Finite Group Databasebeta

← #29590407

Subgroups — #29590407

Order 15616.

420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#14519694C211yesmaximal, characteristic
2#21444137C211yesmaximal, characteristic
3#21443849C212yesmaximal, complemented
4#21443825C212yesmaximal, complemented
5C61×#2638C211yesmaximal, characteristic
6C2×#14519694—21no—
7C2×C22⋊#92418—21no—
8C4×#11758194—21no—
9#16839531C2212yes—
10#16839488C2212yes—
11#16839486—21no—
12C2×C22⋊Q8×C61C411yescharacteristic
13C2×C4×D4×C61C2211yescharacteristic
14C61×#398C2211yescharacteristic
15C61×#397—21no—
16C61×#397C411yescharacteristic
17C61×#395C2211yescharacteristic
18C61×#394—21no—
19C61×#393C411yescharacteristic
20C61×#387—21no—
21C61×#385—21no—
22C61×#381C411yescharacteristic
23C2×#11758194—22no—
24C22×#92418—41no—
25#14519694—24no—
26C22⋊#92418—22no—
27C22⋊#92418—41no—
28#14519688—41no—
29C4×#92418—41no—
30C22×Q8×C61C2×C411yescharacteristic
31C22×D4×C61D411yescharacteristic
32C23×C4×C61C2×C411yescharacteristic
33C23×C4×C61D411yescharacteristic
34C22⋊Q8×C61—41no—
35C22⋊Q8×C61—41no—
36C4×D4×C61—41no—
37C4×D4×C61—41no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61—21no—
47C2×C22⋊C4×C61C2×C411yescharacteristic
48C2×C22⋊C4×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C2×Q8×C61—41no—
60C2×Q8×C61—81no—
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—81no—
73C22×C4×C61—81no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—81no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—81no—
90C22⋊C4×C61—81no—
91C42×C61—21no—
92C42×C61—21no—
93#11758194—24no—
94#11758194—42no—
95C2×#92418—42no—
96C2×#92418—42no—
97C2×#92418—82no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61#10412yes—
108C23×C61C2×C22⋊C411yescharacteristic
109Q8×C61—82no—
110D4×C61—44no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—42no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61#9911yescharacteristic
137C2×C4×C61#9911yescharacteristic
138C2×C4×C61#13512yes—
139#92418—44no—
140#92418—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—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61C2×#9911yescharacteristic
155C22×C61#41611yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—81no—
164C4×C61—81no—
165C4×C61—81no—
166C4×C61—81no—
167#2638D6111yescharacteristic
168C4×#100—611no—
169#1459—611no—
170#1354—612no—
171#1346—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61—42no—
175C2×C61—81no—
176C2×C61#150111yescharacteristic
177C2×C61#212111yescharacteristic
178C2×C61#213511yescharacteristic
179C2×C22⋊Q8Dic6111yescharacteristic
180C2×C4×D4C2×D6111yescharacteristic
181C2×#100—1221no—
182C2×C22⋊C8—1221no—
183C4×M16—1221no—
184#398C2×D6111yescharacteristic
185#397—21no—
186#397Dic6111yescharacteristic
187#395C2×D6111yescharacteristic
188#394—21no—
189#393Dic6111yescharacteristic
190#387—21no—
191#385—21no—
192#381Dic6111yescharacteristic
193#343—612no—
194#324—612no—
195#323—1221no—
196C61#1173911yescharacteristic, complemented, Sylow
197C22×Q8C2×Dic6111yescharacteristic
198C22×D4C22⋊D6111yescharacteristic
199C23×C4C2×Dic6111yescharacteristic
200C23×C4C22⋊D6111yescharacteristic
201C2×M16—1222no—
202C22×C8—2441no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×Dic6111yescharacteristic
211C2×C4⋊C4C22×D6111yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4C2×Dic6111yescharacteristic
217C2×C22⋊C4C22⋊D6111yescharacteristic
218C2×C42C22⋊D6111yescharacteristic
219#100—1224no—
220C22⋊C8—1222no—
221C22⋊C8—2441no—
222#97—2441no—
223C4×C8—2441no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95C2×Dic6111yescharacteristic
230#95C2×Dic6111yescharacteristic
231C24C22⋊Dic6111yescharacteristic
232C24C22⋊Dic6111yescharacteristic
233C2×Q8—41no—
234C2×Q8—81no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4C22⋊Dic6111yescharacteristic
249C22×C4C22⋊Dic6111yescharacteristic
250C22×C4C22×Dic6111yescharacteristic
251C22×C4C2×C22⋊D6111yescharacteristic
252C22×C4C2×C22⋊D6111yescharacteristic
253M16—1224no—
254M16—2442no—
255C2×C8—4882no—
256C2×C8—2442no—
257C2×C8—2442no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—81no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—81no—
269C22⋊C4—81no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#1451970412yes—
282C23C2×C22⋊Dic6111yescharacteristic
283Q8—82no—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4#1451969211yescharacteristic
311C2×C4#1451969211yescharacteristic
312C2×C4#1451979712yes—
313C8—4882no—
314C8—2444no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#1451969211yescharacteristic
328C22#1683975811yescharacteristic
329C22C2×#1451970411yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#2144431011yescharacteristic
345C2#2144746511yescharacteristic
346C2#2144751411yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2638C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C4⋊C4×C61C23
hypercenter#2638D61
hypocenterC61#11739
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2638

Complements

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

NH ≅ G/Ntype
3. #21443849C2semidirect
4. #21443825C2semidirect
196. C61#11739semidirect

Maximal subgroups

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

subgroupindex
C4×#145196942
#214441372
#214438492
#214438252
C61×#26382
#1173961