Finite Group Databasebeta

← #11866788

Subgroups — #11866788

Order 1152.

1089 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 1089 conjugacy classes of subgroups — too many to draw. Only its 188 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×#63802C211yesmaximal, characteristic, complemented
2C2×D32×C8C211yesmaximal, characteristic
3#10594631C212yesmaximal
4C3⋊D3×#107C211yesmaximal, characteristic, complemented
5C3×#4887C212yesmaximal, complemented
6#10590851C212yesmaximal, complemented
7#10590601C212yesmaximal, complemented
8#10590518C214yesmaximal, complemented
9D3×#467—32nomaximal
10C2×C4×D32C2211yescharacteristic
11C2×#3797C2212yes—
12C2×C8×C3⋊D3C2211yescharacteristic
13C4⋊C4×C3⋊D3C2212yes—
14C2×C3×Dic12C2212yescomplemented
15C2×C3×D3×C8C2212yes—
16C3×#897C2214yes—
17#63921—22no—
18#63900—22no—
19#63899—24no—
20#63856C2214yes—
21C2×#3718C2212yescomplemented
22C2×#3710C2211yescharacteristic
23C2×D3×C3⋊C8C2212yes—
24#63802—24no—
25D32×C8—24no—
26C32×#107C2211yescharacteristic, complemented
27#63645C2211yescharacteristic, complemented
28#63634C2212yescomplemented
29C3×#810C2214yescomplemented
30#63566C2214yescomplemented
31C2×D3×Q16—32no—
32C22×D3×C8—32no—
33D3×C22⋊Q8—34no—
34C3×#467—32no—
35#5188—32no—
36#5116—32no—
37#5051—34no—
38#4887D312yescomplemented
39D3×#107—32no—
40D3×#107—61no—
41#4813—34no—
42D3×#103—34no—
43C22×D32D411yescharacteristic
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C3×C4×D3C2312yes—
47C2×C3×Dic6C2314yes—
48C2×#627—22no—
49C2×#624—22no—
50C2×#624D411yescharacteristic
51C2×D3×Dic3D412yes—
52C4×D32—22no—
53C4×D32—22no—
54#3797—24no—
55#3797—24no—
56C2×C32×C8C2311yescharacteristic
57C32×C4⋊C4C2312yes—
58C4⋊(C3⋊Dic3)C2312yes—
59#3750—22no—
60C2×C3⋊(C3⋊C8)C2311yescharacteristic
61C8×C3⋊D3D414yes—
62C3×(C2×D3)⋊C4—24no—
63C3×C4⋊Dic3—24no—
64C2×C3×C3⋊C8C2312yes—
65C3×Dic12—24no—
66C3×D3×C8—24no—
67#3724—24no—
68(C2×D3)⋊Dic3—24no—
69#3718—24no—
70#3710—22no—
71D3×C3⋊C8—24no—
72C2×#467—91noSylow
73C2×D3×Q8—34no—
74C22×C4×D3—32no—
75C2×C3×Q16—32no—
76C22×C3×C8—32no—
77C3×C22⋊Q8—34no—
78#946—34no—
79C2×#216—34no—
80#924—34no—
81C22×C3⋊C8—32no—
82D3×Q16—68no—
83C2×Dic12C2×D312yescomplemented
84C2×D3×C8—32no—
85C2×D3×C8—32no—
86C2×D3×C8—32no—
87C2×D3×C8—61no—
88C2×D3×C8—68no—
89C2×D3×C8C2×D312yes—
90#897C2×D314yes—
91#896—64no—
92D3×C4⋊C4—34no—
93D3×C4⋊C4—62no—
94D3×C4⋊C4—64no—
95D3×C22⋊C4—64no—
96#878—64no—
97C3×#107—21no—
98C3×#107C2×D312yescomplemented
99C3×#103—34no—
100#835—34no—
101#818—32no—
102#818—61no—
103#816—34no—
104#810C2×D314yescomplemented
105#807—34no—
106#807—62no—
107C22×C3⋊D3C2×D411yescharacteristic
108C22×C3×D3C2×D412yes—
109C2×D32—22no—
110C2×D32—22no—
111C2×D32Q1614yescomplemented
112C2×C32×C4—22no—
113C2×C32×C4C2411yescharacteristic
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3C2×D411yescharacteristic
116C4×C3⋊D3—44no—
117C4×C3⋊D3C2×D412yes—
118C4×C3⋊D3#4112yes—
119C2×C3×Dic3—24no—
120C2×C3×Dic3C2×D412yes—
121C3×C4×D3—22no—
122C3×C4×D3—22no—
123C3×Dic6—24no—
124C3×Dic6—24no—
125#627—44no—
126#624—22no—
127#624—44no—
128D3×Dic3—24no—
129C32×C8C2×D412yes—
130C3⋊(C3⋊C8)C2×D412yes—
131C3×C3⋊C8—22no—
132C22×Q16—91no—
133C23×C8—91no—
134C2×C22⋊Q8—92no—
135#467—32no—
136#467—94no—
137#467—92no—
138C2×#107—91no—
139C2×#103—92no—
140C23×D3—32no—
141C2×C3×Q8—34no—
142C22×C3×C4—32no—
143C22×Dic3—32no—
144D3×Q8—68no—
145D3×Q8—68no—
146C2×C4×D3—32no—
147C2×C4×D3—32no—
148C2×C4×D3—32no—
149C2×C4×D3—61no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—64no—
153C2×C4×D3—64no—
154C2×C4×D3—122no—
155C2×C4×D3C22×D312yes—
156C2×Dic6—64no—
157C2×Dic6C22×D314yes—
158C3×Q16—64no—
159C2×C3×C8—21no—
160C2×C3×C8—32no—
161C2×C3×C8—64no—
162C2×C3×C8C22×D312yes—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—64no—
165C3×C4⋊C4C22×D314yes—
166C3×C22⋊C4—64no—
167#217—64no—
168#216—68no—
169(C2×D3)⋊C4—24no—
170(C2×D3)⋊C4—64no—
171C4⋊Dic3—24no—
172C4⋊Dic3—34no—
173C4⋊Dic3—62no—
174Dic3⋊C4—64no—
175Dic3⋊C4—64no—
176Dic3⋊C4—64no—
177Dic3⋊C4—122no—
178C2×C3⋊C8—32no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—64no—
181C2×C3⋊C8C22×D312yes—
182Dic12—24no—
183D3×C8—24no—
184D3×C8—38no—
185D3×C8—64no—
186D3×C8—64no—
187D3×C8—64no—
188C22×C32C22×D411yescharacteristic
189C2×C3⋊D3#12112yes—
190C2×C3⋊D3C2×Q1612yes—
191C2×C3⋊D3#13512yes—
192C2×C3×D3—22no—
193C2×C3×D3—22no—
194C2×C3×D3C2×Q1614yescomplemented
195D32—28no—
196C32×C4—42no—
197C32×C4C22×D411yescharacteristic
198C32×C4C2×#4111yescharacteristic
199C3⋊Dic3—42no—
200C3⋊Dic3#12112yes—
201C3×Dic3—22no—
202C3×Dic3—44no—
203C22×Q8—92no—
204C23×C4—91no—
205C2×Q16—32no—
206C2×Q16—92no—
207C2×Q16—184no—
208C22×C8—32no—
209C22×C8—91no—
210C22×C8—92no—
211C22×C8—91no—
212C22×C8—184no—
213C22⋊Q8—34no—
214C22⋊Q8—94no—
215C22⋊Q8—184no—
216C2×C4⋊C4—92no—
217C2×C4⋊C4—182no—
218C2×C22⋊C4—182no—
219#107—91no—
220#107—92no—
221#107D3211yescharacteristic, complemented
222#103—34no—
223#103—94no—
224C23×C3—32no—
225C22×D3—32no—
226C22×D3—38no—
227C22×D3—61no—
228C22×D3—64no—
229C22×D3—64no—
230C22×D3D3×D412yes—
231C3×Q8—64no—
232C3×Q8—64no—
233C2×C3×C4—24no—
234C2×C3×C4—21no—
235C2×C3×C4—32no—
236C2×C3×C4—42no—
237C2×C3×C4—62no—
238C2×C3×C4—62no—
239C2×C3×C4—64no—
240C2×C3×C4C23×D312yes—
241C2×Dic3—24no—
242C2×Dic3—32no—
243C2×Dic3—61no—
244C2×Dic3—64no—
245C2×Dic3—64no—
246C2×Dic3—122no—
247C2×Dic3D3×D412yes—
248C4×D3—22no—
249C4×D3—22no—
250C4×D3—34no—
251C4×D3—34no—
252C4×D3—62no—
253C4×D3—62no—
254C4×D3—64no—
255C4×D3—64no—
256C4×D3—128no—
257C4×D3—128no—
258C4×D3—244no—
259Dic6—24no—
260Dic6—24no—
261Dic6—128no—
262C3×C8—22no—
263C3×C8—62no—
264C3×C8D3×D414yes—
265C3⋊C8—22no—
266C3⋊C8—34no—
267C3⋊C8—62no—
268C2×C32C2×#12111yescharacteristic
269C2×C32C22×Q1611yescharacteristic
270C2×C32C2×#13511yescharacteristic
271C3⋊D3#46714yescomplemented
272C3×D3—24no—
273C24—91no—
274C2×Q8—34no—
275C2×Q8—182no—
276C2×Q8—184no—
277C2×Q8—184no—
278C22×C4—32no—
279C22×C4—91no—
280C22×C4—92no—
281C22×C4—91no—
282C22×C4—182no—
283C22×C4—182no—
284C22×C4—182no—
285C22×C4—182no—
286Q16—64no—
287Q16—184no—
288C2×C8—32no—
289C2×C8—64no—
290C2×C8—91no—
291C2×C8—94no—
292C2×C8—182no—
293C2×C8—184no—
294C2×C8C2×D3211yescharacteristic
295C4⋊C4—64no—
296C4⋊C4—92no—
297C4⋊C4—182no—
298C4⋊C4—184no—
299C4⋊C4C2×D3212yes—
300C22⋊C4—64no—
301C22⋊C4—184no—
302C22×C3—21no—
303C22×C3—34no—
304C22×C3—62no—
305C22×C3—62no—
306C22×C3C2×D3×D412yes—
307C2×D3—22no—
308C2×D3—22no—
309C2×D3—34no—
310C2×D3—34no—
311C2×D3—34no—
312C2×D3—62no—
313C2×D3—62no—
314C2×D3—62no—
315C2×D3—616no—
316C2×D3D3×Q1614yescomplemented
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—44no—
320C3×C4—62no—
321C3×C4—82no—
322C3×C4—124no—
323C3×C4C2×D3×D412yes—
324C3×C4D3×#4112yes—
325Dic3—22no—
326Dic3—34no—
327Dic3—44no—
328Dic3—62no—
329Dic3—124no—
330Dic3—242no—
331C32C2×#46711yescharacteristic, complemented, Sylow
332C23—32no—
333C23—94no—
334C23—91no—
335C23—182no—
336C23—182no—
337Q8—64no—
338Q8—64no—
339Q8—364no—
340C2×C4—22no—
341C2×C4—32no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—64no—
345C2×C4—91no—
346C2×C4—92no—
347C2×C4—92no—
348C2×C4—182no—
349C2×C4—184no—
350C2×C4—182no—
351C2×C4—364no—
352C2×C4—364no—
353C2×C4C22×D3211yescharacteristic
354C8—62no—
355C8—92no—
356C8#380212yes—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—64no—
361C2×C3D3×#12112yes—
362C2×C3C2×D3×Q1612yes—
363C2×C3D3×#13512yes—
364D3—24no—
365D3—38no—
366D3—64no—
367C22—34no—
368C22—62no—
369C22—62no—
370C22—92no—
371C22—92no—
372C22—92no—
373C22—188no—
374C22D32×D411yescharacteristic
375C4—42no—
376C4—62no—
377C4—92no—
378C4—124no—
379C4—362no—
380C4C2×#380211yescharacteristic
381C4#6431911yescharacteristic
382C3—21no—
383C3D3×#46712yescomplemented
384C2—64no—
385C2—94no—
386C2#1059461211yescharacteristic
387C2#1059473011yescharacteristic
388C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#107D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#63802C2semidirect
4. C3⋊D3×#107C2semidirect
5. C3×#4887C2semidirect
6. #10590851C2semidirect
7. #10590601C2semidirect
8. #10590518C2semidirect
14. C2×C3×Dic12C22semidirect
21. C2×#3718C22semidirect
26. C32×#107C22semidirect
27. #63645C22semidirect
28. #63634C22semidirect
29. C3×#810C22semidirect
30. #63566C22semidirect
38. #4887D3semidirect
83. C2×Dic12C2×D3semidirect
98. C3×#107C2×D3semidirect
104. #810C2×D3semidirect
111. C2×D32Q16semidirect
194. C2×C3×D3C2×Q16semidirect
221. #107D32semidirect
271. C3⋊D3#467semidirect
316. C2×D3D3×Q16semidirect
331. C32C2×#467semidirect
383. C3D3×#467semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
C2×D32×C82
#105946312
C3⋊D3×#1072
C3×#48872
#105908512
#105906012
#105905182
D3×#4673