Finite Group Databasebeta

← #21456694

Subgroups — #21456694

Order 7808.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840341C211yesmaximal, characteristic
2#16840335C211yesmaximal, characteristic, complemented
3#16840106C211yesmaximal, characteristic, complemented
4#16840096C211yesmaximal, characteristic, complemented
5#16840094C211yesmaximal, characteristic, complemented
6#16840084C211yesmaximal, characteristic, complemented
7#16840018C211yesmaximal, characteristic, complemented
8#16840006C211yesmaximal, characteristic, complemented
9#16840003C211yesmaximal, characteristic, complemented
10#16839925C211yesmaximal, characteristic, complemented
11#16839921C211yesmaximal, characteristic, complemented
12#16839919C211yesmaximal, characteristic, complemented
13#16839899C211yesmaximal, characteristic, complemented
14#16839728C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×Dic244C2211yescharacteristic
20C2×#11758202C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758194C2211yescharacteristic
23#14519776—21no—
24#14519763—21no—
25#14519762—21no—
26#14519759—21no—
27#14519757C2211yescharacteristic
28#14519757C2211yescharacteristic
29#14519756C2211yescharacteristic
30#14519756C2211yescharacteristic
31#14519754—21no—
32#14519753C2211yescharacteristic
33#14519750—21no—
34#14519749—21no—
35#14519748—21no—
36#14519748C2211yescharacteristic
37#14519735C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66C2×C22⋊D61D411yescharacteristic
67C22×Dic61—21no—
68Q8×D61—41no—
69Q8×D61—41no—
70#11758224—41no—
71#11758224—41no—
72#11758222—41no—
73#11758222—41no—
74C2×D244D411yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×C4×D61C2311yescharacteristic
79C2×Dic122—21no—
80C2×Dic122D411yescharacteristic
81C2×Dic122C2311yescharacteristic
82C2×Dic122C2311yescharacteristic
83SD16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758202—41no—
96#11758200—41no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110#11758194—41no—
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113Dic244—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61C2×D411yescharacteristic
117C22×D61C2×D411yescharacteristic
118Q8×C61—21no—
119Q8×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—81no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—41no—
131C22⋊D61—41no—
132C22⋊D61—42no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—41no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—42no—
147C4×D61—81no—
148Dic122—21no—
149Dic122—21no—
150Dic122—21no—
151Dic122—21no—
152Dic122—41no—
153Dic122—42no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61H(5,𝔽2)11yescharacteristic
176C4×C61H(5,𝔽2)11yescharacteristic
177Dic61—21no—
178Dic61—21no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183#3201—611nomaximal, Sylow
184C2×C61—41no—
185C2×C61—81no—
186C2×C61#53411yescharacteristic
187C2×C61#57711yescharacteristic
188C2×C61#57811yescharacteristic
189D61—41no—
190D61—41no—
191#537—611no—
192#536—611no—
193#485—611no—
194#484—611no—
195#483—611no—
196#482—611no—
197#470—611no—
198#468—611no—
199#467—611no—
200#465D6111yescharacteristic, complemented
201#452—611no—
202#452—611no—
203#451—611no—
204#448—611no—
205#408—611no—
206C61#320111yescharacteristic, complemented, Sylow
207C2×#41—611no—
208C2×#41—611no—
209C22×Q8—611no—
210C2×Q16—611no—
211C2×Q16—611no—
212C2×SD16—611no—
213C2×SD16C2×D6111yescharacteristic
214C2×M16—611no—
215C22×C8C2×D6111yescharacteristic
216C4⋊Q8—1221no—
217#124—1221no—
218#123—1221no—
219#123—1221no—
220C22⋊Q8—611no—
221C22⋊Q8—611no—
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—611no—
225C22⋊Q8—1221no—
226C22⋊Q8C2×D6111yescharacteristic
227#121—611no—
228#121—1221no—
229#121—1221no—
230#121—1221no—
231#121C2×D6111yescharacteristic
232#117—611no—
233C2×C4⋊C4—611no—
234#107—611no—
235#107—611no—
236#106—611no—
237#106C2×D6111yescharacteristic
238#103—611no—
239#103—611no—
240#103—611no—
241#103—611no—
242#103—611no—
243#103C2×D6111yescharacteristic
244#102—611no—
245#102C2×D6111yescharacteristic
246C22⋊C8—611no—
247C22⋊C8—611no—
248C22⋊C8—611no—
249C22⋊C8—611no—
250#41—2441no—
251#41—2441no—
252#41—2441no—
253#41—2441no—
254C2×Q8—611no—
255C2×Q8—611no—
256C2×Q8—611no—
257C2×Q8—1221no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8C22×D6111yescharacteristic
261C2×D4—21no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4C22×D6111yescharacteristic
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4C22×D6111yescharacteristic
274Q16—2441no—
275Q16—2441no—
276SD16—41no—
277SD16—2441no—
278M16—2441no—
279C2×C8—41no—
280C2×C8—611no—
281C2×C8—611no—
282C2×C8C22×D6111yescharacteristic
283C2×C8C22×D6111yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—611no—
286C4⋊C4—611no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4C22×D6111yescharacteristic
294C4⋊C4C22×D6111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C42—1221no—
305C23—21no—
306C23—611no—
307C23—611no—
308C23D4×D6111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—1221no—
312Q8—1221no—
313Q8—1221no—
314Q8—1221no—
315Q8—2441no—
316Q8—2442no—
317D4—21no—
318D4—21no—
319D4—81no—
320D4—4881no—
321D4—2441no—
322D4—2441no—
323D4—2441no—
324D4—2442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—4881no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4D4×D6111yescharacteristic
344C2×C4C23×D6111yescharacteristic
345C8—21no—
346C8—21no—
347C8—1221no—
348C8—1221no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—1221no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22—1221no—
360C22—1221no—
361C22C2×D4×D6111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—1221no—
367C4—1221no—
368C4—2441no—
369C4—2441no—
370C4—2441no—
371C4—2441no—
372C4#1451982211yescharacteristic
373C4#1451982311yescharacteristic
374C2—41no—
375C2—81no—
376C2—2441no—
377C2—2441no—
378C2#1684032011yescharacteristic
379C2#1684056811yescharacteristic
380C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3201
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. #16840335C2semidirect
3. #16840106C2semidirect
4. #16840096C2semidirect
5. #16840094C2semidirect
6. #16840084C2semidirect
7. #16840018C2semidirect
8. #16840006C2semidirect
9. #16840003C2semidirect
10. #16839925C2semidirect
11. #16839921C2semidirect
12. #16839919C2semidirect
13. #16839899C2semidirect
14. #16839728C2semidirect
15. C61×#465C2semidirect
200. #465D61semidirect
206. C61#3201semidirect