Finite Group Databasebeta

← #21457387

Subgroups — #21457387

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×#14519807C211yesmaximal, characteristic, complemented
2C2×Q16×D61C211yesmaximal, characteristic, complemented
3#16840425C211yesmaximal, characteristic, complemented
4#16840419C211yesmaximal, characteristic
5#16840153C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16839990C211yesmaximal, characteristic, complemented
8#16839983C211yesmaximal, characteristic, complemented
9#16839970C211yesmaximal, characteristic, complemented
10#16839920C211yesmaximal, characteristic, complemented
11#16839919C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839866C211yesmaximal, characteristic, complemented
14#16839836C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19#14519807—24no—
20C2×Dic244C2211yescharacteristic
21C2×Dic244C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758202C2211yescharacteristic
25Q16×D61—24no—
26C2×#11758200C2211yescharacteristic
27C2×#11758200C2211yescharacteristic
28C2×#11758194C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic
30#14519776—21no—
31#14519775C2211yescharacteristic
32#14519764—21no—
33#14519764C2211yescharacteristic
34#14519757C2211yescharacteristic
35#14519756—21no—
36#14519756C2211yescharacteristic
37#14519755—21no—
38#14519754—21no—
39#14519748—21no—
40#14519748C2211yescharacteristic
41Q8×Dic61C2211yescharacteristic
42#14519742C2211yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61C2211yescharacteristic
45#14519737—21no—
46#14519708C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519701C2211yescharacteristic
51#14519700C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519687C2211yescharacteristic
54C2×#41×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic
56C2×SD16×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic
61#41×C61—22no—
62#41×C61—41no—
63C2×Q8×C61C2311yescharacteristic
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C22×Dic61—21no—
72Q8×D61—22no—
73Q8×D61—22no—
74Q8×D61—41no—
75Q8×D61—41no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122—22no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×Dic122—41no—
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87Q16×C61—22no—
88SD16×C61—41no—
89C2×C8×C61C2311yescharacteristic
90C2×C8×C61C2311yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61D411yescharacteristic
99#11758202—22no—
100#11758202—22no—
101#11758202D414yescomplemented
102#11758200—22no—
103#11758200—22no—
104#11758198—21no—
105#11758198D411yescharacteristic
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196D411yescharacteristic
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117#11758194—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120Dic244—22no—
121Dic244—41no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61C2×D411yescharacteristic
125C22×D61C2×D411yescharacteristic
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61C2×D412yes—
130D4×C61—21no—
131D4×C61—21no—
132D4×C61—42no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—42no—
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2411yescharacteristic
141C22⋊D61—22no—
142C22⋊D61—42no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148C2×Dic61C2×D411yescharacteristic
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—42no—
154C4×D61—42no—
155Dic122—21no—
156Dic122—21no—
157Dic122—21no—
158Dic122—21no—
159Dic122—21no—
160Dic122—42no—
161Dic122—42no—
162Dic122—42no—
163Dic122C2×D412yes—
164C8×C61—21no—
165C8×C61—21no—
166#92418—21no—
167#92418C2×D412yes—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61C22×D411yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61#13712yescomplemented
178C4×C61—21no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61C22×D411yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—22no—
185Dic61—21no—
186Dic61—21no—
187Dic61—21no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191#3270—611nomaximal, Sylow
192C2×C61—41no—
193C2×C61—81no—
194C2×C61D4211yescharacteristic
195C2×C61C2×#13711yescharacteristic
196C2×C61#57811yescharacteristic
197D61—22no—
198C2×#137—611no—
199C22×Q16—611no—
200D4×Q8—611no—
201#548—611no—
202#497—611no—
203#470—611no—
204#465—611no—
205#464—611no—
206#462—611no—
207#452D6111yescharacteristic, complemented
208#451—611no—
209#451—611no—
210#448—611no—
211#441—611no—
212#435—611no—
213C61#327011yescharacteristic, complemented, Sylow
214C2×#41C2×D6111yescharacteristic
215C22×Q8—611no—
216C22×Q8—611no—
217C22×Q8—611no—
218#137—1224no—
219C2×Q16—611no—
220C2×Q16—611no—
221C2×Q16—611no—
222C2×Q16—611no—
223C2×Q16—611no—
224C2×Q16—1224no—
225C2×Q16C2×D6111yescharacteristic
226C2×SD16—611no—
227C2×SD16—611no—
228C2×SD16C2×D6111yescharacteristic
229C2×M16—611no—
230C22×C8—611no—
231C4⋊Q8—611no—
232C4⋊Q8—1221no—
233#124—611no—
234#124—1221no—
235C22⋊Q8—611no—
236C22⋊Q8—611no—
237C22⋊Q8—1221no—
238C22⋊Q8—1221no—
239C22⋊Q8—1221no—
240C22⋊Q8C2×D6111yescharacteristic
241#121—611no—
242#121—1221no—
243C4×Q8—611no—
244C4×Q8—611no—
245C4×D4—611no—
246C4×D4—1221no—
247C4×D4—1221no—
248#106—611no—
249C4⋊C8—611no—
250#103—611no—
251#103—611no—
252#103—611no—
253#103—611no—
254#103C2×D6111yescharacteristic
255#102C2×D6111yescharacteristic
256C22⋊C8—611no—
257C22⋊C8C2×D6111yescharacteristic
258#97—611no—
259#41—22no—
260#41—41no—
261C2×Q8—611no—
262C2×Q8—611no—
263C2×Q8—611no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×Q8—1222no—
267C2×Q8—1221no—
268C2×Q8—1222no—
269C2×Q8—1222no—
270C2×Q8—2441no—
271C2×Q8—2441no—
272C2×Q8—2441no—
273C2×Q8C22×D6111yescharacteristic
274C2×Q8C22×D6111yescharacteristic
275C2×D4—21no—
276C2×D4—611no—
277C2×D4—1221no—
278C2×D4C22×D6111yescharacteristic
279C22×C4—21no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C22×D6111yescharacteristic
285Q16—22no—
286Q16—614no—
287Q16—1222no—
288Q16—1222no—
289Q16—1222no—
290Q16—2441no—
291SD16—41no—
292SD16—1222no—
293SD16—1222no—
294M16—1222no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8—1222no—
298C2×C8C22×D6111yescharacteristic
299C2×C8C22×D6111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—611no—
302C4⋊C4—611no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4C22×D6111yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—611no—
312C22⋊C4—611no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C42—611no—
319C42—1221no—
320C42—1221no—
321C23—21no—
322C23—611no—
323C23D4×D6111yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—612no—
328Q8—1221no—
329Q8—1221no—
330Q8—1221no—
331Q8—1221no—
332Q8—1221no—
333Q8—2442no—
334Q8—2442no—
335Q8—2442no—
336Q8D4×D6112yes—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—1222no—
341D4—2442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4D4×D6111yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—21no—
364C8—612no—
365C8—1221no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—612no—
373C22—1221no—
374C22—1221no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—1221no—
381C4—1221no—
382C4—1221no—
383C4—1222no—
384C4—2441no—
385C4—2441no—
386C4—2441no—
387C4C2×D4×D6111yescharacteristic
388C4#1451982211yescharacteristic
389C2—41no—
390C2—81no—
391C2—1222no—
392C2#1684039411yescharacteristic
393C2#137×D6111yescharacteristic
394C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3270
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. C2×Q16×D61C2semidirect
3. #16840425C2semidirect
5. #16840153C2semidirect
6. #16840018C2semidirect
7. #16839990C2semidirect
8. #16839983C2semidirect
9. #16839970C2semidirect
10. #16839920C2semidirect
11. #16839919C2semidirect
12. #16839899C2semidirect
13. #16839866C2semidirect
14. #16839836C2semidirect
15. C61×#452C2semidirect
101. #11758202D4semidirect
177. C2×D61#137semidirect
207. #452D61semidirect
213. C61#3270semidirect