Finite Group Databasebeta

← #21452597

Subgroups — #21452597

Order 7808.

432 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519776C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic
3#16839704C211yesmaximal, characteristic
4#16839701C211yesmaximal, characteristic
5#16839696C211yesmaximal, characteristic
6#16839695C211yesmaximal, characteristic
7#16839682C211yesmaximal, characteristic
8#16839682C211yesmaximal, characteristic
9#16839668C211yesmaximal, characteristic
10#16839666C211yesmaximal, characteristic
11#16839649C211yesmaximal, characteristic
12#16839648C211yesmaximal, characteristic
13#16839648C211yesmaximal, characteristic
14#16839646C211yesmaximal, characteristic
15C61×#389C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18#14519776—24no—
19#14519768—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32#14519684C2211yescharacteristic
33#14519684C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C42×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C2×Dic122—22no—
69C2×Dic122—22no—
70C2×Dic122—22no—
71C2×Dic122—22no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C4⋊C4×C61—22no—
75C4⋊C4×C61—22no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61Q814yescomplemented
78C42×C61—41no—
79C4⋊Dic61—22no—
80C4⋊Dic61—22no—
81C4⋊Dic61—22no—
82C4⋊Dic61—22no—
83#11758196—22no—
84#11758196—22no—
85#11758196—22no—
86#11758196—41no—
87#11758196—41no—
88#11758196D414yes—
89C4×Dic61—22no—
90C4×Dic61—22no—
91C23×C61C2411yescharacteristic
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×C61—21no—
109C2×C4×C61C2×D412yes—
110C2×C4×C61C2×Q812yes—
111C2×C4×C61C2×Q812yes—
112C2×C4×C61C2×Q812yes—
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×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61C2×D412yes—
135C2×Dic61C2×D412yes—
136C2×Dic61#4112yes—
137Dic122—44no—
138Dic122—44no—
139C22×C61C22×D411yescharacteristic
140C22×C61C22×Q811yescharacteristic
141C22×C61C2×#4111yescharacteristic
142C22×C61H(5,𝔽2)11yescharacteristic
143C22×C612−1+411yescharacteristic
144C22×C612−1+411yescharacteristic
145C22×C612−1+411yescharacteristic
146C4×C61—22no—
147C4×C61—22no—
148C4×C61—22no—
149C4×C61—22no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—41no—
153Dic61—22no—
154Dic61—22no—
155Dic61—22no—
156Dic61—41no—
157Dic61—41no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161#2713—611nomaximal, Sylow
162C2×C61#53611yescharacteristic
163C2×C61#54111yescharacteristic
164C2×C61#54411yescharacteristic
165C2×C61#54611yescharacteristic
166C2×C61D4×Q811yescharacteristic
167C2×C61#55711yescharacteristic
168C2×C61#56311yescharacteristic
169C2×C4⋊Q8—611no—
170C2×#125—611no—
171#400—611no—
172#400—611no—
173#398—611no—
174#398—611no—
175#395—611no—
176#395—611no—
177#391—611no—
178#391—611no—
179#389D6111yescharacteristic
180#387—611no—
181#387—611no—
182#387—611no—
183#387—611no—
184C61#271311yescharacteristic, complemented, Sylow
185C22×Q8—611no—
186C22×Q8—611no—
187C4⋊Q8—1224no—
188#125—1224no—
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⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4C2×D6111yescharacteristic
200C2×C4⋊C4C2×D6111yescharacteristic
201C2×C4⋊C4C2×D6111yescharacteristic
202C2×C4⋊C4C2×D6111yescharacteristic
203C2×C42—611no—
204C2×C42—611no—
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#95—611no—
217#95—611no—
218#95—611no—
219#95—611no—
220#95C2×D6111yescharacteristic
221#95C2×D6111yescharacteristic
222C2×Q8—1222no—
223C2×Q8—1222no—
224C2×Q8—1222no—
225C2×Q8—1222no—
226C2×Q8—2441no—
227C2×Q8—2441no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4C22×D6111yescharacteristic
237C22×C4C22×D6111yescharacteristic
238C22×C4C22×D6111yescharacteristic
239C22×C4C22×D6111yescharacteristic
240C22×C4C22×D6111yescharacteristic
241C22×C4C22×D6111yescharacteristic
242C22×C4C22×D6111yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—614no—
247C4⋊C4—1222no—
248C4⋊C4—1222no—
249C4⋊C4—1222no—
250C4⋊C4—1222no—
251C4⋊C4—1222no—
252C4⋊C4—1222no—
253C4⋊C4—1222no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4Dic12214yescomplemented
257C42—41no—
258C42—1222no—
259C42—1222no—
260C23C23×D6111yescharacteristic
261Q8—2444no—
262Q8—2444no—
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—21no—
279C2×C4—21no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—612no—
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×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4C2×Dic12212yes—
305C2×C4C2×Dic12212yes—
306C2×C4C2×Dic12212yes—
307C2×C4D4×D6112yes—
308C22C2×D4×D6111yescharacteristic
309C22C22×Dic12211yescharacteristic
310C22#41×D6111yescharacteristic
311C22#1451982211yescharacteristic
312C22#1451982411yescharacteristic
313C22#1451982511yescharacteristic
314C22#1451982511yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—1222no—
323C4—1222no—
324C4—1222no—
325C4—2441no—
326C4—2441no—
327C4—2441no—
328C4—2441no—
329C4—2441no—
330C2#1684033711yescharacteristic
331C2#1684037111yescharacteristic
332C2#1684039311yescharacteristic
333C2#1684040111yescharacteristic
334C2D4×Dic12211yescharacteristic
335C2#1684048811yescharacteristic
336C2#1684051311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2713
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
77. C4⋊C4×C61Q8semidirect
184. C61#2713semidirect
256. C4⋊C4Dic122semidirect