Finite Group Databasebeta

← C2×#10595427 #11902458

Subgroups — C2×#10595427 #11902458

Order 1152.

3965 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C22×D3×D12C211yesmaximal, characteristic, complemented
3C2×#64156C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5#10595427C2116yesmaximal, direct product factor
6C2×#63922C212yesmaximal, complemented
7C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
8C2×#63909C211yesmaximal, characteristic, complemented
9C2×C4×#625C211yesmaximal, characteristic, complemented
10C2×#63898C211yesmaximal, characteristic, complemented
11C2×#63886C212yesmaximal, complemented
12C2×#63850C212yesmaximal, complemented
13C2×#5829—31nomaximal
14C2×#5630—31nomaximal
15C23×D32C2212yes—
16C22×C32×Q8C2211yescharacteristic, complemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×#239—28no—
19C2×C3×#239C2218yescomplemented
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2212yescomplemented
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2212yescomplemented
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×#626C2212yes—
26C22×#626C2212yescomplemented
27C22×#625C2211yescharacteristic
28C22×D3×Dic3C2212yescomplemented
29C2×D3×D12—28no—
30C2×D3×D12C2218yescomplemented
31#64156C2218yescomplemented
32C2×#3752C2212yescomplemented
33C2×#3752C2212yescomplemented
34C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
35C3×#946C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39C2×#3724C2211yescharacteristic, complemented
40C2×#3722C2212yescomplemented
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
44#63922C22116yescomplemented
45D3×(C2×D3)⋊C4C22116yescomplemented
46#63909C2218yescomplemented
47C4×#625C2218yescomplemented
48#63898C2218yescomplemented
49#63886C22116yescomplemented
50#63850C22116yescomplemented
51C22×C3×#41—31no—
52C22×#239D311yescharacteristic, complemented
53C22×D3×D4—31no—
54C23×D12—31no—
55C2×C3×C22⋊Q8—31no—
56#5829—316no—
57C2×#947—31no—
58C2×#947—31no—
59C2×#947—61no—
60C2×#946D311yescharacteristic, complemented
61C2×#939—32no—
62C2×#937—32no—
63C2×D4×Dic3—31no—
64C2×#930—31no—
65C2×#929—32no—
66C2×C4×#67—31no—
67C2×C4×#67—31no—
68C22×(C2×D3)⋊C4—32no—
69#5630—316no—
70C2×#895—32no—
71C2×#895—31no—
72C2×#894—32no—
73C2×#893—31no—
74C2×#882—32no—
75C2×D3×C22⋊C4—32no—
76C23×C3⋊D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C23×C3×D3C2311yescharacteristic
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C2×C32×Q8—24no—
85C2×C32×Q8C2314yescomplemented
86C22×C32×C4C2312yes—
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C2×C4⋊(C3⋊D3)—24no—
91C2×C4⋊(C3⋊D3)C2314yes—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C3×#239—232no—
96C2×C3×D12—28no—
97C2×C3×D12D418yescomplemented
98C2×C3×D12C2314yes—
99C2×C3×D12C2318yescomplemented
100C2×C3×C4×D3—28no—
101C2×C3×C4×D3—24no—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3C2314yes—
104C2×C3×C4×D3C2318yescomplemented
105C2×C3×C4×D3C2314yescomplemented
106C2×#626—28no—
107C2×#626—44no—
108C2×#626C2318yes—
109C2×#626C2318yescomplemented
110C2×#625—24no—
111C2×#625C2314yes—
112C2×D3×Dic3—44no—
113C2×D3×Dic3C2318yescomplemented
114D3×D12—232no—
115#3752C2318yescomplemented
116#3752C2318yescomplemented
117C4×C3⋊Dic3C2314yescomplemented
118C3×(C2×D3)⋊C4C2318yes—
119C3×C4⋊Dic3C2314yescomplemented
120C3×Dic3⋊C4C2318yescomplemented
121#3724C2314yescomplemented
122#3722C2318yescomplemented
123(C2×D3)⋊Dic3C2314yes—
124(C2×D3)⋊Dic3C2318yescomplemented
125(C2×D3)⋊Dic3C2314yescomplemented
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C2×C3×#41—38no—
130C2×C3×#41—68no—
131C22×C3×Q8—21no—
132C22×C3×Q8C2×D311yescharacteristic, complemented
133C22×C3×Q8C2×D311yescharacteristic, complemented
134C22×C3×D4—31no—
135C22×C3×D4—32no—
136C23×C3×C4—31no—
137C23×C3×C4—32no—
138C23×C3×C4—31no—
139C22×#67—31no—
140C22×#67—31no—
141C22×#67—32no—
142C22×#67—32no—
143C23×Dic3—32no—
144C2×#239—28no—
145C2×#239C2×D318yescomplemented
146C2×D3×D4—38no—
147C2×D3×D4—68no—
148C22×D12—32no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—32no—
152C22×D12—38no—
153C22×D12—61no—
154C22×D12—68no—
155C22×D12C2×D311yescharacteristic
156C22×D12C2×D312yescomplemented
157C22×C4×D3—32no—
158C22×C4×D3C2×D311yescharacteristic
159C22×C4×D3C2×D312yescomplemented
160C22×C4×D3C2×D311yescharacteristic, complemented
161C3×C22⋊Q8—38no—
162C2×C3×C4⋊C4—32no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—32no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—32no—
168#947—38no—
169#947—38no—
170#947—68no—
171#946C2×D318yescomplemented
172#939—316no—
173#937—316no—
174D4×Dic3—38no—
175#930—38no—
176#929—316no—
177C4×#67—38no—
178C4×#67—38no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—316no—
189C2×(C2×D3)⋊C4—62no—
190C2×(C2×D3)⋊C4—62no—
191C2×(C2×D3)⋊C4C2×D312yes—
192C2×C4⋊Dic3C2×D311yescharacteristic, complemented
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4C2×D312yescomplemented
196C2×C4×Dic3—31no—
197C2×C4×Dic3—31no—
198C2×C4×Dic3—61no—
199#895—316no—
200#895—38no—
201#894—316no—
202#893—38no—
203#882—316no—
204D3×C22⋊C4—316no—
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—24no—
207C22×C3⋊D3—24no—
208C22×C3⋊D3—24no—
209C22×C3⋊D3C2414yes—
210C22×C3×D3—22no—
211C22×C3×D3—24no—
212C22×C3×D3—22no—
213C22×C3×D3—24no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3C2×D418yes—
218C22×C3×D3#4114yescomplemented
219C22×C3×D3C2412yes—
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C2×D32—216no—
223C2×D32—216no—
224C2×D32—48no—
225C2×D32—432no—
226C32×Q8—28no—
227C2×C32×C4—24no—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2414yes—
230C2×C32×C4C2412yes—
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3—22no—
233C2×C3⋊Dic3C2412yes—
234C2×C3⋊Dic3C2412yes—
235C4⋊(C3⋊D3)—28no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3C2412yes—
240C2×C3×Dic3C2414yes—
241C2×C3×Dic3C2412yes—
242C3×D12—216no—
243C3×D12C2×D4116yescomplemented
244C3×C4×D3—216no—
245C3×C4×D3—28no—
246C3×C4×D3—28no—
247#626—216no—
248#626—48no—
249#625—28no—
250D3×Dic3—48no—
251C22×#41—31no—
252C23×D4—91no—
253#546—916no—
254C2×#124—91no—
255C2×#123—92no—
256C2×C22⋊Q8—31no—
257C2×#121—91no—
258C2×#121—92no—
259C2×#120—92no—
260C2×C4×D4—91no—
261C2×C4×D4—91no—
262C22×C22⋊C4—92no—
263C24×C3—31no—
264C24×C3—32no—
265C24×C3—31no—
266C23×D3—32no—
267C23×D3—32no—
268C23×D3—38no—
269C23×D3—38no—
270C23×D3—62no—
271C23×D3—68no—
272C23×D3—68no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—124no—
276C23×D3—124no—
277C23×D3C22×D311yescharacteristic
278C23×D3C22×D311yescharacteristic
279C23×D3C22×D312yes—
280C3×#41—632no—
281C2×C3×Q8—24no—
282C2×C3×Q8—24no—
283C2×C3×Q8—24no—
284C2×C3×Q8—44no—
285C2×C3×Q8C22×D314yescomplemented
286C2×C3×Q8C22×D314yescomplemented
287C2×C3×D4—38no—
288C2×C3×D4—34no—
289C2×C3×D4—38no—
290C2×C3×D4—68no—
291C22×C3×C4—21no—
292C22×C3×C4—22no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—32no—
296C22×C3×C4—38no—
297C22×C3×C4—34no—
298C22×C3×C4—34no—
299C22×C3×C4—68no—
300C22×C3×C4—64no—
301C22×C3×C4—64no—
302C22×C3×C4C22×D312yes—
303C22×C3×C4C22×D312yes—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—34no—
307C2×#67—34no—
308C2×#67—38no—
309C2×#67—38no—
310C2×#67—68no—
311C2×#67—64no—
312C2×#67—64no—
313C2×#67—124no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—38no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—124no—
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D312yes—
325#239—232no—
326D3×D4—632no—
327C2×D12—28no—
328C2×D12—38no—
329C2×D12—34no—
330C2×D12—34no—
331C2×D12—38no—
332C2×D12—64no—
333C2×D12—68no—
334C2×D12—64no—
335C2×D12—64no—
336C2×D12—632no—
337C2×D12—124no—
338C2×D12—124no—
339C2×D12#6718yescomplemented
340C2×D12C22×D314yes—
341C2×D12C22×D318yescomplemented
342C2×C4×D3—28no—
343C2×C4×D3—24no—
344C2×C4×D3—24no—
345C2×C4×D3—38no—
346C2×C4×D3—124no—
347C2×C4×D3C22×D314yes—
348C2×C4×D3C22×D318yescomplemented
349C2×C4×D3C22×D314yescomplemented
350C3×C4⋊C4—34no—
351C3×C4⋊C4—38no—
352C3×C22⋊C4—38no—
353#217—34no—
354#217—34no—
355#217—38no—
356(C2×D3)⋊C4—38no—
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—34no—
359(C2×D3)⋊C4—38no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—68no—
366(C2×D3)⋊C4—68no—
367(C2×D3)⋊C4C22×D318yes—
368C4⋊Dic3C22×D314yescomplemented
369Dic3⋊C4—34no—
370Dic3⋊C4—34no—
371Dic3⋊C4C22×D318yescomplemented
372C4×Dic3—34no—
373C4×Dic3—34no—
374C4×Dic3—64no—
375C22×C32C22×D412yes—
376C22×C32C2×#4112yes—
377C22×C32H(5,𝔽2)12yes—
378C22×C32C2511yescharacteristic
379C2×C3⋊D3—24no—
380C2×C3⋊D3—24no—
381C2×C3⋊D3—24no—
382C2×C3⋊D3—48no—
383C2×C3×D3—28no—
384C2×C3×D3—216no—
385C2×C3×D3—22no—
386C2×C3×D3—24no—
387C2×C3×D3—24no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—44no—
393C2×C3×D3C22×D418yes—
394C2×C3×D3C2×#4114yescomplemented
395D32—432no—
396C32×C4—24no—
397C32×C4C22×D414yes—
398C3⋊Dic3—22no—
399C3⋊Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—24no—
403C25—92no—
404C2×#41—38no—
405C2×#41—68no—
406C22×Q8D3211yescharacteristic, complemented
407C22×D4—31no—
408C22×D4—32no—
409C22×D4—98no—
410C22×D4—92no—
411C22×D4—92no—
412C22×D4—91no—
413C22×D4—91no—
414C22×D4—188no—
415C23×C4—32no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—92no—
419#124—98no—
420#123—916no—
421C22⋊Q8—38no—
422#121—98no—
423#121—916no—
424#120—916no—
425C4×D4—98no—
426C4×D4—98no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—32no—
429C2×C4⋊C4—91no—
430C2×C22⋊C4—32no—
431C2×C22⋊C4—916no—
432C2×C22⋊C4—92no—
433C2×C22⋊C4—91no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C2×C42—91no—
439C23×C3—21no—
440C23×C3—38no—
441C23×C3—34no—
442C23×C3—32no—
443C23×C3—34no—
444C23×C3—32no—
445C23×C3—64no—
446C23×C3—64no—
447C23×C3—62no—
448C23×C3—62no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3C23×D311yescharacteristic
453C23×C3C23×D311yescharacteristic
454C22×D3—22no—
455C22×D3—24no—
456C22×D3—24no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—34no—
462C22×D3—34no—
463C22×D3—64no—
464C22×D3—616no—
465C22×D3—616no—
466C22×D3—64no—
467C22×D3—64no—
468C22×D3—64no—
469C22×D3—64no—
470C22×D3—64no—
471C22×D3—64no—
472C22×D3—616no—
473C22×D3—616no—
474C22×D3—124no—
475C22×D3—124no—
476C22×D3—124no—
477C22×D3—128no—
478C22×D3—128no—
479C22×D3—1232no—
480C22×D3—1232no—
481C22×D3#23914yescomplemented
482C22×D3C2×#6718yes—
483C22×D3C23×D312yes—
484C22×D3C23×D312yes—
485C22×D3C23×D314yes—
486C3×Q8—28no—
487C3×Q8—28no—
488C3×Q8—48no—
489C3×D4—316no—
490C3×D4—616no—
491C2×C3×C4—24no—
492C2×C3×C4—24no—
493C2×C3×C4—22no—
494C2×C3×C4—24no—
495C2×C3×C4—24no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—34no—
499C2×C3×C4—44no—
500C2×C3×C4—616no—
501C2×C3×C4—62no—
502C2×C3×C4—64no—
503C2×C3×C4—62no—
504C2×C3×C4—68no—
505C2×C3×C4—68no—
506C2×C3×C4D3×D414yes—
507C2×C3×C4C2×#6714yes—
508C2×C3×C4C23×D314yes—
509C2×C3×C4C23×D314yes—
510C2×C3×C4C23×D312yes—
511C2×C3×C4C23×D312yes—
512#67—616no—
513#67—68no—
514#67—68no—
515#67—128no—
516C2×Dic3—22no—
517C2×Dic3—24no—
518C2×Dic3—22no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—32no—
522C2×Dic3—32no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—62no—
529C2×Dic3—122no—
530C2×Dic3—122no—
531C2×Dic3—128no—
532C2×Dic3C23×D312yes—
533C2×Dic3C23×D312yes—
534C2×Dic3C23×D314yes—
535D12—216no—
536D12—616no—
537D12—68no—
538D12—68no—
539D12—128no—
540D12—128no—
541D12C2×#67116yescomplemented
542C4×D3—216no—
543C4×D3—28no—
544C4×D3—28no—
545C4×D3—128no—
546C2×C32#54614yescomplemented
547C2×C32C23×D411yescharacteristic
548C2×C32C22×#4111yescharacteristic
549C2×C32C2×H(5,𝔽2)11yescharacteristic
550C3⋊D3—44no—
551C3×D3—24no—
552C3×D3—28no—
553C3×D3—42no—
554C24—31no—
555C24—32no—
556C24—31no—
557C24—98no—
558C24—92no—
559C24—188no—
560C24—188no—
561C24—364no—
562#41—632no—
563C2×Q8—24no—
564C2×Q8C2×D3214yescomplemented
565C2×D4—34no—
566C2×D4—38no—
567C2×D4—38no—
568C2×D4—68no—
569C2×D4—98no—
570C2×D4—98no—
571C2×D4—94no—
572C2×D4—94no—
573C2×D4—1832no—
574C2×D4—188no—
575C2×D4—184no—
576C2×D4—184no—
577C2×D4—364no—
578C22×C4—32no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—38no—
582C22×C4—34no—
583C22×C4—34no—
584C22×C4—68no—
585C22×C4—64no—
586C22×C4—64no—
587C22×C4—98no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—364no—
591C22×C4C2×D3212yes—
592C22×C4C2×D3211yescharacteristic
593C4⋊C4—34no—
594C4⋊C4—38no—
595C4⋊C4—94no—
596C22⋊C4—38no—
597C22⋊C4—98no—
598C22⋊C4—94no—
599C22⋊C4—98no—
600C22⋊C4—94no—
601C22⋊C4—98no—
602C22⋊C4—98no—
603C42—94no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—38no—
609C22×C3—34no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—68no—
615C22×C3—616no—
616C22×C3—62no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—124no—
620C22×C3C2×D3×D412yes—
621C22×C3C2×#23912yes—
622C22×C3D3×#4112yes—
623C22×C3#100912yes—
624C22×C3#100912yes—
625C22×C3C22×#6712yes—
626C22×C3C24×D311yescharacteristic
627C22×C3C24×D311yescharacteristic
628C2×D3—22no—
629C2×D3—24no—
630C2×D3—24no—
631C2×D3—22no—
632C2×D3—216no—
633C2×D3—28no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—44no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—64no—
644C2×D3—124no—
645C2×D3—124no—
646C2×D3—124no—
647C2×D3—1232no—
648C2×D3—1232no—
649C2×D3—128no—
650C2×D3—128no—
651C2×D3—248no—
652C2×D3C2×#23914yescomplemented
653C2×D3C22×#6718yes—
654C3×C4—24no—
655C3×C4—24no—
656C3×C4—24no—
657C3×C4—44no—
658C3×C4—62no—
659C3×C4—64no—
660C3×C4—62no—
661C3×C4C2×D3×D414yes—
662C3×C4C22×#6714yes—
663Dic3—22no—
664Dic3—24no—
665Dic3—22no—
666Dic3—62no—
667Dic3—62no—
668Dic3—62no—
669Dic3—62no—
670Dic3—122no—
671Dic3—122no—
672C32C2×#54611yescharacteristic, complemented, Sylow
673C23—34no—
674C23—38no—
675C23—32no—
676C23—34no—
677C23—32no—
678C23—64no—
679C23—64no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—94no—
686C23—1816no—
687C23—1816no—
688C23—184no—
689C23—184no—
690C23—184no—
691C23—368no—
692C23—3632no—
693C23C22×D3211yescharacteristic
694Q8—28no—
695D4—316no—
696D4—616no—
697D4—1816no—
698D4—188no—
699D4—188no—
700D4—368no—
701C2×C4—24no—
702C2×C4—34no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—616no—
706C2×C4—64no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—68no—
710C2×C4—68no—
711C2×C4—92no—
712C2×C4—92no—
713C2×C4—182no—
714C2×C4—182no—
715C2×C4—368no—
716C2×C4D3×#6714yes—
717C2×C4C22×D3214yes—
718C2×C4C22×D3212yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—24no—
723C2×C3—68no—
724C2×C3—64no—
725C2×C3—122no—
726C2×C3#563014yescomplemented
727C2×C3#582914yescomplemented
728C2×C3C22×D3×D411yescharacteristic
729C2×C3C22×#23911yescharacteristic
730C2×C3C2×D3×#4111yescharacteristic
731C2×C3C2×#100911yescharacteristic
732C2×C3C2×#100911yescharacteristic
733C2×C3C23×#6711yescharacteristic
734D3—24no—
735D3—28no—
736D3—42no—
737D3—124no—
738D3—124no—
739D3—244no—
740C22—34no—
741C22—38no—
742C22—64no—
743C22—64no—
744C22—62no—
745C22—62no—
746C22—68no—
747C22—616no—
748C22—62no—
749C22—62no—
750C22—62no—
751C22—124no—
752C22—184no—
753C22—184no—
754C22—184no—
755C22—3632no—
756C22—368no—
757C22D3×#23912yes—
758C22#6432012yes—
759C22C2×D3×#6712yes—
760C22C23×D3211yescharacteristic
761C4—24no—
762C4—64no—
763C4—62no—
764C4—62no—
765C4—182no—
766C4—182no—
767C4C2×D3×#6714yes—
768C3—21no—
769C3C2×#563011yescharacteristic, complemented
770C3C2×#582911yescharacteristic, complemented
771C2—64no—
772C2—68no—
773C2—122no—
774C2—364no—
775C2#1059542714yesdirect product factor
776C2C2×D3×#23911yescharacteristic
777C2C2×#6432011yescharacteristic
778C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C22×D3×D12C2semidirect
3. C2×#64156C2semidirect
4. C2×C3×#946C2semidirect
5. #10595427C2direct (N × H)
6. C2×#63922C2semidirect
7. C2×D3×(C2×D3)⋊C4C2semidirect
8. C2×#63909C2semidirect
9. C2×C4×#625C2semidirect
10. C2×#63898C2semidirect
11. C2×#63886C2semidirect
12. C2×#63850C2semidirect
16. C22×C32×Q8C22semidirect
19. C2×C3×#239C22semidirect
21. C22×C3×D12C22semidirect
23. C22×C3×C4×D3C22semidirect
24. C22×C3×C4×D3C22semidirect
26. C22×#626C22semidirect
28. C22×D3×Dic3C22semidirect
30. C2×D3×D12C22semidirect
31. #64156C22semidirect
32. C2×#3752C22semidirect
33. C2×#3752C22semidirect
34. C2×C4×C3⋊Dic3C22semidirect
35. C3×#946C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×#3724C22semidirect
40. C2×#3722C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. #63922C22semidirect
45. D3×(C2×D3)⋊C4C22semidirect
46. #63909C22semidirect
47. C4×#625C22semidirect
48. #63898C22semidirect
49. #63886C22semidirect
50. #63850C22semidirect
52. C22×#239D3semidirect
60. C2×#946D3semidirect
85. C2×C32×Q8C23semidirect
97. C2×C3×D12D4semidirect
99. C2×C3×D12C23semidirect
104. C2×C3×C4×D3C23semidirect
105. C2×C3×C4×D3C23semidirect
109. C2×#626C23semidirect
113. C2×D3×Dic3C23semidirect
115. #3752C23semidirect
116. #3752C23semidirect
117. C4×C3⋊Dic3C23semidirect
119. C3×C4⋊Dic3C23semidirect
120. C3×Dic3⋊C4C23semidirect
121. #3724C23semidirect
122. #3722C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
132. C22×C3×Q8C2×D3semidirect
133. C22×C3×Q8C2×D3semidirect
145. C2×#239C2×D3semidirect
156. C22×D12C2×D3semidirect
159. C22×C4×D3C2×D3semidirect
160. C22×C4×D3C2×D3semidirect
171. #946C2×D3semidirect
192. C2×C4⋊Dic3C2×D3semidirect
195. C2×Dic3⋊C4C2×D3semidirect
218. C22×C3×D3#41semidirect
243. C3×D12C2×D4semidirect
285. C2×C3×Q8C22×D3semidirect
286. C2×C3×Q8C22×D3semidirect
339. C2×D12#67semidirect
341. C2×D12C22×D3semidirect
348. C2×C4×D3C22×D3semidirect
349. C2×C4×D3C22×D3semidirect
368. C4⋊Dic3C22×D3semidirect
371. Dic3⋊C4C22×D3semidirect
394. C2×C3×D3C2×#41semidirect
406. C22×Q8D32semidirect
481. C22×D3#239semidirect
541. D12C2×#67semidirect
546. C2×C32#546semidirect
564. C2×Q8C2×D32semidirect
652. C2×D3C2×#239semidirect
672. C32C2×#546semidirect
726. C2×C3#5630semidirect
727. C2×C3#5829semidirect
769. C3C2×#5630semidirect
770. C3C2×#5829semidirect
775. C2#10595427direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×D3×D122
C2×#641562
C2×C3×#9462
#105954272
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639092
C2×C4×#6252
C2×#638982
C2×#638862
C2×#638502
C2×#58293
C2×#56303