Finite Group Databasebeta

← #21455934

Subgroups — #21455934

Order 7808.

392 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#16840299C211yesmaximal, characteristic, complemented
2C4×#11758226C211yesmaximal, characteristic, complemented
3#16840101C211yesmaximal, characteristic, complemented
4#16840088C211yesmaximal, characteristic, complemented
5#16840067C211yesmaximal, characteristic, complemented
6#16840061C211yesmaximal, characteristic, complemented
7#16839986C211yesmaximal, characteristic, complemented
8#16839980C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic
11#16839875C211yesmaximal, characteristic, complemented
12#16839860C211yesmaximal, characteristic, complemented
13#16839860C211yesmaximal, characteristic, complemented
14#16839817C211yesmaximal, characteristic, complemented
15C61×#441C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×D488C2211yescharacteristic
20#14519772—21no—
21#14519768C2211yescharacteristic
22#14519766C2211yescharacteristic
23#14519762—21no—
24#14519753C2211yescharacteristic
25#14519752C2211yescharacteristic
26Q8×Dic61C2211yescharacteristic
27C4×D244—21no—
28C4×D244—21no—
29C4×D244C2211yescharacteristic
30C4×D244C2211yescharacteristic
31#14519739—21no—
32#14519739C2211yescharacteristic
33#14519735—21no—
34#14519735C2211yescharacteristic
35#14519734—21no—
36C42×D61—21no—
37C42×D61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61#11758226—22no—
62#11758226—22no—
63C2×D244—21no—
64C2×D244—21no—
65C2×D244C2311yescharacteristic
66C2×D244C2311yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61D411yescharacteristic
72C2×C4×D61D411yescharacteristic
73C2×C4×D61C2311yescharacteristic
74Q16×C61—22no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C42×C61—21no—
82C42×C61—21no—
83C42×C61C2311yescharacteristic
84#11758201—22no—
85#11758201—22no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61D411yescharacteristic
103C4×Dic61D411yescharacteristic
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107D488—22no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61C2×D411yescharacteristic
111Q8×C61—21no—
112Q8×C61—21no—
113Q8×C61—21no—
114Q8×C61#4112yes—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127D244—24no—
128D244—21no—
129D244—21no—
130D244—21no—
131D244—42no—
132D244#4112yes—
133C4×D61—24no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—41no—
137C4×D61—41no—
138C4×D61—42no—
139C4×D61—42no—
140C4×D61—42no—
141C8×C61—21no—
142C8×C61—21no—
143#92418—21no—
144#92418—21no—
145C22×C61C22×D411yescharacteristic
146C2×D61—21no—
147C2×D61—22no—
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C4×C61—22no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61C2×#4111yescharacteristic
162C4×C61C2×#4111yescharacteristic
163Dic61—21no—
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168#3111—611nomaximal, Sylow
169C2×C61#52511yescharacteristic
170C2×C61#57511yescharacteristic
171C2×C61#57511yescharacteristic
172D61—41no—
173D61—42no—
174D61—81no—
175#529—611no—
176C4×#41—611no—
177#485—611no—
178#482—611no—
179#479—611no—
180#478—611no—
181#464—611no—
182#463—611no—
183#452—611no—
184#449—611no—
185#442—611no—
186#441D6111yescharacteristic, complemented
187#440—611no—
188#440—611no—
189#432—611no—
190C61#311111yescharacteristic, complemented, Sylow
191C2×#41—611no—
192C2×Q16C2×D6111yescharacteristic
193C2×SD16—611no—
194C2×SD16—611no—
195C2×D8—611no—
196#126—1221no—
197#125—611no—
198#124—611no—
199#123—1221no—
200C22⋊Q8—611no—
201#121—611no—
202C4×Q8—611no—
203C4×Q8C2×D6111yescharacteristic
204C4×Q8C2×D6111yescharacteristic
205C4×D4—611no—
206C4×D4—611no—
207C4×D4—611no—
208C4×D4—1221no—
209C4×D4—1221no—
210C4×D4—1221no—
211#117—611no—
212#117—1221no—
213#117—1221no—
214C2×C42—611no—
215C2×C42—1221no—
216#107—611no—
217#107—611no—
218#106—611no—
219#106C2×D6111yescharacteristic
220C4⋊C8—611no—
221C4⋊C8—611no—
222#103—611no—
223#103—611no—
224#103C2×D6111yescharacteristic
225#103C2×D6111yescharacteristic
226#102—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230C22⋊C8—611no—
231C22⋊C8—611no—
232#97—611no—
233#97C2×D6111yescharacteristic
234#41—1222no—
235#41—1222no—
236C2×Q8C22×D6111yescharacteristic
237C2×Q8C22×D6111yescharacteristic
238C2×D4—611no—
239C2×D4—611no—
240C2×D4—1221no—
241C2×D4—1221no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249Q16—22no—
250SD16—1222no—
251SD16—1222no—
252D8—1222no—
253C2×C8—611no—
254C2×C8—611no—
255C2×C8C22×D6111yescharacteristic
256C2×C8C22×D6111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4C22×D6111yescharacteristic
266C4⋊C4C22×D6111yescharacteristic
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C42—21no—
276C42—21no—
277C42—611no—
278C42—611no—
279C42—611no—
280C42—1221no—
281C42—1221no—
282C42C22×D6111yescharacteristic
283C23—611no—
284C23—1221no—
285C23—1221no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#1175822212yes—
290D4—612no—
291D4—1224no—
292D4—1221no—
293D4—1221no—
294D4—1221no—
295D4—2442no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—1224no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4D4×D6111yescharacteristic
314C2×C4D4×D6111yescharacteristic
315C2×C4C23×D6111yescharacteristic
316C8—21no—
317C8—21no—
318C8—1221no—
319C8—1221no—
320C22—1222no—
321C22—1221no—
322C22—1221no—
323C22—1221no—
324C22—2441no—
325C22—2441no—
326C22—2441no—
327C22—2441no—
328C22—2441no—
329C22C2×D4×D6111yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—1221no—
337C4—1221no—
338C4—1221no—
339C4—2441no—
340C4—2441no—
341C4#41×D6111yescharacteristic
342C4C2×#1175822211yescharacteristic
343C2—4881no—
344C2—2441no—
345C2—2442no—
346C2#1684027111yescharacteristic
347C2#1684056111yescharacteristic
348C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#441C2
socleC22×C61C22×D4
hypercenter#441D61
hypocenterC61#3111
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #16840299C2semidirect
2. C4×#11758226C2semidirect
3. #16840101C2semidirect
4. #16840088C2semidirect
5. #16840067C2semidirect
6. #16840061C2semidirect
7. #16839986C2semidirect
8. #16839980C2semidirect
9. #16839923C2semidirect
11. #16839875C2semidirect
12. #16839860C2semidirect
13. #16839860C2semidirect
14. #16839817C2semidirect
15. C61×#441C2semidirect
186. #441D61semidirect
190. C61#3111semidirect