Finite Group Databasebeta

← #11788925

Subgroups — #11788925

Order 1152.

751 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 751 conjugacy classes of subgroups — too many to draw. Only its 124 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#10596287C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic
3C2×C3×#836C212yesmaximal, complemented
4#10591078C211yesmaximal, characteristic
5#10589171C212yesmaximal, complemented
6#70124—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9#64156—21no—
10#64155—22no—
11#64153—21no—
12#64138C414yes—
13#64135C2211yescharacteristic
14C2×C3×#208C2212yes—
15C2×C3×#208C2212yes—
16#63818—22no—
17#63817—24no—
18C3×#836—24no—
19#63561—21no—
20#63559—21no—
21#5816—32no—
22#5816—61no—
23#5745—32no—
24C2×C3×#101—32no—
25C2×#836D312yescomplemented
26#5132—32no—
27#4559—32no—
28#4556—32no—
29C2×C32×Q8—21no—
30C2×C32×Q8—21no—
31C2×C32×Q8—22no—
32C2×C32×Q8—22no—
33C22×C32×C4C2×C412yes—
34C22×C32×C4C2311yescharacteristic
35C2×#638C2×C412yes—
36#3828—22no—
37#3828—22no—
38C2×C4⋊(C3⋊D3)D411yescharacteristic
39C2×C4×C3⋊D3D412yes—
40C2×#634D411yescharacteristic
41#3757C2×C412yes—
42#3752—24no—
43C4⋊(C3⋊Dic3)—21no—
44#3750—24no—
45C4×C3⋊Dic3—21no—
46C3×#208—22no—
47C3×#208—22no—
48C3×#208—22no—
49C3×#208D414yes—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52#3712—24no—
53#3710—24no—
54#1915—91noSylow
55C22×C3×Q8—21no—
56C22×C3×Q8C2×D312yes—
57C2×#235—32no—
58C2×#235—61no—
59C2×C3×M16—32no—
60C2×C3×M16—32no—
61#947—62no—
62#947—62no—
63#946—64no—
64#946—64no—
65#944—62no—
66#944—62no—
67#929—38no—
68#929—64no—
69#926—32no—
70#926—61no—
71C2×#208C2×D312yes—
72C2×#208C2×D312yes—
73#907—64no—
74D3×M16—64no—
75#901—64no—
76C3×#101—64no—
77#836—24no—
78#824—62no—
79#823—62no—
80C23×C32C22×C411yescharacteristic
81C22×C3⋊D3C22⋊C412yes—
82C32×Q8—41no—
83C32×Q8—42no—
84C32×Q8—41no—
85C2×C32×C4—22no—
86C2×C32×C4—24no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D412yes—
90C2×C32×C4#4112yes—
91#638—24no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3C22⋊C412yes—
94C4⋊(C3⋊D3)—22no—
95C4×C3⋊D3—22no—
96C4×C3⋊D3—22no—
97#634—22no—
98C3×C3⋊C8—24no—
99C3×C3⋊C8—42no—
100#568—91no—
101#536—91no—
102#413—91no—
103C2×#101—32no—
104#344—92no—
105C2×C3×Q8—22no—
106C2×C3×Q8—22no—
107C2×C3×Q8—22no—
108C2×C3×Q8—22no—
109C2×C3×Q8—22no—
110C2×C3×Q8—22no—
111C2×C3×Q8—22no—
112C2×C3×Q8—22no—
113C2×C3×Q8—42no—
114C2×C3×Q8—42no—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4C4×D314yes—
118C22×C3×C4C22×D312yes—
119C2×#67—34no—
120C2×#67—62no—
121#235—62no—
122#235—62no—
123#235—62no—
124#235—62no—
125#235—122no—
126#235—122no—
127C2×D12—32no—
128C2×D12—61no—
129C2×C4×D3—34no—
130C2×C4×D3—62no—
131C2×Dic6—32no—
132C2×Dic6—61no—
133C3×M16—34no—
134C3×M16—62no—
135C3×M16—62no—
136C3×M16—62no—
137C2×C3×C8—62no—
138C2×C3×C8—62no—
139#217—34no—
140#217—62no—
141(C2×D3)⋊C4—68no—
142(C2×D3)⋊C4—68no—
143C4⋊Dic3—62no—
144C4⋊Dic3—62no—
145Dic3⋊C4—68no—
146Dic3⋊C4—68no—
147C4×Dic3—62no—
148C4×Dic3—62no—
149#208—22no—
150#208—22no—
151#208—22no—
152#208#6714yes—
153C2×C3⋊C8—22no—
154C2×C3⋊C8—22no—
155ΓL(1,𝔽25)—68no—
156D3×C8—68no—
157C22×C32—41no—
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32C4×D412yes—
160C2×C3⋊D3—22no—
161C2×C3⋊D3—42no—
162C32×C4—42no—
163C32×C4#12011yescharacteristic
164C32×C4#12112yes—
165C32×C4#12311yescharacteristic
166C3⋊Dic3—22no—
167C3⋊Dic3—42no—
168C2×#41—91no—
169C22×Q8D3211yescharacteristic
170#131—184no—
171C2×M16—32no—
172C2×M16—32no—
173C2×M16—182no—
174C4⋊Q8—181no—
175#124—181no—
176#123—94no—
177C22⋊Q8—182no—
178#117—91no—
179#101—64no—
180#101—181no—
181#100—181no—
182C23×C3—21no—
183C23×C3C2×C4×D312yes—
184C22×D3—34no—
185C22×D3—62no—
186C3×Q8—44no—
187C3×Q8—42no—
188C3×Q8—42no—
189C3×Q8—42no—
190C3×Q8—42no—
191C3×Q8—42no—
192C3×Q8—42no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—44no—
202C2×C3×C4#23512yes—
203C2×C3×C4D3×D412yes—
204C2×C3×C4D3×D412yes—
205C2×C3×C4D3×D412yes—
206C2×C3×C4#23712yes—
207C2×C3×C4C2×#6712yes—
208#67—64no—
209#67—64no—
210#67—124no—
211C2×Dic3—34no—
212C2×Dic3—62no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215D12—62no—
216D12—62no—
217D12—122no—
218C4×D3—64no—
219C4×D3—64no—
220C4×D3—122no—
221C4×D3—122no—
222Dic6—62no—
223Dic6—62no—
224Dic6—122no—
225C3×C8—64no—
226C3×C8—122no—
227C3⋊C8—24no—
228C3⋊C8—42no—
229C2×C32—21no—
230C2×C32—22no—
231C2×C32#38611yescharacteristic
232C3⋊D3—42no—
233#41—182no—
234#41—182no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—91no—
240C2×D4—92no—
241C2×D4—91no—
242C22×C4—92no—
243C22×C4#62412yes—
244C22×C4C2×D3211yescharacteristic
245M16—34no—
246M16—62no—
247M16—62no—
248M16—62no—
249M16—184no—
250C2×C8—62no—
251C2×C8—62no—
252C2×C8—184no—
253C4⋊C4—184no—
254C4⋊C4—181no—
255C22⋊C4—92no—
256C22⋊C4—184no—
257C42—181no—
258C22×C3—22no—
259C22×C3—21no—
260C22×C3—42no—
261C22×C3—42no—
262C22×C3D3×C22⋊C412yes—
263C22×C3#67⋊C412yes—
264C22×C3C4×#6712yes—
265C2×D3—64no—
266C2×D3—122no—
267C2×D3—124no—
268C2×D3—124no—
269C3×C4—22no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—44no—
273C3×C4—44no—
274C3×C4#88312yes—
275C3×C4#88412yes—
276C3×C4#93712yes—
277C3×C4#93812yes—
278Dic3—64no—
279Dic3—122no—
280Dic3—124no—
281Dic3—124no—
282C32#191511yescharacteristic, complemented, Sylow
283C23—92no—
284C23C2×#62411yescharacteristic
285Q8—42no—
286Q8—41no—
287Q8—41no—
288Q8—182no—
289D4—184no—
290D4—182no—
291C2×C4—24no—
292C2×C4—22no—
293C2×C4—92no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4#380412yes—
298C2×C4D3×#6712yes—
299C2×C4#381111yescharacteristic
300C2×C4#381111yescharacteristic
301C8—64no—
302C8—122no—
303C2×C3—22no—
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—22no—
307C2×C3—21no—
308C2×C3—42no—
309C2×C3#495612yes—
310D3—124no—
311D3—242no—
312C22—41no—
313C22—182no—
314C22—362no—
315C22#6395212yes—
316C22#6397411yescharacteristic
317C4—42no—
318C4—182no—
319C4—362no—
320C4#6395812yes—
321C4#6397511yescharacteristic
322C4#6398311yescharacteristic
323C3—21no—
324C3#7012412yescomplemented
325C2—21no—
326C2—22no—
327C2—362no—
328C2#1059172211yescharacteristic
subgroupG/H
centerC2#10591722
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC2×C32#386
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1915
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#836C2semidirect
5. #10589171C2semidirect
25. C2×#836D3semidirect
282. C32#1915semidirect
324. C3#70124semidirect

Maximal subgroups

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

subgroupindex
#105962872
#105947802
C2×C3×#8362
#105910782
#105891712
#701243