Finite Group Databasebeta

← #30598939

Subgroups — #30598939

Order 15616.

476 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 118 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#21461735C211yesmaximal, characteristic
2#21461735C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal
4#21460697C212yesmaximal
5C4×#14519776C211yesmaximal, characteristic
6C2×#14519844C2212yes—
7C2×#14519844C2212yes—
8#16840628—21no—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840621—24no—
13C2×#14519776C2211yescharacteristic
14C2×C4×Dic122—21no—
15#16839666—21no—
16#16839661C411yescharacteristic
17#16839659—21no—
18#16839658C411yescharacteristic
19#16839631C2211yescharacteristic
20C4×#11758196—21no—
21C4×C4⋊Dic61C411yescharacteristic
22C42×Dic61C2211yescharacteristic
23C4×C4⋊C4×C61C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30C22×Dic122—21no—
31#14519776—21no—
32#14519776—21no—
33#14519776D412yes—
34#14519776Q812yes—
35C4×Dic122—44no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×Dic122—22no—
70C2×Dic122—22no—
71C2×Dic122—42no—
72C2×Dic122—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61C4⋊C412yes—
82C42×C61—22no—
83C42×C61—42no—
84C4⋊Dic61—21no—
85C4⋊Dic61—42no—
86C4⋊Dic61—41no—
87C4⋊Dic61C4⋊C412yes—
88#11758196—22no—
89#11758196—22no—
90#11758196—42no—
91#11758196—42no—
92#11758196—42no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61—42no—
99C4×Dic61C2×D411yescharacteristic
100C4×Dic61C2×Q811yescharacteristic
101C4×Dic61#4111yescharacteristic
102C4×Dic61#4111yescharacteristic
103C23×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61#10112yes—
118C2×C4×C61C2×C4⋊C411yescharacteristic
119C2×C4×C61#11711yescharacteristic
120C2×Dic61—22no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61#12111yescharacteristic
133C2×Dic61#12111yescharacteristic
134C2×Dic61C22⋊Q811yescharacteristic
135C2×Dic61C22⋊Q811yescharacteristic
136C2×Dic61#13512yes—
137C2×Dic61#13512yes—
138C2×Dic61AGL(1,ℤ/8)12yes—
139C2×Dic61#13712yes—
140Dic122—44no—
141Dic122—44no—
142#92420—82no—
143#92420—82no—
144#8593—611nomaximal, Sylow
145C22×C61#38011yescharacteristic
146C22×C61C2×#10111yescharacteristic
147C22×C61#41311yescharacteristic
148C22×C61#41611yescharacteristic
149C22×C61#41611yescharacteristic
150C22×C61#41811yescharacteristic
151C22×C61#41911yescharacteristic
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—22no—
155C4×C61—41no—
156C4×C61—42no—
157C4×C61—81no—
158Dic61—42no—
159Dic61—41no—
160Dic61—41no—
161Dic61—81no—
162Dic61#46312yes—
163Dic61#46412yes—
164Dic61#47812yes—
165Dic61#47912yes—
166C4×C4⋊Q8—611no—
167#1831—611no—
168#1831—611no—
169C2×#332—612no—
170#1296—612no—
171C2×C61#154411yescharacteristic
172C2×C61#155311yescharacteristic
173C2×C61#155411yescharacteristic
174C2×C61#155611yescharacteristic
175C2×C61#180111yescharacteristic
176C2×C61#180411yescharacteristic
177C2×C61#180511yescharacteristic
178C2×C4⋊Q8—611no—
179C2×C4×Q8—1221no—
180C2×C4⋊C8—612no—
181C2×C4⋊C8—612no—
182#391—1221no—
183#389—611no—
184#389—611no—
185#389—1221no—
186#384—611no—
187C4×C4⋊C4—611no—
188C4×C4⋊C4—1221no—
189C4×C4⋊C4#692311yescharacteristic
190C43—611no—
191#336—1221no—
192#336—1221no—
193#336—1221no—
194#336—1221no—
195#332—1224no—
196C61#859311yescharacteristic, complemented, Sylow
197C22×Q8—1221no—
198C22×C8—1222no—
199C22×C8—1222no—
200C4⋊Q8—612no—
201C4⋊Q8—612no—
202C4⋊Q8—1221no—
203C4⋊Q8—1221no—
204C4×Q8—2444no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4C2×#692311yescharacteristic
213C2×C4⋊C4C2×#692311yescharacteristic
214C2×C42—21no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—1221no—
222C2×C42C2×#692311yescharacteristic
223C4⋊C8—1222no—
224C4⋊C8—1222no—
225C4⋊C8—1222no—
226C4⋊C8—1222no—
227#95—21no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231C2×Q8—1222no—
232C2×Q8—1222no—
233C2×Q8—2442no—
234C2×Q8—2442no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4C22⋊#692311yescharacteristic
244C22×C4C22⋊#692311yescharacteristic
245C22×C4C22×#692311yescharacteristic
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C2×C8—2442no—
251C2×C8—2442no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—612no—
255C4⋊C4—1222no—
256C4⋊C4—1222no—
257C4⋊C4—1221no—
258C4⋊C4—2441no—
259C4⋊C4—2442no—
260C4⋊C4—2442no—
261C4⋊C4—2442no—
262C4⋊C4—2442no—
263C4⋊C4C4⋊#692312yes—
264C42—22no—
265C42—42no—
266C42—611no—
267C42—611no—
268C42—611no—
269C42—611no—
270C42—1222no—
271C42—1222no—
272C42—1222no—
273C42—1222no—
274C42—2441no—
275C42—2442no—
276C23C2×C22⋊#692311yescharacteristic
277Q8—2444no—
278Q8—2444no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—611no—
296C2×C4—612no—
297C2×C4—612no—
298C2×C4—612no—
299C2×C4—612no—
300C2×C4—1222no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4#1451983812yes—
313C2×C4C2×C4⋊#692311yescharacteristic
314C2×C4#1451985611yescharacteristic
315C8—4882no—
316C8—4882no—
317C22#1684070411yescharacteristic
318C22C2×#1451983811yescharacteristic
319C22#1684074811yescharacteristic
320C22#1684075211yescharacteristic
321C22#1684075211yescharacteristic
322C22#1684075411yescharacteristic
323C22#1684075511yescharacteristic
324C4—22no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—42no—
329C4—81no—
330C4—612no—
331C4—612no—
332C4—612no—
333C4—612no—
334C4—4881no—
335C4—2441no—
336C4—2441no—
337C4—2442no—
338C2#2146132411yescharacteristic
339C2#2146134211yescharacteristic
340C2#2146134411yescharacteristic
341C2#2146134811yescharacteristic
342C2#2146168511yescharacteristic
343C2#2146168911yescharacteristic
344C2#2146169011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8593
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
196. C61#8593semidirect

Maximal subgroups

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

subgroupindex
#214617352
C2×#168406212
#214606972
C4×#145197762
#859361