Finite Group Databasebeta

← #30598922

Subgroups — #30598922

Order 15616.

456 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461605C211yesmaximal, characteristic
2#21461605C211yesmaximal, characteristic
3C2×#16840619C212yesmaximal
4#21460695C212yesmaximal
5#21448378C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4⋊#92420—21no—
8C2×#14519832C2212yes—
9C2×#14519832C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16840619—24no—
13C2×#14519768C2211yescharacteristic
14#16839660C411yescharacteristic
15#16839647—21no—
16#16839643—21no—
17#16839627C2211yescharacteristic
18C4⋊C4×Dic61—21no—
19C4⋊C4×Dic61C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21#16839613—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26C4⋊#92420—24no—
27C4⋊#92420—24no—
28#14519832—22no—
29#14519832—22no—
30#14519832—22no—
31#14519832—22no—
32#14519768—21no—
33#14519768—21no—
34#14519768D412yes—
35#14519768Q812yes—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58#95×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×#92420—24no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61C4⋊C412yes—
80C42×C61—41no—
81C4⋊Dic61—21no—
82C4⋊Dic61—22no—
83C4⋊Dic61—22no—
84C4⋊Dic61—41no—
85C4⋊Dic61C4⋊C412yes—
86#11758196—22no—
87#11758196—22no—
88#11758196—42no—
89C4×Dic61—22no—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C4×Dic61—41no—
93C4×Dic61—41no—
94C4×Dic61—42no—
95C4×Dic61—42no—
96C4×Dic61C2×D411yescharacteristic
97C4×Dic61C2×Q811yescharacteristic
98C4×Dic61#4111yescharacteristic
99C4×Dic61#4111yescharacteristic
100C23×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#10412yes—
114C2×C4×C61#10412yes—
115C2×C4×C61C2×C4⋊C411yescharacteristic
116C2×C4×C61#11711yescharacteristic
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—22no—
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#10112yes—
133C2×Dic61#12111yescharacteristic
134C2×Dic61#12111yescharacteristic
135C2×Dic61C22⋊Q811yescharacteristic
136C2×Dic61C22⋊Q811yescharacteristic
137#92420—44no—
138#92420—44no—
139#8584—611nomaximal, Sylow
140C22×C61#38011yescharacteristic
141C22×C61C2×#10111yescharacteristic
142C22×C61#41311yescharacteristic
143C22×C61C2×#10411yescharacteristic
144C22×C61C2×#10411yescharacteristic
145C22×C61#42111yescharacteristic
146C22×C61#42111yescharacteristic
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—22no—
150C4×C61—22no—
151C4×C61—42no—
152C4×C61—81no—
153Dic61—21no—
154Dic61—21no—
155Dic61—21no—
156Dic61—21no—
157Dic61—22no—
158Dic61—42no—
159Dic61—41no—
160Dic61—81no—
161C4×#125—611no—
162#1767—611no—
163#1767—611no—
164C2×#330—612no—
165#1295—612no—
166C2×C61#152611yescharacteristic
167C2×C61#153211yescharacteristic
168C2×C61#153211yescharacteristic
169C2×C61#153411yescharacteristic
170C2×C61#180111yescharacteristic
171C2×C61#180611yescharacteristic
172C2×C61#180611yescharacteristic
173C2×#125—611no—
174C2×C4⋊C8—1221no—
175C2×C4⋊C8—1221no—
176C2×#97—612no—
177C2×#97—612no—
178#389—611no—
179#389#692311yescharacteristic
180#387—1221no—
181#387—1221no—
182#382—611no—
183C4×C4⋊C4—611no—
184C4×C4⋊C4—611no—
185C4×C4⋊C4—1221no—
186C4×C4⋊C4—1221no—
187C43—611no—
188#336—1221no—
189#336—1221no—
190#330—1224no—
191C61#858411yescharacteristic, complemented, Sylow
192C22×C8—1222no—
193C22×C8—1222no—
194#125—612no—
195#125—612no—
196#125—1221no—
197#125—1221no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4C2×#692311yescharacteristic
205C2×C4⋊C4C2×#692311yescharacteristic
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—1221no—
213C2×C42—1221no—
214C2×C42C2×#692311yescharacteristic
215C4⋊C8—1224no—
216C4⋊C8—1224no—
217#97—1222no—
218#97—1222no—
219#97—1222no—
220#97—1222no—
221#95—21no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4C22⋊#692311yescharacteristic
236C22×C4C22⋊#692311yescharacteristic
237C22×C4C22×#692311yescharacteristic
238C2×C8—1224no—
239C2×C8—1224no—
240C2×C8—2442no—
241C2×C8—2442no—
242C2×C8—2442no—
243C2×C8—2442no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—612no—
248C4⋊C4—1222no—
249C4⋊C4—1222no—
250C4⋊C4—1222no—
251C4⋊C4—1222no—
252C4⋊C4—1221no—
253C4⋊C4—2441no—
254C4⋊C4—2442no—
255C4⋊C4C4⋊#692312yes—
256C42—41no—
257C42—611no—
258C42—611no—
259C42—611no—
260C42—611no—
261C42—1222no—
262C42—1222no—
263C42—1222no—
264C42—2441no—
265C42—2441no—
266C42—2442no—
267C42—2442no—
268C23C2×C22⋊#692311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—611no—
284C2×C4—611no—
285C2×C4—612no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1222no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4#1451984112yes—
302C2×C4#1451984212yes—
303C2×C4C2×C4⋊#692311yescharacteristic
304C2×C4#1451985611yescharacteristic
305C8—2444no—
306C8—2444no—
307C22#1684070411yescharacteristic
308C22D61⋊#10111yescharacteristic
309C22#1684074911yescharacteristic
310C22C2×#1451984111yescharacteristic
311C22C2×#1451984211yescharacteristic
312C22#1684075911yescharacteristic
313C22#1684075911yescharacteristic
314C4—22no—
315C4—22no—
316C4—21no—
317C4—21no—
318C4—42no—
319C4—81no—
320C4—1222no—
321C4—1221no—
322C4—1221no—
323C4—1221no—
324C4—1221no—
325C4—4881no—
326C4—2441no—
327C4—2442no—
328C2#2146127711yescharacteristic
329C2#2146129511yescharacteristic
330C2#2146129711yescharacteristic
331C2#2146130211yescharacteristic
332C2#2146168611yescharacteristic
333C2#2146169111yescharacteristic
334C2#2146169211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#8584
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
191. C61#8584semidirect

Maximal subgroups

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

subgroupindex
#214616052
C2×#168406192
#214606952
#214483782
#858461