Finite Group Databasebeta

← #11869470

Subgroups — #11869470

Order 1152.

846 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 111 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
2#10594969C211yesmaximal, characteristic, complemented
3#10593800C211yesmaximal, characteristic, complemented
4#10593494C214yesmaximal, complemented
5#10593396C211yesmaximal, characteristic, complemented
6#10593387C211yesmaximal, characteristic, complemented
7#10593365C211yesmaximal, characteristic, complemented
8#10593365C211yesmaximal, characteristic, complemented
9#10593351C214yesmaximal, complemented
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×#3811—21no—
12C2×#3802C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15C3×#930—21no—
16C3×#926—21no—
17#63980C2212yes—
18#63974—21no—
19#63957C2212yescomplemented
20#63921—21no—
21#63916—21no—
22#63912C2212yes—
23#63900C2211yescharacteristic
24#63900C2211yescharacteristic
25#63900C2211yescharacteristic
26C4×#624—21no—
27#63874C2212yescomplemented
28#63849—21no—
29C22⋊#622C2212yescomplemented
30#63778C2212yescomplemented
31#63743C2214yescomplemented
32#63742C2214yescomplemented
33#63739C2214yescomplemented
34#63739C2214yescomplemented
35D3×#121—61no—
36D3×#117—61no—
37C23×C3⋊D3D411yescharacteristic
38C22×D32—21no—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3C2311yescharacteristic
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C4×C3⋊D3C2311yescharacteristic
47C2×C3×#67—22no—
48C2×C3×D12—21no—
49#3811—44no—
50C2×#626—22no—
51C2×#625C2312yes—
52C2×#624—21no—
53C2×#624—21no—
54C2×#624—21no—
55#3802—22no—
56#3802—22no—
57C2×#622C2312yes—
58C2×#622C2312yes—
59#3787—22no—
60#3787—22no—
61C3×#217—22no—
62C3×(C2×D3)⋊C4—22no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4×Dic3—22no—
67#3724C2312yes—
68#3724C2312yes—
69#3724C2312yes—
70#3722—22no—
71(C2×D3)⋊Dic3—22no—
72Dic32—22no—
73C2×#482—91nomaximal, Sylow
74C2×D3×D4—61no—
75C2×D3×D4—62no—
76C22×C4×D3—61no—
77C22×C4×D3—61no—
78C3×#121—61no—
79C3×#117—61no—
80#939—62no—
81#938—61no—
82#930—21no—
83#926—21no—
84#895—61no—
85#892—61no—
86#892—61no—
87D3×C4⋊C4—61no—
88D3×C4⋊C4—61no—
89D3×C4⋊C4—61no—
90#884—62no—
91D3×C22⋊C4—62no—
92D3×C22⋊C4—62no—
93#877—62no—
94#872—62no—
95C42×D3—62no—
96C23×C32C2×D411yescharacteristic
97C22×C3⋊D3—22no—
98C22×C3⋊D3—22no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3C2×D411yescharacteristic
101C22×C3⋊D3C2×D411yescharacteristic
102C22×C3×D3—22no—
103C2×D32—42no—
104C2×D32—42no—
105C2×D32—42no—
106C2×C32×C4—22no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3C2×D411yescharacteristic
112C2×C3⋊Dic3C2411yescharacteristic
113C4×C3⋊D3—22no—
114C4×C3⋊D3—22no—
115C4×C3⋊D3—21no—
116C4×C3⋊D3—21no—
117C4×C3⋊D3#4112yes—
118C4×C3⋊D3#4112yes—
119C3×#67—44no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C3×D12—42no—
124#626—44no—
125#625—22no—
126#625—22no—
127#624—42no—
128#624—42no—
129#624—42no—
130#622—22no—
131#622—22no—
132C2×#121—91no—
133C2×#117—91no—
134#482—94no—
135#482—94no—
136C2×#107—91no—
137C2×#106—91no—
138C2×#102—91no—
139C2×#102—91no—
140C2×C22⋊C8—91no—
141C23×D3—61no—
142C23×D3—61no—
143C23×D3—62no—
144C2×C3×D4—61no—
145C2×C3×D4—62no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C2×#67—22no—
149C2×#67—62no—
150C2×#67—62no—
151C22×Dic3—61no—
152C22×Dic3—61no—
153D3×D4—122no—
154D3×D4—122no—
155D3×D4—128no—
156C2×D12—21no—
157C2×D12—62no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—64no—
167C2×C4×D3—64no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×C4×D3—62no—
171C2×C4×D3—122no—
172C2×C4×D3—122no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—62no—
178C3×C42—62no—
179#217—22no—
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—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191C4×Dic3—22no—
192C4×Dic3—62no—
193C4×Dic3—62no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32C22×D411yescharacteristic
198C2×C3⋊D3—21no—
199C2×C3⋊D3—21no—
200C2×C3⋊D3—21no—
201C2×C3⋊D3—44no—
202C2×C3⋊D3#12312yes—
203C2×C3⋊D3#13512yes—
204C2×C3⋊D3AGL(1,ℤ/8)12yes—
205C2×C3×D3—42no—
206C2×C3×D3—42no—
207C2×C3×D3—42no—
208D32—84no—
209C32×C4—21no—
210C32×C4#12312yes—
211C3⋊Dic3—21no—
212C3⋊Dic3C2×#4111yescharacteristic
213C3⋊Dic3C2×#4111yescharacteristic
214C3×Dic3—42no—
215C3×Dic3—42no—
216C3×Dic3—42no—
217C22×D4—91no—
218C22×D4—181no—
219C23×C4—91no—
220C22×C8—91no—
221C22×C8—91no—
222#121—61no—
223#121—92no—
224#121—92no—
225#121—181no—
226#117—61no—
227#117—92no—
228#117—92no—
229#117—181no—
230C2×C4⋊C4—91no—
231C2×C4⋊C4—91no—
232C2×C4⋊C4—91no—
233C2×C22⋊C4—181no—
234C2×C22⋊C4—181no—
235C2×C42—181no—
236#107—94no—
237#106—94no—
238#102—94no—
239#102—94no—
240C22⋊C8—92no—
241C22⋊C8—92no—
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—62no—
245C22×D3—22no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3—61no—
249C22×D3—61no—
250C22×D3—64no—
251C22×D3—64no—
252C22×D3—122no—
253C22×D3—122no—
254C22×D3—122no—
255C22×D3—122no—
256C22×D3—124no—
257C22×D3—124no—
258C22×D3—124no—
259C3×D4—122no—
260C3×D4—124no—
261C2×C3×C4—24no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—42no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270#67—44no—
271#67—122no—
272#67—122no—
273#67—124no—
274C2×Dic3—22no—
275C2×Dic3—22no—
276C2×Dic3—22no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285D12—42no—
286D12—124no—
287C4×D3—62no—
288C4×D3—62no—
289C4×D3—62no—
290C4×D3—62no—
291C4×D3—62no—
292C4×D3—62no—
293C4×D3—64no—
294C4×D3—64no—
295C4×D3—121no—
296C4×D3—121no—
297C4×D3—122no—
298C4×D3—122no—
299C4×D3—124no—
300C4×D3—124no—
301C4×D3—124no—
302C2×C32—41no—
303C2×C32C2×#12311yescharacteristic
304C2×C32C2×#13511yescharacteristic
305C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
306C3⋊D3—41no—
307C3⋊D3#48214yescomplemented
308C3×D3—82no—
309C24—91no—
310C24—181no—
311C2×D4—62no—
312C2×D4—61no—
313C2×D4—92no—
314C2×D4—182no—
315C2×D4—182no—
316C2×D4—182no—
317C2×D4—364no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—182no—
324C22×C4—182no—
325C22×C4—181no—
326C22×C4—181no—
327C22×C4—181no—
328C22×C4GO+(4,𝔽2)11yescharacteristic
329C2×C8—92no—
330C2×C8—92no—
331C2×C8—182no—
332C2×C8—182no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—92no—
337C4⋊C4—92no—
338C4⋊C4—92no—
339C22⋊C4—62no—
340C22⋊C4—62no—
341C22⋊C4—182no—
342C22⋊C4—182no—
343C42—62no—
344C42—182no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—122no—
354C22×C3—122no—
355C22×C3—122no—
356C2×D3—42no—
357C2×D3—42no—
358C2×D3—42no—
359C2×D3—62no—
360C2×D3—62no—
361C2×D3—62no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—62no—
366C2×D3—62no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—121no—
371C2×D3—128no—
372C2×D3—128no—
373C2×D3—248no—
374C3×C4—22no—
375C3×C4—22no—
376C3×C4—22no—
377C3×C4—41no—
378C3×C4—122no—
379C3×C4—122no—
380C3×C4—122no—
381Dic3—42no—
382Dic3—42no—
383Dic3—42no—
384Dic3—61no—
385Dic3—61no—
386Dic3—61no—
387Dic3—61no—
388Dic3—62no—
389Dic3—121no—
390C32C2×#48211yescharacteristic, complemented, Sylow
391C23—62no—
392C23—91no—
393C23—91no—
394C23—182no—
395C23—182no—
396C23—182no—
397C23—362no—
398C23—362no—
399C23—362no—
400C23C2×GO+(4,𝔽2)11yescharacteristic
401D4—124no—
402D4—122no—
403D4—182no—
404D4—182no—
405D4—364no—
406C2×C4—22no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—91no—
411C2×C4—92no—
412C2×C4—92no—
413C2×C4—91no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4—182no—
417C2×C4—181no—
418C2×C4—181no—
419C2×C4—182no—
420C2×C4—362no—
421C2×C4—362no—
422C2×C4—362no—
423C2×C4C2×GO+(4,𝔽2)11yescharacteristic
424C2×C4C2×GO+(4,𝔽2)11yescharacteristic
425C8—182no—
426C8—182no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—42no—
434C2×C3—42no—
435C2×C3—242no—
436D3—64no—
437D3—64no—
438D3—82no—
439D3—122no—
440D3—122no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—92no—
445C22—92no—
446C22—92no—
447C22—122no—
448C22—122no—
449C22—122no—
450C22—181no—
451C22—181no—
452C22—181no—
453C22—364no—
454C22—724no—
455C22C22×GO+(4,𝔽2)11yescharacteristic
456C4—21no—
457C4—91no—
458C4—91no—
459C4—122no—
460C4—122no—
461C4—122no—
462C4—181no—
463C4#6423312yes—
464C3—21no—
465C3—21no—
466C2—41no—
467C2—94no—
468C2—242no—
469C2—361no—
470C2#1059650011yescharacteristic
471C2#1059650111yescharacteristic
472C2C2×#6423311yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radical#10595081C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#482
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10594969C2semidirect
3. #10593800C2semidirect
4. #10593494C2semidirect
5. #10593396C2semidirect
6. #10593387C2semidirect
7. #10593365C2semidirect
8. #10593365C2semidirect
9. #10593351C2semidirect
19. #63957C22semidirect
27. #63874C22semidirect
29. C22⋊#622C22semidirect
30. #63778C22semidirect
31. #63743C22semidirect
32. #63742C22semidirect
33. #63739C22semidirect
34. #63739C22semidirect
307. C3⋊D3#482semidirect
390. C32C2×#482semidirect

Maximal subgroups

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

subgroupindex
#105950812
#105949692
#105938002
#105934942
#105933962
#105933872
#105933652
#105933512
C2×#4829