Finite Group Databasebeta

← #21457462

Subgroups — #21457462

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519810C211yesmaximal, characteristic, complemented
2C2×#14519809C211yesmaximal, characteristic, complemented
3#16840425C211yesmaximal, characteristic, complemented
4#16840414C211yesmaximal, characteristic
5#16840140C211yesmaximal, characteristic, complemented
6#16840021C211yesmaximal, characteristic, complemented
7#16839971C211yesmaximal, characteristic, complemented
8#16839966C211yesmaximal, characteristic, complemented
9#16839927C211yesmaximal, characteristic, complemented
10#16839922C211yesmaximal, characteristic, complemented
11#16839919C211yesmaximal, characteristic, complemented
12#16839917C211yesmaximal, characteristic, complemented
13#16839849C211yesmaximal, characteristic, complemented
14#16839838C211yesmaximal, characteristic, complemented
15C61×#470C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C22×Dic122C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519810—24no—
21#14519809—24no—
22C2×Dic244C2211yescharacteristic
23C2×Dic244C2211yescharacteristic
24C2×#11758202C2211yescharacteristic
25C2×#11758202C2211yescharacteristic
26C2×#11758202C2211yescharacteristic
27C2×#11758190C2211yescharacteristic
28C2×#11758190C2211yescharacteristic
29C2×#11758201C2211yescharacteristic
30C2×#11758189C2211yescharacteristic
31#14519776—21no—
32#14519775C2211yescharacteristic
33#14519775C2211yescharacteristic
34#14519762—21no—
35#14519759—21no—
36#14519757C2211yescharacteristic
37#14519757C2211yescharacteristic
38#14519755—21no—
39#14519754—21no—
40#14519750—21no—
41#14519742C2211yescharacteristic
42#14519739C2211yescharacteristic
43C4×C22⋊D61C2211yescharacteristic
44#14519737—21no—
45C4⋊C4×D61—21no—
46#14519706C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519700C2211yescharacteristic
50#14519697C2211yescharacteristic
51C22⋊#92418C2211yescharacteristic
52#14519689C2211yescharacteristic
53C8×Dic61C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C2×M16×C61C2211yescharacteristic
56C22⋊Q8×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#106×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#103×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66C22×Dic61—21no—
67#11758226—22no—
68#11758226—41no—
69Q8×D61—22no—
70Q8×D61—41no—
71#11758222—22no—
72#11758222—41no—
73C2×D244—21no—
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—22no—
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×Dic122—41no—
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87Q16×C61—22no—
88M16×C61—22no—
89C2×C8×C61C2311yescharacteristic
90C2×C8×C61C2311yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61C2311yescharacteristic
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊Dic61D411yescharacteristic
98#11758202—22no—
99#11758202—41no—
100#11758202—41no—
101#11758201—22no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198D411yescharacteristic
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108#11758196—21no—
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196D411yescharacteristic
114C4×Dic61—21no—
115C4×Dic61C2311yescharacteristic
116C2×#92418C2311yescharacteristic
117C2×#92418C2311yescharacteristic
118Dic244—22no—
119Dic244—22no—
120#11758190—22no—
121#11758190D414yescomplemented
122#11758189—22no—
123C23×C61C2×D411yescharacteristic
124C22×D61—21no—
125C22×D61C2×D411yescharacteristic
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—22no—
139C22⋊D61—42no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—42no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—21no—
148D244—42no—
149D244C2×D412yes—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—42no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156Dic122—21no—
157Dic122—21no—
158Dic122—21no—
159Dic122—21no—
160Dic122—21no—
161Dic122—42no—
162Dic122—42no—
163Dic122C2×D412yes—
164C8×C61—21no—
165C8×C61C2×D412yes—
166#92418—21no—
167#92418—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61C22×D411yescharacteristic
172C2×D61—21no—
173C2×D61—22no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61C22×D411yescharacteristic
184C4×C61H(5,𝔽2)11yescharacteristic
185Dic61—22no—
186Dic61—21no—
187Dic61—21no—
188Dic61—41no—
189Dic61—41no—
190Dic61#13712yescomplemented
191#3276—611nomaximal, Sylow
192C2×C61—41no—
193C2×C61D4211yescharacteristic
194C2×C61C2×#13711yescharacteristic
195C2×C61#57811yescharacteristic
196D61—41no—
197D61—42no—
198C2×#137—611no—
199C2×#137—611no—
200D4×Q8—611no—
201#547—611no—
202#494—611no—
203#470—611no—
204#470D6111yescharacteristic, complemented
205#462—611no—
206#461—611no—
207#452—611no—
208#452—611no—
209#451—611no—
210#451—611no—
211C4×SD16—611no—
212#436—611no—
213C61#327611yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×#41—611no—
216C22×Q8—611no—
217C22×Q8—611no—
218#137—1224no—
219#137—1224no—
220C2×Q16—611no—
221C2×Q16—611no—
222C2×Q16—611no—
223C2×Q16—611no—
224C2×Q16—611no—
225C2×Q16C2×D6111yescharacteristic
226C2×SD16—611no—
227C2×SD16—611no—
228C2×SD16—611no—
229C2×M16—611no—
230C2×M16C2×D6111yescharacteristic
231C4⋊Q8—611no—
232C4⋊Q8—611no—
233C4⋊Q8—1221no—
234#123—1221no—
235#123—1221no—
236C22⋊Q8—611no—
237C22⋊Q8—611no—
238C22⋊Q8—1221no—
239C22⋊Q8—1221no—
240C22⋊Q8C2×D6111yescharacteristic
241C22⋊Q8C2×D6111yescharacteristic
242#121—1221no—
243C4×Q8—611no—
244C4×D4—611no—
245C4×D4—611no—
246C4×D4—1221no—
247C2×C4⋊C4—1221no—
248#106C2×D6111yescharacteristic
249C4⋊C8—611no—
250#103—611no—
251#103—611no—
252#103—611no—
253#103C2×D6111yescharacteristic
254#103C2×D6111yescharacteristic
255#102—611no—
256C22⋊C8—611no—
257C22⋊C8—611no—
258C4×C8—611no—
259#41—1222no—
260#41—1222no—
261#41—2441no—
262#41—2441no—
263C2×Q8—611no—
264C2×Q8—611no—
265C2×Q8—611no—
266C2×Q8—1221no—
267C2×Q8—1222no—
268C2×Q8—1221no—
269C2×Q8—1222no—
270C2×Q8—2441no—
271C2×Q8—2441no—
272C2×Q8C22×D6111yescharacteristic
273C2×Q8C22×D6111yescharacteristic
274C2×D4—611no—
275C2×D4—611no—
276C2×D4—1221no—
277C2×D4—1221no—
278C22×C4—611no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C22×D6111yescharacteristic
285Q16—22no—
286Q16—1222no—
287Q16—1222no—
288Q16—1222no—
289Q16—2441no—
290Q16—2441no—
291SD16—614no—
292SD16—1222no—
293SD16—1222no—
294M16—22no—
295M16—1222no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8C22×D6111yescharacteristic
299C2×C8C22×D6111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—611no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4C22×D6111yescharacteristic
311C4⋊C4C22×D6111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—611no—
315C22⋊C4—611no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C42—611no—
320C42—1221no—
321C23—611no—
322C23—1221no—
323C23D4×D6111yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—612no—
329Q8—1221no—
330Q8—1221no—
331Q8—1221no—
332Q8—1221no—
333Q8—1221no—
334Q8—2442no—
335Q8—2442no—
336D4—612no—
337D4—1222no—
338D4—1221no—
339D4—2442no—
340D4—2442no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4D4×D6111yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—1221no—
364C8—1221no—
365C8D4×D6112yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—1222no—
373C22—2441no—
374C22—2441no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—612no—
382C4—1221no—
383C4—1221no—
384C4—1222no—
385C4—2441no—
386C4—2441no—
387C4C2×D4×D6111yescharacteristic
388C4#1451982311yescharacteristic
389C2—41no—
390C2—2441no—
391C2—2442no—
392C2#1684039611yescharacteristic
393C2#137×D6111yescharacteristic
394C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3276
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
2. C2×#14519809C2semidirect
3. #16840425C2semidirect
5. #16840140C2semidirect
6. #16840021C2semidirect
7. #16839971C2semidirect
8. #16839966C2semidirect
9. #16839927C2semidirect
10. #16839922C2semidirect
11. #16839919C2semidirect
12. #16839917C2semidirect
13. #16839849C2semidirect
14. #16839838C2semidirect
15. C61×#470C2semidirect
121. #11758190D4semidirect
190. Dic61#137semidirect
204. #470D61semidirect
213. C61#3276semidirect