Finite Group Databasebeta

← #21458777

Subgroups — #21458777

Order 7808.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840471C211yesmaximal, characteristic, complemented
2#16840468C211yesmaximal, characteristic, complemented
3#16840170C211yesmaximal, characteristic, complemented
4#16840169C211yesmaximal, characteristic, complemented
5#16840161C211yesmaximal, characteristic, complemented
6#16840064C211yesmaximal, characteristic, complemented
7#16840063C211yesmaximal, characteristic, complemented
8#16840061C211yesmaximal, characteristic, complemented
9#16840041C211yesmaximal, characteristic, complemented
10#16840040C211yesmaximal, characteristic, complemented
11#16839889C211yesmaximal, characteristic, complemented
12#16839871C211yesmaximal, characteristic
13#16839871C211yesmaximal, characteristic
14C4×#11758199C211yesmaximal, characteristic
15C61×#478C211yesmaximal, characteristic, complemented
16C2×#11758199C2211yescharacteristic
17#14519776C2211yescharacteristic
18#14519776C2211yescharacteristic
19#14519769C2211yescharacteristic
20#14519768C2211yescharacteristic
21#14519768C2211yescharacteristic
22#14519757—21no—
23#14519756—21no—
24#14519755—21no—
25#14519755—21no—
26#14519754—21no—
27#14519754—21no—
28C4×Dic122C2211yescharacteristic
29C4×D244C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic
33#14519739C2211yescharacteristic
34C2×#11758196—21no—
35C4⋊C4×D61—21no—
36#14519711C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519687C2211yescharacteristic
50#14519687C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×D4×C61C2311yescharacteristic
60C22×C4×C61—21no—
61C22×Dic61—21no—
62C22×Dic61—21no—
63C2×D244C2311yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122D411yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C2×C8×C61C2311yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C22⋊C4×C61—21no—
78C42×C61C2311yescharacteristic
79C22⋊Dic61—21no—
80C22⋊Dic61—21no—
81#11758199Q814yescomplemented
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61D411yescharacteristic
88C4⋊Dic61C2311yescharacteristic
89C4⋊Dic61C2311yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196D411yescharacteristic
98#11758196D411yescharacteristic
99C4×Dic61C2311yescharacteristic
100C4×Dic61C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C23×C61—21no—
104C22×D61—21no—
105D4×C61—21no—
106D4×C61C2×Q812yes—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—81no—
111C2×C4×C61C2×D411yescharacteristic
112C2×C4×C61C2×D411yescharacteristic
113C2×C4×C61C2411yescharacteristic
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—42no—
118C2×Dic61—81no—
119C2×Dic61C2×D411yescharacteristic
120C2×Dic61C2×D411yescharacteristic
121C2×Dic61C2×D411yescharacteristic
122C2×Dic61C2×D411yescharacteristic
123D244—21no—
124D244C2×Q812yes—
125C4×D61—42no—
126C4×D61—81no—
127C4×D61—81no—
128Dic122—41no—
129Dic122—81no—
130Dic122—81no—
131C8×C61—21no—
132C8×C61—21no—
133#92418—21no—
134#92418C2×Q812yes—
135C22×C61—22no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61C22×D411yescharacteristic
139C2×D61—22no—
140C2×D61—41no—
141C2×D61—41no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—41no—
147C4×C61C22×Q811yescharacteristic
148C4×C612−1+411yescharacteristic
149Dic61—21no—
150Dic61—21no—
151Dic61—21no—
152Dic61—21no—
153Dic61—41no—
154Dic61—41no—
155Dic61—41no—
156#3389—611nomaximal, Sylow
157C2×C61—42no—
158C2×C61D4×Q811yescharacteristic
159C2×C61#57511yescharacteristic
160C2×C61#57611yescharacteristic
161D61—42no—
162#554—611no—
163#554—611no—
164#501—611no—
165#501—611no—
166#499—611no—
167#478—611no—
168#478—611no—
169#478—611no—
170#478D6111yescharacteristic, complemented
171#474—611no—
172#474—611no—
173#446—611no—
174#442—611no—
175#442—611no—
176C4×D8—611no—
177C61#338911yescharacteristic, complemented, Sylow
178C2×D8—611no—
179C4⋊Q8—611no—
180C4⋊Q8—611no—
181#125—611no—
182#125—611no—
183#125—611no—
184#125C2×D6111yescharacteristic
185C22⋊Q8—1221no—
186C22⋊Q8—1221no—
187C22⋊Q8—1221no—
188C22⋊Q8—1221no—
189C22⋊Q8—1221no—
190C22⋊Q8—1221no—
191C4×Q8—611no—
192C4×D4—611no—
193C4×D4—611no—
194C4×D4—611no—
195C4×D4—611no—
196C4×D4—611no—
197C4×D4C2×D6111yescharacteristic
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200#107—611no—
201#107—611no—
202#107—611no—
203#107—611no—
204#107C2×D6111yescharacteristic
205#106—611no—
206#106—611no—
207#106—611no—
208#106C2×D6111yescharacteristic
209C4⋊C8—611no—
210C4⋊C8—611no—
211C4⋊C8C2×D6111yescharacteristic
212#102—611no—
213#102—611no—
214#102—611no—
215#102—611no—
216#102C2×D6111yescharacteristic
217#102C2×D6111yescharacteristic
218#97—611no—
219#97—611no—
220C4×C8—611no—
221C2×Q8—611no—
222C2×Q8—1221no—
223C2×Q8—1221no—
224C2×D4—611no—
225C2×D4C22×D6111yescharacteristic
226C22×C4—21no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1221no—
232D8—614no—
233C2×C8—611no—
234C2×C8—611no—
235C2×C8C22×D6111yescharacteristic
236C2×C8C22×D6111yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—611no—
240C4⋊C4—611no—
241C4⋊C4—611no—
242C4⋊C4—611no—
243C4⋊C4—611no—
244C4⋊C4—611no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4C22×D6111yescharacteristic
254C4⋊C4C22×D6111yescharacteristic
255C4⋊C4C22×D6111yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—1221no—
258C22⋊C4—1221no—
259C22⋊C4—1221no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C42—611no—
263C42—611no—
264C42C22×D6111yescharacteristic
265C23—21no—
266C23—1221no—
267Q8—4881no—
268Q8—4881no—
269Q8—2441no—
270D4—21no—
271D4—612no—
272D4—1221no—
273D4Q8×D6112yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—81no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—611no—
281C2×C4—611no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—4881no—
286C2×C4—4881no—
287C2×C4—4881no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4D4×D6111yescharacteristic
291C2×C4D4×D6111yescharacteristic
292C2×C4C23×D6111yescharacteristic
293C8—21no—
294C8—21no—
295C8—612no—
296C8—1221no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—1222no—
301C22—2441no—
302C22—2441no—
303C22C2×D4×D6111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—1221no—
310C4—1221no—
311C4—1221no—
312C4—1221no—
313C4—2441no—
314C4—2441no—
315C4—2441no—
316C4C2×Q8×D6111yescharacteristic
317C4#1451982411yescharacteristic
318C2—42no—
319C2—2442no—
320C2#1684042511yescharacteristic
321C2#1684055911yescharacteristic
322C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3389
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840471C2semidirect
2. #16840468C2semidirect
3. #16840170C2semidirect
4. #16840169C2semidirect
5. #16840161C2semidirect
6. #16840064C2semidirect
7. #16840063C2semidirect
8. #16840061C2semidirect
9. #16840041C2semidirect
10. #16840040C2semidirect
11. #16839889C2semidirect
15. C61×#478C2semidirect
81. #11758199Q8semidirect
170. #478D61semidirect
177. C61#3389semidirect