Finite Group Databasebeta

← #21457328

Subgroups — #21457328

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×#14519809C211yesmaximal, characteristic, complemented
2C2×SD16×D61C211yesmaximal, characteristic, complemented
3#16840427C211yesmaximal, characteristic, complemented
4#16840405C211yesmaximal, characteristic
5#16840005C211yesmaximal, characteristic, complemented
6#16840000C211yesmaximal, characteristic, complemented
7#16839981C211yesmaximal, characteristic, complemented
8#16839964C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839916C211yesmaximal, characteristic, complemented
11#16839911C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839864C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#497C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic, complemented
19C2×D4×D61C2211yescharacteristic
20#14519809—24no—
21C2×#11758202C2211yescharacteristic, complemented
22C2×#11758190C2211yescharacteristic
23C2×#11758200C2211yescharacteristic
24C2×#11758201C2211yescharacteristic
25C2×#11758201C2211yescharacteristic
26SD16×D61—24no—
27C2×#11758189C2211yescharacteristic, complemented
28C2×C8×D61C2211yescharacteristic
29#14519776—21no—
30#14519759—21no—
31#14519755—21no—
32#14519755—21no—
33#14519753C2211yescharacteristic
34#14519753C2211yescharacteristic
35#14519753C2211yescharacteristic, complemented
36#14519750—21no—
37#14519748C2211yescharacteristic
38#14519747—21no—
39C4×Dic122C2211yescharacteristic, complemented
40C4×D244C2211yescharacteristic
41C4×D244C2211yescharacteristic
42#14519739—21no—
43C22⋊C4×D61—21no—
44#14519711C2211yescharacteristic, complemented
45C4⋊#92418C2211yescharacteristic, complemented
46#14519702C2211yescharacteristic, complemented
47#14519701C2211yescharacteristic, complemented
48#14519701C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic
51#14519698C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519689C2211yescharacteristic, complemented
54C2×Q16×C61C2211yescharacteristic, complemented
55C2×Q16×C61C2211yescharacteristic, complemented
56C2×SD16×C61C2211yescharacteristic
57C2×SD16×C61C2211yescharacteristic
58C4⋊Q8×C61C2211yescharacteristic, complemented
59#124×C61C2211yescharacteristic
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68#11758226—22no—
69#11758226—41no—
70Q8×D61—22no—
71Q8×D61—22no—
72Q8×D61—41no—
73Q8×D61—41no—
74D4×D61—22no—
75D4×D61—41no—
76C2×D244—21no—
77C2×D244D411yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61C2311yescharacteristic
84C2×C4×D61C2311yescharacteristic
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×Dic122C2311yescharacteristic
88Q16×C61—22no—
89Q16×C61—41no—
90SD16×C61—22no—
91SD16×C61—41no—
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C42×C61C2311yescharacteristic
99C22⋊Dic61—21no—
100#11758202—22no—
101#11758201—22no—
102#11758201—22no—
103#11758200—22no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198D411yescharacteristic
109#11758198D411yescharacteristic
110C4⋊Dic61D411yescharacteristic
111C4⋊Dic61C2311yescharacteristic
112C4⋊Dic61C2311yescharacteristic
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116#11758196—21no—
117C4×Dic61—21no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120#11758190D414yescomplemented
121#11758189—22no—
122C8×D61—22no—
123C23×C61—21no—
124C22×D61—21no—
125C22×D61—42no—
126C22×D61—42no—
127C22×D61—81no—
128C22×D61C2×D411yescharacteristic
129C22×D61C2×D411yescharacteristic
130Q8×C61—21no—
131Q8×C61—21no—
132Q8×C61—21no—
133Q8×C61—21no—
134Q8×C61—21no—
135Q8×C61—21no—
136D4×C61—21no—
137D4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2411yescharacteristic
144C22⋊D61—42no—
145C22⋊D61—81no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151D244—22no—
152D244—21no—
153D244—42no—
154D244C2×D412yes—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—81no—
163Dic122—21no—
164Dic122—42no—
165Dic122—42no—
166Dic122C2×D412yes—
167C8×C61—21no—
168C8×C61C2×D412yes—
169#92418—21no—
170#92418—21no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61C22×D411yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—22no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—84no—
184C2×D61#13712yescomplemented
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61C22×D411yescharacteristic
191C4×C61H(5,𝔽2)11yescharacteristic
192Dic61—22no—
193Dic61—21no—
194Dic61—21no—
195Dic61—41no—
196Dic61—41no—
197#3266—611nomaximal, Sylow
198C2×C61—81no—
199C2×C61D4211yescharacteristic
200C2×C61C2×#13711yescharacteristic
201C2×C61#57711yescharacteristic
202D61—22no—
203D61—41no—
204D61—42no—
205C2×#137—611no—
206C22×SD16—611no—
207D4×Q8—611no—
208#546—611no—
209#497D6111yescharacteristic, complemented
210#468—611no—
211#467—611no—
212#464—611no—
213#461—611no—
214#452—611no—
215#451—611no—
216#450—611no—
217#448—611no—
218#440—611no—
219#435—611no—
220C61#326611yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C22×Q8—611no—
223C22×Q8—611no—
224C22×D4—611no—
225#137—1224no—
226C2×Q16—611no—
227C2×Q16C2×D6111yescharacteristic, complemented
228C2×Q16C2×D6111yescharacteristic, complemented
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16—611no—
233C2×SD16—1224no—
234C2×SD16C2×D6111yescharacteristic
235C2×SD16C2×D6111yescharacteristic
236C2×M16—611no—
237C22×C8—611no—
238C4⋊Q8—1221no—
239C4⋊Q8C2×D6111yescharacteristic, complemented
240#124C2×D6111yescharacteristic
241#123—1221no—
242C22⋊Q8—611no—
243C22⋊Q8—611no—
244C22⋊Q8—611no—
245C22⋊Q8—1221no—
246C22⋊Q8—1221no—
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#103—611no—
261#102—611no—
262#102—611no—
263C22⋊C8—611no—
264C22⋊C8—611no—
265#97C2×D6111yescharacteristic, complemented
266C24—1221no—
267#41—1222no—
268#41—2441no—
269C2×Q8—611no—
270C2×Q8—1221no—
271C2×Q8—1221no—
272C2×Q8—1222no—
273C2×Q8—1222no—
274C2×Q8—2441no—
275C2×Q8—2441no—
276C2×Q8C22×D6111yescharacteristic
277C2×Q8C22×D6111yescharacteristic
278C2×Q8C22×D6111yescharacteristic
279C2×D4—611no—
280C2×D4—611no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1222no—
284C2×D4—1221no—
285C2×D4—2441no—
286C2×D4C22×D6111yescharacteristic
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293Q16—22no—
294Q16—41no—
295Q16—1222no—
296SD16—22no—
297SD16—41no—
298SD16—614no—
299SD16—1222no—
300SD16—1222no—
301SD16—1222no—
302M16—1222no—
303C2×C8—611no—
304C2×C8—611no—
305C2×C8—1222no—
306C2×C8C22×D6111yescharacteristic
307C2×C8C22×D6111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—611no—
311C4⋊C4—611no—
312C4⋊C4—611no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—611no—
320C22⋊C4—611no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C42—1221no—
327C42C22×D6111yescharacteristic
328C23—21no—
329C23—611no—
330C23—611no—
331C23—1221no—
332C23—4881no—
333C23—2442no—
334C23—2442no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—21no—
341Q8—612no—
342Q8—1221no—
343Q8—2442no—
344Q8—2442no—
345D4—21no—
346D4—21no—
347D4—612no—
348D4—1222no—
349D4—1221no—
350D4—4881no—
351D4—2442no—
352D4—2442no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—4881no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4D4×D6111yescharacteristic
370C2×C4D4×D6111yescharacteristic
371C2×C4C23×D6111yescharacteristic
372C8—21no—
373C8—1221no—
374C8—1221no—
375C8D4×D6112yes—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—612no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—1221no—
385C22—1222no—
386C22—4884no—
387C22—2441no—
388C22—2441no—
389C22C2×D4×D6111yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—1221no—
396C4—1221no—
397C4—1222no—
398C4—2441no—
399C4—2441no—
400C4C2×D4×D6111yescharacteristic
401C4#1451982211yescharacteristic
402C2—81no—
403C2—1222no—
404C2—2441no—
405C2—2442no—
406C2#1684039711yescharacteristic
407C2#137×D6111yescharacteristic
408C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#497C2
socleC22×C61C22×D4
hypercenter#497D61
hypocenterC61#3266
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×SD16×D61C2semidirect
3. #16840427C2semidirect
5. #16840005C2semidirect
6. #16840000C2semidirect
7. #16839981C2semidirect
8. #16839964C2semidirect
9. #16839923C2semidirect
10. #16839916C2semidirect
11. #16839911C2semidirect
12. #16839899C2semidirect
13. #16839864C2semidirect
14. #16839835C2semidirect
15. C61×#497C2semidirect
18. C2×Q8×D61C22semidirect
21. C2×#11758202C22semidirect
27. C2×#11758189C22semidirect
35. #14519753C22semidirect
39. C4×Dic122C22semidirect
44. #14519711C22semidirect
45. C4⋊#92418C22semidirect
46. #14519702C22semidirect
47. #14519701C22semidirect
48. #14519701C22semidirect
49. #14519701C22semidirect
53. #14519689C22semidirect
54. C2×Q16×C61C22semidirect
55. C2×Q16×C61C22semidirect
58. C4⋊Q8×C61C22semidirect
60. #97×C61C22semidirect
120. #11758190D4semidirect
184. C2×D61#137semidirect
209. #497D61semidirect
220. C61#3266semidirect
227. C2×Q16C2×D61semidirect
228. C2×Q16C2×D61semidirect
239. C4⋊Q8C2×D61semidirect
265. #97C2×D61semidirect