Finite Group Databasebeta

← #11781636

Subgroups — #11781636

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×#4838C211yesmaximal, characteristic, complemented
2#10590373C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590269C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589099C211yesmaximal, characteristic, complemented
8#70867—31nomaximal
9#68448—31nomaximal
10#64083C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3717—21no—
15C2×#3717—21no—
16C2×#3714—21no—
17C32×C4⋊C8C2211yescharacteristic
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×(C2×D3)⋊C8—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63576—21no—
23#63564—21no—
24#63562—21no—
25C3×#436—31no—
26#5087—31no—
27#5085—31no—
28#5015—31no—
29#5007—31no—
30#4843—31no—
31#4838D311yescharacteristic, complemented
32#4693—31no—
33C3×#332—31no—
34#4485—31no—
35#4485—31no—
36#4485—61no—
37#4482D311yescharacteristic, complemented
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×ΓL(1,𝔽25)—42no—
57#3717—42no—
58#3717—42no—
59#3714—42no—
60#1685—91noSylow
61C2×C3×M16—61no—
62C3×C4⋊Q8—31no—
63C3×C4×D4—31no—
64C2×#215—61no—
65C2×#215—61no—
66C2×#213—61no—
67C2×D24—61no—
68C2×#204—61no—
69C2×#204—61no—
70C2×ΓL(1,𝔽25)—21no—
71#874—31no—
72#874—31no—
73#874—61no—
74C4×D12C2×D311yescharacteristic
75#869C2×D311yescharacteristic
76C3×C4⋊C8—21no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C2×D311yescharacteristic
80C3×C22⋊C8—61no—
81C3×C4×C8—31no—
82#832—61no—
83#821—61no—
84(C2×D3)⋊C8—21no—
85#809—61no—
86#809—61no—
87#807—61no—
88#807—61no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊D3—41no—
95C22×C3×D3—21no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—81no—
104C2×C3×Dic3—21no—
105C2×C3×Dic3—41no—
106C3×D12—21no—
107C3×D12—21no—
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C3×Dic6—41no—
111C3×Dic6—41no—
112C32×C8—41no—
113C3⋊(C3⋊C8)—41no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8D812yescomplemented
117#492—91no—
118#474—91no—
119#459—91no—
120#436—31no—
121#335—91no—
122#332—31no—
123#331—91no—
124C2×C3×Q8—61no—
125C2×C3×D4—31no—
126C22×C3×C4—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—62no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—121no—
135C2×D12—121no—
136C2×D12D1211yescharacteristic
137C2×C4×D3—21no—
138C2×Dic6—21no—
139C3×M16—122no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—31no—
143C2×C3×C8—31no—
144C2×C3×C8—41no—
145C2×C3×C8—61no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C22⋊C4—61no—
150C3×C42—21no—
151C3×C42C22×D311yescharacteristic
152C3×C42C22×D311yescharacteristic
153#215—122no—
154#215—122no—
155#213—122no—
156(C2×D3)⋊C4—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3—21no—
159C4⋊Dic3D1211yescharacteristic
160C2×C3⋊C8—21no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—121no—
164C2×C3⋊C8#6711yescharacteristic
165C2×C3⋊C8#6711yescharacteristic
166D24—122no—
167#204—122no—
168#204—122no—
169ΓL(1,𝔽25)—42no—
170C22×C32#12111yescharacteristic
171C2×C3⋊D3—81no—
172C2×C3⋊D3—81no—
173C2×C3⋊D3—81no—
174C2×C3×D3—41no—
175C2×C3×D3—41no—
176C2×C3×D3—41no—
177C32×C4—21no—
178C32×C4C2×D811yescharacteristic
179C32×C4AGL(1,ℤ/8)11yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4#13711yescharacteristic
182C3×Dic3—41no—
183C3×Dic3—81no—
184C2×SD16—181no—
185C2×SD16—181no—
186C2×D8—181no—
187C2×M16—61no—
188C4⋊Q8—31no—
189#127—91no—
190C4×D4—31no—
191#107—181no—
192C4⋊C8—31no—
193C4⋊C8—91no—
194C4⋊C8D3211yescharacteristic
195#102—181no—
196#102—181no—
197C22⋊C8—61no—
198C4×C8—31no—
199C23×C3—61no—
200C22×D3—21no—
201C22×D3—122no—
202C22×D3—121no—
203C22×D3—121no—
204C3×Q8—121no—
205C3×Q8—121no—
206C3×D4—61no—
207C3×D4—61no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—61no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4C2×D1211yescharacteristic
216C2×C3×C4#23511yescharacteristic
217C2×C3×C4#23511yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×Dic3—21no—
222C2×Dic3—41no—
223D12—21no—
224D12—21no—
225D12—121no—
226D12—121no—
227D12—121no—
228D12—121no—
229D12—121no—
230D12—121no—
231D12—121no—
232D12—121no—
233D12—241no—
234D12—241no—
235D12—241no—
236D12—241no—
237D12—241no—
238D12—241no—
239D12—242no—
240C4×D3—41no—
241C4×D3—41no—
242Dic6—41no—
243Dic6—41no—
244C3×C8—32no—
245C3×C8—41no—
246C3×C8—41no—
247C3×C8—61no—
248C3×C8—81no—
249C3×C8—121no—
250C3⋊C8—21no—
251C3⋊C8—41no—
252C3⋊C8—121no—
253C3⋊C8—121no—
254C3⋊C8—241no—
255C3⋊C8#21312yescomplemented
256C2×C32#45911yescharacteristic
257C2×C32#46811yescharacteristic
258C2×C32#47111yescharacteristic
259C3⋊D3—161no—
260C3×D3—81no—
261C2×Q8—61no—
262C2×D4—31no—
263C2×D4—181no—
264C2×D4—181no—
265C2×D4—181no—
266C22×C4—61no—
267SD16—362no—
268SD16—362no—
269D8—362no—
270M16—122no—
271C2×C8—21no—
272C2×C8—31no—
273C2×C8—31no—
274C2×C8—61no—
275C2×C8—181no—
276C4⋊C4—31no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C22⋊C4—61no—
280C42C2×D3211yescharacteristic
281C22×C3—21no—
282C22×C3—121no—
283C22×C3—121no—
284C22×C3—121no—
285C22×C3#88411yescharacteristic
286C22×C3#93011yescharacteristic
287C2×D3—41no—
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—242no—
291C2×D3—242no—
292C2×D3—242no—
293C2×D3—241no—
294C2×D3—241no—
295C2×D3—241no—
296C2×D3—241no—
297C2×D3—241no—
298C2×D3—241no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—41no—
306C3×C4—121no—
307C3×C4—241no—
308C3×C4#90811yescharacteristic
309C3×C4#90911yescharacteristic
310C3×C4D3×D811yescharacteristic
311C3×C4#91411yescharacteristic
312C3×C4#91411yescharacteristic
313C3×C4#91811yescharacteristic
314C3×C4C2×#21311yescharacteristic
315C3×C4#94911yescharacteristic
316Dic3—41no—
317Dic3—81no—
318C32#168511yescharacteristic, complemented, Sylow
319C23—61no—
320C23—361no—
321Q8—121no—
322Q8—121no—
323D4—61no—
324D4—61no—
325D4—361no—
326D4—361no—
327D4—361no—
328D4—361no—
329D4—721no—
330C2×C4—61no—
331C2×C4—121no—
332C2×C4—121no—
333C2×C4—121no—
334C2×C4#379811yescharacteristic
335C2×C4D3×D1211yescharacteristic
336C2×C4D3×#6711yescharacteristic
337C8—32no—
338C8—41no—
339C8—61no—
340C8—121no—
341C8—361no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—241no—
346C2×C3#475411yescharacteristic
347C2×C3#478611yescharacteristic
348C2×C3#481211yescharacteristic
349C2×C3#501511yescharacteristic
350C2×C3#513411yescharacteristic
351C2×C3#514111yescharacteristic
352D3—81no—
353D3—482no—
354D3—481no—
355D3—481no—
356C22—121no—
357C22—121no—
358C22—121no—
359C22—721no—
360C22—721no—
361C22—721no—
362C22#6390611yescharacteristic
363C4—21no—
364C4—121no—
365C4—241no—
366C4#6379411yescharacteristic
367C4#6380111yescharacteristic
368C4D3×#21311yescharacteristic
369C4#6393911yescharacteristic
370C3—21no—
371C3#6844811yescharacteristic, complemented
372C3#7086711yescharacteristic, complemented
373C2—241no—
374C2—1441no—
375C2#1059054711yescharacteristic
376C2#1059085011yescharacteristic
377C2#1059099811yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590349C2
hypercenterC4⋊C8D32
hypocenterC32#1685
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×#4838C2semidirect
2. #10590373C2semidirect
4. #10590269C2semidirect
5. #10589351C2semidirect
6. C3×#4482C2semidirect
7. #10589099C2semidirect
31. #4838D3semidirect
37. #4482D3semidirect
116. C3×C3⋊C8D8semidirect
255. C3⋊C8#213semidirect
318. C32#1685semidirect
371. C3#68448semidirect
372. C3#70867semidirect

Maximal subgroups

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

subgroupindex
C3×#48382
#105903732
#105903492
#105902692
#105893512
C3×#44822
#105890992
#708673
#684483