Finite Group Databasebeta

← #30604903

Subgroups — #30604903

Order 15616.

420 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461569C211yesmaximal, characteristic
2#21461057C211yesmaximal, characteristic
3#21460819C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#21451741C211yesmaximal, characteristic
6C2×#14519837—21no—
7C2×C22⋊#92420—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519757C411yescharacteristic
13C2×#14519737C2211yescharacteristic
14#16839693C2211yescharacteristic
15#16839689—21no—
16#16839683C2211yescharacteristic
17#16839677—21no—
18#16839674C411yescharacteristic
19#16839649—21no—
20#16839637—21no—
21#16839624C411yescharacteristic
22C61×#397C411yescharacteristic
23C2×#11758217—22no—
24C22×#92420—41no—
25#14519837—24no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28#14519832—41no—
29C4×#92420—41no—
30C22×Dic122C2×C411yescharacteristic
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34#14519757—41no—
35#14519757—41no—
36#14519737—41no—
37#14519737—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×#11758196—21no—
41C2×#11758196C2311yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C2×C22⋊D61—22no—
64C2×C22⋊D61—22no—
65C2×C22⋊D61—41no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—81no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—81no—
77C2×Dic122—41no—
78C2×Dic122—81no—
79#11758217—24no—
80#11758217—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—82no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—42no—
87C22⋊Dic61—81no—
88#11758198—41no—
89#11758198—42no—
90#11758198—81no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—81no—
94#11758196—41no—
95#11758196—42no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61#10412yes—
103C23×C61C2×C22⋊C411yescharacteristic
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—41no—
108C22×D61—41no—
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—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C22⋊D61—44no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—41no—
124C2×Dic61—42no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—81no—
133C2×Dic61#9911yescharacteristic
134C2×Dic61#9911yescharacteristic
135C2×Dic61#13512yes—
136C4×D61—81no—
137C4×D61—81no—
138Dic122—82no—
139#92420—44no—
140#92420—82no—
141#11739—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—22no—
145C22×C61—42no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—81no—
149C22×C61C2×#9911yescharacteristic
150C22×C61#41611yescharacteristic
151C22×C61C2×#10411yescharacteristic
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—81no—
156C2×D61—81no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—81no—
160C4×C61—81no—
161Dic61—21no—
162Dic61—21no—
163Dic61—22no—
164Dic61—41no—
165Dic61—81no—
166Dic61—81no—
167#2638—611no—
168C4×#100—611no—
169#1459—611no—
170#1354—612no—
171#1346—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61—42no—
175C2×C61#150111yescharacteristic
176C2×C61#212111yescharacteristic
177C2×C61#213511yescharacteristic
178D61—81no—
179C2×C22⋊Q8—611no—
180C2×C4×D4—611no—
181C2×#100—1221no—
182C2×C22⋊C8—1221no—
183C4×M16—1221no—
184#398—611no—
185#397—1221no—
186#397#692311yescharacteristic
187#395—611no—
188#394—1221no—
189#393—611no—
190#387—1221no—
191#385—1221no—
192#381—611no—
193#343—612no—
194#324—612no—
195#323—1221no—
196C61#1173911yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×D4—611no—
199C23×C4—611no—
200C23×C4—611no—
201C2×M16—1222no—
202C22×C8—2441no—
203C22⋊Q8—2441no—
204C22⋊Q8—2441no—
205C4×D4—2441no—
206C4×D4—2441no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4C2×#692311yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—611no—
214C2×C22⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4C2×#692311yescharacteristic
218C2×C42—611no—
219#100—1224no—
220C22⋊C8—1222no—
221C22⋊C8—2441no—
222#97—2441no—
223C4×C8—2441no—
224#95—21no—
225#95—611no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95C2×#692311yescharacteristic
231C24—611no—
232C24C22⋊#692311yescharacteristic
233C2×Q8—4881no—
234C2×Q8—2441no—
235C2×D4—1222no—
236C2×D4—1222no—
237C2×D4—2441no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—4881no—
250C22×C4—4881no—
251C22×C4C22⋊#692311yescharacteristic
252C22×C4C22×#692311yescharacteristic
253M16—1224no—
254M16—2442no—
255C2×C8—4882no—
256C2×C8—2442no—
257C2×C8—2442no—
258C4⋊C4—41no—
259C4⋊C4—4881no—
260C4⋊C4—2441no—
261C4⋊C4—2442no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—4881no—
267C22⋊C4—4881no—
268C22⋊C4—2441no—
269C22⋊C4—2442no—
270C42—1221no—
271C42—1221no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23—1221no—
277C23—1221no—
278C23—1221no—
279C23—2441no—
280C23—2441no—
281C23#1451984112yes—
282C23C2×C22⋊#692311yescharacteristic
283Q8—4882no—
284D4—2444no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—611no—
296C2×C4—611no—
297C2×C4—612no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—4881no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4—2441no—
305C2×C4—2442no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C8—4882no—
314C8—2444no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—81no—
322C22—4881no—
323C22—4881no—
324C22—2441no—
325C22—2441no—
326C22—2441no—
327C22D61⋊#9911yescharacteristic
328C22#1684075211yescharacteristic
329C22C2×#1451984111yescharacteristic
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—1221no—
335C4—1221no—
336C4—1222no—
337C4—4881no—
338C4—4881no—
339C4—2441no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—4881no—
344C2#2146119511yescharacteristic
345C2#2146207711yescharacteristic
346C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758196C23
hypercenter#397#6923
hypocenterC61#11739
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #21460819C2semidirect
4. #21460803C2semidirect
196. C61#11739semidirect

Maximal subgroups

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

subgroupindex
#214615692
#214610572
#214608192
#214608032
#214517412
#1173961