Finite Group Databasebeta

← #11779062

Subgroups — #11779062

Order 1152.

488 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic62C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic
3#10590369C211yesmaximal, characteristic
4#10590364C211yesmaximal, characteristic
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71033—31nomaximal
9#68264—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×#204—21no—
12C3×#874C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63918—21no—
16#63918—21no—
17Dic3×Dic6—21no—
18Dic3×Dic6—21no—
19#63840—22no—
20C2×#3716—22no—
21C2×#3715—21no—
22C32×C4⋊C8C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#821—21no—
25C3×C4×C3⋊C8C2211yescharacteristic
26#63562—21no—
27Q8×Dic6—31no—
28Q8×Dic6—31no—
29C3×#460—31no—
30#5076—31no—
31#5075—31no—
32#5027—31no—
33#4848D311yescharacteristic
34#4693—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4484D311yescharacteristic, complemented
38#4481—31no—
39#4481—31no—
40#4481—61no—
41#4456—31no—
42C2×#634D412yes—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D411yescharacteristic
48C2×#627—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C3×#204—42no—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64Dic32—22no—
65#3716—44no—
66#3715—42no—
67#1623—91noSylow
68C2×C3×SD16—61no—
69C3×#127—31no—
70C3×C4×Q8—31no—
71C3×C4×Q8—31no—
72Q8×Dic3—61no—
73Q8×Dic3—61no—
74C2×#215—61no—
75C2×#214—62no—
76C2×#214—61no—
77C2×#204—21no—
78C2×#204—62no—
79#888—61no—
80#888—61no—
81#888—62no—
82#888—62no—
83#874C2×D311yescharacteristic
84#869—31no—
85#869—31no—
86#869—61no—
87#869—61no—
88#869—61no—
89C4×Dic6—61no—
90C4×Dic6—61no—
91C4×Dic6C2×D311yescharacteristic
92C4×Dic6C2×D311yescharacteristic
93C3×C4⋊C8—21no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C2×D311yescharacteristic
96C3×#102—61no—
97C3×C4×C8—31no—
98#832—61no—
99#821—21no—
100#809—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—22no—
110#634—42no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C3×D12—42no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6SD1612yescomplemented
123C3×Dic6SD1612yescomplemented
124#627—82no—
125C32×C8—41no—
126C3⋊(C3⋊C8)—41no—
127C3×C3⋊C8—22no—
128Q82—91no—
129#492—91no—
130#460—31no—
131#460—91no—
132#333—91no—
133Q8⋊C8—31no—
134Q8⋊C8—91no—
135C2×C3×Q8—31no—
136C2×C3×Q8—31no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×D12—21no—
141C2×D12—21no—
142C2×D12—21no—
143C2×Dic6—32no—
144C2×Dic6—32no—
145C2×Dic6—62no—
146C2×Dic6—62no—
147C2×Dic6—62no—
148C2×Dic6D1211yescharacteristic
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—31no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C42—21no—
160C3×C42—61no—
161C3×C42—61no—
162C3×C42C22×D311yescharacteristic
163C3×C42C22×D311yescharacteristic
164#215—122no—
165#214—124no—
166#214—122no—
167C4⋊Dic3—62no—
168C4⋊Dic3—62no—
169C4⋊Dic3—61no—
170C4⋊Dic3—61no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—121no—
174C4⋊Dic3—121no—
175C4⋊Dic3D1211yescharacteristic
176C4⋊Dic3#6711yescharacteristic
177Dic3⋊C4—21no—
178Dic3⋊C4—21no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181C4×Dic3—21no—
182C4×Dic3—21no—
183C4×Dic3—62no—
184C4×Dic3—62no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—121no—
189#204—42no—
190#204—124no—
191C22×C32#12011yescharacteristic
192C2×C3×D3—81no—
193C2×C3×D3—81no—
194C2×C3×D3—81no—
195C32×C4—21no—
196C32×C4C2×SD1611yescharacteristic
197C32×C4C2×SD1611yescharacteristic
198C32×C4#13711yescharacteristic
199C32×C4#13711yescharacteristic
200C3⋊Dic3—42no—
201C3×Dic3—22no—
202C3×Dic3—22no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C2×SD16—61no—
206C2×SD16—182no—
207C2×SD16—181no—
208C4⋊Q8—91no—
209C4⋊Q8—181no—
210C4⋊Q8—181no—
211C4⋊Q8—182no—
212#127—31no—
213C4×Q8—31no—
214C4×Q8—31no—
215C4×Q8—181no—
216C4×Q8—181no—
217C4⋊C8—91no—
218C4⋊C8D3211yescharacteristic
219#102—61no—
220#102—181no—
221C4×C8—31no—
222C23×C3—121no—
223C22×D3—41no—
224C3×Q8—32no—
225C3×Q8—32no—
226C3×Q8—61no—
227C3×Q8—61no—
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—61no—
239C2×C3×C4—61no—
240C2×C3×C4C2×D1211yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4C2×#6711yescharacteristic
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—62no—
251C2×Dic3—62no—
252C2×Dic3—122no—
253D12—42no—
254D12—41no—
255D12—41no—
256D12—41no—
257D12—41no—
258Dic6—21no—
259Dic6—21no—
260Dic6—122no—
261Dic6—122no—
262Dic6—242no—
263Dic6—242no—
264Dic6—242no—
265Dic6#20412yescomplemented
266Dic6#21412yescomplemented
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—62no—
270C3×C8—81no—
271C3⋊C8—22no—
272C3⋊C8—121no—
273C3⋊C8—121no—
274C3⋊C8—241no—
275C2×C32#44811yescharacteristic
276C2×C32#44811yescharacteristic
277C2×C32#45311yescharacteristic
278C3×D3—161no—
279C2×Q8—31no—
280C2×Q8—31no—
281C2×Q8—92no—
282C2×Q8—182no—
283C2×D4—61no—
284C2×D4—61no—
285C2×D4—61no—
286SD16—122no—
287SD16—364no—
288SD16—362no—
289C2×C8—21no—
290C2×C8—61no—
291C2×C8—181no—
292C4⋊C4—31no—
293C4⋊C4—31no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—182no—
297C4⋊C4—182no—
298C4⋊C4—181no—
299C4⋊C4—181no—
300C42—61no—
301C42—61no—
302C42—182no—
303C42C2×D3211yescharacteristic
304C22×C3—21no—
305C22×C3—241no—
306C22×C3—241no—
307C22×C3—241no—
308C22×C3#88211yescharacteristic
309C22×C3#93711yescharacteristic
310C2×D3—81no—
311C2×D3—81no—
312C2×D3—81no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—62no—
321C3×C4—62no—
322C3×C4—121no—
323C3×C4—121no—
324C3×C4C2×#20411yescharacteristic
325C3×C4#90911yescharacteristic
326C3×C4D3×SD1611yescharacteristic
327C3×C4D3×SD1611yescharacteristic
328C3×C4#91511yescharacteristic
329C3×C4#91811yescharacteristic
330C3×C4C2×#21411yescharacteristic
331C3×C4#95111yescharacteristic
332Dic3—22no—
333Dic3—22no—
334Dic3—41no—
335Dic3—41no—
336Dic3—122no—
337Dic3—122no—
338Dic3—242no—
339C32#162311yescharacteristic, complemented, Sylow
340C23—121no—
341Q8—32no—
342Q8—32no—
343Q8—61no—
344Q8—61no—
345Q8—362no—
346Q8—722no—
347D4—122no—
348D4—121no—
349D4—121no—
350D4—121no—
351D4—121no—
352C2×C4—61no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—182no—
357C2×C4D3×D1211yescharacteristic
358C2×C4#380211yescharacteristic
359C2×C4D3×#6711yescharacteristic
360C8—41no—
361C8—62no—
362C8—361no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—481no—
367C2×C3#473811yescharacteristic
368C2×C3#480611yescharacteristic
369C2×C3#482211yescharacteristic
370C2×C3#504011yescharacteristic
371C2×C3#517011yescharacteristic
372C2×C3#519811yescharacteristic
373D3—161no—
374C22—241no—
375C22—241no—
376C22—241no—
377C22#6392211yescharacteristic
378C4—21no—
379C4—62no—
380C4—62no—
381C4—121no—
382C4—121no—
383C4—362no—
384C4D3×#20411yescharacteristic
385C4#6380011yescharacteristic
386C4D3×#21411yescharacteristic
387C4#6394311yescharacteristic
388C3—21no—
389C3#6826411yescharacteristic, complemented
390C3#7103311yescharacteristic, complemented
391C2—481no—
392C2#1059060311yescharacteristic
393C2#1059082211yescharacteristic
394C2#1059101311yescharacteristic
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. Dic62C2semidirect
5. #10589347C2semidirect
6. C3×#4484C2semidirect
7. #10589084C2semidirect
37. #4484D3semidirect
122. C3×Dic6SD16semidirect
123. C3×Dic6SD16semidirect
265. Dic6#204semidirect
266. Dic6#214semidirect
339. C32#1623semidirect
389. C3#68264semidirect
390. C3#71033semidirect

Maximal subgroups

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

subgroupindex
Dic622
C3×#48482
#105903692
#105903642
#105893472
C3×#44842
#105890842
#710333
#682643