Finite Group Databasebeta

← #11878920

Subgroups — #11878920

Order 1152.

827 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 827 conjugacy classes of subgroups — too many to draw. Only its 166 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
1C2×#63873C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4C3×#4739C212yesmaximal
5#10591185C212yesmaximal
6#10590905C212yesmaximal, complemented
7#10590901C212yesmaximal, complemented
8#10590798C214yesmaximal, complemented
9#80178—32nomaximal
10C22×C3×Dic6C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C3×#924C2212yes—
13C2×C3×Dic12C2214yes—
14#63982—21no—
15C2×#3724—21no—
16C2×#3724—21no—
17#63957—21no—
18#63919C2211yescharacteristic
19#63873—21no—
20#63873—21no—
21#63873C2212yes—
22#63873C2212yes—
23#63873C2211yescharacteristic
24#63870—21no—
25#63843C2212yes—
26#63838—21no—
27C2×#3718C2214yes—
28C32×C22⋊C8C2211yescharacteristic
29#63657C2211yescharacteristic
30#63641C2212yes—
31C8×C3⋊Dic3C2212yes—
32C3×#816C2214yes—
33#63565C2214yes—
34C2×#944—32no—
35#5622—32no—
36C3×#451—32no—
37#5228—32no—
38#5183—34no—
39#5182—34no—
40#5050—32no—
41#4795—34no—
42#4792—34no—
43#4739D312yes—
44#4718—32no—
45#4718—61no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C22×C3×Dic3—22no—
50C2×C3×Dic6—22no—
51C2×C3×Dic6—44no—
52C2×C3×Dic6C2312yes—
53C2×C3×Dic6C2314yes—
54C2×#627—21no—
55C2×C32×C8C2312yes—
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C4×C3⋊Dic3C2311yescharacteristic
59C4×C3⋊Dic3C2311yescharacteristic
60C2×C3⋊(C3⋊C8)C2312yes—
61C3×#217—22no—
62C3×C4⋊Dic3C2312yes—
63C3×Dic3⋊C4—22no—
64C3×Dic12—44no—
65#3724—21no—
66#3724—21no—
67#3724—21no—
68#3724—22no—
69#3724—22no—
70#3724—22no—
71#3724—22no—
72Dic3⋊Dic3—22no—
73Dic32—22no—
74#3718—44no—
75#3209—91noSylow
76C22×C3×Q8—32no—
77C22×Dic6C2×D312yes—
78C2×C3×Q16—34no—
79C3×C22⋊Q8—32no—
80Q8×Dic3—32no—
81#944—34no—
82#944—32no—
83#944—34no—
84#944—62no—
85#944—62no—
86C2×#216—34no—
87C2×#216—34no—
88#924C2×D312yes—
89C2×Dic3⋊C4—62no—
90C2×Dic3⋊C4—62no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—61no—
93C2×Dic12C2×D314yes—
94#889—62no—
95#888—32no—
96#887—32no—
97#887—62no—
98#878—62no—
99#877—62no—
100C3×#103—34no—
101C3×C22⋊C8—21no—
102C3×C22⋊C8C2×D312yes—
103#835—34no—
104#830—32no—
105#830—61no—
106#816C2×D314yes—
107Dic3⋊C8—34no—
108Dic3⋊C8—62no—
109C8×Dic3—34no—
110C8×Dic3—62no—
111#810—34no—
112C23×C32C2×D411yescharacteristic
113C2×C32×C4—22no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2411yescharacteristic
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3Q1614yescomplemented
118C2×C3⋊Dic3C2×D411yescharacteristic
119C2×C3⋊Dic3C2×D411yescharacteristic
120C2×C3⋊Dic3C2×D411yescharacteristic
121C2×C3⋊Dic3C2×D411yescharacteristic
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—44no—
126C3×Dic6—24no—
127C3×Dic6—24no—
128C3×Dic6—24no—
129C3×Dic6—44no—
130#627—42no—
131C32×C8—22no—
132C3⋊(C3⋊C8)—22no—
133#533—91no—
134C2×C4⋊Q8—91no—
135#494—92no—
136#487—92no—
137#462—94no—
138#451—32no—
139#451—92no—
140#431—91no—
141C2×C3×Q8—34no—
142C2×C3×Q8—32no—
143C2×C3×Q8—62no—
144C2×C3×Q8—124no—
145C22×C3×C4—21no—
146C22×C3×C4—62no—
147C22×C3×C4C22×D312yes—
148C22×Dic3—22no—
149C22×Dic3—32no—
150C22×Dic3—32no—
151C22×Dic3—61no—
152C22×Dic3—61no—
153C2×Dic6—22no—
154C2×Dic6—44no—
155C2×Dic6—62no—
156C2×Dic6C22×D314yes—
157C2×Dic6C22×D312yes—
158C3×Q16—124no—
159C2×C3×C8—22no—
160C2×C3×C8C22×D314yes—
161C3×C4⋊C4—32no—
162C3×C4⋊C4—62no—
163C3×C22⋊C4—62no—
164#217—22no—
165#216—124no—
166#216—124no—
167C4⋊Dic3—62no—
168C4⋊Dic3C22×D312yes—
169Dic3⋊C4—22no—
170Dic3⋊C4—62no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—64no—
175Dic3⋊C4—64no—
176Dic3⋊C4—64no—
177Dic3⋊C4—64no—
178C4×Dic3—32no—
179C4×Dic3—32no—
180C4×Dic3—32no—
181C4×Dic3—32no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—62no—
187C4×Dic3—62no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—62no—
190Dic12—44no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32C2×Q1612yes—
194C22×C32C22×D411yescharacteristic
195C32×C4—21no—
196C32×C4H(5,𝔽2)12yes—
197C3⋊Dic3—21no—
198C3⋊Dic3C2×Q1612yes—
199C3⋊Dic3C2×Q1612yes—
200C3⋊Dic3#13712yes—
201C3×Dic3—44no—
202C3×Dic3—42no—
203C3×Dic3—42no—
204C22×Q8—32no—
205C2×Q16—34no—
206C2×Q16—94no—
207C4⋊Q8—91no—
208C4⋊Q8—92no—
209C4⋊Q8—92no—
210C4⋊Q8—91no—
211C4⋊Q8—181no—
212C4⋊Q8—181no—
213#125—181no—
214C22⋊Q8—32no—
215C22⋊Q8—181no—
216C4×Q8—92no—
217C4×Q8—181no—
218#117—181no—
219C2×C4⋊C4—181no—
220C2×C4⋊C4—181no—
221C2×C42—91no—
222C4⋊C8—92no—
223#103—34no—
224#103—94no—
225C22⋊C8—91no—
226C22⋊C8D3211yescharacteristic
227C4×C8—92no—
228C23×C3—21no—
229C23×C3D3×D412yes—
230C3×Q8—64no—
231C3×Q8—64no—
232C3×Q8—64no—
233C3×Q8—124no—
234C2×C3×C4—24no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—62no—
239C2×C3×C4—62no—
240C2×C3×C4—64no—
241C2×C3×C4—124no—
242C2×C3×C4D3×D412yes—
243C2×C3×C4C23×D312yes—
244C2×Dic3—22no—
245C2×Dic3—22no—
246C2×Dic3—24no—
247C2×Dic3—38no—
248C2×Dic3—32no—
249C2×Dic3—32no—
250C2×Dic3—32no—
251C2×Dic3—32no—
252C2×Dic3—44no—
253C2×Dic3—64no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—64no—
259C2×Dic3—122no—
260Dic6—24no—
261Dic6—24no—
262Dic6—24no—
263Dic6—44no—
264Dic6—124no—
265C3×C8—24no—
266C3×C8—42no—
267C3⋊C8—64no—
268C3⋊C8—122no—
269C2×C32—22no—
270C2×C32#53511yescharacteristic
271C2×C32C22×Q1611yescharacteristic
272C2×C32C2×#13711yescharacteristic
273C2×Q8—34no—
274C2×Q8—32no—
275C2×Q8—62no—
276C2×Q8—124no—
277C2×Q8—181no—
278C22×C4—62no—
279C22×C4—91no—
280C22×C4—91no—
281C22×C4C2×D3211yescharacteristic
282Q16—124no—
283Q16—364no—
284C2×C8—92no—
285C2×C8C2×D3212yes—
286C4⋊C4—32no—
287C4⋊C4—62no—
288C4⋊C4—182no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—182no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4—182no—
295C4⋊C4—181no—
296C22⋊C4—62no—
297C42—91no—
298C42—91no—
299C42—91no—
300C42—91no—
301C42—182no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3D3×Q1614yes—
309C22×C3C2×D3×D412yes—
310C3×C4—22no—
311C3×C4—22no—
312C3×C4—41no—
313C3×C4—122no—
314C3×C4—124no—
315C3×C4—122no—
316C3×C4#100414yes—
317Dic3—34no—
318Dic3—34no—
319Dic3—34no—
320Dic3—42no—
321Dic3—44no—
322Dic3—42no—
323Dic3—62no—
324Dic3—62no—
325Dic3—62no—
326Dic3—62no—
327Dic3—121no—
328C32#320911yescharacteristic, complemented, Sylow
329C23#380211yescharacteristic
330Q8—64no—
331Q8—64no—
332Q8—64no—
333Q8—124no—
334Q8—362no—
335C2×C4—22no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—64no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—94no—
343C2×C4—91no—
344C2×C4—124no—
345C2×C4—182no—
346C2×C4#380211yescharacteristic
347C2×C4C22×D3211yescharacteristic
348C8—22no—
349C8—182no—
350C2×C3—24no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—42no—
355C2×C3#559212yes—
356C2×C3C2×D3×Q1612yes—
357C2×C3D3×#13712yes—
358C22—21no—
359C22—21no—
360C22#6380212yes—
361C22C2×#380211yescharacteristic
362C4—21no—
363C4—92no—
364C4—92no—
365C4—92no—
366C4—124no—
367C4—122no—
368C4—122no—
369C4—181no—
370C4#6431312yes—
371C3—21no—
372C3#8017812yescomplemented
373C2—22no—
374C2#1059419211yescharacteristic
375C2C2×#6380211yescharacteristic
376C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22⋊C8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
6. #10590905C2semidirect
7. #10590901C2semidirect
8. #10590798C2semidirect
117. C2×C3⋊Dic3Q16semidirect
328. C32#3209semidirect
372. C3#80178semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
#105948102
#105924172
C3×#47392
#105911852
#105909052
#105909012
#105907982
#801783