Finite Group Databasebeta

← #29663339

Subgroups — #29663339

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#21457131C211yesmaximal, characteristic
2#21456144C211yesmaximal, characteristic
3#21454754C211yesmaximal, characteristic, complemented
4#21445375C212yesmaximal, complemented
5#21445361C212yesmaximal, complemented
6#21445279C212yesmaximal, complemented
7#21445265C212yesmaximal, complemented
8C2×#16839514C211yesmaximal, characteristic, complemented
9#21444509C211yesmaximal, characteristic, complemented
10#21444494C211yesmaximal, characteristic
11C61×#3249C211yesmaximal, characteristic, complemented
12#16840312C2211yescharacteristic
13#16840119—21no—
14#16840119—21no—
15#16840114C2211yescharacteristic
16#16840114C2211yescharacteristic
17#16840110C2211yescharacteristic
18#16840110C2211yescharacteristic
19#16840049—21no—
20#16840047C2212yes—
21#16839993—22no—
22#16839964—21no—
23#16839962C2212yes—
24#16839893—21no—
25#16839893C2212yes—
26Q8×#92418—21no—
27Q8×#92418C2212yes—
28#16839789—21no—
29#16839786C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31#16839756—21no—
32#16839756—21no—
33#16839718—21no—
34C2×C4×#92418C2211yescharacteristic
35#16839514C2212yes—
36#16839514C2212yes—
37#16839511C2212yes—
38#16839508C2212yes—
39#16839507C2212yes—
40#16839505C2212yes—
41C61×#533C2211yescharacteristic
42C61×#533C2211yescharacteristic
43C61×#477—21no—
44C61×#477C2212yes—
45C61×#467—22no—
46C61×#462—21no—
47C61×#462C2212yes—
48C2×C4⋊C8×C61C2211yescharacteristic
49C2×#11758222—21no—
50C2×#11758201—22no—
51C2×#11758194—21no—
52C22×#92418—21no—
53C22×#92418D411yescharacteristic
54C22×#92418D411yescharacteristic
55#14519777C2311yescharacteristic
56#14519774C2311yescharacteristic
57#14519765—21no—
58#14519751—21no—
59#14519751—21no—
60C4×D244—21no—
61C4×D244—21no—
62#14519708—22no—
63C4⋊#92418—21no—
64C4⋊#92418—21no—
65C4⋊#92418—22no—
66C4⋊#92418—22no—
67C4⋊#92418C2312yes—
68C4⋊#92418C2312yes—
69#14519701—22no—
70#14519700—21no—
71#14519700—21no—
72#14519700—21no—
73#14519700—21no—
74#14519697—22no—
75#14519697—21no—
76#14519697—21no—
77#14519697—21no—
78#14519697—21no—
79#14519688—22no—
80C4×#92418—22no—
81C4×#92418D411yescharacteristic
82C4×#92418D411yescharacteristic
83C4×#92418C2311yescharacteristic
84C4×#92418C2311yescharacteristic
85C2×Q16×C61—22no—
86C22×C8×C61—21no—
87C4⋊Q8×C61D411yescharacteristic
88C4⋊Q8×C61D411yescharacteristic
89C4⋊Q8×C61C2311yescharacteristic
90C4⋊Q8×C61C2311yescharacteristic
91#125×C61—21no—
92#125×C61—21no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61—21no—
95C22⋊Q8×C61—21no—
96C22⋊Q8×C61D412yes—
97C4×Q8×C61—21no—
98C4×Q8×C61—21no—
99C4×Q8×C61—21no—
100C4×Q8×C61C2312yes—
101#117×C61—21no—
102#117×C61—21no—
103C2×C42×C61C2311yescharacteristic
104#107×C61—22no—
105C4⋊C8×C61—21no—
106C4⋊C8×C61C2312yes—
107#103×C61—22no—
108#103×C61—22no—
109C2×Q8×C61—21no—
110C2×Q8×C61—21no—
111C2×Q8×C61—21no—
112C2×Q8×C61C2×D412yes—
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C2×C22⋊D61—41no—
117#11758222—42no—
118#11758222—42no—
119C2×D244—21no—
120C2×D244—21no—
121C2×D244—21no—
122C2×C4×D61—41no—
123C2×Dic122—21no—
124Q16×C61—82no—
125C2×C8×C61—22no—
126C2×C8×C61—81no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61C2×D412yes—
139C22⋊C4×C61—22no—
140C22⋊C4×C61—41no—
141C42×C61—22no—
142C42×C61—41no—
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61#4111yescharacteristic
146C42×C61C2411yescharacteristic
147#11758201—82no—
148#11758198—41no—
149#11758198—41no—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152#11758194—42no—
153C2×#92418—22no—
154C2×#92418—22no—
155C2×#92418—22no—
156C2×#92418—22no—
157C2×#92418—81no—
158C2×#92418C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162C23×C61#12111yescharacteristic
163C22×D61—41no—
164Q8×C61—22no—
165Q8×C61—22no—
166Q8×C61—42no—
167Q8×C61—41no—
168Q8×C61—41no—
169Q8×C61—81no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#13512yes—
181C2×C4×C61#13712yes—
182C2×C4×C61C22×D411yescharacteristic
183C2×C4×C61C22×D411yescharacteristic
184C2×C4×C61C2×#4111yescharacteristic
185C22⋊D61—82no—
186C2×Dic61—41no—
187D244—41no—
188D244—41no—
189D244—41no—
190D244—41no—
191D244—81no—
192C4×D61—82no—
193Dic122—41no—
194Dic122—41no—
195C8×C61—42no—
196#92418—21no—
197#92418—21no—
198#92418—21no—
199#92418—21no—
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—81no—
216C4×C61—81no—
217C4×C61#46412yes—
218C4×C61C2×#13511yescharacteristic
219C4×C61C2×#13711yescharacteristic
220C4×C61#57611yescharacteristic
221C4×C61#57811yescharacteristic
222Dic61—81no—
223#3249D6111yescharacteristic, complemented
224#3246—611no—
225#3131—611no—
226#2960—611no—
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#533C2×D6111yescharacteristic
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—21no—
249#477C2×D6112yes—
250#476—1221no—
251#475—612no—
252#467—22no—
253#465—1222no—
254#462—21no—
255#462C2×D6112yes—
256#461—1221no—
257#460—612no—
258#446—612no—
259#446—1221no—
260C8×Q8—612no—
261C8×Q8—1221no—
262#424—1221no—
263#423—611no—
264C2×C4⋊C8—611no—
265C2×C4⋊C8C2×D6111yescharacteristic
266#416—1221no—
267#416—1221no—
268#405—1221no—
269C2×C4×C8—611no—
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—22no—
279C2×SD16—1222no—
280C2×M16—1221no—
281C22×C8—21no—
282C22×C8—611no—
283C22×C8—611no—
284C22×C8—1221no—
285C4⋊Q8—611no—
286C4⋊Q8C22⋊D6111yescharacteristic
287C4⋊Q8C22⋊D6111yescharacteristic
288C4⋊Q8C22×D6111yescharacteristic
289C4⋊Q8C22×D6111yescharacteristic
290#127—611no—
291#125—21no—
292#125—21no—
293#124—1221no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8C22⋊D6112yes—
298#121—1221no—
299#121—1221no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8C22×D6112yes—
304C4×D4—1221no—
305C4×D4—1221no—
306#117—21no—
307#117—21no—
308C2×C42C22×D6111yescharacteristic
309#107—22no—
310#106—1222no—
311C4⋊C8—21no—
312C4⋊C8—612no—
313C4⋊C8—612no—
314C4⋊C8—1222no—
315C4⋊C8—1222no—
316C4⋊C8—1221no—
317C4⋊C8—1221no—
318C4⋊C8C22×D6112yes—
319#103—22no—
320#103—22no—
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—1222no—
332C4×C8—611no—
333C4×C8—611no—
334C4×C8—611no—
335C4×C8—611no—
336C4×C8—1222no—
337#41—2442no—
338#41—2442no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—1221no—
343C2×Q8C2×C22⋊D6112yes—
344C2×D4—1221no—
345C2×D4—1221no—
346C2×D4—1221no—
347C2×D4—2441no—
348C22×C4—2441no—
349C22×C4D4×D6111yescharacteristic
350C22×C4#1175822411yescharacteristic
351C22×C4C2×C22⋊D6111yescharacteristic
352Q16—82no—
353SD16—4882no—
354M16—2442no—
355C2×C8—22no—
356C2×C8—81no—
357C2×C8—611no—
358C2×C8—611no—
359C2×C8—611no—
360C2×C8—611no—
361C2×C8—1222no—
362C2×C8—1222no—
363C2×C8—1222no—
364C2×C8—1222no—
365C2×C8—4881no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4C2×C22⋊D6112yes—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C42—22no—
385C42—41no—
386C42D4×D6111yescharacteristic
387C42#1175822411yescharacteristic
388C42C2×C22⋊D6111yescharacteristic
389C42C23×D6111yescharacteristic
390C23—2441no—
391C23#1451974911yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395Q8—41no—
396Q8—41no—
397Q8—81no—
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—41no—
412C2×C4—41no—
413C2×C4—4882no—
414C2×C4—2441no—
415C2×C4#1451974911yescharacteristic
416C2×C4#1451974911yescharacteristic
417C2×C4#1451974911yescharacteristic
418C2×C4#1451980012yes—
419C2×C4#1451980912yes—
420C2×C4C2×D4×D6111yescharacteristic
421C2×C4C22×C22⋊D6111yescharacteristic
422C2×C4C2×#1175822411yescharacteristic
423C8—42no—
424C8—1221no—
425C8—1221no—
426C8—1221no—
427C8—1221no—
428C8—2442no—
429C8—2442no—
430C22—21no—
431C22—21no—
432C22—4881no—
433C22—4881no—
434C22—4881no—
435C22#1683998612yes—
436C22C2×#1451974911yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—81no—
444C4—4881no—
445C4#1683998612yes—
446C4C2×#1451980011yescharacteristic
447C4C2×#1451980911yescharacteristic
448C4#1684056511yescharacteristic
449C4#1684057711yescharacteristic
450C2—22no—
451C2—9761no—
452C2C2×#1683998611yescharacteristic
453C2#2145548611yescharacteristic
454C2#2145553611yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3249C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#3249D61
hypocenterC61#19217
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
3. #21454754C2semidirect
4. #21445375C2semidirect
5. #21445361C2semidirect
6. #21445279C2semidirect
7. #21445265C2semidirect
8. C2×#16839514C2semidirect
9. #21444509C2semidirect
11. C61×#3249C2semidirect
223. #3249D61semidirect
276. C61#19217semidirect

Maximal subgroups

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

subgroupindex
#214571312
#214561442
#214547542
#214453752
#214453612
#214452792
#214452652
C2×#168395142
#214445092
#214444942
C61×#32492
#1921761