Finite Group Databasebeta

← #33057245

Subgroups — #33057245

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620011C211yesmaximal, characteristic
2#22619087C211yesmaximal, characteristic
3#22619020C211yesmaximal, characteristic, complemented
4#22608837C211yesmaximal, characteristic, complemented
5#22608836C211yesmaximal, characteristic, complemented
6#22608784C211yesmaximal, characteristic, complemented
7#22608778C211yesmaximal, characteristic, complemented
8#22608771C211yesmaximal, characteristic, complemented
9#22608770C211yesmaximal, characteristic, complemented
10#22608747C211yesmaximal, characteristic, complemented
11#22608746C211yesmaximal, characteristic, complemented
12#22608714C211yesmaximal, characteristic, complemented
13#22608392C211yesmaximal, characteristic
14#22608223C211yesmaximal, characteristic, complemented
15C2×Q8⋊C8×C73C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988917C411yescharacteristic
18#17988900C411yescharacteristic
19#17988894C411yescharacteristic
20#17988894C411yescharacteristic
21#17988809C411yescharacteristic
22#17988809C411yescharacteristic
23#17988743C411yescharacteristic
24#17988726C411yescharacteristic
25#17988718—21no—
26#17988718—21no—
27#17988718C2211yescharacteristic
28#17988718C2211yescharacteristic
29#17988714C2211yescharacteristic
30Q8×#10596831C2211yescharacteristic
31Q8×#10596831C2211yescharacteristic
32#17988711C2211yescharacteristic
33C4×#11924018C2211yescharacteristic
34C4×#11924018C2211yescharacteristic
35C4×#11924015C2211yescharacteristic
36C4×#11924015C2211yescharacteristic
37#17988664C2211yescharacteristic
38#17988658—21no—
39#17988652C2211yescharacteristic
40C8×C22⋊D73—21no—
41#17988647—21no—
42#17988644—21no—
43#17988644C2211yescharacteristic
44#17988640—21no—
45#17988640C2211yescharacteristic
46#17988640C2211yescharacteristic
47#17988612—21no—
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51#17988337C2211yescharacteristic
52#17988319C2211yescharacteristic
53#17988319C2211yescharacteristic
54#17988316C2211yescharacteristic
55#17988316C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988309C2211yescharacteristic
59#17988309C2211yescharacteristic
60C2×C4×Q8×C73C2211yescharacteristic
61C2×C4⋊C8×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924011—21no—
72C2×C8×D73—21no—
73#14556585—21no—
74#14556583C2×C411yescharacteristic
75#14556579C2×C411yescharacteristic
76#14556574—21no—
77#14556570C2×C411yescharacteristic
78#14556565C2×C411yescharacteristic
79C4×Dic146C2311yescharacteristic
80C4×D292C2311yescharacteristic
81C4×C22⋊D73—21no—
82#14556548—21no—
83#14556524C2×C411yescharacteristic
84#14556524C2×C411yescharacteristic
85#14556522C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87C4⋊#10596831—21no—
88C4⋊#10596831—21no—
89C4⋊#10596831—21no—
90C4⋊#10596831—21no—
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2×C411yescharacteristic
93C4⋊#10596831D411yescharacteristic
94C4⋊#10596831D411yescharacteristic
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556520—21no—
98#14556520—21no—
99#14556515C2×C411yescharacteristic
100#14556515C2×C411yescharacteristic
101#14556515C2×C411yescharacteristic
102#14556515C2×C411yescharacteristic
103#14556514C2×C411yescharacteristic
104#14556514C2×C411yescharacteristic
105#14556511C2×C411yescharacteristic
106#14556511C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831C2×C411yescharacteristic
109C22⋊#10596831C2×C411yescharacteristic
110C22⋊#10596831D411yescharacteristic
111C22⋊#10596831D411yescharacteristic
112#14556503—21no—
113#14556503—21no—
114#14556502—21no—
115#14556502—21no—
116#14556502—21no—
117#14556501—21no—
118C4×#10596831—21no—
119C4×#10596831—21no—
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C8×Dic73—21no—
125C22×Q8×C73C2×C411yescharacteristic
126C22×C8×C73—21no—
127C22×C8×C73—21no—
128C4×Q8×C73—21no—
129C4×Q8×C73—21no—
130C4×Q8×C73C2×C411yescharacteristic
131C4×Q8×C73C2×C411yescharacteristic
132C4×Q8×C73C2311yescharacteristic
133C4×Q8×C73C2311yescharacteristic
134C2×C4⋊C4×C73—21no—
135C2×C4⋊C4×C73C2×C411yescharacteristic
136C2×C42×C73—21no—
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—21no—
139C4⋊C8×C73C2311yescharacteristic
140C4⋊C8×C73C2311yescharacteristic
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292C22×C411yescharacteristic
146C2×C22⋊D73—21no—
147C2×C4×D73—21no—
148#11924018—22no—
149#11924018—41no—
150#11924015—22no—
151#11924015—41no—
152#11924011—81no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831C22×C411yescharacteristic
156C2×#10596831C22×C411yescharacteristic
157C2×#10596831C22×C411yescharacteristic
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C2×D411yescharacteristic
160C2×#10596831C2×D411yescharacteristic
161C2×#10596831C2×D411yescharacteristic
162C2×#10596831C2×D411yescharacteristic
163C8×D73—81no—
164C4⋊Dic73C22×C411yescharacteristic
165C4⋊Dic73C22×C411yescharacteristic
166#11924007—21no—
167#11924007—21no—
168#11924007—21no—
169#11924007—21no—
170C22⋊Dic73—21no—
171#11924005—21no—
172#11924005—21no—
173#11924005—21no—
174#11924005—21no—
175C4×Dic73—21no—
176C2×Q8×C73—21no—
177C2×Q8×C73—22no—
178C2×Q8×C73—41no—
179C2×Q8×C73C22×C411yescharacteristic
180C2×Q8×C73C22×C411yescharacteristic
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73#4111yescharacteristic
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—42no—
191C2×C8×C73—81no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73C22×C411yescharacteristic
198C4⋊C4×C73C22×C411yescharacteristic
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73C22×C411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73#4111yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73C4×D411yescharacteristic
208C22×D73—21no—
209Q8×C73—21no—
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—42no—
213Q8×C73#13112yes—
214C2×C4×C73—21no—
215C2×C4×C73—22no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—42no—
224C2×C4×C73—42no—
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C4×D411yescharacteristic
228C2×C4×C73C23×C411yescharacteristic
229C2×C4×C73C22×D411yescharacteristic
230C2×C4×C73C2×#4111yescharacteristic
231C22⋊D73—42no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235D292—21no—
236D292—21no—
237C4×D73—41no—
238C4×D73—41no—
239Dic146—21no—
240Dic146—21no—
241C8×C73—41no—
242C8×C73—41no—
243C8×C73—41no—
244C8×C73—41no—
245#10596831—21no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—21no—
251#10596831—21no—
252#10596831—21no—
253#10596831—41no—
254#10596831—41no—
255C22×C73—21no—
256C22×C73—21no—
257C22×C73#44412yes—
258C22×C73C2×C4×D411yescharacteristic
259C2×D73—41no—
260C2×D73—41no—
261C2×D73—41no—
262C4×C73—21no—
263C4×C73—22no—
264C4×C73—21no—
265C4×C73—21no—
266C4×C73—21no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73C2×#13111yescharacteristic
271C4×C73#56811yescharacteristic
272C4×C73#57711yescharacteristic
273C4×C73#57811yescharacteristic
274Dic73—41no—
275Dic73—41no—
276Dic73—41no—
277#18023—731nomaximal, Sylow
278C2×C73—22no—
279C2×C73#293311yescharacteristic
280C2×C73#294711yescharacteristic
281C2×C73C2×#44411yescharacteristic
282D73—81no—
283#3108—731no—
284#2994—731no—
285#2984—731no—
286#1593—731no—
287#1592—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1582—731no—
292#1579—731no—
293SD16⋊C8—731no—
294#1573—731no—
295#1494—731no—
296C2×Q8⋊C8D7311yescharacteristic, complemented
297#1452—731no—
298C73#1802311yescharacteristic, complemented, Sylow
299#529—731no—
300C2×C4×Q8C2×D7311yescharacteristic
301#483—731no—
302#480—731no—
303#479—731no—
304#479—731no—
305#464—731no—
306#464—731no—
307#451—731no—
308#448—731no—
309#446—731no—
310#446—731no—
311#446—731no—
312#446—1461no—
313#446—1461no—
314C8×Q8—731no—
315C8×Q8—731no—
316C8×Q8—731no—
317C4×Q16—731no—
318C4×Q16—731no—
319C4×SD16—731no—
320C4×SD16—731no—
321#436—731no—
322#435—1461no—
323C8×D4—731no—
324C8×D4—1461no—
325#433—1461no—
326#432—731no—
327#432—1461no—
328#431—731no—
329#431—731no—
330#431—1461no—
331#424—1461no—
332C2×C4⋊C8C2×D7311yescharacteristic
333C2×C4×C8C2×D7311yescharacteristic
334#335—731no—
335#335—731no—
336#334—731no—
337#334—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8C2×D7311yescharacteristic
341Q8⋊C8C2×D7311yescharacteristic
342Q8⋊C8C2×D7311yescharacteristic
343Q8⋊C8C2×D7311yescharacteristic
344D4⋊C8—731no—
345D4⋊C8—731no—
346#322—731no—
347#322—731no—
348#322—731no—
349#322—731no—
350C22×Q8C4×D7311yescharacteristic
351C2×Q16—731no—
352C2×Q16—731no—
353C2×SD16—731no—
354C2×SD16—731no—
355C2×M16—1461no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—1461no—
359#126—1461no—
360#125—731no—
361#124—731no—
362#123—1461no—
363C22⋊Q8—731no—
364#121—731no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—731no—
368C4×Q8C4×D7311yescharacteristic
369C4×Q8C4×D7311yescharacteristic
370C4×Q8C22×D7311yescharacteristic
371C4×Q8C22×D7311yescharacteristic
372C4×D4—731no—
373C4×D4—1461no—
374#117—1461no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C4×D7311yescharacteristic
377C2×C42—21no—
378C2×C42C22×D7311yescharacteristic
379#107—731no—
380#107—731no—
381#106—731no—
382#106—731no—
383C4⋊C8—21no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8C22×D7311yescharacteristic
397C4⋊C8C22×D7311yescharacteristic
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#103—731no—
403#103—731no—
404#102—731no—
405#102—731no—
406C22⋊C8—731no—
407C22⋊C8—731no—
408C22⋊C8—731no—
409C22⋊C8—731no—
410C22⋊C8—1461no—
411C22⋊C8—1461no—
412C22⋊C8—1461no—
413#97—1461no—
414#97—1461no—
415#97—1461no—
416#97—1461no—
417C4×C8—21no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—731no—
422C4×C8—1461no—
423C4×C8—1461no—
424C4×C8—1461no—
425C4×C8C22×D7311yescharacteristic
426C4×C8C22×D7311yescharacteristic
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—731no—
431C2×Q8C2×C4×D7311yescharacteristic
432C2×Q8C2×C4×D7311yescharacteristic
433C2×D4—731no—
434C2×D4—1461no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—1461no—
438C22×C4C2×C4×D7311yescharacteristic
439C22×C4D4×D7311yescharacteristic
440C22×C4#1192402711yescharacteristic
441Q16—2921no—
442Q16—1462no—
443SD16—2921no—
444SD16—1462no—
445M16—5841no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—81no—
452C2×C8—5841no—
453C2×C8—731no—
454C2×C8—731no—
455C2×C8—731no—
456C2×C8—731no—
457C2×C8—731no—
458C2×C8—731no—
459C2×C8—731no—
460C2×C8—731no—
461C2×C8—1461no—
462C2×C8—1461no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—731no—
469C4⋊C4—731no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4C2×C4×D7311yescharacteristic
475C4⋊C4C2×C4×D7311yescharacteristic
476C22⋊C4—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—1461no—
486C42C2×C4×D7311yescharacteristic
487C42D4×D7311yescharacteristic
488C42#1192402711yescharacteristic
489C42C23×D7311yescharacteristic
490C23—1461no—
491C23#1455655111yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—42no—
496Q8—1461no—
497Q8—1461no—
498Q8#1455659712yes—
499D4—2922no—
500D4—1461no—
501D4—1461no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—2921no—
514C2×C4—2921no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4#1455655111yescharacteristic
519C2×C4#1455655111yescharacteristic
520C2×C4#1455655111yescharacteristic
521C2×C4C22×C4×D7311yescharacteristic
522C2×C4C2×D4×D7311yescharacteristic
523C2×C4C2×#1192402711yescharacteristic
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—2921no—
529C8—2921no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C8—1461no—
535C8—1461no—
536C8—1461no—
537C8—1461no—
538C22—21no—
539C22—21no—
540C22—2921no—
541C22—2921no—
542C22—2921no—
543C22#1798870612yes—
544C22C2×#1455655111yescharacteristic
545C4—21no—
546C4—22no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—2921no—
554C4—2921no—
555C4—2921no—
556C4C2×#1455659711yescharacteristic
557C4#1798935311yescharacteristic
558C4#1798939311yescharacteristic
559C4#1798940011yescharacteristic
560C2—22no—
561C2—5841no—
562C2#2261865211yescharacteristic
563C2#2261876811yescharacteristic
564C2C2×#1798870611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC2×Q8⋊C8×C73C2
socleC22×C73C2×C4×D4
prime radical#14556565C2×C4
cosocleC42×C73C24
hypercenterC2×Q8⋊C8D73
hypocenterC73#18023
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #22619020C2semidirect
4. #22608837C2semidirect
5. #22608836C2semidirect
6. #22608784C2semidirect
7. #22608778C2semidirect
8. #22608771C2semidirect
9. #22608770C2semidirect
10. #22608747C2semidirect
11. #22608746C2semidirect
12. #22608714C2semidirect
14. #22608223C2semidirect
15. C2×Q8⋊C8×C73C2semidirect
296. C2×Q8⋊C8D73semidirect
298. C73#18023semidirect

Maximal subgroups

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

subgroupindex
#226200112
#226190872
#226190202
#226088372
#226088362
#226087842
#226087782
#226087712
#226087702
#226087472
#226087462
#226087142
#226083922
#226082232
C2×Q8⋊C8×C732
#1802373