Finite Group Databasebeta

← #21457327

Subgroups — #21457327

Order 7808.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519807C211yesmaximal, characteristic, complemented
2C2×SD16×D61C211yesmaximal, characteristic, complemented
3#16840425C211yesmaximal, characteristic, complemented
4#16840400C211yesmaximal, characteristic
5#16840155C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16840002C211yesmaximal, characteristic, complemented
8#16839987C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839916C211yesmaximal, characteristic, complemented
11#16839914C211yesmaximal, characteristic, complemented
12#16839903C211yesmaximal, characteristic, complemented
13#16839859C211yesmaximal, characteristic, complemented
14#16839836C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic, complemented
17C2×Q8×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519807—24no—
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758202C2211yescharacteristic, complemented
22C2×#11758190C2211yescharacteristic
23C2×#11758190C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758201C2211yescharacteristic
27SD16×D61—24no—
28C2×#11758194C2211yescharacteristic, complemented
29C2×C8×D61C2211yescharacteristic
30#14519776—21no—
31#14519775C2211yescharacteristic, complemented
32#14519766C2211yescharacteristic
33#14519760—21no—
34#14519757C2211yescharacteristic
35#14519755—21no—
36#14519754—21no—
37#14519753C2211yescharacteristic
38#14519751C2211yescharacteristic
39#14519749—21no—
40#14519745—21no—
41#14519742C2211yescharacteristic, complemented
42D4×Dic61C2211yescharacteristic
43C4×C22⋊D61C2211yescharacteristic
44#14519737—21no—
45C2×#11758198—21no—
46#14519710C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519702C2211yescharacteristic, complemented
50#14519701C2211yescharacteristic, complemented
51#14519697C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519687C2211yescharacteristic, complemented
54C2×#41×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic, complemented
56C2×SD16×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic, complemented
58#103×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62#41×C61—22no—
63#41×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×Q8×C61C2311yescharacteristic
66C2×D4×C61—21no—
67C2×D4×C61C2311yescharacteristic
68C22×C4×C61—21no—
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75Q8×D61—22no—
76Q8×D61—41no—
77D4×D61—22no—
78D4×D61—41no—
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—22no—
83C2×Dic122—21no—
84C2×Dic122—21no—
85C2×Dic122—41no—
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88Q16×C61—41no—
89SD16×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61C2311yescharacteristic
94C22⋊C4×C61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61D411yescharacteristic
97#11758202—22no—
98#11758202—22no—
99#11758201—22no—
100#11758200—22no—
101#11758200D414yescomplemented
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198D411yescharacteristic
108C4⋊Dic61—21no—
109C4⋊Dic61C2311yescharacteristic
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196D411yescharacteristic
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117#11758194—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120#11758190—22no—
121#11758190—41no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—81no—
129C22×D61C2×D411yescharacteristic
130Q8×C61—21no—
131Q8×C61—21no—
132Q8×C61—21no—
133Q8×C61—21no—
134D4×C61—21no—
135D4×C61—42no—
136D4×C61C2×D412yes—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—42no—
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2411yescharacteristic
145C22⋊D61—22no—
146C22⋊D61—42no—
147C22⋊D61—81no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—81no—
153C2×Dic61C2×D411yescharacteristic
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156D244—21no—
157D244—21no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—42no—
161Dic122—21no—
162Dic122—21no—
163Dic122—21no—
164Dic122—42no—
165Dic122—42no—
166Dic122C2×D412yes—
167C8×C61—21no—
168C8×C61—21no—
169#92418—21no—
170#92418C2×D412yes—
171C22×C61—21no—
172C22×C61—22no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61C22×D411yescharacteristic
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—84no—
184C2×D61#13712yescomplemented
185C4×C61—21no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61C22×D411yescharacteristic
190C4×C61H(5,𝔽2)11yescharacteristic
191Dic61—22no—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—41no—
196Dic61—41no—
197#3266—611nomaximal, Sylow
198C2×C61—42no—
199C2×C61—41no—
200C2×C61D4211yescharacteristic
201C2×C61C2×#13711yescharacteristic
202C2×C61#57711yescharacteristic
203D61—22no—
204D61—81no—
205C2×#137—611no—
206C22×SD16—611no—
207D4×Q8—611no—
208#546—611no—
209#497—611no—
210#468—611no—
211#467—611no—
212#464—611no—
213#461—611no—
214#452D6111yescharacteristic, complemented
215#451—611no—
216#450—611no—
217#448—611no—
218#440—611no—
219#435—611no—
220C61#326611yescharacteristic, complemented, Sylow
221C2×#41C2×D6111yescharacteristic
222C22×Q8—611no—
223C22×Q8—611no—
224C22×D4—611no—
225#137—1224no—
226C2×Q16—611no—
227C2×Q16—611no—
228C2×Q16C2×D6111yescharacteristic, complemented
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16—611no—
233C2×SD16—611no—
234C2×SD16—1224no—
235C2×SD16C2×D6111yescharacteristic
236C2×M16—611no—
237C22×C8—611no—
238C4⋊Q8—611no—
239C4⋊Q8—1221no—
240#124—611no—
241#123—1221no—
242C22⋊Q8—611no—
243C22⋊Q8—611no—
244C22⋊Q8—1221no—
245C22⋊Q8—1221no—
246C22⋊Q8C2×D6111yescharacteristic, complemented
247#121—611no—
248#121—1221no—
249#120—1221no—
250C4×Q8—611no—
251C4×D4—611no—
252C4×D4—611no—
253C4×D4—1221no—
254C2×C22⋊C4—1221no—
255#107—611no—
256C4⋊C8—611no—
257#103—611no—
258#103—611no—
259#103—611no—
260#103C2×D6111yescharacteristic, complemented
261#102—611no—
262#102C2×D6111yescharacteristic
263C22⋊C8—611no—
264C22⋊C8C2×D6111yescharacteristic, complemented
265#97—611no—
266C24—1221no—
267#41—22no—
268#41—41no—
269C2×Q8—611no—
270C2×Q8—611no—
271C2×Q8—1221no—
272C2×Q8—1222no—
273C2×Q8—1221no—
274C2×Q8—1222no—
275C2×Q8—2441no—
276C2×Q8—2441no—
277C2×Q8C22×D6111yescharacteristic
278C2×Q8C22×D6111yescharacteristic
279C2×D4—21no—
280C2×D4—611no—
281C2×D4—611no—
282C2×D4—1221no—
283C2×D4—1222no—
284C2×D4—1221no—
285C2×D4—2441no—
286C2×D4C22×D6111yescharacteristic
287C22×C4—21no—
288C22×C4—611no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4C22×D6111yescharacteristic
293Q16—41no—
294Q16—1222no—
295Q16—1222no—
296SD16—22no—
297SD16—614no—
298SD16—1222no—
299SD16—1222no—
300SD16—1222no—
301SD16—2441no—
302M16—1222no—
303C2×C8—611no—
304C2×C8—611no—
305C2×C8—1222no—
306C2×C8C22×D6111yescharacteristic
307C2×C8C22×D6111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—611no—
310C4⋊C4—611no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4C22×D6111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—611no—
319C22⋊C4—611no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C42—611no—
327C42—1221no—
328C23—21no—
329C23—611no—
330C23—1221no—
331C23—4881no—
332C23—2442no—
333C23—2442no—
334C23D4×D6111yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—612no—
340Q8—1221no—
341Q8—1221no—
342Q8—1221no—
343Q8—2442no—
344Q8—2442no—
345D4—21no—
346D4—42no—
347D4—1222no—
348D4—1221no—
349D4—1221no—
350D4—4881no—
351D4—2442no—
352D4D4×D6112yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—4881no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4D4×D6111yescharacteristic
371C2×C4C23×D6111yescharacteristic
372C8—21no—
373C8—21no—
374C8—612no—
375C8—1221no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—612no—
383C22—1221no—
384C22—1221no—
385C22—4884no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22C2×D4×D6111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—1221no—
395C4—1221no—
396C4—1221no—
397C4—1222no—
398C4—2441no—
399C4—2441no—
400C4C2×D4×D6111yescharacteristic
401C4#1451982211yescharacteristic
402C2—41no—
403C2—42no—
404C2—1222no—
405C2—4881no—
406C2#1684039411yescharacteristic
407C2#137×D6111yescharacteristic
408C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3266
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×SD16×D61C2semidirect
3. #16840425C2semidirect
5. #16840155C2semidirect
6. #16840010C2semidirect
7. #16840002C2semidirect
8. #16839987C2semidirect
9. #16839965C2semidirect
10. #16839916C2semidirect
11. #16839914C2semidirect
12. #16839903C2semidirect
13. #16839859C2semidirect
14. #16839836C2semidirect
15. C61×#452C2semidirect
16. C22×Dic122C22semidirect
20. C2×#11758202C22semidirect
21. C2×#11758202C22semidirect
28. C2×#11758194C22semidirect
31. #14519775C22semidirect
41. #14519742C22semidirect
46. #14519710C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519702C22semidirect
50. #14519701C22semidirect
53. #14519687C22semidirect
55. C2×Q16×C61C22semidirect
57. C22⋊Q8×C61C22semidirect
58. #103×C61C22semidirect
60. C22⋊C8×C61C22semidirect
101. #11758200D4semidirect
184. C2×D61#137semidirect
214. #452D61semidirect
220. C61#3266semidirect
228. C2×Q16C2×D61semidirect
246. C22⋊Q8C2×D61semidirect
260. #103C2×D61semidirect
264. C22⋊C8C2×D61semidirect