Finite Group Databasebeta

← #11783842

Subgroups — #11783842

Order 1152.

701 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 701 conjugacy classes of subgroups — too many to draw. Only its 148 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×#64116C211yesmaximal, characteristic
2#10591232C211yesmaximal, characteristic
3#10591078C211yesmaximal, characteristic
4#10591057C212yesmaximal, complemented
5C3×#4556C212yesmaximal, complemented
6#69014—32nomaximal
7C2×#3828C2211yescharacteristic
8C2×C32×M16C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10#64116—22no—
11#64116—22no—
12C2×#3743C412yescomplemented
13C2×C8×C3⋊D3C412yescomplemented
14C3×#926C2212yes—
15C2×C3×#208C2212yes—
16#63581C414yes—
17#63561C412yescomplemented
18#63559C412yescomplemented
19#63554—22no—
20Dic3×C3⋊C8—22no—
21C2×#907—32no—
22C2×#907—61no—
23#5132—32no—
24#5122—32no—
25#5006—32no—
26#4997—32no—
27C3×#344—32no—
28#4556D312yescomplemented
29C22×C32×C4C2311yescharacteristic
30C2×#638C2×C412yes—
31#3828—22no—
32#3828—22no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3C2×C412yes—
35C2×#634C2×C411yescharacteristic
36C32×M16—22no—
37C2×C32×C8C2×C412yes—
38C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
39C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
40C2×C3⋊(C3⋊C8)D412yes—
41C2×C3⋊(C3⋊C8)D412yes—
42#3743—24no—
43C8×C3⋊D3—22no—
44C8×C3⋊D3—22no—
45C3×#217C2×C414yes—
46C3×C4⋊Dic3—22no—
47C3×C4×Dic3—22no—
48C3×#208—22no—
49C3×#208C2×C414yes—
50C2×C3×C3⋊C8—22no—
51#1757—91noSylow
52C2×#235—32no—
53C2×#235—61no—
54C2×C3×M16—21no—
55C2×C3×M16—32no—
56C2×C3×M16C2×D312yes—
57C3×#117—32no—
58#926C2×D312yes—
59C2×#208C2×D312yes—
60C22×C3⋊C8—32no—
61C22×C3⋊C8—61no—
62#907—62no—
63#907—62no—
64#907—62no—
65#907—62no—
66#907—64no—
67#907—64no—
68C2×ΓL(1,𝔽25)—34no—
69C2×ΓL(1,𝔽25)—62no—
70C2×D3×C8—34no—
71C2×D3×C8—62no—
72#824—34no—
73#823—34no—
74#815—62no—
75C8×Dic3—62no—
76#806—38no—
77#803—62no—
78C4×C3⋊C8—62no—
79C23×C32C22×C411yescharacteristic
80C22×C3⋊D3C4212yes—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D412yes—
84C2×C32×C4#4112yes—
85#638—24no—
86C2×C3⋊Dic3C4212yes—
87C4⋊(C3⋊D3)—22no—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90#634—22no—
91C2×C3×Dic3—24no—
92C32×C8—22no—
93C3⋊(C3⋊C8)C22⋊C411yescharacteristic
94C3⋊(C3⋊C8)C22⋊C411yescharacteristic
95C3⋊(C3⋊C8)C22⋊C412yes—
96C3×C3⋊C8—24no—
97C2×#131—91no—
98#413—91no—
99#410—91no—
100#405—92no—
101#344—32no—
102C22×C3×C4—21no—
103C22×C3×C4C22×D312yes—
104C2×#67—34no—
105C2×#67—62no—
106#235—64no—
107#235—64no—
108#235—62no—
109#235—62no—
110#235—62no—
111#235—62no—
112C2×D12—32no—
113C2×D12—61no—
114C2×C4×D3—34no—
115C2×C4×D3—62no—
116C2×Dic6—32no—
117C2×Dic6—61no—
118C3×M16—24no—
119C3×M16—22no—
120C3×M16—22no—
121C3×M16—34no—
122C3×M16—62no—
123C2×C3×C8—22no—
124C2×C3×C8—62no—
125C2×C3×C8C4×D314yes—
126C3×C4⋊C4—62no—
127C3×C22⋊C4—34no—
128C3×C42—62no—
129#217C4×D314yes—
130C4⋊Dic3—22no—
131C4×Dic3—22no—
132#208—22no—
133#208C4×D314yes—
134C2×C3⋊C8—22no—
135C2×C3⋊C8—32no—
136C2×C3⋊C8—32no—
137C2×C3⋊C8—32no—
138C2×C3⋊C8—32no—
139C2×C3⋊C8—32no—
140C2×C3⋊C8—32no—
141C2×C3⋊C8—61no—
142C2×C3⋊C8—61no—
143C2×C3⋊C8—62no—
144C2×C3⋊C8—62no—
145ΓL(1,𝔽25)—64no—
146ΓL(1,𝔽25)—64no—
147ΓL(1,𝔽25)—68no—
148D3×C8—64no—
149D3×C8—64no—
150D3×C8—64no—
151D3×C8—64no—
152C22×C32—41no—
153C22×C32C2×C4211yescharacteristic
154C22×C32C4×D412yes—
155C2×C3⋊D3—22no—
156C2×C3⋊D3—42no—
157C32×C4C2×C22⋊C411yescharacteristic
158C32×C4#11711yescharacteristic
159C32×C4C4×D412yes—
160C3⋊Dic3—22no—
161C3×Dic3—44no—
162C2×#41—91no—
163#131—182no—
164#131—182no—
165C2×M16—32no—
166C2×M16—92no—
167C2×M16D3211yescharacteristic
168C22×C8—91no—
169C22×C8—92no—
170#117—32no—
171#101—92no—
172#100—92no—
173#99—94no—
174#97—182no—
175C4×C8—182no—
176C23×C3—21no—
177C23×C3C2×C4×D312yes—
178C22×D3—34no—
179C22×D3—62no—
180C2×C3×C4—22no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—22no—
184C2×C3×C4—64no—
185C2×C3×C4C2×C4×D312yes—
186C2×C3×C4C2×C4×D312yes—
187C2×C3×C4D3×D412yes—
188C2×C3×C4D3×D412yes—
189C2×C3×C4#23712yes—
190C2×C3×C4#23912yes—
191#67—68no—
192#67—64no—
193#67—64no—
194C2×Dic3—24no—
195C2×Dic3—34no—
196C2×Dic3—62no—
197D12—64no—
198D12—62no—
199D12—62no—
200C4×D3—64no—
201C4×D3—64no—
202C4×D3—64no—
203C4×D3—64no—
204Dic6—64no—
205Dic6—62no—
206Dic6—62no—
207C3×C8—24no—
208C3×C8—24no—
209C3×C8—64no—
210C3⋊C8—24no—
211C3⋊C8—32no—
212C3⋊C8—32no—
213C3⋊C8—32no—
214C3⋊C8—32no—
215C3⋊C8—61no—
216C3⋊C8—61no—
217C3⋊C8—62no—
218C2×C32—21no—
219C2×C32—22no—
220C2×C32C4×C22⋊C411yescharacteristic
221C3⋊D3—42no—
222#41—182no—
223#41—182no—
224C2×Q8—91no—
225C2×D4—92no—
226C2×D4—91no—
227C22×C4—92no—
228C22×C4C2×D3211yescharacteristic
229M16—22no—
230M16—34no—
231M16—62no—
232M16—184no—
233C2×C8—62no—
234C2×C8—91no—
235C2×C8—91no—
236C2×C8—92no—
237C2×C8—92no—
238C2×C8—182no—
239C2×C8—182no—
240C2×C8#62412yes—
241C4⋊C4—62no—
242C22⋊C4—34no—
243C42—62no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—42no—
247C22×C3—42no—
248C22×C3C42×D312yes—
249C22×C3#67⋊C412yes—
250C22×C3#89312yes—
251C2×D3—64no—
252C2×D3—64no—
253C2×D3—124no—
254C2×D3—124no—
255C3×C4—21no—
256C3×C4—22no—
257C3×C4—21no—
258C3×C4—124no—
259C3×C4D3×C22⋊C412yes—
260C3×C4#67⋊C412yes—
261C3×C4#89212yes—
262C3×C4#89312yes—
263Dic3—44no—
264Dic3—64no—
265Dic3—64no—
266C32#175711yescharacteristic, complemented, Sylow
267C23—92no—
268C23C4×D3211yescharacteristic
269Q8—182no—
270D4—184no—
271D4—182no—
272C2×C4—64no—
273C2×C4—92no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4#379612yes—
277C2×C4C4×D3211yescharacteristic
278C2×C4C2×#62411yescharacteristic
279C2×C4#381112yes—
280C8—22no—
281C8—64no—
282C8—91no—
283C8—91no—
284C8—92no—
285C2×C3—22no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—21no—
290C2×C3—42no—
291C2×C3#466612yes—
292D3—124no—
293D3—124no—
294C22—41no—
295C22—182no—
296C22—362no—
297C22#6388112yes—
298C22C4×#62411yescharacteristic
299C4—124no—
300C4—182no—
301C4#6384911yescharacteristic
302C4#6388112yes—
303C4#6397411yescharacteristic
304C3—21no—
305C3#6901412yescomplemented
306C2—22no—
307C2—21no—
308C2—362no—
309C2#1059126011yescharacteristic
subgroupG/H
centerC4#63974
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32C4×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10591057C2semidirect
5. C3×#4556C2semidirect
12. C2×#3743C4semidirect
13. C2×C8×C3⋊D3C4semidirect
17. #63561C4semidirect
18. #63559C4semidirect
28. #4556D3semidirect
266. C32#1757semidirect
305. C3#69014semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
#105912322
#105910782
#105910572
C3×#45562
#690143