Finite Group Databasebeta

← #21457922

Subgroups — #21457922

Order 7808.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840453C211yesmaximal, characteristic, complemented
2#16840415C211yesmaximal, characteristic
3#16840130C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840096C211yesmaximal, characteristic, complemented
6#16840063C211yesmaximal, characteristic, complemented
7#16840017C211yesmaximal, characteristic, complemented
8#16840000C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12#16839832C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839757C211yesmaximal, characteristic, complemented
15C61×#462C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519771—21no—
22#14519769C2211yescharacteristic
23#14519767—21no—
24#14519762—21no—
25#14519762—21no—
26#14519762—21no—
27#14519753C2211yescharacteristic
28#14519753C2211yescharacteristic
29#14519753C2211yescharacteristic
30#14519753C2211yescharacteristic
31#14519752—21no—
32C4×D244C2211yescharacteristic
33C4×D244C2211yescharacteristic
34#14519735C2211yescharacteristic
35#14519734—21no—
36C4⋊C4×D61—21no—
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519701C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C4⋊Q8×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62#11758226—22no—
63#11758226—22no—
64#11758226—41no—
65#11758226—41no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244D411yescharacteristic
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61C2311yescharacteristic
75C2×C4×D61C2311yescharacteristic
76Q16×C61—41no—
77Q16×C61—41no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C42×C61—21no—
85C42×C61C2311yescharacteristic
86#11758201—22no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94#11758198D411yescharacteristic
95C4⋊Dic61D411yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758189—41no—
110C8×D61—41no—
111C22×D61—21no—
112C22×D61C2×D411yescharacteristic
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—21no—
133D244—41no—
134D244—42no—
135D244—42no—
136D244#4112yes—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—42no—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61C22×D411yescharacteristic
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—22no—
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61C2×#4111yescharacteristic
166C4×C61H(5,𝔽2)11yescharacteristic
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3315—611nomaximal, Sylow
173C2×C61#54611yescharacteristic
174C2×C61#57511yescharacteristic
175C2×C61#57811yescharacteristic
176D61—41no—
177D61—41no—
178D61—42no—
179#552—611no—
180#547—611no—
181#491—611no—
182#485—611no—
183#484—611no—
184#478—611no—
185#470—611no—
186#467—611no—
187#462D6111yescharacteristic, complemented
188#452—611no—
189#452—611no—
190#440—611no—
191#435—611no—
192#417—611no—
193#416—611no—
194C61#331511yescharacteristic, complemented, Sylow
195C2×#41—611no—
196C2×#41—611no—
197C2×Q16C2×D6111yescharacteristic
198C2×Q16C2×D6111yescharacteristic
199C2×SD16—611no—
200C2×M16—611no—
201C22×C8—611no—
202C4⋊Q8C2×D6111yescharacteristic
203#126—1221no—
204#125—611no—
205#125—1221no—
206#123—1221no—
207#123—1221no—
208#123—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—611no—
212C22⋊Q8—611no—
213#121—1221no—
214C4×Q8C2×D6111yescharacteristic
215C4×D4—611no—
216C4×D4—611no—
217#117—611no—
218#117—1221no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221#107—611no—
222#107—611no—
223#106—611no—
224C4⋊C8C2×D6111yescharacteristic
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103C2×D6111yescharacteristic
231#103C2×D6111yescharacteristic
232#102—611no—
233#102—611no—
234#102—611no—
235C22⋊C8—611no—
236C22⋊C8—611no—
237#97—611no—
238#41—1222no—
239#41—1222no—
240#41—2441no—
241#41—2441no—
242C2×Q8C22×D6111yescharacteristic
243C2×Q8C22×D6111yescharacteristic
244C2×Q8C22×D6111yescharacteristic
245C2×D4—611no—
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1221no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255Q16—41no—
256Q16—41no—
257SD16—1222no—
258M16—2441no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—2441no—
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4C22×D6111yescharacteristic
279C22⋊C4—611no—
280C22⋊C4—611no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C42—21no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—611no—
291C23—611no—
292C23—1221no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299D4—612no—
300D4—1221no—
301D4—2441no—
302D4—2442no—
303D4—2442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4D4×D6111yescharacteristic
322C2×C4D4×D6111yescharacteristic
323C2×C4C23×D6111yescharacteristic
324C8—21no—
325C8—21no—
326C8—1221no—
327C8—1221no—
328C22—1221no—
329C22—1221no—
330C22—1221no—
331C22—1221no—
332C22—1221no—
333C22—1221no—
334C22—1222no—
335C22—2441no—
336C22—2441no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—1221no—
345C4—1221no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4#41×D6111yescharacteristic
350C4#1451982211yescharacteristic
351C2—2441no—
352C2—2441no—
353C2—2442no—
354C2#1684040911yescharacteristic
355C2#1684056111yescharacteristic
356C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3315
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #16840453C2semidirect
3. #16840130C2semidirect
4. #16840101C2semidirect
5. #16840096C2semidirect
6. #16840063C2semidirect
7. #16840017C2semidirect
8. #16840000C2semidirect
9. #16839923C2semidirect
10. #16839923C2semidirect
11. #16839860C2semidirect
12. #16839832C2semidirect
13. #16839762C2semidirect
14. #16839757C2semidirect
15. C61×#462C2semidirect
187. #462D61semidirect
194. C61#3315semidirect