Finite Group Databasebeta

← #21450320

Subgroups — #21450320

Order 7808.

456 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#16839703C211yesmaximal, characteristic, complemented
2#16839703C211yesmaximal, characteristic, complemented
3#16839702C211yesmaximal, characteristic, complemented
4#16839696C211yesmaximal, characteristic, complemented
5#16839659C211yesmaximal, characteristic, complemented
6#16839647C211yesmaximal, characteristic, complemented
7#16839644C211yesmaximal, characteristic, complemented
8#16839635C211yesmaximal, characteristic
9#16839635C211yesmaximal, characteristic
10#16839635C211yesmaximal, characteristic
11#16839635C211yesmaximal, characteristic
12#16839626C211yesmaximal, characteristic, complemented
13#16839622C211yesmaximal, characteristic
14C4×C22⋊Dic61C211yesmaximal, characteristic
15C2×#95×C61C211yesmaximal, characteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32#14519684C2211yescharacteristic
33#14519684C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44C23×C4×C61C2211yescharacteristic
45C23×C4×C61C2211yescharacteristic
46C23×C4×C61C2211yescharacteristic
47#95×C61C2211yescharacteristic
48#95×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C24×C61C2311yescharacteristic
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61—41no—
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22⋊Dic61—22no—
76C22⋊Dic61—22no—
77C22⋊Dic61—22no—
78C22⋊Dic61Q814yes—
79C4⋊Dic61—22no—
80C4⋊Dic61—41no—
81#11758196—22no—
82#11758196—22no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—22no—
90C4×Dic61—41no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61C2×Q812yes—
96C23×C61#4112yes—
97C23×C61#4112yes—
98C23×C61C2411yescharacteristic
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—44no—
116C2×C4×C61—44no—
117C2×C4×C61—44no—
118C2×C4×C61#4112yes—
119C2×C4×C61#4112yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61C2×Q812yes—
143C2×Dic61C2×Q812yes—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—22no—
149C22×C61—22no—
150C22×C61#12514yes—
151C22×C61C22×Q811yescharacteristic
152C22×C61C2×#4111yescharacteristic
153C22×C61C2×#4111yescharacteristic
154C22×C61C2×#4111yescharacteristic
155C22×C61C2×#4111yescharacteristic
156C22×C61H(5,𝔽2)11yescharacteristic
157C22×C61H(5,𝔽2)11yescharacteristic
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164Dic61—22no—
165Dic61—22no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#2505—611nomaximal, Sylow
173C2×C61—24no—
174C2×C61C2×#12511yescharacteristic
175C2×C61#52911yescharacteristic
176C2×C61#53811yescharacteristic
177C2×C61#55111yescharacteristic
178C2×C61#55111yescharacteristic
179C2×C61#55411yescharacteristic
180C2×C61#55411yescharacteristic
181#400—611no—
182#400—611no—
183#400—611no—
184#398—611no—
185#389—611no—
186#387—611no—
187#387—611no—
188#385—611no—
189#385—611no—
190#385—611no—
191#385—611no—
192#382—611no—
193#380—611no—
194C4×C22⋊C4—611no—
195C2×#95D6111yescharacteristic
196C61#250511yescharacteristic, complemented, Sylow
197C23×C4C2×D6111yescharacteristic
198C23×C4C2×D6111yescharacteristic
199C23×C4C2×D6111yescharacteristic
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C22⋊C4—611no—
211C2×C22⋊C4—611no—
212C2×C22⋊C4—611no—
213C2×C22⋊C4—611no—
214C2×C42—611no—
215C2×C42—611no—
216#95—611no—
217#95—611no—
218#95—611no—
219#95—611no—
220#95—611no—
221#95—611no—
222#95—611no—
223#95—611no—
224#95—611no—
225#95—611no—
226#95—611no—
227#95—611no—
228#95C2×D6111yescharacteristic
229#95C2×D6111yescharacteristic
230#95C2×D6111yescharacteristic
231#95C2×D6111yescharacteristic
232C24C22×D6111yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6111yescharacteristic
252C22×C4C22×D6111yescharacteristic
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255C22×C4C22×D6111yescharacteristic
256C4⋊C4—1222no—
257C4⋊C4—1222no—
258C4⋊C4—1222no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C22⋊C4—614no—
267C22⋊C4—1222no—
268C22⋊C4—1222no—
269C22⋊C4—1222no—
270C42—1222no—
271C42—2441no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23#1175822212yes—
277C23#1175822412yes—
278C23Q8×D6112yes—
279C23C23×D6111yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—612no—
300C2×C4—612no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4#1175822212yes—
324C2×C4#1175822212yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22#1451976714yes—
332C22C2×Q8×D6111yescharacteristic
333C22C2×#1175822411yescharacteristic
334C22C2×#1175822211yescharacteristic
335C22C2×#1175822211yescharacteristic
336C22C2×#1175822211yescharacteristic
337C22#1451982211yescharacteristic
338C22#1451982211yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—1222no—
346C4—1222no—
347C4—2441no—
348C4—2441no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C2—24no—
354C2C2×#1451976711yescharacteristic
355C2#1684029611yescharacteristic
356C2#1684035011yescharacteristic
357C2#1684043811yescharacteristic
358C2#1684043811yescharacteristic
359C2#1684046711yescharacteristic
360C2#1684046711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#95×C61C2
hypercenterC2×#95D61
hypocenterC61#2505
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. #16839703C2semidirect
2. #16839703C2semidirect
3. #16839702C2semidirect
4. #16839696C2semidirect
5. #16839659C2semidirect
6. #16839647C2semidirect
7. #16839644C2semidirect
12. #16839626C2semidirect
196. C61#2505semidirect