Finite Group Databasebeta

← #11781627

Subgroups — #11781627

Order 1152.

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

normal subgroups only

This group has 434 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#10592714C211yesmaximal, characteristic
2C3×#5012C211yesmaximal, characteristic, complemented
3C3×#5007C211yesmaximal, characteristic, complemented
4#10590373C211yesmaximal, characteristic, complemented
5#10589099C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#71104—31nomaximal
9#70867—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3753—21no—
12#64083C2211yescharacteristic
13C2×C3×#208—21no—
14C3×#869C2211yescharacteristic
15C2×#3717—21no—
16C2×#3717—21no—
17#63636—21no—
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×#832—21no—
20C3×#830—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#474—31no—
26C3×#436—31no—
27#5085—31no—
28#5015—31no—
29#5015—31no—
30#5015—61no—
31#5012D311yescharacteristic, complemented
32#5007D311yescharacteristic, complemented
33#4693—31no—
34#4547—31no—
35#4485—31no—
36#4485—31no—
37#4482—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C3×Dic6—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C22⋊C4—21no—
48C32×C42C2311yescharacteristic
49#3753—42no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×#208—42no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#3717—42no—
59#3717—42no—
60#1685—91noSylow
61C2×C3×M16—61no—
62C3×C4⋊Q8—31no—
63C3×C4×D4—21no—
64C3×C4×D4C2×D311yescharacteristic
65C3×C4×D4C2×D311yescharacteristic
66C2×#215—61no—
67C2×#215—61no—
68C2×#213—62no—
69C2×#213—61no—
70C2×#213—61no—
71C2×#208—21no—
72C2×#204—61no—
73C2×#204—61no—
74#874—31no—
75#874—31no—
76#874—61no—
77#869C2×D311yescharacteristic
78C3×#107—61no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8—31no—
81C3×#102—61no—
82C3×C22⋊C8—61no—
83C3×C4×C8—31no—
84#832—21no—
85#830—21no—
86#809—62no—
87#809—61no—
88#809—61no—
89#807—21no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—31no—
92C4⋊(C3⋊C8)—61no—
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4⋊(C3⋊C8)C2×D311yescharacteristic
95C4×C3⋊C8C2×D311yescharacteristic
96C23×C32—21no—
97C22×C3⋊D3—41no—
98C32×D4—21no—
99C32×D4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—41no—
108C4⋊(C3⋊D3)—41no—
109C4⋊(C3⋊D3)—41no—
110C4⋊(C3⋊D3)—81no—
111C2×C3×Dic3—41no—
112C3×Dic6—41no—
113C3×Dic6—41no—
114C3⋊(C3⋊C8)—41no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118C3×C3⋊C8D812yescomplemented
119#492—91no—
120#474—31no—
121#459—91no—
122#436—31no—
123#335—91no—
124#332—91no—
125#331—91no—
126C2×C3×Q8—61no—
127C2×C3×D4—21no—
128C2×C3×D4D1211yescharacteristic
129C2×C3×D4#6711yescharacteristic
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—41no—
133C2×D12—62no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—61no—
140C2×D12—121no—
141C2×D12—121no—
142C2×Dic6—21no—
143C3×M16—122no—
144C2×C3×C8—31no—
145C2×C3×C8—31no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4D1211yescharacteristic
152C3×C4⋊C4#6711yescharacteristic
153C3×C22⋊C4—21no—
154C3×C22⋊C4—21no—
155C3×C22⋊C4—41no—
156C3×C42—21no—
157C3×C42C22×D311yescharacteristic
158C3×C42C22×D311yescharacteristic
159#215—122no—
160#215—122no—
161#213—124no—
162#213—122no—
163#213—122no—
164C4⋊Dic3—21no—
165C4⋊Dic3—21no—
166#208—42no—
167C2×C3⋊C8—21no—
168C2×C3⋊C8—21no—
169C2×C3⋊C8—62no—
170C2×C3⋊C8—61no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8#6711yescharacteristic
173C2×C3⋊C8#6711yescharacteristic
174#204—122no—
175#204—122no—
176C22×C32—41no—
177C22×C32—41no—
178C22×C32—41no—
179C22×C32#12111yescharacteristic
180C2×C3⋊D3—81no—
181C2×C3⋊D3—81no—
182C2×C3⋊D3—81no—
183C32×C4—21no—
184C32×C4—41no—
185C32×C4C2×D811yescharacteristic
186C32×C4AGL(1,ℤ/8)11yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C32×C4#13711yescharacteristic
189C3×Dic3—81no—
190C2×SD16—181no—
191C2×SD16—181no—
192C2×D8—181no—
193C2×M16—61no—
194C4⋊Q8—31no—
195#127—91no—
196C4×D4D3211yescharacteristic
197#107—61no—
198C4⋊C8—31no—
199C4⋊C8—31no—
200C4⋊C8—91no—
201#102—61no—
202#102—181no—
203C22⋊C8—61no—
204C4×C8—31no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—41no—
208C22×D3—122no—
209C22×D3—121no—
210C22×D3—121no—
211C3×Q8—121no—
212C3×Q8—121no—
213C3×D4—22no—
214C3×D4—21no—
215C3×D4—21no—
216C3×D4—21no—
217C3×D4—21no—
218C3×D4—41no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—81no—
230C2×C3×C4—81no—
231C2×C3×C4—121no—
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4#23511yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4#23711yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—41no—
239D12—122no—
240D12—122no—
241D12—121no—
242D12—121no—
243D12—121no—
244D12—121no—
245D12—121no—
246D12—121no—
247D12—121no—
248D12—121no—
249D12—241no—
250D12—241no—
251D12—241no—
252D12—241no—
253D12—242no—
254Dic6—41no—
255Dic6—41no—
256C3×C8—32no—
257C3×C8—61no—
258C3×C8—121no—
259C3×C8—121no—
260C3⋊C8—21no—
261C3⋊C8—41no—
262C3⋊C8—41no—
263C3⋊C8—122no—
264C3⋊C8—121no—
265C3⋊C8—121no—
266C3⋊C8#21312yescomplemented
267C2×C32—81no—
268C2×C32#45911yescharacteristic
269C2×C32#46811yescharacteristic
270C2×C32#47111yescharacteristic
271C3⋊D3—161no—
272C2×Q8—61no—
273C2×D4—181no—
274C2×D4—181no—
275C2×D4—181no—
276C2×D4#62611yescharacteristic
277C22×C4—21no—
278SD16—362no—
279SD16—362no—
280D8—362no—
281M16—122no—
282C2×C8—31no—
283C2×C8—31no—
284C2×C8—61no—
285C2×C8—61no—
286C2×C8—181no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4#62611yescharacteristic
290C22⋊C4—21no—
291C42C2×D3211yescharacteristic
292C22×C3—21no—
293C22×C3—42no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—81no—
301C22×C3—81no—
302C22×C3#93011yescharacteristic
303C22×C3#93911yescharacteristic
304C2×D3—242no—
305C2×D3—242no—
306C2×D3—242no—
307C2×D3—241no—
308C2×D3—241no—
309C2×D3—241no—
310C2×D3—241no—
311C2×D3—241no—
312C2×D3—241no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—81no—
323C3×C4—241no—
324C3×C4#90811yescharacteristic
325C3×C4#90911yescharacteristic
326C3×C4D3×D811yescharacteristic
327C3×C4#91111yescharacteristic
328C3×C4C2×#21311yescharacteristic
329C3×C4#94211yescharacteristic
330C3×C4#94911yescharacteristic
331C3×C4#94911yescharacteristic
332Dic3—81no—
333C32#168511yescharacteristic, complemented, Sylow
334C23—21no—
335C23—361no—
336Q8—121no—
337Q8—121no—
338D4—21no—
339D4—21no—
340D4—361no—
341D4—361no—
342D4—361no—
343D4—361no—
344D4—721no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—121no—
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—82no—
361C2×C3—81no—
362C2×C3—81no—
363C2×C3#501511yescharacteristic
364C2×C3#504911yescharacteristic
365C2×C3#513411yescharacteristic
366C2×C3#514111yescharacteristic
367C2×C3#515011yescharacteristic
368C2×C3#520311yescharacteristic
369D3—482no—
370D3—481no—
371D3—481no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—721no—
376C22—721no—
377C22—721no—
378C22#6397811yescharacteristic
379C4—21no—
380C4—41no—
381C4—241no—
382C4#6382511yescharacteristic
383C4#6383311yescharacteristic
384C4D3×#21311yescharacteristic
385C4#6392511yescharacteristic
386C3—21no—
387C3#7086711yescharacteristic, complemented
388C3#7110411yescharacteristic, complemented
389C2—81no—
390C2—1441no—
391C2#1059117811yescharacteristic
392C2#1059148111yescharacteristic
393C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radical#10592714C2
hypercenterC4×D4D32
hypocenterC32#1685
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
2. C3×#5012C2semidirect
3. C3×#5007C2semidirect
4. #10590373C2semidirect
5. #10589099C2semidirect
6. #10589093C2semidirect
7. #10589091C2semidirect
31. #5012D3semidirect
32. #5007D3semidirect
118. C3×C3⋊C8D8semidirect
266. C3⋊C8#213semidirect
333. C32#1685semidirect
387. C3#70867semidirect
388. C3#71104semidirect

Maximal subgroups

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

subgroupindex
#105927142
C3×#50122
C3×#50072
#105903732
#105890992
#105890932
#105890912
#711043
#708673