Finite Group Databasebeta

← #11860554

Subgroups — #11860554

Order 1152.

822 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 151 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×#64224C211yesmaximal, characteristic
2#10594606C211yesmaximal, characteristic, complemented
3#10594509C211yesmaximal, characteristic, complemented
4#10593748C211yesmaximal, characteristic, complemented
5#10593433C212yesmaximal, complemented
6#10593431C212yesmaximal, complemented
7#10593419C212yesmaximal, complemented
8C4×#3774C212yesmaximal, complemented
9#10593394C211yesmaximal, characteristic, complemented
10#10593365C211yesmaximal, characteristic, complemented
11#10593349C211yesmaximal, characteristic, complemented
12C2×#3802C2211yescharacteristic
13C2×#3798C2211yescharacteristic
14C2×#3788C2211yescharacteristic
15C2×#3787C2211yescharacteristic
16C2×#3775C2212yes—
17C2×#3774C2212yes—
18#64224C418yescomplemented
19#64101C2211yescharacteristic
20C3×#893—21no—
21C3×D3×C4⋊C4—21no—
22D3×(C2×D3)⋊C4—22no—
23#63904—22no—
24#63902C2212yes—
25C4×#625C2212yes—
26C4×#625C2212yescomplemented
27#63900C2211yescharacteristic
28Dic3×D12—21no—
29#63874C2211yescharacteristic
30#63841—21no—
31#63838C2212yescomplemented
32#63777C2212yescomplemented
33C4×#622C2212yescomplemented
34#63743C2212yescomplemented
35#63742C2212yescomplemented
36#63740C2211yescharacteristic, complemented
37#63740C2211yescharacteristic, complemented
38#63739C2212yes—
39#63739C2212yes—
40#63739C2211yescharacteristic, complemented
41#63739C2211yescharacteristic, complemented
42#5545—61no—
43#5504—61no—
44C22×D32—21no—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C3×D12—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—22no—
49C2×C3×C4×D3—22no—
50C2×#627C2311yescharacteristic
51C2×#626—21no—
52C2×#625C2311yescharacteristic
53C2×#625C2312yes—
54C2×#624—21no—
55C2×D3×Dic3—22no—
56#3802—22no—
57#3802C2×C414yescomplemented
58#3798—22no—
59#3798C2×C414yescomplemented
60C2×#622C2311yescharacteristic
61C2×#622C2311yescharacteristic
62C2×#622C2312yes—
63#3788C2×C414yescomplemented
64#3787—22no—
65#3775C2×C418yescomplemented
66#3774C2×C418yescomplemented
67C32×C4⋊C4D411yescharacteristic
68#3752D412yes—
69C4⋊(C3⋊Dic3)D411yescharacteristic
70C4×C3⋊Dic3C2312yes—
71C3×(C2×D3)⋊C4—22no—
72C3×C4⋊Dic3—21no—
73C3×Dic3⋊C4—22no—
74C3×C4×Dic3—21no—
75#3724C2312yes—
76#3724C2311yescharacteristic
77#3724C2311yescharacteristic
78#3722—21no—
79(C2×D3)⋊Dic3—22no—
80(C2×D3)⋊Dic3—22no—
81Dic32—22no—
82#2946—91nomaximal, Sylow
83C2×D3×D4—61no—
84C2×#235—61no—
85C3×C4×D4—61no—
86C2×C3×C4⋊C4—61no—
87D4×Dic3—61no—
88C4×#67—62no—
89C4×#67—62no—
90C4×#67—62no—
91C2×(C2×D3)⋊C4—62no—
92#926—61no—
93#893—21no—
94#893—62no—
95#892—61no—
96#892—61no—
97#892—61no—
98D3×C4⋊C4—21no—
99D3×C4⋊C4—61no—
100#887—62no—
101#67⋊C4—62no—
102D3×C22⋊C4—62no—
103C4×D12—61no—
104#872—61no—
105C22×C3⋊D3C2×D411yescharacteristic
106C22×C3×D3—22no—
107C22×C3×D3—21no—
108C2×D32—24no—
109C2×D32—81no—
110C2×D32—81no—
111C2×C32×C4C2×D412yes—
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3C2×D412yes—
114C2×C3⋊Dic3C2411yescharacteristic
115C4×C3⋊D3C22×C412yes—
116C4×C3⋊D3#4112yes—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C3×D12—24no—
122C3×C4×D3—24no—
123C3×C4×D3—82no—
124C3×C4×D3—82no—
125#627—21no—
126#627C22×C412yes—
127#626—24no—
128#625—21no—
129#625—22no—
130#625C22×C412yes—
131#625C22×C414yes—
132#624—81no—
133D3×Dic3—82no—
134#622—21no—
135#622—21no—
136#622C22×C414yes—
137C2×AGL(1,ℤ/8)—91no—
138#520—91no—
139#518—91no—
140#442—92no—
141#440—92no—
142C4×SD16—92no—
143C4×D8—92no—
144#428—91no—
145#416—91no—
146C2×#102—91no—
147#405—91no—
148C23×D3—62no—
149C2×C3×D4—61no—
150C22×C3×C4—61no—
151C22×C3×C4—62no—
152C22×C3×C4—62no—
153C2×#67—62no—
154C2×#67—61no—
155C2×#67—61no—
156C22×Dic3—62no—
157D3×D4—64no—
158D3×D4—64no—
159#235—64no—
160#235—64no—
161C2×D12—21no—
162C2×D12—61no—
163C2×C4×D3—21no—
164C2×C4×D3—22no—
165C2×C4×D3—22no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×Dic6—61no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—61no—
175C3×C22⋊C4—62no—
176C3×C42—61no—
177#217—62no—
178#217—62no—
179(C2×D3)⋊C4—22no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—62no—
186C4⋊Dic3—21no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189Dic3⋊C4—22no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—62no—
193C4×Dic3—21no—
194C4×Dic3—62no—
195C4×Dic3—62no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C22×C32C22×D411yescharacteristic
199C2×C3⋊D3—21no—
200C2×C3⋊D3—21no—
201C2×C3⋊D3C4×D412yes—
202C2×C3×D3—22no—
203C2×C3×D3—24no—
204C2×C3×D3—41no—
205C2×C3×D3—42no—
206C2×C3×D3—42no—
207C2×C3×D3—41no—
208D32—84no—
209C32×C4—22no—
210C32×C4C4×D412yes—
211C3⋊Dic3—22no—
212C3⋊Dic3C23×C411yescharacteristic
213C3⋊Dic3C2×#4111yescharacteristic
214C3×Dic3—22no—
215C3×Dic3—42no—
216C3×Dic3—41no—
217C3×Dic3—41no—
218C2×#41—91no—
219C22×D4—91no—
220AGL(1,ℤ/8)—98no—
221C2×SD16—92no—
222C2×D8—92no—
223C2×M16—91no—
224C22×C8—91no—
225C4×Q8—92no—
226C4×D4—61no—
227C4×D4—92no—
228C4×D4—92no—
229C4×D4—92no—
230C4×D4—181no—
231C4×D4—182no—
232#117—91no—
233#117—91no—
234#117—181no—
235C2×C4⋊C4—61no—
236C2×C4⋊C4—91no—
237C2×C22⋊C4—182no—
238#107—92no—
239#106—92no—
240#103—91no—
241#103—91no—
242#102—92no—
243#102—92no—
244#102—91no—
245#102—91no—
246#97—92no—
247C4×C8—92no—
248C23×C3—61no—
249C23×C3—62no—
250C22×D3—22no—
251C22×D3—21no—
252C22×D3—61no—
253C22×D3—61no—
254C22×D3—68no—
255C22×D3—242no—
256C22×D3—242no—
257C3×D4—64no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—64no—
263C2×C3×C4—61no—
264C2×C3×C4—62no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—242no—
268C2×C3×C4—242no—
269#67—62no—
270#67—64no—
271#67—64no—
272#67—62no—
273#67—64no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—22no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—242no—
283D12—24no—
284D12—64no—
285C4×D3—24no—
286C4×D3—62no—
287C4×D3—62no—
288C4×D3—62no—
289C4×D3—62no—
290C4×D3—82no—
291C4×D3—82no—
292C4×D3—242no—
293C4×D3—242no—
294Dic6—62no—
295Dic6—62no—
296C2×C32C2×C4×D411yescharacteristic
297C2×C32#57611yescharacteristic
298C2×C32#57711yescharacteristic
299C3⋊D3—22no—
300C3×D3—44no—
301C3×D3—42no—
302C24—181no—
303#41—94no—
304#41—182no—
305C2×Q8—91no—
306C2×D4—61no—
307C2×D4—94no—
308C2×D4—91no—
309C2×D4—92no—
310C2×D4—181no—
311C2×D4—182no—
312C22×C4—61no—
313C22×C4—62no—
314C22×C4—62no—
315C22×C4—91no—
316C22×C4—181no—
317C22×C4—182no—
318SD16—98no—
319D8—98no—
320M16—94no—
321C2×C8—92no—
322C2×C8—91no—
323C2×C8—91no—
324C2×C8—182no—
325C4⋊C4—61no—
326C4⋊C4—62no—
327C4⋊C4—92no—
328C4⋊C4—91no—
329C4⋊C4—91no—
330C4⋊C4—91no—
331C4⋊C4GO+(4,𝔽2)11yescharacteristic
332C22⋊C4—62no—
333C22⋊C4—92no—
334C22⋊C4—181no—
335C22⋊C4—182no—
336C22⋊C4—182no—
337C42—61no—
338C42—92no—
339C42—182no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—62no—
343C22×C3—64no—
344C22×C3—122no—
345C22×C3—121no—
346C22×C3—122no—
347C22×C3—121no—
348C2×D3—22no—
349C2×D3—24no—
350C2×D3—41no—
351C2×D3—42no—
352C2×D3—42no—
353C2×D3—41no—
354C2×D3—62no—
355C2×D3—62no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—121no—
360C2×D3—248no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—62no—
366C3×C4—121no—
367C3×C4—122no—
368C3×C4—121no—
369Dic3—22no—
370Dic3—41no—
371Dic3—42no—
372Dic3—41no—
373Dic3—61no—
374Dic3—61no—
375Dic3—61no—
376Dic3—61no—
377Dic3—122no—
378Dic3—122no—
379C32#294611yescharacteristic, complemented, Sylow
380C23—62no—
381C23—61no—
382C23—91no—
383C23—184no—
384C23—721no—
385C23—721no—
386Q8—92no—
387Q8—181no—
388D4—64no—
389D4—92no—
390D4—94no—
391D4—184no—
392D4—182no—
393D4—181no—
394C2×C4—61no—
395C2×C4—64no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—62no—
399C2×C4—91no—
400C2×C4—92no—
401C2×C4—92no—
402C2×C4—92no—
403C2×C4—242no—
404C2×C4—242no—
405C2×C4—721no—
406C2×C4—722no—
407C2×C4C2×GO+(4,𝔽2)12yes—
408C2×C4C2×GO+(4,𝔽2)11yescharacteristic
409C8—94no—
410C8—181no—
411C8—181no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—124no—
419C2×C3—122no—
420D3—44no—
421D3—42no—
422D3—122no—
423D3—122no—
424C22—62no—
425C22—64no—
426C22—92no—
427C22—121no—
428C22—122no—
429C22—122no—
430C22—121no—
431C22—181no—
432C22—181no—
433C22—724no—
434C22C22×GO+(4,𝔽2)11yescharacteristic
435C4—22no—
436C4—62no—
437C4—91no—
438C4—91no—
439C4—121no—
440C4—122no—
441C4—121no—
442C4—182no—
443C4C4×GO+(4,𝔽2)12yes—
444C3—21no—
445C3—21no—
446C2—124no—
447C2—122no—
448C2—182no—
449C2C2×C4×GO+(4,𝔽2)11yescharacteristic
450C2#1059651411yescharacteristic
451C2#1059652111yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#64224C2
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2946
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594606C2semidirect
3. #10594509C2semidirect
4. #10593748C2semidirect
5. #10593433C2semidirect
6. #10593431C2semidirect
7. #10593419C2semidirect
8. C4×#3774C2semidirect
9. #10593394C2semidirect
10. #10593365C2semidirect
11. #10593349C2semidirect
18. #64224C4semidirect
26. C4×#625C22semidirect
31. #63838C22semidirect
32. #63777C22semidirect
33. C4×#622C22semidirect
34. #63743C22semidirect
35. #63742C22semidirect
36. #63740C22semidirect
37. #63740C22semidirect
40. #63739C22semidirect
41. #63739C22semidirect
57. #3802C2×C4semidirect
59. #3798C2×C4semidirect
63. #3788C2×C4semidirect
65. #3775C2×C4semidirect
66. #3774C2×C4semidirect
379. C32#2946semidirect

Maximal subgroups

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

subgroupindex
C2×#642242
#105946062
#105945092
#105937482
#105934332
#105934312
#105934192
C4×#37742
#105933942
#105933652
#105933492
#29469