Finite Group Databasebeta

← #21448564

Subgroups — #21448564

Order 7808.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519776C211yesmaximal, characteristic
2#16839668C211yesmaximal, characteristic
3#16839667C211yesmaximal, characteristic
4#16839666C211yesmaximal, characteristic
5#16839666C211yesmaximal, characteristic
6#16839659C211yesmaximal, characteristic
7#16839657C211yesmaximal, characteristic
8#16839648C211yesmaximal, characteristic
9#16839647C211yesmaximal, characteristic
10#16839645C211yesmaximal, characteristic
11#16839626C211yesmaximal, characteristic
12C4×#11758196C211yesmaximal, characteristic
13#16839613C211yesmaximal, characteristic
14#16839607C211yesmaximal, characteristic
15C61×#387C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18#14519776C418yescomplemented
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×C4×Dic61C2211yescharacteristic
28C2×C4×Dic61C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
33#14519684C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45C2×C4⋊C4×C61C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C42×C61C2211yescharacteristic
48#95×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52C22×C4×C61C2311yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×Dic61C2311yescharacteristic
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C2×Dic122—41no—
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122C2×C414yes—
72C2×Dic122C2×C414yes—
73C4⋊C4×C61—41no—
74C4⋊C4×C61C2×C414yes—
75C42×C61—41no—
76C4⋊Dic61—41no—
77C4⋊Dic61C2×C414yes—
78#11758196—22no—
79#11758196—22no—
80#11758196—41no—
81#11758196—41no—
82#11758196C2×C414yes—
83#11758196C2×C414yes—
84C4×Dic61—22no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C4×Dic61C2×C414yes—
89C4×Dic61Q814yescomplemented
90C23×C61C2411yescharacteristic
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
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×C61C22×C412yes—
109C2×C4×C61C22×C412yes—
110C2×C4×C61C22×C412yes—
111C2×C4×C61C2×Q812yes—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C22×C412yes—
130C2×Dic61C22×C412yes—
131C2×Dic61C22×C412yes—
132C2×Dic61C22×C412yes—
133C2×Dic61C2×Q812yes—
134C2×Dic61C2×Q812yes—
135C2×Dic61#4112yes—
136Dic122—44no—
137Dic122—44no—
138C22×C61C23×C411yescharacteristic
139C22×C61C22×Q811yescharacteristic
140C22×C61C2×#4111yescharacteristic
141C22×C61H(5,𝔽2)11yescharacteristic
142C22×C61H(5,𝔽2)11yescharacteristic
143C22×C612−1+411yescharacteristic
144C22×C612−1+411yescharacteristic
145C4×C61—22no—
146C4×C61—22no—
147C4×C61—22no—
148C4×C61—22no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152Dic61—22no—
153Dic61—22no—
154Dic61—22no—
155Dic61—22no—
156Dic61—41no—
157Dic61—41no—
158Dic61—41no—
159Dic61C4×Q814yes—
160#2331—611nomaximal, Sylow
161C2×C61C2×C4×Q811yescharacteristic
162C2×C61#51811yescharacteristic
163C2×C61#51911yescharacteristic
164C2×C61#54211yescharacteristic
165C2×C61#54211yescharacteristic
166C2×C61#54411yescharacteristic
167C2×C61#54411yescharacteristic
168C2×C4⋊Q8—611no—
169#391—611no—
170#391—611no—
171#391—611no—
172#391—611no—
173#389—611no—
174#389—611no—
175#387—611no—
176#387—611no—
177#387—611no—
178#387D6111yescharacteristic
179#382—611no—
180C4×C4⋊C4—611no—
181C4×C4⋊C4—611no—
182#376—611no—
183C61#233111yescharacteristic, complemented, Sylow
184C22×Q8—611no—
185C22×Q8—611no—
186C4⋊Q8—618no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4C2×D6111yescharacteristic
196C2×C4⋊C4C2×D6111yescharacteristic
197C2×C42—611no—
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42C2×D6111yescharacteristic
204#95—611no—
205#95—611no—
206#95—611no—
207#95—611no—
208#95—611no—
209#95—611no—
210#95—611no—
211#95—611no—
212#95—611no—
213#95—611no—
214#95—611no—
215#95—611no—
216#95C2×D6111yescharacteristic
217#95C2×D6111yescharacteristic
218#95C2×D6111yescharacteristic
219#95C2×D6111yescharacteristic
220C2×Q8—614no—
221C2×Q8—614no—
222C2×Q8—2441no—
223C2×Q8—2441no—
224C2×Q8—2441no—
225C2×Q8—2441no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4C22×D6111yescharacteristic
235C22×C4C22×D6111yescharacteristic
236C22×C4C22×D6111yescharacteristic
237C22×C4C22×D6111yescharacteristic
238C22×C4C22×D6111yescharacteristic
239C22×C4C22×D6111yescharacteristic
240C22×C4C22×D6111yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—614no—
243C4⋊C4—614no—
244C4⋊C4—614no—
245C4⋊C4—1222no—
246C4⋊C4—1222no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C4⋊C4—2441no—
250C4⋊C4C4×D6114yes—
251C42—41no—
252C42—614no—
253C42—614no—
254C42—1222no—
255C42—2441no—
256C42—2441no—
257C42—2441no—
258C23C23×D6111yescharacteristic
259Q8—2444no—
260Q8—2444no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—612no—
279C2×C4—612no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—612no—
283C2×C4—612no—
284C2×C4—612no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4C2×C4×D6112yes—
303C2×C4C2×C4×D6112yes—
304C2×C4C2×C4×D6112yes—
305C2×C4Q8×D6112yes—
306C22C22×C4×D6111yescharacteristic
307C22C2×Q8×D6111yescharacteristic
308C22#41×D6111yescharacteristic
309C22#1451982211yescharacteristic
310C22#1451982311yescharacteristic
311C22#1451982411yescharacteristic
312C22#1451982411yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—614no—
321C4—1222no—
322C4—1222no—
323C4—1222no—
324C4—1222no—
325C4—2441no—
326C4—2441no—
327C4—2441no—
328C2C4×Q8×D6111yescharacteristic
329C2#1684023411yescharacteristic
330C2#1684023911yescharacteristic
331C2#1684037811yescharacteristic
332C2#1684038011yescharacteristic
333C2#1684039111yescharacteristic
334C2#1684039211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#387C2
socleC23×C61C24
hypercenter#387D61
hypocenterC61#2331
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #14519776C4semidirect
89. C4×Dic61Q8semidirect
183. C61#2331semidirect