Finite Group Databasebeta

← #30598868

Subgroups — #30598868

Order 15616.

472 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461734C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3C2×#16840612C212yesmaximal
4#21460655C212yesmaximal
5#21448290C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420C2212yes—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840612—24no—
13C2×#14519742C2211yescharacteristic
14#16839668C411yescharacteristic
15#16839667C411yescharacteristic
16#16839661C411yescharacteristic
17#16839649—21no—
18#16839643—21no—
19C4⋊C4×Dic61—21no—
20C4⋊C4×Dic61C2211yescharacteristic
21#16839607—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—24no—
27C4⋊#92420—22no—
28C4⋊#92420—22no—
29C4×#92420—22no—
30C4×#92420—22no—
31C22×Dic122C2×C411yescharacteristic
32#14519742—21no—
33#14519742—21no—
34#14519742D412yes—
35#14519742Q812yes—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×Dic122—22no—
70C2×Dic122—22no—
71C2×Dic122—21no—
72C2×Dic122C4⋊C412yes—
73C2×#92420—24no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—22no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61C4⋊C412yes—
83C42×C61—22no—
84C4⋊Dic61—22no—
85C4⋊Dic61—42no—
86#11758196—22no—
87#11758196—22no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—41no—
95C4×Dic61—42no—
96C4×Dic61C2×D411yescharacteristic
97C4×Dic61C2×Q811yescharacteristic
98C4×Dic61#4111yescharacteristic
99C4×Dic61#4111yescharacteristic
100C23×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61C2×C4⋊C411yescharacteristic
114C2×C4×C61#11711yescharacteristic
115C2×C4×C61#13112yes—
116C2×C4×C61#13112yes—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—22no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#10412yes—
131C2×Dic61#12111yescharacteristic
132C2×Dic61#12111yescharacteristic
133C2×Dic61C22⋊Q811yescharacteristic
134C2×Dic61C22⋊Q811yescharacteristic
135C2×Dic61#13512yes—
136C2×Dic61#13712yes—
137Dic122—24no—
138Dic122—42no—
139#92420—44no—
140#92420—82no—
141#8570—611nomaximal, Sylow
142C22×C61#38011yescharacteristic
143C22×C61#40811yescharacteristic
144C22×C61#40811yescharacteristic
145C22×C61#41611yescharacteristic
146C22×C61#41911yescharacteristic
147C22×C61C2×#10411yescharacteristic
148C22×C61#42111yescharacteristic
149C4×C61—42no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—81no—
153C4×C61#42412yes—
154C4×C61#43312yes—
155Dic61—21no—
156Dic61—21no—
157Dic61—22no—
158Dic61—42no—
159Dic61—41no—
160Dic61—81no—
161Dic61#46412yes—
162Dic61#47912yes—
163#2295—611no—
164#1831—611no—
165C4×C4⋊C8—611no—
166C2×Q8⋊C8—612no—
167#1279—612no—
168C2×C61#148211yescharacteristic
169C2×C61#148511yescharacteristic
170C2×C61#149411yescharacteristic
171C2×C61#149711yescharacteristic
172C2×C61#179811yescharacteristic
173C2×C61#180511yescharacteristic
174C2×C61#180611yescharacteristic
175C2×C4×Q8—611no—
176C2×C4⋊C8—612no—
177C2×C4⋊C8—1221no—
178C2×C4×C8—612no—
179#391—611no—
180#391—611no—
181#389—611no—
182#389#692311yescharacteristic
183#387—1221no—
184#387—1221no—
185C4×C4⋊C4—611no—
186C4×C4⋊C4—1221no—
187#376—1221no—
188C43—611no—
189#336—1221no—
190#336—1221no—
191#336—1221no—
192Q8⋊C8—1224no—
193C61#857011yescharacteristic, complemented, Sylow
194C22×Q8—611no—
195C22×C8—1222no—
196C22×C8—1222no—
197C4×Q8—612no—
198C4×Q8—612no—
199C4×Q8—1221no—
200C4×Q8—1221no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4C2×#692311yescharacteristic
206C2×C4⋊C4C2×#692311yescharacteristic
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—1221no—
214C2×C42—1221no—
215C2×C42C2×#692311yescharacteristic
216C4⋊C8—1222no—
217C4⋊C8—1222no—
218C4⋊C8—1224no—
219C4×C8—1222no—
220C4×C8—1222no—
221#95—21no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228C2×Q8—612no—
229C2×Q8—1221no—
230C2×Q8—1222no—
231C2×Q8—1222no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4C22⋊#692311yescharacteristic
241C22×C4C22⋊#692311yescharacteristic
242C22×C4C22×#692311yescharacteristic
243C2×C8—1224no—
244C2×C8—2442no—
245C2×C8—2442no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—42no—
252C4⋊C4—1222no—
253C4⋊C4—1222no—
254C4⋊C4—1222no—
255C4⋊C4—2442no—
256C4⋊C4C4⋊#692312yes—
257C42—22no—
258C42—611no—
259C42—611no—
260C42—611no—
261C42—611no—
262C42—1222no—
263C42—1222no—
264C42—1222no—
265C42—1222no—
266C42—1222no—
267C42—1222no—
268C42—2441no—
269C42—2442no—
270C23C2×C22⋊#692311yescharacteristic
271Q8—1224no—
272Q8—2442no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—612no—
288C2×C4—612no—
289C2×C4—611no—
290C2×C4—611no—
291C2×C4—612no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1222no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4C2×C4⋊#692311yescharacteristic
306C2×C4#1451985611yescharacteristic
307C2×C4#1451986412yes—
308C2×C4#1451986512yes—
309C8—4882no—
310C8—2444no—
311C22#1684070411yescharacteristic
312C22#1684073511yescharacteristic
313C22#1684073711yescharacteristic
314C22#1684075211yescharacteristic
315C22#1684075511yescharacteristic
316C22D61⋊#10411yescharacteristic
317C22#1684076011yescharacteristic
318C4—41no—
319C4—41no—
320C4—42no—
321C4—81no—
322C4—612no—
323C4—612no—
324C4—1222no—
325C4—1221no—
326C4—1221no—
327C4—4881no—
328C4—2442no—
329C4—2441no—
330C4#1684076912yes—
331C4#1684078712yes—
332C2#2146113011yescharacteristic
333C2#2146114111yescharacteristic
334C2#2146117311yescharacteristic
335C2#2146118311yescharacteristic
336C2#2146167811yescharacteristic
337C2#2146169011yescharacteristic
338C2#2146169311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#8570
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
193. C61#8570semidirect

Maximal subgroups

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

subgroupindex
#214617342
C4×#145198442
C2×#168406122
#214606552
#214482902
#857061