Finite Group Databasebeta

← #29699467

Subgroups — #29699467

Order 15616.

740 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519799C211yesmaximal, characteristic
2#21454484C211yesmaximal, characteristic, complemented
3#21454384C211yesmaximal, characteristic, complemented
4#21446530C212yesmaximal, complemented
5#21446419C212yesmaximal, complemented
6#21446145C212yesmaximal
7#21445957C211yesmaximal, characteristic, complemented
8#21445840C211yesmaximal, characteristic, complemented
9#21445840C211yesmaximal, characteristic, complemented
10#21445663C212yesmaximal, complemented
11C61×#1770C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C2×#14519783C2212yes—
14C4×#11758222C2211yescharacteristic
15C4×#11758222C2211yescharacteristic
16C4×Dic244C411yescharacteristic, complemented
17C4×Dic244C411yescharacteristic, complemented
18C4×#11758190C411yescharacteristic, complemented
19C4×#11758190C411yescharacteristic, complemented
20C4×#11758190C411yescharacteristic, complemented
21C4×#11758190C411yescharacteristic, complemented
22C4×D488C411yescharacteristic, complemented
23C4×D488C411yescharacteristic, complemented
24#16839822—22no—
25#16839818—21no—
26#16839814—21no—
27#16839800C2211yescharacteristic
28#16839788C2212yes—
29#16839787—22no—
30#16839786C2211yescharacteristic
31#16839786C2211yescharacteristic
32#16839784—21no—
33C4⋊C8×D61—21no—
34C2×#14519705C2212yes—
35C2×#14519705C2212yes—
36#16839759C2211yescharacteristic
37#16839759C2211yescharacteristic
38#16839728C2212yes—
39#16839717C2212yes—
40#16839527C2212yes—
41#16839527C2212yes—
42#16839522C2212yes—
43#16839522C2212yes—
44C2×C4⋊C8×C61C2211yescharacteristic
45C2×#97×C61C2212yes—
46C2×C4×C8×C61C2211yescharacteristic
47C4×C4⋊C4×C61C2211yescharacteristic
48C61×#336C2212yes—
49C2×#11758222C2311yescharacteristic
50C2×#11758222C2311yescharacteristic
51#14519799—22no—
52#14519799—22no—
53C2×Dic244C2×C411yescharacteristic
54C2×#11758190C2×C411yescharacteristic
55C2×#11758190C2×C411yescharacteristic
56C2×D488C2×C411yescharacteristic
57#14519783—24no—
58#14519783—42no—
59C2×#11758194C2312yes—
60C2×#11758194C2312yes—
61C2×#11758189—22no—
62C2×C8×D61—22no—
63C4×Dic122C2×C411yescharacteristic
64C4×Dic122C2×C411yescharacteristic
65C4×Dic122C2×C411yescharacteristic
66C4×Dic122C2×C411yescharacteristic
67C4×D244C2×C411yescharacteristic
68C4×D244C2×C411yescharacteristic
69C4×D244C2×C411yescharacteristic
70C4×D244C2×C411yescharacteristic
71C4×C22⋊D61—21no—
72C4×C22⋊D61—21no—
73C4×C22⋊D61—21no—
74C4×C22⋊D61—21no—
75#14519736C2311yescharacteristic
76#14519736C2311yescharacteristic
77#14519734—21no—
78#14519734—21no—
79C42×D61—21no—
80C42×D61—21no—
81#14519711C2×C411yescharacteristic
82#14519711C2×C411yescharacteristic
83#14519709C2×C411yescharacteristic
84#14519709C2×C411yescharacteristic
85C4⋊#92418—21no—
86C4⋊#92418—21no—
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89#14519706—22no—
90#14519706—22no—
91#14519705—24no—
92#14519705—42no—
93#14519702C2×C411yescharacteristic
94#14519702C2×C411yescharacteristic
95#14519702C2×C411yescharacteristic
96#14519702C2×C411yescharacteristic
97#14519699C2×C411yescharacteristic
98#14519699C2×C411yescharacteristic
99#14519699C2×C411yescharacteristic
100#14519699C2×C411yescharacteristic
101#14519689—22no—
102#14519689—22no—
103#14519687—22no—
104C8×Dic61—22no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2312yes—
108C2×C4⋊C4×C61—21no—
109C2×C42×C61C2312yes—
110C2×C42×C61C2311yescharacteristic
111C4⋊C8×C61D411yescharacteristic
112C4⋊C8×C61D411yescharacteristic
113C4⋊C8×C61D412yes—
114#97×C61—42no—
115C4×C8×C61C2×C411yescharacteristic
116C4×C8×C61C2×C411yescharacteristic
117C4×C8×C61C2×C411yescharacteristic
118C4×C8×C61C2×C411yescharacteristic
119#95×C61—21no—
120C22×C4×C61—22no—
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61C2411yescharacteristic
124C2×C22⋊D61—21no—
125C2×C22⋊D61—21no—
126#11758222—21no—
127#11758222—21no—
128#11758222—21no—
129#11758222—21no—
130#11758222—21no—
131#11758222—21no—
132#11758222#4112yes—
133#11758222#4112yes—
134C2×D244C22×C411yescharacteristic
135C2×D244C22×C411yescharacteristic
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×Dic122C22×C411yescharacteristic
143C2×Dic122C22×C411yescharacteristic
144C2×C8×C61—22no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—22no—
149C2×C8×C61—21no—
150C2×C8×C61C22×C411yescharacteristic
151C2×C8×C61C22×C411yescharacteristic
152C2×C8×C61C22×C411yescharacteristic
153C2×C8×C61C22×C411yescharacteristic
154C2×C8×C61C2×D412yes—
155C2×C8×C61C2×D412yes—
156C4⋊C4×C61—42no—
157C42×C61—22no—
158C42×C61—22no—
159C42×C61C22×C411yescharacteristic
160C42×C61C22×C411yescharacteristic
161C42×C61C2×D411yescharacteristic
162C42×C61C2×D411yescharacteristic
163C22⋊Dic61—21no—
164C22⋊Dic61—21no—
165#11758198—21no—
166#11758198—21no—
167#11758198—21no—
168#11758198—21no—
169C4⋊Dic61C22×C411yescharacteristic
170C4⋊Dic61C22×C411yescharacteristic
171C4⋊Dic61C22×C411yescharacteristic
172C4⋊Dic61C22×C411yescharacteristic
173#11758196—21no—
174#11758196—21no—
175#11758196—21no—
176#11758196—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C4×Dic61—21no—
181C4×Dic61—21no—
182C4×Dic61—21no—
183#11758194—22no—
184#11758194—22no—
185#11758194—22no—
186#11758194—22no—
187C2×#92418—22no—
188C2×#92418—22no—
189Dic244—22no—
190D488—22no—
191#11758190—22no—
192#11758190—22no—
193#11758189—44no—
194C8×D61—44no—
195C23×C61C2×#4111yescharacteristic
196C22×D61—21no—
197C22×D61—21no—
198C2×C4×C61—22no—
199C2×C4×C61—41no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61C4×D411yescharacteristic
204C2×C4×C61C4×D411yescharacteristic
205C2×C4×C61C4×D411yescharacteristic
206C2×C4×C61C4×D411yescharacteristic
207C2×C4×C61C23×C411yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C2×C4×C61C2×#4111yescharacteristic
210C2×C4×C61C2×#4111yescharacteristic
211C2×C4×C61H(5,𝔽2)11yescharacteristic
212C2×C4×C612−1+411yescharacteristic
213C22⋊D61—22no—
214C22⋊D61—22no—
215C22⋊D61—41no—
216C22⋊D61—41no—
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223D244—21no—
224D244—21no—
225D244—21no—
226D244#11712yes—
227C4×D61—22no—
228C4×D61—22no—
229C4×D61—41no—
230C4×D61—41no—
231C4×D61—42no—
232C4×D61—42no—
233C4×D61—81no—
234C4×D61—81no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122#11712yes—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—22no—
244C8×C61—22no—
245#92418—42no—
246#92418—42no—
247#22782—611nomaximal, Sylow
248C22×C61—21no—
249C22×C61—21no—
250C22×C61C2×C4×D411yescharacteristic
251C22×C61#55211yescharacteristic
252C22×C61#55311yescharacteristic
253C2×D61—22no—
254C2×D61—41no—
255C2×D61—41no—
256C2×D61—41no—
257C2×D61—41no—
258C2×D61—41no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—82no—
263C4×C61#44412yes—
264C4×C61C2×#11711yescharacteristic
265C4×C61#52011yescharacteristic
266C4×C61#54611yescharacteristic
267C4×C61#54811yescharacteristic
268Dic61—22no—
269Dic61—41no—
270Dic61—41no—
271Dic61—41no—
272Dic61—41no—
273Dic61—41no—
274C4×#135—611no—
275#2925—611no—
276#2906—611no—
277#1938—612no—
278#1922—612no—
279#1876—612no—
280#1837—611no—
281#1806—611no—
282#1806—611no—
283#1770D6111yescharacteristic, complemented
284#1765—612no—
285C2×C61—21no—
286C2×C61—21no—
287C2×C61#235211yescharacteristic
288C2×C61C2×#44411yescharacteristic
289C2×C61#295711yescharacteristic
290D61—42no—
291D61—81no—
292C2×#135—611no—
293C2×#131—612no—
294C4×#41—611no—
295C4×#41—611no—
296C4×Q16—611no—
297C4×Q16—611no—
298C4×SD16—611no—
299C4×SD16—611no—
300C4×SD16—611no—
301C4×SD16—611no—
302C4×D8—611no—
303C4×D8—611no—
304#433—1222no—
305#432—1221no—
306#431—1221no—
307#427—611no—
308#424—612no—
309#424—1222no—
310#423—611no—
311#423—611no—
312#423—1221no—
313C2×C4⋊C8—1221no—
314C2×C4⋊C8C2×D6111yescharacteristic
315C2×#104—612no—
316C2×#104—612no—
317#416—611no—
318#416—611no—
319#408—612no—
320#405—612no—
321C2×#97C2×D6112yes—
322C2×C4×C8C2×D6111yescharacteristic
323C4×C4⋊C4C2×D6111yescharacteristic
324#341—612no—
325#341—612no—
326#339—612no—
327#339—612no—
328#336C2×D6112yes—
329C61#2278211yescharacteristic, complemented, Sylow
330C2×#41—611no—
331C2×#41—611no—
332#135—1222no—
333#135—1222no—
334C2×Q16—611no—
335C2×SD16—611no—
336C2×SD16—611no—
337C2×D8—611no—
338#131—1224no—
339#131—2442no—
340C2×M16—612no—
341C2×M16—612no—
342C2×M16—1222no—
343C22×C8—1222no—
344C22×C8C22×D6111yescharacteristic
345C22×C8C22×D6111yescharacteristic
346C22×C8C22×D6112yes—
347C4×Q8—611no—
348C4×Q8—611no—
349C4×Q8—611no—
350C4×Q8—611no—
351C4×D4—611no—
352C4×D4—611no—
353C4×D4—611no—
354C4×D4—611no—
355C4×D4—1221no—
356C4×D4—1221no—
357C4×D4—1221no—
358C4×D4—1221no—
359#117—611no—
360#117—611no—
361#117—1221no—
362#117—1221no—
363C2×C4⋊C4—21no—
364C2×C42—1221no—
365C2×C42—1221no—
366C2×C42C22×D6112yes—
367C2×C42C22×D6111yescharacteristic
368#107—611no—
369#107—611no—
370#106—611no—
371#106—611no—
372C4⋊C8—1222no—
373C4⋊C8—1222no—
374C4⋊C8—1221no—
375C4⋊C8—1221no—
376C4⋊C8—1221no—
377C4⋊C8—1221no—
378C4⋊C8D24411yescharacteristic
379C4⋊C8D24411yescharacteristic
380C4⋊C8D24412yes—
381#104—1224no—
382#104—2442no—
383#103—611no—
384#103—611no—
385#103—611no—
386#103—611no—
387#102—611no—
388#102—611no—
389#102—611no—
390#102—611no—
391C22⋊C8—1222no—
392C22⋊C8—1222no—
393#97—42no—
394#97—1222no—
395C4×C8—1222no—
396C4×C8C4×D6111yescharacteristic
397C4×C8C4×D6111yescharacteristic
398C4×C8C4×D6111yescharacteristic
399C4×C8C4×D6111yescharacteristic
400#95—21no—
401#41—612no—
402#41—612no—
403#41—1221no—
404#41—1221no—
405#41—1221no—
406#41—1221no—
407#41—1221no—
408#41—1221no—
409C2×Q8—611no—
410C2×Q8—611no—
411C2×D4—611no—
412C2×D4—611no—
413C2×D4—1221no—
414C2×D4—1221no—
415C22×C4—22no—
416C22×C4—1221no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—1221no—
420C22×C4—1221no—
421C22×C4—1221no—
422C22×C4#1175822211yescharacteristic
423C22×C4#1175822211yescharacteristic
424C22×C4C23×D6111yescharacteristic
425Q16—1222no—
426SD16—1222no—
427SD16—1222no—
428D8—1222no—
429M16—1222no—
430M16—1222no—
431M16—1222no—
432M16—1222no—
433M16—2444no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—22no—
439C2×C8—21no—
440C2×C8—1222no—
441C2×C8—1222no—
442C2×C8—2444no—
443C2×C8C2×C4×D6111yescharacteristic
444C2×C8C2×C4×D6111yescharacteristic
445C2×C8C2×C4×D6111yescharacteristic
446C2×C8C2×C4×D6111yescharacteristic
447C2×C8C2×D24412yes—
448C2×C8C2×D24412yes—
449C4⋊C4—42no—
450C4⋊C4—611no—
451C4⋊C4—611no—
452C4⋊C4—611no—
453C4⋊C4—611no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C22⋊C4—1221no—
459C22⋊C4—1221no—
460C22⋊C4—1221no—
461C22⋊C4—1221no—
462C22⋊C4—1221no—
463C22⋊C4—1221no—
464C42—22no—
465C42—22no—
466C42—1221no—
467C42—1221no—
468C42—1221no—
469C42—1221no—
470C42—1221no—
471C42—1221no—
472C42C2×C4×D6111yescharacteristic
473C42C2×C4×D6111yescharacteristic
474C42C2×D24411yescharacteristic
475C42C2×D24411yescharacteristic
476C23—1221no—
477C23—1221no—
478C23C2×#1175822211yescharacteristic
479Q8—612no—
480Q8—1221no—
481Q8—1221no—
482Q8—1221no—
483D4—612no—
484D4—1222no—
485D4—1222no—
486D4—1221no—
487D4—1221no—
488D4—1221no—
489D4—2441no—
490D4—2441no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—1221no—
497C2×C4—1222no—
498C2×C4—1222no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—4881no—
505C2×C4—4881no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4C4×D24411yescharacteristic
511C2×C4C4×D24411yescharacteristic
512C2×C4C4×D24411yescharacteristic
513C2×C4C4×D24411yescharacteristic
514C2×C4C22×C4×D6111yescharacteristic
515C2×C4C22×D24411yescharacteristic
516C2×C4#41×D6111yescharacteristic
517C2×C4#41×D6111yescharacteristic
518C2×C4#1451982211yescharacteristic
519C2×C4#1451982511yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—22no—
525C8—22no—
526C8—2442no—
527C8—2442no—
528C22—21no—
529C22—21no—
530C22—1222no—
531C22—2441no—
532C22—2441no—
533C22—2441no—
534C22—2441no—
535C22—2441no—
536C22C2×C4×D24411yescharacteristic
537C22#1684045311yescharacteristic
538C22#1684046211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—82no—
543C4—1222no—
544C4—2441no—
545C4—2441no—
546C4—2441no—
547C4—2441no—
548C4—2441no—
549C4#1683988512yes—
550C4#117×D6111yescharacteristic
551C4#1684024311yescharacteristic
552C4#1684040711yescharacteristic
553C4#1684042411yescharacteristic
554C2—21no—
555C2—21no—
556C2—4881no—
557C2—2442no—
558C2#2144875111yescharacteristic
559C2C2×#1683988511yescharacteristic
560C2#2145473711yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1770C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519799C22
cosocleC22×C4×C61C24
hypercenter#1770D61
hypocenterC61#22782
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #1770

Complements

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

NH ≅ G/Ntype
2. #21454484C2semidirect
3. #21454384C2semidirect
4. #21446530C2semidirect
5. #21446419C2semidirect
7. #21445957C2semidirect
8. #21445840C2semidirect
9. #21445840C2semidirect
10. #21445663C2semidirect
11. C61×#1770C2semidirect
16. C4×Dic244C4semidirect
17. C4×Dic244C4semidirect
18. C4×#11758190C4semidirect
19. C4×#11758190C4semidirect
20. C4×#11758190C4semidirect
21. C4×#11758190C4semidirect
22. C4×D488C4semidirect
23. C4×D488C4semidirect
283. #1770D61semidirect
329. C61#22782semidirect

Maximal subgroups

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

subgroupindex
C4×#145197992
#214544842
#214543842
#214465302
#214464192
#214461452
#214459572
#214458402
#214456632
C61×#17702
#2278261