Finite Group Databasebeta

← #11779064

Subgroups — #11779064

Order 1152.

491 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 491 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593856C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic
3#10590377C211yesmaximal, characteristic
4#10590375C211yesmaximal, characteristic
5#10589350C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71033—31nomaximal
9#68504—31nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×#204—21no—
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63919—21no—
16#63918—21no—
17#63844—21no—
18#63843—21no—
19#63839—22no—
20C2×#3716—21no—
21C2×#3715—22no—
22C32×C4⋊C8C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#821—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26#63563—21no—
27#5722—31no—
28Q8×Dic6—31no—
29C3×#460—31no—
30#5085—31no—
31#5076—31no—
32#5075—31no—
33#4848—31no—
34#4848D311yescharacteristic
35C3×#333—31no—
36#4535—31no—
37#4484—31no—
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4481D311yescharacteristic, complemented
42C2×#634D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D412yes—
48C2×#627—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C3×#204—42no—
62#3724—22no—
63Dic3⋊Dic3—22no—
64Dic32—22no—
65#3716—42no—
66#3715—44no—
67#1623—91noSylow
68C2×C3×SD16—61no—
69C3×C4⋊Q8—31no—
70C3×#127—31no—
71C3×C4×Q8—31no—
72Q8×Dic3—61no—
73#944—62no—
74C2×#215—62no—
75C2×#214—61no—
76C2×#214—62no—
77C2×#204—21no—
78C2×#204—61no—
79#888—61no—
80#888—61no—
81#888—62no—
82#888—61no—
83#887—61no—
84#887—61no—
85#874C2×D311yescharacteristic
86#869—61no—
87#869C2×D311yescharacteristic
88C4×Dic6—31no—
89C4×Dic6—31no—
90C4×Dic6—61no—
91C4×Dic6—61no—
92C4×Dic6C2×D311yescharacteristic
93C3×C4⋊C8—21no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8C2×D311yescharacteristic
96C3×C4⋊C8C2×D311yescharacteristic
97C3×#102—61no—
98#832—61no—
99#821—21no—
100#821—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C22×C3×D3—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111#634—21no—
112#634SD1612yescomplemented
113C2×C3×Dic3—21no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—21no—
116C3×D12—42no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×Dic6—21no—
122C3×Dic6—42no—
123C3×Dic6SD1612yescomplemented
124#627—82no—
125C32×C8—41no—
126C3⋊(C3⋊C8)—22no—
127C3×C3⋊C8—41no—
128Q82—91no—
129#492—91no—
130#460—31no—
131#460—91no—
132#333—31no—
133Q8⋊C8—91no—
134Q8⋊C8—91no—
135C2×C3×Q8—31no—
136C2×C3×Q8—32no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×D12—21no—
141C2×D12—21no—
142C2×D12—21no—
143C2×Dic6—31no—
144C2×Dic6—31no—
145C2×Dic6—61no—
146C2×Dic6—62no—
147C2×Dic6—62no—
148C2×Dic6D1212yes—
149C2×Dic6#6711yescharacteristic
150C3×SD16—122no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—41no—
154C2×C3×C8—61no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C42—21no—
160C3×C42—61no—
161C3×C42C22×D311yescharacteristic
162C3×C42C22×D311yescharacteristic
163#215—124no—
164#214—122no—
165#214—124no—
166C4⋊Dic3—21no—
167C4⋊Dic3—21no—
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—61no—
171C4⋊Dic3—62no—
172C4⋊Dic3#6711yescharacteristic
173Dic3⋊C4—21no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—121no—
180C4×Dic3—21no—
181C4×Dic3—62no—
182C4×Dic3—62no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—121no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—121no—
190#204—42no—
191#204—122no—
192C22×C32#12011yescharacteristic
193C2×C3×D3—81no—
194C2×C3×D3—81no—
195C2×C3×D3—81no—
196C32×C4—21no—
197C32×C4C2×SD1611yescharacteristic
198C32×C4C2×SD1611yescharacteristic
199C32×C4#13711yescharacteristic
200C32×C4#13711yescharacteristic
201C3⋊Dic3—22no—
202C3⋊Dic3—41no—
203C3×Dic3—22no—
204C3×Dic3—41no—
205C3×Dic3—42no—
206C2×SD16—61no—
207C2×SD16—181no—
208C2×SD16—182no—
209C4⋊Q8—31no—
210C4⋊Q8—181no—
211C4⋊Q8—181no—
212C4⋊Q8—182no—
213#127—31no—
214C4×Q8—31no—
215C4×Q8—91no—
216C4×Q8—181no—
217C4×Q8—181no—
218C4⋊C8—31no—
219C4⋊C8D3211yescharacteristic
220#102—61no—
221#102—181no—
222C4×C8—91no—
223C23×C3—121no—
224C22×D3—41no—
225C3×Q8—32no—
226C3×Q8—61no—
227C3×Q8—122no—
228C3×D4—122no—
229C3×D4—121no—
230C3×D4—121no—
231C3×D4—121no—
232C3×D4—121no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4—62no—
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—22no—
247C2×Dic3—21no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—121no—
253C2×Dic3—121no—
254D12—42no—
255D12—41no—
256D12—41no—
257D12—41no—
258D12—41no—
259Dic6—21no—
260Dic6—32no—
261Dic6—32no—
262Dic6—42no—
263Dic6—62no—
264Dic6—61no—
265Dic6—61no—
266Dic6—121no—
267Dic6—242no—
268Dic6—242no—
269Dic6#21412yescomplemented
270C3×C8—41no—
271C3×C8—41no—
272C3×C8—81no—
273C3×C8—121no—
274C3⋊C8—41no—
275C3⋊C8—62no—
276C3⋊C8—62no—
277C3⋊C8—122no—
278C2×C32#44811yescharacteristic
279C2×C32#44811yescharacteristic
280C2×C32#45311yescharacteristic
281C3×D3—161no—
282C2×Q8—32no—
283C2×Q8—31no—
284C2×Q8—91no—
285C2×Q8—182no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289SD16—122no—
290SD16—362no—
291SD16—364no—
292C2×C8—21no—
293C2×C8—61no—
294C2×C8—181no—
295C4⋊C4—31no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—91no—
300C4⋊C4—182no—
301C4⋊C4—182no—
302C4⋊C4—181no—
303C42—61no—
304C42—182no—
305C42—181no—
306C42C2×D3211yescharacteristic
307C22×C3—21no—
308C22×C3—241no—
309C22×C3—241no—
310C22×C3—241no—
311C22×C3#88211yescharacteristic
312C22×C3#93711yescharacteristic
313C2×D3—81no—
314C2×D3—81no—
315C2×D3—81no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—41no—
323C3×C4—62no—
324C3×C4—122no—
325C3×C4—121no—
326C3×C4D3×SD1611yescharacteristic
327C3×C4D3×SD1611yescharacteristic
328C3×C4D3×SD1611yescharacteristic
329C3×C4#91511yescharacteristic
330C3×C4#91811yescharacteristic
331C3×C4#91811yescharacteristic
332C3×C4C2×#21411yescharacteristic
333C3×C4#95111yescharacteristic
334Dic3—22no—
335Dic3—41no—
336Dic3—42no—
337Dic3—62no—
338Dic3—62no—
339Dic3—122no—
340Dic3—121no—
341Dic3—121no—
342Dic3—241no—
343C32#162311yescharacteristic, complemented, Sylow
344C23—121no—
345Q8—32no—
346Q8—61no—
347Q8—92no—
348Q8—122no—
349Q8—181no—
350Q8—722no—
351D4—122no—
352D4—121no—
353D4—121no—
354D4—121no—
355D4—121no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—62no—
359C2×C4—181no—
360C2×C4—181no—
361C2×C4D3×D1211yescharacteristic
362C2×C4#380211yescharacteristic
363C2×C4D3×#6711yescharacteristic
364C8—41no—
365C8—121no—
366C8—182no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—481no—
371C2×C3#474711yescharacteristic
372C2×C3#480611yescharacteristic
373C2×C3#480611yescharacteristic
374C2×C3#504011yescharacteristic
375C2×C3#517011yescharacteristic
376C2×C3#519811yescharacteristic
377D3—161no—
378C22—241no—
379C22—241no—
380C22—241no—
381C22#6392211yescharacteristic
382C4—21no—
383C4—62no—
384C4—122no—
385C4—121no—
386C4—182no—
387C4—361no—
388C4#6379611yescharacteristic
389C4#6381111yescharacteristic
390C4D3×#21411yescharacteristic
391C4#6394311yescharacteristic
392C3—21no—
393C3#6850411yescharacteristic, complemented
394C3#7103311yescharacteristic, complemented
395C2—481no—
396C2#1059060311yescharacteristic
397C2#1059082411yescharacteristic
398C2#1059101411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1623
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593856C2semidirect
5. #10589350C2semidirect
6. C3×#4481C2semidirect
7. #10589083C2semidirect
41. #4481D3semidirect
112. #634SD16semidirect
123. C3×Dic6SD16semidirect
269. Dic6#214semidirect
343. C32#1623semidirect
393. C3#68504semidirect
394. C3#71033semidirect

Maximal subgroups

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

subgroupindex
#105938562
C3×#48482
#105903772
#105903752
#105893502
C3×#44812
#105890832
#710333
#685043