Finite Group Databasebeta

← #11775588

Subgroups — #11775588

Order 1152.

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

normal subgroups only

This group has 654 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×#63912C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic, complemented
3#10591152C211yesmaximal, characteristic, complemented
4#10590033C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#626—21no—
7C22×#625C411yescharacteristic, complemented
8C2×C22⋊#157—21no—
9C2×C4⋊#157—21no—
10C2×C3×(C2×D3)⋊C4—21no—
11C2×#3724C411yescharacteristic, complemented
12#63912—21no—
13#63912—21no—
14#63912C412yescomplemented
15#63912C2212yes—
16C2×#3710—21no—
17#63781C2212yescomplemented
18C3×#830—21no—
19#63557C2212yescomplemented
20C2×#884—61no—
21D3×C22⋊C8—61no—
22C23×C3⋊D3D411yescharacteristic
23C23×C3×D3—21no—
24C22×#157—22no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C2×C4×C3⋊D3—42no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C22×C3×Dic3—21no—
33C2×#626—22no—
34C2×#626—22no—
35C2×#626—42no—
36C2×#626—42no—
37C2×#625—21no—
38C2×#625—42no—
39C2×#625C2×C412yes—
40C22⋊#157—42no—
41C4⋊#157—42no—
42C3×(C2×D3)⋊C4—22no—
43C3×(C2×D3)⋊C4—22no—
44C2×C3×C3⋊C8—22no—
45#3724—21no—
46#3724C2×C412yes—
47#3710—42no—
48#1519—91nomaximal, Sylow
49C22×#67—61no—
50C22×#67—61no—
51C22×D12—61no—
52C22×C4×D3—61no—
53C22×C4×D3—61no—
54C2×C3×C22⋊C4—61no—
55C2×(C2×D3)⋊C4—21no—
56C2×Dic3⋊C4—61no—
57C2×D3×C8—62no—
58#884—62no—
59#884—62no—
60#884—62no—
61#884—62no—
62C3×C22⋊C8—61no—
63#830—21no—
64(C2×D3)⋊C8—62no—
65C23×C32C22⋊C411yescharacteristic
66C22×C3⋊D3—41no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3C22⋊C411yescharacteristic
69C22×C3⋊D3D812yes—
70C22×C3⋊D3SD1612yes—
71C22×C3⋊D3C2×D411yescharacteristic
72C22×C3×D3—22no—
73C22×C3×D3—42no—
74C22×C3×D3—42no—
75C22×C3×D3—42no—
76C2×#157—42no—
77C2×#157—42no—
78C2×#157—42no—
79C2×C32×C4—41no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22×C411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—41no—
88C4×C3⋊D3—41no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—42no—
91#626—44no—
92#626—42no—
93#626—42no—
94#625—42no—
95#625—42no—
96C3×C3⋊C8—42no—
97C2×#121—91no—
98C2×C22⋊C8—91no—
99#380—91no—
100#327—94no—
101C24×C3—61no—
102C23×D3—21no—
103C23×D3—61no—
104C23×D3—61no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4—61no—
108C2×#67—62no—
109C2×#67—62no—
110C2×#67—62no—
111C2×#67—62no—
112C2×#67—122no—
113C2×#67—122no—
114C2×#67—124no—
115C22×Dic3—21no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118C2×D12—62no—
119C2×D12—62no—
120C2×D12—122no—
121C2×D12—122no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×C4×D3—61no—
130C2×C4×D3—124no—
131C2×C4×D3—124no—
132C2×C3×C8—62no—
133C3×C22⋊C4—62no—
134C3×C22⋊C4—62no—
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—22no—
137Dic3⋊C4—62no—
138Dic3⋊C4—62no—
139C2×C3⋊C8—22no—
140D3×C8—124no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32#10212yes—
144C22×C32C2×C22⋊C411yescharacteristic
145C2×C3⋊D3—21no—
146C2×C3⋊D3—21no—
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3—42no—
150C2×C3⋊D3—42no—
151C2×C3⋊D3#10212yes—
152C2×C3⋊D3C2×D811yescharacteristic
153C2×C3⋊D3C2×SD1611yescharacteristic
154C2×C3×D3—42no—
155C2×C3×D3—42no—
156C2×C3×D3—42no—
157C2×C3×D3—84no—
158#157—82no—
159C32×C4—21no—
160C32×C4—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3#9912yes—
163C3×Dic3—42no—
164C22×D4—91no—
165C22×D4—181no—
166C23×C4—91no—
167C22×C8—181no—
168#121—92no—
169#121—92no—
170#121—181no—
171#121—181no—
172C2×C4⋊C4—91no—
173C2×C4⋊C4—181no—
174C2×C22⋊C4—61no—
175C2×C22⋊C4—181no—
176C22⋊C8—61no—
177C22⋊C8—92no—
178#95—92no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—62no—
182C23×C3—122no—
183C23×C3—122no—
184C23×C3—122no—
185C22×D3—22no—
186C22×D3—42no—
187C22×D3—42no—
188C22×D3—42no—
189C22×D3—61no—
190C22×D3—61no—
191C22×D3—62no—
192C22×D3—62no—
193C22×D3—62no—
194C22×D3—62no—
195C22×D3—61no—
196C22×D3—61no—
197C22×D3—122no—
198C22×D3—122no—
199C22×D3—122no—
200C22×D3—122no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—42no—
206C2×C3×C4—42no—
207C2×C3×C4—62no—
208C2×C3×C4—122no—
209#67—124no—
210#67—122no—
211#67—122no—
212#67—124no—
213#67—124no—
214C2×Dic3—22no—
215C2×Dic3—42no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—64no—
221C2×Dic3—122no—
222D12—124no—
223D12—122no—
224D12—122no—
225C4×D3—64no—
226C4×D3—122no—
227C4×D3—122no—
228C4×D3—122no—
229C4×D3—122no—
230C4×D3—122no—
231C4×D3—122no—
232C4×D3—122no—
233C3×C8—122no—
234C3⋊C8—42no—
235C2×C32—22no—
236C2×C32C2×#9911yescharacteristic
237C2×C32C2×#10211yescharacteristic
238C2×C32#42111yescharacteristic
239C3⋊D3—22no—
240C3⋊D3—21no—
241C3⋊D3—21no—
242C3×D3—82no—
243C24—61no—
244C24—91no—
245C2×D4—92no—
246C2×D4—182no—
247C2×D4—182no—
248C2×D4—181no—
249C2×D4—362no—
250C2×D4—362no—
251C2×D4—362no—
252C22×C4—61no—
253C22×C4—91no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—182no—
259C22×C4—362no—
260C22×C4GO+(4,𝔽2)11yescharacteristic
261C2×C8—62no—
262C2×C8—362no—
263C4⋊C4—92no—
264C4⋊C4—181no—
265C4⋊C4—362no—
266C22⋊C4—62no—
267C22⋊C4—62no—
268C22⋊C4—362no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—122no—
278C22×C3—122no—
279C22×C3—122no—
280C22×C3—244no—
281C2×D3—42no—
282C2×D3—42no—
283C2×D3—42no—
284C2×D3—62no—
285C2×D3—62no—
286C2×D3—61no—
287C2×D3—61no—
288C2×D3—61no—
289C2×D3—61no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—84no—
293C2×D3—121no—
294C2×D3—121no—
295C2×D3—121no—
296C2×D3—121no—
297C2×D3—121no—
298C2×D3—121no—
299C2×D3—124no—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C3×C4—22no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—122no—
308Dic3—42no—
309Dic3—62no—
310Dic3—62no—
311Dic3—62no—
312Dic3—121no—
313C32#151911yescharacteristic, complemented, Sylow
314C23—62no—
315C23—91no—
316C23—91no—
317C23—92no—
318C23—92no—
319C23—122no—
320C23—122no—
321C23—122no—
322C23—361no—
323C23—361no—
324C23D32⋊C411yescharacteristic
325D4—362no—
326D4—362no—
327D4—364no—
328D4—362no—
329D4—362no—
330C2×C4—41no—
331C2×C4—62no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—122no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—361no—
339C2×C4—361no—
340C2×C4—362no—
341C2×C4—362no—
342C2×C4—362no—
343C2×C4D32⋊C411yescharacteristic
344C2×C4C2×GO+(4,𝔽2)11yescharacteristic
345C8—122no—
346C2×C3—24no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—42no—
354C2×C3—242no—
355D3—64no—
356D3—82no—
357D3—121no—
358D3—121no—
359D3—122no—
360D3—121no—
361D3—121no—
362C22—21no—
363C22—21no—
364C22—91no—
365C22—92no—
366C22—91no—
367C22—122no—
368C22—122no—
369C22—122no—
370C22—181no—
371C22—181no—
372C22—181no—
373C22—181no—
374C22—244no—
375C22—362no—
376C22—362no—
377C22#6372912yes—
378C22C2×D32⋊C411yescharacteristic
379C4—21no—
380C4—21no—
381C4—92no—
382C4—122no—
383C4—181no—
384C4—722no—
385C3—21no—
386C3—21no—
387C2—22no—
388C2—181no—
389C2—182no—
390C2—181no—
391C2—242no—
392C2C2×#6372911yescharacteristic
393C2#1059332311yescharacteristic
394C2#1059349011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#63912C2
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1519
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
2. #10593812C2semidirect
3. #10591152C2semidirect
4. #10590033C2semidirect
7. C22×#625C4semidirect
11. C2×#3724C4semidirect
14. #63912C4semidirect
17. #63781C22semidirect
19. #63557C22semidirect
313. C32#1519semidirect

Maximal subgroups

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

subgroupindex
C2×#639122
#105938122
#105911522
#105900332
#15199