Finite Group Databasebeta

← #21448701

Subgroups — #21448701

Order 7808.

504 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519733C211yesmaximal, characteristic
2#16839659C211yesmaximal, characteristic, complemented
3#16839657C211yesmaximal, characteristic, complemented
4#16839656C211yesmaximal, characteristic
5#16839655C211yesmaximal, characteristic
6#16839650C211yesmaximal, characteristic
7#16839627C211yesmaximal, characteristic, complemented
8#16839626C211yesmaximal, characteristic, complemented
9#16839620C211yesmaximal, characteristic
10C4×#11758196C211yesmaximal, characteristic, complemented
11#16839613C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic61C211yesmaximal, characteristic
13#16839608C211yesmaximal, characteristic, complemented
14#16839607C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic
16C23×Dic61C2211yescharacteristic
17#14519733C418yescomplemented
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C4×Dic61C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
33C2×C4×Dic61C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45C2×C4⋊C4×C61C2211yescharacteristic
46C2×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C42×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52C24×C61C2311yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×Dic61—22no—
60C22×Dic61—22no—
61C22×Dic61C2×C414yes—
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C4⋊C4×C61—41no—
71C22⋊C4×C61—22no—
72C22⋊C4×C61—41no—
73C22⋊C4×C61C2×C414yes—
74C42×C61—22no—
75C22⋊Dic61—22no—
76C22⋊Dic61—41no—
77C22⋊Dic61C2×C414yes—
78C4⋊Dic61—41no—
79#11758196—22no—
80#11758196—22no—
81#11758196—41no—
82#11758196—41no—
83#11758196C2×C414yes—
84#11758196C2×C414yes—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—22no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61C2×C414yes—
91C4×Dic61C2×C414yes—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61C22×C412yes—
99C23×C61C2411yescharacteristic
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×C61C22×C412yes—
116C2×C4×C61C22×C412yes—
117C2×C4×C61#4112yes—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—28no—
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×Dic61C22×C412yes—
137C2×Dic61C22×C412yes—
138C2×Dic61C22×C412yes—
139C2×Dic61C22×C412yes—
140C2×Dic61#4112yes—
141C2×Dic61#4112yes—
142C2×Dic61#4112yes—
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61C23×C411yescharacteristic
151C22×C61C2×#4111yescharacteristic
152C22×C61C2×#4111yescharacteristic
153C22×C61C2×#4111yescharacteristic
154C22×C61C2×#4111yescharacteristic
155C22×C61H(5,𝔽2)11yescharacteristic
156C22×C612−1+411yescharacteristic
157C4×C61—22no—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163Dic61—22no—
164Dic61—22no—
165Dic61—22no—
166Dic61—22no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61#11714yes—
171#2346—611nomaximal, Sylow
172C2×C61—42no—
173C2×C61C2×#11711yescharacteristic
174C2×C61C4×#4111yescharacteristic
175C2×C61#52011yescharacteristic
176C2×C61#55211yescharacteristic
177C2×C61#55211yescharacteristic
178C2×C61#55511yescharacteristic
179C2×C61#55511yescharacteristic
180C2×#117—611no—
181#389—611no—
182#389—611no—
183#388—611no—
184#388—611no—
185#388—611no—
186#388D6111yescharacteristic
187#382—611no—
188#382—611no—
189#380—611no—
190C4×C4⋊C4—611no—
191C4×C4⋊C4—611no—
192C4×C22⋊C4—611no—
193#376—611no—
194#376—611no—
195C61#234611yescharacteristic, complemented, Sylow
196C23×C4—611no—
197#117—618no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4C2×D6111yescharacteristic
206C2×C22⋊C4—611no—
207C2×C22⋊C4—611no—
208C2×C22⋊C4—611no—
209C2×C22⋊C4C2×D6111yescharacteristic
210C2×C22⋊C4C2×D6111yescharacteristic
211C2×C22⋊C4C2×D6111yescharacteristic
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—611no—
219C2×C42C2×D6111yescharacteristic
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#95—611no—
229#95—611no—
230#95C2×D6111yescharacteristic
231#95C2×D6111yescharacteristic
232C24C22×D6111yescharacteristic
233C22×C4—611no—
234C22×C4—614no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—1222no—
243C22×C4—1222no—
244C22×C4C22×D6111yescharacteristic
245C22×C4C22×D6111yescharacteristic
246C22×C4C22×D6111yescharacteristic
247C22×C4C22×D6111yescharacteristic
248C22×C4C22×D6111yescharacteristic
249C22×C4C22×D6111yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—614no—
252C4⋊C4—614no—
253C4⋊C4—1222no—
254C4⋊C4—1222no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C22⋊C4—22no—
259C22⋊C4—41no—
260C22⋊C4—614no—
261C22⋊C4—1222no—
262C22⋊C4—2441no—
263C22⋊C4C4×D6114yes—
264C42—22no—
265C42—614no—
266C42—614no—
267C42—1222no—
268C42—1222no—
269C42—1222no—
270C42—1222no—
271C42—1222no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×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—612no—
296C2×C4—612no—
297C2×C4—612no—
298C2×C4—612no—
299C2×C4—612no—
300C2×C4—612no—
301C2×C4—612no—
302C2×C4—1228no—
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×C4C2×C4×D6112yes—
321C2×C4C2×C4×D6112yes—
322C2×C4#1175822412yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D6111yescharacteristic
331C22#41×D6111yescharacteristic
332C22#41×D6111yescharacteristic
333C22#41×D6111yescharacteristic
334C22C2×#1175822411yescharacteristic
335C22#1451982211yescharacteristic
336C22#1451982411yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—614no—
344C4—1222no—
345C4—1222no—
346C4—1222no—
347C4—1222no—
348C4—2441no—
349C4—2441no—
350C4—2441no—
351C2—42no—
352C2#117×D6111yescharacteristic
353C2C4×#1175822411yescharacteristic
354C2#1684024111yescharacteristic
355C2#1684044811yescharacteristic
356C2#1684044911yescharacteristic
357C2#1684047411yescharacteristic
358C2#1684047611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#388C2
socleC23×C61C24
hypercenter#388D61
hypocenterC61#2346
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #16839659C2semidirect
3. #16839657C2semidirect
7. #16839627C2semidirect
8. #16839626C2semidirect
10. C4×#11758196C2semidirect
11. #16839613C2semidirect
13. #16839608C2semidirect
14. #16839607C2semidirect
17. #14519733C4semidirect
195. C61#2346semidirect