Finite Group Databasebeta

← #11781624

Subgroups — #11781624

Order 1152.

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

normal subgroups only

This group has 435 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#10592392C211yesmaximal, characteristic, complemented
2C3×#4688C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590272C211yesmaximal, characteristic, complemented
5C3×#4458C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#70867—31nomaximal
9#68582—31nomaximal
10C2×#3744—21no—
11C2×#3744—21no—
12#64083C2211yescharacteristic
13#64078C2211yescharacteristic
14C2×C3×ΓL(1,𝔽25)—21no—
15C3×C4×D12C2211yescharacteristic
16C2×#3714—21no—
17C32×C4×C8C2211yescharacteristic
18C3×(C2×D3)⋊C8—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63575—21no—
23#63564—21no—
24#63563—21no—
25C3×#436—31no—
26#5015—31no—
27#5007—31no—
28#4846—31no—
29#4843—31no—
30#4693—31no—
31#4693—31no—
32#4693—61no—
33#4688D311yescharacteristic, complemented
34C3×#335—31no—
35#4486—31no—
36#4485—31no—
37#4485—31no—
38#4482—31no—
39#4458D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51#3744—42no—
52#3744—42no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58C3×ΓL(1,𝔽25)—42no—
59#3714—42no—
60#1685—91noSylow
61C2×C3×M16—61no—
62C3×C4×D4—31no—
63C2×#213—61no—
64C2×D24—61no—
65C2×#204—62no—
66C2×#204—62no—
67C2×#204—61no—
68C2×#204—61no—
69C2×#204—61no—
70C2×#204—61no—
71C2×ΓL(1,𝔽25)—21no—
72#874—31no—
73#874—31no—
74#874—61no—
75C4×D12C2×D311yescharacteristic
76#869—31no—
77#869—31no—
78#869—61no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8—31no—
81C3×C4⋊C8—31no—
82C3×C22⋊C8—61no—
83C3×C4×C8—21no—
84C3×C4×C8C2×D311yescharacteristic
85C3×C4×C8C2×D311yescharacteristic
86#832—61no—
87#821—61no—
88#821—61no—
89(C2×D3)⋊C8—21no—
90#818—61no—
91#809—61no—
92#807—61no—
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4⋊(C3⋊C8)C2×D311yescharacteristic
95C4⋊(C3⋊C8)C2×D311yescharacteristic
96C22×C3⋊D3—41no—
97C22×C3×D3—21no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—81no—
107#634—41no—
108#634—41no—
109C2×C3×Dic3—21no—
110C3×D12—21no—
111C3×D12—21no—
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C32×C8—21no—
115C32×C8D812yescomplemented
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118C3×C3⋊C8—41no—
119#492—91no—
120#474—91no—
121#459—91no—
122#436—31no—
123#335—31no—
124#332—91no—
125#331—91no—
126C2×C3×D4—31no—
127C22×C3×C4—61no—
128C2×D12—62no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—121no—
136C2×D12—121no—
137C2×D12D1211yescharacteristic
138C2×C4×D3—21no—
139C2×Dic6—62no—
140C2×Dic6—61no—
141C2×Dic6—61no—
142C3×M16—122no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C2×C3×C8D1211yescharacteristic
149C2×C3×C8D1211yescharacteristic
150C2×C3×C8#6711yescharacteristic
151C2×C3×C8#6711yescharacteristic
152C3×C4⋊C4—31no—
153C3×C22⋊C4—61no—
154C3×C42—21no—
155C3×C42C22×D311yescharacteristic
156C3×C42C22×D311yescharacteristic
157#213—122no—
158(C2×D3)⋊C4—21no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—121no—
164C4⋊Dic3—121no—
165C4⋊Dic3D1211yescharacteristic
166C2×C3⋊C8—21no—
167C2×C3⋊C8—21no—
168C2×C3⋊C8—21no—
169D24—122no—
170#204—124no—
171#204—122no—
172#204—122no—
173#204—124no—
174#204—122no—
175#204—122no—
176ΓL(1,𝔽25)—42no—
177C22×C32#12111yescharacteristic
178C2×C3⋊D3—81no—
179C2×C3⋊D3—81no—
180C2×C3⋊D3—81no—
181C2×C3×D3—41no—
182C2×C3×D3—41no—
183C2×C3×D3—41no—
184C32×C4—21no—
185C32×C4C2×D811yescharacteristic
186C32×C4AGL(1,ℤ/8)11yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C32×C4#13711yescharacteristic
189C3⋊Dic3—81no—
190C3×Dic3—41no—
191C2×SD16—181no—
192C2×SD16—181no—
193C2×D8—181no—
194C2×M16—61no—
195C4⋊Q8—91no—
196#127—91no—
197C4×D4—31no—
198#107—181no—
199C4⋊C8—31no—
200C4⋊C8—31no—
201C4⋊C8—31no—
202#102—181no—
203#102—181no—
204C22⋊C8—61no—
205C4×C8D3211yescharacteristic
206C23×C3—61no—
207C22×D3—21no—
208C22×D3—122no—
209C22×D3—121no—
210C22×D3—121no—
211C3×D4—61no—
212C3×D4—61no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—61no—
217C2×C3×C4—121no—
218C2×C3×C4—121no—
219C2×C3×C4C2×D1211yescharacteristic
220C2×C3×C4C2×D1211yescharacteristic
221C2×C3×C4#23511yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4#23911yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×Dic3—21no—
226C2×Dic3—122no—
227C2×Dic3—121no—
228C2×Dic3—121no—
229D12—21no—
230D12—21no—
231D12—122no—
232D12—122no—
233D12—121no—
234D12—121no—
235D12—121no—
236D12—121no—
237D12—121no—
238D12—121no—
239D12—121no—
240D12—121no—
241D12—241no—
242D12—241no—
243D12—241no—
244D12—241no—
245D12—242no—
246C4×D3—41no—
247C4×D3—41no—
248Dic6—122no—
249Dic6—122no—
250Dic6—121no—
251Dic6—121no—
252Dic6—121no—
253Dic6—121no—
254C3×C8—22no—
255C3×C8—21no—
256C3×C8—21no—
257C3×C8—22no—
258C3×C8—121no—
259C3×C8—121no—
260C3×C8—121no—
261C3×C8D2412yescomplemented
262C3×C8#21312yescomplemented
263C3⋊C8—41no—
264C3⋊C8—41no—
265C3⋊C8—41no—
266C2×C32#45911yescharacteristic
267C2×C32#46811yescharacteristic
268C2×C32#47111yescharacteristic
269C3⋊D3—161no—
270C3×D3—81no—
271C2×Q8—181no—
272C2×D4—31no—
273C2×D4—181no—
274C2×D4—181no—
275C2×D4—181no—
276C22×C4—61no—
277SD16—362no—
278SD16—362no—
279D8—362no—
280M16—122no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8#62611yescharacteristic
285C2×C8#62611yescharacteristic
286C4⋊C4—31no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C22⋊C4—61no—
290C42C2×D3211yescharacteristic
291C22×C3—21no—
292C22×C3—121no—
293C22×C3—121no—
294C22×C3—121no—
295C22×C3#89511yescharacteristic
296C22×C3#93011yescharacteristic
297C2×D3—41no—
298C2×D3—41no—
299C2×D3—41no—
300C2×D3—242no—
301C2×D3—242no—
302C2×D3—242no—
303C2×D3—241no—
304C2×D3—241no—
305C2×D3—241no—
306C2×D3—241no—
307C2×D3—241no—
308C2×D3—241no—
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—121no—
317C3×C4C2×D2411yescharacteristic
318C3×C4#90811yescharacteristic
319C3×C4#90811yescharacteristic
320C3×C4#90911yescharacteristic
321C3×C4#91111yescharacteristic
322C3×C4#91811yescharacteristic
323C3×C4C2×#21311yescharacteristic
324C3×C4#94911yescharacteristic
325Dic3—41no—
326Dic3—242no—
327Dic3—241no—
328Dic3—241no—
329C32#168511yescharacteristic, complemented, Sylow
330C23—61no—
331C23—361no—
332Q8—361no—
333Q8—361no—
334D4—61no—
335D4—61no—
336D4—361no—
337D4—361no—
338D4—361no—
339D4—361no—
340D4—721no—
341C2×C4—61no—
342C2×C4—121no—
343C2×C4—121no—
344C2×C4—361no—
345C2×C4#379911yescharacteristic
346C2×C4D3×D1211yescharacteristic
347C2×C4C2×#62611yescharacteristic
348C8—21no—
349C8—121no—
350C8—121no—
351C8—121no—
352C8#371412yescomplemented
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—241no—
357C2×C3#484311yescharacteristic
358C2×C3#488611yescharacteristic
359C2×C3#489811yescharacteristic
360C2×C3#501511yescharacteristic
361C2×C3#513411yescharacteristic
362C2×C3#514111yescharacteristic
363D3—81no—
364D3—482no—
365D3—481no—
366D3—481no—
367C22—121no—
368C22—121no—
369C22—121no—
370C22—721no—
371C22—721no—
372C22—721no—
373C22#6390911yescharacteristic
374C4—21no—
375C4—121no—
376C4—721no—
377C4#6379511yescharacteristic
378C4#6380111yescharacteristic
379C4C2×#371411yescharacteristic
380C4#6382511yescharacteristic
381C3—21no—
382C3#6858211yescharacteristic, complemented
383C3#7086711yescharacteristic, complemented
384C2—241no—
385C2—1441no—
386C2#1059034911yescharacteristic
387C2#1059083811yescharacteristic
388C2#1059093111yescharacteristic
subgroupG/H
centerC22#63909
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. #10592392C2semidirect
2. C3×#4688C2semidirect
4. #10590272C2semidirect
5. C3×#4458C2semidirect
6. #10589094C2semidirect
7. #10589091C2semidirect
33. #4688D3semidirect
39. #4458D3semidirect
115. C32×C8D8semidirect
261. C3×C8D24semidirect
262. C3×C8#213semidirect
329. C32#1685semidirect
352. C8#3714semidirect
382. C3#68582semidirect
383. C3#70867semidirect

Maximal subgroups

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

subgroupindex
#105923922
C3×#46882
#105903492
#105902722
C3×#44582
#105890942
#105890912
#708673
#685823