Finite Group Databasebeta

← #29662492

Subgroups — #29662492

Order 15616.

620 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455884C212yesmaximal
2C8×#11758222C211yesmaximal, characteristic
3#21445246C212yesmaximal, complemented
4#21445239C212yesmaximal, complemented
5#21445210C211yesmaximal, characteristic, complemented
6#21445205C211yesmaximal, characteristic, complemented
7#21445186C211yesmaximal, characteristic, complemented
8#21445181C211yesmaximal, characteristic, complemented
9#21444567C211yesmaximal, characteristic, complemented
10#21444484C212yesmaximal, complemented
11C61×#3170C211yesmaximal, characteristic, complemented
12C4×#11758222C2211yescharacteristic
13#16840100—22no—
14#16840044C2212yes—
15#16840039C2212yes—
16#16839969C2212yes—
17#16839964C2212yes—
18#16839922—22no—
19C8×Dic122C2211yescharacteristic
20C8×Dic122C2211yescharacteristic
21C4×#11758202—22no—
22C4×#11758201—22no—
23C8×D244C2211yescharacteristic
24C8×D244C2211yescharacteristic
25C8×C22⋊D61—21no—
26C8×C22⋊D61—21no—
27#16839815C2212yes—
28#16839815C2211yescharacteristic
29#16839813—21no—
30C4×C8×D61—21no—
31#16839515C2211yescharacteristic
32#16839515C2211yescharacteristic
33#16839513C2212yes—
34#16839508C2212yes—
35#16839508C2212yes—
36#16839508C2212yes—
37#16839508C2212yes—
38C61×#533C2212yes—
39C61×#500C2211yescharacteristic
40C61×#494C2211yescharacteristic
41C61×#487C2212yes—
42C61×#467—21no—
43C61×#467—21no—
44C4×Q16×C61—21no—
45C4×Q16×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758222D411yescharacteristic
48C2×#11758202—22no—
49C2×#11758201—22no—
50C2×C8×D61—21no—
51C2×C8×D61—21no—
52C4×Dic122D411yescharacteristic
53C4×Dic122C2311yescharacteristic
54C4×D244D411yescharacteristic
55C4×D244C2311yescharacteristic
56C4×C22⋊D61—21no—
57C4×C22⋊D61—21no—
58#14519736D411yescharacteristic
59#14519734—21no—
60C42×D61—21no—
61#14519710—22no—
62#14519708—22no—
63C4⋊#92418C2312yes—
64C4⋊#92418C2312yes—
65C4⋊#92418C2311yescharacteristic
66C4⋊#92418C2311yescharacteristic
67#14519706—21no—
68#14519706—21no—
69#14519701—22no—
70#14519701—22no—
71#14519700—22no—
72#14519697—22no—
73C22⋊#92418—21no—
74C22⋊#92418—22no—
75#14519689—21no—
76#14519689—21no—
77C4×#92418—21no—
78C4×#92418—22no—
79C8×Dic61—21no—
80C8×Dic61—21no—
81C2×Q16×C61—21no—
82C2×Q16×C61—21no—
83C22×C8×C61D411yescharacteristic
84C22×C8×C61D411yescharacteristic
85C4⋊Q8×C61C2312yes—
86C4⋊Q8×C61C2312yes—
87#125×C61—22no—
88C22⋊Q8×C61—22no—
89C22⋊Q8×C61—22no—
90C4×Q8×C61—22no—
91C4×Q8×C61—22no—
92#117×C61—22no—
93C2×C42×C61C2311yescharacteristic
94#107×C61—21no—
95#107×C61—21no—
96#103×C61—22no—
97#103×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C2×C22⋊D61—21no—
108#11758222—22no—
109#11758222—22no—
110C2×D244C2×D411yescharacteristic
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×Dic122C2×D411yescharacteristic
115Q16×C61—42no—
116Q16×C61—42no—
117C2×C8×C61—22no—
118C2×C8×C61—41no—
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C4⋊C4×C61—22no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—42no—
128C4⋊C4×C61—42no—
129C22⋊C4×C61—42no—
130C42×C61—42no—
131C42×C61C2×D411yescharacteristic
132C42×C61C2×D411yescharacteristic
133C42×C61#4111yescharacteristic
134C42×C61C2411yescharacteristic
135C22⋊Dic61—21no—
136#11758202—44no—
137#11758201—44no—
138#11758198—21no—
139#11758198—21no—
140C4⋊Dic61C2×D411yescharacteristic
141C4⋊Dic61C2×D411yescharacteristic
142#11758196—21no—
143#11758196—21no—
144C4×Dic61—21no—
145C4×Dic61—21no—
146C4×Dic61—21no—
147C2×#92418—21no—
148C2×#92418—21no—
149C2×#92418—22no—
150C2×#92418—22no—
151C8×D61—42no—
152C8×D61—42no—
153C23×C61#12111yescharacteristic
154C22×D61—21no—
155Q8×C61—42no—
156Q8×C61—42no—
157Q8×C61—42no—
158Q8×C61—42no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—22no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61C22×D411yescharacteristic
170C2×C4×C61C22×D411yescharacteristic
171C2×C4×C61C2×#4111yescharacteristic
172C22⋊D61—24no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176D244—21no—
177D244#13512yes—
178C4×D61—24no—
179C4×D61—41no—
180C4×D61—41no—
181C4×D61—42no—
182Dic122—21no—
183Dic122#13512yes—
184C8×C61—21no—
185C8×C61—21no—
186C8×C61—21no—
187C8×C61#13512yes—
188#92418—41no—
189#92418—42no—
190#92418—42no—
191#92418—41no—
192#19129—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61C2×#12111yescharacteristic
197C2×D61—22no—
198C2×D61—41no—
199C2×D61—41no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—82no—
204C4×C61—82no—
205C4×C61#47312yes—
206C4×C61C2×#13511yescharacteristic
207C4×C61C2×#13511yescharacteristic
208C4×C61C2×#13511yescharacteristic
209C4×C61#57511yescharacteristic
210Dic61—22no—
211Dic61—41no—
212Dic61—41no—
213#3170D6111yescharacteristic, complemented
214#3107—612no—
215C8×#41—611no—
216#1680—612no—
217#1679—612no—
218#1674—611no—
219#1673—611no—
220#1670—611no—
221#1669—611no—
222#1564—611no—
223#1544—612no—
224C2×C61—41no—
225C2×C61#303511yescharacteristic
226C2×C61#305011yescharacteristic
227C2×C61C2×#47311yescharacteristic
228D61—42no—
229#533C2×D6112yes—
230C4×#41—611no—
231#500C2×D6111yescharacteristic
232#494C2×D6111yescharacteristic
233#487C2×D6112yes—
234#485—1222no—
235#475—612no—
236#474—612no—
237#467—21no—
238#467—21no—
239#462—612no—
240#461—612no—
241#452—1222no—
242C8×Q8—611no—
243C8×Q8—611no—
244C4×Q16—21no—
245C4×Q16—21no—
246C4×Q16—1222no—
247C4×SD16—1222no—
248C8×D4—611no—
249C8×D4—611no—
250C8×D4—1221no—
251C8×D4—1221no—
252#431—611no—
253#431—612no—
254#431—1221no—
255C2×C4×C8—1221no—
256C2×C4×C8C2×D6111yescharacteristic
257#335—611no—
258#335—611no—
259#334—612no—
260#332—612no—
261#332—612no—
262#332—612no—
263#332—612no—
264C61#1912911yescharacteristic, complemented, Sylow
265C2×#41—611no—
266C2×Q16—21no—
267C2×Q16—21no—
268C2×Q16—1222no—
269C2×SD16—1222no—
270C22×C8—1221no—
271C22×C8—1221no—
272C22×C8C22⋊D6111yescharacteristic
273C22×C8C22⋊D6111yescharacteristic
274C4⋊Q8C22×D6112yes—
275C4⋊Q8C22×D6112yes—
276#125—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C4×Q8—22no—
280C4×Q8—22no—
281C4×Q8—611no—
282C4×Q8—611no—
283C4×D4—611no—
284C4×D4—611no—
285C4×D4—1221no—
286C4×D4—1221no—
287#117—22no—
288#117—611no—
289#117—1221no—
290C2×C42—1221no—
291C2×C42C22×D6111yescharacteristic
292#107—21no—
293#107—21no—
294#107—1222no—
295#106—1222no—
296C4⋊C8—611no—
297C4⋊C8—611no—
298C4⋊C8—612no—
299C4⋊C8—612no—
300C4⋊C8—1221no—
301C4⋊C8—1221no—
302#103—22no—
303#103—22no—
304#103—1222no—
305#103—1222no—
306#103—1222no—
307#102—1222no—
308C22⋊C8—1222no—
309C22⋊C8—1221no—
310C22⋊C8—1221no—
311C22⋊C8—1221no—
312C4×C8—1221no—
313C4×C8—1221no—
314C4×C8—1222no—
315C4×C8—1221no—
316C4×C8C22⋊D6111yescharacteristic
317C4×C8C22⋊D6111yescharacteristic
318C4×C8C22×D6111yescharacteristic
319C4×C8C22×D6111yescharacteristic
320#41—1222no—
321#41—1222no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—611no—
325C2×D4—611no—
326C2×D4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4D4×D6111yescharacteristic
331C22×C4#1175822411yescharacteristic
332C22×C4C2×C22⋊D6111yescharacteristic
333Q16—42no—
334Q16—42no—
335Q16—2444no—
336SD16—2444no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—1222no—
340C2×C8—1222no—
341C2×C8—1221no—
342C2×C8—1221no—
343C2×C8—2442no—
344C2×C8—2442no—
345C2×C8C2×C22⋊D6111yescharacteristic
346C2×C8C2×C22⋊D6111yescharacteristic
347C2×C8C2×C22⋊D6111yescharacteristic
348C2×C8C2×C22⋊D6111yescharacteristic
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—611no—
356C4⋊C4—611no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C22⋊C4—42no—
360C22⋊C4—1221no—
361C22⋊C4—1221no—
362C22⋊C4—1221no—
363C42—42no—
364C42—1221no—
365C42—1221no—
366C42—1221no—
367C42D4×D6111yescharacteristic
368C42#1175822411yescharacteristic
369C42C2×C22⋊D6111yescharacteristic
370C42C23×D6111yescharacteristic
371C23—1221no—
372C23#1451974811yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—42no—
376Q8—42no—
377Q8—612no—
378Q8—1221no—
379D4—612no—
380D4—1224no—
381D4—1221no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—1224no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—2441no—
394C2×C4—2442no—
395C2×C4—2441no—
396C2×C4#1451974811yescharacteristic
397C2×C4#1451974811yescharacteristic
398C2×C4#1451974811yescharacteristic
399C2×C4C2×D4×D6111yescharacteristic
400C2×C4C22×C22⋊D6111yescharacteristic
401C2×C4C2×#1175822411yescharacteristic
402C8—21no—
403C8—21no—
404C8—21no—
405C8—2442no—
406C8—2442no—
407C8—2441no—
408C8—2441no—
409C8#1451979712yes—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—1222no—
414C22—2441no—
415C22—2441no—
416C22C2×#1451974811yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—82no—
421C4—82no—
422C4—1222no—
423C4—2441no—
424C4—2441no—
425C4#1684003412yes—
426C4#135×D6111yescharacteristic
427C4#135×D6111yescharacteristic
428C4C2×#1451979711yescharacteristic
429C4#1684056011yescharacteristic
430C2—41no—
431C2—2442no—
432C2#2145526811yescharacteristic
433C2#2145539611yescharacteristic
434C2C2×#1684003411yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3170C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#3170D61
hypocenterC61#19129
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #21445246C2semidirect
4. #21445239C2semidirect
5. #21445210C2semidirect
6. #21445205C2semidirect
7. #21445186C2semidirect
8. #21445181C2semidirect
9. #21444567C2semidirect
10. #21444484C2semidirect
11. C61×#3170C2semidirect
213. #3170D61semidirect
264. C61#19129semidirect

Maximal subgroups

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

subgroupindex
#214558842
C8×#117582222
#214452462
#214452392
#214452102
#214452052
#214451862
#214451812
#214445672
#214444842
C61×#31702
#1912961