Finite Group Databasebeta

← #11791856

Subgroups — #11791856

Order 1152.

614 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 69 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
3#10591260C211yesmaximal, characteristic
4#10590076C214yesmaximal
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3797C411yescharacteristic, complemented
7C2×C22⋊#157C2212yes—
8C2×C4⋊#157—21no—
9C3×#924—21no—
10#63982—21no—
11#63974C2212yes—
12C2×#3722C2212yes—
13C2×Dic32—21no—
14#63900C411yescharacteristic, complemented
15#63883C412yescomplemented
16#63871—21no—
17#63865—21no—
18#63781—21no—
19C3×C3⋊#95—21no—
20D3×C22⋊Q8—61no—
21#4666—61no—
22C23×C3⋊D3C2311yescharacteristic
23C22×#157—22no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C4×C3⋊D3—42no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C22×C3×Dic3—22no—
32C2×C3×Dic6—21no—
33C2×#627—21no—
34C2×#624C2×C412yes—
35C2×#624C2×C412yes—
36#3797—42no—
37C22⋊#157—24no—
38C4⋊#157—42no—
39C3×#217—22no—
40C3×C4⋊Dic3—21no—
41C3×Dic3⋊C4—22no—
42#3724—21no—
43Dic3⋊Dic3—22no—
44#3722—22no—
45#3722—22no—
46#3722Q814yescomplemented
47Dic32—42no—
48#1996—91nomaximal, Sylow
49C2×D3×Q8—61no—
50C22×C4×D3—61no—
51C22×C4×D3—61no—
52C3×C22⋊Q8—61no—
53#946—61no—
54C2×(C2×D3)⋊C4—62no—
55#924—21no—
56C2×C4×Dic3—62no—
57#897—61no—
58#896—62no—
59D3×C4⋊C4—62no—
60D3×C4⋊C4—61no—
61D3×C22⋊C4—62no—
62#878—62no—
63C3×#95—61no—
64C3⋊#95—21no—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3—41no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3C22×C411yescharacteristic
69C22×C3⋊D3C2×D411yescharacteristic
70C22×C3⋊D3C2×Q812yes—
71C22×C3⋊D3#4112yes—
72C2×#157—42no—
73C2×#157—42no—
74C2×#157—42no—
75C2×C32×C4—41no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C4×C3⋊D3—22no—
82C4×C3⋊D3—22no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3—41no—
85C2×C3×Dic3—22no—
86C2×C3×Dic3—22no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C3×Dic6—42no—
91#627—42no—
92#624—42no—
93#624—42no—
94C2×C22⋊Q8—91no—
95#380—91no—
96C4×C22⋊C4—91no—
97#342—94no—
98C23×D3—61no—
99C23×D3—61no—
100C2×C3×Q8—61no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4—62no—
104C22×Dic3—22no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107D3×Q8—124no—
108C2×C4×D3—61no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—124no—
119C2×C4×D3—124no—
120C2×Dic6—21no—
121C2×Dic6—62no—
122C3×C4⋊C4—62no—
123C3×C4⋊C4—61no—
124C3×C22⋊C4—62no—
125#217—22no—
126(C2×D3)⋊C4—64no—
127(C2×D3)⋊C4—62no—
128(C2×D3)⋊C4—62no—
129(C2×D3)⋊C4—64no—
130C4⋊Dic3—21no—
131C4⋊Dic3—62no—
132Dic3⋊C4—22no—
133Dic3⋊C4—62no—
134Dic3⋊C4—62no—
135C4×Dic3—124no—
136C22×C32—21no—
137C22×C32—21no—
138C22×C32C2×C22⋊C411yescharacteristic
139C22×C32C22⋊Q812yes—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3—42no—
145C2×C3⋊D3—42no—
146C2×C3⋊D3C4×Q812yes—
147C2×C3⋊D3#12411yescharacteristic
148C2×C3⋊D3C4⋊Q811yescharacteristic
149#157—82no—
150C32×C4—21no—
151C32×C4—21no—
152C3⋊Dic3—21no—
153C3⋊Dic3#9912yes—
154C3×Dic3—44no—
155C3×Dic3—42no—
156C3×Dic3—42no—
157C22×Q8—91no—
158C23×C4—91no—
159C22⋊Q8—61no—
160C22⋊Q8—181no—
161C22⋊Q8—181no—
162C22⋊Q8—181no—
163C2×C4⋊C4—92no—
164C2×C4⋊C4—91no—
165C2×C4⋊C4—181no—
166C2×C22⋊C4—92no—
167C2×C22⋊C4—92no—
168C2×C22⋊C4—92no—
169C2×C42—181no—
170#95—61no—
171#95—181no—
172C23×C3—21no—
173C23×C3—21no—
174C22×D3—61no—
175C22×D3—61no—
176C22×D3—61no—
177C22×D3—61no—
178C22×D3—62no—
179C22×D3—62no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—122no—
183C22×D3—122no—
184C22×D3—122no—
185C22×D3—121no—
186C22×D3—121no—
187C3×Q8—122no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—42no—
193C2×C3×C4—42no—
194C2×C3×C4—62no—
195C2×C3×C4—62no—
196C2×C3×C4—64no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×Dic3—22no—
200C2×Dic3—22no—
201C2×Dic3—24no—
202C2×Dic3—42no—
203C2×Dic3—42no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—64no—
209C2×Dic3—122no—
210C4×D3—64no—
211C4×D3—122no—
212C4×D3—122no—
213C4×D3—122no—
214C4×D3—124no—
215C4×D3—124no—
216C4×D3—122no—
217C4×D3—122no—
218C4×D3—122no—
219C4×D3—122no—
220Dic6—42no—
221Dic6—124no—
222C2×C32—22no—
223C2×C32#39111yescharacteristic
224C2×C32C2×#9911yescharacteristic
225C2×C32#41011yescharacteristic
226C3⋊D3—22no—
227C3⋊D3—21no—
228C3⋊D3—21no—
229C24—91no—
230C2×Q8—61no—
231C2×Q8—181no—
232C2×Q8—362no—
233C22×C4—62no—
234C22×C4—92no—
235C22×C4—92no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—182no—
242C22×C4—362no—
243C22×C4GO+(4,𝔽2)11yescharacteristic
244C4⋊C4—62no—
245C4⋊C4—61no—
246C4⋊C4—181no—
247C4⋊C4—182no—
248C4⋊C4—362no—
249C22⋊C4—62no—
250C22⋊C4—94no—
251C22⋊C4—182no—
252C22⋊C4—182no—
253C22⋊C4—184no—
254C42—362no—
255C22×C3—21no—
256C22×C3—22no—
257C22×C3—21no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—41no—
263C22×C3—41no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—61no—
267C2×D3—61no—
268C2×D3—61no—
269C2×D3—61no—
270C2×D3—62no—
271C2×D3—62no—
272C2×D3—121no—
273C2×D3—121no—
274C2×D3—121no—
275C2×D3—121no—
276C2×D3—121no—
277C2×D3—121no—
278C2×D3—124no—
279C2×D3—124no—
280C2×D3—122no—
281C2×D3—122no—
282C2×D3—122no—
283C2×D3—122no—
284C3×C4—22no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—122no—
289C3×C4—122no—
290C3×C4—124no—
291Dic3—42no—
292Dic3—42no—
293Dic3—44no—
294Dic3—62no—
295Dic3—62no—
296Dic3—62no—
297Dic3—121no—
298C32#199611yescharacteristic, complemented, Sylow
299C23—91no—
300C23—91no—
301C23—92no—
302C23—92no—
303C23—361no—
304C23—361no—
305C23C2×GO+(4,𝔽2)11yescharacteristic
306Q8—122no—
307Q8—362no—
308C2×C4—41no—
309C2×C4—64no—
310C2×C4—62no—
311C2×C4—62no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—122no—
315C2×C4—122no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—182no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4—362no—
322C2×C4—362no—
323C2×C4—362no—
324C2×C4—362no—
325C2×C4—362no—
326C2×C4D32⋊C411yescharacteristic
327C2×C4D32⋊C411yescharacteristic
328C2×C3—22no—
329C2×C3—22no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—42no—
337D3—64no—
338D3—121no—
339D3—121no—
340D3—122no—
341D3—121no—
342D3—121no—
343C22—21no—
344C22—21no—
345C22—91no—
346C22—92no—
347C22—91no—
348C22—181no—
349C22—181no—
350C22—181no—
351C22—181no—
352C22—362no—
353C22—362no—
354C22D32⋊Q812yes—
355C22C2×D32⋊C411yescharacteristic
356C4—21no—
357C4—21no—
358C4—92no—
359C4—124no—
360C4—122no—
361C4—122no—
362C4—181no—
363C4—722no—
364C3—21no—
365C3—21no—
366C2—22no—
367C2—181no—
368C2—182no—
369C2—181no—
370C2#1059334111yescharacteristic
371C2#1059334611yescharacteristic
372C2#1059349011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1996
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. C2×#3797C4semidirect
14. #63900C4semidirect
15. #63883C4semidirect
46. #3722Q8semidirect
298. C32#1996semidirect

Maximal subgroups

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

subgroupindex
#105949252
#105938122
#105912602
#105900762
#19969