Finite Group Databasebeta

← #30595683

Subgroups — #30595683

Order 15616.

566 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 120 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#21461736C211yesmaximal, characteristic, complemented
2C4×#14519844C211yesmaximal, characteristic, complemented
3#21460636C214yesmaximal, complemented
4#21454177C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×C4⋊#92420—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519774C411yescharacteristic
12C2×#14519766—21no—
13C2×#14519766—21no—
14#16839663—21no—
15#16839663—21no—
16#16839663C412yes—
17#16839663C2212yes—
18C42×Dic61C2211yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—24no—
23C4⋊#92420—42no—
24C4×#92420—42no—
25C22×D244—21no—
26C22×D244—21no—
27C22×D244C2×C412yes—
28#14519774—42no—
29#14519766—42no—
30#14519766—42no—
31#14519766—42no—
32#14519766—42no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C2×#11758198—22no—
36C2×#11758198—22no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43C22×Q8×C61—21no—
44C4⋊Q8×C61—42no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61C2×C412yes—
47C2×C42×C61C2×C411yescharacteristic
48C23×D61—22no—
49C2×Q8×C61—42no—
50C2×Q8×C61—42no—
51C2×Q8×C61—42no—
52C22×C4×C61—22no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C2×D244—24no—
61C2×D244—42no—
62C2×D244—42no—
63C2×D244—42no—
64C2×D244—42no—
65C2×D244—42no—
66C2×D244—42no—
67C2×D244—42no—
68C2×D244—42no—
69C2×#92420—24no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C4⋊C4×C61—42no—
76C4⋊C4×C61—42no—
77C42×C61—22no—
78#11758198—44no—
79#11758198—44no—
80#11758198—42no—
81#11758198—42no—
82#11758198—42no—
83#11758198—42no—
84C4×Dic61—22no—
85C4×Dic61—22no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C4×Dic61D812yes—
89C4×Dic61D812yes—
90C4×Dic61SD1612yes—
91C4×Dic61SD1612yes—
92C23×C61C2×C22⋊C411yescharacteristic
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—42no—
96C22×D61—42no—
97C22×D61—42no—
98C22×D61—42no—
99C22×D61—42no—
100Q8×C61—84no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61#10012yes—
109C2×C4×C61#10212yes—
110C2×C4×C61#10212yes—
111C2×C4×C61#10412yes—
112C2×C4×C61#13112yes—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61#10212yes—
122C2×Dic61#10212yes—
123C2×Dic61C2×D811yescharacteristic
124C2×Dic61C2×D811yescharacteristic
125C2×Dic61C2×SD1611yescharacteristic
126C2×Dic61C2×SD1611yescharacteristic
127D244—84no—
128D244—84no—
129D244—84no—
130#92420—44no—
131#92420—82no—
132#7659—611nomaximal, Sylow
133C22×C61#40811yescharacteristic
134C22×C61#41011yescharacteristic
135C22×C61C2×#10011yescharacteristic
136C22×C61C2×#10211yescharacteristic
137C22×C61C2×#10211yescharacteristic
138C22×C61C2×#10411yescharacteristic
139C22×C61#42111yescharacteristic
140C2×D61—82no—
141C2×D61—82no—
142C2×D61—82no—
143C2×D61—82no—
144C2×D61—82no—
145C2×D61—82no—
146C2×D61—82no—
147C4×C61—22no—
148C4×C61—22no—
149C4×C61—82no—
150C4×C61#33114yes—
151Dic61—22no—
152Dic61—22no—
153Dic61—21no—
154Dic61—21no—
155Dic61—21no—
156Dic61—21no—
157#2858—611no—
158#1831—611no—
159C4×C4⋊C8—611no—
160#1270—614no—
161C2×C61#146911yescharacteristic
162C2×C61#148011yescharacteristic
163C2×C61#149211yescharacteristic
164C2×C61#150211yescharacteristic
165C2×C61#151711yescharacteristic
166C2×C61#152711yescharacteristic
167C2×C61C2×#33111yescharacteristic
168D61—162no—
169C2×C4⋊Q8#692311yescharacteristic
170C2×#127—611no—
171C2×#124—1221no—
172C2×#124—1221no—
173C2×C4⋊C8—1221no—
174C2×C4⋊C8—1221no—
175C2×C4×C8—1221no—
176#390—612no—
177#390—612no—
178#390—1221no—
179#390—1221no—
180C43—611no—
181#336—612no—
182#336—612no—
183#336—1221no—
184C61#765911yescharacteristic, complemented, Sylow
185C22×Q8—21no—
186C22×D4—612no—
187C22×D4—1221no—
188C22×D4—1221no—
189C22×C8—1222no—
190C22×C8—1222no—
191C4⋊Q8—42no—
192#127—2442no—
193#124—2442no—
194#124—2442no—
195#124—2442no—
196#124—2442no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×#692312yes—
199C2×C22⋊C4—1222no—
200C2×C22⋊C4—1222no—
201C2×C22⋊C4—1222no—
202C2×C22⋊C4—1222no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42C2×#692311yescharacteristic
210C4⋊C8—1224no—
211C4⋊C8—2442no—
212C4×C8—2442no—
213C24—1222no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—42no—
217C2×D4—1224no—
218C2×D4—2442no—
219C2×D4—2442no—
220C2×D4—2442no—
221C2×D4—2442no—
222C2×D4—2442no—
223C2×D4—2442no—
224C2×D4—2442no—
225C2×D4—2442no—
226C22×C4—22no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22⋊#692311yescharacteristic
233C22×C4C22×#692311yescharacteristic
234C2×C8—1224no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C2×C8—2442no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C22⋊C4—2444no—
243C22⋊C4—2444no—
244C22⋊C4—2442no—
245C22⋊C4—2442no—
246C22⋊C4—2442no—
247C22⋊C4—2442no—
248C42—22no—
249C42—612no—
250C42—612no—
251C42—612no—
252C42—612no—
253C42—1222no—
254C42—1222no—
255C42—2441no—
256C42—2441no—
257C23—2442no—
258C23—2442no—
259C23—2442no—
260C23—2442no—
261C23—2442no—
262C23—2442no—
263C23—2442no—
264C23C2×C22⋊#692311yescharacteristic
265Q8—84no—
266D4—4884no—
267D4—4884no—
268D4—4884no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—612no—
277C2×C4—612no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—611no—
281C2×C4—611no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4#1451983712yes—
291C2×C4#1451983912yes—
292C2×C4#1451983912yes—
293C2×C4#1451984212yes—
294C2×C4#1451986512yes—
295C8—4882no—
296C8—2444no—
297C22—4882no—
298C22—4882no—
299C22—4882no—
300C22—4882no—
301C22—4882no—
302C22—4882no—
303C22—4882no—
304C22#1684073711yescharacteristic
305C22#1684074311yescharacteristic
306C22C2×#1451983711yescharacteristic
307C22C2×#1451983911yescharacteristic
308C22C2×#1451983911yescharacteristic
309C22C2×#1451984211yescharacteristic
310C22#1684076111yescharacteristic
311C4—22no—
312C4—22no—
313C4—82no—
314C4—1221no—
315C4—1221no—
316C4—1222no—
317C4—1222no—
318C4—1221no—
319C4—1221no—
320C4#1684062014yes—
321C2—9762no—
322C2#2146109011yescharacteristic
323C2#2146112611yescharacteristic
324C2#2146116611yescharacteristic
325C2#2146120011yescharacteristic
326C2#2146125011yescharacteristic
327C2#2146128011yescharacteristic
328C2C2×#1684062011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519774C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#7659
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21461736C2semidirect
2. C4×#14519844C2semidirect
3. #21460636C2semidirect
184. C61#7659semidirect

Maximal subgroups

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

subgroupindex
#214617362
C4×#145198442
#214606362
#214541772
#765961