Finite Group Databasebeta

← #21448754

Subgroups — #21448754

Order 7808.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519737C211yesmaximal, characteristic
2#16839655C211yesmaximal, characteristic, complemented
3#16839649C211yesmaximal, characteristic, complemented
4#16839643C211yesmaximal, characteristic, complemented
5#16839638C211yesmaximal, characteristic
6#16839638C211yesmaximal, characteristic
7#16839629C211yesmaximal, characteristic, complemented
8#16839623C211yesmaximal, characteristic, complemented
9#16839619C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
11C4×#11758198C211yesmaximal, characteristic, complemented
12#16839609C211yesmaximal, characteristic, complemented
13#16839608C211yesmaximal, characteristic, complemented
14#95×D61C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519737C418yescomplemented
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
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×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C42×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52C24×C61C2311yescharacteristic
53C23×D61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C2×C22⋊D61—22no—
61C2×C22⋊D61—22no—
62C2×C22⋊D61C2×C414yes—
63C22×Dic61—41no—
64C22×Dic61—41no—
65C22×Dic61C2×C414yescomplemented
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61C2×C414yes—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—22no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61C2×C414yescomplemented
86C42×C61—22no—
87C22⋊Dic61—22no—
88C22⋊Dic61—41no—
89#11758198—22no—
90#11758198—22no—
91#11758198C2×C414yes—
92C4⋊Dic61—41no—
93#11758196C2×C414yescomplemented
94C4×Dic61—22no—
95C4×Dic61—41no—
96C4×Dic61—41no—
97C4×Dic61C2×C414yescomplemented
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61C22×C412yes—
105C23×C61C2411yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61C22×C412yes—
111C22×D61#4112yes—
112C22×D61#4112yes—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C22×C412yes—
129C2×C4×C61C22×C412yes—
130C2×C4×C61#4112yes—
131C22⋊D61—28no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—44no—
150C2×Dic61C22×C412yes—
151C2×Dic61C22×C412yes—
152C2×Dic61C22×C412yes—
153C2×Dic61#4112yes—
154C4×D61—44no—
155C4×D61—44no—
156C4×D61—44no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C23×C411yescharacteristic
165C22×C61C2×#4111yescharacteristic
166C22×C61C2×#4111yescharacteristic
167C22×C61C2×#4111yescharacteristic
168C22×C61C2×#4111yescharacteristic
169C22×C61H(5,𝔽2)11yescharacteristic
170C22×C61H(5,𝔽2)11yescharacteristic
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61#11714yes—
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—22no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184Dic61—22no—
185Dic61—22no—
186Dic61—22no—
187Dic61—22no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191#2353—611nomaximal, Sylow
192C2×C61—42no—
193C2×C61C2×#11711yescharacteristic
194C2×C61C4×#4111yescharacteristic
195C2×C61#51811yescharacteristic
196C2×C61#55111yescharacteristic
197C2×C61#55111yescharacteristic
198C2×C61#55311yescharacteristic
199C2×C61#55311yescharacteristic
200D61—24no—
201C2×C4×D4—611no—
202#388—611no—
203#388D6111yescharacteristic, complemented
204#387—611no—
205#387—611no—
206#386—611no—
207#386—611no—
208#383—611no—
209#381—611no—
210#380—611no—
211C4×C22⋊C4—611no—
212C4×C22⋊C4—611no—
213C4×C22⋊C4—611no—
214#376—611no—
215C2×#95—611no—
216C61#235311yescharacteristic, complemented, Sylow
217C22×D4—611no—
218C23×C4—611no—
219C23×C4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C4×D4—618no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4C2×D6111yescharacteristic
226C2×C22⋊C4—611no—
227C2×C22⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4C2×D6111yescharacteristic
232C2×C22⋊C4C2×D6111yescharacteristic
233C2×C22⋊C4C2×D6111yescharacteristic
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42C2×D6111yescharacteristic
239#95—611no—
240#95—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95—611no—
246#95—611no—
247#95—611no—
248#95—611no—
249#95—611no—
250#95—611no—
251#95C2×D6111yescharacteristic
252#95C2×D6111yescharacteristic
253C24—611no—
254C24C22×D6111yescharacteristic
255C2×D4—614no—
256C2×D4—1222no—
257C2×D4—1222no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—614no—
263C22×C4—614no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1222no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4C22×D6111yescharacteristic
278C22×C4C22×D6111yescharacteristic
279C22×C4C22×D6111yescharacteristic
280C22×C4C22×D6111yescharacteristic
281C22×C4C22×D6111yescharacteristic
282C22×C4C22×D6111yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—614no—
285C4⋊C4—2441no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—614no—
289C22⋊C4—1222no—
290C22⋊C4—1222no—
291C22⋊C4—1222no—
292C22⋊C4—2441no—
293C22⋊C4C4×D6114yescomplemented
294C42—22no—
295C42—614no—
296C42—1222no—
297C42—2441no—
298C42—2441no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—612no—
306C23—612no—
307C23—612no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23C2×C4×D6112yes—
313C23C23×D6111yescharacteristic
314D4—1228no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—612no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—612no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—2444no—
352C2×C4—2444no—
353C2×C4—2444no—
354C2×C4—2444no—
355C2×C4C2×C4×D6112yes—
356C2×C4C2×C4×D6112yes—
357C2×C4#1175822412yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—614no—
366C22—1222no—
367C22—1222no—
368C22—1222no—
369C22—1222no—
370C22—1222no—
371C22—1222no—
372C22C22×C4×D6111yescharacteristic
373C22#41×D6111yescharacteristic
374C22#41×D6111yescharacteristic
375C22#41×D6111yescharacteristic
376C22C2×#1175822411yescharacteristic
377C22#1451982211yescharacteristic
378C22#1451982311yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—1222no—
386C4—1222no—
387C4—1222no—
388C4—1222no—
389C4—2441no—
390C4—2441no—
391C4—2441no—
392C2—42no—
393C2—1224no—
394C2#117×D6111yescharacteristic
395C2C4×#1175822411yescharacteristic
396C2#1684023411yescharacteristic
397C2#1684043511yescharacteristic
398C2#1684044211yescharacteristic
399C2#1684045911yescharacteristic
400C2#1684046311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#388C2
socleC23×C61C24
hypercenter#388D61
hypocenterC61#2353
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #16839655C2semidirect
3. #16839649C2semidirect
4. #16839643C2semidirect
7. #16839629C2semidirect
8. #16839623C2semidirect
9. #16839619C2semidirect
10. C22⋊C4×Dic61C2semidirect
11. C4×#11758198C2semidirect
12. #16839609C2semidirect
13. #16839608C2semidirect
14. #95×D61C2semidirect
15. C61×#388C2semidirect
21. #14519737C4semidirect
65. C22×Dic61C2×C4semidirect
85. C22⋊C4×C61C2×C4semidirect
93. #11758196C2×C4semidirect
97. C4×Dic61C2×C4semidirect
203. #388D61semidirect
216. C61#2353semidirect
293. C22⋊C4C4×D61semidirect