Finite Group Databasebeta

← #21456647

Subgroups — #21456647

Order 7808.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840269C211yesmaximal, characteristic
2C22⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840104C211yesmaximal, characteristic, complemented
4#16840100C211yesmaximal, characteristic, complemented
5#16840096C211yesmaximal, characteristic, complemented
6#16840079C211yesmaximal, characteristic, complemented
7#16840019C211yesmaximal, characteristic, complemented
8#16840017C211yesmaximal, characteristic, complemented
9#16840007C211yesmaximal, characteristic, complemented
10#16840005C211yesmaximal, characteristic, complemented
11#16839924C211yesmaximal, characteristic, complemented
12#16839916C211yesmaximal, characteristic, complemented
13#16839899C211yesmaximal, characteristic, complemented
14#16839724C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C2×#11758202C2211yescharacteristic, complemented
19C2×#11758200C2211yescharacteristic, complemented
20C2×#11758189C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22#14519758—21no—
23#14519757C2211yescharacteristic
24#14519756C2211yescharacteristic
25#14519755—21no—
26#14519754—21no—
27#14519753C2211yescharacteristic
28#14519753C2211yescharacteristic
29#14519753C2211yescharacteristic
30#14519748C2211yescharacteristic
31#14519748C2211yescharacteristic
32#14519745—21no—
33C4×C22⋊D61—21no—
34C4×C22⋊D61—21no—
35#14519736C2211yescharacteristic
36C4⋊C4×D61—21no—
37C4⋊C4×D61C2211yescharacteristic
38C22⋊C4×D61—21no—
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519701C2211yescharacteristic, complemented
47#14519701C2211yescharacteristic, complemented
48#14519698C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C22⋊Q8×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61D411yescharacteristic
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C22×Dic61D411yescharacteristic
71Q8×D61—41no—
72Q8×D61—41no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61D411yescharacteristic
78C2×C4×D61D411yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122C2311yescharacteristic
83Q16×C61—41no—
84SD16×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94#11758202—41no—
95#11758200—41no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112#11758189—41no—
113#11758189—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—22no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61C2×D411yescharacteristic
120C22×D61C2×D411yescharacteristic
121Q8×C61—21no—
122Q8×C61—21no—
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—42no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—42no—
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—41no—
150C4×D61—41no—
151C4×D61—42no—
152C4×D61—42no—
153Dic122—21no—
154Dic122—21no—
155Dic122—42no—
156C8×C61—21no—
157C8×C61—21no—
158#92418—21no—
159#92418—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61C22×D411yescharacteristic
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—44no—
173C2×D61#13712yes—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61H(5,𝔽2)11yescharacteristic
179C4×C61H(5,𝔽2)11yescharacteristic
180Dic61—21no—
181Dic61—21no—
182Dic61—41no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186#3196—611nomaximal, Sylow
187C2×C61—41no—
188C2×C61—81no—
189C2×C61#53411yescharacteristic
190C2×C61C2×#13711yescharacteristic
191C2×C61#57511yescharacteristic
192D61—22no—
193D61—41no—
194#525—611no—
195C2×C22⋊Q8—611no—
196#485—611no—
197#485—611no—
198#484—611no—
199#481—611no—
200#470—611no—
201#470—611no—
202#468—611no—
203#468—611no—
204#452—611no—
205#452D6111yescharacteristic, complemented
206#451—611no—
207#448—611no—
208#407—611no—
209C61#319611yescharacteristic, complemented, Sylow
210C2×#41C2×D6111yescharacteristic
211C22×Q8—611no—
212C23×C4—611no—
213C2×Q16—611no—
214C2×Q16C2×D6111yescharacteristic, complemented
215C2×SD16—611no—
216C2×SD16C2×D6111yescharacteristic, complemented
217C2×M16—611no—
218C2×M16—611no—
219#123—1221no—
220C22⋊Q8—611no—
221C22⋊Q8—611no—
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—611no—
225C22⋊Q8—1221no—
226C22⋊Q8—1221no—
227C22⋊Q8C2×D6111yescharacteristic
228#121—611no—
229#121—611no—
230#120—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233#117—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C22⋊C4—1221no—
237#107—611no—
238#107—611no—
239#106—611no—
240#106—611no—
241#103—611no—
242#103—611no—
243#103—611no—
244#103—611no—
245#103—611no—
246#103C2×D6111yescharacteristic, complemented
247#102—611no—
248#102C2×D6111yescharacteristic, complemented
249C22⋊C8—611no—
250C22⋊C8—611no—
251C22⋊C8—611no—
252C22⋊C8C2×D6111yescharacteristic
253C24—611no—
254#41—41no—
255#41—41no—
256C2×Q8—611no—
257C2×Q8—1221no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8C22×D6111yescharacteristic
261C2×Q8C22×D6111yescharacteristic
262C2×D4—21no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4C22×D6111yescharacteristic
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4C22×D6111yescharacteristic
277Q16—41no—
278Q16—2441no—
279SD16—41no—
280SD16—2441no—
281M16—2441no—
282M16—2441no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8C22×D6111yescharacteristic
286C2×C8C22×D6111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4C22×D6111yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C42—1221no—
308C23—21no—
309C23—611no—
310C23—611no—
311C23—1222no—
312C23—2441no—
313C23—2441no—
314C23D4×D6111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—1221no—
320Q8—1221no—
321Q8—2442no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—2442no—
326D4—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2441no—
348C2×C4D4×D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—1221no—
353C8—1221no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—612no—
361C22—1221no—
362C22—1221no—
363C22—1221no—
364C22—1221no—
365C22—1221no—
366C22—2444no—
367C22C2×D4×D6111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—1221no—
373C4—1221no—
374C4—2441no—
375C4—2441no—
376C4—2441no—
377C4—2441no—
378C4#1451982211yescharacteristic
379C4#1451982211yescharacteristic
380C2—41no—
381C2—81no—
382C2—1222no—
383C2—2441no—
384C2#1684032211yescharacteristic
385C2#137×D6111yescharacteristic
386C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3196
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
2. C22⋊Q8×D61C2semidirect
3. #16840104C2semidirect
4. #16840100C2semidirect
5. #16840096C2semidirect
6. #16840079C2semidirect
7. #16840019C2semidirect
8. #16840017C2semidirect
9. #16840007C2semidirect
10. #16840005C2semidirect
11. #16839924C2semidirect
12. #16839916C2semidirect
13. #16839899C2semidirect
14. #16839724C2semidirect
15. C61×#452C2semidirect
18. C2×#11758202C22semidirect
19. C2×#11758200C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519709C22semidirect
42. #14519708C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
45. #14519701C22semidirect
46. #14519701C22semidirect
47. #14519701C22semidirect
48. #14519698C22semidirect
53. C2×Q16×C61C22semidirect
54. C2×SD16×C61C22semidirect
56. #103×C61C22semidirect
57. #102×C61C22semidirect
205. #452D61semidirect
209. C61#3196semidirect
214. C2×Q16C2×D61semidirect
216. C2×SD16C2×D61semidirect
246. #103C2×D61semidirect
248. #102C2×D61semidirect