Finite Group Databasebeta

← #21458357

Subgroups — #21458357

Order 7808.

348 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#16840480C211yesmaximal, characteristic, complemented
2#16840464C211yesmaximal, characteristic
3#16840170C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840093C211yesmaximal, characteristic, complemented
6#16840085C211yesmaximal, characteristic, complemented
7#16840072C211yesmaximal, characteristic, complemented
8#16840050C211yesmaximal, characteristic, complemented
9#16840006C211yesmaximal, characteristic, complemented
10#16839990C211yesmaximal, characteristic, complemented
11#16839859C211yesmaximal, characteristic, complemented
12#16839836C211yesmaximal, characteristic, complemented
13#16839805C211yesmaximal, characteristic, complemented
14#16839797C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C2×#11758200C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18C2×C8×D61C2211yescharacteristic
19#14519776C2211yescharacteristic
20#14519771—21no—
21#14519770—21no—
22#14519770—21no—
23#14519768C2211yescharacteristic
24#14519763—21no—
25#14519761—21no—
26#14519757C2211yescharacteristic
27#14519756C2211yescharacteristic
28#14519749—21no—
29#14519748C2211yescharacteristic
30C4×Dic122—21no—
31#14519742C2211yescharacteristic
32D4×Dic61—21no—
33D4×Dic61C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35#14519735C2211yescharacteristic
36#14519735C2211yescharacteristic
37C2×C4⋊Dic61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519708C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61D411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C2×C4×D61C2311yescharacteristic
67C2×Dic122—21no—
68C2×Dic122C2311yescharacteristic
69C2×C8×C61C2311yescharacteristic
70C2×C8×C61C2311yescharacteristic
71C4⋊C4×C61C2311yescharacteristic
72C4⋊C4×C61C2311yescharacteristic
73C4⋊C4×C61C2311yescharacteristic
74C22⋊C4×C61—21no—
75C22⋊C4×C61—21no—
76C42×C61—21no—
77C22⋊Dic61—21no—
78C22⋊Dic61—21no—
79C22⋊Dic61—21no—
80C22⋊Dic61D411yescharacteristic
81#11758200—22no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198D411yescharacteristic
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61C2311yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196D411yescharacteristic
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61C2311yescharacteristic
101#11758194—22no—
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C8×D61—22no—
105C23×C61—21no—
106C23×C61C2×D411yescharacteristic
107C22×D61C2×D411yescharacteristic
108D4×C61—21no—
109D4×C61—21no—
110D4×C61—42no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2411yescharacteristic
118C22⋊D61—41no—
119C22⋊D61—81no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—81no—
125C2×Dic61—81no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C4×D61—21no—
130C4×D61—21no—
131Dic122—21no—
132Dic122—21no—
133Dic122—42no—
134C8×C61—21no—
135C8×C61—21no—
136#92418—21no—
137#92418#4112yes—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61C22×D411yescharacteristic
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C4×C61—21no—
149C4×C61—41no—
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—
161#3350—611nomaximal, Sylow
162C2×C61—41no—
163C2×C61—81no—
164C2×C61#54711yescharacteristic
165C2×C61#57511yescharacteristic
166C2×C61#57711yescharacteristic
167D61—41no—
168#556—611no—
169#553—611no—
170#501—611no—
171#485—611no—
172#483—611no—
173#482—611no—
174#482D6111yescharacteristic, complemented
175#479—611no—
176#476—611no—
177#468—611no—
178#465—611no—
179#440—611no—
180#435—611no—
181#428—611no—
182#427—611no—
183C61#335011yescharacteristic, complemented, Sylow
184C2×SD16—611no—
185C2×M16—611no—
186C22×C8—611no—
187C4⋊Q8—611no—
188#126—1221no—
189#126—1221no—
190#126—1221no—
191#125—611no—
192#124—1221no—
193#123—1221no—
194C22⋊Q8—611no—
195C22⋊Q8—611no—
196#121—611no—
197#121—1221no—
198#121C2×D6111yescharacteristic
199C4×Q8—611no—
200C4×Q8—1221no—
201C4×D4—611no—
202C4×D4—611no—
203C4×D4—1221no—
204#117—611no—
205#117—611no—
206#117C2×D6111yescharacteristic
207C2×C4⋊C4—611no—
208#107—611no—
209#107—611no—
210#107—611no—
211#107C2×D6111yescharacteristic
212#106—611no—
213#106—611no—
214#106—611no—
215#106—611no—
216#106C2×D6111yescharacteristic
217C4⋊C8—611no—
218#103—611no—
219#103—611no—
220#103—611no—
221#102—611no—
222#102C2×D6111yescharacteristic
223#102C2×D6111yescharacteristic
224C22⋊C8—611no—
225C22⋊C8C2×D6111yescharacteristic
226#97—611no—
227C2×Q8—611no—
228C2×Q8—1221no—
229C2×D4—21no—
230C2×D4—611no—
231C2×D4—1221no—
232C2×D4C22×D6111yescharacteristic
233C22×C4—611no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4C22×D6111yescharacteristic
237SD16—1222no—
238M16—1222no—
239C2×C8—611no—
240C2×C8—611no—
241C2×C8—1222no—
242C2×C8C22×D6111yescharacteristic
243C2×C8C22×D6111yescharacteristic
244C4⋊C4—611no—
245C4⋊C4—611no—
246C4⋊C4—611no—
247C4⋊C4—611no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C4⋊C4C22×D6111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—611no—
261C22⋊C4—611no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C42—21no—
269C42—611no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C23—21no—
274C23—611no—
275C23D4×D6111yescharacteristic
276Q8—1221no—
277Q8—1221no—
278Q8—2442no—
279D4—21no—
280D4—21no—
281D4—42no—
282D4—4881no—
283D4—2441no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—611no—
290C2×C4—611no—
291C2×C4—611no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—4881no—
299C2×C4—4881no—
300C2×C4D4×D6111yescharacteristic
301C2×C4C23×D6111yescharacteristic
302C8—21no—
303C8—21no—
304C8—612no—
305C8—1221no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—1221no—
313C22—1221no—
314C22—1221no—
315C22C2×D4×D6111yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—1221no—
321C4—1221no—
322C4—1221no—
323C4—2441no—
324C4—2441no—
325C4—2441no—
326C4—2441no—
327C4#41×D6111yescharacteristic
328C4#1451982411yescharacteristic
329C2—41no—
330C2—81no—
331C2—2441no—
332C2#1684041011yescharacteristic
333C2#1684055811yescharacteristic
334C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3350
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16840480C2semidirect
3. #16840170C2semidirect
4. #16840105C2semidirect
5. #16840093C2semidirect
6. #16840085C2semidirect
7. #16840072C2semidirect
8. #16840050C2semidirect
9. #16840006C2semidirect
10. #16839990C2semidirect
11. #16839859C2semidirect
12. #16839836C2semidirect
13. #16839805C2semidirect
14. #16839797C2semidirect
15. C61×#482C2semidirect
174. #482D61semidirect
183. C61#3350semidirect