Finite Group Databasebeta

← #11781685

Subgroups — #11781685

Order 1152.

363 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 363 conjugacy classes of subgroups — too many to draw. Only its 84 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×#4851C211yesmaximal, characteristic, complemented
2#10590375C211yesmaximal, characteristic
3#10590364C211yesmaximal, characteristic
4#10590259C211yesmaximal, characteristic, complemented
5#10589345C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic, complemented
8#71120—31nomaximal
9#68412—31nomaximal
10C3×#874C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3715—21no—
14C2×#3715—21no—
15C2×#3715—21no—
16C32×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#817—21no—
20C3×#816—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22Dic3⋊(C3⋊C8)—21no—
23#63562—21no—
24#63554—21no—
25C3×#475—31no—
26#5085—31no—
27#5076—31no—
28#5075—31no—
29#5027—31no—
30#5024—31no—
31#4851D311yescharacteristic, complemented
32#4831—31no—
33C3×#331—31no—
34#4547—31no—
35#4485D311yescharacteristic
36#4482—31no—
37#4479—31no—
38#4479—31no—
39#4479—61no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56#3715—42no—
57#3715—42no—
58#3715—42no—
59#1686—91noSylow
60C3×C4⋊Q8—31no—
61C3×#127—31no—
62C3×C4×Q8—31no—
63C2×#215—61no—
64C2×#215—61no—
65C2×#215—61no—
66C2×#214—61no—
67C2×#214—61no—
68C2×#214—61no—
69#874C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71C4×Dic6C2×D311yescharacteristic
72C3×#106—61no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×#103—61no—
78#832—61no—
79#817—21no—
80#816—21no—
81#815—61no—
82Dic3⋊C8—61no—
83#809—61no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89#803—61no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C22×C3×D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C3×D12—41no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—81no—
105C3×Dic6—21no—
106C3×Dic6—21no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)—41no—
112C3⋊(C3⋊C8)SD1612yescomplemented
113C3×C3⋊C8—41no—
114#492—91no—
115#475—31no—
116#460—91no—
117#446—91no—
118#335—91no—
119#332—91no—
120#331—31no—
121C2×C3×Q8—31no—
122C2×C3×Q8—61no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×D12—21no—
127C2×D12—21no—
128C2×D12—21no—
129C2×Dic6—21no—
130C2×Dic6#6711yescharacteristic
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—41no—
134C2×C3×C8—61no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—61no—
139C3×C42—21no—
140C3×C42—61no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143#215—122no—
144#215—122no—
145#215—122no—
146#214—122no—
147#214—122no—
148#214—122no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3#6711yescharacteristic
152Dic3⋊C4—21no—
153C4×Dic3—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—121no—
164C22×C32#12111yescharacteristic
165C2×C3×D3—81no—
166C2×C3×D3—81no—
167C2×C3×D3—81no—
168C32×C4—21no—
169C32×C4C2×SD1611yescharacteristic
170C32×C4AGL(1,ℤ/8)11yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C32×C4#13711yescharacteristic
173C3×Dic3—41no—
174C3×Dic3—41no—
175C3×Dic3—81no—
176C2×SD16—181no—
177C2×SD16—181no—
178C2×SD16—181no—
179C4⋊Q8—31no—
180#127—31no—
181C4×Q8—31no—
182#106—61no—
183C4⋊C8—31no—
184C4⋊C8—91no—
185C4⋊C8—181no—
186C4⋊C8D3211yescharacteristic
187#103—61no—
188#102—181no—
189#97—181no—
190C4×C8—91no—
191C23×C3—121no—
192C22×D3—41no—
193C3×Q8—61no—
194C3×Q8—61no—
195C3×Q8—121no—
196C3×Q8—121no—
197C3×D4—121no—
198C3×D4—121no—
199C3×D4—121no—
200C3×D4—121no—
201C3×D4—241no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—61no—
206C2×C3×C4—61no—
207C2×C3×C4—121no—
208C2×C3×C4#23511yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4#23711yescharacteristic
213C2×C3×C4C2×#6711yescharacteristic
214C2×Dic3—21no—
215C2×Dic3—21no—
216C2×Dic3—41no—
217D12—41no—
218D12—41no—
219D12—41no—
220D12—41no—
221D12—81no—
222Dic6—21no—
223Dic6—21no—
224Dic6—41no—
225Dic6—41no—
226C3×C8—41no—
227C3×C8—41no—
228C3×C8—81no—
229C3×C8—121no—
230C3⋊C8—32no—
231C3⋊C8—32no—
232C3⋊C8—41no—
233C3⋊C8—62no—
234C3⋊C8—61no—
235C3⋊C8—61no—
236C3⋊C8—121no—
237C3⋊C8—121no—
238C3⋊C8—121no—
239C3⋊C8—241no—
240C2×C32#46011yescharacteristic
241C2×C32#46811yescharacteristic
242C2×C32#47111yescharacteristic
243C3×D3—161no—
244C2×Q8—31no—
245C2×Q8—61no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249SD16—362no—
250SD16—362no—
251SD16—362no—
252C2×C8—21no—
253C2×C8—61no—
254C2×C8—91no—
255C2×C8—91no—
256C2×C8—181no—
257C4⋊C4—31no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C42—61no—
262C42C2×D3211yescharacteristic
263C22×C3—21no—
264C22×C3—241no—
265C22×C3—241no—
266C22×C3—241no—
267C22×C3#88411yescharacteristic
268C22×C3#93911yescharacteristic
269C2×D3—81no—
270C2×D3—81no—
271C2×D3—81no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—121no—
280C3×C4—121no—
281C3×C4—241no—
282C3×C4#91111yescharacteristic
283C3×C4#91111yescharacteristic
284C3×C4D3×SD1611yescharacteristic
285C3×C4D3×SD1611yescharacteristic
286C3×C4#91411yescharacteristic
287C3×C4#91511yescharacteristic
288C3×C4#94211yescharacteristic
289C3×C4#94911yescharacteristic
290Dic3—41no—
291Dic3—41no—
292Dic3—81no—
293C32#168611yescharacteristic, complemented, Sylow
294C23—121no—
295Q8—61no—
296Q8—61no—
297Q8—121no—
298Q8—121no—
299D4—121no—
300D4—121no—
301D4—121no—
302D4—121no—
303D4—241no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—121no—
307C2×C4#379511yescharacteristic
308C2×C4#380211yescharacteristic
309C2×C4D3×#6711yescharacteristic
310C8—41no—
311C8—92no—
312C8—121no—
313C8—181no—
314C8—361no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—481no—
319C2×C3#474811yescharacteristic
320C2×C3#476211yescharacteristic
321C2×C3#478011yescharacteristic
322C2×C3#504911yescharacteristic
323C2×C3#516311yescharacteristic
324C2×C3#520311yescharacteristic
325D3—161no—
326C22—241no—
327C22—241no—
328C22—241no—
329C22#6388511yescharacteristic
330C4—21no—
331C4—121no—
332C4—121no—
333C4—241no—
334C4#6379611yescharacteristic
335C4#6379811yescharacteristic
336C4#6392511yescharacteristic
337C4#6394611yescharacteristic
338C3—21no—
339C3#6841211yescharacteristic, complemented
340C3#7112011yescharacteristic, complemented
341C2—481no—
342C2#1059050311yescharacteristic
343C2#1059087611yescharacteristic
344C2#1059097911yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1686
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. C3×#4851C2semidirect
4. #10590259C2semidirect
5. #10589345C2semidirect
7. #10589093C2semidirect
31. #4851D3semidirect
112. C3⋊(C3⋊C8)SD16semidirect
293. C32#1686semidirect
339. C3#68412semidirect
340. C3#71120semidirect

Maximal subgroups

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

subgroupindex
C3×#48512
#105903752
#105903642
#105902592
#105893452
C3×#44852
#105890932
#711203
#684123