Finite Group Databasebeta

← #29663336

Subgroups — #29663336

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457161C211yesmaximal, characteristic, complemented
2#21457131C211yesmaximal, characteristic
3#21456142C211yesmaximal, characteristic
4#21445373C212yesmaximal, complemented
5#21445359C212yesmaximal, complemented
6#21445277C212yesmaximal, complemented
7#21445263C212yesmaximal, complemented
8C2×#16839515C211yesmaximal, characteristic, complemented
9#21444510C211yesmaximal, characteristic, complemented
10#21444497C211yesmaximal, characteristic
11C61×#2960C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13#16840312C2211yescharacteristic
14#16840117—21no—
15#16840117—21no—
16#16840113C2211yescharacteristic
17#16840113C2211yescharacteristic
18#16840109C2211yescharacteristic
19#16840109C2211yescharacteristic
20#16840057C2212yes—
21#16840054—21no—
22#16840049—21no—
23#16840047C2212yes—
24#16840001—22no—
25#16839993—22no—
26#16839972C2212yes—
27#16839969—21no—
28#16839964—21no—
29#16839962C2212yes—
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32#16839759—21no—
33#16839759—21no—
34#16839515C2212yes—
35#16839515C2212yes—
36#16839510C2212yes—
37#16839509C2212yes—
38#16839507C2212yes—
39#16839505C2212yes—
40C61×#533C2211yescharacteristic
41C61×#446—21no—
42C61×#446C2212yes—
43C8×Q8×C61—21no—
44C8×Q8×C61C2212yes—
45C61×#424—21no—
46C61×#423C2211yescharacteristic
47C61×#405—21no—
48C2×C4×C8×C61C2211yescharacteristic
49C2×#11758222—21no—
50C2×#11758202—22no—
51C2×#11758201—22no—
52C22×#92418—21no—
53C22×#92418—21no—
54#14519777C2311yescharacteristic
55#14519777C2311yescharacteristic
56#14519777C2311yescharacteristic
57#14519774C2311yescharacteristic
58#14519769—21no—
59#14519765—21no—
60#14519756—21no—
61#14519756—21no—
62#14519751—21no—
63#14519751—21no—
64C4×Dic122—21no—
65C4×Dic122—21no—
66C4×D244—21no—
67C4×D244—21no—
68#14519736—21no—
69#14519710—22no—
70#14519708—22no—
71C4⋊#92418—21no—
72C4⋊#92418—21no—
73C4⋊#92418C2312yes—
74C4⋊#92418C2312yes—
75#14519702—21no—
76#14519702—21no—
77#14519702—21no—
78#14519702—21no—
79#14519701—22no—
80#14519701—22no—
81#14519700—22no—
82#14519699—21no—
83#14519699—21no—
84#14519699—21no—
85#14519699—21no—
86#14519697—22no—
87C2×M16×C61—21no—
88C22×C8×C61D411yescharacteristic
89C22×C8×C61D411yescharacteristic
90C4⋊Q8×C61D411yescharacteristic
91C4⋊Q8×C61D411yescharacteristic
92#125×C61—21no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61D412yes—
95C4×Q8×C61—21no—
96C4×Q8×C61C2312yes—
97#117×C61—21no—
98C2×C42×C61C2311yescharacteristic
99C4⋊C8×C61—22no—
100C4⋊C8×C61—22no—
101C4⋊C8×C61—21no—
102C4⋊C8×C61C2312yes—
103#97×C61—22no—
104C4×C8×C61—22no—
105C4×C8×C61D411yescharacteristic
106C4×C8×C61D411yescharacteristic
107C4×C8×C61C2311yescharacteristic
108C4×C8×C61C2311yescharacteristic
109C2×Q8×C61—21no—
110C2×Q8×C61C2×D412yes—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—41no—
115#11758222—42no—
116#11758222—42no—
117C2×D244—21no—
118C2×D244—21no—
119C2×D244—21no—
120C2×C4×D61—41no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—21no—
124M16×C61—42no—
125C2×C8×C61—22no—
126C2×C8×C61—22no—
127C2×C8×C61—22no—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2×D411yescharacteristic
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61C2×D412yes—
138C22⋊C4×C61—22no—
139C42×C61—22no—
140C42×C61C2×D411yescharacteristic
141C42×C61C2×D411yescharacteristic
142C42×C61#4111yescharacteristic
143C42×C61C2411yescharacteristic
144C22⋊Dic61—41no—
145#11758202—82no—
146#11758201—82no—
147#11758198—41no—
148#11758198—41no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155#11758196—41no—
156#11758196—41no—
157C4×Dic61—41no—
158C2×#92418—22no—
159C2×#92418—22no—
160C2×#92418—81no—
161C2×#92418—81no—
162C23×C61#12111yescharacteristic
163C22×D61—41no—
164Q8×C61—22no—
165Q8×C61—22no—
166Q8×C61—42no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—22no—
170C2×C4×C61—22no—
171C2×C4×C61—41no—
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#13512yes—
176C2×C4×C61#13712yes—
177C2×C4×C61C22×D411yescharacteristic
178C2×C4×C61C22×D411yescharacteristic
179C2×C4×C61C2×#4111yescharacteristic
180C22⋊D61—82no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184D244—41no—
185D244—41no—
186D244—41no—
187D244—41no—
188D244—81no—
189C4×D61—82no—
190Dic122—41no—
191Dic122—41no—
192Dic122—41no—
193Dic122—41no—
194Dic122—81no—
195C8×C61—21no—
196C8×C61—21no—
197C8×C61—21no—
198C8×C61—21no—
199C8×C61—42no—
200#92418—42no—
201#92418—42no—
202#19217—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61#46412yes—
206C22×C61C2×#12111yescharacteristic
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—42no—
214C4×C61—42no—
215C4×C61#46412yes—
216C4×C61C2×#13511yescharacteristic
217C4×C61C2×#13711yescharacteristic
218C4×C61#57611yescharacteristic
219C4×C61#57811yescharacteristic
220Dic61—81no—
221Dic61—81no—
222Dic61—81no—
223#3249—611no—
224#3246—611no—
225#3131—611no—
226#2960D6111yescharacteristic, complemented
227#1700—612no—
228#1698—612no—
229#1684—612no—
230#1682—612no—
231C2×#335—611no—
232#1550—611no—
233#1547—611no—
234C2×C61—22no—
235C2×C61C2×#46411yescharacteristic
236C2×C61#306111yescharacteristic
237C2×C61#306711yescharacteristic
238D61—161no—
239#533—611no—
240#533C2×D6111yescharacteristic
241#532—611no—
242#488—1221no—
243#488—1221no—
244#487—611no—
245#487—611no—
246#486—611no—
247#486—611no—
248#477—612no—
249#477—1221no—
250#476—1221no—
251#475—612no—
252#467—1222no—
253#465—1222no—
254#462—612no—
255#462—1221no—
256#461—1221no—
257#460—612no—
258#446—21no—
259#446C2×D6112yes—
260C8×Q8—21no—
261C8×Q8C2×D6112yes—
262#424—21no—
263#423C2×D6111yescharacteristic
264C2×C4⋊C8—611no—
265C2×C4⋊C8—611no—
266#416—1221no—
267#416—1221no—
268#405—21no—
269C2×C4×C8C2×D6111yescharacteristic
270#335—612no—
271#335—612no—
272#333—612no—
273#332—612no—
274#332—612no—
275#331—612no—
276C61#1921711yescharacteristic, complemented, Sylow
277C2×#41—1221no—
278C2×Q16—1222no—
279C2×SD16—1222no—
280C2×M16—21no—
281C22×C8—1221no—
282C22×C8—1221no—
283C22×C8C22⋊D6111yescharacteristic
284C22×C8C22⋊D6111yescharacteristic
285C4⋊Q8—611no—
286C4⋊Q8—611no—
287C4⋊Q8—611no—
288C4⋊Q8D24411yescharacteristic
289C4⋊Q8D24411yescharacteristic
290#127—611no—
291#125—21no—
292#125—1221no—
293#124—1221no—
294C22⋊Q8—21no—
295C22⋊Q8—1221no—
296C22⋊Q8—1221no—
297C22⋊Q8D24412yes—
298#121—1221no—
299#121—1221no—
300C4×Q8—21no—
301C4×Q8—1221no—
302C4×Q8—1221no—
303C4×Q8C22×D6112yes—
304C4×D4—1221no—
305C4×D4—1221no—
306#117—21no—
307#117—1221no—
308C2×C42C22×D6111yescharacteristic
309#107—1222no—
310#106—1222no—
311C4⋊C8—22no—
312C4⋊C8—22no—
313C4⋊C8—21no—
314C4⋊C8—612no—
315C4⋊C8—612no—
316C4⋊C8—1221no—
317C4⋊C8—1221no—
318C4⋊C8C22×D6112yes—
319#103—1222no—
320#103—1222no—
321#103—1221no—
322#103—1221no—
323#103—1221no—
324#103—1221no—
325#103—1222no—
326#102—1221no—
327#102—1221no—
328#102—1221no—
329#102—1221no—
330#102—1222no—
331#97—22no—
332C4×C8—22no—
333C4×C8C22⋊D6111yescharacteristic
334C4×C8C22⋊D6111yescharacteristic
335C4×C8C22×D6111yescharacteristic
336C4×C8C22×D6111yescharacteristic
337#41—2442no—
338#41—2442no—
339C2×Q8—21no—
340C2×Q8—1221no—
341C2×Q8—1221no—
342C2×Q8—1221no—
343C2×Q8C2×D24412yes—
344C2×D4—1221no—
345C2×D4—1221no—
346C2×D4—1221no—
347C2×D4—2441no—
348C22×C4—2441no—
349C22×C4C2×D24411yescharacteristic
350C22×C4#1175822211yescharacteristic
351C22×C4C2×C22⋊D6111yescharacteristic
352Q16—4882no—
353SD16—4882no—
354M16—42no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—1222no—
359C2×C8—1222no—
360C2×C8—4881no—
361C2×C8—4881no—
362C2×C8C2×C22⋊D6111yescharacteristic
363C2×C8C2×C22⋊D6111yescharacteristic
364C2×C8C2×C22⋊D6111yescharacteristic
365C2×C8C2×C22⋊D6111yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4C2×D24412yes—
380C22⋊C4—22no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C42—22no—
385C42—2441no—
386C42C2×D24411yescharacteristic
387C42#1175822211yescharacteristic
388C42C2×C22⋊D6111yescharacteristic
389C42C23×D6111yescharacteristic
390C23—2441no—
391C23#1451975111yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395Q8—4881no—
396Q8—2441no—
397Q8—2441no—
398Q8—2441no—
399Q8—2441no—
400D4—4881no—
401D4—4882no—
402D4—2441no—
403D4—2441no—
404D4—2441no—
405D4—2441no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—4882no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4#1451975111yescharacteristic
416C2×C4#1451975111yescharacteristic
417C2×C4#1451975111yescharacteristic
418C2×C4#1451979712yes—
419C2×C4#1451980812yes—
420C2×C4C22×C22⋊D6111yescharacteristic
421C2×C4C22×D24411yescharacteristic
422C2×C4C2×#1175822211yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8—21no—
427C8—42no—
428C8—2442no—
429C8—2442no—
430C22—21no—
431C22—21no—
432C22—4881no—
433C22—4881no—
434C22—4881no—
435C22#1683998412yes—
436C22C2×#1451975111yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—42no—
442C4—4881no—
443C4—4881no—
444C4—4881no—
445C4#1683998412yes—
446C4C2×#1451979711yescharacteristic
447C4C2×#1451980811yescharacteristic
448C4#1684056711yescharacteristic
449C4#1684057911yescharacteristic
450C2—22no—
451C2—9761no—
452C2C2×#1683998411yescharacteristic
453C2#2145548911yescharacteristic
454C2#2145553911yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2960C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#2960D61
hypocenterC61#19217
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960

Complements

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

NH ≅ G/Ntype
1. #21457161C2semidirect
4. #21445373C2semidirect
5. #21445359C2semidirect
6. #21445277C2semidirect
7. #21445263C2semidirect
8. C2×#16839515C2semidirect
9. #21444510C2semidirect
11. C61×#2960C2semidirect
226. #2960D61semidirect
276. C61#19217semidirect

Maximal subgroups

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

subgroupindex
#214571612
#214571312
#214561422
#214453732
#214453592
#214452772
#214452632
C2×#168395152
#214445102
#214444972
C61×#29602
#1921761