Finite Group Databasebeta

← #11878931

Subgroups — #11878931

Order 1152.

1182 conjugacy classes of subgroups; only the 233 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 233 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#10596199C211yesmaximal, characteristic, complemented
2#10596187C211yesmaximal, characteristic
3C32×#492C211yesmaximal, characteristic, complemented
4#10592872C214yesmaximal, complemented
5#10592865C214yesmaximal, complemented
6#10592791C211yesmaximal, characteristic, complemented
7#10592769C211yesmaximal, characteristic, complemented
8#10592384C211yesmaximal, characteristic, complemented
9#10592380C211yesmaximal, characteristic, complemented
10#81767—34nomaximal
11C2×#3830C2212yes—
12C2×C32×SD16C2214yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×#127C2211yescharacteristic
15#64155C2212yes—
16Q8×C3⋊Dic3C2212yes—
17C2×#3756C2214yes—
18#64147—21no—
19#64147—21no—
20#64145C2212yes—
21D4×C3⋊Dic3—21no—
22D4×C3⋊Dic3—21no—
23#64106—21no—
24#64101—21no—
25#64099—21no—
26#64096—21no—
27C42×C3⋊D3C2211yescharacteristic
28#64078C2211yescharacteristic
29#64078C2211yescharacteristic
30C32×C4×C8C2211yescharacteristic
31#63659C2214yes—
32#63647C2212yes—
33#63643C2214yes—
34#63641C2212yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36#5728—34no—
37#5716—34no—
38C3×#492D314yescomplemented
39#5173—316no—
40#5166—316no—
41#5092—34no—
42#5070—34no—
43#4685—34no—
44#4681—34no—
45C2×C32×Q8C2312yes—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2312yes—
49C2×#638—22no—
50C22×C3⋊Dic3—22no—
51#3830—44no—
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×#634—21no—
56C2×#634C2312yes—
57C32×SD16—44no—
58C2×C32×C8C2312yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C42C2311yescharacteristic
62#3757—22no—
63#3757—22no—
64#3756—44no—
65#3752—22no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—22no—
70C4⋊(C3⋊Dic3)C2312yes—
71#3750—22no—
72C4×C3⋊Dic3—22no—
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2312yes—
77#3210—91noSylow
78C2×#237—38no—
79C2×C3×SD16C2×D3116yes—
80C3×C4⋊Q8C2×D314yes—
81C3×#127C2×D314yes—
82#946—38no—
83Q8×Dic3—38no—
84C2×#216—316no—
85#938—64no—
86#938—64no—
87#936—38no—
88D4×Dic3—64no—
89D4×Dic3—64no—
90#897—64no—
91#892—64no—
92#890—64no—
93#887—64no—
94C42×D3—34no—
95#869—34no—
96#869—34no—
97C3×C4×C8C2×D314yes—
98#832—316no—
99(C2×D3)⋊C8—38no—
100#816—316no—
101Dic3⋊C8—38no—
102C4×C3⋊C8—34no—
103C23×C32—22no—
104C22×C3⋊D3C2×D411yescharacteristic
105C32×Q8—24no—
106C32×D4—24no—
107C32×D4—42no—
108C32×D4—42no—
109C2×C32×C4—22no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2411yescharacteristic
113#638—44no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—44no—
117C2×C3⋊Dic3C2×D411yescharacteristic
118C2×C3⋊Dic3C2×D411yescharacteristic
119C2×C3⋊Dic3C2×D411yescharacteristic
120C4×C3⋊D3—22no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123#634—24no—
124#634—42no—
125C32×C8—22no—
126C3⋊(C3⋊C8)—22no—
127#533—91no—
128#532—91no—
129#494—91no—
130#492C3⋊D311yescharacteristic, complemented
131#487—91no—
132#486—91no—
133#464—94no—
134#452—94no—
135#431—91no—
136C2×C3×Q8C22×D318yes—
137C2×C3×D4—24no—
138C2×C3×D4—24no—
139C2×C3×D4C22×D318yes—
140C2×#67—68no—
141C22×Dic3—68no—
142#237—1216no—
143C2×C4×D3—34no—
144C2×C4×D3—34no—
145C2×C4×D3—34no—
146C2×Dic6—38no—
147C2×Dic6—64no—
148C3×SD16—416no—
149C2×C3×C8C22×D318yes—
150C3×C4⋊C4—24no—
151C3×C4⋊C4—24no—
152C3×C42C22×D314yes—
153#217—68no—
154#217—68no—
155#216—1216no—
156(C2×D3)⋊C4—68no—
157C4⋊Dic3—38no—
158C4⋊Dic3—68no—
159C4⋊Dic3—64no—
160C4⋊Dic3—64no—
161C4⋊Dic3—64no—
162Dic3⋊C4—68no—
163C4×Dic3—34no—
164C4×Dic3—34no—
165C4×Dic3—34no—
166C4×Dic3—68no—
167C2×C3⋊C8—38no—
168C22×C32—42no—
169C22×C32—42no—
170C22×C32—42no—
171C22×C32C22×D411yescharacteristic
172C2×C3⋊D3—21no—
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C32×C4—42no—
176C32×C4#13512yes—
177C32×C4#13712yes—
178C32×C4H(5,𝔽2)12yes—
179C3⋊Dic3—21no—
180C3⋊Dic3—21no—
181C3⋊Dic3—21no—
182C3⋊Dic3—42no—
183C3⋊Dic3—42no—
184C2×#41—92no—
185C2×Q16—94no—
186C2×SD16C2×C3⋊D314yes—
187C4⋊Q8—91no—
188C4⋊Q8—91no—
189C4⋊Q8C2×C3⋊D311yescharacteristic
190#127C2×C3⋊D311yescharacteristic
191#125—181no—
192#124—92no—
193C22⋊Q8—92no—
194C22⋊Q8—181no—
195#121—181no—
196#121—181no—
197C4×Q8—92no—
198C4×Q8—181no—
199C4×D4—181no—
200C4×D4—181no—
201#117—181no—
202C2×C42—91no—
203C4⋊C8—92no—
204#103—94no—
205#102—94no—
206C22⋊C8—92no—
207C4×C8—91no—
208C4×C8C2×C3⋊D311yescharacteristic
209C23×C3—28no—
210C22×D3—34no—
211C3×Q8—216no—
212C3×D4—216no—
213C3×D4—48no—
214C3×D4—48no—
215C2×C3×C4—28no—
216C2×C3×C4D3×D414yes—
217C2×C3×C4D3×D414yes—
218C2×C3×C4C23×D314yes—
219#67—1216no—
220C2×Dic3—34no—
221C2×Dic3—34no—
222C2×Dic3—34no—
223C2×Dic3—68no—
224C2×Dic3—68no—
225C2×Dic3—1216no—
226C4×D3—68no—
227C4×D3—68no—
228C4×D3—68no—
229Dic6—616no—
230Dic6—128no—
231C3×C8—28no—
232C3⋊C8—68no—
233C2×C32—82no—
234C2×C32#53511yescharacteristic
235C2×C32C2×#13511yescharacteristic
236C2×C32C2×#13711yescharacteristic
237C3⋊D3—41no—
238#41—364no—
239C2×Q8—92no—
240C2×Q8—181no—
241C2×Q8C22×C3⋊D312yes—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—182no—
245C2×D4C22×C3⋊D312yes—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—182no—
250Q16—364no—
251SD16—44no—
252C2×C8—92no—
253C2×C8C22×C3⋊D312yes—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—92no—
257C4⋊C4—182no—
258C4⋊C4—182no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C22⋊C4—182no—
263C22⋊C4—182no—
264C22⋊C4—182no—
265C42—91no—
266C42—91no—
267C42—91no—
268C42—182no—
269C42C22×C3⋊D311yescharacteristic
270C22×C3—48no—
271C22×C3—48no—
272C22×C3—48no—
273C22×C3C2×D3×D414yes—
274C2×D3—64no—
275C2×D3—64no—
276C2×D3—64no—
277C3×C4—48no—
278C3×C4#91518yes—
279C3×C4#91618yes—
280C3×C4#100418yes—
281Dic3—64no—
282Dic3—64no—
283Dic3—64no—
284Dic3—128no—
285Dic3—128no—
286C32#321011yescharacteristic, complemented, Sylow
287C23—22no—
288C23—91no—
289Q8—24no—
290Q8—184no—
291Q8—362no—
292D4—24no—
293D4—42no—
294D4—42no—
295D4—364no—
296C2×C4—22no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—364no—
306C2×C4D4×C3⋊D311yescharacteristic
307C2×C4D4×C3⋊D311yescharacteristic
308C2×C4C23×C3⋊D311yescharacteristic
309C8—22no—
310C8—182no—
311C2×C3—88no—
312C2×C3#571514yes—
313C2×C3C2×#91514yes—
314C2×C3C2×#91614yes—
315D3—124no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—181no—
320C22—181no—
321C22—181no—
322C22C2×D4×C3⋊D311yescharacteristic
323C4—42no—
324C4—181no—
325C4—181no—
326C4—181no—
327C4—362no—
328C4—362no—
329C4#6412412yes—
330C4#6412512yes—
331C4#6436112yes—
332C3#8176714yescomplemented
333C2—82no—
334C2—361no—
335C2#1059618611yescharacteristic
336C2C2×#6412411yescharacteristic
337C2C2×#6412511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#492C2
socleC22×C32C22×D4
prime radical#10596187C2
hypercenter#492C3⋊D3
hypocenterC32#3210
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#492C2semidirect
4. #10592872C2semidirect
5. #10592865C2semidirect
6. #10592791C2semidirect
7. #10592769C2semidirect
8. #10592384C2semidirect
9. #10592380C2semidirect
38. C3×#492D3semidirect
130. #492C3⋊D3semidirect
286. C32#3210semidirect
332. C3#81767semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105961872
C32×#4922
#105928722
#105928652
#105927912
#105927692
#105923842
#105923802
#817673