Finite Group Databasebeta

← #30605236

Subgroups — #30605236

Order 15616.

382 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461685C211yesmaximal, characteristic, complemented
2#21461081C211yesmaximal, characteristic, complemented
3#21460820C212yesmaximal, complemented
4#21460801C212yesmaximal
5#21451680C211yesmaximal, characteristic
6#16840783—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×C4×Dic122C2211yescharacteristic
13#16839698—21no—
14#16839681C411yescharacteristic
15#16839681C2211yescharacteristic
16#16839676C411yescharacteristic
17#16839676C2211yescharacteristic
18#16839674—21no—
19#16839650—21no—
20#16839650—21no—
21#16839630C411yescharacteristic
22C2×#124×C61C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27#14519838—42no—
28C22⋊#92420—22no—
29#14519832—41no—
30C22×Dic122D411yescharacteristic
31C4×Dic122—41no—
32C4×Dic122—41no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196C2×C411yescharacteristic
37C2×#11758196C2311yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C22×Q8×C61C2×C411yescharacteristic
51C22×D4×C61C2×C411yescharacteristic
52#124×C61—41no—
53#124×C61—41no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C24×C61—21no—
58C2×Q8×C61—41no—
59C2×Q8×C61—81no—
60C2×D4×C61—41no—
61C2×D4×C61—81no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76#11758217—42no—
77#11758217—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C22⋊C4×C61—42no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61—21no—
84C42×C61—21no—
85C22⋊Dic61—42no—
86C22⋊Dic61—41no—
87C22⋊Dic61—41no—
88C22⋊Dic61—81no—
89C22⋊Dic61—81no—
90C4⋊Dic61—41no—
91#11758196—41no—
92#11758196—41no—
93#11758196—81no—
94#11758196—81no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C23×C61—41no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61C2×C22⋊C411yescharacteristic
107Q8×C61—82no—
108D4×C61—82no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61#9911yescharacteristic
119C2×C4×C61#9911yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
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—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61AGL(1,ℤ/8)11yescharacteristic
136C2×Dic61#13711yescharacteristic
137Dic122—42no—
138Dic122—42no—
139#92420—82no—
140#92420—82no—
141#11833—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—81no—
145C22×C61—81no—
146C22×C61—81no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61—81no—
150C22×C61—81no—
151C22×C61C2×#9911yescharacteristic
152C22×C61#41711yescharacteristic
153C22×C61#42111yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—81no—
159Dic61—21no—
160Dic61—21no—
161Dic61—41no—
162Dic61—41no—
163Dic61—41no—
164Dic61—81no—
165Dic61—81no—
166#2632—611no—
167#1801—611no—
168#1467—611no—
169#1354—612no—
170#1345—612no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61—161no—
174C2×C61#151311yescharacteristic
175C2×C61#212211yescharacteristic
176C2×C61#213311yescharacteristic
177C2×#124#692311yescharacteristic
178C2×C4×Q8—611no—
179#432—1221no—
180#423—1221no—
181C2×#101—1221no—
182#399—1221no—
183#395—611no—
184#395—611no—
185#394—611no—
186#394—611no—
187#393—1221no—
188#388—1221no—
189#388—1221no—
190#383—611no—
191#343—612no—
192#324—612no—
193#324—1221no—
194C61#1183311yescharacteristic, complemented, Sylow
195C22×Q8—611no—
196C22×Q8C2×#692311yescharacteristic
197C22×D4C2×#692311yescharacteristic
198C2×M16—1222no—
199#124—41no—
200#124—41no—
201C4×Q8—2441no—
202C4×Q8—2441no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—1221no—
211C2×C22⋊C4—1221no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—1221no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42C2×#692311yescharacteristic
217C4⋊C8—2441no—
218C4⋊C8—2441no—
219C4⋊C8—2441no—
220#101—2442no—
221C22⋊C8—1222no—
222#97—2441no—
223#95—611no—
224#95—611no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229C24—21no—
230C2×Q8—41no—
231C2×Q8—81no—
232C2×Q8—1221no—
233C2×Q8—1221no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C2×D4—41no—
237C2×D4—81no—
238C22×C4—21no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22⋊#692311yescharacteristic
247C22×C4C22×#692311yescharacteristic
248M16—2442no—
249M16—2442no—
250C2×C8—2442no—
251C2×C8—2442no—
252C4⋊C4—4881no—
253C4⋊C4—4881no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—4881no—
261C22⋊C4—4881no—
262C22⋊C4—2441no—
263C22⋊C4—2441no—
264C22⋊C4—2442no—
265C42—21no—
266C42—21no—
267C42—1221no—
268C42—1221no—
269C42—1221no—
270C42—1221no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊#692311yescharacteristic
279Q8—82no—
280Q8—2442no—
281Q8—2442no—
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4#1451983511yescharacteristic
310C2×C4#1451983511yescharacteristic
311C8—4882no—
312C8—4882no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C2×#1451983511yescharacteristic
323C22#1684075311yescharacteristic
324C22#1684075911yescharacteristic
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—81no—
330C4—1221no—
331C4—1221no—
332C4—4881no—
333C4—4881no—
334C4—2441no—
335C4—2441no—
336C4—2441no—
337C2—21no—
338C2—21no—
339C2—161no—
340C2#2146123411yescharacteristic
341C2#2146207811yescharacteristic
342C2#2146211411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×#11758196C23
hypercenterC2×#124#6923
hypocenterC61#11833
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461685C2semidirect
2. #21461081C2semidirect
3. #21460820C2semidirect
194. C61#11833semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610812
#214608202
#214608012
#214516802
#1183361