Finite Group Databasebeta

← #11785597

Subgroups — #11785597

Order 1152.

661 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 661 conjugacy classes of subgroups — too many to draw. Only its 132 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
2C2×#63578C211yesmaximal, characteristic, complemented
3C2×#63574C211yesmaximal, characteristic, complemented
4#10591106C212yesmaximal
5C3×#4554C212yesmaximal, complemented
6#69000—32nomaximal
7C2×#3828C2211yescharacteristic
8C2×C32×M16C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10#64116—22no—
11#64116C414yescomplemented
12C2×#3743—21no—
13C2×C8×C3⋊D3—21no—
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×#208C2212yes—
16#63578—22no—
17#63574—21no—
18#63574—21no—
19#63567—22no—
20#63564—22no—
21C2×#907—32no—
22C2×#907—61no—
23#5133—32no—
24C2×#822—32no—
25#4966—32no—
26C2×#808—32no—
27C3×#343—32no—
28#4554D312yescomplemented
29C22×C32×C4C2311yescharacteristic
30C2×#638—21no—
31#3828—21no—
32#3828—21no—
33#3828C2×C412yes—
34#3828Q812yes—
35C2×C4⋊(C3⋊D3)D411yescharacteristic
36C2×C4×C3⋊D3—21no—
37C2×#634D411yescharacteristic
38C22×C3×Dic3—22no—
39C32×M16—21no—
40C32×M16C2×C412yes—
41C2×C32×C8—21no—
42C2×C3⋊(C3⋊C8)C2×C412yes—
43C2×C3⋊(C3⋊C8)D411yescharacteristic
44C2×C3⋊(C3⋊C8)D411yescharacteristic
45C2×C3⋊(C3⋊C8)D412yes—
46#3743—24no—
47C8×C3⋊D3—24no—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3—22no—
50C3×#208—22no—
51C3×#208—22no—
52C2×C3×C3⋊C8—22no—
53#1815—91noSylow
54C2×#235—32no—
55C2×#235—61no—
56C2×C3×M16—21no—
57C2×C3×M16—32no—
58C2×C3×M16C2×D312yes—
59C2×C3×C4⋊C4—32no—
60C2×C4⋊Dic3C2×D312yes—
61C2×#208C2×D312yes—
62C22×C3⋊C8—32no—
63C22×C3⋊C8—61no—
64#907—38no—
65#907—64no—
66#907—64no—
67#907—64no—
68C2×ΓL(1,𝔽25)—62no—
69C2×ΓL(1,𝔽25)—62no—
70C2×D3×C8—62no—
71C2×D3×C8—62no—
72#822—64no—
73#821—62no—
74#816—62no—
75#810—62no—
76#809—62no—
77#808—62no—
78#808—62no—
79C23×C32#4111yescharacteristic
80C22×C3⋊D3—21no—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×Q811yescharacteristic
86C2×C32×C4#4111yescharacteristic
87#638—22no—
88#638—22no—
89C2×C3⋊Dic3—21no—
90C4⋊(C3⋊D3)—21no—
91C4⋊(C3⋊D3)C4⋊C412yes—
92C4×C3⋊D3—22no—
93C4×C3⋊D3—22no—
94#634—21no—
95#634C4⋊C412yes—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—82no—
98C32×C8—22no—
99C3⋊(C3⋊C8)C22⋊C412yes—
100C3⋊(C3⋊C8)C22⋊C412yes—
101C3×C3⋊C8—42no—
102C2×#131—91no—
103C2×#108—91no—
104C2×#106—91no—
105#417—92no—
106#343—32no—
107C22×C3×C4—21no—
108C22×C3×C4—62no—
109C22×C3×C4C22×D312yes—
110C2×#67—62no—
111C2×#67—62no—
112C22×Dic3—22no—
113#235—34no—
114#235—34no—
115#235—62no—
116#235—62no—
117#235—62no—
118#235—62no—
119#235—62no—
120#235—62no—
121C2×D12—32no—
122C2×D12—61no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×Dic6—32no—
126C2×Dic6—61no—
127C3×M16—22no—
128C3×M16—22no—
129C3×M16—22no—
130C3×M16—62no—
131C3×M16—62no—
132C3×M16C4×D314yes—
133C2×C3×C8—22no—
134C2×C3×C8—22no—
135C2×C3×C8—62no—
136C3×C4⋊C4—62no—
137C3×C4⋊C4—62no—
138C4⋊Dic3—22no—
139C4⋊Dic3—22no—
140#208—22no—
141#208—22no—
142C2×C3⋊C8—22no—
143C2×C3⋊C8—34no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—32no—
146C2×C3⋊C8—34no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8—62no—
151ΓL(1,𝔽25)—68no—
152ΓL(1,𝔽25)—68no—
153D3×C8—68no—
154D3×C8—68no—
155C22×C32—22no—
156C22×C32#11711yescharacteristic
157C22×C32#12111yescharacteristic
158C22×C32C22⋊Q811yescharacteristic
159C2×C3⋊D3—22no—
160C2×C3⋊D3—42no—
161C32×C4C2×C22⋊C411yescharacteristic
162C32×C4C2×C4⋊C411yescharacteristic
163C32×C4#12111yescharacteristic
164C32×C4C22⋊Q811yescharacteristic
165C3⋊Dic3—22no—
166C3×Dic3—82no—
167C2×#41—91no—
168#131—94no—
169#131—182no—
170C2×M16—32no—
171C2×M16—181no—
172C2×M16D3211yescharacteristic
173C22×C8—91no—
174C22×C8—181no—
175C2×C4⋊C4—32no—
176#108—182no—
177#106—181no—
178#106—181no—
179#103—182no—
180#102—182no—
181C23×C3—21no—
182C23×C3#23512yes—
183C22×D3—62no—
184C22×D3—62no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—122no—
192C2×C3×C4—242no—
193C2×C3×C4C2×C4×D312yes—
194C2×C3×C4#23512yes—
195C2×C3×C4D3×D412yes—
196C2×C3×C4D3×D412yes—
197C2×C3×C4D3×D412yes—
198C2×C3×C4D3×Q812yes—
199#67—64no—
200#67—64no—
201#67—64no—
202#67—64no—
203C2×Dic3—42no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—82no—
207D12—34no—
208D12—62no—
209D12—62no—
210D12—62no—
211C4×D3—64no—
212C4×D3—64no—
213C4×D3—64no—
214C4×D3—64no—
215Dic6—34no—
216Dic6—62no—
217Dic6—62no—
218Dic6—62no—
219C3×C8—24no—
220C3×C8—24no—
221C3×C8—122no—
222C3⋊C8—34no—
223C3⋊C8—34no—
224C3⋊C8—42no—
225C3⋊C8—62no—
226C3⋊C8—62no—
227C2×C32—21no—
228C2×C32—21no—
229C2×C32#38011yescharacteristic
230C2×C32#47112yes—
231C3⋊D3—42no—
232#41—92no—
233#41—92no—
234#41—181no—
235#41—181no—
236C2×Q8—91no—
237C2×D4—91no—
238C2×D4—181no—
239C22×C4—62no—
240C22×C4—181no—
241C22×C4C2×D3211yescharacteristic
242M16—21no—
243M16—62no—
244M16—62no—
245M16—184no—
246M16#62412yes—
247C2×C8—21no—
248C2×C8—62no—
249C2×C8—92no—
250C2×C8—91no—
251C2×C8—91no—
252C2×C8—92no—
253C2×C8—184no—
254C4⋊C4—62no—
255C4⋊C4—62no—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—42no—
262C22×C3#87212yes—
263C22×C3#88412yes—
264C22×C3#89612yes—
265C2×D3—64no—
266C2×D3—64no—
267C2×D3—124no—
268C2×D3—122no—
269C2×D3—122no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—242no—
275C3×C4D3×C22⋊C412yes—
276C3×C4#88412yes—
277C3×C4D3×C4⋊C412yes—
278C3×C4#89612yes—
279Dic3—64no—
280Dic3—64no—
281Dic3—82no—
282C32#181511yescharacteristic, complemented, Sylow
283C23—181no—
284C23#379811yescharacteristic
285Q8—92no—
286Q8—181no—
287D4—92no—
288D4—182no—
289D4—182no—
290D4—181no—
291C2×C4—122no—
292C2×C4—181no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—242no—
296C2×C4#379711yescharacteristic
297C2×C4#379811yescharacteristic
298C2×C4#380211yescharacteristic
299C2×C4C2×#62411yescharacteristic
300C2×C4#381111yescharacteristic
301C2×C4#381111yescharacteristic
302C8—22no—
303C8—92no—
304C8—92no—
305C8—122no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—21no—
310C2×C3—41no—
311C2×C3—41no—
312C2×C3#466712yes—
313C2×C3#474812yes—
314C2×C3#475412yes—
315D3—124no—
316D3—124no—
317C22—22no—
318C22—182no—
319C22—362no—
320C22#6386511yescharacteristic
321C22#6387411yescharacteristic
322C22#6391211yescharacteristic
323C4—182no—
324C4—242no—
325C4#6386511yescharacteristic
326C4#6390011yescharacteristic
327C4#6391211yescharacteristic
328C4#6397411yescharacteristic
329C3—21no—
330C3#6900012yescomplemented
331C2—21no—
332C2—21no—
333C2—362no—
334C2#1059099112yes—
335C2#1059135511yescharacteristic
subgroupG/H
centerC22#63912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1815
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63578C2semidirect
3. C2×#63574C2semidirect
5. C3×#4554C2semidirect
11. #64116C4semidirect
28. #4554D3semidirect
282. C32#1815semidirect
330. C3#69000semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×#635782
C2×#635742
#105911062
C3×#45542
#690003