Finite Group Databasebeta

← #29595068

Subgroups — #29595068

Order 15616.

482 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#131×Dic61C211yesmaximal, characteristic
2C2×#16839546C211yesmaximal, characteristic
3M32×Dic61C211yesmaximal, characteristic, complemented
4C2×#16839537C211yesmaximal, characteristic, complemented
5#21443909C211yesmaximal, characteristic, complemented
6#21443907C211yesmaximal, characteristic, complemented
7C2×C61×#350C211yesmaximal, characteristic
8C2×#14519784C411yescharacteristic
9#41×Dic61C411yescharacteristic
10C2×#14519717C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12#16839720—21no—
13#16839720C411yescharacteristic
14#16839717—21no—
15#16839717C2211yescharacteristic
16M16×Dic61—21no—
17M16×Dic61C411yescharacteristic
18C2×C8×Dic61—21no—
19C2×C8×Dic61C2211yescharacteristic
20#16839546C414yescomplemented
21#16839537—21no—
22#16839537—21no—
23#16839537—21no—
24C16×Dic61—21no—
25C2×#131×C61C2211yescharacteristic
26C2×M32×C61C2211yescharacteristic
27C22×C16×C61C2211yescharacteristic
28C61×#350C414yescomplemented
29#14519784—22no—
30#14519784C814yes—
31C2×#11758194—21no—
32C2×#11758194C2×C411yescharacteristic
33C22×#92418—21no—
34C22×#92418C2×C411yescharacteristic
35Q8×Dic61C812yes—
36D4×Dic61—22no—
37D4×Dic61C812yes—
38#14519736—21no—
39#14519736C2×C411yescharacteristic
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42#14519717—21no—
43#14519717C2×C412yescomplemented
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185C2×C412yescomplemented
48#14519687—21no—
49#14519687—21no—
50#14519687—21no—
51C8×Dic61—21no—
52C8×Dic61—21no—
53C8×Dic61—21no—
54C8×Dic61D411yescharacteristic
55C8×Dic61D411yescharacteristic
56C8×Dic61D411yescharacteristic
57C8×Dic61D411yescharacteristic
58C2×#41×C61C2×C411yescharacteristic
59#131×C61—21no—
60#131×C61—21no—
61#131×C61C2×C412yes—
62#131×C61C2×C412yes—
63C2×M16×C61—21no—
64C2×M16×C61C2×C411yescharacteristic
65C22×C8×C61—21no—
66C22×C8×C61C2311yescharacteristic
67M32×C61—21no—
68M32×C61C2×C412yescomplemented
69C2×C16×C61—21no—
70C2×C16×C61—21no—
71C2×C16×C61—21no—
72C2×C16×C61C2×C412yescomplemented
73#41×C61—21no—
74#41×C61—21no—
75#41×C61C4212yes—
76#41×C61C2×C812yes—
77C2×Q8×C61C2×C811yescharacteristic
78C2×D4×C61—21no—
79C2×D4×C61C2×C811yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61C22×C411yescharacteristic
82C22×Dic61—22no—
83C22×Dic61M1612yes—
84M16×C61—21no—
85M16×C61—22no—
86M16×C61—22no—
87M16×C61C4212yes—
88C2×C8×C61—21no—
89C2×C8×C61—22no—
90C2×C8×C61—22no—
91C2×C8×C61C22×C411yescharacteristic
92C2×C8×C61C22×C411yescharacteristic
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61#4111yescharacteristic
96C2×C8×C61#4111yescharacteristic
97C22⋊Dic61—21no—
98C22⋊Dic61—22no—
99C4⋊Dic61—22no—
100C4⋊Dic61C2×C812yes—
101C4×Dic61—21no—
102C4×Dic61—22no—
103C4×Dic61C22⋊C411yescharacteristic
104C4×Dic61C22⋊C411yescharacteristic
105C4×Dic61C2×C812yes—
106#11758194—21no—
107#11758194—24no—
108#11758194C2×C812yes—
109C2×#92418—21no—
110C2×#92418—24no—
111C2×#92418C22⋊C411yescharacteristic
112C2×#92418C22⋊C411yescharacteristic
113C2×#92418C2×C812yes—
114C2×#92418M1612yes—
115C16×C61—22no—
116C16×C61—22no—
117#11758185—22no—
118#11758185—22no—
119C23×C61—21no—
120C23×C61C2×M1611yescharacteristic
121Q8×C61—21no—
122Q8×C61C4×C812yes—
123D4×C61—22no—
124D4×C61—22no—
125D4×C61—21no—
126D4×C61C4×C812yes—
127C2×C4×C61—21no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61C2×C4211yescharacteristic
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×C4×C61#11711yescharacteristic
133C2×C4×C61C22×C811yescharacteristic
134C2×C4×C61C22×C811yescharacteristic
135C2×C4×C61C2×M1611yescharacteristic
136C2×Dic61—22no—
137C2×Dic61—42no—
138C2×Dic61—44no—
139C2×Dic61C22⋊C812yes—
140C2×Dic61C22⋊C812yes—
141C8×C61—22no—
142C8×C61C4×D411yescharacteristic
143C8×C61C4×D411yescharacteristic
144C8×C61C4×D411yescharacteristic
145C8×C61C4×D411yescharacteristic
146#92418—22no—
147#92418C22⋊C812yes—
148#92418C22⋊C812yes—
149#12604—611nomaximal, Sylow
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—42no—
153C22×C61C4×M1611yescharacteristic
154C22×C61C2×C22⋊C811yescharacteristic
155C22×C61#43111yescharacteristic
156C4×C61—22no—
157C4×C61C4×C22⋊C411yescharacteristic
158C4×C61C2×C4×C811yescharacteristic
159C4×C61C2×C22⋊C811yescharacteristic
160C4×C61#43111yescharacteristic
161Dic61—22no—
162Dic61—22no—
163Dic61—42no—
164C4×#131—611no—
165C2×#350—611no—
166C2×#350D6111yescharacteristic
167C4×M32—611no—
168C2×#346—611no—
169#1379—611no—
170#1379—611no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61—42no—
174C2×C61C4×C22⋊C811yescharacteristic
175C2×C61#211712yes—
176C2×#131—611no—
177C2×#131C2×D6111yescharacteristic
178C4×#41—611no—
179C2×M32—611no—
180C2×M32C2×D6111yescharacteristic
181C22×C16—611no—
182C22×C16C2×D6111yescharacteristic
183#405—611no—
184#405—611no—
185#405—1221no—
186#405—1221no—
187C4×M16—611no—
188C4×M16—1221no—
189C2×C4×C8—611no—
190C2×C4×C8—1221no—
191#350—614no—
192#350Dic6114yescomplemented
193#346—1221no—
194#346—1221no—
195#346—1221no—
196C4×C16—1221no—
197C61#1260411yescharacteristic, complemented, Sylow
198C2×#41C4×D6111yescharacteristic
199#131—21no—
200#131—21no—
201#131—614no—
202#131—1222no—
203#131C4×D6112yes—
204#131C2×Dic6112yes—
205C2×M16—21no—
206C2×M16—611no—
207C2×M16—1221no—
208C2×M16C4×D6111yescharacteristic
209C22×C8—21no—
210C22×C8—611no—
211C22×C8—1221no—
212C22×C8C22×D6111yescharacteristic
213C4×Q8—612no—
214C4×D4—612no—
215C4×D4—1222no—
216#117—611no—
217#117—1221no—
218C2×C42—611no—
219C2×C42—1221no—
220M32—21no—
221M32—612no—
222M32—1221no—
223M32C2×Dic6112yescomplemented
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—612no—
228C2×C16—1221no—
229C2×C16—1221no—
230C2×C16—1221no—
231C2×C16C2×Dic6112yescomplemented
232#97—1221no—
233#97—1221no—
234#97—1221no—
235C4×C8—611no—
236C4×C8—611no—
237C4×C8—611no—
238C4×C8—611no—
239C4×C8—1221no—
240C4×C8—1221no—
241C4×C8—1221no—
242#41—21no—
243#41—21no—
244#41C8×D6112yes—
245#41C4×Dic6112yes—
246C2×Q8C8×D6111yescharacteristic
247C2×D4—21no—
248C2×D4C8×D6111yescharacteristic
249C22×C4—21no—
250C22×C4—612no—
251C22×C4—1222no—
252C22×C4C2×C4×D6111yescharacteristic
253M16—21no—
254M16—22no—
255M16—22no—
256M16—612no—
257M16—1224no—
258M16—1221no—
259M16C4×Dic6112yes—
260C2×C8—21no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—612no—
266C2×C8—612no—
267C2×C8—1224no—
268C2×C8—1221no—
269C2×C8C2×C4×D6111yescharacteristic
270C2×C8D4×D6111yescharacteristic
271C2×C8D4×D6111yescharacteristic
272C2×C8#1175822411yescharacteristic
273C2×C8#1175822411yescharacteristic
274C2×C8C22×Dic6111yescharacteristic
275C4⋊C4—612no—
276C4⋊C4—1222no—
277C22⋊C4—1222no—
278C22⋊C4—1221no—
279C42—611no—
280C42—611no—
281C42—612no—
282C42—1222no—
283C42—1221no—
284C16—22no—
285C16—22no—
286C16—1222no—
287C16—1222no—
288C23—21no—
289C23M16×D6111yescharacteristic
290Q8—21no—
291Q8C8×Dic6112yes—
292D4—22no—
293D4—22no—
294D4—21no—
295D4C8×Dic6112yes—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—612no—
300C2×C4—612no—
301C2×C4—1222no—
302C2×C4—2442no—
303C2×C4—2444no—
304C2×C4C2×C4×Dic6111yescharacteristic
305C2×C4C22⋊C4×D6111yescharacteristic
306C2×C4#1451973311yescharacteristic
307C2×C4C2×C8×D6111yescharacteristic
308C2×C4C2×C8×D6111yescharacteristic
309C2×C4M16×D6111yescharacteristic
310C8—22no—
311C8—612no—
312C8—612no—
313C8—1222no—
314C8#1451973711yescharacteristic
315C8#1451973711yescharacteristic
316C8D4×Dic6111yescharacteristic
317C8D4×Dic6111yescharacteristic
318C22—22no—
319C22—22no—
320C22—42no—
321C22M16×Dic6111yescharacteristic
322C22C22⋊C8×D6111yescharacteristic
323C22#1683981211yescharacteristic
324C4—22no—
325C4—1222no—
326C4—1222no—
327C4—2442no—
328C4C22⋊C4×Dic6111yescharacteristic
329C4C2×C8×Dic6111yescharacteristic
330C4C22⋊C8×D6111yescharacteristic
331C4#1683981211yescharacteristic
332C2—21no—
333C2—21no—
334C2—42no—
335C2C22⋊C8×Dic6111yescharacteristic
336C2#2144744512yes—
subgroupG/H
centerC2×C8D4×D61
commutatorC4×C61C2×C4×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#350C2
socleC22×C61C2×C22⋊C8
prime radicalC2×#41×C61C2×C4
cosocleC22×C8×C61C23
hypercenterC2×#350D61
hypocenterC61#12604
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
3. M32×Dic61C2semidirect
4. C2×#16839537C2semidirect
5. #21443909C2semidirect
6. #21443907C2semidirect
20. #16839546C4semidirect
28. C61×#350C4semidirect
43. #14519717C2×C4semidirect
47. C2×#11758185C2×C4semidirect
68. M32×C61C2×C4semidirect
72. C2×C16×C61C2×C4semidirect
192. #350Dic61semidirect
197. C61#12604semidirect
223. M32C2×Dic61semidirect
231. C2×C16C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
#131×Dic612
C2×#168395462
M32×Dic612
C2×#168395372
#214439092
#214439072
C2×C61×#3502
#1260461