Finite Group Databasebeta

← #21456101

Subgroups — #21456101

Order 7808.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840386C211yesmaximal, characteristic, complemented
2#16840241C211yesmaximal, characteristic, complemented
3#16840094C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840044C211yesmaximal, characteristic, complemented
6#16839985C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839925C211yesmaximal, characteristic, complemented
9#16839908C211yesmaximal, characteristic
10#16839871C211yesmaximal, characteristic, complemented
11#16839868C211yesmaximal, characteristic, complemented
12#16839853C211yesmaximal, characteristic, complemented
13#16839849C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#476C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21#14519772—21no—
22#14519766—21no—
23#14519765C2211yescharacteristic
24#14519762—21no—
25#14519757C2211yescharacteristic
26#14519753—21no—
27#14519752C2211yescharacteristic
28C4×Dic122C2211yescharacteristic
29#14519742C2211yescharacteristic
30#14519742C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic
33C4×C22⋊D61—21no—
34#14519737—21no—
35#14519734C2211yescharacteristic
36#14519733—21no—
37C2×#11758196—21no—
38C4⋊C4×D61C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54#106×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65#11758224—22no—
66#11758224—22no—
67C2×D244—21no—
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C2311yescharacteristic
72C2×Dic122C2311yescharacteristic
73C2×Dic122C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C42×C61C2311yescharacteristic
82C22⋊Dic61—21no—
83#11758200—22no—
84#11758199—22no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198D411yescharacteristic
91#11758198D411yescharacteristic
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196D411yescharacteristic
99#11758196D411yescharacteristic
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106Dic244—22no—
107#11758190—22no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61C2×D411yescharacteristic
111Q8×C61—81no—
112D4×C61—21no—
113D4×C61#4112yes—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—81no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C22⋊D61—24no—
122C2×Dic61—24no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—81no—
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—21no—
131D244—21no—
132D244—81no—
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—81no—
136C4×D61—81no—
137Dic122—21no—
138Dic122—21no—
139Dic122—21no—
140Dic122#4112yes—
141C8×C61—21no—
142C8×C61—21no—
143#92418—21no—
144#92418—21no—
145C22×C61—22no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61C22×D411yescharacteristic
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61C2×#4111yescharacteristic
161C4×C61C2×#4111yescharacteristic
162Dic61—22no—
163Dic61—21no—
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168#3125—611nomaximal, Sylow
169C2×C61—42no—
170C2×C61#52511yescharacteristic
171C2×C61#57711yescharacteristic
172C2×C61#57711yescharacteristic
173D61—41no—
174D61—81no—
175#542—611no—
176#520—611no—
177#483—611no—
178#481—611no—
179#476D6111yescharacteristic, complemented
180#475—611no—
181#464—611no—
182#463—611no—
183#452—611no—
184#449—611no—
185#442—611no—
186#441—611no—
187C4×SD16—611no—
188C4×SD16—611no—
189#433—611no—
190C61#312511yescharacteristic, complemented, Sylow
191C2×#41—611no—
192C2×Q16—611no—
193C2×SD16—611no—
194C2×SD16—611no—
195C2×D8—611no—
196C4⋊Q8C2×D6111yescharacteristic
197#126—1221no—
198#124—611no—
199#124—1221no—
200#123—1221no—
201C22⋊Q8—611no—
202C22⋊Q8—1221no—
203#121—611no—
204C4×Q8—611no—
205C4×Q8—611no—
206C4×Q8—611no—
207C4×D4—611no—
208C4×D4—611no—
209C4×D4—1221no—
210C4×D4—1221no—
211C4×D4C2×D6111yescharacteristic
212#117—611no—
213#117—1221no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216#106—611no—
217#106—611no—
218#106C2×D6111yescharacteristic
219#106C2×D6111yescharacteristic
220C4⋊C8—611no—
221C4⋊C8C2×D6111yescharacteristic
222#103—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#102—611no—
227#102—611no—
228#102C2×D6111yescharacteristic
229#102C2×D6111yescharacteristic
230C22⋊C8—611no—
231C22⋊C8—611no—
232#97—611no—
233C4×C8—611no—
234#41—1222no—
235#41—1222no—
236C2×Q8—21no—
237C2×Q8—611no—
238C2×Q8—611no—
239C2×D4—611no—
240C2×D4—1221no—
241C2×D4—1221no—
242C2×D4C22×D6111yescharacteristic
243C22×C4—21no—
244C22×C4—611no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249Q16—1222no—
250SD16—1222no—
251SD16—1222no—
252D8—1222no—
253C2×C8—611no—
254C2×C8—611no—
255C2×C8C22×D6111yescharacteristic
256C2×C8C22×D6111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4C22×D6111yescharacteristic
267C4⋊C4C22×D6111yescharacteristic
268C4⋊C4C22×D6111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—611no—
271C22⋊C4—611no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C42—611no—
279C42—1221no—
280C42—1221no—
281C42—1221no—
282C42C22×D6111yescharacteristic
283C23—21no—
284C23—611no—
285C23—1221no—
286Q8—81no—
287Q8—612no—
288Q8—1221no—
289Q8—1221no—
290Q8—1221no—
291D4—21no—
292D4—1224no—
293D4—1221no—
294D4—1221no—
295D4—4881no—
296D4#1175822612yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—1224no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—4881no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4D4×D6111yescharacteristic
314C2×C4D4×D6111yescharacteristic
315C2×C4C23×D6111yescharacteristic
316C8—21no—
317C8—21no—
318C8—1221no—
319C8—1221no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—1221no—
324C22—1221no—
325C22—1221no—
326C22—2441no—
327C22—2441no—
328C22—2441no—
329C22C2×D4×D6111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—1221no—
336C4—1222no—
337C4—1221no—
338C4—1221no—
339C4—2441no—
340C4—2441no—
341C4#41×D6111yescharacteristic
342C4C2×#1175822611yescharacteristic
343C2—42no—
344C2—4881no—
345C2—2441no—
346C2#1684027511yescharacteristic
347C2#1684056811yescharacteristic
348C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61#3125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16840386C2semidirect
2. #16840241C2semidirect
3. #16840094C2semidirect
4. #16840082C2semidirect
5. #16840044C2semidirect
6. #16839985C2semidirect
7. #16839977C2semidirect
8. #16839925C2semidirect
10. #16839871C2semidirect
11. #16839868C2semidirect
12. #16839853C2semidirect
13. #16839849C2semidirect
14. #16839822C2semidirect
15. C61×#476C2semidirect
179. #476D61semidirect
190. C61#3125semidirect