Finite Group Databasebeta

← #11781452

Subgroups — #11781452

Order 1152.

406 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4834C211yesmaximal, characteristic, complemented
2#10590363C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590281C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589099C211yesmaximal, characteristic, complemented
8#70849—31nomaximal
9#68446—31nomaximal
10#64083C2211yescharacteristic
11C2×C3×D3×C8—21no—
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3715—21no—
15C2×#3714—21no—
16C32×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×(C2×D3)⋊C8—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63565—21no—
22#63564—21no—
23#63564—21no—
24#63564—21no—
25C3×C8×D4—31no—
26#5088—31no—
27#5083—31no—
28#5019—31no—
29#5015—31no—
30#4843—31no—
31#4834D311yescharacteristic, complemented
32#4694—31no—
33C3×#332—31no—
34#4486D311yescharacteristic, complemented
35#4485—31no—
36#4485—31no—
37#4485—61no—
38#4479—31no—
39#4458—31no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×D3×C8—42no—
57#3715—42no—
58#3714—42no—
59#1681—91noSylow
60C22×C3×C8—61no—
61C3×C4⋊Q8—31no—
62C3×C4×D4—31no—
63C2×#215—61no—
64C2×#214—61no—
65C2×#213—61no—
66C2×D24—61no—
67C2×D3×C8—21no—
68#874—31no—
69#874—31no—
70#874—61no—
71C4×D12C2×D311yescharacteristic
72#869C2×D311yescharacteristic
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C22⋊C8—61no—
78C3×C4×C8—31no—
79#835—61no—
80#821—61no—
81#821—61no—
82#821—61no—
83(C2×D3)⋊C8—21no—
84#810—61no—
85#809—61no—
86#809—61no—
87#809—61no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊D3—41no—
94C22×C3×D3—21no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—81no—
103C2×C3×Dic3—21no—
104C2×C3×Dic3—41no—
105C3×D12—21no—
106C3×D12D812yes—
107C3×C4×D3—41no—
108C3×C4×D3—41no—
109C3×Dic6—41no—
110C3×Dic6—41no—
111C32×C8—41no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116#486—91no—
117#461—91no—
118#459—91no—
119C8×D4—31no—
120#335—91no—
121#332—31no—
122#331—91no—
123C2×C3×Q8—61no—
124C2×C3×D4—31no—
125C22×C3×C4—61no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—62no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—121no—
134C2×D12—121no—
135C2×D12D1211yescharacteristic
136C2×C4×D3—21no—
137C2×Dic6—21no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—31no—
141C2×C3×C8—31no—
142C2×C3×C8—41no—
143C2×C3×C8—61no—
144C2×C3×C8—122no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C22⋊C4—61no—
149C3×C42—21no—
150C3×C42C22×D311yescharacteristic
151C3×C42C22×D311yescharacteristic
152#215—122no—
153#214—122no—
154#213—122no—
155(C2×D3)⋊C4—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3D1211yescharacteristic
159C2×C3⋊C8—21no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—121no—
163C2×C3⋊C8#6711yescharacteristic
164C2×C3⋊C8#6711yescharacteristic
165D24—122no—
166D3×C8—42no—
167C22×C32#12111yescharacteristic
168C2×C3⋊D3—81no—
169C2×C3⋊D3—81no—
170C2×C3⋊D3—81no—
171C2×C3×D3—22no—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C32×C4—21no—
175C32×C4C2×D811yescharacteristic
176C32×C4#13511yescharacteristic
177C32×C4#13511yescharacteristic
178C32×C4AGL(1,ℤ/8)11yescharacteristic
179C3×Dic3—41no—
180C3×Dic3—81no—
181C2×SD16—181no—
182C2×D8—181no—
183C22×C8—61no—
184C4⋊Q8—31no—
185#127—91no—
186C4×D4—31no—
187C4⋊C8—31no—
188C4⋊C8—91no—
189C4⋊C8D3211yescharacteristic
190#103—181no—
191#102—181no—
192#102—181no—
193#102—181no—
194C22⋊C8—61no—
195C4×C8—31no—
196C23×C3—61no—
197C22×D3—21no—
198C22×D3—122no—
199C22×D3—121no—
200C22×D3—121no—
201C3×Q8—121no—
202C3×Q8—121no—
203C3×D4—32no—
204C3×D4—61no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—61no—
209C2×C3×C4—121no—
210C2×C3×C4—121no—
211C2×C3×C4—121no—
212C2×C3×C4C2×D1211yescharacteristic
213C2×C3×C4#23511yescharacteristic
214C2×C3×C4#23511yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4C2×#6711yescharacteristic
218C2×Dic3—21no—
219C2×Dic3—41no—
220D12—21no—
221D12—121no—
222D12—121no—
223D12—121no—
224D12—121no—
225D12—121no—
226D12—121no—
227D12—121no—
228D12—121no—
229D12—241no—
230D12—241no—
231D12—241no—
232D12—241no—
233D12—241no—
234D12—241no—
235D12—242no—
236D12D2412yes—
237C4×D3—41no—
238C4×D3—41no—
239Dic6—41no—
240Dic6—41no—
241C3×C8—41no—
242C3×C8—41no—
243C3×C8—61no—
244C3×C8—61no—
245C3×C8—81no—
246C3×C8—121no—
247C3⋊C8—21no—
248C3⋊C8—21no—
249C3⋊C8—41no—
250C3⋊C8—121no—
251C3⋊C8—121no—
252C3⋊C8—241no—
253C2×C32#46311yescharacteristic
254C2×C32#46611yescharacteristic
255C2×C32#47111yescharacteristic
256C3⋊D3—161no—
257C3×D3—42no—
258C2×Q8—61no—
259C2×D4—31no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263C22×C4—61no—
264SD16—362no—
265D8—362no—
266C2×C8—21no—
267C2×C8—31no—
268C2×C8—31no—
269C2×C8—61no—
270C2×C8—122no—
271C2×C8—181no—
272C4⋊C4—31no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C22⋊C4—61no—
276C42C2×D3211yescharacteristic
277C22×C3—21no—
278C22×C3—62no—
279C22×C3—121no—
280C22×C3—121no—
281C22×C3#88411yescharacteristic
282C22×C3#93011yescharacteristic
283C2×D3—22no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—242no—
287C2×D3—242no—
288C2×D3—242no—
289C2×D3—241no—
290C2×D3—241no—
291C2×D3—241no—
292C2×D3—241no—
293C2×D3—241no—
294C2×D3—241no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—41no—
302C3×C4—121no—
303C3×C4—241no—
304C3×C4C2×D2411yescharacteristic
305C3×C4#90411yescharacteristic
306C3×C4D3×D811yescharacteristic
307C3×C4#91411yescharacteristic
308C3×C4#91611yescharacteristic
309C3×C4#91911yescharacteristic
310C3×C4#93211yescharacteristic
311C3×C4#95011yescharacteristic
312Dic3—41no—
313Dic3—81no—
314C32#168111yescharacteristic, complemented, Sylow
315C23—61no—
316C23—361no—
317Q8—121no—
318Q8—121no—
319D4—32no—
320D4—61no—
321D4—361no—
322D4—361no—
323D4—361no—
324D4—361no—
325D4—721no—
326C2×C4—61no—
327C2×C4—121no—
328C2×C4—121no—
329C2×C4—121no—
330C2×C4#379811yescharacteristic
331C2×C4D3×D1211yescharacteristic
332C2×C4D3×#6711yescharacteristic
333C8—41no—
334C8—61no—
335C8—61no—
336C8—121no—
337C8—361no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—122no—
342C2×C3#475411yescharacteristic
343C2×C3#477511yescharacteristic
344C2×C3#481911yescharacteristic
345C2×C3#501611yescharacteristic
346C2×C3#511511yescharacteristic
347C2×C3#514111yescharacteristic
348D3—42no—
349D3—482no—
350D3—481no—
351D3—481no—
352C22—62no—
353C22—121no—
354C22—121no—
355C22—721no—
356C22—721no—
357C22—721no—
358C22#6390611yescharacteristic
359C4—21no—
360C4—121no—
361C4—241no—
362C4D3×D2411yescharacteristic
363C4#6380611yescharacteristic
364C4#6393411yescharacteristic
365C4#6394911yescharacteristic
366C3—21no—
367C3#6844611yescharacteristic, complemented
368C3#7084911yescharacteristic, complemented
369C2—122no—
370C2—1441no—
371C2#1059053411yescharacteristic
372C2#1059082611yescharacteristic
373C2#1059099811yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590349C2
hypercenterC4⋊C8D32
hypocenterC32#1681
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×#4834C2semidirect
2. #10590363C2semidirect
4. #10590281C2semidirect
5. #10589351C2semidirect
6. C3×#4486C2semidirect
7. #10589099C2semidirect
31. #4834D3semidirect
34. #4486D3semidirect
314. C32#1681semidirect
367. C3#68446semidirect
368. C3#70849semidirect

Maximal subgroups

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

subgroupindex
C3×#48342
#105903632
#105903492
#105902812
#105893512
C3×#44862
#105890992
#708493
#684463