Finite Group Databasebeta

← #11857810

Subgroups — #11857810

Order 1152.

1402 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1402 conjugacy classes of subgroups — too many to draw. Only its 199 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×#64306C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic, complemented
3#10594969C211yesmaximal, characteristic, complemented
4#10593498C214yesmaximal, complemented
5#10593375C212yesmaximal, complemented
6#10593365C212yesmaximal, complemented
7#10593349C214yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C3×#235—21no—
10C2×#3811—21no—
11C2×#3805C2212yes—
12#64306—24no—
13#64306C418yescomplemented
14C2×#3802C2211yescharacteristic
15C2×C4×D32—21no—
16C2×#3798C2212yes—
17C2×#3797C2211yescharacteristic
18C2×#3796—21no—
19C22×#622C2212yescomplemented
20C2×#3787—24no—
21C2×#3787C2212yes—
22C2×#3787C2212yescomplemented
23C3×#926—21no—
24#63974—21no—
25#63957C2212yescomplemented
26#63900C2212yes—
27C4×#624—21no—
28#63874C2212yescomplemented
29#63849—21no—
30#63740C2218yescomplemented
31#63739C2218yescomplemented
32C2×D3×#41—61no—
33D3×#117—61no—
34C23×C3⋊D3D411yescharacteristic
35C22×D32—21no—
36C22×C32×C4D411yescharacteristic
37C22×C3⋊Dic3C2311yescharacteristic
38C2×C4×C3⋊D3C2×C414yes—
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D414yes—
42C2×C4×C3⋊D3C2311yescharacteristic
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C3×#67—22no—
45C3×#235—28no—
46C2×C3×D12—21no—
47C2×C3×C4×D3—22no—
48C2×C3×Dic6—21no—
49#3811—28no—
50C2×#627C2312yes—
51C2×#626—22no—
52C2×#625C2312yes—
53C2×#624—21no—
54C2×#624—22no—
55#3805—24no—
56#3805C2×C418yescomplemented
57C2×D3×Dic3—22no—
58#3802—22no—
59#3802C2×C414yes—
60C4×D32—28no—
61#3798—24no—
62#3798C2×C418yescomplemented
63#3797—22no—
64#3797C2×C414yes—
65#3796—28no—
66C2×#622—24no—
67C2×#622C2314yes—
68#3787—24no—
69#3787—24no—
70C3×#217—22no—
71C3×C4⋊Dic3—22no—
72C3×C4×Dic3—22no—
73#3724C2314yes—
74#3722—22no—
75Dic32—22no—
76C2×#416—91nomaximal, Sylow
77C2×C3×#41—61no—
78D3×#41—68no—
79D3×#41—68no—
80C2×#239—61no—
81C2×D3×Q8—61no—
82C2×#237—62no—
83C2×#237—61no—
84C2×D3×D4—61no—
85C2×D3×D4—62no—
86C2×#235—21no—
87C2×#235—62no—
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C22×C4×D3—62no—
91C3×#117—61no—
92#926—21no—
93#892—62no—
94D3×C4⋊C4—62no—
95D3×C22⋊C4—62no—
96#877—62no—
97#872—62no—
98C42×D3—62no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—24no—
101C22×C3⋊D3C22⋊C414yes—
102C22×C3⋊D3C2×D411yescharacteristic
103C22×C3⋊D3C2×D411yescharacteristic
104C22×C3×D3—22no—
105C2×D32—24no—
106C2×D32—44no—
107C2×C32×C4C22⋊C414yes—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3C22×C412yes—
111C2×C3⋊Dic3C2×D411yescharacteristic
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2411yescharacteristic
114C4×C3⋊D3C22⋊C414yes—
115C4×C3⋊D3C22⋊C414yes—
116C4×C3⋊D3C22×C412yes—
117C4×C3⋊D3C22×C412yes—
118C4×C3⋊D3C2×D412yes—
119C4×C3⋊D3C2×D412yes—
120C3×#67—28no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—24no—
123C3×D12—24no—
124C3×C4×D3—28no—
125C3×Dic6—24no—
126#627—22no—
127#627C22×C414yes—
128#626—28no—
129#625—22no—
130#625C22×C414yes—
131#624—24no—
132#624—44no—
133D3×Dic3—28no—
134#622—24no—
135C22×#41—91no—
136C23×C8—91no—
137C2×#117—91no—
138#416—94no—
139#416—94no—
140C2×#103—92no—
141C2×#102—92no—
142C23×D3—61no—
143C23×D3—61no—
144C23×D3—62no—
145C3×#41—68no—
146C2×C3×Q8—61no—
147C2×C3×D4—61no—
148C2×C3×D4—62no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—62no—
152C2×#67—22no—
153C2×#67—62no—
154C2×#67—62no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C22×Dic3—62no—
158#239—68no—
159D3×Q8—64no—
160D3×Q8—64no—
161#237—68no—
162#237—68no—
163#237—68no—
164D3×D4—64no—
165D3×D4—64no—
166D3×D4—616no—
167#235—28no—
168#235—68no—
169#235—68no—
170C2×D12—21no—
171C2×D12—62no—
172C2×C4×D3—22no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—61no—
181C2×C4×D3—64no—
182C2×C4×D3—64no—
183C2×C4×D3—64no—
184C2×C4×D3—64no—
185C2×C4×D3—616no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×C4×D3—64no—
189C2×Dic6—21no—
190C2×Dic6—62no—
191C3×C4⋊C4—62no—
192C3×C22⋊C4—62no—
193C3×C42—62no—
194#217—22no—
195(C2×D3)⋊C4—64no—
196C4⋊Dic3—22no—
197Dic3⋊C4—64no—
198C4×Dic3—22no—
199C4×Dic3—64no—
200C22×C32—22no—
201C22×C32C2×C22⋊C412yes—
202C22×C32C22×D411yescharacteristic
203C2×C3⋊D3—22no—
204C2×C3⋊D3—28no—
205C2×C3⋊D3C2×C22⋊C412yes—
206C2×C3⋊D3C2×C22⋊C412yes—
207C2×C3⋊D3#13514yes—
208C2×C3×D3—24no—
209C2×C3×D3—44no—
210D32—48no—
211C32×C4C2×C22⋊C412yes—
212C32×C4C2×C22⋊C412yes—
213C3⋊Dic3C2×C22⋊C412yes—
214C3⋊Dic3C23×C411yescharacteristic
215C3⋊Dic3C22×D411yescharacteristic
216C3×Dic3—24no—
217C3×Dic3—44no—
218C2×#41—61no—
219C2×#41—92no—
220C2×#41—92no—
221C2×#41—98no—
222C2×#41—181no—
223C2×#41—184no—
224C22×Q8—91no—
225C22×D4—91no—
226C22×D4—181no—
227C23×C4—91no—
228C23×C4—181no—
229C22×C8—92no—
230C22×C8—92no—
231C22×C8—92no—
232C22×C8—184no—
233#117—61no—
234#117—92no—
235#117—92no—
236#117—181no—
237C2×C4⋊C4—92no—
238C2×C22⋊C4—181no—
239C2×C42—181no—
240#103—98no—
241#102—98no—
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—62no—
245C22×D3—22no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3—64no—
249C22×D3—64no—
250C22×D3—61no—
251C22×D3—61no—
252C22×D3—68no—
253C22×D3—124no—
254C22×D3—124no—
255C22×D3—128no—
256C3×Q8—64no—
257C3×D4—64no—
258C3×D4—68no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—24no—
264C2×C3×C4—24no—
265C2×C3×C4—68no—
266C2×C3×C4—62no—
267C2×C3×C4—64no—
268#67—28no—
269#67—64no—
270#67—68no—
271#67—64no—
272C2×Dic3—22no—
273C2×Dic3—24no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—68no—
283D12—24no—
284D12—68no—
285C4×D3—28no—
286C4×D3—64no—
287C4×D3—64no—
288C4×D3—64no—
289C4×D3—64no—
290C4×D3—62no—
291C4×D3—62no—
292C4×D3—62no—
293C4×D3—62no—
294C4×D3—62no—
295C4×D3—62no—
296C4×D3—62no—
297C4×D3—62no—
298C4×D3—68no—
299C4×D3—68no—
300C4×D3—128no—
301Dic6—24no—
302Dic6—64no—
303Dic6—64no—
304C2×C32—22no—
305C2×C32C22×C22⋊C411yescharacteristic
306C2×C32C2×#13512yes—
307C3⋊D3—22no—
308C3⋊D3#41614yescomplemented
309C3×D3—44no—
310C24—91no—
311C24—181no—
312#41—68no—
313#41—98no—
314#41—98no—
315#41—184no—
316#41—184no—
317#41—188no—
318C2×Q8—61no—
319C2×Q8—92no—
320C2×Q8—94no—
321C2×Q8—182no—
322C2×D4—62no—
323C2×D4—61no—
324C2×D4—94no—
325C2×D4—92no—
326C2×D4—182no—
327C2×D4—182no—
328C2×D4—188no—
329C22×C4—62no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—94no—
336C22×C4—94no—
337C22×C4—188no—
338C22×C4—181no—
339C22×C4—182no—
340C22×C4—182no—
341C22×C4GO+(4,𝔽2)11yescharacteristic
342C2×C8—94no—
343C2×C8—184no—
344C2×C8—184no—
345C2×C8—184no—
346C4⋊C4—62no—
347C4⋊C4—94no—
348C22⋊C4—62no—
349C22⋊C4—182no—
350C42—62no—
351C42—182no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—64no—
359C22×C3—124no—
360C2×D3—24no—
361C2×D3—44no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—64no—
365C2×D3—64no—
366C2×D3—62no—
367C2×D3—62no—
368C2×D3—128no—
369C2×D3—128no—
370C2×D3—122no—
371C2×D3—122no—
372C2×D3—1216no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—22no—
376C3×C4—22no—
377C3×C4—64no—
378C3×C4—124no—
379Dic3—24no—
380Dic3—44no—
381Dic3—61no—
382Dic3—61no—
383Dic3—62no—
384Dic3—62no—
385Dic3—61no—
386Dic3—61no—
387C32C2×#41611yescharacteristic, complemented, Sylow
388C23—62no—
389C23—91no—
390C23—91no—
391C23—94no—
392C23—184no—
393C23—184no—
394C23—364no—
395C23C2×GO+(4,𝔽2)11yescharacteristic
396Q8—64no—
397Q8—94no—
398Q8—182no—
399D4—68no—
400D4—64no—
401D4—94no—
402D4—188no—
403D4—182no—
404C2×C4—62no—
405C2×C4—68no—
406C2×C4—64no—
407C2×C4—91no—
408C2×C4—91no—
409C2×C4—92no—
410C2×C4—92no—
411C2×C4—92no—
412C2×C4—92no—
413C2×C4—94no—
414C2×C4—92no—
415C2×C4—92no—
416C2×C4—94no—
417C2×C4—184no—
418C2×C4—188no—
419C2×C4—364no—
420C2×C4D32⋊C414yes—
421C2×C4C2×GO+(4,𝔽2)11yescharacteristic
422C2×C4C2×GO+(4,𝔽2)11yescharacteristic
423C8—184no—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—42no—
429C2×C3—42no—
430C2×C3—124no—
431D3—44no—
432D3—64no—
433D3—64no—
434D3—122no—
435D3—122no—
436C22—22no—
437C22—64no—
438C22—94no—
439C22—92no—
440C22—92no—
441C22—124no—
442C22—188no—
443C22—182no—
444C22—368no—
445C22C2×D32⋊C412yes—
446C22C22×GO+(4,𝔽2)11yescharacteristic
447C4—64no—
448C4—91no—
449C4—92no—
450C4—91no—
451C4—124no—
452C4C2×D32⋊C412yes—
453C4C2×D32⋊C412yes—
454C3—21no—
455C3—21no—
456C2—22no—
457C2—94no—
458C2—124no—
459C2—182no—
460C2#1059650012yes—
461C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#64306C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#416
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3787C2semidirect
3. #10594969C2semidirect
4. #10593498C2semidirect
5. #10593375C2semidirect
6. #10593365C2semidirect
7. #10593349C2semidirect
13. #64306C4semidirect
19. C22×#622C22semidirect
22. C2×#3787C22semidirect
25. #63957C22semidirect
28. #63874C22semidirect
30. #63740C22semidirect
31. #63739C22semidirect
56. #3805C2×C4semidirect
62. #3798C2×C4semidirect
308. C3⋊D3#416semidirect
387. C32C2×#416semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C22×#37872
#105949692
#105934982
#105933752
#105933652
#105933492
C2×#4169