Finite Group Databasebeta

← C2×#10595242 #11900963

Subgroups — C2×#10595242 #11900963

Order 1152.

4649 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C23×#626C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×C3×#935C211yesmaximal, characteristic, complemented
5C2×#63981C212yesmaximal, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63974C211yesmaximal, characteristic, complemented
8C2×#63966C211yesmaximal, characteristic, complemented
9C2×#63958C212yesmaximal, complemented
10#10595242C2116yesmaximal, direct product factor
11C2×#63910C212yesmaximal, complemented
12C2×#63853C212yesmaximal, complemented
13C2×#5653—31nomaximal
14C2×#5589—31nomaximal
15C24×C3⋊D3C2211yescharacteristic
16C24×C3⋊D3C2211yescharacteristic, complemented
17C24×C3×D3C2211yescharacteristic, complemented
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic, complemented
21C2×D4×C3⋊D3—28no—
22C2×D4×C3⋊D3C2218yescomplemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C3×#67C2212yescomplemented
26C23×C3×Dic3C2211yescharacteristic, complemented
27C22×#626—28no—
28C22×#626C2212yes—
29C22×#626C2212yescomplemented
30C22×#626C2212yescomplemented
31C22×#626C2218yescomplemented
32C22×#624C2212yescomplemented
33C2×C3×#217C2212yescomplemented
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic, complemented
36C3×#937C2218yescomplemented
37C3×#935C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×Dic3⋊C4C2212yescomplemented
40#63981C22116yescomplemented
41#63977C2218yescomplemented
42#63974C2218yescomplemented
43#63966C2218yescomplemented
44C2×Dic3⋊Dic3C2212yescomplemented
45C2×#3722C2212yescomplemented
46C2×#3722C2212yescomplemented
47C2×(C2×D3)⋊Dic3C2212yescomplemented
48#63958C22116yescomplemented
49#63910C22116yescomplemented
50#63853C22116yescomplemented
51C23×#67—31no—
52C22×D3×D4—31no—
53C22×D3×D4—31no—
54C22×D3×D4—61no—
55C23×D12—31no—
56C2×C3×#123—31no—
57C2×C3×#120—31no—
58C2×#953—31no—
59C2×#938—32no—
60C2×#937—32no—
61C2×#937D311yescharacteristic, complemented
62C2×#935D311yescharacteristic, complemented
63C2×#929—31no—
64#5653—316no—
65#5589—316no—
66C2×#895—32no—
67C2×#894—32no—
68C2×#886—31no—
69C2×#884—32no—
70C2×#884—32no—
71C2×#883—32no—
72C2×#882—31no—
73C2×#882—32no—
74C2×D3×C22⋊C4—31no—
75C2×D3×C22⋊C4—31no—
76C24×C32C2311yescharacteristic
77C24×C32C2311yescharacteristic
78C23×C3⋊D3—24no—
79C23×C3⋊D3—44no—
80C23×C3⋊D3—44no—
81C23×C3⋊D3D418yescomplemented
82C23×C3⋊D3C2311yescharacteristic
83C23×C3⋊D3C2311yescharacteristic
84C23×C3⋊D3C2311yescharacteristic
85C23×C3⋊D3C2314yes—
86C23×C3⋊D3C2314yescomplemented
87C23×C3×D3—24no—
88C23×C3×D3—44no—
89C23×C3×D3C2312yes—
90C23×C3×D3C2314yescomplemented
91C2×C32×D4—24no—
92C2×C32×D4C2314yes—
93C22×C32×C4C2311yescharacteristic
94C2×#638—24no—
95C2×#638—24no—
96C2×#638C2314yes—
97C2×#638C2314yescomplemented
98C22×C3⋊Dic3C2311yescharacteristic
99D4×C3⋊D3—232no—
100C2×C4⋊(C3⋊D3)—24no—
101C2×C4⋊(C3⋊D3)C2314yescomplemented
102C2×C4×C3⋊D3—24no—
103C2×C4×C3⋊D3C2314yescomplemented
104C2×C3×#67—44no—
105C2×C3×#67C2318yescomplemented
106C22×C3×Dic3—24no—
107C22×C3×Dic3C2312yes—
108C22×C3×Dic3C2312yes—
109C22×C3×Dic3C2312yes—
110C22×C3×Dic3C2314yescomplemented
111C2×#626—28no—
112C2×#626—28no—
113C2×#626—232no—
114C2×#626—44no—
115C2×#626C2318yes—
116C2×#626C2318yescomplemented
117C2×#626C2318yescomplemented
118C2×#624—44no—
119C2×#624C2318yescomplemented
120C3×#217C2318yescomplemented
121C3×#217C2314yescomplemented
122C3×#217C2314yescomplemented
123C3×(C2×D3)⋊C4C2318yescomplemented
124C3×Dic3⋊C4C2318yescomplemented
125Dic3⋊Dic3C2318yescomplemented
126#3722C2318yescomplemented
127#3722C2318yescomplemented
128(C2×D3)⋊Dic3C2318yescomplemented
129C2×#534—91noSylow
130C25×C3—31no—
131C24×D3—31no—
132C24×D3—31no—
133C24×D3—31no—
134C24×D3—31no—
135C24×D3—61no—
136C24×D3—61no—
137C24×D3C2×D311yescharacteristic, complemented
138C22×C3×D4—21no—
139C22×C3×D4—32no—
140C22×C3×D4C2×D311yescharacteristic
141C22×C3×D4C2×D311yescharacteristic
142C23×C3×C4—31no—
143C22×#67—31no—
144C22×#67—31no—
145C22×#67—31no—
146C22×#67—31no—
147C22×#67—32no—
148C22×#67—32no—
149C22×#67—32no—
150C22×#67—38no—
151C22×#67—61no—
152C22×#67—61no—
153C22×#67—68no—
154C22×#67C2×D312yescomplemented
155C23×Dic3C2×D311yescharacteristic, complemented
156C2×D3×D4—38no—
157C2×D3×D4—38no—
158C2×D3×D4—68no—
159C2×D3×D4—68no—
160C2×D3×D4—68no—
161C2×D3×D4—616no—
162C22×D12—32no—
163C22×D12—32no—
164C22×D12—38no—
165C22×D12—31no—
166C22×D12—31no—
167C22×D12—32no—
168C22×D12—61no—
169C22×D12—68no—
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—32no—
173C22×C4×D3—32no—
174C22×C4×D3—61no—
175C3×#123—38no—
176C3×#120—38no—
177C2×C3×C4⋊C4—32no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—32no—
181C2×C3×C22⋊C4—32no—
182#953—38no—
183C2×#217—32no—
184C2×#217C2×D311yescharacteristic, complemented
185C2×#217C2×D311yescharacteristic, complemented
186C2×#217C2×D312yescomplemented
187#938—316no—
188#937—316no—
189#937C2×D318yescomplemented
190#935C2×D318yescomplemented
191#929—38no—
192C2×(C2×D3)⋊C4—32no—
193C2×(C2×D3)⋊C4—32no—
194C2×(C2×D3)⋊C4—32no—
195C2×(C2×D3)⋊C4—32no—
196C2×(C2×D3)⋊C4—32no—
197C2×(C2×D3)⋊C4C2×D312yescomplemented
198C2×C4⋊Dic3—32no—
199C2×Dic3⋊C4—32no—
200C2×Dic3⋊C4C2×D312yescomplemented
201#895—316no—
202#894—316no—
203#886—38no—
204#884—316no—
205#884—316no—
206#883—316no—
207#882—38no—
208#882—316no—
209D3×C22⋊C4—38no—
210D3×C22⋊C4—38no—
211C23×C32—22no—
212C23×C32—24no—
213C23×C32—24no—
214C23×C32C2×D414yes—
215C23×C32C2412yes—
216C23×C32C2412yes—
217C23×C32C2411yescharacteristic
218C22×C3⋊D3—24no—
219C22×C3⋊D3—22no—
220C22×C3⋊D3—28no—
221C22×C3⋊D3—24no—
222C22×C3⋊D3—24no—
223C22×C3⋊D3—416no—
224C22×C3⋊D3—48no—
225C22×C3⋊D3—48no—
226C22×C3⋊D3—416no—
227C22×C3⋊D3C2×D414yes—
228C22×C3⋊D3C2×D414yes—
229C22×C3⋊D3C2×D4116yescomplemented
230C22×C3⋊D3C2412yes—
231C22×C3⋊D3C2412yes—
232C22×C3⋊D3C2412yes—
233C22×C3×D3—24no—
234C22×C3×D3—28no—
235C22×C3×D3—24no—
236C22×C3×D3—24no—
237C22×C3×D3—48no—
238C22×C3×D3—416no—
239C22×C3×D3C2414yes—
240C32×D4—28no—
241C2×C32×C4—22no—
242C2×C32×C4C2412yes—
243#638—28no—
244#638—28no—
245C2×C3⋊Dic3—22no—
246C2×C3⋊Dic3C2412yes—
247C4⋊(C3⋊D3)—28no—
248C4×C3⋊D3—28no—
249C3×#67—48no—
250C2×C3×Dic3—24no—
251C2×C3×Dic3—28no—
252C2×C3×Dic3—24no—
253C2×C3×Dic3—24no—
254C2×C3×Dic3C2414yes—
255C2×C3×Dic3C2414yes—
256C2×C3×Dic3C2414yes—
257#626—216no—
258#626—216no—
259#626—48no—
260#624—48no—
261C23×D4—91no—
262C23×D4—91no—
263#534—916no—
264C2×#123—31no—
265C2×#123—92no—
266C2×#123—91no—
267C2×#121—92no—
268C2×#121—92no—
269C2×#120—31no—
270C2×#120—92no—
271C2×#120—91no—
272C22×C22⋊C4—91no—
273C24×C3—21no—
274C24×C3—21no—
275C24×C3—32no—
276C24×C3—34no—
277C24×C3—64no—
278C24×C3—124no—
279C24×C3C22×D311yescharacteristic
280C24×C3C22×D311yescharacteristic
281C24×C3C22×D311yescharacteristic
282C24×C3C22×D311yescharacteristic
283C23×D3—24no—
284C23×D3—31no—
285C23×D3—31no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—38no—
289C23×D3—38no—
290C23×D3—34no—
291C23×D3—34no—
292C23×D3—31no—
293C23×D3—31no—
294C23×D3—34no—
295C23×D3—34no—
296C23×D3—44no—
297C23×D3—61no—
298C23×D3—68no—
299C23×D3—61no—
300C23×D3—61no—
301C23×D3—64no—
302C23×D3—64no—
303C23×D3—64no—
304C23×D3—64no—
305C23×D3—68no—
306C23×D3—124no—
307C23×D3—124no—
308C23×D3—124no—
309C23×D3—124no—
310C23×D3—128no—
311C23×D3—128no—
312C23×D3C22×D312yes—
313C23×D3C22×D314yescomplemented
314C2×C3×D4—28no—
315C2×C3×D4—24no—
316C2×C3×D4—24no—
317C2×C3×D4—24no—
318C2×C3×D4—38no—
319C2×C3×D4—124no—
320C2×C3×D4C22×D314yes—
321C2×C3×D4C22×D314yes—
322C22×C3×C4—21no—
323C22×C3×C4—32no—
324C22×C3×C4—32no—
325C22×C3×C4—32no—
326C22×C3×C4—34no—
327C22×C3×C4—64no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—34no—
331C2×#67—34no—
332C2×#67—34no—
333C2×#67—34no—
334C2×#67—38no—
335C2×#67—38no—
336C2×#67—38no—
337C2×#67—44no—
338C2×#67—64no—
339C2×#67—64no—
340C2×#67—68no—
341C2×#67—68no—
342C2×#67—632no—
343C2×#67—64no—
344C2×#67—64no—
345C2×#67—68no—
346C2×#67—68no—
347C2×#67—64no—
348C2×#67—64no—
349C2×#67—124no—
350C2×#67C22×D318yescomplemented
351C22×Dic3—24no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—61no—
355C22×Dic3C22×D312yes—
356C22×Dic3C22×D312yes—
357C22×Dic3C22×D312yes—
358C22×Dic3C22×D314yescomplemented
359D3×D4—632no—
360D3×D4—632no—
361D3×D4—664no—
362C2×D12—38no—
363C2×D12—38no—
364C2×D12—34no—
365C2×D12—34no—
366C2×D12—38no—
367C2×D12—64no—
368C2×D12—64no—
369C2×D12—64no—
370C2×D12—68no—
371C2×D12—68no—
372C2×D12—68no—
373C2×D12—632no—
374C2×D12—124no—
375C2×C4×D3—34no—
376C2×C4×D3—34no—
377C2×C4×D3—38no—
378C2×C4×D3—38no—
379C2×C4×D3—64no—
380C2×C4×D3—64no—
381C2×C4×D3—64no—
382C2×C4×D3—68no—
383C2×C4×D3—124no—
384C2×C4×D3—124no—
385C3×C4⋊C4—38no—
386C3×C22⋊C4—34no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—38no—
389C3×C22⋊C4—38no—
390#217—38no—
391#217C22×D314yescomplemented
392#217C22×D314yescomplemented
393#217C22×D318yescomplemented
394(C2×D3)⋊C4—38no—
395(C2×D3)⋊C4—38no—
396(C2×D3)⋊C4—38no—
397(C2×D3)⋊C4—38no—
398(C2×D3)⋊C4—38no—
399(C2×D3)⋊C4C22×D318yescomplemented
400C4⋊Dic3—38no—
401Dic3⋊C4—38no—
402Dic3⋊C4C22×D318yescomplemented
403C22×C32—22no—
404C22×C32—28no—
405C22×C32—24no—
406C22×C32—24no—
407C22×C32—44no—
408C22×C32C22×D414yes—
409C22×C32C22×D412yes—
410C22×C32H(5,𝔽2)14yes—
411C22×C32C2511yescharacteristic
412C2×C3⋊D3—28no—
413C2×C3⋊D3—24no—
414C2×C3⋊D3—22no—
415C2×C3⋊D3—28no—
416C2×C3⋊D3—24no—
417C2×C3⋊D3—24no—
418C2×C3⋊D3—416no—
419C2×C3⋊D3—416no—
420C2×C3⋊D3—44no—
421C2×C3⋊D3C22×D414yes—
422C2×C3⋊D3C22×D414yes—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—24no—
426C2×C3×D3—416no—
427C2×C3×D3—48no—
428C32×C4—22no—
429C3⋊Dic3—22no—
430C3×Dic3—24no—
431C3×Dic3—24no—
432C3×Dic3—24no—
433C25—31no—
434C25—91no—
435C25—91no—
436C22×D4—32no—
437C22×D4—92no—
438C22×D4—92no—
439C22×D4—98no—
440C22×D4—92no—
441C22×D4—91no—
442C22×D4—91no—
443C22×D4—98no—
444C22×D4—91no—
445C22×D4—188no—
446C22×D4—188no—
447C22×D4D3211yescharacteristic
448C23×C4—31no—
449C23×C4—92no—
450C23×C4—91no—
451#123—38no—
452#123—916no—
453#123—98no—
454#121—916no—
455#121—916no—
456#120—38no—
457#120—916no—
458#120—98no—
459C2×C4⋊C4—32no—
460C2×C4⋊C4—92no—
461C2×C22⋊C4—31no—
462C2×C22⋊C4—31no—
463C2×C22⋊C4—32no—
464C2×C22⋊C4—32no—
465C2×C22⋊C4—98no—
466C2×C22⋊C4—92no—
467C2×C22⋊C4—92no—
468C2×C22⋊C4—92no—
469C23×C3—24no—
470C23×C3—24no—
471C23×C3—24no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—24no—
475C23×C3—24no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—21no—
479C23×C3—24no—
480C23×C3—34no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—68no—
484C23×C3—64no—
485C23×C3—64no—
486C23×C3—64no—
487C23×C3—128no—
488C23×C3—1216no—
489C23×C3D3×D414yes—
490C23×C3D3×D414yes—
491C23×C3C23×D312yes—
492C23×C3C23×D312yes—
493C23×C3C23×D312yes—
494C23×C3C23×D312yes—
495C23×C3C23×D311yescharacteristic
496C23×C3C23×D311yescharacteristic
497C22×D3—24no—
498C22×D3—28no—
499C22×D3—24no—
500C22×D3—24no—
501C22×D3—34no—
502C22×D3—34no—
503C22×D3—34no—
504C22×D3—34no—
505C22×D3—32no—
506C22×D3—32no—
507C22×D3—32no—
508C22×D3—32no—
509C22×D3—316no—
510C22×D3—316no—
511C22×D3—32no—
512C22×D3—32no—
513C22×D3—48no—
514C22×D3—416no—
515C22×D3—64no—
516C22×D3—62no—
517C22×D3—64no—
518C22×D3—616no—
519C22×D3—62no—
520C22×D3—62no—
521C22×D3—68no—
522C22×D3—68no—
523C22×D3—68no—
524C22×D3—64no—
525C22×D3—64no—
526C22×D3—64no—
527C22×D3—64no—
528C22×D3—64no—
529C22×D3—616no—
530C22×D3—62no—
531C22×D3—62no—
532C22×D3—64no—
533C22×D3—64no—
534C22×D3—124no—
535C22×D3—124no—
536C22×D3—1216no—
537C22×D3—128no—
538C22×D3—128no—
539C22×D3—128no—
540C22×D3—128no—
541C22×D3—1216no—
542C22×D3—1232no—
543C22×D3—1216no—
544C22×D3—1216no—
545C22×D3—1232no—
546C22×D3—1216no—
547C22×D3—1216no—
548C22×D3C23×D314yes—
549C3×D4—216no—
550C3×D4—28no—
551C3×D4—28no—
552C3×D4—128no—
553C2×C3×C4—24no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—34no—
558C2×C3×C4—34no—
559C2×C3×C4—34no—
560C2×C3×C4—68no—
561C2×C3×C4—64no—
562C2×C3×C4—64no—
563C2×C3×C4—64no—
564C2×C3×C4C23×D312yes—
565C2×C3×C4C23×D312yes—
566#67—48no—
567#67—616no—
568#67—616no—
569#67—68no—
570#67—68no—
571#67—616no—
572#67—616no—
573#67—68no—
574#67—68no—
575#67—128no—
576C2×Dic3—24no—
577C2×Dic3—28no—
578C2×Dic3—24no—
579C2×Dic3—24no—
580C2×Dic3—32no—
581C2×Dic3—32no—
582C2×Dic3—62no—
583C2×Dic3—64no—
584C2×Dic3—62no—
585C2×Dic3—62no—
586C2×Dic3C23×D314yes—
587C2×Dic3C23×D314yes—
588C2×Dic3C23×D314yes—
589D12—68no—
590D12—68no—
591D12—616no—
592D12—616no—
593D12—616no—
594D12—128no—
595C4×D3—68no—
596C4×D3—68no—
597C4×D3—616no—
598C4×D3—128no—
599C4×D3—128no—
600C2×C32—24no—
601C2×C32—42no—
602C2×C32#53414yescomplemented
603C2×C32C23×D411yescharacteristic
604C2×C32C2×H(5,𝔽2)12yes—
605C3⋊D3—24no—
606C3⋊D3—24no—
607C3⋊D3—42no—
608C3×D3—44no—
609C24—32no—
610C24—34no—
611C24—64no—
612C24—91no—
613C24—91no—
614C24—94no—
615C24—98no—
616C24—91no—
617C24—94no—
618C24—124no—
619C24—184no—
620C24—364no—
621C24—364no—
622C24C2×D3211yescharacteristic
623C24C2×D3211yescharacteristic
624C2×D4—24no—
625C2×D4—38no—
626C2×D4—98no—
627C2×D4—98no—
628C2×D4—98no—
629C2×D4—94no—
630C2×D4—94no—
631C2×D4—94no—
632C2×D4—124no—
633C2×D4—184no—
634C2×D4—188no—
635C2×D4—188no—
636C2×D4—1832no—
637C2×D4—1832no—
638C2×D4—184no—
639C2×D4—184no—
640C2×D4—364no—
641C2×D4C2×D3214yes—
642C22×C4—34no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—64no—
647C22×C4—98no—
648C22×C4—91no—
649C22×C4—94no—
650C22×C4—184no—
651C22×C4—364no—
652C22×C4C2×D3211yescharacteristic
653C4⋊C4—38no—
654C4⋊C4—98no—
655C22⋊C4—34no—
656C22⋊C4—34no—
657C22⋊C4—38no—
658C22⋊C4—38no—
659C22⋊C4—98no—
660C22⋊C4—98no—
661C22⋊C4—98no—
662C22×C3—28no—
663C22×C3—24no—
664C22×C3—24no—
665C22×C3—28no—
666C22×C3—24no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—24no—
670C22×C3—24no—
671C22×C3—24no—
672C22×C3—22no—
673C22×C3—24no—
674C22×C3—21no—
675C22×C3—44no—
676C22×C3—48no—
677C22×C3—44no—
678C22×C3—48no—
679C22×C3—44no—
680C22×C3—44no—
681C22×C3—64no—
682C22×C3—64no—
683C22×C3—64no—
684C22×C3—1216no—
685C22×C3—128no—
686C22×C3C2×D3×D414yes—
687C22×C3C2×D3×D414yes—
688C22×C3C2×D3×D412yes—
689C22×C3C2×D3×D412yes—
690C22×C3#100414yes—
691C22×C3#100914yes—
692C22×C3C24×D311yescharacteristic
693C22×C3C24×D311yescharacteristic
694C2×D3—24no—
695C2×D3—24no—
696C2×D3—24no—
697C2×D3—34no—
698C2×D3—34no—
699C2×D3—34no—
700C2×D3—34no—
701C2×D3—416no—
702C2×D3—48no—
703C2×D3—64no—
704C2×D3—64no—
705C2×D3—68no—
706C2×D3—616no—
707C2×D3—68no—
708C2×D3—68no—
709C2×D3—64no—
710C2×D3—64no—
711C2×D3—64no—
712C2×D3—64no—
713C2×D3—68no—
714C2×D3—68no—
715C2×D3—64no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—64no—
719C2×D3—64no—
720C2×D3—124no—
721C2×D3—128no—
722C2×D3—124no—
723C2×D3—1216no—
724C2×D3—1216no—
725C2×D3—1232no—
726C2×D3—1232no—
727C2×D3—1216no—
728C2×D3—1216no—
729C2×D3—128no—
730C2×D3—124no—
731C2×D3—124no—
732C3×C4—24no—
733C3×C4—22no—
734C3×C4—22no—
735C3×C4—64no—
736C3×C4—64no—
737C3×C4—64no—
738Dic3—24no—
739Dic3—24no—
740Dic3—24no—
741Dic3—64no—
742Dic3—62no—
743Dic3—62no—
744C32C2×#53411yescharacteristic, complemented, Sylow
745C23—24no—
746C23—24no—
747C23—22no—
748C23—34no—
749C23—64no—
750C23—64no—
751C23—68no—
752C23—64no—
753C23—94no—
754C23—94no—
755C23—92no—
756C23—92no—
757C23—916no—
758C23—92no—
759C23—128no—
760C23—1216no—
761C23—188no—
762C23—184no—
763C23—184no—
764C23—184no—
765C23—182no—
766C23—368no—
767C23—3616no—
768C23—368no—
769C23—3616no—
770C23#381114yes—
771C23C22×D3212yes—
772C23C22×D3212yes—
773C23C22×D3211yescharacteristic
774D4—28no—
775D4—128no—
776D4—188no—
777D4—1816no—
778D4—1816no—
779D4—188no—
780D4—188no—
781D4—368no—
782C2×C4—22no—
783C2×C4—34no—
784C2×C4—34no—
785C2×C4—34no—
786C2×C4—64no—
787C2×C4—64no—
788C2×C4—68no—
789C2×C4—64no—
790C2×C4—92no—
791C2×C4—188no—
792C2×C4—182no—
793C2×C4—368no—
794C2×C4C22×D3212yes—
795C2×C3—24no—
796C2×C3—24no—
797C2×C3—22no—
798C2×C3—21no—
799C2×C3—24no—
800C2×C3—44no—
801C2×C3—44no—
802C2×C3—42no—
803C2×C3—42no—
804C2×C3—124no—
805C2×C3#558914yescomplemented
806C2×C3#565314yescomplemented
807C2×C3C22×D3×D411yescharacteristic
808C2×C3C22×D3×D411yescharacteristic
809C2×C3C2×#100412yes—
810C2×C3C2×#100912yes—
811D3—44no—
812D3—68no—
813D3—64no—
814D3—64no—
815D3—64no—
816D3—64no—
817D3—124no—
818D3—124no—
819D3—122no—
820D3—122no—
821C22—24no—
822C22—28no—
823C22—24no—
824C22—22no—
825C22—44no—
826C22—64no—
827C22—64no—
828C22—64no—
829C22—94no—
830C22—94no—
831C22—1216no—
832C22—128no—
833C22—184no—
834C22—184no—
835C22—188no—
836C22—188no—
837C22—184no—
838C22—182no—
839C22—3616no—
840C22—3616no—
841C22—364no—
842C22#6431414yes—
843C22C2×#381114yes—
844C22C2×#381112yes—
845C22C23×D3211yescharacteristic
846C4—22no—
847C4—64no—
848C4—64no—
849C4—64no—
850C4—182no—
851C3—21no—
852C3C2×#558911yescharacteristic, complemented
853C3C2×#565311yescharacteristic, complemented
854C2—24no—
855C2—42no—
856C2—124no—
857C2—184no—
858C2—184no—
859C2—362no—
860C2#1059524214yesdirect product factor
861C2C2×#6431412yes—
862C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C3⋊D3C2semidirect
2. C23×#626C2semidirect
3. C2×C3×#937C2semidirect
4. C2×C3×#935C2semidirect
5. C2×#63981C2semidirect
6. C2×#63977C2semidirect
7. C2×#63974C2semidirect
8. C2×#63966C2semidirect
9. C2×#63958C2semidirect
10. #10595242C2direct (N × H)
11. C2×#63910C2semidirect
12. C2×#63853C2semidirect
16. C24×C3⋊D3C22semidirect
17. C24×C3×D3C22semidirect
20. C22×#638C22semidirect
22. C2×D4×C3⋊D3C22semidirect
23. C22×C4⋊(C3⋊D3)C22semidirect
24. C22×C4×C3⋊D3C22semidirect
25. C22×C3×#67C22semidirect
26. C23×C3×Dic3C22semidirect
29. C22×#626C22semidirect
30. C22×#626C22semidirect
31. C22×#626C22semidirect
32. C22×#624C22semidirect
33. C2×C3×#217C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
36. C3×#937C22semidirect
37. C3×#935C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
40. #63981C22semidirect
41. #63977C22semidirect
42. #63974C22semidirect
43. #63966C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
45. C2×#3722C22semidirect
46. C2×#3722C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. #63958C22semidirect
49. #63910C22semidirect
50. #63853C22semidirect
61. C2×#937D3semidirect
62. C2×#935D3semidirect
81. C23×C3⋊D3D4semidirect
86. C23×C3⋊D3C23semidirect
90. C23×C3×D3C23semidirect
97. C2×#638C23semidirect
101. C2×C4⋊(C3⋊D3)C23semidirect
103. C2×C4×C3⋊D3C23semidirect
105. C2×C3×#67C23semidirect
110. C22×C3×Dic3C23semidirect
116. C2×#626C23semidirect
117. C2×#626C23semidirect
119. C2×#624C23semidirect
120. C3×#217C23semidirect
121. C3×#217C23semidirect
122. C3×#217C23semidirect
123. C3×(C2×D3)⋊C4C23semidirect
124. C3×Dic3⋊C4C23semidirect
125. Dic3⋊Dic3C23semidirect
126. #3722C23semidirect
127. #3722C23semidirect
128. (C2×D3)⋊Dic3C23semidirect
137. C24×D3C2×D3semidirect
154. C22×#67C2×D3semidirect
155. C23×Dic3C2×D3semidirect
184. C2×#217C2×D3semidirect
185. C2×#217C2×D3semidirect
186. C2×#217C2×D3semidirect
189. #937C2×D3semidirect
190. #935C2×D3semidirect
197. C2×(C2×D3)⋊C4C2×D3semidirect
200. C2×Dic3⋊C4C2×D3semidirect
229. C22×C3⋊D3C2×D4semidirect
313. C23×D3C22×D3semidirect
350. C2×#67C22×D3semidirect
358. C22×Dic3C22×D3semidirect
391. #217C22×D3semidirect
392. #217C22×D3semidirect
393. #217C22×D3semidirect
399. (C2×D3)⋊C4C22×D3semidirect
402. Dic3⋊C4C22×D3semidirect
602. C2×C32#534semidirect
744. C32C2×#534semidirect
805. C2×C3#5589semidirect
806. C2×C3#5653semidirect
852. C3C2×#5589semidirect
853. C3C2×#5653semidirect
860. C2#10595242direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C23×#6262
C2×C3×#9372
C2×C3×#9352
C2×#639812
C2×#639772
C2×#639742
C2×#639662
C2×#639582
#105952422
C2×#639102
C2×#638532
C2×#56533
C2×#55893