Finite Group Databasebeta

← C2×#10595244 #11902440

Subgroups — C2×#10595244 #11902440

Order 1152.

4013 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×#237C211yesmaximal, characteristic, complemented
2C22×C3×D3×D4C211yesmaximal, characteristic, complemented
3C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63980C212yesmaximal, complemented
5C2×#63976C212yesmaximal, complemented
6C2×#63961C212yesmaximal, complemented
7C22×(C2×D3)⋊Dic3C212yesmaximal, complemented
8#10595244C2116yesmaximal, direct product factor
9C2×#63908C211yesmaximal, characteristic, complemented
10C2×C4×#625C211yesmaximal, characteristic, complemented
11C2×#63863C211yesmaximal, characteristic, complemented
12C2×#63856C211yesmaximal, characteristic, complemented
13C2×#5829—31nomaximal
14C2×#5806—31nomaximal
15C24×C3×D3C2212yes—
16C22×C32×D4C2211yescharacteristic
17C23×C3⋊Dic3C2212yescomplemented
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yescomplemented
20C23×C3×Dic3C2212yescomplemented
21C2×C3×#237—28no—
22C2×C3×#237C2218yescomplemented
23C2×C3×D3×D4—28no—
24C2×C3×D3×D4C2218yescomplemented
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×Dic6C2211yescharacteristic, complemented
29C22×#625C2211yescharacteristic
30C22×#625C2212yescomplemented
31C2×#3757C2212yescomplemented
32D4×C3⋊Dic3C2218yescomplemented
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
35#63980C22116yescomplemented
36#63976C22116yescomplemented
37C2×#3724C2212yescomplemented
38C2×#3724C2211yescharacteristic, complemented
39#63961C22116yescomplemented
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C22116yescomplemented
43C2×(C2×D3)⋊Dic3C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47#63908C2218yescomplemented
48C4×#625C2218yescomplemented
49#63863C2218yescomplemented
50#63856C2218yescomplemented
51C22×C3×#41—31no—
52C23×C3×D4—31no—
53C22×#237D311yescharacteristic, complemented
54C22×D3×D4D311yescharacteristic, complemented
55C2×#953—32no—
56C22×#217—32no—
57#5829—316no—
58C2×#947—31no—
59C2×#946—31no—
60#5806—316no—
61C2×#939—32no—
62C2×#939—32no—
63C2×#938—31no—
64C2×#937—32no—
65C2×#936—31no—
66C2×#935—32no—
67C2×D4×Dic3—31no—
68C2×D4×Dic3—31no—
69C2×D4×Dic3—61no—
70C2×#930—31no—
71C2×#929—32no—
72C2×C4×#67—31no—
73C2×C4×#67—31no—
74C22×(C2×D3)⋊C4—32no—
75C2×#924—31no—
76C24×C32C2312yes—
77C23×C3×D3—28no—
78C23×C3×D3—28no—
79C23×C3×D3—44no—
80C23×C3×D3C2311yescharacteristic
81C23×C3×D3C2312yes—
82C23×C3×D3C2318yes—
83C23×C3×D3C2311yescharacteristic
84C2×C32×D4D418yescomplemented
85C2×C32×D4C2314yes—
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3—44no—
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2312yes—
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2318yescomplemented
92C2×C3×#67—28no—
93C2×C3×#67—28no—
94C2×C3×#67C2318yes—
95C2×C3×#67C2318yescomplemented
96C22×C3×Dic3—28no—
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2318yescomplemented
101C3×#237—232no—
102C3×D3×D4—232no—
103C2×C3×D12—24no—
104C2×C3×D12C2314yes—
105C2×C3×C4×D3—24no—
106C2×C3×C4×D3—24no—
107C2×C3×C4×D3C2314yes—
108C2×C3×C4×D3C2314yescomplemented
109C2×C3×Dic6—24no—
110C2×C3×Dic6C2314yescomplemented
111C2×#625—24no—
112C2×#625—44no—
113C2×#625C2314yes—
114C2×#625C2318yescomplemented
115#3757C2318yescomplemented
116C4⋊(C3⋊Dic3)C2314yescomplemented
117C4×C3⋊Dic3C2314yescomplemented
118#3724C2318yescomplemented
119#3724C2314yescomplemented
120(C2×D3)⋊Dic3C2318yes—
121(C2×D3)⋊Dic3C2314yes—
122(C2×D3)⋊Dic3C2318yescomplemented
123(C2×D3)⋊Dic3C2318yescomplemented
124(C2×D3)⋊Dic3C2314yescomplemented
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C25×C3—32no—
128C24×D3C2×D312yes—
129C2×C3×#41—38no—
130C2×C3×#41—68no—
131C22×C3×Q8—31no—
132C22×C3×D4—21no—
133C22×C3×D4—32no—
134C22×C3×D4—32no—
135C22×C3×D4—38no—
136C22×C3×D4—31no—
137C22×C3×D4—68no—
138C22×C3×D4C2×D311yescharacteristic
139C22×C3×D4C2×D311yescharacteristic
140C23×C3×C4—32no—
141C23×C3×C4—31no—
142C23×C3×C4—31no—
143C22×#67—31no—
144C22×#67—31no—
145C22×#67—32no—
146C22×#67—32no—
147C22×#67C2×D312yes—
148C22×#67C2×D312yescomplemented
149C23×Dic3—32no—
150C23×Dic3—32no—
151C23×Dic3—62no—
152C23×Dic3C2×D312yescomplemented
153C2×#237—28no—
154C2×#237C2×D318yescomplemented
155C2×D3×D4—28no—
156C2×D3×D4C2×D318yescomplemented
157C22×D12C2×D311yescharacteristic
158C22×C4×D3C2×D311yescharacteristic
159C22×C4×D3C2×D311yescharacteristic, complemented
160C22×Dic6C2×D311yescharacteristic, complemented
161#953—316no—
162C2×#217—32no—
163C2×#217—32no—
164C2×#217—32no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—32no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—316no—
171C2×#217—62no—
172#947—38no—
173#946—38no—
174#939—316no—
175#939—316no—
176#938—38no—
177#937—316no—
178#936—38no—
179#935—316no—
180D4×Dic3—38no—
181D4×Dic3—38no—
182D4×Dic3—68no—
183#930—38no—
184#929—316no—
185C4×#67—38no—
186C4×#67—38no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—32no—
191C2×(C2×D3)⋊C4—316no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—32no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—61no—
197#924—38no—
198C2×Dic3⋊C4—32no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—32no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—61no—
205C23×C32—24no—
206C23×C32—24no—
207C23×C32C2×D418yes—
208C23×C32C2414yes—
209C23×C32C2411yescharacteristic
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—24no—
213C22×C3×D3—216no—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3—22no—
219C22×C3×D3—216no—
220C22×C3×D3—48no—
221C22×C3×D3—432no—
222C22×C3×D3#4114yescomplemented
223C22×C3×D3C2414yes—
224C22×C3×D3C2412yes—
225C22×C3×D3C2412yes—
226C32×D4C2×D4116yescomplemented
227C2×C32×C4C2×D414yes—
228C2×C32×C4C2412yes—
229C2×C3⋊Dic3—22no—
230C2×C3⋊Dic3—22no—
231C2×C3⋊Dic3—24no—
232C2×C3⋊Dic3—48no—
233C2×C3⋊Dic3C2412yes—
234C2×C3⋊Dic3C2414yes—
235C2×C3⋊Dic3C2412yes—
236C3×#67—216no—
237C3×#67—216no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—216no—
242C2×C3×Dic3C2414yes—
243C2×C3×Dic3C2412yes—
244C2×C3×Dic3C2412yes—
245C3×D12—28no—
246C3×C4×D3—28no—
247C3×C4×D3—28no—
248C3×Dic6—28no—
249#625—28no—
250#625—48no—
251C22×#41—31no—
252C23×D4—31no—
253#546—916no—
254C2×#124—91no—
255C2×#123—92no—
256C2×C22⋊Q8—91no—
257C2×#121—91no—
258C2×#121—92no—
259C2×#120—92no—
260C2×C4×D4—91no—
261C2×C4×D4—91no—
262C22×C22⋊C4—92no—
263C24×C3—22no—
264C24×C3—31no—
265C24×C3—32no—
266C24×C3—31no—
267C24×C3—38no—
268C24×C3—68no—
269C24×C3—68no—
270C24×C3—124no—
271C24×C3C22×D312yes—
272C24×C3C22×D312yes—
273C23×D3—28no—
274C23×D3—28no—
275C23×D3—44no—
276C23×D3C22×D312yes—
277C23×D3C22×D311yescharacteristic
278C23×D3C22×D318yes—
279C23×D3C22×D311yescharacteristic
280C3×#41—632no—
281C2×C3×Q8—34no—
282C2×C3×Q8—64no—
283C2×C3×D4—28no—
284C2×C3×D4—24no—
285C2×C3×D4—38no—
286C2×C3×D4—38no—
287C2×C3×D4—34no—
288C2×C3×D4—68no—
289C2×C3×D4—68no—
290C2×C3×D4—632no—
291C2×C3×D4—64no—
292C2×C3×D4#6718yescomplemented
293C2×C3×D4#6718yescomplemented
294C2×C3×D4C22×D314yes—
295C2×C3×D4C22×D314yes—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—32no—
300C22×C3×C4—38no—
301C22×C3×C4—34no—
302C22×C3×C4—34no—
303C22×C3×C4—68no—
304C22×C3×C4—64no—
305C22×C3×C4—64no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—28no—
309C2×#67—28no—
310C2×#67—34no—
311C2×#67—34no—
312C2×#67—38no—
313C2×#67—38no—
314C2×#67—64no—
315C2×#67—64no—
316C2×#67—124no—
317C2×#67—124no—
318C2×#67C22×D318yes—
319C2×#67C22×D318yescomplemented
320C22×Dic3—28no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—32no—
326C22×Dic3—32no—
327C22×Dic3—38no—
328C22×Dic3—38no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—62no—
332C22×Dic3—68no—
333C22×Dic3—124no—
334C22×Dic3—124no—
335C22×Dic3—128no—
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D312yes—
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D318yescomplemented
340#237—232no—
341D3×D4—232no—
342C2×D12—24no—
343C2×D12C22×D314yes—
344C2×C4×D3—24no—
345C2×C4×D3—24no—
346C2×C4×D3C22×D314yes—
347C2×C4×D3C22×D314yescomplemented
348C2×Dic6—24no—
349C2×Dic6C22×D314yescomplemented
350#217—38no—
351#217—38no—
352#217—38no—
353#217—34no—
354#217—34no—
355#217—38no—
356#217—38no—
357#217—38no—
358#217—68no—
359(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—38no—
365C4⋊Dic3—34no—
366C4⋊Dic3—34no—
367C4⋊Dic3—64no—
368Dic3⋊C4—38no—
369Dic3⋊C4—34no—
370Dic3⋊C4—34no—
371Dic3⋊C4—38no—
372C4×Dic3—34no—
373C4×Dic3—34no—
374C4×Dic3—64no—
375C22×C32—216no—
376C22×C32—24no—
377C22×C32—24no—
378C22×C32C22×D418yes—
379C22×C32C22×D412yes—
380C22×C32C2×#4112yes—
381C22×C32H(5,𝔽2)12yes—
382C22×C32C2511yescharacteristic
383C2×C3×D3—28no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—24no—
388C2×C3×D3—22no—
389C2×C3×D3—24no—
390C2×C3×D3—22no—
391C2×C3×D3—24no—
392C2×C3×D3—432no—
393C2×C3×D3—44no—
394C2×C3×D3—48no—
395C2×C3×D3C2×#4114yescomplemented
396C32×C4C22×D414yes—
397C3⋊Dic3—22no—
398C3⋊Dic3—22no—
399C3⋊Dic3—24no—
400C3×Dic3—24no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C25—32no—
404C2×#41—38no—
405C2×#41—68no—
406C22×Q8—31no—
407C22×D4—32no—
408C22×D4—32no—
409C22×D4—38no—
410C22×D4—31no—
411C22×D4—68no—
412C22×D4—91no—
413C22×D4—92no—
414C22×D4D3211yescharacteristic
415C23×C4—32no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—92no—
419#124—98no—
420#123—916no—
421C22⋊Q8—98no—
422#121—98no—
423#121—916no—
424#120—916no—
425C4×D4—98no—
426C4×D4—98no—
427C2×C4⋊C4—91no—
428C2×C4⋊C4—92no—
429C2×C4⋊C4—91no—
430C2×C22⋊C4—91no—
431C2×C22⋊C4—92no—
432C2×C22⋊C4—92no—
433C2×C22⋊C4—92no—
434C2×C22⋊C4—916no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C2×C42—91no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—21no—
445C23×C3—28no—
446C23×C3—34no—
447C23×C3—32no—
448C23×C3—34no—
449C23×C3—32no—
450C23×C3—44no—
451C23×C3—44no—
452C23×C3—616no—
453C23×C3—62no—
454C23×C3—62no—
455C23×C3—62no—
456C23×C3—62no—
457C23×C3—64no—
458C23×C3—64no—
459C23×C3—62no—
460C23×C3—616no—
461C23×C3—64no—
462C23×C3—128no—
463C23×C3—1232no—
464C23×C3C2×#6718yes—
465C23×C3C2×#6718yes—
466C23×C3C23×D314yes—
467C23×C3C23×D314yes—
468C23×C3C23×D311yescharacteristic
469C23×C3C23×D311yescharacteristic
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—24no—
473C22×D3—24no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—24no—
478C22×D3—216no—
479C22×D3—216no—
480C22×D3—48no—
481C22×D3—432no—
482C22×D3#23714yescomplemented
483C22×D3C23×D314yes—
484C22×D3C23×D312yes—
485C22×D3C23×D312yes—
486C3×Q8—68no—
487C3×D4—216no—
488C3×D4—616no—
489C3×D4—616no—
490C3×D4—68no—
491C3×D4C2×#67116yescomplemented
492C3×D4C2×#67116yescomplemented
493C2×C3×C4—22no—
494C2×C3×C4—24no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—34no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—64no—
501C2×C3×C4—616no—
502C2×C3×C4—68no—
503C2×C3×C4—68no—
504C2×C3×C4C2×#6714yes—
505C2×C3×C4C2×#6714yes—
506C2×C3×C4C23×D312yes—
507C2×C3×C4C23×D312yes—
508#67—216no—
509#67—216no—
510#67—68no—
511#67—68no—
512#67—128no—
513#67—128no—
514C2×Dic3—24no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—216no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—32no—
522C2×Dic3—34no—
523C2×Dic3—34no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—64no—
527C2×Dic3—64no—
528C2×Dic3—62no—
529C2×Dic3—62no—
530C2×Dic3—64no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—64no—
534C2×Dic3—122no—
535C2×Dic3—124no—
536C2×Dic3—128no—
537C2×Dic3—128no—
538C2×Dic3—1216no—
539C2×Dic3C23×D312yes—
540C2×Dic3C23×D314yes—
541C2×Dic3C23×D312yes—
542D12—28no—
543C4×D3—28no—
544C4×D3—28no—
545Dic6—28no—
546C2×C32—28no—
547C2×C32#54614yescomplemented
548C2×C32C23×D411yescharacteristic
549C2×C32C22×#4111yescharacteristic
550C2×C32C2×H(5,𝔽2)11yescharacteristic
551C3×D3—24no—
552C3×D3—42no—
553C3×D3—44no—
554C24—31no—
555C24—32no—
556C24—31no—
557C24—38no—
558C24—68no—
559C24—68no—
560C24—124no—
561C24C2×D3212yes—
562#41—632no—
563C2×Q8—34no—
564C2×Q8—64no—
565C2×D4—38no—
566C2×D4—38no—
567C2×D4—34no—
568C2×D4—68no—
569C2×D4—68no—
570C2×D4—632no—
571C2×D4—64no—
572C2×D4—94no—
573C2×D4—98no—
574C2×D4—184no—
575C2×D4—364no—
576C2×D4#62518yescomplemented
577C2×D4C2×D3214yes—
578C22×C4—38no—
579C22×C4—31no—
580C22×C4—32no—
581C22×C4—31no—
582C22×C4—34no—
583C22×C4—34no—
584C22×C4—68no—
585C22×C4—64no—
586C22×C4—64no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—92no—
590C22×C4—98no—
591C22×C4—364no—
592C22×C4C2×D3211yescharacteristic
593C4⋊C4—94no—
594C4⋊C4—98no—
595C4⋊C4—94no—
596C22⋊C4—94no—
597C22⋊C4—98no—
598C22⋊C4—98no—
599C22⋊C4—98no—
600C22⋊C4—94no—
601C22⋊C4—98no—
602C22⋊C4—98no—
603C42—94no—
604C22×C3—24no—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—216no—
609C22×C3—216no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—28no—
614C22×C3—21no—
615C22×C3—34no—
616C22×C3—44no—
617C22×C3—44no—
618C22×C3—416no—
619C22×C3—62no—
620C22×C3—62no—
621C22×C3—68no—
622C22×C3—62no—
623C22×C3—62no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—62no—
627C22×C3—64no—
628C22×C3—1232no—
629C22×C3—124no—
630C22×C3—128no—
631C22×C3C2×#23712yes—
632C22×C3#100412yes—
633C22×C3D3×#4112yes—
634C22×C3#100912yes—
635C22×C3C22×#6718yes—
636C22×C3C22×#6718yes—
637C22×C3C22×#6712yes—
638C22×C3C22×#6712yes—
639C22×C3C24×D311yescharacteristic
640C22×C3C24×D311yescharacteristic
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—28no—
644C2×D3—24no—
645C2×D3—24no—
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—24no—
650C2×D3—432no—
651C2×D3—48no—
652C2×D3—44no—
653C2×D3C2×#23714yescomplemented
654C3×C4—24no—
655C3×C4—62no—
656C3×C4—62no—
657C3×C4—64no—
658C3×C4C22×#6714yes—
659C3×C4C22×#6714yes—
660Dic3—24no—
661Dic3—22no—
662Dic3—22no—
663Dic3—64no—
664Dic3—62no—
665Dic3—62no—
666Dic3—64no—
667Dic3—62no—
668Dic3—62no—
669Dic3—64no—
670Dic3—124no—
671Dic3—122no—
672C32C2×#54611yescharacteristic, complemented, Sylow
673C23—24no—
674C23—24no—
675C23—34no—
676C23—32no—
677C23—34no—
678C23—32no—
679C23—616no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—64no—
684C23—62no—
685C23—64no—
686C23—62no—
687C23—616no—
688C23—64no—
689C23—128no—
690C23—1232no—
691C23C2×#62518yes—
692C23C22×D3214yes—
693C23C22×D3211yescharacteristic
694Q8—68no—
695D4—616no—
696D4—616no—
697D4—68no—
698D4—188no—
699D4—368no—
700D4C2×#625116yescomplemented
701C2×C4—32no—
702C2×C4—34no—
703C2×C4—32no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—64no—
707C2×C4—616no—
708C2×C4—68no—
709C2×C4—68no—
710C2×C4—92no—
711C2×C4—92no—
712C2×C4—94no—
713C2×C4—182no—
714C2×C4—182no—
715C2×C4—184no—
716C2×C4—368no—
717C2×C4C2×#62514yes—
718C2×C4C22×D3212yes—
719C2×C3—28no—
720C2×C3—28no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—24no—
725C2×C3—48no—
726C2×C3—64no—
727C2×C3—122no—
728C2×C3—124no—
729C2×C3#580614yescomplemented
730C2×C3#582914yescomplemented
731C2×C3C22×#23711yescharacteristic
732C2×C3C2×#100411yescharacteristic
733C2×C3C2×D3×#4111yescharacteristic
734C2×C3C2×#100911yescharacteristic
735C2×C3C23×#6711yescharacteristic
736C2×C3C23×#6711yescharacteristic
737D3—24no—
738D3—44no—
739D3—42no—
740C22—24no—
741C22—24no—
742C22—216no—
743C22—34no—
744C22—62no—
745C22—62no—
746C22—68no—
747C22—62no—
748C22—64no—
749C22—62no—
750C22—64no—
751C22—62no—
752C22—64no—
753C22—1232no—
754C22—128no—
755C22—124no—
756C22D3×#23712yes—
757C22#6431412yes—
758C22C22×#62518yes—
759C22C22×#62512yes—
760C22C23×D3211yescharacteristic
761C4—62no—
762C4—62no—
763C4—64no—
764C4—182no—
765C4—182no—
766C4—184no—
767C4C22×#62514yes—
768C3—21no—
769C3C2×#580611yescharacteristic, complemented
770C3C2×#582911yescharacteristic, complemented
771C2—28no—
772C2—64no—
773C2—124no—
774C2—122no—
775C2#1059524414yesdirect product factor
776C2C2×D3×#23711yescharacteristic
777C2C2×#6431411yescharacteristic
778C2C23×#62511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×C3×D3×D4C2semidirect
3. C2×D4×C3⋊Dic3C2semidirect
4. C2×#63980C2semidirect
5. C2×#63976C2semidirect
6. C2×#63961C2semidirect
7. C22×(C2×D3)⋊Dic3C2semidirect
8. #10595244C2direct (N × H)
9. C2×#63908C2semidirect
10. C2×C4×#625C2semidirect
11. C2×#63863C2semidirect
12. C2×#63856C2semidirect
17. C23×C3⋊Dic3C22semidirect
19. C22×C3×#67C22semidirect
20. C23×C3×Dic3C22semidirect
22. C2×C3×#237C22semidirect
24. C2×C3×D3×D4C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×Dic6C22semidirect
30. C22×#625C22semidirect
31. C2×#3757C22semidirect
32. D4×C3⋊Dic3C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. C2×C4×C3⋊Dic3C22semidirect
35. #63980C22semidirect
36. #63976C22semidirect
37. C2×#3724C22semidirect
38. C2×#3724C22semidirect
39. #63961C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. #63908C22semidirect
48. C4×#625C22semidirect
49. #63863C22semidirect
50. #63856C22semidirect
53. C22×#237D3semidirect
54. C22×D3×D4D3semidirect
84. C2×C32×D4D4semidirect
91. C22×C3⋊Dic3C23semidirect
95. C2×C3×#67C23semidirect
100. C22×C3×Dic3C23semidirect
108. C2×C3×C4×D3C23semidirect
110. C2×C3×Dic6C23semidirect
114. C2×#625C23semidirect
115. #3757C23semidirect
116. C4⋊(C3⋊Dic3)C23semidirect
117. C4×C3⋊Dic3C23semidirect
118. #3724C23semidirect
119. #3724C23semidirect
122. (C2×D3)⋊Dic3C23semidirect
123. (C2×D3)⋊Dic3C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
148. C22×#67C2×D3semidirect
152. C23×Dic3C2×D3semidirect
154. C2×#237C2×D3semidirect
156. C2×D3×D4C2×D3semidirect
159. C22×C4×D3C2×D3semidirect
160. C22×Dic6C2×D3semidirect
222. C22×C3×D3#41semidirect
226. C32×D4C2×D4semidirect
292. C2×C3×D4#67semidirect
293. C2×C3×D4#67semidirect
319. C2×#67C22×D3semidirect
339. C22×Dic3C22×D3semidirect
347. C2×C4×D3C22×D3semidirect
349. C2×Dic6C22×D3semidirect
395. C2×C3×D3C2×#41semidirect
482. C22×D3#237semidirect
491. C3×D4C2×#67semidirect
492. C3×D4C2×#67semidirect
547. C2×C32#546semidirect
576. C2×D4#625semidirect
653. C2×D3C2×#237semidirect
672. C32C2×#546semidirect
700. D4C2×#625semidirect
729. C2×C3#5806semidirect
730. C2×C3#5829semidirect
769. C3C2×#5806semidirect
770. C3C2×#5829semidirect
775. C2#10595244direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×C3×D3×D42
C2×D4×C3⋊Dic32
C2×#639802
C2×#639762
C2×#639612
C22×(C2×D3)⋊Dic32
#105952442
C2×#639082
C2×C4×#6252
C2×#638632
C2×#638562
C2×#58293
C2×#58063