Finite Group Databasebeta

← #29650438

Subgroups — #29650438

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455884C211yesmaximal, characteristic
2#21454932C211yesmaximal, characteristic
3#21444726C211yesmaximal, characteristic, complemented
4#21444719C211yesmaximal, characteristic, complemented
5#21444714C211yesmaximal, characteristic, complemented
6#21444709C211yesmaximal, characteristic, complemented
7#21444697C211yesmaximal, characteristic, complemented
8#21444690C211yesmaximal, characteristic, complemented
9#21444669C211yesmaximal, characteristic, complemented
10#21444662C211yesmaximal, characteristic, complemented
11#21444605C211yesmaximal, characteristic, complemented
12#21444251C211yesmaximal, characteristic
13#21444222C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#2985C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840100C411yescharacteristic
18#16840100C411yescharacteristic
19#16840044C411yescharacteristic
20#16840039C411yescharacteristic
21#16839969C411yescharacteristic
22#16839964C411yescharacteristic
23#16839922C411yescharacteristic
24#16839922C411yescharacteristic
25#16839892C2211yescharacteristic
26#16839892C2211yescharacteristic
27C4×#11758202C2211yescharacteristic
28C4×#11758202C2211yescharacteristic
29C4×#11758201C2211yescharacteristic
30C4×#11758201C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839841C2211yescharacteristic
33#16839830—21no—
34#16839830—21no—
35#16839818—21no—
36#16839815C2211yescharacteristic
37#16839815C2211yescharacteristic
38#16839784—21no—
39C2×C4⋊#92418C2211yescharacteristic
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44Q8⋊#92418C2211yescharacteristic
45Q8⋊#92418C2211yescharacteristic
46Q8⋊#92418C2211yescharacteristic
47Q8⋊#92418C2211yescharacteristic
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839484C2211yescharacteristic
53#16839484C2211yescharacteristic
54#16839483C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#446—21no—
58C61×#446—21no—
59C61×#446C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C8×Q8×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#433—21no—
65C61×#432C2211yescharacteristic
66C61×#431C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71C2×#11758201C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C4×Dic122C2×C411yescharacteristic
76C4×Dic122C2311yescharacteristic
77C4×D244C2×C411yescharacteristic
78C4×D244C2311yescharacteristic
79C4×C22⋊D61—21no—
80C4×C22⋊D61—21no—
81#14519736C2×C411yescharacteristic
82#14519734—21no—
83C42×D61—21no—
84#14519710C2×C411yescharacteristic
85#14519710C2×C411yescharacteristic
86#14519708C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90C4⋊#92418C2×C411yescharacteristic
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519706—21no—
95#14519706—21no—
96#14519701C2×C411yescharacteristic
97#14519701C2×C411yescharacteristic
98#14519701C2×C411yescharacteristic
99#14519701C2×C411yescharacteristic
100#14519700C2×C411yescharacteristic
101#14519700C2×C411yescharacteristic
102#14519697C2×C411yescharacteristic
103#14519697C2×C411yescharacteristic
104C22⋊#92418—21no—
105C22⋊#92418C2×C411yescharacteristic
106C22⋊#92418C2×C411yescharacteristic
107#14519689—21no—
108#14519689—21no—
109#14519687—21no—
110#14519687—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C4⋊Q8×C61C2×C411yescharacteristic
116C4⋊Q8×C61C2×C411yescharacteristic
117#125×C61—21no—
118C22⋊Q8×C61—21no—
119C22⋊Q8×C61C2×C411yescharacteristic
120C22⋊Q8×C61C2×C411yescharacteristic
121C4×Q8×C61—21no—
122C4×Q8×C61C2311yescharacteristic
123C4×Q8×C61C2311yescharacteristic
124#117×C61—21no—
125C2×C42×C61C2311yescharacteristic
126C4⋊C8×C61—21no—
127C4⋊C8×C61—21no—
128C4⋊C8×C61—21no—
129C4⋊C8×C61—21no—
130C4⋊C8×C61D411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61D411yescharacteristic
136C22⋊C8×C61D411yescharacteristic
137#97×C61—21no—
138#97×C61—21no—
139#97×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61#4111yescharacteristic
150C2×C22⋊D61—21no—
151#11758222—41no—
152#11758222—41no—
153C2×D244C22×C411yescharacteristic
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×Dic122C22×C411yescharacteristic
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C22×C411yescharacteristic
172C4⋊C4×C61C22×C411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61C22×C411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61#4111yescharacteristic
180C42×C61C2411yescharacteristic
181C22⋊Dic61—21no—
182#11758202—41no—
183#11758202—41no—
184#11758201—41no—
185#11758201—41no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204#11758189—81no—
205#11758189—81no—
206C23×C61C4×D411yescharacteristic
207C22×D61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—81no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C23×C411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C22⋊D61—42no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232D244—21no—
233D244—21no—
234C4×D61—42no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—81no—
238Dic122—21no—
239Dic122—21no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245C8×C61—41no—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#17949—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61C2×C4×D411yescharacteristic
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61#56811yescharacteristic
271C4×C61#56811yescharacteristic
272C4×C61#57711yescharacteristic
273C4×C61#57811yescharacteristic
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277#3107—611no—
278#2989—611no—
279#2985D6111yescharacteristic, complemented
280#1593—611no—
281#1592—611no—
282#1591—611no—
283#1590—611no—
284#1588—611no—
285#1587—611no—
286#1584—611no—
287#1583—611no—
288#1573—611no—
289#1488—611no—
290#1481—611no—
291#1454—611no—
292C2×C61—41no—
293C2×C61#293011yescharacteristic
294C2×C61#294711yescharacteristic
295C2×C61#295711yescharacteristic
296D61—81no—
297#533C2×D6111yescharacteristic
298C4×#41—611no—
299#485—611no—
300#485—611no—
301#475—611no—
302#474—611no—
303#462—611no—
304#461—611no—
305#452—611no—
306#452—611no—
307#446—21no—
308#446—21no—
309#446—611no—
310#446—611no—
311#446C2×D6111yescharacteristic
312#446C2×D6111yescharacteristic
313C8×Q8C2×D6111yescharacteristic
314C8×Q8C2×D6111yescharacteristic
315C4×Q16—611no—
316C4×Q16—611no—
317C4×SD16—611no—
318C4×SD16—611no—
319#436—611no—
320#436—611no—
321#435—1221no—
322#435—1221no—
323#433—21no—
324#433—21no—
325#432—1221no—
326#432C2×D6111yescharacteristic
327#431—611no—
328#431—611no—
329#431C2×D6111yescharacteristic
330#423—1221no—
331C2×C4⋊C8—611no—
332#335—611no—
333#335—611no—
334#334—611no—
335#334—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345#322—611no—
346#322—611no—
347C82—611no—
348C61#1794911yescharacteristic, complemented, Sylow
349C2×#41—611no—
350C2×Q16—611no—
351C2×Q16—611no—
352C2×SD16—611no—
353C2×SD16—611no—
354C2×M16—1221no—
355C2×M16—1221no—
356C22×C8—1221no—
357C4⋊Q8C4×D6111yescharacteristic
358C4⋊Q8C4×D6111yescharacteristic
359#125—21no—
360C22⋊Q8—21no—
361C22⋊Q8C4×D6111yescharacteristic
362C22⋊Q8C4×D6111yescharacteristic
363C4×Q8—21no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8C22×D6111yescharacteristic
367C4×Q8C22×D6111yescharacteristic
368C4×D4—611no—
369C4×D4—611no—
370C4×D4—1221no—
371C4×D4—1221no—
372#117—21no—
373#117—611no—
374#117—1221no—
375C2×C42—1221no—
376C2×C42C22×D6111yescharacteristic
377#107—611no—
378#107—611no—
379#106—611no—
380#106—611no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8C22⋊D6111yescharacteristic
394C4⋊C8C22⋊D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#102—611no—
404#102—611no—
405C22⋊C8—21no—
406C22⋊C8—611no—
407C22⋊C8—611no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C22⋊D6111yescharacteristic
412C22⋊C8C22⋊D6111yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416#97—1221no—
417#97—1221no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426#41—2441no—
427#41—2441no—
428C2×Q8—21no—
429C2×Q8—611no—
430C2×Q8C2×C4×D6111yescharacteristic
431C2×Q8C2×C4×D6111yescharacteristic
432C2×D4—611no—
433C2×D4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4#1175822211yescharacteristic
439C22×C4C2×C22⋊D6111yescharacteristic
440Q16—2441no—
441Q16—2441no—
442SD16—2441no—
443SD16—2441no—
444M16—4881no—
445M16—4881no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—4881no—
457C2×C8C2×C22⋊D6111yescharacteristic
458C2×C8C2×C22⋊D6111yescharacteristic
459C2×C8C2×C22⋊D6111yescharacteristic
460C2×C8C2×C22⋊D6111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—611no—
469C4⋊C4—611no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4C2×C4×D6111yescharacteristic
473C4⋊C4C2×C4×D6111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C42—21no—
480C42—21no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42#1175822211yescharacteristic
486C42C2×C22⋊D6111yescharacteristic
487C42C23×D6111yescharacteristic
488C23—1221no—
489C23C4×C22⋊D6111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—1221no—
496Q8—1221no—
497D4—1221no—
498D4—1221no—
499D4—2442no—
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—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—4881no—
513C2×C4—2442no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4C4×C22⋊D6111yescharacteristic
517C2×C4C4×C22⋊D6111yescharacteristic
518C2×C4C4×C22⋊D6111yescharacteristic
519C2×C4C22×C4×D6111yescharacteristic
520C2×C4C22×C22⋊D6111yescharacteristic
521C2×C4C2×#1175822211yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—1221no—
529C8—1221no—
530C8—1221no—
531C8—1221no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—2441no—
540C22—2441no—
541C22—2441no—
542C22C2×C4×C22⋊D6111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4#1684052711yescharacteristic
555C4#1684052711yescharacteristic
556C4#1684057011yescharacteristic
557C4#1684057711yescharacteristic
558C2—41no—
559C2—4881no—
560C2#2145452011yescharacteristic
561C2#2145466211yescharacteristic
562C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2985C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#2985D61
hypocenterC61#17949
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2985

Complements

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

NH ≅ G/Ntype
3. #21444726C2semidirect
4. #21444719C2semidirect
5. #21444714C2semidirect
6. #21444709C2semidirect
7. #21444697C2semidirect
8. #21444690C2semidirect
9. #21444669C2semidirect
10. #21444662C2semidirect
11. #21444605C2semidirect
13. #21444222C2semidirect
14. #21444119C2semidirect
15. C61×#2985C2semidirect
279. #2985D61semidirect
348. C61#17949semidirect

Maximal subgroups

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

subgroupindex
#214558842
#214549322
#214447262
#214447192
#214447142
#214447092
#214446972
#214446902
#214446692
#214446622
#214446052
#214442512
#214442222
#214441192
C61×#29852
#1794961