Finite Group Databasebeta

← #11775908

Subgroups — #11775908

Order 1152.

535 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 535 conjugacy classes of subgroups — too many to draw. Only its 88 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#10596159C211yesmaximal, characteristic
2#10590322C211yesmaximal, characteristic
3#10590299C211yesmaximal, characteristic
4C3×#4543C212yesmaximal, complemented
5#10589089C212yesmaximal, complemented
6#68365—32nomaximal
7C32×#125C2211yescharacteristic
8#64105—21no—
9#64105—21no—
10#64101C411yescharacteristic
11#64101C411yescharacteristic
12#64097C411yescharacteristic
13#64097C411yescharacteristic
14#64096—21no—
15#64096—21no—
16C42×C3⋊D3C2211yescharacteristic
17#64079C2211yescharacteristic
18C2×#3710—21no—
19C3×#803C2212yes—
20C3×#803C2212yes—
21#63572—21no—
22#63557—21no—
23#63555—21no—
24#5688—32no—
25#5688—61no—
26#4705—32no—
27D3×#97—32no—
28C3×#330—32no—
29#4543D312yescomplemented
30#4465—32no—
31#4465—32no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×#634—21no—
36C2×#634—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4C2×C411yescharacteristic
40C32×C4⋊C4C2×C411yescharacteristic
41C32×C42C2311yescharacteristic
42#3752—21no—
43#3752—21no—
44C4⋊(C3⋊Dic3)C2×C411yescharacteristic
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46#3750—21no—
47#3750—21no—
48#3750—21no—
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—22no—
57#3710—24no—
58#1531—91noSylow
59C3×#125—21no—
60C3×#125C2×D312yes—
61C2×D3×C8—62no—
62#896—62no—
63#896—62no—
64#896—62no—
65#896—62no—
66#892—32no—
67#892—32no—
68#892—61no—
69#892—61no—
70#888—32no—
71#888—32no—
72#888—61no—
73#888—61no—
74#887—62no—
75#887—62no—
76#887—62no—
77#887—62no—
78C42×D3—32no—
79C42×D3—61no—
80#870—32no—
81#870—61no—
82C3×#97—32no—
83C3×#97—32no—
84(C2×D3)⋊C8—62no—
85#815—62no—
86Dic3⋊C8—62no—
87#803C2×D312yes—
88#803C2×D312yes—
89C22×C3⋊D3C22⋊C411yescharacteristic
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4C22×C411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C4×C3⋊D3—22no—
101C4×C3⋊D3—22no—
102C4×C3⋊D3—41no—
103#634—42no—
104#634—42no—
105C3×C3⋊C8—24no—
106C3×C3⋊C8—42no—
107#533—91no—
108#432—91no—
109C2×#97—91no—
110#330—32no—
111#330—92no—
112C2×C4×D3—32no—
113C2×C4×D3—32no—
114C2×C4×D3—32no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×Dic6—62no—
119C2×Dic6—62no—
120C2×Dic6—62no—
121C2×Dic6—62no—
122C2×C3×C8—62no—
123C2×C3×C8—62no—
124C3×C4⋊C4—22no—
125C3×C4⋊C4—22no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4C4×D312yes—
131C3×C4⋊C4C4×D312yes—
132C3×C42—21no—
133C3×C42C22×D312yes—
134(C2×D3)⋊C4—62no—
135(C2×D3)⋊C4—62no—
136(C2×D3)⋊C4—62no—
137(C2×D3)⋊C4—62no—
138C4⋊Dic3—32no—
139C4⋊Dic3—32no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142Dic3⋊C4—62no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150C4×Dic3—32no—
151C4×Dic3—32no—
152C4×Dic3—32no—
153C4×Dic3—61no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C4×Dic3—62no—
157C4×Dic3—62no—
158C4×Dic3—62no—
159C4×Dic3—62no—
160C2×C3⋊C8—22no—
161C2×C3⋊C8—22no—
162D3×C8—68no—
163C22×C32C2×C22⋊C411yescharacteristic
164C2×C3⋊D3—21no—
165C2×C3⋊D3—21no—
166C2×C3⋊D3#10112yes—
167C32×C4—21no—
168C32×C4—21no—
169C32×C4—21no—
170C32×C4—41no—
171C32×C4—41no—
172C3⋊Dic3—21no—
173C3⋊Dic3—21no—
174C3⋊Dic3—41no—
175C3⋊Dic3—41no—
176C3⋊Dic3#10412yes—
177C22×C8—181no—
178C4⋊Q8—91no—
179C4⋊Q8—91no—
180#125—91no—
181#125D3211yescharacteristic
182C22⋊Q8—181no—
183C22⋊Q8—181no—
184C4×Q8—181no—
185C4×Q8—181no—
186#117—91no—
187#117—91no—
188C2×C42—91no—
189C4⋊C8—181no—
190C22⋊C8—181no—
191#97—32no—
192#97—32no—
193#97—181no—
194C22×D3—32no—
195C22×D3—61no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4C2×C4×D312yes—
204C2×C3×C4D3×D412yes—
205C2×C3×C4D3×D412yes—
206C2×Dic3—32no—
207C2×Dic3—32no—
208C2×Dic3—32no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C4×D3—64no—
217C4×D3—64no—
218C4×D3—64no—
219C4×D3—122no—
220C4×D3—122no—
221C4×D3—122no—
222Dic6—124no—
223Dic6—124no—
224Dic6—124no—
225Dic6—124no—
226C3×C8—64no—
227C3×C8—122no—
228C3⋊C8—24no—
229C3⋊C8—42no—
230C2×C32C2×#10111yescharacteristic
231C2×C32C2×#10411yescharacteristic
232C2×C32#42111yescharacteristic
233C3⋊D3—22no—
234C2×Q8—181no—
235C2×Q8—181no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—91no—
239C2×C8—62no—
240C2×C8—62no—
241C2×C8—184no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—91no—
245C4⋊C4—91no—
246C4⋊C4—181no—
247C4⋊C4—181no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C4⋊C4#62411yescharacteristic
251C4⋊C4#62411yescharacteristic
252C22⋊C4—181no—
253C22⋊C4—181no—
254C42—91no—
255C42—91no—
256C42—91no—
257C42—181no—
258C42—181no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3D3×C22⋊C412yes—
262C2×D3—34no—
263C2×D3—62no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—121no—
267C2×D3—121no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—42no—
275C3×C4—42no—
276C3×C4—42no—
277C3×C4—42no—
278Dic3—34no—
279Dic3—62no—
280Dic3—62no—
281Dic3—62no—
282Dic3—62no—
283Dic3—62no—
284Dic3—122no—
285Dic3—122no—
286Dic3—122no—
287Dic3—122no—
288C32#153111yescharacteristic, complemented, Sylow
289C23—91no—
290Q8—362no—
291Q8—362no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4—181no—
300C2×C4—181no—
301C2×C4—361no—
302C2×C4C2×#62411yescharacteristic
303C2×C4#381111yescharacteristic
304C2×C4#381111yescharacteristic
305C8—64no—
306C8—122no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3D3×#10112yes—
311C2×C3D3×#10412yes—
312C2×C3#482112yes—
313D3—64no—
314D3—122no—
315C22—92no—
316C22—181no—
317C22—181no—
318C22#6397411yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—92no—
325C4—181no—
326C4—181no—
327C4—361no—
328C4—361no—
329C3—21no—
330C3#6836512yescomplemented
331C2—182no—
332C2#1059163911yescharacteristic
333C2#1059167111yescharacteristic
334C2#1059167211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenter#125D32
hypocenterC32#1531
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
4. C3×#4543C2semidirect
5. #10589089C2semidirect
29. #4543D3semidirect
288. C32#1531semidirect
330. C3#68365semidirect

Maximal subgroups

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

subgroupindex
#105961592
#105903222
#105902992
C3×#45432
#105890892
#683653