Finite Group Databasebeta

← #21459496

Subgroups — #21459496

Order 7808.

1522 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519825C211yesmaximal, characteristic, complemented
2C22×#11758226C211yesmaximal, characteristic, complemented
3Q8×C22⋊D61C211yesmaximal, characteristic, complemented
4#16840424C211yesmaximal, characteristic, complemented
5#16840423C211yesmaximal, characteristic, complemented
6#16840415C213yesmaximal, complemented
7#16840414C213yesmaximal, complemented
8#16840408C213yesmaximal, complemented
9#16840403C213yesmaximal, complemented
10#16840342C213yesmaximal, complemented
11#16840337C213yesmaximal, complemented
12#16840271C213yesmaximal, complemented
13C22⋊Q8×D61C213yesmaximal, complemented
14#16840244C211yesmaximal, characteristic, complemented
15D4×Q8×C61C211yesmaximal, characteristic, complemented
16#14519825—28no—
17C2×#11758226—28no—
18C2×#11758226C2213yes—
19C2×#11758226C2213yes—
20C2×#11758226C2211yescharacteristic
21C2×#11758226C2211yescharacteristic
22C2×#11758226C2213yescomplemented
23C2×#11758222C2213yescomplemented
24C2×#11758222C2213yescomplemented
25C2×Q8×D61C2213yescomplemented
26C2×Q8×D61C2211yescharacteristic, complemented
27C22×D244C2213yes—
28C22×C4×D61C2213yes—
29#14519775C2213yescomplemented
30#14519766C2213yescomplemented
31#14519765C2213yescomplemented
32#14519762C2213yescomplemented
33#14519762C2216yescomplemented
34#14519762C2216yescomplemented
35#14519759C2213yescomplemented
36#14519757C2213yescomplemented
37#14519756C2213yes—
38#14519755C2216yescomplemented
39#14519755C2213yescomplemented
40#14519754C2213yes—
41#14519753C2213yescomplemented
42#14519753C2213yescomplemented
43#14519752C2216yescomplemented
44#14519752C2213yescomplemented
45#14519751C2213yescomplemented
46#14519750C2213yescomplemented
47#14519750C2216yescomplemented
48#14519749C2211yescharacteristic
49#14519747C2213yes—
50#14519745C2213yes—
51Q8×Dic61C2211yescharacteristic, complemented
52C4×D244C2213yescomplemented
53C4×D244C2213yescomplemented
54#14519739C2213yescomplemented
55C4×C22⋊D61C2213yes—
56C4×C22⋊D61C2213yescomplemented
57#14519734C2213yescomplemented
58C4⋊C4×D61C2213yescomplemented
59C4⋊C4×D61C2216yescomplemented
60C22⋊C4×D61C2216yes—
61C22×Q8×C61C2211yescharacteristic
62C22×Q8×C61C2211yescharacteristic, complemented
63C4⋊Q8×C61C2213yescomplemented
64C22⋊Q8×C61C2213yes—
65C22⋊Q8×C61C2213yescomplemented
66C4×Q8×C61C2211yescharacteristic, complemented
67C4×D4×C61C2213yes—
68C23×D61C2313yes—
69C2×Q8×C61—24no—
70C2×Q8×C61—24no—
71C2×Q8×C61C2313yes—
72C2×Q8×C61C2313yes—
73C2×Q8×C61C2311yescharacteristic
74C2×D4×C61C2311yescharacteristic
75C22×C4×C61C2313yes—
76C22×C4×C61C2313yes—
77C2×C22⋊D61C2313yes—
78C2×C22⋊D61C2311yescharacteristic
79C2×C22⋊D61C2311yescharacteristic
80C2×C22⋊D61C2313yes—
81C22×Dic61C2311yescharacteristic
82#11758226—24no—
83#11758226—212no—
84#11758226—212no—
85#11758226—212no—
86#11758226D418yescomplemented
87Q8×D61—24no—
88Q8×D61—212no—
89#11758222—212no—
90#11758222—212no—
91C2×D244—212no—
92C2×D244C2316yes—
93C2×D244C2313yes—
94C2×D244C2313yes—
95C2×D244C2313yes—
96C2×D244C2313yes—
97C2×C4×D61—212no—
98C2×C4×D61C2313yes—
99C2×C4×D61C2313yes—
100C2×C4×D61C2313yes—
101C2×C4×D61C2316yes—
102C2×C4×D61C2313yes—
103C2×C4×D61C2316yes—
104C2×C4×D61C2313yes—
105C2×Dic122C2313yes—
106C2×Dic122C2313yes—
107C4⋊C4×C61C2313yes—
108C4⋊C4×C61C2313yes—
109C4⋊C4×C61C2316yes—
110C22⋊C4×C61C2313yes—
111C22⋊C4×C61C2313yes—
112C42×C61C2313yes—
113C22⋊Dic61C2313yes—
114C22⋊Dic61C2311yescharacteristic
115#11758198C2316yes—
116#11758198C2316yes—
117#11758198C2313yes—
118#11758198C2313yes—
119#11758198C2313yes—
120#11758198C2313yes—
121#11758198C2311yescharacteristic
122#11758198C2313yes—
123C4⋊Dic61C2313yes—
124C4⋊Dic61C2313yes—
125#11758196C2313yes—
126#11758196C2313yes—
127#11758196C2316yes—
128#11758196C2311yescharacteristic
129#11758196C2313yes—
130C4×Dic61C2313yes—
131C23×C61C2411yescharacteristic
132C23×C61C2411yescharacteristic
133C22×D61—26no—
134C22×D61—26no—
135C22×D61—43no—
136C22×D61C2413yes—
137C22×D61C2411yescharacteristic
138C22×D61C2413yes—
139Q8×C61—26no—
140Q8×C61—26no—
141Q8×C61C2×D414yes—
142D4×C61—22no—
143C2×C4×C61—26no—
144C2×C4×C61—26no—
145C2×C4×C61C2413yes—
146C2×C4×C61C2413yes—
147C2×C4×C61C2411yescharacteristic
148C2×C4×C61C2413yes—
149C2×C4×C61C2413yes—
150C22⋊D61—22no—
151C22⋊D61—26no—
152C22⋊D61—22no—
153C22⋊D61—43no—
154C2×Dic61—22no—
155C2×Dic61C2411yescharacteristic
156C2×Dic61C2413yes—
157C2×Dic61C2411yescharacteristic
158C2×Dic61C2413yes—
159C2×Dic61C2411yescharacteristic
160D244—212no—
161D244—26no—
162D244—26no—
163D244—43no—
164D244C2×D4112yes—
165C4×D61—26no—
166C4×D61—212no—
167C4×D61—26no—
168C4×D61—26no—
169C4×D61—26no—
170C4×D61—46no—
171C4×D61C2×D4112yes—
172Dic122—26no—
173Dic122—26no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C612−1+412yescomplemented
180C22×C61C2511yescharacteristic
181C2×D61—23no—
182C2×D61—23no—
183C2×D61—21no—
184C2×D61—23no—
185C2×D61—21no—
186C2×D61—23no—
187C2×D61—21no—
188C2×D61—23no—
189C2×D61—412no—
190C2×D61C22×D416yes—
191C4×C61—23no—
192C4×C61—23no—
193C4×C61—21no—
194C4×C61—23no—
195C4×C61C22×D416yes—
196Dic61—23no—
197Dic61—21no—
198Dic61—21no—
199Dic61—23no—
200Dic61C22×D412yes—
201#3489—611nomaximal, Sylow
202C2×C61—22no—
203C2×C61—41no—
204C2×C61C23×D411yescharacteristic
205C2×C61C2×2−1+411yescharacteristic
206C2×C61#58511yescharacteristic
207D61—26no—
208D61—41no—
209D61—43no—
210C2×2−1+4—611no—
211C22×#41—611no—
212D4×Q8—611no—
213D4×Q8D6111yescharacteristic, complemented
214#548—611no—
215#548—611no—
216#547—613no—
217#547—613no—
218#546—613no—
219#546—613no—
220#537—613no—
221#536—613no—
222#525—613no—
223C2×C22⋊Q8—613no—
224#520—611no—
225C61#348911yescharacteristic, complemented, Sylow
2262−1+4—1228no—
227C2×#41—611no—
228C2×#41—613no—
229C2×#41—613no—
230C2×#41—611no—
231C2×#41—613no—
232C2×#41—613no—
233C2×#41—613no—
234C2×#41—1228no—
235C22×Q8—613no—
236C22×Q8—611no—
237C22×Q8C2×D6111yescharacteristic
238C22×Q8C2×D6111yescharacteristic, complemented
239C22×D4—613no—
240C23×C4—613no—
241C4⋊Q8—613no—
242C4⋊Q8C2×D6113yescomplemented
243#124—613no—
244#124—613no—
245#123—613no—
246#123—616no—
247#123—616no—
248#123—613no—
249C22⋊Q8—613no—
250C22⋊Q8—613no—
251C22⋊Q8—613no—
252C22⋊Q8—616no—
253C22⋊Q8—613no—
254C22⋊Q8—613no—
255C22⋊Q8—613no—
256C22⋊Q8C2×D6113yes—
257C22⋊Q8C2×D6113yescomplemented
258#121—611no—
259#121—613no—
260#121—616no—
261#121—613no—
262#121—613no—
263#121—616no—
264#120—613no—
265#120—613no—
266C4×Q8—611no—
267C4×Q8C2×D6111yescharacteristic, complemented
268C4×D4—613no—
269C4×D4—613no—
270C4×D4—613no—
271C4×D4—613no—
272C4×D4—613no—
273C4×D4C2×D6113yes—
274#117—613no—
275C2×C4⋊C4—613no—
276C2×C4⋊C4—616no—
277C2×C22⋊C4—616no—
278C24—613no—
279#41—618no—
280#41—12212no—
281#41—12212no—
282#41—12212no—
283#41—12212no—
284#41—12212no—
285#41—1224no—
286C2×Q8—24no—
287C2×Q8—24no—
288C2×Q8—613no—
289C2×Q8—613no—
290C2×Q8—12212no—
291C2×Q8—1224no—
292C2×Q8C22×D6113yes—
293C2×Q8C22×D6113yes—
294C2×Q8C22×D6111yescharacteristic
295C2×D4—611no—
296C2×D4—613no—
297C2×D4—611no—
298C2×D4—613no—
299C2×D4—613no—
300C2×D4—613no—
301C2×D4—616no—
302C2×D4—613no—
303C2×D4—613no—
304C2×D4—12212no—
305C2×D4C22×D6111yescharacteristic
306C22×C4—613no—
307C22×C4—611no—
308C22×C4—616no—
309C22×C4—613no—
310C22×C4—613no—
311C22×C4—613no—
312C22×C4—613no—
313C22×C4—616no—
314C22×C4—12212no—
315C22×C4C22×D6113yes—
316C22×C4C22×D6113yes—
317C4⋊C4—613no—
318C4⋊C4—613no—
319C4⋊C4—613no—
320C4⋊C4—616no—
321C4⋊C4—613no—
322C4⋊C4—611no—
323C4⋊C4—613no—
324C4⋊C4C22×D6113yes—
325C4⋊C4C22×D6116yes—
326C4⋊C4C22×D6113yes—
327C22⋊C4—613no—
328C22⋊C4—611no—
329C22⋊C4—616no—
330C22⋊C4—616no—
331C22⋊C4—613no—
332C22⋊C4—613no—
333C22⋊C4—611no—
334C22⋊C4—613no—
335C22⋊C4—613no—
336C22⋊C4—613no—
337C22⋊C4C22×D6113yes—
338C22⋊C4C22×D6113yes—
339C42—613no—
340C42C22×D6113yes—
341C23—613no—
342C23—613no—
343C23—611no—
344C23—1226no—
345C23—1226no—
346C23—2443no—
347C23C23×D6111yescharacteristic
348C23C23×D6111yescharacteristic
349Q8—26no—
350Q8—26no—
351Q8—1226no—
352Q8—1226no—
353Q8D4×D6114yes—
354D4—22no—
355D4—6112no—
356D4—12212no—
357D4—1226no—
358D4—1222no—
359D4—1226no—
360D4—1222no—
361D4—1226no—
362D4—2443no—
363D4—2443no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—611no—
367C2×C4—6112no—
368C2×C4—611no—
369C2×C4—613no—
370C2×C4—613no—
371C2×C4—611no—
372C2×C4—1226no—
373C2×C4—1226no—
374C2×C4—12212no—
375C2×C4—1222no—
376C2×C4—1226no—
377C2×C4—1226no—
378C2×C4—2446no—
379C2×C4C23×D6111yescharacteristic
380C2×C4C23×D6113yes—
381C2×C4C23×D6113yes—
382C2×C4C23×D6113yes—
383C2×C4C23×D6113yes—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—616no—
390C22—1223no—
391C22—1223no—
392C22—1221no—
393C22—1223no—
394C22—1221no—
395C22—1223no—
396C22—1221no—
397C22—1223no—
398C22—24412no—
399C22#1451982512yescomplemented
400C22C24×D6111yescharacteristic
401C4—23no—
402C4—23no—
403C4—21no—
404C4—23no—
405C4—612no—
406C4—1221no—
407C4—1223no—
408C4—1221no—
409C4—1223no—
410C4C2×D4×D6116yes—
411C2—22no—
412C2—41no—
413C2—1226no—
414C2—2443no—
415C2—2441no—
416C2C22×D4×D6111yescharacteristic
417C2C2×#1451982511yescharacteristic
418C2#1684059911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingD4×Q8×C61C2
hypercenterD4×Q8D61
hypocenterC61#3489
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14519825C2semidirect
2. C22×#11758226C2semidirect
3. Q8×C22⋊D61C2semidirect
4. #16840424C2semidirect
5. #16840423C2semidirect
6. #16840415C2semidirect
7. #16840414C2semidirect
8. #16840408C2semidirect
9. #16840403C2semidirect
10. #16840342C2semidirect
11. #16840337C2semidirect
12. #16840271C2semidirect
13. C22⋊Q8×D61C2semidirect
14. #16840244C2semidirect
15. D4×Q8×C61C2semidirect
22. C2×#11758226C22semidirect
23. C2×#11758222C22semidirect
24. C2×#11758222C22semidirect
25. C2×Q8×D61C22semidirect
26. C2×Q8×D61C22semidirect
29. #14519775C22semidirect
30. #14519766C22semidirect
31. #14519765C22semidirect
32. #14519762C22semidirect
33. #14519762C22semidirect
34. #14519762C22semidirect
35. #14519759C22semidirect
36. #14519757C22semidirect
38. #14519755C22semidirect
39. #14519755C22semidirect
41. #14519753C22semidirect
42. #14519753C22semidirect
43. #14519752C22semidirect
44. #14519752C22semidirect
45. #14519751C22semidirect
46. #14519750C22semidirect
47. #14519750C22semidirect
51. Q8×Dic61C22semidirect
52. C4×D244C22semidirect
53. C4×D244C22semidirect
54. #14519739C22semidirect
56. C4×C22⋊D61C22semidirect
57. #14519734C22semidirect
58. C4⋊C4×D61C22semidirect
59. C4⋊C4×D61C22semidirect
62. C22×Q8×C61C22semidirect
63. C4⋊Q8×C61C22semidirect
65. C22⋊Q8×C61C22semidirect
66. C4×Q8×C61C22semidirect
86. #11758226D4semidirect
179. C22×C612−1+4semidirect
213. D4×Q8D61semidirect
225. C61#3489semidirect
238. C22×Q8C2×D61semidirect
242. C4⋊Q8C2×D61semidirect
257. C22⋊Q8C2×D61semidirect
267. C4×Q8C2×D61semidirect
399. C22#14519825semidirect