Finite Group Databasebeta

← #11860246

Subgroups — #11860246

Order 1152.

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

normal subgroups only

This group has 802 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×#64223C211yesmaximal, characteristic
2#10593966C211yesmaximal, characteristic, complemented
3C4×#3798C211yesmaximal, characteristic, complemented
4#10593723C211yesmaximal, characteristic, complemented
5#10593432C212yesmaximal, complemented
6#10593431C212yesmaximal, complemented
7#10593419C212yesmaximal, complemented
8#10593389C211yesmaximal, characteristic, complemented
9#10593369C212yesmaximal, complemented
10#10593349C211yesmaximal, characteristic, complemented
11#10593349C211yesmaximal, characteristic, complemented
12C2×#3798C2211yescharacteristic
13C2×#3798C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15C2×#3787C2211yescharacteristic
16C2×#3776C2211yescharacteristic
17C2×#3775C2211yescharacteristic
18C2×#3775C2211yescharacteristic
19C2×#3774C2211yescharacteristic
20#64223C418yescomplemented
21C42×C3⋊D3C2211yescharacteristic
22C3×#872—21no—
23C3×C42×D3—21no—
24C4×#627C2212yes—
25C4×#626—22no—
26#63902C2212yes—
27C4×#625C2212yes—
28#63881—22no—
29C4×D3×Dic3—21no—
30#63874C2211yescharacteristic
31#63874C2211yescharacteristic
32#63855—21no—
33#63838C2212yes—
34#63777C2212yes—
35#63777C2212yes—
36#63743C2212yes—
37#63742C2212yes—
38#63740C2212yes—
39#63740C2212yes—
40#63739C2212yes—
41#63739C2212yes—
42#5522—61no—
43C4×#235—61no—
44C2×C4×C3⋊D3D412yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—22no—
49C2×#627C2311yescharacteristic
50C2×#627C2311yescharacteristic
51C2×#626—21no—
52C2×#626—21no—
53C2×#625C2311yescharacteristic
54C2×#625C2311yescharacteristic
55C2×D3×Dic3—22no—
56#3798—22no—
57#3798—22no—
58#3798C2×C414yescomplemented
59#3798C2×C414yescomplemented
60C2×#622C2312yes—
61C2×#622C2311yescharacteristic
62C2×#622C2311yescharacteristic
63#3787—22no—
64#3787C2×C414yescomplemented
65#3776C2×C414yescomplemented
66#3775C2×C414yescomplemented
67#3775C2×C414yescomplemented
68#3774C2×C414yescomplemented
69C32×C42D411yescharacteristic
70C4×C3⋊Dic3D411yescharacteristic
71C4×C3⋊Dic3C2312yes—
72C3×(C2×D3)⋊C4—22no—
73C3×Dic3⋊C4—22no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—22no—
77#3724C2312yes—
78#3724C2312yes—
79Dic3⋊Dic3—22no—
80#3722—21no—
81#3722—21no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#2943—91nomaximal, Sylow
85C2×#235—61no—
86C2×#235—61no—
87C3×#117—61no—
88C2×C3×C42—61no—
89C4×#67—62no—
90C4×#67—62no—
91#926—61no—
92C2×C4×Dic3—61no—
93#893—62no—
94#887—62no—
95#67⋊C4—62no—
96#67⋊C4—62no—
97C4×D12—62no—
98#872—21no—
99#872—61no—
100#872—61no—
101#872—61no—
102C42×D3—21no—
103C42×D3—61no—
104C42×D3—61no—
105C42×D3—61no—
106C4×Dic6—62no—
107C22×C3⋊D3C2×D411yescharacteristic
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C2×C32×C4C2×D412yes—
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2411yescharacteristic
114C4×C3⋊D3—42no—
115C4×C3⋊D3C22×C412yes—
116C4×C3⋊D3#4112yes—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C3×C4×D3—24no—
122C3×C4×D3—24no—
123C3×C4×D3—44no—
124#627—21no—
125#627—21no—
126#627C22×C412yes—
127#627C22×C412yes—
128#626—24no—
129#626—24no—
130#625—21no—
131#625—21no—
132#625C22×C412yes—
133#625C22×C412yes—
134D3×Dic3—44no—
135#622—22no—
136#622C22×C412yes—
137#622C22×C412yes—
138C2×#135—91no—
139C4×#41—91no—
140C4×#41—91no—
141#442—92no—
142#441—92no—
143#440—92no—
144#440—92no—
145#427—91no—
146#416—91no—
147#416—91no—
148C2×#97—91no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4—62no—
152C2×#67—61no—
153C2×#67—61no—
154C2×#67—61no—
155C2×#67—61no—
156C22×Dic3—62no—
157#235—64no—
158#235—64no—
159#235—64no—
160#235—64no—
161C2×D12—61no—
162C2×D12—61no—
163C2×C4×D3—21no—
164C2×C4×D3—21no—
165C2×C4×D3—22no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×C4×D3—62no—
171C2×Dic6—61no—
172C2×Dic6—61no—
173C3×C4⋊C4—62no—
174C3×C22⋊C4—62no—
175C3×C42—21no—
176C3×C42—21no—
177C3×C42—62no—
178C3×C42—61no—
179C3×C42—61no—
180#217—62no—
181(C2×D3)⋊C4—22no—
182(C2×D3)⋊C4—62no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185C4⋊Dic3—62no—
186Dic3⋊C4—22no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190C4×Dic3—22no—
191C4×Dic3—21no—
192C4×Dic3—21no—
193C4×Dic3—62no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C4×Dic3—62no—
199C22×C32C22×D411yescharacteristic
200C2×C3⋊D3—22no—
201C2×C3⋊D3C4×D412yes—
202C2×C3×D3—22no—
203C2×C3×D3—22no—
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C32×C4—22no—
207C32×C4C4×D412yes—
208C3⋊Dic3—22no—
209C3⋊Dic3C23×C411yescharacteristic
210C3⋊Dic3C2×#4111yescharacteristic
211C3×Dic3—22no—
212C3×Dic3—22no—
213C3×Dic3—42no—
214C3×Dic3—42no—
215C2×#41—91no—
216C2×#41—91no—
217#135—98no—
218C2×Q16—91no—
219C2×SD16—91no—
220C2×SD16—91no—
221C2×D8—91no—
222C22×C8—91no—
223C22×C8—91no—
224C4×Q8—92no—
225C4×Q8—92no—
226C4×D4—92no—
227C4×D4—92no—
228C4×D4—182no—
229C4×D4—182no—
230#117—61no—
231#117—91no—
232#117—91no—
233#117—181no—
234C2×C42—61no—
235C2×C42—91no—
236C2×C42—181no—
237#107—92no—
238#106—92no—
239#103—92no—
240#103—92no—
241#102—92no—
242#102—92no—
243#97—92no—
244#97—92no—
245C23×C3—61no—
246C23×C3—61no—
247C22×D3—21no—
248C22×D3—21no—
249C22×D3—61no—
250C22×D3—61no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—64no—
256C2×C3×C4—64no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—124no—
262#67—62no—
263#67—62no—
264#67—64no—
265#67—64no—
266#67—62no—
267#67—62no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—62no—
276C2×Dic3—124no—
277D12—64no—
278D12—64no—
279C4×D3—24no—
280C4×D3—24no—
281C4×D3—44no—
282C4×D3—62no—
283C4×D3—62no—
284C4×D3—62no—
285C4×D3—62no—
286C4×D3—124no—
287C4×D3—124no—
288C4×D3—124no—
289Dic6—62no—
290Dic6—62no—
291Dic6—62no—
292Dic6—62no—
293C2×C32C2×C4×D411yescharacteristic
294C2×C32#57512yes—
295C3⋊D3—22no—
296C3×D3—42no—
297C3×D3—42no—
298#41—94no—
299#41—94no—
300#41—182no—
301#41—182no—
302C2×Q8—91no—
303C2×Q8—91no—
304C2×D4—91no—
305C2×D4—91no—
306C2×D4—181no—
307C2×D4—181no—
308C22×C4—61no—
309C22×C4—61no—
310C22×C4—62no—
311C22×C4—91no—
312C22×C4—92no—
313C22×C4—182no—
314Q16—94no—
315SD16—94no—
316SD16—94no—
317D8—94no—
318C2×C8—91no—
319C2×C8—91no—
320C2×C8—94no—
321C2×C8—92no—
322C2×C8—182no—
323C4⋊C4—62no—
324C4⋊C4—92no—
325C4⋊C4—92no—
326C4⋊C4—182no—
327C22⋊C4—62no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C22⋊C4—182no—
331C42—62no—
332C42—61no—
333C42—61no—
334C42—92no—
335C42—91no—
336C42—182no—
337C42GO+(4,𝔽2)11yescharacteristic
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—62no—
341C22×C3—62no—
342C22×C3—122no—
343C22×C3—122no—
344C2×D3—22no—
345C2×D3—22no—
346C2×D3—42no—
347C2×D3—42no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—122no—
351C2×D3—122no—
352C3×C4—24no—
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—42no—
356C3×C4—62no—
357C3×C4—62no—
358C3×C4—122no—
359C3×C4—122no—
360Dic3—22no—
361Dic3—22no—
362Dic3—42no—
363Dic3—42no—
364Dic3—61no—
365Dic3—61no—
366Dic3—61no—
367Dic3—61no—
368Dic3—64no—
369Dic3—122no—
370C32#294311yescharacteristic, complemented, Sylow
371C23—61no—
372C23—61no—
373C23—91no—
374Q8—92no—
375Q8—92no—
376Q8—181no—
377Q8—181no—
378D4—92no—
379D4—92no—
380D4—184no—
381D4—184no—
382D4—181no—
383D4—181no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—64no—
387C2×C4—64no—
388C2×C4—62no—
389C2×C4—62no—
390C2×C4—91no—
391C2×C4—92no—
392C2×C4—92no—
393C2×C4—92no—
394C2×C4—124no—
395C2×C4—362no—
396C2×C4—364no—
397C2×C4C2×GO+(4,𝔽2)12yes—
398C2×C4C2×GO+(4,𝔽2)11yescharacteristic
399C8—92no—
400C8—92no—
401C8—182no—
402C2×C3—22no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—122no—
407C2×C3—122no—
408D3—42no—
409D3—42no—
410D3—122no—
411D3—122no—
412C22—62no—
413C22—62no—
414C22—92no—
415C22—122no—
416C22—122no—
417C22—182no—
418C22C22×GO+(4,𝔽2)11yescharacteristic
419C4—22no—
420C4—62no—
421C4—62no—
422C4—91no—
423C4—91no—
424C4—122no—
425C4—122no—
426C4—182no—
427C4C4×GO+(4,𝔽2)12yes—
428C3—21no—
429C3—21no—
430C2—122no—
431C2—122no—
432C2—182no—
433C2#1059649912yes—
434C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#64223C2
cosocleC2×C3⋊Dic3C24
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2943
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593966C2semidirect
3. C4×#3798C2semidirect
4. #10593723C2semidirect
5. #10593432C2semidirect
6. #10593431C2semidirect
7. #10593419C2semidirect
8. #10593389C2semidirect
9. #10593369C2semidirect
10. #10593349C2semidirect
11. #10593349C2semidirect
20. #64223C4semidirect
58. #3798C2×C4semidirect
59. #3798C2×C4semidirect
64. #3787C2×C4semidirect
65. #3776C2×C4semidirect
66. #3775C2×C4semidirect
67. #3775C2×C4semidirect
68. #3774C2×C4semidirect
370. C32#2943semidirect

Maximal subgroups

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

subgroupindex
C2×#642232
#105939662
C4×#37982
#105937232
#105934322
#105934312
#105934192
#105933892
#105933692
#105933492
#29439