Finite Group Databasebeta

← #29650951

Subgroups — #29650951

Order 15616.

602 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#21455856C211yesmaximal, characteristic
2#21454771C211yesmaximal, characteristic
3#21454767C211yesmaximal, characteristic
4#21444713C211yesmaximal, characteristic, complemented
5#21444670C211yesmaximal, characteristic, complemented
6#21444668C211yesmaximal, characteristic, complemented
7#21444667C211yesmaximal, characteristic, complemented
8#21444667C211yesmaximal, characteristic, complemented
9C8×Dic244C211yesmaximal, characteristic, complemented
10#21444623C211yesmaximal, characteristic, complemented
11#21444592C211yesmaximal, characteristic
12#21444272C211yesmaximal, characteristic
13Q8⋊C8×D61C211yesmaximal, characteristic
14C8×#11758189C211yesmaximal, characteristic
15C61×#1591C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17C4×Q8×D61C2211yescharacteristic
18#16840099C411yescharacteristic
19#16840096C411yescharacteristic
20#16840056C411yescharacteristic
21#16840055C411yescharacteristic
22#16839971C411yescharacteristic
23#16839970C411yescharacteristic
24#16839919C411yescharacteristic
25#16839916C411yescharacteristic
26#16839893C2211yescharacteristic
27#16839891—21no—
28#16839890—21no—
29#16839890—21no—
30#16839889—21no—
31#16839889C2211yescharacteristic
32Q8×#92418C2211yescharacteristic
33C8×Dic122C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839886C2211yescharacteristic
36C4×Dic244C2211yescharacteristic
37C4×#11758202C2211yescharacteristic
38C4×#11758202C2211yescharacteristic
39#16839813C2211yescharacteristic
40#16839787—21no—
41#16839784—21no—
42#16839784C2211yescharacteristic
43C4⋊C8×D61C2211yescharacteristic
44#16839719—21no—
45#16839714—21no—
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54Q8⋊#92418C2211yescharacteristic
55#16839492C2211yescharacteristic
56#16839492C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C61×#446C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×Q8×D61C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758202C2×C411yescharacteristic
71C2×#11758189—21no—
72C2×#11758189D411yescharacteristic
73C2×#11758189D411yescharacteristic
74C2×C8×D61—21no—
75C2×C8×D61—21no—
76#14519776C2×C411yescharacteristic
77#14519775C2×C411yescharacteristic
78#14519767—21no—
79#14519757C2×C411yescharacteristic
80#14519755—21no—
81#14519753C2×C411yescharacteristic
82Q8×Dic61C2×C411yescharacteristic
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×Dic122C2311yescharacteristic
86C4×Dic122C2311yescharacteristic
87#14519742—21no—
88#14519742C2×C411yescharacteristic
89#14519734—21no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61C2×C411yescharacteristic
92C42×D61—21no—
93C42×D61C2311yescharacteristic
94#14519711C2×C411yescharacteristic
95#14519710C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97C4⋊#92418—21no—
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706C2×C411yescharacteristic
108#14519706C2×C411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519701C2×C411yescharacteristic
112#14519701C2×C411yescharacteristic
113#14519700C2×C411yescharacteristic
114#14519700C2×C411yescharacteristic
115#14519689C2×C411yescharacteristic
116#14519689C2×C411yescharacteristic
117#14519688—21no—
118#14519687—21no—
119#14519687D411yescharacteristic
120#14519687D411yescharacteristic
121C4×#92418—21no—
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×Q16×C61C2×C411yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61C2×C411yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#103×C61C2×C411yescharacteristic
139#97×C61—21no—
140#97×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146Q8×D61—22no—
147Q8×D61—41no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61C22×C411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61#4111yescharacteristic
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122C22×C411yescharacteristic
156C2×Dic122C22×C411yescharacteristic
157Q16×C61—41no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C411yescharacteristic
168C4⋊C4×C61C22×C411yescharacteristic
169C42×C61—21no—
170C42×C61—21no—
171C42×C61C2411yescharacteristic
172#11758202—22no—
173#11758202—41no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61C22×C411yescharacteristic
179C4⋊Dic61C22×C411yescharacteristic
180#11758196—21no—
181#11758196—21no—
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61C22×C411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61#4111yescharacteristic
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202Dic244—22no—
203#11758189—22no—
204#11758189—42no—
205#11758189Q1614yescomplemented
206C8×D61—42no—
207C8×D61—42no—
208C22×D61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61C4×D411yescharacteristic
225C2×Dic61C4×D411yescharacteristic
226C2×Dic61C4×D411yescharacteristic
227C4×D61—21no—
228C4×D61—21no—
229C4×D61—41no—
230C4×D61—42no—
231C4×D61—81no—
232C4×D61C2×Q1612yes—
233C4×D61#13512yes—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—42no—
238Dic122—81no—
239Dic122#13112yes—
240C8×C61—22no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61C2×Q1612yes—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418C2×Q1612yes—
254#17998—611nomaximal, Sylow
255C22×C61C2×C4×D411yescharacteristic
256C2×D61—21no—
257C2×D61—21no—
258C2×D61C4×Q1612yes—
259C4×C61—21no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61C2×#13111yescharacteristic
265C4×C61#56811yescharacteristic
266C4×C61C22×Q1611yescharacteristic
267C4×C61C2×#13511yescharacteristic
268Dic61—22no—
269Dic61—21no—
270Dic61—21no—
271Dic61—41no—
272Dic61—41no—
273Dic61—41no—
274Dic61C4×Q1612yes—
275#3104—611no—
276Q8×M16—611no—
277#2962—611no—
278#1591—611no—
279#1591D6111yescharacteristic, complemented
280#1584—611no—
281#1584—611no—
282#1584—611no—
283#1584—611no—
284C8×Q16—611no—
285C8×Q16—611no—
286#1571—611no—
287#1493—611no—
288C2×Q8⋊C8—611no—
289C8×M16—611no—
290C2×C61#293311yescharacteristic
291C2×C61C2×C4×Q1611yescharacteristic
292C2×C61#295611yescharacteristic
293D61—22no—
294#533—611no—
295C2×C4×Q8—611no—
296#484—611no—
297#484—611no—
298#477—611no—
299#477—611no—
300#462—611no—
301#462—611no—
302#451—611no—
303#451—611no—
304#446—611no—
305#446—611no—
306#446—1221no—
307#446—1221no—
308#446—1221no—
309#446—1221no—
310#446C2×D6111yescharacteristic
311#446C2×D6111yescharacteristic
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—611no—
315C8×Q8—611no—
316C4×Q16—611no—
317C4×Q16—611no—
318C4×Q16—611no—
319C4×Q16C2×D6111yescharacteristic
320#431—611no—
321#424—1221no—
322#423—611no—
323#423—1221no—
324C2×C4⋊C8—611no—
325#405—1221no—
326C4×M16—611no—
327C4×M16—1221no—
328C2×C4×C8—611no—
329#335—611no—
330#335—611no—
331#335—611no—
332#335C2×D6111yescharacteristic
333Q8⋊C8—611no—
334Q8⋊C8—611no—
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8C2×D6111yescharacteristic
340Q8⋊C8C2×D6111yescharacteristic
341#322—611no—
342#322—611no—
343C82—611no—
344C82C2×D6111yescharacteristic
345C61#1799811yescharacteristic, complemented, Sylow
346C22×Q8—611no—
347C2×Q16—611no—
348C2×Q16—611no—
349C2×Q16—611no—
350C2×Q16C4×D6111yescharacteristic
351C2×M16—611no—
352C2×M16—611no—
353C2×M16—1221no—
354C22×C8—1221no—
355C22×C8—1221no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358#125—1221no—
359C22⋊Q8—611no—
360C22⋊Q8—611no—
361C22⋊Q8—1221no—
362C4×Q8—611no—
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8—1221no—
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×Q8C22×D6111yescharacteristic
370C4×Q8C22×D6111yescharacteristic
371#117—1221no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—1221no—
374C2×C42—611no—
375C2×C42—1221no—
376#107—611no—
377#107—611no—
378#107—611no—
379#107C4×D6111yescharacteristic
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—611no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103C4×D6111yescharacteristic
403#103C4×D6111yescharacteristic
404C22⋊C8—611no—
405C22⋊C8—611no—
406#97—21no—
407#97—21no—
408#97—611no—
409#97—611no—
410#97—1221no—
411#97—1221no—
412C4×C8—611no—
413C4×C8—611no—
414C4×C8—611no—
415C4×C8—1221no—
416C4×C8—1221no—
417C4×C8—1221no—
418C4×C8—1221no—
419C4×C8—1221no—
420C4×C8C22×D6111yescharacteristic
421C4×C8C22×D6111yescharacteristic
422C4×C8C22×D6111yescharacteristic
423C2×Q8—611no—
424C2×Q8—611no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1222no—
428C2×Q8—2441no—
429C2×Q8C2×C4×D6111yescharacteristic
430C2×Q8C2×C4×D6111yescharacteristic
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—1221no—
435C22×C4—1221no—
436Q16—41no—
437Q16—1222no—
438Q16—1222no—
439Q16—2441no—
440M16—614no—
441M16—1222no—
442M16—2442no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—2442no—
454C2×C8—2442no—
455C2×C8C2×C4×D6111yescharacteristic
456C2×C8C2×C4×D6111yescharacteristic
457C2×C8D4×D6111yescharacteristic
458C2×C8D4×D6111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—611no—
462C4⋊C4—611no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4C2×C4×D6111yescharacteristic
474C4⋊C4C2×C4×D6111yescharacteristic
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C42—21no—
478C42—21no—
479C42—611no—
480C42—611no—
481C42—611no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42C23×D6111yescharacteristic
487C23—611no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—612no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—4881no—
497Q8—2442no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—611no—
503C2×C4—612no—
504C2×C4—612no—
505C2×C4—611no—
506C2×C4—611no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—4881no—
514C2×C4—2441no—
515C2×C4—2442no—
516C2×C4C22×C4×D6111yescharacteristic
517C2×C4C2×D4×D6111yescharacteristic
518C2×C4#41×D6111yescharacteristic
519C8—22no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—612no—
526C8—1221no—
527C8—1221no—
528C8—1221no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C8Q16×D6112yes—
533C22—612no—
534C22—1221no—
535C22—1221no—
536C22C4×D4×D6111yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—612no—
543C4—1221no—
544C4—1221no—
545C4—1222no—
546C4—2441no—
547C4—2441no—
548C4—2441no—
549C4#131×D6111yescharacteristic
550C4#1684052811yescharacteristic
551C4C2×Q16×D6111yescharacteristic
552C4#135×D6111yescharacteristic
553C2—1222no—
554C2#2145454811yescharacteristic
555C2C4×Q16×D6111yescharacteristic
556C2#2145472411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1591C2
socleC22×C61C2×C4×D4
prime radicalC22×D61C4×D4
cosocleC42×C61C24
hypercenter#1591D61
hypocenterC61#17998
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1591

Complements

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

NH ≅ G/Ntype
4. #21444713C2semidirect
5. #21444670C2semidirect
6. #21444668C2semidirect
7. #21444667C2semidirect
8. #21444667C2semidirect
9. C8×Dic244C2semidirect
10. #21444623C2semidirect
15. C61×#1591C2semidirect
205. #11758189Q16semidirect
279. #1591D61semidirect
345. C61#17998semidirect

Maximal subgroups

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

subgroupindex
#214558562
#214547712
#214547672
#214447132
#214446702
#214446682
#214446672
C8×Dic2442
#214446232
#214445922
#214442722
Q8⋊C8×D612
C8×#117581892
C61×#15912
#1799861