Finite Group Databasebeta

← #11788223

Subgroups — #11788223

Order 1152.

1794 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 1794 conjugacy classes of subgroups — too many to draw. Only its 195 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×#64146C211yesmaximal, characteristic
2C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×#99C211yesmaximal, characteristic, complemented
4C2×#63661C211yesmaximal, characteristic, complemented
5#10592654C211yesmaximal, characteristic, complemented
6#10589393C211yesmaximal, characteristic, complemented
7#10589393C211yesmaximal, characteristic, complemented
8#70036—34nomaximal
9C24×C3⋊D3C2211yescharacteristic
10C22×C32×D4C2211yescharacteristic
11C22×#638C412yescomplemented
12C22×C4×C3⋊D3—21no—
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16C2×#3757C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18#64146—21no—
19#64146—22no—
20#64146—21no—
21C2×#3752—21no—
22C2×#3752—22no—
23C2×#3752C412yescomplemented
24C22⋊C4×C3⋊D3—22no—
25C22⋊C4×C3⋊D3—22no—
26C32×#99—22no—
27#63661—22no—
28C2×#937—34no—
29C2×D3×C22⋊C4—34no—
30C2×C3×#99D314yescomplemented
31C2×#834—34no—
32#4955—34no—
33#4527—34no—
34#4527—34no—
35C24×C32C2×C411yescharacteristic, complemented
36C24×C32C2311yescharacteristic
37C23×C3⋊D3—21no—
38C23×C3⋊D3—21no—
39C23×C3⋊D3—21no—
40C23×C3⋊D3—21no—
41C23×C3⋊D3—44no—
42C23×C3⋊D3C2×C412yes—
43C23×C3⋊D3D411yescharacteristic
44C23×C3⋊D3D412yes—
45C23×C3⋊D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4C2×C411yescharacteristic, complemented
55C2×#638—22no—
56C2×#638—22no—
57C2×#638—44no—
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3C2×C412yescomplemented
61C2×C4×C3⋊D3—24no—
62C2×C4×C3⋊D3—44no—
63C32×C22⋊C4—21no—
64C32×C22⋊C4—21no—
65C32×C22⋊C4—21no—
66C32×C22⋊C4D412yescomplemented
67#3757—21no—
68#3757—21no—
69#3757—21no—
70#3757—21no—
71#3757—21no—
72#3757D412yescomplemented
73#3752—24no—
74#3752—22no—
75#3752—22no—
76#3752—44no—
77#1898—91noSylow
78C24×D3—34no—
79C22×C3×D4C2×D314yes—
80C22×#67—38no—
81C22×C4×D3—64no—
82C2×C3×C22⋊C4C2×D314yes—
83C2×C3×C22⋊C4C2×D314yes—
84C2×#217—34no—
85C2×#217—34no—
86C2×#217—34no—
87#937—64no—
88#937—68no—
89#937—64no—
90C2×(C2×D3)⋊C4—38no—
91C2×(C2×D3)⋊C4—64no—
92C2×(C2×D3)⋊C4—68no—
93D3×C22⋊C4—68no—
94D3×C22⋊C4—68no—
95C3×#99—28no—
96#834—68no—
97C23×C32—21no—
98C23×C32—21no—
99C23×C32—21no—
100C23×C32—42no—
101C23×C32—42no—
102C23×C32C22×C411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C23×C32C2×D411yescharacteristic
105C23×C32C2×D411yescharacteristic
106C23×C32C2×D411yescharacteristic
107C23×C32#4111yescharacteristic
108C23×C32#4111yescharacteristic
109C22×C3⋊D3—21no—
110C22×C3⋊D3—21no—
111C22×C3⋊D3—24no—
112C22×C3⋊D3—22no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—24no—
119C22×C3⋊D3—24no—
120C22×C3⋊D3—42no—
121C22×C3⋊D3—42no—
122C22×C3⋊D3—42no—
123C22×C3⋊D3—44no—
124C22×C3⋊D3—44no—
125C22×C3⋊D3—44no—
126C22×C3⋊D3—44no—
127C22×C3⋊D3C22⋊C412yes—
128C22×C3⋊D3C22⋊C412yes—
129C32×D4—41no—
130C32×D4—41no—
131C32×D4—41no—
132C32×D4—41no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—22no—
137C2×C32×C4—42no—
138C2×C32×C4—42no—
139C2×C32×C4—41no—
140#638—44no—
141#638—44no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145C2×C3⋊Dic3—42no—
146C2×C3⋊Dic3—42no—
147C2×C3⋊Dic3—41no—
148C4×C3⋊D3—48no—
149C2×#120—91no—
150C22×C22⋊C4—91no—
151C2×#99—91no—
152C2×#99C3⋊D311yescharacteristic, complemented
153#379—91no—
154#342—91no—
155#342—91no—
156C24×C3C4×D314yescomplemented
157C24×C3C22×D314yes—
158C23×D3—34no—
159C23×D3—38no—
160C23×D3—38no—
161C23×D3—34no—
162C23×D3—64no—
163C23×D3—64no—
164C23×D3—64no—
165C23×D3—64no—
166C23×D3—1216no—
167C2×C3×D4—24no—
168C2×C3×D4—24no—
169C2×C3×D4—24no—
170C2×C3×D4—24no—
171C2×C3×D4—24no—
172C2×C3×D4—24no—
173C22×C3×C4—24no—
174C22×C3×C4—24no—
175C22×C3×C4C4×D314yescomplemented
176C2×#67—68no—
177C2×#67—68no—
178C2×#67—1216no—
179C22×Dic3—38no—
180C22×Dic3—64no—
181C22×Dic3—64no—
182C2×C4×D3—616no—
183C2×C4×D3—1216no—
184C3×C22⋊C4—24no—
185C3×C22⋊C4—24no—
186C3×C22⋊C4—24no—
187C3×C22⋊C4#6718yescomplemented
188#217—38no—
189#217—64no—
190#217—64no—
191#217—64no—
192#217—64no—
193#217—64no—
194(C2×D3)⋊C4—68no—
195(C2×D3)⋊C4—68no—
196(C2×D3)⋊C4—616no—
197(C2×D3)⋊C4—1216no—
198C22×C32—22no—
199C22×C32—22no—
200C22×C32—22no—
201C22×C32—41no—
202C22×C32—41no—
203C22×C32—41no—
204C22×C32—41no—
205C22×C32—41no—
206C22×C32—42no—
207C22×C32—81no—
208C22×C32—81no—
209C22×C32C2×C22⋊C411yescharacteristic
210C22×C32C4×D411yescharacteristic
211C22×C32C4×D411yescharacteristic
212C22×C32#12011yescharacteristic
213C22×C32#12111yescharacteristic
214C22×C32#12111yescharacteristic
215C22×C32#12311yescharacteristic
216C2×C3⋊D3—24no—
217C2×C3⋊D3—24no—
218C2×C3⋊D3—22no—
219C2×C3⋊D3—22no—
220C2×C3⋊D3—22no—
221C2×C3⋊D3—22no—
222C2×C3⋊D3—22no—
223C2×C3⋊D3—44no—
224C2×C3⋊D3—44no—
225C2×C3⋊D3—44no—
226C2×C3⋊D3—44no—
227C2×C3⋊D3—42no—
228C2×C3⋊D3—42no—
229C2×C3⋊D3#9914yescomplemented
230C32×C4—42no—
231C32×C4—41no—
232C32×C4—81no—
233C3⋊Dic3—42no—
234C3⋊Dic3—42no—
235C3⋊Dic3—81no—
236C25—91no—
237C22×D4—92no—
238C22×D4C2×C3⋊D311yescharacteristic
239C23×C4—181no—
240#120—181no—
241#120—182no—
242#120—181no—
243C2×C22⋊C4—91no—
244C2×C22⋊C4—91no—
245C2×C22⋊C4—92no—
246C2×C22⋊C4—91no—
247C2×C22⋊C4—182no—
248C2×C22⋊C4—181no—
249C2×C22⋊C4—182no—
250C2×C22⋊C4—182no—
251C2×C22⋊C4C2×C3⋊D311yescharacteristic
252C2×C22⋊C4C2×C3⋊D311yescharacteristic
253#99—22no—
254#99—182no—
255C23×C3—24no—
256C23×C3—24no—
257C23×C3—24no—
258C23×C3—48no—
259C23×C3—48no—
260C23×C3C2×C4×D314yes—
261C23×C3#23514yes—
262C23×C3D3×D414yes—
263C23×C3D3×D414yes—
264C23×C3D3×D414yes—
265C23×C3#23714yes—
266C23×C3C2×#6714yes—
267C22×D3—38no—
268C22×D3—38no—
269C22×D3—616no—
270C22×D3—616no—
271C22×D3—616no—
272C22×D3—64no—
273C22×D3—64no—
274C22×D3—68no—
275C22×D3—64no—
276C22×D3—68no—
277C22×D3—68no—
278C22×D3—64no—
279C22×D3—68no—
280C22×D3—128no—
281C22×D3—128no—
282C22×D3—128no—
283C22×D3—1216no—
284C22×D3—1216no—
285C22×D3—1216no—
286C22×D3—1216no—
287C3×D4—44no—
288C3×D4—44no—
289C3×D4—44no—
290C3×D4—44no—
291C2×C3×C4—24no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—28no—
295C2×C3×C4—48no—
296C2×C3×C4—48no—
297C2×C3×C4—44no—
298#67—1216no—
299#67—1216no—
300C2×Dic3—68no—
301C2×Dic3—68no—
302C2×Dic3—128no—
303C2×Dic3—128no—
304C2×Dic3—128no—
305C2×Dic3—124no—
306C4×D3—1232no—
307C2×C32—21no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32—21no—
312C2×C32—21no—
313C2×C32—81no—
314C2×C32#38611yescharacteristic
315C2×C32C2×#9912yes—
316C3⋊D3—24no—
317C3⋊D3—42no—
318C24—91no—
319C24—92no—
320C24—92no—
321C24—91no—
322C24—181no—
323C24—181no—
324C24—181no—
325C24—181no—
326C24—364no—
327C24C4×C3⋊D311yescharacteristic, complemented
328C24C22×C3⋊D311yescharacteristic
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—182no—
336C2×D4—182no—
337C2×D4—364no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—92no—
341C22×C4—184no—
342C22×C4—181no—
343C22×C4—181no—
344C22×C4—364no—
345C22×C4C4×C3⋊D311yescharacteristic, complemented
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—92no—
350C22⋊C4—182no—
351C22⋊C4—182no—
352C22⋊C4—184no—
353C22⋊C4—181no—
354C22⋊C4—181no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C22⋊C4—364no—
359C22⋊C4#63812yescomplemented
360C22×C3—28no—
361C22×C3—28no—
362C22×C3—28no—
363C22×C3—44no—
364C22×C3—44no—
365C22×C3—44no—
366C22×C3—44no—
367C22×C3—44no—
368C22×C3—48no—
369C22×C3—84no—
370C22×C3—84no—
371C22×C3D3×C22⋊C414yes—
372C22×C3#67⋊C414yes—
373C22×C3#88314yes—
374C22×C3#88414yes—
375C22×C3C4×#6714yes—
376C22×C3#93714yes—
377C22×C3#93814yes—
378C2×D3—316no—
379C2×D3—616no—
380C2×D3—616no—
381C2×D3—68no—
382C2×D3—68no—
383C2×D3—68no—
384C2×D3—68no—
385C2×D3—68no—
386C2×D3—1216no—
387C2×D3—1216no—
388C2×D3—1216no—
389C2×D3—1216no—
390C2×D3—128no—
391C2×D3—128no—
392C3×C4—48no—
393C3×C4—44no—
394C3×C4—84no—
395Dic3—128no—
396Dic3—128no—
397Dic3—244no—
398C32#189811yescharacteristic, complemented, Sylow
399C23—21no—
400C23—21no—
401C23—21no—
402C23—42no—
403C23—42no—
404C23—92no—
405C23—92no—
406C23—184no—
407C23—184no—
408C23—184no—
409C23—181no—
410C23—181no—
411C23—182no—
412C23—181no—
413C23—182no—
414C23—182no—
415C23—181no—
416C23—182no—
417C23—362no—
418C23—362no—
419C23—362no—
420C23—364no—
421C23—364no—
422C23—364no—
423C23—364no—
424C23C2×C4×C3⋊D311yescharacteristic
425C23#382811yescharacteristic
426C23D4×C3⋊D311yescharacteristic
427C23D4×C3⋊D311yescharacteristic
428C23D4×C3⋊D311yescharacteristic
429C23#383011yescharacteristic
430C23C2×#63811yescharacteristic
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—364no—
436D4—364no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—368no—
447C2×C4—362no—
448C2×C4—362no—
449C2×C4—362no—
450C2×C4—361no—
451C2×C3—24no—
452C2×C3—24no—
453C2×C3—24no—
454C2×C3—24no—
455C2×C3—24no—
456C2×C3—24no—
457C2×C3—84no—
458C2×C3D3×#9918yes—
459C2×C3#495614yes—
460D3—616no—
461D3—128no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22—94no—
474C22—184no—
475C22—184no—
476C22—182no—
477C22—182no—
478C22—182no—
479C22—182no—
480C22—182no—
481C22—364no—
482C22—364no—
483C22—364no—
484C22—364no—
485C22—362no—
486C22—362no—
487C22C22⋊C4×C3⋊D311yescharacteristic
488C22#6409011yescharacteristic
489C22#6409211yescharacteristic
490C22#6409311yescharacteristic
491C22C4×#63811yescharacteristic
492C22#6414611yescharacteristic
493C22#6414711yescharacteristic
494C4—42no—
495C4—41no—
496C4—81no—
497C4—362no—
498C4—362no—
499C4—721no—
500C3#7003614yescomplemented
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—21no—
506C2—21no—
507C2—81no—
508C2—184no—
509C2—362no—
510C2C3⋊D3×#9912yes—
511C2#1059265511yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC24C22×C3⋊D3
FittingC2×C32×#99C2
socleC22×C32C2×C22⋊C4
prime radicalC2×#64146C2
cosocleC24×C32C23
hypercenterC2×#99C3⋊D3
hypocenterC32#1898
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×C3⋊D3C2semidirect
3. C2×C32×#99C2semidirect
4. C2×#63661C2semidirect
5. #10592654C2semidirect
6. #10589393C2semidirect
7. #10589393C2semidirect
11. C22×#638C4semidirect
23. C2×#3752C4semidirect
30. C2×C3×#99D3semidirect
35. C24×C32C2×C4semidirect
54. C22×C32×C4C2×C4semidirect
60. C22×C3⋊Dic3C2×C4semidirect
66. C32×C22⋊C4D4semidirect
72. #3757D4semidirect
152. C2×#99C3⋊D3semidirect
156. C24×C3C4×D3semidirect
175. C22×C3×C4C4×D3semidirect
187. C3×C22⋊C4#67semidirect
229. C2×C3⋊D3#99semidirect
327. C24C4×C3⋊D3semidirect
345. C22×C4C4×C3⋊D3semidirect
359. C22⋊C4#638semidirect
398. C32#1898semidirect
500. C3#70036semidirect

Maximal subgroups

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

subgroupindex
C2×#641462
C2×C22⋊C4×C3⋊D32
C2×C32×#992
C2×#636612
#105926542
#105893932
#700363