Finite Group Databasebeta

← #21457677

Subgroups — #21457677

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D61C211yesmaximal, characteristic, complemented
2#16840412C211yesmaximal, characteristic
3#16840111C211yesmaximal, characteristic, complemented
4#16840093C211yesmaximal, characteristic, complemented
5#16840091C211yesmaximal, characteristic, complemented
6#16840045C211yesmaximal, characteristic, complemented
7#16839989C211yesmaximal, characteristic, complemented
8#16839988C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839899C211yesmaximal, characteristic, complemented
11SD16×Dic61C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13C2×#14519701C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#448C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×Q8×D61C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C22×#92418C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519776C2211yescharacteristic
22#14519775—21no—
23#14519775C2211yescharacteristic
24#14519759—21no—
25#14519758—21no—
26#14519756—21no—
27#14519756C2211yescharacteristic
28#14519754—21no—
29#14519753—21no—
30#14519753C2211yescharacteristic
31#14519748C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33D4×Dic61C2211yescharacteristic
34C4×C22⋊D61—21no—
35C4×C22⋊D61C2211yescharacteristic
36C2×C4⋊Dic61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519709C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72Q8×D61—22no—
73Q8×D61—41no—
74#11758224—44no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×Dic122—21no—
79C2×Dic122—21no—
80C2×Dic122C2311yescharacteristic
81SD16×C61—22no—
82SD16×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61D411yescharacteristic
91#11758200—41no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
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#11758196D411yescharacteristic
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418—41no—
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C8×D61—41no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—42no—
119Q8×C61#4112yescomplemented
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—42no—
132C22⋊D61SD1614yescomplemented
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—42no—
145C4×D61—42no—
146Dic122—21no—
147Dic122—21no—
148Dic122—42no—
149Dic122—42no—
150C8×C61—21no—
151C8×C61—21no—
152#92418—21no—
153#92418—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61C2×SD1612yes—
160C22×C61C22×D411yescharacteristic
161C2×D61—21no—
162C2×D61—21no—
163C2×D61C2×SD1612yes—
164C4×C61—22no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C2×#4111yescharacteristic
169C4×C61H(5,𝔽2)11yescharacteristic
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61C2×SD1612yes—
177#3298—611nomaximal, Sylow
178C2×C61—22no—
179C2×C61—81no—
180C2×C61#54611yescharacteristic
181C2×C61C22×SD1611yescharacteristic
182C2×C61#57811yescharacteristic
183D61—22no—
184D4×Q8—611no—
185#547—611no—
186#487—611no—
187#483—611no—
188#483—611no—
189#475—611no—
190#465—611no—
191#465—611no—
192#461—611no—
193#448—611no—
194#448D6111yescharacteristic, complemented
195C4×SD16—611no—
196C8×D4—611no—
197C2×#103—611no—
198C2×#103—611no—
199C61#329811yescharacteristic, complemented, Sylow
200C2×#41—1221no—
201C22×Q8—611no—
202C22×Q8C2×D6111yescharacteristic
203C2×SD16—611no—
204C2×SD16C2×D6111yescharacteristic
205C2×SD16C2×D6111yescharacteristic
206C22×C8—611no—
207C22×C8—611no—
208C4⋊Q8—611no—
209C4⋊Q8—611no—
210C4⋊Q8—1221no—
211#123—1221no—
212#123—1221no—
213C22⋊Q8—611no—
214C22⋊Q8—611no—
215C22⋊Q8—1221no—
216C22⋊Q8—1221no—
217C22⋊Q8—1221no—
218#121—611no—
219#121C2×D6111yescharacteristic
220C4×Q8—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—1221no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226#106—611no—
227#106—611no—
228#106—611no—
229C4⋊C8—611no—
230#103—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103C2×D6111yescharacteristic
238#103C2×D6111yescharacteristic
239#102—611no—
240C22⋊C8—611no—
241C22⋊C8C2×D6111yescharacteristic
242C4×C8—611no—
243#41—2444no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—611no—
248C2×Q8—1221no—
249C2×Q8—1221no—
250C2×Q8—1222no—
251C2×Q8—2441no—
252C2×Q8C22×D6111yescharacteristic
253C2×Q8C22×D6111yescharacteristic
254C2×D4—21no—
255C2×D4—611no—
256C2×D4—1221no—
257C2×D4C22×D6111yescharacteristic
258C22×C4—21no—
259C22×C4—611no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4C22×D6111yescharacteristic
265SD16—22no—
266SD16—41no—
267SD16—2441no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8C22×D6111yescharacteristic
273C2×C8C22×D6111yescharacteristic
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—611no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4C22×D6111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—611no—
289C22⋊C4—611no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—611no—
295C42—1221no—
296C23—21no—
297C23—611no—
298C23D4×D6111yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—1221no—
304Q8—1221no—
305Q8—2442no—
306Q8—2442no—
307Q8#1175822412yescomplemented
308D4—21no—
309D4—21no—
310D4—42no—
311D4—614no—
312D4—2442no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4D4×D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—612no—
344C22—1221no—
345C22—1221no—
346C22SD16×D6112yes—
347C22C2×D4×D6111yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—612no—
353C4—1221no—
354C4—1221no—
355C4—2441no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4C2×#1175822411yescharacteristic
360C4#1451982211yescharacteristic
361C2—22no—
362C2—81no—
363C2—1222no—
364C2#1684039911yescharacteristic
365C2C2×SD16×D6111yescharacteristic
366C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#448C2
socleC22×C61C22×D4
hypercenter#448D61
hypocenterC61#3298
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D61C2semidirect
3. #16840111C2semidirect
4. #16840093C2semidirect
5. #16840091C2semidirect
6. #16840045C2semidirect
7. #16839989C2semidirect
8. #16839988C2semidirect
9. #16839965C2semidirect
10. #16839899C2semidirect
11. SD16×Dic61C2semidirect
12. #16839825C2semidirect
13. C2×#14519701C2semidirect
14. #103×D61C2semidirect
15. C61×#448C2semidirect
119. Q8×C61#41semidirect
132. C22⋊D61SD16semidirect
194. #448D61semidirect
199. C61#3298semidirect
307. Q8#11758224semidirect