Finite Group Databasebeta

← #21451648

Subgroups — #21451648

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519767C211yesmaximal, characteristic, complemented
2C2×#14519733C211yesmaximal, characteristic
3#16839696C211yesmaximal, characteristic, complemented
4#16839695C211yesmaximal, characteristic, complemented
5#16839693C211yesmaximal, characteristic, complemented
6#16839692C211yesmaximal, characteristic, complemented
7#16839685C211yesmaximal, characteristic
8#16839685C211yesmaximal, characteristic
9#16839685C211yesmaximal, characteristic
10#16839659C211yesmaximal, characteristic, complemented
11#16839657C211yesmaximal, characteristic, complemented
12#16839631C211yesmaximal, characteristic, complemented
13#16839620C211yesmaximal, characteristic
14#16839620C211yesmaximal, characteristic
15C61×#396C211yesmaximal, characteristic
16C23×Dic61C2211yescharacteristic
17#14519767—24no—
18#14519733—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758196C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C4×Dic61C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×Dic61—22no—
61C22×Dic61—22no—
62C22×Dic61Q814yes—
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C4⋊C4×C61—22no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—22no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊Dic61—22no—
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80C4⋊Dic61—22no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758196—22no—
84#11758196—22no—
85#11758196—22no—
86#11758196—22no—
87#11758196—22no—
88#11758196—22no—
89#11758196—22no—
90#11758196—22no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196—41no—
95C4×Dic61—22no—
96C4×Dic61D414yes—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61C2×Q812yes—
104C23×C61C2411yescharacteristic
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—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D412yes—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—28no—
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×Dic61—21no—
143C2×Dic61C2×D412yes—
144C2×Dic61C2×D412yes—
145C2×Dic61C2×Q812yes—
146C2×Dic61C2×Q812yes—
147C2×Dic61#4112yes—
148C22×C61—22no—
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C22×D411yescharacteristic
156C22×C61C22×Q811yescharacteristic
157C22×C61C2×#4111yescharacteristic
158C22×C61H(5,𝔽2)11yescharacteristic
159C22×C61H(5,𝔽2)11yescharacteristic
160C22×C612−1+411yescharacteristic
161C22×C612−1+411yescharacteristic
162C4×C61—22no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168Dic61—22no—
169Dic61—22no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175Dic61C22⋊Q814yes—
176#2629—611nomaximal, Sylow
177C2×C61—42no—
178C2×C61C2×C22⋊Q811yescharacteristic
179C2×C61#53711yescharacteristic
180C2×C61#53711yescharacteristic
181C2×C61#54011yescharacteristic
182C2×C61#54111yescharacteristic
183C2×C61#54411yescharacteristic
184C2×C61#54411yescharacteristic
185C2×#125—611no—
186C2×#117—611no—
187#398—611no—
188#398—611no—
189#398—611no—
190#398—611no—
191#396—611no—
192#396—611no—
193#396—611no—
194#396D6111yescharacteristic
195#389—611no—
196#389—611no—
197#384—611no—
198#380—611no—
199#380—611no—
200C61#262911yescharacteristic, complemented, Sylow
201C23×C4—611no—
202#125—1224no—
203#117—1224no—
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×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4C2×D6111yescharacteristic
220C2×C4⋊C4C2×D6111yescharacteristic
221C2×C4⋊C4C2×D6111yescharacteristic
222C2×C22⋊C4—611no—
223C2×C22⋊C4—611no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4C2×D6111yescharacteristic
226C2×C22⋊C4C2×D6111yescharacteristic
227C2×C22⋊C4C2×D6111yescharacteristic
228C2×C42—611no—
229C2×C42—611no—
230#95—611no—
231#95—611no—
232#95—611no—
233#95—611no—
234#95—611no—
235#95—611no—
236#95—611no—
237#95C2×D6111yescharacteristic
238C24C22×D6111yescharacteristic
239C22×C4—611no—
240C22×C4—614no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6111yescharacteristic
252C22×C4C22×D6111yescharacteristic
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255C22×C4C22×D6111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—1222no—
260C4⋊C4—1222no—
261C4⋊C4—1222no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C4⋊C4—1222no—
266C4⋊C4—1222no—
267C4⋊C4—1222no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C22⋊C4—22no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—1222no—
278C22⋊C4—2441no—
279C22⋊C4—2441no—
280C42—614no—
281C42—1222no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23Q8×D6112yes—
289C23C23×D6111yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—612no—
308C2×C4—612no—
309C2×C4—612no—
310C2×C4—612no—
311C2×C4—612no—
312C2×C4—1228no—
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—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4D4×D6112yes—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22C2×D4×D6111yescharacteristic
341C22C2×Q8×D6111yescharacteristic
342C22#41×D6111yescharacteristic
343C22#1451982211yescharacteristic
344C22#1451982211yescharacteristic
345C22#1451982411yescharacteristic
346C22#1451982411yescharacteristic
347C4—22no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—614no—
354C4—1222no—
355C4—1222no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4—2441no—
361C2—42no—
362C2C22⋊Q8×D6111yescharacteristic
363C2#1684033911yescharacteristic
364C2#1684034111yescharacteristic
365C2#1684036211yescharacteristic
366C2#1684036911yescharacteristic
367C2#1684039111yescharacteristic
368C2#1684039111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#396C2
hypercenter#396D61
hypocenterC61#2629
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14519767C2semidirect
3. #16839696C2semidirect
4. #16839695C2semidirect
5. #16839693C2semidirect
6. #16839692C2semidirect
10. #16839659C2semidirect
11. #16839657C2semidirect
12. #16839631C2semidirect
200. C61#2629semidirect