Finite Group Databasebeta

← C2×#10594886 #11902435

Subgroups — C2×#10594886 #11902435

Order 1152.

3961 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
1C23×C3×D12C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64133C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63976C212yesmaximal, complemented
6C2×D3×#217C212yesmaximal, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8C2×Dic3×D12C211yesmaximal, characteristic, complemented
9C2×#63885C212yesmaximal, complemented
10#10594886C2116yesmaximal, direct product factor
11C2×#63884C212yesmaximal, complemented
12C2×#63860C211yesmaximal, characteristic, complemented
13C2×#5806—31nomaximal
14C2×#5550—31nomaximal
15C24×C3×D3C2212yes—
16C23×C32×C4C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C22×C3×#67C2211yescharacteristic
19C22×C3×D12—28no—
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2212yes—
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2218yescomplemented
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×#625C2212yescomplemented
26C22×#625C2212yescomplemented
27C22×D3×Dic3C2212yescomplemented
28C22×D3×Dic3C2212yescomplemented
29C2×#3795—28no—
30C2×#3795C2218yescomplemented
31C2×#3757C2212yes—
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33#64133C2218yescomplemented
34C2×#3750C2212yescomplemented
35C2×C3×#217C2211yescharacteristic
36C3×C4×#67C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×C4×Dic3C2211yescharacteristic, complemented
40#63976C22116yescomplemented
41D3×#217C22116yescomplemented
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43C2×(C2×D3)⋊Dic3C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46#63908C2218yescomplemented
47Dic3×D12C2218yescomplemented
48#63885C22116yescomplemented
49#63884C22116yescomplemented
50#63860C2218yescomplemented
51C23×C3×D4—31no—
52C22×#237—31no—
53C22×#235—31no—
54C23×D12D311yescharacteristic, complemented
55C2×C3×C4×D4—31no—
56C2×#953—32no—
57C22×#217—32no—
58#5806—316no—
59C2×#939—32no—
60C2×#938—31no—
61C2×#937—32no—
62C2×#936—31no—
63C2×#935—32no—
64C2×D4×Dic3—31no—
65C2×#930—31no—
66C2×C4×#67D311yescharacteristic, complemented
67C2×#924—31no—
68C2×#924—31no—
69C2×#924—61no—
70#5550—316no—
71C2×#894—32no—
72C2×#884—32no—
73C2×D3×C22⋊C4—32no—
74C2×#875—31no—
75C2×C4×D12—31no—
76C24×C32C2311yescharacteristic
77C23×C3×D3—28no—
78C23×C3×D3—28no—
79C23×C3×D3—44no—
80C23×C3×D3C2311yescharacteristic
81C23×C3×D3C2312yes—
82C23×C3×D3C2318yes—
83C23×C3×D3C2312yes—
84C22×C32×C4—24no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2312yes—
89C22×C3⋊Dic3C2312yes—
90C2×#634—24no—
91C2×#634C2314yescomplemented
92C2×C3×#67—24no—
93C2×C3×#67C2314yes—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C2×C3×D12—28no—
98C2×C3×D12—24no—
99C2×C3×D12—232no—
100C2×C3×D12D418yescomplemented
101C2×C3×D12C2314yes—
102C2×C3×D12C2318yes—
103C2×C3×D12C2314yes—
104C2×C3×C4×D3—24no—
105C2×C3×C4×D3C2314yescomplemented
106C2×#625—28no—
107C2×#625—44no—
108C2×#625C2318yescomplemented
109C2×#625C2318yescomplemented
110C2×D3×Dic3—28no—
111C2×D3×Dic3—44no—
112C2×D3×Dic3C2318yescomplemented
113C2×D3×Dic3C2318yescomplemented
114#3795—232no—
115#3757C2318yes—
116C4⋊(C3⋊Dic3)C2314yescomplemented
117#3750C2318yescomplemented
118C3×#217C2314yes—
119C3×(C2×D3)⋊C4C2314yescomplemented
120C3×Dic3⋊C4C2314yescomplemented
121C3×C4×Dic3C2314yescomplemented
122(C2×D3)⋊Dic3C2318yescomplemented
123(C2×D3)⋊Dic3C2318yescomplemented
124(C2×D3)⋊Dic3C2318yescomplemented
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C25×C3—32no—
128C24×D3C2×D312yes—
129C22×C3×D4—31no—
130C22×C3×D4—31no—
131C22×C3×D4—32no—
132C22×C3×D4—31no—
133C22×C3×D4—38no—
134C22×C3×D4—68no—
135C23×C3×C4—21no—
136C23×C3×C4—31no—
137C23×C3×C4C2×D311yescharacteristic
138C23×C3×C4C2×D311yescharacteristic
139C22×#67—32no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67C2×D311yescharacteristic
144C23×Dic3—32no—
145C23×Dic3—32no—
146C2×#237—38no—
147C2×#237—68no—
148C2×#235—38no—
149C2×#235—68no—
150C22×D12—28no—
151C22×D12C2×D311yescharacteristic
152C22×D12C2×D312yes—
153C22×D12C2×D311yescharacteristic
154C22×D12C2×D318yescomplemented
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3C2×D311yescharacteristic, complemented
158C22×Dic6—31no—
159C22×Dic6—31no—
160C22×Dic6—61no—
161C3×C4×D4—38no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C42—31no—
166#953—316no—
167C2×#217—32no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—32no—
171C2×#217—32no—
172C2×#217—32no—
173C2×#217—316no—
174C2×#217—62no—
175C2×#217C2×D311yescharacteristic
176#939—316no—
177#938—38no—
178#937—316no—
179#936—38no—
180#935—316no—
181D4×Dic3—38no—
182#930—38no—
183C4×#67C2×D318yescomplemented
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—61no—
192#924—38no—
193#924—38no—
194#924—68no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—62no—
198C2×Dic3⋊C4C2×D311yescharacteristic, complemented
199C2×C4×Dic3C2×D311yescharacteristic, complemented
200#894—316no—
201#884—316no—
202D3×C22⋊C4—316no—
203#875—38no—
204C4×D12—38no—
205C23×C32—22no—
206C23×C32—22no—
207C23×C32#4114yescomplemented
208C23×C32C2412yes—
209C23×C32C2411yescharacteristic
210C22×C3×D3—24no—
211C22×C3×D3—24no—
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—24no—
215C22×C3×D3—22no—
216C22×C3×D3—216no—
217C22×C3×D3—24no—
218C22×C3×D3—22no—
219C22×C3×D3—216no—
220C22×C3×D3—48no—
221C22×C3×D3—432no—
222C22×C3×D3C2×D418yes—
223C22×C3×D3C2414yes—
224C22×C3×D3C2412yes—
225C22×C3×D3C2414yes—
226C2×C32×C4—22no—
227C2×C32×C4—28no—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2412yes—
230C2×C32×C4C2412yes—
231C2×C3⋊Dic3—24no—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3C2414yes—
234C2×C3⋊Dic3C2414yes—
235#634—28no—
236C3×#67—28no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2412yes—
242C2×C3×Dic3C2412yes—
243C3×D12—216no—
244C3×D12—28no—
245C3×D12C2×D4116yescomplemented
246C3×C4×D3—28no—
247#625—216no—
248#625—48no—
249D3×Dic3—216no—
250D3×Dic3—48no—
251C22×#41—91no—
252C23×D4—31no—
253#546—916no—
254C2×#124—91no—
255C2×#123—92no—
256C2×C22⋊Q8—91no—
257C2×#121—92no—
258C2×#121—91no—
259C2×#120—92no—
260C2×C4×D4—31no—
261C2×C4×D4—91no—
262C22×C22⋊C4—92no—
263C24×C3—21no—
264C24×C3—32no—
265C24×C3—32no—
266C24×C3—31no—
267C24×C3—38no—
268C24×C3—68no—
269C24×C3—68no—
270C24×C3—124no—
271C24×C3C22×D311yescharacteristic
272C24×C3C22×D311yescharacteristic
273C23×D3—28no—
274C23×D3—28no—
275C23×D3—44no—
276C23×D3C22×D312yes—
277C23×D3C22×D311yescharacteristic
278C23×D3C22×D318yes—
279C23×D3C22×D312yes—
280C2×C3×D4—34no—
281C2×C3×D4—38no—
282C2×C3×D4—34no—
283C2×C3×D4—38no—
284C2×C3×D4—34no—
285C2×C3×D4—632no—
286C2×C3×D4—68no—
287C2×C3×D4—64no—
288C2×C3×D4—64no—
289C22×C3×C4—24no—
290C22×C3×C4—24no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—24no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—34no—
298C22×C3×C4—44no—
299C22×C3×C4—64no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D314yes—
303C22×C3×C4C22×D314yes—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—24no—
307C2×#67—38no—
308C2×#67—38no—
309C2×#67—38no—
310C2×#67—38no—
311C2×#67—68no—
312C2×#67—68no—
313C2×#67—124no—
314C2×#67—124no—
315C2×#67C22×D314yes—
316C22×Dic3—32no—
317C22×Dic3—32no—
318C22×Dic3—32no—
319C22×Dic3—32no—
320C22×Dic3—38no—
321C22×Dic3—38no—
322C22×Dic3—62no—
323C22×Dic3—62no—
324C22×Dic3—68no—
325C22×Dic3—124no—
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329#237—632no—
330#235—632no—
331C2×D12—28no—
332C2×D12—24no—
333C2×D12—232no—
334C2×D12#6718yescomplemented
335C2×D12C22×D314yes—
336C2×D12C22×D318yes—
337C2×D12C22×D314yes—
338C2×C4×D3—24no—
339C2×C4×D3—38no—
340C2×C4×D3—38no—
341C2×C4×D3—68no—
342C2×C4×D3—124no—
343C2×C4×D3C22×D314yescomplemented
344C2×Dic6—34no—
345C2×Dic6—34no—
346C2×Dic6—64no—
347C2×Dic6—64no—
348C2×Dic6—64no—
349C2×Dic6—124no—
350C3×C4⋊C4—34no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4—34no—
353C3×C42—34no—
354#217—38no—
355#217—38no—
356#217—38no—
357#217—38no—
358#217—38no—
359#217—38no—
360#217—68no—
361#217C22×D314yes—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4C22×D314yescomplemented
367C4⋊Dic3—34no—
368C4⋊Dic3—34no—
369C4⋊Dic3—64no—
370Dic3⋊C4—38no—
371Dic3⋊C4—38no—
372Dic3⋊C4—68no—
373Dic3⋊C4C22×D314yescomplemented
374C4×Dic3C22×D314yescomplemented
375C22×C32—28no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32C22×D412yes—
379C22×C32C2×#4112yes—
380C22×C32C2×#4114yescomplemented
381C22×C32H(5,𝔽2)12yes—
382C22×C32C2511yescharacteristic
383C2×C3×D3—216no—
384C2×C3×D3—24no—
385C2×C3×D3—24no—
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×D3C22×D418yes—
396C32×C4—22no—
397C32×C4C22×D414yes—
398C3⋊Dic3—24no—
399C3⋊Dic3—24no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C25—32no—
404C2×#41—98no—
405C2×#41—188no—
406C22×Q8—91no—
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—32no—
410C22×D4—31no—
411C22×D4—38no—
412C22×D4—68no—
413C22×D4—92no—
414C22×D4—92no—
415C23×C4—31no—
416C23×C4—92no—
417C23×C4—92no—
418C23×C4D3211yescharacteristic
419#124—98no—
420#123—916no—
421C22⋊Q8—98no—
422#121—916no—
423#121—98no—
424#120—916no—
425C4×D4—38no—
426C4×D4—98no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—91no—
429C2×C4⋊C4—92no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—916no—
433C2×C22⋊C4—92no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C2×C42—31no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—21no—
445C23×C3—24no—
446C23×C3—38no—
447C23×C3—34no—
448C23×C3—34no—
449C23×C3—32no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—616no—
453C23×C3—64no—
454C23×C3—64no—
455C23×C3—64no—
456C23×C3—616no—
457C23×C3—64no—
458C23×C3—62no—
459C23×C3—62no—
460C23×C3—64no—
461C23×C3—62no—
462C23×C3—128no—
463C23×C3—1232no—
464C23×C3#23514yescomplemented
465C23×C3#23714yescomplemented
466C23×C3C23×D312yes—
467C23×C3C23×D312yes—
468C23×C3C23×D311yescharacteristic
469C23×C3C23×D311yescharacteristic
470C22×D3—24no—
471C22×D3—24no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—24no—
475C22×D3—216no—
476C22×D3—24no—
477C22×D3—22no—
478C22×D3—24no—
479C22×D3—216no—
480C22×D3—48no—
481C22×D3—432no—
482C22×D3C2×#6718yes—
483C22×D3C23×D314yes—
484C22×D3C23×D312yes—
485C22×D3C23×D314yes—
486C3×D4—316no—
487C3×D4—616no—
488C3×D4—68no—
489C3×D4—68no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—28no—
493C2×C3×C4—28no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—24no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—48no—
501C2×C3×C4—42no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—68no—
506C2×C3×C4D3×D414yes—
507C2×C3×C4C2×#6714yes—
508C2×C3×C4C23×D312yes—
509C2×C3×C4C23×D312yes—
510C2×C3×C4C23×D312yes—
511C2×C3×C4C23×D312yes—
512#67—28no—
513#67—616no—
514#67—616no—
515#67—128no—
516#67—128no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—34no—
521C2×Dic3—34no—
522C2×Dic3—34no—
523C2×Dic3—34no—
524C2×Dic3—64no—
525C2×Dic3—64no—
526C2×Dic3—616no—
527C2×Dic3—64no—
528C2×Dic3—64no—
529C2×Dic3—64no—
530C2×Dic3—64no—
531C2×Dic3—124no—
532C2×Dic3—124no—
533C2×Dic3—128no—
534C2×Dic3C23×D312yes—
535C2×Dic3C23×D312yes—
536C2×Dic3C23×D312yes—
537D12—216no—
538D12—28no—
539D12C2×#67116yescomplemented
540C4×D3—28no—
541C4×D3—616no—
542C4×D3—128no—
543Dic6—68no—
544Dic6—68no—
545Dic6—128no—
546C2×C32—24no—
547C2×C32#54614yescomplemented
548C2×C32C23×D411yescharacteristic
549C2×C32C22×#4111yescharacteristic
550C2×C32C2×H(5,𝔽2)11yescharacteristic
551C3×D3—28no—
552C3×D3—42no—
553C3×D3—44no—
554C24—32no—
555C24—31no—
556C24—32no—
557C24—38no—
558C24—68no—
559C24—68no—
560C24—124no—
561C24C2×D3211yescharacteristic
562#41—1832no—
563C2×Q8—94no—
564C2×Q8—184no—
565C2×D4—34no—
566C2×D4—34no—
567C2×D4—38no—
568C2×D4—34no—
569C2×D4—38no—
570C2×D4—632no—
571C2×D4—68no—
572C2×D4—64no—
573C2×D4—64no—
574C2×D4—98no—
575C2×D4—98no—
576C2×D4—188no—
577C2×D4—364no—
578C22×C4—24no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—34no—
583C22×C4—64no—
584C22×C4—98no—
585C22×C4—98no—
586C22×C4—92no—
587C22×C4—92no—
588C22×C4—188no—
589C22×C4—364no—
590C22×C4C2×D3214yes—
591C22×C4C2×D3211yescharacteristic
592C22×C4C2×D3211yescharacteristic
593C4⋊C4—34no—
594C4⋊C4—94no—
595C4⋊C4—98no—
596C22⋊C4—34no—
597C22⋊C4—34no—
598C22⋊C4—98no—
599C22⋊C4—98no—
600C22⋊C4—98no—
601C22⋊C4—98no—
602C22⋊C4—98no—
603C42—34no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—28no—
609C22×C3—28no—
610C22×C3—22no—
611C22×C3—24no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—21no—
615C22×C3—38no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—48no—
619C22×C3—64no—
620C22×C3—64no—
621C22×C3—616no—
622C22×C3—64no—
623C22×C3—64no—
624C22×C3—62no—
625C22×C3—62no—
626C22×C3—64no—
627C22×C3—62no—
628C22×C3—1232no—
629C22×C3—128no—
630C22×C3—124no—
631C22×C3C2×#23512yes—
632C22×C3C2×#23514yescomplemented
633C22×C3C2×D3×D412yes—
634C22×C3C2×#23712yes—
635C22×C3C2×#23714yescomplemented
636C22×C3#100412yes—
637C22×C3#100912yes—
638C22×C3C22×#6712yes—
639C22×C3C24×D311yescharacteristic
640C22×C3C24×D311yescharacteristic
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—216no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—24no—
647C2×D3—24no—
648C2×D3—22no—
649C2×D3—24no—
650C2×D3—432no—
651C2×D3—44no—
652C2×D3—48no—
653C2×D3C22×#6718yes—
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—24no—
657C3×C4—42no—
658C3×C4—62no—
659C3×C4—62no—
660C3×C4—62no—
661C3×C4C2×D3×D414yes—
662C3×C4C22×#6714yes—
663Dic3—22no—
664Dic3—22no—
665Dic3—22no—
666Dic3—64no—
667Dic3—64no—
668Dic3—64no—
669Dic3—64no—
670Dic3—124no—
671Dic3—124no—
672C32C2×#54611yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—38no—
676C23—34no—
677C23—32no—
678C23—34no—
679C23—616no—
680C23—64no—
681C23—64no—
682C23—62no—
683C23—64no—
684C23—616no—
685C23—62no—
686C23—64no—
687C23—62no—
688C23—64no—
689C23—128no—
690C23—1232no—
691C23#379514yescomplemented
692C23C22×D3212yes—
693C23C22×D3211yescharacteristic
694Q8—188no—
695D4—316no—
696D4—616no—
697D4—68no—
698D4—68no—
699D4—1816no—
700D4—368no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—68no—
710C2×C4—94no—
711C2×C4—94no—
712C2×C4—1816no—
713C2×C4—184no—
714C2×C4—184no—
715C2×C4—368no—
716C2×C4D3×#6714yes—
717C2×C4C22×D3212yes—
718C2×C4C22×D3212yes—
719C2×C3—24no—
720C2×C3—24no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—24no—
724C2×C3—21no—
725C2×C3—44no—
726C2×C3—68no—
727C2×C3—124no—
728C2×C3—122no—
729C2×C3#555014yescomplemented
730C2×C3#580614yescomplemented
731C2×C3C22×#23511yescharacteristic
732C2×C3C22×D3×D411yescharacteristic
733C2×C3C22×#23711yescharacteristic
734C2×C3C2×#100411yescharacteristic
735C2×C3C2×#100911yescharacteristic
736C2×C3C23×#6711yescharacteristic
737D3—28no—
738D3—42no—
739D3—44no—
740C22—22no—
741C22—28no—
742C22—22no—
743C22—38no—
744C22—64no—
745C22—64no—
746C22—616no—
747C22—62no—
748C22—64no—
749C22—62no—
750C22—64no—
751C22—62no—
752C22—64no—
753C22—1232no—
754C22—128no—
755C22—124no—
756C22C2×#379512yes—
757C22C2×#379514yescomplemented
758C22#6430712yes—
759C22C2×D3×#6712yes—
760C22C23×D3211yescharacteristic
761C4—22no—
762C4—62no—
763C4—62no—
764C4—62no—
765C4—184no—
766C4—184no—
767C4C2×D3×#6714yes—
768C3—21no—
769C3C2×#555011yescharacteristic, complemented
770C3C2×#580611yescharacteristic, complemented
771C2—24no—
772C2—68no—
773C2—124no—
774C2—122no—
775C2#1059488614yesdirect product factor
776C2C22×#379511yescharacteristic
777C2C2×#6430711yescharacteristic
778C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#546
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×D12C2semidirect
2. C22×#3795C2semidirect
3. C2×#64133C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63976C2semidirect
6. C2×D3×#217C2semidirect
7. C2×#63908C2semidirect
8. C2×Dic3×D12C2semidirect
9. C2×#63885C2semidirect
10. #10594886C2direct (N × H)
11. C2×#63884C2semidirect
12. C2×#63860C2semidirect
17. C22×#634C22semidirect
23. C22×C3×D12C22semidirect
24. C22×C3×C4×D3C22semidirect
25. C22×#625C22semidirect
26. C22×#625C22semidirect
27. C22×D3×Dic3C22semidirect
28. C22×D3×Dic3C22semidirect
30. C2×#3795C22semidirect
32. C2×C4⋊(C3⋊Dic3)C22semidirect
33. #64133C22semidirect
34. C2×#3750C22semidirect
36. C3×C4×#67C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. #63976C22semidirect
41. D3×#217C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. #63908C22semidirect
47. Dic3×D12C22semidirect
48. #63885C22semidirect
49. #63884C22semidirect
50. #63860C22semidirect
54. C23×D12D3semidirect
66. C2×C4×#67D3semidirect
91. C2×#634C23semidirect
100. C2×C3×D12D4semidirect
105. C2×C3×C4×D3C23semidirect
108. C2×#625C23semidirect
109. C2×#625C23semidirect
112. C2×D3×Dic3C23semidirect
113. C2×D3×Dic3C23semidirect
116. C4⋊(C3⋊Dic3)C23semidirect
117. #3750C23semidirect
119. C3×(C2×D3)⋊C4C23semidirect
120. C3×Dic3⋊C4C23semidirect
121. C3×C4×Dic3C23semidirect
122. (C2×D3)⋊Dic3C23semidirect
123. (C2×D3)⋊Dic3C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
154. C22×D12C2×D3semidirect
157. C22×C4×D3C2×D3semidirect
183. C4×#67C2×D3semidirect
188. C2×(C2×D3)⋊C4C2×D3semidirect
198. C2×Dic3⋊C4C2×D3semidirect
199. C2×C4×Dic3C2×D3semidirect
207. C23×C32#41semidirect
245. C3×D12C2×D4semidirect
334. C2×D12#67semidirect
343. C2×C4×D3C22×D3semidirect
366. (C2×D3)⋊C4C22×D3semidirect
373. Dic3⋊C4C22×D3semidirect
374. C4×Dic3C22×D3semidirect
380. C22×C32C2×#41semidirect
464. C23×C3#235semidirect
465. C23×C3#237semidirect
539. D12C2×#67semidirect
547. C2×C32#546semidirect
632. C22×C3C2×#235semidirect
635. C22×C3C2×#237semidirect
672. C32C2×#546semidirect
691. C23#3795semidirect
729. C2×C3#5550semidirect
730. C2×C3#5806semidirect
757. C22C2×#3795semidirect
769. C3C2×#5550semidirect
770. C3C2×#5806semidirect
775. C2#10594886direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D122
C22×#37952
C2×#641332
C2×C3×C4×#672
C2×#639762
C2×D3×#2172
C2×#639082
C2×Dic3×D122
C2×#638852
#105948862
C2×#638842
C2×#638602
C2×#58063
C2×#55503