Finite Group Databasebeta

← #11779059

Subgroups — #11779059

Order 1152.

491 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 491 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic
3#10590375C211yesmaximal, characteristic
4#10590364C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71939—31nomaximal
9#71033—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×Q8×Dic3—21no—
12C2×C3×#215—21no—
13C3×#888—22no—
14C3×#888—21no—
15C3×#874C2211yescharacteristic
16C3×#869—21no—
17C3×#869C2211yescharacteristic
18C3×C4×Dic6—21no—
19C3×C4×Dic6C2211yescharacteristic
20C2×#3715—21no—
21C2×#3715—22no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#809—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26#63562—21no—
27C3×Q82—31no—
28Q8×Dic6D311yescharacteristic, complemented
29C3×#460—31no—
30#5085—31no—
31#5076—31no—
32#5075—31no—
33#5027—31no—
34#5027D311yescharacteristic
35#4546—31no—
36#4535—31no—
37#4535—31no—
38#4535—31no—
39#4535—61no—
40#4484—31no—
41#4481—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6D411yescharacteristic
48C2×C3×Dic6D412yes—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C42—21no—
52C32×C42C2311yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#215—42no—
56C3×C4⋊Dic3—22no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—22no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65#3715—44no—
66#3715—42no—
67#1623—91noSylow
68C2×C3×SD16—61no—
69C3×C4⋊Q8—31no—
70C3×C4⋊Q8—61no—
71C3×C4⋊Q8—62no—
72C3×C4⋊Q8—61no—
73C3×#127—31no—
74C3×C4×Q8—21no—
75C3×C4×Q8—31no—
76C3×C4×Q8—61no—
77C3×C4×Q8—61no—
78C3×C4×Q8C2×D311yescharacteristic
79C3×C4×Q8C2×D311yescharacteristic
80Q8×Dic3—21no—
81C2×#215—21no—
82C2×#215—61no—
83C2×#215—62no—
84C2×#214—61no—
85C2×#214—62no—
86#888—22no—
87#888—21no—
88#874C2×D311yescharacteristic
89#869—21no—
90#869C2×D311yescharacteristic
91C4×Dic6—21no—
92C4×Dic6C2×D311yescharacteristic
93C3×C4⋊C8—31no—
94C3×#102—61no—
95#832—61no—
96#809—21no—
97#809—61no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C22×C3×D3—41no—
106C32×Q8—21no—
107C32×Q8SD1612yescomplemented
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
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×Dic6—82no—
124C3×Dic6SD1612yescomplemented
125C3⋊(C3⋊C8)—22no—
126C3⋊(C3⋊C8)—41no—
127C3×C3⋊C8—41no—
128Q82—31no—
129#492—91no—
130#460—31no—
131#460—91no—
132#333—91no—
133Q8⋊C8—91no—
134Q8⋊C8—91no—
135C2×C3×Q8—21no—
136C2×C3×Q8—31no—
137C2×C3×Q8—32no—
138C2×C3×Q8—62no—
139C2×C3×Q8#6711yescharacteristic
140C2×C3×Q8#6711yescharacteristic
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×D12—21no—
145C2×D12—21no—
146C2×D12—21no—
147C2×Dic6—22no—
148C2×Dic6#6711yescharacteristic
149C2×Dic6#6712yes—
150C3×SD16—122no—
151C2×C3×C8—61no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—62no—
158C3×C4⋊C4—62no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4#6711yescharacteristic
163C3×C4⋊C4#6711yescharacteristic
164C3×C42—21no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—41no—
168C3×C42—62no—
169C3×C42—61no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#215—42no—
173#215—124no—
174#215—122no—
175#214—124no—
176#214—122no—
177C4⋊Dic3—22no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3#6711yescharacteristic
181Dic3⋊C4—22no—
182Dic3⋊C4—21no—
183C4×Dic3—22no—
184C4×Dic3—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—121no—
191C2×C3⋊C8—121no—
192C22×C32#12011yescharacteristic
193C2×C3×D3—81no—
194C2×C3×D3—81no—
195C2×C3×D3—81no—
196C32×C4—22no—
197C32×C4—21no—
198C32×C4—41no—
199C32×C4C2×SD1611yescharacteristic
200C32×C4C2×SD1611yescharacteristic
201C32×C4#13711yescharacteristic
202C32×C4#13711yescharacteristic
203C3×Dic3—22no—
204C3×Dic3—42no—
205C3×Dic3—41no—
206C2×SD16—61no—
207C2×SD16—181no—
208C2×SD16—182no—
209C4⋊Q8—31no—
210C4⋊Q8—61no—
211C4⋊Q8—62no—
212C4⋊Q8—61no—
213#127—31no—
214C4×Q8—31no—
215C4×Q8—61no—
216C4×Q8—61no—
217C4×Q8D3211yescharacteristic
218C4⋊C8—31no—
219C4⋊C8—91no—
220#102—61no—
221#102—181no—
222C4×C8—91no—
223C23×C3—121no—
224C22×D3—41no—
225C3×Q8—21no—
226C3×Q8—21no—
227C3×Q8—22no—
228C3×Q8—32no—
229C3×Q8—41no—
230C3×Q8—61no—
231C3×Q8—122no—
232C3×Q8—242no—
233C3×Q8#21412yescomplemented
234C3×Q8#21512yescomplemented
235C3×D4—122no—
236C3×D4—121no—
237C3×D4—121no—
238C3×D4—121no—
239C3×D4—121no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—62no—
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×Dic3—21no—
259C2×Dic3—22no—
260C2×Dic3—21no—
261D12—42no—
262D12—41no—
263D12—41no—
264D12—41no—
265D12—41no—
266Dic6—21no—
267Dic6—42no—
268Dic6—82no—
269Dic6#21512yescomplemented
270C3×C8—121no—
271C3⋊C8—41no—
272C3⋊C8—62no—
273C3⋊C8—62no—
274C3⋊C8—122no—
275C3⋊C8—121no—
276C3⋊C8—121no—
277C3⋊C8—241no—
278C2×C32#44811yescharacteristic
279C2×C32#44811yescharacteristic
280C2×C32#45311yescharacteristic
281C3×D3—161no—
282C2×Q8—31no—
283C2×Q8—32no—
284C2×Q8—62no—
285C2×Q8#62511yescharacteristic
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289SD16—122no—
290SD16—364no—
291SD16—362no—
292C2×C8—61no—
293C2×C8—181no—
294C2×C8—181no—
295C4⋊C4—21no—
296C4⋊C4—31no—
297C4⋊C4—62no—
298C4⋊C4—62no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4#62511yescharacteristic
303C42—21no—
304C42—62no—
305C42—61no—
306C42C2×D3211yescharacteristic
307C22×C3—21no—
308C22×C3—241no—
309C22×C3—241no—
310C22×C3—241no—
311C22×C3#93711yescharacteristic
312C22×C3#95311yescharacteristic
313C2×D3—81no—
314C2×D3—81no—
315C2×D3—81no—
316C3×C4—21no—
317C3×C4—22no—
318C3×C4—21no—
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—41no—
325C3×C4—42no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—62no—
329C3×C4—81no—
330C3×C4—122no—
331C3×C4—121no—
332C3×C4D3×SD1611yescharacteristic
333C3×C4#91511yescharacteristic
334C3×C4C2×#21411yescharacteristic
335C3×C4C2×#21511yescharacteristic
336C3×C4C2×#21511yescharacteristic
337C3×C4#94211yescharacteristic
338C3×C4#94211yescharacteristic
339C3×C4#95111yescharacteristic
340Dic3—22no—
341Dic3—42no—
342Dic3—41no—
343C32#162311yescharacteristic, complemented, Sylow
344C23—121no—
345Q8—21no—
346Q8—32no—
347Q8—61no—
348Q8—122no—
349Q8—242no—
350Q8#371512yescomplemented
351D4—122no—
352D4—121no—
353D4—121no—
354D4—121no—
355D4—121no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—62no—
361C2×C4C2×#62511yescharacteristic
362C2×C4D3×#6711yescharacteristic
363C2×C4D3×#6711yescharacteristic
364C8—121no—
365C8—182no—
366C8—361no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—481no—
371C2×C3#504011yescharacteristic
372C2×C3#517011yescharacteristic
373C2×C3#519811yescharacteristic
374C2×C3#522711yescharacteristic
375C2×C3#522711yescharacteristic
376C2×C3#524111yescharacteristic
377D3—161no—
378C22—241no—
379C22—241no—
380C22—241no—
381C22#6397611yescharacteristic
382C4—21no—
383C4—22no—
384C4—41no—
385C4—62no—
386C4—122no—
387C4—121no—
388C4C2×#371511yescharacteristic
389C4#6382711yescharacteristic
390C4D3×#21511yescharacteristic
391C4#6394611yescharacteristic
392C3—21no—
393C3#7103311yescharacteristic, complemented
394C3#7193911yescharacteristic, complemented
395C2—481no—
396C2#1059117111yescharacteristic
397C2#1059158311yescharacteristic
398C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC4×Q8D32
hypocenterC32#1623
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. C3×Q8×Dic6C2semidirect
5. #10589401C2semidirect
6. #10589095C2semidirect
7. #10589083C2semidirect
28. Q8×Dic6D3semidirect
107. C32×Q8SD16semidirect
124. C3×Dic6SD16semidirect
233. C3×Q8#214semidirect
234. C3×Q8#215semidirect
269. Dic6#215semidirect
343. C32#1623semidirect
350. Q8#3715semidirect
393. C3#71033semidirect
394. C3#71939semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
C3×#50272
#105903752
#105903642
#105894012
#105890952
#105890832
#719393
#710333