Finite Group Databasebeta

← #30607444

Subgroups — #30607444

Order 15616.

380 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462580C211yesmaximal, characteristic
2#21462167C211yesmaximal, characteristic
3C2×#16840681C211yesmaximal, characteristic
4#21461938C211yesmaximal, characteristic
5#21460899C211yesmaximal, characteristic
6#21460871C211yesmaximal, characteristic
7#362×D61C211yesmaximal, characteristic
8#16840830—21no—
9C2×#14519852C2211yescharacteristic
10#16840802—21no—
11#16840802—21no—
12Q16×#6923—22no—
13#16840777—21no—
14C2×#14519847C2211yescharacteristic
15#16840772C2211yescharacteristic
16#16840755—21no—
17#16840725C2211yescharacteristic
18#16840687—21no—
19#16840686—21no—
20#16840681—22no—
21#16840645—21no—
22C2×Q16×D61C2211yescharacteristic
23M32×D61C2211yescharacteristic
24#108×D61C2211yescharacteristic
25#16839579C411yescharacteristic, complemented
26#16839578C411yescharacteristic, complemented
27#16839577C411yescharacteristic, complemented
28C61×#362C411yescharacteristic, complemented
29C2×#11758213—21no—
30D61⋊M16D411yescharacteristic
31Q8×#6923—22no—
32Q8×#6923—22no—
33Q8×#6923—41no—
34Q8×#6923—41no—
35#14519856—21no—
36#14519856—42no—
37#14519856D411yescharacteristic
38#14519852—21no—
39#14519852—21no—
40C2×#11758187—21no—
41#14519848—41no—
42#14519847—21no—
43#14519847—21no—
44#14519847—41no—
45#14519846—21no—
46#14519845D411yescharacteristic
47#14519845D411yescharacteristic
48#14519840—22no—
49#14519840—22no—
50#14519831—21no—
51C8×#6923—21no—
52C2×Q8×D61—21no—
53C2×Dic244C2×C411yescharacteristic
54C2×#11758202—21no—
55Q16×D61—21no—
56Q16×D61—21no—
57Q16×D61D412yes—
58Q16×D61Q812yes—
59M16×D61—21no—
60C2×C8×D61C2311yescharacteristic
61#14519717C2×C411yescharacteristic
62#14519716—21no—
63C16×D61—21no—
64#14519713C2×C411yescharacteristic
65#14519712—21no—
66C2×Q16×C61C2×C411yescharacteristic
67M32×C61C2×C411yescharacteristic
68#108×C61C2×C411yescharacteristic
69C2×Q8×C61—21no—
70Q8×D61—22no—
71Q8×D61—22no—
72Q8×D61—41no—
73Q8×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61C2×D411yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—41no—
78C22⋊#6923—41no—
79C22⋊#6923SD1612yes—
80#11758217—21no—
81C2×#92420—41no—
82C4⋊#6923—21no—
83C4⋊#6923—21no—
84C4⋊#6923—21no—
85C4⋊#6923—42no—
86C4⋊#6923—42no—
87C4×#6923—21no—
88C4×#6923—42no—
89C4×#6923—42no—
90C4×#6923—41no—
91#11758213—21no—
92#11758213—41no—
93#11758213—41no—
94D61⋊C8—21no—
95Q16×C61—21no—
96Q16×C61C4⋊C412yes—
97M16×C61—21no—
98C2×C8×C61C22×C411yescharacteristic
99#11758202—22no—
100#11758202—22no—
101#11758194—21no—
102C2×#92418#4111yescharacteristic
103Dic244—21no—
104Dic244C4⋊C412yes—
105#11758189—41no—
106C8×D61—41no—
107C8×D61C2×D411yescharacteristic
108C8×D61C2×D411yescharacteristic
109C8×D61C2×Q811yescharacteristic
110C8×D61#4111yescharacteristic
111#11758187—41no—
112C16×C61—21no—
113#11758185—21no—
114C22×D61C2×SD1611yescharacteristic
115C2×#6923—22no—
116C2×#6923—41no—
117C2×#6923—41no—
118Q8×C61—22no—
119Q8×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61C4×D411yescharacteristic
122C2×Dic61—41no—
123C2×Dic61#13511yescharacteristic
124C4×D61—42no—
125C4×D61—42no—
126C4×D61#12011yescharacteristic
127C4×D61C22⋊Q811yescharacteristic
128C4×D61AGL(1,ℤ/8)11yescharacteristic
129C4×D61AGL(1,ℤ/8)11yescharacteristic
130Dic122—22no—
131Dic122—41no—
132Dic122—42no—
133Dic122—42no—
134#92420—41no—
135#92420—81no—
136C8×C61—41no—
137C8×C61C2×C4⋊C411yescharacteristic
138C8×C61C4×D411yescharacteristic
139#92418—41no—
140#92418C22⋊Q811yescharacteristic
141#92418#12311yescharacteristic
142#12954—611nomaximal, Sylow
143C22×C61C4×SD1611yescharacteristic
144C2×D61—41no—
145C2×D61#45011yescharacteristic
146C2×D61#47611yescharacteristic
147#6923—42no—
148#6923—81no—
149#6923—81no—
150C4×C61—42no—
151C4×C61#38511yescharacteristic
152C4×C61#44211yescharacteristic
153Dic61—42no—
154Dic61#44911yescharacteristic
155Dic61#47811yescharacteristic
156#2950—611no—
157#2155—611no—
158C2×#362—611no—
159C2×#362—611no—
160#1953—611no—
161#1389—611no—
162#1378—611no—
163C2×C61—21no—
164C2×C61#186411yescharacteristic
165D61—21no—
166D61—21no—
167C22×Q16—611no—
168#519—1221no—
169C2×M32—611no—
170C2×M32—611no—
171#441—1221no—
172#441—1221no—
173C4×Q16—1222no—
174#430—1221no—
175C2×#108—611no—
176C2×#108—611no—
177#427—611no—
178#419—1221no—
179#405—611no—
180#365—1221no—
181#365—1221no—
182#362—611no—
183#362—611no—
184#362—611no—
185#362—1222no—
186#362#692311yescharacteristic, complemented
187#344—1221no—
188C61#1295411yescharacteristic, complemented, Sylow
189C22×Q8—1221no—
190C2×Q16—612no—
191C2×Q16—612no—
192C2×Q16—611no—
193C2×Q16—1221no—
194C2×Q16—1221no—
195C2×Q16—1221no—
196C2×Q16C2×#692311yescharacteristic
197C2×M16—611no—
198C2×M16—1221no—
199C2×M16—1221no—
200C22×C8—611no—
201C4×Q8—1222no—
202C4×Q8—1222no—
203C4×Q8—2441no—
204C4×Q8—2441no—
205#117—611no—
206#117—1221no—
207#117—2442no—
208M32—611no—
209M32—1221no—
210M32—1221no—
211M32—1221no—
212M32C2×#692311yescharacteristic
213C2×C16—1221no—
214C2×C16—1221no—
215#108—611no—
216#108—1221no—
217#108—1221no—
218#108—1221no—
219#108—2441no—
220#108—2441no—
221#108C2×#692311yescharacteristic
222#107—1221no—
223#106—611no—
224#106—611no—
225#103—1222no—
226#103—1222no—
227#97—1221no—
228C4×C8—1221no—
229C2×Q8—21no—
230C2×Q8—1222no—
231C2×Q8—1222no—
232C2×Q8—1221no—
233C2×Q8—2441no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C22×C4—611no—
237C22×C4—2441no—
238Q16—21no—
239Q16—612no—
240Q16—1222no—
241Q16—1222no—
242Q16—1221no—
243Q16C4⋊#692312yes—
244M16—21no—
245M16—1221no—
246M16—1221no—
247M16—1221no—
248M16—2441no—
249M16—2441no—
250M16—2441no—
251C2×C8—611no—
252C2×C8—611no—
253C2×C8—611no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—1221no—
257C2×C8—2441no—
258C2×C8—2441no—
259C2×C8C22×#692311yescharacteristic
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—2442no—
264C4⋊C4—2442no—
265C22⋊C4—612no—
266C22⋊C4—2441no—
267C42—1221no—
268C42—2441no—
269C42—2442no—
270C42—2442no—
271C16—21no—
272C16—1221no—
273C16—2441no—
274C23—611no—
275Q8—22no—
276Q8—41no—
277Q8—1222no—
278Q8—2442no—
279Q8—2442no—
280Q8—2441no—
281C2×C4—41no—
282C2×C4—611no—
283C2×C4—611no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—1222no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4D4×#692311yescharacteristic
294C8—41no—
295C8—611no—
296C8—611no—
297C8—4881no—
298C8—2441no—
299C8—2441no—
300C8C2×C4⋊#692311yescharacteristic
301C8D4×#692311yescharacteristic
302C22—611no—
303C22—611no—
304C22—2441no—
305C22SD16×#692311yescharacteristic
306C4—42no—
307C4—611no—
308C4—611no—
309C4—4881no—
310C4—4881no—
311C4—2442no—
312C4—2442no—
313C4#1684070911yescharacteristic
314C4#1684080311yescharacteristic
315C2—21no—
316C2—1221no—
317C2—1221no—
318C2#2146178411yescharacteristic
subgroupG/H
centerC2#21461784
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#362C4
socleC2×C61#1864
prime radicalC22×D61C2×SD16
cosocleC2×C8×D61C23
hypercenter#362#6923
hypocenterC61#12954
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
25. #16839579C4semidirect
26. #16839578C4semidirect
27. #16839577C4semidirect
28. C61×#362C4semidirect
186. #362#6923semidirect
188. C61#12954semidirect

Maximal subgroups

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

subgroupindex
#214625802
#214621672
C2×#168406812
#214619382
#214608992
#214608712
#362×D612
#1295461