Finite Group Databasebeta

← #11856283

Subgroups — #11856283

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63981C211yesmaximal, characteristic
3C2×#63853C212yesmaximal, complemented
4C3×#5213C211yesmaximal, characteristic, complemented
5C3×#5210C211yesmaximal, characteristic, complemented
6#10591719C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591387C212yesmaximal, complemented
10#10591290C212yesmaximal, complemented
11#10591219C212yesmaximal, complemented
12#74936—31nomaximal
13#74656—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C4×C3⋊D3—28no—
18C22×C4×C3⋊D3—24no—
19C22×C4×C3⋊D3C2212yes—
20C22×C4×C3⋊D3C2212yes—
21C22×C3×#67C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2212yescomplemented
28C2×C3×Dic3⋊C4C2212yescomplemented
29#63981—24no—
30C2×Dic3⋊Dic3C2212yescomplemented
31C2×#3722C2212yes—
32C2×#3722C2211yescharacteristic
33C2×#3722C2212yes—
34C2×#3722C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36#63853—28no—
37C3×C3⋊#95C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39#63579C2212yescomplemented
40#63579C2212yescomplemented
41C23×C4×D3—31no—
42C23×C4×D3—31no—
43C23×C4×D3—61no—
44C2×#937—31no—
45C2×#894—32no—
46C2×#883—32no—
47C2×#882—31no—
48C3×#386—31no—
49C3×#385—31no—
50#5220—31no—
51#5213D311yescharacteristic, complemented
52#5210D311yescharacteristic, complemented
53#4989—32no—
54#4958—31no—
55#4956—32no—
56#4955—31no—
57#4955—31no—
58#4950—31no—
59#4946—31no—
60#4668—32no—
61#4665—32no—
62#4664—32no—
63#4664—32no—
64C24×C32C2311yescharacteristic
65C23×C3⋊D3—22no—
66C23×C3⋊D3—22no—
67C23×C3⋊D3—24no—
68C23×C3⋊D3—24no—
69C23×C3⋊D3D414yes—
70C23×C3⋊D3C2311yescharacteristic
71C23×C3⋊D3C2311yescharacteristic
72C23×C3×D3C2311yescharacteristic
73C22×C32×C4—22no—
74C22×C32×C4—24no—
75C22×C32×C4C2312yes—
76C22×C3⋊Dic3—22no—
77C22×C3⋊Dic3—24no—
78C22×C3⋊Dic3C2312yes—
79C2×C4×C3⋊D3—232no—
80C2×C4×C3⋊D3—24no—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3D418yescomplemented
86C2×C3×#67—22no—
87C2×C3×#67—22no—
88C2×C3×#67—22no—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C2×#626—24no—
95C2×#626—22no—
96C2×#626—22no—
97C2×#626—24no—
98C3×#217—22no—
99C3×#217—22no—
100C3×#217—22no—
101C3×(C2×D3)⋊C4—24no—
102C3×Dic3⋊C4—24no—
103Dic3⋊Dic3—24no—
104#3722—24no—
105#3722—22no—
106#3722—22no—
107#3722—24no—
108(C2×D3)⋊Dic3—24no—
109#2849—91noSylow
110C24×D3—31no—
111C24×D3—31no—
112C24×D3—61no—
113C22×C3×D4—31no—
114C23×C3×C4—21no—
115C23×C3×C4C2×D311yescharacteristic
116C23×C3×C4C2×D311yescharacteristic
117C22×#67—31no—
118C22×#67—31no—
119C22×#67C2×D311yescharacteristic
120C23×Dic3—31no—
121C23×Dic3—31no—
122C23×Dic3—61no—
123C22×D12—31no—
124C22×D12—31no—
125C22×C4×D3—32no—
126C22×C4×D3—32no—
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3—62no—
130C22×C4×D3—62no—
131C22×C4×D3—68no—
132C22×C4×D3—68no—
133C22×C4×D3—64no—
134C22×C4×D3—64no—
135C22×C4×D3—616no—
136C22×C4×D3—68no—
137C2×C3×C4⋊C4—32no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—32no—
142C2×#217—32no—
143C2×#217C2×D311yescharacteristic
144C2×#217C2×D311yescharacteristic
145C2×#217C2×D311yescharacteristic
146#937—64no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4C2×D312yescomplemented
157C2×C4⋊Dic3—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4C2×D312yescomplemented
160#894—68no—
161#883—68no—
162#882—64no—
163C3×#95—32no—
164C3×#95—32no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95—32no—
168C3⋊#95—32no—
169C3⋊#95C2×D312yescomplemented
170C3⋊#95C2×D312yescomplemented
171C23×C32—22no—
172C23×C32—22no—
173C23×C32C2×D412yes—
174C23×C32#4112yes—
175C23×C32#4112yes—
176C23×C32C2411yescharacteristic
177C22×C3⋊D3—216no—
178C22×C3⋊D3—216no—
179C22×C3⋊D3—28no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—21no—
182C22×C3⋊D3—21no—
183C22×C3⋊D3—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3—28no—
187C22×C3⋊D3—28no—
188C22×C3⋊D3C2×D414yes—
189C22×C3⋊D3C2×D412yes—
190C22×C3⋊D3C2×D412yes—
191C22×C3⋊D3#4114yes—
192C22×C3×D3—22no—
193C22×C3×D3—21no—
194C22×C3×D3—22no—
195C22×C3×D3—21no—
196C22×C3×D3—21no—
197C2×C32×C4—28no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4C2×D414yes—
201C2×C3⋊Dic3—28no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3C2×D414yes—
205C4×C3⋊D3—216no—
206C4×C3⋊D3—216no—
207C3×#67—44no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221#626—44no—
222#626—44no—
223C24×C4—91no—
224C2×#123—92no—
225C2×#120—91no—
226#386—31no—
227#386—92no—
228#386—91no—
229#385—31no—
230#385—92no—
231#385—91no—
232#381—92no—
233#379—91no—
234C24×C3—21no—
235C24×C3—31no—
236C24×C3C22×D311yescharacteristic
237C24×C3C22×D311yescharacteristic
238C23×D3—31no—
239C23×D3—31no—
240C23×D3—31no—
241C23×D3—31no—
242C23×D3—34no—
243C23×D3—34no—
244C23×D3—64no—
245C23×D3—61no—
246C23×D3—61no—
247C23×D3—64no—
248C23×D3—64no—
249C23×D3—64no—
250C23×D3—64no—
251C23×D3—68no—
252C23×D3—68no—
253C23×D3—64no—
254C23×D3—64no—
255C23×D3—62no—
256C23×D3—62no—
257C23×D3—62no—
258C23×D3—62no—
259C23×D3C22×D311yescharacteristic
260C2×C3×D4—62no—
261C2×C3×D4—62no—
262C2×C3×D4—62no—
263C22×C3×C4—24no—
264C22×C3×C4—28no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—22no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—32no—
273C22×C3×C4—32no—
274C22×C3×C4—31no—
275C22×C3×C4C22×D312yes—
276C22×C3×C4C22×D312yes—
277C2×#67—22no—
278C2×#67—22no—
279C2×#67—22no—
280C2×#67—64no—
281C2×#67—62no—
282C2×#67—62no—
283C2×#67—64no—
284C22×Dic3—32no—
285C22×Dic3—32no—
286C22×Dic3—62no—
287C22×Dic3—64no—
288C22×Dic3—64no—
289C22×Dic3—68no—
290C22×Dic3—64no—
291C22×Dic3—62no—
292C22×Dic3—62no—
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D312yes—
296C22×Dic3C22×D312yes—
297C22×Dic3C22×D311yescharacteristic
298C2×D12—62no—
299C2×D12—62no—
300C2×D12—64no—
301C2×D12—64no—
302C2×C4×D3—38no—
303C2×C4×D3—38no—
304C2×C4×D3—68no—
305C2×C4×D3—64no—
306C2×C4×D3—64no—
307C2×C4×D3—64no—
308C2×C4×D3—64no—
309C2×C4×D3—64no—
310C2×C4×D3—64no—
311C2×C4×D3—64no—
312C2×C4×D3—64no—
313C2×C4×D3—68no—
314C2×C4×D3—68no—
315C2×C4×D3—68no—
316C2×C4×D3—68no—
317C2×C4×D3—632no—
318C2×C4×D3—632no—
319C2×C4×D3—664no—
320C2×C4×D3—68no—
321C2×C4×D3—64no—
322C2×C4×D3—64no—
323C3×C4⋊C4—64no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—62no—
326C3×C22⋊C4—62no—
327C3×C22⋊C4—64no—
328#217—22no—
329#217—22no—
330#217—22no—
331#217—64no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—62no—
334(C2×D3)⋊C4—62no—
335(C2×D3)⋊C4—64no—
336(C2×D3)⋊C4—64no—
337(C2×D3)⋊C4—64no—
338(C2×D3)⋊C4—64no—
339(C2×D3)⋊C4—62no—
340(C2×D3)⋊C4—62no—
341(C2×D3)⋊C4—64no—
342C4⋊Dic3—64no—
343Dic3⋊C4—24no—
344Dic3⋊C4—64no—
345C22×C32—22no—
346C22×C32—22no—
347C22×C32—24no—
348C22×C32—24no—
349C22×C32#12314yescomplemented
350C22×C32C22×D411yescharacteristic
351C22×C32C22×D412yes—
352C22×C32C2×#4111yescharacteristic
353C22×C32C2×#4111yescharacteristic
354C22×C32C2×#4112yes—
355C2×C3⋊D3—232no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3—24no—
361C2×C3⋊D3—24no—
362C2×C3⋊D3—24no—
363C2×C3⋊D3—24no—
364C2×C3⋊D3#12014yes—
365C2×C3⋊D3#12314yescomplemented
366C2×C3×D3—41no—
367C2×C3×D3—41no—
368C2×C3×D3—41no—
369C2×C3×D3—42no—
370C2×C3×D3—42no—
371C32×C4—24no—
372C3⋊Dic3—24no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3—42no—
377C3×Dic3—42no—
378C25—91no—
379C22×D4—31no—
380C22×D4—91no—
381C22×D4—91no—
382C23×C4—92no—
383C23×C4—91no—
384C23×C4—92no—
385C23×C4—188no—
386C23×C4—184no—
387C23×C4D3211yescharacteristic
388#123—188no—
389#120—184no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—92no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—91no—
397C2×C22⋊C4—91no—
398C2×C22⋊C4—92no—
399C2×C22⋊C4—92no—
400C2×C22⋊C4—92no—
401#95—32no—
402#95—32no—
403#95—92no—
404#95—92no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—21no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—61no—
416C23×C3—62no—
417C23×C3—61no—
418C23×C3—61no—
419C23×C3—62no—
420C23×C3#23512yes—
421C23×C3#23512yes—
422C23×C3D3×D412yes—
423C23×C3D3×D412yes—
424C23×C3#23712yes—
425C23×C3#23912yes—
426C23×C3C23×D311yescharacteristic
427C23×C3C23×D311yescharacteristic
428C22×D3—21no—
429C22×D3—22no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—22no—
433C22×D3—34no—
434C22×D3—34no—
435C22×D3—32no—
436C22×D3—32no—
437C22×D3—32no—
438C22×D3—32no—
439C22×D3—34no—
440C22×D3—34no—
441C22×D3—64no—
442C22×D3—62no—
443C22×D3—62no—
444C22×D3—64no—
445C22×D3—68no—
446C22×D3—68no—
447C22×D3—68no—
448C22×D3—68no—
449C22×D3—616no—
450C22×D3—64no—
451C22×D3—616no—
452C22×D3—632no—
453C22×D3—632no—
454C22×D3—616no—
455C22×D3—616no—
456C22×D3—616no—
457C22×D3—616no—
458C22×D3—62no—
459C22×D3—62no—
460C22×D3—62no—
461C22×D3—62no—
462C22×D3—64no—
463C22×D3—616no—
464C22×D3—68no—
465C22×D3—68no—
466C22×D3—61no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—62no—
477C22×D3—62no—
478C3×D4—124no—
479C2×C3×C4—216no—
480C2×C3×C4—28no—
481C2×C3×C4—28no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—24no—
489C2×C3×C4—62no—
490C2×C3×C4—61no—
491C2×C3×C4—62no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—62no—
498C2×C3×C4—61no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4D3×D414yes—
503C2×C3×C4D3×D414yes—
504#67—44no—
505#67—124no—
506#67—124no—
507C2×Dic3—22no—
508C2×Dic3—21no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—22no—
516C2×Dic3—21no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—34no—
521C2×Dic3—34no—
522C2×Dic3—64no—
523C2×Dic3—616no—
524C2×Dic3—68no—
525C2×Dic3—68no—
526C2×Dic3—64no—
527C2×Dic3—64no—
528C2×Dic3—62no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532D12—124no—
533D12—124no—
534C4×D3—616no—
535C4×D3—616no—
536C4×D3—632no—
537C4×D3—632no—
538C4×D3—616no—
539C4×D3—616no—
540C2×C32—24no—
541C2×C32C2×#12011yescharacteristic
542C2×C32C2×#12311yescharacteristic
543C2×C32C2×#12311yescharacteristic
544C2×C32#52512yes—
545C2×C32#52512yes—
546C3⋊D3—24no—
547C3⋊D3—24no—
548C3×D3—81no—
549C24—31no—
550C24—91no—
551C24—91no—
552C24—94no—
553C24—184no—
554C24—184no—
555C24—182no—
556C24—182no—
557C24C2×D3211yescharacteristic
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—182no—
562C2×D4—182no—
563C2×D4—184no—
564C2×D4—184no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—31no—
572C22×C4—92no—
573C22×C4—98no—
574C22×C4—184no—
575C22×C4—184no—
576C22×C4—184no—
577C22×C4—184no—
578C22×C4—1832no—
579C22×C4—184no—
580C22×C4—182no—
581C22×C4—184no—
582C22×C4C2×D3212yes—
583C4⋊C4—64no—
584C4⋊C4—184no—
585C22⋊C4—62no—
586C22⋊C4—62no—
587C22⋊C4—62no—
588C22⋊C4—64no—
589C22⋊C4—182no—
590C22⋊C4—182no—
591C22⋊C4—184no—
592C22⋊C4—184no—
593C22⋊C4—184no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—28no—
597C22×C3—28no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—24no—
605C22×C3—24no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—22no—
611C22×C3—24no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3—122no—
615C22×C3—121no—
616C22×C3—122no—
617C22×C3#88314yescomplemented
618C22×C3#89414yescomplemented
619C22×C3C2×#23511yescharacteristic
620C22×C3C2×#23511yescharacteristic
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C2×D3×D412yes—
624C22×C3C2×D3×D412yes—
625C22×C3C2×#23711yescharacteristic
626C22×C3C2×#23911yescharacteristic
627C22×C3D3×#4112yes—
628C22×C3D3×#4112yes—
629C2×D3—34no—
630C2×D3—34no—
631C2×D3—34no—
632C2×D3—34no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—42no—
636C2×D3—41no—
637C2×D3—42no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—664no—
642C2×D3—632no—
643C2×D3—632no—
644C2×D3—64no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—68no—
648C2×D3—68no—
649C2×D3—68no—
650C2×D3—68no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—64no—
658C2×D3—64no—
659C2×D3—64no—
660C2×D3—64no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—64no—
666C2×D3—64no—
667C3×C4—28no—
668C3×C4—24no—
669C3×C4—24no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—122no—
673C3×C4—121no—
674C3×C4—122no—
675Dic3—41no—
676Dic3—41no—
677Dic3—42no—
678Dic3—41no—
679Dic3—42no—
680Dic3—68no—
681Dic3—64no—
682Dic3—64no—
683C32#284911yescharacteristic, complemented, Sylow
684C23—22no—
685C23—22no—
686C23—61no—
687C23—61no—
688C23—62no—
689C23—62no—
690C23—61no—
691C23—94no—
692C23—94no—
693C23—92no—
694C23—92no—
695C23—188no—
696C23—188no—
697C23—1816no—
698C23—1816no—
699C23—181no—
700C23—181no—
701C23—181no—
702C23—181no—
703C23—182no—
704C23—182no—
705C23—188no—
706C23#379612yes—
707C23#379812yes—
708C23#381112yes—
709C23C22×D3211yescharacteristic
710D4—124no—
711D4—364no—
712D4—364no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—62no—
727C2×C4—61no—
728C2×C4—62no—
729C2×C4—94no—
730C2×C4—1816no—
731C2×C4—1816no—
732C2×C4—188no—
733C2×C4—182no—
734C2×C4—182no—
735C2×C4#381114yes—
736C2×C3—28no—
737C2×C3—24no—
738C2×C3—24no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—22no—
742C2×C3—21no—
743C2×C3—22no—
744C2×C3—241no—
745C2×C3C2×#88311yescharacteristic
746C2×C3C2×#89411yescharacteristic
747C2×C3#554712yes—
748C2×C3#554712yes—
749C2×C3D3×#12011yescharacteristic
750C2×C3D3×#12011yescharacteristic
751C2×C3#560612yes—
752C2×C3#562712yes—
753C2×C3D3×#12311yescharacteristic
754C2×C3D3×#12311yescharacteristic
755D3—68no—
756D3—68no—
757D3—64no—
758D3—64no—
759D3—64no—
760D3—64no—
761D3—81no—
762C22—22no—
763C22—24no—
764C22—22no—
765C22—24no—
766C22—94no—
767C22—94no—
768C22—121no—
769C22—121no—
770C22—122no—
771C22—121no—
772C22—122no—
773C22—1832no—
774C22—182no—
775C22—182no—
776C22—182no—
777C22—184no—
778C22—184no—
779C22—182no—
780C22—184no—
781C22—184no—
782C22#6385314yescomplemented
783C22C2×#379611yescharacteristic
784C22C2×#379811yescharacteristic
785C22#6430612yes—
786C22C2×#381111yescharacteristic
787C22C2×#381112yes—
788C4—24no—
789C4—121no—
790C4—121no—
791C4—122no—
792C4—121no—
793C4—122no—
794C4—184no—
795C3—21no—
796C3#7465611yescharacteristic, complemented
797C3#7493611yescharacteristic, complemented
798C2—24no—
799C2—184no—
800C2—184no—
801C2—241no—
802C2C2×#6385311yescharacteristic
803C2#1059492212yes—
804C2#1059501612yes—
805C2#1059507911yescharacteristic
806C2#1059552711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC2×#63981C2
hypercenterC23×C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4×C3⋊D3C2semidirect
3. C2×#63853C2semidirect
4. C3×#5213C2semidirect
5. C3×#5210C2semidirect
6. #10591719C2semidirect
7. #10591714C2semidirect
8. #10591713C2semidirect
9. #10591387C2semidirect
10. #10591290C2semidirect
11. #10591219C2semidirect
27. C2×C3×(C2×D3)⋊C4C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
30. C2×Dic3⋊Dic3C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
37. C3×C3⋊#95C22semidirect
38. C3×C3⋊#95C22semidirect
39. #63579C22semidirect
40. #63579C22semidirect
51. #5213D3semidirect
52. #5210D3semidirect
85. C2×C4×C3⋊D3D4semidirect
156. C2×(C2×D3)⋊C4C2×D3semidirect
159. C2×Dic3⋊C4C2×D3semidirect
169. C3⋊#95C2×D3semidirect
170. C3⋊#95C2×D3semidirect
349. C22×C32#123semidirect
365. C2×C3⋊D3#123semidirect
617. C22×C3#883semidirect
618. C22×C3#894semidirect
683. C32#2849semidirect
782. C22#63853semidirect
796. C3#74656semidirect
797. C3#74936semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×#639812
C2×#638532
C3×#52132
C3×#52102
#105917192
#105917142
#105917132
#105913872
#105912902
#105912192
#749363
#746563