Finite Group Databasebeta

← #21455423

Subgroups — #21455423

Order 7808.

500 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519798C211yesmaximal, characteristic, complemented
2C2×M16×D61C211yesmaximal, characteristic, complemented
3#16840275C211yesmaximal, characteristic, complemented
4#16840272C211yesmaximal, characteristic, complemented
5#16840019C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16840013C211yesmaximal, characteristic, complemented
9#16840009C211yesmaximal, characteristic, complemented
10#16840008C211yesmaximal, characteristic, complemented
11#16840005C211yesmaximal, characteristic, complemented
12#16839799C211yesmaximal, characteristic, complemented
13#16839757C211yesmaximal, characteristic, complemented
14#16839755C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19#14519798—24no—
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758190C2211yescharacteristic, complemented
22C2×#11758199C2211yescharacteristic, complemented
23C2×#11758194C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25C2×#11758189C2211yescharacteristic
26M16×D61—24no—
27C2×C8×D61C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519762—21no—
30#14519759—21no—
31#14519757C2211yescharacteristic
32#14519756C2211yescharacteristic
33#14519753C2211yescharacteristic
34#14519752C2211yescharacteristic
35#14519751C2211yescharacteristic
36#14519748C2211yescharacteristic
37#14519747—21no—
38#14519745—21no—
39D4×Dic61—21no—
40#14519739—21no—
41#14519737—21no—
42#14519737—21no—
43#14519735C2211yescharacteristic
44#14519735C2211yescharacteristic
45#14519711C2211yescharacteristic, complemented
46#14519708C2211yescharacteristic, complemented
47#14519708C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519700C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52#14519698C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×M16×C61C2211yescharacteristic
56C22⋊Q8×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic
58#107×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61D411yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70C22×Dic61D411yescharacteristic
71#11758226—22no—
72#11758226—22no—
73#11758224—22no—
74#11758224—22no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244C2311yescharacteristic
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61D411yescharacteristic
82C2×C4×D61D411yescharacteristic
83C2×C4×D61C2311yescharacteristic
84C2×C4×D61C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86SD16×C61—22no—
87M16×C61—22no—
88C2×C8×C61C2311yescharacteristic
89C2×C8×C61C2311yescharacteristic
90C4⋊C4×C61—21no—
91C4⋊C4×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97#11758202—22no—
98#11758199—22no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61C2311yescharacteristic
107C4⋊Dic61C2311yescharacteristic
108#11758196—21no—
109#11758196—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112#11758194—22no—
113C2×#92418C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115#11758190—22no—
116#11758189—22no—
117#11758189—22no—
118C8×D61—22no—
119C8×D61D414yescomplemented
120C23×C61—21no—
121C23×C61C2×D411yescharacteristic
122C22×D61—22no—
123C22×D61—21no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61C2×D411yescharacteristic
127C22×D61C2×D411yescharacteristic
128Q8×C61—21no—
129Q8×C61—21no—
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×C61C2×D411yescharacteristic
139C2×C4×C61C2411yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—42no—
143C2×Dic61—22no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148C2×Dic61C2×D411yescharacteristic
149C2×Dic61C2×D411yescharacteristic
150D244—21no—
151D244—21no—
152D244—42no—
153D244—42no—
154C4×D61—22no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—22no—
158C4×D61—42no—
159C4×D61C2×D412yes—
160C4×D61#4112yes—
161Dic122—21no—
162Dic122—21no—
163C8×C61—21no—
164C8×C61C2×D412yes—
165#92418—21no—
166#92418C2×D412yes—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61C22×D411yescharacteristic
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—44no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61#12112yes—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61C22×D411yescharacteristic
189C4×C61C2×#4111yescharacteristic
190Dic61—21no—
191Dic61—41no—
192Dic61—41no—
193Dic61—41no—
194Dic61#12112yes—
195#3054—611nomaximal, Sylow
196C2×C61—41no—
197C2×C61—81no—
198C2×C61C2×#12111yescharacteristic
199C2×C61#57511yescharacteristic
200C2×C61#57511yescharacteristic
201D61—22no—
202D61—41no—
203D61—81no—
204C2×#135—611no—
205C22×M16—611no—
206#525—611no—
207#525—611no—
208#470—611no—
209#470—611no—
210#469—611no—
211#469—611no—
212#468—611no—
213#468—611no—
214#468—611no—
215#468D6111yescharacteristic, complemented
216#427—611no—
217#416—611no—
218#416—611no—
219C61#305411yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41—611no—
222C23×C4—611no—
223#135—1224no—
224C2×Q16—611no—
225C2×SD16—611no—
226C2×SD16C2×D6111yescharacteristic, complemented
227C2×D8—611no—
228C2×M16—611no—
229C2×M16—611no—
230C2×M16—611no—
231C2×M16—1224no—
232C2×M16C2×D6111yescharacteristic
233C22×C8—611no—
234C22×C8—611no—
235#123—1221no—
236#123—1221no—
237C22⋊Q8—611no—
238C22⋊Q8—611no—
239C22⋊Q8—611no—
240C22⋊Q8C2×D6111yescharacteristic
241#121—611no—
242#121—611no—
243#121—611no—
244#121C2×D6111yescharacteristic
245#120—1221no—
246#120—1221no—
247C4×D4—1221no—
248C4×D4—1221no—
249C4×D4—1221no—
250C4×D4—1221no—
251#117—611no—
252#117—611no—
253#107—611no—
254#107C2×D6111yescharacteristic, complemented
255#106—611no—
256#106—611no—
257#103—611no—
258#103—611no—
259#103—611no—
260#103C2×D6111yescharacteristic, complemented
261#102—611no—
262#102—611no—
263#102—611no—
264#102C2×D6111yescharacteristic, complemented
265C24—611no—
266#41—1222no—
267#41—1222no—
268#41—1222no—
269#41—1222no—
270C2×Q8—611no—
271C2×Q8C22×D6111yescharacteristic
272C2×D4—21no—
273C2×D4—611no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4C22×D6111yescharacteristic
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1222no—
286C22×C4—1222no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4C22×D6111yescharacteristic
290Q16—1222no—
291SD16—22no—
292SD16—1222no—
293D8—1222no—
294M16—22no—
295M16—1222no—
296M16—1222no—
297M16—1222no—
298C2×C8—611no—
299C2×C8—614no—
300C2×C8—611no—
301C2×C8—1222no—
302C2×C8C22×D6111yescharacteristic
303C2×C8C22×D6111yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—611no—
306C4⋊C4—611no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4C22×D6111yescharacteristic
311C4⋊C4C22×D6111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C42—1221no—
323C42—1221no—
324C23—21no—
325C23—611no—
326C23—611no—
327C23—1222no—
328C23—1221no—
329C23—2441no—
330C23—2441no—
331C23D4×D6111yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—1221no—
335Q8—1221no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—1221no—
340D4—1221no—
341D4—2442no—
342D4—2442no—
343D4—2442no—
344D4—2442no—
345D4—2442no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—611no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—611no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—2442no—
364C2×C4—2442no—
365C2×C4D4×D6111yescharacteristic
366C2×C4C23×D6111yescharacteristic
367C8—21no—
368C8—612no—
369C8—1221no—
370C8D4×D6112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—612no—
378C22—1221no—
379C22—1221no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—2444no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22C2×D4×D6111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—612no—
393C4—1221no—
394C4—2441no—
395C4—2441no—
396C4—2441no—
397C4C2×D4×D6111yescharacteristic
398C4#41×D6111yescharacteristic
399C2—41no—
400C2—81no—
401C2—1222no—
402C2—4881no—
403C2—2441no—
404C2#121×D6111yescharacteristic
405C2#1684055811yescharacteristic
406C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3054
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14519798C2semidirect
2. C2×M16×D61C2semidirect
3. #16840275C2semidirect
4. #16840272C2semidirect
5. #16840019C2semidirect
6. #16840018C2semidirect
7. #16840014C2semidirect
8. #16840013C2semidirect
9. #16840009C2semidirect
10. #16840008C2semidirect
11. #16840005C2semidirect
12. #16839799C2semidirect
13. #16839757C2semidirect
14. #16839755C2semidirect
15. C61×#468C2semidirect
20. C2×#11758202C22semidirect
21. C2×#11758190C22semidirect
22. C2×#11758199C22semidirect
45. #14519711C22semidirect
46. #14519708C22semidirect
47. #14519708C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519700C22semidirect
51. #14519699C22semidirect
52. #14519698C22semidirect
53. #14519697C22semidirect
54. C2×SD16×C61C22semidirect
58. #107×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
119. C8×D61D4semidirect
215. #468D61semidirect
219. C61#3054semidirect
226. C2×SD16C2×D61semidirect
254. #107C2×D61semidirect
260. #103C2×D61semidirect
264. #102C2×D61semidirect