Finite Group Databasebeta

← #11775310

Subgroups — #11775310

Order 1152.

634 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593811C211yesmaximal, characteristic, complemented
3#10591074C211yesmaximal, characteristic, complemented
4#10590033C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#626—21no—
7C22×#625C411yescharacteristic, complemented
8C2×C22⋊#157—21no—
9C2×C3×(C2×D3)⋊C4—21no—
10C2×C3×#208—21no—
11C2×#3724C411yescharacteristic, complemented
12#63912—21no—
13#63912—21no—
14#63912C412yescomplemented
15#63912C2212yes—
16#63781—21no—
17#63781C2212yescomplemented
18#63557—21no—
19#63557C2212yescomplemented
20C2×#884—61no—
21#5126—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—44no—
36C2×#625—21no—
37C2×#625—42no—
38C2×#625C2×C412yes—
39C22⋊#157—42no—
40C3×(C2×D3)⋊C4—22no—
41C3×(C2×D3)⋊C4—22no—
42C3×#208—42no—
43C2×C3×C3⋊C8—22no—
44#3724—21no—
45#3724C2×C412yes—
46#1510—91nomaximal, Sylow
47C22×#67—61no—
48C22×#67—61no—
49C22×D12—61no—
50C22×C4×D3—61no—
51C22×C4×D3—61no—
52C2×C3×M16—61no—
53C2×C3×C22⋊C4—61no—
54C2×(C2×D3)⋊C4—21no—
55C2×Dic3⋊C4—61no—
56C2×#208—21no—
57#884—62no—
58#884—62no—
59#884—62no—
60#884—62no—
61(C2×D3)⋊C8—62no—
62(C2×D3)⋊C8—62no—
63C23×C32C22⋊C411yescharacteristic
64C22×C3⋊D3—22no—
65C22×C3⋊D3—22no—
66C22×C3⋊D3—41no—
67C22×C3⋊D3C22⋊C411yescharacteristic
68C22×C3⋊D3C2×D411yescharacteristic
69C22×C3×D3—22no—
70C22×C3×D3—42no—
71C22×C3×D3—42no—
72C22×C3×D3—42no—
73C2×#157—42no—
74C2×#157—42no—
75C2×#157—42no—
76C2×C32×C4—22no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22×C411yescharacteristic
82C4×C3⋊D3—41no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3—41no—
86C2×C3×Dic3—22no—
87C2×C3×Dic3—42no—
88#626—44no—
89#626—44no—
90#625—42no—
91#625—42no—
92C3×C3⋊C8—42no—
93C2×#121—91no—
94#407—91no—
95#381—91no—
96#327—94no—
97C24×C3—61no—
98C23×D3—21no—
99C23×D3—61no—
100C23×D3—61no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4—61no—
104C2×#67—62no—
105C2×#67—62no—
106C2×#67—62no—
107C2×#67—62no—
108C2×#67—124no—
109C2×#67—124no—
110C22×Dic3—21no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C2×D12—62no—
114C2×D12—62no—
115C2×D12—124no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—124no—
125C2×C4×D3—122no—
126C2×C4×D3—122no—
127C3×M16—122no—
128C2×C3×C8—62no—
129C3×C22⋊C4—62no—
130C3×C22⋊C4—62no—
131(C2×D3)⋊C4—22no—
132(C2×D3)⋊C4—22no—
133Dic3⋊C4—62no—
134Dic3⋊C4—62no—
135#208—42no—
136C2×C3⋊C8—22no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32#9912yes—
140C22×C32C2×C22⋊C411yescharacteristic
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3⋊D3—21no—
146C2×C3⋊D3—44no—
147C2×C3⋊D3AGL(1,ℤ/8)12yes—
148C2×C3×D3—42no—
149C2×C3×D3—42no—
150C2×C3×D3—42no—
151C2×C3×D3—84no—
152#157—82no—
153C32×C4—21no—
154C32×C4—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3—21no—
157C3×Dic3—42no—
158C22×D4—91no—
159C22×D4—181no—
160C23×C4—91no—
161C2×M16—61no—
162#121—92no—
163#121—92no—
164#121—181no—
165#121—181no—
166C2×C4⋊C4—91no—
167C2×C22⋊C4—61no—
168C2×C22⋊C4—181no—
169C22⋊C8—92no—
170C22⋊C8—181no—
171#95—92no—
172#95—181no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—62no—
176C23×C3—122no—
177C23×C3—122no—
178C23×C3—122no—
179C22×D3—22no—
180C22×D3—42no—
181C22×D3—42no—
182C22×D3—42no—
183C22×D3—61no—
184C22×D3—61no—
185C22×D3—61no—
186C22×D3—61no—
187C22×D3—64no—
188C22×D3—122no—
189C22×D3—122no—
190C22×D3—122no—
191C22×D3—122no—
192C22×D3—122no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—42no—
200C2×C3×C4—62no—
201C2×C3×C4—122no—
202#67—124no—
203#67—124no—
204#67—124no—
205#67—124no—
206C2×Dic3—22no—
207C2×Dic3—42no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—64no—
213C2×Dic3—122no—
214D12—124no—
215D12—124no—
216C4×D3—122no—
217C4×D3—122no—
218C4×D3—122no—
219C4×D3—122no—
220C4×D3—121no—
221C4×D3—121no—
222C4×D3—121no—
223C4×D3—121no—
224C4×D3—122no—
225C4×D3—122no—
226C3×C8—122no—
227C3⋊C8—42no—
228C2×C32—22no—
229C2×C32C2×#9911yescharacteristic
230C2×C32#41811yescharacteristic
231C2×C32#42111yescharacteristic
232C3⋊D3—22no—
233C3⋊D3—41no—
234C3×D3—82no—
235C24—61no—
236C24—91no—
237C2×D4—92no—
238C2×D4—182no—
239C2×D4—182no—
240C2×D4—181no—
241C2×D4—364no—
242C2×D4—362no—
243C22×C4—61no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—182no—
250C22×C4—362no—
251C22×C4GO+(4,𝔽2)11yescharacteristic
252M16—122no—
253C2×C8—62no—
254C4⋊C4—92no—
255C4⋊C4—181no—
256C22⋊C4—62no—
257C22⋊C4—62no—
258C22⋊C4—362no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—122no—
268C22×C3—122no—
269C22×C3—122no—
270C22×C3—244no—
271C2×D3—42no—
272C2×D3—42no—
273C2×D3—42no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—62no—
277C2×D3—62no—
278C2×D3—84no—
279C2×D3—121no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—121no—
283C2×D3—121no—
284C2×D3—121no—
285C2×D3—121no—
286C2×D3—121no—
287C2×D3—128no—
288C2×D3—128no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—22no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—122no—
295Dic3—42no—
296Dic3—62no—
297Dic3—62no—
298Dic3—121no—
299Dic3—121no—
300C32#151011yescharacteristic, complemented, Sylow
301C23—62no—
302C23—91no—
303C23—91no—
304C23—122no—
305C23—122no—
306C23—122no—
307C23—182no—
308C23—182no—
309C23—361no—
310C23D32⋊C411yescharacteristic
311D4—364no—
312D4—364no—
313D4—362no—
314D4—362no—
315C2×C4—22no—
316C2×C4—62no—
317C2×C4—91no—
318C2×C4—91no—
319C2×C4—122no—
320C2×C4—182no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4—361no—
324C2×C4—361no—
325C2×C4—362no—
326C2×C4—362no—
327C2×C4—362no—
328C2×C4D32⋊C411yescharacteristic
329C2×C4C2×GO+(4,𝔽2)11yescharacteristic
330C8—122no—
331C2×C3—24no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—42no—
339C2×C3—242no—
340D3—82no—
341D3—122no—
342D3—122no—
343D3—122no—
344D3—122no—
345C22—21no—
346C22—21no—
347C22—92no—
348C22—122no—
349C22—122no—
350C22—122no—
351C22—181no—
352C22—181no—
353C22—181no—
354C22—181no—
355C22—181no—
356C22—244no—
357C22—364no—
358C22#6373812yes—
359C22C2×D32⋊C411yescharacteristic
360C4—21no—
361C4—21no—
362C4—122no—
363C4—181no—
364C4—181no—
365C4—722no—
366C3—21no—
367C3—21no—
368C2—22no—
369C2—182no—
370C2—242no—
371C2—361no—
372C2#1059331811yescharacteristic
373C2#1059332311yescharacteristic
374C2C2×#6373811yescharacteristic
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#1510
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. #10593811C2semidirect
3. #10591074C2semidirect
4. #10590033C2semidirect
7. C22×#625C4semidirect
11. C2×#3724C4semidirect
14. #63912C4semidirect
17. #63781C22semidirect
19. #63557C22semidirect
300. C32#1510semidirect

Maximal subgroups

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

subgroupindex
C2×#639122
#105938112
#105910742
#105900332
#15109