Finite Group Databasebeta

← #33056810

Subgroups — #33056810

Order 18688.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620538C211yesmaximal, characteristic
2#22619025C211yesmaximal, characteristic, complemented
3#22608807C211yesmaximal, characteristic, complemented
4#22608802C211yesmaximal, characteristic, complemented
5#22608800C211yesmaximal, characteristic, complemented
6#22608788C211yesmaximal, characteristic, complemented
7#22608781C211yesmaximal, characteristic, complemented
8#22608779C211yesmaximal, characteristic, complemented
9#22608772C211yesmaximal, characteristic, complemented
10#22608767C211yesmaximal, characteristic, complemented
11#22608696C211yesmaximal, characteristic, complemented
12#22608391C211yesmaximal, characteristic
13#22608385C211yesmaximal, characteristic, complemented
14#22608221C211yesmaximal, characteristic, complemented
15C73×#2993C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17#17988997C411yescharacteristic
18#17988982C411yescharacteristic
19#17988957C411yescharacteristic
20#17988946C411yescharacteristic
21#17988843C411yescharacteristic
22#17988843C411yescharacteristic
23#17988831C411yescharacteristic
24#17988831C411yescharacteristic
25#17988717C2211yescharacteristic
26#17988717C2211yescharacteristic
27#17988716—21no—
28#17988716—21no—
29C8×Dic146C2211yescharacteristic
30C8×Dic146C2211yescharacteristic
31C4×#11924018C2211yescharacteristic
32C4×#11924018C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34C4×#11924016C2211yescharacteristic
35#17988645—21no—
36#17988645—21no—
37#17988644C2211yescharacteristic
38C4×#11924012C2211yescharacteristic
39C2×C4×#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46#17988317C2211yescharacteristic
47#17988317C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50D4⋊#10596831C2211yescharacteristic
51D4⋊#10596831C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55#17988308C2211yescharacteristic
56#529×C73C2211yescharacteristic
57#446×C73C2211yescharacteristic
58C8×Q8×C73C2211yescharacteristic
59#436×C73—21no—
60#436×C73C2211yescharacteristic
61#435×C73—21no—
62C8×D4×C73C2211yescharacteristic
63#433×C73—21no—
64#431×C73C2211yescharacteristic
65#424×C73—21no—
66#423×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924012C2×C411yescharacteristic
72C2×#11924012C2×C411yescharacteristic
73C22×#10596831—21no—
74#14556591C2×C411yescharacteristic
75#14556591C2×C411yescharacteristic
76#14556583—21no—
77#14556570—21no—
78#14556570C2×C411yescharacteristic
79#14556570C2×C411yescharacteristic
80C4×Dic146—21no—
81C4×Dic146C2311yescharacteristic
82C4×Dic146C2311yescharacteristic
83#14556550—21no—
84#14556524C2×C411yescharacteristic
85#14556524C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88C4⋊#10596831C2311yescharacteristic
89C4⋊#10596831C2311yescharacteristic
90#14556520—21no—
91#14556520—21no—
92#14556520—21no—
93#14556520—21no—
94#14556515C2×C411yescharacteristic
95#14556515C2×C411yescharacteristic
96#14556514C2×C411yescharacteristic
97#14556514C2×C411yescharacteristic
98#14556514C2×C411yescharacteristic
99#14556514C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102C22⋊#10596831—21no—
103#14556502—21no—
104#14556502C2×C411yescharacteristic
105#14556502C2×C411yescharacteristic
106#14556501—21no—
107#14556501—21no—
108C4×#10596831—21no—
109C4×#10596831C2311yescharacteristic
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C8×Dic73—21no—
114C8×Dic73—21no—
115C2×M16×C73—21no—
116C2×M16×C73—21no—
117C22×C8×C73—21no—
118#126×C73—21no—
119#125×C73C2×C411yescharacteristic
120#124×C73C2×C411yescharacteristic
121#123×C73—21no—
122C22⋊Q8×C73C2×C411yescharacteristic
123#121×C73C2×C411yescharacteristic
124C4×Q8×C73C2311yescharacteristic
125C4×D4×C73—21no—
126C4×D4×C73C2311yescharacteristic
127#117×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—21no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73D411yescharacteristic
133C4⋊C8×C73D411yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73D411yescharacteristic
139C22⋊C8×C73D411yescharacteristic
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×Dic146C22×C411yescharacteristic
147#11924018—41no—
148#11924018—41no—
149#11924016—41no—
150#11924016—41no—
151#11924012—41no—
152#11924012—41no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—42no—
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73C22×C411yescharacteristic
166C4⋊Dic73C22×C411yescharacteristic
167#11924007—21no—
168#11924007—21no—
169#11924007—21no—
170#11924007—21no—
171C22⋊Dic73—21no—
172C22⋊Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—21no—
175C2×Q8×C73C22×C411yescharacteristic
176C2×D4×C73—21no—
177C2×D4×C73C22×C411yescharacteristic
178C22×C4×C73—21no—
179C22×C4×C73C22×C411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73#4111yescharacteristic
182M16×C73—81no—
183M16×C73—81no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—81no—
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
190C2×C8×C73C2×D411yescharacteristic
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73C22×C411yescharacteristic
196C4⋊C4×C73C22×C411yescharacteristic
197C22⋊C4×C73—21no—
198C22⋊C4×C73—21no—
199C22⋊C4×C73—21no—
200C22⋊C4×C73—21no—
201C22⋊C4×C73—21no—
202C42×C73—21no—
203C42×C73C22×C411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73#4111yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C23×C73C4×D411yescharacteristic
209Q8×C73—21no—
210Q8×C73—21no—
211D4×C73—21no—
212D4×C73—21no—
213D4×C73—81no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C23×C411yescharacteristic
228C2×C4×C73C22×D411yescharacteristic
229C2×C4×C73C2×#4111yescharacteristic
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234Dic146—21no—
235Dic146—21no—
236Dic146—21no—
237Dic146—21no—
238Dic146—81no—
239C8×C73—21no—
240C8×C73—21no—
241C8×C73—21no—
242C8×C73—21no—
243C8×C73—41no—
244C8×C73—41no—
245#10596831—22no—
246#10596831—21no—
247#10596831—21no—
248#10596831—21no—
249#10596831—21no—
250#10596831—41no—
251#10596831—41no—
252#10596831—41no—
253C22×C73—21no—
254C22×C73—21no—
255C22×C73—21no—
256C22×C73—41no—
257C22×C73—41no—
258C22×C73—41no—
259C22×C73C2×C4×D411yescharacteristic
260C4×C73—21no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73—21no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73#56811yescharacteristic
268C4×C73#56811yescharacteristic
269C4×C73#57711yescharacteristic
270C4×C73#57811yescharacteristic
271Dic73—41no—
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275#17988—731nomaximal, Sylow
276C2×C73—41no—
277C2×C73—81no—
278C2×C73#293211yescharacteristic
279C2×C73#294711yescharacteristic
280C2×C73#295611yescharacteristic
281#3172—731no—
282#2993D7311yescharacteristic
283#2985—731no—
284#1588—731no—
285#1587—731no—
286#1587—731no—
287#1585—731no—
288#1584—731no—
289#1584—731no—
290#1583—731no—
291#1582—731no—
292#1569—731no—
293#1494—731no—
294#1493—731no—
295#1451—731no—
296C73#1798811yescharacteristic, complemented, Sylow
297#533—731no—
298#529C2×D7311yescharacteristic
299#501—731no—
300#497—731no—
301#491—731no—
302#489—731no—
303#470—731no—
304#470—731no—
305#468—731no—
306#468—731no—
307#446—731no—
308#446—731no—
309#446—1461no—
310#446—1461no—
311#446C2×D7311yescharacteristic
312C8×Q8—731no—
313C8×Q8—731no—
314C8×Q8C2×D7311yescharacteristic
315C4×Q16—731no—
316C4×Q16—731no—
317C4×SD16—731no—
318C4×SD16—731no—
319#436—21no—
320#436C2×D7311yescharacteristic
321#435—21no—
322C8×D4C2×D7311yescharacteristic
323#433—21no—
324#433—1461no—
325#433—1461no—
326#432—731no—
327#431C2×D7311yescharacteristic
328#424—21no—
329#423C2×D7311yescharacteristic
330C4×M16—731no—
331C2×C4×C8—731no—
332#335—731no—
333#335—731no—
334#334—731no—
335#334—731no—
336Q8⋊C8—731no—
337Q8⋊C8—731no—
338Q8⋊C8—731no—
339Q8⋊C8—731no—
340Q8⋊C8—731no—
341Q8⋊C8—731no—
342D4⋊C8—731no—
343D4⋊C8—731no—
344#322—731no—
345#322—731no—
346#322—731no—
347#322—731no—
348C2×Q16—731no—
349C2×Q16—731no—
350C2×SD16—731no—
351C2×SD16—731no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—731no—
355C2×M16—731no—
356C22×C8—21no—
357C22×C8—1461no—
358C4⋊Q8—731no—
359C4⋊Q8—731no—
360#126—21no—
361#125—1461no—
362#125C4×D7311yescharacteristic
363#124C4×D7311yescharacteristic
364#123—21no—
365C22⋊Q8—731no—
366C22⋊Q8—731no—
367C22⋊Q8—1461no—
368C22⋊Q8C4×D7311yescharacteristic
369#121C4×D7311yescharacteristic
370C4×Q8—731no—
371C4×Q8—731no—
372C4×Q8—1461no—
373C4×Q8C22×D7311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D7311yescharacteristic
376#117—21no—
377#117—1461no—
378C2×C42C22×D7311yescharacteristic
379#107—731no—
380#107—731no—
381#106—731no—
382#106—731no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—1461no—
389C4⋊C8—1461no—
390C4⋊C8—1461no—
391C4⋊C8—1461no—
392C4⋊C8C22⋊D7311yescharacteristic
393C4⋊C8C22⋊D7311yescharacteristic
394C4⋊C8C22×D7311yescharacteristic
395C4⋊C8C22×D7311yescharacteristic
396#103—731no—
397#103—731no—
398#103—731no—
399#103—731no—
400#103—731no—
401#103—731no—
402#102—731no—
403#102—731no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—1461no—
407C22⋊C8C22⋊D7311yescharacteristic
408C22⋊C8C22⋊D7311yescharacteristic
409#97—21no—
410#97—731no—
411#97—731no—
412#97—1461no—
413#97—1461no—
414#97—1461no—
415C4×C8—21no—
416C4×C8—731no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—1461no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C2×Q8—731no—
426C2×Q8—731no—
427C2×Q8—1461no—
428C2×Q8C2×C4×D7311yescharacteristic
429C2×D4—21no—
430C2×D4C2×C4×D7311yescharacteristic
431C22×C4—21no—
432C22×C4C2×C4×D7311yescharacteristic
433C22×C4C2×C22⋊D7311yescharacteristic
434C22×C4#1192402811yescharacteristic
435Q16—2921no—
436Q16—2921no—
437SD16—2921no—
438SD16—2921no—
439M16—81no—
440M16—81no—
441M16—2921no—
442M16—2921no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—2922no—
447C2×C8—731no—
448C2×C8—731no—
449C2×C8—731no—
450C2×C8—731no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8C2×C22⋊D7311yescharacteristic
456C2×C8C2×C22⋊D7311yescharacteristic
457C2×C8C2×C22⋊D7311yescharacteristic
458C2×C8C2×C22⋊D7311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—731no—
464C4⋊C4—731no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4C2×C4×D7311yescharacteristic
473C4⋊C4C2×C4×D7311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—21no—
482C42—1461no—
483C42—1461no—
484C42C2×C4×D7311yescharacteristic
485C42C2×C22⋊D7311yescharacteristic
486C42#1192402811yescharacteristic
487C42C23×D7311yescharacteristic
488C23—21no—
489C23C4×C22⋊D7311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—5841no—
493Q8—1461no—
494Q8—1461no—
495Q8—1461no—
496Q8—1461no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—1461no—
511C2×C4—1461no—
512C2×C4—1461no—
513C2×C4—1461no—
514C2×C4C4×C22⋊D7311yescharacteristic
515C2×C4C4×C22⋊D7311yescharacteristic
516C2×C4C4×C22⋊D7311yescharacteristic
517C2×C4C22×C4×D7311yescharacteristic
518C2×C4C22×C22⋊D7311yescharacteristic
519C2×C4C2×#1192402811yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—2921no—
527C8—2921no—
528C8—2921no—
529C8—1462no—
530C8—1461no—
531C8—1461no—
532C8—1461no—
533C8—1461no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×C4×C22⋊D7311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—2921no—
549C4—2921no—
550C4—2921no—
551C4—2921no—
552C4#1798935211yescharacteristic
553C4#1798935211yescharacteristic
554C4#1798939811yescharacteristic
555C4#1798940211yescharacteristic
556C2—41no—
557C2—81no—
558C2#2261864711yescharacteristic
559C2#2261877011yescharacteristic
560C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2993C2
socleC22×C73C2×C4×D4
prime radical#121×C73C2×C4
cosocleC42×C73C24
hypercenter#2993D73
hypocenterC73#17988
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #22619025C2semidirect
3. #22608807C2semidirect
4. #22608802C2semidirect
5. #22608800C2semidirect
6. #22608788C2semidirect
7. #22608781C2semidirect
8. #22608779C2semidirect
9. #22608772C2semidirect
10. #22608767C2semidirect
11. #22608696C2semidirect
13. #22608385C2semidirect
14. #22608221C2semidirect
296. C73#17988semidirect

Maximal subgroups

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

subgroupindex
#226205382
#226190252
#226088072
#226088022
#226088002
#226087882
#226087812
#226087792
#226087722
#226087672
#226086962
#226083912
#226083852
#226082212
C73×#29932
#1798873