Finite Group Databasebeta

← #34030398

Subgroups — #34030398

Order 18688.

574 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626317C211yesmaximal, characteristic, complemented
2#22626316C211yesmaximal, characteristic, complemented
3#22626314C211yesmaximal, characteristic, complemented
4#22626313C211yesmaximal, characteristic, complemented
5#22626313C211yesmaximal, characteristic, complemented
6#22626311C211yesmaximal, characteristic, complemented
7#22626309C211yesmaximal, characteristic, complemented
8D4×#11924031C211yesmaximal, characteristic, complemented
9#22626299C211yesmaximal, characteristic, complemented
10#22626298C211yesmaximal, characteristic, complemented
11#22626163C211yesmaximal, characteristic, complemented
12#22626162C211yesmaximal, characteristic, complemented
13#22626159C211yesmaximal, characteristic, complemented
14C2×#17989482C211yesmaximal, characteristic, complemented
15#22618622C211yesmaximal, characteristic
16C2×#14556666C2211yescharacteristic
17C2×#14556666C2211yescharacteristic
18C2×#14556666C2211yescharacteristic, complemented
19C2×#14556665C2211yescharacteristic, complemented
20C2×#14556664C2211yescharacteristic, complemented
21C22×#11924031C2211yescharacteristic
22C22×#11924031C2211yescharacteristic
23C22×#11924031C2211yescharacteristic, complemented
24#17989508C2211yescharacteristic, complemented
25#17989508C2211yescharacteristic, complemented
26C4⋊#11924031C2211yescharacteristic, complemented
27C4⋊#11924031C2211yescharacteristic, complemented
28#17989482C2211yescharacteristic
29#17989482C2211yescharacteristic
30#17989482C2211yescharacteristic
31#17989482C2211yescharacteristic
32#17989482C2211yescharacteristic
33#17989482C2211yescharacteristic
34#17989482C2211yescharacteristic, complemented
35#17989482C2211yescharacteristic, complemented
36C22⋊#11924031C2211yescharacteristic
37C22⋊#11924031C2211yescharacteristic
38C22⋊#11924031C2211yescharacteristic, complemented
39C22⋊#11924031C2211yescharacteristic, complemented
40#17989476C2211yescharacteristic, complemented
41#17989475C2211yescharacteristic, complemented
42#17989473C2211yescharacteristic, complemented
43C4×#11924031C2211yescharacteristic, complemented
44C2×#14556599C2211yescharacteristic
45C22×C8×D73C2211yescharacteristic
46#17989096C411yescharacteristic
47#17988660C411yescharacteristic
48#17988658C411yescharacteristic
49#17988656C411yescharacteristic
50D4×#10596831C2211yescharacteristic
51#17988652C2211yescharacteristic
52#17988650C2211yescharacteristic
53#17988650C2211yescharacteristic
54#17988612C411yescharacteristic
55#17988552C411yescharacteristic
56#17988549C411yescharacteristic
57#17988544C2211yescharacteristic
58#435×C73C411yescharacteristic
59#14556666—41no—
60#14556666—41no—
61#14556666—41no—
62#14556665—41no—
63#14556664—41no—
64C2×#11924031—41no—
65C2×#11924031—41no—
66C2×#11924031—41no—
67C2×#11924031C2311yescharacteristic
68C2×#11924031C2311yescharacteristic
69C2×#11924031C2311yescharacteristic
70C2×#11924031C2311yescharacteristic
71C2×#11924031C2311yescharacteristic
72C2×#11924031C2311yescharacteristic
73C2×#11924031C2311yescharacteristic
74C2×#11924031C2311yescharacteristic
75C2×#11924028C2×C411yescharacteristic
76C22×C4×D73C2×C411yescharacteristic
77#14556599—41no—
78#14556599—41no—
79C2×#11924011C2×C411yescharacteristic
80C2×#11924011C2×C411yescharacteristic
81C2×#11924011C2×C411yescharacteristic
82C22×#10596831C2311yescharacteristic
83C22×#10596831C2311yescharacteristic
84C2×C8×D73—41no—
85C2×C8×D73—41no—
86C2×C8×D73C2×C411yescharacteristic
87C2×C8×D73C2×C411yescharacteristic
88C2×C8×D73C2311yescharacteristic
89C2×C8×D73C2311yescharacteristic
90C2×C8×D73C2311yescharacteristic
91#14556576C811yescharacteristic
92#14556573C811yescharacteristic
93#14556569C811yescharacteristic
94#14556568C811yescharacteristic
95#14556564C811yescharacteristic
96#14556563C811yescharacteristic
97#14556561C811yescharacteristic
98#14556559C811yescharacteristic
99C4×D292C2×C411yescharacteristic
100C4×C22⋊D73C2×C411yescharacteristic
101C4×C22⋊D73C2×C411yescharacteristic
102#14556548C2×C411yescharacteristic
103C4⋊#10596831C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520C2×C411yescharacteristic
106C22⋊#10596831C2×C411yescharacteristic
107C22⋊#10596831C2×C411yescharacteristic
108#14556503C2×C411yescharacteristic
109#14556503C2×C411yescharacteristic
110#14556503C2×C411yescharacteristic
111#14556503C2×C411yescharacteristic
112#14556501C2×C411yescharacteristic
113C4×#10596831C2311yescharacteristic
114C8×Dic73C2311yescharacteristic
115C2×M16×C73C2×C411yescharacteristic
116C22×C8×C73C2×C411yescharacteristic
117C4×D4×C73C2×C411yescharacteristic
118C4⋊C8×C73C2×C411yescharacteristic
119C22⋊C8×C73C2×C411yescharacteristic
120C22⋊C8×C73C2×C411yescharacteristic
121#97×C73C2×C411yescharacteristic
122#11924031—21no—
123#11924031—21no—
124#11924031—21no—
125#11924031—21no—
126#11924031—21no—
127#11924031—21no—
128#11924031—21no—
129#11924031—21no—
130C23×D73C2×C811yescharacteristic
131#11924028—41no—
132#11924028—41no—
133C2×Dic146C2×C811yescharacteristic
134C2×D292C2×C811yescharacteristic
135C2×D292C2×C811yescharacteristic
136C2×C22⋊D73C2×C811yescharacteristic
137C2×C22⋊D73C2×C811yescharacteristic
138C2×C22⋊D73C2×C811yescharacteristic
139C2×C22⋊D73C2×C811yescharacteristic
140C22×Dic73C2×C811yescharacteristic
141C2×C4×D73—41no—
142C2×C4×D73—41no—
143C2×C4×D73C2×C811yescharacteristic
144C2×C4×D73C2×C811yescharacteristic
145C2×C4×D73C22×C411yescharacteristic
146C2×C4×D73C22×C411yescharacteristic
147C2×C4×D73C22×C411yescharacteristic
148#11924011—41no—
149#11924011—41no—
150#11924011—41no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831C22×C411yescharacteristic
156C2×#10596831C22×C411yescharacteristic
157C2×#10596831C22×C411yescharacteristic
158C2×#10596831C2411yescharacteristic
159C8×D73—21no—
160C8×D73—21no—
161C8×D73—21no—
162C8×D73—21no—
163C8×D73—21no—
164C8×D73—21no—
165C8×D73—41no—
166C8×D73—41no—
167C4⋊Dic73C2×C811yescharacteristic
168#11924007C2×C811yescharacteristic
169#11924007C2×C811yescharacteristic
170#11924007C2×C811yescharacteristic
171#11924007C2×C811yescharacteristic
172C22⋊Dic73C2×C811yescharacteristic
173C22⋊Dic73C2×C811yescharacteristic
174#11924005C2×C811yescharacteristic
175#11924005C2×C811yescharacteristic
176#11924005C2×C811yescharacteristic
177#11924005C2×C811yescharacteristic
178#11924005C2×C811yescharacteristic
179#11924005C2×C811yescharacteristic
180C4×Dic73C22×C411yescharacteristic
181C2×D4×C73C2×C811yescharacteristic
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C22×C411yescharacteristic
184M16×C73—41no—
185C2×C8×C73—41no—
186C2×C8×C73C22×C411yescharacteristic
187C2×C8×C73C22×C411yescharacteristic
188C2×C8×C73C22×C411yescharacteristic
189C2×C8×C73C22×C411yescharacteristic
190C4⋊C4×C73C2×C811yescharacteristic
191C22⋊C4×C73C2×C811yescharacteristic
192C22⋊C4×C73C2×C811yescharacteristic
193C42×C73C22×C411yescharacteristic
194C23×C73C22×C811yescharacteristic
195C23×C73C22×C811yescharacteristic
196C22×D73—22no—
197C22×D73—41no—
198C22×D73—41no—
199C22×D73C22×C811yescharacteristic
200C22×D73C22×C811yescharacteristic
201C22×D73C22×C811yescharacteristic
202D4×C73—22no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73C22×C811yescharacteristic
208C2×C4×C73C22×C811yescharacteristic
209C2×C4×C73C22×C811yescharacteristic
210C2×C4×C73C22×C811yescharacteristic
211C2×C4×C73C23×C411yescharacteristic
212C22⋊D73—22no—
213C22⋊D73—41no—
214C22⋊D73—41no—
215C22⋊D73—41no—
216C2×Dic73—41no—
217C2×Dic73C22×C811yescharacteristic
218C2×Dic73C22×C811yescharacteristic
219C2×Dic73C22×C811yescharacteristic
220C2×Dic73C22×C811yescharacteristic
221C2×Dic73C22×C811yescharacteristic
222D292—41no—
223D292—41no—
224C4×D73—21no—
225C4×D73—21no—
226C4×D73—21no—
227C4×D73—21no—
228C4×D73—21no—
229C4×D73—21no—
230C4×D73—41no—
231C4×D73—41no—
232Dic146—41no—
233C8×C73—21no—
234C8×C73—21no—
235C8×C73—21no—
236C8×C73—21no—
237#10596831—21no—
238#10596831—21no—
239#10596831—21no—
240#10596831H(5,𝔽2)11yescharacteristic
241#10596831H(5,𝔽2)11yescharacteristic
242C22×C73—21no—
243C22×C73—21no—
244C22×C73—21no—
245C22×C73—21no—
246C22×C73—21no—
247C22×C73#50412yes—
248C22×C73C23×C811yescharacteristic
249C2×D73—21no—
250C2×D73—21no—
251C2×D73—21no—
252C2×D73—21no—
253C2×D73—21no—
254C2×D73—21no—
255C2×D73—21no—
256C2×D73—21no—
257C2×D73—21no—
258C2×D73—44no—
259C4×C73—21no—
260C4×C73—21no—
261C4×C73—21no—
262C4×C73—21no—
263C4×C73#51811yescharacteristic
264C4×C73#56811yescharacteristic
265Dic73—21no—
266Dic73—21no—
267Dic73—21no—
268Dic73—21no—
269Dic73—21no—
270#33490—731nomaximal, Sylow
271C2×C73—22no—
272C2×C73—41no—
273C2×C73#297211yescharacteristic
274C2×C73C2×#50411yescharacteristic
275C2×C73#340711yescharacteristic
276D73—41no—
277D73—41no—
278D73—41no—
279#2929—731no—
280#2169—731no—
281#2169—731no—
282#2168—731no—
283#2168—731no—
284#2168—731no—
285#2168—731no—
286D4×C16—731no—
287D4×C16—731no—
288#2164—731no—
289#2164—731no—
290#2113—731no—
291#2113—731no—
292#2112—731no—
293C2×C22⋊C16—731no—
294C73#3349011yescharacteristic, complemented, Sylow
295C2×#131—731no—
296C23×C8—731no—
297#525—731no—
298C2×M32—731no—
299C2×M32—731no—
300C2×M32—731no—
301C2×M32—731no—
302C22×C16—731no—
303C22×C16—731no—
304C22×C16—731no—
305C22×C16—731no—
306#435—731no—
307#435—731no—
308#435—731no—
309#435#6440811yescharacteristic
310C8×D4—731no—
311C8×D4—731no—
312C8×D4—731no—
313C8×D4—731no—
314#424—731no—
315#408—731no—
316#407—731no—
317#405—731no—
318C4⋊C16—731no—
319C4⋊C16—731no—
320C4⋊C16—731no—
321C4⋊C16—731no—
322C22⋊C16—731no—
323C22⋊C16—731no—
324C22⋊C16—731no—
325C22⋊C16—731no—
326C22⋊C16—731no—
327C22⋊C16—731no—
328C22⋊C16—731no—
329C22⋊C16—731no—
330C22⋊C16—731no—
331C22⋊C16—731no—
332C22⋊C16—731no—
333C22⋊C16—731no—
334#346—731no—
335#346—731no—
336C4×C16—731no—
337C4×C16—731no—
338C2×#41—731no—
339C23×C4—731no—
340#131—2921no—
341#131—2921no—
342C2×M16—731no—
343C2×M16—731no—
344C2×M16—731no—
345C2×M16C2×#6440811yescharacteristic
346C22×C8—2921no—
347C22×C8—2921no—
348C22×C8—731no—
349C22×C8—731no—
350C22×C8—731no—
351C22×C8—731no—
352C22×C8—731no—
353C22×C8—731no—
354C22×C8—731no—
355C22×C8C2×#6440811yescharacteristic
356#123—731no—
357#123—731no—
358C22⋊Q8—731no—
359C22⋊Q8—731no—
360#121—731no—
361#121—731no—
362#120—731no—
363#120—731no—
364C4×D4—731no—
365C4×D4—731no—
366C4×D4—731no—
367C4×D4C2×#6440811yescharacteristic
368#117—731no—
369M32—2921no—
370M32—2921no—
371M32—2921no—
372M32—2921no—
373C2×C16—2921no—
374C2×C16—2921no—
375C2×C16—2921no—
376C2×C16—2921no—
377C2×C16—731no—
378C2×C16—731no—
379C2×C16—731no—
380C2×C16—731no—
381C2×C16—731no—
382C2×C16—731no—
383C2×C16—731no—
384C2×C16—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8C2×#6440811yescharacteristic
389C22⋊C8—731no—
390C22⋊C8—731no—
391C22⋊C8—731no—
392C22⋊C8—731no—
393C22⋊C8—731no—
394C22⋊C8—731no—
395C22⋊C8C2×#6440811yescharacteristic
396C22⋊C8C2×#6440811yescharacteristic
397#97—731no—
398#97C2×#6440811yescharacteristic
399C4×C8—731no—
400C4×C8—731no—
401C24—731no—
402#41—2921no—
403#41—2921no—
404C2×Q8—731no—
405C2×D4—731no—
406C2×D4—731no—
407C2×D4—731no—
408C2×D4—731no—
409C2×D4—731no—
410C2×D4—731no—
411C2×D4#1192403611yescharacteristic
412C22×C4—2921no—
413C22×C4—2921no—
414C22×C4—731no—
415C22×C4—731no—
416C22×C4—731no—
417C22×C4—731no—
418C22×C4—731no—
419C22×C4—731no—
420C22×C4C22×#6440811yescharacteristic
421C22×C4C22×#6440811yescharacteristic
422M16—41no—
423M16—2921no—
424M16—2921no—
425M16—2921no—
426C2×C8—41no—
427C2×C8—2921no—
428C2×C8—2921no—
429C2×C8—731no—
430C2×C8—731no—
431C2×C8—731no—
432C2×C8—731no—
433C2×C8—1461no—
434C2×C8—1461no—
435C2×C8—1461no—
436C2×C8—1461no—
437C2×C8—1461no—
438C2×C8—1461no—
439C2×C8—1461no—
440C2×C8—1461no—
441C2×C8—1461no—
442C2×C8—1461no—
443C2×C8C22×#6440811yescharacteristic
444C2×C8C22×#6440811yescharacteristic
445C2×C8C22×#6440811yescharacteristic
446C2×C8C22×#6440811yescharacteristic
447C4⋊C4—731no—
448C4⋊C4—731no—
449C4⋊C4—731no—
450C4⋊C4—731no—
451C4⋊C4—731no—
452C4⋊C4#1192403611yescharacteristic
453C22⋊C4—731no—
454C22⋊C4—731no—
455C22⋊C4—731no—
456C22⋊C4—731no—
457C22⋊C4—731no—
458C22⋊C4—731no—
459C22⋊C4—731no—
460C22⋊C4—731no—
461C22⋊C4#1192403611yescharacteristic
462C22⋊C4#1192403611yescharacteristic
463C42—731no—
464C42C22×#6440811yescharacteristic
465C16—1461no—
466C16—1461no—
467C16—1461no—
468C16—1461no—
469C16—1461no—
470C16—1461no—
471C16—1461no—
472C16—1461no—
473C23—2921no—
474C23—2921no—
475C23—731no—
476C23—731no—
477C23—731no—
478C23—1462no—
479C23C2×#1192403611yescharacteristic
480C23C2×#1192403611yescharacteristic
481Q8—2921no—
482D4—22no—
483D4—2921no—
484D4—2921no—
485D4—2921no—
486D4—2921no—
487D4—2921no—
488D4—1462no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—2921no—
494C2×C4—2921no—
495C2×C4—2921no—
496C2×C4—731no—
497C2×C4—731no—
498C2×C4—731no—
499C2×C4—731no—
500C2×C4—731no—
501C2×C4—1461no—
502C2×C4—1461no—
503C2×C4—1461no—
504C2×C4—1461no—
505C2×C4—1461no—
506C2×C4—1461no—
507C2×C4C2×#1192403611yescharacteristic
508C2×C4C2×#1192403611yescharacteristic
509C2×C4C2×#1192403611yescharacteristic
510C2×C4C2×#1192403611yescharacteristic
511C2×C4C23×#6440811yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—731no—
517C8—731no—
518C8—1461no—
519C8—1461no—
520C8—1461no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—2924no—
527C22—1461no—
528C22—1461no—
529C22—1461no—
530C22—1461no—
531C22—1461no—
532C22—1461no—
533C22—1461no—
534C22—1461no—
535C22—1461no—
536C22#1798964612yes—
537C22C22×#1192403611yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—1461no—
543C4—1461no—
544C4—1461no—
545C4—1461no—
546C4—1461no—
547C4#1798965411yescharacteristic
548C4#1798966611yescharacteristic
549C2—22no—
550C2—41no—
551C2—2921no—
552C2—2921no—
553C2—2921no—
554C2#2262677911yescharacteristic
555C2C2×#1798964611yescharacteristic
556C2#2262689911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#64408
commutator, socleC22×C73C23×C8
Fitting#435×C73C4
prime radical#17989096C4
cosocleC2×#10596831C24
hypercenter#435#64408
hypocenterC73#33490
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #22626317C2semidirect
2. #22626316C2semidirect
3. #22626314C2semidirect
4. #22626313C2semidirect
5. #22626313C2semidirect
6. #22626311C2semidirect
7. #22626309C2semidirect
8. D4×#11924031C2semidirect
9. #22626299C2semidirect
10. #22626298C2semidirect
11. #22626163C2semidirect
12. #22626162C2semidirect
13. #22626159C2semidirect
14. C2×#17989482C2semidirect
18. C2×#14556666C22semidirect
19. C2×#14556665C22semidirect
20. C2×#14556664C22semidirect
23. C22×#11924031C22semidirect
24. #17989508C22semidirect
25. #17989508C22semidirect
26. C4⋊#11924031C22semidirect
27. C4⋊#11924031C22semidirect
34. #17989482C22semidirect
35. #17989482C22semidirect
38. C22⋊#11924031C22semidirect
39. C22⋊#11924031C22semidirect
40. #17989476C22semidirect
41. #17989475C22semidirect
42. #17989473C22semidirect
43. C4×#11924031C22semidirect
294. C73#33490semidirect

Maximal subgroups

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

subgroupindex
#226263172
#226263162
#226263142
#226263132
#226263112
#226263092
D4×#119240312
#226262992
#226262982
#226261632
#226261622
#226261592
C2×#179894822
#226186222
#3349073