Finite Group Databasebeta

← #29699460

Subgroups — #29699460

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×#14519797C211yesmaximal, characteristic
2#21454484C211yesmaximal, characteristic, complemented
3#21446529C212yesmaximal, complemented
4#21446415C212yesmaximal, complemented
5#21446146C212yesmaximal
6#21445956C211yesmaximal, characteristic, complemented
7#21445839C211yesmaximal, characteristic, complemented
8#21445836C211yesmaximal, characteristic, complemented
9#21445689C211yesmaximal, characteristic, complemented
10#21445661C212yesmaximal, complemented
11C61×#2906C211yesmaximal, characteristic, complemented
12C2×#14519797C2211yescharacteristic
13C4×#11758222C2211yescharacteristic
14C4×#11758202C411yescharacteristic, complemented
15C4×#11758202C411yescharacteristic, complemented
16C4×#11758201C411yescharacteristic, complemented
17C4×#11758201C411yescharacteristic, complemented
18C4×#11758200C411yescharacteristic, complemented
19C4×#11758200C411yescharacteristic, complemented
20C4×#11758199C411yescharacteristic, complemented
21C4×#11758199C411yescharacteristic, complemented
22#16839822—22no—
23#16839818—21no—
24#16839814—21no—
25#16839798C2211yescharacteristic
26#16839786C2211yescharacteristic
27C2×#14519704C2212yes—
28C2×#14519703C2212yes—
29#16839758C2211yescharacteristic
30#16839756C2211yescharacteristic
31#16839728C2212yes—
32#16839717C2212yes—
33C2×#14519687C2212yes—
34C2×C4×#92418C2211yescharacteristic
35C4×C4⋊Dic61C2211yescharacteristic
36#16839526C2212yes—
37#16839526C2212yes—
38#16839523C2212yes—
39#16839521C2212yes—
40#16839516C2212yes—
41C2×#131×C61C2212yes—
42C4×#41×C61C2211yescharacteristic
43C61×#424—22no—
44C61×#424C2212yes—
45C61×#423—21no—
46C61×#423C2211yescharacteristic
47C2×C4⋊C8×C61—21no—
48C2×C4⋊C8×C61C2211yescharacteristic
49C2×#11758222C2311yescharacteristic
50#14519797—22no—
51#14519797—22no—
52C2×#11758202C2×C411yescharacteristic
53C2×#11758200C2×C411yescharacteristic
54C2×#11758201C2×C411yescharacteristic
55C2×#11758199C2×C411yescharacteristic
56C2×#11758194C2312yes—
57C22×#92418C2311yescharacteristic
58C22×#92418C2311yescharacteristic
59C4×Dic122C2×C411yescharacteristic
60C4×Dic122C2×C411yescharacteristic
61C4×D244C2×C411yescharacteristic
62C4×D244C2×C411yescharacteristic
63C4×C22⋊D61—21no—
64C4×C22⋊D61—21no—
65#14519736C2311yescharacteristic
66#14519734—21no—
67C2×C4⋊Dic61—21no—
68C2×C4×Dic61C2312yes—
69C42×D61—21no—
70#14519710C2×C411yescharacteristic
71#14519710C2×C411yescharacteristic
72#14519708C2×C411yescharacteristic
73#14519708C2×C411yescharacteristic
74C4⋊#92418—21no—
75C4⋊#92418—21no—
76#14519704—24no—
77#14519703—42no—
78#14519701C2×C411yescharacteristic
79#14519701C2×C411yescharacteristic
80#14519700C2×C411yescharacteristic
81#14519700C2×C411yescharacteristic
82#14519698C2×C411yescharacteristic
83#14519698C2×C411yescharacteristic
84#14519697C2×C411yescharacteristic
85#14519697C2×C411yescharacteristic
86#14519689—22no—
87#14519689—22no—
88#14519687—22no—
89#14519687—42no—
90C4×#92418C2×C411yescharacteristic
91C4×#92418C2×C411yescharacteristic
92C4×#92418C2×C411yescharacteristic
93C4×#92418C2×C411yescharacteristic
94C8×Dic61—22no—
95#14519684—21no—
96C2×#41×C61C2311yescharacteristic
97#131×C61—24no—
98#131×C61—42no—
99C2×M16×C61—22no—
100C2×M16×C61C2312yes—
101C22×C8×C61—22no—
102C22×C8×C61C2312yes—
103C4×Q8×C61C2×C411yescharacteristic
104C4×Q8×C61C2×C411yescharacteristic
105C4×D4×C61—21no—
106C4×D4×C61—21no—
107C4×D4×C61C2×C411yescharacteristic
108C4×D4×C61C2×C411yescharacteristic
109#117×C61—21no—
110#117×C61C2311yescharacteristic
111C2×C42×C61—21no—
112C2×C42×C61C2311yescharacteristic
113C4⋊C8×C61—22no—
114C4⋊C8×C61—22no—
115C4⋊C8×C61—21no—
116C4⋊C8×C61—21no—
117C4⋊C8×C61D411yescharacteristic
118C4⋊C8×C61D411yescharacteristic
119C4⋊C8×C61D412yes—
120#41×C61—21no—
121#41×C61—21no—
122#41×C61#4112yes—
123#41×C61#4112yes—
124C2×Q8×C61C22×C411yescharacteristic
125C2×D4×C61—21no—
126C2×D4×C61C22×C411yescharacteristic
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61#4111yescharacteristic
131C22×C4×C61#4111yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C2×C22⋊D61—21no—
134C22×Dic61—22no—
135#11758222—21no—
136#11758222—21no—
137#11758222—21no—
138#11758222—21no—
139C2×D244C22×C411yescharacteristic
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×Dic122C22×C411yescharacteristic
144M16×C61—22no—
145M16×C61—22no—
146M16×C61—44no—
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61—22no—
150C2×C8×C61—44no—
151C2×C8×C61C2×D412yes—
152C2×C8×C61C2×D412yes—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61C22×C411yescharacteristic
156C4⋊C4×C61C22×C411yescharacteristic
157C22⋊C4×C61—21no—
158C22⋊C4×C61—21no—
159C22⋊C4×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61C22×C411yescharacteristic
164C42×C61C22×C411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C22⋊Dic61—21no—
168#11758202—22no—
169#11758201—22no—
170#11758200—22no—
171#11758199—22no—
172#11758198—21no—
173#11758198—21no—
174C4⋊Dic61—42no—
175C4⋊Dic61C22×C411yescharacteristic
176C4⋊Dic61C22×C411yescharacteristic
177#11758196—21no—
178#11758196—21no—
179C4×Dic61—21no—
180C4×Dic61—21no—
181C4×Dic61—21no—
182C4×Dic61—22no—
183C4×Dic61—22no—
184#11758194—22no—
185#11758194—22no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—22no—
191C2×#92418C22×C411yescharacteristic
192C2×#92418C22×C411yescharacteristic
193C2×#92418C22×C411yescharacteristic
194C2×#92418C22×C411yescharacteristic
195C23×C61—21no—
196C23×C61C2×#4111yescharacteristic
197C22×D61—21no—
198Q8×C61—21no—
199Q8×C61#11712yes—
200D4×C61—22no—
201D4×C61—22no—
202D4×C61—21no—
203D4×C61#11712yes—
204C2×C4×C61—21no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—41no—
211C2×C4×C61—42no—
212C2×C4×C61—81no—
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61H(5,𝔽2)11yescharacteristic
222C2×C4×C612−1+411yescharacteristic
223C22⋊D61—41no—
224C22⋊D61—41no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—42no—
231D244—21no—
232D244—21no—
233C4×D61—41no—
234C4×D61—41no—
235C4×D61—42no—
236C4×D61—81no—
237Dic122—21no—
238Dic122—21no—
239C8×C61—22no—
240C8×C61—22no—
241C8×C61—42no—
242#92418—21no—
243#92418—21no—
244#92418—21no—
245#92418—21no—
246#92418—42no—
247#22782—611nomaximal, Sylow
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—22no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61C2×C4×D411yescharacteristic
254C22×C61#55211yescharacteristic
255C22×C61#55311yescharacteristic
256C2×D61—41no—
257C2×D61—41no—
258C2×D61—41no—
259C4×C61—22no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61#44412yes—
266C4×C61C2×#11711yescharacteristic
267C4×C61#52011yescharacteristic
268C4×C61#54611yescharacteristic
269C4×C61#54811yescharacteristic
270Dic61—41no—
271Dic61—41no—
272Dic61—41no—
273Dic61—82no—
274C4×#135—611no—
275#2925—611no—
276#2906D6111yescharacteristic, complemented
277#1938—612no—
278#1922—612no—
279#1876—612no—
280#1837—611no—
281#1806—611no—
282#1806—611no—
283#1770—611no—
284#1765—612no—
285C2×C61—21no—
286C2×C61—21no—
287C2×C61—42no—
288C2×C61#235211yescharacteristic
289C2×C61C2×#44411yescharacteristic
290C2×C61#295711yescharacteristic
291D61—81no—
292C2×#135—611no—
293C2×#131C2×D6112yes—
294C4×#41—611no—
295C4×#41C2×D6111yescharacteristic
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—22no—
309#424C2×D6112yes—
310#423—21no—
311#423—611no—
312#423C2×D6111yescharacteristic
313C2×C4⋊C8—21no—
314C2×C4⋊C8C2×D6111yescharacteristic
315C2×#104—612no—
316C2×#104—612no—
317#416—611no—
318#416—611no—
319#408—612no—
320#405—612no—
321C2×#97—612no—
322C2×C4×C8—611no—
323C4×C4⋊C4—611no—
324#341—612no—
325#341—612no—
326#339—612no—
327#339—612no—
328#336—612no—
329C61#2278211yescharacteristic, complemented, Sylow
330C2×#41—611no—
331C2×#41C22×D6111yescharacteristic
332#135—1222no—
333#135—1222no—
334C2×Q16—611no—
335C2×SD16—611no—
336C2×SD16—611no—
337C2×D8—611no—
338#131—24no—
339#131—42no—
340C2×M16—22no—
341C2×M16—612no—
342C2×M16C22×D6112yes—
343C22×C8—22no—
344C22×C8—611no—
345C22×C8—611no—
346C22×C8C22×D6112yes—
347C4×Q8—611no—
348C4×Q8—611no—
349C4×Q8C4×D6111yescharacteristic
350C4×Q8C4×D6111yescharacteristic
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—611no—
354C4×D4—611no—
355C4×D4—1221no—
356C4×D4—1221no—
357C4×D4C4×D6111yescharacteristic
358C4×D4C4×D6111yescharacteristic
359#117—21no—
360#117—611no—
361#117—1221no—
362#117C22×D6111yescharacteristic
363C2×C4⋊C4—1221no—
364C2×C42—21no—
365C2×C42—612no—
366C2×C42—1221no—
367C2×C42C22×D6111yescharacteristic
368#107—611no—
369#107—611no—
370#106—611no—
371#106—611no—
372C4⋊C8—22no—
373C4⋊C8—22no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—1221no—
377C4⋊C8—1221no—
378C4⋊C8C22⋊D6111yescharacteristic
379C4⋊C8C22⋊D6111yescharacteristic
380C4⋊C8C22⋊D6112yes—
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—1222no—
394#97—2442no—
395C4×C8—611no—
396C4×C8—611no—
397C4×C8—611no—
398C4×C8—611no—
399C4×C8—1222no—
400#95—1221no—
401#41—21no—
402#41—21no—
403#41—1221no—
404#41—1221no—
405#41—1221no—
406#41—1221no—
407#41#1175822412yes—
408#41#1175822612yes—
409C2×Q8—611no—
410C2×Q8C2×C4×D6111yescharacteristic
411C2×D4—21no—
412C2×D4—611no—
413C2×D4—1221no—
414C2×D4C2×C4×D6111yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—1221no—
419C22×C4—1221no—
420C22×C4—1221no—
421C22×C4—1222no—
422C22×C4#1175822211yescharacteristic
423C22×C4#1175822211yescharacteristic
424C22×C4C23×D6111yescharacteristic
425Q16—1222no—
426SD16—1222no—
427SD16—1222no—
428D8—1222no—
429M16—22no—
430M16—22no—
431M16—44no—
432M16—1222no—
433M16—1222no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—44no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—1222no—
447C2×C8C2×C22⋊D6112yes—
448C2×C8C2×C22⋊D6112yes—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—611no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—2442no—
456C4⋊C4C2×C4×D6111yescharacteristic
457C4⋊C4C2×C4×D6111yescharacteristic
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—1221no—
462C22⋊C4—1221no—
463C22⋊C4—1221no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—1221no—
468C42—1221no—
469C42—1221no—
470C42—1222no—
471C42—1222no—
472C42C2×C4×D6111yescharacteristic
473C42C2×C4×D6111yescharacteristic
474C42C2×C22⋊D6111yescharacteristic
475C42C2×C22⋊D6111yescharacteristic
476C23—21no—
477C23—1221no—
478C23C2×#1175822211yescharacteristic
479Q8—21no—
480Q8—1221no—
481Q8—1221no—
482Q8#1451973512yes—
483D4—22no—
484D4—22no—
485D4—21no—
486D4—1221no—
487D4—1221no—
488D4—2441no—
489D4—2441no—
490D4#1451973512yes—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—81no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—4881no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4C4×C22⋊D6111yescharacteristic
511C2×C4C4×C22⋊D6111yescharacteristic
512C2×C4C4×C22⋊D6111yescharacteristic
513C2×C4C4×C22⋊D6111yescharacteristic
514C2×C4C22×C4×D6111yescharacteristic
515C2×C4C22×C22⋊D6111yescharacteristic
516C2×C4C2×#1175822411yescharacteristic
517C2×C4C2×#1175822611yescharacteristic
518C2×C4#1451982211yescharacteristic
519C2×C4#1451982511yescharacteristic
520C8—22no—
521C8—22no—
522C8—42no—
523C8—1221no—
524C8—1221no—
525C8—1221no—
526C8—1221no—
527C8—2442no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—2441no—
534C22—2441no—
535C22—2441no—
536C22C2×C4×C22⋊D6111yescharacteristic
537C22#1684044711yescharacteristic
538C22#1684046011yescharacteristic
539C4—22no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—4882no—
546C4—2441no—
547C4—2441no—
548C4—2441no—
549C4#1683988212yes—
550C4C2×#1451973511yescharacteristic
551C4#1684024311yescharacteristic
552C4#1684040611yescharacteristic
553C4#1684042311yescharacteristic
554C2—21no—
555C2—21no—
556C2—42no—
557C2—4881no—
558C2#2144874411yescharacteristic
559C2C2×#1683988211yescharacteristic
560C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2906C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#2906D61
hypocenterC61#22782
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #21454484C2semidirect
3. #21446529C2semidirect
4. #21446415C2semidirect
6. #21445956C2semidirect
7. #21445839C2semidirect
8. #21445836C2semidirect
9. #21445689C2semidirect
10. #21445661C2semidirect
11. C61×#2906C2semidirect
14. C4×#11758202C4semidirect
15. C4×#11758202C4semidirect
16. C4×#11758201C4semidirect
17. C4×#11758201C4semidirect
18. C4×#11758200C4semidirect
19. C4×#11758200C4semidirect
20. C4×#11758199C4semidirect
21. C4×#11758199C4semidirect
276. #2906D61semidirect
329. C61#22782semidirect

Maximal subgroups

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

subgroupindex
C4×#145197972
#214544842
#214465292
#214464152
#214461462
#214459562
#214458392
#214458362
#214456892
#214456612
C61×#29062
#2278261