Finite Group Databasebeta

← #21452795

Subgroups — #21452795

Order 7808.

480 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519753C211yesmaximal, characteristic
2#16839701C211yesmaximal, characteristic, complemented
3#16839695C211yesmaximal, characteristic, complemented
4#16839692C211yesmaximal, characteristic, complemented
5#16839684C211yesmaximal, characteristic
6#16839681C211yesmaximal, characteristic, complemented
7#16839673C211yesmaximal, characteristic
8#16839669C211yesmaximal, characteristic, complemented
9#16839657C211yesmaximal, characteristic, complemented
10#16839653C211yesmaximal, characteristic
11#16839652C211yesmaximal, characteristic
12#16839646C211yesmaximal, characteristic, complemented
13#16839633C211yesmaximal, characteristic
14#16839633C211yesmaximal, characteristic
15C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
16C22×C4×D61C2211yescharacteristic
17#14519753—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
33#14519684C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45C22×Q8×C61C2211yescharacteristic
46C22×Q8×C61C2211yescharacteristic
47C4⋊Q8×C61—24no—
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C4⋊C4×C61C2211yescharacteristic
51C2×C4⋊C4×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic
53C23×D61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×Q8×C61—41no—
56C2×Q8×C61—41no—
57C2×Q8×C61—41no—
58C2×Q8×C61—41no—
59C2×Q8×C61D414yes—
60C22×C4×C61C2311yescharacteristic
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
74C2×C4×D61—22no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C4⋊C4×C61—22no—
78C4⋊C4×C61—22no—
79C4⋊C4×C61—22no—
80C4⋊C4×C61—22no—
81C42×C61—22no—
82#11758198—22no—
83#11758198—22no—
84#11758198—22no—
85#11758198—41no—
86#11758198—41no—
87#11758198Q814yescomplemented
88C4⋊Dic61—22no—
89C4⋊Dic61—41no—
90#11758196—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196—22no—
94#11758196—41no—
95#11758196—41no—
96C4×Dic61—41no—
97C23×C61C2411yescharacteristic
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61C2×Q812yes—
105Q8×C61—44no—
106Q8×C61—44no—
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×C61—21no—
123C2×C4×C61C2×D412yes—
124C2×C4×C61C2×D412yes—
125C2×C4×C61C2×D412yes—
126C2×C4×C61C2×Q812yes—
127C2×C4×C61#4112yes—
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×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61C2×Q812yes—
149C4×D61—44no—
150C22×C61C22×D411yescharacteristic
151C22×C61C22×Q811yescharacteristic
152C22×C61C2×#4111yescharacteristic
153C22×C61H(5,𝔽2)11yescharacteristic
154C22×C61H(5,𝔽2)11yescharacteristic
155C22×C612−1+411yescharacteristic
156C22×C612−1+411yescharacteristic
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—22no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—22no—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—41no—
170C4×C61—41no—
171Dic61—22no—
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#2729—611nomaximal, Sylow
179C2×C61#53411yescharacteristic
180C2×C61#54211yescharacteristic
181C2×C61#54411yescharacteristic
182C2×C61#54811yescharacteristic
183C2×C61D4×Q811yescharacteristic
184C2×C61#55411yescharacteristic
185C2×C61#56311yescharacteristic
186D61—42no—
187C2×C4⋊Q8D6111yescharacteristic, complemented
188C2×C22⋊Q8—611no—
189#400—611no—
190#398—611no—
191#398—611no—
192#396—611no—
193#395—611no—
194#393—611no—
195#391—611no—
196#389—611no—
197#388—611no—
198#388—611no—
199#387—611no—
200#385—611no—
201#385—611no—
202C61#272911yescharacteristic, complemented, Sylow
203C22×Q8C2×D6111yescharacteristic
204C22×Q8C2×D6111yescharacteristic
205C23×C4—611no—
206C4⋊Q8—24no—
207C22⋊Q8—1224no—
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⋊C4C2×D6111yescharacteristic
217C2×C4⋊C4C2×D6111yescharacteristic
218C2×C4⋊C4C2×D6111yescharacteristic
219C2×C4⋊C4C2×D6111yescharacteristic
220C2×C22⋊C4—611no—
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—611no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4—611no—
226C2×C42—611no—
227C2×C42C2×D6111yescharacteristic
228#95—611no—
229#95—611no—
230#95—611no—
231#95—611no—
232#95—611no—
233#95—611no—
234#95—611no—
235#95—611no—
236#95—611no—
237#95—611no—
238#95—611no—
239#95—611no—
240C24—611no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C22⋊D6114yes—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—1222no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6111yescharacteristic
259C22×C4C22×D6111yescharacteristic
260C22×C4C22×D6111yescharacteristic
261C22×C4C22×D6111yescharacteristic
262C22×C4C22×D6111yescharacteristic
263C22×C4C22×D6111yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—1222no—
269C4⋊C4—1222no—
270C4⋊C4—1222no—
271C4⋊C4—1222no—
272C4⋊C4—1222no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C22⋊C4—614no—
277C22⋊C4—1222no—
278C22⋊C4—1222no—
279C22⋊C4—1222no—
280C22⋊C4—2441no—
281C22⋊C4—2441no—
282C42—22no—
283C42—2441no—
284C23—612no—
285C23—1221no—
286C23—1221no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23—1221no—
291C23C23×D6111yescharacteristic
292Q8—44no—
293Q8—44no—
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—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—612no—
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—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—2444no—
332C2×C4Q8×D6112yes—
333C2×C4#1175822612yes—
334C2×C4C2×C22⋊D6112yes—
335C2×C4C2×C22⋊D6112yes—
336C2×C4C2×C22⋊D6112yes—
337C22—1222no—
338C22—1222no—
339C22—1222no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22C22×C22⋊D6111yescharacteristic
345C22C2×Q8×D6111yescharacteristic
346C22C2×#1175822611yescharacteristic
347C22#1451982211yescharacteristic
348C22#1451982211yescharacteristic
349C22#1451982511yescharacteristic
350C22#1451982511yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—1222no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C2—2442no—
366C2#1684032111yescharacteristic
367C2#1684038611yescharacteristic
368C2#1684038911yescharacteristic
369C2#1684042311yescharacteristic
370C2Q8×C22⋊D6111yescharacteristic
371C2#1684047311yescharacteristic
372C2#1684051111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4⋊Q8×C61C2
hypercenterC2×C4⋊Q8D61
hypocenterC61#2729
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839701C2semidirect
3. #16839695C2semidirect
4. #16839692C2semidirect
6. #16839681C2semidirect
8. #16839669C2semidirect
9. #16839657C2semidirect
12. #16839646C2semidirect
15. C2×C4⋊Q8×C61C2semidirect
87. #11758198Q8semidirect
187. C2×C4⋊Q8D61semidirect
202. C61#2729semidirect