Finite Group Databasebeta

← #21450014

Subgroups — #21450014

Order 7808.

540 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×#14519755C211yesmaximal, characteristic, complemented
2#16839700C211yesmaximal, characteristic, complemented
3#16839688C211yesmaximal, characteristic, complemented
4#16839678C211yesmaximal, characteristic
5#16839674C211yesmaximal, characteristic, complemented
6#16839668C211yesmaximal, characteristic, complemented
7#16839656C211yesmaximal, characteristic, complemented
8#16839653C211yesmaximal, characteristic, complemented
9#16839648C211yesmaximal, characteristic, complemented
10#16839646C211yesmaximal, characteristic, complemented
11#16839641C211yesmaximal, characteristic
12#16839638C211yesmaximal, characteristic
13#16839635C211yesmaximal, characteristic, complemented
14C4×#11758198C211yesmaximal, characteristic, complemented
15C2×#117×C61C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19#14519755—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
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
45C23×C4×C61C2211yescharacteristic
46#117×C61—24no—
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C42×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C23×D61C2311yescharacteristic
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—22no—
65C2×C22⋊D61—22no—
66C2×C22⋊D61—41no—
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—41no—
77C2×Dic122—22no—
78C2×Dic122—22no—
79C2×Dic122—41no—
80C4⋊C4×C61—22no—
81C4⋊C4×C61D414yescomplemented
82C22⋊C4×C61—22no—
83C22⋊C4×C61—22no—
84C42×C61—22no—
85C42×C61—22no—
86C22⋊Dic61—22no—
87C22⋊Dic61—22no—
88C22⋊Dic61—41no—
89#11758198—22no—
90#11758198—22no—
91#11758198—22no—
92#11758198—22no—
93#11758198—22no—
94C4⋊Dic61—41no—
95#11758196—22no—
96#11758196—22no—
97#11758196—22no—
98C4×Dic61—41no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61#4112yes—
106C23×C61C2411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61#4112yes—
114C2×C4×C61—28no—
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×C61—21no—
129C2×C4×C61C2×D412yes—
130C2×C4×C61C2×D412yes—
131C2×C4×C61C2×D412yes—
132C2×C4×C61#4112yes—
133C22⋊D61—44no—
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—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61#4112yes—
155C4×D61—44no—
156Dic122—44no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C22×C61C2×#4111yescharacteristic
166C22×C61C2×#4111yescharacteristic
167C22×C61C2×#4111yescharacteristic
168C22×C61C2×#4111yescharacteristic
169C22×C61H(5,𝔽2)11yescharacteristic
170C22×C612−1+411yescharacteristic
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—22no—
181C4×C61—22no—
182C4×C61—41no—
183C4×C61—41no—
184Dic61—22no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191#2477—611nomaximal, Sylow
192C2×C61—42no—
193C2×C61#52511yescharacteristic
194C2×C61#52911yescharacteristic
195C2×C61#54211yescharacteristic
196C2×C61#54611yescharacteristic
197C2×C61#54811yescharacteristic
198C2×C61#55111yescharacteristic
199C2×C61#55211yescharacteristic
200D61—42no—
201C2×C22⋊Q8—611no—
202C2×#117D6111yescharacteristic, complemented
203#400—611no—
204#397—611no—
205#394—611no—
206#393—611no—
207#391—611no—
208#388—611no—
209#388—611no—
210#387—611no—
211#387—611no—
212#386—611no—
213#386—611no—
214#385—611no—
215C4×C22⋊C4—611no—
216C61#247711yescharacteristic, complemented, Sylow
217C22×Q8—611no—
218C22×D4—611no—
219C23×C4—611no—
220C23×C4C2×D6111yescharacteristic
221C22⋊Q8—1224no—
222#117—24no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4C2×D6111yescharacteristic
228C2×C4⋊C4C2×D6111yescharacteristic
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4C2×D6111yescharacteristic
238C2×C22⋊C4C2×D6111yescharacteristic
239C2×C42—611no—
240C2×C42C2×D6111yescharacteristic
241C2×C42C2×D6111yescharacteristic
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#95—611no—
252#95—611no—
253#95—611no—
254C24—611no—
255C24C22×D6111yescharacteristic
256C2×Q8—1222no—
257C2×Q8—1222no—
258C2×Q8—2441no—
259C2×D4—1222no—
260C2×D4—1222no—
261C2×D4—2441no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1222no—
273C22×C4—1222no—
274C22×C4—2441no—
275C22×C4C22×D6111yescharacteristic
276C22×C4C22×D6111yescharacteristic
277C22×C4C22×D6111yescharacteristic
278C22×C4C22×D6111yescharacteristic
279C22×C4C22×D6111yescharacteristic
280C22×C4C22×D6111yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—1222no—
283C4⋊C4—1222no—
284C4⋊C4—1222no—
285C4⋊C4—2441no—
286C4⋊C4C22⋊D6114yescomplemented
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—1222no—
290C22⋊C4—1222no—
291C22⋊C4—1222no—
292C22⋊C4—1222no—
293C22⋊C4—1222no—
294C22⋊C4—1222no—
295C22⋊C4—1222no—
296C22⋊C4—2441no—
297C42—22no—
298C42—22no—
299C42—2441no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—612no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23—1221no—
313C23#1175822212yes—
314C23C23×D6111yescharacteristic
315Q8—2444no—
316D4—2444no—
317C2×C4—28no—
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—21no—
331C2×C4—21no—
332C2×C4—612no—
333C2×C4—1221no—
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—1221no—
352C2×C4—1221no—
353C2×C4—2444no—
354C2×C4#1175822212yes—
355C2×C4C2×C22⋊D6112yes—
356C2×C4C2×C22⋊D6112yes—
357C2×C4C2×C22⋊D6112yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—1222no—
366C22—1222no—
367C22—1222no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22C22×C22⋊D6111yescharacteristic
373C22#41×D6111yescharacteristic
374C22#41×D6111yescharacteristic
375C22C2×#1175822211yescharacteristic
376C22C2×#1175822211yescharacteristic
377C22#1451982311yescharacteristic
378C22#1451982411yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—1222no—
386C4—2441no—
387C4—2441no—
388C4—2441no—
389C4—2441no—
390C4—2441no—
391C4—2441no—
392C2—42no—
393C2—2442no—
394C2#1684027311yescharacteristic
395C2#1684029011yescharacteristic
396C2#1684038311yescharacteristic
397C2#1684040011yescharacteristic
398C2#1684041911yescharacteristic
399C2#1684043611yescharacteristic
400C2#1684044511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#117×C61C2
hypercenterC2×#117D61
hypocenterC61#2477
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
2. #16839700C2semidirect
3. #16839688C2semidirect
5. #16839674C2semidirect
6. #16839668C2semidirect
7. #16839656C2semidirect
8. #16839653C2semidirect
9. #16839648C2semidirect
10. #16839646C2semidirect
13. #16839635C2semidirect
14. C4×#11758198C2semidirect
15. C2×#117×C61C2semidirect
81. C4⋊C4×C61D4semidirect
202. C2×#117D61semidirect
216. C61#2477semidirect
286. C4⋊C4C22⋊D61semidirect