Finite Group Databasebeta

← #21455448

Subgroups — #21455448

Order 7808.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic, complemented
2C2×M16×D61C211yesmaximal, characteristic, complemented
3#16840275C211yesmaximal, characteristic
4C22⋊Q8×D61C211yesmaximal, characteristic, complemented
5#16840018C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16840008C211yesmaximal, characteristic, complemented
8#16840002C211yesmaximal, characteristic, complemented
9#16840000C211yesmaximal, characteristic, complemented
10#16839994C211yesmaximal, characteristic, complemented
11#16839992C211yesmaximal, characteristic, complemented
12#16839801C211yesmaximal, characteristic, complemented
13#16839769C211yesmaximal, characteristic, complemented
14#16839762C211yesmaximal, characteristic, complemented
15C61×#470C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19#14519809—24no—
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758190C2211yescharacteristic, complemented
22C2×#11758201C2211yescharacteristic, complemented
23C2×#11758194C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25C2×#11758189C2211yescharacteristic
26M16×D61—24no—
27C2×C8×D61C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519762—21no—
30#14519757C2211yescharacteristic
31#14519756C2211yescharacteristic
32#14519755—21no—
33#14519754—21no—
34#14519753C2211yescharacteristic
35#14519753C2211yescharacteristic
36#14519752C2211yescharacteristic
37#14519751C2211yescharacteristic
38#14519747—21no—
39#14519739—21no—
40#14519737—21no—
41#14519735C2211yescharacteristic
42C4⋊C4×D61—21no—
43C4⋊C4×D61C2211yescharacteristic
44C22⋊C4×D61—21no—
45#14519711C2211yescharacteristic, complemented
46#14519710C2211yescharacteristic, complemented
47#14519708C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519701C2211yescharacteristic, complemented
51#14519700C2211yescharacteristic, complemented
52#14519699C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic, complemented
54C2×Q16×C61C2211yescharacteristic, complemented
55C2×M16×C61C2211yescharacteristic
56C22⋊Q8×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#106×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#103×C61C2211yescharacteristic, complemented
61C23×D61D411yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C22×Dic61D411yescharacteristic
67#11758226—22no—
68#11758226—22no—
69Q8×D61—22no—
70Q8×D61—22no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244C2311yescharacteristic
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61D411yescharacteristic
80C2×C4×D61D411yescharacteristic
81C2×C4×D61C2311yescharacteristic
82C2×C4×D61C2311yescharacteristic
83C2×Dic122—21no—
84C2×Dic122C2311yescharacteristic
85Q16×C61—22no—
86M16×C61—22no—
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊Dic61—21no—
96#11758202—22no—
97#11758201—22no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109#11758196—21no—
110#11758196—21no—
111C4×Dic61—21no—
112#11758194—22no—
113C2×#92418C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115#11758190—22no—
116#11758189—22no—
117#11758189D414yescomplemented
118C8×D61—22no—
119C8×D61—22no—
120C23×C61C2×D411yescharacteristic
121C22×D61—22no—
122C22×D61—22no—
123C22×D61—21no—
124C22×D61—41no—
125C22×D61C2×D411yescharacteristic
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2411yescharacteristic
139C22⋊D61—42no—
140C2×Dic61—22no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146D244—21no—
147D244—21no—
148D244—42no—
149D244—42no—
150C4×D61—22no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—22no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61C2×D412yes—
158C4×D61#4112yes—
159Dic122—21no—
160Dic122—21no—
161Dic122—42no—
162C8×C61—21no—
163C8×C61C2×D412yes—
164#92418—21no—
165#92418C2×D412yes—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61C22×D411yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—44no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61#12112yes—
179C2×D61#13712yescomplemented
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61C22×D411yescharacteristic
186C4×C61C2×#4111yescharacteristic
187Dic61—21no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191Dic61#12112yes—
192#3056—611nomaximal, Sylow
193C2×C61—41no—
194C2×C61C2×#12111yescharacteristic
195C2×C61C2×#13711yescharacteristic
196C2×C61#57511yescharacteristic
197D61—22no—
198D61—22no—
199D61—81no—
200C2×#137—611no—
201C22×M16—611no—
202#525—611no—
203C2×C22⋊Q8—611no—
204#470—611no—
205#470D6111yescharacteristic, complemented
206#468—611no—
207#468—611no—
208#467—611no—
209#467—611no—
210#465—611no—
211#465—611no—
212#428—611no—
213#419—611no—
214#417—611no—
215C61#305611yescharacteristic, complemented, Sylow
216C2×#41—611no—
217C22×Q8—611no—
218C23×C4—611no—
219#137—1224no—
220C2×Q16—611no—
221C2×Q16C2×D6111yescharacteristic, complemented
222C2×SD16—611no—
223C2×SD16—611no—
224C2×M16—611no—
225C2×M16—611no—
226C2×M16—611no—
227C2×M16—1224no—
228C2×M16C2×D6111yescharacteristic
229C22×C8—611no—
230C22×C8—611no—
231#123—1221no—
232C22⋊Q8—611no—
233C22⋊Q8—611no—
234C22⋊Q8—611no—
235C22⋊Q8—611no—
236C22⋊Q8—1221no—
237C22⋊Q8—1221no—
238C22⋊Q8C2×D6111yescharacteristic
239C22⋊Q8C2×D6111yescharacteristic
240#121—611no—
241#121—611no—
242#120—1221no—
243C4×D4—1221no—
244C4×D4—1221no—
245#117—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—1221no—
248C2×C22⋊C4—1221no—
249#107—611no—
250#107—611no—
251#106—611no—
252#106C2×D6111yescharacteristic, complemented
253#103—611no—
254#103—611no—
255#103—611no—
256#103—611no—
257#103C2×D6111yescharacteristic, complemented
258#103C2×D6111yescharacteristic, complemented
259#102—611no—
260#102—611no—
261C24—611no—
262#41—1222no—
263#41—1222no—
264C2×Q8—611no—
265C2×Q8—1221no—
266C2×Q8—1222no—
267C2×Q8—1222no—
268C2×Q8C22×D6111yescharacteristic
269C2×Q8C22×D6111yescharacteristic
270C2×D4—611no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C22×D6111yescharacteristic
285Q16—22no—
286Q16—1222no—
287SD16—1222no—
288SD16—1222no—
289M16—22no—
290M16—614no—
291M16—1222no—
292M16—1222no—
293C2×C8—611no—
294C2×C8—611no—
295C2×C8—1222no—
296C2×C8—1222no—
297C2×C8C22×D6111yescharacteristic
298C2×C8C22×D6111yescharacteristic
299C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
309C4⋊C4C22×D6111yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C42—1221no—
320C23—611no—
321C23—611no—
322C23—1222no—
323C23—1222no—
324C23—1221no—
325C23—2441no—
326C23D4×D6111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—21no—
331Q8—1221no—
332Q8—1221no—
333Q8—2442no—
334D4—1221no—
335D4—1221no—
336D4—2442no—
337D4—2442no—
338D4—2442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—611no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
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—612no—
364C8—1221no—
365C8D4×D6112yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—612no—
370C22—612no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—2444no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22C2×D4×D6111yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—612no—
386C4—1221no—
387C4—2441no—
388C4—2441no—
389C4—2441no—
390C4C2×D4×D6111yescharacteristic
391C4#41×D6111yescharacteristic
392C2—41no—
393C2—1222no—
394C2—1222no—
395C2—4881no—
396C2#121×D6111yescharacteristic
397C2#137×D6111yescharacteristic
398C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3056
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×#14519809C2semidirect
2. C2×M16×D61C2semidirect
4. C22⋊Q8×D61C2semidirect
5. #16840018C2semidirect
6. #16840010C2semidirect
7. #16840008C2semidirect
8. #16840002C2semidirect
9. #16840000C2semidirect
10. #16839994C2semidirect
11. #16839992C2semidirect
12. #16839801C2semidirect
13. #16839769C2semidirect
14. #16839762C2semidirect
15. C61×#470C2semidirect
20. C2×#11758202C22semidirect
21. C2×#11758190C22semidirect
22. C2×#11758201C22semidirect
45. #14519711C22semidirect
46. #14519710C22semidirect
47. #14519708C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519701C22semidirect
51. #14519700C22semidirect
52. #14519699C22semidirect
53. #14519697C22semidirect
54. C2×Q16×C61C22semidirect
58. #106×C61C22semidirect
59. #103×C61C22semidirect
60. #103×C61C22semidirect
117. #11758189D4semidirect
179. C2×D61#137semidirect
205. #470D61semidirect
215. C61#3056semidirect
221. C2×Q16C2×D61semidirect
252. #106C2×D61semidirect
257. #103C2×D61semidirect
258. #103C2×D61semidirect