Finite Group Databasebeta

← #11869385

Subgroups — #11869385

Order 1152.

1021 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 1021 conjugacy classes of subgroups — too many to draw. Only its 178 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×#63900C211yesmaximal, characteristic
2#10594925C211yesmaximal, characteristic
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic
4C3×#4721C212yesmaximal, complemented
5#10591101C212yesmaximal, complemented
6#10590686C214yesmaximal, complemented
7#10590685C212yesmaximal, complemented
8#10590672C212yesmaximal, complemented
9D3×#483—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×#624—21no—
12C2×#3797C2211yescharacteristic
13C2×C8×C3⋊D3C2212yes—
14C2×C3×C4⋊Dic3C2212yes—
15C3×#924C2212yes—
16#63982—21no—
17#63974—21no—
18C2×#3724—21no—
19#63900—21no—
20#63900—21no—
21#63900C2211yescharacteristic
22#63900C2212yes—
23#63900C2212yes—
24#63883—21no—
25#63871C2212yes—
26#63865—21no—
27C32×C22⋊C8C2211yescharacteristic
28#63657C2211yescharacteristic
29#63647C2212yes—
30C3×#817C2214yescomplemented
31C3×#816C2214yescomplemented
32#63574C2214yescomplemented
33#63565C2214yescomplemented
34D3×C22⋊Q8—32no—
35C2×D3×C4⋊C4—32no—
36C3×#483—32no—
37#5043—32no—
38#4971—32no—
39#4862—34no—
40D3×#106—34no—
41#4805—34no—
42D3×#103—34no—
43D3×C22⋊C8—32no—
44D3×C22⋊C8—61no—
45#4721D312yescomplemented
46C23×C3⋊D3D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3C2311yescharacteristic
53C2×C4×C3⋊D3C2311yescharacteristic
54C22×C3×Dic3—22no—
55C2×C3×Dic6C2312yes—
56C2×#627—21no—
57C2×#624—21no—
58C2×#624—22no—
59C2×#624—22no—
60C2×#624—21no—
61C2×#624—44no—
62#3797—24no—
63C2×C32×C8C2312yes—
64C2×C3⋊(C3⋊C8)C2312yes—
65C8×C3⋊D3—24no—
66C3×#217—22no—
67C3×C4⋊Dic3—22no—
68C3×C4⋊Dic3C2312yes—
69C3×C4⋊Dic3C2314yes—
70C3×Dic3⋊C4—22no—
71#3724—21no—
72#3724—22no—
73#3724—22no—
74Dic3⋊Dic3—22no—
75#3722—22no—
76C2×#483—91noSylow
77C2×D3×Q8—32no—
78C22×C4×D3—32no—
79C22×C4×D3—61no—
80C22×C4×D3—62no—
81C3×C22⋊Q8—32no—
82C2×C3×C4⋊C4—32no—
83#946—32no—
84C2×C4⋊Dic3C2×D312yes—
85#924C2×D312yes—
86C2×Dic3⋊C4—62no—
87C2×D3×C8—34no—
88C2×D3×C8—62no—
89#897—32no—
90#896—62no—
91D3×C4⋊C4—34no—
92D3×C4⋊C4—34no—
93D3×C4⋊C4—32no—
94D3×C4⋊C4—62no—
95D3×C4⋊C4—62no—
96D3×C4⋊C4—62no—
97D3×C22⋊C4—62no—
98#878—62no—
99C3×#106—34no—
100C3×#103—34no—
101C3×C22⋊C8—21no—
102C3×C22⋊C8C2×D312yes—
103#835—34no—
104#830—32no—
105#830—61no—
106(C2×D3)⋊C8—34no—
107(C2×D3)⋊C8—62no—
108#817C2×D314yescomplemented
109#816C2×D314yescomplemented
110#810—34no—
111#808—34no—
112#808—34no—
113C23×C32C2×D411yescharacteristic
114C22×C3⋊D3—22no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3SD1614yes—
117C22×C3⋊D3C2×D411yescharacteristic
118C22×C3⋊D3C2×D411yescharacteristic
119C2×C32×C4—22no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2411yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3C2×D411yescharacteristic
124C2×C3⋊Dic3C2×D411yescharacteristic
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127C4×C3⋊D3—22no—
128C4×C3⋊D3#4114yes—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—44no—
133C3×Dic6—24no—
134#627—42no—
135#624—42no—
136#624—44no—
137#624—44no—
138#624—42no—
139C32×C8—22no—
140C3⋊(C3⋊C8)—22no—
141C2×C22⋊Q8—91no—
142C22×C4⋊C4—91no—
143#483—32no—
144#483—94no—
145#483—92no—
146C2×#106—92no—
147C2×#103—92no—
148C2×C22⋊C8—91no—
149C23×D3—32no—
150C23×D3—61no—
151C2×C3×Q8—32no—
152C22×C3×C4—21no—
153C22×C3×C4—62no—
154C22×C3×C4C22×D312yes—
155C22×Dic3—22no—
156C22×Dic3—32no—
157C22×Dic3—61no—
158D3×Q8—68no—
159C2×C4×D3—32no—
160C2×C4×D3—32no—
161C2×C4×D3—32no—
162C2×C4×D3—32no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—68no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×C4×D3—64no—
171C2×C4×D3—64no—
172C2×C4×D3—124no—
173C2×C4×D3—128no—
174C2×Dic6—62no—
175C2×Dic6C22×D312yes—
176C2×C3×C8—22no—
177C2×C3×C8C22×D314yes—
178C3×C4⋊C4—32no—
179C3×C4⋊C4—34no—
180C3×C4⋊C4—62no—
181C3×C4⋊C4—62no—
182C3×C22⋊C4—62no—
183#217—22no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—62no—
186C4⋊Dic3—22no—
187C4⋊Dic3—62no—
188C4⋊Dic3C22×D312yes—
189C4⋊Dic3C22×D314yes—
190Dic3⋊C4—22no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193Dic3⋊C4—64no—
194Dic3⋊C4—64no—
195C2×C3⋊C8—34no—
196C2×C3⋊C8—62no—
197D3×C8—68no—
198D3×C8—124no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32C2×SD1612yes—
202C22×C32C22×D411yescharacteristic
203C2×C3⋊D3—21no—
204C2×C3⋊D3—21no—
205C2×C3⋊D3—28no—
206C2×C3⋊D3#12312yes—
207C2×C3⋊D3C2×SD1612yes—
208C2×C3⋊D3C2×SD1612yes—
209C2×C3⋊D3#13712yes—
210C32×C4—21no—
211C32×C4C2×#4112yes—
212C3⋊Dic3—21no—
213C3⋊Dic3#12312yes—
214C3×Dic3—42no—
215C3×Dic3—44no—
216C3×Dic3—42no—
217C22×Q8—91no—
218C23×C4—91no—
219C23×C4—181no—
220C22×C8—92no—
221C22⋊Q8—32no—
222C22⋊Q8—92no—
223C22⋊Q8—181no—
224C22⋊Q8—181no—
225C2×C4⋊C4—32no—
226C2×C4⋊C4—92no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—181no—
230C2×C4⋊C4—181no—
231C2×C4⋊C4—181no—
232C2×C4⋊C4—181no—
233C2×C22⋊C4—181no—
234#106—34no—
235#106—94no—
236#103—34no—
237#103—94no—
238C22⋊C8—91no—
239C22⋊C8—92no—
240C22⋊C8D3211yescharacteristic
241C23×C3—21no—
242C23×C3D3×D412yes—
243C22×D3—32no—
244C22×D3—38no—
245C22×D3—32no—
246C22×D3—61no—
247C22×D3—64no—
248C22×D3—61no—
249C22×D3—64no—
250C22×D3—64no—
251C22×D3—122no—
252C22×D3—122no—
253C3×Q8—64no—
254C2×C3×C4—24no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—42no—
258C2×C3×C4—64no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—124no—
262C2×C3×C4D3×D412yes—
263C2×C3×C4C23×D312yes—
264C2×Dic3—22no—
265C2×Dic3—22no—
266C2×Dic3—24no—
267C2×Dic3—32no—
268C2×Dic3—32no—
269C2×Dic3—44no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—64no—
273C2×Dic3—122no—
274C4×D3—38no—
275C4×D3—64no—
276C4×D3—64no—
277C4×D3—64no—
278C4×D3—64no—
279C4×D3—122no—
280C4×D3—122no—
281C4×D3—122no—
282C4×D3—124no—
283C4×D3—128no—
284C4×D3—128no—
285C4×D3—124no—
286Dic6—24no—
287Dic6—124no—
288C3×C8—24no—
289C3×C8—42no—
290C3⋊C8—64no—
291C3⋊C8—122no—
292C2×C32—22no—
293C2×C32C2×#12311yescharacteristic
294C2×C32C22×SD1611yescharacteristic
295C2×C32C2×#13711yescharacteristic
296C3⋊D3—22no—
297C3⋊D3#48314yescomplemented
298C24—91no—
299C2×Q8—32no—
300C2×Q8—181no—
301C2×Q8—184no—
302C22×C4—62no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—184no—
309C22×C4—181no—
310C22×C4—181no—
311C22×C4—182no—
312C22×C4—182no—
313C22×C4—364no—
314C22×C4C2×D3211yescharacteristic
315C2×C8—92no—
316C2×C8—184no—
317C2×C8C2×D3212yes—
318C4⋊C4—34no—
319C4⋊C4—32no—
320C4⋊C4—62no—
321C4⋊C4—62no—
322C4⋊C4—182no—
323C4⋊C4—182no—
324C4⋊C4—181no—
325C4⋊C4—182no—
326C22⋊C4—62no—
327C22⋊C4—182no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—22no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3D3×SD1614yes—
335C22×C3C2×D3×D412yes—
336C2×D3—34no—
337C2×D3—34no—
338C2×D3—34no—
339C2×D3—34no—
340C2×D3—62no—
341C2×D3—62no—
342C2×D3—62no—
343C2×D3—62no—
344C2×D3—616no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—128no—
348C2×D3—121no—
349C2×D3—121no—
350C3×C4—22no—
351C3×C4—22no—
352C3×C4—41no—
353C3×C4—122no—
354C3×C4—124no—
355C3×C4—122no—
356C3×C4D3×#4114yes—
357Dic3—34no—
358Dic3—42no—
359Dic3—44no—
360Dic3—42no—
361Dic3—62no—
362Dic3—62no—
363Dic3—121no—
364C32C2×#48311yescharacteristic, complemented, Sylow
365C23—91no—
366C23—91no—
367C23—94no—
368C23—182no—
369C23—182no—
370C23#380211yescharacteristic
371Q8—64no—
372Q8—362no—
373C2×C4—22no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—64no—
377C2×C4—91no—
378C2×C4—94no—
379C2×C4—91no—
380C2×C4—124no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4—364no—
386C2×C4—364no—
387C2×C4—362no—
388C2×C4—362no—
389C2×C4#380211yescharacteristic
390C2×C4C22×D3211yescharacteristic
391C8—22no—
392C8—182no—
393C2×C3—24no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—42no—
398C2×C3D3×#12312yes—
399C2×C3C2×D3×SD1612yes—
400C2×C3D3×#13712yes—
401D3—38no—
402D3—64no—
403D3—64no—
404D3—122no—
405C22—21no—
406C22—21no—
407C22—92no—
408C22—92no—
409C22—92no—
410C22—92no—
411C22—188no—
412C22—181no—
413C22—181no—
414C22#6379612yes—
415C22C2×#380211yescharacteristic
416C4—21no—
417C4—92no—
418C4—124no—
419C4—122no—
420C4—122no—
421C4—181no—
422C4#6431212yes—
423C3—21no—
424C3D3×#48312yescomplemented
425C2—22no—
426C2—94no—
427C2—182no—
428C2#1059429511yescharacteristic
429C2C2×#6379611yescharacteristic
430C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22⋊C8D32
hypocenterC32C2×#483
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
4. C3×#4721C2semidirect
5. #10591101C2semidirect
6. #10590686C2semidirect
7. #10590685C2semidirect
8. #10590672C2semidirect
30. C3×#817C22semidirect
31. C3×#816C22semidirect
32. #63574C22semidirect
33. #63565C22semidirect
45. #4721D3semidirect
108. #817C2×D3semidirect
109. #816C2×D3semidirect
297. C3⋊D3#483semidirect
364. C32C2×#483semidirect
424. C3D3×#483semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105949252
C3⋊D3×C22⋊C82
C3×#47212
#105911012
#105906862
#105906852
#105906722
D3×#4833