Finite Group Databasebeta

← #11781970

Subgroups — #11781970

Order 1152.

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

normal subgroups only

This group has 358 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#10592730C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic
3C3×#5024C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic
5#10589097C211yesmaximal, characteristic
6#10589094C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71057—31nomaximal
9#70964—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×#3756—21no—
12#64078C2211yescharacteristic
13C2×C3×#216—21no—
14C3×#869C2211yescharacteristic
15#63637—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#810—21no—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#803—21no—
22C3×C4×C3⋊C8C2211yescharacteristic
23#63575—21no—
24#63575—21no—
25C3×#462—31no—
26C3×#446—31no—
27#5078—31no—
28#5031—31no—
29#5031—31no—
30#5031—61no—
31#5031D311yescharacteristic
32#5024D311yescharacteristic
33#4682—31no—
34#4547—31no—
35#4486—31no—
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8D411yescharacteristic
41C2×#634—21no—
42C2×C3×Dic6—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47#3756—42no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×#216—42no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1694—91noSylow
59C2×C3×Q16—61no—
60C3×C4⋊Q8—31no—
61C3×C4×Q8—21no—
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×Q8C2×D311yescharacteristic
64C2×#216—21no—
65C2×#216—62no—
66C2×#216—61no—
67C2×#216—61no—
68#869—31no—
69#869—31no—
70#869—61no—
71#869C2×D311yescharacteristic
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—61no—
75C3×#103—61no—
76C3×#97—61no—
77C3×C4×C8—31no—
78#818—61no—
79#818—61no—
80#810—21no—
81#810—62no—
82#810—61no—
83#810—61no—
84#807—61no—
85#807—61no—
86C4⋊(C3⋊C8)—21no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92#803—21no—
93C4×C3⋊C8C2×D311yescharacteristic
94C32×Q8—21no—
95C32×Q8—21no—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—41no—
102#634—41no—
103#634—41no—
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8Q1612yescomplemented
112#500—91no—
113#462—31no—
114#462—91no—
115#446—31no—
116#334—91no—
117#332—91no—
118#332—91no—
119C2×C3×Q8—21no—
120C2×C3×Q8—61no—
121C2×C3×Q8D1211yescharacteristic
122C2×C3×Q8#6711yescharacteristic
123C2×Dic6—21no—
124C2×Dic6—62no—
125C2×Dic6—61no—
126C2×Dic6—61no—
127C3×Q16—122no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—61no—
131C2×C3×C8—61no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—41no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4D1211yescharacteristic
139C3×C4⋊C4#6711yescharacteristic
140C3×C42—21no—
141C3×C42—21no—
142C3×C42—21no—
143C3×C42—41no—
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146#216—42no—
147#216—124no—
148#216—122no—
149#216—122no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—121no—
157C4⋊Dic3—121no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—62no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8#6711yescharacteristic
164C2×C3⋊C8#6711yescharacteristic
165C22×C32#12111yescharacteristic
166C32×C4—21no—
167C32×C4—41no—
168C32×C4—41no—
169C32×C4C2×Q1611yescharacteristic
170C32×C4AGL(1,ℤ/8)11yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C32×C4#13711yescharacteristic
173C3⋊Dic3—81no—
174C3×Dic3—81no—
175C2×Q16—61no—
176C2×Q16—181no—
177C4⋊Q8—31no—
178C4⋊Q8—91no—
179C4×Q8D3211yescharacteristic
180#107—181no—
181#107—181no—
182C4⋊C8—31no—
183C4⋊C8—31no—
184C4⋊C8—61no—
185C4⋊C8—91no—
186#103—61no—
187#103—181no—
188#97—61no—
189C4×C8—31no—
190C3×Q8—22no—
191C3×Q8—21no—
192C3×Q8—21no—
193C3×Q8—21no—
194C3×Q8—21no—
195C3×Q8—41no—
196C3×Q8—121no—
197C3×Q8—121no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—121no—
208C2×C3×C4C2×D1211yescharacteristic
209C2×C3×C4#23511yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4#23711yescharacteristic
212C2×C3×C4C2×#6711yescharacteristic
213C2×C3×C4C2×#6711yescharacteristic
214C2×Dic3—41no—
215C2×Dic3—122no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218Dic6—41no—
219Dic6—41no—
220Dic6—122no—
221Dic6—122no—
222Dic6—121no—
223Dic6—121no—
224Dic6—121no—
225Dic6—121no—
226C3×C8—32no—
227C3×C8—61no—
228C3×C8—121no—
229C3×C8—121no—
230C3⋊C8—21no—
231C3⋊C8—41no—
232C3⋊C8—41no—
233C3⋊C8—122no—
234C3⋊C8—121no—
235C3⋊C8—121no—
236C3⋊C8#21612yescomplemented
237C2×C32#46211yescharacteristic
238C2×C32#46911yescharacteristic
239C2×C32#47311yescharacteristic
240C2×Q8—61no—
241C2×Q8—181no—
242C2×Q8#62611yescharacteristic
243Q16—122no—
244Q16—362no—
245C2×C8—31no—
246C2×C8—31no—
247C2×C8—61no—
248C2×C8—61no—
249C2×C8—181no—
250C4⋊C4—21no—
251C4⋊C4—61no—
252C4⋊C4—61no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4#62611yescharacteristic
256C42—21no—
257C42C2×D3211yescharacteristic
258C22×C3—21no—
259C22×C3#93011yescharacteristic
260C22×C3#93911yescharacteristic
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—41no—
268C3×C4—42no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4—81no—
274C3×C4—241no—
275C3×C4#90811yescharacteristic
276C3×C4#90811yescharacteristic
277C3×C4D3×Q1611yescharacteristic
278C3×C4#91811yescharacteristic
279C3×C4#93211yescharacteristic
280C3×C4C2×#21611yescharacteristic
281C3×C4#94911yescharacteristic
282C3×C4#95111yescharacteristic
283Dic3—81no—
284Dic3—242no—
285Dic3—241no—
286Dic3—241no—
287C32#169411yescharacteristic, complemented, Sylow
288Q8—21no—
289Q8—21no—
290Q8—121no—
291Q8—121no—
292Q8—361no—
293Q8—361no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—121no—
297C2×C4—361no—
298C2×C4#380411yescharacteristic
299C2×C4C2×#62611yescharacteristic
300C2×C4D3×#6711yescharacteristic
301C8—32no—
302C8—61no—
303C8—121no—
304C8—121no—
305C8—361no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3#503111yescharacteristic
310C2×C3#503911yescharacteristic
311C2×C3#513511yescharacteristic
312C2×C3#514311yescharacteristic
313C2×C3#518211yescharacteristic
314C2×C3#520411yescharacteristic
315C22#6397811yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—241no—
320C4—721no—
321C4#6382511yescharacteristic
322C4#6383011yescharacteristic
323C4D3×#21611yescharacteristic
324C4#6394311yescharacteristic
325C3—21no—
326C3#7096411yescharacteristic, complemented
327C3#7105711yescharacteristic, complemented
328C2#1059116511yescharacteristic
329C2#1059162511yescharacteristic
330C2#1059168211yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1694
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
111. C3×C3⋊C8Q16semidirect
236. C3⋊C8#216semidirect
287. C32#1694semidirect
326. C3#70964semidirect
327. C3#71057semidirect

Maximal subgroups

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

subgroupindex
#105927302
C3×#50312
C3×#50242
#105903112
#105890972
#105890942
#105890922
#710573
#709643