Finite Group Databasebeta

← #30604883

Subgroups — #30604883

Order 15616.

434 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461572C211yesmaximal, characteristic, complemented
2#21461063C211yesmaximal, characteristic, complemented
3#21460817C212yesmaximal, complemented
4#21460801C212yesmaximal
5#21449107C211yesmaximal, characteristic
6#16840778—21no—
7C2×#14519838—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519742C2211yescharacteristic
13C2×D4×Dic61C411yescharacteristic
14#16839702C2211yescharacteristic
15#16839701C411yescharacteristic
16#16839690—21no—
17#16839676C2211yescharacteristic
18#16839674—21no—
19C22⋊C4×Dic61—21no—
20C22⋊C4×Dic61—21no—
21#16839607C411yescharacteristic
22C61×#394C411yescharacteristic
23C2×#11758217—22no—
24C4⋊#92420—41no—
25#14519838—24no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29C4×#92420—41no—
30C22×Dic122D411yescharacteristic
31C23×Dic61—21no—
32#14519742—41no—
33#14519742—41no—
34D4×Dic61—41no—
35D4×Dic61—41no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×#11758196C2311yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56#95×C61C2×C411yescharacteristic
57C24×C61—21no—
58C2×D4×C61—41no—
59C2×D4×C61—42no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—42no—
67C22×Dic61—42no—
68C22×Dic61—41no—
69C22×Dic61—41no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—41no—
77#11758217—24no—
78#11758217—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—42no—
83C22⋊C4×C61—42no—
84C22⋊Dic61—42no—
85C22⋊Dic61—42no—
86C22⋊Dic61—42no—
87C4⋊Dic61—41no—
88#11758196—41no—
89#11758196—41no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—42no—
97C23×C61—22no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105D4×C61—42no—
106D4×C61—42no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61#10412yes—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—22no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—82no—
132C2×Dic61—82no—
133C2×Dic61#9911yescharacteristic
134C2×Dic61#9911yescharacteristic
135C2×Dic61#13512yes—
136Dic122—44no—
137#92420—44no—
138#92420—82no—
139#11734—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—42no—
143C22×C61—42no—
144C22×C61—42no—
145C22×C61—81no—
146C22×C61—81no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61C2×#9911yescharacteristic
150C22×C61#41611yescharacteristic
151C22×C61C2×#10411yescharacteristic
152C4×C61—22no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—81no—
156Dic61—21no—
157Dic61—22no—
158Dic61—41no—
159Dic61—41no—
160Dic61—81no—
161Dic61—81no—
162Dic61#35512yes—
163#2398—611no—
164C4×#101—611no—
165#1461—611no—
166#1353—612no—
167#1345—612no—
168C2×C61—21no—
169C2×C61—21no—
170C2×C61—82no—
171C2×C61#150111yescharacteristic
172C2×C61#212011yescharacteristic
173C2×C61C2×#35511yescharacteristic
174C2×C4×Q8—611no—
175C2×C4×D4—611no—
176#431—1221no—
177C2×#101—1221no—
178C4×M16—1221no—
179#400—611no—
180#400—611no—
181#397—1221no—
182#394—611no—
183#394#692311yescharacteristic
184#393—1221no—
185C4×C22⋊C4—1221no—
186C4×C22⋊C4—1221no—
187#376—611no—
188#343—612no—
189#324—612no—
190#324—1221no—
191C61#1173411yescharacteristic, complemented, Sylow
192C22×Q8—611no—
193C22×D4C2×#692311yescharacteristic
194C23×C4—1221no—
195C2×M16—1222no—
196C4×Q8—2441no—
197C4×Q8—2441no—
198C4×D4—2441no—
199C4×D4—2441no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4C2×#692311yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—1221no—
207C2×C22⋊C4—1221no—
208C2×C22⋊C4—1221no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—1221no—
213C4⋊C8—2441no—
214#101—1224no—
215C22⋊C8—1222no—
216#97—2441no—
217C4×C8—2441no—
218C4×C8—2441no—
219#95—611no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95C2×#692311yescharacteristic
226C24—21no—
227C2×Q8—1222no—
228C2×Q8—1222no—
229C2×Q8—2441no—
230C2×D4—41no—
231C2×D4—42no—
232C22×C4—21no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—2441no—
240C22×C4—2441no—
241C22×C4—2442no—
242C22×C4—2442no—
243C22×C4C22⋊#692311yescharacteristic
244C22×C4C22⋊#692311yescharacteristic
245C22×C4C22×#692311yescharacteristic
246M16—1224no—
247M16—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C4⋊C4—41no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—2442no—
257C22⋊C4—2442no—
258C22⋊C4—2442no—
259C42—1221no—
260C42—1221no—
261C42—1221no—
262C42—1221no—
263C42—1221no—
264C42—1221no—
265C42—2442no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23C2×C22⋊#692311yescharacteristic
274Q8—2444no—
275D4—42no—
276D4—42no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—612no—
289C2×C4—1222no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—4882no—
297C2×C4—4882no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4#1451984112yes—
306C8—4882no—
307C8—2444no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22D61⋊#9911yescharacteristic
318C22#1684075211yescharacteristic
319C22C2×#1451984111yescharacteristic
320C4—22no—
321C4—41no—
322C4—41no—
323C4—81no—
324C4—612no—
325C4—1221no—
326C4—1222no—
327C4—4881no—
328C4—4881no—
329C4—2441no—
330C4—2441no—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#2146119511yescharacteristic
335C2#2146207111yescharacteristic
336C2D61⋊#35511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#394C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×#11758196C23
hypercenter#394#6923
hypocenterC61#11734
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #21461572C2semidirect
2. #21461063C2semidirect
3. #21460817C2semidirect
191. C61#11734semidirect

Maximal subgroups

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

subgroupindex
#214615722
#214610632
#214608172
#214608012
#214491072
#1173461