Finite Group Databasebeta

← #11861129

Subgroups — #11861129

Order 1152.

722 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 147 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#10596499C211yesmaximal, characteristic
2C2×#63805C211yesmaximal, characteristic, complemented
3#10594669C211yesmaximal, characteristic, complemented
4#10593765C211yesmaximal, characteristic, complemented
5#10593330C211yesmaximal, characteristic, complemented
6#10593324C211yesmaximal, characteristic, complemented
7#10593323C211yesmaximal, characteristic, complemented
8#10593299C214yesmaximal, complemented
9#10593298C214yesmaximal, complemented
10#64306C2211yescharacteristic
11C2×#3798C2211yescharacteristic
12#64286C2211yescharacteristic
13#64283C2211yescharacteristic
14#64239C412yescomplemented
15#64236C412yescomplemented
16#64226C412yescomplemented
17#64224C412yescomplemented
18#64223C2214yes—
19C2×C8×C3⋊D3C2211yescharacteristic
20C3×#901—21no—
21C2×C3×ΓL(1,𝔽25)—21no—
22C2×#3712C2211yescharacteristic
23#63818C2211yescharacteristic
24#63815—21no—
25C2×D3×C3⋊C8—21no—
26#63805—21no—
27#63805—21no—
28#63805C2212yescomplemented
29#63805C2212yescomplemented
30#63805C2212yescomplemented
31#63803C2212yescomplemented
32#63791—21no—
33D32×C8—21no—
34#63767C2212yescomplemented
35C8×#157C2212yescomplemented
36#63733C2214yescomplemented
37#63731C2214yescomplemented
38#63731C2214yescomplemented
39D3×#131—61no—
40C2×#907—61no—
41C2×C4×C3⋊D3C2311yescharacteristic
42C3×#235—21no—
43C2×C3×C4×D3—21no—
44#3811—21no—
45C2×#627C2×C411yescharacteristic
46C2×#626—21no—
47C2×#625C2×C411yescharacteristic
48#3805C2×C412yes—
49#3802C2×C411yescharacteristic
50C4×D32—21no—
51#3798—21no—
52#3798—21no—
53#3798C2×C412yes—
54#3798C2312yes—
55#3798C2312yes—
56#3797C2×C411yescharacteristic
57#3796—21no—
58C22⋊#157—21no—
59#3792C2×C412yes—
60C4⋊#157—21no—
61C4×#157C2312yes—
62#3788C2×C412yes—
63#3787C2312yes—
64#3776C2×C414yes—
65#3775C2×C414yes—
66#3775C2×C414yes—
67#3774C2×C414yes—
68C2×C32×C8D411yescharacteristic
69C2×C3⋊(C3⋊C8)D411yescharacteristic
70C8×C3⋊D3D411yescharacteristic
71C8×C3⋊D3D411yescharacteristic
72C8×C3⋊D3C2311yescharacteristic
73C8×C3⋊D3C2311yescharacteristic
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76C3×ΓL(1,𝔽25)—22no—
77C3×ΓL(1,𝔽25)—22no—
78C3×ΓL(1,𝔽25)—22no—
79C3×D3×C8—22no—
80#3712—21no—
81#3712C2312yes—
82#3712C2312yes—
83#3711—22no—
84#3710—21no—
85D3×C3⋊C8—22no—
86D3×C3⋊C8—22no—
87D3×C3⋊C8—22no—
88#2955—91nomaximal, Sylow
89D3×#41—61no—
90C2×#235—61no—
91C3×#131—61no—
92C2×C3×M16—61no—
93#948—61no—
94C22×C3⋊C8—61no—
95#907—62no—
96#907—62no—
97#907—62no—
98#907—62no—
99#907—62no—
100#907—61no—
101D3×M16—61no—
102D3×M16—62no—
103#901—21no—
104#901—62no—
105C2×ΓL(1,𝔽25)—21no—
106C2×ΓL(1,𝔽25)—61no—
107C2×D3×C8—61no—
108C2×D3×C8—61no—
109C2×D3×C8—62no—
110C2×D3×C8—61no—
111C22×C3⋊D3#4111yescharacteristic
112C22×C3×D3—21no—
113C2×D32—21no—
114C2×#157—22no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3C22×C411yescharacteristic
117C4×C3⋊D3C22×C411yescharacteristic
118C4×C3⋊D3C2×D411yescharacteristic
119C4×C3⋊D3#4111yescharacteristic
120C4×C3⋊D3C2411yescharacteristic
121C3×#67—22no—
122C2×C3×Dic3—21no—
123C3×D12—21no—
124C3×C4×D3—22no—
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×Dic6—21no—
128#627—21no—
129#627C22×C412yes—
130#627C22×C412yes—
131#626—22no—
132#626—22no—
133#626—22no—
134#625—21no—
135#625C22×C412yes—
136#625C22×C412yes—
137#624—21no—
138D3×Dic3—22no—
139#622C22×C414yes—
140C32×C8C2×D411yescharacteristic
141C32×C8C2×D411yescharacteristic
142C3⋊(C3⋊C8)C2×D411yescharacteristic
143C3⋊(C3⋊C8)C2×D411yescharacteristic
144C3×C3⋊C8—22no—
145C3×C3⋊C8—22no—
146#575—91no—
147C2×#131—91no—
148C2×#131—91no—
149#444—94no—
150#443—94no—
151#430—91no—
152#421—91no—
153#421—91no—
154#405—91no—
155C3×#41—61no—
156C22×C3×C4—61no—
157C2×#67—61no—
158C2×#67—61no—
159#239—61no—
160D3×Q8—61no—
161#237—62no—
162#237—61no—
163D3×D4—61no—
164D3×D4—62no—
165#235—21no—
166#235—62no—
167#235—62no—
168#235—62no—
169#235—62no—
170#235—62no—
171C2×D12—61no—
172C2×C4×D3—21no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—62no—
176C2×Dic6—61no—
177C3×M16—62no—
178C3×M16—62no—
179C3×M16—62no—
180C3×M16—61no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—62no—
184C2×C3×C8—61no—
185#208—21no—
186#208—62no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—62no—
192C2×C3⋊C8—62no—
193ΓL(1,𝔽25)—22no—
194ΓL(1,𝔽25)—22no—
195ΓL(1,𝔽25)—22no—
196ΓL(1,𝔽25)—62no—
197ΓL(1,𝔽25)—62no—
198ΓL(1,𝔽25)—62no—
199ΓL(1,𝔽25)—62no—
200D3×C8—22no—
201D3×C8—61no—
202D3×C8—61no—
203D3×C8—61no—
204D3×C8—61no—
205D3×C8—61no—
206D3×C8—61no—
207D3×C8—61no—
208D3×C8—61no—
209D3×C8—62no—
210D3×C8—62no—
211D3×C8—62no—
212D3×C8—62no—
213C22×C32C4×D411yescharacteristic
214C2×C3⋊D3—41no—
215C2×C3⋊D3C4×D411yescharacteristic
216C2×C3⋊D3C2×#4111yescharacteristic
217C2×C3×D3—22no—
218C2×C3×D3—22no—
219C2×C3×D3—42no—
220D32—42no—
221#157—42no—
222C32×C4C4×D411yescharacteristic
223C32×C4C22×D411yescharacteristic
224C3⋊Dic3C4×D411yescharacteristic
225C3⋊Dic3C23×C411yescharacteristic
226C3×Dic3—22no—
227C3×Dic3—22no—
228C2×#41—91no—
229C2×#41—91no—
230#137—92no—
231#137—92no—
232AGL(1,ℤ/8)—92no—
233AGL(1,ℤ/8)—92no—
234#135—94no—
235#131—61no—
236#131—92no—
237#131—92no—
238#131—92no—
239#131—92no—
240#131—181no—
241#131—181no—
242#131—181no—
243C2×M16—61no—
244C2×M16—91no—
245C2×M16—91no—
246C2×M16—91no—
247C2×M16—181no—
248C22×C8—91no—
249C22×C8—181no—
250C22×C8—181no—
251#117—91no—
252#108—94no—
253#104—94no—
254#104—94no—
255#97—92no—
256C4×C8—92no—
257C23×C3—61no—
258C22×D3—21no—
259C22×D3—61no—
260C22×D3—61no—
261C22×D3—62no—
262C3×Q8—61no—
263C3×D4—61no—
264C3×D4—62no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—61no—
271#67—22no—
272#67—62no—
273#67—62no—
274#67—62no—
275#67—62no—
276#67—62no—
277#67—62no—
278C2×Dic3—21no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—62no—
282D12—21no—
283D12—62no—
284D12—62no—
285D12—62no—
286C4×D3—22no—
287C4×D3—22no—
288C4×D3—22no—
289C4×D3—61no—
290C4×D3—61no—
291C4×D3—61no—
292C4×D3—61no—
293C4×D3—61no—
294C4×D3—61no—
295C4×D3—61no—
296C4×D3—61no—
297C4×D3—62no—
298C4×D3—62no—
299Dic6—21no—
300Dic6—62no—
301Dic6—62no—
302Dic6—62no—
303C3×C8—21no—
304C3×C8—21no—
305C3×C8—21no—
306C3×C8—21no—
307C3×C8—62no—
308C3×C8—62no—
309C3⋊C8—22no—
310C3⋊C8—22no—
311C3⋊C8—61no—
312C3⋊C8—61no—
313C3⋊C8—61no—
314C3⋊C8—61no—
315C2×C32—21no—
316C2×C32C2×C4×D411yescharacteristic
317C3⋊D3—21no—
318C3⋊D3—21no—
319C3×D3—42no—
320C3×D3—42no—
321#41—61no—
322#41—92no—
323#41—92no—
324#41—92no—
325#41—92no—
326#41—181no—
327#41—181no—
328#41—181no—
329C2×Q8—91no—
330C2×Q8—91no—
331C2×D4—91no—
332C2×D4—91no—
333C2×D4—181no—
334C2×D4—181no—
335C22×C4—61no—
336C22×C4—91no—
337C22×C4—181no—
338Q16—94no—
339SD16—94no—
340SD16—94no—
341D8—94no—
342M16—61no—
343M16—62no—
344M16—62no—
345M16—62no—
346M16—92no—
347M16—92no—
348M16—92no—
349M16—92no—
350M16—181no—
351M16—182no—
352C2×C8—61no—
353C2×C8—62no—
354C2×C8—92no—
355C2×C8—91no—
356C2×C8—91no—
357C2×C8—91no—
358C2×C8—91no—
359C2×C8—91no—
360C2×C8—181no—
361C2×C8—182no—
362C2×C8—182no—
363C2×C8—182no—
364C2×C8GO+(4,𝔽2)11yescharacteristic
365C4⋊C4—181no—
366C22⋊C4—181no—
367C42—92no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—62no—
371C22×C3—62no—
372C22×C3—122no—
373C2×D3—22no—
374C2×D3—22no—
375C2×D3—42no—
376C2×D3—61no—
377C2×D3—61no—
378C2×D3—61no—
379C2×D3—61no—
380C2×D3—124no—
381C2×D3—122no—
382C2×D3—122no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—62no—
388C3×C4—62no—
389Dic3—22no—
390Dic3—22no—
391Dic3—61no—
392Dic3—61no—
393Dic3—61no—
394Dic3—61no—
395C32#295511yescharacteristic, complemented, Sylow
396C23—61no—
397C23—91no—
398C23—181no—
399Q8—61no—
400Q8—92no—
401Q8—92no—
402Q8—181no—
403D4—62no—
404D4—61no—
405D4—92no—
406D4—92no—
407D4—182no—
408D4—182no—
409D4—182no—
410D4—181no—
411C2×C4—61no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—91no—
416C2×C4—91no—
417C2×C4—91no—
418C2×C4—91no—
419C2×C4—91no—
420C2×C4—181no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4C2×GO+(4,𝔽2)11yescharacteristic
424C8—62no—
425C8—62no—
426C8—94no—
427C8—91no—
428C8—91no—
429C8C2×GO+(4,𝔽2)11yescharacteristic
430C8C2×GO+(4,𝔽2)11yescharacteristic
431C2×C3—22no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—122no—
436C2×C3—122no—
437D3—42no—
438D3—42no—
439D3—62no—
440D3—121no—
441D3—121no—
442D3—121no—
443C22—62no—
444C22—62no—
445C22—91no—
446C22—91no—
447C22—122no—
448C22—361no—
449C22—362no—
450C22C4×GO+(4,𝔽2)11yescharacteristic
451C4—62no—
452C4—62no—
453C4—91no—
454C4—91no—
455C4—362no—
456C4C4×GO+(4,𝔽2)11yescharacteristic
457C4C22×GO+(4,𝔽2)11yescharacteristic
458C3—21no—
459C3—21no—
460C2—21no—
461C2—122no—
462C2—122no—
463C2—181no—
464C2—181no—
465C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC2×C32×C8D4
socleC2×C32C2×C4×D4
prime radical#10596499C2
cosocleC4×C3⋊D3C24
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2955
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63805C2semidirect
3. #10594669C2semidirect
4. #10593765C2semidirect
5. #10593330C2semidirect
6. #10593324C2semidirect
7. #10593323C2semidirect
8. #10593299C2semidirect
9. #10593298C2semidirect
14. #64239C4semidirect
15. #64236C4semidirect
16. #64226C4semidirect
17. #64224C4semidirect
28. #63805C22semidirect
29. #63805C22semidirect
30. #63805C22semidirect
31. #63803C22semidirect
34. #63767C22semidirect
35. C8×#157C22semidirect
36. #63733C22semidirect
37. #63731C22semidirect
38. #63731C22semidirect
395. C32#2955semidirect

Maximal subgroups

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

subgroupindex
#105964992
C2×#638052
#105946692
#105937652
#105933302
#105933242
#105933232
#105932992
#105932982
#29559