Finite Group Databasebeta

← #11781537

Subgroups — #11781537

Order 1152.

374 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 96 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#10592707C211yesmaximal, characteristic
2C3×D4×C3⋊C8C211yesmaximal, characteristic
3C3×#5007C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic, complemented
5#10589099C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#71103—31nomaximal
9#70855—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64078C2211yescharacteristic
12C22×C3×C3⋊C8—21no—
13C3×#869C2211yescharacteristic
14#63659—21no—
15#63635—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#832—21no—
18C3×#830—21no—
19C3×#807—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63566—21no—
24#63566—21no—
25C3×#474—31no—
26C3×C8×D4—31no—
27#5079—31no—
28D4×C3⋊C8D311yescharacteristic
29#5008—31no—
30#5008—31no—
31#5008—61no—
32#5007D311yescharacteristic
33#4681—31no—
34#4547—31no—
35#4482—31no—
36#4481—31no—
37#4481—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—42no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1683—91noSylow
58C22×C3×C8—61no—
59C3×C4⋊Q8—31no—
60C3×C4×D4—21no—
61C3×C4×D4C2×D311yescharacteristic
62C3×C4×D4C2×D311yescharacteristic
63C22×C3⋊C8—21no—
64#869—31no—
65#869—31no—
66#869—61no—
67#869C2×D311yescharacteristic
68C3×#107—61no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×#102—61no—
72C3×C22⋊C8—61no—
73C3×C4×C8—31no—
74#835—61no—
75#835—61no—
76#832—21no—
77#832—62no—
78#832—61no—
79#832—61no—
80#830—21no—
81#816—61no—
82#816—61no—
83#808—62no—
84#808—61no—
85#808—61no—
86#807—21no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C23×C32—21no—
94C32×D4—21no—
95C32×D4Q1612yes—
96C2×C32×C4—21no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3⋊Dic3—41no—
103#634—81no—
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—91no—
113#476—91no—
114#474—31no—
115C8×D4—31no—
116#335—91no—
117#333—91no—
118#332—91no—
119C2×C3×Q8—61no—
120C2×C3×D4—21no—
121C2×C3×D4D1211yescharacteristic
122C2×C3×D4#6711yescharacteristic
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—41no—
126C2×Dic6—21no—
127C2×Dic6—61no—
128C2×Dic6—61no—
129C2×Dic6—121no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C2×C3×C8—122no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4D1211yescharacteristic
139C3×C4⋊C4#6711yescharacteristic
140C3×C22⋊C4—21no—
141C3×C22⋊C4—21no—
142C3×C22⋊C4—41no—
143C3×C42—21no—
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—62no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—121no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—42no—
157C2×C3⋊C8—62no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8#6711yescharacteristic
161C2×C3⋊C8#6711yescharacteristic
162C22×C32—22no—
163C22×C32—41no—
164C22×C32—41no—
165C22×C32#12111yescharacteristic
166C32×C4—21no—
167C32×C4—41no—
168C32×C4C2×Q1611yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C3⋊Dic3—81no—
173C3×Dic3—81no—
174C22×C8—61no—
175C4⋊Q8—31no—
176C4⋊Q8—91no—
177C4×D4D3211yescharacteristic
178#107—61no—
179#106—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—91no—
183#103—181no—
184#103—181no—
185#102—61no—
186#102—181no—
187C22⋊C8—61no—
188C4×C8—31no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—41no—
192C3×Q8—121no—
193C3×Q8—121no—
194C3×D4—21no—
195C3×D4—21no—
196C3×D4—22no—
197C3×D4—41no—
198C3×D4Dic1212yes—
199C3×D4#21612yes—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—81no—
211C2×C3×C4—81no—
212C2×C3×C4—121no—
213C2×C3×C4C2×D1211yescharacteristic
214C2×C3×C4#23511yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4#23711yescharacteristic
217C2×C3×C4C2×#6711yescharacteristic
218C2×C3×C4C2×#6711yescharacteristic
219C2×Dic3—41no—
220C2×Dic3—122no—
221C2×Dic3—121no—
222C2×Dic3—121no—
223Dic6—41no—
224Dic6—41no—
225Dic6—242no—
226Dic6—241no—
227Dic6—241no—
228C3×C8—61no—
229C3×C8—61no—
230C3×C8—121no—
231C3×C8—121no—
232C3⋊C8—21no—
233C3⋊C8—21no—
234C3⋊C8—41no—
235C3⋊C8—41no—
236C3⋊C8—122no—
237C3⋊C8—121no—
238C3⋊C8—121no—
239C2×C32—42no—
240C2×C32#46311yescharacteristic
241C2×C32#46711yescharacteristic
242C2×C32#47111yescharacteristic
243C2×Q8—61no—
244C2×Q8—181no—
245C2×D4#62611yescharacteristic
246C22×C4—21no—
247C2×C8—31no—
248C2×C8—31no—
249C2×C8—61no—
250C2×C8—61no—
251C2×C8—122no—
252C2×C8—181no—
253C4⋊C4—61no—
254C4⋊C4—61no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C4⋊C4#62611yescharacteristic
258C22⋊C4—21no—
259C42C2×D3211yescharacteristic
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—21no—
263C22×C3—42no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—81no—
269C22×C3—81no—
270C22×C3#93011yescharacteristic
271C22×C3#93911yescharacteristic
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—81no—
282C3×C4—241no—
283C3×C4#90411yescharacteristic
284C3×C4C2×Dic1211yescharacteristic
285C3×C4#91111yescharacteristic
286C3×C4#91211yescharacteristic
287C3×C4#93211yescharacteristic
288C3×C4C2×#21611yescharacteristic
289C3×C4#95011yescharacteristic
290C3×C4#95011yescharacteristic
291Dic3—81no—
292Dic3—242no—
293Dic3—241no—
294Dic3—241no—
295C32#168311yescharacteristic, complemented, Sylow
296C23—21no—
297Q8—121no—
298Q8—121no—
299Q8—721no—
300D4—21no—
301D4#371912yes—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—121no—
306C2×C4—361no—
307C2×C4#380411yescharacteristic
308C2×C4C2×#62611yescharacteristic
309C2×C4D3×#6711yescharacteristic
310C8—61no—
311C8—61no—
312C8—121no—
313C8—121no—
314C8—361no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—42no—
319C2×C3—42no—
320C2×C3—82no—
321C2×C3#501611yescharacteristic
322C2×C3#505111yescharacteristic
323C2×C3#511611yescharacteristic
324C2×C3#514111yescharacteristic
325C2×C3#515311yescharacteristic
326C2×C3#520311yescharacteristic
327C22—22no—
328C22—41no—
329C22—41no—
330C22#6397811yescharacteristic
331C4—21no—
332C4—41no—
333C4—241no—
334C4—721no—
335C4#6382911yescharacteristic
336C4C2×#371911yescharacteristic
337C4#6393211yescharacteristic
338C4#6393311yescharacteristic
339C3—21no—
340C3#7085511yescharacteristic, complemented
341C3#7110311yescharacteristic, complemented
342C2—42no—
343C2#1059118711yescharacteristic
344C2#1059146811yescharacteristic
345C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1683
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10590287C2semidirect
5. #10589099C2semidirect
6. #10589096C2semidirect
7. #10589093C2semidirect
295. C32#1683semidirect
340. C3#70855semidirect
341. C3#71103semidirect

Maximal subgroups

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

subgroupindex
#105927072
C3×D4×C3⋊C82
C3×#50072
#105902872
#105890992
#105890962
#105890932
#711033
#708553