Finite Group Databasebeta

← #29836886

Subgroups — #29836886

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458164C211yesmaximal, characteristic
2#21457568C211yesmaximal, characteristic, complemented
3#21448045C211yesmaximal, characteristic, complemented
4#21448018C211yesmaximal, characteristic, complemented
5#21447960C211yesmaximal, characteristic, complemented
6#21447917C211yesmaximal, characteristic, complemented
7#21447916C211yesmaximal, characteristic, complemented
8#21447863C211yesmaximal, characteristic, complemented
9#21447738C211yesmaximal, characteristic, complemented
10#21447737C211yesmaximal, characteristic, complemented
11#21447670C211yesmaximal, characteristic, complemented
12#21447636C211yesmaximal, characteristic, complemented
13C2×#16839565C211yesmaximal, characteristic, complemented
14#358×D61C211yesmaximal, characteristic, complemented
15C61×#2235C211yesmaximal, characteristic, complemented
16C22×Dic244C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18#16840425—21no—
19#16840413—21no—
20C2×#14519722C2211yescharacteristic
21C2×#14519722C2211yescharacteristic
22C2×#14519720C2211yescharacteristic
23C22×#11758185C2211yescharacteristic
24C2×C16×D61C2211yescharacteristic
25#16840166C2211yescharacteristic
26#16840140C2211yescharacteristic
27#16840077—21no—
28#16840075—21no—
29#16840041—21no—
30#16840004C2211yescharacteristic
31#16839999C2211yescharacteristic
32#16839998C2211yescharacteristic
33#16839971—21no—
34#16839919—21no—
35#16839917—21no—
36#16839856C2211yescharacteristic
37#16839844C2211yescharacteristic
38C8×C22⋊D61C2211yescharacteristic
39#107×D61C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#367C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758222—41no—
60C22×Dic122—21no—
61C2×Q8×D61—21no—
62C2×Dic244—22no—
63C2×Dic244—21no—
64C2×Dic244—41no—
65C2×Dic244C2311yescharacteristic
66C2×Dic244C2311yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69Q16×D61—22no—
70Q16×D61—41no—
71C2×D488C2311yescharacteristic
72C2×C8×D61C2311yescharacteristic
73#14519776—21no—
74#14519776—41no—
75#14519775—21no—
76#14519762—41no—
77#14519760—41no—
78#14519757—21no—
79#14519755—41no—
80#14519755—41no—
81#14519754—41no—
82#14519752—21no—
83#14519751—21no—
84#14519742—21no—
85#14519739—21no—
86C4×C22⋊D61D411yescharacteristic
87#14519737—41no—
88C4⋊C4×D61—21no—
89#14519722—22no—
90#14519722—41no—
91#14519720—41no—
92C2×#11758185—41no—
93C2×#11758185C2311yescharacteristic
94C2×#11758185C2311yescharacteristic
95C16×D61—41no—
96#14519711C2311yescharacteristic
97#14519710—21no—
98#14519710—21no—
99#14519706D411yescharacteristic
100#14519700—21no—
101#14519700—21no—
102#14519699—21no—
103#14519697—21no—
104#14519697—21no—
105C22⋊#92418D411yescharacteristic
106#14519689D411yescharacteristic
107C8×Dic61C2311yescharacteristic
108C2×Q16×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22⋊Q8×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C16×C61C2311yescharacteristic
113C2×C16×C61C2311yescharacteristic
114#107×C61—21no—
115#107×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#103×C61—21no—
119C2×Q8×C61—21no—
120C22×C4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—41no—
123C2×C22⋊D61D811yescharacteristic
124C22×Dic61—41no—
125Q8×D61—42no—
126Q8×D61—81no—
127#11758222—84no—
128C2×D244—21no—
129C2×D244—41no—
130C2×C4×D61—41no—
131C2×C4×D61—41no—
132C2×C4×D61—41no—
133C2×C4×D61C2×D411yescharacteristic
134C2×Dic122—21no—
135C2×Dic122—21no—
136C2×Dic122—42no—
137C2×Dic122—41no—
138C2×Dic122—41no—
139C2×Dic122—41no—
140C2×Dic122—81no—
141Q16×C61—21no—
142Q16×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2411yescharacteristic
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—41no—
151C4⋊C4×C61—41no—
152C22⋊C4×C61—41no—
153C22⋊Dic61D811yescharacteristic
154#11758202—42no—
155#11758202—81no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198D811yescharacteristic
161C4⋊Dic61—21no—
162C4⋊Dic61—41no—
163#11758196—41no—
164#11758196—41no—
165#11758196—41no—
166#11758196—41no—
167#11758196—41no—
168#11758196D811yescharacteristic
169C4×Dic61—41no—
170C4×Dic61C2×D411yescharacteristic
171C2×#92418C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173Dic244—21no—
174Dic244—21no—
175Dic244—21no—
176Dic244—42no—
177Dic244#4112yescomplemented
178D488—21no—
179D488—21no—
180C8×D61—21no—
181C8×D61—21no—
182C16×C61—21no—
183C16×C61—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61C2×D811yescharacteristic
187C22×D61—41no—
188C22×D61C2×D811yescharacteristic
189Q8×C61—41no—
190Q8×C61—41no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—82no—
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C22⋊D61—82no—
201C22⋊D61SD3214yescomplemented
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—82no—
206C2×Dic61C2×D811yescharacteristic
207C2×Dic61C2×D811yescharacteristic
208C2×Dic61C2×D811yescharacteristic
209D244—41no—
210D244—41no—
211D244—82no—
212C4×D61—21no—
213C4×D61—21no—
214C4×D61—82no—
215C4×D61—82no—
216C4×D61—82no—
217Dic122—22no—
218Dic122—41no—
219Dic122—41no—
220Dic122—41no—
221Dic122—82no—
222Dic122—82no—
223Dic122—82no—
224C8×C61—21no—
225C8×C61C2×#4111yescharacteristic
226C8×C61H(5,𝔽2)11yescharacteristic
227#92418—21no—
228#92418—21no—
229#33865—611nomaximal, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61C2×SD3212yes—
233C22×C61C22×D811yescharacteristic
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—81no—
237C2×D61—81no—
238C2×D61—81no—
239C2×D61C2×SD3212yes—
240C4×C61—21no—
241C4×C61—81no—
242C4×C61—81no—
243C4×C61—81no—
244C4×C61—81no—
245C4×C61#54611yescharacteristic
246C4×C61#57711yescharacteristic
247Dic61—21no—
248Dic61—21no—
249Dic61—42no—
250Dic61—81no—
251Dic61—81no—
252Dic61C2×SD3212yes—
253#3334—611no—
254D4×Q16—611no—
255#2241—611no—
256#2235—611no—
257#2235D6111yescharacteristic, complemented
258#2225—611no—
259#2217—611no—
260#2217—611no—
261#2208—611no—
262#2185—611no—
263#2185—611no—
264C4×SD32—611no—
265D4×C16—611no—
266C2×#358—611no—
267C2×#358—611no—
268C2×C61—22no—
269C2×C61#329411yescharacteristic
270C2×C61C22×SD3211yescharacteristic
271C2×C61#341711yescharacteristic
272D61—22no—
273D61—161no—
274C22×Q16—611no—
275C22×Q16—611no—
276D4×Q8—1221no—
277#547—1221no—
278C2×SD32—611no—
279C2×SD32—611no—
280C2×SD32—611no—
281C22×C16—611no—
282C22×C16—611no—
283#500—611no—
284#494—611no—
285#480—1221no—
286#480—1221no—
287#474—1221no—
288#467—611no—
289#467C2×D6111yescharacteristic
290#466—611no—
291#466—611no—
292#462—1221no—
293#451—1221no—
294#451—1221no—
295C4×Q16—611no—
296C4×D8—611no—
297C8×D4—611no—
298C2×#107—611no—
299C2×#107C2×D6111yescharacteristic
300#367—611no—
301#367C2×D6111yescharacteristic
302#367C2×D6111yescharacteristic
303C4⋊C16—611no—
304#358—611no—
305#358—611no—
306#358—611no—
307#358—611no—
308#358—611no—
309#358—611no—
310#358—611no—
311#358C2×D6111yescharacteristic
312#358C2×D6111yescharacteristic
313#357—611no—
314C22⋊C16—611no—
315C22⋊C16C2×D6111yescharacteristic
316C4×C16—611no—
317C61#3386511yescharacteristic, complemented, Sylow
318C2×#41—2441no—
319C22×Q8—1221no—
320C22×Q8—1221no—
321C2×Q16—611no—
322C2×Q16—611no—
323C2×Q16—1222no—
324C2×Q16—1221no—
325C2×Q16—1221no—
326C2×Q16—1222no—
327C2×Q16—1221no—
328C2×Q16—2441no—
329C2×Q16—2441no—
330C2×Q16C22×D6111yescharacteristic
331C2×D8—611no—
332C22×C8—611no—
333C22×C8C22×D6111yescharacteristic
334C4⋊Q8—1221no—
335C4⋊Q8—1221no—
336C4⋊Q8—2441no—
337#123—2441no—
338#123—2441no—
339C22⋊Q8—21no—
340C22⋊Q8—1221no—
341C22⋊Q8—2441no—
342C22⋊Q8—2441no—
343C22⋊Q8—2441no—
344#121—1221no—
345#121—1221no—
346C4×Q8—1221no—
347C4×D4—611no—
348C4×D4—1221no—
349C4×D4—2441no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—1221no—
352SD32—1222no—
353SD32—2441no—
354SD32—2441no—
355C2×C16—611no—
356C2×C16—611no—
357C2×C16—2441no—
358C2×C16—2441no—
359C2×C16C22×D6111yescharacteristic
360C2×C16C22×D6111yescharacteristic
361#107—21no—
362#107—611no—
363#107—1221no—
364#107—1221no—
365#107C22×D6111yescharacteristic
366#107C22×D6111yescharacteristic
367#107C22×D6111yescharacteristic
368C4⋊C8—611no—
369#103—21no—
370#103—1221no—
371#103—1221no—
372#102—1221no—
373#102—1221no—
374#102—1221no—
375C22⋊C8—611no—
376C22⋊C8—611no—
377C4×C8—611no—
378#41—4884no—
379C2×Q8—21no—
380C2×Q8—1221no—
381C2×Q8—1221no—
382C2×Q8—4881no—
383C2×Q8—4881no—
384C2×Q8—2442no—
385C2×Q8—2441no—
386C2×Q8—2441no—
387C2×Q8—2442no—
388C2×Q8—2441no—
389C2×D4—611no—
390C2×D4—1221no—
391C2×D4—2441no—
392C2×D4—2441no—
393C22×C4—41no—
394C22×C4—611no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4D4×D6111yescharacteristic
400Q16—21no—
401Q16—21no—
402Q16—612no—
403Q16—1221no—
404Q16—1221no—
405Q16—1221no—
406Q16—4881no—
407Q16—2442no—
408Q16—2442no—
409D8—1221no—
410D8—1221no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—611no—
414C2×C8—611no—
415C2×C8—1221no—
416C2×C8—1221no—
417C2×C8D4×D6111yescharacteristic
418C2×C8C23×D6111yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—611no—
425C4⋊C4—1221no—
426C4⋊C4—2441no—
427C4⋊C4—2441no—
428C4⋊C4—2441no—
429C4⋊C4—2441no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C22⋊C4—41no—
433C22⋊C4—611no—
434C22⋊C4—611no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C42—611no—
440C42—2441no—
441C16—21no—
442C16—21no—
443C16—1221no—
444C16—1221no—
445C23—611no—
446C23—2441no—
447C23D8×D6111yescharacteristic
448Q8—41no—
449Q8—41no—
450Q8—1222no—
451Q8—4882no—
452Q8—4882no—
453Q8—4882no—
454Q8—2441no—
455Q8—2441no—
456Q8—2441no—
457D4—614no—
458D4—4882no—
459D4—4882no—
460D4—2441no—
461D4—2441no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—82no—
469C2×C4—611no—
470C2×C4—611no—
471C2×C4—611no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—4882no—
475C2×C4—4882no—
476C2×C4—4882no—
477C2×C4—4882no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4D8×D6111yescharacteristic
482C2×C4C2×D4×D6111yescharacteristic
483C8—21no—
484C8—1221no—
485C8—1221no—
486C8#41×D6111yescharacteristic
487C8#1451982311yescharacteristic
488C22—21no—
489C22—21no—
490C22—612no—
491C22—1221no—
492C22—1221no—
493C22—4881no—
494C22—4881no—
495C22—4881no—
496C22SD32×D6112yes—
497C22C2×D8×D6111yescharacteristic
498C4—21no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—612no—
504C4—1221no—
505C4—1221no—
506C4—4881no—
507C4—4881no—
508C4—2442no—
509C4#1684040411yescharacteristic
510C4#1684057111yescharacteristic
511C2—22no—
512C2—1222no—
513C2—9761no—
514C2#2145763011yescharacteristic
515C2C2×SD32×D6111yescharacteristic
516C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2235C2
socleC22×C61C22×D8
prime radical#21458164C2
hypercenter#2235D61
hypocenterC61#33865
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
2. #21457568C2semidirect
3. #21448045C2semidirect
4. #21448018C2semidirect
5. #21447960C2semidirect
6. #21447917C2semidirect
7. #21447916C2semidirect
8. #21447863C2semidirect
9. #21447738C2semidirect
10. #21447737C2semidirect
11. #21447670C2semidirect
12. #21447636C2semidirect
13. C2×#16839565C2semidirect
14. #358×D61C2semidirect
15. C61×#2235C2semidirect
177. Dic244#41semidirect
201. C22⋊D61SD32semidirect
257. #2235D61semidirect
317. C61#33865semidirect

Maximal subgroups

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

subgroupindex
#214581642
#214575682
#214480452
#214480182
#214479602
#214479172
#214479162
#214478632
#214477382
#214477372
#214476702
#214476362
C2×#168395652
#358×D612
C61×#22352
#3386561