Finite Group Databasebeta

← #21448916

Subgroups — #21448916

Order 7808.

464 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519767C211yesmaximal, characteristic
2#16839660C211yesmaximal, characteristic
3#16839659C211yesmaximal, characteristic
4#16839657C211yesmaximal, characteristic
5#16839657C211yesmaximal, characteristic
6#16839648C211yesmaximal, characteristic
7#16839647C211yesmaximal, characteristic
8#16839646C211yesmaximal, characteristic
9#16839646C211yesmaximal, characteristic
10C4×#11758196C211yesmaximal, characteristic
11C4×#11758196C211yesmaximal, characteristic
12C4×#11758196C211yesmaximal, characteristic
13#16839613C211yesmaximal, characteristic
14#16839613C211yesmaximal, characteristic
15C4×C4⋊C4×C61C211yesmaximal, characteristic
16#14519767C418yescomplemented
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
33C2×C4×Dic61C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
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
48C2×C42×C61C2211yescharacteristic
49C2×C42×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
67C4⋊C4×C61—22no—
68C4⋊C4×C61C2×C414yes—
69C42×C61—22no—
70C42×C61—41no—
71C42×C61—41no—
72C4⋊Dic61—41no—
73C4⋊Dic61C2×C414yes—
74#11758196—22no—
75#11758196—22no—
76#11758196—22no—
77#11758196—22no—
78#11758196—41no—
79#11758196C2×C414yes—
80#11758196C2×C414yes—
81#11758196C2×C414yes—
82#11758196C2×C414yes—
83#11758196Q814yes—
84C4×Dic61—22no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C4×Dic61C2×C414yes—
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×C61C22×C412yes—
107C2×C4×C61C22×C412yes—
108C2×C4×C61C22×C412yes—
109C2×C4×C61C2×Q812yes—
110C2×C4×C61#4112yes—
111C2×C4×C61#4112yes—
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—
136C22×C61C23×C411yescharacteristic
137C22×C61C22×Q811yescharacteristic
138C22×C61C2×#4111yescharacteristic
139C22×C61C2×#4111yescharacteristic
140C22×C61C2×#4111yescharacteristic
141C22×C61H(5,𝔽2)11yescharacteristic
142C22×C612−1+411yescharacteristic
143C4×C61—22no—
144C4×C61—22no—
145C4×C61—22no—
146C4×C61—22no—
147C4×C61—22no—
148C4×C61—22no—
149C4×C61—41no—
150Dic61—22no—
151Dic61—22no—
152Dic61—22no—
153Dic61—22no—
154Dic61—41no—
155Dic61—41no—
156Dic61—41no—
157Dic61C4×Q814yes—
158#2370—611nomaximal, Sylow
159C2×C61C2×C4×Q811yescharacteristic
160C2×C61C4×#4111yescharacteristic
161C2×C61#52011yescharacteristic
162C2×C61#55211yescharacteristic
163C2×C61#55311yescharacteristic
164C2×C61#55411yescharacteristic
165C2×C61#55711yescharacteristic
166C2×#125—611no—
167#389—611no—
168#389—611no—
169#389—611no—
170#389—611no—
171#387—611no—
172#387—611no—
173#387—611no—
174#387—611no—
175C4×C4⋊C4—611no—
176C4×C4⋊C4—611no—
177C4×C4⋊C4—611no—
178C4×C4⋊C4—611no—
179C4×C4⋊C4—611no—
180C4×C4⋊C4D6111yescharacteristic
181C61#237011yescharacteristic, complemented, Sylow
182#125—618no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—611no—
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
204C2×C42C2×D6111yescharacteristic
205C2×C42C2×D6111yescharacteristic
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
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4C22×D6111yescharacteristic
227C22×C4C22×D6111yescharacteristic
228C22×C4C22×D6111yescharacteristic
229C22×C4C22×D6111yescharacteristic
230C22×C4C22×D6111yescharacteristic
231C22×C4C22×D6111yescharacteristic
232C22×C4C22×D6111yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—614no—
235C4⋊C4—614no—
236C4⋊C4—614no—
237C4⋊C4—614no—
238C4⋊C4—614no—
239C4⋊C4—614no—
240C4⋊C4—1222no—
241C4⋊C4—1222no—
242C4⋊C4—1222no—
243C4⋊C4—1222no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4C4×D6114yes—
247C42—22no—
248C42—41no—
249C42—41no—
250C42—614no—
251C42—1222no—
252C42—1222no—
253C42—1222no—
254C42—2441no—
255C42—2441no—
256C23C23×D6111yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
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—612no—
273C2×C4—612no—
274C2×C4—612no—
275C2×C4—612no—
276C2×C4—612no—
277C2×C4—612no—
278C2×C4—612no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
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×C4C2×C4×D6112yes—
297C2×C4C2×C4×D6112yes—
298C2×C4C2×C4×D6112yes—
299C2×C4#1175822212yes—
300C2×C4#1175822212yes—
301C2×C4Q8×D6112yes—
302C22C22×C4×D6111yescharacteristic
303C22C2×Q8×D6111yescharacteristic
304C22#41×D6111yescharacteristic
305C22C2×#1175822211yescharacteristic
306C22C2×#1175822211yescharacteristic
307C22#1451982211yescharacteristic
308C22#1451982411yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—614no—
317C4—1222no—
318C4—1222no—
319C4—1222no—
320C4—1222no—
321C4—2441no—
322C4—2441no—
323C4—2441no—
324C2C4×Q8×D6111yescharacteristic
325C2C4×#1175822211yescharacteristic
326C2#1684024111yescharacteristic
327C2#1684044511yescharacteristic
328C2#1684046111yescharacteristic
329C2#1684046711yescharacteristic
330C2#1684049011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC4×C4⋊C4×C61C2
socleC23×C61C24
hypercenterC4×C4⋊C4D61
hypocenterC61#2370
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #14519767C4semidirect
181. C61#2370semidirect