Finite Group Databasebeta

← #11869341

Subgroups — #11869341

Order 1152.

1125 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 1125 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
1#10595081C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic, complemented
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
4C3×#4736C212yesmaximal, complemented
5#10591089C212yesmaximal, complemented
6#10590940C212yesmaximal, complemented
7#10590687C212yesmaximal, complemented
8#10590650C214yesmaximal, complemented
9D3×#480—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×#3811—21no—
12C22×#624—21no—
13C2×#3802C2211yescharacteristic
14C2×C8×C3⋊D3C2212yes—
15C3×#930C2212yes—
16C2×C3×C4⋊Dic3C2212yescomplemented
17#63980—21no—
18C2×#3724—21no—
19#63921—21no—
20#63916C2212yes—
21#63912—21no—
22#63900—21no—
23#63900—21no—
24#63900C2211yescharacteristic
25#63900C2212yes—
26#63900C2212yescomplemented
27C32×C22⋊C8C2211yescharacteristic, complemented
28#63657C2211yescharacteristic, complemented
29#63647C2212yescomplemented
30C3×#821C2214yescomplemented
31C3×#818C2214yescomplemented
32#63576C2214yescomplemented
33#63562C2214yescomplemented
34D3×#121—32no—
35C2×D3×C4⋊C4—32no—
36C3×#480—32no—
37#5033—32no—
38#4967—32no—
39#4882—34no—
40D3×#107—34no—
41#4774—34no—
42D3×#102—34no—
43#4736D312yescomplemented
44D3×C22⋊C8—32no—
45D3×C22⋊C8—61no—
46C23×C3⋊D3D411yescharacteristic
47C22×D32—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C2×C4×C3⋊D3—24no—
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×C3×#67—22no—
56C22×C3×Dic3—22no—
57C2×C3×D12C2312yes—
58#3811—44no—
59C2×#626—22no—
60C2×#625—21no—
61C2×#624—22no—
62C2×#624—22no—
63C2×#624—21no—
64C2×#624—44no—
65#3802—24no—
66C2×C32×C8C2312yes—
67C2×C3⋊(C3⋊C8)C2312yes—
68C8×C3⋊D3—24no—
69C3×(C2×D3)⋊C4—22no—
70C3×C4⋊Dic3—22no—
71C3×C4⋊Dic3C2314yes—
72C3×C4⋊Dic3C2312yes—
73#3724—22no—
74#3724—22no—
75#3724—21no—
76(C2×D3)⋊Dic3—22no—
77C2×#480—91noSylow
78C2×D3×D4—32no—
79C2×D3×D4—62no—
80C22×C4×D3—32no—
81C22×C4×D3—61no—
82C22×C4×D3—62no—
83C3×#121—32no—
84C2×C3×C4⋊C4—32no—
85#939—62no—
86#938—32no—
87#930C2×D312yes—
88C2×C4⋊Dic3C2×D312yescomplemented
89C2×Dic3⋊C4—62no—
90C2×D3×C8—34no—
91C2×D3×C8—62no—
92#895—32no—
93D3×C4⋊C4—32no—
94D3×C4⋊C4—34no—
95D3×C4⋊C4—34no—
96D3×C4⋊C4—62no—
97D3×C4⋊C4—62no—
98#884—62no—
99D3×C22⋊C4—62no—
100C3×#107—34no—
101C3×#102—34no—
102C3×C22⋊C8—21no—
103C3×C22⋊C8C2×D312yescomplemented
104#832—34no—
105#830—32no—
106#830—61no—
107#821C2×D314yescomplemented
108(C2×D3)⋊C8—34no—
109(C2×D3)⋊C8—62no—
110#818C2×D314yescomplemented
111#809—34no—
112#807—34no—
113#807—34no—
114C23×C32C2×D411yescharacteristic
115C22×C3⋊D3—22no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3D814yes—
118C22×C3⋊D3C2×D411yescharacteristic
119C22×C3⋊D3C2×D411yescharacteristic
120C22×C3×D3—22no—
121C2×D32—42no—
122C2×D32—42no—
123C2×D32—42no—
124C2×C32×C4—22no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2411yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3C2×D411yescharacteristic
129C2×C3⋊Dic3C2×D411yescharacteristic
130C4×C3⋊D3—22no—
131C4×C3⋊D3—22no—
132C4×C3⋊D3—22no—
133C4×C3⋊D3#4114yes—
134C3×#67—44no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—24no—
137C2×C3×Dic3—44no—
138C3×D12—24no—
139#626—44no—
140#625—42no—
141#624—44no—
142#624—44no—
143#624—42no—
144C32×C8—22no—
145C3⋊(C3⋊C8)—22no—
146C2×#121—91no—
147C22×C4⋊C4—91no—
148#480—32no—
149#480—94no—
150#480—92no—
151C2×#107—92no—
152C2×#102—92no—
153C2×C22⋊C8—91no—
154C23×D3—32no—
155C23×D3—61no—
156C23×D3—62no—
157C2×C3×D4—32no—
158C2×C3×D4—62no—
159C22×C3×C4—21no—
160C22×C3×C4—62no—
161C22×C3×C4C22×D312yes—
162C2×#67—22no—
163C2×#67—62no—
164C2×#67—62no—
165C22×Dic3—22no—
166C22×Dic3—32no—
167C22×Dic3—61no—
168D3×D4—68no—
169D3×D4—128no—
170C2×D12—62no—
171C2×D12C22×D312yes—
172C2×C4×D3—32no—
173C2×C4×D3—32no—
174C2×C4×D3—32no—
175C2×C4×D3—32no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—68no—
181C2×C4×D3—62no—
182C2×C4×D3—64no—
183C2×C4×D3—64no—
184C2×C4×D3—124no—
185C2×C4×D3—128no—
186C2×C3×C8—22no—
187C2×C3×C8C22×D314yes—
188C3×C4⋊C4—32no—
189C3×C4⋊C4—34no—
190C3×C4⋊C4—62no—
191C3×C22⋊C4—62no—
192#217—62no—
193(C2×D3)⋊C4—22no—
194(C2×D3)⋊C4—62no—
195C4⋊Dic3—22no—
196C4⋊Dic3C22×D312yes—
197C4⋊Dic3C22×D314yes—
198Dic3⋊C4—62no—
199Dic3⋊C4—64no—
200Dic3⋊C4—64no—
201C2×C3⋊C8—34no—
202C2×C3⋊C8—62no—
203D3×C8—68no—
204D3×C8—124no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32C2×D812yes—
208C22×C32C22×D411yescharacteristic
209C2×C3⋊D3—21no—
210C2×C3⋊D3—21no—
211C2×C3⋊D3—28no—
212C2×C3⋊D3#12312yes—
213C2×C3⋊D3C2×D812yes—
214C2×C3⋊D3C2×D812yes—
215C2×C3⋊D3#13712yes—
216C2×C3×D3—42no—
217C2×C3×D3—42no—
218C2×C3×D3—42no—
219D32—84no—
220C32×C4—21no—
221C32×C4C2×#4112yes—
222C3⋊Dic3—21no—
223C3⋊Dic3#12312yes—
224C3×Dic3—44no—
225C3×Dic3—42no—
226C22×D4—91no—
227C22×D4—181no—
228C23×C4—91no—
229C23×C4—181no—
230C22×C8—92no—
231#121—32no—
232#121—92no—
233#121—181no—
234#121—181no—
235C2×C4⋊C4—32no—
236C2×C4⋊C4—92no—
237C2×C4⋊C4—92no—
238C2×C4⋊C4—91no—
239C2×C4⋊C4—181no—
240C2×C4⋊C4—181no—
241C2×C4⋊C4—181no—
242C2×C22⋊C4—181no—
243#107—34no—
244#107—94no—
245#102—34no—
246#102—94no—
247C22⋊C8—91no—
248C22⋊C8—92no—
249C22⋊C8D3211yescharacteristic, complemented
250C23×C3—21no—
251C23×C3—62no—
252C23×C3D3×D412yes—
253C22×D3—22no—
254C22×D3—32no—
255C22×D3—38no—
256C22×D3—32no—
257C22×D3—61no—
258C22×D3—64no—
259C22×D3—61no—
260C22×D3—64no—
261C22×D3—64no—
262C22×D3—122no—
263C22×D3—122no—
264C22×D3—124no—
265C22×D3—124no—
266C22×D3—124no—
267C3×D4—64no—
268C3×D4—124no—
269C2×C3×C4—24no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—42no—
273C2×C3×C4—64no—
274C2×C3×C4—62no—
275C2×C3×C4—124no—
276C2×C3×C4D3×D412yes—
277C2×C3×C4C23×D312yes—
278#67—44no—
279#67—124no—
280#67—124no—
281C2×Dic3—24no—
282C2×Dic3—22no—
283C2×Dic3—32no—
284C2×Dic3—32no—
285C2×Dic3—44no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—64no—
289C2×Dic3—122no—
290D12—24no—
291D12—124no—
292C4×D3—38no—
293C4×D3—64no—
294C4×D3—64no—
295C4×D3—64no—
296C4×D3—64no—
297C4×D3—122no—
298C4×D3—122no—
299C4×D3—122no—
300C4×D3—128no—
301C4×D3—128no—
302C4×D3—124no—
303C3×C8—24no—
304C3×C8—42no—
305C3⋊C8—64no—
306C3⋊C8—122no—
307C2×C32—22no—
308C2×C32C2×#12311yescharacteristic
309C2×C32C22×D811yescharacteristic
310C2×C32C2×#13711yescharacteristic
311C3⋊D3—22no—
312C3⋊D3#48014yescomplemented
313C3×D3—82no—
314C24—91no—
315C24—181no—
316C2×D4—32no—
317C2×D4—62no—
318C2×D4—182no—
319C2×D4—184no—
320C2×D4—181no—
321C2×D4—364no—
322C22×C4—62no—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—184no—
329C22×C4—181no—
330C22×C4—182no—
331C22×C4—182no—
332C22×C4—364no—
333C22×C4C2×D3211yescharacteristic
334C2×C8—92no—
335C2×C8—184no—
336C2×C8C2×D3212yes—
337C4⋊C4—34no—
338C4⋊C4—32no—
339C4⋊C4—62no—
340C4⋊C4—182no—
341C4⋊C4—182no—
342C4⋊C4—181no—
343C22⋊C4—62no—
344C22⋊C4—182no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—21no—
348C22×C3—22no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—122no—
352C22×C3—122no—
353C22×C3—122no—
354C22×C3D3×D814yes—
355C22×C3C2×D3×D412yes—
356C2×D3—34no—
357C2×D3—34no—
358C2×D3—34no—
359C2×D3—34no—
360C2×D3—42no—
361C2×D3—42no—
362C2×D3—42no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—62no—
366C2×D3—62no—
367C2×D3—616no—
368C2×D3—62no—
369C2×D3—62no—
370C2×D3—128no—
371C2×D3—121no—
372C2×D3—121no—
373C2×D3—248no—
374C3×C4—22no—
375C3×C4—22no—
376C3×C4—41no—
377C3×C4—124no—
378C3×C4—122no—
379C3×C4D3×#4114yes—
380Dic3—34no—
381Dic3—44no—
382Dic3—42no—
383Dic3—62no—
384Dic3—62no—
385Dic3—121no—
386C32C2×#48011yescharacteristic, complemented, Sylow
387C23—62no—
388C23—91no—
389C23—91no—
390C23—94no—
391C23—182no—
392C23—182no—
393C23—362no—
394C23—362no—
395C23—362no—
396C23#380211yescharacteristic
397D4—64no—
398D4—124no—
399D4—362no—
400D4—364no—
401C2×C4—22no—
402C2×C4—62no—
403C2×C4—64no—
404C2×C4—91no—
405C2×C4—94no—
406C2×C4—91no—
407C2×C4—124no—
408C2×C4—182no—
409C2×C4—182no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—364no—
413C2×C4—364no—
414C2×C4—362no—
415C2×C4#380211yescharacteristic
416C2×C4C22×D3211yescharacteristic
417C8—22no—
418C8—182no—
419C2×C3—24no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—42no—
424C2×C3—242no—
425C2×C3D3×#12312yes—
426C2×C3C2×D3×D812yes—
427C2×C3D3×#13712yes—
428D3—38no—
429D3—64no—
430D3—64no—
431D3—82no—
432D3—122no—
433C22—21no—
434C22—21no—
435C22—92no—
436C22—92no—
437C22—92no—
438C22—92no—
439C22—122no—
440C22—122no—
441C22—122no—
442C22—188no—
443C22—181no—
444C22—181no—
445C22—724no—
446C22#6379712yes—
447C22C2×#380211yescharacteristic
448C4—21no—
449C4—92no—
450C4—124no—
451C4—122no—
452C4—181no—
453C4#6431212yes—
454C3—21no—
455C3D3×#48012yescomplemented
456C2—22no—
457C2—94no—
458C2—182no—
459C2—242no—
460C2#1059429511yescharacteristic
461C2C2×#6379711yescharacteristic
462C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595081C2
hypercenterC22⋊C8D32
hypocenterC32C2×#480
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
2. C2×#63900C2semidirect
3. C3⋊D3×C22⋊C8C2semidirect
4. C3×#4736C2semidirect
5. #10591089C2semidirect
6. #10590940C2semidirect
7. #10590687C2semidirect
8. #10590650C2semidirect
16. C2×C3×C4⋊Dic3C22semidirect
26. #63900C22semidirect
27. C32×C22⋊C8C22semidirect
28. #63657C22semidirect
29. #63647C22semidirect
30. C3×#821C22semidirect
31. C3×#818C22semidirect
32. #63576C22semidirect
33. #63562C22semidirect
43. #4736D3semidirect
88. C2×C4⋊Dic3C2×D3semidirect
103. C3×C22⋊C8C2×D3semidirect
107. #821C2×D3semidirect
110. #818C2×D3semidirect
249. C22⋊C8D32semidirect
312. C3⋊D3#480semidirect
386. C32C2×#480semidirect
455. C3D3×#480semidirect

Maximal subgroups

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

subgroupindex
#105950812
C2×#639002
C3⋊D3×C22⋊C82
C3×#47362
#105910892
#105909402
#105906872
#105906502
D3×#4803