Finite Group Databasebeta

← #21457395

Subgroups — #21457395

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×#14519809C211yesmaximal, characteristic, complemented
2C2×Q16×D61C211yesmaximal, characteristic, complemented
3#16840427C211yesmaximal, characteristic, complemented
4#16840424C211yesmaximal, characteristic
5#16840154C211yesmaximal, characteristic, complemented
6#16840019C211yesmaximal, characteristic, complemented
7#16839994C211yesmaximal, characteristic, complemented
8#16839985C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839919C211yesmaximal, characteristic, complemented
11#16839916C211yesmaximal, characteristic, complemented
12#16839902C211yesmaximal, characteristic, complemented
13#16839867C211yesmaximal, characteristic, complemented
14#16839832C211yesmaximal, characteristic, complemented
15C61×#462C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519809—24no—
21C2×Dic244C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758202C2211yescharacteristic
25Q16×D61—24no—
26C2×#11758190C2211yescharacteristic
27C2×#11758201C2211yescharacteristic
28C2×#11758201C2211yescharacteristic
29C2×#11758189C2211yescharacteristic
30C2×C8×D61C2211yescharacteristic
31#14519776—21no—
32#14519765—21no—
33#14519765C2211yescharacteristic
34#14519757—21no—
35#14519757C2211yescharacteristic
36#14519755—21no—
37#14519755—21no—
38#14519753C2211yescharacteristic
39#14519753C2211yescharacteristic
40#14519752—21no—
41#14519752C2211yescharacteristic
42C4×Dic122C2211yescharacteristic
43C4×D244—21no—
44C4×D244C2211yescharacteristic
45#14519739—21no—
46#14519708C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519700C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519689C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519688C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic
56C4⋊Q8×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#103×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64#11758226—22no—
65#11758226—41no—
66Q8×D61—22no—
67Q8×D61—22no—
68Q8×D61—22no—
69Q8×D61—41no—
70Q8×D61—41no—
71Q8×D61—41no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244D411yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61C2311yescharacteristic
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83C2×Dic122—21no—
84C2×Dic122—21no—
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87Q16×C61—22no—
88Q16×C61—22no—
89C2×C8×C61C2311yescharacteristic
90C2×C8×C61C2311yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61C2311yescharacteristic
95C42×C61—21no—
96C42×C61C2311yescharacteristic
97#11758202—22no—
98#11758202—41no—
99#11758202D414yescomplemented
100#11758201—22no—
101#11758201—41no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198D411yescharacteristic
109#11758198D411yescharacteristic
110C4⋊Dic61—21no—
111C4⋊Dic61D411yescharacteristic
112C4⋊Dic61C2311yescharacteristic
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116C4×Dic61—21no—
117C2×#92418C2311yescharacteristic
118C2×#92418C2311yescharacteristic
119Dic244—22no—
120#11758190—22no—
121#11758189—22no—
122C8×D61—22no—
123C22×D61—21no—
124C22×D61C2×D411yescharacteristic
125C22×D61C2×D411yescharacteristic
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131Q8×C61C2×D412yes—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2411yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—22no—
145D244—21no—
146D244—21no—
147D244—42no—
148D244—42no—
149C4×D61—21no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
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×C61C22×D411yescharacteristic
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61#13712yescomplemented
178C4×C61—22no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61C22×D411yescharacteristic
185C4×C61H(5,𝔽2)11yescharacteristic
186Dic61—22no—
187Dic61—21no—
188Dic61—21no—
189Dic61—41no—
190Dic61—41no—
191#3270—611nomaximal, Sylow
192C2×C61D4211yescharacteristic
193C2×C61C2×#13711yescharacteristic
194C2×C61#57811yescharacteristic
195D61—22no—
196D61—41no—
197D61—81no—
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#462D6111yescharacteristic, complemented
207#452—611no—
208#451—611no—
209#451—611no—
210#448—611no—
211#441—611no—
212#435—611no—
213C61#327011yescharacteristic, complemented, Sylow
214C2×#41—611no—
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—1224no—
224C2×Q16C2×D6111yescharacteristic
225C2×Q16C2×D6111yescharacteristic
226C2×SD16—611no—
227C2×SD16—611no—
228C2×SD16—611no—
229C2×M16—611no—
230C22×C8—611no—
231C4⋊Q8—1221no—
232C4⋊Q8C2×D6111yescharacteristic
233#124—611no—
234#124—1221no—
235C22⋊Q8—611no—
236C22⋊Q8—611no—
237C22⋊Q8—611no—
238C22⋊Q8—1221no—
239C22⋊Q8—1221no—
240C22⋊Q8—1221no—
241#121—611no—
242#121—1221no—
243C4×Q8—611no—
244C4×Q8C2×D6111yescharacteristic
245C4×D4—611no—
246C4×D4—1221no—
247C4×D4—1221no—
248#106—611no—
249C4⋊C8C2×D6111yescharacteristic
250#103—611no—
251#103—611no—
252#103—611no—
253#103C2×D6111yescharacteristic
254#103C2×D6111yescharacteristic
255#102—611no—
256C22⋊C8—611no—
257C22⋊C8—611no—
258#97—611no—
259#41—1222no—
260#41—2441no—
261C2×Q8—611no—
262C2×Q8—611no—
263C2×Q8—1221no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×Q8—1222no—
267C2×Q8—1222no—
268C2×Q8—1222no—
269C2×Q8—2441no—
270C2×Q8—2441no—
271C2×Q8—2441no—
272C2×Q8C22×D6111yescharacteristic
273C2×Q8C22×D6111yescharacteristic
274C2×Q8C22×D6111yescharacteristic
275C2×D4—611no—
276C2×D4—611no—
277C2×D4—1221no—
278C2×D4—1221no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285Q16—22no—
286Q16—22no—
287Q16—614no—
288Q16—1222no—
289Q16—1222no—
290Q16—2441no—
291SD16—1222no—
292SD16—1222no—
293SD16—2441no—
294M16—1222no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8—1222no—
298C2×C8C22×D6111yescharacteristic
299C2×C8C22×D6111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—611no—
304C4⋊C4—611no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4C22×D6111yescharacteristic
310C22⋊C4—611no—
311C22⋊C4—611no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C42—21no—
319C42—1221no—
320C42C22×D6111yescharacteristic
321C23—611no—
322C23—611no—
323C23—1221no—
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—612no—
330Q8—1221no—
331Q8—1221no—
332Q8—1221no—
333Q8—2442no—
334Q8—2442no—
335Q8—2442no—
336Q8D4×D6112yes—
337D4—1222no—
338D4—1221no—
339D4—1221no—
340D4—2442no—
341D4—2442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—1221no—
349C2×C4—1221no—
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×C4D4×D6111yescharacteristic
360C2×C4D4×D6111yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—21no—
364C8—612no—
365C8—1221no—
366C22—612no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—1221no—
383C4—1221no—
384C4—1222no—
385C4—2441no—
386C4—2441no—
387C4C2×D4×D6111yescharacteristic
388C4#1451982311yescharacteristic
389C2—1222no—
390C2—4881no—
391C2—2441no—
392C2#1684039611yescharacteristic
393C2#137×D6111yescharacteristic
394C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3270
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×Q16×D61C2semidirect
3. #16840427C2semidirect
5. #16840154C2semidirect
6. #16840019C2semidirect
7. #16839994C2semidirect
8. #16839985C2semidirect
9. #16839923C2semidirect
10. #16839919C2semidirect
11. #16839916C2semidirect
12. #16839902C2semidirect
13. #16839867C2semidirect
14. #16839832C2semidirect
15. C61×#462C2semidirect
99. #11758202D4semidirect
177. C2×D61#137semidirect
206. #462D61semidirect
213. C61#3270semidirect