Finite Group Databasebeta

← C2×#10594900 #11902622

Subgroups — C2×#10594900 #11902622

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C2×#63978C212yesmaximal, complemented
6C2×Dic3×#67C212yesmaximal, complemented
7C2×#63907C212yesmaximal, complemented
8#10594900C2116yesmaximal, direct product factor
9C2×#63887C212yesmaximal, complemented
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63863C211yesmaximal, characteristic, complemented
12C2×#63843C211yesmaximal, characteristic, complemented
13C2×#5817—31nomaximal
14C2×#5598—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yes—
20C22×C3×D12C2211yescharacteristic
21C22×C3×Dic6—28no—
22C22×C3×Dic6C2211yescharacteristic
23C22×C3×Dic6C2212yes—
24C22×C3×Dic6C2211yescharacteristic
25C22×C3×Dic6C2218yescomplemented
26C22×#626C2212yes—
27C22×D3×Dic3C2212yes—
28C2×#3796—28no—
29C2×#3796C2218yescomplemented
30C2×#3757C2211yescharacteristic
31C4×#638C2218yescomplemented
32C2×#3752C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C3×#930C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic
38#63978C22116yescomplemented
39Dic3×#67C22116yescomplemented
40C2×Dic3⋊Dic3C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42C2×#3722C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×Dic32C2212yes—
46#63907C22116yescomplemented
47#63887C22116yescomplemented
48#63871C2218yescomplemented
49#63863C2218yescomplemented
50#63843C2218yescomplemented
51C23×C3×Q8—31no—
52C22×#239—31no—
53C22×#237—31no—
54C23×Dic6D311yescharacteristic, complemented
55C2×C3×#121—31no—
56#5817—316no—
57C2×#947—31no—
58C2×#947—32no—
59C2×#946—32no—
60C2×#946—31no—
61C2×Q8×Dic3—31no—
62C2×#939—32no—
63C2×#936—31no—
64C2×D4×Dic3—32no—
65C2×#930—32no—
66C2×#930D311yescharacteristic, complemented
67C2×C4×#67—31no—
68C2×C4×#67—31no—
69C2×C4×#67—32no—
70C2×C4×#67—61no—
71#5598—316no—
72C2×#897—31no—
73C2×#887—31no—
74C2×#885—32no—
75C2×#878—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C22×C32×C4—24no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2314yes—
82C22×C32×C4C2311yescharacteristic
83C2×#638—24no—
84C2×#638C2314yes—
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C2×C4×C3⋊D3—24no—
89C2×C4×C3⋊D3C2314yes—
90C2×C3×#67—28no—
91C2×C3×#67C2318yes—
92C22×C3×Dic3—28no—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2318yes—
96C22×C3×Dic3C2312yes—
97C2×C3×D12—24no—
98C2×C3×D12C2314yes—
99C2×C3×Dic6—24no—
100C2×C3×Dic6—28no—
101C2×C3×Dic6—232no—
102C2×C3×Dic6D418yescomplemented
103C2×C3×Dic6C2314yes—
104C2×C3×Dic6C2318yes—
105C2×C3×Dic6C2314yes—
106C2×#626—28no—
107C2×#626C2318yes—
108C2×D3×Dic3—28no—
109C2×D3×Dic3C2318yes—
110#3796—232no—
111#3757C2314yes—
112#3752C2314yes—
113#3750C2314yes—
114C4×C3⋊Dic3C2314yes—
115C3×(C2×D3)⋊C4C2318yes—
116C3×C4⋊Dic3C2314yes—
117Dic3⋊Dic3C2318yes—
118Dic3⋊Dic3C2318yes—
119#3722C2318yes—
120(C2×D3)⋊Dic3C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122Dic32C2318yes—
123C2×#548—91noSylow
124C22×C3×Q8—31no—
125C22×C3×Q8—32no—
126C22×C3×Q8—31no—
127C22×C3×Q8—38no—
128C22×C3×Q8—68no—
129C22×C3×D4—32no—
130C22×C3×D4—31no—
131C23×C3×C4—21no—
132C23×C3×C4—32no—
133C23×C3×C4C2×D311yescharacteristic
134C23×C3×C4C2×D311yescharacteristic
135C22×#67—31no—
136C22×#67—31no—
137C22×#67—32no—
138C22×#67—61no—
139C22×#67C2×D312yes—
140C23×Dic3—32no—
141C23×Dic3C2×D312yes—
142C2×#239—38no—
143C2×#239—68no—
144C2×#237—38no—
145C2×#237—68no—
146C22×D12—32no—
147C22×D12C2×D311yescharacteristic
148C22×C4×D3—32no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—61no—
152C22×Dic6—28no—
153C22×Dic6C2×D312yes—
154C22×Dic6C2×D311yescharacteristic
155C22×Dic6C2×D311yescharacteristic
156C22×Dic6C2×D318yescomplemented
157C3×#121—38no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—32no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—32no—
163C2×#217—32no—
164C2×#217—61no—
165#947—38no—
166#947—316no—
167#946—316no—
168#946—38no—
169Q8×Dic3—38no—
170#939—316no—
171#936—38no—
172D4×Dic3—316no—
173#930—316no—
174#930C2×D318yescomplemented
175C4×#67—38no—
176C4×#67—38no—
177C4×#67—316no—
178C4×#67—68no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4C2×D312yes—
187C2×C4⋊Dic3—32no—
188C2×C4⋊Dic3—32no—
189C2×C4⋊Dic3C2×D311yescharacteristic
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—32no—
193C2×Dic3⋊C4—32no—
194C2×Dic3⋊C4—61no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—31no—
197C2×C4×Dic3—32no—
198C2×C4×Dic3—32no—
199C2×C4×Dic3—61no—
200#897—38no—
201#887—38no—
202#885—316no—
203#878—316no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32#4114yescomplemented
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3⋊D3—22no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3C2412yes—
213C22×C3×D3—24no—
214C22×C3×D3—24no—
215C22×C3×D3—24no—
216C22×C3×D3C2414yes—
217C2×C32×C4—22no—
218C2×C32×C4—28no—
219C2×C32×C4C2×D414yes—
220C2×C32×C4C2412yes—
221C2×C32×C4C2412yes—
222#638—28no—
223C2×C3⋊Dic3—22no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3C2412yes—
227C2×C3⋊Dic3C2412yes—
228C2×C3⋊Dic3C2412yes—
229C4×C3⋊D3—28no—
230C3×#67—216no—
231C2×C3×Dic3—24no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—216no—
234C2×C3×Dic3C2×D418yes—
235C2×C3×Dic3C2414yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2414yes—
238C3×D12—28no—
239C3×Dic6—28no—
240C3×Dic6—216no—
241C3×Dic6C2×D4116yescomplemented
242#626—216no—
243D3×Dic3—216no—
244C22×#41—91no—
245C23×Q8—31no—
246#548—916no—
247C2×#124—92no—
248C2×#124—91no—
249C2×C22⋊Q8—92no—
250C2×C22⋊Q8—91no—
251C2×#121—31no—
252C2×#121—92no—
253C2×C4×Q8—91no—
254C2×C4×D4—92no—
255C2×C4×D4—91no—
256C24×C3—21no—
257C24×C3—32no—
258C24×C3C22×D311yescharacteristic
259C24×C3C22×D311yescharacteristic
260C23×D3—31no—
261C23×D3—31no—
262C23×D3—61no—
263C23×D3C22×D312yes—
264C2×C3×Q8—38no—
265C2×C3×Q8—34no—
266C2×C3×Q8—38no—
267C2×C3×Q8—34no—
268C2×C3×Q8—68no—
269C2×C3×Q8—632no—
270C2×C3×Q8—64no—
271C2×C3×D4—38no—
272C2×C3×D4—34no—
273C2×C3×D4—68no—
274C2×C3×D4—64no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—24no—
280C22×C3×C4—32no—
281C22×C3×C4—32no—
282C22×C3×C4—32no—
283C22×C3×C4—38no—
284C22×C3×C4—44no—
285C22×C3×C4—68no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D314yes—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C2×#67—28no—
293C2×#67—34no—
294C2×#67—34no—
295C2×#67—38no—
296C2×#67—64no—
297C2×#67—68no—
298C2×#67—64no—
299C2×#67—64no—
300C2×#67—68no—
301C2×#67C22×D318yes—
302C22×Dic3—28no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—38no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—68no—
314C22×Dic3C22×D312yes—
315C22×Dic3C22×D312yes—
316C22×Dic3C22×D318yes—
317C22×Dic3C22×D312yes—
318#239—632no—
319#237—632no—
320C2×D12—24no—
321C2×D12—38no—
322C2×D12—68no—
323C2×D12C22×D314yes—
324C2×C4×D3—38no—
325C2×C4×D3—34no—
326C2×C4×D3—34no—
327C2×C4×D3—64no—
328C2×C4×D3—68no—
329C2×C4×D3—64no—
330C2×C4×D3—64no—
331C2×C4×D3—124no—
332C2×Dic6—24no—
333C2×Dic6—28no—
334C2×Dic6—232no—
335C2×Dic6#6718yescomplemented
336C2×Dic6C22×D318yes—
337C2×Dic6C22×D314yes—
338C2×Dic6C22×D314yes—
339C3×C4⋊C4—34no—
340C3×C22⋊C4—38no—
341#217—34no—
342#217—34no—
343#217—38no—
344#217—38no—
345#217—64no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—38no—
348(C2×D3)⋊C4—34no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—38no—
351(C2×D3)⋊C4—38no—
352(C2×D3)⋊C4—64no—
353(C2×D3)⋊C4C22×D318yes—
354C4⋊Dic3—38no—
355C4⋊Dic3—38no—
356C4⋊Dic3C22×D314yes—
357Dic3⋊C4—34no—
358Dic3⋊C4—34no—
359Dic3⋊C4—38no—
360Dic3⋊C4—38no—
361Dic3⋊C4—64no—
362C4×Dic3—34no—
363C4×Dic3—34no—
364C4×Dic3—38no—
365C4×Dic3—38no—
366C4×Dic3—64no—
367C22×C32—28no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32C22×D412yes—
371C22×C32C2×#4112yes—
372C22×C32C2×#4114yescomplemented
373C22×C322−1+412yes—
374C22×C32C2511yescharacteristic
375C2×C3⋊D3—22no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—22no—
378C2×C3⋊D3—44no—
379C2×C3×D3—24no—
380C2×C3×D3—24no—
381C2×C3×D3—24no—
382C2×C3×D3—48no—
383C32×C4—22no—
384C32×C4C22×D414yes—
385C3⋊Dic3—22no—
386C3⋊Dic3—22no—
387C3⋊Dic3—22no—
388C3×Dic3—24no—
389C3×Dic3—24no—
390C3×Dic3C22×D418yes—
391C2×#41—98no—
392C2×#41—188no—
393C22×Q8—31no—
394C22×Q8—32no—
395C22×Q8—31no—
396C22×Q8—38no—
397C22×Q8—68no—
398C22×D4—32no—
399C22×D4—31no—
400C22×D4—92no—
401C22×D4—91no—
402C23×C4—32no—
403C23×C4—92no—
404C23×C4—91no—
405C23×C4D3211yescharacteristic
406#124—916no—
407#124—98no—
408C22⋊Q8—916no—
409C22⋊Q8—98no—
410#121—38no—
411#121—916no—
412C4×Q8—98no—
413C4×D4—916no—
414C4×D4—98no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—92no—
417C2×C4⋊C4—92no—
418C2×C4⋊C4—91no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—92no—
421C2×C22⋊C4—92no—
422C2×C22⋊C4—92no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C42—92no—
426C2×C42—91no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—21no—
433C23×C3—24no—
434C23×C3—34no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—64no—
438C23×C3—64no—
439C23×C3—64no—
440C23×C3#23714yescomplemented
441C23×C3#23914yescomplemented
442C23×C3C23×D312yes—
443C23×C3C23×D312yes—
444C23×C3C23×D311yescharacteristic
445C23×C3C23×D311yescharacteristic
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—24no—
449C22×D3—32no—
450C22×D3—32no—
451C22×D3—62no—
452C22×D3—64no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—62no—
457C22×D3—62no—
458C22×D3—62no—
459C22×D3—122no—
460C22×D3—122no—
461C22×D3C23×D314yes—
462C3×Q8—316no—
463C3×Q8—616no—
464C3×Q8—68no—
465C3×D4—616no—
466C3×D4—68no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—28no—
470C2×C3×C4—28no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—24no—
474C2×C3×C4—38no—
475C2×C3×C4—34no—
476C2×C3×C4—34no—
477C2×C3×C4—34no—
478C2×C3×C4—48no—
479C2×C3×C4—42no—
480C2×C3×C4—616no—
481C2×C3×C4—64no—
482C2×C3×C4—64no—
483C2×C3×C4D3×D414yes—
484C2×C3×C4C2×#6714yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C23×D312yes—
487C2×C3×C4C23×D312yes—
488C2×C3×C4C23×D312yes—
489#67—216no—
490#67—616no—
491#67—68no—
492#67—68no—
493#67—616no—
494C2×Dic3—24no—
495C2×Dic3—24no—
496C2×Dic3—216no—
497C2×Dic3—32no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—62no—
506C2×Dic3—64no—
507C2×Dic3—62no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—62no—
513C2×Dic3—616no—
514C2×Dic3—122no—
515C2×Dic3—122no—
516C2×Dic3C2×#6718yes—
517C2×Dic3C23×D314yes—
518C2×Dic3C23×D314yes—
519C2×Dic3C23×D314yes—
520D12—28no—
521D12—616no—
522C4×D3—616no—
523C4×D3—68no—
524C4×D3—68no—
525C4×D3—128no—
526Dic6—28no—
527Dic6—216no—
528Dic6C2×#67116yescomplemented
529C2×C32—24no—
530C2×C32#54814yescomplemented
531C2×C32C23×D411yescharacteristic
532C2×C32C22×#4111yescharacteristic
533C2×C32C2×2−1+411yescharacteristic
534C3⋊D3—42no—
535C3×D3—44no—
536C24—32no—
537C24—91no—
538C24C2×D3211yescharacteristic
539#41—1832no—
540C2×Q8—34no—
541C2×Q8—38no—
542C2×Q8—34no—
543C2×Q8—38no—
544C2×Q8—68no—
545C2×Q8—632no—
546C2×Q8—64no—
547C2×D4—38no—
548C2×D4—34no—
549C2×D4—68no—
550C2×D4—64no—
551C2×D4—98no—
552C2×D4—94no—
553C2×D4—188no—
554C2×D4—184no—
555C22×C4—24no—
556C22×C4—32no—
557C22×C4—38no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—68no—
561C22×C4—98no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4—91no—
565C22×C4—94no—
566C22×C4—188no—
567C22×C4—184no—
568C22×C4C2×D3214yes—
569C22×C4C2×D3211yescharacteristic
570C22×C4C2×D3211yescharacteristic
571C4⋊C4—34no—
572C4⋊C4—98no—
573C4⋊C4—98no—
574C4⋊C4—94no—
575C22⋊C4—38no—
576C22⋊C4—98no—
577C22⋊C4—98no—
578C22⋊C4—98no—
579C22⋊C4—94no—
580C22⋊C4—94no—
581C42—98no—
582C42—94no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—28no—
588C22×C3—28no—
589C22×C3—22no—
590C22×C3—24no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—21no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—48no—
597C22×C3—64no—
598C22×C3—64no—
599C22×C3—64no—
600C22×C3—128no—
601C22×C3C2×D3×D412yes—
602C22×C3C2×#23712yes—
603C22×C3C2×#23714yescomplemented
604C22×C3C2×#23912yes—
605C22×C3C2×#23914yescomplemented
606C22×C3#100712yes—
607C22×C3#101012yes—
608C22×C3C22×#6712yes—
609C22×C3C24×D311yescharacteristic
610C22×C3C24×D311yescharacteristic
611C2×D3—24no—
612C2×D3—24no—
613C2×D3—24no—
614C2×D3—48no—
615C2×D3—64no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—62no—
622C2×D3—122no—
623C2×D3—122no—
624C2×D3—128no—
625C2×D3—124no—
626C2×D3—124no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—24no—
630C3×C4—38no—
631C3×C4—42no—
632C3×C4—64no—
633C3×C4—64no—
634C3×C4C2×D3×D414yes—
635C3×C4C22×#6714yes—
636Dic3—24no—
637Dic3—24no—
638Dic3—64no—
639Dic3—62no—
640Dic3—62no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646Dic3—122no—
647Dic3C22×#6718yes—
648C32C2×#54811yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—34no—
652C23—64no—
653C23—64no—
654C23—64no—
655C23—92no—
656C23—182no—
657C23—182no—
658C23—182no—
659C23#379614yescomplemented
660C23C22×D3212yes—
661C23C22×D3211yescharacteristic
662Q8—316no—
663Q8—616no—
664Q8—68no—
665D4—616no—
666D4—68no—
667D4—1816no—
668D4—188no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—38no—
672C2×C4—34no—
673C2×C4—34no—
674C2×C4—34no—
675C2×C4—616no—
676C2×C4—64no—
677C2×C4—64no—
678C2×C4—92no—
679C2×C4—92no—
680C2×C4—92no—
681C2×C4—1816no—
682C2×C4—182no—
683C2×C4—182no—
684C2×C4—182no—
685C2×C4—188no—
686C2×C4D3×#6714yes—
687C2×C4C22×D3212yes—
688C2×C4C22×D3212yes—
689C2×C3—24no—
690C2×C3—24no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—24no—
694C2×C3—21no—
695C2×C3—44no—
696C2×C3—124no—
697C2×C3#559814yescomplemented
698C2×C3#581714yescomplemented
699C2×C3C22×D3×D411yescharacteristic
700C2×C3C22×#23711yescharacteristic
701C2×C3C22×#23911yescharacteristic
702C2×C3C2×#100711yescharacteristic
703C2×C3C2×#101011yescharacteristic
704C2×C3C23×#6711yescharacteristic
705D3—44no—
706D3—124no—
707D3—122no—
708D3—122no—
709C22—22no—
710C22—28no—
711C22—22no—
712C22—64no—
713C22—64no—
714C22—64no—
715C22—128no—
716C22—182no—
717C22—182no—
718C22—182no—
719C22—364no—
720C22C2×#379612yes—
721C22C2×#379614yescomplemented
722C22#6429712yes—
723C22C2×D3×#6712yes—
724C22C23×D3211yescharacteristic
725C4—22no—
726C4—38no—
727C4—64no—
728C4—64no—
729C4—182no—
730C4—182no—
731C4—182no—
732C4C2×D3×#6714yes—
733C3—21no—
734C3C2×#559811yescharacteristic, complemented
735C3C2×#581711yescharacteristic, complemented
736C2—24no—
737C2—124no—
738C2—362no—
739C2#1059490014yesdirect product factor
740C2C22×#379611yescharacteristic
741C2C2×#6429711yescharacteristic
742C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×Dic6C2semidirect
2. C22×#3796C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×#930C2semidirect
5. C2×#63978C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×#63907C2semidirect
8. #10594900C2direct (N × H)
9. C2×#63887C2semidirect
10. C2×#63871C2semidirect
11. C2×#63863C2semidirect
12. C2×#63843C2semidirect
25. C22×C3×Dic6C22semidirect
29. C2×#3796C22semidirect
31. C4×#638C22semidirect
35. C3×#930C22semidirect
38. #63978C22semidirect
39. Dic3×#67C22semidirect
46. #63907C22semidirect
47. #63887C22semidirect
48. #63871C22semidirect
49. #63863C22semidirect
50. #63843C22semidirect
54. C23×Dic6D3semidirect
66. C2×#930D3semidirect
102. C2×C3×Dic6D4semidirect
156. C22×Dic6C2×D3semidirect
174. #930C2×D3semidirect
206. C23×C32#41semidirect
241. C3×Dic6C2×D4semidirect
335. C2×Dic6#67semidirect
372. C22×C32C2×#41semidirect
440. C23×C3#237semidirect
441. C23×C3#239semidirect
528. Dic6C2×#67semidirect
530. C2×C32#548semidirect
603. C22×C3C2×#237semidirect
605. C22×C3C2×#239semidirect
648. C32C2×#548semidirect
659. C23#3796semidirect
697. C2×C3#5598semidirect
698. C2×C3#5817semidirect
721. C22C2×#3796semidirect
734. C3C2×#5598semidirect
735. C3C2×#5817semidirect
739. C2#10594900direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C22×#37962
C2×C4×#6382
C2×C3×#9302
C2×#639782
C2×Dic3×#672
C2×#639072
#105949002
C2×#638872
C2×#638712
C2×#638632
C2×#638432
C2×#58173
C2×#55983