Finite Group Databasebeta

← #30603968

Subgroups — #30603968

Order 15616.

392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 88 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#21462047C211yesmaximal, characteristic, complemented
2D61⋊(C22⋊C16)C211yesmaximal, characteristic, complemented
3#21460758C212yesmaximal, complemented
4#21460741C212yesmaximal, complemented
5#21454511C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×D61⋊C16—21no—
8#16840657—21no—
9#16840657—21no—
10C22⋊#11758187C2212yes—
11C22⋊#11758187C2212yes—
12C22×C8×D61C2211yescharacteristic
13#16840269C411yescharacteristic
14#16839831—21no—
15#16839831—21no—
16C8×C22⋊D61—21no—
17C8×C22⋊D61—21no—
18#16839790C2211yescharacteristic
19#16839729C2211yescharacteristic
20#16839725C411yescharacteristic
21#16839717C411yescharacteristic
22C2×#131×C61C411yescharacteristic
23#14519852—42no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C22×C4×D61C2×C411yescharacteristic
28C2×#11758194C2×C411yescharacteristic
29C22×#92418C2311yescharacteristic
30C2×C8×D61—42no—
31C2×C8×D61D411yescharacteristic
32C2×C8×D61D411yescharacteristic
33C2×C8×D61D411yescharacteristic
34C2×C8×D61D411yescharacteristic
35#14519758—21no—
36#14519753C811yescharacteristic
37#14519753C811yescharacteristic
38#14519748C811yescharacteristic
39#14519748C811yescharacteristic
40#14519745—21no—
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43#14519736C2×C411yescharacteristic
44#14519706—21no—
45#14519706—21no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519689—21no—
49#14519689—21no—
50#14519687—21no—
51C8×Dic61—21no—
52C2×#41×C61C2×C411yescharacteristic
53#131×C61—42no—
54C2×M16×C61—21no—
55C2×M16×C61C2×C411yescharacteristic
56C22×C8×C61—21no—
57C22×C8×C61C2×C411yescharacteristic
58C23×D61M1611yescharacteristic
59#41×C61—41no—
60#41×C61—41no—
61C2×Q8×C61C2×C811yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2×C811yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61M1611yescharacteristic
69C2×C4×D61—41no—
70C2×C4×D61—41no—
71C2×C4×D61C22⋊C411yescharacteristic
72C2×C4×D61C22⋊C411yescharacteristic
73C2×C4×D61C2×C811yescharacteristic
74C2×C4×D61C2×C811yescharacteristic
75M16×C61—42no—
76M16×C61—41no—
77C2×C8×C61—22no—
78C2×C8×C61—21no—
79C2×C8×C61—42no—
80C2×C8×C61C22⋊C411yescharacteristic
81C2×C8×C61C22⋊C411yescharacteristic
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85#11758198—21no—
86#11758198—21no—
87C4⋊Dic61C2×C811yescharacteristic
88C4⋊Dic61C2×C811yescharacteristic
89#11758196—21no—
90#11758196—21no—
91C4×Dic61—21no—
92#11758194—41no—
93C2×#92418—21no—
94C2×#92418—41no—
95C2×#92418C2×D411yescharacteristic
96C2×#92418C2×D411yescharacteristic
97C8×D61—22no—
98C8×D61—22no—
99C8×D61—41no—
100C8×D61—41no—
101#11758187—42no—
102#11758187—42no—
103C23×C61—21no—
104C23×C61C2×M1611yescharacteristic
105C22×D61—22no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61C22⋊C811yescharacteristic
109C22×D61C22⋊C811yescharacteristic
110Q8×C61—41no—
111D4×C61—41no—
112D4×C61—42no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61C2×C22⋊C411yescharacteristic
119C2×C4×C61C22×C811yescharacteristic
120C22⋊D61—42no—
121C22⋊D61—42no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—41no—
125C2×Dic61C22⋊C811yescharacteristic
126C2×Dic61C22⋊C811yescharacteristic
127C4×D61—21no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—41no—
132C4×D61—41no—
133C8×C61—21no—
134C8×C61—41no—
135C8×C61#9912yes—
136#92418—21no—
137#92418—21no—
138#92418—41no—
139#11470—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61C2×C22⋊C811yescharacteristic
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—44no—
153C2×D61#35012yes—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61C2×#9911yescharacteristic
157C4×C61#41311yescharacteristic
158Dic61—21no—
159Dic61—21no—
160Dic61—41no—
161Dic61—41no—
162#2929—611no—
163#2112—611no—
164C2×C22⋊C16—611no—
165#1323—612no—
166#1315—612no—
167C2×C61—41no—
168C2×C61—81no—
169C2×C61#145911yescharacteristic
170C2×C61C2×#35011yescharacteristic
171C2×C61#211711yescharacteristic
172D61—22no—
173D61—41no—
174C2×#131#692311yescharacteristic
175C23×C8—611no—
176#525—611no—
177C2×M32—1221no—
178C22×C16—1221no—
179#435—1221no—
180#435—1221no—
181C8×D4—1221no—
182C8×D4—1221no—
183#424—611no—
184#408—611no—
185#407—611no—
186#405—611no—
187C22⋊C16—612no—
188C22⋊C16—612no—
189C22⋊C16—1221no—
190C22⋊C16—1221no—
191C61#1147011yescharacteristic, complemented, Sylow
192C2×#41C2×#692311yescharacteristic
193C23×C4—611no—
194#131—42no—
195C2×M16—21no—
196C2×M16—611no—
197C2×M16C2×#692311yescharacteristic
198C22×C8—21no—
199C22×C8—611no—
200C22×C8—611no—
201C22×C8—611no—
202C22×C8—611no—
203C22×C8—611no—
204C22×C8—2442no—
205C22×C8C2×#692311yescharacteristic
206#123—1221no—
207C22⋊Q8—611no—
208C22⋊Q8—611no—
209#121—611no—
210#121—611no—
211#120—1221no—
212C4×D4—1221no—
213C4×D4—1221no—
214#117—611no—
215M32—2442no—
216C2×C16—1222no—
217C2×C16—1222no—
218C2×C16—2442no—
219C4⋊C8—1221no—
220C4⋊C8—1221no—
221C22⋊C8—1221no—
222C22⋊C8—1221no—
223C22⋊C8—1221no—
224C22⋊C8—1221no—
225#97—1221no—
226C4×C8—1221no—
227C24—611no—
228#41—41no—
229#41—41no—
230C2×Q8D61⋊C811yescharacteristic
231C2×D4—21no—
232C2×D4—1221no—
233C2×D4—1221no—
234C2×D4D61⋊C811yescharacteristic
235C22×C4—21no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—2441no—
242C22×C4—2441no—
243C22×C4C22×#692311yescharacteristic
244M16—42no—
245M16—41no—
246M16—2441no—
247C2×C8—22no—
248C2×C8—21no—
249C2×C8—42no—
250C2×C8—611no—
251C2×C8—611no—
252C2×C8—1222no—
253C2×C8—1222no—
254C2×C8—1221no—
255C2×C8—2441no—
256C2×C8—2441no—
257C2×C8—2441no—
258C2×C8C22⋊#692311yescharacteristic
259C2×C8C22⋊#692311yescharacteristic
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C42—1221no—
270C16—2442no—
271C16—2442no—
272C23—21no—
273C23—611no—
274C23—611no—
275C23—1222no—
276C23—2441no—
277C23—2441no—
278C23D61⋊M1611yescharacteristic
279Q8—41no—
280D4—41no—
281D4—42no—
282D4—2442no—
283D4—2442no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—611no—
290C2×C4—611no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4C2×C22⋊#692311yescharacteristic
301C2×C4C2×D61⋊C811yescharacteristic
302C8—21no—
303C8—41no—
304C8—1221no—
305C8—1221no—
306C8—2441no—
307C8#1451983512yes—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—612no—
315C22—1221no—
316C22—1221no—
317C22—1221no—
318C22—1221no—
319C22—1221no—
320C22—2444no—
321C22D61⋊(C22⋊C8)11yescharacteristic
322C4—21no—
323C4—41no—
324C4—1221no—
325C4—1221no—
326C4—2441no—
327C4—2441no—
328C4C2×#1451983511yescharacteristic
329C4#1684074811yescharacteristic
330C2—41no—
331C2—81no—
332C2—1222no—
333C2—2441no—
334C2#2146105411yescharacteristic
335C2D61⋊#35011yescharacteristic
336C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#131×C61C4
socleC22×C61C2×C22⋊C8
prime radical#16840269C4
cosocleC22×#92418C23
hypercenterC2×#131#6923
hypocenterC61#11470
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #21462047C2semidirect
2. D61⋊(C22⋊C16)C2semidirect
3. #21460758C2semidirect
4. #21460741C2semidirect
191. C61#11470semidirect

Maximal subgroups

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

subgroupindex
#214620472
D61⋊(C22⋊C16)2
#214607582
#214607412
#214545112
#1147061