Finite Group Databasebeta

← #17205323

Subgroups — #17205323

Order 4352.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534494C211yesmaximal, characteristic, complemented
2#14534491C211yesmaximal, characteristic, complemented
3#14534490C211yesmaximal, characteristic, complemented
4#14534489C211yesmaximal, characteristic, complemented
5#14534440C211yesmaximal, characteristic, complemented
6#14534438C211yesmaximal, characteristic, complemented
7#14534431C211yesmaximal, characteristic, complemented
8#14534429C211yesmaximal, characteristic, complemented
9#14534010C211yesmaximal, characteristic
10#14534005C211yesmaximal, characteristic
11#14533797C211yesmaximal, characteristic
12#14533792C211yesmaximal, characteristic
13#14532466C211yesmaximal, characteristic
14#14532464C211yesmaximal, characteristic
15#14532458C211yesmaximal, characteristic
16#14532456C211yesmaximal, characteristic
17#14532091C211yesmaximal, characteristic, complemented
18#14532091C211yesmaximal, characteristic, complemented
19#14532078C211yesmaximal, characteristic, complemented
20#14532075C211yesmaximal, characteristic, complemented
21C4×#10587610C211yesmaximal, characteristic
22C4×#10587564C211yesmaximal, characteristic
23C4×#10587564C211yesmaximal, characteristic
24#14531262C211yesmaximal, characteristic, complemented
25#14531260C211yesmaximal, characteristic, complemented
26#14531260C211yesmaximal, characteristic, complemented
27#14531258C211yesmaximal, characteristic, complemented
28#14531178C211yesmaximal, characteristic
29C4×#10587563C211yesmaximal, characteristic
30C2×#11762655C211yesmaximal, characteristic
31C4×C17×C22⋊Q8C211yesmaximal, characteristic
32C2×#10587610C2211yescharacteristic
33C2×#10587564C2211yescharacteristic
34C2×#10587564C2211yescharacteristic
35C2×C4×Dic34C2211yescharacteristic
36C2×C4×Dic34C2211yescharacteristic
37C2×C4×Dic34C2211yescharacteristic
38C2×#10587563C2211yescharacteristic
39C2×#10587563C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41C22×C4×Dic17C2211yescharacteristic
42#11762750C2211yescharacteristic
43#11762750C2211yescharacteristic
44#11762750C2211yescharacteristic
45#11762750C2211yescharacteristic
46#11762749C2211yescharacteristic
47#11762749C2211yescharacteristic
48#11762747C2211yescharacteristic
49#11762747C2211yescharacteristic
50#11762743C2211yescharacteristic
51#11762743C2211yescharacteristic
52#11762743C2211yescharacteristic
53#11762743C2211yescharacteristic
54#11762742C2211yescharacteristic
55#11762742C2211yescharacteristic
56#11762742C2211yescharacteristic
57#11762742C2211yescharacteristic
58#11762740C2211yescharacteristic
59#11762740C2211yescharacteristic
60#11762740C2211yescharacteristic
61#11762740C2211yescharacteristic
62#11762739C2211yescharacteristic
63#11762739C2211yescharacteristic
64#11762739C2211yescharacteristic
65#11762739C2211yescharacteristic
66#11762730C2211yescharacteristic
67#11762730C2211yescharacteristic
68#11762729C2211yescharacteristic
69#11762729C2211yescharacteristic
70#11762729C2211yescharacteristic
71#11762729C2211yescharacteristic
72#11762728C2211yescharacteristic
73#11762728C2211yescharacteristic
74#11762716C2211yescharacteristic
75#11762716C2211yescharacteristic
76#11762715C2211yescharacteristic
77#11762714C2211yescharacteristic
78#11762714C2211yescharacteristic
79#11762713C2211yescharacteristic
80#11762713C2211yescharacteristic
81#11762713C2211yescharacteristic
82#11762713C2211yescharacteristic
83#11762713C2211yescharacteristic
84#11762713C2211yescharacteristic
85#11762708C2211yescharacteristic
86#11762708C2211yescharacteristic
87#11762707C2211yescharacteristic
88#11762706C2211yescharacteristic
89#11762706C2211yescharacteristic
90#11762705C2211yescharacteristic
91#11762705C2211yescharacteristic
92#11762704C2211yescharacteristic
93#11762704C2211yescharacteristic
94#11762704C2211yescharacteristic
95#11762704C2211yescharacteristic
96#11762696C2211yescharacteristic
97#11762696C2211yescharacteristic
98#11762695C2211yescharacteristic
99#11762695C2211yescharacteristic
100#11762695C2211yescharacteristic
101#11762695C2211yescharacteristic
102#11762694C2211yescharacteristic
103#11762694C2211yescharacteristic
104#11762694C2211yescharacteristic
105#11762694C2211yescharacteristic
106#11762693C2211yescharacteristic
107#11762693C2211yescharacteristic
108#11762692C2211yescharacteristic
109#11762692C2211yescharacteristic
110#11762691C2211yescharacteristic
111#11762691C2211yescharacteristic
112#11762691C2211yescharacteristic
113#11762691C2211yescharacteristic
114#11762690C2211yescharacteristic
115#11762690C2211yescharacteristic
116#11762690C2211yescharacteristic
117#11762690C2211yescharacteristic
118#11762684C2211yescharacteristic
119#11762684C2211yescharacteristic
120#11762682C2211yescharacteristic
121#11762682C2211yescharacteristic
122#11762681C2211yescharacteristic
123#11762681C2211yescharacteristic
124#11762676C2211yescharacteristic
125#11762676C2211yescharacteristic
126#11762673C2211yescharacteristic
127#11762673C2211yescharacteristic
128#11762670C2211yescharacteristic
129#11762670C2211yescharacteristic
130#11762669C2211yescharacteristic
131#11762667C2211yescharacteristic
132#11762667C2211yescharacteristic
133#11762667C2211yescharacteristic
134#11762667C2211yescharacteristic
135C4×#63225C2211yescharacteristic
136C4×#63225C2211yescharacteristic
137C4×#63225C2211yescharacteristic
138C4×#63225C2211yescharacteristic
139C4×#63225C2211yescharacteristic
140C4×#63225C2211yescharacteristic
141C4×#63225C2211yescharacteristic
142C4×#63225C2211yescharacteristic
143C4×#63225C2211yescharacteristic
144C4×#63225C2211yescharacteristic
145C4×C4⋊Dic17C2211yescharacteristic
146C4×C4⋊Dic17C2211yescharacteristic
147C4×C4⋊Dic17C2211yescharacteristic
148#11762660C2211yescharacteristic
149#11762660C2211yescharacteristic
150C22⋊C4×Dic17C2211yescharacteristic
151C22⋊C4×Dic17C2211yescharacteristic
152C4×C22⋊Dic17C2211yescharacteristic
153C4×C22⋊Dic17C2211yescharacteristic
154#11762655C2211yescharacteristic
155#11762655C2211yescharacteristic
156#11762655C2211yescharacteristic
157#11762655C2211yescharacteristic
158#11762655C2211yescharacteristic
159#11762655C2211yescharacteristic
160#11762655C2211yescharacteristic
161#11762655C2211yescharacteristic
162#11762655C2211yescharacteristic
163#11762655C2211yescharacteristic
164#11762654C2211yescharacteristic
165#11762654C2211yescharacteristic
166C2×#10587502C2211yescharacteristic
167C2×#10587502C2211yescharacteristic
168C2×#10587502C2211yescharacteristic
169C2×#10587502C2211yescharacteristic
170C42×Dic17C2211yescharacteristic
171C42×Dic17C2211yescharacteristic
172C2×C17×C22⋊Q8C2211yescharacteristic
173C2×C4×Q8×C17C2211yescharacteristic
174C22×C42×C17C2211yescharacteristic
175C17×#391C2211yescharacteristic
176C17×#389C2211yescharacteristic
177C17×#387C2211yescharacteristic
178C17×#387C2211yescharacteristic
179C17×#385C2211yescharacteristic
180C17×#385C2211yescharacteristic
181C17×#380C2211yescharacteristic
182C4×C4⋊C4×C17C2211yescharacteristic
183C4×C4⋊C4×C17C2211yescharacteristic
184C4×C4⋊C4×C17C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic
187C22×Q8×C17C2311yescharacteristic
188C23×C4×C17C2311yescharacteristic
189C23×C4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×Dic17C2311yescharacteristic
192C23×Dic17C2311yescharacteristic
193C23×Dic17C2311yescharacteristic
194C23×Dic17C2311yescharacteristic
195C22×Dic34C2311yescharacteristic
196C22×Dic34C2311yescharacteristic
197C22×Dic34C2311yescharacteristic
198C17×C22⋊Q8—24no—
199C4×Q8×C17—24no—
200C2×C4⋊C4×C17C2311yescharacteristic
201C2×C4⋊C4×C17C2311yescharacteristic
202C2×C4⋊C4×C17C2311yescharacteristic
203C2×C4⋊C4×C17C2311yescharacteristic
204C2×C4⋊C4×C17C2311yescharacteristic
205C2×C4⋊C4×C17C2311yescharacteristic
206C2×C4⋊C4×C17C2311yescharacteristic
207C2×C4⋊C4×C17C2311yescharacteristic
208C2×C4⋊C4×C17C2311yescharacteristic
209C2×C22⋊C4×C17C2311yescharacteristic
210C2×C22⋊C4×C17C2311yescharacteristic
211C2×C22⋊C4×C17C2311yescharacteristic
212C2×C22⋊C4×C17C2311yescharacteristic
213C2×C42×C17—24no—
214C2×C42×C17C2311yescharacteristic
215C2×C42×C17C2311yescharacteristic
216C2×C42×C17C2311yescharacteristic
217C2×C42×C17C2311yescharacteristic
218C2×C42×C17C2311yescharacteristic
219C2×C42×C17C2311yescharacteristic
220C2×C42×C17C2311yescharacteristic
221C2×C42×C17C2311yescharacteristic
222C2×C22⋊Dic17C2311yescharacteristic
223C2×C22⋊Dic17C2311yescharacteristic
224C2×C22⋊Dic17C2311yescharacteristic
225C2×C22⋊Dic17C2311yescharacteristic
226C2×C4⋊Dic17C2311yescharacteristic
227C2×C4⋊Dic17C2311yescharacteristic
228C2×C4⋊Dic17C2311yescharacteristic
229C2×C4⋊Dic17C2311yescharacteristic
230C2×C4⋊Dic17C2311yescharacteristic
231C2×C4⋊Dic17C2311yescharacteristic
232C2×C4⋊Dic17C2311yescharacteristic
233C2×C4⋊Dic17C2311yescharacteristic
234C2×C4⋊Dic17C2311yescharacteristic
235#10587610—24no—
236C2×#63225C2311yescharacteristic
237C2×#63225C2311yescharacteristic
238C2×#63225C2311yescharacteristic
239C2×#63225C2311yescharacteristic
240C2×#63225C2311yescharacteristic
241C2×#63225C2311yescharacteristic
242C2×#63225C2311yescharacteristic
243C2×#63225C2311yescharacteristic
244C2×#63225C2311yescharacteristic
245C2×#63225C2311yescharacteristic
246C2×#63225C2311yescharacteristic
247C2×#63225C2311yescharacteristic
248C2×#63225C2311yescharacteristic
249C2×#63225C2311yescharacteristic
250C2×#63225C2311yescharacteristic
251C2×#63225C2311yescharacteristic
252C2×#63225C2311yescharacteristic
253C2×#63225C2311yescharacteristic
254C2×#63225C2311yescharacteristic
255C2×#63225C2311yescharacteristic
256C2×#63225C2311yescharacteristic
257C2×#63225C2311yescharacteristic
258C2×#63225C2311yescharacteristic
259C2×#63225C2311yescharacteristic
260C2×#63225C2311yescharacteristic
261C2×#63225C2311yescharacteristic
262C2×C4×Dic17—24no—
263C2×C4×Dic17Q818yescomplemented
264C2×C4×Dic17C2311yescharacteristic
265C2×C4×Dic17C2311yescharacteristic
266C2×C4×Dic17C2311yescharacteristic
267C2×C4×Dic17C2311yescharacteristic
268C2×C4×Dic17C2311yescharacteristic
269C2×C4×Dic17C2311yescharacteristic
270C2×C4×Dic17C2311yescharacteristic
271C2×C4×Dic17C2311yescharacteristic
272C2×C4×Dic17C2311yescharacteristic
273C2×C4×Dic17C2311yescharacteristic
274C2×C4×Dic17C2311yescharacteristic
275C2×C4×Dic17C2311yescharacteristic
276C2×C4×Dic17C2311yescharacteristic
277C2×C4×Dic17C2311yescharacteristic
278C2×C4×Dic17C2311yescharacteristic
279C2×C4×Dic17C2311yescharacteristic
280C2×C4×Dic17C2311yescharacteristic
281C2×C4×Dic17C2311yescharacteristic
282C2×C4×Dic17C2311yescharacteristic
283C2×C4×Dic17C2311yescharacteristic
284#10587564—24no—
285#10587564—24no—
286#10587563—24no—
287#10587563—24no—
288C4×Dic34—24no—
289C4×Dic34—24no—
290C4×Dic34—24no—
291C17×#95C2311yescharacteristic
292C17×#95C2311yescharacteristic
293C17×#95C2311yescharacteristic
294C17×#95C2311yescharacteristic
295C17×#95C2311yescharacteristic
296C17×#95C2311yescharacteristic
297C17×#95C2311yescharacteristic
298C17×#95C2311yescharacteristic
299C17×#95C2311yescharacteristic
300C17×#95C2311yescharacteristic
301#10587502C2311yescharacteristic
302#10587502C2311yescharacteristic
303#10587502C2311yescharacteristic
304#10587502C2311yescharacteristic
305#10587502C2311yescharacteristic
306#10587502C2311yescharacteristic
307#10587502C2311yescharacteristic
308#10587502C2311yescharacteristic
309#10587502C2311yescharacteristic
310#10587502C2311yescharacteristic
311#10587502C2311yescharacteristic
312#10587502C2311yescharacteristic
313#10587502C2311yescharacteristic
314#10587502C2311yescharacteristic
315#10587502C2311yescharacteristic
316#10587502C2311yescharacteristic
317#10587502C2311yescharacteristic
318#10587502C2311yescharacteristic
319#10587502C2311yescharacteristic
320#10587502C2311yescharacteristic
321#10587502C2311yescharacteristic
322#10587502C2311yescharacteristic
323#10587502C2311yescharacteristic
324#10587502C2311yescharacteristic
325#10587502C2311yescharacteristic
326#10587502C2311yescharacteristic
327#10587502C2311yescharacteristic
328#10587502C2311yescharacteristic
329#10587502C2311yescharacteristic
330#10587502C2311yescharacteristic
331#10587502C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355C24×C17C2411yescharacteristic
356C2×Q8×C17—22no—
357C2×Q8×C17—22no—
358C2×Q8×C17—41no—
359C22×C4×C17—22no—
360C22×C4×C17—22no—
361C22×C4×C17—22no—
362C22×C4×C17—22no—
363C22×C4×C17—22no—
364C22×C4×C17—22no—
365C22×C4×C17—41no—
366C22×C4×C17—41no—
367C22×C4×C17C2×Q814yes—
368C22×C4×C17C2411yescharacteristic
369C22×C4×C17C2411yescharacteristic
370C22×C4×C17C2411yescharacteristic
371C22×C4×C17C2411yescharacteristic
372C22×C4×C17C2411yescharacteristic
373C22×C4×C17C2411yescharacteristic
374C22×C4×C17C2411yescharacteristic
375C22×C4×C17C2411yescharacteristic
376C22×C4×C17C2411yescharacteristic
377C22×C4×C17C2411yescharacteristic
378C22×C4×C17C2411yescharacteristic
379C22×C4×C17C2411yescharacteristic
380C22×C4×C17C2411yescharacteristic
381C22×C4×C17C2411yescharacteristic
382C22×Dic17—22no—
383C22×Dic17—22no—
384C22×Dic17—22no—
385C22×Dic17—22no—
386C22×Dic17—22no—
387C22×Dic17—22no—
388C22×Dic17—41no—
389C22×Dic17—41no—
390C22×Dic17—41no—
391C22×Dic17—41no—
392C22×Dic17C2×Q814yes—
393C22×Dic17C2×Q814yes—
394C22×Dic17C2411yescharacteristic
395C22×Dic17C2411yescharacteristic
396C22×Dic17C2411yescharacteristic
397C22×Dic17C2411yescharacteristic
398C22×Dic17C2411yescharacteristic
399C22×Dic17C2411yescharacteristic
400C22×Dic17C2411yescharacteristic
401C22×Dic17C2411yescharacteristic
402C22×Dic17C2411yescharacteristic
403C22×Dic17C2411yescharacteristic
404C22×Dic17C2411yescharacteristic
405C22×Dic17C2411yescharacteristic
406C22×Dic17C2411yescharacteristic
407C22×Dic17C2411yescharacteristic
408C22×Dic17C2411yescharacteristic
409C22×Dic17C2411yescharacteristic
410C2×Dic34—22no—
411C2×Dic34—22no—
412C2×Dic34—22no—
413C2×Dic34—22no—
414C2×Dic34—22no—
415C2×Dic34—22no—
416C2×Dic34—41no—
417C2×Dic34—41no—
418C2×Dic34—41no—
419C4⋊C4×C17—22no—
420C4⋊C4×C17—22no—
421C4⋊C4×C17—22no—
422C4⋊C4×C17—22no—
423C4⋊C4×C17—22no—
424C4⋊C4×C17—22no—
425C4⋊C4×C17—41no—
426C4⋊C4×C17—41no—
427C4⋊C4×C17—41no—
428C22⋊C4×C17—22no—
429C22⋊C4×C17—22no—
430C22⋊C4×C17—22no—
431C22⋊C4×C17#4114yes—
432C42×C17—22no—
433C42×C17—22no—
434C42×C17—22no—
435C42×C17—22no—
436C42×C17—22no—
437C42×C17—22no—
438C42×C17—22no—
439C42×C17#4114yes—
440C22⋊Dic17—22no—
441C22⋊Dic17—22no—
442C22⋊Dic17—22no—
443C22⋊Dic17#4114yes—
444C4⋊Dic17—22no—
445C4⋊Dic17—22no—
446C4⋊Dic17—22no—
447C4⋊Dic17—22no—
448C4⋊Dic17—22no—
449C4⋊Dic17—22no—
450C4⋊Dic17—41no—
451C4⋊Dic17—41no—
452C4⋊Dic17—41no—
453#63225—22no—
454#63225—22no—
455#63225—22no—
456#63225—22no—
457#63225—22no—
458#63225—22no—
459#63225—22no—
460#63225—22no—
461#63225—22no—
462#63225—22no—
463#63225—22no—
464#63225—22no—
465#63225—22no—
466#63225—22no—
467#63225—22no—
468#63225—22no—
469#63225—41no—
470#63225—41no—
471#63225—41no—
472#63225—41no—
473#63225—41no—
474#63225—41no—
475#63225—41no—
476#63225—41no—
477#63225—41no—
478#63225—41no—
479C4×Dic17—22no—
480C4×Dic17—22no—
481C4×Dic17—22no—
482C4×Dic17—22no—
483C4×Dic17—22no—
484C4×Dic17—22no—
485C4×Dic17—22no—
486C4×Dic17—22no—
487C4×Dic17—22no—
488C4×Dic17—22no—
489C4×Dic17—22no—
490C4×Dic17—41no—
491C4×Dic17—41no—
492C4×Dic17—41no—
493C4×Dic17—41no—
494C4×Dic17C2×Q814yes—
495C4×Dic17C2×Q814yes—
496C4×Dic17C2×Q814yes—
497C4×Dic17C2×Q814yes—
498C4×Dic17#4114yes—
499#34878—171nomaximal, Sylow
500C23×C17—21no—
501C23×C17—21no—
502C23×C17—21no—
503C23×C17—21no—
504C23×C17C22×Q812yes—
505C23×C17C2×#4112yes—
506C23×C17C2×#4112yes—
507C23×C17C2511yescharacteristic
508Q8×C17—44no—
509C2×C4×C17—21no—
510C2×C4×C17—21no—
511C2×C4×C17—21no—
512C2×C4×C17—21no—
513C2×C4×C17—21no—
514C2×C4×C17—21no—
515C2×C4×C17—21no—
516C2×C4×C17—21no—
517C2×C4×C17—21no—
518C2×C4×C17—21no—
519C2×C4×C17—28no—
520C2×C4×C17—21no—
521C2×C4×C17—21no—
522C2×C4×C17—21no—
523C2×C4×C17—21no—
524C2×C4×C17—21no—
525C2×C4×C17—21no—
526C2×C4×C17—21no—
527C2×C4×C17—21no—
528C2×C4×C17—21no—
529C2×C4×C17—21no—
530C2×C4×C17—21no—
531C2×C4×C17—21no—
532C2×C4×C17—21no—
533C2×C4×C17—21no—
534C2×C4×C17—21no—
535C2×C4×C17—21no—
536C2×C4×C17—21no—
537C2×C4×C17—21no—
538C2×C4×C17—21no—
539C2×C4×C17—21no—
540C2×C4×C17—21no—
541C2×C4×C17—21no—
542C2×C4×C17—21no—
543C2×C4×C17—21no—
544C2×C4×C17—44no—
545C2×C4×C17—44no—
546C2×C4×C17C22×Q812yes—
547C2×C4×C17C22×Q812yes—
548C2×C4×C17C2×#4112yes—
549C2×C4×C17C2×#4112yes—
550C2×C4×C17C2×#4112yes—
551C2×C4×C17C2×#4112yes—
552C2×C4×C17C2×#4112yes—
553C2×C4×C17C2×#4112yes—
554C2×Dic17—28no—
555C2×Dic17—21no—
556C2×Dic17—21no—
557C2×Dic17—21no—
558C2×Dic17—21no—
559C2×Dic17—21no—
560C2×Dic17—21no—
561C2×Dic17—21no—
562C2×Dic17—21no—
563C2×Dic17—21no—
564C2×Dic17—21no—
565C2×Dic17—21no—
566C2×Dic17—21no—
567C2×Dic17—21no—
568C2×Dic17—21no—
569C2×Dic17—21no—
570C2×Dic17—21no—
571C2×Dic17—21no—
572C2×Dic17—21no—
573C2×Dic17—21no—
574C2×Dic17—21no—
575C2×Dic17—21no—
576C2×Dic17—21no—
577C2×Dic17—21no—
578C2×Dic17—21no—
579C2×Dic17—21no—
580C2×Dic17—21no—
581C2×Dic17—21no—
582C2×Dic17—21no—
583C2×Dic17—21no—
584C2×Dic17—21no—
585C2×Dic17—21no—
586C2×Dic17—21no—
587C2×Dic17—21no—
588C2×Dic17—21no—
589C2×Dic17—21no—
590C2×Dic17—21no—
591C2×Dic17—21no—
592C2×Dic17—21no—
593C2×Dic17—21no—
594C2×Dic17—21no—
595C2×Dic17—44no—
596C2×Dic17—44no—
597C2×Dic17—44no—
598C2×Dic17C22×Q812yes—
599C2×Dic17C22×Q812yes—
600C2×Dic17C22×Q812yes—
601C2×Dic17C22×Q812yes—
602C2×Dic17C2×#4112yes—
603C2×Dic17C2×#4112yes—
604C2×Dic17C2×#4112yes—
605C2×Dic17C2×#4112yes—
606Dic34—44no—
607Dic34—44no—
608Dic34—44no—
609#2612—171no—
610#2612—171no—
611#2612—171no—
612#2612—171no—
613#2606—171no—
614#2606—171no—
615#2605—171no—
616#2605—171no—
617#2569—171no—
618#2569—171no—
619#2549—171no—
620#2549—171no—
621#2438—171no—
622#2438—171no—
623#2438—171no—
624#2438—171no—
625#2402—171no—
626#2402—171no—
627#2399—171no—
628#2399—171no—
629C4×C22⋊Q8—171no—
630C4×C22⋊Q8—171no—
631C4×C22⋊Q8—171no—
632C4×C22⋊Q8D1711yescharacteristic
633#2295—171no—
634#2295—171no—
635#2295—171no—
636#2295—171no—
637#2283—171no—
638C4×#117—171no—
639C2×#376—171no—
640C22×C17—22no—
641C22×C17—22no—
642C22×C17—22no—
643C22×C17—22no—
644C22×C17—22no—
645C22×C17—22no—
646C22×C17#53314yes—
647C22×C17C23×Q811yescharacteristic
648C22×C17C22×#4111yescharacteristic
649C22×C17C22×#4111yescharacteristic
650C22×C17C22×#4111yescharacteristic
651C22×C17C22×#4111yescharacteristic
652C22×C17#58511yescharacteristic
653C22×C17#58511yescharacteristic
654C4×C17—22no—
655C4×C17—22no—
656C4×C17—22no—
657C4×C17—22no—
658C4×C17—22no—
659C4×C17—41no—
660C4×C17—41no—
661C4×C17—41no—
662C4×C17—41no—
663C4×C17—41no—
664C4×C17—41no—
665C4×C17—41no—
666C4×C17—41no—
667C4×C17#53314yes—
668Dic17—22no—
669Dic17—22no—
670Dic17—22no—
671Dic17—22no—
672Dic17—22no—
673Dic17—22no—
674Dic17—22no—
675Dic17—22no—
676Dic17—41no—
677Dic17—41no—
678Dic17—41no—
679Dic17—41no—
680Dic17—41no—
681Dic17—41no—
682Dic17—41no—
683Dic17—41no—
684C2×C22⋊Q8—171no—
685C2×C22⋊Q8—171no—
686C2×C22⋊Q8—171no—
687C2×C22⋊Q8C2×D1711yescharacteristic
688C2×C4×Q8—171no—
689C2×C4×Q8—171no—
690C2×C4×Q8—171no—
691C2×C4×Q8C2×D1711yescharacteristic
692C2×#117—171no—
693C2×#117—171no—
694C22×C42—171no—
695C22×C42—171no—
696C22×C42C2×D1711yescharacteristic
697#400—171no—
698#400—171no—
699#400—171no—
700#400—171no—
701#400—171no—
702#400—171no—
703#400—171no—
704#400—171no—
705#398—171no—
706#398—171no—
707#398—171no—
708#398—171no—
709#398—171no—
710#398—171no—
711#398—171no—
712#398—171no—
713#398—171no—
714#398—171no—
715#398—171no—
716#398—171no—
717#398—171no—
718#398—171no—
719#398—171no—
720#398—171no—
721#395—171no—
722#395—171no—
723#395—171no—
724#395—171no—
725#395—171no—
726#395—171no—
727#395—171no—
728#395—171no—
729#391—171no—
730#391—171no—
731#391—171no—
732#391—171no—
733#391—171no—
734#391—171no—
735#391—171no—
736#391—171no—
737#391—171no—
738#391—171no—
739#391—171no—
740#391C2×D1711yescharacteristic
741#389—171no—
742#389—171no—
743#389—171no—
744#389—171no—
745#389—171no—
746#389—171no—
747#389—171no—
748#389—171no—
749#389—171no—
750#389—171no—
751#389—171no—
752#389C2×D1711yescharacteristic
753#387—171no—
754#387—171no—
755#387—171no—
756#387—171no—
757#387—171no—
758#387—171no—
759#387—171no—
760#387—171no—
761#387—171no—
762#387—171no—
763#387—171no—
764#387—171no—
765#387—171no—
766#387—171no—
767#387—171no—
768#387—171no—
769#387—171no—
770#387—171no—
771#387—171no—
772#387—171no—
773#387—171no—
774#387—171no—
775#387C2×D1711yescharacteristic
776#387C2×D1711yescharacteristic
777#385—171no—
778#385—171no—
779#385—171no—
780#385—171no—
781#385—171no—
782#385—171no—
783#385C2×D1711yescharacteristic
784#385C2×D1711yescharacteristic
785#383—171no—
786#383—171no—
787#382—171no—
788#382—171no—
789#381—171no—
790#381—171no—
791#380—171no—
792#380—171no—
793#380—171no—
794#380—171no—
795#380—171no—
796#380C2×D1711yescharacteristic
797C4×C4⋊C4—171no—
798C4×C4⋊C4—171no—
799C4×C4⋊C4—171no—
800C4×C4⋊C4—171no—
801C4×C4⋊C4—171no—
802C4×C4⋊C4—171no—
803C4×C4⋊C4—171no—
804C4×C4⋊C4—171no—
805C4×C4⋊C4—171no—
806C4×C4⋊C4—171no—
807C4×C4⋊C4—171no—
808C4×C4⋊C4—171no—
809C4×C4⋊C4—171no—
810C4×C4⋊C4—171no—
811C4×C4⋊C4—171no—
812C4×C4⋊C4C2×D1711yescharacteristic
813C4×C4⋊C4C2×D1711yescharacteristic
814C4×C4⋊C4C2×D1711yescharacteristic
815C4×C22⋊C4—171no—
816C4×C22⋊C4—171no—
817C4×C22⋊C4—171no—
818C4×C22⋊C4—171no—
819C4×C22⋊C4C2×D1711yescharacteristic
820C4×C22⋊C4C2×D1711yescharacteristic
821#376—171no—
822#376—171no—
823#376—171no—
824#376—171no—
825#376—171no—
826#376—171no—
827#376—171no—
828#376—171no—
829#376—171no—
830#376—171no—
831#376—171no—
832#376—171no—
833C2×#95—171no—
834C2×#95—171no—
835C2×#95—171no—
836C2×#95—171no—
837C43—171no—
838C43—171no—
839C2×C17—24no—
840C2×C17C2×#53311yescharacteristic
841C2×C17C2×#53311yescharacteristic
842C2×C17#345811yescharacteristic
843C2×C17#347511yescharacteristic
844C2×C17#347511yescharacteristic
845C2×C17#347511yescharacteristic
846C2×C17#347511yescharacteristic
847C22×Q8—171no—
848C22×Q8—171no—
849C22×Q8—171no—
850C22×Q8C22×D1711yescharacteristic
851C23×C4—171no—
852C23×C4—171no—
853C23×C4—171no—
854C23×C4—171no—
855C23×C4C22×D1711yescharacteristic
856C23×C4C22×D1711yescharacteristic
857C23×C4C22×D1711yescharacteristic
858C22⋊Q8—24no—
859C22⋊Q8—344no—
860C22⋊Q8—344no—
861C22⋊Q8—344no—
862C4×Q8—24no—
863C4×Q8—344no—
864C4×Q8—344no—
865C4×Q8—344no—
866#117—344no—
867#117—344no—
868C2×C4⋊C4—171no—
869C2×C4⋊C4—171no—
870C2×C4⋊C4—171no—
871C2×C4⋊C4—171no—
872C2×C4⋊C4—171no—
873C2×C4⋊C4—171no—
874C2×C4⋊C4—171no—
875C2×C4⋊C4—171no—
876C2×C4⋊C4—171no—
877C2×C4⋊C4—171no—
878C2×C4⋊C4—171no—
879C2×C4⋊C4—171no—
880C2×C4⋊C4—171no—
881C2×C4⋊C4—171no—
882C2×C4⋊C4—171no—
883C2×C4⋊C4—171no—
884C2×C4⋊C4—171no—
885C2×C4⋊C4—171no—
886C2×C4⋊C4—171no—
887C2×C4⋊C4—171no—
888C2×C4⋊C4—171no—
889C2×C4⋊C4—171no—
890C2×C4⋊C4—171no—
891C2×C4⋊C4—171no—
892C2×C4⋊C4—171no—
893C2×C4⋊C4—171no—
894C2×C4⋊C4—171no—
895C2×C4⋊C4—171no—
896C2×C4⋊C4—171no—
897C2×C4⋊C4—171no—
898C2×C4⋊C4—171no—
899C2×C4⋊C4—171no—
900C2×C4⋊C4—171no—
901C2×C4⋊C4—171no—
902C2×C4⋊C4—171no—
903C2×C4⋊C4C22×D1711yescharacteristic
904C2×C4⋊C4C22×D1711yescharacteristic
905C2×C4⋊C4C22×D1711yescharacteristic
906C2×C4⋊C4C22×D1711yescharacteristic
907C2×C4⋊C4C22×D1711yescharacteristic
908C2×C4⋊C4C22×D1711yescharacteristic
909C2×C4⋊C4C22×D1711yescharacteristic
910C2×C4⋊C4C22×D1711yescharacteristic
911C2×C4⋊C4C22×D1711yescharacteristic
912C2×C22⋊C4—171no—
913C2×C22⋊C4—171no—
914C2×C22⋊C4—171no—
915C2×C22⋊C4—171no—
916C2×C22⋊C4C22×D1711yescharacteristic
917C2×C22⋊C4C22×D1711yescharacteristic
918C2×C22⋊C4C22×D1711yescharacteristic
919C2×C22⋊C4C22×D1711yescharacteristic
920C2×C42—24no—
921C2×C42—178no—
922C2×C42—171no—
923C2×C42—171no—
924C2×C42—171no—
925C2×C42—171no—
926C2×C42—171no—
927C2×C42—171no—
928C2×C42—171no—
929C2×C42—171no—
930C2×C42—171no—
931C2×C42—171no—
932C2×C42—171no—
933C2×C42—171no—
934C2×C42—171no—
935C2×C42—171no—
936C2×C42—171no—
937C2×C42—171no—
938C2×C42—171no—
939C2×C42—171no—
940C2×C42—171no—
941C2×C42—171no—
942C2×C42—344no—
943C2×C42C22×D1711yescharacteristic
944C2×C42C22×D1711yescharacteristic
945C2×C42C22×D1711yescharacteristic
946C2×C42C22×D1711yescharacteristic
947C2×C42C22×D1711yescharacteristic
948C2×C42C22×D1711yescharacteristic
949C2×C42C22×D1711yescharacteristic
950C2×C42C22×D1711yescharacteristic
951#95—171no—
952#95—171no—
953#95—171no—
954#95—171no—
955#95—171no—
956#95—171no—
957#95—171no—
958#95—171no—
959#95—171no—
960#95—171no—
961#95—171no—
962#95—171no—
963#95—171no—
964#95—171no—
965#95—171no—
966#95—171no—
967#95—171no—
968#95—171no—
969#95—171no—
970#95—171no—
971#95—171no—
972#95—171no—
973#95—171no—
974#95—171no—
975#95—171no—
976#95—171no—
977#95—171no—
978#95—171no—
979#95—171no—
980#95—171no—
981#95—171no—
982#95—171no—
983#95—171no—
984#95—171no—
985#95—171no—
986#95—171no—
987#95—171no—
988#95—171no—
989#95—171no—
990#95—171no—
991#95—171no—
992#95—171no—
993#95—171no—
994#95—171no—
995#95—171no—
996#95—171no—
997#95—171no—
998#95—171no—
999#95—171no—
1000#95—171no—
1001#95—171no—
1002#95—171no—
1003#95—171no—
1004#95—171no—
1005#95C22×D1711yescharacteristic
1006#95C22×D1711yescharacteristic
1007#95C22×D1711yescharacteristic
1008#95C22×D1711yescharacteristic
1009#95C22×D1711yescharacteristic
1010#95C22×D1711yescharacteristic
1011#95C22×D1711yescharacteristic
1012#95C22×D1711yescharacteristic
1013#95C22×D1711yescharacteristic
1014#95C22×D1711yescharacteristic
1015C17#3487811yescharacteristic, complemented, Sylow
1016C24C23×D1711yescharacteristic
1017C2×Q8—22no—
1018C2×Q8—22no—
1019C2×Q8—41no—
1020C2×Q8—342no—
1021C2×Q8—342no—
1022C2×Q8—342no—
1023C2×Q8—342no—
1024C2×Q8—342no—
1025C2×Q8—342no—
1026C2×Q8—681no—
1027C2×Q8—681no—
1028C2×Q8—681no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—174no—
1038C22×C4—171no—
1039C22×C4—171no—
1040C22×C4—171no—
1041C22×C4—171no—
1042C22×C4—171no—
1043C22×C4—171no—
1044C22×C4—171no—
1045C22×C4—171no—
1046C22×C4—174no—
1047C22×C4—171no—
1048C22×C4—171no—
1049C22×C4—171no—
1050C22×C4—171no—
1051C22×C4—171no—
1052C22×C4—171no—
1053C22×C4—171no—
1054C22×C4—171no—
1055C22×C4—342no—
1056C22×C4—342no—
1057C22×C4—342no—
1058C22×C4—342no—
1059C22×C4—342no—
1060C22×C4—342no—
1061C22×C4—681no—
1062C22×C4—681no—
1063C22×C4—681no—
1064C22×C4—681no—
1065C22×C4Q8×D1714yes—
1066C22×C4C23×D1711yescharacteristic
1067C22×C4C23×D1711yescharacteristic
1068C22×C4C23×D1711yescharacteristic
1069C22×C4C23×D1711yescharacteristic
1070C22×C4C23×D1711yescharacteristic
1071C22×C4C23×D1711yescharacteristic
1072C22×C4C23×D1711yescharacteristic
1073C22×C4C23×D1711yescharacteristic
1074C22×C4C23×D1711yescharacteristic
1075C22×C4C23×D1711yescharacteristic
1076C22×C4C23×D1711yescharacteristic
1077C22×C4C23×D1711yescharacteristic
1078C22×C4C23×D1711yescharacteristic
1079C22×C4C23×D1711yescharacteristic
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—342no—
1090C4⋊C4—342no—
1091C4⋊C4—342no—
1092C4⋊C4—342no—
1093C4⋊C4—342no—
1094C4⋊C4—342no—
1095C4⋊C4—342no—
1096C4⋊C4—342no—
1097C4⋊C4—342no—
1098C4⋊C4—342no—
1099C4⋊C4—342no—
1100C4⋊C4—342no—
1101C4⋊C4—342no—
1102C4⋊C4—342no—
1103C4⋊C4—342no—
1104C4⋊C4—342no—
1105C4⋊C4—342no—
1106C4⋊C4—342no—
1107C4⋊C4—342no—
1108C4⋊C4—342no—
1109C4⋊C4—342no—
1110C4⋊C4—342no—
1111C4⋊C4—681no—
1112C4⋊C4—681no—
1113C4⋊C4—681no—
1114C4⋊C4—681no—
1115C4⋊C4—681no—
1116C4⋊C4—681no—
1117C4⋊C4—681no—
1118C4⋊C4—681no—
1119C4⋊C4—681no—
1120C4⋊C4—681no—
1121C4⋊C4—681no—
1122C4⋊C4—681no—
1123C4⋊C4—681no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—174no—
1128C22⋊C4—342no—
1129C22⋊C4—342no—
1130C22⋊C4—342no—
1131C22⋊C4#6325214yes—
1132C42—22no—
1133C42—22no—
1134C42—22no—
1135C42—22no—
1136C42—22no—
1137C42—22no—
1138C42—22no—
1139C42—174no—
1140C42—174no—
1141C42—174no—
1142C42—174no—
1143C42—174no—
1144C42—342no—
1145C42—342no—
1146C42—342no—
1147C42—342no—
1148C42—342no—
1149C42—342no—
1150C42—342no—
1151C42—342no—
1152C42—342no—
1153C42—342no—
1154C42—342no—
1155C42—681no—
1156C42—681no—
1157C42—681no—
1158C42—681no—
1159C42#6325414yes—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23C2×#6325212yes—
1165C23C2×Q8×D1712yes—
1166C23#41×D1712yes—
1167C23C24×D1711yescharacteristic
1168Q8—44no—
1169Q8—684no—
1170Q8—684no—
1171Q8—684no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—28no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—172no—
1210C2×C4—172no—
1211C2×C4—172no—
1212C2×C4—172no—
1213C2×C4—172no—
1214C2×C4—172no—
1215C2×C4—172no—
1216C2×C4—172no—
1217C2×C4—348no—
1218C2×C4—341no—
1219C2×C4—341no—
1220C2×C4—341no—
1221C2×C4—341no—
1222C2×C4—341no—
1223C2×C4—341no—
1224C2×C4—341no—
1225C2×C4—341no—
1226C2×C4—341no—
1227C2×C4—341no—
1228C2×C4—341no—
1229C2×C4—341no—
1230C2×C4—341no—
1231C2×C4—341no—
1232C2×C4—341no—
1233C2×C4—341no—
1234C2×C4—341no—
1235C2×C4—341no—
1236C2×C4—341no—
1237C2×C4—341no—
1238C2×C4—341no—
1239C2×C4—341no—
1240C2×C4—341no—
1241C2×C4—341no—
1242C2×C4—341no—
1243C2×C4—341no—
1244C2×C4—341no—
1245C2×C4—341no—
1246C2×C4—341no—
1247C2×C4—341no—
1248C2×C4—341no—
1249C2×C4—341no—
1250C2×C4—341no—
1251C2×C4—341no—
1252C2×C4—341no—
1253C2×C4—341no—
1254C2×C4—341no—
1255C2×C4—341no—
1256C2×C4—341no—
1257C2×C4—341no—
1258C2×C4—684no—
1259C2×C4—684no—
1260C2×C4—684no—
1261C2×C4C2×#6325212yes—
1262C2×C4C2×#6325212yes—
1263C2×C4C2×#6325412yes—
1264C2×C4C2×#6325412yes—
1265C2×C4C2×#6325412yes—
1266C2×C4C2×Q8×D1712yes—
1267C2×C4C2×Q8×D1712yes—
1268C2×C4#41×D1712yes—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22#1176336314yes—
1276C22C22×Q8×D1711yescharacteristic
1277C22C2×#41×D1711yescharacteristic
1278C22C2×#41×D1711yescharacteristic
1279C22C22×#6325411yescharacteristic
1280C22C22×#6325211yescharacteristic
1281C22#1176364511yescharacteristic
1282C22#1176364511yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—22no—
1287C4—22no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—342no—
1297C4—342no—
1298C4—342no—
1299C4—342no—
1300C4—342no—
1301C4—342no—
1302C4—342no—
1303C4—342no—
1304C4—681no—
1305C4—681no—
1306C4—681no—
1307C4—681no—
1308C4—681no—
1309C4—681no—
1310C4—681no—
1311C4—681no—
1312C4#1176336114yes—
1313C2—24no—
1314C2C2×#1176336111yescharacteristic
1315C2C2×#1176336311yescharacteristic
1316C2#1454218711yescharacteristic
1317C2#1454233611yescharacteristic
1318C2#1454234211yescharacteristic
1319C2#1454234411yescharacteristic
1320C2#1454234611yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutator, socle, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC4×C17×C22⋊Q8C2
prime radicalC24×C17C24
hypercenterC4×C22⋊Q8D17
hypocenterC17#34878
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14534494C2semidirect
2. #14534491C2semidirect
3. #14534490C2semidirect
4. #14534489C2semidirect
5. #14534440C2semidirect
6. #14534438C2semidirect
7. #14534431C2semidirect
8. #14534429C2semidirect
17. #14532091C2semidirect
18. #14532091C2semidirect
19. #14532078C2semidirect
20. #14532075C2semidirect
24. #14531262C2semidirect
25. #14531260C2semidirect
26. #14531260C2semidirect
27. #14531258C2semidirect
263. C2×C4×Dic17Q8semidirect
1015. C17#34878semidirect

Maximal subgroups

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

subgroupindex
#145344942
#145344912
#145344902
#145344892
#145344402
#145344382
#145344312
#145344292
#145340102
#145340052
#145337972
#145337922
#145324662
#145324642
#145324582
#145324562
#145320912
#145320782
#145320752
C4×#105876102
C4×#105875642
#145312622
#145312602
#145312582
#145311782
C4×#105875632
C2×#117626552
C4×C17×C22⋊Q82
#3487817