Finite Group Databasebeta

← #21457930

Subgroups — #21457930

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840469C211yesmaximal, characteristic, complemented
2#16840121C211yesmaximal, characteristic, complemented
3#16840090C211yesmaximal, characteristic, complemented
4#16840078C211yesmaximal, characteristic, complemented
5#16840047C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16839989C211yesmaximal, characteristic, complemented
8#16839981C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839918C211yesmaximal, characteristic, complemented
11#16839867C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839763C211yesmaximal, characteristic, complemented
14C2×#14519701C211yesmaximal, characteristic, complemented
15C61×#548C211yesmaximal, characteristic
16C2×#11758202C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20C22×#92418C2211yescharacteristic
21#14519777C2211yescharacteristic
22#14519768—21no—
23#14519756C2211yescharacteristic
24#14519756C2211yescharacteristic
25#14519754—21no—
26#14519754—21no—
27C4×Dic122C2211yescharacteristic
28D4×Dic61—21no—
29C2×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊Dic61C2211yescharacteristic
31#14519708C2211yescharacteristic
32#14519708C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519701C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519701C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519701C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519698C2211yescharacteristic
43#14519698C2211yescharacteristic
44#14519698C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48C2×#41×C61C2211yescharacteristic
49C22×Q8×C61C2211yescharacteristic
50#124×C61—21no—
51#124×C61C2211yescharacteristic
52C22⋊Q8×C61—21no—
53C22⋊Q8×C61C2211yescharacteristic
54#121×C61—21no—
55#121×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57C4×D4×C61—21no—
58C4×D4×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61—21no—
62C2×Q8×C61—22no—
63C2×Q8×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×Q8×C61C2311yescharacteristic
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61D411yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61D411yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61D411yescharacteristic
87C22⋊C4×C61D411yescharacteristic
88C42×C61—21no—
89C42×C61C2311yescharacteristic
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758202—22no—
93#11758202—41no—
94#11758200—41no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—42no—
118Q8×C61#4112yes—
119D4×C61—22no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123D4×C61—42no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144Dic122—21no—
145Dic122—21no—
146Dic122—81no—
147#92418—21no—
148#92418—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61#13712yes—
160C22×C61C22×D411yescharacteristic
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—22no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C2×#4111yescharacteristic
169C4×C61H(5,𝔽2)11yescharacteristic
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3316—611nomaximal, Sylow
175C2×C61—22no—
176C2×C61—41no—
177C2×C61—81no—
178C2×C61#54611yescharacteristic
179C2×C61C2×#13711yescharacteristic
180C2×C61#57711yescharacteristic
181#554—611no—
182#548D6111yescharacteristic
183#489—611no—
184#483—611no—
185#481—611no—
186#475—611no—
187#470—611no—
188#465—611no—
189#464—611no—
190#452—611no—
191#451—611no—
192#441—611no—
193#435—611no—
194#417—611no—
195C2×#103—611no—
196C61#331611yescharacteristic, complemented, Sylow
197C2×#41C2×D6111yescharacteristic
198C22×Q8C2×D6111yescharacteristic
199C2×Q16—611no—
200C2×Q16—611no—
201C2×SD16—611no—
202C2×M16—611no—
203C22×C8—611no—
204C4⋊Q8—611no—
205#125—1221no—
206#124—21no—
207#124C2×D6111yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212C22⋊Q8—1221no—
213C22⋊Q8C2×D6111yescharacteristic
214#121—21no—
215#121C2×D6111yescharacteristic
216C4×Q8—611no—
217C4×Q8C2×D6111yescharacteristic
218C4×D4—21no—
219C4×D4—1221no—
220C4×D4C2×D6111yescharacteristic
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223#106—611no—
224#106—611no—
225#106—611no—
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#102—611no—
235#102—611no—
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97—611no—
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—611no—
246C2×Q8—1221no—
247C2×Q8C22×D6111yescharacteristic
248C2×Q8C22×D6111yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D6111yescharacteristic
252C2×D4C22×D6111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6111yescharacteristic
259Q16—1222no—
260Q16—2441no—
261SD16—2441no—
262M16—2441no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—2441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—611no—
271C4⋊C4—611no—
272C4⋊C4—611no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22⋊D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4C22⋊D6111yescharacteristic
288C22⋊C4C22⋊D6111yescharacteristic
289C42—21no—
290C42—1221no—
291C42C22×D6111yescharacteristic
292C23—21no—
293C23C2×C22⋊D6111yescharacteristic
294C23C2×C22⋊D6111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—1221no—
300Q8—1221no—
301Q8—4881no—
302Q8#1175822412yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4C2×C22⋊D6111yescharacteristic
324C2×C4C2×C22⋊D6111yescharacteristic
325C2×C4C2×C22⋊D6111yescharacteristic
326C2×C4C2×C22⋊D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—1221no—
329C8—1221no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1451980712yes—
341C22C22×C22⋊D6111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4C2×#1175822411yescharacteristic
354C4#1451982211yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1684040611yescharacteristic
359C2C2×#1451980711yescharacteristic
360C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#548C2
socleC22×C61C22×D4
hypercenter#548D61
hypocenterC61#3316
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #16840469C2semidirect
2. #16840121C2semidirect
3. #16840090C2semidirect
4. #16840078C2semidirect
5. #16840047C2semidirect
6. #16840018C2semidirect
7. #16839989C2semidirect
8. #16839981C2semidirect
9. #16839924C2semidirect
10. #16839918C2semidirect
11. #16839867C2semidirect
12. #16839834C2semidirect
13. #16839763C2semidirect
14. C2×#14519701C2semidirect
196. C61#3316semidirect