Finite Group Databasebeta

← #11801999

Subgroups — #11801999

Order 1152.

2779 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#624C211yesmaximal, characteristic, complemented
2C2×#64091C211yesmaximal, characteristic
3C2×#63952C211yesmaximal, characteristic, complemented
4C2×#63894C212yesmaximal, complemented
5C3×#4950C211yesmaximal, characteristic, complemented
6C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591711C211yesmaximal, characteristic, complemented
9#10591380C212yesmaximal, complemented
10#10591378C212yesmaximal, complemented
11#10591233C212yesmaximal, complemented
12#74379—31nomaximal
13C4×#882—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2212yes—
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×#624—24no—
20C22×#624—28no—
21C22×#624C2212yes—
22C22×#624C2212yes—
23C22×#624C2211yescharacteristic, complemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3752C2212yes—
26#64091C418yescomplemented
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×C4⋊Dic3C2212yescomplemented
30C2×C3×C4×Dic3C2212yescomplemented
31C2×#3724C2211yescharacteristic, complemented
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yescomplemented
35C2×#3722C2211yescharacteristic, complemented
36C2×Dic32C2211yescharacteristic, complemented
37#63952—24no—
38#63894—28no—
39C3×C3⋊#95C2212yescomplemented
40C3×C3⋊#95C2212yescomplemented
41#63579C2212yescomplemented
42C23×C4×D3—31no—
43C23×C4×D3—31no—
44C2×C4×#67—31no—
45C2×#893—32no—
46C2×#882—31no—
47C2×#882—31no—
48C2×#882—61no—
49C2×#67⋊C4—31no—
50C2×C4×D12—32no—
51C3×#385—31no—
52C3×C4×C22⋊C4—31no—
53#5213—31no—
54#4989—32no—
55#4958—31no—
56#4955—31no—
57#4955—31no—
58#4950D311yescharacteristic, complemented
59Dic3×C22⋊C4D311yescharacteristic, complemented
60C4×(C2×D3)⋊C4—32no—
61#4668—32no—
62#4666—32no—
63#4665—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⋊D3C2311yescharacteristic
72C23×C3⋊D3C2312yes—
73C22×C32×C4C2312yes—
74C2×#638—22no—
75C2×#638—22no—
76C2×#638C2×C414yescomplemented
77C22×C3⋊Dic3C2311yescharacteristic
78C2×C4⋊(C3⋊D3)—24no—
79C2×C4⋊(C3⋊D3)—24no—
80C2×C4⋊(C3⋊D3)C2×C418yescomplemented
81C22×C3×Dic3—22no—
82C22×C3×Dic3—24no—
83C22×C3×Dic3—24no—
84C22×C3×Dic3D414yescomplemented
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C2×#624—232no—
92C2×#624—24no—
93C2×#624—24no—
94C2×#624—24no—
95C2×#624—24no—
96C2×#624—24no—
97C2×#624—24no—
98C2×#624—22no—
99C2×#624D418yescomplemented
100C32×C22⋊C4C2×C414yescomplemented
101#3752C2×C418yescomplemented
102C3×#217—22no—
103C3×#217—22no—
104C3×C4⋊Dic3—24no—
105C3×C4×Dic3—24no—
106#3724—22no—
107#3722—24no—
108#3722—24no—
109#3722—24no—
110#3722—22no—
111Dic32—22no—
112C4×#120—91noSylow
113C24×D3—31no—
114C24×D3—31no—
115C24×D3—61no—
116C23×C3×C4—31no—
117C23×C3×C4—31no—
118C22×#67—31no—
119C22×#67—31no—
120C22×#67—61no—
121C23×Dic3C2×D311yescharacteristic
122C23×Dic3C2×D311yescharacteristic
123C22×D12—32no—
124C22×D12—32no—
125C22×D12—62no—
126C22×C4×D3—32no—
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C22×C4×D3—31no—
131C22×C4×D3—31no—
132C22×C4×D3—68no—
133C22×C4×D3—68no—
134C22×C4×D3—64no—
135C22×C4×D3—64no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4C2×D311yescharacteristic
141C2×C3×C22⋊C4C2×D311yescharacteristic
142C2×C3×C42—32no—
143C2×#217C2×D311yescharacteristic
144C2×#217C2×D311yescharacteristic
145C4×#67—64no—
146C2×(C2×D3)⋊C4—32no—
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—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—62no—
157C2×C4⋊Dic3C2×D312yescomplemented
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3C2×D312yescomplemented
163#893—68no—
164#882—38no—
165#882—38no—
166#882—68no—
167#67⋊C4—64no—
168C4×D12—68no—
169C3×#95—32no—
170C3×#95—32no—
171C3⋊#95—32no—
172C3⋊#95—32no—
173C3⋊#95C2×D312yescomplemented
174C3⋊#95C2×D312yescomplemented
175C23×C32—22no—
176C23×C32—22no—
177C23×C32C22×C412yes—
178C23×C32C2×D412yes—
179C23×C32#4112yes—
180C23×C32C2411yescharacteristic
181C22×C3⋊D3—216no—
182C22×C3⋊D3—28no—
183C22×C3⋊D3—28no—
184C22×C3⋊D3—28no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3—22no—
187C22×C3⋊D3—22no—
188C22×C3⋊D3—22no—
189C22×C3⋊D3—216no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3—21no—
192C22×C3⋊D3—22no—
193C22×C3⋊D3—21no—
194C22×C3⋊D3C22×C414yes—
195C22×C3⋊D3C22×C412yescomplemented
196C22×C3⋊D3C2×D414yes—
197C22×C3⋊D3#4114yes—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4C22×C414yescomplemented
201#638—28no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3C22×C412yescomplemented
205C4⋊(C3⋊D3)—216no—
206C2×C3×Dic3—28no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—28no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3C2×D412yes—
219C2×C3×Dic3C2×D412yes—
220C2×C3×Dic3C2×D414yes—
221C2×C3×Dic3C2×D414yes—
222#624—216no—
223#624—216no—
224#624—44no—
225C24×C4—91no—
226C2×#120—91no—
227C2×C4×D4—92no—
228C2×C4×D4—91no—
229#386—92no—
230#386—91no—
231#385—31no—
232#385—92no—
233#379—91no—
234C4×C22⋊C4—31no—
235C4×C22⋊C4—92no—
236C24×C3—21no—
237C24×C3C22×D311yescharacteristic
238C24×C3C22×D311yescharacteristic
239C23×D3—32no—
240C23×D3—32no—
241C23×D3—34no—
242C23×D3—34no—
243C23×D3—31no—
244C23×D3—31no—
245C23×D3—62no—
246C23×D3—64no—
247C23×D3—61no—
248C23×D3—64no—
249C23×D3—64no—
250C23×D3—64no—
251C23×D3—64no—
252C23×D3—62no—
253C23×D3—62no—
254C23×D3—62no—
255C23×D3—62no—
256C23×D3—124no—
257C23×D3—124no—
258C23×D3—122no—
259C23×D3—122no—
260C22×C3×C4—22no—
261C22×C3×C4—31no—
262C22×C3×C4—34no—
263C22×C3×C4—32no—
264C22×C3×C4—31no—
265C22×C3×C4—32no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—64no—
269C22×C3×C4—64no—
270C22×C3×C4—62no—
271C22×C3×C4C22×D312yes—
272C22×C3×C4C22×D312yes—
273C2×#67—34no—
274C2×#67—34no—
275C2×#67—64no—
276C2×#67—62no—
277C2×#67—62no—
278C2×#67—62no—
279C2×#67—62no—
280C2×#67—122no—
281C2×#67—122no—
282C22×Dic3—22no—
283C22×Dic3—24no—
284C22×Dic3—24no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—61no—
288C22×Dic3D1214yescomplemented
289C22×Dic3C22×D312yes—
290C22×Dic3C22×D311yescharacteristic
291C22×Dic3C22×D311yescharacteristic
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D312yes—
294C22×Dic3C22×D311yescharacteristic
295C2×D12—38no—
296C2×D12—38no—
297C2×D12—68no—
298C2×D12—64no—
299C2×D12—64no—
300C2×D12—64no—
301C2×D12—64no—
302C2×D12—124no—
303C2×D12—124no—
304C2×C4×D3—38no—
305C2×C4×D3—38no—
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—632no—
313C2×C4×D3—632no—
314C2×C4×D3—64no—
315C2×C4×D3—64no—
316C2×C4×D3—64no—
317C2×C4×D3—64no—
318C2×C4×D3—64no—
319C2×C4×D3—62no—
320C2×C4×D3—62no—
321C2×C4×D3—64no—
322C3×C4⋊C4—64no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—62no—
326C3×C22⋊C4C4×D314yescomplemented
327C3×C22⋊C4C4×D314yescomplemented
328C3×C42—64no—
329#217—22no—
330#217—22no—
331(C2×D3)⋊C4—38no—
332(C2×D3)⋊C4—38no—
333(C2×D3)⋊C4—68no—
334(C2×D3)⋊C4—64no—
335(C2×D3)⋊C4—62no—
336(C2×D3)⋊C4—64no—
337(C2×D3)⋊C4—64no—
338(C2×D3)⋊C4—64no—
339(C2×D3)⋊C4—64no—
340(C2×D3)⋊C4—62no—
341(C2×D3)⋊C4—64no—
342C4⋊Dic3—24no—
343Dic3⋊C4—62no—
344Dic3⋊C4—62no—
345C4×Dic3—24no—
346C4×Dic3—62no—
347C4×Dic3—62no—
348C22×C32—24no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—24no—
352C22×C32C4×D414yescomplemented
353C22×C32C23×C411yescharacteristic
354C22×C32C22×D411yescharacteristic
355C22×C32C22×D412yes—
356C22×C32C2×#4111yescharacteristic
357C22×C32C2×#4112yes—
358C2×C3⋊D3—232no—
359C2×C3⋊D3—24no—
360C2×C3⋊D3—24no—
361C2×C3⋊D3—24no—
362C2×C3⋊D3—24no—
363C2×C3⋊D3—24no—
364C2×C3⋊D3—24no—
365C2×C3⋊D3—24no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—41no—
368C2×C3⋊D3—41no—
369C2×C3⋊D3—42no—
370C2×C3⋊D3C4×D418yescomplemented
371C32×C4—24no—
372C3⋊Dic3—22no—
373C3×Dic3—22no—
374C3×Dic3—24no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—42no—
378C3×Dic3#12014yescomplemented
379C25—91no—
380C22×D4—91no—
381C22×D4—92no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—92no—
385C23×C4—91no—
386C23×C4—92no—
387C23×C4—184no—
388C23×C4—188no—
389#120—98no—
390C4×D4—188no—
391C4×D4—184no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—91no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—31no—
396C2×C22⋊C4—92no—
397C2×C22⋊C4—92no—
398C2×C22⋊C4—91no—
399C2×C22⋊C4—92no—
400C2×C22⋊C4—92no—
401C2×C22⋊C4D3211yescharacteristic
402C2×C42—32no—
403C2×C42—91no—
404#95—32no—
405#95—32no—
406#95—92no—
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—42no—
416C23×C3—42no—
417C23×C3C2×C4×D312yes—
418C23×C3C2×C4×D312yes—
419C23×C3C2×D1212yes—
420C23×C3#23512yes—
421C23×C3D3×D412yes—
422C23×C3#23912yes—
423C23×C3C23×D311yescharacteristic
424C23×C3C23×D311yescharacteristic
425C22×D3—34no—
426C22×D3—34no—
427C22×D3—34no—
428C22×D3—34no—
429C22×D3—34no—
430C22×D3—34no—
431C22×D3—32no—
432C22×D3—32no—
433C22×D3—64no—
434C22×D3—64no—
435C22×D3—64no—
436C22×D3—62no—
437C22×D3—616no—
438C22×D3—616no—
439C22×D3—68no—
440C22×D3—68no—
441C22×D3—68no—
442C22×D3—68no—
443C22×D3—616no—
444C22×D3—616no—
445C22×D3—68no—
446C22×D3—68no—
447C22×D3—62no—
448C22×D3—62no—
449C22×D3—62no—
450C22×D3—62no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—61no—
456C22×D3—61no—
457C22×D3—62no—
458C22×D3—62no—
459C22×D3—61no—
460C22×D3—61no—
461C22×D3—62no—
462C22×D3—62no—
463C22×D3—1216no—
464C22×D3—122no—
465C22×D3—122no—
466C22×D3—122no—
467C22×D3—122no—
468C22×D3—128no—
469C22×D3—128no—
470C22×D3—1216no—
471C22×D3—128no—
472C22×D3—122no—
473C22×D3—122no—
474C22×D3—121no—
475C22×D3—121no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—24no—
481C2×C3×C4—32no—
482C2×C3×C4—34no—
483C2×C3×C4—32no—
484C2×C3×C4—34no—
485C2×C3×C4—42no—
486C2×C3×C4—42no—
487C2×C3×C4—68no—
488C2×C3×C4—68no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4C2×C4×D314yescomplemented
500C2×C3×C4C2×C4×D314yescomplemented
501#67—68no—
502#67—68no—
503#67—128no—
504C2×Dic3—28no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—28no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—62no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3C2×D1212yes—
526C2×Dic3C2×D1212yes—
527C2×Dic3D3×D414yes—
528C2×Dic3D3×D414yes—
529D12—616no—
530D12—616no—
531D12—1216no—
532C4×D3—616no—
533C4×D3—616no—
534C4×D3—616no—
535C4×D3—616no—
536C4×D3—124no—
537C4×D3—124no—
538C2×C32—24no—
539C2×C32C2×C4×D411yescharacteristic
540C2×C32C2×C4×D412yes—
541C2×C32C2×#12011yescharacteristic
542C2×C32#52511yescharacteristic
543C2×C32#52512yes—
544C3⋊D3—28no—
545C3⋊D3—42no—
546C24—92no—
547C24—91no—
548C24—94no—
549C24—184no—
550C24—184no—
551C24—182no—
552C24—182no—
553C24C2×D3211yescharacteristic
554C2×D4—94no—
555C2×D4—98no—
556C2×D4—184no—
557C2×D4—184no—
558C2×D4—182no—
559C2×D4—182no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—32no—
563C22×C4—34no—
564C22×C4—31no—
565C22×C4—32no—
566C22×C4—31no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—62no—
570C22×C4—98no—
571C22×C4—91no—
572C22×C4—184no—
573C22×C4—184no—
574C22×C4—184no—
575C22×C4—184no—
576C22×C4—182no—
577C22×C4—184no—
578C22×C4—184no—
579C22×C4—1832no—
580C22×C4C2×D3212yes—
581C4⋊C4—64no—
582C4⋊C4—182no—
583C22⋊C4—62no—
584C22⋊C4—62no—
585C22⋊C4—98no—
586C22⋊C4—182no—
587C22⋊C4—184no—
588C22⋊C4—184no—
589C22⋊C4—184no—
590C22⋊C4#62414yescomplemented
591C42—64no—
592C42—182no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—22no—
600C22×C3—24no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—21no—
606C22×C3—24no—
607C22×C3—44no—
608C22×C3—42no—
609C22×C3—44no—
610C22×C3—42no—
611C22×C3C4×D1214yescomplemented
612C22×C3#89314yescomplemented
613C22×C3C22×C4×D311yescharacteristic
614C22×C3C22×C4×D311yescharacteristic
615C22×C3C22×D1211yescharacteristic
616C22×C3C2×#23511yescharacteristic
617C22×C3C2×D3×D411yescharacteristic
618C22×C3C2×D3×D412yes—
619C22×C3C2×D3×D412yes—
620C22×C3C2×#23911yescharacteristic
621C22×C3D3×#4112yes—
622C22×C3D3×#4112yes—
623C2×D3—38no—
624C2×D3—38no—
625C2×D3—68no—
626C2×D3—632no—
627C2×D3—632no—
628C2×D3—64no—
629C2×D3—64no—
630C2×D3—64no—
631C2×D3—64no—
632C2×D3—64no—
633C2×D3—64no—
634C2×D3—64no—
635C2×D3—64no—
636C2×D3—64no—
637C2×D3—64no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—64no—
643C2×D3—64no—
644C2×D3—124no—
645C2×D3—124no—
646C2×D3—124no—
647C2×D3—124no—
648C2×D3—124no—
649C2×D3—124no—
650C2×D3—1232no—
651C2×D3—124no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—122no—
657C2×D3—121no—
658C2×D3—122no—
659C2×D3—242no—
660C2×D3—241no—
661C2×D3—241no—
662C3×C4—24no—
663C3×C4—24no—
664C3×C4—34no—
665C3×C4—44no—
666C3×C4—64no—
667C3×C4—62no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—122no—
671Dic3—22no—
672Dic3—24no—
673Dic3—41no—
674Dic3—42no—
675Dic3—41no—
676Dic3—62no—
677Dic3—62no—
678Dic3—122no—
679Dic3#88214yescomplemented
680C32C4×#12011yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—94no—
684C23—94no—
685C23—94no—
686C23—92no—
687C23—1816no—
688C23—188no—
689C23—1816no—
690C23—188no—
691C23—182no—
692C23—182no—
693C23—182no—
694C23—182no—
695C23—188no—
696C23—181no—
697C23—181no—
698C23—182no—
699C23—182no—
700C23#379912yes—
701C23D3×D1212yes—
702C23C2×#62412yes—
703C23C22×D3211yescharacteristic
704D4—1816no—
705D4—188no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—32no—
709C2×C4—34no—
710C2×C4—32no—
711C2×C4—34no—
712C2×C4—68no—
713C2×C4—68no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—92no—
725C2×C4—1816no—
726C2×C4—1816no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—364no—
730C2×C4C2×#62414yescomplemented
731C2×C3—24no—
732C2×C3—24no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—22no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—44no—
739C2×C3C2×C4×D1211yescharacteristic
740C2×C3C2×#88211yescharacteristic
741C2×C3C2×#89311yescharacteristic
742C2×C3#552411yescharacteristic
743C2×C3C4×D3×D412yes—
744C2×C3C4×D3×D412yes—
745C2×C3#554712yes—
746C2×C3D3×#12011yescharacteristic
747C2×C3#562712yes—
748C2×C3#565611yescharacteristic
749D3—68no—
750D3—68no—
751D3—128no—
752D3—122no—
753D3—122no—
754D3—242no—
755C22—24no—
756C22—22no—
757C22—24no—
758C22—22no—
759C22—98no—
760C22—1832no—
761C22—184no—
762C22—184no—
763C22—184no—
764C22—184no—
765C22—184no—
766C22—184no—
767C22—184no—
768C22—182no—
769C22—362no—
770C22—361no—
771C22—361no—
772C22#6389414yescomplemented
773C22C2×#379911yescharacteristic
774C22C2×D3×D1211yescharacteristic
775C22D32×D412yes—
776C22#6431212yes—
777C22C22×#62411yescharacteristic
778C4—24no—
779C4—34no—
780C4—62no—
781C4—64no—
782C4—122no—
783C4—121no—
784C4—121no—
785C4—182no—
786C3—21no—
787C3C4×#88211yescharacteristic, complemented
788C3#7437911yescharacteristic, complemented
789C2—24no—
790C2—188no—
791C2—362no—
792C2#1059406612yes—
793C2#1059407911yescharacteristic
794C2D3×#88211yescharacteristic
795C2C2×#6389411yescharacteristic
796C2D4×#62412yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64091C2
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#624C2semidirect
3. C2×#63952C2semidirect
4. C2×#63894C2semidirect
5. C3×#4950C2semidirect
6. C3×Dic3×C22⋊C4C2semidirect
7. #10591714C2semidirect
8. #10591711C2semidirect
9. #10591380C2semidirect
10. #10591378C2semidirect
11. #10591233C2semidirect
23. C22×#624C22semidirect
26. #64091C4semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. C2×#3724C22semidirect
34. C2×#3722C22semidirect
35. C2×#3722C22semidirect
36. C2×Dic32C22semidirect
39. C3×C3⋊#95C22semidirect
40. C3×C3⋊#95C22semidirect
41. #63579C22semidirect
58. #4950D3semidirect
59. Dic3×C22⋊C4D3semidirect
70. C23×C3⋊D3C2×C4semidirect
76. C2×#638C2×C4semidirect
80. C2×C4⋊(C3⋊D3)C2×C4semidirect
84. C22×C3×Dic3D4semidirect
99. C2×#624D4semidirect
100. C32×C22⋊C4C2×C4semidirect
101. #3752C2×C4semidirect
157. C2×C4⋊Dic3C2×D3semidirect
162. C2×C4×Dic3C2×D3semidirect
173. C3⋊#95C2×D3semidirect
174. C3⋊#95C2×D3semidirect
195. C22×C3⋊D3C22×C4semidirect
200. C2×C32×C4C22×C4semidirect
204. C2×C3⋊Dic3C22×C4semidirect
288. C22×Dic3D12semidirect
326. C3×C22⋊C4C4×D3semidirect
327. C3×C22⋊C4C4×D3semidirect
352. C22×C32C4×D4semidirect
370. C2×C3⋊D3C4×D4semidirect
378. C3×Dic3#120semidirect
499. C2×C3×C4C2×C4×D3semidirect
500. C2×C3×C4C2×C4×D3semidirect
590. C22⋊C4#624semidirect
611. C22×C3C4×D12semidirect
612. C22×C3#893semidirect
679. Dic3#882semidirect
680. C32C4×#120semidirect
730. C2×C4C2×#624semidirect
772. C22#63894semidirect
787. C3C4×#882semidirect
788. C3#74379semidirect

Maximal subgroups

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

subgroupindex
C23×#6242
C2×#640912
C2×#639522
C2×#638942
C3×#49502
C3×Dic3×C22⋊C42
#105917142
#105917112
#105913802
#105913782
#105912332
#743793
C4×#8823