Finite Group Databasebeta

← #21458313

Subgroups — #21458313

Order 7808.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840477C211yesmaximal, characteristic, complemented
2#16840172C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840083C211yesmaximal, characteristic, complemented
5#16840083C211yesmaximal, characteristic, complemented
6#16840075C211yesmaximal, characteristic, complemented
7#16840059C211yesmaximal, characteristic, complemented
8#16840042C211yesmaximal, characteristic, complemented
9#16840013C211yesmaximal, characteristic, complemented
10#16839996C211yesmaximal, characteristic, complemented
11#16839872C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839802C211yesmaximal, characteristic, complemented
14#16839798C211yesmaximal, characteristic, complemented
15C61×#553C211yesmaximal, characteristic, complemented
16C2×#11758199C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519763—21no—
21#14519763—21no—
22#14519751C2211yescharacteristic
23#14519751C2211yescharacteristic
24#14519748—21no—
25C4×D244C2211yescharacteristic
26#14519736C2211yescharacteristic
27#14519736C2211yescharacteristic
28#14519735—21no—
29#14519710C2211yescharacteristic
30#14519710C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519710C2211yescharacteristic
34#14519708C2211yescharacteristic
35#14519708C2211yescharacteristic
36#14519708C2211yescharacteristic
37#14519708C2211yescharacteristic
38C4⋊#92418C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48#126×C61—21no—
49#125×C61C2211yescharacteristic
50#123×C61—21no—
51#121×C61—21no—
52#121×C61C2211yescharacteristic
53#121×C61C2211yescharacteristic
54C4×D4×C61—21no—
55C4×D4×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57#117×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61D411yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×Dic122—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61D411yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊C4×C61D411yescharacteristic
84C22⋊C4×C61D411yescharacteristic
85C42×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758199—22no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4×Dic61—21no—
98C4×Dic61—21no—
99#11758194—22no—
100C2×#92418—22no—
101C2×#92418C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C23×C61—21no—
106C23×C61C2×D411yescharacteristic
107C23×C61C2×D411yescharacteristic
108C22×D61—21no—
109D4×C61—21no—
110D4×C61—21no—
111D4×C61—41no—
112D4×C61—42no—
113D4×C61—81no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—81no—
122C2×C4×C61—81no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—81no—
129C22⋊D61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133D244—21no—
134D244—21no—
135C4×D61—42no—
136Dic122—81no—
137#92418—21no—
138#92418—21no—
139#92418—21no—
140#92418#4112yes—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61C22×D411yescharacteristic
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61C2×#4111yescharacteristic
162C4×C612−1+411yescharacteristic
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166#3347—611nomaximal, Sylow
167C2×C61—41no—
168C2×C61—41no—
169C2×C61—81no—
170C2×C61#54711yescharacteristic
171C2×C61#57511yescharacteristic
172C2×C61#57611yescharacteristic
173D61—81no—
174#555—611no—
175#553D6111yescharacteristic, complemented
176#501—611no—
177#482—611no—
178#482—611no—
179#482—611no—
180#480—611no—
181#478—611no—
182#474—611no—
183#469—611no—
184#466—611no—
185#442—611no—
186#435—611no—
187#428—611no—
188#427—611no—
189C61#334711yescharacteristic, complemented, Sylow
190C2×D8—611no—
191C2×M16—611no—
192C22×C8—611no—
193C4⋊Q8—611no—
194#126—21no—
195#125C2×D6111yescharacteristic
196#124—1221no—
197#124—1221no—
198#123—21no—
199#121—21no—
200#121—611no—
201#121—611no—
202#121—1221no—
203#121C2×D6111yescharacteristic
204#121C2×D6111yescharacteristic
205C4×D4—21no—
206C4×D4—611no—
207C4×D4C2×D6111yescharacteristic
208C4×D4C2×D6111yescharacteristic
209#117—611no—
210#117—611no—
211#117—1221no—
212#117C2×D6111yescharacteristic
213C2×C4⋊C4C2×D6111yescharacteristic
214#107—611no—
215#107—611no—
216#107—611no—
217#107—611no—
218#107—611no—
219#106—611no—
220#106—611no—
221#106—611no—
222#106—611no—
223C4⋊C8—611no—
224#102—611no—
225#102—611no—
226#102—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230C22⋊C8—611no—
231C22⋊C8—611no—
232#97—611no—
233C2×Q8—1221no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—611no—
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4C22⋊D6111yescharacteristic
240C2×D4C22×D6111yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—1221no—
244C22×C4C22×D6111yescharacteristic
245C22×C4C22×D6111yescharacteristic
246D8—1222no—
247M16—1222no—
248C2×C8—611no—
249C2×C8—611no—
250C2×C8—611no—
251C2×C8—611no—
252C2×C8—1222no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—611no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—1221no—
260C4⋊C4C22⋊D6111yescharacteristic
261C4⋊C4C22×D6111yescharacteristic
262C4⋊C4C22×D6111yescharacteristic
263C4⋊C4C22×D6111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4C22⋊D6111yescharacteristic
274C22⋊C4C22⋊D6111yescharacteristic
275C42—21no—
276C42—1221no—
277C42—1221no—
278C42C22×D6111yescharacteristic
279C23—21no—
280C23—1221no—
281C23C2×C22⋊D6111yescharacteristic
282C23C2×C22⋊D6111yescharacteristic
283Q8—4881no—
284D4—21no—
285D4—21no—
286D4—41no—
287D4—42no—
288D4—81no—
289D4—1221no—
290D4—1221no—
291D4—4881no—
292D4—4881no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—2442no—
306C2×C4C2×C22⋊D6111yescharacteristic
307C2×C4C2×C22⋊D6111yescharacteristic
308C2×C4C2×C22⋊D6111yescharacteristic
309C2×C4C2×C22⋊D6111yescharacteristic
310C2×C4C23×D6111yescharacteristic
311C8—612no—
312C8—1221no—
313C8—1221no—
314C8—1221no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—2441no—
325C22—2441no—
326C22—2441no—
327C22C22×C22⋊D6111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—2441no—
336C4—2441no—
337C4—2441no—
338C4#41×D6111yescharacteristic
339C4#1451982411yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—4881no—
344C2#1684041111yescharacteristic
345C2#1684056011yescharacteristic
346C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#553C2
socleC22×C61C22×D4
hypercenter#553D61
hypocenterC61#3347
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #16840477C2semidirect
2. #16840172C2semidirect
3. #16840086C2semidirect
4. #16840083C2semidirect
5. #16840083C2semidirect
6. #16840075C2semidirect
7. #16840059C2semidirect
8. #16840042C2semidirect
9. #16840013C2semidirect
10. #16839996C2semidirect
11. #16839872C2semidirect
12. #16839834C2semidirect
13. #16839802C2semidirect
14. #16839798C2semidirect
15. C61×#553C2semidirect
175. #553D61semidirect
189. C61#3347semidirect