Finite Group Databasebeta

← #21450151

Subgroups — #21450151

Order 7808.

546 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519761C211yesmaximal, characteristic
2#16839701C211yesmaximal, characteristic, complemented
3#16839701C211yesmaximal, characteristic, complemented
4#16839688C211yesmaximal, characteristic, complemented
5#16839673C211yesmaximal, characteristic, complemented
6#16839669C211yesmaximal, characteristic, complemented
7#16839652C211yesmaximal, characteristic, complemented
8#16839652C211yesmaximal, characteristic, complemented
9#16839641C211yesmaximal, characteristic
10#16839639C211yesmaximal, characteristic
11#16839627C211yesmaximal, characteristic, complemented
12#16839623C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C2×#14519684C211yesmaximal, characteristic, complemented
15C2×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19#14519761—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
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
54C23×D61C2311yescharacteristic
55C2×Q8×C61—22no—
56C2×Q8×C61—22no—
57C2×Q8×C61—41no—
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—41no—
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—22no—
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—41no—
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C4⋊C4×C61—22no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—22no—
86C22⋊C4×C61—22no—
87C22⋊C4×C61D414yes—
88C22⋊Dic61—22no—
89#11758198—22no—
90#11758198—22no—
91#11758198—22no—
92#11758198—22no—
93#11758198—41no—
94#11758198—41no—
95C4⋊Dic61—22no—
96C4⋊Dic61—22no—
97C4×Dic61—22no—
98C4×Dic61—41no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61C2×D412yes—
104C23×C61#4112yes—
105C23×C61#4112yes—
106C23×C61C2411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114Q8×C61—44no—
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×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—44no—
131C2×C4×C61C2×D412yes—
132C2×C4×C61C2×D412yes—
133C2×C4×C61#4112yes—
134C22⋊D61—44no—
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—21no—
154C2×Dic61—21no—
155C2×Dic61—44no—
156C2×Dic61—44no—
157C2×Dic61#4112yes—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—22no—
163C22×C61—22no—
164C22×C61#12414yes—
165C22×C61C22×D411yescharacteristic
166C22×C61C2×#4111yescharacteristic
167C22×C61C2×#4111yescharacteristic
168C22×C61C2×#4111yescharacteristic
169C22×C61C2×#4111yescharacteristic
170C22×C61H(5,𝔽2)11yescharacteristic
171C22×C612−1+411yescharacteristic
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C4×C61—22no—
180C4×C61—22no—
181C4×C61—22no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—41no—
185Dic61—22no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191Dic61—41no—
192#2488—611nomaximal, Sylow
193C2×C61—24no—
194C2×C61C2×#12411yescharacteristic
195C2×C61#52911yescharacteristic
196C2×C61#53911yescharacteristic
197C2×C61#54611yescharacteristic
198C2×C61#54711yescharacteristic
199C2×C61#55111yescharacteristic
200C2×C61#55211yescharacteristic
201D61—81no—
202C2×#123—611no—
203C2×C22⋊Q8D6111yescharacteristic, complemented
204#400—611no—
205#400—611no—
206#397—611no—
207#393—611no—
208#391—611no—
209#388—611no—
210#388—611no—
211#386—611no—
212#386—611no—
213#382—611no—
214#381—611no—
215C4×C22⋊C4—611no—
216C2×#95—611no—
217C61#248811yescharacteristic, complemented, Sylow
218C22×Q8C2×D6111yescharacteristic
219C22×D4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C23×C4C2×D6111yescharacteristic
223#123—1224no—
224C22⋊Q8—24no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4C2×D6111yescharacteristic
228C2×C4⋊C4C2×D6111yescharacteristic
229C2×C4⋊C4C2×D6111yescharacteristic
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4C2×D6111yescharacteristic
238C2×C22⋊C4C2×D6111yescharacteristic
239C2×C42—611no—
240C2×C42—611no—
241#95—611no—
242#95—611no—
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—
253#95—611no—
254#95—611no—
255C24—611no—
256C24C22×D6111yescharacteristic
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—41no—
260C2×D4—1222no—
261C2×D4—1222no—
262C2×D4—1222no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1222no—
278C22×C4—2441no—
279C22×C4C22×D6111yescharacteristic
280C22×C4C22×D6111yescharacteristic
281C22×C4C22×D6111yescharacteristic
282C22×C4C22×D6111yescharacteristic
283C22×C4C22×D6111yescharacteristic
284C22×C4C22×D6111yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—1222no—
289C4⋊C4—1222no—
290C22⋊C4—22no—
291C22⋊C4—1222no—
292C22⋊C4—1222no—
293C22⋊C4—1222no—
294C22⋊C4—1222no—
295C22⋊C4—1222no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C22⋊C4C22⋊D6114yes—
299C42—1222no—
300C42—2441no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23#1175822612yes—
313C23#1175822612yes—
314C23C2×C22⋊D6112yes—
315C23C23×D6111yescharacteristic
316Q8—44no—
317D4—2444no—
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—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—44no—
334C2×C4—612no—
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—1221no—
354C2×C4—1221no—
355C2×C4—2444no—
356C2×C4—2444no—
357C2×C4#1175822412yes—
358C2×C4C2×C22⋊D6112yes—
359C2×C4C2×C22⋊D6112yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22#1451976614yes—
374C22C22×C22⋊D6111yescharacteristic
375C22#41×D6111yescharacteristic
376C22C2×#1175822411yescharacteristic
377C22C2×#1175822611yescharacteristic
378C22C2×#1175822611yescharacteristic
379C22#1451982211yescharacteristic
380C22#1451982411yescharacteristic
381C4—22no—
382C4—22no—
383C4—22no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—1222no—
388C4—2441no—
389C4—2441no—
390C4—2441no—
391C4—2441no—
392C4—2441no—
393C4—2441no—
394C2—24no—
395C2—4881no—
396C2C2×#1451976611yescharacteristic
397C2#1684029811yescharacteristic
398C2#1684036111yescharacteristic
399C2#1684040611yescharacteristic
400C2#1684041111yescharacteristic
401C2#1684043911yescharacteristic
402C2#1684045411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C22⋊Q8×C61C2
hypercenterC2×C22⋊Q8D61
hypocenterC61#2488
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839701C2semidirect
3. #16839701C2semidirect
4. #16839688C2semidirect
5. #16839673C2semidirect
6. #16839669C2semidirect
7. #16839652C2semidirect
8. #16839652C2semidirect
11. #16839627C2semidirect
12. #16839623C2semidirect
13. C22⋊C4×Dic61C2semidirect
14. C2×#14519684C2semidirect
15. C2×C22⋊Q8×C61C2semidirect
203. C2×C22⋊Q8D61semidirect
217. C61#2488semidirect