Finite Group Databasebeta

← #21461819

Subgroups — #21461819

Order 7808.

370 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840831C211yesmaximal, characteristic, complemented
2D61⋊#104C211yesmaximal, characteristic, complemented
3#16840754C211yesmaximal, characteristic, complemented
4#16840714C211yesmaximal, characteristic, complemented
5#16840641C211yesmaximal, characteristic, complemented
6#16840634C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×D61C211yesmaximal, characteristic
8D61⋊M16C2211yescharacteristic
9Q8×#6923—21no—
10D4×#6923—22no—
11D4×#6923—21no—
12#14519856—21no—
13#14519856C2211yescharacteristic
14C2×C4⋊#6923—21no—
15C2×C4⋊#6923C2211yescharacteristic
16C2×C22⋊#6923—22no—
17C2×C4×#6923C2211yescharacteristic
18#14519842—21no—
19#14519841—21no—
20#14519839—21no—
21#14519839—21no—
22#41×D61C2211yescharacteristic
23C2×D4×D61C2211yescharacteristic
24#14519805C411yescharacteristic, complemented
25#14519804—21no—
26#14519803C411yescharacteristic, complemented
27#14519802C411yescharacteristic, complemented
28#14519801—21no—
29SD16×D61—21no—
30D8×D61—21no—
31M16×D61C2211yescharacteristic
32AGL(1,ℤ/8)×C61C411yescharacteristic, complemented
33C23×D61—21no—
34C22×#6923—21no—
35C22×#6923—22no—
36C22×#6923D412yes—
37#41×C61C2×C411yescharacteristic
38C2×D4×C61C2×C411yescharacteristic, complemented
39C2×C22⋊D61—21no—
40#11758226D411yescharacteristic
41Q8×D61D411yescharacteristic
42#11758224—21no—
43#11758224D411yescharacteristic
44D4×D61—21no—
45D4×D61—21no—
46D4×D61—21no—
47D4×D61—21no—
48D4×D61—21no—
49D4×D61D411yescharacteristic
50#11758222—21no—
51#11758222C2×C411yescharacteristic
52C2×D244C2×C411yescharacteristic, complemented
53C2×C4×D61—21no—
54C2×C4×D61C2311yescharacteristic
55C22⋊#6923—22no—
56C22⋊#6923—21no—
57C22⋊#6923—44no—
58#11758217—21no—
59C4⋊#6923—22no—
60C4⋊#6923—21no—
61C4⋊#6923—21no—
62C4⋊#6923D411yescharacteristic
63C4⋊#6923D411yescharacteristic
64C4×#6923—22no—
65C4×#6923—21no—
66C4×#6923—21no—
67C4×#6923—21no—
68#11758213—21no—
69D61⋊C8—21no—
70SD16×C61—21no—
71D8×C61—21no—
72M16×C61C2×C411yescharacteristic, complemented
73#11758201—21no—
74#11758200—21no—
75#11758199—21no—
76#11758199—21no—
77#11758194C2×C411yescharacteristic, complemented
78D488—21no—
79#11758190—21no—
80#11758189—21no—
81C8×D61—21no—
82C23×C61—21no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—42no—
86C22×D61—42no—
87C22×D61—41no—
88C22×D61—41no—
89C22×D61C2×D411yescharacteristic
90C2×#6923—22no—
91C2×#6923—21no—
92C2×#6923—22no—
93C2×#6923—21no—
94C2×#6923—41no—
95C2×#6923—41no—
96C2×#6923—42no—
97C2×#6923—82no—
98Q8×C61C22⋊C411yescharacteristic, complemented
99D4×C61—21no—
100D4×C61—21no—
101D4×C61—21no—
102D4×C61C22⋊C411yescharacteristic, complemented
103C2×C4×C61—21no—
104C2×C4×C61C22×C411yescharacteristic
105C22⋊D61—21no—
106C22⋊D61—21no—
107C22⋊D61—21no—
108C22⋊D61—41no—
109C22⋊D61—41no—
110C2×Dic61—21no—
111C2×Dic61#4111yescharacteristic
112D244—21no—
113D244—21no—
114D244—21no—
115D244C22⋊C411yescharacteristic, complemented
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—21no—
119C4×D61C2×D411yescharacteristic
120C4×D61C2×D411yescharacteristic
121C4×D61C2×D411yescharacteristic
122C4×D61#4111yescharacteristic
123Dic122—21no—
124Dic122C22⋊C411yescharacteristic, complemented
125#92420—41no—
126C8×C61—21no—
127#92418—21no—
128C22×C61—21no—
129C22×C61—42no—
130C22×C61—41no—
131C22×C61C4×D411yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—42no—
138C2×D61—41no—
139C2×D61—82no—
140C2×D61—81no—
141C2×D61—81no—
142C2×D61#12011yescharacteristic
143C2×D61#12111yescharacteristic
144#6923—42no—
145#6923—42no—
146#6923—41no—
147#6923—41no—
148C4×C61—21no—
149C4×C61C2×C22⋊C411yescharacteristic
150C4×C61C4×D411yescharacteristic
151Dic61—21no—
152Dic61#12111yescharacteristic
153Dic61#12311yescharacteristic
154#1883—611nomaximal, Sylow
155C2×C61—21no—
156C2×C61—41no—
157C2×C61—81no—
158C2×C61#38611yescharacteristic
159D61—21no—
160D61—41no—
161D61—81no—
162D61#45311yescharacteristic
163D61#45411yescharacteristic
164C2×AGL(1,ℤ/8)—611no—
165#520—611no—
166C2×#104—611no—
167#418—611no—
168#390—611no—
169#343—611no—
170#339—611no—
171C61#188311yescharacteristic, complemented, Sylow
172C2×#41—611no—
173C22×D4—611no—
174AGL(1,ℤ/8)—611no—
175AGL(1,ℤ/8)—611no—
176AGL(1,ℤ/8)—611no—
177AGL(1,ℤ/8)—1221no—
178AGL(1,ℤ/8)—1221no—
179AGL(1,ℤ/8)#692311yescharacteristic, complemented
180C2×SD16—1221no—
181C2×D8—1221no—
182C2×M16—611no—
183C2×M16—611no—
184C4×Q8—1221no—
185C4×D4—1222no—
186C4×D4—1221no—
187#117—611no—
188#117—1221no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—1221no—
191C2×C22⋊C4—1222no—
192C2×C42—611no—
193#104—1221no—
194#104—1221no—
195#102—1221no—
196#102—1221no—
197C24—1221no—
198#41—611no—
199#41—611no—
200#41—611no—
201#41—1221no—
202#41—1221no—
203#41C2×#692311yescharacteristic
204C2×Q8—611no—
205C2×D4—611no—
206C2×D4—611no—
207C2×D4—1221no—
208C2×D4—1221no—
209C2×D4—1221no—
210C2×D4—1221no—
211C2×D4—1221no—
212C2×D4—1221no—
213C2×D4C2×#692311yescharacteristic, complemented
214C22×C4—611no—
215C22×C4—612no—
216C22×C4—1221no—
217C22×C4—1222no—
218C22×C4—1221no—
219SD16—21no—
220SD16—1221no—
221SD16—1221no—
222SD16—1221no—
223D8—21no—
224D8—1221no—
225D8—1221no—
226D8—1221no—
227M16—611no—
228M16—1221no—
229M16—1221no—
230M16—1221no—
231M16C2×#692311yescharacteristic, complemented
232C2×C8—1221no—
233C2×C8—1221no—
234C4⋊C4—611no—
235C4⋊C4—611no—
236C4⋊C4—1221no—
237C4⋊C4—1221no—
238C4⋊C4—1222no—
239C22⋊C4—1221no—
240C22⋊C4—1222no—
241C22⋊C4—2444no—
242C42—1221no—
243C42—1221no—
244C42—1221no—
245C42—1222no—
246C23—21no—
247C23—611no—
248C23—1221no—
249C23—1221no—
250C23—2441no—
251C23—2441no—
252C23—2442no—
253C23—2442no—
254Q8—611no—
255Q8—1221no—
256Q8C22⋊#692311yescharacteristic, complemented
257D4—21no—
258D4—21no—
259D4—21no—
260D4—611no—
261D4—1221no—
262D4—1221no—
263D4—1221no—
264D4—1221no—
265D4—1221no—
266D4—1221no—
267D4—2441no—
268D4—2441no—
269D4C22⋊#692311yescharacteristic, complemented
270C2×C4—21no—
271C2×C4—611no—
272C2×C4—611no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1222no—
283C2×C4—1222no—
284C2×C4—4882no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2442no—
288C2×C4C22×#692311yescharacteristic
289C8—21no—
290C8—1221no—
291C8—2441no—
292C22—21no—
293C22—42no—
294C22—41no—
295C22—611no—
296C22—611no—
297C22—1221no—
298C22—1221no—
299C22—1221no—
300C22—4881no—
301C22—4881no—
302C22—4882no—
303C22—2442no—
304C22—2441no—
305C22—2441no—
306C22—2441no—
307C22D4×#692311yescharacteristic
308C4—21no—
309C4—611no—
310C4—611no—
311C4—1221no—
312C4—2441no—
313C4—2442no—
314C4—2441no—
315C4—2442no—
316C4C2×C22⋊#692311yescharacteristic
317C4D4×#692311yescharacteristic
318C2—21no—
319C2—41no—
320C2—81no—
321C2—611no—
322C2—611no—
323C2—1221no—
324C2—4881no—
325C2—2441no—
326C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingAGL(1,ℤ/8)×C61C4
socleC2×C61#386
hypercenterAGL(1,ℤ/8)#6923
hypocenterC61#1883
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #16840831C2semidirect
2. D61⋊#104C2semidirect
3. #16840754C2semidirect
4. #16840714C2semidirect
5. #16840641C2semidirect
6. #16840634C2semidirect
24. #14519805C4semidirect
26. #14519803C4semidirect
27. #14519802C4semidirect
32. AGL(1,ℤ/8)×C61C4semidirect
38. C2×D4×C61C2×C4semidirect
52. C2×D244C2×C4semidirect
72. M16×C61C2×C4semidirect
77. #11758194C2×C4semidirect
98. Q8×C61C22⋊C4semidirect
102. D4×C61C22⋊C4semidirect
115. D244C22⋊C4semidirect
124. Dic122C22⋊C4semidirect
171. C61#1883semidirect
179. AGL(1,ℤ/8)#6923semidirect
213. C2×D4C2×#6923semidirect
231. M16C2×#6923semidirect
256. Q8C22⋊#6923semidirect
269. D4C22⋊#6923semidirect