Finite Group Databasebeta

← #11774928

Subgroups — #11774928

Order 1152.

941 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 941 conjugacy classes of subgroups — too many to draw. Only its 106 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#10595081C211yesmaximal, characteristic
2C3⋊D3×#95C211yesmaximal, characteristic, complemented
3#10591152C211yesmaximal, characteristic, complemented
4C3×#4451C212yesmaximal, complemented
5#10589150C212yesmaximal, complemented
6D3×#327—32nomaximal
7C22×C4×C3⋊D3—21no—
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×#3811—21no—
10C2×#3802C411yescharacteristic, complemented
11C3×#930C2212yes—
12#63980—21no—
13#63921—21no—
14#63916C412yescomplemented
15#63912—21no—
16#63900C411yescharacteristic, complemented
17C2×#3710—21no—
18C32×#95C2211yescharacteristic, complemented
19#63658—21no—
20#63658C2211yescharacteristic, complemented
21C3×#830C2212yescomplemented
22#63557—21no—
23D3×#121—32no—
24D3×C22⋊C8—32no—
25D3×#95—32no—
26D3×#95—61no—
27C3×#327—32no—
28#4537—32no—
29#4470—32no—
30#4451D312yescomplemented
31C23×C3⋊D3D411yescharacteristic
32C22×D32—21no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C2×C4×C3⋊D3—24no—
38C2×C4×C3⋊D3—42no—
39C2×C4×C3⋊D3—42no—
40C2×C4×C3⋊D3—42no—
41C2×C4×C3⋊D3C2×C411yescharacteristic
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C3×#67—22no—
46C2×C3×D12C2×C412yescomplemented
47#3811—42no—
48#3811—42no—
49C2×#626—22no—
50C2×#625—21no—
51C2×#624—21no—
52#3802—42no—
53C3×(C2×D3)⋊C4—22no—
54C3×C4⋊Dic3C2×C412yescomplemented
55C2×C3×C3⋊C8—22no—
56#3724—21no—
57(C2×D3)⋊Dic3—22no—
58#3710—42no—
59C2×#327—91noSylow
60C2×D3×D4—32no—
61C2×D3×D4—62no—
62C22×C4×D3—32no—
63C22×C4×D3—61no—
64C22×C4×D3—62no—
65C22×C4×D3—62no—
66C3×#121—32no—
67#939—62no—
68#938—32no—
69#930C2×D312yes—
70C2×D3×C8—62no—
71#895—32no—
72D3×C4⋊C4—32no—
73#884—62no—
74D3×C22⋊C4—62no—
75C3×C22⋊C8—32no—
76C3×#95—21no—
77C3×#95C2×D312yescomplemented
78C3⋊#95—32no—
79C3⋊#95—61no—
80C3⋊#95—62no—
81C3⋊#95—62no—
82#830C2×D312yescomplemented
83(C2×D3)⋊C8—62no—
84C23×C32C2×D411yescharacteristic
85C22×C3⋊D3—22no—
86C22×C3⋊D3—22no—
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3⋊D3C22⋊C411yescharacteristic
89C22×C3⋊D3D812yes—
90C22×C3⋊D3SD1612yes—
91C22×C3×D3—22no—
92C2×D32—42no—
93C2×D32—42no—
94C2×D32—42no—
95C2×C32×C4—22no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—41no—
110C4×C3⋊D3—41no—
111C4×C3⋊D3—48no—
112C3×#67—42no—
113C3×#67—42no—
114C2×C3×Dic3—22no—
115C3×D12—42no—
116#626—44no—
117#625—42no—
118#624—42no—
119C3×C3⋊C8—42no—
120C2×#121—91no—
121C2×C22⋊C8—91no—
122C2×#95—91no—
123#327—32no—
124#327—92no—
125C23×D3—32no—
126C23×D3—61no—
127C23×D3—62no—
128C2×C3×D4—32no—
129C2×C3×D4—62no—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C22×C3×C4—21no—
133C22×C3×C4C22×D312yes—
134C2×#67—22no—
135C2×#67—62no—
136C2×#67—62no—
137C22×Dic3—32no—
138C22×Dic3—61no—
139C22×Dic3—62no—
140C22×Dic3—62no—
141D3×D4—124no—
142D3×D4—124no—
143D3×D4—124no—
144C2×D12—62no—
145C2×D12C4×D312yescomplemented
146C2×C4×D3—32no—
147C2×C4×D3—32no—
148C2×C4×D3—32no—
149C2×C4×D3—32no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—62no—
155C2×C4×D3—68no—
156C2×C4×D3—68no—
157C2×C4×D3—124no—
158C2×C4×D3—124no—
159C2×C4×D3—124no—
160C2×C4×D3—124no—
161C2×C4×D3—124no—
162C2×C4×D3—124no—
163C2×C3×C8—62no—
164C3×C4⋊C4—32no—
165C3×C22⋊C4—62no—
166#217—62no—
167(C2×D3)⋊C4—22no—
168(C2×D3)⋊C4—62no—
169C4⋊Dic3C4×D312yescomplemented
170Dic3⋊C4—62no—
171C2×C3⋊C8—22no—
172D3×C8—124no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32C2×C22⋊C411yescharacteristic
176C22×C32C2×D811yescharacteristic
177C22×C32C2×SD1611yescharacteristic
178C2×C3⋊D3—21no—
179C2×C3⋊D3—21no—
180C2×C3⋊D3—24no—
181C2×C3⋊D3—24no—
182C2×C3⋊D3#9912yes—
183C2×C3⋊D3#10212yes—
184C2×C3⋊D3#10212yes—
185C2×C3⋊D3#10412yes—
186C2×C3×D3—42no—
187C2×C3×D3—42no—
188C2×C3×D3—42no—
189D32—84no—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4—42no—
193C3⋊Dic3—21no—
194C3⋊Dic3—21no—
195C3⋊Dic3—42no—
196C3×Dic3—42no—
197C22×D4—91no—
198C22×D4—181no—
199C23×C4—91no—
200C23×C4—181no—
201C22×C8—181no—
202#121—32no—
203#121—92no—
204#121—181no—
205#121—181no—
206C2×C4⋊C4—91no—
207C2×C22⋊C4—181no—
208C22⋊C8—32no—
209C22⋊C8—181no—
210#95—91no—
211#95—181no—
212#95D3211yescharacteristic, complemented
213C23×C3—21no—
214C23×C3—62no—
215C23×C3D3×D412yes—
216C22×D3—22no—
217C22×D3—32no—
218C22×D3—32no—
219C22×D3—34no—
220C22×D3—34no—
221C22×D3—61no—
222C22×D3—61no—
223C22×D3—62no—
224C22×D3—62no—
225C22×D3—64no—
226C22×D3—64no—
227C22×D3—64no—
228C22×D3—64no—
229C22×D3—124no—
230C22×D3—124no—
231C22×D3—124no—
232C3×D4—122no—
233C3×D4—122no—
234C3×D4—122no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—62no—
246C2×C3×C4C2×C4×D312yes—
247C2×C3×C4D3×D412yes—
248#67—42no—
249#67—42no—
250#67—124no—
251#67—124no—
252C2×Dic3—22no—
253C2×Dic3—32no—
254C2×Dic3—32no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—122no—
260C2×Dic3—122no—
261C2×Dic3—122no—
262C2×Dic3—122no—
263C2×Dic3—122no—
264C2×Dic3—122no—
265D12—42no—
266D12—124no—
267C4×D3—64no—
268C4×D3—64no—
269C4×D3—122no—
270C4×D3—122no—
271C4×D3—124no—
272C4×D3—122no—
273C4×D3—122no—
274C4×D3—122no—
275C4×D3—122no—
276C4×D3—1216no—
277C4×D3—1216no—
278C3×C8—122no—
279C3⋊C8—42no—
280C2×C32—21no—
281C2×C32—21no—
282C2×C32C2×#9911yescharacteristic
283C2×C32C2×#10211yescharacteristic
284C2×C32C2×#10411yescharacteristic
285C3⋊D3—22no—
286C3⋊D3#32714yescomplemented
287C3×D3—82no—
288C24—91no—
289C24—181no—
290C2×D4—32no—
291C2×D4—62no—
292C2×D4—182no—
293C2×D4—181no—
294C2×D4—362no—
295C2×D4—362no—
296C2×D4—362no—
297C22×C4—21no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—184no—
304C22×C4—181no—
305C22×C4—181no—
306C22×C4—362no—
307C22×C4—362no—
308C22×C4—362no—
309C22×C4C2×D3211yescharacteristic
310C2×C8—62no—
311C2×C8—362no—
312C4⋊C4—32no—
313C4⋊C4—181no—
314C22⋊C4—62no—
315C22⋊C4—182no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—122no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3D3×C22⋊C412yes—
327C22×C3D3×D812yes—
328C22×C3D3×SD1612yes—
329C2×D3—34no—
330C2×D3—34no—
331C2×D3—34no—
332C2×D3—34no—
333C2×D3—42no—
334C2×D3—42no—
335C2×D3—42no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C2×D3—62no—
340C2×D3—68no—
341C2×D3—68no—
342C2×D3—68no—
343C2×D3—62no—
344C2×D3—68no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—62no—
348C2×D3—248no—
349C3×C4—22no—
350C3×C4—22no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—44no—
354C3×C4—44no—
355C3×C4—122no—
356Dic3—42no—
357Dic3—62no—
358Dic3—62no—
359Dic3—121no—
360Dic3—121no—
361Dic3—124no—
362Dic3—124no—
363C32C2×#32711yescharacteristic, complemented, Sylow
364C23—62no—
365C23—91no—
366C23—91no—
367C23—92no—
368C23—92no—
369C23—182no—
370C23—182no—
371C23—362no—
372C23—362no—
373C23—362no—
374C23#381111yescharacteristic
375D4—122no—
376D4—122no—
377D4—122no—
378D4—364no—
379D4—362no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—62no—
385C2×C4—91no—
386C2×C4—91no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4—361no—
391C2×C4—361no—
392C2×C4—368no—
393C2×C4—362no—
394C2×C4—361no—
395C2×C4—361no—
396C2×C4—361no—
397C2×C4C4×D3211yescharacteristic
398C2×C4#380211yescharacteristic
399C8—122no—
400C2×C3—22no—
401C2×C3—22no—
402C2×C3—22no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—242no—
408C2×C3D3×#9912yes—
409C2×C3D3×#10212yes—
410C2×C3D3×#10412yes—
411D3—38no—
412D3—64no—
413D3—64no—
414D3—64no—
415D3—82no—
416C22—21no—
417C22—21no—
418C22—92no—
419C22—92no—
420C22—92no—
421C22—92no—
422C22—122no—
423C22—122no—
424C22—122no—
425C22—184no—
426C22—184no—
427C22—181no—
428C22—181no—
429C22—724no—
430C22#6392111yescharacteristic
431C22#6392611yescharacteristic
432C22#6394011yescharacteristic
433C4—21no—
434C4—21no—
435C4—42no—
436C4—122no—
437C4—181no—
438C4—181no—
439C4—362no—
440C3—21no—
441C3D3×#32712yescomplemented
442C2—21no—
443C2—21no—
444C2—94no—
445C2—182no—
446C2—242no—
447C2#1059039311yescharacteristic
448C2#1059040411yescharacteristic
449C2#1059059311yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32C2×#327
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#95C2semidirect
3. #10591152C2semidirect
4. C3×#4451C2semidirect
5. #10589150C2semidirect
10. C2×#3802C4semidirect
14. #63916C4semidirect
16. #63900C4semidirect
18. C32×#95C22semidirect
20. #63658C22semidirect
21. C3×#830C22semidirect
30. #4451D3semidirect
46. C2×C3×D12C2×C4semidirect
54. C3×C4⋊Dic3C2×C4semidirect
77. C3×#95C2×D3semidirect
82. #830C2×D3semidirect
145. C2×D12C4×D3semidirect
169. C4⋊Dic3C4×D3semidirect
212. #95D32semidirect
286. C3⋊D3#327semidirect
363. C32C2×#327semidirect
441. C3D3×#327semidirect

Maximal subgroups

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

subgroupindex
#105950812
C3⋊D3×#952
#105911522
C3×#44512
#105891502
D3×#3273