Finite Group Databasebeta

← #34018646

Subgroups — #34018646

Order 18688.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×#10596833C211yesmaximal, characteristic
2#22626719C211yesmaximal, characteristic, complemented
3#22625544C211yesmaximal, characteristic, complemented
4#22625542C211yesmaximal, characteristic, complemented
5#22625536C211yesmaximal, characteristic, complemented
6#22625534C211yesmaximal, characteristic, complemented
7#22625525C211yesmaximal, characteristic, complemented
8#22625524C211yesmaximal, characteristic, complemented
9#22625522C211yesmaximal, characteristic, complemented
10SD16⋊#10596833C211yesmaximal, characteristic, complemented
11#22625507C211yesmaximal, characteristic, complemented
12#22625266C211yesmaximal, characteristic
13#22625253C211yesmaximal, characteristic, complemented
14#22625142C211yesmaximal, characteristic, complemented
15#22619995C211yesmaximal, characteristic
16#17989639—21no—
17#17989638C2211yescharacteristic
18#17989637C2211yescharacteristic
19#17989636—21no—
20#17989636C2211yescharacteristic
21Q8×#10596833C2211yescharacteristic
22Q8×#10596833C2211yescharacteristic
23Q8×#10596833C2211yescharacteristic
24D4×#10596833—21no—
25D4×#10596833—21no—
26D4×#10596833C2211yescharacteristic
27D4×#10596833C2211yescharacteristic
28#17989603—21no—
29#17989603C2211yescharacteristic
30#17989593—21no—
31#17989590C2211yescharacteristic
32#17989551—21no—
33C4×#11924037C2211yescharacteristic
34C2×C4×#10596833—21no—
35C2×C4×#10596833C2211yescharacteristic
36#17989451C2211yescharacteristic
37#17989450C2211yescharacteristic
38#17989449C2211yescharacteristic
39#17989448C2211yescharacteristic
40#17989437C2211yescharacteristic
41#17989437C2211yescharacteristic
42Q8⋊#10596833C2211yescharacteristic
43Q8⋊#10596833C2211yescharacteristic
44Q8⋊#10596833C2211yescharacteristic
45Q8⋊#10596833C2211yescharacteristic
46D4⋊#10596833C2211yescharacteristic
47D4⋊#10596833C2211yescharacteristic
48#17989429C2211yescharacteristic
49#17989429C2211yescharacteristic
50#17989428C2211yescharacteristic
51#17989428C2211yescharacteristic
52#17989139C2211yescharacteristic
53#41×Dic73C2211yescharacteristic
54#17988929C411yescharacteristic
55#17988925C411yescharacteristic
56#17988870C411yescharacteristic
57#17988865C411yescharacteristic
58#17988795C411yescharacteristic
59#17988790C411yescharacteristic
60#17988749C411yescharacteristic
61Q16×Dic73C2211yescharacteristic
62#17988679C2211yescharacteristic
63#17988678C2211yescharacteristic
64SD16×Dic73C2211yescharacteristic
65#17988637C2211yescharacteristic
66#452×C73C411yescharacteristic
67C2×#11924037—21no—
68C2×#11924037—21no—
69C22×#10596833—21no—
70C22×#10596833—21no—
71C22×#10596833D411yescharacteristic
72C22×#10596833D411yescharacteristic
73#14556658—21no—
74#14556658—21no—
75#14556658—21no—
76C4⋊#10596833—21no—
77C4⋊#10596833—21no—
78C4⋊#10596833—21no—
79C4⋊#10596833—21no—
80C4⋊#10596833C2311yescharacteristic
81C4⋊#10596833C2311yescharacteristic
82C4⋊#10596833C2311yescharacteristic
83C4⋊#10596833C2311yescharacteristic
84C22⋊#10596833—21no—
85C22⋊#10596833—21no—
86C22⋊#10596833—21no—
87#14556646—21no—
88#14556646—21no—
89#14556646—21no—
90C4×#10596833—21no—
91C4×#10596833—21no—
92C4×#10596833—21no—
93C4×#10596833—21no—
94C4×#10596833—21no—
95C4×#10596833D411yescharacteristic
96C4×#10596833D411yescharacteristic
97C4×#10596833C2311yescharacteristic
98C4×#10596833C2311yescharacteristic
99C4×#10596833C2311yescharacteristic
100C4×#10596833C2311yescharacteristic
101C2×#11924018C2×C411yescharacteristic
102C2×#11924016C2×C411yescharacteristic
103#14556590C2×C411yescharacteristic
104#14556589C2×C411yescharacteristic
105#14556581—21no—
106#14556570C2×C411yescharacteristic
107#14556568—21no—
108Q8×Dic73C2×C411yescharacteristic
109Q8×Dic73C2311yescharacteristic
110Q8×Dic73C2311yescharacteristic
111#14556556—21no—
112#14556556C2311yescharacteristic
113D4×Dic73—21no—
114D4×Dic73—21no—
115D4×Dic73C2×C411yescharacteristic
116D4×Dic73C2311yescharacteristic
117#14556550—21no—
118#14556550C2×C411yescharacteristic
119#14556547—21no—
120C2×C4×Dic73—21no—
121C2×C4×Dic73C2311yescharacteristic
122#14556525C2×C411yescharacteristic
123#14556524C2×C411yescharacteristic
124#14556523C2×C411yescharacteristic
125#14556522C2×C411yescharacteristic
126#14556520C2×C411yescharacteristic
127#14556520C2×C411yescharacteristic
128#14556516C2×C411yescharacteristic
129#14556516C2×C411yescharacteristic
130#14556515C2×C411yescharacteristic
131#14556515C2×C411yescharacteristic
132#14556515C2×C411yescharacteristic
133#14556512C2×C411yescharacteristic
134C22⋊#10596831C2×C411yescharacteristic
135C8×Dic73C2311yescharacteristic
136C8×Dic73C2311yescharacteristic
137C2×#41×C73C2×C411yescharacteristic
138C2×Q16×C73C2×C411yescharacteristic
139C2×SD16×C73C2×C411yescharacteristic
140C22⋊Q8×C73C2×C411yescharacteristic
141#103×C73C2×C411yescharacteristic
142#102×C73C2×C411yescharacteristic
143C22⋊C8×C73C2×C411yescharacteristic
144#11924037—42no—
145#11924037—42no—
146C2×#10596833—22no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—41no—
154C2×#10596833—42no—
155C2×#10596833—42no—
156C2×#10596833C2×D411yescharacteristic
157C2×#10596833C2×D411yescharacteristic
158C2×#10596833C2×D411yescharacteristic
159C2×#10596833C2×D411yescharacteristic
160C2×Dic146—21no—
161C2×Dic146C22×C411yescharacteristic
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73C2×D411yescharacteristic
165C22×Dic73#4111yescharacteristic
166#11924018—22no—
167#11924016—22no—
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C22×C411yescharacteristic
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73C22×C411yescharacteristic
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181C22⋊Dic73—21no—
182C22⋊Dic73—21no—
183C22⋊Dic73—21no—
184C22⋊Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73C22×C411yescharacteristic
191C4×Dic73C2×D411yescharacteristic
192C4×Dic73#4111yescharacteristic
193C4×Dic73C2411yescharacteristic
194#41×C73—22no—
195#41×C73—22no—
196C2×Q8×C73C22×C411yescharacteristic
197C2×Q8×C73C22×C411yescharacteristic
198C2×D4×C73—21no—
199C2×D4×C73C22×C411yescharacteristic
200C22×C4×C73—21no—
201C22×C4×C73C22×C411yescharacteristic
202Q16×C73—22no—
203SD16×C73—22no—
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C4⋊C4×C73—21no—
207C4⋊C4×C73C22×C411yescharacteristic
208C22⋊C4×C73—21no—
209C23×C73—21no—
210C23×C73C4×D411yescharacteristic
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—21no—
214Q8×C73#13112yes—
215D4×C73—24no—
216D4×C73—21no—
217D4×C73#13112yes—
218C2×C4×C73—24no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C23×C411yescharacteristic
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—22no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—41no—
234C2×Dic73—41no—
235C2×Dic73—42no—
236C2×Dic73C4×D411yescharacteristic
237C2×Dic73C4×D411yescharacteristic
238C2×Dic73C22×D411yescharacteristic
239C2×Dic73C2×#4111yescharacteristic
240Dic146—21no—
241Dic146—21no—
242Dic146—42no—
243#10596833—21no—
244#10596833—21no—
245#10596833—21no—
246#10596833—41no—
247#10596833—41no—
248#10596833—41no—
249#10596833—41no—
250#10596833—41no—
251#10596833—41no—
252#10596833#13712yes—
253C8×C73—21no—
254C8×C73—21no—
255#10596831—21no—
256#10596831—21no—
257C22×C73—21no—
258C22×C73—22no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—41no—
262C22×C73—41no—
263C22×C73C2×C4×D411yescharacteristic
264C4×C73—21no—
265C4×C73—22no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73C2×#13111yescharacteristic
269C4×C73C2×#13111yescharacteristic
270Dic73—21no—
271Dic73—21no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275Dic73—41no—
276Dic73#44412yes—
277Dic73C2×#13711yescharacteristic
278Dic73#57511yescharacteristic
279#17916—731nomaximal, Sylow
280C2×C73—41no—
281C2×C73—42no—
282C2×C73#292911yescharacteristic
283C2×C73C4×#13711yescharacteristic
284C2×C73C2×#44411yescharacteristic
285#3107—731no—
286C8×#41—731no—
287#2960—731no—
288#1584—731no—
289#1584—731no—
290#1582—731no—
291#1582—731no—
292#1579—731no—
293#1579—731no—
294SD16⋊C8—731no—
295SD16⋊C8—731no—
296#1574—731no—
297#1489—731no—
298#1485—731no—
299#1451—731no—
300C73#1791611yescharacteristic, complemented, Sylow
301#533—731no—
302C4×#41—731no—
303#485—731no—
304#485—731no—
305#475—731no—
306#474—731no—
307#462—731no—
308#461—731no—
309#452—731no—
310#452#6440811yescharacteristic
311#446—731no—
312#446—731no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C8×Q8—731no—
318C8×Q8—1461no—
319C4×Q16—731no—
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16—731no—
323C8×D4—731no—
324C8×D4—731no—
325C8×D4—1461no—
326C8×D4—1461no—
327#431—731no—
328#431—731no—
329#431—1461no—
330#424—1461no—
331#423—731no—
332#405—1461no—
333C4×M16—731no—
334C2×C4×C8—731no—
335C2×C4×C8—1461no—
336#335—731no—
337#335—731no—
338#334—731no—
339#334—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342Q8⋊C8—731no—
343Q8⋊C8—731no—
344Q8⋊C8—731no—
345Q8⋊C8—731no—
346D4⋊C8—731no—
347D4⋊C8—731no—
348#322—731no—
349#322—731no—
350#322—731no—
351#322—731no—
352C2×#41C2×#6440811yescharacteristic
353C2×Q16—731no—
354C2×Q16C2×#6440811yescharacteristic
355C2×SD16—731no—
356C2×SD16C2×#6440811yescharacteristic
357C2×M16—1461no—
358C2×M16—1461no—
359C22×C8—731no—
360C22×C8—731no—
361C22×C8—1461no—
362C22×C8—1461no—
363C4⋊Q8—731no—
364C4⋊Q8—731no—
365#125—1461no—
366C22⋊Q8—731no—
367C22⋊Q8—1461no—
368C22⋊Q8C2×#6440811yescharacteristic
369C4×Q8—731no—
370C4×Q8—731no—
371C4×Q8—731no—
372C4×Q8—731no—
373C4×Q8—1461no—
374C4×D4—731no—
375C4×D4—731no—
376C4×D4—1461no—
377C4×D4—1461no—
378#117—731no—
379#117—1461no—
380#117—1461no—
381C2×C42—731no—
382C2×C42—1461no—
383#107—731no—
384#107—731no—
385#106—731no—
386#106—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—731no—
392C4⋊C8—731no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8—1461no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400#103—731no—
401#103—731no—
402#103—731no—
403#103—731no—
404#103—731no—
405#103C2×#6440811yescharacteristic
406#102—731no—
407#102C2×#6440811yescharacteristic
408C22⋊C8—731no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8C2×#6440811yescharacteristic
413#97—1461no—
414#97—1461no—
415#97—1461no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—1461no—
425C4×C8—1461no—
426C4×C8—1461no—
427C4×C8—1461no—
428C4×C8—1461no—
429#41—22no—
430#41—22no—
431C2×Q8—731no—
432C2×Q8—1461no—
433C2×Q8C22×#6440811yescharacteristic
434C2×Q8C22×#6440811yescharacteristic
435C2×D4—21no—
436C2×D4C22×#6440811yescharacteristic
437C22×C4—21no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4C22×#6440811yescharacteristic
443Q16—22no—
444Q16—1462no—
445SD16—22no—
446SD16—1462no—
447M16—2922no—
448M16—2922no—
449C2×C8—2922no—
450C2×C8—2922no—
451C2×C8—2921no—
452C2×C8—731no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—731no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1462no—
465C2×C8C22×#6440811yescharacteristic
466C2×C8C22×#6440811yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—731no—
469C4⋊C4—731no—
470C4⋊C4—731no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4C22×#6440811yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—1461no—
482C22⋊C4—1461no—
483C22⋊C4—1461no—
484C22⋊C4—1461no—
485C42—731no—
486C42—731no—
487C42—731no—
488C42—731no—
489C42—1461no—
490C42—1461no—
491C42—1461no—
492C42—1461no—
493C42—1461no—
494C23—21no—
495C23D4×#6440811yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—2922no—
500Q8—1461no—
501Q8—1461no—
502Q8#1455667812yes—
503D4—24no—
504D4—21no—
505D4#1455667812yes—
506C2×C4—24no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—2921no—
513C2×C4—2921no—
514C2×C4—2922no—
515C2×C4—731no—
516C2×C4—731no—
517C2×C4—731no—
518C2×C4—731no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1462no—
526C2×C4D4×#6440811yescharacteristic
527C2×C4C23×#6440811yescharacteristic
528C8—21no—
529C8—21no—
530C8—2921no—
531C8—2921no—
532C8—2921no—
533C8—2921no—
534C8—2921no—
535C8—2921no—
536C8—732no—
537C8—1461no—
538C8—1461no—
539C8—1461no—
540C8—1461no—
541C8—1461no—
542C22—21no—
543C22—22no—
544C22—21no—
545C22—21no—
546C22—41no—
547C22—41no—
548C22C2×D4×#6440811yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—2921no—
554C4—2921no—
555C4—2921no—
556C4—2921no—
557C4—731no—
558C4—731no—
559C4—732no—
560C4—1461no—
561C4—1461no—
562C4C2×#1455667811yescharacteristic
563C4C2×#1455667811yescharacteristic
564C2—41no—
565C2—42no—
566C2#2262664611yescharacteristic
567C2#137×#6440811yescharacteristic
568C2D73⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#452×C73C4
socleC22×C73C2×C4×D4
prime radicalC2×#41×C73C2×C4
cosocleC4×Dic73C24
hypercenter#452#64408
hypocenterC73#17916
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #22626719C2semidirect
3. #22625544C2semidirect
4. #22625542C2semidirect
5. #22625536C2semidirect
6. #22625534C2semidirect
7. #22625525C2semidirect
8. #22625524C2semidirect
9. #22625522C2semidirect
10. SD16⋊#10596833C2semidirect
11. #22625507C2semidirect
13. #22625253C2semidirect
14. #22625142C2semidirect
300. C73#17916semidirect

Maximal subgroups

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

subgroupindex
#41×#105968332
#226267192
#226255442
#226255422
#226255362
#226255342
#226255252
#226255242
#226255222
SD16⋊#105968332
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