Finite Group Databasebeta

← #11778444

Subgroups — #11778444

Order 1152.

645 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 80 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#10595084C211yesmaximal, characteristic
2#10592691C211yesmaximal, characteristic, complemented
3C3×#4967C212yesmaximal, complemented
4#10589150C212yesmaximal, complemented
5#10589146C211yesmaximal, characteristic, complemented
6#71164—32nomaximal
7C2×#3811—21no—
8C2×C32×C4⋊C4C2211yescharacteristic, complemented
9C2×#3752—21no—
10C2×#3752C2211yescharacteristic
11C3×#930C2212yes—
12#63980—21no—
13#63922—22no—
14#63854—22no—
15#63658—21no—
16#63658C2211yescharacteristic, complemented
17C3×#830C2212yescomplemented
18C3×#809—22no—
19C3×#807—22no—
20#5605—32no—
21C3×#480—32no—
22#4992—32no—
23#4992—61no—
24#4967D312yescomplemented
25#4537—32no—
26#4470—32no—
27#4468—32no—
28C23×C3⋊D3D411yescharacteristic
29C22×D32—21no—
30C22×C32×C4—21no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3D411yescharacteristic
34C2×C3×#67—22no—
35C2×C3×D12D412yes—
36#3811—42no—
37#3811—42no—
38C2×#626—22no—
39C2×#625—21no—
40C2×#624—21no—
41C32×C4⋊C4—22no—
42#3752—22no—
43#3752—42no—
44C3×(C2×D3)⋊C4—22no—
45C3×C4⋊Dic3D412yes—
46C2×C3×C3⋊C8—22no—
47#3724—21no—
48(C2×D3)⋊Dic3—22no—
49#1607—91noSylow
50C2×D3×D4—62no—
51C3×#121—32no—
52C2×C3×C4⋊C4—21no—
53C2×C3×C4⋊C4C2×D312yescomplemented
54#939—62no—
55#937—62no—
56#930C2×D312yes—
57C2×(C2×D3)⋊C4—32no—
58C2×(C2×D3)⋊C4—61no—
59C2×(C2×D3)⋊C4—62no—
60C2×(C2×D3)⋊C4—62no—
61#894—62no—
62#883—62no—
63#882—62no—
64C3×#107—62no—
65C3×#102—62no—
66C3×C22⋊C8—32no—
67C3⋊#95—32no—
68C3⋊#95—61no—
69C3⋊#95—62no—
70C3⋊#95—62no—
71#830C2×D312yescomplemented
72#809—22no—
73#807—22no—
74C23×C32C2×D411yescharacteristic
75C22×C3⋊D3—21no—
76C22×C3⋊D3—21no—
77C22×C3⋊D3—41no—
78C22×C3⋊D3—41no—
79C22×C3⋊D3D812yes—
80C22×C3×D3—22no—
81C2×D32—42no—
82C2×D32—81no—
83C2×D32—81no—
84C2×C32×C4—41no—
85C2×C32×C4—41no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4C2×D412yes—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3—41no—
94C3×#67—42no—
95C3×#67—42no—
96C2×C3×Dic3—22no—
97C3×D12—42no—
98#626—44no—
99#625—81no—
100#624—42no—
101C3×C3⋊C8—42no—
102#534—91no—
103#480—32no—
104#397—91no—
105#327—92no—
106#323—91no—
107C23×D3—32no—
108C23×D3—61no—
109C23×D3—62no—
110C2×C3×D4—32no—
111C2×C3×D4—62no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—21no—
115C22×C3×C4C22×D312yes—
116C2×#67—22no—
117C2×#67—62no—
118C2×#67—62no—
119C22×Dic3—32no—
120C22×Dic3—61no—
121C22×Dic3—62no—
122C22×Dic3—62no—
123D3×D4—124no—
124D3×D4—124no—
125C2×D12—62no—
126C2×D12#6712yes—
127C2×C4×D3—62no—
128C2×C3×C8—62no—
129C3×C4⋊C4—22no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—32no—
132C3×C4⋊C4—42no—
133C3×C22⋊C4—62no—
134#217—62no—
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—62no—
137(C2×D3)⋊C4—62no—
138(C2×D3)⋊C4—62no—
139(C2×D3)⋊C4—122no—
140(C2×D3)⋊C4—124no—
141(C2×D3)⋊C4—124no—
142C4⋊Dic3#6712yes—
143Dic3⋊C4—62no—
144C2×C3⋊C8—22no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32#12011yescharacteristic
148C22×C32C2×D811yescharacteristic
149C22×C32AGL(1,ℤ/8)11yescharacteristic
150C2×C3⋊D3—22no—
151C2×C3⋊D3—42no—
152C2×C3⋊D3—41no—
153C2×C3⋊D3—41no—
154C2×C3⋊D3—81no—
155C2×C3×D3—42no—
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158D32—84no—
159C32×C4—22no—
160C32×C4—81no—
161C3⋊Dic3—41no—
162C3⋊Dic3—81no—
163C3×Dic3—42no—
164C22×D4—181no—
165#123—182no—
166#121—32no—
167#121—181no—
168#120—182no—
169C2×C4⋊C4D3211yescharacteristic, complemented
170C2×C22⋊C4—91no—
171C2×C22⋊C4—181no—
172#107—62no—
173#102—62no—
174C22⋊C8—32no—
175#95—91no—
176#95—181no—
177C23×C3—21no—
178C23×C3—62no—
179C23×C3D3×D412yes—
180C22×D3—22no—
181C22×D3—34no—
182C22×D3—62no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—121no—
186C22×D3—121no—
187C22×D3—124no—
188C22×D3—122no—
189C22×D3—122no—
190C22×D3—122no—
191C22×D3—122no—
192C22×D3—242no—
193C22×D3—242no—
194C3×D4—122no—
195C3×D4—122no—
196C3×D4—122no—
197C2×C3×C4—22no—
198C2×C3×C4—42no—
199C2×C3×C4—42no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—62no—
207C2×C3×C4D3×D412yes—
208C2×C3×C4C2×#6712yes—
209#67—42no—
210#67—42no—
211#67—124no—
212#67—242no—
213C2×Dic3—22no—
214C2×Dic3—62no—
215C2×Dic3—121no—
216C2×Dic3—122no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C2×Dic3—122no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C2×Dic3—122no—
224D12—42no—
225D12—124no—
226C4×D3—124no—
227C3×C8—122no—
228C3⋊C8—42no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32#44711yescharacteristic
232C2×C32#45511yescharacteristic
233C2×C32#45811yescharacteristic
234C3⋊D3—42no—
235C3×D3—82no—
236C24—91no—
237C24—181no—
238C2×D4—32no—
239C2×D4—62no—
240C2×D4—182no—
241C2×D4—181no—
242C2×D4—362no—
243C2×D4—362no—
244C22×C4—21no—
245C22×C4—91no—
246C22×C4—181no—
247C22×C4—181no—
248C22×C4C2×D3211yescharacteristic
249C2×C8—62no—
250C4⋊C4—22no—
251C4⋊C4—32no—
252C4⋊C4—181no—
253C22⋊C4—62no—
254C22⋊C4—182no—
255C22⋊C4—182no—
256C22⋊C4—362no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—122no—
265C22×C3—122no—
266C22×C3—122no—
267C22×C3D3×D812yes—
268C22×C3#91112yes—
269C22×C3#93712yes—
270C2×D3—42no—
271C2×D3—42no—
272C2×D3—42no—
273C2×D3—64no—
274C2×D3—122no—
275C2×D3—122no—
276C2×D3—122no—
277C2×D3—124no—
278C2×D3—124no—
279C2×D3—241no—
280C2×D3—241no—
281C2×D3—248no—
282C2×D3—242no—
283C2×D3—242no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—42no—
287C3×C4—82no—
288C3×C4—82no—
289C3×C4—122no—
290Dic3—42no—
291Dic3—122no—
292Dic3—241no—
293Dic3—242no—
294Dic3—242no—
295C32#160711yescharacteristic, complemented, Sylow
296C23—62no—
297C23—92no—
298C23—181no—
299C23—181no—
300C23—361no—
301C23—361no—
302C23—362no—
303C23—721no—
304C23—721no—
305C23#381111yescharacteristic
306D4—122no—
307D4—122no—
308D4—122no—
309D4—364no—
310D4—721no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—62no—
316C2×C4—181no—
317C2×C4—362no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4D3×#6712yes—
323C8—122no—
324C2×C3—22no—
325C2×C3—22no—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—242no—
332C2×C3#505312yes—
333C2×C3#515612yes—
334C2×C3#520212yes—
335D3—82no—
336D3—124no—
337D3—242no—
338C22—21no—
339C22—21no—
340C22—122no—
341C22—122no—
342C22—122no—
343C22—182no—
344C22—362no—
345C22—361no—
346C22—361no—
347C22—721no—
348C22—724no—
349C22#6392611yescharacteristic
350C22#6392711yescharacteristic
351C22#6398311yescharacteristic
352C4—22no—
353C4—81no—
354C4—122no—
355C4—361no—
356C4—721no—
357C3—21no—
358C3#7116412yescomplemented
359C2—21no—
360C2—21no—
361C2—242no—
362C2—362no—
363C2#1059139811yescharacteristic
364C2#1059151611yescharacteristic
365C2#1059165811yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#10595084C2
hypercenterC2×C4⋊C4D32
hypocenterC32#1607
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592691C2semidirect
3. C3×#4967C2semidirect
4. #10589150C2semidirect
5. #10589146C2semidirect
8. C2×C32×C4⋊C4C22semidirect
16. #63658C22semidirect
17. C3×#830C22semidirect
24. #4967D3semidirect
53. C2×C3×C4⋊C4C2×D3semidirect
71. #830C2×D3semidirect
169. C2×C4⋊C4D32semidirect
295. C32#1607semidirect
358. C3#71164semidirect

Maximal subgroups

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

subgroupindex
#105950842
#105926912
C3×#49672
#105891502
#105891462
#711643