Finite Group Databasebeta

← #29575105

Subgroups — #29575105

Order 15616.

482 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 111 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#21454457C211yesmaximal, characteristic
2#21449087C211yesmaximal, characteristic
3#21444249C212yesmaximal, complemented
4#21443721C212yesmaximal, complemented
5C61×#1458C211yesmaximal, characteristic
6C2×C4×Dic122C2211yescharacteristic
7#16839823—24no—
8#16839786C2212yes—
9#16839726—21no—
10C4×#11758194—21no—
11#16839701C411yescharacteristic
12#16839698C411yescharacteristic
13#16839695—21no—
14#16839685—21no—
15#16839682C411yescharacteristic
16#16839674C411yescharacteristic
17C4×#11758196—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19C4×C22⋊Dic61—21no—
20#16839494—24no—
21C2×#117×C61C2211yescharacteristic
22C61×#431C2212yes—
23C61×#324—21no—
24C61×#323—21no—
25C22×Dic122C2×C411yescharacteristic
26C2×#11758194—22no—
27C4×Dic122—22no—
28C4×Dic122—22no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C4⋊#92418—22no—
39C4⋊#92418D414yes—
40C22⋊#92418—24no—
41#14519688—22no—
42C4×#92418—22no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684C2×C411yescharacteristic
48#14519684C2×C411yescharacteristic
49C23×C4×C61D411yescharacteristic
50#117×C61—22no—
51#117×C61—22no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61D411yescharacteristic
56C2×C42×C61D411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—22no—
59C22⋊C8×C61—22no—
60C4×C8×C61—22no—
61C24×C61C22⋊C411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C2×Dic122—22no—
77C2×Dic122—42no—
78C2×C8×C61—42no—
79C4⋊C4×C61—22no—
80C4⋊C4×C61—22no—
81C22⋊C4×C61—22no—
82C22⋊C4×C61—22no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61C2×D412yes—
86C42×C61#4112yes—
87C22⋊Dic61—42no—
88C22⋊Dic61—42no—
89C4⋊Dic61—22no—
90C4⋊Dic61—42no—
91#11758196—42no—
92#11758196—42no—
93#11758196—42no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C4×Dic61—42no—
97#11758194—42no—
98#11758194—42no—
99C2×#92418—24no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61C4×D412yes—
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61#12112yes—
120C2×C4×C61#12311yescharacteristic
121C2×C4×C61#13512yes—
122C2×C4×C61#13712yes—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135Dic122—24no—
136Dic122—42no—
137C8×C61—82no—
138#92418—44no—
139#9034—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—42no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—81no—
147C22×C61#38611yescharacteristic
148C22×C61#41611yescharacteristic
149C22×C61#41911yescharacteristic
150C4×C61—22no—
151C4×C61—22no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61#45212yes—
156C4×C61#48512yes—
157Dic61—42no—
158Dic61—42no—
159Dic61—81no—
160Dic61—81no—
161#2921—611no—
162#2396—611no—
163#1487—612no—
164#1458D6111yescharacteristic
165#1303—612no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61—81no—
169C2×C61#187311yescharacteristic
170C2×C61#188411yescharacteristic
171C2×C61#189111yescharacteristic
172C2×C4×Q8—611no—
173C2×#117C2×D6111yescharacteristic
174#433—1224no—
175#431C2×D6112yes—
176#423—612no—
177#407—1221no—
178C4×M16—1221no—
179#400—611no—
180#399—611no—
181#398—1221no—
182#396—1221no—
183#395—611no—
184#393—611no—
185C4×C4⋊C4—611no—
186C4×C4⋊C4—1221no—
187C4×C22⋊C4—1221no—
188Q8⋊C8—1224no—
189#324—21no—
190#323—21no—
191C61#903411yescharacteristic, complemented, Sylow
192C22×Q8—611no—
193C23×C4D24411yescharacteristic
194C2×M16—1222no—
195C4×Q8—1222no—
196C4×Q8—1222no—
197#117—22no—
198#117—22no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4C4×D6111yescharacteristic
205C2×C4⋊C4C22⋊D6111yescharacteristic
206C2×C22⋊C4—1221no—
207C2×C22⋊C4—1221no—
208C2×C22⋊C4C4×D6111yescharacteristic
209C2×C22⋊C4C22⋊D6111yescharacteristic
210C2×C42—1221no—
211C2×C42—1221no—
212C2×C42D24411yescharacteristic
213C2×C42C22×D6111yescharacteristic
214C4⋊C8—22no—
215C4⋊C8—614no—
216C4⋊C8—1222no—
217C22⋊C8—22no—
218C22⋊C8—1224no—
219#97—1222no—
220C4×C8—22no—
221C4×C8—1222no—
222#95—611no—
223#95—611no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228C24#1175819811yescharacteristic
229C2×Q8—1222no—
230C2×Q8—2442no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4#1175819811yescharacteristic
240C22×C4#1175819811yescharacteristic
241C22×C4#1175819811yescharacteristic
242C22×C4C2×C4×D6111yescharacteristic
243C22×C4C2×D24411yescharacteristic
244C22×C4C2×C22⋊D6111yescharacteristic
245M16—2442no—
246M16—2442no—
247C2×C8—42no—
248C2×C8—1224no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—1222no—
252C4⋊C4—2442no—
253C4⋊C4—2442no—
254C4⋊C4—2442no—
255C4⋊C4—2442no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—2442no—
259C22⋊C4—2442no—
260C42—21no—
261C42—21no—
262C42—2441no—
263C42—2441no—
264C42—2442no—
265C42D4×D6112yes—
266C42#1175822412yes—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—41no—
271C23—41no—
272C23C2×#1175819811yescharacteristic
273Q8—1224no—
274Q8—2442no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—1222no—
287C2×C4—1222no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4#1451973712yes—
299C2×C4#1451974711yescharacteristic
300C2×C4#1451974912yes—
301C2×C4#1451976111yescharacteristic
302C2×C4#1451979912yes—
303C2×C4#1451981012yes—
304C8—82no—
305C8—2444no—
306C22—21no—
307C22—21no—
308C22—42no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—81no—
313C22#1683963911yescharacteristic
314C22#1683975911yescharacteristic
315C22#1683977211yescharacteristic
316C4—22no—
317C4—22no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—4881no—
322C4—4881no—
323C4—2442no—
324C4—2442no—
325C4#1683992612yes—
326C4#1684010412yes—
327C2—21no—
328C2—21no—
329C2—81no—
330C2#2144612911yescharacteristic
331C2#2144620011yescharacteristic
332C2#2144623511yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#386
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#9034
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #21444249C2semidirect
4. #21443721C2semidirect
191. C61#9034semidirect

Maximal subgroups

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

subgroupindex
#214544572
#214490872
#214442492
#214437212
C61×#14582
#903461