Finite Group Databasebeta

← #46811267

Subgroups — #46811267

Order 34432.

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

normal subgroups only

This group has 332 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
1#31771371C211yesmaximal, characteristic, complemented
2#31771155C211yesmaximal, characteristic
3#31770623C211yesmaximal, characteristic, complemented
4#31770621C211yesmaximal, characteristic, complemented
5#31770578C211yesmaximal, characteristic, complemented
6#31770365C211yesmaximal, characteristic, complemented
7#339×C269C211yesmaximal, characteristic, complemented
8C2×#16864402C2211yescharacteristic
9C2×#16864402C2211yescharacteristic
10#22575461—22no—
11#22575459—22no—
12C2×#16864386C2211yescharacteristic
13M16×D269—22no—
14#22575453C411yescharacteristic, complemented
15#22575450C411yescharacteristic, complemented
16#22575441C411yescharacteristic, complemented
17#22575441C411yescharacteristic, complemented
18#22575427—22no—
19C4×D1076—22no—
20#22575412C2211yescharacteristic
21#22575381—22no—
22#22575379—22no—
23#22575367—22no—
24C2×M16×C269C2211yescharacteristic
25#117×C269C2211yescharacteristic
26C2×C42×C269C2211yescharacteristic
27#16864402—21no—
28#16864402—21no—
29#16864402—21no—
30#16864402—21no—
31#16864402—21no—
32#16864402—21no—
33#16864402—21no—
34#16864402—21no—
35C2×Dic538C2×C411yescharacteristic
36C2×Dic538C2×C411yescharacteristic
37C2×D1076—22no—
38C2×D1076C2×C411yescharacteristic
39C2×D1076C2×C411yescharacteristic
40C2×C22⋊D269—21no—
41C2×C22⋊D269D412yes—
42C2×C4×D269—21no—
43C2×C4×D269D412yes—
44#16864386—21no—
45#16864386D412yescomplemented
46#16864385—24no—
47C2×#14524130—21no—
48C8×D269—24no—
49C4⋊Dic269—22no—
50C4⋊Dic269—21no—
51C22⋊Dic269—21no—
52#16864379—22no—
53#16864379—22no—
54C4×Dic269—21no—
55C22×C4×C269—21no—
56C22×C4×C269C2311yescharacteristic
57M16×C269—21no—
58M16×C269D412yescomplemented
59C2×C8×C269—21no—
60C4⋊C4×C269—21no—
61C22⋊C4×C269—21no—
62C42×C269—21no—
63C42×C269—21no—
64C42×C269C2×C411yescharacteristic
65C42×C269C2×C411yescharacteristic
66C22×D269—21no—
67C22×D269C22⋊C412yes—
68Dic538—21no—
69Dic538—21no—
70Dic538—21no—
71Dic538—21no—
72D1076—21no—
73D1076—21no—
74D1076—21no—
75D1076—21no—
76D1076—44no—
77C22⋊D269—22no—
78C22⋊D269—22no—
79C22⋊D269—41no—
80C22⋊D269—41no—
81C2×Dic269—21no—
82C2×Dic269—41no—
83C2×Dic269C22⋊C412yes—
84C4×D269—22no—
85C4×D269—22no—
86C4×D269—41no—
87C4×D269—41no—
88#14524130—22no—
89C23×C269C2×D411yescharacteristic
90C2×C4×C269—21no—
91C2×C4×C269—21no—
92C2×C4×C269—42no—
93C2×C4×C269—41no—
94C2×C4×C269C22×C411yescharacteristic
95C2×C4×C269C2×D411yescharacteristic
96C2×C4×C269C2×D411yescharacteristic
97C2×C4×C269C2×D411yescharacteristic
98C2×C4×C269#4111yescharacteristic
99C2×C4×C269#4111yescharacteristic
100C8×C269—22no—
101C22×C269—41no—
102C22×C269C2×C22⋊C411yescharacteristic
103C22×C269#12111yescharacteristic
104C22×C269#12111yescharacteristic
105C2×D269—22no—
106C2×D269—42no—
107C2×D269—42no—
108C2×D269—41no—
109C4×C269—22no—
110C4×C269—41no—
111C4×C269—81no—
112C4×C269C4×D411yescharacteristic
113C4×C269C4×D411yescharacteristic
114C4×C269#12011yescharacteristic
115C4×C269#12311yescharacteristic
116Dic269—22no—
117Dic269—41no—
118Dic269—81no—
119C2×C269—21no—
120C2×C269—21no—
121C2×C269—21no—
122C2×C269#38611yescharacteristic
123D269—42no—
124D269—81no—
125C269#188411yescharacteristic, complemented, Sylow
126#1884—2691nomaximal, Sylow
127#568—2691no—
128#532—2691no—
129#421—2691no—
130#421—2691no—
131#410—2691no—
132#339—2691no—
133#339D26911yescharacteristic, complemented
134C2×#41—2691no—
135C2×#41—2691no—
136#131—5382no—
137#131—5382no—
138C2×M16—2691no—
139C2×M16—5382no—
140C2×M16C2×D26911yescharacteristic
141C4⋊Q8—2691no—
142#127—2691no—
143#124—2691no—
144#124—2691no—
145#121—5382no—
146C4×D4—5382no—
147#117—2691no—
148#117C2×D26911yescharacteristic
149C2×C42C2×D26911yescharacteristic
150#104—5382no—
151#104—5382no—
152#99—5382no—
153#41—5381no—
154#41—5381no—
155#41—5381no—
156#41—5381no—
157#41—5381no—
158#41—5381no—
159#41—5381no—
160#41—5381no—
161C2×Q8—2691no—
162C2×Q8—2691no—
163C2×D4—2692no—
164C2×D4—2691no—
165C2×D4—2691no—
166C2×D4—5382no—
167C2×D4—5381no—
168C22×C4—21no—
169C22×C4—2692no—
170C22×C4—5381no—
171C22×C4C22×D26911yescharacteristic
172M16—21no—
173M16—2692no—
174M16—5384no—
175M16—5381no—
176M16D107612yescomplemented
177C2×C8—21no—
178C2×C8—5384no—
179C2×C8—5381no—
180C4⋊C4—21no—
181C4⋊C4—5382no—
182C4⋊C4—5381no—
183C22⋊C4—21no—
184C22⋊C4—5382no—
185C22⋊C4—5382no—
186C22⋊C4—5381no—
187C42—21no—
188C42—21no—
189C42—5381no—
190C42C4×D26911yescharacteristic
191C42C4×D26911yescharacteristic
192C23—2692no—
193C23—5381no—
194C23D4×D26911yescharacteristic
195Q8—5381no—
196Q8—5381no—
197Q8—5381no—
198Q8—5381no—
199D4—5382no—
200D4—5382no—
201D4—5381no—
202D4—5381no—
203D4—5381no—
204D4—5381no—
205D4—10764no—
206D4—10761no—
207D4—10761no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—2692no—
213C2×C4—5382no—
214C2×C4—5382no—
215C2×C4—5381no—
216C2×C4—10761no—
217C2×C4—10761no—
218C2×C4—10761no—
219C2×C4C2×C4×D26911yescharacteristic
220C2×C4D4×D26911yescharacteristic
221C2×C4D4×D26911yescharacteristic
222C2×C4C2×D107611yescharacteristic
223C2×C4#1686440211yescharacteristic
224C2×C4#1686440311yescharacteristic
225C8—22no—
226C8—5382no—
227C22—41no—
228C22—5382no—
229C22—10762no—
230C22—10762no—
231C22—10761no—
232C22C22⋊C4×D26911yescharacteristic
233C22#2257542611yescharacteristic
234C22#2257542811yescharacteristic
235C4—22no—
236C4—41no—
237C4—81no—
238C4—5382no—
239C4—10761no—
240C4—21521no—
241C4#2257541511yescharacteristic
242C4C4×D107611yescharacteristic
243C4#2257542311yescharacteristic
244C4#2257543811yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—10762no—
249C2—21521no—
250C2#3177048311yescharacteristic
subgroupG/H
centerC4#22575423
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#339×C269C2
socleC2×C269#386
prime radical#31771155C2
cosocleC22×C4×C269C23
hypercenter#339D269
hypocenterC269#1884
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #31771371C2semidirect
3. #31770623C2semidirect
4. #31770621C2semidirect
5. #31770578C2semidirect
6. #31770365C2semidirect
7. #339×C269C2semidirect
14. #22575453C4semidirect
15. #22575450C4semidirect
16. #22575441C4semidirect
17. #22575441C4semidirect
45. #16864386D4semidirect
58. M16×C269D4semidirect
125. C269#1884semidirect
133. #339D269semidirect
176. M16D1076semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#317713712
#317711552
#317706232
#317706212
#317705782
#317703652
#339×C2692
#1884269