Finite Group Databasebeta

← #21458532

Subgroups — #21458532

Order 7808.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840481C211yesmaximal, characteristic, complemented
2D4×Dic122C211yesmaximal, characteristic, complemented
3#16840121C211yesmaximal, characteristic, complemented
4#16840120C211yesmaximal, characteristic, complemented
5#16840111C211yesmaximal, characteristic, complemented
6#16840058C211yesmaximal, characteristic, complemented
7#16840055C211yesmaximal, characteristic, complemented
8#16840040C211yesmaximal, characteristic, complemented
9#16839975C211yesmaximal, characteristic
10#16839965C211yesmaximal, characteristic, complemented
11#16839891C211yesmaximal, characteristic, complemented
12#16839863C211yesmaximal, characteristic, complemented
13#16839862C211yesmaximal, characteristic, complemented
14D8×Dic61C211yesmaximal, characteristic
15C61×#463C211yesmaximal, characteristic
16C22×Dic122—21no—
17C2×#11758200C2211yescharacteristic
18#14519777C2211yescharacteristic
19#14519776C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519775C2211yescharacteristic
22#14519770—21no—
23#14519770—21no—
24#14519764C2211yescharacteristic
25#14519756—21no—
26#14519754—21no—
27#14519754—21no—
28#14519754—21no—
29Q8×Dic61C2211yescharacteristic
30C4×Dic122C2211yescharacteristic
31C4×Dic122C2211yescharacteristic
32D4×Dic61C2211yescharacteristic
33D4×Dic61C2211yescharacteristic
34D4×Dic61C2211yescharacteristic
35#14519733—21no—
36#14519711C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519706C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519688C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C2×Dic122—21no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—44no—
70C2×Dic122D411yescharacteristic
71C2×Dic122C2311yescharacteristic
72SD16×C61—22no—
73D8×C61—22no—
74C2×C8×C61C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C22⋊C4×C61—21no—
78C22⋊C4×C61—21no—
79C22⋊C4×C61—21no—
80C42×C61C2311yescharacteristic
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86#11758200—22no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61D411yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196D411yescharacteristic
99#11758196D411yescharacteristic
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61C2311yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C23×C61—21no—
107C23×C61—21no—
108Q8×C61—21no—
109Q8×C61—21no—
110D4×C61—21no—
111D4×C61—21no—
112D4×C61—21no—
113D4×C61#4112yes—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—42no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131Dic122—22no—
132Dic122—21no—
133Dic122—21no—
134Dic122—42no—
135Dic122—42no—
136Dic122—42no—
137C8×C61—21no—
138C8×C61—21no—
139#92418—21no—
140#92418—21no—
141C22×C61—22no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61C22×D411yescharacteristic
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61C2×#4111yescharacteristic
153C4×C612−1+411yescharacteristic
154Dic61—21no—
155Dic61—21no—
156Dic61—21no—
157Dic61—41no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161Dic61AGL(1,ℤ/8)12yes—
162#3367—611nomaximal, Sylow
163C2×C61—42no—
164C2×C61—81no—
165C2×C61#54811yescharacteristic
166C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C61#57811yescharacteristic
168#556—611no—
169D4×Q8—611no—
170#489—611no—
171#489—611no—
172#487—611no—
173#477—611no—
174#477—611no—
175#474—611no—
176#463—611no—
177#463D6111yescharacteristic
178#461—611no—
179#446—611no—
180#440—611no—
181#440—611no—
182C4×D8—611no—
183C61#336711yescharacteristic, complemented, Sylow
184C22×Q8—1221no—
185C2×SD16—611no—
186C2×SD16C2×D6111yescharacteristic
187C2×D8C2×D6111yescharacteristic
188C4⋊Q8—611no—
189C4⋊Q8—611no—
190C4⋊Q8—611no—
191C4⋊Q8—611no—
192#126—1221no—
193#126—1221no—
194#124—611no—
195#124C2×D6111yescharacteristic
196C22⋊Q8—1221no—
197C22⋊Q8—1221no—
198C22⋊Q8—1221no—
199C22⋊Q8—1221no—
200C4×Q8—611no—
201C4×Q8—611no—
202C4×Q8—611no—
203C4×D4—611no—
204C4×D4—611no—
205C4×D4—611no—
206C4×D4C2×D6111yescharacteristic
207#117—1221no—
208#107—611no—
209#107—611no—
210#107—611no—
211C4⋊C8—611no—
212C4⋊C8—611no—
213C4⋊C8C2×D6111yescharacteristic
214#103—611no—
215#103—611no—
216#103—611no—
217#103—611no—
218#103—611no—
219#103C2×D6111yescharacteristic
220#102—611no—
221#102—611no—
222#102—611no—
223#102C2×D6111yescharacteristic
224#97—611no—
225#97—611no—
226C4×C8—611no—
227C2×Q8—611no—
228C2×Q8—611no—
229C2×Q8—1221no—
230C2×Q8—1221no—
231C2×Q8—1221no—
232C2×Q8—2444no—
233C2×Q8C22×D6111yescharacteristic
234C2×D4C22×D6111yescharacteristic
235C2×D4C22×D6111yescharacteristic
236C22×C4—21no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240SD16—22no—
241SD16—1222no—
242D8—22no—
243C2×C8—611no—
244C2×C8—611no—
245C2×C8C22×D6111yescharacteristic
246C2×C8C22×D6111yescharacteristic
247C4⋊C4—611no—
248C4⋊C4—611no—
249C4⋊C4—611no—
250C4⋊C4—611no—
251C4⋊C4—611no—
252C4⋊C4—611no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4C22×D6111yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C42—611no—
270C42—611no—
271C42—1221no—
272C42—1221no—
273C42C22×D6111yescharacteristic
274C23—21no—
275C23—21no—
276Q8—21no—
277Q8—21no—
278Q8—1222no—
279Q8—1221no—
280Q8—1221no—
281Q8—2442no—
282Q8—2442no—
283Q8—2442no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4#1175822412yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4D4×D6111yescharacteristic
303C2×C4D4×D6111yescharacteristic
304C2×C4C23×D6111yescharacteristic
305C8—21no—
306C8—21no—
307C8—1221no—
308C8—1221no—
309C22—22no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C2×D4×D6111yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—612no—
321C4—1221no—
322C4—1221no—
323C4—1221no—
324C4—2441no—
325C4—2441no—
326C4—2441no—
327C4—2441no—
328C4C2×#1175822411yescharacteristic
329C4#1451982411yescharacteristic
330C2—42no—
331C2—81no—
332C2#1684041811yescharacteristic
333C2AGL(1,ℤ/8)×D6111yescharacteristic
334C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3367
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16840481C2semidirect
2. D4×Dic122C2semidirect
3. #16840121C2semidirect
4. #16840120C2semidirect
5. #16840111C2semidirect
6. #16840058C2semidirect
7. #16840055C2semidirect
8. #16840040C2semidirect
10. #16839965C2semidirect
11. #16839891C2semidirect
12. #16839863C2semidirect
13. #16839862C2semidirect
183. C61#3367semidirect