Finite Group Databasebeta

← #21456773

Subgroups — #21456773

Order 7808.

394 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840314C211yesmaximal, characteristic, complemented
2#16840308C211yesmaximal, characteristic
3#16840140C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840111C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16839987C211yesmaximal, characteristic, complemented
8#16839986C211yesmaximal, characteristic, complemented
9#16839983C211yesmaximal, characteristic, complemented
10#16839982C211yesmaximal, characteristic, complemented
11#16839926C211yesmaximal, characteristic, complemented
12#16839924C211yesmaximal, characteristic, complemented
13#16839922C211yesmaximal, characteristic, complemented
14#16839812C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23#14519776C2211yescharacteristic
24#14519775C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519773C2211yescharacteristic
27#14519767—21no—
28#14519766C2211yescharacteristic
29#14519764C2211yescharacteristic
30#14519756C2211yescharacteristic
31#14519754—21no—
32#14519749—21no—
33#14519749—21no—
34Q8×Dic61C2211yescharacteristic
35#14519742—21no—
36#14519742C2211yescharacteristic
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39#14519733—21no—
40C2×C4×Dic61C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—41no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C22×Dic61D411yescharacteristic
71C22×Dic61D411yescharacteristic
72#11758222—41no—
73#11758222—41no—
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79Q16×C61—41no—
80SD16×C61—41no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758202—41no—
90#11758202—41no—
91#11758201—41no—
92#11758200—41no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61D411yescharacteristic
107C4×Dic61D411yescharacteristic
108C4×Dic61C2311yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112Dic244—41no—
113#11758190—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—42no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—42no—
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—42no—
133C22⋊D61—42no—
134C22⋊D61—42no—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146C4×D61—42no—
147Dic122—21no—
148Dic122—21no—
149Dic122—21no—
150Dic122—21no—
151Dic122—42no—
152C8×C61—21no—
153C8×C61—21no—
154#92418—21no—
155#92418—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61C22×D411yescharacteristic
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61H(5,𝔽2)11yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61#13512yes—
178Dic61#13712yes—
179#3210—611nomaximal, Sylow
180C2×C61—41no—
181C2×C61—81no—
182C2×C61#53511yescharacteristic
183C2×C61C2×#13511yescharacteristic
184C2×C61C2×#13711yescharacteristic
185D61—81no—
186#533—611no—
187#532—611no—
188#494—611no—
189#492—611no—
190#487—611no—
191#486—611no—
192#464—611no—
193#464—611no—
194#464—611no—
195#464—611no—
196#452—611no—
197#452—611no—
198#452—611no—
199#452D6111yescharacteristic, complemented
200#431—611no—
201C61#321011yescharacteristic, complemented, Sylow
202C2×#41—611no—
203C2×#41C2×D6111yescharacteristic
204C2×Q16—611no—
205C2×Q16—611no—
206C2×Q16—611no—
207C2×Q16C2×D6111yescharacteristic
208C2×SD16—611no—
209C2×SD16—611no—
210C2×SD16—611no—
211C2×SD16C2×D6111yescharacteristic
212C4⋊Q8—611no—
213C4⋊Q8—611no—
214C4⋊Q8—611no—
215#127—611no—
216#125—1221no—
217#124—611no—
218#124—611no—
219C22⋊Q8—611no—
220C22⋊Q8—1221no—
221C22⋊Q8C2×D6111yescharacteristic
222#121—1221no—
223#121—1221no—
224C4×Q8—611no—
225C4×Q8—611no—
226C4×Q8—1221no—
227C4×D4—1221no—
228C4×D4—1221no—
229#117—1221no—
230C2×C42—611no—
231C4⋊C8—611no—
232C4⋊C8—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103C2×D6111yescharacteristic
237#102—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241C22⋊C8—611no—
242C22⋊C8C2×D6111yescharacteristic
243C4×C8—611no—
244C4×C8—611no—
245#41—41no—
246#41—41no—
247#41—2441no—
248#41—2441no—
249C2×Q8—611no—
250C2×Q8—611no—
251C2×Q8—1221no—
252C2×Q8C22×D6111yescharacteristic
253C2×Q8C22×D6111yescharacteristic
254C2×D4—21no—
255C2×D4—611no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4C22×D6111yescharacteristic
260C22×C4—21no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4C22×D6111yescharacteristic
265Q16—41no—
266Q16—2441no—
267Q16—2441no—
268Q16—2441no—
269SD16—41no—
270SD16—2441no—
271SD16—2441no—
272SD16—2441no—
273C2×C8—611no—
274C2×C8—611no—
275C2×C8C22×D6111yescharacteristic
276C2×C8C22×D6111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—611no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4C22×D6111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—611no—
295C42—611no—
296C42—611no—
297C42—611no—
298C42—1221no—
299C42—1221no—
300C23—21no—
301C23—1221no—
302C23D4×D6111yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—1221no—
308Q8—1221no—
309Q8—1221no—
310Q8—1221no—
311Q8—2442no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—1221no—
316D4—1221no—
317D4—2442no—
318D4—2442no—
319D4—2442no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—1222no—
331C2×C4—1222no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—2442no—
336C2×C4D4×D6111yescharacteristic
337C2×C4C23×D6111yescharacteristic
338C8—21no—
339C8—21no—
340C8—1221no—
341C8—1221no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22C2×D4×D6111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—612no—
357C4—612no—
358C4—1221no—
359C4—1221no—
360C4—2441no—
361C4—2441no—
362C4—2441no—
363C4#1451982211yescharacteristic
364C4#1451982211yescharacteristic
365C2—41no—
366C2—81no—
367C2—4881no—
368C2#1684032711yescharacteristic
369C2#135×D6111yescharacteristic
370C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3210
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16840314C2semidirect
3. #16840140C2semidirect
4. #16840133C2semidirect
5. #16840111C2semidirect
6. #16840107C2semidirect
7. #16839987C2semidirect
8. #16839986C2semidirect
9. #16839983C2semidirect
10. #16839982C2semidirect
11. #16839926C2semidirect
12. #16839924C2semidirect
13. #16839922C2semidirect
14. #16839812C2semidirect
15. C61×#452C2semidirect
199. #452D61semidirect
201. C61#3210semidirect