Finite Group Databasebeta

← #21456185

Subgroups — #21456185

Order 7808.

372 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#16840392C211yesmaximal, characteristic, complemented
2#16840337C211yesmaximal, characteristic
3#16840129C211yesmaximal, characteristic, complemented
4#16840123C211yesmaximal, characteristic, complemented
5#16840122C211yesmaximal, characteristic, complemented
6#16840119C211yesmaximal, characteristic, complemented
7#16840118C211yesmaximal, characteristic, complemented
8#16840112C211yesmaximal, characteristic, complemented
9#16840111C211yesmaximal, characteristic, complemented
10#16839769C211yesmaximal, characteristic, complemented
11#16839762C211yesmaximal, characteristic
12#16839757C211yesmaximal, characteristic
13#103×D61C211yesmaximal, characteristic, complemented
14#16839719C211yesmaximal, characteristic, complemented
15C61×#491C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519777C2211yescharacteristic
21#14519776—21no—
22#14519776C2211yescharacteristic
23#14519775C2211yescharacteristic
24#14519768C2211yescharacteristic
25#14519767—21no—
26#14519766C2211yescharacteristic
27#14519765C2211yescharacteristic
28#14519762—21no—
29#14519762—21no—
30#14519757—21no—
31#14519755—21no—
32#14519755—21no—
33#14519755—21no—
34#14519735C2211yescharacteristic
35#14519734C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic
37#14519702C2211yescharacteristic
38#14519702C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519701C2211yescharacteristic
41#14519701C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519687C2211yescharacteristic
50C4×#92418C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61#11758226—22no—
62#11758226—22no—
63Q8×D61—22no—
64Q8×D61—22no—
65C2×D244—21no—
66C2×D244C2311yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61C2311yescharacteristic
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C42×C61C2311yescharacteristic
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198D411yescharacteristic
90#11758198D411yescharacteristic
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107C8×D61—22no—
108C22×D61—21no—
109C22×D61C2×D411yescharacteristic
110Q8×C61—21no—
111Q8×C61—21no—
112Q8×C61—21no—
113Q8×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127D244—21no—
128D244—21no—
129D244—42no—
130C4×D61—42no—
131C4×D61—42no—
132C4×D61—81no—
133C4×D61#4112yes—
134C4×D61#4112yes—
135Dic122—21no—
136Dic122—21no—
137Dic122—42no—
138Dic122—81no—
139Dic122—81no—
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#12412yes—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61C2×#4111yescharacteristic
158C4×C61C2×#4111yescharacteristic
159Dic61—21no—
160Dic61—21no—
161Dic61—41no—
162Dic61—41no—
163Dic61—41no—
164Dic61#12412yes—
165#3137—611nomaximal, Sylow
166C2×C61C2×#12411yescharacteristic
167C2×C61#57711yescharacteristic
168C2×C61#57811yescharacteristic
169D61—22no—
170D61—81no—
171#544—611no—
172#536—611no—
173#491—611no—
174#491D6111yescharacteristic, complemented
175#489—611no—
176#489—611no—
177#488—611no—
178#488—611no—
179#487—611no—
180#487—611no—
181#419—611no—
182#417—611no—
183#416—611no—
184C2×#103—611no—
185#405—611no—
186C61#313711yescharacteristic, complemented, Sylow
187C2×#41—611no—
188C22×Q8—611no—
189C2×M16—611no—
190C22×C8—611no—
191C4⋊Q8—611no—
192C4⋊Q8—611no—
193C4⋊Q8—611no—
194C4⋊Q8—1221no—
195C4⋊Q8C2×D6111yescharacteristic
196#125—611no—
197#125—1221no—
198#125C2×D6111yescharacteristic
199#124—611no—
200#124—611no—
201#123—1221no—
202#123—1221no—
203C22⋊Q8—1221no—
204C22⋊Q8—1221no—
205C22⋊Q8—1221no—
206C22⋊Q8—1221no—
207#117—611no—
208#117—611no—
209C2×C4⋊C4—611no—
210#103—611no—
211#103—611no—
212#103—611no—
213#103—611no—
214#103—611no—
215#103—611no—
216#103—611no—
217#103—611no—
218#103C2×D6111yescharacteristic
219#103C2×D6111yescharacteristic
220#103C2×D6111yescharacteristic
221#103C2×D6111yescharacteristic
222#102—611no—
223#102—611no—
224#102—611no—
225#102—611no—
226#97—611no—
227#97C2×D6111yescharacteristic
228C4×C8—611no—
229C4×C8—611no—
230#41—1222no—
231#41—1222no—
232C2×Q8—611no—
233C2×Q8—1221no—
234C2×Q8—1221no—
235C2×Q8—1222no—
236C2×Q8—1222no—
237C2×Q8—1221no—
238C2×Q8C22×D6111yescharacteristic
239C2×Q8C22×D6111yescharacteristic
240C2×D4—611no—
241C2×D4—1221no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246M16—1222no—
247C2×C8—611no—
248C2×C8—611no—
249C2×C8—1222no—
250C2×C8C22×D6111yescharacteristic
251C2×C8C22×D6111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—611no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4C22×D6111yescharacteristic
268C4⋊C4C22×D6111yescharacteristic
269C22⋊C4—611no—
270C22⋊C4—611no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C42—611no—
277C42—1221no—
278C42C22×D6111yescharacteristic
279C23—611no—
280C23—1221no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—1221no—
286Q8—1221no—
287Q8—4881no—
288Q8—4881no—
289Q8—2442no—
290D4—1221no—
291D4—1221no—
292D4—2442no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—611no—
298C2×C4—612no—
299C2×C4—612no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—4881no—
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—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—612no—
329C4—1221no—
330C4—1221no—
331C4—2441no—
332C4—2441no—
333C4—2441no—
334C4#41×D6111yescharacteristic
335C4#41×D6111yescharacteristic
336C2—1222no—
337C2—4881no—
338C2#124×D6111yescharacteristic
339C2#1684057111yescharacteristic
340C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#491C2
socleC22×C61C22×D4
hypercenter#491D61
hypocenterC61#3137
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #16840392C2semidirect
3. #16840129C2semidirect
4. #16840123C2semidirect
5. #16840122C2semidirect
6. #16840119C2semidirect
7. #16840118C2semidirect
8. #16840112C2semidirect
9. #16840111C2semidirect
10. #16839769C2semidirect
13. #103×D61C2semidirect
14. #16839719C2semidirect
15. C61×#491C2semidirect
174. #491D61semidirect
186. C61#3137semidirect