Finite Group Databasebeta

← #21458100

Subgroups — #21458100

Order 7808.

374 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840480C211yesmaximal, characteristic
2#16840425C211yesmaximal, characteristic
3#16840111C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840046C211yesmaximal, characteristic, complemented
6#16840021C211yesmaximal, characteristic, complemented
7#16840018C211yesmaximal, characteristic, complemented
8#16839971C211yesmaximal, characteristic, complemented
9#16839920C211yesmaximal, characteristic, complemented
10#16839919C211yesmaximal, characteristic, complemented
11#16839856C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic
13#16839770C211yesmaximal, characteristic, complemented
14#16839769C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×Dic244C2211yescharacteristic
20C2×#11758202C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23#14519776—21no—
24#14519776C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519771—21no—
27#14519770—21no—
28#14519763—21no—
29#14519757C2211yescharacteristic
30#14519757C2211yescharacteristic
31#14519756C2211yescharacteristic
32#14519755—21no—
33#14519754—21no—
34C4×Dic122—21no—
35#14519742C2211yescharacteristic
36#14519742C2211yescharacteristic
37C4×C22⋊D61C2211yescharacteristic
38#14519737—21no—
39#14519735C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519700C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61D411yescharacteristic
62C22×Dic61—21no—
63Q8×D61—22no—
64Q8×D61—41no—
65C2×C4×D61—21no—
66C2×C4×D61C2311yescharacteristic
67C2×Dic122—22no—
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122—41no—
72C2×Dic122C2311yescharacteristic
73C2×Dic122C2311yescharacteristic
74C2×Dic122C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C42×C61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61D411yescharacteristic
86#11758202—41no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198D411yescharacteristic
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105#11758194—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108Dic244—22no—
109Dic244—41no—
110#11758189—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61C2×D411yescharacteristic
113Q8×C61—21no—
114Q8×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2411yescharacteristic
123C22⋊D61—22no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—42no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—42no—
135Dic122—21no—
136Dic122—21no—
137Dic122—21no—
138Dic122—21no—
139Dic122—21no—
140Dic122—42no—
141Dic122—42no—
142Dic122—42no—
143Dic122#4112yes—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
155C4×C61—21no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61C2×#4111yescharacteristic
161C4×C61H(5,𝔽2)11yescharacteristic
162Dic61—22no—
163Dic61—21no—
164Dic61—21no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61#13712yes—
169#3328—611nomaximal, Sylow
170C2×C61—41no—
171C2×C61#54611yescharacteristic
172C2×C61C2×#13711yescharacteristic
173C2×C61#57811yescharacteristic
174D61—41no—
175#556—611no—
176D4×Q8—611no—
177#487—611no—
178#485—611no—
179#485D6111yescharacteristic, complemented
180#475—611no—
181#470—611no—
182#470—611no—
183#462—611no—
184#451—611no—
185#451—611no—
186C4×Q16—611no—
187#436—611no—
188#419—611no—
189#419—611no—
190C61#332811yescharacteristic, complemented, Sylow
191C22×Q8—611no—
192C22×Q8—611no—
193C2×Q16—611no—
194C2×Q16—611no—
195C2×Q16—611no—
196C2×M16—611no—
197C2×M16—611no—
198C4⋊Q8—611no—
199C4⋊Q8—611no—
200C4⋊Q8—1221no—
201#126—1221no—
202#126—1221no—
203#124—1221no—
204C22⋊Q8—611no—
205C22⋊Q8—611no—
206C22⋊Q8—611no—
207C22⋊Q8—1221no—
208C22⋊Q8—1221no—
209C22⋊Q8C2×D6111yescharacteristic
210C4×Q8—611no—
211C4×Q8—611no—
212C4×Q8—1221no—
213C4×D4—611no—
214C4×D4—1221no—
215#117—611no—
216#117C2×D6111yescharacteristic
217#107C2×D6111yescharacteristic
218#106—611no—
219#106C2×D6111yescharacteristic
220C4⋊C8—611no—
221#103—611no—
222#103—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103C2×D6111yescharacteristic
230#103C2×D6111yescharacteristic
231C22⋊C8—611no—
232C22⋊C8C2×D6111yescharacteristic
233C4×C8—611no—
234C2×Q8—611no—
235C2×Q8—611no—
236C2×Q8—611no—
237C2×Q8—1221no—
238C2×Q8—1221no—
239C2×Q8—1222no—
240C2×Q8—1221no—
241C2×Q8—1222no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C2×Q8C22×D6111yescharacteristic
245C2×D4—611no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4C22×D6111yescharacteristic
250Q16—1222no—
251Q16—2441no—
252Q16—2441no—
253M16—2441no—
254M16—2441no—
255C2×C8—611no—
256C2×C8—611no—
257C2×C8C22×D6111yescharacteristic
258C2×C8C22×D6111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4C22×D6111yescharacteristic
271C4⋊C4C22×D6111yescharacteristic
272C4⋊C4C22×D6111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—611no—
276C22⋊C4—611no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C42—21no—
282C42—611no—
283C42—1221no—
284C42—1221no—
285C42—1221no—
286C23—611no—
287C23D4×D6111yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—612no—
291Q8—1221no—
292Q8—1221no—
293Q8—1221no—
294Q8—1221no—
295Q8—1221no—
296Q8—2442no—
297Q8—2442no—
298Q8—2442no—
299D4—1222no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—2442no—
316C2×C4—2442no—
317C2×C4D4×D6111yescharacteristic
318C2×C4C23×D6111yescharacteristic
319C8—21no—
320C8—21no—
321C8—1221no—
322C8—1221no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—1221no—
327C22—1221no—
328C22—1221no—
329C22C2×D4×D6111yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—612no—
336C4—1221no—
337C4—1221no—
338C4—1222no—
339C4—2441no—
340C4—2441no—
341C4—2441no—
342C4#41×D6111yescharacteristic
343C4#1451982311yescharacteristic
344C2—41no—
345C2—2441no—
346C2#1684040411yescharacteristic
347C2#137×D6111yescharacteristic
348C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3328
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #16840111C2semidirect
4. #16840105C2semidirect
5. #16840046C2semidirect
6. #16840021C2semidirect
7. #16840018C2semidirect
8. #16839971C2semidirect
9. #16839920C2semidirect
10. #16839919C2semidirect
11. #16839856C2semidirect
13. #16839770C2semidirect
14. #16839769C2semidirect
15. C61×#485C2semidirect
179. #485D61semidirect
190. C61#3328semidirect