Finite Group Databasebeta

← #11775617

Subgroups — #11775617

Order 1152.

550 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 65 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×#63865C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3#10591152C211yesmaximal, characteristic
4#10590034C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#627C411yescharacteristic, complemented
7C2×C22⋊#157—21no—
8C2×C4⋊#157—21no—
9C2×C3×Dic3⋊C4—21no—
10C2×#3724C411yescharacteristic, complemented
11C2×#3722—21no—
12#63865—21no—
13#63865—21no—
14#63865C412yescomplemented
15#63865C2212yes—
16C2×#3710—21no—
17#63781C2212yes—
18C3×#830—21no—
19#63557C2212yes—
20C2×#896—61no—
21D3×C22⋊C8—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×#157—22no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C2×C4×C3⋊D3—42no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C22×C3×Dic3—21no—
32C22×C3×Dic3—21no—
33C2×#627—21no—
34C2×#627—42no—
35C2×#627C2×C412yes—
36C22⋊#157—42no—
37C4⋊#157—42no—
38C3×Dic3⋊C4—22no—
39C3×Dic3⋊C4—22no—
40C2×C3×C3⋊C8—22no—
41#3724—21no—
42#3724C2×C412yes—
43#3722—22no—
44#3722—22no—
45#3710—42no—
46#1520—91nomaximal, Sylow
47C22×C4×D3—61no—
48C22×C4×D3—61no—
49C22×Dic6—61no—
50C2×C3×C4⋊C4—61no—
51C2×(C2×D3)⋊C4—61no—
52C2×(C2×D3)⋊C4—61no—
53C2×Dic3⋊C4—21no—
54C2×Dic3⋊C4—61no—
55C2×D3×C8—62no—
56#896—62no—
57#896—62no—
58#896—62no—
59#896—62no—
60C3×C22⋊C8—61no—
61#830—21no—
62(C2×D3)⋊C8—62no—
63C23×C32C22⋊C411yescharacteristic
64C22×C3⋊D3—41no—
65C22×C3⋊D3—41no—
66C22×C3⋊D3C22⋊C411yescharacteristic
67C22×C3⋊D3SD1612yes—
68C22×C3⋊D3Q1612yes—
69C22×C3⋊D3C2×D411yescharacteristic
70C2×#157—42no—
71C2×#157—42no—
72C2×#157—42no—
73C2×C32×C4—41no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22×C411yescharacteristic
79C4×C3⋊D3—22no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3—41no—
83C2×C3×Dic3—22no—
84C2×C3×Dic3—22no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—42no—
87#627—42no—
88#627—42no—
89C3×C3⋊C8—42no—
90C2×C22⋊Q8—91no—
91C2×C22⋊C8—91no—
92#380—91no—
93#328—94no—
94C23×D3—61no—
95C23×D3—61no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—61no—
99C22×C3×C4—61no—
100C22×Dic3—21no—
101C22×Dic3—21no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—124no—
113C2×C4×D3—124no—
114C2×Dic6—62no—
115C2×Dic6—62no—
116C2×Dic6—124no—
117C2×C3×C8—62no—
118C3×C4⋊C4—62no—
119C3×C4⋊C4—62no—
120(C2×D3)⋊C4—62no—
121(C2×D3)⋊C4—62no—
122(C2×D3)⋊C4—62no—
123(C2×D3)⋊C4—62no—
124Dic3⋊C4—22no—
125Dic3⋊C4—22no—
126Dic3⋊C4—62no—
127Dic3⋊C4—62no—
128C2×C3⋊C8—22no—
129D3×C8—124no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32#10312yes—
133C22×C32C2×C22⋊C411yescharacteristic
134C2×C3⋊D3—21no—
135C2×C3⋊D3—21no—
136C2×C3⋊D3—21no—
137C2×C3⋊D3—21no—
138C2×C3⋊D3—42no—
139C2×C3⋊D3—42no—
140C2×C3⋊D3#10312yes—
141C2×C3⋊D3C2×SD1611yescharacteristic
142C2×C3⋊D3C2×Q1611yescharacteristic
143#157—82no—
144C32×C4—21no—
145C32×C4—21no—
146C3⋊Dic3—21no—
147C3⋊Dic3#9912yes—
148C3×Dic3—42no—
149C3×Dic3—42no—
150C22×Q8—91no—
151C23×C4—91no—
152C22×C8—181no—
153C22⋊Q8—92no—
154C22⋊Q8—92no—
155C22⋊Q8—181no—
156C22⋊Q8—181no—
157C2×C4⋊C4—61no—
158C2×C4⋊C4—91no—
159C2×C4⋊C4—181no—
160C2×C22⋊C4—181no—
161C2×C22⋊C4—181no—
162C22⋊C8—61no—
163C22⋊C8—92no—
164#95—92no—
165C23×C3—21no—
166C23×C3—21no—
167C22×D3—61no—
168C22×D3—61no—
169C22×D3—62no—
170C22×D3—62no—
171C22×D3—62no—
172C22×D3—62no—
173C22×D3—61no—
174C22×D3—61no—
175C22×D3—122no—
176C22×D3—122no—
177C22×D3—122no—
178C22×D3—122no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—62no—
186C2×C3×C4—62no—
187C2×C3×C4—122no—
188C2×C3×C4—122no—
189C2×Dic3—22no—
190C2×Dic3—22no—
191C2×Dic3—42no—
192C2×Dic3—42no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—64no—
198C2×Dic3—122no—
199C4×D3—64no—
200C4×D3—122no—
201C4×D3—122no—
202C4×D3—122no—
203C4×D3—122no—
204C4×D3—122no—
205C4×D3—122no—
206C4×D3—122no—
207Dic6—124no—
208Dic6—124no—
209C3×C8—122no—
210C3⋊C8—42no—
211C2×C32—22no—
212C2×C32C2×#9911yescharacteristic
213C2×C32C2×#10311yescharacteristic
214C2×C32#42111yescharacteristic
215C3⋊D3—22no—
216C3⋊D3—21no—
217C3⋊D3—21no—
218C24—91no—
219C2×Q8—92no—
220C2×Q8—181no—
221C2×Q8—362no—
222C22×C4—61no—
223C22×C4—61no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—182no—
230C22×C4—362no—
231C22×C4GO+(4,𝔽2)11yescharacteristic
232C2×C8—62no—
233C2×C8—362no—
234C4⋊C4—62no—
235C4⋊C4—62no—
236C4⋊C4—92no—
237C4⋊C4—181no—
238C4⋊C4—362no—
239C22⋊C4—182no—
240C22⋊C4—182no—
241C22⋊C4—362no—
242C22×C3—22no—
243C22×C3—22no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—41no—
249C22×C3—41no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—61no—
253C2×D3—61no—
254C2×D3—61no—
255C2×D3—61no—
256C2×D3—62no—
257C2×D3—62no—
258C2×D3—121no—
259C2×D3—121no—
260C2×D3—121no—
261C2×D3—121no—
262C2×D3—121no—
263C2×D3—121no—
264C2×D3—124no—
265C2×D3—124no—
266C2×D3—124no—
267C2×D3—124no—
268C3×C4—22no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—122no—
273C3×C4—122no—
274Dic3—42no—
275Dic3—42no—
276Dic3—62no—
277Dic3—62no—
278Dic3—62no—
279Dic3—121no—
280C32#152011yescharacteristic, complemented, Sylow
281C23—91no—
282C23—91no—
283C23—92no—
284C23—92no—
285C23—361no—
286C23—361no—
287C23D32⋊C411yescharacteristic
288Q8—362no—
289Q8—362no—
290C2×C4—41no—
291C2×C4—62no—
292C2×C4—62no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—122no—
296C2×C4—122no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4—182no—
300C2×C4—361no—
301C2×C4—361no—
302C2×C4—362no—
303C2×C4—362no—
304C2×C4—362no—
305C2×C4D32⋊C411yescharacteristic
306C2×C4C2×GO+(4,𝔽2)11yescharacteristic
307C8—122no—
308C2×C3—24no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—42no—
316D3—64no—
317D3—121no—
318D3—121no—
319D3—122no—
320D3—121no—
321D3—121no—
322C22—21no—
323C22—21no—
324C22—91no—
325C22—92no—
326C22—91no—
327C22—181no—
328C22—181no—
329C22—181no—
330C22—181no—
331C22—362no—
332C22—362no—
333C22#6373012yes—
334C22C2×D32⋊C411yescharacteristic
335C4—21no—
336C4—21no—
337C4—92no—
338C4—122no—
339C4—122no—
340C4—181no—
341C4—722no—
342C3—21no—
343C3—21no—
344C2—22no—
345C2—181no—
346C2—182no—
347C2—181no—
348C2C2×#6373011yescharacteristic
349C2#1059332311yescharacteristic
350C2#1059349011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1520
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590034C2semidirect
6. C22×#627C4semidirect
10. C2×#3724C4semidirect
14. #63865C4semidirect
280. C32#1520semidirect

Maximal subgroups

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

subgroupindex
C2×#638652
#105938122
#105911522
#105900342
#15209