Finite Group Databasebeta

← #11775618

Subgroups — #11775618

Order 1152.

550 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 67 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#10594925C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3C2×#63557C211yesmaximal, characteristic
4#10590034C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3797C411yescharacteristic, complemented
7C2×C22⋊#157—21no—
8C2×C4⋊#157—21no—
9C3×#924—21no—
10C22×C3×C3⋊C8—21no—
11#63982C412yescomplemented
12#63974—21no—
13#63900C411yescharacteristic, complemented
14#63883—21no—
15#63871—21no—
16#63865C2212yes—
17#63781C2212yes—
18#63557—21no—
19#63557C2212yes—
20D3×C22⋊Q8—61no—
21C2×(C2×D3)⋊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
31C2×C3×Dic6—21no—
32C2×#627C2×C412yes—
33C2×#624—21no—
34C2×#624—21no—
35#3797—42no—
36C22⋊#157—42no—
37C4⋊#157—42no—
38C3×#217—22no—
39C3×C4⋊Dic3—21no—
40C3×Dic3⋊C4—22no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—42no—
43#3724C2×C412yes—
44Dic3⋊Dic3—22no—
45#3722—22no—
46#1520—91nomaximal, Sylow
47C2×D3×Q8—61no—
48C22×C4×D3—61no—
49C22×C4×D3—61no—
50C22×C3×C8—61no—
51C3×C22⋊Q8—61no—
52#946—61no—
53#924—21no—
54C22×C3⋊C8—21no—
55#897—61no—
56#896—62no—
57D3×C4⋊C4—61no—
58D3×C4⋊C4—62no—
59D3×C22⋊C4—62no—
60#878—62no—
61(C2×D3)⋊C8—62no—
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—22no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3—41no—
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—
85C3×Dic6—42no—
86#627—42no—
87#624—42no—
88#624—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—
96C2×C3×Q8—61no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101D3×Q8—124no—
102C2×C4×D3—61no—
103C2×C4×D3—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—62no—
111C2×C4×D3—62no—
112C2×C4×D3—124no—
113C2×C4×D3—122no—
114C2×C4×D3—122no—
115C2×Dic6—21no—
116C2×Dic6—62no—
117C2×C3×C8—62no—
118C2×C3×C8—122no—
119C3×C4⋊C4—62no—
120C3×C4⋊C4—61no—
121C3×C22⋊C4—62no—
122#217—22no—
123(C2×D3)⋊C4—62no—
124(C2×D3)⋊C4—62no—
125C4⋊Dic3—21no—
126C4⋊Dic3—62no—
127Dic3⋊C4—22no—
128Dic3⋊C4—62no—
129Dic3⋊C4—62no—
130C2×C3⋊C8—22no—
131C2×C3⋊C8—42no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32#10312yes—
135C22×C32C2×C22⋊C411yescharacteristic
136C2×C3⋊D3—21no—
137C2×C3⋊D3—21no—
138C2×C3⋊D3—21no—
139C2×C3⋊D3—21no—
140C2×C3⋊D3—42no—
141C2×C3⋊D3—42no—
142C2×C3⋊D3#10312yes—
143C2×C3⋊D3C2×SD1611yescharacteristic
144C2×C3⋊D3C2×Q1611yescharacteristic
145#157—82no—
146C32×C4—21no—
147C32×C4#9912yes—
148C3⋊Dic3—21no—
149C3⋊Dic3—21no—
150C3×Dic3—42no—
151C3×Dic3—42no—
152C22×Q8—91no—
153C23×C4—91no—
154C22×C8—61no—
155C22⋊Q8—61no—
156C22⋊Q8—92no—
157C22⋊Q8—92no—
158C22⋊Q8—181no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—181no—
161C2×C4⋊C4—181no—
162C2×C22⋊C4—181no—
163C2×C22⋊C4—181no—
164C22⋊C8—92no—
165C22⋊C8—181no—
166#95—92no—
167C23×C3—21no—
168C23×C3—21no—
169C22×D3—61no—
170C22×D3—61no—
171C22×D3—62no—
172C22×D3—62no—
173C22×D3—62no—
174C22×D3—62no—
175C22×D3—61no—
176C22×D3—61no—
177C22×D3—122no—
178C22×D3—122no—
179C22×D3—122no—
180C22×D3—122no—
181C3×Q8—122no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—42no—
189C2×C3×C4—62no—
190C2×C3×C4—62no—
191C2×Dic3—22no—
192C2×Dic3—22no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—122no—
198C2×Dic3—122no—
199C4×D3—64no—
200C4×D3—122no—
201C4×D3—122no—
202C4×D3—122no—
203C4×D3—124no—
204C4×D3—124no—
205C4×D3—122no—
206C4×D3—121no—
207C4×D3—121no—
208C4×D3—121no—
209C4×D3—121no—
210C4×D3—122no—
211Dic6—42no—
212Dic6—124no—
213C3×C8—122no—
214C3⋊C8—42no—
215C2×C32—22no—
216C2×C32C2×#9911yescharacteristic
217C2×C32C2×#10311yescharacteristic
218C2×C32#42111yescharacteristic
219C3⋊D3—22no—
220C3⋊D3—21no—
221C3⋊D3—21no—
222C24—91no—
223C2×Q8—61no—
224C2×Q8—92no—
225C2×Q8—362no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—181no—
232C22×C4—181no—
233C22×C4—182no—
234C22×C4—362no—
235C22×C4GO+(4,𝔽2)11yescharacteristic
236C2×C8—62no—
237C2×C8—122no—
238C4⋊C4—62no—
239C4⋊C4—61no—
240C4⋊C4—92no—
241C4⋊C4—182no—
242C4⋊C4—362no—
243C22⋊C4—62no—
244C22⋊C4—182no—
245C22⋊C4—362no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—41no—
253C22×C3—41no—
254C2×D3—62no—
255C2×D3—62no—
256C2×D3—61no—
257C2×D3—61no—
258C2×D3—61no—
259C2×D3—61no—
260C2×D3—62no—
261C2×D3—62no—
262C2×D3—121no—
263C2×D3—121no—
264C2×D3—121no—
265C2×D3—121no—
266C2×D3—121no—
267C2×D3—121no—
268C2×D3—124no—
269C2×D3—124no—
270C2×D3—124no—
271C2×D3—124no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—41no—
277C3×C4—122no—
278C3×C4—122no—
279Dic3—42no—
280Dic3—42no—
281Dic3—62no—
282Dic3—121no—
283Dic3—121no—
284Dic3—121no—
285C32#152011yescharacteristic, complemented, Sylow
286C23—91no—
287C23—91no—
288C23—92no—
289C23—92no—
290C23—361no—
291C23—361no—
292C23D32⋊C411yescharacteristic
293Q8—122no—
294Q8—362no—
295C2×C4—22no—
296C2×C4—62no—
297C2×C4—62no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—361no—
303C2×C4—361no—
304C2×C4—362no—
305C2×C4—362no—
306C2×C4—361no—
307C2×C4—362no—
308C2×C4—362no—
309C2×C4—362no—
310C2×C4D32⋊C411yescharacteristic
311C2×C4C2×GO+(4,𝔽2)11yescharacteristic
312C8—122no—
313C2×C3—24no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—42no—
321D3—64no—
322D3—121no—
323D3—121no—
324D3—122no—
325D3—121no—
326D3—121no—
327C22—21no—
328C22—21no—
329C22—91no—
330C22—92no—
331C22—91no—
332C22—181no—
333C22—181no—
334C22—181no—
335C22—181no—
336C22—362no—
337C22—362no—
338C22#6373012yes—
339C22C2×D32⋊C411yescharacteristic
340C4—21no—
341C4—122no—
342C4—122no—
343C4—181no—
344C4—181no—
345C4—722no—
346C4#6373812yes—
347C3—21no—
348C3—21no—
349C2—22no—
350C2—181no—
351C2—182no—
352C2—181no—
353C2C2×#6373011yescharacteristic
354C2#1059332411yescharacteristic
355C2C2×#6373811yescharacteristic
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. C2×#3797C4semidirect
11. #63982C4semidirect
13. #63900C4semidirect
285. C32#1520semidirect

Maximal subgroups

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

subgroupindex
#105949252
#105938122
C2×#635572
#105900342
#15209