Finite Group Databasebeta

← #11781746

Subgroups — #11781746

Order 1152.

432 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592726C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590350C211yesmaximal, characteristic
5#10589097C211yesmaximal, characteristic, complemented
6#10589091C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71025—31nomaximal
9#70959—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×#3755—21no—
12#64083C2211yescharacteristic
13C2×C3×#215—21no—
14C3×#874C2211yescharacteristic
15C2×#3714—21no—
16C2×#3714—21no—
17#63636—21no—
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×#809—21no—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#803—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#460—31no—
26C3×#446—31no—
27#5073—31no—
28#5027—31no—
29#5027—31no—
30#5027—61no—
31#5027D311yescharacteristic, complemented
32#5024D311yescharacteristic, complemented
33#4695—31no—
34#4544—31no—
35#4485—31no—
36#4485—31no—
37#4485—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8D411yescharacteristic
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51#3755—42no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×#215—42no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#3714—42no—
59#3714—42no—
60#1688—91noSylow
61C2×C3×SD16—61no—
62C3×#127—31no—
63C3×C4×Q8—21no—
64C3×C4×Q8C2×D311yescharacteristic
65C3×C4×Q8C2×D311yescharacteristic
66C2×#215—21no—
67C2×#215—62no—
68C2×#215—61no—
69C2×#215—61no—
70C2×#213—61no—
71C2×#213—61no—
72C2×D24—61no—
73C2×D24—61no—
74#874—31no—
75#874—31no—
76#874—61no—
77#874C2×D311yescharacteristic
78C3×C4⋊C8—31no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8—61no—
81C3×#102—61no—
82C3×#97—61no—
83C3×C4×C8—31no—
84#809—21no—
85#809—62no—
86#809—61no—
87#809—61no—
88C4⋊(C3⋊C8)—21no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94#803—21no—
95C4×C3⋊C8C2×D311yescharacteristic
96C22×C3⋊D3—41no—
97C22×C3×D3—41no—
98C32×Q8—21no—
99C32×Q8—21no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—41no—
108C4⋊(C3⋊D3)—41no—
109C4⋊(C3⋊D3)—81no—
110C3×D12—41no—
111C3×D12—41no—
112C3×D12—41no—
113C3×D12—41no—
114C3×D12—81no—
115C3⋊(C3⋊C8)—41no—
116C3×C3⋊C8—21no—
117C3×C3⋊C8—41no—
118C3×C3⋊C8—41no—
119C3×C3⋊C8SD1612yescomplemented
120#493—91no—
121#460—31no—
122#460—91no—
123#446—31no—
124#334—91no—
125#331—91no—
126#331—91no—
127C2×C3×Q8—21no—
128C2×C3×Q8D1211yescharacteristic
129C2×C3×Q8#6711yescharacteristic
130C2×C3×D4—61no—
131C2×C3×D4—61no—
132C2×C3×D4—61no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—62no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—121no—
144C2×D12—121no—
145C3×SD16—122no—
146C2×C3×C8—31no—
147C2×C3×C8—31no—
148C2×C3×C8—61no—
149C2×C3×C8—61no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4D1211yescharacteristic
155C3×C4⋊C4#6711yescharacteristic
156C3×C42—21no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—41no—
160C3×C42C22×D311yescharacteristic
161C3×C42C22×D311yescharacteristic
162#215—42no—
163#215—124no—
164#215—122no—
165#215—122no—
166#213—122no—
167#213—122no—
168C2×C3⋊C8—21no—
169C2×C3⋊C8—21no—
170C2×C3⋊C8—62no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8—61no—
173C2×C3⋊C8#6711yescharacteristic
174C2×C3⋊C8#6711yescharacteristic
175D24—122no—
176D24—122no—
177C22×C32#12111yescharacteristic
178C2×C3⋊D3—81no—
179C2×C3⋊D3—81no—
180C2×C3⋊D3—81no—
181C2×C3×D3—81no—
182C2×C3×D3—81no—
183C2×C3×D3—81no—
184C32×C4—21no—
185C32×C4—41no—
186C32×C4—41no—
187C32×C4C2×SD1611yescharacteristic
188C32×C4AGL(1,ℤ/8)11yescharacteristic
189C32×C4AGL(1,ℤ/8)11yescharacteristic
190C32×C4AGL(1,ℤ/8)11yescharacteristic
191C2×SD16—61no—
192C2×SD16—181no—
193C2×D8—181no—
194C2×D8—181no—
195#127—31no—
196#127—91no—
197C4×Q8D3211yescharacteristic
198C4⋊C8—31no—
199C4⋊C8—31no—
200C4⋊C8—61no—
201C4⋊C8—91no—
202#102—61no—
203#102—181no—
204#97—61no—
205C4×C8—31no—
206C23×C3—121no—
207C22×D3—41no—
208C22×D3—122no—
209C22×D3—121no—
210C22×D3—121no—
211C3×Q8—22no—
212C3×Q8—21no—
213C3×Q8—21no—
214C3×Q8—21no—
215C3×Q8—21no—
216C3×Q8—41no—
217C3×D4—121no—
218C3×D4—121no—
219C3×D4—121no—
220C3×D4—121no—
221C3×D4—241no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4C2×D1211yescharacteristic
232C2×C3×C4#23511yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4#23711yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237D12—41no—
238D12—41no—
239D12—41no—
240D12—41no—
241D12—81no—
242D12—122no—
243D12—122no—
244D12—121no—
245D12—121no—
246D12—121no—
247D12—121no—
248D12—121no—
249D12—121no—
250D12—121no—
251D12—121no—
252D12—241no—
253D12—241no—
254D12—241no—
255D12—241no—
256D12—242no—
257C3×C8—32no—
258C3×C8—61no—
259C3×C8—121no—
260C3×C8—121no—
261C3⋊C8—21no—
262C3⋊C8—41no—
263C3⋊C8—41no—
264C3⋊C8—122no—
265C3⋊C8—121no—
266C3⋊C8—121no—
267C3⋊C8#21512yescomplemented
268C2×C32#46011yescharacteristic
269C2×C32#46911yescharacteristic
270C2×C32#47211yescharacteristic
271C3⋊D3—161no—
272C3×D3—161no—
273C2×Q8#62611yescharacteristic
274C2×D4—61no—
275C2×D4—61no—
276C2×D4—61no—
277C2×D4—181no—
278C2×D4—181no—
279C2×D4—181no—
280SD16—122no—
281SD16—362no—
282D8—362no—
283D8—362no—
284C2×C8—31no—
285C2×C8—31no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—181no—
289C4⋊C4—21no—
290C4⋊C4#62611yescharacteristic
291C42—21no—
292C42C2×D3211yescharacteristic
293C22×C3—21no—
294C22×C3—241no—
295C22×C3—241no—
296C22×C3—241no—
297C22×C3#93011yescharacteristic
298C22×C3#93911yescharacteristic
299C2×D3—81no—
300C2×D3—81no—
301C2×D3—81no—
302C2×D3—242no—
303C2×D3—242no—
304C2×D3—242no—
305C2×D3—241no—
306C2×D3—241no—
307C2×D3—241no—
308C2×D3—241no—
309C2×D3—241no—
310C2×D3—241no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—42no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—81no—
324C3×C4#90811yescharacteristic
325C3×C4#90811yescharacteristic
326C3×C4D3×SD1611yescharacteristic
327C3×C4#91411yescharacteristic
328C3×C4#93211yescharacteristic
329C3×C4C2×#21511yescharacteristic
330C3×C4#94911yescharacteristic
331C3×C4#94911yescharacteristic
332C32#168811yescharacteristic, complemented, Sylow
333C23—121no—
334C23—361no—
335Q8—21no—
336Q8—21no—
337D4—121no—
338D4—121no—
339D4—121no—
340D4—121no—
341D4—241no—
342D4—361no—
343D4—361no—
344D4—361no—
345D4—361no—
346D4—721no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4#380411yescharacteristic
350C2×C4C2×#62611yescharacteristic
351C2×C4D3×#6711yescharacteristic
352C8—32no—
353C8—61no—
354C8—121no—
355C8—121no—
356C8—361no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—481no—
361C2×C3#502711yescharacteristic
362C2×C3#503911yescharacteristic
363C2×C3#513511yescharacteristic
364C2×C3#514211yescharacteristic
365C2×C3#516311yescharacteristic
366C2×C3#519911yescharacteristic
367D3—161no—
368D3—482no—
369D3—481no—
370D3—481no—
371C22—241no—
372C22—241no—
373C22—241no—
374C22—721no—
375C22—721no—
376C22—721no—
377C22#6397811yescharacteristic
378C4—21no—
379C4—41no—
380C4—41no—
381C4#6382511yescharacteristic
382C4#6383011yescharacteristic
383C4D3×#21511yescharacteristic
384C4#6393911yescharacteristic
385C3—21no—
386C3#7095911yescharacteristic, complemented
387C3#7102511yescharacteristic, complemented
388C2—481no—
389C2—1441no—
390C2#1059116511yescharacteristic
391C2#1059161711yescharacteristic
392C2#1059167711yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#121
prime radical#10590350C2
hypercenterC4×Q8D32
hypocenterC32#1688
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10592726C2semidirect
2. C3×#5027C2semidirect
3. C3×#5024C2semidirect
5. #10589097C2semidirect
6. #10589091C2semidirect
7. #10589090C2semidirect
31. #5027D3semidirect
32. #5024D3semidirect
119. C3×C3⋊C8SD16semidirect
267. C3⋊C8#215semidirect
332. C32#1688semidirect
386. C3#70959semidirect
387. C3#71025semidirect

Maximal subgroups

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

subgroupindex
#105927262
C3×#50272
C3×#50242
#105903502
#105890972
#105890912
#105890902
#710253
#709593