Finite Group Databasebeta

← #11802006

Subgroups — #11802006

Order 1152.

3129 conjugacy classes of subgroups.

The subgroup lattice has 795 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×#67⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63881C212yesmaximal, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6C3×#5210C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591705C211yesmaximal, characteristic, complemented
9#10591387C212yesmaximal, complemented
10#10591290C212yesmaximal, complemented
11#10591260C212yesmaximal, complemented
12#74659—31nomaximal
13#74379—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C4×C3⋊D3—24no—
18C22×C4×C3⋊D3—28no—
19C22×C4×C3⋊D3C2212yes—
20C22×C4×C3⋊D3C2212yes—
21C22×C3×#67C2211yescharacteristic
22C22×#626C2212yes—
23C22×D3×Dic3C2211yescharacteristic, complemented
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2212yescomplemented
28C2×C3×Dic3⋊C4C2212yescomplemented
29#63981C418yescomplemented
30#67⋊Dic3—24no—
31C2×Dic3⋊Dic3C2211yescharacteristic, complemented
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
36C2×Dic32C2211yescharacteristic, complemented
37C2×Dic32C2212yescomplemented
38#63881—28no—
39C3×C3⋊#95C2212yescomplemented
40C3×C3⋊#95C2212yescomplemented
41#63579C2212yescomplemented
42C23×C4×D3—31no—
43C23×C4×D3—31no—
44C23×C4×D3—61no—
45C2×#937—31no—
46C2×D4×Dic3—31no—
47C2×#893—32no—
48C2×#882—31no—
49C2×#67⋊C4—31no—
50C2×#67⋊C4—32no—
51C3×#386—31no—
52C3×#385—31no—
53#5213D311yescharacteristic, complemented
54#5210D311yescharacteristic, complemented
55#4989—32no—
56#4956—32no—
57#4955—31no—
58#4955—31no—
59Dic3×C22⋊C4—31no—
60Dic3×C22⋊C4—31no—
61#4668—32no—
62#4666—32no—
63#4666—32no—
64#4665—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3—22no—
67C23×C3⋊D3—22no—
68C23×C3⋊D3—24no—
69C23×C3⋊D3—24no—
70C23×C3⋊D3C2×C414yescomplemented
71C23×C3⋊D3C2312yes—
72C23×C3×D3C2311yescharacteristic
73C22×C32×C4—22no—
74C22×C32×C4—24no—
75C22×C32×C4C2312yes—
76C22×C3⋊Dic3—24no—
77C22×C3⋊Dic3D414yescomplemented
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C2×C4×C3⋊D3—232no—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3D418yescomplemented
87C2×C3×#67—22no—
88C2×C3×#67—22no—
89C2×C3×#67C2×C414yescomplemented
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C2×#626—24no—
96C2×#626—24no—
97C2×#626C2×C418yescomplemented
98C2×D3×Dic3—24no—
99C2×D3×Dic3—22no—
100C3×#217—22no—
101C3×#217—22no—
102C3×#217C2×C414yescomplemented
103C3×(C2×D3)⋊C4—24no—
104C3×Dic3⋊C4—24no—
105Dic3⋊Dic3—22no—
106#3722—24no—
107#3722—24no—
108#3722C2×C418yescomplemented
109(C2×D3)⋊Dic3—22no—
110Dic32—24no—
111Dic32—22no—
112C4×#120—91noSylow
113C24×D3—31no—
114C24×D3—31no—
115C24×D3—61no—
116C22×C3×D4—31no—
117C23×C3×C4—21no—
118C23×C3×C4C2×D311yescharacteristic
119C23×C3×C4C2×D311yescharacteristic
120C22×#67—32no—
121C22×#67C2×D311yescharacteristic
122C23×Dic3—31no—
123C23×Dic3—31no—
124C23×Dic3—31no—
125C23×Dic3—61no—
126C22×D12—32no—
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3—31no—
130C22×C4×D3—32no—
131C22×C4×D3—32no—
132C22×C4×D3—62no—
133C22×C4×D3—62no—
134C22×C4×D3—68no—
135C22×C4×D3—68no—
136C22×C4×D3—64no—
137C22×C4×D3—64no—
138C22×C4×D3—616no—
139C22×C4×D3—68no—
140C2×C3×C4⋊C4—32no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—32no—
145C2×#217—31no—
146C2×#217C2×D311yescharacteristic
147C2×#217C2×D311yescharacteristic
148C2×#217C2×D311yescharacteristic
149#937—38no—
150D4×Dic3—64no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4C2×D312yescomplemented
159C2×C4⋊Dic3—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4C2×D312yescomplemented
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—32no—
165C2×C4×Dic3—32no—
166#893—68no—
167#882—38no—
168#67⋊C4—68no—
169#67⋊C4—64no—
170C3×#95—32no—
171C3×#95—32no—
172C3⋊#95—32no—
173C3⋊#95—32no—
174C3⋊#95C2×D312yescomplemented
175C3⋊#95C2×D312yescomplemented
176C23×C32—22no—
177C23×C32—22no—
178C23×C32C22×C412yes—
179C23×C32C2×D412yes—
180C23×C32#4112yes—
181C23×C32C2411yescharacteristic
182C22×C3⋊D3—216no—
183C22×C3⋊D3—28no—
184C22×C3⋊D3—28no—
185C22×C3⋊D3—28no—
186C22×C3⋊D3—22no—
187C22×C3⋊D3—22no—
188C22×C3⋊D3—22no—
189C22×C3⋊D3—22no—
190C22×C3⋊D3—216no—
191C22×C3⋊D3C22×C414yes—
192C22×C3⋊D3C2×D414yes—
193C22×C3⋊D3#4114yes—
194C22×C3×D3—21no—
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3—21no—
198C22×C3×D3C22×C412yescomplemented
199C2×C32×C4—28no—
200C2×C32×C4—22no—
201C2×C32×C4—22no—
202C2×C32×C4C2×D414yes—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—28no—
205C2×C3⋊Dic3C2×D412yes—
206C2×C3⋊Dic3C2×D412yes—
207C2×C3⋊Dic3C2×D414yes—
208C4×C3⋊D3—216no—
209C4×C3⋊D3—216no—
210C3×#67—28no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3C22×C412yescomplemented
223C2×C3×Dic3C22×C414yescomplemented
224#626—216no—
225D3×Dic3—44no—
226C24×C4—91no—
227C2×#120—91no—
228C2×C4×D4—92no—
229C2×C4×D4—91no—
230#386—31no—
231#386—92no—
232#385—31no—
233#385—92no—
234#379—91no—
235C4×C22⋊C4—92no—
236C4×C22⋊C4—91no—
237C24×C3—21no—
238C24×C3—31no—
239C24×C3C22×D311yescharacteristic
240C24×C3C22×D311yescharacteristic
241C23×D3—32no—
242C23×D3—32no—
243C23×D3—34no—
244C23×D3—34no—
245C23×D3—64no—
246C23×D3—62no—
247C23×D3—64no—
248C23×D3—64no—
249C23×D3—64no—
250C23×D3—64no—
251C23×D3—68no—
252C23×D3—64no—
253C23×D3—68no—
254C23×D3—64no—
255C23×D3—62no—
256C23×D3—62no—
257C23×D3—62no—
258C23×D3—62no—
259C23×D3C22×D311yescharacteristic
260C2×C3×D4—34no—
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—32no—
271C22×C3×C4—31no—
272C22×C3×C4—32no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4C22×D312yes—
276C22×C3×C4C22×D312yes—
277C2×#67—22no—
278C2×#67—22no—
279C2×#67—38no—
280C2×#67—64no—
281C2×#67—64no—
282C2×#67C4×D314yescomplemented
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—34no—
286C22×Dic3—34no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—64no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—64no—
293C22×Dic3—62no—
294C22×Dic3—64no—
295C22×Dic3—64no—
296C22×Dic3—68no—
297C22×Dic3C22×D312yes—
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D312yes—
301C22×Dic3C22×D311yescharacteristic
302C2×D12—38no—
303C2×D12—64no—
304C2×D12—64no—
305C2×C4×D3—38no—
306C2×C4×D3—38no—
307C2×C4×D3—68no—
308C2×C4×D3—64no—
309C2×C4×D3—64no—
310C2×C4×D3—64no—
311C2×C4×D3—64no—
312C2×C4×D3—64no—
313C2×C4×D3—64no—
314C2×C4×D3—64no—
315C2×C4×D3—64no—
316C2×C4×D3—68no—
317C2×C4×D3—68no—
318C2×C4×D3—68no—
319C2×C4×D3—68no—
320C2×C4×D3—632no—
321C2×C4×D3—632no—
322C2×C4×D3—664no—
323C2×C4×D3—68no—
324C2×C4×D3—64no—
325C2×C4×D3—64no—
326C2×C4×D3—62no—
327C2×C4×D3—64no—
328C3×C4⋊C4—64no—
329C3×C22⋊C4—34no—
330C3×C22⋊C4—62no—
331C3×C22⋊C4—62no—
332C3×C22⋊C4—64no—
333#217—22no—
334#217—22no—
335#217—62no—
336#217C4×D314yescomplemented
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—38no—
339(C2×D3)⋊C4—38no—
340(C2×D3)⋊C4—64no—
341(C2×D3)⋊C4—64no—
342(C2×D3)⋊C4—64no—
343(C2×D3)⋊C4—64no—
344(C2×D3)⋊C4—62no—
345C4⋊Dic3—62no—
346Dic3⋊C4—24no—
347Dic3⋊C4—62no—
348C4×Dic3—64no—
349C4×Dic3—62no—
350C4×Dic3—64no—
351C4×Dic3—62no—
352C22×C32—24no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—24no—
356C22×C32C4×D414yescomplemented
357C22×C32C23×C411yescharacteristic
358C22×C32C22×D412yes—
359C22×C32C22×D411yescharacteristic
360C22×C32C2×#4111yescharacteristic
361C22×C32C2×#4112yes—
362C2×C3⋊D3—232no—
363C2×C3⋊D3—24no—
364C2×C3⋊D3—24no—
365C2×C3⋊D3—24no—
366C2×C3⋊D3—24no—
367C2×C3⋊D3—24no—
368C2×C3⋊D3—24no—
369C2×C3⋊D3C4×D418yescomplemented
370C2×C3×D3—24no—
371C2×C3×D3—22no—
372C2×C3×D3—41no—
373C2×C3×D3—41no—
374C2×C3×D3—42no—
375C32×C4—24no—
376C3⋊Dic3—22no—
377C3⋊Dic3#12014yescomplemented
378C3×Dic3—24no—
379C3×Dic3—22no—
380C3×Dic3—41no—
381C3×Dic3—41no—
382C3×Dic3—42no—
383C25—91no—
384C22×D4—31no—
385C22×D4—92no—
386C23×C4—91no—
387C23×C4—91no—
388C23×C4—92no—
389C23×C4—92no—
390C23×C4—184no—
391C23×C4—188no—
392C23×C4D3211yescharacteristic
393#120—98no—
394C4×D4—188no—
395C4×D4—184no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—91no—
398C2×C22⋊C4—31no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—32no—
402C2×C22⋊C4—92no—
403C2×C22⋊C4—92no—
404C2×C22⋊C4—92no—
405C2×C22⋊C4—91no—
406C2×C42—91no—
407C2×C42—92no—
408#95—32no—
409#95—32no—
410#95—92no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—32no—
422C23×C3—61no—
423C23×C3—62no—
424C23×C3—61no—
425C23×C3—62no—
426C23×C3C2×C4×D312yes—
427C23×C3C2×C4×D312yes—
428C23×C3D3×D412yes—
429C23×C3D3×D412yes—
430C23×C3#23712yes—
431C23×C3#23912yes—
432C23×C3C23×D311yescharacteristic
433C23×C3C23×D311yescharacteristic
434C22×D3—22no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—22no—
438C22×D3—34no—
439C22×D3—34no—
440C22×D3—34no—
441C22×D3—34no—
442C22×D3—34no—
443C22×D3—34no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C22×D3—616no—
448C22×D3—616no—
449C22×D3—616no—
450C22×D3—68no—
451C22×D3—68no—
452C22×D3—64no—
453C22×D3—64no—
454C22×D3—632no—
455C22×D3—616no—
456C22×D3—632no—
457C22×D3—68no—
458C22×D3—68no—
459C22×D3—616no—
460C22×D3—616no—
461C22×D3—64no—
462C22×D3—64no—
463C22×D3—616no—
464C22×D3—68no—
465C22×D3—68no—
466C22×D3—62no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—62no—
473C22×D3—62no—
474C22×D3C2×C4×D312yescomplemented
475C3×D4—68no—
476C2×C3×C4—216no—
477C2×C3×C4—28no—
478C2×C3×C4—28no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
486C2×C3×C4—32no—
487C2×C3×C4—34no—
488C2×C3×C4—61no—
489C2×C3×C4—62no—
490C2×C3×C4—61no—
491C2×C3×C4—62no—
492C2×C3×C4—61no—
493C2×C3×C4—62no—
494C2×C3×C4—61no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4D3×D414yes—
500C2×C3×C4D3×D414yes—
501#67—28no—
502#67—616no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—21no—
509C2×Dic3—22no—
510C2×Dic3—21no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—34no—
515C2×Dic3—34no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—62no—
521C2×Dic3—64no—
522C2×Dic3—62no—
523C2×Dic3—68no—
524C2×Dic3—68no—
525C2×Dic3—616no—
526C2×Dic3—64no—
527C2×Dic3—62no—
528C2×Dic3—62no—
529C2×Dic3—124no—
530C2×Dic3C2×C4×D312yescomplemented
531C2×Dic3C2×C4×D314yescomplemented
532D12—616no—
533C4×D3—616no—
534C4×D3—616no—
535C4×D3—632no—
536C4×D3—632no—
537C4×D3—616no—
538C4×D3—616no—
539C4×D3—124no—
540C2×C32—24no—
541C2×C32C2×C4×D411yescharacteristic
542C2×C32C2×C4×D412yes—
543C2×C32C2×#12011yescharacteristic
544C2×C32#52511yescharacteristic
545C2×C32#52512yes—
546C3⋊D3—28no—
547C3×D3—42no—
548C24—31no—
549C24—92no—
550C24—94no—
551C24—184no—
552C24—184no—
553C24—182no—
554C24—182no—
555C24C2×D3211yescharacteristic
556C2×D4—34no—
557C2×D4—62no—
558C2×D4—62no—
559C2×D4—98no—
560C2×D4—184no—
561C2×D4—184no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—31no—
565C22×C4—32no—
566C22×C4—31no—
567C22×C4—32no—
568C22×C4—31no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4—94no—
572C22×C4—98no—
573C22×C4—184no—
574C22×C4—184no—
575C22×C4—184no—
576C22×C4—184no—
577C22×C4—1832no—
578C22×C4—182no—
579C22×C4—184no—
580C22×C4—184no—
581C22×C4—184no—
582C22×C4C2×D3212yes—
583C4⋊C4—64no—
584C4⋊C4—182no—
585C22⋊C4—34no—
586C22⋊C4—62no—
587C22⋊C4—62no—
588C22⋊C4—64no—
589C22⋊C4—98no—
590C22⋊C4—184no—
591C22⋊C4—184no—
592C22⋊C4—182no—
593C42—184no—
594C42—182no—
595C22×C3—24no—
596C22×C3—24no—
597C22×C3—28no—
598C22×C3—28no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—24no—
602C22×C3—24no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—22no—
610C22×C3—21no—
611C22×C3—22no—
612C22×C3—24no—
613C22×C3—62no—
614C22×C3—64no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3—122no—
618C22×C3#67⋊C414yescomplemented
619C22×C3#89314yescomplemented
620C22×C3C22×C4×D311yescharacteristic
621C22×C3C22×C4×D311yescharacteristic
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C2×D3×D411yescharacteristic
624C22×C3C2×D3×D412yes—
625C22×C3C2×D3×D412yes—
626C22×C3C2×#23711yescharacteristic
627C22×C3C2×#23911yescharacteristic
628C22×C3D3×#4112yes—
629C22×C3D3×#4112yes—
630C2×D3—22no—
631C2×D3—24no—
632C2×D3—38no—
633C2×D3—38no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—42no—
637C2×D3—68no—
638C2×D3—68no—
639C2×D3—664no—
640C2×D3—632no—
641C2×D3—632no—
642C2×D3—68no—
643C2×D3—68no—
644C2×D3—68no—
645C2×D3—68no—
646C2×D3—68no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—64no—
650C2×D3—64no—
651C2×D3—64no—
652C2×D3—64no—
653C2×D3—64no—
654C2×D3—64no—
655C2×D3—64no—
656C2×D3—64no—
657C2×D3—64no—
658C2×D3—64no—
659C3×C4—28no—
660C3×C4—24no—
661C3×C4—24no—
662C3×C4—62no—
663C3×C4—64no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—122no—
667Dic3—22no—
668Dic3—24no—
669Dic3—34no—
670Dic3—34no—
671Dic3—41no—
672Dic3—41no—
673Dic3—42no—
674Dic3—64no—
675Dic3—64no—
676Dic3—62no—
677Dic3—62no—
678C32C4×#12011yescharacteristic, complemented, Sylow
679C23—22no—
680C23—22no—
681C23—32no—
682C23—61no—
683C23—62no—
684C23—62no—
685C23—61no—
686C23—94no—
687C23—94no—
688C23—94no—
689C23—1816no—
690C23—188no—
691C23—188no—
692C23—1816no—
693C23—182no—
694C23—182no—
695C23—182no—
696C23—182no—
697C23—188no—
698C23#379612yes—
699C23C4×D3212yes—
700C23#381112yes—
701C23C22×D3211yescharacteristic
702D4—68no—
703D4—1816no—
704C2×C4—28no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—34no—
708C2×C4—32no—
709C2×C4—61no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—61no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—92no—
721C2×C4—94no—
722C2×C4—92no—
723C2×C4—1816no—
724C2×C4—1816no—
725C2×C4—188no—
726C2×C4—182no—
727C2×C4—364no—
728C2×C4#381114yes—
729C2×C3—28no—
730C2×C3—24no—
731C2×C3—24no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—22no—
735C2×C3—21no—
736C2×C3—22no—
737C2×C3—122no—
738C2×C3C2×#67⋊C411yescharacteristic
739C2×C3C2×#89311yescharacteristic
740C2×C3C4×D3×D412yes—
741C2×C3C4×D3×D412yes—
742C2×C3D3×#12011yescharacteristic
743C2×C3D3×#12011yescharacteristic
744C2×C3#560612yes—
745C2×C3#562712yes—
746C2×C3#565611yescharacteristic
747C2×C3#565611yescharacteristic
748D3—42no—
749D3—616no—
750D3—68no—
751D3—68no—
752C22—22no—
753C22—24no—
754C22—22no—
755C22—24no—
756C22—62no—
757C22—64no—
758C22—98no—
759C22—121no—
760C22—122no—
761C22—121no—
762C22—1832no—
763C22—184no—
764C22—184no—
765C22—184no—
766C22—184no—
767C22—184no—
768C22—184no—
769C22#6388114yescomplemented
770C22C2×#379611yescharacteristic
771C22C2×C4×D3211yescharacteristic
772C22#6430612yes—
773C22C2×#381111yescharacteristic
774C22C2×#381112yes—
775C4—24no—
776C4—62no—
777C4—64no—
778C4—94no—
779C4—121no—
780C4—122no—
781C4—121no—
782C4—182no—
783C3—21no—
784C3#7437911yescharacteristic, complemented
785C3#7465911yescharacteristic, complemented
786C2—24no—
787C2—122no—
788C2—188no—
789C2C2×#6388111yescharacteristic
790C2#1059492011yescharacteristic
791C2#1059492212yes—
792C2C4×#381112yes—
793C2#1059552711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63981C2
hypercenterC23×C4D32
hypocenterC32C4×#120
LCSG ▷ C22×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×#67⋊Dic3C2semidirect
4. C2×#63881C2semidirect
5. C3×#5213C2semidirect
6. C3×#5210C2semidirect
7. #10591714C2semidirect
8. #10591705C2semidirect
9. #10591387C2semidirect
10. #10591290C2semidirect
11. #10591260C2semidirect
23. C22×D3×Dic3C22semidirect
27. C2×C3×(C2×D3)⋊C4C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. #63981C4semidirect
31. C2×Dic3⋊Dic3C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. C2×Dic32C22semidirect
37. C2×Dic32C22semidirect
39. C3×C3⋊#95C22semidirect
40. C3×C3⋊#95C22semidirect
41. #63579C22semidirect
53. #5213D3semidirect
54. #5210D3semidirect
70. C23×C3⋊D3C2×C4semidirect
77. C22×C3⋊Dic3D4semidirect
86. C2×C4×C3⋊D3D4semidirect
89. C2×C3×#67C2×C4semidirect
97. C2×#626C2×C4semidirect
102. C3×#217C2×C4semidirect
108. #3722C2×C4semidirect
158. C2×(C2×D3)⋊C4C2×D3semidirect
161. C2×Dic3⋊C4C2×D3semidirect
174. C3⋊#95C2×D3semidirect
175. C3⋊#95C2×D3semidirect
198. C22×C3×D3C22×C4semidirect
222. C2×C3×Dic3C22×C4semidirect
223. C2×C3×Dic3C22×C4semidirect
282. C2×#67C4×D3semidirect
336. #217C4×D3semidirect
356. C22×C32C4×D4semidirect
369. C2×C3⋊D3C4×D4semidirect
377. C3⋊Dic3#120semidirect
474. C22×D3C2×C4×D3semidirect
530. C2×Dic3C2×C4×D3semidirect
531. C2×Dic3C2×C4×D3semidirect
618. C22×C3#67⋊C4semidirect
619. C22×C3#893semidirect
678. C32C4×#120semidirect
769. C22#63881semidirect
784. C3#74379semidirect
785. C3#74659semidirect

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×#67⋊Dic32
C2×#638812
C3×#52132
C3×#52102
#105917142
#105917052
#105913872
#105912902
#105912602
#746593
#743793