Finite Group Databasebeta

← #14542805

Subgroups — #14542805

Order 2176.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763521C211yesmaximal, characteristic, complemented
2#11763513C211yesmaximal, characteristic, complemented
3#11763508C211yesmaximal, characteristic, complemented
4#11763508C211yesmaximal, characteristic, complemented
5#11763504C211yesmaximal, characteristic, complemented
6#11763502C211yesmaximal, characteristic, complemented
7#11763477C211yesmaximal, characteristic, complemented
8#11763451C211yesmaximal, characteristic, complemented
9#11763449C211yesmaximal, characteristic, complemented
10#11763449C211yesmaximal, characteristic, complemented
11#11763448C211yesmaximal, characteristic, complemented
12#11763447C211yesmaximal, characteristic, complemented
13D4×C22⋊D17C211yesmaximal, characteristic, complemented
14#11763441C211yesmaximal, characteristic, complemented
15#11763441C211yesmaximal, characteristic, complemented
16#11763411C211yesmaximal, characteristic, complemented
17#11763409C211yesmaximal, characteristic, complemented
18#11763399C211yesmaximal, characteristic, complemented
19#11763394C211yesmaximal, characteristic, complemented
20#11763393C211yesmaximal, characteristic, complemented
21#11763391C211yesmaximal, characteristic, complemented
22#11763355C211yesmaximal, characteristic, complemented
23#11763336C211yesmaximal, characteristic, complemented
24#11763318C211yesmaximal, characteristic, complemented
25#11763315C211yesmaximal, characteristic, complemented
26C2×#10587625C211yesmaximal, characteristic, complemented
27#121×D17C211yesmaximal, characteristic, complemented
28#11763282C211yesmaximal, characteristic, complemented
29#11763281C211yesmaximal, characteristic, complemented
30C2×#10587567C211yesmaximal, characteristic, complemented
31C17×#546C211yesmaximal, characteristic, complemented
32C2×#41×C17C2211yescharacteristic, complemented
33C22×D4×C17C2211yescharacteristic, complemented
34C22×C22⋊D17C2211yescharacteristic
35C22×C22⋊D17C2211yescharacteristic
36C22×C22⋊D17C2211yescharacteristic, complemented
37C22×C22⋊D17C2211yescharacteristic, complemented
38C23×Dic17C2211yescharacteristic, complemented
39C2×#63254C2211yescharacteristic, complemented
40C2×D4×D17C2211yescharacteristic
41C2×D4×D17C2211yescharacteristic, complemented
42C2×D4×D17C2211yescharacteristic, complemented
43C2×D4×D17C2211yescharacteristic, complemented
44C2×#63252C2211yescharacteristic, complemented
45C2×#63252C2211yescharacteristic, complemented
46C22×C4×D17C2211yescharacteristic, complemented
47C17×#124C2211yescharacteristic, complemented
48C17×#123C2211yescharacteristic, complemented
49C17×#123C2211yescharacteristic, complemented
50C17×C22⋊Q8C2211yescharacteristic, complemented
51C17×#121C2211yescharacteristic, complemented
52C17×#121C2211yescharacteristic, complemented
53C17×#121C2211yescharacteristic, complemented
54C17×#120C2211yescharacteristic, complemented
55C17×#120C2211yescharacteristic, complemented
56C4×D4×C17C2211yescharacteristic, complemented
57C4×D4×C17C2211yescharacteristic, complemented
58C2×C22⋊C4×C17C2211yescharacteristic, complemented
59C2×C22⋊C4×C17C2211yescharacteristic, complemented
60#10587639C2211yescharacteristic, complemented
61#10587639C2211yescharacteristic, complemented
62C2×C22⋊Dic17C2211yescharacteristic, complemented
63#10587633C2211yescharacteristic, complemented
64#10587633C2211yescharacteristic, complemented
65#10587632C2211yescharacteristic, complemented
66#10587630C2211yescharacteristic, complemented
67#10587626C2211yescharacteristic, complemented
68#10587626C2211yescharacteristic, complemented
69#10587626C2211yescharacteristic, complemented
70#10587625C2211yescharacteristic
71#10587625C2211yescharacteristic, complemented
72#10587625C2211yescharacteristic, complemented
73#10587625C2211yescharacteristic, complemented
74#10587625C2211yescharacteristic, complemented
75#10587625C2211yescharacteristic, complemented
76#10587625C2211yescharacteristic, complemented
77#10587625C2211yescharacteristic, complemented
78#10587625C2211yescharacteristic, complemented
79#10587625C2211yescharacteristic, complemented
80#10587625C2211yescharacteristic, complemented
81#10587625C2211yescharacteristic, complemented
82#10587625C2211yescharacteristic, complemented
83#10587625C2211yescharacteristic, complemented
84#10587625C2211yescharacteristic, complemented
85#10587625C2211yescharacteristic, complemented
86#10587624C2211yescharacteristic, complemented
87#10587624C2211yescharacteristic, complemented
88#10587623C2211yescharacteristic, complemented
89#10587623C2211yescharacteristic, complemented
90#10587623C2211yescharacteristic, complemented
91#10587623C2211yescharacteristic, complemented
92#10587622C2211yescharacteristic, complemented
93#10587621C2211yescharacteristic, complemented
94#10587621C2211yescharacteristic, complemented
95D4×Dic17C2211yescharacteristic, complemented
96D4×Dic17C2211yescharacteristic, complemented
97D4×Dic17C2211yescharacteristic, complemented
98#10587616C2211yescharacteristic, complemented
99#10587616C2211yescharacteristic, complemented
100#10587616C2211yescharacteristic, complemented
101#10587615C2211yescharacteristic, complemented
102#10587615C2211yescharacteristic, complemented
103#10587615C2211yescharacteristic, complemented
104C4×C22⋊D17C2211yescharacteristic
105C4×C22⋊D17C2211yescharacteristic, complemented
106C4×C22⋊D17C2211yescharacteristic, complemented
107C4×C22⋊D17C2211yescharacteristic, complemented
108C4×C22⋊D17C2211yescharacteristic, complemented
109C4×C22⋊D17C2211yescharacteristic, complemented
110C4×C22⋊D17C2211yescharacteristic, complemented
111C4×C22⋊D17C2211yescharacteristic, complemented
112C4×C22⋊D17C2211yescharacteristic, complemented
113C2×#63227C2211yescharacteristic, complemented
114C2×#63227C2211yescharacteristic, complemented
115C2×#63227C2211yescharacteristic, complemented
116C2×#63225C2211yescharacteristic, complemented
117C2×#63225C2211yescharacteristic, complemented
118C2×C4×Dic17C2211yescharacteristic, complemented
119#10587584C2211yescharacteristic, complemented
120#10587584C2211yescharacteristic, complemented
121#10587582C2211yescharacteristic, complemented
122#10587582C2211yescharacteristic, complemented
123#10587581C2211yescharacteristic, complemented
124#10587581C2211yescharacteristic, complemented
125#10587580C2211yescharacteristic, complemented
126#10587580C2211yescharacteristic, complemented
127#10587580C2211yescharacteristic, complemented
128#10587579C2211yescharacteristic, complemented
129#10587578C2211yescharacteristic, complemented
130C4⋊C4×D17C2211yescharacteristic, complemented
131#10587575C2211yescharacteristic, complemented
132#10587575C2211yescharacteristic, complemented
133#10587575C2211yescharacteristic, complemented
134#10587573C2211yescharacteristic, complemented
135#10587572C2211yescharacteristic, complemented
136#10587571C2211yescharacteristic, complemented
137#10587571C2211yescharacteristic, complemented
138#10587571C2211yescharacteristic, complemented
139#10587570C2211yescharacteristic, complemented
140#10587570C2211yescharacteristic, complemented
141#10587570C2211yescharacteristic, complemented
142#10587570C2211yescharacteristic, complemented
143#10587570C2211yescharacteristic, complemented
144#10587570C2211yescharacteristic, complemented
145#10587570C2211yescharacteristic, complemented
146#10587570C2211yescharacteristic, complemented
147#10587570C2211yescharacteristic, complemented
148#10587569C2211yescharacteristic, complemented
149#10587569C2211yescharacteristic, complemented
150#10587569C2211yescharacteristic, complemented
151#10587568C2211yescharacteristic, complemented
152#10587568C2211yescharacteristic, complemented
153#10587568C2211yescharacteristic, complemented
154#10587568C2211yescharacteristic, complemented
155#10587567C2211yescharacteristic
156#10587567C2211yescharacteristic
157#10587567C2211yescharacteristic
158#10587567C2211yescharacteristic, complemented
159#10587567C2211yescharacteristic, complemented
160#10587567C2211yescharacteristic, complemented
161#10587567C2211yescharacteristic, complemented
162#10587567C2211yescharacteristic, complemented
163#10587567C2211yescharacteristic, complemented
164#10587567C2211yescharacteristic, complemented
165#10587567C2211yescharacteristic, complemented
166#10587567C2211yescharacteristic, complemented
167#10587567C2211yescharacteristic, complemented
168#10587567C2211yescharacteristic, complemented
169#10587567C2211yescharacteristic, complemented
170C22⋊C4×D17C2211yescharacteristic, complemented
171C22⋊C4×D17C2211yescharacteristic, complemented
172C22⋊C4×D17C2211yescharacteristic, complemented
173C22⋊C4×D17C2211yescharacteristic, complemented
174#10587565C2211yescharacteristic, complemented
175#10587565C2211yescharacteristic, complemented
176#10587565C2211yescharacteristic, complemented
177#10587564C2211yescharacteristic, complemented
178#10587564C2211yescharacteristic, complemented
179#10587564C2211yescharacteristic, complemented
180#10587563C2211yescharacteristic, complemented
181#10587563C2211yescharacteristic, complemented
182#10587563C2211yescharacteristic, complemented
183#10587562C2211yescharacteristic, complemented
184C4×D68C2211yescharacteristic, complemented
185#10587558C2211yescharacteristic, complemented
186#10587558C2211yescharacteristic, complemented
187C24×C17C2311yescharacteristic
188C24×C17C2311yescharacteristic
189C23×D17C2311yescharacteristic
190C23×D17C2311yescharacteristic
191C23×D17C2311yescharacteristic
192C23×D17C2311yescharacteristic
193#41×C17—42no—
194C2×Q8×C17C2311yescharacteristic
195C2×D4×C17—42no—
196C2×D4×C17C2311yescharacteristic
197C2×D4×C17C2311yescharacteristic
198C2×D4×C17C2311yescharacteristic
199C2×D4×C17C2311yescharacteristic
200C2×D4×C17C2311yescharacteristic
201C2×D4×C17C2311yescharacteristic
202C2×D4×C17C2311yescharacteristic
203C2×D4×C17C2311yescharacteristic
204C2×D4×C17C2311yescharacteristic
205C22×C4×C17C2311yescharacteristic
206C22×C4×C17C2311yescharacteristic
207C22×C4×C17C2311yescharacteristic
208C22×C4×C17C2311yescharacteristic
209C22×C4×C17C2311yescharacteristic
210C22×C4×C17C2311yescharacteristic
211C2×C22⋊D17—24no—
212C2×C22⋊D17—24no—
213C2×C22⋊D17—42no—
214C2×C22⋊D17—42no—
215C2×C22⋊D17C2311yescharacteristic
216C2×C22⋊D17C2311yescharacteristic
217C2×C22⋊D17C2311yescharacteristic
218C2×C22⋊D17C2311yescharacteristic
219C2×C22⋊D17C2311yescharacteristic
220C2×C22⋊D17C2311yescharacteristic
221C2×C22⋊D17C2311yescharacteristic
222C2×C22⋊D17C2311yescharacteristic
223C2×C22⋊D17C2311yescharacteristic
224C2×C22⋊D17C2311yescharacteristic
225C2×C22⋊D17C2311yescharacteristic
226C2×C22⋊D17C2311yescharacteristic
227C2×C22⋊D17C2311yescharacteristic
228C2×C22⋊D17C2311yescharacteristic
229C2×C22⋊D17C2311yescharacteristic
230C2×C22⋊D17C2311yescharacteristic
231C2×C22⋊D17C2311yescharacteristic
232C2×C22⋊D17C2311yescharacteristic
233C2×C22⋊D17C2311yescharacteristic
234C2×C22⋊D17C2311yescharacteristic
235C2×C22⋊D17C2311yescharacteristic
236C2×C22⋊D17C2311yescharacteristic
237C22×Dic17—42no—
238C22×Dic17C2311yescharacteristic
239C22×Dic17C2311yescharacteristic
240C22×Dic17C2311yescharacteristic
241C22×Dic17C2311yescharacteristic
242C22×Dic17C2311yescharacteristic
243C22×Dic17C2311yescharacteristic
244C22×Dic17C2311yescharacteristic
245C22×Dic17C2311yescharacteristic
246C22×Dic17C2311yescharacteristic
247C22×Dic17C2311yescharacteristic
248#63254—42no—
249D4×D17—24no—
250D4×D17—42no—
251D4×D17—42no—
252D4×D17—42no—
253#63252—42no—
254#63252—42no—
255C2×D68C2311yescharacteristic
256C2×D68C2311yescharacteristic
257C2×D68C2311yescharacteristic
258C2×D68C2311yescharacteristic
259C2×D68C2311yescharacteristic
260C2×D68C2311yescharacteristic
261C2×C4×D17—42no—
262C2×C4×D17C2311yescharacteristic
263C2×C4×D17C2311yescharacteristic
264C2×C4×D17C2311yescharacteristic
265C2×C4×D17C2311yescharacteristic
266C2×C4×D17C2311yescharacteristic
267C2×C4×D17C2311yescharacteristic
268C2×C4×D17C2311yescharacteristic
269C2×C4×D17C2311yescharacteristic
270C2×C4×D17C2311yescharacteristic
271C2×C4×D17C2311yescharacteristic
272C2×C4×D17C2311yescharacteristic
273C2×Dic34C2311yescharacteristic
274C2×Dic34C2311yescharacteristic
275C4⋊C4×C17C2311yescharacteristic
276C4⋊C4×C17C2311yescharacteristic
277C4⋊C4×C17C2311yescharacteristic
278C4⋊C4×C17C2311yescharacteristic
279C22⋊C4×C17C2311yescharacteristic
280C22⋊C4×C17C2311yescharacteristic
281C22⋊C4×C17C2311yescharacteristic
282C22⋊C4×C17C2311yescharacteristic
283C22⋊C4×C17C2311yescharacteristic
284C22⋊C4×C17C2311yescharacteristic
285C22⋊C4×C17C2311yescharacteristic
286C22⋊C4×C17C2311yescharacteristic
287C22⋊C4×C17C2311yescharacteristic
288C22⋊C4×C17C2311yescharacteristic
289C22⋊C4×C17C2311yescharacteristic
290C22⋊C4×C17C2311yescharacteristic
291C42×C17C2311yescharacteristic
292C22⋊Dic17C2311yescharacteristic
293C22⋊Dic17C2311yescharacteristic
294C22⋊Dic17C2311yescharacteristic
295C22⋊Dic17C2311yescharacteristic
296C22⋊Dic17C2311yescharacteristic
297C22⋊Dic17C2311yescharacteristic
298C22⋊Dic17C2311yescharacteristic
299C22⋊Dic17C2311yescharacteristic
300C22⋊Dic17C2311yescharacteristic
301C22⋊Dic17C2311yescharacteristic
302C22⋊Dic17C2311yescharacteristic
303C22⋊Dic17C2311yescharacteristic
304#63227C2311yescharacteristic
305#63227C2311yescharacteristic
306#63227C2311yescharacteristic
307#63227C2311yescharacteristic
308#63227C2311yescharacteristic
309#63227C2311yescharacteristic
310#63227C2311yescharacteristic
311#63227C2311yescharacteristic
312#63227C2311yescharacteristic
313#63227C2311yescharacteristic
314#63227C2311yescharacteristic
315#63227C2311yescharacteristic
316#63227C2311yescharacteristic
317#63227C2311yescharacteristic
318#63227C2311yescharacteristic
319#63227C2311yescharacteristic
320#63227C2311yescharacteristic
321#63227C2311yescharacteristic
322#63227C2311yescharacteristic
323#63227C2311yescharacteristic
324#63227C2311yescharacteristic
325#63227C2311yescharacteristic
326C4⋊Dic17C2311yescharacteristic
327C4⋊Dic17C2311yescharacteristic
328C4⋊Dic17C2311yescharacteristic
329C4⋊Dic17C2311yescharacteristic
330#63225C2311yescharacteristic
331#63225C2311yescharacteristic
332#63225C2311yescharacteristic
333#63225C2311yescharacteristic
334#63225C2311yescharacteristic
335#63225C2311yescharacteristic
336#63225C2311yescharacteristic
337#63225C2311yescharacteristic
338#63225C2311yescharacteristic
339#63225C2311yescharacteristic
340#63225C2311yescharacteristic
341#63225C2311yescharacteristic
342#63225C2311yescharacteristic
343#63225C2311yescharacteristic
344#63225C2311yescharacteristic
345#63225C2311yescharacteristic
346#63225C2311yescharacteristic
347#63225C2311yescharacteristic
348C4×Dic17C2311yescharacteristic
349C4×Dic17C2311yescharacteristic
350C4×Dic17C2311yescharacteristic
351C4×Dic17C2311yescharacteristic
352C4×Dic17C2311yescharacteristic
353C4×Dic17C2311yescharacteristic
354C4×Dic17C2311yescharacteristic
355C4×Dic17C2311yescharacteristic
356C4×Dic17C2311yescharacteristic
357C23×C17—22no—
358C23×C17—22no—
359C23×C17—22no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17C2411yescharacteristic
364C23×C17C2411yescharacteristic
365C23×C17C2411yescharacteristic
366C23×C17C2411yescharacteristic
367C23×C17C2411yescharacteristic
368C23×C17C2411yescharacteristic
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17C2411yescharacteristic
382C22×D17C2411yescharacteristic
383C22×D17C2411yescharacteristic
384C22×D17C2411yescharacteristic
385C22×D17C2411yescharacteristic
386Q8×C17—41no—
387D4×C17—22no—
388D4×C17—22no—
389D4×C17—22no—
390D4×C17—22no—
391D4×C17—41no—
392D4×C17—41no—
393D4×C17—41no—
394D4×C17—41no—
395D4×C17—41no—
396C2×C4×C17—22no—
397C2×C4×C17—41no—
398C2×C4×C17—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17C2411yescharacteristic
403C2×C4×C17C2411yescharacteristic
404C2×C4×C17C2411yescharacteristic
405C2×C4×C17C2411yescharacteristic
406C2×C4×C17C2411yescharacteristic
407C2×C4×C17C2411yescharacteristic
408C2×C4×C17C2411yescharacteristic
409C2×C4×C17C2411yescharacteristic
410C2×C4×C17C2411yescharacteristic
411C22⋊D17—22no—
412C22⋊D17—22no—
413C22⋊D17—22no—
414C22⋊D17—22no—
415C22⋊D17—22no—
416C22⋊D17—22no—
417C22⋊D17—22no—
418C22⋊D17—22no—
419C22⋊D17—22no—
420C22⋊D17—22no—
421C22⋊D17—22no—
422C22⋊D17—22no—
423C22⋊D17—22no—
424C22⋊D17—41no—
425C22⋊D17—41no—
426C22⋊D17—41no—
427C22⋊D17—41no—
428C22⋊D17—41no—
429C22⋊D17—41no—
430C22⋊D17—41no—
431C22⋊D17—41no—
432C22⋊D17#4114yescomplemented
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17—41no—
441C2×Dic17—41no—
442C2×Dic17—41no—
443C2×Dic17C2411yescharacteristic
444C2×Dic17C2411yescharacteristic
445C2×Dic17C2411yescharacteristic
446C2×Dic17C2411yescharacteristic
447C2×Dic17C2411yescharacteristic
448C2×Dic17C2411yescharacteristic
449C2×Dic17C2411yescharacteristic
450C2×Dic17C2411yescharacteristic
451C2×Dic17C2411yescharacteristic
452C2×Dic17C2411yescharacteristic
453C2×Dic17C2411yescharacteristic
454D68—22no—
455D68—41no—
456D68—41no—
457D68—41no—
458D68—41no—
459D68—41no—
460C4×D17—22no—
461C4×D17—22no—
462C4×D17—22no—
463C4×D17—41no—
464C4×D17—41no—
465C4×D17—41no—
466C4×D17—41no—
467C4×D17—41no—
468C4×D17—41no—
469C4×D17—41no—
470C4×D17—41no—
471Dic34—22no—
472Dic34—41no—
473#3519—171nomaximal, Sylow
474C22×C17—21no—
475C22×C17—21no—
476C22×C17—21no—
477C22×C17—21no—
478C22×C17—21no—
479C22×C17—21no—
480C22×C17—21no—
481C22×C17—21no—
482C22×C17—21no—
483C22×C17—21no—
484C22×C17—21no—
485C22×C17—21no—
486C22×C17—21no—
487C22×C17—21no—
488C22×C17—21no—
489C22×C17—21no—
490C22×C17—44no—
491C22×C17—82no—
492C22×C17C2×#4112yes—
493C22×C17H(5,𝔽2)12yes—
494C22×C17C2511yescharacteristic
495C2×D17—21no—
496C2×D17—21no—
497C2×D17—21no—
498C2×D17—21no—
499C2×D17—21no—
500C2×D17—21no—
501C2×D17—21no—
502C2×D17—21no—
503C2×D17—21no—
504C2×D17—21no—
505C2×D17—21no—
506C2×D17—21no—
507C2×D17—21no—
508C2×D17—21no—
509C2×D17—44no—
510C2×D17—82no—
511C2×D17—82no—
512C2×D17—82no—
513C2×D17C2×#4112yes—
514C4×C17—21no—
515C4×C17—21no—
516C4×C17—21no—
517C4×C17—21no—
518C4×C17—21no—
519C4×C17—21no—
520C4×C17—21no—
521C4×C17—21no—
522C4×C17—21no—
523Dic17—21no—
524Dic17—21no—
525Dic17—21no—
526Dic17—21no—
527Dic17—21no—
528Dic17—21no—
529Dic17—21no—
530Dic17—21no—
531Dic17—21no—
532Dic17C2×#4112yes—
533Dic17H(5,𝔽2)12yes—
534#555—171no—
535#554—171no—
536#553—171no—
537#553—171no—
538#553—171no—
539#553—171no—
540#550—171no—
541#546—171no—
542#546—171no—
543#546—171no—
544#546—171no—
545#546—171no—
546#546D1711yescharacteristic, complemented
547D42—171no—
548D42—171no—
549D42—171no—
550#540—171no—
551#540—171no—
552#538—171no—
553#538—171no—
554#538—171no—
555#538—171no—
556#532—171no—
557#529—171no—
558#525—171no—
559#525—171no—
560C2×#121—171no—
561C2×#121—171no—
562#518—171no—
563#518—171no—
564C2×C4×D4—171no—
565C2×C17—22no—
566C2×C17—22no—
567C2×C17—41no—
568C2×C17—41no—
569C2×C17—41no—
570C2×C17—41no—
571C2×C17C22×#4111yescharacteristic
572C2×C17C2×H(5,𝔽2)11yescharacteristic
573C2×C17C2×H(5,𝔽2)11yescharacteristic
574D17—22no—
575D17—41no—
576D17—41no—
577D17—41no—
578D17—41no—
579C2×#41—171no—
580C2×#41—171no—
581C2×#41—171no—
582C2×#41C2×D1711yescharacteristic, complemented
583C22×D4—171no—
584C22×D4—171no—
585C22×D4—171no—
586C22×D4—171no—
587C22×D4—171no—
588C22×D4—171no—
589C22×D4—171no—
590C22×D4—171no—
591C22×D4C2×D1711yescharacteristic, complemented
592C23×C4—171no—
593C23×C4—171no—
594C4⋊Q8—171no—
595#127—171no—
596#127—171no—
597#127—171no—
598#126—171no—
599#126—171no—
600#126—171no—
601#126—171no—
602#126—171no—
603#126—171no—
604#125—171no—
605#125—171no—
606#125—171no—
607#124—171no—
608#124—171no—
609#124—171no—
610#124—171no—
611#124—171no—
612#124—171no—
613#124C2×D1711yescharacteristic, complemented
614#123—171no—
615#123—171no—
616#123—171no—
617#123—171no—
618#123—171no—
619#123—171no—
620#123—171no—
621#123—171no—
622#123—171no—
623#123—171no—
624#123—171no—
625#123—171no—
626#123C2×D1711yescharacteristic, complemented
627#123C2×D1711yescharacteristic, complemented
628C22⋊Q8—171no—
629C22⋊Q8—171no—
630C22⋊Q8—171no—
631C22⋊Q8—171no—
632C22⋊Q8—171no—
633C22⋊Q8—171no—
634C22⋊Q8C2×D1711yescharacteristic, complemented
635#121—171no—
636#121—171no—
637#121—171no—
638#121—171no—
639#121—171no—
640#121—171no—
641#121—171no—
642#121—171no—
643#121—171no—
644#121—171no—
645#121—171no—
646#121—171no—
647#121—171no—
648#121—171no—
649#121—171no—
650#121—171no—
651#121—171no—
652#121—171no—
653#121—171no—
654#121—171no—
655#121—171no—
656#121—171no—
657#121—171no—
658#121—171no—
659#121—171no—
660#121—171no—
661#121—171no—
662#121—171no—
663#121—171no—
664#121—171no—
665#121—171no—
666#121—171no—
667#121C2×D1711yescharacteristic, complemented
668#121C2×D1711yescharacteristic, complemented
669#121C2×D1711yescharacteristic, complemented
670#120—171no—
671#120—171no—
672#120—171no—
673#120—171no—
674#120—171no—
675#120—171no—
676#120—171no—
677#120—171no—
678#120—171no—
679#120—171no—
680#120C2×D1711yescharacteristic, complemented
681#120C2×D1711yescharacteristic, complemented
682C4×Q8—171no—
683C4×D4—171no—
684C4×D4—171no—
685C4×D4—171no—
686C4×D4—171no—
687C4×D4—171no—
688C4×D4—171no—
689C4×D4—171no—
690C4×D4—171no—
691C4×D4—171no—
692C4×D4—171no—
693C4×D4—171no—
694C4×D4—171no—
695C4×D4—171no—
696C4×D4—171no—
697C4×D4—171no—
698C4×D4—171no—
699C4×D4—171no—
700C4×D4—171no—
701C4×D4—171no—
702C4×D4—171no—
703C4×D4—171no—
704C4×D4—171no—
705C4×D4—171no—
706C4×D4—171no—
707C4×D4—171no—
708C4×D4—171no—
709C4×D4—171no—
710C4×D4—171no—
711C4×D4—171no—
712C4×D4C2×D1711yescharacteristic, complemented
713C4×D4C2×D1711yescharacteristic, complemented
714#117—171no—
715#117—171no—
716#117—171no—
717#117—171no—
718#117—171no—
719#117—171no—
720C2×C4⋊C4—171no—
721C2×C4⋊C4—171no—
722C2×C4⋊C4—171no—
723C2×C22⋊C4—171no—
724C2×C22⋊C4—171no—
725C2×C22⋊C4—171no—
726C2×C22⋊C4—171no—
727C2×C22⋊C4—171no—
728C2×C22⋊C4—171no—
729C2×C22⋊C4—171no—
730C2×C22⋊C4—171no—
731C2×C22⋊C4C2×D1711yescharacteristic, complemented
732C2×C22⋊C4C2×D1711yescharacteristic, complemented
733C2×C42—171no—
734C17#351911yescharacteristic, complemented, Sylow
735C24—171no—
736C24—171no—
737C24—171no—
738C24—171no—
739C24C22×D1711yescharacteristic
740C24C22×D1711yescharacteristic
741#41—42no—
742#41—682no—
743#41—682no—
744#41—682no—
745C2×Q8—171no—
746C2×Q8—171no—
747C2×Q8C22×D1711yescharacteristic
748C2×D4—42no—
749C2×D4—171no—
750C2×D4—171no—
751C2×D4—171no—
752C2×D4—171no—
753C2×D4—171no—
754C2×D4—171no—
755C2×D4—171no—
756C2×D4—171no—
757C2×D4—171no—
758C2×D4—171no—
759C2×D4—171no—
760C2×D4—171no—
761C2×D4—171no—
762C2×D4—171no—
763C2×D4—171no—
764C2×D4—171no—
765C2×D4—171no—
766C2×D4—171no—
767C2×D4—171no—
768C2×D4—171no—
769C2×D4—171no—
770C2×D4—171no—
771C2×D4—171no—
772C2×D4—171no—
773C2×D4—171no—
774C2×D4—171no—
775C2×D4—171no—
776C2×D4—171no—
777C2×D4—344no—
778C2×D4—344no—
779C2×D4—344no—
780C2×D4—682no—
781C2×D4—682no—
782C2×D4—682no—
783C2×D4—682no—
784C2×D4—682no—
785C2×D4C22×D1711yescharacteristic
786C2×D4C22×D1711yescharacteristic
787C2×D4C22×D1711yescharacteristic
788C2×D4C22×D1711yescharacteristic
789C2×D4C22×D1711yescharacteristic
790C2×D4C22×D1711yescharacteristic
791C2×D4C22×D1711yescharacteristic
792C2×D4C22×D1711yescharacteristic
793C2×D4C22×D1711yescharacteristic
794C22×C4—171no—
795C22×C4—171no—
796C22×C4—171no—
797C22×C4—171no—
798C22×C4—171no—
799C22×C4—171no—
800C22×C4—171no—
801C22×C4—171no—
802C22×C4—171no—
803C22×C4—171no—
804C22×C4—171no—
805C22×C4—171no—
806C22×C4—171no—
807C22×C4—171no—
808C22×C4—171no—
809C22×C4—171no—
810C22×C4—171no—
811C22×C4—171no—
812C22×C4—171no—
813C22×C4—171no—
814C22×C4—171no—
815C22×C4—682no—
816C22×C4—682no—
817C22×C4C22×D1711yescharacteristic
818C22×C4C22×D1711yescharacteristic
819C22×C4C22×D1711yescharacteristic
820C22×C4C22×D1711yescharacteristic
821C22×C4C22×D1711yescharacteristic
822C22×C4C22×D1711yescharacteristic
823C4⋊C4—171no—
824C4⋊C4—171no—
825C4⋊C4—171no—
826C4⋊C4—171no—
827C4⋊C4—171no—
828C4⋊C4—171no—
829C4⋊C4—171no—
830C4⋊C4—171no—
831C4⋊C4—171no—
832C4⋊C4—171no—
833C4⋊C4—171no—
834C4⋊C4—171no—
835C4⋊C4—171no—
836C4⋊C4—171no—
837C4⋊C4—171no—
838C4⋊C4—171no—
839C4⋊C4—171no—
840C4⋊C4—171no—
841C4⋊C4—171no—
842C4⋊C4—171no—
843C4⋊C4—171no—
844C4⋊C4—171no—
845C4⋊C4C22×D1711yescharacteristic
846C4⋊C4C22×D1711yescharacteristic
847C4⋊C4C22×D1711yescharacteristic
848C4⋊C4C22×D1711yescharacteristic
849C22⋊C4—171no—
850C22⋊C4—171no—
851C22⋊C4—171no—
852C22⋊C4—171no—
853C22⋊C4—171no—
854C22⋊C4—171no—
855C22⋊C4—171no—
856C22⋊C4—171no—
857C22⋊C4—171no—
858C22⋊C4—171no—
859C22⋊C4—171no—
860C22⋊C4—171no—
861C22⋊C4—171no—
862C22⋊C4—171no—
863C22⋊C4—171no—
864C22⋊C4—171no—
865C22⋊C4—171no—
866C22⋊C4—171no—
867C22⋊C4—171no—
868C22⋊C4—171no—
869C22⋊C4—171no—
870C22⋊C4—171no—
871C22⋊C4—171no—
872C22⋊C4—171no—
873C22⋊C4—171no—
874C22⋊C4—171no—
875C22⋊C4—171no—
876C22⋊C4—171no—
877C22⋊C4—171no—
878C22⋊C4—171no—
879C22⋊C4—171no—
880C22⋊C4—171no—
881C22⋊C4—171no—
882C22⋊C4—171no—
883C22⋊C4C22×D1711yescharacteristic
884C22⋊C4C22×D1711yescharacteristic
885C22⋊C4C22×D1711yescharacteristic
886C22⋊C4C22×D1711yescharacteristic
887C22⋊C4C22×D1711yescharacteristic
888C22⋊C4C22×D1711yescharacteristic
889C22⋊C4C22×D1711yescharacteristic
890C22⋊C4C22×D1711yescharacteristic
891C22⋊C4C22×D1711yescharacteristic
892C22⋊C4C22×D1711yescharacteristic
893C22⋊C4C22×D1711yescharacteristic
894C22⋊C4C22×D1711yescharacteristic
895C42—171no—
896C42—171no—
897C42—171no—
898C42—171no—
899C42—171no—
900C42—171no—
901C42—171no—
902C42—171no—
903C42—171no—
904C42C22×D1711yescharacteristic
905C23—22no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—171no—
912C23—171no—
913C23—171no—
914C23—171no—
915C23—171no—
916C23—342no—
917C23—342no—
918C23—342no—
919C23—342no—
920C23—342no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23C23×D1711yescharacteristic
929C23C23×D1711yescharacteristic
930C23C23×D1711yescharacteristic
931C23C23×D1711yescharacteristic
932C23C23×D1711yescharacteristic
933C23C23×D1711yescharacteristic
934Q8—41no—
935Q8—342no—
936Q8—681no—
937D4—22no—
938D4—22no—
939D4—22no—
940D4—22no—
941D4—41no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—174no—
947D4—342no—
948D4—342no—
949D4—342no—
950D4—342no—
951D4—342no—
952D4—342no—
953D4—342no—
954D4—342no—
955D4—342no—
956D4—342no—
957D4—342no—
958D4—342no—
959D4—342no—
960D4—342no—
961D4—681no—
962D4—681no—
963D4—681no—
964D4—681no—
965D4—681no—
966D4—681no—
967D4—681no—
968D4—681no—
969D4—681no—
970D4—681no—
971D4—681no—
972D4—681no—
973D4—681no—
974C2×C4—22no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—171no—
981C2×C4—171no—
982C2×C4—171no—
983C2×C4—171no—
984C2×C4—171no—
985C2×C4—171no—
986C2×C4—171no—
987C2×C4—171no—
988C2×C4—171no—
989C2×C4—171no—
990C2×C4—171no—
991C2×C4—342no—
992C2×C4—342no—
993C2×C4—342no—
994C2×C4—342no—
995C2×C4—342no—
996C2×C4—342no—
997C2×C4—342no—
998C2×C4—342no—
999C2×C4—681no—
1000C2×C4—681no—
1001C2×C4—681no—
1002C2×C4—681no—
1003C2×C4—681no—
1004C2×C4—681no—
1005C2×C4—681no—
1006C2×C4—681no—
1007C2×C4—681no—
1008C2×C4—681no—
1009C2×C4—681no—
1010C2×C4—681no—
1011C2×C4—681no—
1012C2×C4C23×D1711yescharacteristic
1013C2×C4C23×D1711yescharacteristic
1014C2×C4C23×D1711yescharacteristic
1015C2×C4C23×D1711yescharacteristic
1016C2×C4C23×D1711yescharacteristic
1017C2×C4C23×D1711yescharacteristic
1018C2×C4C23×D1711yescharacteristic
1019C2×C4C23×D1711yescharacteristic
1020C2×C4C23×D1711yescharacteristic
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—44no—
1038C22—82no—
1039C22—172no—
1040C22—341no—
1041C22—341no—
1042C22—341no—
1043C22—341no—
1044C22—341no—
1045C22—341no—
1046C22—341no—
1047C22—341no—
1048C22—341no—
1049C22—341no—
1050C22—341no—
1051C22—341no—
1052C22—341no—
1053C22—341no—
1054C22—684no—
1055C22—1362no—
1056C22—1362no—
1057C22—1362no—
1058C22#1058769112yes—
1059C22#41×D1712yes—
1060C22C24×D1711yescharacteristic
1061C4—21no—
1062C4—21no—
1063C4—21no—
1064C4—21no—
1065C4—21no—
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—172no—
1071C4—172no—
1072C4—341no—
1073C4—341no—
1074C4—341no—
1075C4—341no—
1076C4—341no—
1077C4—341no—
1078C4—341no—
1079C4—341no—
1080C4—341no—
1081C2—22no—
1082C2—22no—
1083C2—41no—
1084C2—41no—
1085C2—41no—
1086C2—41no—
1087C2—342no—
1088C2—681no—
1089C2—681no—
1090C2—681no—
1091C2—681no—
1092C2C2×#41×D1711yescharacteristic
1093C2H(5,𝔽2)×D1711yescharacteristic
1094C2C2×#1058769111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D17
commutator, socle, cosocleC22×C17C25
FittingC17×#546C2
hypercenter#546D17
hypocenterC17#3519
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11763521C2semidirect
2. #11763513C2semidirect
3. #11763508C2semidirect
4. #11763508C2semidirect
5. #11763504C2semidirect
6. #11763502C2semidirect
7. #11763477C2semidirect
8. #11763451C2semidirect
9. #11763449C2semidirect
10. #11763449C2semidirect
11. #11763448C2semidirect
12. #11763447C2semidirect
13. D4×C22⋊D17C2semidirect
14. #11763441C2semidirect
15. #11763441C2semidirect
16. #11763411C2semidirect
17. #11763409C2semidirect
18. #11763399C2semidirect
19. #11763394C2semidirect
20. #11763393C2semidirect
21. #11763391C2semidirect
22. #11763355C2semidirect
23. #11763336C2semidirect
24. #11763318C2semidirect
25. #11763315C2semidirect
26. C2×#10587625C2semidirect
27. #121×D17C2semidirect
28. #11763282C2semidirect
29. #11763281C2semidirect
30. C2×#10587567C2semidirect
31. C17×#546C2semidirect
32. C2×#41×C17C22semidirect
33. C22×D4×C17C22semidirect
36. C22×C22⋊D17C22semidirect
37. C22×C22⋊D17C22semidirect
38. C23×Dic17C22semidirect
39. C2×#63254C22semidirect
41. C2×D4×D17C22semidirect
42. C2×D4×D17C22semidirect
43. C2×D4×D17C22semidirect
44. C2×#63252C22semidirect
45. C2×#63252C22semidirect
46. C22×C4×D17C22semidirect
47. C17×#124C22semidirect
48. C17×#123C22semidirect
49. C17×#123C22semidirect
50. C17×C22⋊Q8C22semidirect
51. C17×#121C22semidirect
52. C17×#121C22semidirect
53. C17×#121C22semidirect
54. C17×#120C22semidirect
55. C17×#120C22semidirect
56. C4×D4×C17C22semidirect
57. C4×D4×C17C22semidirect
58. C2×C22⋊C4×C17C22semidirect
59. C2×C22⋊C4×C17C22semidirect
60. #10587639C22semidirect
61. #10587639C22semidirect
62. C2×C22⋊Dic17C22semidirect
63. #10587633C22semidirect
64. #10587633C22semidirect
65. #10587632C22semidirect
66. #10587630C22semidirect
67. #10587626C22semidirect
68. #10587626C22semidirect
69. #10587626C22semidirect
71. #10587625C22semidirect
72. #10587625C22semidirect
73. #10587625C22semidirect
74. #10587625C22semidirect
75. #10587625C22semidirect
76. #10587625C22semidirect
77. #10587625C22semidirect
78. #10587625C22semidirect
79. #10587625C22semidirect
80. #10587625C22semidirect
81. #10587625C22semidirect
82. #10587625C22semidirect
83. #10587625C22semidirect
84. #10587625C22semidirect
85. #10587625C22semidirect
86. #10587624C22semidirect
87. #10587624C22semidirect
88. #10587623C22semidirect
89. #10587623C22semidirect
90. #10587623C22semidirect
91. #10587623C22semidirect
92. #10587622C22semidirect
93. #10587621C22semidirect
94. #10587621C22semidirect
95. D4×Dic17C22semidirect
96. D4×Dic17C22semidirect
97. D4×Dic17C22semidirect
98. #10587616C22semidirect
99. #10587616C22semidirect
100. #10587616C22semidirect
101. #10587615C22semidirect
102. #10587615C22semidirect
103. #10587615C22semidirect
105. C4×C22⋊D17C22semidirect
106. C4×C22⋊D17C22semidirect
107. C4×C22⋊D17C22semidirect
108. C4×C22⋊D17C22semidirect
109. C4×C22⋊D17C22semidirect
110. C4×C22⋊D17C22semidirect
111. C4×C22⋊D17C22semidirect
112. C4×C22⋊D17C22semidirect
113. C2×#63227C22semidirect
114. C2×#63227C22semidirect
115. C2×#63227C22semidirect
116. C2×#63225C22semidirect
117. C2×#63225C22semidirect
118. C2×C4×Dic17C22semidirect
119. #10587584C22semidirect
120. #10587584C22semidirect
121. #10587582C22semidirect
122. #10587582C22semidirect
123. #10587581C22semidirect
124. #10587581C22semidirect
125. #10587580C22semidirect
126. #10587580C22semidirect
127. #10587580C22semidirect
128. #10587579C22semidirect
129. #10587578C22semidirect
130. C4⋊C4×D17C22semidirect
131. #10587575C22semidirect
132. #10587575C22semidirect
133. #10587575C22semidirect
134. #10587573C22semidirect
135. #10587572C22semidirect
136. #10587571C22semidirect
137. #10587571C22semidirect
138. #10587571C22semidirect
139. #10587570C22semidirect
140. #10587570C22semidirect
141. #10587570C22semidirect
142. #10587570C22semidirect
143. #10587570C22semidirect
144. #10587570C22semidirect
145. #10587570C22semidirect
146. #10587570C22semidirect
147. #10587570C22semidirect
148. #10587569C22semidirect
149. #10587569C22semidirect
150. #10587569C22semidirect
151. #10587568C22semidirect
152. #10587568C22semidirect
153. #10587568C22semidirect
154. #10587568C22semidirect
158. #10587567C22semidirect
159. #10587567C22semidirect
160. #10587567C22semidirect
161. #10587567C22semidirect
162. #10587567C22semidirect
163. #10587567C22semidirect
164. #10587567C22semidirect
165. #10587567C22semidirect
166. #10587567C22semidirect
167. #10587567C22semidirect
168. #10587567C22semidirect
169. #10587567C22semidirect
170. C22⋊C4×D17C22semidirect
171. C22⋊C4×D17C22semidirect
172. C22⋊C4×D17C22semidirect
173. C22⋊C4×D17C22semidirect
174. #10587565C22semidirect
175. #10587565C22semidirect
176. #10587565C22semidirect
177. #10587564C22semidirect
178. #10587564C22semidirect
179. #10587564C22semidirect
180. #10587563C22semidirect
181. #10587563C22semidirect
182. #10587563C22semidirect
183. #10587562C22semidirect
184. C4×D68C22semidirect
185. #10587558C22semidirect
186. #10587558C22semidirect
432. C22⋊D17#41semidirect
546. #546D17semidirect
582. C2×#41C2×D17semidirect
591. C22×D4C2×D17semidirect
613. #124C2×D17semidirect
626. #123C2×D17semidirect
627. #123C2×D17semidirect
634. C22⋊Q8C2×D17semidirect
667. #121C2×D17semidirect
668. #121C2×D17semidirect
669. #121C2×D17semidirect
680. #120C2×D17semidirect
681. #120C2×D17semidirect
712. C4×D4C2×D17semidirect
713. C4×D4C2×D17semidirect
731. C2×C22⋊C4C2×D17semidirect
732. C2×C22⋊C4C2×D17semidirect
734. C17#3519semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117635212
#117635132
#117635082
#117635042
#117635022
#117634772
#117634512
#117634492
#117634482
#117634472
D4×C22⋊D172
#117634412
#117634112
#117634092
#117633992
#117633942
#117633932
#117633912
#117633552
#117633362
#117633182
#117633152
C2×#105876252
#121×D172
#117632822
#117632812
C2×#105875672
C17×#5462
#351917