Finite Group Databasebeta

← #21449971

Subgroups — #21449971

Order 7808.

526 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519733C211yesmaximal, characteristic, complemented
2#16839690C211yesmaximal, characteristic, complemented
3#16839685C211yesmaximal, characteristic, complemented
4#16839681C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic
6#16839669C211yesmaximal, characteristic, complemented
7#16839656C211yesmaximal, characteristic, complemented
8#16839655C211yesmaximal, characteristic, complemented
9#16839650C211yesmaximal, characteristic, complemented
10#16839650C211yesmaximal, characteristic, complemented
11#16839646C211yesmaximal, characteristic, complemented
12#16839642C211yesmaximal, characteristic
13#16839634C211yesmaximal, characteristic, complemented
14C4×#11758196C211yesmaximal, characteristic, complemented
15C2×#124×C61C211yesmaximal, characteristic
16C23×Dic61C2211yescharacteristic
17#14519733—24no—
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×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊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
45C22×Q8×C61C2211yescharacteristic
46C22×D4×C61C2211yescharacteristic
47#124×C61—24no—
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C24×C61C2311yescharacteristic
55C2×Q8×C61—22no—
56C2×Q8×C61—22no—
57C2×Q8×C61—41no—
58C2×D4×C61—22no—
59C2×D4×C61—22no—
60C2×D4×C61—41no—
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×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22⋊C4×C61—22no—
78C22⋊C4×C61—22no—
79C22⋊C4×C61—22no—
80C22⋊C4×C61D414yes—
81C42×C61—22no—
82C22⋊Dic61—22no—
83C22⋊Dic61—22no—
84C22⋊Dic61—22no—
85C22⋊Dic61—22no—
86C22⋊Dic61—22no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196—22no—
94#11758196—22no—
95#11758196—41no—
96C4×Dic61—22no—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61C2×D412yes—
113C23×C61C2411yescharacteristic
114Q8×C61—44no—
115D4×C61—44no—
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×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D412yes—
129C2×C4×C61C2×D412yes—
130C2×C4×C61#4112yes—
131C2×Dic61—28no—
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×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61#4112yes—
154C2×Dic61#4112yes—
155C2×Dic61#4112yes—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61C22×D411yescharacteristic
171C22×C61C2×#4111yescharacteristic
172C22×C61C2×#4111yescharacteristic
173C22×C61C2×#4111yescharacteristic
174C22×C61C2×#4111yescharacteristic
175C22×C61H(5,𝔽2)11yescharacteristic
176C22×C612−1+411yescharacteristic
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—41no—
182Dic61—22no—
183Dic61—22no—
184Dic61—22no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190#2474—611nomaximal, Sylow
191C2×C61—42no—
192C2×C61—81no—
193C2×C61#52511yescharacteristic
194C2×C61#52911yescharacteristic
195C2×C61#54211yescharacteristic
196C2×C61#54611yescharacteristic
197C2×C61#54711yescharacteristic
198C2×C61#55511yescharacteristic
199C2×C61#55611yescharacteristic
200C2×#124D6111yescharacteristic
201C2×#117—611no—
202#397—611no—
203#396—611no—
204#395—611no—
205#394—611no—
206#391—611no—
207#388—611no—
208#388—611no—
209#388—611no—
210#388—611no—
211#387—611no—
212#386—611no—
213#385—611no—
214C4×C4⋊C4—611no—
215C61#247411yescharacteristic, complemented, Sylow
216C22×Q8C2×D6111yescharacteristic
217C22×D4C2×D6111yescharacteristic
218C23×C4—611no—
219#124—24no—
220#117—1224no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4C2×D6111yescharacteristic
236C2×C22⋊C4C2×D6111yescharacteristic
237C2×C22⋊C4C2×D6111yescharacteristic
238C2×C22⋊C4C2×D6111yescharacteristic
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42C2×D6111yescharacteristic
243#95—611no—
244#95—611no—
245#95—611no—
246#95—611no—
247#95—611no—
248#95—611no—
249#95—611no—
250#95—611no—
251#95—611no—
252#95—611no—
253C24C22×D6111yescharacteristic
254C24C22×D6111yescharacteristic
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—41no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4C22×D6111yescharacteristic
273C22×C4C22×D6111yescharacteristic
274C22×C4C22×D6111yescharacteristic
275C22×C4C22×D6111yescharacteristic
276C22×C4C22×D6111yescharacteristic
277C4⋊C4—1222no—
278C4⋊C4—1222no—
279C4⋊C4—1222no—
280C4⋊C4—1222no—
281C4⋊C4—1222no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—1222no—
288C22⋊C4—1222no—
289C22⋊C4—1222no—
290C22⋊C4—1222no—
291C22⋊C4—1222no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4C22⋊D6114yes—
295C42—22no—
296C42—1222no—
297C42—1222no—
298C42—1222no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23C2×C22⋊D6112yes—
313C23C23×D6111yescharacteristic
314Q8—44no—
315D4—44no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—612no—
331C2×C4—1228no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4#1175822412yes—
354C2×C4C2×C22⋊D6112yes—
355C2×C4C2×C22⋊D6112yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C22×C22⋊D6111yescharacteristic
371C22#41×D6111yescharacteristic
372C22#41×D6111yescharacteristic
373C22#41×D6111yescharacteristic
374C22C2×#1175822411yescharacteristic
375C22#1451982211yescharacteristic
376C22#1451982411yescharacteristic
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—1222no—
383C4—1222no—
384C4—1222no—
385C4—2441no—
386C4—2441no—
387C4—2441no—
388C4—2441no—
389C4—2441no—
390C2—42no—
391C2—81no—
392C2#1684026911yescharacteristic
393C2#1684029111yescharacteristic
394C2#1684037611yescharacteristic
395C2#1684040611yescharacteristic
396C2#1684041111yescharacteristic
397C2#1684047411yescharacteristic
398C2#1684048111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2474
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519733C2semidirect
2. #16839690C2semidirect
3. #16839685C2semidirect
4. #16839681C2semidirect
6. #16839669C2semidirect
7. #16839656C2semidirect
8. #16839655C2semidirect
9. #16839650C2semidirect
10. #16839650C2semidirect
11. #16839646C2semidirect
13. #16839634C2semidirect
14. C4×#11758196C2semidirect
215. C61#2474semidirect