Finite Group Databasebeta

← #21454648

Subgroups — #21454648

Order 7808.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519801C211yesmaximal, characteristic
2#16840241C211yesmaximal, characteristic, complemented
3#16840234C211yesmaximal, characteristic, complemented
4#16839871C211yesmaximal, characteristic, complemented
5#16839864C211yesmaximal, characteristic, complemented
6#16839859C211yesmaximal, characteristic, complemented
7#16839849C211yesmaximal, characteristic, complemented
8C4×#11758200C211yesmaximal, characteristic, complemented
9D8×Dic61C211yesmaximal, characteristic, complemented
10C4×#11758199C211yesmaximal, characteristic, complemented
11#16839801C211yesmaximal, characteristic, complemented
12#16839755C211yesmaximal, characteristic, complemented
13#102×D61C211yesmaximal, characteristic, complemented
14#16839719C211yesmaximal, characteristic, complemented
15C61×#442C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18#14519801C418yescomplemented
19C2×#11758190C2211yescharacteristic
20C2×#11758200C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23C2×C8×D61C2211yescharacteristic
24C4×Dic122C2211yescharacteristic, complemented
25#14519742C2211yescharacteristic, complemented
26C4×D244C2211yescharacteristic
27D4×Dic61C2211yescharacteristic
28D4×Dic61C2211yescharacteristic, complemented
29#14519739C2211yescharacteristic
30C4×C22⋊D61—21no—
31C4×C22⋊D61—21no—
32#14519737—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic
35#14519734C2211yescharacteristic
36#14519733—21no—
37C2×#11758196—21no—
38C4⋊C4×D61C2211yescharacteristic
39C2×#11758198—21no—
40C22⋊C4×D61—21no—
41#14519711C2211yescharacteristic, complemented
42#14519710C2211yescharacteristic, complemented
43#14519708C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C4×#92418C2211yescharacteristic, complemented
52C8×Dic61C2211yescharacteristic, complemented
53C2×D8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56#106×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic, complemented
59#97×C61C2211yescharacteristic, complemented
60C23×D61—21no—
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70#11758224—22no—
71#11758224C2×C414yescomplemented
72D4×D61—22no—
73D4×D61C2×C414yescomplemented
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122C2311yescharacteristic
80D8×C61C2×C414yescomplemented
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758200C2×C414yescomplemented
91#11758199C2×C414yescomplemented
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198D411yescharacteristic
96#11758198D411yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196D411yescharacteristic
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758190C2×C414yescomplemented
111#11758189C2×C414yescomplemented
112C8×D61—22no—
113C23×C61—21no—
114C23×C61—21no—
115C22×D61—21no—
116C22×D61—24no—
117C22×D61—81no—
118C22×D61—81no—
119C22×D61C2×D411yescharacteristic
120D4×C61—21no—
121D4×C61—21no—
122D4×C61C22×C412yes—
123D4×C61C22×C412yes—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—24no—
132C22⋊D61—24no—
133C2×Dic61—21no—
134C2×Dic61—24no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—81no—
138C2×Dic61—81no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142D244—21no—
143D244C22×C412yes—
144C4×D61—81no—
145C4×D61—81no—
146C4×D61—81no—
147C4×D61C22×C412yes—
148C4×D61#4112yes—
149Dic122—21no—
150Dic122C22×C412yes—
151C8×C61—21no—
152C8×C61C22×C412yes—
153#92418—21no—
154#92418C22×C412yes—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—22no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C2×D61C4×D412yes—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61C23×C411yescharacteristic
174C4×C61C2×#4111yescharacteristic
175Dic61—22no—
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179Dic61—41no—
180Dic61C4×D412yes—
181#2946—611nomaximal, Sylow
182C2×C61—42no—
183C2×C61—42no—
184C2×C61C2×C4×D411yescharacteristic
185C2×C61#57611yescharacteristic
186C2×C61#57711yescharacteristic
187D61—22no—
188D61—42no—
189C2×AGL(1,ℤ/8)—611no—
190#520—611no—
191#518—611no—
192#442—611no—
193#442D6111yescharacteristic, complemented
194#440—611no—
195#440—611no—
196C4×SD16—611no—
197C4×SD16—611no—
198C4×D8—611no—
199C4×D8—611no—
200#428—611no—
201#416—611no—
202C2×#102—611no—
203#405—611no—
204C61#294611yescharacteristic, complemented, Sylow
205C2×#41—611no—
206C22×D4—611no—
207AGL(1,ℤ/8)—618no—
208C2×SD16—611no—
209C2×SD16—611no—
210C2×D8—611no—
211C2×D8C2×D6111yescharacteristic
212C2×M16—611no—
213C22×C8—611no—
214C4×Q8—611no—
215C4×Q8—611no—
216C4×D4—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—1221no—
221C4×D4—1221no—
222C4×D4—1221no—
223C4×D4—1221no—
224C4×D4C2×D6111yescharacteristic
225C4×D4C2×D6111yescharacteristic, complemented
226#117—611no—
227#117—611no—
228#117—1221no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233#107—611no—
234#107—611no—
235#106—611no—
236#106C2×D6111yescharacteristic, complemented
237#103—611no—
238#103—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102C2×D6111yescharacteristic
244#102C2×D6111yescharacteristic, complemented
245#97—611no—
246#97C2×D6111yescharacteristic, complemented
247C4×C8—611no—
248C4×C8—611no—
249C24—1221no—
250#41—614no—
251#41—1222no—
252C2×Q8—611no—
253C2×D4—614no—
254C2×D4—611no—
255C2×D4—1222no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4C22×D6111yescharacteristic
259C2×D4C22×D6111yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269SD16—614no—
270SD16—614no—
271D8—614no—
272D8C4×D6114yescomplemented
273M16—614no—
274C2×C8—611no—
275C2×C8—611no—
276C2×C8—1222no—
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C4⋊C4—611no—
280C4⋊C4—611no—
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4C22×D6111yescharacteristic
287C4⋊C4C22×D6111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—611no—
291C22⋊C4—611no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C42—611no—
298C42—1221no—
299C42—1221no—
300C42—1221no—
301C42C22×D6111yescharacteristic
302C23—21no—
303C23—21no—
304C23—611no—
305C23—1224no—
306C23—1221no—
307C23—4881no—
308C23—4881no—
309Q8—612no—
310Q8—1221no—
311D4—21no—
312D4—21no—
313D4—612no—
314D4—1224no—
315D4—1224no—
316D4—1221no—
317D4C2×C4×D6112yes—
318D4C2×C4×D6112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—611no—
324C2×C4—612no—
325C2×C4—612no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1224no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4D4×D6111yescharacteristic
338C2×C4D4×D6111yescharacteristic
339C2×C4C23×D6111yescharacteristic
340C8—21no—
341C8—612no—
342C8—1221no—
343C8C2×C4×D6112yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—612no—
351C22—1221no—
352C22—1221no—
353C22—1222no—
354C22—4884no—
355C22—2441no—
356C22—2441no—
357C22C2×D4×D6111yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—612no—
363C4—1222no—
364C4—1221no—
365C4—1221no—
366C4—2441no—
367C4—2441no—
368C4C22×C4×D6111yescharacteristic
369C4#41×D6111yescharacteristic
370C2—42no—
371C2—42no—
372C2—1222no—
373C2—2442no—
374C2C4×D4×D6111yescharacteristic
375C2#1684056611yescharacteristic
376C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#2946
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #16840241C2semidirect
3. #16840234C2semidirect
4. #16839871C2semidirect
5. #16839864C2semidirect
6. #16839859C2semidirect
7. #16839849C2semidirect
8. C4×#11758200C2semidirect
9. D8×Dic61C2semidirect
10. C4×#11758199C2semidirect
11. #16839801C2semidirect
12. #16839755C2semidirect
13. #102×D61C2semidirect
14. #16839719C2semidirect
15. C61×#442C2semidirect
18. #14519801C4semidirect
24. C4×Dic122C22semidirect
25. #14519742C22semidirect
28. D4×Dic61C22semidirect
41. #14519711C22semidirect
42. #14519710C22semidirect
43. #14519708C22semidirect
44. #14519702C22semidirect
45. #14519700C22semidirect
48. #14519698C22semidirect
50. #14519687C22semidirect
51. C4×#92418C22semidirect
52. C8×Dic61C22semidirect
55. C4×D4×C61C22semidirect
56. #106×C61C22semidirect
58. #102×C61C22semidirect
59. #97×C61C22semidirect
71. #11758224C2×C4semidirect
73. D4×D61C2×C4semidirect
80. D8×C61C2×C4semidirect
90. #11758200C2×C4semidirect
91. #11758199C2×C4semidirect
110. #11758190C2×C4semidirect
111. #11758189C2×C4semidirect
193. #442D61semidirect
204. C61#2946semidirect
225. C4×D4C2×D61semidirect
236. #106C2×D61semidirect
244. #102C2×D61semidirect
246. #97C2×D61semidirect
272. D8C4×D61semidirect