Finite Group Databasebeta

← #11782002

Subgroups — #11782002

Order 1152.

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

normal subgroups only

This group has 362 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#10592707C211yesmaximal, characteristic
2C3×#5012C211yesmaximal, characteristic
3C3×#5008C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589095C211yesmaximal, characteristic, complemented
8#71137—31nomaximal
9#70874—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#208—21no—
13C3×#869C2211yescharacteristic
14#63659—21no—
15#63635—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#832—21no—
18C3×#830—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63575—21no—
24#63575—21no—
25C3×#476—31no—
26C3×#436—31no—
27#5078—31no—
28#5012D311yescharacteristic
29#5008—31no—
30#5008—31no—
31#5008—61no—
32#5008D311yescharacteristic
33#4682—31no—
34#4546—31no—
35#4481—31no—
36#4481—31no—
37#4481—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×#208—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1695—91noSylow
58C2×C3×M16—61no—
59C3×C4⋊Q8—31no—
60C3×C4×D4—21no—
61C3×C4×D4C2×D311yescharacteristic
62C3×C4×D4C2×D311yescharacteristic
63C2×#208—21no—
64#869—31no—
65#869—31no—
66#869—61no—
67#869C2×D311yescharacteristic
68C3×#106—61no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×#102—61no—
72C3×C22⋊C8—61no—
73C3×C4×C8—31no—
74#832—21no—
75#832—62no—
76#832—61no—
77#832—61no—
78#830—21no—
79#818—61no—
80#818—61no—
81#808—21no—
82#808—62no—
83#808—61no—
84#808—61no—
85#807—61no—
86#807—61no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C23×C32—21no—
94C32×D4—21no—
95C32×D4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3⋊Dic3—41no—
103#634—81no—
104C2×C3×Dic3—41no—
105C3×Dic6—81no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8SD1612yes—
111#500—91no—
112#476—31no—
113#476—91no—
114#436—31no—
115#334—91no—
116#333—91no—
117#333—91no—
118C2×C3×Q8—61no—
119C2×C3×D4—21no—
120C2×C3×D4D1211yescharacteristic
121C2×C3×D4#6711yescharacteristic
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—41no—
125C2×Dic6—21no—
126C2×Dic6—61no—
127C2×Dic6—61no—
128C2×Dic6—121no—
129C3×M16—122no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4D1211yescharacteristic
138C3×C4⋊C4#6711yescharacteristic
139C3×C22⋊C4—21no—
140C3×C22⋊C4—21no—
141C3×C22⋊C4—41no—
142C3×C42—21no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—62no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—121no—
153#208—42no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8#6711yescharacteristic
160C2×C3⋊C8#6711yescharacteristic
161C22×C32—41no—
162C22×C32—41no—
163C22×C32—41no—
164C22×C32#12111yescharacteristic
165C32×C4—21no—
166C32×C4—41no—
167C32×C4C2×SD1611yescharacteristic
168C32×C4#13711yescharacteristic
169C32×C4#13711yescharacteristic
170C32×C4#13711yescharacteristic
171C3⋊Dic3—81no—
172C3×Dic3—81no—
173C2×M16—61no—
174C4⋊Q8—31no—
175C4⋊Q8—91no—
176C4×D4D3211yescharacteristic
177#107—181no—
178#107—181no—
179#106—61no—
180#106—181no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183C4⋊C8—91no—
184#102—61no—
185#102—181no—
186C22⋊C8—61no—
187C4×C8—31no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—41no—
191C3×Q8—241no—
192C3×D4—22no—
193C3×D4—21no—
194C3×D4—21no—
195C3×D4—21no—
196C3×D4—21no—
197C3×D4—41no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—81no—
209C2×C3×C4—81no—
210C2×C3×C4—121no—
211C2×C3×C4C2×D1211yescharacteristic
212C2×C3×C4#23511yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4#23711yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216C2×C3×C4C2×#6711yescharacteristic
217C2×Dic3—41no—
218C2×Dic3—122no—
219C2×Dic3—121no—
220C2×Dic3—121no—
221Dic6—81no—
222Dic6—242no—
223Dic6—241no—
224Dic6—241no—
225C3×C8—32no—
226C3×C8—61no—
227C3×C8—121no—
228C3×C8—121no—
229C3⋊C8—21no—
230C3⋊C8—41no—
231C3⋊C8—41no—
232C3⋊C8—122no—
233C3⋊C8—121no—
234C3⋊C8—121no—
235C3⋊C8#21412yes—
236C2×C32—81no—
237C2×C32#46111yescharacteristic
238C2×C32#47011yescharacteristic
239C2×C32#47211yescharacteristic
240C2×Q8—61no—
241C2×Q8—181no—
242C2×D4#62611yescharacteristic
243C22×C4—21no—
244M16—122no—
245C2×C8—31no—
246C2×C8—31no—
247C2×C8—61no—
248C2×C8—61no—
249C2×C8—181no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4#62611yescharacteristic
255C22⋊C4—21no—
256C42C2×D3211yescharacteristic
257C22×C3—21no—
258C22×C3—42no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—81no—
266C22×C3—81no—
267C22×C3#93011yescharacteristic
268C22×C3#93911yescharacteristic
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—41no—
278C3×C4—81no—
279C3×C4—241no—
280C3×C4#90911yescharacteristic
281C3×C4#90911yescharacteristic
282C3×C4D3×SD1611yescharacteristic
283C3×C4#91511yescharacteristic
284C3×C4C2×#21411yescharacteristic
285C3×C4#94211yescharacteristic
286C3×C4#95111yescharacteristic
287C3×C4#95111yescharacteristic
288Dic3—81no—
289Dic3—242no—
290Dic3—241no—
291Dic3—241no—
292C32#169511yescharacteristic, complemented, Sylow
293C23—21no—
294Q8—241no—
295Q8—721no—
296D4—21no—
297D4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—121no—
302C2×C4—361no—
303C2×C4#380411yescharacteristic
304C2×C4C2×#62611yescharacteristic
305C2×C4D3×#6711yescharacteristic
306C8—32no—
307C8—61no—
308C8—121no—
309C8—121no—
310C8—361no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—82no—
315C2×C3—81no—
316C2×C3—81no—
317C2×C3#501911yescharacteristic
318C2×C3#505211yescharacteristic
319C2×C3#513711yescharacteristic
320C2×C3#514211yescharacteristic
321C2×C3#516211yescharacteristic
322C2×C3#519911yescharacteristic
323C22—41no—
324C22—41no—
325C22—41no—
326C22#6397811yescharacteristic
327C4—21no—
328C4—41no—
329C4—241no—
330C4—721no—
331C4#6383111yescharacteristic
332C4#6383311yescharacteristic
333C4D3×#21411yescharacteristic
334C4#6392911yescharacteristic
335C3—21no—
336C3#7087411yescharacteristic, complemented
337C3#7113711yescharacteristic, complemented
338C2—81no—
339C2#1059112111yescharacteristic
340C2#1059148911yescharacteristic
341C2#1059167711yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1695
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
4. #10590311C2semidirect
5. #10589097C2semidirect
6. #10589096C2semidirect
7. #10589095C2semidirect
292. C32#1695semidirect
336. C3#70874semidirect
337. C3#71137semidirect

Maximal subgroups

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

subgroupindex
#105927072
C3×#50122
C3×#50082
#105903112
#105890972
#105890962
#105890952
#711373
#708743