Finite Group Databasebeta

← #30603869

Subgroups — #30603869

Order 15616.

392 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 94 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
2D61⋊(C22⋊C16)C211yesmaximal, characteristic
3#21460756C212yesmaximal, complemented
4#21460755C212yesmaximal, complemented
5C2×#16839787C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×D61⋊C16—21no—
8#16840657—21no—
9#16840657—21no—
10C22⋊#11758187C2212yes—
11C22⋊#11758187C2212yes—
12C22×#11758189C411yescharacteristic
13C22×C8×D61C2211yescharacteristic
14C2×#14519734C411yescharacteristic
15#16839787—21no—
16#16839787—21no—
17#16839787—21no—
18#16839787—21no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519706C411yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×C4⋊C8×C61C411yescharacteristic
23#14519852—42no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C22×C4×D61C2×C411yescharacteristic
28C2×#11758189—21no—
29C2×#11758189—21no—
30C2×#11758189—42no—
31C22×#92418C2×C411yescharacteristic
32C22×#92418C2311yescharacteristic
33C2×C8×D61—42no—
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38#14519734—21no—
39#14519734—21no—
40#14519734—21no—
41#14519734—21no—
42C2×#11758196C811yescharacteristic
43C2×#11758196C811yescharacteristic
44C2×#11758198C811yescharacteristic
45C2×#11758198C811yescharacteristic
46C2×C4×Dic61C2×C411yescharacteristic
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49#14519706—21no—
50#14519706—21no—
51#14519706—21no—
52#14519706—21no—
53C22×C8×C61C2×C411yescharacteristic
54C22×C8×C61C2×C411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C23×D61C2×C811yescharacteristic
59C22×C4×C61C2×C811yescharacteristic
60C22×C4×C61C2×C811yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61C2×C811yescharacteristic
63C22×Dic61C2×C811yescharacteristic
64C22×Dic61C2×C811yescharacteristic
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61C22⋊C411yescharacteristic
68C2×C4×D61C22⋊C411yescharacteristic
69C2×C4×D61M1611yescharacteristic
70C2×C4×D61M1611yescharacteristic
71C2×C8×C61—21no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61C22⋊C411yescharacteristic
75C2×C8×C61C22⋊C411yescharacteristic
76C42×C61—21no—
77C42×C61—21no—
78#11758198—21no—
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82#11758196—21no—
83#11758196—21no—
84#11758196—21no—
85#11758196—21no—
86C4×Dic61—21no—
87C4×Dic61—21no—
88C2×#92418—21no—
89C2×#92418—41no—
90C2×#92418—41no—
91C2×#92418C2×D411yescharacteristic
92C2×#92418C2×D411yescharacteristic
93#11758189—42no—
94#11758189—42no—
95C8×D61—22no—
96C8×D61—22no—
97C8×D61—41no—
98C8×D61—41no—
99#11758187—42no—
100#11758187—42no—
101C23×C61C22×C811yescharacteristic
102C22×D61—22no—
103C22×D61—22no—
104C22×D61—41no—
105C22×D61C22⋊C811yescharacteristic
106C22×D61C22⋊C811yescharacteristic
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—22no—
112C2×C4×C61—41no—
113C2×C4×C61C2×C22⋊C411yescharacteristic
114C2×C4×C61C2×M1611yescharacteristic
115C2×Dic61—22no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—22no—
119C2×Dic61—41no—
120C2×Dic61C22⋊C811yescharacteristic
121C2×Dic61C22⋊C811yescharacteristic
122C4×D61—22no—
123C4×D61—21no—
124C4×D61—21no—
125C4×D61—22no—
126C4×D61#9912yes—
127C4×D61#10112yes—
128C8×C61—21no—
129C8×C61—21no—
130C8×C61—41no—
131#92418—21no—
132#92418—21no—
133#92418—41no—
134#11441—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61C2×C22⋊C811yescharacteristic
138C22×C61#50412yes—
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—21no—
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—44no—
145C2×D61#32412yes—
146C4×C61—21no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61C2×#9911yescharacteristic
150C4×C61C2×#10111yescharacteristic
151Dic61—21no—
152Dic61—41no—
153Dic61—41no—
154Dic61#32412yes—
155C2×#424—611no—
156#2112—611no—
157C2×C22⋊C16—611no—
158#1322—612no—
159#1322—612no—
160C2×C61—22no—
161C2×C61C2×#32411yescharacteristic
162C2×C61#211311yescharacteristic
163C2×C61#211511yescharacteristic
164D61—22no—
165D61—41no—
166C22×M16—611no—
167C23×C8—611no—
168C2×#117—611no—
169C2×M32—1221no—
170C22×C16—1221no—
171#424—1221no—
172#424—1221no—
173#424—1221no—
174#424—1221no—
175C2×C4⋊C8—611no—
176C2×C4⋊C8—611no—
177C2×C4⋊C8—611no—
178C2×C4⋊C8#692311yescharacteristic
179C22⋊C16—612no—
180C22⋊C16—612no—
181C22⋊C16—1221no—
182C22⋊C16—1221no—
183C61#1144111yescharacteristic, complemented, Sylow
184C23×C4—611no—
185C2×M16—1221no—
186C2×M16—1221no—
187C2×M16—2442no—
188C22×C8—611no—
189C22×C8—611no—
190C22×C8—611no—
191C22×C8—611no—
192C22×C8—611no—
193C22×C8—611no—
194C22×C8—2442no—
195C22×C8C2×#692311yescharacteristic
196C22×C8C2×#692311yescharacteristic
197#117—1221no—
198#117—1221no—
199#117—1221no—
200#117—1221no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C22⋊C4—611no—
204C2×C22⋊C4—611no—
205C2×C42—611no—
206C2×C42C2×#692311yescharacteristic
207M32—2442no—
208C2×C16—1222no—
209C2×C16—1222no—
210C2×C16—2442no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—1221no—
214C4⋊C8—1221no—
215C4⋊C8—1221no—
216C4⋊C8—1221no—
217C4⋊C8—1221no—
218C4⋊C8—1221no—
219C24—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1222no—
228C22×C4—1222no—
229C22×C4D61⋊C811yescharacteristic
230C22×C4D61⋊C811yescharacteristic
231C22×C4C22×#692311yescharacteristic
232M16—2442no—
233M16—2442no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—611no—
238C2×C8—611no—
239C2×C8—1222no—
240C2×C8—1222no—
241C2×C8—1221no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C2×C8—2441no—
246C2×C8C22⋊#692311yescharacteristic
247C2×C8C22⋊#692311yescharacteristic
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C22⋊C4—1221no—
253C22⋊C4—1221no—
254C22⋊C4—1221no—
255C22⋊C4—1221no—
256C42—21no—
257C42—21no—
258C42—1221no—
259C42—1221no—
260C16—2442no—
261C16—2442no—
262C23—611no—
263C23—611no—
264C23—1222no—
265C23—1222no—
266C23—2441no—
267C23C2×D61⋊C811yescharacteristic
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—611no—
275C2×C4—612no—
276C2×C4—612no—
277C2×C4—611no—
278C2×C4—1222no—
279C2×C4—1222no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1222no—
286C2×C4—2441no—
287C2×C4C2×C22⋊#692311yescharacteristic
288C2×C4D61⋊M1611yescharacteristic
289C8—21no—
290C8—21no—
291C8—41no—
292C8—1221no—
293C8—1221no—
294C8—2441no—
295C22—21no—
296C22—21no—
297C22—612no—
298C22—1221no—
299C22—1221no—
300C22—1221no—
301C22—1221no—
302C22—1221no—
303C22—2444no—
304C22D61⋊(C22⋊C8)11yescharacteristic
305C22#1684082112yes—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—612no—
310C4—1221no—
311C4—2441no—
312C4—2441no—
313C4D61⋊#9911yescharacteristic
314C4D61⋊#10111yescharacteristic
315C2—22no—
316C2—1222no—
317C2—2441no—
318C2D61⋊#32411yescharacteristic
319C2#2146205011yescharacteristic
320C2#2146205611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC23×D61C2×C8
cosocleC22×#92418C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#11441
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #21460756C2semidirect
4. #21460755C2semidirect
183. C61#11441semidirect

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
#214607562
#214607552
C2×#168397872
#1144161