Finite Group Databasebeta

← #21449491

Subgroups — #21449491

Order 7808.

528 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519733C211yesmaximal, characteristic
2#16839700C211yesmaximal, characteristic, complemented
3#16839695C211yesmaximal, characteristic, complemented
4#16839695C211yesmaximal, characteristic, complemented
5#16839681C211yesmaximal, characteristic, complemented
6#16839669C211yesmaximal, characteristic, complemented
7#16839658C211yesmaximal, characteristic, complemented
8#16839643C211yesmaximal, characteristic, complemented
9#16839643C211yesmaximal, characteristic, complemented
10#16839637C211yesmaximal, characteristic
11#16839635C211yesmaximal, characteristic
12#16839623C211yesmaximal, characteristic
13#16839620C211yesmaximal, characteristic
14C2×#14519684C211yesmaximal, characteristic
15C2×C22⋊Q8×C61C211yesmaximal, characteristic
16C23×Dic61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18#14519733—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31#14519684C2211yescharacteristic
32#14519684C2211yescharacteristic
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
46C23×C4×C61C2211yescharacteristic
47C22⋊Q8×C61—24no—
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C4⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×Q8×C61—22no—
56C2×Q8×C61—41no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—41no—
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—41no—
71C22×Dic61Q814yescomplemented
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C4⋊C4×C61—22no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—22no—
83C22⋊C4×C61—22no—
84C22⋊C4×C61D414yes—
85C22⋊Dic61—22no—
86C22⋊Dic61—22no—
87C4⋊Dic61—22no—
88C4⋊Dic61—41no—
89#11758196—22no—
90#11758196—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196—41no—
94#11758196—41no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61C2×D412yes—
102C23×C61C2×Q812yes—
103C23×C61#4112yes—
104C23×C61C2411yescharacteristic
105Q8×C61—44no—
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—44no—
122C2×C4×C61C2×D412yes—
123C2×C4×C61C2×D412yes—
124C2×C4×C61#4112yes—
125C2×Dic61—28no—
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×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—44no—
148C2×Dic61C2×Q812yes—
149C2×Dic61C2×Q812yes—
150C2×Dic61#4112yes—
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61C22⋊Q814yes—
158C22×C61C22×D411yescharacteristic
159C22×C61C22×Q811yescharacteristic
160C22×C61C2×#4111yescharacteristic
161C22×C61C2×#4111yescharacteristic
162C22×C61C2×#4111yescharacteristic
163C22×C61H(5,𝔽2)11yescharacteristic
164C22×C612−1+411yescharacteristic
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—41no—
171Dic61—22no—
172Dic61—22no—
173Dic61—22no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178Dic61—41no—
179#2438—611nomaximal, Sylow
180C2×C61—24no—
181C2×C61C2×C22⋊Q811yescharacteristic
182C2×C61#53311yescharacteristic
183C2×C61#54411yescharacteristic
184C2×C61#54611yescharacteristic
185C2×C61#54711yescharacteristic
186C2×C61#55111yescharacteristic
187C2×C61#55211yescharacteristic
188C2×C22⋊Q8D6111yescharacteristic
189C2×#117—611no—
190#400—611no—
191#398—611no—
192#398—611no—
193#395—611no—
194#391—611no—
195#389—611no—
196#387—611no—
197#387—611no—
198#385—611no—
199#385—611no—
200#381—611no—
201#380—611no—
202C2×#95—611no—
203C61#243811yescharacteristic, complemented, Sylow
204C22×Q8C2×D6111yescharacteristic
205C23×C4—611no—
206C23×C4—611no—
207C23×C4C2×D6111yescharacteristic
208C22⋊Q8—24no—
209#117—1224no—
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⋊C4C2×D6111yescharacteristic
219C2×C4⋊C4C2×D6111yescharacteristic
220C2×C4⋊C4C2×D6111yescharacteristic
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4C2×D6111yescharacteristic
224C2×C22⋊C4C2×D6111yescharacteristic
225C2×C42—611no—
226C2×C42—611no—
227#95—611no—
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—
240#95—611no—
241C24C22×D6111yescharacteristic
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—41no—
248C22×C4—614no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—2441no—
262C22×C4C22×D6111yescharacteristic
263C22×C4C22×D6111yescharacteristic
264C22×C4C22×D6111yescharacteristic
265C22×C4C22×D6111yescharacteristic
266C22×C4C22×D6111yescharacteristic
267C22×C4C22×D6111yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—1222no—
272C4⋊C4—1222no—
273C4⋊C4—1222no—
274C4⋊C4—1222no—
275C4⋊C4—1222no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C22⋊C4—22no—
280C22⋊C4—1222no—
281C22⋊C4—1222no—
282C22⋊C4C22⋊D6114yes—
283C42—1222no—
284C42—1222no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23Q8×D6112yes—
290C23#1175822612yes—
291C23C2×C22⋊D6112yes—
292C23C23×D6111yescharacteristic
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—44no—
310C2×C4—612no—
311C2×C4—612no—
312C2×C4—612no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1228no—
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×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—2444no—
336C2×C4#1175822412yes—
337C2×C4C2×C22⋊D6112yes—
338C2×C4C2×C22⋊D6112yes—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22#1451975314yes—
346C22C22×C22⋊D6111yescharacteristic
347C22C2×Q8×D6111yescharacteristic
348C22#41×D6111yescharacteristic
349C22C2×#1175822411yescharacteristic
350C22C2×#1175822611yescharacteristic
351C22#1451982211yescharacteristic
352C22#1451982411yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—1222no—
360C4—1222no—
361C4—1222no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C4—2441no—
366C4—2441no—
367C2—24no—
368C2C2×#1451975311yescharacteristic
369C2#1684031411yescharacteristic
370C2#1684039111yescharacteristic
371C2#1684040611yescharacteristic
372C2#1684041111yescharacteristic
373C2#1684043911yescharacteristic
374C2#1684045411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C22⋊Q8×C61C2
hypercenterC2×C22⋊Q8D61
hypocenterC61#2438
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839700C2semidirect
3. #16839695C2semidirect
4. #16839695C2semidirect
5. #16839681C2semidirect
6. #16839669C2semidirect
7. #16839658C2semidirect
8. #16839643C2semidirect
9. #16839643C2semidirect
71. C22×Dic61Q8semidirect
203. C61#2438semidirect