Finite Group Databasebeta

← #11860655

Subgroups — #11860655

Order 1152.

750 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64239C211yesmaximal, characteristic
2#10594245C211yesmaximal, characteristic, complemented
3#10594051C211yesmaximal, characteristic
4#10593738C211yesmaximal, characteristic, complemented
5#10593507C211yesmaximal, characteristic, complemented
6C2×#63740C211yesmaximal, characteristic, complemented
7#10593498C211yesmaximal, characteristic
8#10593445C211yesmaximal, characteristic, complemented
9C4×#3776C211yesmaximal, characteristic, complemented
10#10593433C211yesmaximal, characteristic, complemented
11#10593432C211yesmaximal, characteristic, complemented
12#10593431C211yesmaximal, characteristic, complemented
13C4×#3775C211yesmaximal, characteristic, complemented
14#10593369C211yesmaximal, characteristic, complemented
15#10593369C211yesmaximal, characteristic, complemented
16C22×#627C2211yescharacteristic
17C2×#3805C2211yescharacteristic
18C2×#3792C2211yescharacteristic
19C22×#622C2211yescharacteristic
20C2×#3776C2211yescharacteristic
21C2×#3776C2211yescharacteristic
22#64239C418yescomplemented
23C2×#3775C2211yescharacteristic
24C2×#3775C2211yescharacteristic
25#64086C2211yescharacteristic
26C3×#67⋊C4—21no—
27C3×#877—21no—
28Dic3×#67—21no—
29C2×#3724C2211yescharacteristic
30#63957C2211yescharacteristic
31#63955—21no—
32C4×#627C2211yescharacteristic
33C4×#627C2211yescharacteristic
34C4×#627C2211yescharacteristic
35#63902C2211yescharacteristic
36C4×#625C2211yescharacteristic
37#63877—21no—
38D3×Dic3⋊C4—21no—
39#63838C2211yescharacteristic
40#63838C2211yescharacteristic
41#63838C2211yescharacteristic
42#63837—21no—
43#63837—21no—
44#63777C2211yescharacteristic
45#63777C2211yescharacteristic
46C4×#622C2211yescharacteristic
47C4×#622C2211yescharacteristic
48#63743C2211yescharacteristic
49#63743C2211yescharacteristic
50#63742C2211yescharacteristic
51#63742C2211yescharacteristic
52#63740C2211yescharacteristic
53#63740C2211yescharacteristic
54#63740C2211yescharacteristic
55#63740C2211yescharacteristic
56#63740C2211yescharacteristic
57#63740C2211yescharacteristic
58#63739C2211yescharacteristic
59#63739C2211yescharacteristic
60#5546—61no—
61#5516—61no—
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C3×#67—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C2×C3×C4×D3—21no—
67C2×#627—21no—
68C2×#627—22no—
69C2×#627C2×C414yescomplemented
70C2×#627C2311yescharacteristic
71C2×#627C2311yescharacteristic
72C2×#627C2311yescharacteristic
73C2×#625C2311yescharacteristic
74#3805—22no—
75#3805C2×C414yes—
76C2×D3×Dic3—21no—
77C2×D3×Dic3—21no—
78#3792C2×C414yescomplemented
79C2×#622—22no—
80C2×#622C2311yescharacteristic
81C2×#622C2311yescharacteristic
82C2×#622C2311yescharacteristic
83C2×#622C2311yescharacteristic
84#3776C2×C414yescomplemented
85#3776C2×C414yescomplemented
86#3775C2×C414yescomplemented
87#3775C2×C414yescomplemented
88C32×C22⋊C4D411yescharacteristic
89#3757D411yescharacteristic
90#3750D411yescharacteristic
91#3750D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C3×#217—21no—
95C3×(C2×D3)⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102#3724—21no—
103#3724C2311yescharacteristic
104#3724C2311yescharacteristic
105#3724C2311yescharacteristic
106#3724C2311yescharacteristic
107Dic3⋊Dic3—21no—
108Dic3⋊Dic3—21no—
109Dic3⋊Dic3—21no—
110(C2×D3)⋊Dic3—21no—
111Dic32—21no—
112Dic32—21no—
113Dic32—21no—
114Dic32—21no—
115#2947—91nomaximal, Sylow
116C2×#237—61no—
117C22×Dic6—61no—
118C3×C4×D4—61no—
119C3×#117—61no—
120D4×Dic3—61no—
121C4×#67—61no—
122C4×#67—61no—
123#926—61no—
124C2×Dic3⋊C4—61no—
125C2×Dic3⋊C4—61no—
126D3×C4⋊C4—61no—
127#887—61no—
128#887—61no—
129#887—61no—
130#887—61no—
131#887—61no—
132#67⋊C4—21no—
133#67⋊C4—61no—
134#877—21no—
135#877—61no—
136#877—61no—
137#877—61no—
138#877—61no—
139#877—61no—
140#872—61no—
141C4×Dic6—61no—
142C4×Dic6—61no—
143C4×Dic6—61no—
144C4×Dic6—61no—
145C4×Dic6—61no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—21no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C3⋊Dic3C22×C412yes—
151C2×C3⋊Dic3C2×D411yescharacteristic
152C2×C3⋊Dic3C2×D411yescharacteristic
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3⋊Dic3#4112yes—
155C2×C3⋊Dic3C2411yescharacteristic
156C3×#67—24no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—81no—
166C3×C4×D3—81no—
167#627—24no—
168#627—21no—
169#627—21no—
170#627—21no—
171#627C22×C412yes—
172#627C22×C412yes—
173#627C22×C412yes—
174#625—21no—
175#625C22×C412yes—
176D3×Dic3—24no—
177D3×Dic3—81no—
178#622—21no—
179#622—21no—
180#622C22×C412yes—
181#622C22×C412yes—
182C2×#137—91no—
183#520—91no—
184#519—91no—
185#441—91no—
186#441—91no—
187#440—91no—
188#440—91no—
189C4×Q16—91no—
190C4×Q16—91no—
191C4×SD16—91no—
192C4×SD16—91no—
193#428—91no—
194#416—91no—
195C2×#103—91no—
196#405—91no—
197C2×C3×D4—61no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C2×#67—21no—
202C2×#67—61no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209#237—64no—
210#237—64no—
211C2×C4×D3—21no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—64no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—64no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C3×C22⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—61no—
227C3×C22⋊C4—61no—
228C3×C42—61no—
229C3×C42—61no—
230C3×C42—61no—
231#217—21no—
232#217—61no—
233#217—61no—
234#217—61no—
235(C2×D3)⋊C4—21no—
236(C2×D3)⋊C4—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240Dic3⋊C4—21no—
241Dic3⋊C4—21no—
242Dic3⋊C4—21no—
243Dic3⋊C4—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247Dic3⋊C4—61no—
248Dic3⋊C4—61no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252Dic3⋊C4—61no—
253Dic3⋊C4—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—61no—
256C4×Dic3—21no—
257C4×Dic3—21no—
258C4×Dic3—21no—
259C4×Dic3—61no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32C4×D412yes—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—21no—
280C3⋊Dic3—21no—
281C3⋊Dic3—21no—
282C3⋊Dic3C4×D412yes—
283C3⋊Dic3C23×C411yescharacteristic
284C3⋊Dic3C2×#4111yescharacteristic
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3—41no—
291C3×Dic3—41no—
292C2×#41—91no—
293C22×Q8—91no—
294#137—98no—
295C2×Q16—91no—
296C2×Q16—91no—
297C2×SD16—91no—
298C2×SD16—91no—
299C2×M16—91no—
300C22×C8—91no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—91no—
306C4×Q8—91no—
307C4×Q8—181no—
308C4×Q8—181no—
309C4×D4—61no—
310C4×D4—91no—
311C4×D4—91no—
312C4×D4—181no—
313#117—61no—
314#117—91no—
315#117—91no—
316#117—181no—
317#117—181no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—181no—
320#107—91no—
321#107—91no—
322#106—91no—
323#106—91no—
324#103—91no—
325#103—91no—
326#103—91no—
327#103—91no—
328#103—91no—
329#103—91no—
330#102—91no—
331#102—91no—
332#97—91no—
333#97—91no—
334C4×C8—91no—
335C4×C8—91no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—61no—
339C22×D3—21no—
340C3×D4—64no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—64no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—241no—
354C2×C3×C4—241no—
355#67—24no—
356#67—62no—
357#67—62no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—24no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—64no—
379C2×Dic3—81no—
380C2×Dic3—241no—
381C4×D3—64no—
382C4×D3—81no—
383C4×D3—241no—
384Dic6—62no—
385Dic6—62no—
386Dic6—62no—
387Dic6—64no—
388Dic6—64no—
389Dic6—62no—
390Dic6—62no—
391Dic6—62no—
392C2×C32—22no—
393C2×C32C2×C4×D411yescharacteristic
394C2×C32#57711yescharacteristic
395C2×C32#57811yescharacteristic
396C3×D3—42no—
397#41—94no—
398#41—182no—
399C2×Q8—91no—
400C2×Q8—91no—
401C2×Q8—91no—
402C2×Q8—94no—
403C2×Q8—181no—
404C2×Q8—182no—
405C2×D4—61no—
406C2×D4—91no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413Q16—94no—
414Q16—94no—
415SD16—94no—
416SD16—94no—
417M16—94no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8—182no—
423C4⋊C4—61no—
424C4⋊C4—61no—
425C4⋊C4—61no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—91no—
429C4⋊C4—91no—
430C4⋊C4—91no—
431C4⋊C4—91no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4—181no—
435C4⋊C4—181no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C22⋊C4—91no—
439C22⋊C4—181no—
440C22⋊C4GO+(4,𝔽2)11yescharacteristic
441C42—61no—
442C42—61no—
443C42—61no—
444C42—91no—
445C42—91no—
446C42—181no—
447C42—181no—
448C42—181no—
449C42—181no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—62no—
459C22×C3—121no—
460C22×C3—121no—
461C2×D3—22no—
462C2×D3—41no—
463C2×D3—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—62no—
469C3×C4—62no—
470C3×C4—62no—
471C3×C4—121no—
472C3×C4—121no—
473C3×C4—121no—
474C3×C4—121no—
475Dic3—22no—
476Dic3—22no—
477Dic3—22no—
478Dic3—41no—
479Dic3—41no—
480Dic3—41no—
481Dic3—41no—
482Dic3—62no—
483Dic3—61no—
484Dic3—61no—
485Dic3—61no—
486Dic3—61no—
487Dic3—62no—
488Dic3—121no—
489Dic3—121no—
490Dic3—121no—
491Dic3—121no—
492C32#294711yescharacteristic, complemented, Sylow
493C23—61no—
494C23C2×GO+(4,𝔽2)11yescharacteristic
495Q8—92no—
496Q8—92no—
497Q8—92no—
498Q8—181no—
499Q8—181no—
500Q8—184no—
501Q8—181no—
502D4—64no—
503D4—92no—
504D4—181no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—64no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—91no—
514C2×C4—91no—
515C2×C4—92no—
516C2×C4—92no—
517C2×C4—91no—
518C2×C4—91no—
519C2×C4—184no—
520C2×C4—241no—
521C2×C4—241no—
522C2×C4—721no—
523C2×C4C2×GO+(4,𝔽2)11yescharacteristic
524C2×C4C2×GO+(4,𝔽2)11yescharacteristic
525C8—92no—
526C8—92no—
527C8—181no—
528C8—181no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—42no—
536C2×C3—42no—
537C2×C3—122no—
538D3—42no—
539C22—21no—
540C22—21no—
541C22—62no—
542C22—121no—
543C22—121no—
544C22C4×GO+(4,𝔽2)12yes—
545C22C22×GO+(4,𝔽2)11yescharacteristic
546C4—21no—
547C4—21no—
548C4—62no—
549C4—62no—
550C4—62no—
551C4—91no—
552C4—91no—
553C4—92no—
554C4—121no—
555C4—121no—
556C4—121no—
557C4—121no—
558C4—181no—
559C4—181no—
560C3—21no—
561C3—21no—
562C2—22no—
563C2—122no—
564C2C2×C4×GO+(4,𝔽2)11yescharacteristic
565C2#1059651511yescharacteristic
566C2#1059651611yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C22⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#3805C22
cosocleC2×C3⋊Dic3C24
hypercenterC22⋊C4GO+(4,𝔽2)
hypocenterC32#2947
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594245C2semidirect
4. #10593738C2semidirect
5. #10593507C2semidirect
6. C2×#63740C2semidirect
8. #10593445C2semidirect
9. C4×#3776C2semidirect
10. #10593433C2semidirect
11. #10593432C2semidirect
12. #10593431C2semidirect
13. C4×#3775C2semidirect
14. #10593369C2semidirect
15. #10593369C2semidirect
22. #64239C4semidirect
69. C2×#627C2×C4semidirect
78. #3792C2×C4semidirect
84. #3776C2×C4semidirect
85. #3776C2×C4semidirect
86. #3775C2×C4semidirect
87. #3775C2×C4semidirect
492. C32#2947semidirect

Maximal subgroups

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

subgroupindex
C2×#642392
#105942452
#105940512
#105937382
#105935072
C2×#637402
#105934982
#105934452
C4×#37762
#105934332
#105934322
#105934312
C4×#37752
#105933692
#29479