Finite Group Databasebeta

← #34018227

Subgroups — #34018227

Order 18688.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626859C211yesmaximal, characteristic
2#22626856C211yesmaximal, characteristic
3#22625506C211yesmaximal, characteristic, complemented
4#22625504C211yesmaximal, characteristic, complemented
5#22625503C211yesmaximal, characteristic, complemented
6#22625502C211yesmaximal, characteristic, complemented
7#22625501C211yesmaximal, characteristic, complemented
8#22625500C211yesmaximal, characteristic, complemented
9#22625497C211yesmaximal, characteristic, complemented
10#22625495C211yesmaximal, characteristic, complemented
11#22625493C211yesmaximal, characteristic, complemented
12#22625484C211yesmaximal, characteristic, complemented
13#22625483C211yesmaximal, characteristic, complemented
14C2×#17989451C211yesmaximal, characteristic, complemented
15#22618891C211yesmaximal, characteristic
16#17989639—21no—
17#17989637—21no—
18#17989619—21no—
19#17989618—21no—
20#17989616—21no—
21#17989616—21no—
22#17989614—21no—
23D4×#10596833—21no—
24#17989609C2211yescharacteristic
25#17989608C2211yescharacteristic
26#17989608C2211yescharacteristic
27#17989608C2211yescharacteristic
28#17989606C2211yescharacteristic
29#17989603C2211yescharacteristic
30#17989591C2211yescharacteristic
31#17989590C2211yescharacteristic
32#17989588C2211yescharacteristic
33C2×C4⋊#10596833C2211yescharacteristic
34C2×C4⋊#10596833C2211yescharacteristic
35C2×C4⋊#10596833C2211yescharacteristic
36#17989451C2211yescharacteristic
37#17989451C2211yescharacteristic
38#17989451C2211yescharacteristic
39#17989451C2211yescharacteristic
40#17989451C2211yescharacteristic
41#17989451C2211yescharacteristic
42#17989450C2211yescharacteristic
43#17989450C2211yescharacteristic
44#17989450C2211yescharacteristic
45#17989450C2211yescharacteristic
46#17989449C2211yescharacteristic
47#17989449C2211yescharacteristic
48#17989449C2211yescharacteristic
49#17989449C2211yescharacteristic
50#17989448C2211yescharacteristic
51#17989448C2211yescharacteristic
52C4×#11924027C2211yescharacteristic
53#17988716C411yescharacteristic
54#17988715C411yescharacteristic
55#17988663C411yescharacteristic
56#17988662C411yescharacteristic
57#17988659C411yescharacteristic
58#17988658C411yescharacteristic
59#17988655C411yescharacteristic
60#17988639C2211yescharacteristic
61#17988637C2211yescharacteristic
62#17988637C2211yescharacteristic
63#17988539C2211yescharacteristic
64M16×Dic73C2211yescharacteristic
65C2×C8×Dic73C2211yescharacteristic
66#435×C73C411yescharacteristic
67C2×#11924038—21no—
68C2×#11924037—21no—
69C2×#11924036—21no—
70C22×#10596833—21no—
71C22×#10596833—21no—
72C22×#10596833—21no—
73#14556658—21no—
74#14556658—21no—
75C4⋊#10596833—21no—
76C4⋊#10596833—21no—
77C4⋊#10596833—21no—
78C4⋊#10596833—21no—
79C4⋊#10596833C2311yescharacteristic
80C4⋊#10596833C2311yescharacteristic
81C4⋊#10596833C2311yescharacteristic
82C4⋊#10596833C2311yescharacteristic
83C4⋊#10596833C2311yescharacteristic
84C4⋊#10596833C2311yescharacteristic
85C4⋊#10596833C2311yescharacteristic
86C4⋊#10596833C2311yescharacteristic
87#14556648—21no—
88#14556648—21no—
89C22⋊#10596833—21no—
90C22⋊#10596833—21no—
91C22⋊#10596833—21no—
92C22⋊#10596833—21no—
93#14556646—21no—
94#14556646—21no—
95#14556646—21no—
96#14556646—21no—
97C4×#10596833—21no—
98C4×#10596833—21no—
99C2×#11924027Q811yescharacteristic
100C2×#11924012C2×C411yescharacteristic
101C2×#11924011C2×C411yescharacteristic
102C2×#11924011C2×C411yescharacteristic
103C22×#10596831C2×C411yescharacteristic
104C4×Dic146C2×C411yescharacteristic
105#14556556D411yescharacteristic
106D4×Dic73D411yescharacteristic
107C4×C22⋊D73C2×C411yescharacteristic
108C4×C22⋊D73C2×C411yescharacteristic
109#14556551D411yescharacteristic
110#14556551D411yescharacteristic
111#14556549Q811yescharacteristic
112#14556547Q811yescharacteristic
113#14556547Q811yescharacteristic
114C2×C4×Dic73C2311yescharacteristic
115C2×C4×Dic73C2311yescharacteristic
116C42×D73C2311yescharacteristic
117C4⋊#10596831C2×C411yescharacteristic
118#14556520C2×C411yescharacteristic
119#14556520C2×C411yescharacteristic
120#14556520C2×C411yescharacteristic
121#14556520C2×C411yescharacteristic
122C22⋊#10596831C2×C411yescharacteristic
123C22⋊#10596831C2×C411yescharacteristic
124#14556503C2×C411yescharacteristic
125#14556503C2×C411yescharacteristic
126#14556502C2×C411yescharacteristic
127#14556501C2×C411yescharacteristic
128#14556501C2×C411yescharacteristic
129C8×Dic73C2×C411yescharacteristic
130C8×Dic73C2×C411yescharacteristic
131C8×Dic73C2311yescharacteristic
132C8×Dic73C2311yescharacteristic
133C8×Dic73C2311yescharacteristic
134C8×Dic73C2311yescharacteristic
135C2×M16×C73C2×C411yescharacteristic
136C22×C8×C73C2×C411yescharacteristic
137C4×D4×C73C2×C411yescharacteristic
138C4⋊C8×C73C2×C411yescharacteristic
139C22⋊C8×C73C2×C411yescharacteristic
140C22⋊C8×C73C2×C411yescharacteristic
141#97×C73C2×C411yescharacteristic
142#11924038—81no—
143#11924037—81no—
144#11924036—81no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—81no—
154C2×#10596833—81no—
155C2×#10596833—81no—
156#11924027—42no—
157C2×Dic146C4⋊C411yescharacteristic
158C2×C22⋊D73C4⋊C411yescharacteristic
159C2×C22⋊D73C4⋊C411yescharacteristic
160C22×Dic73C2×D411yescharacteristic
161C22×Dic73C2×D411yescharacteristic
162C22×Dic73C2×Q811yescharacteristic
163C22×Dic73C2×Q811yescharacteristic
164C2×C4×D73C22×C411yescharacteristic
165C2×C4×D73C2×D411yescharacteristic
166C2×C4×D73C2×Q811yescharacteristic
167#11924012—22no—
168#11924011—22no—
169#11924011—41no—
170C2×#10596831—22no—
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C22×C411yescharacteristic
174C2×#10596831C22×C411yescharacteristic
175C4⋊Dic73C4⋊C411yescharacteristic
176#11924007C4⋊C411yescharacteristic
177#11924007C4⋊C411yescharacteristic
178#11924007C4⋊C411yescharacteristic
179#11924007C4⋊C411yescharacteristic
180C22⋊Dic73C4⋊C411yescharacteristic
181C22⋊Dic73C4⋊C411yescharacteristic
182#11924005C4⋊C411yescharacteristic
183#11924005C4⋊C411yescharacteristic
184C4×Dic73C22×C411yescharacteristic
185C4×Dic73C22×C411yescharacteristic
186C4×Dic73C2×D411yescharacteristic
187C4×Dic73C2×D411yescharacteristic
188C4×Dic73C2×D411yescharacteristic
189C4×Dic73C2×Q811yescharacteristic
190C4×Dic73C2×Q811yescharacteristic
191C4×Dic73C2×Q811yescharacteristic
192C4×Dic73C2411yescharacteristic
193C2×D4×C73C4⋊C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C22×C411yescharacteristic
196M16×C73—41no—
197C2×C8×C73—41no—
198C2×C8×C73C22×C411yescharacteristic
199C2×C8×C73C22×C411yescharacteristic
200C2×C8×C73C22×C411yescharacteristic
201C2×C8×C73C22×C411yescharacteristic
202C4⋊C4×C73C4⋊C411yescharacteristic
203C22⋊C4×C73C4⋊C411yescharacteristic
204C22⋊C4×C73C4⋊C411yescharacteristic
205C42×C73C22×C411yescharacteristic
206C23×C73C2×C4⋊C411yescharacteristic
207C23×C73C2×C4⋊C411yescharacteristic
208C22×D73C2×C4⋊C411yescharacteristic
209D4×C73—22no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73C2×C4⋊C411yescharacteristic
215C2×C4×C73C2×C4⋊C411yescharacteristic
216C2×C4×C73C2×C4⋊C411yescharacteristic
217C2×C4×C73C2×C4⋊C411yescharacteristic
218C2×C4×C73C23×C411yescharacteristic
219C22⋊D73—22no—
220C22⋊D73—41no—
221C2×Dic73—22no—
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—41no—
227C2×Dic73C2×C4⋊C411yescharacteristic
228C2×Dic73C2×C4⋊C411yescharacteristic
229C2×Dic73C2×C4⋊C411yescharacteristic
230C2×Dic73C2×C4⋊C411yescharacteristic
231C2×Dic73C2×C4⋊C411yescharacteristic
232C2×Dic73C22×D411yescharacteristic
233C2×Dic73C22×Q811yescharacteristic
234C4×D73—21no—
235C4×D73—21no—
236C4×D73—21no—
237C4×D73—21no—
238C4×D73—41no—
239Dic146—41no—
240#10596833—41no—
241#10596833—41no—
242#10596833—41no—
243#10596833—41no—
244#10596833—41no—
245#10596833—41no—
246#10596833—41no—
247#10596833—41no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—21no—
252#10596831—21no—
253#10596831—21no—
254#10596831—21no—
255#10596831#13112yes—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73#43012yes—
262C22×C73C22×C4⋊C411yescharacteristic
263C2×D73—21no—
264C2×D73—21no—
265C2×D73—21no—
266C4×C73—21no—
267C4×C73—21no—
268C4×C73—21no—
269C4×C73—21no—
270C4×C73C2×#13111yescharacteristic
271C4×C73#56811yescharacteristic
272Dic73—21no—
273Dic73—21no—
274Dic73—21no—
275Dic73—21no—
276Dic73—21no—
277Dic73—21no—
278Dic73#57611yescharacteristic
279Dic73#57811yescharacteristic
280#17840—731nomaximal, Sylow
281C2×C73—22no—
282C2×C73—41no—
283C2×C73#290611yescharacteristic
284C2×C73#291311yescharacteristic
285C2×C73C2×#43011yescharacteristic
286D73—41no—
287#2990—731no—
288#2990—731no—
289#2965—731no—
290#1573—731no—
291#1573—731no—
292#1572—731no—
293#1572—731no—
294#1571—731no—
295#1571—731no—
296#1569—731no—
297#1569—731no—
298#1568—731no—
299#1565—731no—
300#1565—731no—
301C2×#335—731no—
302C73#1784011yescharacteristic, complemented, Sylow
303C4×#41—731no—
304#446—731no—
305#446—731no—
306#446—1461no—
307#446—1461no—
308#436—731no—
309#436—731no—
310#435—731no—
311#435—731no—
312#435—731no—
313#435—1461no—
314#435—1461no—
315#435—1461no—
316#435—1461no—
317#435#6440811yescharacteristic
318C8×D4—1461no—
319C8×D4—1461no—
320#432—731no—
321#432—731no—
322#432—731no—
323#432—731no—
324#431—731no—
325#431—731no—
326#431—731no—
327#431—731no—
328#431—731no—
329#423—731no—
330#423—731no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C4×M16—731no—
336C4×M16—731no—
337C2×C4×C8—731no—
338#335—731no—
339#335—731no—
340#335—731no—
341#335—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345#335—731no—
346#335—731no—
347#335—731no—
348#334—731no—
349#334—731no—
350#334—731no—
351#334—731no—
352#334—731no—
353#334—731no—
354C2×#41—731no—
355C2×M16—731no—
356C2×M16—731no—
357C2×M16—731no—
358C2×M16—1461no—
359C2×M16—1461no—
360C2×M16C2×#6440811yescharacteristic
361C22×C8—731no—
362C22×C8—1461no—
363C22×C8—1461no—
364C22×C8—1461no—
365C22×C8—1461no—
366C22×C8C2×#6440811yescharacteristic
367C4×Q8—731no—
368C4×Q8—731no—
369C4×D4—731no—
370C4×D4—731no—
371C4×D4—731no—
372C4×D4—731no—
373C4×D4—731no—
374C4×D4C2×#6440811yescharacteristic
375#117—731no—
376#117—731no—
377#117—731no—
378C2×C42—731no—
379C2×C42—731no—
380C2×C42—731no—
381C4⋊C8—731no—
382C4⋊C8—731no—
383C4⋊C8—731no—
384C4⋊C8—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—731no—
392C4⋊C8—731no—
393C4⋊C8—731no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8—1461no—
398C4⋊C8—1461no—
399C4⋊C8—1461no—
400C4⋊C8C2×#6440811yescharacteristic
401C22⋊C8—731no—
402C22⋊C8—731no—
403C22⋊C8—731no—
404C22⋊C8—731no—
405C22⋊C8—1461no—
406C22⋊C8—1461no—
407C22⋊C8—1461no—
408C22⋊C8—1461no—
409C22⋊C8—1461no—
410C22⋊C8—1461no—
411C22⋊C8C2×#6440811yescharacteristic
412C22⋊C8C2×#6440811yescharacteristic
413#97—731no—
414#97—731no—
415#97—731no—
416#97—1461no—
417#97—1461no—
418#97—1461no—
419#97—1461no—
420#97C2×#6440811yescharacteristic
421C4×C8—731no—
422C4×C8—731no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—1461no—
428C4×C8—1461no—
429#41—2922no—
430C2×Q8—731no—
431C2×D4—731no—
432C2×D4—731no—
433C2×D4C4⋊#6440811yescharacteristic
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4C22×#6440811yescharacteristic
442C22×C4C22×#6440811yescharacteristic
443M16—41no—
444M16—2921no—
445M16—5841no—
446M16—5841no—
447M16—1462no—
448M16—1462no—
449C2×C8—41no—
450C2×C8—5841no—
451C2×C8—5841no—
452C2×C8—5841no—
453C2×C8—5841no—
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—1461no—
465C2×C8—1461no—
466C2×C8—1462no—
467C2×C8C22×#6440811yescharacteristic
468C2×C8C22×#6440811yescharacteristic
469C2×C8C22×#6440811yescharacteristic
470C2×C8C22×#6440811yescharacteristic
471C4⋊C4—731no—
472C4⋊C4—731no—
473C4⋊C4—731no—
474C4⋊C4—731no—
475C4⋊C4—731no—
476C4⋊C4C4⋊#6440811yescharacteristic
477C22⋊C4—731no—
478C22⋊C4—731no—
479C22⋊C4—731no—
480C22⋊C4—731no—
481C22⋊C4C4⋊#6440811yescharacteristic
482C22⋊C4C4⋊#6440811yescharacteristic
483C42—731no—
484C42—731no—
485C42—731no—
486C42—731no—
487C42—731no—
488C42—731no—
489C42—731no—
490C42—731no—
491C42—731no—
492C42C22×#6440811yescharacteristic
493C23—731no—
494C23C2×C4⋊#6440811yescharacteristic
495C23C2×C4⋊#6440811yescharacteristic
496Q8—2921no—
497D4—22no—
498D4—2921no—
499D4—1462no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—2921no—
505C2×C4—2921no—
506C2×C4—731no—
507C2×C4—731no—
508C2×C4—731no—
509C2×C4—731no—
510C2×C4—731no—
511C2×C4—731no—
512C2×C4—731no—
513C2×C4—1461no—
514C2×C4—1461no—
515C2×C4—1461no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1462no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4C2×C4⋊#6440811yescharacteristic
523C2×C4C2×C4⋊#6440811yescharacteristic
524C2×C4C2×C4⋊#6440811yescharacteristic
525C2×C4C2×C4⋊#6440811yescharacteristic
526C2×C4C23×#6440811yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—2921no—
532C8—2921no—
533C8—2921no—
534C8—2921no—
535C8—2921no—
536C8—2921no—
537C8—2921no—
538C8—2921no—
539C8—732no—
540C8—1461no—
541C8—1461no—
542C8—1461no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—1461no—
549C22—1461no—
550C22—1461no—
551C22#1798960212yes—
552C22C22×C4⋊#6440811yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—731no—
558C4—731no—
559C4—1461no—
560C4—1461no—
561C4—1461no—
562C4—1461no—
563C4—1461no—
564C4—1461no—
565C4D73⋊#13111yescharacteristic
566C4#1798966511yescharacteristic
567C2—22no—
568C2—41no—
569C2—2921no—
570C2#2262657811yescharacteristic
571C2#2262658611yescharacteristic
572C2C2×#1798960211yescharacteristic
subgroupG/H
centerC22C22×C4⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#435×C73C4
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924027Q8
cosocleC4×Dic73C24
hypercenter#435#64408
hypocenterC73#17840
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #22625506C2semidirect
4. #22625504C2semidirect
5. #22625503C2semidirect
6. #22625502C2semidirect
7. #22625501C2semidirect
8. #22625500C2semidirect
9. #22625497C2semidirect
10. #22625495C2semidirect
11. #22625493C2semidirect
12. #22625484C2semidirect
13. #22625483C2semidirect
14. C2×#17989451C2semidirect
302. C73#17840semidirect

Maximal subgroups

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

subgroupindex
#226268592
#226268562
#226255062
#226255042
#226255032
#226255022
#226255012
#226255002
#226254972
#226254952
#226254932
#226254842
#226254832
C2×#179894512
#226188912
#1784073