Finite Group Databasebeta

← #29651206

Subgroups — #29651206

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455899C211yesmaximal, characteristic
2#21454981C211yesmaximal, characteristic
3#21444714C211yesmaximal, characteristic, complemented
4#21444709C211yesmaximal, characteristic, complemented
5#21444697C211yesmaximal, characteristic, complemented
6#21444690C211yesmaximal, characteristic, complemented
7#21444688C211yesmaximal, characteristic, complemented
8#21444674C211yesmaximal, characteristic, complemented
9C8×#11758202C211yesmaximal, characteristic, complemented
10C8×#11758201C211yesmaximal, characteristic, complemented
11#21444605C211yesmaximal, characteristic, complemented
12#21444277C211yesmaximal, characteristic
13C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
14#21444103C211yesmaximal, characteristic, complemented
15C61×#2984C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840092C411yescharacteristic
18#16840075C411yescharacteristic
19#16840069C411yescharacteristic
20#16840069C411yescharacteristic
21#16839984C411yescharacteristic
22#16839984C411yescharacteristic
23#16839918C411yescharacteristic
24#16839901C411yescharacteristic
25#16839892C2211yescharacteristic
26C8×Dic122C2211yescharacteristic
27C4×#11758202C2211yescharacteristic
28C4×#11758202C2211yescharacteristic
29C4×#11758201C2211yescharacteristic
30C4×#11758201C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839830—21no—
33C8×D244C2211yescharacteristic
34#16839825—21no—
35#16839822—21no—
36#16839815C2211yescharacteristic
37#16839787—21no—
38C2×C4⋊#92418C2211yescharacteristic
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
54C8×#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C61×#446—21no—
58C61×#446—21no—
59C61×#446C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C8×Q8×C61C2211yescharacteristic
63C61×#432—21no—
64C61×#432C2211yescharacteristic
65C61×#431—21no—
66C61×#431C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71C2×#11758189—21no—
72C22×#92418—21no—
73C22×#92418—21no—
74C2×C8×D61—21no—
75#14519771—21no—
76#14519769C2×C411yescharacteristic
77#14519765C2×C411yescharacteristic
78#14519760—21no—
79#14519756C2×C411yescharacteristic
80#14519751C2×C411yescharacteristic
81C4×Dic122C2311yescharacteristic
82C4×D244C2311yescharacteristic
83C4×C22⋊D61—21no—
84#14519734—21no—
85#14519710C2×C411yescharacteristic
86#14519710C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88#14519708C2×C411yescharacteristic
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⋊#92418C2×C411yescharacteristic
105C22⋊#92418C2×C411yescharacteristic
106#14519689—21no—
107#14519689—21no—
108#14519687—21no—
109C4×#92418—21no—
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C22×Q8×C61C2×C411yescharacteristic
116C4×Q8×C61—21no—
117C4×Q8×C61—21no—
118C4×Q8×C61C2×C411yescharacteristic
119C4×Q8×C61C2×C411yescharacteristic
120C4×Q8×C61C2311yescharacteristic
121C4×Q8×C61C2311yescharacteristic
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61C2×C411yescharacteristic
124C2×C42×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×C61—22no—
146C2×Q8×C61—41no—
147C2×Q8×C61C22×C411yescharacteristic
148C2×Q8×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C2×C22⋊D61—21no—
155C2×D244C22×C411yescharacteristic
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×C61C22×C411yescharacteristic
170C4⋊C4×C61C22×C411yescharacteristic
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61C22×C411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758202—22no—
181#11758202—41no—
182#11758201—22no—
183#11758201—41no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194C4×Dic61—21no—
195C2×#92418—24no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—81no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205#11758189—81no—
206C8×D61—81no—
207C23×C61C4×D411yescharacteristic
208C22×D61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—42no—
213Q8×C61#13112yes—
214C2×C4×C61—21no—
215C2×C4×C61—22no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C22⋊D61—42no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235D244—21no—
236D244—21no—
237C4×D61—41no—
238C4×D61—41no—
239Dic122—21no—
240Dic122—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—41no—
246C8×C61—41no—
247#92418—22no—
248#92418—22no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#18017—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61#44312yes—
259C22×C61C2×C4×D411yescharacteristic
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
263C4×C61—21no—
264C4×C61—22no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61C2×#13111yescharacteristic
272C4×C61#56811yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57811yescharacteristic
275Dic61—41no—
276Dic61—41no—
277Dic61—41no—
278#3108—611no—
279#2994—611no—
280#2984D6111yescharacteristic, complemented
281#1591—611no—
282#1590—611no—
283#1588—611no—
284#1587—611no—
285#1587—611no—
286#1585—611no—
287C8×Q16—611no—
288C8×SD16—611no—
289#1573—611no—
290#1494—611no—
291C2×Q8⋊C8—611no—
292#1450—611no—
293C2×C61—22no—
294C2×C61#293311yescharacteristic
295C2×C61#294711yescharacteristic
296C2×C61C2×#44311yescharacteristic
297D61—81no—
298#529—611no—
299C2×C4×Q8C2×D6111yescharacteristic
300#483—611no—
301#480—611no—
302#479—611no—
303#479—611no—
304#464—611no—
305#464—611no—
306#451—611no—
307#448—611no—
308#446—21no—
309#446—21no—
310#446—611no—
311#446C2×D6111yescharacteristic
312#446C2×D6111yescharacteristic
313C8×Q8—611no—
314C8×Q8C2×D6111yescharacteristic
315C8×Q8C2×D6111yescharacteristic
316C4×Q16—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320#436—611no—
321#435—1221no—
322C8×D4—611no—
323C8×D4—1221no—
324#433—1221no—
325#432—21no—
326#432C2×D6111yescharacteristic
327#431—21no—
328#431—611no—
329#431C2×D6111yescharacteristic
330#424—1221no—
331C2×C4⋊C8—611no—
332C2×C4×C8—611no—
333#335—611no—
334#335—611no—
335#334—611no—
336#334—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343D4⋊C8—611no—
344D4⋊C8—611no—
345#322—611no—
346#322—611no—
347C82—611no—
348C82—611no—
349C61#1801711yescharacteristic, complemented, Sylow
350C22×Q8C4×D6111yescharacteristic
351C2×Q16—611no—
352C2×Q16—611no—
353C2×SD16—611no—
354C2×SD16—611no—
355C2×M16—1221no—
356C22×C8—1221no—
357C22×C8—1221no—
358C22×C8—1221no—
359#126—1221no—
360#125—611no—
361#124—611no—
362#123—1221no—
363C22⋊Q8—611no—
364#121—611no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—611no—
368C4×Q8C4×D6111yescharacteristic
369C4×Q8C4×D6111yescharacteristic
370C4×Q8C22×D6111yescharacteristic
371C4×Q8C22×D6111yescharacteristic
372C4×D4—611no—
373C4×D4—1221no—
374#117—1221no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C4×D6111yescharacteristic
377C2×C42—21no—
378C2×C42C22×D6111yescharacteristic
379#107—611no—
380#107—611no—
381#106—611no—
382#106—611no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22⋊D6111yescharacteristic
395C4⋊C8C22⋊D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#103—611no—
404#102—611no—
405#102—611no—
406C22⋊C8—21no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C22⋊D6111yescharacteristic
412C22⋊C8C22⋊D6111yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416#97—1221no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8C22×D6111yescharacteristic
426C4×C8C22×D6111yescharacteristic
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—611no—
431C2×Q8C2×C4×D6111yescharacteristic
432C2×Q8C2×C4×D6111yescharacteristic
433C2×D4—611no—
434C2×D4—1221no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—1221no—
438C22×C4C2×C4×D6111yescharacteristic
439C22×C4#1175822211yescharacteristic
440C22×C4C2×C22⋊D6111yescharacteristic
441Q16—1222no—
442Q16—2441no—
443SD16—1222no—
444SD16—2441no—
445M16—4881no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—1224no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—4881no—
458C2×C8—4881no—
459C2×C8C2×C22⋊D6111yescharacteristic
460C2×C8C2×C22⋊D6111yescharacteristic
461C2×C8C2×C22⋊D6111yescharacteristic
462C2×C8C2×C22⋊D6111yescharacteristic
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⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4C2×C4×D6111yescharacteristic
475C4⋊C4C2×C4×D6111yescharacteristic
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—1221no—
486C42C2×C4×D6111yescharacteristic
487C42#1175822211yescharacteristic
488C42C2×C22⋊D6111yescharacteristic
489C42C23×D6111yescharacteristic
490C23—1221no—
491C23C4×C22⋊D6111yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—42no—
496Q8—1221no—
497Q8—1221no—
498Q8#1451978512yes—
499D4—1221no—
500D4—1221no—
501D4—2442no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4C4×C22⋊D6111yescharacteristic
519C2×C4C4×C22⋊D6111yescharacteristic
520C2×C4C4×C22⋊D6111yescharacteristic
521C2×C4C22×C4×D6111yescharacteristic
522C2×C4C22×C22⋊D6111yescharacteristic
523C2×C4C2×#1175822211yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—1222no—
531C8—1222no—
532C8—1221no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—2441no—
537C8—2441no—
538C22—21no—
539C22—21no—
540C22—2441no—
541C22—2441no—
542C22—2441no—
543C22#1683987712yes—
544C22C2×C4×C22⋊D6111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—2441no—
554C4—2441no—
555C4—2441no—
556C4C2×#1451978511yescharacteristic
557C4#1684052811yescharacteristic
558C4#1684057011yescharacteristic
559C4#1684057711yescharacteristic
560C2—22no—
561C2—4881no—
562C2#2145454411yescharacteristic
563C2#2145466211yescharacteristic
564C2C2×#1683987711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2984C2
socleC22×C61C2×C4×D4
prime radical#14519751C2×C4
cosocleC42×C61C24
hypercenter#2984D61
hypocenterC61#18017
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #21444714C2semidirect
4. #21444709C2semidirect
5. #21444697C2semidirect
6. #21444690C2semidirect
7. #21444688C2semidirect
8. #21444674C2semidirect
9. C8×#11758202C2semidirect
10. C8×#11758201C2semidirect
11. #21444605C2semidirect
13. C2×Q8⋊#92418C2semidirect
14. #21444103C2semidirect
15. C61×#2984C2semidirect
280. #2984D61semidirect
349. C61#18017semidirect

Maximal subgroups

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

subgroupindex
#214558992
#214549812
#214447142
#214447092
#214446972
#214446902
#214446882
#214446742
C8×#117582022
C8×#117582012
#214446052
#214442772
C2×Q8⋊#924182
#214441032
C61×#29842
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