Finite Group Databasebeta

← #11782446

Subgroups — #11782446

Order 1152.

529 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 529 conjugacy classes of subgroups — too many to draw. Only its 106 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#10592772C211yesmaximal, characteristic
2C3×#5076C211yesmaximal, characteristic, complemented
3C3×#5070C211yesmaximal, characteristic, complemented
4#10590373C211yesmaximal, characteristic, complemented
5#10590312C211yesmaximal, characteristic, complemented
6#10590281C211yesmaximal, characteristic, complemented
7C3⋊C82C211yesmaximal, characteristic, complemented
8#71255—31nomaximal
9#71180—31nomaximal
10C32×#127C2211yescharacteristic
11C2×#3753—22no—
12#64083C2211yescharacteristic
13C2×C3×#214—22no—
14C3×#869C2211yescharacteristic
15C3×#869C2211yescharacteristic
16C2×#3717—22no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#832—22no—
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63576—22no—
22#63564—22no—
23C3×#492—31no—
24C3×#486—31no—
25#5088—31no—
26#5085—31no—
27#5078—31no—
28#5078—31no—
29#5076D311yescharacteristic, complemented
30#5073—31no—
31#5073—31no—
32#5073—61no—
33#5070D311yescharacteristic, complemented
34#4694—31no—
35#4693—31no—
36C8×C3⋊C8—31no—
37C8×C3⋊C8—31no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6—21no—
46C32×C42C2311yescharacteristic
47#3753—44no—
48C2×C3⋊(C3⋊C8)D412yes—
49C3×#214—44no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8D412yes—
55C2×C3×C3⋊C8D412yes—
56#3717—44no—
57#1706—91noSylow
58C2×C3×SD16—62no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C3×#127—21no—
62C3×#127C2×D311yescharacteristic
63C3×#127C2×D311yescharacteristic
64C2×#215—62no—
65C2×#214—22no—
66C2×#213—62no—
67C2×#213—62no—
68C2×#213—64no—
69C2×#204—62no—
70#874—31no—
71#874—31no—
72#874—61no—
73#869C2×D311yescharacteristic
74#869C2×D311yescharacteristic
75C3×#102—62no—
76C3×C4×C8—31no—
77C3×C4×C8—31no—
78#832—22no—
79#821—62no—
80#809—62no—
81#807—62no—
82#807—62no—
83C4×C3⋊C8—31no—
84C4×C3⋊C8—31no—
85C4×C3⋊C8—61no—
86C4×C3⋊C8C2×D311yescharacteristic
87C4×C3⋊C8C2×D311yescharacteristic
88C23×C32—41no—
89C22×C3⋊D3—41no—
90C32×D4—42no—
91C32×D4—42no—
92C32×D4—42no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C4⋊(C3⋊D3)—42no—
97C4⋊(C3⋊D3)—42no—
98C4⋊(C3⋊D3)—42no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C3×Dic6—42no—
102C3×Dic6—42no—
103C3⋊(C3⋊C8)SD1614yescomplemented
104C3×C3⋊C8—22no—
105C3×C3⋊C8D814yescomplemented
106#500—91no—
107#493—91no—
108#492—31no—
109#492—91no—
110#486—31no—
111#486—91no—
112C82—91no—
113C2×C3×Q8—61no—
114C2×C3×Q8—61no—
115C2×C3×D4—22no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—21no—
119C2×C3×D4—21no—
120C2×C3×D4—21no—
121C2×C3×D4—21no—
122C2×C3×D4—41no—
123C2×C3×D4—41no—
124C2×D12—62no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—121no—
132C2×D12—121no—
133C2×Dic6—21no—
134C2×Dic6—21no—
135C3×SD16—124no—
136C2×C3×C8—32no—
137C2×C3×C8—32no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C4⋊C4—61no—
142C3×C42—21no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#215—124no—
146#214—44no—
147#213—124no—
148#213—124no—
149#213—128no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C2×C3⋊C8—32no—
155C2×C3⋊C8—32no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8#6712yes—
158C2×C3⋊C8#6712yes—
159#204—124no—
160C22×C32—81no—
161C22×C32—81no—
162C22×C32—81no—
163C22×C32#12711yescharacteristic
164C2×C3⋊D3—81no—
165C2×C3⋊D3—81no—
166C2×C3⋊D3—81no—
167C32×C4C2×D812yes—
168C32×C4C2×SD1612yes—
169C32×C4#13512yes—
170C3×Dic3—81no—
171C3×Dic3—81no—
172C2×SD16—62no—
173C2×SD16—182no—
174C2×D8—182no—
175C4⋊Q8—31no—
176C4⋊Q8—31no—
177#127—91no—
178#127D3211yescharacteristic
179#107—182no—
180#102—62no—
181#102—182no—
182C4×C8—31no—
183C4×C8—31no—
184C4×C8—91no—
185C23×C3—42no—
186C23×C3—41no—
187C23×C3—41no—
188C22×D3—122no—
189C22×D3—121no—
190C22×D3—121no—
191C3×Q8—122no—
192C3×Q8—122no—
193C3×D4—44no—
194C3×D4—42no—
195C3×D4—42no—
196C3×D4—42no—
197C3×D4—42no—
198C3×D4—42no—
199C3×D4—42no—
200C3×D4—82no—
201C3×D4—82no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—121no—
206C2×C3×C4—121no—
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×C3×C4C2×#6711yescharacteristic
213C2×Dic3—41no—
214C2×Dic3—41no—
215D12—124no—
216D12—122no—
217D12—122no—
218D12—122no—
219D12—122no—
220D12—122no—
221D12—122no—
222D12—242no—
223D12—242no—
224Dic6—42no—
225Dic6—42no—
226C3×C8—34no—
227C3×C8—62no—
228C3⋊C8—22no—
229C3⋊C8—34no—
230C3⋊C8—34no—
231C3⋊C8—64no—
232C3⋊C8#21314yescomplemented
233C2×C32—161no—
234C2×C32#49211yescharacteristic
235C2×C32#49311yescharacteristic
236C2×C32#49511yescharacteristic
237C3⋊D3—161no—
238C2×Q8—61no—
239C2×Q8—61no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—181no—
244C2×D4—181no—
245C2×D4—181no—
246SD16—124no—
247SD16—364no—
248D8—364no—
249C2×C8—32no—
250C2×C8—32no—
251C2×C8—92no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C42C2×D3211yescharacteristic
257C22×C3—21no—
258C22×C3—82no—
259C22×C3—82no—
260C22×C3—82no—
261C22×C3—81no—
262C22×C3—81no—
263C22×C3—81no—
264C22×C3—81no—
265C22×C3—81no—
266C22×C3—81no—
267C22×C3#94011yescharacteristic
268C22×C3#94011yescharacteristic
269C2×D3—242no—
270C2×D3—242no—
271C2×D3—242no—
272C2×D3—241no—
273C2×D3—241no—
274C2×D3—241no—
275C2×D3—241no—
276C2×D3—241no—
277C2×D3—241no—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—241no—
282C3×C4—241no—
283C3×C4D3×D812yes—
284C3×C4D3×SD1612yes—
285C3×C4D3×SD1612yes—
286C3×C4#91612yes—
287C3×C4C2×#21312yes—
288C3×C4#95012yes—
289Dic3—81no—
290Dic3—81no—
291C32#170611yescharacteristic, complemented, Sylow
292C23—41no—
293C23—361no—
294Q8—122no—
295Q8—122no—
296D4—42no—
297D4—42no—
298D4—42no—
299D4—362no—
300D4—362no—
301D4—362no—
302C2×C4—121no—
303C2×C4—121no—
304C2×C4D3×#6711yescharacteristic
305C2×C4D3×#6711yescharacteristic
306C2×C4#381111yescharacteristic
307C8—34no—
308C8—62no—
309C8—94no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—162no—
314C2×C3—161no—
315C2×C3—161no—
316C2×C3#505911yescharacteristic
317C2×C3#507311yescharacteristic
318C2×C3#515111yescharacteristic
319C2×C3#516811yescharacteristic
320C2×C3#517511yescharacteristic
321C2×C3#517511yescharacteristic
322D3—482no—
323D3—481no—
324D3—481no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—721no—
329C22—721no—
330C22—721no—
331C22#6397911yescharacteristic
332C4—241no—
333C4—241no—
334C4D3×#21312yes—
335C4#6393012yes—
336C4#6393512yes—
337C3—21no—
338C3#7118011yescharacteristic, complemented
339C3#7125511yescharacteristic, complemented
340C2—161no—
341C2—1441no—
342C2#1059147311yescharacteristic
343C2#1059148211yescharacteristic
344C2#1059149211yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#127
prime radical#10592772C2
hypercenter#127D32
hypocenterC32#1706
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C3×#5076C2semidirect
3. C3×#5070C2semidirect
4. #10590373C2semidirect
5. #10590312C2semidirect
6. #10590281C2semidirect
7. C3⋊C82C2semidirect
29. #5076D3semidirect
33. #5070D3semidirect
103. C3⋊(C3⋊C8)SD16semidirect
105. C3×C3⋊C8D8semidirect
232. C3⋊C8#213semidirect
291. C32#1706semidirect
338. C3#71180semidirect
339. C3#71255semidirect

Maximal subgroups

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

subgroupindex
#105927722
C3×#50762
C3×#50702
#105903732
#105903122
#105902812
C3⋊C822
#712553
#711803