Finite Group Databasebeta

← #33056814

Subgroups — #33056814

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#22620531C211yesmaximal, characteristic
2#22619082C211yesmaximal, characteristic
3#22608809C211yesmaximal, characteristic, complemented
4#22608802C211yesmaximal, characteristic, complemented
5#22608800C211yesmaximal, characteristic, complemented
6#22608786C211yesmaximal, characteristic, complemented
7#22608781C211yesmaximal, characteristic, complemented
8#22608779C211yesmaximal, characteristic, complemented
9#22608774C211yesmaximal, characteristic, complemented
10#22608765C211yesmaximal, characteristic, complemented
11#22608699C211yesmaximal, characteristic, complemented
12#22608389C211yesmaximal, characteristic
13#22608386C211yesmaximal, characteristic, complemented
14#22608221C211yesmaximal, characteristic, complemented
15C73×#2985C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988993C411yescharacteristic
18#17988979C411yescharacteristic
19#17988955C411yescharacteristic
20#17988949C411yescharacteristic
21#17988843C411yescharacteristic
22#17988843C411yescharacteristic
23#17988835C411yescharacteristic
24#17988835C411yescharacteristic
25#17988717C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924018C2211yescharacteristic
28C4×#11924018C2211yescharacteristic
29C4×#11924015C2211yescharacteristic
30C4×#11924015C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988662—21no—
33#17988661—21no—
34C8×D292C2211yescharacteristic
35#17988647—21no—
36#17988612—21no—
37#17988611C2211yescharacteristic
38C4×#11924012C2211yescharacteristic
39C2×C4×#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46Q8⋊#10596831C2211yescharacteristic
47Q8⋊#10596831C2211yescharacteristic
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55#17988308C2211yescharacteristic
56#533×C73C2211yescharacteristic
57#446×C73—21no—
58#446×C73—21no—
59#446×C73C2211yescharacteristic
60#446×C73C2211yescharacteristic
61C8×Q8×C73C2211yescharacteristic
62C8×Q8×C73C2211yescharacteristic
63#433×C73—21no—
64#433×C73—21no—
65#432×C73C2211yescharacteristic
66#431×C73C2211yescharacteristic
67C2×#11924018C2×C411yescharacteristic
68C2×#11924018C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924012C2×C411yescharacteristic
73C2×#11924012C2×C411yescharacteristic
74C2×#11924011—21no—
75C22×#10596831—21no—
76C2×C8×D73—21no—
77#14556585—21no—
78#14556583C2×C411yescharacteristic
79#14556579C2×C411yescharacteristic
80#14556574—21no—
81#14556570C2×C411yescharacteristic
82#14556565C2×C411yescharacteristic
83C4×Dic146C2311yescharacteristic
84C4×D292C2311yescharacteristic
85C4×C22⋊D73—21no—
86#14556548—21no—
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91C4⋊#10596831—21no—
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556520—21no—
95#14556520—21no—
96#14556515C2×C411yescharacteristic
97#14556515C2×C411yescharacteristic
98#14556515C2×C411yescharacteristic
99#14556515C2×C411yescharacteristic
100#14556514C2×C411yescharacteristic
101#14556514C2×C411yescharacteristic
102#14556511C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104#14556503—21no—
105#14556503—21no—
106#14556502C2×C411yescharacteristic
107#14556502C2×C411yescharacteristic
108#14556501—21no—
109C4×#10596831—21no—
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C8×Dic73—21no—
115C4⋊Q8×C73C2×C411yescharacteristic
116C4⋊Q8×C73C2×C411yescharacteristic
117#125×C73—21no—
118C22⋊Q8×C73—21no—
119C22⋊Q8×C73C2×C411yescharacteristic
120C22⋊Q8×C73C2×C411yescharacteristic
121C4×Q8×C73—21no—
122C4×Q8×C73C2311yescharacteristic
123C4×Q8×C73C2311yescharacteristic
124#117×C73—21no—
125C2×C42×C73C2311yescharacteristic
126C4⋊C8×C73—21no—
127C4⋊C8×C73—21no—
128C4⋊C8×C73—21no—
129C4⋊C8×C73—21no—
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73D411yescharacteristic
136C22⋊C8×C73D411yescharacteristic
137#97×C73—21no—
138#97×C73—21no—
139#97×C73—21no—
140C4×C8×C73—21no—
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—41no—
149#11924018—41no—
150#11924015—41no—
151#11924015—41no—
152#11924012—41no—
153#11924012—41no—
154#11924012—81no—
155#11924011—81no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—42no—
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C8×D73—81no—
166C4⋊Dic73C22×C411yescharacteristic
167C4⋊Dic73C22×C411yescharacteristic
168#11924007—21no—
169#11924007—21no—
170#11924007—21no—
171#11924007—21no—
172C22⋊Dic73—21no—
173#11924005—21no—
174#11924005—21no—
175#11924005—21no—
176#11924005—21no—
177C4×Dic73—21no—
178C2×Q8×C73—21no—
179C2×Q8×C73C22×C411yescharacteristic
180C2×Q8×C73C22×C411yescharacteristic
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73#4111yescharacteristic
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73C2×D411yescharacteristic
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C2×C8×C73C2×D411yescharacteristic
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
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
199C22⋊C4×C73—21no—
200C22⋊C4×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—21no—
213Q8×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—21no—
222C2×C4×C73—41no—
223C2×C4×C73C4×D411yescharacteristic
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C23×C411yescharacteristic
227C2×C4×C73C22×D411yescharacteristic
228C2×C4×C73C2×#4111yescharacteristic
229C22⋊D73—81no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233D292—21no—
234D292—21no—
235C4×D73—41no—
236C4×D73—41no—
237Dic146—21no—
238Dic146—21no—
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×C73C2×C4×D411yescharacteristic
257C2×D73—41no—
258C2×D73—41no—
259C2×D73—41no—
260C4×C73—21no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73—21no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73#56811yescharacteristic
269C4×C73#56811yescharacteristic
270C4×C73#57711yescharacteristic
271C4×C73#57811yescharacteristic
272Dic73—41no—
273Dic73—41no—
274Dic73—41no—
275#17988—731nomaximal, Sylow
276C2×C73—41no—
277C2×C73#293211yescharacteristic
278C2×C73#294711yescharacteristic
279C2×C73#295611yescharacteristic
280D73—81no—
281#3172—731no—
282#2993—731no—
283#2985D7311yescharacteristic, complemented
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#533C2×D7311yescharacteristic
298#529—731no—
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—21no—
308#446—21no—
309#446—731no—
310#446C2×D7311yescharacteristic
311#446C2×D7311yescharacteristic
312C8×Q8—731no—
313C8×Q8C2×D7311yescharacteristic
314C8×Q8C2×D7311yescharacteristic
315C4×Q16—731no—
316C4×Q16—731no—
317C4×SD16—731no—
318C4×SD16—731no—
319#436—731no—
320#436—1461no—
321#435—1461no—
322C8×D4—731no—
323#433—21no—
324#433—21no—
325#433—1461no—
326#432C2×D7311yescharacteristic
327#431C2×D7311yescharacteristic
328#424—1461no—
329#423—731no—
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—731no—
353C2×M16—731no—
354C2×M16—1461no—
355C2×M16—1461no—
356C22×C8—1461no—
357C22×C8—1461no—
358C4⋊Q8C4×D7311yescharacteristic
359C4⋊Q8C4×D7311yescharacteristic
360#126—1461no—
361#125—21no—
362#125—731no—
363#124—731no—
364#123—1461no—
365C22⋊Q8—21no—
366C22⋊Q8—731no—
367C22⋊Q8C4×D7311yescharacteristic
368C22⋊Q8C4×D7311yescharacteristic
369#121—731no—
370C4×Q8—21no—
371C4×Q8—731no—
372C4×Q8C22×D7311yescharacteristic
373C4×Q8C22×D7311yescharacteristic
374C4×D4—731no—
375C4×D4—1461no—
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—21no—
387C4⋊C8—731no—
388C4⋊C8—731no—
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—1461no—
406C22⋊C8—1461no—
407C22⋊C8C22⋊D7311yescharacteristic
408C22⋊C8C22⋊D7311yescharacteristic
409#97—21no—
410#97—21no—
411#97—21no—
412#97—731no—
413#97—731no—
414#97—1461no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—731no—
418C4×C8—731no—
419C4×C8—731no—
420C4×C8—731no—
421C4×C8—1461no—
422C4×C8—1461no—
423C4×C8C22×D7311yescharacteristic
424C4×C8C22×D7311yescharacteristic
425C2×Q8—21no—
426C2×Q8—731no—
427C2×Q8C2×C4×D7311yescharacteristic
428C2×Q8C2×C4×D7311yescharacteristic
429C2×D4—731no—
430C2×D4—1461no—
431C22×C4—1461no—
432C22×C4C2×C4×D7311yescharacteristic
433C22×C4C2×C22⋊D7311yescharacteristic
434C22×C4#1192402811yescharacteristic
435Q16—2921no—
436Q16—2921no—
437SD16—2921no—
438SD16—2921no—
439M16—2921no—
440M16—2921no—
441M16—5841no—
442M16—5841no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—2922no—
446C2×C8—5841no—
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—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—731no—
467C4⋊C4—731no—
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—1461no—
477C22⋊C4—1461no—
478C22⋊C4—1461no—
479C22⋊C4—1461no—
480C22⋊C4—1461no—
481C42—21no—
482C42—21no—
483C42—1461no—
484C42C2×C4×D7311yescharacteristic
485C42C2×C22⋊D7311yescharacteristic
486C42#1192402811yescharacteristic
487C42C23×D7311yescharacteristic
488C23—1461no—
489C23C4×C22⋊D7311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—1461no—
496Q8—1461no—
497D4—5841no—
498D4—1461no—
499D4—1461no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—2921no—
510C2×C4—2921no—
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—2921no—
538C22—2921no—
539C22—2921no—
540C22C2×C4×C22⋊D7311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—2921no—
550C4—2921no—
551C4—2921no—
552C4#1798935211yescharacteristic
553C4#1798935211yescharacteristic
554C4#1798939511yescharacteristic
555C4#1798940211yescharacteristic
556C2—41no—
557C2—5841no—
558C2#2261864711yescharacteristic
559C2#2261877411yescharacteristic
560C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2985C2
socleC22×C73C2×C4×D4
prime radical#14556565C2×C4
cosocleC42×C73C24
hypercenter#2985D73
hypocenterC73#17988
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2985

Complements

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

NH ≅ G/Ntype
3. #22608809C2semidirect
4. #22608802C2semidirect
5. #22608800C2semidirect
6. #22608786C2semidirect
7. #22608781C2semidirect
8. #22608779C2semidirect
9. #22608774C2semidirect
10. #22608765C2semidirect
11. #22608699C2semidirect
13. #22608386C2semidirect
14. #22608221C2semidirect
15. C73×#2985C2semidirect
283. #2985D73semidirect
296. C73#17988semidirect

Maximal subgroups

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

subgroupindex
#226205312
#226190822
#226088092
#226088022
#226088002
#226087862
#226087812
#226087792
#226087742
#226087652
#226086992
#226083892
#226083862
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C73×#29852
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