Finite Group Databasebeta

← #21457680

Subgroups — #21457680

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#16840413C211yesmaximal, characteristic
3#16840111C211yesmaximal, characteristic, complemented
4#16840092C211yesmaximal, characteristic, complemented
5#16840091C211yesmaximal, characteristic, complemented
6#16840045C211yesmaximal, characteristic, complemented
7#16839994C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839966C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic, complemented
11#16839901C211yesmaximal, characteristic, complemented
12#16839847C211yesmaximal, characteristic, complemented
13C8×C22⋊D61C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C2×#103×C61C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×Q8×D61C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519775—21no—
24#14519775C2211yescharacteristic
25#14519762—21no—
26#14519760—21no—
27#14519756—21no—
28#14519756C2211yescharacteristic
29#14519755—21no—
30#14519753—21no—
31#14519753C2211yescharacteristic
32#14519752C2211yescharacteristic
33#14519751C2211yescharacteristic
34Q8×Dic61C2211yescharacteristic
35#14519739C2211yescharacteristic
36C4×C22⋊D61—21no—
37C4×C22⋊D61C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61D411yescharacteristic
69Q8×D61—22no—
70Q8×D61—41no—
71#11758222—44no—
72C2×D244—21no—
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×Dic122—21no—
79C2×Dic122—21no—
80C2×Dic122C2311yescharacteristic
81C2×C8×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61—21no—
85C4⋊C4×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61D411yescharacteristic
89#11758201—22no—
90#11758201—41no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
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×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758190—41no—
111C8×D61—41no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—42no—
119Q8×C61#4112yescomplemented
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—42no—
131C22⋊D61SD1614yescomplemented
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—21no—
139D244—21no—
140D244—42no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—42no—
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×C61C2×SD1612yes—
157C22×C61C22×D411yescharacteristic
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61C2×SD1612yes—
164C4×C61—22no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61C2×SD1612yes—
177#3298—611nomaximal, Sylow
178C2×C61—22no—
179C2×C61#54611yescharacteristic
180C2×C61C22×SD1611yescharacteristic
181C2×C61#57811yescharacteristic
182D61—22no—
183D61—81no—
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#448—611no—
195C4×SD16—611no—
196C8×D4—611no—
197C2×#103—611no—
198C2×#103D6111yescharacteristic, complemented
199C61#329811yescharacteristic, complemented, Sylow
200C2×#41—1221no—
201C22×Q8—611no—
202C22×Q8C2×D6111yescharacteristic
203C2×SD16—611no—
204C2×SD16—611no—
205C2×SD16—611no—
206C22×C8—611no—
207C22×C8C2×D6111yescharacteristic
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#121—611no—
220C4×Q8—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—1221no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4C2×D6111yescharacteristic
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#103C2×D6111yescharacteristic
236#103C2×D6111yescharacteristic
237#103C2×D6111yescharacteristic
238#103C2×D6111yescharacteristic
239#102—611no—
240C22⋊C8—611no—
241C22⋊C8—611no—
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—611no—
255C2×D4—611no—
256C2×D4—1221no—
257C2×D4—1221no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4C22×D6111yescharacteristic
265SD16—1222no—
266SD16—2441no—
267SD16—2441no—
268C2×C8—41no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8—2441no—
272C2×C8C22×D6111yescharacteristic
273C2×C8C22×D6111yescharacteristic
274C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
286C4⋊C4C22×D6111yescharacteristic
287C22⋊C4—611no—
288C22⋊C4—611no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—611no—
295C42—1221no—
296C23—611no—
297C23—1221no—
298C23D4×D6111yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—1221no—
304Q8—1221no—
305Q8—2442no—
306Q8—2442no—
307Q8#1175822212yescomplemented
308D4—614no—
309D4—1221no—
310D4—1221no—
311D4—2442no—
312D4—2442no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
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—612no—
341C22—1221no—
342C22—1221no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22SD16×D6112yes—
347C22C2×D4×D6111yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—612no—
354C4—1221no—
355C4—1221no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4C2×#1175822211yescharacteristic
360C4#1451982211yescharacteristic
361C2—22no—
362C2—1222no—
363C2—4881no—
364C2#1684040211yescharacteristic
365C2C2×SD16×D6111yescharacteristic
366C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#103×C61C2
socleC22×C61C22×D4
hypercenterC2×#103D61
hypocenterC61#3298
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D61C2semidirect
3. #16840111C2semidirect
4. #16840092C2semidirect
5. #16840091C2semidirect
6. #16840045C2semidirect
7. #16839994C2semidirect
8. #16839991C2semidirect
9. #16839966C2semidirect
10. #16839902C2semidirect
11. #16839901C2semidirect
12. #16839847C2semidirect
13. C8×C22⋊D61C2semidirect
14. #103×D61C2semidirect
15. C2×#103×C61C2semidirect
119. Q8×C61#41semidirect
131. C22⋊D61SD16semidirect
198. C2×#103D61semidirect
199. C61#3298semidirect
307. Q8#11758222semidirect