Finite Group Databasebeta

← #21458133

Subgroups — #21458133

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#16840467C211yesmaximal, characteristic, complemented
2#16840414C211yesmaximal, characteristic
3#16840111C211yesmaximal, characteristic, complemented
4#16840094C211yesmaximal, characteristic, complemented
5#16840051C211yesmaximal, characteristic, complemented
6#16840021C211yesmaximal, characteristic, complemented
7#16840018C211yesmaximal, characteristic, complemented
8#16839971C211yesmaximal, characteristic, complemented
9#16839927C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839849C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839761C211yesmaximal, characteristic, complemented
15C61×#483C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23#14519776C2211yescharacteristic
24#14519775C2211yescharacteristic
25#14519767—21no—
26#14519762—21no—
27#14519759—21no—
28#14519757C2211yescharacteristic
29#14519757C2211yescharacteristic
30#14519756—21no—
31#14519756C2211yescharacteristic
32#14519755—21no—
33#14519750—21no—
34#14519742C2211yescharacteristic
35#14519739C2211yescharacteristic
36C4×C22⋊D61—21no—
37C4×C22⋊D61C2211yescharacteristic
38C4⋊C4×D61—21no—
39C4⋊C4×D61C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54#106×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61D411yescharacteristic
64#11758226—22no—
65#11758226—41no—
66#11758222—22no—
67#11758222—41no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C2311yescharacteristic
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61D411yescharacteristic
88#11758202—41no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198D411yescharacteristic
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105#11758194—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108Dic244—41no—
109#11758190—22no—
110#11758189—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61—21no—
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×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—81no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—22no—
126C22⋊D61—42no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—42no—
135D244#4112yes—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—42no—
139C4×D61—42no—
140C4×D61—42no—
141C4×D61—81no—
142Dic122—21no—
143Dic122—21no—
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#483D6111yescharacteristic, complemented
186#476—611no—
187#470—611no—
188#470—611no—
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×Q16—611no—
201C2×SD16—611no—
202C2×M16—611no—
203C2×M16—611no—
204C4⋊Q8—611no—
205C4⋊Q8—611no—
206#125—1221no—
207#123—1221no—
208#123—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—611no—
212C22⋊Q8—1221no—
213C22⋊Q8—1221no—
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—1221no—
222C2×C4⋊C4C2×D6111yescharacteristic
223#106—611no—
224#106C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
239C4×C8—611no—
240#41—1222no—
241#41—1222no—
242#41—2441no—
243#41—2441no—
244C2×Q8—611no—
245C2×Q8—611no—
246C2×Q8—1221no—
247C2×Q8C22×D6111yescharacteristic
248C2×D4—611no—
249C2×D4—611no—
250C2×D4—1221no—
251C2×D4—1221no—
252C22×C4—21no—
253C22×C4—611no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C22×D6111yescharacteristic
259Q16—2441no—
260Q16—2441no—
261SD16—1222no—
262M16—2441no—
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—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4C22×D6111yescharacteristic
281C4⋊C4C22×D6111yescharacteristic
282C4⋊C4C22×D6111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—611no—
285C22⋊C4—611no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C42—611no—
291C42—1221no—
292C23—611no—
293C23—1221no—
294C23D4×D6111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—1221no—
298Q8—1221no—
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—81no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
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#1451982311yescharacteristic
355C2—41no—
356C2—2441no—
357C2—2442no—
358C2#1684040411yescharacteristic
359C2#137×D6111yescharacteristic
360C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#483C2
socleC22×C61C22×D4
hypercenter#483D61
hypocenterC61#3331
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #16840467C2semidirect
3. #16840111C2semidirect
4. #16840094C2semidirect
5. #16840051C2semidirect
6. #16840021C2semidirect
7. #16840018C2semidirect
8. #16839971C2semidirect
9. #16839927C2semidirect
10. #16839926C2semidirect
11. #16839849C2semidirect
12. #16839837C2semidirect
13. #16839762C2semidirect
14. #16839761C2semidirect
15. C61×#483C2semidirect
185. #483D61semidirect
196. C61#3331semidirect