Finite Group Databasebeta

← #30598244

Subgroups — #30598244

Order 15616.

814 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 120 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#21461546C211yesmaximal, characteristic
2#21461546C211yesmaximal, characteristic
3C2×#16840619C214yesmaximal, complemented
4C2×#16840317C211yesmaximal, characteristic
5C2×#14519834—21no—
6C2×#14519834—21no—
7C2×#14519832C2212yes—
8C2×#14519832C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840619—28no—
12#16840317—28no—
13C2×#14519777C411yescharacteristic
14C2×#14519768C2212yes—
15C2×#14519757—21no—
16C2×#14519753—21no—
17C2×Q8×Dic61—21no—
18C2×#14519742—21no—
19C2×#14519735C412yes—
20C2×C42×D61C2211yescharacteristic
21C2×C4⋊Q8×C61C411yescharacteristic
22C22×#92420—22no—
23C22×#92420—22no—
24#14519834—24no—
25#14519834—24no—
26#14519832—24no—
27#14519832—24no—
28C22×Dic122—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32#14519777—24no—
33#14519768—24no—
34#14519768D418yes—
35#14519757—28no—
36#14519753—28no—
37Q8×Dic61—28no—
38#14519742—28no—
39#14519735—24no—
40#14519735—24no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61C2×C412yes—
44C2×#11758196—22no—
45C2×#11758198—22no—
46C2×C4×Dic61—22no—
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50C42×D61—24no—
51C22×Q8×C61—21no—
52C4⋊Q8×C61—24no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C412yes—
55C2×C42×C61C2×C411yescharacteristic
56C23×D61C22⋊C411yescharacteristic
57C2×Q8×C61—24no—
58C2×Q8×C61—42no—
59C2×Q8×C61—42no—
60C22×C4×C61—22no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—22no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×Dic122—24no—
78C2×Dic122—42no—
79C2×Dic122—42no—
80C2×#92420—24no—
81C2×#92420—24no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C4⋊C4×C61—24no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61C22⋊C414yes—
89C42×C61—22no—
90#11758198—28no—
91C4⋊Dic61—24no—
92C4⋊Dic61—22no—
93C4⋊Dic61—28no—
94C4⋊Dic61C22⋊C414yes—
95#11758196—28no—
96C4×Dic61—28no—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C4×Dic61C2×D414yes—
100C23×C61C2×C22⋊C411yescharacteristic
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61#10112yes—
108Q8×C61—48no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—24no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61#10412yes—
119C2×C4×C61#10412yes—
120C2×C4×C61C2×C22⋊C412yes—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—24no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61#10112yes—
131C2×Dic61#12012yes—
132C2×Dic61#12012yes—
133C4×D61—28no—
134C4×D61—44no—
135C4×D61—44no—
136Dic122—48no—
137#92420—44no—
138#92420—44no—
139#8338—611nomaximal, Sylow
140C22×C61#37911yescharacteristic
141C22×C61C2×#10111yescharacteristic
142C22×C61C2×#10111yescharacteristic
143C22×C61C2×#10411yescharacteristic
144C22×C61C2×#10411yescharacteristic
145C22×C61#42111yescharacteristic
146C22×C61#42111yescharacteristic
147C2×D61—22no—
148C2×D61—22no—
149C2×D61—22no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C4×C61—22no—
155C4×C61—22no—
156C4×C61—22no—
157C4×C61—44no—
158Dic61—22no—
159Dic61—22no—
160Dic61—22no—
161Dic61—44no—
162C2×#533—611no—
163#1749—611no—
164#1749—611no—
165C2×#330—614no—
166C2×C61#152611yescharacteristic
167C2×C61#153111yescharacteristic
168C2×C61#153111yescharacteristic
169C2×C61#153711yescharacteristic
170C2×C61#178411yescharacteristic
171C2×C61#178911yescharacteristic
172C2×C61#178911yescharacteristic
173D61—42no—
174#533—1228no—
175C2×C4⋊Q8—611no—
176C2×C4⋊Q8#692311yescharacteristic
177C2×#125—612no—
178C2×C22⋊Q8—1221no—
179C2×C22⋊Q8—1221no—
180C2×C4×Q8—1221no—
181C2×C4×Q8—1221no—
182C2×#117—612no—
183C22×C42—611no—
184C2×C22⋊C8—1221no—
185C2×C22⋊C8—1221no—
186C2×#97—612no—
187C2×#97—612no—
188#336—1221no—
189#336—1221no—
190#330—1228no—
191C61#833811yescharacteristic, complemented, Sylow
192C22×Q8—21no—
193C22×Q8—1221no—
194C23×C4—611no—
195C23×C4—611no—
196C23×C4—611no—
197C22×C8—1222no—
198C22×C8—1222no—
199C4⋊Q8—24no—
200C4⋊Q8—1224no—
201#125—618no—
202#125—1224no—
203C22⋊Q8—1228no—
204C22⋊Q8—1228no—
205C4×Q8—1228no—
206C4×Q8—1228no—
207#117—1224no—
208#117—1224no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—612no—
211C2×C4⋊C4—1222no—
212C2×C4⋊C4—1222no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C2×#692312yes—
215C2×C22⋊C4—1222no—
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—1224no—
220C2×C42—1222no—
221C2×C42C2×#692311yescharacteristic
222C22⋊C8—1224no—
223C22⋊C8—1224no—
224#97—1224no—
225#97—1224no—
226C24—611no—
227C2×Q8—24no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—1224no—
231C2×Q8—2442no—
232C2×Q8—2442no—
233C22×C4—22no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1222no—
238C22×C4—1222no—
239C22×C4—1222no—
240C22×C4—1222no—
241C22×C4—1222no—
242C22×C4—1222no—
243C22×C4—1222no—
244C22×C4—1222no—
245C22×C4—2441no—
246C22×C4—2441no—
247C22×C4C22⋊#692311yescharacteristic
248C22×C4C22⋊#692311yescharacteristic
249C22×C4C22×#692311yescharacteristic
250C2×C8—1224no—
251C2×C8—1224no—
252C2×C8—2442no—
253C2×C8—2442no—
254C2×C8—2442no—
255C2×C8—2442no—
256C4⋊C4—24no—
257C4⋊C4—22no—
258C4⋊C4—614no—
259C4⋊C4—1228no—
260C4⋊C4—1228no—
261C4⋊C4—1224no—
262C4⋊C4—1222no—
263C4⋊C4C22⋊#692314yes—
264C22⋊C4—1228no—
265C42—22no—
266C42—614no—
267C42—1222no—
268C42—1222no—
269C42—1228no—
270C23—612no—
271C23—1221no—
272C23—1221no—
273C23—1221no—
274C23—1221no—
275C23—1221no—
276C23—1221no—
277C23C2×C22⋊#692311yescharacteristic
278Q8—48no—
279Q8—2448no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—24no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—612no—
290C2×C4—612no—
291C2×C4—612no—
292C2×C4—1228no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1224no—
300C2×C4—2444no—
301C2×C4—2444no—
302C2×C4—2442no—
303C2×C4—2442no—
304C2×C4#1451984112yes—
305C2×C4#1451984212yes—
306C2×C4C2×C22⋊#692312yes—
307C8—2444no—
308C8—2444no—
309C22—1222no—
310C22—1222no—
311C22—1222no—
312C22—2441no—
313C22—2441no—
314C22—2441no—
315C22—2441no—
316C22#1684070311yescharacteristic
317C22D61⋊#10111yescharacteristic
318C22D61⋊#10111yescharacteristic
319C22C2×#1451984111yescharacteristic
320C22C2×#1451984211yescharacteristic
321C22#1684076011yescharacteristic
322C22#1684076111yescharacteristic
323C4—22no—
324C4—22no—
325C4—22no—
326C4—44no—
327C4—1222no—
328C4—1222no—
329C4—1222no—
330C4—2444no—
331C2—2442no—
332C2#2146127711yescharacteristic
333C2#2146129211yescharacteristic
334C2#2146129311yescharacteristic
335C2#2146131111yescharacteristic
336C2#2146165411yescharacteristic
337C2#2146166011yescharacteristic
338C2#2146166211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#8338
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#16840619C2semidirect
191. C61#8338semidirect

Maximal subgroups

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

subgroupindex
#214615462
C2×#168406192
C2×#168403172
#833861