Finite Group Databasebeta

← #11867008

Subgroups — #11867008

Order 1152.

1113 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 1113 conjugacy classes of subgroups — too many to draw. Only its 176 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×Q16×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595429C212yesmaximal
3C2×#63791C211yesmaximal, characteristic
4C3×#5189C212yesmaximal, complemented
5#10591598C214yesmaximal, complemented
6#10591552C212yesmaximal, complemented
7#10590853C212yesmaximal, complemented
8#10590685C211yesmaximal, characteristic, complemented
9D3×#470—32nomaximal
10C2×Q8×C3⋊D3C2212yes—
11C2×C4×D32C2211yescharacteristic
12C2×C32×Q16C2211yescharacteristic, complemented
13C2×#3756C2212yescomplemented
14Q16×C3⋊D3—24no—
15C2×#3746C2211yescharacteristic, complemented
16C2×C8×C3⋊D3C2211yescharacteristic
17C3×#946C2214yes—
18C2×C3×ΓL(1,𝔽25)C2212yes—
19#63921—22no—
20#63900C2212yes—
21#63896—24no—
22#63883—22no—
23#63857C2214yes—
24C2×#3711C2212yes—
25C2×#3710C2211yescharacteristic
26#63791—24no—
27C3×#835C2214yescomplemented
28C3×#817C2212yescomplemented
29#63574C2212yescomplemented
30#63567C2214yescomplemented
31C2×D3×Q16—32no—
32C2×D3×Q16—61no—
33C2×D3×M16—32no—
34D3×C22⋊Q8—34no—
35C3×#470—32no—
36#5189D312yescomplemented
37#5137—32no—
38#5052—34no—
39#4867—32no—
40D3×#106—32no—
41#4816—34no—
42D3×#103—34no—
43C22×D32D411yescharacteristic
44C2×C32×Q8C2312yes—
45Q8×C3⋊D3—24no—
46Q8×C3⋊D3—24no—
47C2×C4×C3⋊D3—22no—
48C2×C4×C3⋊D3C2311yescharacteristic
49C2×#634—22no—
50C2×#634C2312yes—
51C2×C3×C4×D3C2312yes—
52C2×#624—22no—
53C2×#624D411yescharacteristic
54C2×D3×Dic3D412yes—
55C4×D32—22no—
56C4×D32—22no—
57C32×Q16—22no—
58C2×C32×C8C2311yescharacteristic
59#3756—24no—
60C2×C3⋊(C3⋊C8)C2311yescharacteristic
61#3746—22no—
62C8×C3⋊D3D414yes—
63C3×(C2×D3)⋊C4—24no—
64C3×C4⋊Dic3C2314yes—
65C3×Dic3⋊C4—24no—
66C2×C3×C3⋊C8C2312yes—
67C3×ΓL(1,𝔽25)—24no—
68#3724—22no—
69Dic3⋊Dic3—24no—
70(C2×D3)⋊Dic3—24no—
71#3711—24no—
72#3710—22no—
73C2×#470—91noSylow
74C2×D3×Q8—34no—
75C2×D3×Q8—62no—
76C22×C4×D3—32no—
77C2×C3×Q16—21no—
78C2×C3×Q16C2×D312yescomplemented
79C2×C3×M16—32no—
80C3×C22⋊Q8—34no—
81#946C2×D314yes—
82C2×#216—34no—
83C2×#216—62no—
84#924—34no—
85C2×#208—32no—
86D3×Q16—68no—
87D3×Q16—68no—
88D3×M16—68no—
89C2×Dic12—32no—
90C2×Dic12—61no—
91C2×ΓL(1,𝔽25)—32no—
92C2×ΓL(1,𝔽25)C2×D312yes—
93C2×D3×C8—32no—
94C2×D3×C8—32no—
95C2×D3×C8—61no—
96#897—34no—
97#896—64no—
98D3×C4⋊C4—34no—
99D3×C4⋊C4—64no—
100D3×C22⋊C4—64no—
101#878—64no—
102C3×#106—32no—
103C3×#103—34no—
104#835C2×D314yescomplemented
105#817C2×D312yescomplemented
106#816—34no—
107#810—34no—
108#808—34no—
109C22×C3⋊D3C2×D411yescharacteristic
110C22×C3×D3C2×D412yes—
111C2×D32—22no—
112C2×D32—24no—
113C32×Q8—22no—
114C32×Q8—22no—
115C2×C32×C4—22no—
116C2×C32×C4C2411yescharacteristic
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3C2×D411yescharacteristic
119C4×C3⋊D3—44no—
120C4×C3⋊D3C2×D412yes—
121C4×C3⋊D3#4112yes—
122#634—22no—
123#634—22no—
124#634—44no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3C2×D412yes—
127C3×C4×D3—22no—
128C3×C4×D3—22no—
129#624—22no—
130#624—44no—
131D3×Dic3—24no—
132C32×C8C2×D412yes—
133C3⋊(C3⋊C8)C2×D412yes—
134C3×C3⋊C8—22no—
135C22×Q16—91no—
136C22×M16—91no—
137C2×C22⋊Q8—92no—
138#470—32no—
139#470—94no—
140#470—92no—
141C2×#106—91no—
142C2×#103—92no—
143C23×D3—32no—
144C2×C3×Q8—22no—
145C2×C3×Q8C22×D314yes—
146C22×C3×C4—32no—
147C22×Dic3—32no—
148D3×Q8—68no—
149D3×Q8—68no—
150D3×Q8—68no—
151D3×Q8—124no—
152C2×C4×D3—32no—
153C2×C4×D3—32no—
154C2×C4×D3—32no—
155C2×C4×D3—61no—
156C2×C4×D3—64no—
157C2×C4×D3—64no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C4×D3—122no—
161C2×C4×D3C22×D312yes—
162C2×Dic6—34no—
163C2×Dic6—62no—
164C2×Dic6—64no—
165C2×Dic6—122no—
166C3×Q16—24no—
167C3×Q16—24no—
168C3×M16—64no—
169C2×C3×C8—21no—
170C2×C3×C8—32no—
171C2×C3×C8C22×D312yes—
172C3×C4⋊C4—34no—
173C3×C4⋊C4—64no—
174C3×C22⋊C4—64no—
175#217—64no—
176#216—68no—
177#216—68no—
178(C2×D3)⋊C4—24no—
179(C2×D3)⋊C4—64no—
180C4⋊Dic3—64no—
181C4⋊Dic3C22×D314yes—
182Dic3⋊C4—24no—
183Dic3⋊C4—64no—
184Dic3⋊C4—64no—
185#208—64no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8C22×D312yes—
189Dic12—64no—
190Dic12—64no—
191ΓL(1,𝔽25)—24no—
192ΓL(1,𝔽25)—64no—
193D3×C8—38no—
194D3×C8—64no—
195D3×C8—64no—
196C22×C32C22×D411yescharacteristic
197C2×C3⋊D3#12112yes—
198C2×C3⋊D3#13714yes—
199C2×C3×D3—22no—
200C2×C3×D3—24no—
201D32—44no—
202C32×C4—42no—
203C32×C4C22×D411yescharacteristic
204C32×C4C2×#4111yescharacteristic
205C3⋊Dic3—42no—
206C3⋊Dic3#12112yes—
207C3×Dic3—22no—
208C3×Dic3—44no—
209C22×Q8—92no—
210C23×C4—91no—
211C2×Q16—92no—
212C2×Q16—91no—
213C2×Q16—184no—
214C2×Q16D3211yescharacteristic, complemented
215C2×M16—32no—
216C2×M16—92no—
217C2×M16—184no—
218C22×C8—91no—
219C22×C8—91no—
220C22⋊Q8—34no—
221C22⋊Q8—94no—
222C22⋊Q8—184no—
223C2×C4⋊C4—92no—
224C2×C4⋊C4—182no—
225C2×C22⋊C4—182no—
226#106—32no—
227#106—92no—
228#103—34no—
229#103—94no—
230C23×C3—32no—
231C22×D3—32no—
232C22×D3—61no—
233C22×D3—64no—
234C22×D3—68no—
235C22×D3D3×D412yes—
236C3×Q8—24no—
237C3×Q8—24no—
238C3×Q8—24no—
239C3×Q8—42no—
240C2×C3×C4—24no—
241C2×C3×C4—21no—
242C2×C3×C4—32no—
243C2×C3×C4—42no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—64no—
247C2×C3×C4C23×D312yes—
248C2×Dic3—24no—
249C2×Dic3—32no—
250C2×Dic3—61no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—122no—
254C2×Dic3D3×D412yes—
255C4×D3—22no—
256C4×D3—22no—
257C4×D3—34no—
258C4×D3—34no—
259C4×D3—62no—
260C4×D3—62no—
261C4×D3—64no—
262C4×D3—64no—
263C4×D3—128no—
264C4×D3—128no—
265C4×D3—128no—
266Dic6—64no—
267Dic6—64no—
268Dic6—64no—
269Dic6—122no—
270Dic6—128no—
271Dic6—128no—
272C3×C8—22no—
273C3×C8—62no—
274C3×C8D3×D414yes—
275C3⋊C8—22no—
276C3⋊C8—34no—
277C3⋊C8—62no—
278C2×C32C2×#12111yescharacteristic
279C2×C32C2×#13712yes—
280C3⋊D3#47014yescomplemented
281C3×D3—42no—
282C24—91no—
283C2×Q8—92no—
284C2×Q8—182no—
285C2×Q8—184no—
286C2×Q8—184no—
287C2×Q8C2×D3212yes—
288C22×C4—32no—
289C22×C4—91no—
290C22×C4—92no—
291C22×C4—91no—
292C22×C4—182no—
293C22×C4—182no—
294C22×C4—182no—
295C22×C4—182no—
296Q16—22no—
297Q16—184no—
298Q16—182no—
299M16—64no—
300M16—184no—
301C2×C8—32no—
302C2×C8—91no—
303C2×C8—94no—
304C2×C8—182no—
305C2×C8C2×D3211yescharacteristic
306C4⋊C4—34no—
307C4⋊C4—64no—
308C4⋊C4—184no—
309C4⋊C4—182no—
310C22⋊C4—64no—
311C22⋊C4—184no—
312C22×C3—21no—
313C22×C3—64no—
314C22×C3—62no—
315C22×C3C2×D3×D412yes—
316C2×D3—24no—
317C2×D3—22no—
318C2×D3—38no—
319C2×D3—34no—
320C2×D3—62no—
321C2×D3—64no—
322C2×D3—128no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—44no—
326C3×C4—44no—
327C3×C4—62no—
328C3×C4—124no—
329C3×C4C2×D3×D412yes—
330C3×C4D3×#4112yes—
331Dic3—22no—
332Dic3—34no—
333Dic3—44no—
334Dic3—62no—
335Dic3—124no—
336Dic3—124no—
337C32C2×#47011yescharacteristic, complemented, Sylow
338C23—32no—
339C23—91no—
340C23—182no—
341C23—184no—
342Q8—22no—
343Q8—22no—
344Q8—182no—
345Q8—182no—
346Q8—364no—
347C2×C4—22no—
348C2×C4—32no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—64no—
352C2×C4—91no—
353C2×C4—92no—
354C2×C4—92no—
355C2×C4—182no—
356C2×C4—184no—
357C2×C4—182no—
358C2×C4—364no—
359C2×C4—364no—
360C2×C4C22×D3211yescharacteristic
361C8—62no—
362C8—92no—
363C8#381112yes—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3—122no—
367C2×C3D3×#12112yes—
368C2×C3D3×#13714yes—
369D3—38no—
370D3—42no—
371D3—64no—
372C22—64no—
373C22—62no—
374C22—94no—
375C22—92no—
376C22—364no—
377C22D32×D411yescharacteristic
378C4—42no—
379C4—62no—
380C4—92no—
381C4—124no—
382C4—362no—
383C4#6431211yescharacteristic
384C4C2×#381111yescharacteristic
385C3—21no—
386C3D3×#47012yescomplemented
387C2—94no—
388C2—122no—
389C2#1059476012yes—
390C2#1059528211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenterC2×Q16D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×Q16×C3⋊D3C2semidirect
4. C3×#5189C2semidirect
5. #10591598C2semidirect
6. #10591552C2semidirect
7. #10590853C2semidirect
8. #10590685C2semidirect
12. C2×C32×Q16C22semidirect
13. C2×#3756C22semidirect
15. C2×#3746C22semidirect
27. C3×#835C22semidirect
28. C3×#817C22semidirect
29. #63574C22semidirect
30. #63567C22semidirect
36. #5189D3semidirect
78. C2×C3×Q16C2×D3semidirect
104. #835C2×D3semidirect
105. #817C2×D3semidirect
214. C2×Q16D32semidirect
280. C3⋊D3#470semidirect
337. C32C2×#470semidirect
386. C3D3×#470semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
#105954292
C2×#637912
C3×#51892
#105915982
#105915522
#105908532
#105906852
D3×#4703