Finite Group Databasebeta

← #11866786

Subgroups — #11866786

Order 1152.

1153 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 1153 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×Q16×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595429C212yesmaximal
3C2×D32×C8C211yesmaximal, characteristic
4C3×#5188C212yesmaximal, complemented
5#10591596C214yesmaximal, complemented
6#10591552C212yesmaximal, complemented
7#10590852C212yesmaximal, complemented
8#10590687C211yesmaximal, characteristic, complemented
9D3×#467—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×D3×C8C2212yes—
19#63921—22no—
20#63900C2212yes—
21#63896—24no—
22#63883—22no—
23#63857C2214yes—
24C2×#3710C2211yescharacteristic
25C2×D3×C3⋊C8C2212yes—
26D32×C8—24no—
27C3×#835C2214yescomplemented
28C3×#818C2212yescomplemented
29#63576C2212yescomplemented
30#63567C2214yescomplemented
31C2×D3×Q16—32no—
32C2×D3×Q16—61no—
33C22×D3×C8—32no—
34D3×C22⋊Q8—34no—
35C3×#467—32no—
36#5188D312yescomplemented
37#5116—32no—
38#5051—34no—
39#4887—32no—
40D3×#107—32no—
41#4813—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×D3×C8—24no—
68#3724—22no—
69Dic3⋊Dic3—24no—
70(C2×D3)⋊Dic3—24no—
71#3710—22no—
72D3×C3⋊C8—24no—
73C2×#467—91noSylow
74C2×D3×Q8—34no—
75C2×D3×Q8—62no—
76C22×C4×D3—32no—
77C2×C3×Q16—21no—
78C2×C3×Q16C2×D312yescomplemented
79C22×C3×C8—32no—
80C3×C22⋊Q8—34no—
81#946C2×D314yes—
82C2×#216—34no—
83C2×#216—62no—
84#924—34no—
85C22×C3⋊C8—32no—
86D3×Q16—68no—
87D3×Q16—68no—
88C2×Dic12—32no—
89C2×Dic12—61no—
90C2×D3×C8—32no—
91C2×D3×C8—32no—
92C2×D3×C8—32no—
93C2×D3×C8—61no—
94C2×D3×C8—68no—
95C2×D3×C8C2×D312yes—
96#897—34no—
97#896—64no—
98D3×C4⋊C4—34no—
99D3×C4⋊C4—64no—
100D3×C22⋊C4—64no—
101#878—64no—
102C3×#107—32no—
103C3×#103—34no—
104#835C2×D314yescomplemented
105#818C2×D312yescomplemented
106#816—34no—
107#810—34no—
108#807—34no—
109C22×C3⋊D3C2×D411yescharacteristic
110C22×C3×D3C2×D412yes—
111C2×D32—22no—
112C2×D32—22no—
113C2×D32Q1614yescomplemented
114C32×Q8—22no—
115C32×Q8—22no—
116C2×C32×C4—22no—
117C2×C32×C4C2411yescharacteristic
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3C2×D411yescharacteristic
120C4×C3⋊D3—44no—
121C4×C3⋊D3C2×D412yes—
122C4×C3⋊D3#4112yes—
123#634—22no—
124#634—22no—
125#634—44no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3C2×D412yes—
128C3×C4×D3—22no—
129C3×C4×D3—22no—
130#624—22no—
131#624—44no—
132D3×Dic3—24no—
133C32×C8C2×D412yes—
134C3⋊(C3⋊C8)C2×D412yes—
135C3×C3⋊C8—22no—
136C22×Q16—91no—
137C23×C8—91no—
138C2×C22⋊Q8—92no—
139#467—32no—
140#467—94no—
141#467—92no—
142C2×#107—91no—
143C2×#103—92no—
144C23×D3—32no—
145C2×C3×Q8—22no—
146C2×C3×Q8C22×D314yes—
147C22×C3×C4—32no—
148C22×Dic3—32no—
149D3×Q8—68no—
150D3×Q8—68no—
151D3×Q8—68no—
152D3×Q8—124no—
153C2×C4×D3—32no—
154C2×C4×D3—32no—
155C2×C4×D3—32no—
156C2×C4×D3—61no—
157C2×C4×D3—64no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C4×D3—64no—
161C2×C4×D3—122no—
162C2×C4×D3C22×D312yes—
163C2×Dic6—34no—
164C2×Dic6—62no—
165C2×Dic6—64no—
166C2×Dic6—122no—
167C3×Q16—24no—
168C3×Q16—24no—
169C2×C3×C8—21no—
170C2×C3×C8—32no—
171C2×C3×C8—64no—
172C2×C3×C8C22×D312yes—
173C3×C4⋊C4—34no—
174C3×C4⋊C4—64no—
175C3×C22⋊C4—64no—
176#217—64no—
177#216—68no—
178#216—68no—
179(C2×D3)⋊C4—24no—
180(C2×D3)⋊C4—64no—
181C4⋊Dic3—64no—
182C4⋊Dic3C22×D314yes—
183Dic3⋊C4—24no—
184Dic3⋊C4—64no—
185Dic3⋊C4—64no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—64no—
189C2×C3⋊C8C22×D312yes—
190Dic12—64no—
191Dic12—64no—
192D3×C8—24no—
193D3×C8—38no—
194D3×C8—64no—
195D3×C8—64no—
196D3×C8—64no—
197C22×C32C22×D411yescharacteristic
198C2×C3⋊D3#12112yes—
199C2×C3⋊D3C2×Q1612yes—
200C2×C3⋊D3#13512yes—
201C2×C3×D3—22no—
202C2×C3×D3—22no—
203C2×C3×D3C2×Q1614yescomplemented
204D32—28no—
205C32×C4—42no—
206C32×C4C22×D411yescharacteristic
207C32×C4C2×#4111yescharacteristic
208C3⋊Dic3—42no—
209C3⋊Dic3#12112yes—
210C3×Dic3—22no—
211C3×Dic3—44no—
212C22×Q8—92no—
213C23×C4—91no—
214C2×Q16—92no—
215C2×Q16—91no—
216C2×Q16—184no—
217C2×Q16D3211yescharacteristic, complemented
218C22×C8—32no—
219C22×C8—91no—
220C22×C8—92no—
221C22×C8—91no—
222C22×C8—184no—
223C22⋊Q8—34no—
224C22⋊Q8—94no—
225C22⋊Q8—184no—
226C2×C4⋊C4—92no—
227C2×C4⋊C4—182no—
228C2×C22⋊C4—182no—
229#107—32no—
230#107—92no—
231#103—34no—
232#103—94no—
233C23×C3—32no—
234C22×D3—32no—
235C22×D3—38no—
236C22×D3—61no—
237C22×D3—64no—
238C22×D3—64no—
239C22×D3D3×D412yes—
240C3×Q8—24no—
241C3×Q8—24no—
242C3×Q8—24no—
243C3×Q8—42no—
244C2×C3×C4—24no—
245C2×C3×C4—21no—
246C2×C3×C4—32no—
247C2×C3×C4—42no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—64no—
251C2×C3×C4C23×D312yes—
252C2×Dic3—24no—
253C2×Dic3—32no—
254C2×Dic3—61no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—122no—
258C2×Dic3D3×D412yes—
259C4×D3—22no—
260C4×D3—22no—
261C4×D3—34no—
262C4×D3—34no—
263C4×D3—62no—
264C4×D3—62no—
265C4×D3—64no—
266C4×D3—64no—
267C4×D3—128no—
268C4×D3—128no—
269C4×D3—128no—
270Dic6—64no—
271Dic6—64no—
272Dic6—64no—
273Dic6—122no—
274Dic6—128no—
275Dic6—128no—
276C3×C8—22no—
277C3×C8—62no—
278C3×C8D3×D414yes—
279C3⋊C8—22no—
280C3⋊C8—34no—
281C3⋊C8—62no—
282C2×C32C2×#12111yescharacteristic
283C2×C32C22×Q1611yescharacteristic
284C2×C32C2×#13511yescharacteristic
285C3⋊D3#46714yescomplemented
286C3×D3—24no—
287C24—91no—
288C2×Q8—92no—
289C2×Q8—182no—
290C2×Q8—184no—
291C2×Q8—184no—
292C2×Q8C2×D3212yes—
293C22×C4—32no—
294C22×C4—91no—
295C22×C4—92no—
296C22×C4—91no—
297C22×C4—182no—
298C22×C4—182no—
299C22×C4—182no—
300C22×C4—182no—
301Q16—22no—
302Q16—184no—
303Q16—182no—
304C2×C8—32no—
305C2×C8—64no—
306C2×C8—91no—
307C2×C8—94no—
308C2×C8—182no—
309C2×C8—184no—
310C2×C8C2×D3211yescharacteristic
311C4⋊C4—34no—
312C4⋊C4—64no—
313C4⋊C4—184no—
314C4⋊C4—182no—
315C22⋊C4—64no—
316C22⋊C4—184no—
317C22×C3—21no—
318C22×C3—34no—
319C22×C3—62no—
320C22×C3—62no—
321C22×C3C2×D3×D412yes—
322C2×D3—22no—
323C2×D3—22no—
324C2×D3—34no—
325C2×D3—34no—
326C2×D3—34no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—62no—
330C2×D3—616no—
331C2×D3D3×Q1614yescomplemented
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—44no—
335C3×C4—44no—
336C3×C4—62no—
337C3×C4—124no—
338C3×C4C2×D3×D412yes—
339C3×C4D3×#4112yes—
340Dic3—22no—
341Dic3—34no—
342Dic3—44no—
343Dic3—62no—
344Dic3—124no—
345Dic3—124no—
346C32C2×#46711yescharacteristic, complemented, Sylow
347C23—32no—
348C23—94no—
349C23—91no—
350C23—182no—
351C23—182no—
352Q8—22no—
353Q8—22no—
354Q8—182no—
355Q8—182no—
356Q8—364no—
357C2×C4—22no—
358C2×C4—32no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—64no—
362C2×C4—91no—
363C2×C4—92no—
364C2×C4—92no—
365C2×C4—182no—
366C2×C4—184no—
367C2×C4—182no—
368C2×C4—364no—
369C2×C4—364no—
370C2×C4C22×D3211yescharacteristic
371C8—62no—
372C8—92no—
373C8#381112yes—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—64no—
378C2×C3D3×#12112yes—
379C2×C3C2×D3×Q1612yes—
380C2×C3D3×#13512yes—
381D3—24no—
382D3—38no—
383D3—64no—
384C22—34no—
385C22—62no—
386C22—62no—
387C22—92no—
388C22—92no—
389C22—92no—
390C22—188no—
391C22D32×D411yescharacteristic
392C4—42no—
393C4—62no—
394C4—92no—
395C4—124no—
396C4—362no—
397C4#6431211yescharacteristic
398C4C2×#381111yescharacteristic
399C3—21no—
400C3D3×#46712yescomplemented
401C2—64no—
402C2—94no—
403C2D32×Q1611yescharacteristic
404C2#1059476411yescharacteristic
405C2#1059528211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenterC2×Q16D32
hypocenterC32C2×#467
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×#5188C2semidirect
5. #10591596C2semidirect
6. #10591552C2semidirect
7. #10590852C2semidirect
8. #10590687C2semidirect
12. C2×C32×Q16C22semidirect
13. C2×#3756C22semidirect
15. C2×#3746C22semidirect
27. C3×#835C22semidirect
28. C3×#818C22semidirect
29. #63576C22semidirect
30. #63567C22semidirect
36. #5188D3semidirect
78. C2×C3×Q16C2×D3semidirect
104. #835C2×D3semidirect
105. #818C2×D3semidirect
113. C2×D32Q16semidirect
203. C2×C3×D3C2×Q16semidirect
217. C2×Q16D32semidirect
285. C3⋊D3#467semidirect
331. C2×D3D3×Q16semidirect
346. C32C2×#467semidirect
400. C3D3×#467semidirect

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×D32×C82
C3×#51882
#105915962
#105915522
#105908522
#105906872
D3×#4673