Finite Group Databasebeta

← #21455995

Subgroups — #21455995

Order 7808.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840297C211yesmaximal, characteristic
2C4×Q8×D61C211yesmaximal, characteristic, complemented
3#16840099C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic
5#16840066C211yesmaximal, characteristic, complemented
6#16839985C211yesmaximal, characteristic, complemented
7#16839984C211yesmaximal, characteristic, complemented
8#16839919C211yesmaximal, characteristic, complemented
9#16839902C211yesmaximal, characteristic
10#16839868C211yesmaximal, characteristic, complemented
11#16839866C211yesmaximal, characteristic, complemented
12#16839865C211yesmaximal, characteristic, complemented
13#16839861C211yesmaximal, characteristic, complemented
14#16839818C211yesmaximal, characteristic, complemented
15C61×#479C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21#14519772—21no—
22#14519765C2211yescharacteristic
23#14519762—21no—
24#14519757C2211yescharacteristic
25#14519752C2211yescharacteristic
26Q8×Dic61C2211yescharacteristic
27C4×Dic122—21no—
28C4×Dic122C2211yescharacteristic
29#14519742—21no—
30#14519742C2211yescharacteristic
31#14519742C2211yescharacteristic
32#14519739—21no—
33#14519739C2211yescharacteristic
34#14519735—21no—
35C4⋊C4×D61—21no—
36C4⋊C4×D61C2211yescharacteristic
37C42×D61—21no—
38C42×D61C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic
51#14519687C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60Q8×D61—22no—
61Q8×D61—22no—
62C2×D244—21no—
63C2×D244C2311yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61D411yescharacteristic
68C2×C4×D61D411yescharacteristic
69C2×C4×D61C2311yescharacteristic
70C2×Dic122—21no—
71C2×Dic122C2311yescharacteristic
72C2×Dic122C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C42×C61—21no—
82C42×C61C2311yescharacteristic
83#11758202—22no—
84#11758201—22no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61C2311yescharacteristic
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61D411yescharacteristic
102C4×Dic61D411yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106Dic244—22no—
107#11758190—22no—
108C22×D61—21no—
109C22×D61C2×D411yescharacteristic
110Q8×C61—21no—
111Q8×C61#4112yes—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2411yescharacteristic
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124C2×Dic61C2×D411yescharacteristic
125D244—21no—
126D244—21no—
127D244—42no—
128C4×D61—24no—
129C4×D61—22no—
130C4×D61—21no—
131C4×D61—21no—
132C4×D61—41no—
133C4×D61—42no—
134C4×D61—42no—
135Dic122—24no—
136Dic122—21no—
137Dic122—21no—
138Dic122—21no—
139Dic122#4112yes—
140C8×C61—21no—
141C8×C61—21no—
142#92418—21no—
143#92418—21no—
144C22×C61C22×D411yescharacteristic
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—41no—
150C2×D61#13712yes—
151C4×C61—22no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61C2×#4111yescharacteristic
158C4×C61C2×#4111yescharacteristic
159Dic61—21no—
160Dic61—22no—
161Dic61—21no—
162Dic61—21no—
163Dic61—41no—
164Dic61—41no—
165#3117—611nomaximal, Sylow
166C2×C61#52511yescharacteristic
167C2×C61C2×#13711yescharacteristic
168C2×C61#57511yescharacteristic
169D61—22no—
170D61—81no—
171#529—611no—
172C2×C4×Q8—611no—
173#484—611no—
174#481—611no—
175#479—611no—
176#479D6111yescharacteristic, complemented
177#464—611no—
178#464—611no—
179#451—611no—
180#448—611no—
181#441—611no—
182#441—611no—
183#440—611no—
184#440—611no—
185#432—611no—
186C61#311711yescharacteristic, complemented, Sylow
187C22×Q8—611no—
188C2×Q16—611no—
189C2×Q16—611no—
190C2×SD16—611no—
191C2×SD16—611no—
192#126—1221no—
193#125C2×D6111yescharacteristic
194#124—611no—
195#123—1221no—
196C22⋊Q8—611no—
197#121—611no—
198C4×Q8—611no—
199C4×Q8—611no—
200C4×Q8—611no—
201C4×Q8—611no—
202C4×Q8—1221no—
203C4×Q8—1221no—
204C4×Q8C2×D6111yescharacteristic
205C4×D4—611no—
206C4×D4—1221no—
207#117—1221no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—1221no—
210C2×C42—611no—
211C2×C42—1221no—
212#107—611no—
213#107C2×D6111yescharacteristic
214#106—611no—
215#106C2×D6111yescharacteristic
216C4⋊C8—611no—
217C4⋊C8C2×D6111yescharacteristic
218#103—611no—
219#103—611no—
220#103—611no—
221#103—611no—
222#103C2×D6111yescharacteristic
223#103C2×D6111yescharacteristic
224#102—611no—
225#102—611no—
226C22⋊C8—611no—
227C22⋊C8—611no—
228#97—611no—
229#97—611no—
230C2×Q8—611no—
231C2×Q8—611no—
232C2×Q8—1221no—
233C2×Q8—1222no—
234C2×Q8—1222no—
235C2×Q8C22×D6111yescharacteristic
236C2×D4—611no—
237C2×D4—1221no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244Q16—1222no—
245Q16—1222no—
246SD16—1222no—
247SD16—1222no—
248C2×C8—611no—
249C2×C8—611no—
250C2×C8C22×D6111yescharacteristic
251C2×C8C22×D6111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—611no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4C22×D6111yescharacteristic
263C4⋊C4C22×D6111yescharacteristic
264C4⋊C4C22×D6111yescharacteristic
265C22⋊C4—1221no—
266C22⋊C4—1221no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C42—21no—
271C42—611no—
272C42—611no—
273C42—611no—
274C42—1221no—
275C42—1221no—
276C42—1221no—
277C42—1221no—
278C42C22×D6111yescharacteristic
279C23—611no—
280C23—1221no—
281Q8—21no—
282Q8—612no—
283Q8—1224no—
284Q8—1221no—
285Q8—1221no—
286Q8—1221no—
287Q8#1175822612yes—
288D4—1221no—
289D4—1221no—
290D4—2442no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—611no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—1222no—
299C2×C4—1224no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—2441no—
306C2×C4—2442no—
307C2×C4—2442no—
308C2×C4D4×D6111yescharacteristic
309C2×C4D4×D6111yescharacteristic
310C2×C4C23×D6111yescharacteristic
311C8—21no—
312C8—21no—
313C8—1221no—
314C8—1221no—
315C22—612no—
316C22—1221no—
317C22—1221no—
318C22—2441no—
319C22—2441no—
320C22—2441no—
321C22C2×D4×D6111yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—1221no—
329C4—1222no—
330C4—1221no—
331C4—1221no—
332C4—2441no—
333C4—2441no—
334C4#41×D6111yescharacteristic
335C4C2×#1175822611yescharacteristic
336C2—1222no—
337C2—4881no—
338C2#1684027511yescharacteristic
339C2#137×D6111yescharacteristic
340C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#479C2
socleC22×C61C22×D4
hypercenter#479D61
hypocenterC61#3117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D61C2semidirect
3. #16840099C2semidirect
5. #16840066C2semidirect
6. #16839985C2semidirect
7. #16839984C2semidirect
8. #16839919C2semidirect
10. #16839868C2semidirect
11. #16839866C2semidirect
12. #16839865C2semidirect
13. #16839861C2semidirect
14. #16839818C2semidirect
15. C61×#479C2semidirect
176. #479D61semidirect
186. C61#3117semidirect