Finite Group Databasebeta

← #21446877

Subgroups — #21446877

Order 7808.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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#16840560C211yesmaximal, characteristic
2#16840336C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4#16839771C211yesmaximal, characteristic, complemented
5#16839736C211yesmaximal, characteristic, complemented
6#16839534C211yesmaximal, characteristic, complemented
7C2×#137×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—21no—
10#14519807—21no—
11#14519803—21no—
12#14519802—21no—
13#14519797—22no—
14C2×#11758194C2211yescharacteristic
15#14519775—21no—
16#14519766—21no—
17#14519760—22no—
18#14519753—22no—
19#14519736C2211yescharacteristic
20#14519736C2211yescharacteristic
21#14519703—22no—
22#14519701—22no—
23#14519692—22no—
24C2×#41×C61C2211yescharacteristic
25C22×Q8×C61C2211yescharacteristic
26#137×C61—22no—
27#137×C61—22no—
28C2×Q16×C61—21no—
29C2×SD16×C61—21no—
30C2×M16×C61C2211yescharacteristic
31#41×C61—21no—
32#41×C61—21no—
33#41×C61—21no—
34#41×C61—21no—
35C2×Q8×C61—21no—
36C2×Q8×C61—21no—
37C2×Q8×C61—21no—
38C2×Q8×C61—21no—
39C2×Q8×C61—21no—
40C2×Q8×C61D411yescharacteristic
41C2×Q8×C61D412yes—
42C2×D4×C61—21no—
43C2×D4×C61D411yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48#11758222—21no—
49#11758222—21no—
50#11758222—21no—
51#11758222—21no—
52C2×D244D411yescharacteristic
53C2×C4×D61—21no—
54C2×Dic122D411yescharacteristic
55Q16×C61—24no—
56SD16×C61—24no—
57M16×C61—21no—
58M16×C61D412yes—
59C2×C8×C61—21no—
60C22⋊Dic61—21no—
61C22⋊Dic61D412yes—
62#11758202—22no—
63#11758201—22no—
64#11758200—22no—
65#11758199—22no—
66#11758198—24no—
67C4⋊Dic61—21no—
68C4⋊Dic61—21no—
69#11758196—24no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72#11758194—21no—
73#11758194—21no—
74C2×#92418D412yes—
75C23×C61—21no—
76C23×C61C2×D411yescharacteristic
77C22×D61—21no—
78Q8×C61—21no—
79Q8×C61—22no—
80Q8×C61—21no—
81Q8×C61—22no—
82Q8×C61—41no—
83Q8×C61—41no—
84D4×C61—21no—
85D4×C61—21no—
86D4×C61—41no—
87D4×C61—41no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61#4111yescharacteristic
100C22⋊D61—41no—
101C22⋊D61—41no—
102C2×Dic61—22no—
103C2×Dic61—21no—
104C2×Dic61—41no—
105D244—21no—
106D244—21no—
107C4×D61—41no—
108C4×D61—41no—
109Dic122—21no—
110Dic122—21no—
111C8×C61—22no—
112#92418—22no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—81no—
116C22×C61#12011yescharacteristic
117C22×C61#12111yescharacteristic
118C22×C61#12711yescharacteristic
119C2×D61—42no—
120C2×D61—41no—
121C4×C61—41no—
122C4×C61—42no—
123C4×C61#12011yescharacteristic
124C4×C61#12011yescharacteristic
125C4×C61#12111yescharacteristic
126C4×C61#12111yescharacteristic
127Dic61—42no—
128Dic61—41no—
129Dic61—81no—
130#2009—611nomaximal, Sylow
131C2×C61—21no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—81no—
135C2×C61#39211yescharacteristic
136D61—81no—
137#575—611no—
138C2×#137D6111yescharacteristic, complemented
139#536—611no—
140#421—611no—
141#419—611no—
142#410—611no—
143#344—611no—
144C61#200911yescharacteristic, complemented, Sylow
145C2×#41—611no—
146C2×#41C2×D6111yescharacteristic
147C22×Q8C2×D6111yescharacteristic
148#137—22no—
149#137—22no—
150#137—1221no—
151#137—1221no—
152AGL(1,ℤ/8)—1221no—
153AGL(1,ℤ/8)—1221no—
154#135—1222no—
155C2×Q16—21no—
156C2×SD16—21no—
157C2×M16—611no—
158C2×M16C2×D6111yescharacteristic
159C4⋊Q8—1221no—
160#124—1221no—
161#123—1222no—
162C22⋊Q8—1222no—
163#117—611no—
164#117—611no—
165#104—1222no—
166#103—1222no—
167#99—1222no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—1221no—
173#41—1221no—
174#41—1221no—
175#41—1221no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—21no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—611no—
182C2×Q8C22⋊D6112yes—
183C2×Q8C22⋊D6111yescharacteristic
184C2×D4—21no—
185C2×D4—611no—
186C2×D4—1221no—
187C2×D4C22⋊D6111yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—1221no—
191C22×C4C22×D6111yescharacteristic
192Q16—24no—
193Q16—1222no—
194SD16—24no—
195SD16—1222no—
196SD16—1222no—
197D8—1222no—
198M16—21no—
199M16—1221no—
200M16—1221no—
201M16C22⋊D6112yes—
202C2×C8—21no—
203C2×C8—612no—
204C4⋊C4—1224no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C22⋊C4—612no—
208C22⋊C4—1224no—
209C22⋊C4—1221no—
210C42—1221no—
211C42—1221no—
212C23—21no—
213C23—1221no—
214C23D4×D6111yescharacteristic
215Q8—21no—
216Q8—22no—
217Q8—21no—
218Q8—22no—
219Q8—41no—
220Q8—41no—
221Q8—1221no—
222Q8—1221no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—1221no—
228D4—1221no—
229D4—2441no—
230D4—2441no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—1222no—
238C2×C4—1221no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4D4×D6111yescharacteristic
243C2×C4D4×D6111yescharacteristic
244C2×C4#1175822411yescharacteristic
245C2×C4C2×C22⋊D6111yescharacteristic
246C2×C4C2×C22⋊D6111yescharacteristic
247C2×C4C2×C22⋊D6111yescharacteristic
248C8—22no—
249C8—1222no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—2442no—
254C22—2441no—
255C22#1451974511yescharacteristic
256C22#1451974911yescharacteristic
257C22#1451977311yescharacteristic
258C4—41no—
259C4—42no—
260C4—4881no—
261C4—2442no—
262C4—2441no—
263C4#1451974511yescharacteristic
264C4#1451974611yescharacteristic
265C4#1451974811yescharacteristic
266C4#1451974911yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—4881no—
272C2#1683967011yescharacteristic
subgroupG/H
centerC2#16839670
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#137×C61C2
socleC2×C61#392
hypercenterC2×#137D61
hypocenterC61#2009
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. #16840336C2semidirect
3. #16839778C2semidirect
4. #16839771C2semidirect
5. #16839736C2semidirect
6. #16839534C2semidirect
7. C2×#137×C61C2semidirect
138. C2×#137D61semidirect
144. C61#2009semidirect