Finite Group Databasebeta

← #30601207

Subgroups — #30601207

Order 15616.

454 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 84 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#21462718C211yesmaximal, characteristic
2#21461686C211yesmaximal, characteristic
3#21461147C212yesmaximal
4#21460672C212yesmaximal
5#21451180C211yesmaximal, characteristic
6#16840814—24no—
7#16840783—21no—
8#16840782—21no—
9#16840779C2212yes—
10#16840765C2212yes—
11C2×#14519838—21no—
12#16840642—21no—
13Q8⋊#92420—24no—
14C2×Q8×Dic61C2211yescharacteristic
15C2×#14519742C2211yescharacteristic
16#16839702C411yescharacteristic
17#16839701C411yescharacteristic
18#16839681C411yescharacteristic
19#16839666—21no—
20#16839657—21no—
21#16839649—21no—
22#16839648—21no—
23#16839626C2211yescharacteristic
24C61×#395C411yescharacteristic
25C2×#11758217—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844—22no—
29C4⋊#92420—22no—
30C4⋊#92420—22no—
31#14519838—42no—
32C22⋊#92420—22no—
33#14519832—22no—
34#14519832—22no—
35C4×#92420D414yes—
36C22×Dic122D411yescharacteristic
37Q8×Dic61—22no—
38Q8×Dic61—22no—
39#14519742—22no—
40#14519742—22no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196C2×C411yescharacteristic
46C2×#11758196D411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C22×Q8×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C2×Q8×C61—22no—
64C2×Q8×C61—42no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×Dic122—22no—
77C2×Dic122—21no—
78C2×Dic122—22no—
79C2×Dic122—21no—
80#11758217—42no—
81#11758217—42no—
82C2×#92420—24no—
83C2×#92420—42no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—42no—
86C4⋊Dic61—22no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89#11758196—22no—
90#11758196—22no—
91#11758196—42no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—42no—
99C4×Dic61C2×D412yes—
100C4×Dic61#4112yes—
101C23×C61C2×C22⋊C411yescharacteristic
102Q8×C61—24no—
103Q8×C61—42no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61C4×D412yes—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—42no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61#12011yescharacteristic
129C2×Dic61#12112yes—
130C2×Dic61#12311yescharacteristic
131C2×Dic61AGL(1,ℤ/8)11yescharacteristic
132C2×Dic61#13712yes—
133C2×Dic61#13711yescharacteristic
134Dic122—42no—
135Dic122—42no—
136#92420—44no—
137#92420—82no—
138#9488—611nomaximal, Sylow
139C22×C61—21no—
140C22×C61—21no—
141C22×C61#38611yescharacteristic
142C22×C61#41711yescharacteristic
143C22×C61#41911yescharacteristic
144C4×C61—22no—
145C4×C61—41no—
146C4×C61—42no—
147C4×C61—41no—
148C4×C61—81no—
149Dic61—21no—
150Dic61—21no—
151Dic61—41no—
152Dic61—41no—
153Dic61—81no—
154Dic61—81no—
155Dic61#46812yes—
156Dic61#47012yes—
157#2983—611no—
158#2581—611no—
159#1801—611no—
160#1487—612no—
161#1286—612no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61#189111yescharacteristic
165C2×C61#189411yescharacteristic
166C2×C61#191211yescharacteristic
167C2×C4×Q8—611no—
168C2×C4×Q8—611no—
169#446—1224no—
170#432—1221no—
171#432—1221no—
172#431—612no—
173#423—612no—
174C2×#101—1221no—
175#400—611no—
176#400—611no—
177#395—611no—
178#395#692311yescharacteristic
179#391—1221no—
180#389—1221no—
181#387—1221no—
182#387—1221no—
183#382—611no—
184#343—1221no—
185Q8⋊C8—1224no—
186C61#948811yescharacteristic, complemented, Sylow
187C22×Q8—611no—
188C22×Q8C2×#692311yescharacteristic
189C2×M16—1222no—
190C4×Q8—1222no—
191C4×Q8—1222no—
192C4×Q8—1222no—
193C4×Q8—1222no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4C2×#692311yescharacteristic
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—1221no—
206C4⋊C8—1222no—
207C4⋊C8—1222no—
208C4⋊C8—1222no—
209C4⋊C8—1222no—
210C4⋊C8—1222no—
211#101—2442no—
212C22⋊C8—1222no—
213#97—1222no—
214#97—1222no—
215C4×C8—614no—
216#95—21no—
217#95—611no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95C2×#692311yescharacteristic
225C2×Q8—22no—
226C2×Q8—42no—
227C2×Q8—1221no—
228C2×Q8—1222no—
229C2×Q8—1221no—
230C2×Q8—1222no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4C22⋊#692311yescharacteristic
240C22×C4C22⋊#692311yescharacteristic
241C22×C4C22×#692311yescharacteristic
242M16—2442no—
243M16—2442no—
244C2×C8—1224no—
245C2×C8—2442no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—1222no—
249C4⋊C4—1222no—
250C4⋊C4—1222no—
251C4⋊C4—2442no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C42—612no—
257C42—612no—
258C42—1221no—
259C42—1221no—
260C42—1221no—
261C42—1221no—
262C42—2442no—
263C23C2×C22⋊#692311yescharacteristic
264Q8—24no—
265Q8—42no—
266Q8—2442no—
267Q8—2442no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—612no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—612no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2442no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4D4×#692312yes—
298C8—4882no—
299C8—2444no—
300C22—21no—
301C22—21no—
302C22#1684071011yescharacteristic
303C22#1684075311yescharacteristic
304C22#1684075511yescharacteristic
305C4—22no—
306C4—41no—
307C4—42no—
308C4—41no—
309C4—81no—
310C4—612no—
311C4—612no—
312C4—1221no—
313C4—1221no—
314C4—4881no—
315C4—4881no—
316C4—2441no—
317C4—2441no—
318C2—21no—
319C2—21no—
320C2#2146183011yescharacteristic
321C2#2146183411yescharacteristic
322C2#2146186611yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#395#6923
hypocenterC61#9488
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
186. C61#9488semidirect

Maximal subgroups

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

subgroupindex
#214627182
#214616862
#214611472
#214606722
#214511802
#948861