Finite Group Databasebeta

← #11781351

Subgroups — #11781351

Order 1152.

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

normal subgroups only

This group has 392 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#10592718C211yesmaximal, characteristic
2C3×D4×C3⋊C8C211yesmaximal, characteristic
3C3×#5007C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#71102—31nomaximal
9#70854—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3754—21no—
12#64078C2211yescharacteristic
13C22×C3×C3⋊C8—21no—
14C3×#869C2211yescharacteristic
15#63637—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#832—21no—
18C3×#830—21no—
19C3×#807—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63566—21no—
24#63566—21no—
25C3×#474—31no—
26C3×C8×D4—31no—
27#5079—31no—
28#5019—31no—
29#5019—31no—
30#5019—61no—
31D4×C3⋊C8D311yescharacteristic
32#5007D311yescharacteristic
33#4681—31no—
34#4547—31no—
35#4486—31no—
36#4482—31no—
37#4482—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
47#3754—42no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—42no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1679—91noSylow
59C22×C3×C8—61no—
60C3×C4⋊Q8—31no—
61C3×C4×D4—21no—
62C3×C4×D4C2×D311yescharacteristic
63C3×C4×D4C2×D311yescharacteristic
64C2×#214—62no—
65C2×#214—61no—
66C2×#214—61no—
67C22×C3⋊C8—21no—
68#869—31no—
69#869—31no—
70#869—61no—
71#869C2×D311yescharacteristic
72C3×#107—61no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×#102—61no—
76C3×C22⋊C8—61no—
77C3×C4×C8—31no—
78#835—61no—
79#835—61no—
80#832—21no—
81#830—21no—
82#816—61no—
83#816—61no—
84#810—62no—
85#810—61no—
86#810—61no—
87#807—21no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C23×C32—21no—
95C32×D4—21no—
96C32×D4SD1612yes—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3⋊Dic3—41no—
104#634—41no—
105#634—41no—
106C2×C3×Dic3—41no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C3⋊(C3⋊C8)—41no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#487—91no—
115#474—31no—
116#461—91no—
117C8×D4—31no—
118#334—91no—
119#332—91no—
120#332—91no—
121C2×C3×Q8—61no—
122C2×C3×D4—21no—
123C2×C3×D4D1211yescharacteristic
124C2×C3×D4#6711yescharacteristic
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—41no—
128C2×Dic6—21no—
129C2×Dic6—62no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C2×C3×C8—122no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4D1211yescharacteristic
141C3×C4⋊C4#6711yescharacteristic
142C3×C22⋊C4—21no—
143C3×C22⋊C4—21no—
144C3×C22⋊C4—41no—
145C3×C42—21no—
146C3×C42C22×D311yescharacteristic
147C3×C42C22×D311yescharacteristic
148#214—124no—
149#214—122no—
150#214—122no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—121no—
158C4⋊Dic3—121no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—42no—
162C2×C3⋊C8—62no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8#6711yescharacteristic
166C2×C3⋊C8#6711yescharacteristic
167C22×C32—22no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32#12111yescharacteristic
171C32×C4—21no—
172C32×C4—41no—
173C32×C4C2×SD1611yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4#13511yescharacteristic
176C32×C4AGL(1,ℤ/8)11yescharacteristic
177C3⋊Dic3—81no—
178C3×Dic3—81no—
179C2×SD16—181no—
180C22×C8—61no—
181C4⋊Q8—31no—
182C4⋊Q8—91no—
183C4×D4D3211yescharacteristic
184#107—61no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—91no—
188#103—181no—
189#103—181no—
190#103—181no—
191#102—61no—
192C22⋊C8—61no—
193C4×C8—31no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—41no—
197C3×Q8—121no—
198C3×Q8—121no—
199C3×D4—21no—
200C3×D4—21no—
201C3×D4—22no—
202C3×D4—41no—
203C3×D4#20412yes—
204C3×D4#21512yes—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—81no—
216C2×C3×C4—81no—
217C2×C3×C4—121no—
218C2×C3×C4C2×D1211yescharacteristic
219C2×C3×C4#23511yescharacteristic
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4#23711yescharacteristic
222C2×C3×C4C2×#6711yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×Dic3—41no—
225C2×Dic3—122no—
226C2×Dic3—121no—
227C2×Dic3—121no—
228Dic6—41no—
229Dic6—41no—
230Dic6—122no—
231Dic6—122no—
232Dic6—121no—
233Dic6—121no—
234Dic6—121no—
235Dic6—121no—
236C3×C8—61no—
237C3×C8—61no—
238C3×C8—121no—
239C3×C8—121no—
240C3⋊C8—21no—
241C3⋊C8—21no—
242C3⋊C8—41no—
243C3⋊C8—41no—
244C3⋊C8—122no—
245C3⋊C8—121no—
246C3⋊C8—121no—
247C2×C32—42no—
248C2×C32#46311yescharacteristic
249C2×C32#46511yescharacteristic
250C2×C32#47311yescharacteristic
251C2×Q8—61no—
252C2×Q8—181no—
253C2×D4#62611yescharacteristic
254C22×C4—21no—
255SD16—362no—
256C2×C8—31no—
257C2×C8—31no—
258C2×C8—61no—
259C2×C8—61no—
260C2×C8—122no—
261C2×C8—181no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4#62611yescharacteristic
267C22⋊C4—21no—
268C42C2×D3211yescharacteristic
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—42no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—81no—
278C22×C3—81no—
279C22×C3#93011yescharacteristic
280C22×C3#93911yescharacteristic
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—81no—
291C3×C4—241no—
292C3×C4C2×#20411yescharacteristic
293C3×C4#90411yescharacteristic
294C3×C4#91111yescharacteristic
295C3×C4#91211yescharacteristic
296C3×C4#93211yescharacteristic
297C3×C4C2×#21511yescharacteristic
298C3×C4#95011yescharacteristic
299C3×C4#95011yescharacteristic
300Dic3—81no—
301Dic3—242no—
302Dic3—241no—
303Dic3—241no—
304C32#167911yescharacteristic, complemented, Sylow
305C23—21no—
306Q8—121no—
307Q8—121no—
308Q8—361no—
309Q8—361no—
310D4—21no—
311D4#371712yes—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—121no—
316C2×C4—361no—
317C2×C4#380411yescharacteristic
318C2×C4C2×#62611yescharacteristic
319C2×C4D3×#6711yescharacteristic
320C8—61no—
321C8—61no—
322C8—121no—
323C8—121no—
324C8—361no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—42no—
329C2×C3—42no—
330C2×C3—82no—
331C2×C3#501611yescharacteristic
332C2×C3#504811yescharacteristic
333C2×C3#511411yescharacteristic
334C2×C3#514311yescharacteristic
335C2×C3#515311yescharacteristic
336C2×C3#520411yescharacteristic
337C22—22no—
338C22—41no—
339C22—41no—
340C22#6397811yescharacteristic
341C4—21no—
342C4—41no—
343C4—241no—
344C4—721no—
345C4#6382911yescharacteristic
346C4C2×#371711yescharacteristic
347C4#6393211yescharacteristic
348C4#6393311yescharacteristic
349C3—21no—
350C3#7085411yescharacteristic, complemented
351C3#7110211yescharacteristic, complemented
352C2—42no—
353C2#1059117711yescharacteristic
354C2#1059146811yescharacteristic
355C2#1059168211yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1679
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. #10590287C2semidirect
5. #10589097C2semidirect
6. #10589094C2semidirect
7. #10589093C2semidirect
304. C32#1679semidirect
350. C3#70854semidirect
351. C3#71102semidirect

Maximal subgroups

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

subgroupindex
#105927182
C3×D4×C3⋊C82
C3×#50072
#105902872
#105890972
#105890942
#105890932
#711023
#708543