Finite Group Databasebeta

← #21446716

Subgroups — #21446716

Order 7808.

284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#14519797C211yesmaximal, characteristic
2#16839798C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4#16839736C211yesmaximal, characteristic, complemented
5#16839735C211yesmaximal, characteristic, complemented
6#16839720C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519797—21no—
10#14519797—21no—
11#14519797—21no—
12#14519797—21no—
13C2×#11758202C411yescharacteristic, complemented
14C2×#11758200C411yescharacteristic, complemented
15C2×#11758201C411yescharacteristic, complemented
16C2×#11758199C411yescharacteristic, complemented
17C22×#92418C2211yescharacteristic
18#14519736C2211yescharacteristic
19#14519736C2211yescharacteristic
20#14519710—21no—
21#14519708—21no—
22#14519703—22no—
23#14519692—22no—
24#14519691—22no—
25#14519687—21no—
26C8×Dic61—21no—
27C2×#41×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#104×C61—22no—
31#41×C61—21no—
32#41×C61—21no—
33#41×C61—21no—
34#41×C61—21no—
35C2×Q8×C61C2×C411yescharacteristic
36C2×D4×C61—21no—
37C2×D4×C61C2×C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—21no—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44#11758222—21no—
45C2×D244C2×C411yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122C2×C411yescharacteristic
48M16×C61—21no—
49M16×C61D412yes—
50C2×C8×C61—21no—
51C4⋊C4×C61—21no—
52C22⋊C4×C61—21no—
53C42×C61—21no—
54C22⋊Dic61—21no—
55C22⋊Dic61D412yes—
56#11758202—21no—
57#11758202—21no—
58#11758201—21no—
59#11758201—21no—
60#11758200—21no—
61#11758200—21no—
62#11758199—21no—
63#11758199—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—21no—
66C4×Dic61—21no—
67C4×Dic61—21no—
68C2×#92418C2×C411yescharacteristic
69C2×#92418C2×C411yescharacteristic
70C2×#92418D411yescharacteristic
71C2×#92418D411yescharacteristic
72C2×#92418D411yescharacteristic
73C2×#92418D411yescharacteristic
74C23×C61—21no—
75C23×C61C2×D411yescharacteristic
76C22×D61—21no—
77Q8×C61—21no—
78Q8×C61—21no—
79D4×C61—21no—
80D4×C61—21no—
81D4×C61—41no—
82D4×C61—41no—
83C2×C4×C61—21no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61C22×C411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61#4111yescharacteristic
92C2×C4×C61#4111yescharacteristic
93C22⋊D61—41no—
94C22⋊D61—41no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—41no—
98D244—21no—
99D244—21no—
100C4×D61—41no—
101C4×D61—41no—
102Dic122—21no—
103Dic122—21no—
104C8×C61—22no—
105#92418C22⋊C411yescharacteristic
106#92418C22⋊C411yescharacteristic
107#92418C22⋊C411yescharacteristic
108#92418C22⋊C411yescharacteristic
109C22×C61—41no—
110C22×C61—41no—
111C22×C61—81no—
112C22×C61C4×D411yescharacteristic
113C22×C61#12111yescharacteristic
114C22×C61#12711yescharacteristic
115C2×D61—41no—
116C2×D61—81no—
117C4×C61—41no—
118C4×C61—81no—
119C4×C61C2×C22⋊C411yescharacteristic
120C4×C61C4×D411yescharacteristic
121C4×C61#12111yescharacteristic
122C4×C61#12411yescharacteristic
123Dic61—42no—
124Dic61—41no—
125Dic61—81no—
126#1976—611nomaximal, Sylow
127C2×C61—21no—
128C2×C61—21no—
129C2×C61—21no—
130C2×C61—81no—
131C2×C61#39011yescharacteristic
132D61—81no—
133C2×#135—611no—
134#427—611no—
135#421—611no—
136#421D6111yescharacteristic, complemented
137#410—611no—
138#410—611no—
139#405—611no—
140C61#197611yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C2×#41C2×D6111yescharacteristic
143#135—1221no—
144#135—1221no—
145#135—1221no—
146#135—1221no—
147C2×Q16—611no—
148C2×SD16—611no—
149C2×SD16—611no—
150C2×D8—611no—
151C2×M16C2×D6111yescharacteristic
152C22×C8—611no—
153#117—611no—
154#117—611no—
155#117C2×D6111yescharacteristic
156#107—1221no—
157#106—1221no—
158#104—22no—
159#104—1222no—
160#99—1222no—
161#99—1222no—
162#97—1221no—
163C4×C8—1221no—
164#41—21no—
165#41—21no—
166#41—21no—
167#41—21no—
168#41—1221no—
169#41—1221no—
170#41—1221no—
171#41—1221no—
172C2×Q8—611no—
173C2×Q8C4×D6111yescharacteristic
174C2×D4—21no—
175C2×D4—611no—
176C2×D4—1221no—
177C2×D4C4×D6111yescharacteristic
178C22×C4—21no—
179C22×C4—1221no—
180C22×C4C22×D6111yescharacteristic
181Q16—1221no—
182Q16—1221no—
183SD16—1221no—
184SD16—1221no—
185SD16—1221no—
186SD16—1221no—
187D8—1221no—
188D8—1221no—
189M16—21no—
190M16C22⋊D6112yes—
191C2×C8—21no—
192C2×C8—611no—
193C2×C8—611no—
194C2×C8—611no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—611no—
198C4⋊C4—21no—
199C4⋊C4—1221no—
200C4⋊C4—1221no—
201C22⋊C4—21no—
202C22⋊C4—612no—
203C22⋊C4—1221no—
204C42—21no—
205C42—1221no—
206C42—1221no—
207C23—21no—
208C23—1221no—
209C23D4×D6111yescharacteristic
210Q8—21no—
211Q8—21no—
212Q8—1221no—
213Q8—1221no—
214D4—21no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—1221no—
219D4—1221no—
220D4—2441no—
221D4—2441no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—1221no—
227C2×C4—1222no—
228C2×C4—2441no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4C2×C4×D6111yescharacteristic
232C2×C4#1175822211yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4D4×D6111yescharacteristic
235C2×C4#1175822411yescharacteristic
236C2×C4C2×C22⋊D6111yescharacteristic
237C8—22no—
238C8—611no—
239C8—611no—
240C8—611no—
241C8—611no—
242C22—41no—
243C22—41no—
244C22—81no—
245C22—4881no—
246C22—2441no—
247C22#1451973711yescharacteristic
248C22#1451975011yescharacteristic
249C22#1451977311yescharacteristic
250C4—41no—
251C4—81no—
252C4—4881no—
253C4—2442no—
254C4—2441no—
255C4C22⋊C4×D6111yescharacteristic
256C4C4×C22⋊D6111yescharacteristic
257C4#1451974911yescharacteristic
258C4#1451976311yescharacteristic
259C2—21no—
260C2—21no—
261C2—21no—
262C2—81no—
263C2—4881no—
264C2#1683966211yescharacteristic
subgroupG/H
centerC4#14519749
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#390
hypercenter#421D61
hypocenterC61#1976
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #16839798C2semidirect
3. #16839778C2semidirect
4. #16839736C2semidirect
5. #16839735C2semidirect
6. #16839720C2semidirect
7. C61×#421C2semidirect
13. C2×#11758202C4semidirect
14. C2×#11758200C4semidirect
15. C2×#11758201C4semidirect
16. C2×#11758199C4semidirect
136. #421D61semidirect
140. C61#1976semidirect