Finite Group Databasebeta

← #11878685

Subgroups — #11878685

Order 1152.

1284 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 241 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10596187C211yesmaximal, characteristic
3C32×#492C211yesmaximal, characteristic, complemented
4#10592869C214yesmaximal, complemented
5#10592861C214yesmaximal, complemented
6#10592778C211yesmaximal, characteristic, complemented
7#10592775C211yesmaximal, characteristic, complemented
8#10592384C211yesmaximal, characteristic, complemented
9#10592380C211yesmaximal, characteristic, complemented
10#81764—34nomaximal
11C2×Q8×C3⋊D3C2212yes—
12C2×#3830—21no—
13C2×C32×SD16C2214yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#127C2211yescharacteristic
16#64153C2212yes—
17#64147—21no—
18#64147C2212yes—
19#64145—21no—
20D4×C3⋊Dic3—21no—
21D4×C3⋊Dic3C2212yes—
22C2×#3754C2214yes—
23C4⋊C4×C3⋊D3—21no—
24C4⋊C4×C3⋊D3—21no—
25#64097—21no—
26#64097—21no—
27C42×C3⋊D3C2211yescharacteristic
28#64078C2211yescharacteristic
29#64078C2211yescharacteristic
30C32×C4×C8C2211yescharacteristic
31#63662C2214yes—
32#63647C2212yes—
33#63643C2214yes—
34#63641C2212yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36D3×C4⋊Q8—34no—
37#5716—34no—
38C3×#492D314yescomplemented
39#5170—316no—
40#5162—316no—
41#5079—34no—
42#5076—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—
51Q8×C3⋊D3—44no—
52#3830—44no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3C2311yescharacteristic
57C2×#634—21no—
58C2×#634—22no—
59C2×#634C2312yes—
60C32×SD16—44no—
61C2×C32×C8C2312yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C32×C42C2311yescharacteristic
65#3757—22no—
66#3757—22no—
67#3754—44no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2312yes—
72#3750—22no—
73#3750—22no—
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3D411yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2312yes—
78#3206—91noSylow
79C2×D3×Q8—38no—
80C2×#237—64no—
81C2×C3×SD16C2×D3116yes—
82C3×C4⋊Q8C2×D314yes—
83C3×#127C2×D314yes—
84#944—38no—
85#938—38no—
86#938—64no—
87#936—64no—
88D4×Dic3—38no—
89D4×Dic3—64no—
90C2×#214—316no—
91D3×C4⋊C4—64no—
92D3×C4⋊C4—64no—
93#888—64no—
94#888—64no—
95C42×D3—34no—
96#869—34no—
97#869—34no—
98C3×C4×C8C2×D314yes—
99#835—316no—
100(C2×D3)⋊C8—38no—
101#816—316no—
102Dic3⋊C8—38no—
103C4×C3⋊C8—34no—
104C23×C32—22no—
105C22×C3⋊D3C2×D411yescharacteristic
106C32×Q8—24no—
107C32×D4—24no—
108C32×D4—42no—
109C32×D4—42no—
110C2×C32×C4—22no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2411yescharacteristic
114#638—44no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—44no—
118C2×C3⋊Dic3C2×D411yescharacteristic
119C2×C3⋊Dic3C2×D411yescharacteristic
120C2×C3⋊Dic3C2×D411yescharacteristic
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—44no—
124C4×C3⋊D3SD1614yescomplemented
125#634—24no—
126#634—44no—
127#634—42no—
128C32×C8—22no—
129C3⋊(C3⋊C8)—22no—
130#532—91no—
131C2×C4⋊Q8—91no—
132#492—91no—
133#492C3⋊D311yescharacteristic, complemented
134#487—91no—
135#487—91no—
136#461—94no—
137#448—94no—
138#431—91no—
139C2×C3×Q8C22×D318yes—
140C2×C3×D4—24no—
141C2×C3×D4—24no—
142C2×C3×D4C22×D318yes—
143C2×#67—68no—
144C22×Dic3—68no—
145D3×Q8—1216no—
146#237—1216no—
147C2×C4×D3—34no—
148C2×C4×D3—34no—
149C2×C4×D3—34no—
150C2×C4×D3—68no—
151C2×Dic6—38no—
152C2×Dic6—68no—
153C2×Dic6—64no—
154C3×SD16—416no—
155C2×C3×C8C22×D318yes—
156C3×C4⋊C4—24no—
157C3×C4⋊C4—24no—
158C3×C42C22×D314yes—
159#217—68no—
160#217—68no—
161#214—1216no—
162C4⋊Dic3—38no—
163C4⋊Dic3—64no—
164C4⋊Dic3—64no—
165C4⋊Dic3—64no—
166Dic3⋊C4—68no—
167Dic3⋊C4—68no—
168C4×Dic3—34no—
169C4×Dic3—34no—
170C4×Dic3—34no—
171C2×C3⋊C8—38no—
172C22×C32—42no—
173C22×C32—42no—
174C22×C32—42no—
175C22×C32C22×D411yescharacteristic
176C2×C3⋊D3—21no—
177C2×C3⋊D3—21no—
178C2×C3⋊D3C2×SD1612yes—
179C32×C4—42no—
180C32×C4C2×SD1612yes—
181C32×C4#13712yes—
182C32×C4H(5,𝔽2)12yes—
183C3⋊Dic3—21no—
184C3⋊Dic3—21no—
185C3⋊Dic3—42no—
186C3⋊Dic3—42no—
187C3⋊Dic3C2×SD1612yes—
188C2×#41—181no—
189C22×Q8—92no—
190C2×SD16—94no—
191C2×SD16C2×C3⋊D314yes—
192C4⋊Q8—92no—
193C4⋊Q8—91no—
194C4⋊Q8—91no—
195C4⋊Q8—181no—
196C4⋊Q8—181no—
197C4⋊Q8C2×C3⋊D311yescharacteristic
198#127C2×C3⋊D311yescharacteristic
199#124—181no—
200#121—92no—
201#121—181no—
202C4×D4—92no—
203C4×D4—181no—
204C2×C4⋊C4—181no—
205C2×C4⋊C4—181no—
206C2×C42—91no—
207C4⋊C8—92no—
208#103—94no—
209#103—94no—
210C22⋊C8—92no—
211C4×C8—91no—
212C4×C8C2×C3⋊D311yescharacteristic
213C23×C3—28no—
214C22×D3—34no—
215C3×Q8—216no—
216C3×D4—216no—
217C3×D4—48no—
218C3×D4—48no—
219C2×C3×C4—28no—
220C2×C3×C4D3×D414yes—
221C2×C3×C4D3×D414yes—
222C2×C3×C4C23×D314yes—
223#67—1216no—
224C2×Dic3—34no—
225C2×Dic3—34no—
226C2×Dic3—34no—
227C2×Dic3—68no—
228C2×Dic3—68no—
229C2×Dic3—1216no—
230C4×D3—316no—
231C4×D3—68no—
232C4×D3—68no—
233C4×D3—1216no—
234Dic6—616no—
235Dic6—1216no—
236Dic6—128no—
237C3×C8—28no—
238C3⋊C8—68no—
239C2×C32—82no—
240C2×C32#53511yescharacteristic
241C2×C32C22×SD1611yescharacteristic
242C2×C32C2×#13711yescharacteristic
243C3⋊D3—22no—
244#41—364no—
245C2×Q8—92no—
246C2×Q8—182no—
247C2×Q8—181no—
248C2×Q8—364no—
249C2×Q8C22×C3⋊D312yes—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—182no—
253C2×D4C22×C3⋊D312yes—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—182no—
258C22×C4—182no—
259SD16—44no—
260SD16—364no—
261C2×C8—92no—
262C2×C8C22×C3⋊D312yes—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—92no—
266C4⋊C4—182no—
267C4⋊C4—182no—
268C4⋊C4—181no—
269C4⋊C4—181no—
270C4⋊C4—181no—
271C22⋊C4—182no—
272C22⋊C4—182no—
273C42—91no—
274C42—91no—
275C42—91no—
276C42C22×C3⋊D311yescharacteristic
277C22×C3—48no—
278C22×C3—48no—
279C22×C3—48no—
280C22×C3C2×D3×D414yes—
281C2×D3—38no—
282C2×D3—64no—
283C2×D3—64no—
284C3×C4—48no—
285C3×C4D3×SD1618yes—
286C3×C4#91518yes—
287C3×C4#100418yes—
288Dic3—38no—
289Dic3—64no—
290Dic3—64no—
291Dic3—128no—
292Dic3—128no—
293C32#320611yescharacteristic, complemented, Sylow
294C23—22no—
295C23—91no—
296Q8—24no—
297Q8—184no—
298Q8—364no—
299Q8—362no—
300D4—24no—
301D4—42no—
302D4—42no—
303D4—364no—
304C2×C4—22no—
305C2×C4—91no—
306C2×C4—94no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4—364no—
314C2×C4—364no—
315C2×C4D4×C3⋊D311yescharacteristic
316C2×C4D4×C3⋊D311yescharacteristic
317C2×C4C23×C3⋊D311yescharacteristic
318C8—22no—
319C8—182no—
320C2×C3—88no—
321C2×C3#571514yes—
322C2×C3C2×D3×SD1614yes—
323C2×C3C2×#91514yes—
324D3—68no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—92no—
329C22—181no—
330C22—181no—
331C22C2×D4×C3⋊D311yescharacteristic
332C4—42no—
333C4—92no—
334C4—181no—
335C4—181no—
336C4—362no—
337C4—362no—
338C4SD16×C3⋊D312yes—
339C4#6412412yes—
340C4#6436112yes—
341C3#8176414yescomplemented
342C2—82no—
343C2—182no—
344C2#1059618611yescharacteristic
345C2C2×SD16×C3⋊D311yescharacteristic
346C2C2×#6412411yescharacteristic
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#3206
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. C3⋊D3×C4⋊Q8C2semidirect
3. C32×#492C2semidirect
4. #10592869C2semidirect
5. #10592861C2semidirect
6. #10592778C2semidirect
7. #10592775C2semidirect
8. #10592384C2semidirect
9. #10592380C2semidirect
38. C3×#492D3semidirect
124. C4×C3⋊D3SD16semidirect
133. #492C3⋊D3semidirect
293. C32#3206semidirect
341. C3#81764semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105961872
C32×#4922
#105928692
#105928612
#105927782
#105927752
#105923842
#105923802
#817643