Finite Group Databasebeta

← #21449151

Subgroups — #21449151

Order 7808.

864 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11758224C211yesmaximal, characteristic
2C2×#14519760C211yesmaximal, characteristic, complemented
3C22×#11758196C211yesmaximal, characteristic, complemented
4#16839682C212yesmaximal, complemented
5#16839677C212yesmaximal, complemented
6#16839642C211yesmaximal, characteristic, complemented
7#16839639C211yesmaximal, characteristic, complemented
8#16839634C212yesmaximal, complemented
9#16839633C212yesmaximal, complemented
10#16839623C211yesmaximal, characteristic, complemented
11C2×#123×C61C211yesmaximal, characteristic, complemented
12C2×#11758224—24no—
13C2×#11758224—24no—
14C2×#11758224—24no—
15C22×Dic122C2211yescharacteristic
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22#14519760—24no—
23C2×#11758196—24no—
24C2×#11758196C2212yes—
25C2×#11758196C2212yes—
26C2×#11758196C2212yes—
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2212yes—
29C2×#11758198C2212yes—
30C2×#11758198C2212yes—
31#14519684C2212yes—
32#14519684C2212yes—
33#14519684C2212yes—
34#14519684C2212yes—
35C22×D4×C61C2211yescharacteristic
36C23×C4×C61C2211yescharacteristic
37#123×C61—24no—
38C2×C4⋊C4×C61C2212yes—
39C2×C22⋊C4×C61C2211yescharacteristic
40C2×C22⋊C4×C61C2212yes—
41C24×C61C2311yescharacteristic
42C24×C61C2311yescharacteristic
43C23×D61C2311yescharacteristic
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61D414yes—
47C22×C4×C61—22no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61C2312yes—
51C22×C4×C61C2312yes—
52C22×C4×C61C2311yescharacteristic
53C2×C22⋊D61—22no—
54C2×C22⋊D61—22no—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—22no—
57C2×C22⋊D61—22no—
58C2×C22⋊D61D414yes—
59C22×Dic61—22no—
60C22×Dic61—22no—
61C22×Dic61—22no—
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—24no—
66C22×Dic61D414yes—
67C22×Dic61C2312yes—
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2312yes—
72#11758224—232no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×Dic122—22no—
77C2×Dic122—22no—
78C2×Dic122—22no—
79C4⋊C4×C61—24no—
80C22⋊C4×C61—22no—
81C22⋊C4×C61—24no—
82C22⋊Dic61—22no—
83C22⋊Dic61—24no—
84#11758198—24no—
85#11758198—24no—
86#11758196—24no—
87#11758196—24no—
88#11758196—24no—
89C23×C61—22no—
90C23×C61—22no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—22no—
94C23×C61—22no—
95C23×C61C2×D412yes—
96C23×C61C2×D412yes—
97C23×C61C2×D412yes—
98C23×C61C2×D412yes—
99C23×C61C2411yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—22no—
103C22×D61—22no—
104C22×D61C2×D412yes—
105D4×C61—28no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—44no—
115C2×C4×C61C2×D412yes—
116C22⋊D61—28no—
117C22⋊D61—28no—
118C2×Dic61—28no—
119C2×Dic61—28no—
120C2×Dic61—28no—
121C2×Dic61—22no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61C2×D412yes—
133C2×Dic61C2×D412yes—
134C2×Dic61C2×D412yes—
135C2×Dic61#4114yescomplemented
136C4×D61—28no—
137Dic122—28no—
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—24no—
141C22×C61—24no—
142C22×C61—22no—
143C22×C61—24no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—42no—
147C22×C61#12014yes—
148C22×C61C22×D411yescharacteristic
149C22×C61C22×D411yescharacteristic
150C22×C61C22×D411yescharacteristic
151C22×C61C2×#4112yes—
152C22×C612−1+412yes—
153C2×D61—22no—
154C2×D61—24no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—42no—
158C4×C61—22no—
159C4×C61—42no—
160C4×C61—42no—
161Dic61—22no—
162Dic61—22no—
163Dic61—22no—
164Dic61—24no—
165Dic61—42no—
166#2406—611nomaximal, Sylow
167C2×C61—24no—
168C2×C61—42no—
169C2×C61C2×#12011yescharacteristic
170C2×C61#52511yescharacteristic
171C2×C61#53611yescharacteristic
172C2×C61#54712yes—
173C2×C61#54712yes—
174D61—42no—
175C22×#41—611no—
176C2×#123—611no—
177C2×#123D6111yescharacteristic, complemented
178C22×C4⋊C4—611no—
179#395—612no—
180#394—612no—
181#386—611no—
182#386—611no—
183#385—612no—
184#385—612no—
185#381—611no—
186C61#240611yescharacteristic, complemented, Sylow
187C2×#41—1224no—
188C2×#41—1224no—
189C2×#41—1224no—
190C22×Q8—611no—
191C22×D4—611no—
192C22×D4—611no—
193C22×D4C2×D6111yescharacteristic
194C23×C4—611no—
195C23×C4—611no—
196C23×C4—611no—
197C23×C4—611no—
198C23×C4C2×D6111yescharacteristic
199#123—24no—
200#123—1224no—
201C2×C4⋊C4—612no—
202C2×C4⋊C4—612no—
203C2×C4⋊C4—612no—
204C2×C4⋊C4—1224no—
205C2×C4⋊C4C2×D6112yes—
206C2×C22⋊C4—611no—
207C2×C22⋊C4—612no—
208C2×C22⋊C4—612no—
209C2×C22⋊C4—612no—
210C2×C22⋊C4C2×D6111yescharacteristic
211C2×C22⋊C4C2×D6112yes—
212#95—612no—
213#95—612no—
214#95—612no—
215#95—612no—
216C24—611no—
217C24C22×D6111yescharacteristic
218C24C22×D6111yescharacteristic
219#41—12232no—
220C2×Q8—1222no—
221C2×Q8—1222no—
222C2×Q8—1222no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—614no—
226C2×D4—1222no—
227C2×D4—1222no—
228C2×D4—1222no—
229C2×D4—1222no—
230C2×D4—1222no—
231C2×D4C22⋊D6114yes—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—614no—
236C22×C4—612no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—612no—
241C22×C4—1222no—
242C22×C4—1222no—
243C22×C4—1222no—
244C22×C4—1222no—
245C22×C4—1224no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4C22×D6112yes—
252C22×C4C22×D6112yes—
253C22×C4C22×D6111yescharacteristic
254C4⋊C4—24no—
255C4⋊C4—1224no—
256C4⋊C4—1224no—
257C4⋊C4—1224no—
258C22⋊C4—22no—
259C22⋊C4—24no—
260C22⋊C4—1224no—
261C22⋊C4—1224no—
262C22⋊C4—1224no—
263C22⋊C4—1222no—
264C23—22no—
265C23—22no—
266C23—21no—
267C23—21no—
268C23—22no—
269C23—22no—
270C23—612no—
271C23—1221no—
272C23—1221no—
273C23—1222no—
274C23—1222no—
275C23D4×D6112yes—
276C23D4×D6112yes—
277C23C2×C22⋊D6112yes—
278C23C2×C22⋊D6112yes—
279C23C23×D6111yescharacteristic
280Q8—1228no—
281D4—28no—
282D4—1228no—
283D4—1228no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—44no—
293C2×C4—612no—
294C2×C4—612no—
295C2×C4—612no—
296C2×C4—614no—
297C2×C4—1228no—
298C2×C4—1228no—
299C2×C4—1228no—
300C2×C4—1222no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1222no—
308C2×C4—1228no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—1222no—
312C2×C4C2×C22⋊D6112yes—
313C22—22no—
314C22—22no—
315C22—24no—
316C22—24no—
317C22—22no—
318C22—24no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—1222no—
323C22—1224no—
324C22—2441no—
325C22—2441no—
326C22—2442no—
327C22#1451974514yes—
328C22C2×D4×D6111yescharacteristic
329C22C2×D4×D6111yescharacteristic
330C22C22×C22⋊D6111yescharacteristic
331C22#41×D6112yes—
332C22#1451982412yes—
333C4—22no—
334C4—42no—
335C4—42no—
336C4—1222no—
337C4—1222no—
338C4—1222no—
339C4—1224no—
340C4—2442no—
341C2—24no—
342C2—42no—
343C2—2442no—
344C2C2×#1451974511yescharacteristic
345C2#1684027011yescharacteristic
346C2#1684033411yescharacteristic
347C2#1684041012yes—
348C2#1684041112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#123×C61C2
hypercenterC2×#123D61
hypocenterC61#2406
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#14519760C2semidirect
3. C22×#11758196C2semidirect
4. #16839682C2semidirect
5. #16839677C2semidirect
6. #16839642C2semidirect
7. #16839639C2semidirect
8. #16839634C2semidirect
9. #16839633C2semidirect
10. #16839623C2semidirect
11. C2×#123×C61C2semidirect
135. C2×Dic61#41semidirect
177. C2×#123D61semidirect
186. C61#2406semidirect