Finite Group Databasebeta

← #21458130

Subgroups — #21458130

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840470C211yesmaximal, characteristic, complemented
2#16840414C211yesmaximal, characteristic
3#16840111C211yesmaximal, characteristic, complemented
4#16840094C211yesmaximal, characteristic, complemented
5#16840090C211yesmaximal, characteristic, complemented
6#16840051C211yesmaximal, characteristic, complemented
7#16840019C211yesmaximal, characteristic, complemented
8#16839970C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839922C211yesmaximal, characteristic, complemented
11#16839847C211yesmaximal, characteristic, complemented
12#16839838C211yesmaximal, characteristic, complemented
13#16839764C211yesmaximal, characteristic, complemented
14#16839762C211yesmaximal, characteristic, complemented
15C61×#470C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519775C2211yescharacteristic
23#14519767—21no—
24#14519762—21no—
25#14519759—21no—
26#14519757—21no—
27#14519757C2211yescharacteristic
28#14519754—21no—
29#14519753C2211yescharacteristic
30#14519750—21no—
31Q8×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34#14519737—21no—
35C2×C4⋊Dic61C2211yescharacteristic
36C4⋊C4×D61—21no—
37C4⋊C4×D61C2211yescharacteristic
38#14519708C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61D411yescharacteristic
64C22×Dic61—21no—
65#11758226—22no—
66#11758226—41no—
67#11758222—22no—
68#11758222—41no—
69C2×D244—21no—
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78Q16×C61—41no—
79M16×C61—41no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C22⋊Dic61D411yescharacteristic
89#11758202—41no—
90#11758201—22no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198D411yescharacteristic
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196D411yescharacteristic
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61—21no—
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×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×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—22no—
127C22⋊D61—42no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—81no—
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—21no—
136D244—42no—
137D244#4112yes—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—42no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61—81no—
144Dic122—21no—
145Dic122—21no—
146Dic122—81no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61C22×D411yescharacteristic
155C2×D61—21no—
156C2×D61—22no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61H(5,𝔽2)11yescharacteristic
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61#13712yes—
174#3331—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61#54611yescharacteristic
177C2×C61C2×#13711yescharacteristic
178C2×C61#57711yescharacteristic
179D61—41no—
180D61—42no—
181#554—611no—
182#547—611no—
183#487—611no—
184#483—611no—
185#483—611no—
186#476—611no—
187#470—611no—
188#470D6111yescharacteristic, complemented
189#462—611no—
190#452—611no—
191#452—611no—
192C4×SD16—611no—
193#436—611no—
194#417—611no—
195#417—611no—
196C61#333111yescharacteristic, complemented, Sylow
197C2×#41—611no—
198C2×#41—611no—
199C2×Q16—611no—
200C2×Q16C2×D6111yescharacteristic
201C2×SD16—611no—
202C2×M16—611no—
203C2×M16C2×D6111yescharacteristic
204C4⋊Q8—611no—
205C4⋊Q8—611no—
206#125—1221no—
207#123—1221no—
208#123—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212C22⋊Q8—1221no—
213C22⋊Q8C2×D6111yescharacteristic
214C22⋊Q8C2×D6111yescharacteristic
215#121—1221no—
216C4×Q8—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—1221no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223#106—611no—
224#106—611no—
225#106C2×D6111yescharacteristic
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103C2×D6111yescharacteristic
233#103C2×D6111yescharacteristic
234#102—611no—
235#102—611no—
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8—611no—
239C4×C8—611no—
240#41—1222no—
241#41—1222no—
242#41—2441no—
243#41—2441no—
244C2×Q8—611no—
245C2×Q8—1221no—
246C2×Q8C22×D6111yescharacteristic
247C2×Q8C22×D6111yescharacteristic
248C2×D4—611no—
249C2×D4—611no—
250C2×D4—1221no—
251C2×D4—1221no—
252C22×C4—611no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C22×D6111yescharacteristic
259Q16—41no—
260Q16—2441no—
261SD16—1222no—
262M16—41no—
263M16—2441no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—611no—
271C4⋊C4—611no—
272C4⋊C4—611no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4C22×D6111yescharacteristic
282C4⋊C4C22×D6111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—611no—
286C22⋊C4—611no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C42—611no—
291C42—1221no—
292C23—611no—
293C23—1221no—
294C23D4×D6111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—1221no—
300Q8—1221no—
301Q8—4881no—
302D4—612no—
303D4—1222no—
304D4—1221no—
305D4—2442no—
306D4—2442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4D4×D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—1221no—
336C22—1221no—
337C22—1221no—
338C22—1222no—
339C22—2441no—
340C22—2441no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—612no—
348C4—1221no—
349C4—1221no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4#41×D6111yescharacteristic
354C4#1451982211yescharacteristic
355C2—41no—
356C2—2441no—
357C2—2442no—
358C2#1684040111yescharacteristic
359C2#137×D6111yescharacteristic
360C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3331
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #16840470C2semidirect
3. #16840111C2semidirect
4. #16840094C2semidirect
5. #16840090C2semidirect
6. #16840051C2semidirect
7. #16840019C2semidirect
8. #16839970C2semidirect
9. #16839923C2semidirect
10. #16839922C2semidirect
11. #16839847C2semidirect
12. #16839838C2semidirect
13. #16839764C2semidirect
14. #16839762C2semidirect
15. C61×#470C2semidirect
188. #470D61semidirect
196. C61#3331semidirect