Finite Group Databasebeta

← #11779280

Subgroups — #11779280

Order 1152.

538 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 88 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#10596055C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3#10590355C211yesmaximal, characteristic
4#10590273C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71029—31nomaximal
9#68245—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64155—21no—
12#64107—22no—
13#64101—21no—
14#64084—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078C2211yescharacteristic
17C4×#634—21no—
18C2×C3×#215—21no—
19C3×#874C2211yescharacteristic
20C2×#3714—21no—
21C3×#809—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—22no—
26#63563—21no—
27#5584—31no—
28#5584—31no—
29#5584—61no—
30C3×#460—31no—
31#5072—31no—
32#5070—31no—
33#5027D311yescharacteristic, complemented
34#4843—31no—
35#4694—31no—
36C3×Q8⋊C8—31no—
37#4535D311yescharacteristic, complemented
38#4486—31no—
39#4483—31no—
40#4482—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×#634—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C42—21no—
52C32×C42C2311yescharacteristic
53#3752—22no—
54#3752—22no—
55#3752—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C4⋊(C3⋊Dic3)D412yes—
59#3750—22no—
60C4×C3⋊Dic3—22no—
61C3×#215—42no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3714—42no—
66#1628—91noSylow
67C2×C3×SD16—61no—
68C3×#127—31no—
69C3×C4×Q8—21no—
70C3×C4×Q8C2×D311yescharacteristic
71C3×C4×Q8C2×D311yescharacteristic
72#946—62no—
73#946—61no—
74#946—61no—
75C2×#215—21no—
76C2×#213—61no—
77C2×D24—61no—
78#898—62no—
79#898—62no—
80#898—64no—
81#892—62no—
82#892—61no—
83#892—61no—
84#875—61no—
85#875—61no—
86#875—62no—
87#874C2×D311yescharacteristic
88C4×D12—31no—
89C4×D12—31no—
90C4×D12—61no—
91#869—31no—
92#869—31no—
93#869—61no—
94C4×Dic6—61no—
95C4×Dic6—61no—
96C4×Dic6—62no—
97C3×C4⋊C8—31no—
98C3×C4⋊C8—31no—
99C3×#102—61no—
100C3×C4×C8—31no—
101#832—62no—
102#832—61no—
103#821—62no—
104#821—61no—
105#809—21no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊D3—21no—
110C22×C3×D3—41no—
111C32×Q8—21no—
112C32×Q8—21no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—22no—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)—21no—
122C4×C3⋊D3—41no—
123C4×C3⋊D3—41no—
124#634—41no—
125#634—41no—
126C3×D12—42no—
127C3×D12—41no—
128C3×D12—41no—
129C3×D12—41no—
130C3×D12—41no—
131C3×C3⋊C8—41no—
132C3×C3⋊C8—41no—
133C3×C3⋊C8—41no—
134#556—91no—
135#486—91no—
136#460—31no—
137#459—91no—
138#332—91no—
139Q8⋊C8—31no—
140D4⋊C8—91no—
141C2×C3×Q8—21no—
142C2×C3×Q8D1211yescharacteristic
143C2×C3×Q8#6711yescharacteristic
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—31no—
151C2×D12—31no—
152C2×D12—61no—
153C2×C4×D3—62no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×Dic6—62no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C3×SD16—122no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4D1211yescharacteristic
168C3×C4⋊C4#6711yescharacteristic
169C3×C42—22no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#215—42no—
176#213—122no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—64no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—64no—
182(C2×D3)⋊C4—62no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186C4⋊Dic3—31no—
187C4⋊Dic3—32no—
188C4⋊Dic3—31no—
189C4⋊Dic3—32no—
190C4⋊Dic3—61no—
191C4⋊Dic3—62no—
192C4⋊Dic3—62no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195Dic3⋊C4—64no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198C4×Dic3—64no—
199C4×Dic3—62no—
200C4×Dic3—62no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204D24—122no—
205C22×C32#12011yescharacteristic
206C2×C3⋊D3—41no—
207C2×C3⋊D3—41no—
208C2×C3⋊D3—41no—
209C2×C3×D3—81no—
210C2×C3×D3—81no—
211C2×C3×D3—81no—
212C32×C4—21no—
213C32×C4—41no—
214C32×C4—41no—
215C32×C4#13511yescharacteristic
216C32×C4#13511yescharacteristic
217C32×C4AGL(1,ℤ/8)11yescharacteristic
218C32×C4AGL(1,ℤ/8)11yescharacteristic
219C3⋊Dic3—42no—
220C3⋊Dic3—41no—
221C2×SD16—61no—
222C2×D8—181no—
223C4⋊Q8—91no—
224#127—31no—
225#126—182no—
226#124—181no—
227C22⋊Q8—181no—
228C4×Q8—181no—
229C4×Q8D3211yescharacteristic
230C4×D4—91no—
231#117—181no—
232C4⋊C8—31no—
233C4⋊C8—31no—
234#102—61no—
235#102—181no—
236#102—182no—
237C4×C8—31no—
238C23×C3—121no—
239C22×D3—41no—
240C22×D3—62no—
241C22×D3—61no—
242C22×D3—61no—
243C3×Q8—21no—
244C3×Q8—21no—
245C3×Q8—21no—
246C3×Q8—21no—
247C3×Q8—41no—
248C3×Q8—41no—
249C3×D4—122no—
250C3×D4—121no—
251C3×D4—121no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×Dic3—62no—
270C2×Dic3—64no—
271C2×Dic3—61no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—62no—
275D12—42no—
276D12—41no—
277D12—41no—
278D12—41no—
279D12—41no—
280D12—61no—
281D12—61no—
282D12—61no—
283D12—61no—
284D12—121no—
285D12—121no—
286C4×D3—122no—
287C4×D3—122no—
288C4×D3—121no—
289C4×D3—121no—
290C4×D3—121no—
291C4×D3—121no—
292Dic6—122no—
293Dic6—122no—
294Dic6—121no—
295Dic6—121no—
296Dic6—121no—
297Dic6—121no—
298C3×C8—121no—
299C3×C8—121no—
300C3×C8—121no—
301C3⋊C8—41no—
302C3⋊C8—41no—
303C3⋊C8—41no—
304C2×C32#44911yescharacteristic
305C2×C32#44911yescharacteristic
306C2×C32#45411yescharacteristic
307C3⋊D3—81no—
308C3×D3—161no—
309C2×Q8—181no—
310C2×Q8#62611yescharacteristic
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—61no—
314C2×D4—91no—
315C22×C4—181no—
316SD16—122no—
317D8—362no—
318C2×C8—61no—
319C2×C8—61no—
320C2×C8—61no—
321C4⋊C4—21no—
322C4⋊C4—91no—
323C4⋊C4—92no—
324C4⋊C4—182no—
325C4⋊C4—181no—
326C4⋊C4#62611yescharacteristic
327C22⋊C4—182no—
328C22⋊C4—182no—
329C22⋊C4—181no—
330C42—21no—
331C42—182no—
332C42C2×D3211yescharacteristic
333C22×C3—21no—
334C22×C3—241no—
335C22×C3—241no—
336C22×C3—241no—
337C22×C3#88211yescharacteristic
338C22×C3#93711yescharacteristic
339C2×D3—81no—
340C2×D3—81no—
341C2×D3—81no—
342C2×D3—122no—
343C2×D3—122no—
344C2×D3—122no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—121no—
349C2×D3—121no—
350C2×D3—121no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—41no—
358C3×C4—42no—
359C3×C4—42no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4#90411yescharacteristic
365C3×C4#90811yescharacteristic
366C3×C4#91411yescharacteristic
367C3×C4#91411yescharacteristic
368C3×C4#91611yescharacteristic
369C3×C4#91911yescharacteristic
370C3×C4#93211yescharacteristic
371C3×C4#95011yescharacteristic
372Dic3—124no—
373Dic3—122no—
374Dic3—122no—
375Dic3—121no—
376Dic3—121no—
377Dic3—122no—
378C32#162811yescharacteristic, complemented, Sylow
379C23—121no—
380C23—181no—
381Q8—21no—
382Q8—21no—
383Q8—361no—
384Q8—361no—
385D4—122no—
386D4—121no—
387D4—121no—
388D4—121no—
389D4—121no—
390D4—181no—
391D4—181no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—181no—
395C2×C4—182no—
396C2×C4—361no—
397C2×C4—361no—
398C2×C4C2×#62611yescharacteristic
399C2×C4#381111yescharacteristic
400C2×C4#381111yescharacteristic
401C8—121no—
402C8—121no—
403C8—121no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—481no—
408C2×C3#473411yescharacteristic
409C2×C3#481011yescharacteristic
410C2×C3#482711yescharacteristic
411C2×C3#503711yescharacteristic
412C2×C3#517211yescharacteristic
413C2×C3#520111yescharacteristic
414D3—161no—
415D3—242no—
416D3—241no—
417D3—241no—
418C22—241no—
419C22—241no—
420C22—241no—
421C22—361no—
422C22—361no—
423C22—361no—
424C22#6398111yescharacteristic
425C4—21no—
426C4—41no—
427C4—41no—
428C4—362no—
429C4—361no—
430C4#6382911yescharacteristic
431C4#6383011yescharacteristic
432C4#6394111yescharacteristic
433C4#6395011yescharacteristic
434C3—21no—
435C3#6824511yescharacteristic, complemented
436C3#7102911yescharacteristic, complemented
437C2—481no—
438C2—721no—
439C2#1059118211yescharacteristic
440C2#1059159311yescharacteristic
441C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#10590355C2
hypercenterC4×Q8D32
hypocenterC32#1628
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596055C2semidirect
2. C3×#5027C2semidirect
4. #10590273C2semidirect
5. C3×#4535C2semidirect
6. #10589094C2semidirect
7. #10589082C2semidirect
33. #5027D3semidirect
37. #4535D3semidirect
378. C32#1628semidirect
435. C3#68245semidirect
436. C3#71029semidirect

Maximal subgroups

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

subgroupindex
#105960552
C3×#50272
#105903552
#105902732
C3×#45352
#105890942
#105890822
#710293
#682453