Finite Group Databasebeta

← #11791849

Subgroups — #11791849

Order 1152.

777 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 777 conjugacy classes of subgroups — too many to draw. Only its 134 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×#63982C211yesmaximal, characteristic
2C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
3#10591720C211yesmaximal, characteristic
4C3×#4527C212yesmaximal
5#10589186C212yesmaximal
6#68955—32nomaximal
7C23×C3⋊Dic3C2211yescharacteristic
8C22×#627C411yescharacteristic, complemented
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757C2211yescharacteristic
11C2×C4×C3⋊Dic3—21no—
12C2×C3×#217C2212yes—
13C2×C3×#217C2212yes—
14#63982—21no—
15#63982—21no—
16#63982—21no—
17#63982—21no—
18C2×#3724—21no—
19C2×#3724C411yescharacteristic, complemented
20C2×Dic3⋊Dic3C412yescomplemented
21#63658—21no—
22#63579—21no—
23C2×#878—32no—
24#4942—32no—
25Dic3×C22⋊C4—32no—
26Dic3×C22⋊C4—61no—
27C3×#342—32no—
28#4527—32no—
29#4527D312yes—
30#4526—32no—
31C24×C32C2311yescharacteristic
32C22×C32×C4—21no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—42no—
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3×Dic3—22no—
42C22×C3×Dic3C2×C412yes—
43C22×C3×Dic3C2×C412yes—
44C2×#627—21no—
45C2×#627—21no—
46C2×#627—42no—
47C32×C22⋊C4—21no—
48C32×C22⋊C4Q812yescomplemented
49#3757—21no—
50#3757Q812yescomplemented
51C4×C3⋊Dic3—42no—
52C3×#217—22no—
53C3×#217—22no—
54C3×#217—22no—
55C3×#217—22no—
56#3724—21no—
57#3724—21no—
58#3724—42no—
59Dic3⋊Dic3—22no—
60Dic3⋊Dic3—22no—
61#1996—91noSylow
62C23×Dic3—32no—
63C23×Dic3—61no—
64C22×Dic6—32no—
65C2×C3×C22⋊C4—21no—
66C2×C3×C22⋊C4—32no—
67C2×C3×C22⋊C4—32no—
68C2×C3×C22⋊C4C2×D312yes—
69C2×#217—32no—
70C2×#217—61no—
71C2×#217C2×D312yes—
72C2×#217C2×D312yes—
73C2×C4⋊Dic3—32no—
74C2×Dic3⋊C4—32no—
75C2×Dic3⋊C4—32no—
76C2×Dic3⋊C4—62no—
77C2×C4×Dic3—62no—
78C2×C4×Dic3—62no—
79#878—62no—
80#878—62no—
81#878—62no—
82#878—62no—
83C3⋊#95—62no—
84C3⋊#95—62no—
85C3⋊#95—62no—
86C23×C32—41no—
87C23×C32—41no—
88C23×C32C22×C411yescharacteristic
89C23×C32C2×D411yescharacteristic
90C23×C32C2×D411yescharacteristic
91C23×C32C2×Q811yescharacteristic
92C23×C32C2×Q811yescharacteristic
93C23×C32#4111yescharacteristic
94C23×C32#4111yescharacteristic
95C2×C32×C4—22no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—42no—
118#627—42no—
119#627—42no—
120C2×C22⋊Q8—91no—
121#380—91no—
122C4×C22⋊C4—91no—
123#342—32no—
124#342—92no—
125C24×C3—21no—
126C24×C3C22×D312yes—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—32no—
130C22×C3×C4—32no—
131C22×C3×C4—62no—
132C22×Dic3—22no—
133C22×Dic3—32no—
134C22×Dic3—32no—
135C22×Dic3—32no—
136C22×Dic3—32no—
137C22×Dic3—32no—
138C22×Dic3—32no—
139C22×Dic3—61no—
140C22×Dic3—61no—
141C22×Dic3—61no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C22×Dic3—61no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147C22×Dic3—124no—
148C22×Dic3—124no—
149C22×Dic3C4×D312yes—
150C22×Dic3C4×D312yes—
151C2×Dic6—62no—
152C2×Dic6—62no—
153C2×Dic6—124no—
154C3×C22⋊C4—22no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—62no—
158C3×C22⋊C4—62no—
159C3×C22⋊C4—62no—
160C3×C22⋊C4—62no—
161C3×C22⋊C4Dic614yescomplemented
162#217—22no—
163#217—22no—
164#217—22no—
165#217—22no—
166#217—34no—
167#217—62no—
168#217—62no—
169#217—62no—
170C4⋊Dic3—62no—
171C4⋊Dic3—62no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176Dic3⋊C4—124no—
177C4×Dic3—124no—
178C4×Dic3—124no—
179C22×C32—21no—
180C22×C32—21no—
181C22×C32—21no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—41no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32—41no—
189C22×C32C2×C22⋊C411yescharacteristic
190C22×C32C4×Q811yescharacteristic
191C22×C32C4×Q811yescharacteristic
192C22×C32C22⋊Q811yescharacteristic
193C22×C32C22⋊Q811yescharacteristic
194C22×C32#12411yescharacteristic
195C22×C32C4⋊Q811yescharacteristic
196C32×C4—42no—
197C3⋊Dic3—21no—
198C3⋊Dic3—21no—
199C3⋊Dic3—21no—
200C3⋊Dic3—42no—
201C3⋊Dic3#9912yes—
202C3×Dic3—42no—
203C3×Dic3—42no—
204C3×Dic3—82no—
205C22×Q8—91no—
206C23×C4—91no—
207C22⋊Q8—181no—
208C22⋊Q8—181no—
209C22⋊Q8—181no—
210C22⋊Q8—181no—
211C2×C4⋊C4—91no—
212C2×C4⋊C4—92no—
213C2×C4⋊C4—181no—
214C2×C22⋊C4—32no—
215C2×C22⋊C4—32no—
216C2×C22⋊C4—91no—
217C2×C22⋊C4D3211yescharacteristic
218C2×C42—181no—
219#95—181no—
220#95—181no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—21no—
227C23×C3—21no—
228C23×C3—42no—
229C23×C3—42no—
230C23×C3—42no—
231C23×C3—42no—
232C23×C3C2×Dic612yes—
233C23×C3C2×C4×D312yes—
234C23×C3#23512yes—
235C23×C3D3×D412yes—
236C23×C3D3×D412yes—
237C23×C3#23712yes—
238C23×C3D3×Q812yes—
239C2×C3×C4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—122no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4—122no—
251C2×C3×C4—122no—
252C2×Dic3—22no—
253C2×Dic3—22no—
254C2×Dic3—32no—
255C2×Dic3—32no—
256C2×Dic3—32no—
257C2×Dic3—32no—
258C2×Dic3—42no—
259C2×Dic3—42no—
260C2×Dic3—42no—
261C2×Dic3—42no—
262C2×Dic3—42no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C2×Dic3—64no—
273C2×Dic3—122no—
274C2×Dic3—122no—
275C2×Dic3—122no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—122no—
281C2×Dic3—122no—
282C2×Dic3—122no—
283C2×Dic3—122no—
284C2×Dic3—122no—
285Dic6—124no—
286Dic6—124no—
287C2×C32—21no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32#39111yescharacteristic
294C2×C32C2×#9911yescharacteristic
295C2×C32#41011yescharacteristic
296C24C2×D3211yescharacteristic
297C2×Q8—181no—
298C2×Q8—181no—
299C2×Q8—362no—
300C22×C4—21no—
301C22×C4—32no—
302C22×C4—32no—
303C22×C4—62no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—181no—
311C22×C4—362no—
312C4⋊C4—181no—
313C4⋊C4—181no—
314C4⋊C4—182no—
315C4⋊C4—182no—
316C4⋊C4—362no—
317C22⋊C4—21no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—62no—
321C22⋊C4—62no—
322C22⋊C4—92no—
323C22⋊C4—181no—
324C22⋊C4#62712yescomplemented
325C42—362no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3C4×Dic612yes—
354C22×C3#87812yes—
355C22×C3D3×C22⋊C412yes—
356C22×C3#88512yes—
357C22×C3#88712yes—
358C22×C3#88812yes—
359C22×C3#89612yes—
360C3×C4—44no—
361C3×C4—44no—
362C3×C4—122no—
363C3×C4—122no—
364C3×C4—242no—
365Dic3—34no—
366Dic3—42no—
367Dic3—42no—
368Dic3—62no—
369Dic3—62no—
370Dic3—62no—
371Dic3—62no—
372Dic3—62no—
373Dic3—82no—
374Dic3—121no—
375Dic3—121no—
376Dic3—124no—
377Dic3—124no—
378C32#199611yescharacteristic, complemented, Sylow
379C23—41no—
380C23—41no—
381C23#379711yescharacteristic
382C23#379811yescharacteristic
383C23C4×D3211yescharacteristic
384C23#380211yescharacteristic
385C23#380511yescharacteristic
386C23C2×#62711yescharacteristic
387C23#381111yescharacteristic
388Q8—362no—
389Q8—362no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—91no—
396C2×C4—91no—
397C2×C4—91no—
398C2×C4—91no—
399C2×C4—122no—
400C2×C4—122no—
401C2×C4—122no—
402C2×C4—122no—
403C2×C4—122no—
404C2×C4—182no—
405C2×C4—182no—
406C2×C4—182no—
407C2×C4—182no—
408C2×C4—361no—
409C2×C4—361no—
410C2×C4—361no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—22no—
418C2×C3—22no—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—41no—
428C2×C3#464612yes—
429C2×C3#474012yes—
430C2×C3D3×#9912yes—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22#6383811yescharacteristic
442C22#6386511yescharacteristic
443C22#6391511yescharacteristic
444C22C4×#62711yescharacteristic
445C22#6391911yescharacteristic
446C22#6392111yescharacteristic
447C22#6398211yescharacteristic
448C4—42no—
449C4—92no—
450C4—122no—
451C4—122no—
452C4—181no—
453C4—181no—
454C4—181no—
455C4—242no—
456C4—362no—
457C3—21no—
458C3#6895512yescomplemented
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—21no—
464C2—21no—
465C2#1059040411yescharacteristic
466C2#1059040611yescharacteristic
467C2#1059139611yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radical, cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1996
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C22×#627C4semidirect
19. C2×#3724C4semidirect
20. C2×Dic3⋊Dic3C4semidirect
48. C32×C22⋊C4Q8semidirect
50. #3757Q8semidirect
161. C3×C22⋊C4Dic6semidirect
324. C22⋊C4#627semidirect
378. C32#1996semidirect
458. C3#68955semidirect

Maximal subgroups

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

subgroupindex
C2×#639822
C22⋊C4×C3⋊Dic32
#105917202
C3×#45272
#105891862
#689553