Finite Group Databasebeta

← #30601979

Subgroups — #30601979

Order 15616.

392 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461381C211yesmaximal, characteristic, complemented
2#21461283C211yesmaximal, characteristic, complemented
3#21461280C211yesmaximal, characteristic
4#21461093C211yesmaximal, characteristic, complemented
5#21461090C211yesmaximal, characteristic
6C8×#11758217C211yesmaximal, characteristic, complemented
7C2×#16840118C211yesmaximal, characteristic
8#16840783C2211yescharacteristic
9#16840783C2211yescharacteristic
10#16840779C2211yescharacteristic
11C4×#11758217C2211yescharacteristic
12#16840625—21no—
13#16840624—21no—
14#16840619—22no—
15#16840618—22no—
16#16840608—22no—
17#16840606—22no—
18#92420⋊C8—21no—
19C8×#92420—21no—
20C2×#14519768C2211yescharacteristic
21C2×#14519766C2211yescharacteristic
22#16840118—21no—
23#16840118—21no—
24#16840118—21no—
25#16840118—21no—
26C2×#14519701C411yescharacteristic
27C2×#14519699C411yescharacteristic
28C2×#14519697C411yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30C2×#103×C61C411yescharacteristic
31C2×#11758217—21no—
32#14519844—21no—
33C4⋊#92420—21no—
34C4⋊#92420—21no—
35C22⋊#92420—21no—
36C22⋊#92420—21no—
37C22⋊#92420D412yes—
38#14519832—21no—
39#14519832—21no—
40#14519832D412yes—
41C4×#92420—21no—
42C4×#92420—21no—
43C22×D244C2×C411yescharacteristic
44C22×#92418C2×C411yescharacteristic
45#14519768—21no—
46#14519768—21no—
47#14519768—21no—
48#14519768—21no—
49#14519766—21no—
50#14519766—21no—
51#14519766—21no—
52#14519766—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×#11758196—21no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×C4×Dic61C2311yescharacteristic
59#14519701—21no—
60#14519701—21no—
61#14519699—21no—
62#14519699—21no—
63#14519697—21no—
64#14519697—21no—
65C8×Dic61D411yescharacteristic
66C8×Dic61D411yescharacteristic
67C8×Dic61D411yescharacteristic
68C8×Dic61D411yescharacteristic
69C22×Q8×C61C2×C411yescharacteristic
70C22×C8×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72#103×C61—21no—
73#103×C61—21no—
74C23×D61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61C22×C411yescharacteristic
82C22×Dic61—21no—
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61#4111yescharacteristic
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—41no—
88C2×D244—41no—
89#11758217—24no—
90C2×#92420—22no—
91C2×#92420—22no—
92C2×#92420—41no—
93C2×#92420—41no—
94C2×C8×C61—41no—
95C2×C8×C61C22⋊C411yescharacteristic
96C2×C8×C61C22⋊C411yescharacteristic
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99#11758198—41no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107#11758196—41no—
108#11758196—41no—
109C4×Dic61C2×D411yescharacteristic
110C4×Dic61C2×D411yescharacteristic
111C4×Dic61C2×D411yescharacteristic
112C4×Dic61#4111yescharacteristic
113C2×#92418—41no—
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C22⋊C411yescharacteristic
116C23×C61C4×D411yescharacteristic
117C22×D61—41no—
118C22×D61—42no—
119C22×D61—81no—
120C22×D61—81no—
121Q8×C61—41no—
122Q8×C61—41no—
123Q8×C61—81no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×Dic61—22no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—42no—
136C2×Dic61#12111yescharacteristic
137C2×Dic61#12111yescharacteristic
138C2×Dic61#12411yescharacteristic
139C2×Dic61#12711yescharacteristic
140D244—41no—
141D244—41no—
142D244—81no—
143#92420—24no—
144#92420—42no—
145#92420—81no—
146#92420—81no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151#9789—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61#39011yescharacteristic
155C22×C61#44312yes—
156C2×D61—81no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—162no—
160C4×C61—21no—
161C4×C61—81no—
162C4×C61—81no—
163C4×C61#41311yescharacteristic
164C4×C61#41311yescharacteristic
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—81no—
170C2×#488—611no—
171#1568—611no—
172#1528—611no—
173#1527—611no—
174#1470—611no—
175#1469—611no—
176C8×M16—611no—
177C2×C61—22no—
178C2×C61#196711yescharacteristic
179C2×C61#197411yescharacteristic
180C2×C61#197611yescharacteristic
181D61—161no—
182C2×#125—611no—
183C2×#124—611no—
184#488—1221no—
185#488—1221no—
186#488—1221no—
187#488—1221no—
188#432—611no—
189#432—611no—
190#431—611no—
191C2×#103—611no—
192C2×#103#692311yescharacteristic
193C2×#102—611no—
194C2×#102—611no—
195C4×M16—611no—
196C2×C4×C8—611no—
197#335—1221no—
198#334—1221no—
199#330—1222no—
200#329—1222no—
201#324—1222no—
202#323—1222no—
203#322—1221no—
204C82—1221no—
205C61#978911yescharacteristic, complemented, Sylow
206C22×Q8C2×#692311yescharacteristic
207C22×D4—611no—
208C2×M16—1221no—
209C22×C8—611no—
210C22×C8C2×#692311yescharacteristic
211#125—1221no—
212#125—1221no—
213#125—1221no—
214#125—1221no—
215#124—1221no—
216#124—1221no—
217#124—1221no—
218#124—1221no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C42—611no—
226C4⋊C8—1221no—
227C4⋊C8—1221no—
228C4⋊C8—1221no—
229#103—21no—
230#103—21no—
231#103—1221no—
232#103—1221no—
233#102—1221no—
234#102—1221no—
235#102—1221no—
236#102—1221no—
237C22⋊C8—612no—
238C22⋊C8—1221no—
239C22⋊C8—1221no—
240#97—612no—
241#97—1221no—
242#97—1221no—
243C4×C8—611no—
244C4×C8—611no—
245C4×C8—611no—
246C4×C8—611no—
247C4×C8—1221no—
248C4×C8—1221no—
249C24—1221no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—2441no—
257C2×D4—2441no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4C22×#692311yescharacteristic
264M16—1224no—
265C2×C8—41no—
266C2×C8—611no—
267C2×C8—611no—
268C2×C8—1222no—
269C2×C8—1222no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8—2441no—
273C2×C8C22⋊#692311yescharacteristic
274C2×C8C22⋊#692311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C42—611no—
288C42—611no—
289C42—611no—
290C42—611no—
291C23—4881no—
292C23—4881no—
293C23—2442no—
294C23—2441no—
295C23D4×#692311yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—81no—
299D4—4881no—
300D4—2441no—
301D4—2441no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—1222no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2442no—
316C2×C4C2×C22⋊#692311yescharacteristic
317C2×C4D4×#692311yescharacteristic
318C8—21no—
319C8—21no—
320C8—1224no—
321C8—1221no—
322C8—1221no—
323C8—4881no—
324C8—4881no—
325C8—2442no—
326C22—21no—
327C22—21no—
328C22—9762no—
329C22—4881no—
330C22—4881no—
331C22—4881no—
332C22#1684071411yescharacteristic
333C22#1684080612yes—
334C4—21no—
335C4—81no—
336C4—81no—
337C4—1221no—
338C4—1221no—
339C4—1221no—
340C4—1221no—
341C4—4881no—
342C4#1684074811yescharacteristic
343C4#1684074911yescharacteristic
344C2—22no—
345C2—9761no—
346C2#2146196311yescharacteristic
347C2#2146197011yescharacteristic
348C2#2146197711yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#103×C61C4
socleC22×C61#390
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×#103#6923
hypocenterC61#9789
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #21461381C2semidirect
2. #21461283C2semidirect
4. #21461093C2semidirect
6. C8×#11758217C2semidirect
205. C61#9789semidirect

Maximal subgroups

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

subgroupindex
#214613812
#214612832
#214612802
#214610932
#214610902
C8×#117582172
C2×#168401182
#978961