Finite Group Databasebeta

← #11874392

Subgroups — #11874392

Order 1152.

1273 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 1273 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#63944C212yesmaximal, complemented
3C2×#63940C212yesmaximal
4#10594009C211yesmaximal, characteristic
5C3×#5086C212yesmaximal, complemented
6#10591611C214yesmaximal, complemented
7#10590372C212yesmaximal, complemented
8#10590322C211yesmaximal, characteristic, complemented
9D3×#497—32nomaximal
10C2×Q8×C3⋊D3C2212yes—
11C2×#3802C2211yescharacteristic
12C2×#3797C2211yescharacteristic
13C32×C4⋊Q8C2211yescharacteristic, complemented
14#64153C2212yescomplemented
15C4⋊C4×C3⋊D3—22no—
16#64097—22no—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C2×C3×#216C2214yescomplemented
20C2×C3×#215C2214yes—
21C3×#875C2212yes—
22#63944—28no—
23#63940—28no—
24#63921—22no—
25#63915—22no—
26#63863C2212yes—
27C2×#3719C2214yescomplemented
28C2×#3716C2214yes—
29C2×#3710C2212yes—
30C3×#803C2212yescomplemented
31#63555C2212yescomplemented
32C2×D3×Q16—34no—
33C2×D3×SD16—34no—
34D3×C4⋊Q8—32no—
35D3×C4⋊Q8—61no—
36D3×#124—32no—
37C3×#497—32no—
38#5190—34no—
39#5167—34no—
40#5086D312yescomplemented
41#5060—32no—
42#4715—32no—
43D3×#97—32no—
44C22×D32—21no—
45C2×C32×Q8C2312yes—
46Q8×C3⋊D3—24no—
47Q8×C3⋊D3—24no—
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3D412yes—
50C2×C4×C3⋊D3C2311yescharacteristic
51C2×#634—22no—
52C2×#634C2312yes—
53C2×C3×D12C2312yes—
54C2×C3×Dic6C2312yes—
55C2×#627—21no—
56C2×#625—21no—
57C2×#624—21no—
58#3802—24no—
59#3797—24no—
60C32×C4⋊C4—22no—
61C32×C42C2311yescharacteristic
62C4⋊(C3⋊Dic3)—22no—
63#3750—24no—
64C4×C3⋊Dic3D412yes—
65C4×C3⋊Dic3C2311yescharacteristic
66C3×#216—28no—
67C3×#215—28no—
68C3×(C2×D3)⋊C4—24no—
69C2×C3×C3⋊C8C2314yes—
70(C2×D3)⋊Dic3—24no—
71#3719—28no—
72#3716—28no—
73#3710D418yes—
74C2×#497—91noSylow
75C2×D3×Q8—34no—
76C2×D3×Q8—32no—
77C2×D3×Q8—62no—
78C2×D3×D4—32no—
79C2×C3×Q16—34no—
80C2×C3×SD16—34no—
81C3×C4⋊Q8—21no—
82C3×C4⋊Q8C2×D312yescomplemented
83C3×#124—32no—
84#947—32no—
85#944—34no—
86#944—62no—
87C2×#216—34no—
88C2×#216C2×D314yescomplemented
89C2×#215C2×D314yes—
90#936—32no—
91C2×#214—34no—
92D3×Q16—616no—
93D3×SD16—616no—
94C2×Dic12—34no—
95C2×#204—34no—
96C2×D3×C8—34no—
97D3×C4⋊C4—64no—
98D3×C4⋊C4—64no—
99#888—64no—
100#888—64no—
101#885—64no—
102D3×C22⋊C4—64no—
103#875C2×D312yes—
104C42×D3—32no—
105C42×D3—61no—
106#869—32no—
107#869—61no—
108C3×#97—32no—
109#815—34no—
110#803C2×D312yescomplemented
111C22×C3⋊D3C2×D411yescharacteristic
112C22×C3×D3—22no—
113C2×D32—42no—
114C2×D32—44no—
115C32×Q8—22no—
116C32×Q8—22no—
117C2×C32×C4—22no—
118C2×C32×C4C2×D412yes—
119C2×C32×C4C2411yescharacteristic
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3C2×D412yes—
122C2×C3⋊Dic3C2×D411yescharacteristic
123C4×C3⋊D3—24no—
124C4×C3⋊D3—44no—
125C4×C3⋊D3C2×D414yes—
126#634—22no—
127#634—22no—
128#634—44no—
129C2×C3×Dic3—22no—
130C3×D12—24no—
131C3×Dic6—24no—
132#627—42no—
133#625—42no—
134#624—42no—
135C3×C3⋊C8C2×D418yes—
136C22×Q16—92no—
137C22×SD16—92no—
138C2×C4⋊Q8—91no—
139C2×#124—91no—
140#497—32no—
141#497—92no—
142#497—94no—
143C2×#97—91no—
144C23×D3—62no—
145C2×C3×Q8—22no—
146C2×C3×Q8—32no—
147C2×C3×Q8C22×D314yes—
148C2×C3×D4—32no—
149C2×#67—62no—
150D3×Q8—68no—
151D3×Q8—68no—
152D3×Q8—68no—
153D3×Q8—124no—
154D3×Q8—124no—
155D3×D4—68no—
156C2×D12C22×D312yes—
157C2×C4×D3—32no—
158C2×C4×D3—34no—
159C2×C4×D3—62no—
160C2×C4×D3—61no—
161C2×C4×D3—62no—
162C2×C4×D3—64no—
163C2×C4×D3—64no—
164C2×Dic6—34no—
165C2×Dic6—62no—
166C2×Dic6—62no—
167C2×Dic6—64no—
168C2×Dic6—64no—
169C2×Dic6C22×D312yes—
170C3×Q16—68no—
171C3×SD16—68no—
172C2×C3×C8—34no—
173C3×C4⋊C4—24no—
174C3×C4⋊C4—24no—
175C3×C22⋊C4—64no—
176C3×C42—21no—
177C3×C42C22×D312yes—
178#217—64no—
179#216—28no—
180#216—68no—
181#215—28no—
182#214—68no—
183(C2×D3)⋊C4—24no—
184(C2×D3)⋊C4—64no—
185C4⋊Dic3—64no—
186C4⋊Dic3—64no—
187Dic3⋊C4—68no—
188Dic3⋊C4—68no—
189C4×Dic3—34no—
190C4×Dic3—32no—
191C4×Dic3—62no—
192C4×Dic3—61no—
193C2×C3⋊C8C22×D314yes—
194Dic12—68no—
195#204—68no—
196D3×C8—316no—
197C22×C32C22×D411yescharacteristic
198C2×C3⋊D3#12712yes—
199C2×C3⋊D3#13714yes—
200C2×C3×D3—42no—
201C2×C3×D3—44no—
202D32—84no—
203C32×C4—22no—
204C32×C4—42no—
205C32×C4C22×D412yes—
206C3⋊Dic3—22no—
207C3⋊Dic3—42no—
208C3⋊Dic3#12712yes—
209C3×Dic3—42no—
210C22×Q8—91no—
211C22×Q8—92no—
212C22×D4—91no—
213C2×Q16—34no—
214C2×Q16—94no—
215C2×Q16—188no—
216C2×SD16—34no—
217C2×SD16—94no—
218C2×SD16—188no—
219C22×C8—92no—
220C4⋊Q8—92no—
221C4⋊Q8—91no—
222C4⋊Q8—182no—
223C4⋊Q8D3211yescharacteristic, complemented
224#124—32no—
225#124—92no—
226#124—182no—
227C2×C4⋊C4—182no—
228C2×C22⋊C4—182no—
229C2×C42—91no—
230#97—32no—
231#97—92no—
232C23×C3—62no—
233C22×D3—22no—
234C22×D3—32no—
235C22×D3—61no—
236C22×D3—124no—
237C22×D3—128no—
238C3×Q8—24no—
239C3×Q8—24no—
240C3×Q8—42no—
241C3×Q8—42no—
242C3×Q8—64no—
243C3×D4—64no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4—62no—
249C2×C3×C4D3×D414yes—
250C2×C3×C4C23×D312yes—
251#67—124no—
252C2×Dic3—22no—
253C2×Dic3—32no—
254C2×Dic3—34no—
255C2×Dic3—62no—
256C2×Dic3—61no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259D12—24no—
260C4×D3—38no—
261C4×D3—64no—
262C4×D3—68no—
263C4×D3—68no—
264C4×D3—124no—
265C4×D3—128no—
266C4×D3—128no—
267Dic6—24no—
268Dic6—64no—
269Dic6—64no—
270Dic6—122no—
271Dic6—122no—
272Dic6—124no—
273Dic6—128no—
274Dic6—128no—
275C3×C8—38no—
276C3⋊C8D3×D418yes—
277C2×C32C2×#12711yescharacteristic
278C2×C32C2×#13712yes—
279C3⋊D3#49714yescomplemented
280C3×D3—82no—
281C24—181no—
282C2×Q8—32no—
283C2×Q8—92no—
284C2×Q8—182no—
285C2×Q8—181no—
286C2×Q8—184no—
287C2×Q8—184no—
288C2×Q8—184no—
289C2×Q8C2×D3212yes—
290C2×D4—32no—
291C2×D4—184no—
292C2×D4—181no—
293C22×C4—91no—
294C22×C4—92no—
295C22×C4—182no—
296C22×C4—181no—
297Q16—68no—
298Q16—188no—
299SD16—68no—
300SD16—188no—
301C2×C8—34no—
302C2×C8—98no—
303C4⋊C4—22no—
304C4⋊C4—184no—
305C4⋊C4—182no—
306C22⋊C4—64no—
307C22⋊C4—184no—
308C42—91no—
309C42—92no—
310C42C2×D3211yescharacteristic
311C22×C3—21no—
312C22×C3—122no—
313C22×C3—124no—
314C22×C3C2×D3×D412yes—
315C2×D3—34no—
316C2×D3—38no—
317C2×D3—42no—
318C2×D3—44no—
319C2×D3—62no—
320C2×D3—64no—
321C2×D3—248no—
322C3×C4—24no—
323C3×C4—24no—
324C3×C4—22no—
325C3×C4—44no—
326C3×C4—44no—
327C3×C4—122no—
328C3×C4C2×D3×D414yes—
329Dic3—34no—
330Dic3—42no—
331Dic3—62no—
332Dic3—64no—
333Dic3—64no—
334Dic3—124no—
335Dic3—124no—
336C32C2×#49711yescharacteristic, complemented, Sylow
337C23—62no—
338C23—91no—
339C23—362no—
340C23—364no—
341Q8—22no—
342Q8—22no—
343Q8—64no—
344Q8—182no—
345Q8—182no—
346Q8—364no—
347Q8—362no—
348D4—64no—
349D4—362no—
350C2×C4—22no—
351C2×C4—62no—
352C2×C4—91no—
353C2×C4—94no—
354C2×C4—92no—
355C2×C4—184no—
356C2×C4—182no—
357C2×C4—364no—
358C2×C4—362no—
359C2×C4#381112yes—
360C2×C4C22×D3211yescharacteristic
361C8—38no—
362C2×C3—21no—
363C2×C3—22no—
364C2×C3—242no—
365C2×C3D3×#12712yes—
366C2×C3D3×#13714yes—
367D3—38no—
368D3—64no—
369D3—82no—
370C22—92no—
371C22—94no—
372C22—122no—
373C22—124no—
374C22—724no—
375C22C2×#381111yescharacteristic
376C4—22no—
377C4—42no—
378C4—92no—
379C4—122no—
380C4—182no—
381C4—362no—
382C4D32×D412yes—
383C3—21no—
384C3D3×#49712yescomplemented
385C2—94no—
386C2—242no—
387C2#1059530011yescharacteristic
388C2#1059532212yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊Q8D32
hypocenterC32C2×#497
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C4⋊Q8C2semidirect
2. C2×#63944C2semidirect
5. C3×#5086C2semidirect
6. #10591611C2semidirect
7. #10590372C2semidirect
8. #10590322C2semidirect
13. C32×C4⋊Q8C22semidirect
14. #64153C22semidirect
18. #64078C22semidirect
19. C2×C3×#216C22semidirect
27. C2×#3719C22semidirect
30. C3×#803C22semidirect
31. #63555C22semidirect
40. #5086D3semidirect
82. C3×C4⋊Q8C2×D3semidirect
88. C2×#216C2×D3semidirect
110. #803C2×D3semidirect
223. C4⋊Q8D32semidirect
279. C3⋊D3#497semidirect
336. C32C2×#497semidirect
384. C3D3×#497semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C2×#639442
C2×#639402
#105940092
C3×#50862
#105916112
#105903722
#105903222
D3×#4973