Finite Group Databasebeta

← #17201675

Subgroups — #17201675

Order 4352.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534883C211yesmaximal, characteristic, complemented
2#14534876C211yesmaximal, characteristic, complemented
3#14534869C211yesmaximal, characteristic, complemented
4#14534860C211yesmaximal, characteristic, complemented
5#14534849C211yesmaximal, characteristic, complemented
6#14534842C211yesmaximal, characteristic, complemented
7#14534835C211yesmaximal, characteristic, complemented
8#14534826C211yesmaximal, characteristic, complemented
9#14534821C211yesmaximal, characteristic, complemented
10#14534814C211yesmaximal, characteristic, complemented
11#14534807C211yesmaximal, characteristic, complemented
12#14534798C211yesmaximal, characteristic, complemented
13#14534787C211yesmaximal, characteristic, complemented
14#14534780C211yesmaximal, characteristic, complemented
15#14534773C211yesmaximal, characteristic
16#14532090C211yesmaximal, characteristic, complemented
17#14532081C211yesmaximal, characteristic, complemented
18#14532081C211yesmaximal, characteristic, complemented
19#14532072C211yesmaximal, characteristic, complemented
20#14532059C211yesmaximal, characteristic, complemented
21#14532040C211yesmaximal, characteristic, complemented
22#14532040C211yesmaximal, characteristic, complemented
23#14532019C211yesmaximal, characteristic
24#14531278C211yesmaximal, characteristic, complemented
25#14531278C211yesmaximal, characteristic, complemented
26#14531257C211yesmaximal, characteristic, complemented
27#14531246C211yesmaximal, characteristic, complemented
28#14531224C211yesmaximal, characteristic, complemented
29#14531224C211yesmaximal, characteristic, complemented
30C4×#10587563C211yesmaximal, characteristic, complemented
31C17×#2648C211yesmaximal, characteristic
32C2×#10587573C2211yescharacteristic
33C2×D4×Dic17C2211yescharacteristic
34C2×D4×Dic17C2211yescharacteristic
35C2×D4×Dic17C2211yescharacteristic
36C2×#10587563C2211yescharacteristic
37C2×#10587563C2211yescharacteristic
38C2×#10587563C2211yescharacteristic
39C2×#10587563C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41C17⋊#401C2211yescharacteristic
42C17⋊#401C2211yescharacteristic
43#11762751C2211yescharacteristic
44#11762751C2211yescharacteristic
45#11762751C2211yescharacteristic
46#11762751C2211yescharacteristic
47#11762751C2211yescharacteristic
48#11762750C2211yescharacteristic
49#11762750C2211yescharacteristic
50#11762750C2211yescharacteristic
51#11762750C2211yescharacteristic
52#11762750C2211yescharacteristic
53#11762749C2211yescharacteristic
54#11762748C2211yescharacteristic
55#11762747C2211yescharacteristic
56#11762747C2211yescharacteristic
57#11762745C2211yescharacteristic
58#11762745C2211yescharacteristic
59#11762745C2211yescharacteristic
60#11762743C2211yescharacteristic
61#11762743C2211yescharacteristic
62#11762742C2211yescharacteristic
63#11762742C2211yescharacteristic
64#11762742C2211yescharacteristic
65#11762742C2211yescharacteristic
66#11762741C2211yescharacteristic
67#11762740C2211yescharacteristic
68#11762739C2211yescharacteristic
69#11762737C2211yescharacteristic
70#11762737C2211yescharacteristic
71#11762737C2211yescharacteristic
72#11762737C2211yescharacteristic
73#11762737C2211yescharacteristic
74#11762737C2211yescharacteristic
75#11762737C2211yescharacteristic
76#11762737C2211yescharacteristic
77#11762737C2211yescharacteristic
78#11762737C2211yescharacteristic
79#11762734C2211yescharacteristic
80#11762734C2211yescharacteristic
81#11762734C2211yescharacteristic
82#11762732C2211yescharacteristic
83#11762732C2211yescharacteristic
84#11762732C2211yescharacteristic
85#11762732C2211yescharacteristic
86#11762732C2211yescharacteristic
87#11762729C2211yescharacteristic
88#11762723C2211yescharacteristic
89#11762723C2211yescharacteristic
90#11762723C2211yescharacteristic
91#11762723C2211yescharacteristic
92#11762723C2211yescharacteristic
93#11762723C2211yescharacteristic
94#11762721C2211yescharacteristic
95#11762721C2211yescharacteristic
96#11762721C2211yescharacteristic
97#11762713C2211yescharacteristic
98#11762713C2211yescharacteristic
99#11762712C2211yescharacteristic
100#11762707C2211yescharacteristic
101#11762706C2211yescharacteristic
102#11762705C2211yescharacteristic
103#11762704C2211yescharacteristic
104#11762703C2211yescharacteristic
105#11762703C2211yescharacteristic
106#11762703C2211yescharacteristic
107#11762703C2211yescharacteristic
108#11762703C2211yescharacteristic
109#11762703C2211yescharacteristic
110#11762702C2211yescharacteristic
111#11762702C2211yescharacteristic
112#11762697C2211yescharacteristic
113#11762697C2211yescharacteristic
114#11762697C2211yescharacteristic
115#11762697C2211yescharacteristic
116#11762697C2211yescharacteristic
117#11762697C2211yescharacteristic
118#11762696C2211yescharacteristic
119#11762696C2211yescharacteristic
120#11762695C2211yescharacteristic
121#11762694C2211yescharacteristic
122#11762694C2211yescharacteristic
123#11762693C2211yescharacteristic
124#11762693C2211yescharacteristic
125#11762693C2211yescharacteristic
126#11762692C2211yescharacteristic
127#11762692C2211yescharacteristic
128#11762691C2211yescharacteristic
129#11762691C2211yescharacteristic
130#11762691C2211yescharacteristic
131#11762690C2211yescharacteristic
132#11762690C2211yescharacteristic
133#11762689C2211yescharacteristic
134#11762689C2211yescharacteristic
135#11762682C2211yescharacteristic
136#11762682C2211yescharacteristic
137#11762681C2211yescharacteristic
138#11762681C2211yescharacteristic
139C4⋊C4×Dic17C2211yescharacteristic
140C4⋊C4×Dic17C2211yescharacteristic
141C4⋊C4×Dic17C2211yescharacteristic
142C4⋊C4×Dic17C2211yescharacteristic
143C4×#63225C2211yescharacteristic
144C4×#63225C2211yescharacteristic
145#11762660C2211yescharacteristic
146#11762660C2211yescharacteristic
147#11762660C2211yescharacteristic
148#11762660C2211yescharacteristic
149#11762660C2211yescharacteristic
150#11762660C2211yescharacteristic
151#11762660C2211yescharacteristic
152#11762660C2211yescharacteristic
153C22⋊C4×Dic17C2211yescharacteristic
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic
164C22⋊C4×Dic17C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic
166#11762654C2211yescharacteristic
167#11762654C2211yescharacteristic
168#11762654C2211yescharacteristic
169#11762654C2211yescharacteristic
170C42×Dic17C2211yescharacteristic
171C42×Dic17C2211yescharacteristic
172C17×#400C2211yescharacteristic
173C17×#397C2211yescharacteristic
174C17×#397C2211yescharacteristic
175C17×#396C2211yescharacteristic
176C17×#394C2211yescharacteristic
177C17×#394C2211yescharacteristic
178C17×#394C2211yescharacteristic
179C17×#392C2211yescharacteristic
180C17×#390C2211yescharacteristic
181C17×#388C2211yescharacteristic
182C17×#388C2211yescharacteristic
183C17×#387C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic
187C22×D4×C17C2311yescharacteristic
188C22×D4×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×Dic17C2311yescharacteristic
192C23×Dic17C2311yescharacteristic
193C23×Dic17C2311yescharacteristic
194C23×Dic17C2311yescharacteristic
195C22×Dic34C2311yescharacteristic
196C2×C4⋊C4×C17C2311yescharacteristic
197C2×C4⋊C4×C17C2311yescharacteristic
198C2×C4⋊C4×C17C2311yescharacteristic
199C2×C4⋊C4×C17C2311yescharacteristic
200C2×C4⋊C4×C17C2311yescharacteristic
201C2×C22⋊C4×C17C2311yescharacteristic
202C2×C22⋊C4×C17C2311yescharacteristic
203C2×C22⋊C4×C17C2311yescharacteristic
204C2×C22⋊C4×C17C2311yescharacteristic
205C2×C22⋊C4×C17C2311yescharacteristic
206C2×C22⋊C4×C17C2311yescharacteristic
207C2×C22⋊C4×C17C2311yescharacteristic
208C2×C22⋊C4×C17C2311yescharacteristic
209C2×C22⋊C4×C17C2311yescharacteristic
210C2×C22⋊C4×C17C2311yescharacteristic
211C2×C22⋊C4×C17C2311yescharacteristic
212C2×C22⋊C4×C17C2311yescharacteristic
213C2×C22⋊C4×C17C2311yescharacteristic
214C2×C22⋊C4×C17C2311yescharacteristic
215C2×C42×C17C2311yescharacteristic
216C2×C42×C17C2311yescharacteristic
217C2×C22⋊Dic17C2311yescharacteristic
218C2×C22⋊Dic17C2311yescharacteristic
219C2×C22⋊Dic17C2311yescharacteristic
220C2×C22⋊Dic17C2311yescharacteristic
221C2×C22⋊Dic17C2311yescharacteristic
222C2×C22⋊Dic17C2311yescharacteristic
223C2×C22⋊Dic17C2311yescharacteristic
224C2×C22⋊Dic17C2311yescharacteristic
225C2×C22⋊Dic17C2311yescharacteristic
226C2×C22⋊Dic17C2311yescharacteristic
227C2×C22⋊Dic17C2311yescharacteristic
228C2×C22⋊Dic17C2311yescharacteristic
229C2×C22⋊Dic17C2311yescharacteristic
230C2×C22⋊Dic17C2311yescharacteristic
231C2×C22⋊Dic17C2311yescharacteristic
232C2×C22⋊Dic17C2311yescharacteristic
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237D4×Dic17—24no—
238D4×Dic17—24no—
239D4×Dic17—24no—
240C2×C4⋊Dic17C2311yescharacteristic
241C2×C4⋊Dic17C2311yescharacteristic
242C2×C4⋊Dic17C2311yescharacteristic
243C2×C4⋊Dic17C2311yescharacteristic
244C2×C4⋊Dic17C2311yescharacteristic
245C2×C4⋊Dic17C2311yescharacteristic
246C2×C4⋊Dic17C2311yescharacteristic
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×#63225C2311yescharacteristic
263C2×#63225C2311yescharacteristic
264C2×#63225C2311yescharacteristic
265C2×#63225C2311yescharacteristic
266C2×#63225C2311yescharacteristic
267C2×#63225C2311yescharacteristic
268C2×#63225C2311yescharacteristic
269C2×C4×Dic17—24no—
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
284C2×C4×Dic17C2311yescharacteristic
285C2×C4×Dic17C2311yescharacteristic
286C2×C4×Dic17C2311yescharacteristic
287C2×C4×Dic17C2311yescharacteristic
288C2×C4×Dic17C2311yescharacteristic
289C2×C4×Dic17C2311yescharacteristic
290#10587573—24no—
291#10587563—24no—
292#10587563—24no—
293#10587563—24no—
294#10587563—24no—
295C17×#95C2311yescharacteristic
296C17×#95C2311yescharacteristic
297C17×#95C2311yescharacteristic
298C17×#95C2311yescharacteristic
299C17×#95C2311yescharacteristic
300C17×#95C2311yescharacteristic
301C17×#95C2311yescharacteristic
302C17×#95C2311yescharacteristic
303C17×#95C2311yescharacteristic
304C17×#95C2311yescharacteristic
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
351C24×C17C2411yescharacteristic
352C24×C17C2411yescharacteristic
353C24×C17C2411yescharacteristic
354C2×D4×C17—22no—
355C2×D4×C17—22no—
356C2×D4×C17—22no—
357C2×D4×C17—41no—
358C2×D4×C17—41no—
359C2×D4×C17—41no—
360C2×D4×C17—41no—
361C2×D4×C17—41no—
362C2×D4×C17—41no—
363C22×C4×C17—22no—
364C22×C4×C17—41no—
365C22×C4×C17—41no—
366C22×C4×C17C2411yescharacteristic
367C22×C4×C17C2411yescharacteristic
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×Dic17—22no—
379C22×Dic17—22no—
380C22×Dic17—22no—
381C22×Dic17—22no—
382C22×Dic17—22no—
383C22×Dic17—22no—
384C22×Dic17—22no—
385C22×Dic17—22no—
386C22×Dic17—22no—
387C22×Dic17—41no—
388C22×Dic17—41no—
389C22×Dic17#4114yes—
390C22×Dic17C2411yescharacteristic
391C22×Dic17C2411yescharacteristic
392C22×Dic17C2411yescharacteristic
393C22×Dic17C2411yescharacteristic
394C22×Dic17C2411yescharacteristic
395C22×Dic17C2411yescharacteristic
396C22×Dic17C2411yescharacteristic
397C22×Dic17C2411yescharacteristic
398C22×Dic17C2411yescharacteristic
399C22×Dic17C2411yescharacteristic
400C22×Dic17C2411yescharacteristic
401C22×Dic17C2411yescharacteristic
402C22×Dic17C2411yescharacteristic
403C22×Dic17C2411yescharacteristic
404C22×Dic17C2411yescharacteristic
405C22×Dic17C2411yescharacteristic
406C2×Dic34—22no—
407C2×Dic34—41no—
408C2×Dic34—41no—
409C4⋊C4×C17—22no—
410C4⋊C4×C17—41no—
411C4⋊C4×C17—41no—
412C4⋊C4×C17—41no—
413C4⋊C4×C17—41no—
414C22⋊C4×C17—22no—
415C22⋊C4×C17—22no—
416C22⋊C4×C17—22no—
417C22⋊C4×C17—22no—
418C22⋊C4×C17—41no—
419C22⋊C4×C17—41no—
420C22⋊C4×C17—41no—
421C22⋊C4×C17—41no—
422C22⋊C4×C17—41no—
423C22⋊C4×C17—41no—
424C22⋊C4×C17—41no—
425C22⋊C4×C17—41no—
426C22⋊C4×C17—41no—
427C22⋊C4×C17—41no—
428C42×C17—41no—
429C42×C17—41no—
430C22⋊Dic17—22no—
431C22⋊Dic17—22no—
432C22⋊Dic17—22no—
433C22⋊Dic17—22no—
434C22⋊Dic17—22no—
435C22⋊Dic17—22no—
436C22⋊Dic17—22no—
437C22⋊Dic17—22no—
438C22⋊Dic17—22no—
439C22⋊Dic17—22no—
440C22⋊Dic17—41no—
441C22⋊Dic17—41no—
442C22⋊Dic17—41no—
443C22⋊Dic17—41no—
444C22⋊Dic17—41no—
445C22⋊Dic17—41no—
446C22⋊Dic17—41no—
447C22⋊Dic17—41no—
448C22⋊Dic17—41no—
449C22⋊Dic17—41no—
450C4⋊Dic17—22no—
451C4⋊Dic17—22no—
452C4⋊Dic17—22no—
453C4⋊Dic17—41no—
454C4⋊Dic17—41no—
455C4⋊Dic17—41no—
456C4⋊Dic17—41no—
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—41no—
468#63225—41no—
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—22no—
491C4×Dic17—41no—
492C4×Dic17—41no—
493C4×Dic17—41no—
494C4×Dic17—41no—
495C4×Dic17—41no—
496C4×Dic17—41no—
497C4×Dic17#4114yes—
498C4×Dic17#4114yes—
499#34640—171nomaximal, Sylow
500C23×C17—21no—
501C23×C17—21no—
502C23×C17—21no—
503C23×C17—21no—
504C23×C17—21no—
505C23×C17—21no—
506C23×C17—21no—
507C23×C17—21no—
508C23×C17—21no—
509C23×C17—21no—
510C23×C17—21no—
511C23×C17—21no—
512C23×C17—21no—
513C23×C17—21no—
514C23×C17—21no—
515C23×C17—21no—
516C23×C17—21no—
517C23×C17—21no—
518C23×C17—21no—
519C23×C17—21no—
520C23×C17C2×#4112yes—
521C23×C17C2511yescharacteristic
522D4×C17—44no—
523D4×C17—44no—
524D4×C17—44no—
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—21no—
545C2×C4×C17—21no—
546C2×C4×C17—21no—
547C2×C4×C17—21no—
548C2×C4×C17—21no—
549C2×C4×C17—21no—
550C2×C4×C17—21no—
551C2×C4×C17—21no—
552C2×C4×C17—21no—
553C2×C4×C17—21no—
554C2×C4×C17—21no—
555C2×C4×C17—21no—
556C2×C4×C17—21no—
557C2×C4×C17—21no—
558C2×C4×C17—21no—
559C2×C4×C17—44no—
560C2×C4×C17C2×#4112yes—
561C2×C4×C17C2×#4112yes—
562C2×Dic17—21no—
563C2×Dic17—21no—
564C2×Dic17—21no—
565C2×Dic17—21no—
566C2×Dic17—21no—
567C2×Dic17—21no—
568C2×Dic17—28no—
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—21no—
596C2×Dic17—21no—
597C2×Dic17—21no—
598C2×Dic17—21no—
599C2×Dic17—21no—
600C2×Dic17—21no—
601C2×Dic17—21no—
602C2×Dic17—21no—
603C2×Dic17—21no—
604C2×Dic17—21no—
605C2×Dic17—44no—
606C2×Dic17—44no—
607C2×Dic17—44no—
608C2×Dic17C2×#4112yes—
609C2×Dic17C2×#4112yes—
610C2×Dic17C2×#4112yes—
611C2×Dic17C2×#4112yes—
612C2×Dic17C2×#4112yes—
613C2×Dic17C2×#4112yes—
614Dic34—44no—
615#2655—171no—
616#2655—171no—
617#2654—171no—
618#2654—171no—
619#2653—171no—
620#2653—171no—
621#2652—171no—
622#2652—171no—
623#2651—171no—
624#2651—171no—
625#2650—171no—
626#2650—171no—
627#2649—171no—
628#2649—171no—
629#2648—171no—
630#2648D1711yescharacteristic
631#2402—171no—
632#2401—171no—
633#2401—171no—
634#2398—171no—
635#2396—171no—
636#2395—171no—
637#2395—171no—
638#2392—171no—
639#2298—171no—
640#2298—171no—
641#2295—171no—
642#2293—171no—
643#2290—171no—
644#2290—171no—
645C4×#117—171no—
646C22×C17—22no—
647C22×C17—22no—
648C22×C17—22no—
649C22×C17—41no—
650C22×C17—41no—
651C22×C17—41no—
652C22×C17—41no—
653C22×C17—41no—
654C22×C17—41no—
655C22×C17—41no—
656C22×C17—41no—
657C22×C17—41no—
658C22×C17—41no—
659C22×C17—41no—
660C22×C17—41no—
661C22×C17—41no—
662C22×C17—41no—
663C22×C17—41no—
664C22×C17—41no—
665C22×C17—41no—
666C22×C17—41no—
667C22×C17C22×#4111yescharacteristic
668C22×C17C22×#4111yescharacteristic
669C22×C17C22×#4111yescharacteristic
670C22×C17#58511yescharacteristic
671C22×C17#58511yescharacteristic
672C22×C17#58511yescharacteristic
673C22×C17#58511yescharacteristic
674C4×C17—22no—
675C4×C17—22no—
676C4×C17—41no—
677C4×C17—41no—
678C4×C17—41no—
679C4×C17—41no—
680C4×C17—41no—
681C4×C17—41no—
682C4×C17—41no—
683C4×C17—41no—
684C4×C17—41no—
685C4×C17—41no—
686Dic17—22no—
687Dic17—22no—
688Dic17—22no—
689Dic17—41no—
690Dic17—41no—
691Dic17—41no—
692Dic17—41no—
693Dic17—41no—
694Dic17—41no—
695Dic17—41no—
696Dic17—41no—
697Dic17—41no—
698Dic17—41no—
699Dic17—41no—
700Dic17—41no—
701Dic17#52914yes—
702C2×C4×Q8—171no—
703C2×C4×D4—171no—
704C2×C4×D4—171no—
705C2×C4×D4—171no—
706C2×#117—171no—
707C2×#117—171no—
708C2×#117—171no—
709C2×#117—171no—
710C22×C42—171no—
711#401—171no—
712#401—171no—
713#400—171no—
714#400—171no—
715#400—171no—
716#400—171no—
717#400—171no—
718#400—171no—
719#400—171no—
720#400—171no—
721#400—171no—
722#400—171no—
723#400—171no—
724#400—171no—
725#400—171no—
726#400—171no—
727#400C2×D1711yescharacteristic
728#399—171no—
729#399—171no—
730#399—171no—
731#398—171no—
732#398—171no—
733#398—171no—
734#398—171no—
735#398—171no—
736#398—171no—
737#398—171no—
738#398—171no—
739#398—171no—
740#397—171no—
741#397—171no—
742#397—171no—
743#397—171no—
744#397—171no—
745#397—171no—
746#397—171no—
747#397—171no—
748#397—171no—
749#397—171no—
750#397—171no—
751#397—171no—
752#397—171no—
753#397C2×D1711yescharacteristic
754#397C2×D1711yescharacteristic
755#396—171no—
756#396—171no—
757#396—171no—
758#396—171no—
759#396—171no—
760#396C2×D1711yescharacteristic
761#395—171no—
762#394—171no—
763#394—171no—
764#394—171no—
765#394—171no—
766#394—171no—
767#394—171no—
768#394C2×D1711yescharacteristic
769#394C2×D1711yescharacteristic
770#394C2×D1711yescharacteristic
771#393—171no—
772#393—171no—
773#393—171no—
774#392C2×D1711yescharacteristic
775#391—171no—
776#391—171no—
777#390—171no—
778#390C2×D1711yescharacteristic
779#389—171no—
780#389—171no—
781#389—171no—
782#389—171no—
783#388—171no—
784#388—171no—
785#388—171no—
786#388—171no—
787#388—171no—
788#388—171no—
789#388—171no—
790#388—171no—
791#388—171no—
792#388—171no—
793#388—171no—
794#388—171no—
795#388—171no—
796#388—171no—
797#388C2×D1711yescharacteristic
798#388C2×D1711yescharacteristic
799#387—171no—
800#387—171no—
801#387—171no—
802#387—171no—
803#387—171no—
804#387—171no—
805#387—171no—
806#387—171no—
807#387—171no—
808#387—171no—
809#387—171no—
810#387—171no—
811#387—171no—
812#387—171no—
813#387—171no—
814#387C2×D1711yescharacteristic
815#386—171no—
816#386—171no—
817#386C2×D1711yescharacteristic
818#386C2×D1711yescharacteristic
819#385—171no—
820#385—171no—
821#385—171no—
822#385—171no—
823C4×C4⋊C4—171no—
824C4×C4⋊C4—171no—
825C4×C4⋊C4—171no—
826C4×C4⋊C4—171no—
827C4×C4⋊C4—171no—
828C4×C4⋊C4—171no—
829C4×C4⋊C4—171no—
830C4×C4⋊C4—171no—
831C4×C4⋊C4—171no—
832C4×C4⋊C4—171no—
833C4×C4⋊C4—171no—
834C4×C4⋊C4—171no—
835C4×C4⋊C4—171no—
836C4×C4⋊C4—171no—
837C4×C22⋊C4—171no—
838C4×C22⋊C4—171no—
839C4×C22⋊C4—171no—
840C4×C22⋊C4—171no—
841C4×C22⋊C4—171no—
842C4×C22⋊C4—171no—
843C4×C22⋊C4—171no—
844C4×C22⋊C4—171no—
845C4×C22⋊C4—171no—
846C4×C22⋊C4—171no—
847C4×C22⋊C4—171no—
848C4×C22⋊C4—171no—
849C4×C22⋊C4—171no—
850C4×C22⋊C4C2×D1711yescharacteristic
851#376—171no—
852#376—171no—
853#376—171no—
854#376—171no—
855C43—171no—
856C43—171no—
857C2×C17—42no—
858C2×C17—81no—
859C2×C17—81no—
860C2×C17C2×#52911yescharacteristic
861C2×C17#345511yescharacteristic
862C2×C17#345511yescharacteristic
863C2×C17#345511yescharacteristic
864C2×C17#345511yescharacteristic
865C2×C17#345511yescharacteristic
866C2×C17#345511yescharacteristic
867C22×Q8—171no—
868C22×D4C22×D1711yescharacteristic
869C22×D4C22×D1711yescharacteristic
870C22×D4C22×D1711yescharacteristic
871C23×C4—171no—
872C23×C4—171no—
873C23×C4—171no—
874C23×C4—171no—
875C23×C4C22×D1711yescharacteristic
876C4×Q8—344no—
877C4×D4—344no—
878C4×D4—344no—
879C4×D4—344no—
880#117—344no—
881#117—344no—
882#117—344no—
883#117—344no—
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⋊C4—171no—
904C2×C4⋊C4—171no—
905C2×C4⋊C4—171no—
906C2×C4⋊C4—171no—
907C2×C4⋊C4—171no—
908C2×C4⋊C4—171no—
909C2×C4⋊C4—171no—
910C2×C4⋊C4—171no—
911C2×C4⋊C4—171no—
912C2×C4⋊C4—171no—
913C2×C4⋊C4C22×D1711yescharacteristic
914C2×C4⋊C4C22×D1711yescharacteristic
915C2×C4⋊C4C22×D1711yescharacteristic
916C2×C4⋊C4C22×D1711yescharacteristic
917C2×C4⋊C4C22×D1711yescharacteristic
918C2×C22⋊C4—171no—
919C2×C22⋊C4—171no—
920C2×C22⋊C4—171no—
921C2×C22⋊C4—171no—
922C2×C22⋊C4—171no—
923C2×C22⋊C4—171no—
924C2×C22⋊C4—171no—
925C2×C22⋊C4—171no—
926C2×C22⋊C4—171no—
927C2×C22⋊C4—171no—
928C2×C22⋊C4—171no—
929C2×C22⋊C4—171no—
930C2×C22⋊C4—171no—
931C2×C22⋊C4—171no—
932C2×C22⋊C4—171no—
933C2×C22⋊C4—171no—
934C2×C22⋊C4—171no—
935C2×C22⋊C4—171no—
936C2×C22⋊C4—171no—
937C2×C22⋊C4—171no—
938C2×C22⋊C4C22×D1711yescharacteristic
939C2×C22⋊C4C22×D1711yescharacteristic
940C2×C22⋊C4C22×D1711yescharacteristic
941C2×C22⋊C4C22×D1711yescharacteristic
942C2×C22⋊C4C22×D1711yescharacteristic
943C2×C22⋊C4C22×D1711yescharacteristic
944C2×C22⋊C4C22×D1711yescharacteristic
945C2×C22⋊C4C22×D1711yescharacteristic
946C2×C22⋊C4C22×D1711yescharacteristic
947C2×C22⋊C4C22×D1711yescharacteristic
948C2×C22⋊C4C22×D1711yescharacteristic
949C2×C22⋊C4C22×D1711yescharacteristic
950C2×C22⋊C4C22×D1711yescharacteristic
951C2×C22⋊C4C22×D1711yescharacteristic
952C2×C42—171no—
953C2×C42—171no—
954C2×C42—171no—
955C2×C42—171no—
956C2×C42—171no—
957C2×C42—171no—
958C2×C42—171no—
959C2×C42—171no—
960C2×C42—171no—
961C2×C42—171no—
962C2×C42—171no—
963C2×C42—171no—
964C2×C42—171no—
965C2×C42—171no—
966C2×C42—171no—
967C2×C42—171no—
968C2×C42—171no—
969C2×C42—171no—
970C2×C42—171no—
971C2×C42—171no—
972C2×C42—344no—
973C2×C42C22×D1711yescharacteristic
974C2×C42C22×D1711yescharacteristic
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#95—171no—
1006#95—171no—
1007#95—171no—
1008#95—171no—
1009#95—171no—
1010#95—171no—
1011#95—171no—
1012#95—171no—
1013#95—171no—
1014#95—171no—
1015#95—171no—
1016#95—171no—
1017#95—171no—
1018#95—171no—
1019#95—171no—
1020#95—171no—
1021#95C22×D1711yescharacteristic
1022#95C22×D1711yescharacteristic
1023#95C22×D1711yescharacteristic
1024#95C22×D1711yescharacteristic
1025#95C22×D1711yescharacteristic
1026#95C22×D1711yescharacteristic
1027#95C22×D1711yescharacteristic
1028#95C22×D1711yescharacteristic
1029#95C22×D1711yescharacteristic
1030#95C22×D1711yescharacteristic
1031C17#3464011yescharacteristic, complemented, Sylow
1032C24C23×D1711yescharacteristic
1033C24C23×D1711yescharacteristic
1034C24C23×D1711yescharacteristic
1035C2×Q8—342no—
1036C2×Q8—681no—
1037C2×Q8—681no—
1038C2×D4—22no—
1039C2×D4—22no—
1040C2×D4—22no—
1041C2×D4—41no—
1042C2×D4—41no—
1043C2×D4—41no—
1044C2×D4—41no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C22×C4—22no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—171no—
1051C22×C4—174no—
1052C22×C4—171no—
1053C22×C4—171no—
1054C22×C4—171no—
1055C22×C4—171no—
1056C22×C4—171no—
1057C22×C4—171no—
1058C22×C4—171no—
1059C22×C4—171no—
1060C22×C4—171no—
1061C22×C4—171no—
1062C22×C4—171no—
1063C22×C4—171no—
1064C22×C4—171no—
1065C22×C4—171no—
1066C22×C4—171no—
1067C22×C4—342no—
1068C22×C4—342no—
1069C22×C4—342no—
1070C22×C4—342no—
1071C22×C4—342no—
1072C22×C4—342no—
1073C22×C4—342no—
1074C22×C4—342no—
1075C22×C4—342no—
1076C22×C4—681no—
1077C22×C4—681no—
1078C22×C4C23×D1711yescharacteristic
1079C22×C4C23×D1711yescharacteristic
1080C22×C4C23×D1711yescharacteristic
1081C22×C4C23×D1711yescharacteristic
1082C22×C4C23×D1711yescharacteristic
1083C22×C4C23×D1711yescharacteristic
1084C22×C4C23×D1711yescharacteristic
1085C22×C4C23×D1711yescharacteristic
1086C22×C4C23×D1711yescharacteristic
1087C22×C4C23×D1711yescharacteristic
1088C22×C4C23×D1711yescharacteristic
1089C22×C4C23×D1711yescharacteristic
1090C4⋊C4—22no—
1091C4⋊C4—41no—
1092C4⋊C4—41no—
1093C4⋊C4—41no—
1094C4⋊C4—41no—
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—681no—
1109C4⋊C4—681no—
1110C4⋊C4—681no—
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—22no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—41no—
1138C22⋊C4—342no—
1139C22⋊C4—342no—
1140C22⋊C4—342no—
1141C22⋊C4—342no—
1142C22⋊C4—342no—
1143C22⋊C4—342no—
1144C22⋊C4—342no—
1145C22⋊C4—342no—
1146C22⋊C4—342no—
1147C22⋊C4—342no—
1148C22⋊C4—681no—
1149C22⋊C4—681no—
1150C22⋊C4—681no—
1151C22⋊C4—681no—
1152C22⋊C4—681no—
1153C22⋊C4—681no—
1154C22⋊C4—681no—
1155C22⋊C4—681no—
1156C22⋊C4—681no—
1157C22⋊C4—681no—
1158C42—41no—
1159C42—41no—
1160C42—174no—
1161C42—174no—
1162C42—342no—
1163C42—342no—
1164C42—342no—
1165C42—342no—
1166C42—342no—
1167C42—342no—
1168C42—342no—
1169C42—342no—
1170C42—342no—
1171C42—342no—
1172C42—342no—
1173C42—342no—
1174C42—681no—
1175C42—681no—
1176C42—681no—
1177C42—681no—
1178C42—681no—
1179C42—681no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23#41×D1712yes—
1201C23C24×D1711yescharacteristic
1202Q8—684no—
1203D4—44no—
1204D4—44no—
1205D4—44no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—44no—
1241C2×C4—172no—
1242C2×C4—172no—
1243C2×C4—172no—
1244C2×C4—172no—
1245C2×C4—172no—
1246C2×C4—172no—
1247C2×C4—348no—
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—341no—
1259C2×C4—341no—
1260C2×C4—341no—
1261C2×C4—341no—
1262C2×C4—341no—
1263C2×C4—341no—
1264C2×C4—341no—
1265C2×C4—341no—
1266C2×C4—341no—
1267C2×C4—341no—
1268C2×C4—341no—
1269C2×C4—341no—
1270C2×C4—341no—
1271C2×C4—341no—
1272C2×C4—341no—
1273C2×C4—341no—
1274C2×C4—341no—
1275C2×C4—341no—
1276C2×C4—341no—
1277C2×C4—341no—
1278C2×C4—341no—
1279C2×C4—341no—
1280C2×C4—341no—
1281C2×C4—341no—
1282C2×C4—341no—
1283C2×C4—341no—
1284C2×C4—341no—
1285C2×C4—341no—
1286C2×C4—341no—
1287C2×C4—341no—
1288C2×C4—341no—
1289C2×C4—341no—
1290C2×C4—684no—
1291C2×C4—684no—
1292C2×C4—684no—
1293C2×C4#41×D1712yes—
1294C2×C4#41×D1712yes—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22C2×#41×D1711yescharacteristic
1317C22C2×#41×D1711yescharacteristic
1318C22C2×#41×D1711yescharacteristic
1319C22#1176364411yescharacteristic
1320C22#1176364411yescharacteristic
1321C22#1176364411yescharacteristic
1322C22#1176364411yescharacteristic
1323C4—22no—
1324C4—22no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—174no—
1336C4—342no—
1337C4—342no—
1338C4—342no—
1339C4—681no—
1340C4—681no—
1341C4—681no—
1342C4—681no—
1343C4—681no—
1344C4—681no—
1345C4—681no—
1346C4—681no—
1347C4—681no—
1348C4—681no—
1349C4—681no—
1350C4—681no—
1351C2—42no—
1352C2—81no—
1353C2—81no—
1354C2D17×#52911yescharacteristic
1355C2#1454216611yescharacteristic
1356C2#1454216611yescharacteristic
1357C2#1454216611yescharacteristic
1358C2#1454216611yescharacteristic
1359C2#1454216811yescharacteristic
1360C2#1454216811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2648C2
prime radicalC17×#392C22
hypercenter#2648D17
hypocenterC17#34640
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2648

Complements

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

NH ≅ G/Ntype
1. #14534883C2semidirect
2. #14534876C2semidirect
3. #14534869C2semidirect
4. #14534860C2semidirect
5. #14534849C2semidirect
6. #14534842C2semidirect
7. #14534835C2semidirect
8. #14534826C2semidirect
9. #14534821C2semidirect
10. #14534814C2semidirect
11. #14534807C2semidirect
12. #14534798C2semidirect
13. #14534787C2semidirect
14. #14534780C2semidirect
16. #14532090C2semidirect
17. #14532081C2semidirect
18. #14532081C2semidirect
19. #14532072C2semidirect
20. #14532059C2semidirect
21. #14532040C2semidirect
22. #14532040C2semidirect
24. #14531278C2semidirect
25. #14531278C2semidirect
26. #14531257C2semidirect
27. #14531246C2semidirect
28. #14531224C2semidirect
29. #14531224C2semidirect
30. C4×#10587563C2semidirect
1031. C17#34640semidirect

Maximal subgroups

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

subgroupindex
#145348832
#145348762
#145348692
#145348602
#145348492
#145348422
#145348352
#145348262
#145348212
#145348142
#145348072
#145347982
#145347872
#145347802
#145347732
#145320902
#145320812
#145320722
#145320592
#145320402
#145320192
#145312782
#145312572
#145312462
#145312242
C4×#105875632
C17×#26482
#3464017