Finite Group Databasebeta

← #21459472

Subgroups — #21459472

Order 7808.

1536 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519824C211yesmaximal, characteristic, complemented
2C2×#41×D61C211yesmaximal, characteristic, complemented
3#16840432C213yesmaximal, complemented
4#16840431C211yesmaximal, characteristic, complemented
5#16840430C213yesmaximal, complemented
6#16840424C211yesmaximal, characteristic, complemented
7#16840421C213yesmaximal, complemented
8#16840419C211yesmaximal, characteristic, complemented
9#16840418C213yesmaximal, complemented
10#16840328C213yesmaximal, complemented
11#16840325C213yesmaximal, complemented
12#16840272C213yesmaximal, complemented
13#16840271C213yesmaximal, complemented
14#16840238C211yesmaximal, characteristic, complemented
15C61×#550C211yesmaximal, characteristic, complemented
16#14519824—28no—
17C2×#11758226C2211yescharacteristic
18C2×#11758222C2213yes—
19C2×#11758222C2213yes—
20C2×#11758224C2213yes—
21C2×#11758224C2213yes—
22C2×#11758224C2213yescomplemented
23#41×D61—28no—
24C22×Dic122C2213yescomplemented
25C2×Q8×D61C2211yescharacteristic
26C2×Q8×D61C2211yescharacteristic, complemented
27C2×D4×D61C2213yes—
28C22×C4×D61C2213yes—
29#14519773C2213yescomplemented
30#14519773C2216yescomplemented
31#14519765C2213yescomplemented
32#14519764C2213yescomplemented
33#14519763C2216yescomplemented
34#14519762C2211yescharacteristic
35#14519759C2213yes—
36#14519757C2213yescomplemented
37#14519756C2213yescomplemented
38#14519755C2213yescomplemented
39#14519754C2213yescomplemented
40#14519752C2213yescomplemented
41#14519751C2213yescomplemented
42#14519750C2213yescomplemented
43#14519749C2213yescomplemented
44#14519749C2216yescomplemented
45#14519749C2216yescomplemented
46#14519748C2213yescomplemented
47#14519748C2213yescomplemented
48#14519747C2213yes—
49#14519745C2213yes—
50#14519745C2216yes—
51Q8×Dic61C2211yescharacteristic, complemented
52C4×Dic122C2213yescomplemented
53#14519742C2213yescomplemented
54C4×D244C2213yescomplemented
55D4×Dic61C2216yescomplemented
56C4×C22⋊D61C2213yescomplemented
57C4×C22⋊D61C2213yescomplemented
58#14519737C2216yescomplemented
59#14519735C2213yes—
60#14519734C2213yes—
61C2×#41×C61C2211yescharacteristic
62C2×#41×C61C2211yescharacteristic, complemented
63#127×C61C2213yescomplemented
64#121×C61C2213yescomplemented
65#121×C61C2213yescomplemented
66C4×Q8×C61C2211yescharacteristic, complemented
67C4×D4×C61C2213yescomplemented
68C23×D61C2313yes—
69#41×C61—24no—
70#41×C61—24no—
71C2×Q8×C61C2311yescharacteristic
72C2×D4×C61C2313yes—
73C2×D4×C61C2313yes—
74C2×D4×C61C2313yes—
75C2×D4×C61C2316yes—
76C22×C4×C61C2313yes—
77C22×C4×C61C2313yes—
78C2×C22⋊D61C2316yes—
79C2×C22⋊D61C2313yes—
80C2×C22⋊D61C2313yes—
81C2×C22⋊D61C2316yes—
82C2×C22⋊D61C2313yes—
83C2×C22⋊D61C2313yes—
84C22×Dic61C2313yes—
85C22×Dic61C2316yes—
86#11758226—24no—
87Q8×D61—24no—
88Q8×D61D418yescomplemented
89#11758224—212no—
90#11758224—212no—
91#11758224—212no—
92D4×D61—212no—
93#11758222—212no—
94#11758222—212no—
95C2×D244C2313yes—
96C2×D244C2311yescharacteristic
97C2×D244C2313yes—
98C2×C4×D61—212no—
99C2×C4×D61C2311yescharacteristic
100C2×C4×D61C2313yes—
101C2×C4×D61C2313yes—
102C2×C4×D61C2313yes—
103C2×C4×D61C2313yes—
104C2×Dic122—212no—
105C2×Dic122C2313yes—
106C2×Dic122C2313yes—
107C2×Dic122C2313yes—
108C4⋊C4×C61C2311yescharacteristic
109C4⋊C4×C61C2313yes—
110C22⋊C4×C61C2313yes—
111C22⋊C4×C61C2313yes—
112C42×C61C2313yes—
113C22⋊Dic61C2313yes—
114C22⋊Dic61C2313yes—
115C22⋊Dic61C2316yes—
116#11758198C2311yescharacteristic
117#11758198C2313yes—
118#11758198C2316yes—
119#11758198C2311yescharacteristic
120#11758198C2313yes—
121#11758198C2311yescharacteristic
122#11758198C2313yes—
123C4⋊Dic61C2313yes—
124C4⋊Dic61C2313yes—
125#11758196C2313yes—
126#11758196C2313yes—
127#11758196C2313yes—
128#11758196C2311yescharacteristic
129C4×Dic61C2313yes—
130C4×Dic61C2316yes—
131C23×C61C2413yes—
132C23×C61C2413yes—
133C22×D61—26no—
134C22×D61—43no—
135C22×D61—43no—
136C22×D61C2413yes—
137C22×D61C2411yescharacteristic
138C22×D61C2411yescharacteristic
139Q8×C61C2×D414yes—
140D4×C61—26no—
141D4×C61—26no—
142D4×C61—46no—
143D4×C61—43no—
144C2×C4×C61—26no—
145C2×C4×C61—26no—
146C2×C4×C61C2413yes—
147C2×C4×C61C2411yescharacteristic
148C2×C4×C61C2411yescharacteristic
149C2×C4×C61C2411yescharacteristic
150C2×C4×C61C2413yes—
151C22⋊D61—26no—
152C22⋊D61—212no—
153C22⋊D61—26no—
154C22⋊D61—43no—
155C22⋊D61—43no—
156C22⋊D61—46no—
157C2×Dic61—212no—
158C2×Dic61—26no—
159C2×Dic61C2411yescharacteristic
160C2×Dic61C2413yes—
161C2×Dic61C2411yescharacteristic
162C2×Dic61C2413yes—
163C2×Dic61C2413yes—
164D244—22no—
165D244—26no—
166D244—43no—
167C4×D61—22no—
168C4×D61—26no—
169C4×D61—26no—
170C4×D61—26no—
171C4×D61C2×D4112yes—
172Dic122—26no—
173Dic122—26no—
174Dic122C2×D4112yes—
175C22×C61—23no—
176C22×C61—23no—
177C22×C61—23no—
178C22×C61—23no—
179C22×C61—23no—
180C22×C61—23no—
181C22×C61C2511yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—23no—
186C2×D61—21no—
187C2×D61—23no—
188C2×D61—21no—
189C2×D61—23no—
190C2×D61—412no—
191C2×D61C22×D412yes—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—23no—
195C4×C61—21no—
196C4×C61C22×D416yes—
197Dic61—23no—
198Dic61—21no—
199Dic61—21no—
200Dic61—23no—
201Dic61C22×D416yes—
202#3487—611nomaximal, Sylow
203C2×C61—43no—
204C2×C61—43no—
205C2×C61C23×D411yescharacteristic
206C2×C61#58511yescharacteristic
207C2×C61#58511yescharacteristic
208D61—22no—
209D61—41no—
210D61—43no—
211C2×2−1+4—611no—
212C22×#41—611no—
213#550—611no—
214#550—613no—
215#550—613no—
216#550D6111yescharacteristic, complemented
217#548—611no—
218#548—613no—
219#548—611no—
220#548—613no—
221#535—613no—
222#535—613no—
223#525—613no—
224#525—613no—
225#519—611no—
226C61#348711yescharacteristic, complemented, Sylow
2272−1+4—1228no—
228C2×#41—611no—
229C2×#41—613no—
230C2×#41—613no—
231C2×#41—613no—
232C2×#41—613no—
233C2×#41—613no—
234C2×#41—1228no—
235C2×#41C2×D6111yescharacteristic
236C2×#41C2×D6111yescharacteristic, complemented
237C22×Q8—611no—
238C22×Q8—611no—
239C22×Q8—613no—
240C22×D4—613no—
241C23×C4—613no—
242#127—616no—
243#127—613no—
244#127C2×D6113yescomplemented
245#124—613no—
246#124—616no—
247#124—613no—
248#123—611no—
249#123—613no—
250C22⋊Q8—613no—
251C22⋊Q8—613no—
252C22⋊Q8—613no—
253C22⋊Q8—613no—
254#121—613no—
255#121—613no—
256#121—613no—
257#121—616no—
258#121—616no—
259#121—613no—
260#121—613no—
261#121—613no—
262#121C2×D6113yescomplemented
263#121C2×D6113yescomplemented
264#120—616no—
265#120—613no—
266#120—613no—
267C4×Q8—611no—
268C4×Q8—613no—
269C4×Q8—613no—
270C4×Q8C2×D6111yescharacteristic, complemented
271C4×D4—616no—
272C4×D4—613no—
273C4×D4—613no—
274C4×D4—616no—
275C4×D4—613no—
276C4×D4C2×D6113yescomplemented
277#117—613no—
278#117—613no—
279C24—613no—
280#41—24no—
281#41—24no—
282#41—12212no—
283#41—12212no—
284#41—12212no—
285#41—12212no—
286#41—12212no—
287#41—1224no—
288C2×Q8—618no—
289C2×Q8—613no—
290C2×Q8—613no—
291C2×Q8—613no—
292C2×Q8—12212no—
293C2×Q8—1224no—
294C2×Q8C22×D6111yescharacteristic
295C2×D4—613no—
296C2×D4—616no—
297C2×D4—613no—
298C2×D4—613no—
299C2×D4—616no—
300C2×D4—613no—
301C2×D4—611no—
302C2×D4—613no—
303C2×D4—613no—
304C2×D4—12212no—
305C2×D4C22×D6113yes—
306C2×D4C22×D6113yes—
307C2×D4C22×D6116yes—
308C2×D4C22×D6113yes—
309C22×C4—613no—
310C22×C4—616no—
311C22×C4—613no—
312C22×C4—613no—
313C22×C4—613no—
314C22×C4—613no—
315C22×C4—611no—
316C22×C4—12212no—
317C22×C4C22×D6113yes—
318C22×C4C22×D6113yes—
319C4⋊C4—613no—
320C4⋊C4—613no—
321C4⋊C4—613no—
322C4⋊C4—611no—
323C4⋊C4—613no—
324C4⋊C4—613no—
325C4⋊C4C22×D6113yes—
326C4⋊C4C22×D6111yescharacteristic
327C22⋊C4—613no—
328C22⋊C4—616no—
329C22⋊C4—613no—
330C22⋊C4—613no—
331C22⋊C4—611no—
332C22⋊C4—611no—
333C22⋊C4—611no—
334C22⋊C4—613no—
335C22⋊C4—616no—
336C22⋊C4—613no—
337C22⋊C4C22×D6113yes—
338C22⋊C4C22×D6113yes—
339C42—616no—
340C42—613no—
341C42C22×D6113yes—
342C23—611no—
343C23—613no—
344C23—611no—
345C23—1226no—
346C23—2443no—
347C23—2443no—
348C23C23×D6113yes—
349C23C23×D6113yes—
350Q8—6112no—
351Q8—1226no—
352Q8—1226no—
353Q8D4×D6114yes—
354D4—26no—
355D4—26no—
356D4—46no—
357D4—43no—
358D4—1222no—
359D4—12212no—
360D4—1226no—
361D4—1226no—
362D4—1226no—
363D4—2443no—
364D4—2443no—
365D4—2446no—
366D4—2443no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—613no—
370C2×C4—6112no—
371C2×C4—611no—
372C2×C4—613no—
373C2×C4—613no—
374C2×C4—611no—
375C2×C4—1226no—
376C2×C4—1222no—
377C2×C4—1226no—
378C2×C4—12212no—
379C2×C4—1226no—
380C2×C4—1226no—
381C2×C4C23×D6113yes—
382C2×C4C23×D6111yescharacteristic
383C2×C4C23×D6111yescharacteristic
384C2×C4C23×D6111yescharacteristic
385C2×C4C23×D6113yes—
386C22—23no—
387C22—23no—
388C22—23no—
389C22—23no—
390C22—23no—
391C22—23no—
392C22—612no—
393C22—1221no—
394C22—1221no—
395C22—1221no—
396C22—1223no—
397C22—1221no—
398C22—1223no—
399C22—1221no—
400C22—1223no—
401C22—24412no—
402C22C24×D6111yescharacteristic
403C4—21no—
404C4—21no—
405C4—23no—
406C4—21no—
407C4—616no—
408C4—1221no—
409C4—1223no—
410C4—1221no—
411C4—1223no—
412C4C2×D4×D6116yes—
413C2—43no—
414C2—43no—
415C2—1222no—
416C2—2443no—
417C2—2441no—
418C2C22×D4×D6111yescharacteristic
419C2#1684059711yescharacteristic
420C2#1684059811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC61×#550C2
hypercenter#550D61
hypocenterC61#3487
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#14519824C2semidirect
2. C2×#41×D61C2semidirect
3. #16840432C2semidirect
4. #16840431C2semidirect
5. #16840430C2semidirect
6. #16840424C2semidirect
7. #16840421C2semidirect
8. #16840419C2semidirect
9. #16840418C2semidirect
10. #16840328C2semidirect
11. #16840325C2semidirect
12. #16840272C2semidirect
13. #16840271C2semidirect
14. #16840238C2semidirect
15. C61×#550C2semidirect
22. C2×#11758224C22semidirect
24. C22×Dic122C22semidirect
26. C2×Q8×D61C22semidirect
29. #14519773C22semidirect
30. #14519773C22semidirect
31. #14519765C22semidirect
32. #14519764C22semidirect
33. #14519763C22semidirect
36. #14519757C22semidirect
37. #14519756C22semidirect
38. #14519755C22semidirect
39. #14519754C22semidirect
40. #14519752C22semidirect
41. #14519751C22semidirect
42. #14519750C22semidirect
43. #14519749C22semidirect
44. #14519749C22semidirect
45. #14519749C22semidirect
46. #14519748C22semidirect
47. #14519748C22semidirect
51. Q8×Dic61C22semidirect
52. C4×Dic122C22semidirect
53. #14519742C22semidirect
54. C4×D244C22semidirect
55. D4×Dic61C22semidirect
56. C4×C22⋊D61C22semidirect
57. C4×C22⋊D61C22semidirect
58. #14519737C22semidirect
62. C2×#41×C61C22semidirect
63. #127×C61C22semidirect
64. #121×C61C22semidirect
65. #121×C61C22semidirect
66. C4×Q8×C61C22semidirect
67. C4×D4×C61C22semidirect
88. Q8×D61D4semidirect
216. #550D61semidirect
226. C61#3487semidirect
236. C2×#41C2×D61semidirect
244. #127C2×D61semidirect
262. #121C2×D61semidirect
263. #121C2×D61semidirect
270. C4×Q8C2×D61semidirect
276. C4×D4C2×D61semidirect