Finite Group Databasebeta

← C2×#10595067 #11902464

Subgroups — C2×#10595067 #11902464

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×D3×D12C211yesmaximal, characteristic, complemented
3C2×#64139C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63983C212yesmaximal, complemented
6C2×#63971C212yesmaximal, complemented
7#10595067C2116yesmaximal, direct product factor
8C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
9C2×Dic3×D12C211yesmaximal, characteristic, complemented
10C2×#63864C211yesmaximal, characteristic, complemented
11C2×#63856C211yesmaximal, characteristic, complemented
12C2×#63850C212yesmaximal, complemented
13C2×#5829—31nomaximal
14C2×#5550—31nomaximal
15C23×D32C2212yes—
16C23×C32×C4C2211yescharacteristic, complemented
17C22×#638C2212yescomplemented
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2212yescomplemented
21C2×C3×#235—28no—
22C2×C3×#235C2218yescomplemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2212yescomplemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#626C2212yes—
28C22×D3×Dic3C2212yescomplemented
29C2×D3×D12—28no—
30C2×D3×D12C2218yescomplemented
31#64139C2218yescomplemented
32C2×#3752C2212yescomplemented
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C2×C3×#217C2211yescharacteristic, complemented
35C3×C4×#67C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×C4×Dic3C2211yescharacteristic, complemented
39#63983C22116yescomplemented
40#63971C22116yescomplemented
41C2×#3724C2212yescomplemented
42C2×#3722C2212yescomplemented
43C2×#3722C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46D3×(C2×D3)⋊C4C22116yescomplemented
47Dic3×D12C2218yescomplemented
48#63864C2218yescomplemented
49#63856C2218yescomplemented
50#63850C22116yescomplemented
51C22×C3×#41—31no—
52C22×D3×D4—31no—
53C22×#235D311yescharacteristic, complemented
54C23×D12—31no—
55C2×C3×C4×D4—31no—
56#5829—316no—
57C2×#947—31no—
58C2×#946—31no—
59C2×#939—32no—
60C2×#937—32no—
61C2×#937—32no—
62C2×D4×Dic3—31no—
63C2×#930—31no—
64C2×#930—31no—
65C2×#930—61no—
66C2×#929—32no—
67C2×C4×#67D311yescharacteristic, complemented
68C22×(C2×D3)⋊C4—32no—
69C2×#924—31no—
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⋊D3C2312yes—
78C23×C3×D3C2312yes—
79C23×C3×D3C2311yescharacteristic
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C22×C32×C4—24no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2314yescomplemented
88C2×#638—44no—
89C2×#638C2318yescomplemented
90C22×C3⋊Dic3C2312yes—
91C2×C4⋊(C3⋊D3)—24no—
92C2×C4⋊(C3⋊D3)C2314yes—
93C2×C3×#67—28no—
94C2×C3×#67—24no—
95C2×C3×#67C2314yes—
96C2×C3×#67C2318yescomplemented
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2312yes—
101C3×#235—232no—
102C2×C3×D12D418yescomplemented
103C2×C3×D12C2314yes—
104C2×C3×C4×D3—28no—
105C2×C3×C4×D3—24no—
106C2×C3×C4×D3C2314yes—
107C2×C3×C4×D3C2318yescomplemented
108C2×C3×Dic6—24no—
109C2×C3×Dic6C2314yescomplemented
110C2×#626—28no—
111C2×#626C2318yes—
112C2×D3×Dic3—44no—
113C2×D3×Dic3C2318yescomplemented
114D3×D12—232no—
115#3752C2318yescomplemented
116C4⋊(C3⋊Dic3)C2314yescomplemented
117C3×#217C2314yescomplemented
118C3×(C2×D3)⋊C4C2314yes—
119C3×Dic3⋊C4C2314yescomplemented
120C3×C4×Dic3C2314yescomplemented
121#3724C2318yescomplemented
122#3722C2318yescomplemented
123#3722C2318yescomplemented
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C2×C3×#41—38no—
130C2×C3×#41—68no—
131C22×C3×Q8—31no—
132C22×C3×D4—32no—
133C22×C3×D4—31no—
134C22×C3×D4—31no—
135C23×C3×C4—21no—
136C23×C3×C4—31no—
137C23×C3×C4—32no—
138C23×C3×C4C2×D311yescharacteristic, complemented
139C23×C3×C4C2×D311yescharacteristic, complemented
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—62no—
144C22×#67C2×D311yescharacteristic
145C22×#67C2×D312yescomplemented
146C23×Dic3—32no—
147C2×D3×D4—38no—
148C2×D3×D4—68no—
149C2×#235—28no—
150C2×#235C2×D318yescomplemented
151C22×D12—32no—
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—38no—
155C22×D12—61no—
156C22×D12—68no—
157C22×D12C2×D311yescharacteristic
158C22×C4×D3—32no—
159C22×C4×D3C2×D311yescharacteristic
160C22×C4×D3C2×D312yescomplemented
161C22×Dic6C2×D311yescharacteristic, complemented
162C3×C4×D4—38no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C42—31no—
167C2×#217—32no—
168C2×#217—32no—
169C2×#217C2×D311yescharacteristic, complemented
170#947—38no—
171#946—38no—
172#939—316no—
173#937—316no—
174#937—316no—
175D4×Dic3—38no—
176#930—38no—
177#930—38no—
178#930—68no—
179#929—316no—
180C4×#67C2×D318yescomplemented
181C2×(C2×D3)⋊C4—32no—
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—32no—
189C2×(C2×D3)⋊C4—316no—
190C2×(C2×D3)⋊C4—62no—
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—61no—
195#924—38no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—32no—
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—22no—
208C23×C32C2412yes—
209C23×C32C2411yescharacteristic
210C22×C3⋊D3—24no—
211C22×C3⋊D3—24no—
212C22×C3⋊D3—24no—
213C22×C3⋊D3C2414yes—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3C2×D418yes—
219C22×C3×D3#4114yescomplemented
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C2×D32—216no—
223C2×D32—216no—
224C2×D32—48no—
225C2×D32—432no—
226C2×C32×C4—22no—
227C2×C32×C4—28no—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2412yes—
230C2×C32×C4C2412yes—
231#638—48no—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3C2414yes—
234C4⋊(C3⋊D3)—28no—
235C3×#67—216no—
236C3×#67—28no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3C2414yes—
242C2×C3×Dic3C2412yes—
243C2×C3×Dic3C2412yes—
244C2×C3×Dic3C2412yes—
245C3×D12C2×D4116yescomplemented
246C3×C4×D3—216no—
247C3×C4×D3—28no—
248C3×Dic6—28no—
249#626—216no—
250D3×Dic3—48no—
251C22×#41—31no—
252C23×D4—91no—
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—31no—
265C24×C3—32no—
266C24×C3C22×D311yescharacteristic
267C24×C3C22×D311yescharacteristic
268C23×D3—32no—
269C23×D3—32no—
270C23×D3—38no—
271C23×D3—38no—
272C23×D3—62no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—68no—
276C23×D3—68no—
277C23×D3—124no—
278C23×D3—124no—
279C23×D3C22×D311yescharacteristic
280C23×D3C22×D312yes—
281C3×#41—632no—
282C2×C3×Q8—34no—
283C2×C3×Q8—64no—
284C2×C3×D4—34no—
285C2×C3×D4—38no—
286C2×C3×D4—38no—
287C2×C3×D4—34no—
288C2×C3×D4—64no—
289C2×C3×D4—68no—
290C22×C3×C4—24no—
291C22×C3×C4—24no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—24no—
295C22×C3×C4—31no—
296C22×C3×C4—32no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—34no—
300C22×C3×C4—38no—
301C22×C3×C4—44no—
302C22×C3×C4—68no—
303C22×C3×C4—64no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D314yescomplemented
309C22×C3×C4C22×D314yescomplemented
310C2×#67—24no—
311C2×#67—28no—
312C2×#67—38no—
313C2×#67—38no—
314C2×#67—38no—
315C2×#67—68no—
316C2×#67—68no—
317C2×#67—124no—
318C2×#67—124no—
319C2×#67—128no—
320C2×#67C22×D314yes—
321C2×#67C22×D318yescomplemented
322C22×Dic3—32no—
323C22×Dic3—32no—
324C22×Dic3—38no—
325C22×Dic3—62no—
326C22×Dic3—124no—
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D312yes—
331D3×D4—632no—
332#235—232no—
333C2×D12—38no—
334C2×D12—34no—
335C2×D12—34no—
336C2×D12—64no—
337C2×D12—68no—
338C2×D12—64no—
339C2×D12—64no—
340C2×D12—632no—
341C2×D12—124no—
342C2×D12#6718yescomplemented
343C2×D12C22×D314yes—
344C2×C4×D3—28no—
345C2×C4×D3—24no—
346C2×C4×D3—38no—
347C2×C4×D3—124no—
348C2×C4×D3C22×D314yes—
349C2×C4×D3C22×D318yescomplemented
350C2×Dic6—24no—
351C2×Dic6C22×D314yescomplemented
352C3×C4⋊C4—34no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—34no—
355C3×C42—34no—
356#217—38no—
357#217—38no—
358#217C22×D314yescomplemented
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—38no—
366(C2×D3)⋊C4—38no—
367(C2×D3)⋊C4—68no—
368(C2×D3)⋊C4C22×D314yes—
369C4⋊Dic3—34no—
370C4⋊Dic3—34no—
371C4⋊Dic3—64no—
372Dic3⋊C4—38no—
373Dic3⋊C4—38no—
374Dic3⋊C4C22×D314yescomplemented
375C4×Dic3C22×D314yescomplemented
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—22no—
379C22×C32—44no—
380C22×C32C22×D412yes—
381C22×C32C2×#4112yes—
382C22×C32H(5,𝔽2)12yes—
383C22×C32C2511yescharacteristic
384C2×C3⋊D3—24no—
385C2×C3⋊D3—24no—
386C2×C3⋊D3—24no—
387C2×C3⋊D3—48no—
388C2×C3×D3—28no—
389C2×C3×D3—216no—
390C2×C3×D3—22no—
391C2×C3×D3—24no—
392C2×C3×D3—24no—
393C2×C3×D3—22no—
394C2×C3×D3C22×D418yes—
395C2×C3×D3C2×#4114yescomplemented
396D32—432no—
397C32×C4—22no—
398C32×C4C22×D414yes—
399C3⋊Dic3—24no—
400C3×Dic3—22no—
401C3×Dic3—24no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C25—92no—
405C2×#41—38no—
406C2×#41—68no—
407C22×Q8—31no—
408C22×D4—31no—
409C22×D4—32no—
410C22×D4—31no—
411C22×D4—98no—
412C22×D4—92no—
413C22×D4—92no—
414C22×D4—91no—
415C22×D4—188no—
416C23×C4—32no—
417C23×C4—31no—
418C23×C4—92no—
419C23×C4D3211yescharacteristic, complemented
420#124—98no—
421#123—916no—
422C22⋊Q8—98no—
423#121—916no—
424#121—98no—
425#120—916no—
426C4×D4—38no—
427C4×D4—98no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—92no—
430C2×C4⋊C4—91no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—916no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C2×C22⋊C4—92no—
439C2×C42—31no—
440C23×C3—24no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—21no—
449C23×C3—38no—
450C23×C3—34no—
451C23×C3—32no—
452C23×C3—34no—
453C23×C3—42no—
454C23×C3—42no—
455C23×C3—64no—
456C23×C3—64no—
457C23×C3—62no—
458C23×C3—62no—
459C23×C3C23×D312yes—
460C23×C3C23×D312yes—
461C23×C3C23×D311yescharacteristic
462C23×C3C23×D311yescharacteristic
463C22×D3—22no—
464C22×D3—24no—
465C22×D3—24no—
466C22×D3—22no—
467C22×D3—34no—
468C22×D3—34no—
469C22×D3—64no—
470C22×D3—616no—
471C22×D3—616no—
472C22×D3—64no—
473C22×D3—64no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—64no—
478C22×D3—616no—
479C22×D3—616no—
480C22×D3—124no—
481C22×D3—124no—
482C22×D3—124no—
483C22×D3—128no—
484C22×D3—128no—
485C22×D3—1232no—
486C22×D3—1232no—
487C22×D3#23514yescomplemented
488C22×D3C2×#6718yes—
489C22×D3C23×D312yes—
490C22×D3C23×D314yes—
491C3×Q8—68no—
492C3×D4—316no—
493C3×D4—68no—
494C3×D4—616no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—28no—
498C2×C3×C4—28no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—24no—
502C2×C3×C4—32no—
503C2×C3×C4—34no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—48no—
507C2×C3×C4—42no—
508C2×C3×C4—616no—
509C2×C3×C4—64no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—68no—
514C2×C3×C4D3×D414yes—
515C2×C3×C4C2×#6714yes—
516C2×C3×C4C23×D312yes—
517C2×C3×C4C23×D312yes—
518C2×C3×C4C23×D312yes—
519C2×C3×C4C23×D312yes—
520#67—28no—
521#67—216no—
522#67—616no—
523#67—128no—
524#67—128no—
525#67—1216no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—24no—
530C2×Dic3—34no—
531C2×Dic3—34no—
532C2×Dic3—64no—
533C2×Dic3—64no—
534C2×Dic3—64no—
535C2×Dic3—124no—
536C2×Dic3—128no—
537C2×Dic3C23×D312yes—
538C2×Dic3C23×D312yes—
539C2×Dic3C23×D312yes—
540C2×Dic3C23×D314yes—
541D12—616no—
542D12—68no—
543D12—68no—
544D12—128no—
545D12C2×#67116yescomplemented
546C4×D3—216no—
547C4×D3—28no—
548C4×D3—128no—
549Dic6—28no—
550C2×C32—42no—
551C2×C32#54614yescomplemented
552C2×C32C23×D411yescharacteristic
553C2×C32C22×#4111yescharacteristic
554C2×C32C2×H(5,𝔽2)11yescharacteristic
555C3⋊D3—44no—
556C3×D3—24no—
557C3×D3—28no—
558C24—31no—
559C24—32no—
560C24—98no—
561C24—92no—
562C24—188no—
563C24—188no—
564C24—364no—
565C24C2×D3211yescharacteristic
566#41—632no—
567C2×Q8—34no—
568C2×Q8—64no—
569C2×D4—34no—
570C2×D4—38no—
571C2×D4—34no—
572C2×D4—38no—
573C2×D4—68no—
574C2×D4—64no—
575C2×D4—98no—
576C2×D4—98no—
577C2×D4—94no—
578C2×D4—1832no—
579C2×D4—188no—
580C2×D4—184no—
581C2×D4—364no—
582C22×C4—24no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—32no—
587C22×C4—38no—
588C22×C4—34no—
589C22×C4—68no—
590C22×C4—64no—
591C22×C4—98no—
592C22×C4—92no—
593C22×C4—364no—
594C22×C4C2×D3211yescharacteristic
595C22×C4C2×D3211yescharacteristic
596C22×C4C2×D3214yescomplemented
597C4⋊C4—34no—
598C4⋊C4—98no—
599C4⋊C4—94no—
600C22⋊C4—34no—
601C22⋊C4—34no—
602C22⋊C4—98no—
603C22⋊C4—98no—
604C22⋊C4—98no—
605C22⋊C4—98no—
606C22⋊C4—98no—
607C42—34no—
608C22×C3—24no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—38no—
620C22×C3—34no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—48no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—62no—
629C22×C3—62no—
630C22×C3—616no—
631C22×C3—68no—
632C22×C3C2×#23512yes—
633C22×C3C2×D3×D412yes—
634C22×C3D3×#4112yes—
635C22×C3#100912yes—
636C22×C3#100912yes—
637C22×C3C22×#6712yes—
638C22×C3C24×D311yescharacteristic
639C22×C3C24×D311yescharacteristic
640C2×D3—22no—
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—22no—
644C2×D3—28no—
645C2×D3—216no—
646C2×D3—64no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—64no—
650C2×D3—64no—
651C2×D3—64no—
652C2×D3—124no—
653C2×D3—124no—
654C2×D3—124no—
655C2×D3—1232no—
656C2×D3—1232no—
657C2×D3—128no—
658C2×D3—128no—
659C2×D3—248no—
660C2×D3C2×#23514yescomplemented
661C2×D3C22×#6718yes—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—24no—
665C3×C4—42no—
666C3×C4—64no—
667C3×C4—62no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4C2×D3×D414yes—
671C3×C4C22×#6714yes—
672Dic3—22no—
673Dic3—22no—
674Dic3—22no—
675Dic3—24no—
676Dic3—64no—
677Dic3—64no—
678Dic3—124no—
679C32C2×#54611yescharacteristic, complemented, Sylow
680C23—22no—
681C23—22no—
682C23—22no—
683C23—34no—
684C23—38no—
685C23—32no—
686C23—34no—
687C23—64no—
688C23—64no—
689C23—62no—
690C23—62no—
691C23—94no—
692C23—1816no—
693C23—1816no—
694C23—184no—
695C23—184no—
696C23—184no—
697C23—368no—
698C23—3632no—
699C23C22×D3212yes—
700C23C22×D3211yescharacteristic
701Q8—68no—
702D4—316no—
703D4—616no—
704D4—68no—
705D4—1816no—
706D4—188no—
707D4—368no—
708C2×C4—22no—
709C2×C4—28no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—34no—
714C2×C4—616no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—64no—
718C2×C4—62no—
719C2×C4—68no—
720C2×C4—94no—
721C2×C4—184no—
722C2×C4—368no—
723C2×C4D3×#6714yes—
724C2×C4C22×D3212yes—
725C2×C4C22×D3212yes—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—24no—
730C2×C3—44no—
731C2×C3—42no—
732C2×C3—42no—
733C2×C3—68no—
734C2×C3—64no—
735C2×C3#555014yescomplemented
736C2×C3#582914yescomplemented
737C2×C3C22×#23511yescharacteristic
738C2×C3C22×D3×D411yescharacteristic
739C2×C3C2×D3×#4111yescharacteristic
740C2×C3C2×#100911yescharacteristic
741C2×C3C2×#100911yescharacteristic
742C2×C3C23×#6711yescharacteristic
743D3—24no—
744D3—28no—
745D3—124no—
746D3—124no—
747D3—244no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—34no—
752C22—38no—
753C22—44no—
754C22—64no—
755C22—64no—
756C22—62no—
757C22—62no—
758C22—68no—
759C22—616no—
760C22—184no—
761C22—184no—
762C22—184no—
763C22—3632no—
764C22—368no—
765C22D3×#23512yes—
766C22#6430812yes—
767C22C2×D3×#6712yes—
768C22C23×D3211yescharacteristic
769C4—22no—
770C4—62no—
771C4—62no—
772C4—64no—
773C4—62no—
774C4—184no—
775C4C2×D3×#6714yes—
776C3—21no—
777C3C2×#555011yescharacteristic, complemented
778C3C2×#582911yescharacteristic, complemented
779C2—42no—
780C2—64no—
781C2—68no—
782C2—364no—
783C2#1059506714yesdirect product factor
784C2C2×D3×#23511yescharacteristic
785C2C2×#6430811yescharacteristic
786C2C22×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. C22×C3×#235C2semidirect
2. C22×D3×D12C2semidirect
3. C2×#64139C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63983C2semidirect
6. C2×#63971C2semidirect
7. #10595067C2direct (N × H)
8. C2×D3×(C2×D3)⋊C4C2semidirect
9. C2×Dic3×D12C2semidirect
10. C2×#63864C2semidirect
11. C2×#63856C2semidirect
12. C2×#63850C2semidirect
16. C23×C32×C4C22semidirect
17. C22×#638C22semidirect
20. C22×C3×#67C22semidirect
22. C2×C3×#235C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C22×C3×Dic6C22semidirect
28. C22×D3×Dic3C22semidirect
30. C2×D3×D12C22semidirect
31. #64139C22semidirect
32. C2×#3752C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. C2×C3×#217C22semidirect
35. C3×C4×#67C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×C4×Dic3C22semidirect
39. #63983C22semidirect
40. #63971C22semidirect
41. C2×#3724C22semidirect
42. C2×#3722C22semidirect
43. C2×#3722C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. D3×(C2×D3)⋊C4C22semidirect
47. Dic3×D12C22semidirect
48. #63864C22semidirect
49. #63856C22semidirect
50. #63850C22semidirect
53. C22×#235D3semidirect
67. C2×C4×#67D3semidirect
87. C22×C32×C4C23semidirect
89. C2×#638C23semidirect
96. C2×C3×#67C23semidirect
102. C2×C3×D12D4semidirect
107. C2×C3×C4×D3C23semidirect
109. C2×C3×Dic6C23semidirect
113. C2×D3×Dic3C23semidirect
115. #3752C23semidirect
116. C4⋊(C3⋊Dic3)C23semidirect
117. C3×#217C23semidirect
119. C3×Dic3⋊C4C23semidirect
120. C3×C4×Dic3C23semidirect
121. #3724C23semidirect
122. #3722C23semidirect
123. #3722C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
138. C23×C3×C4C2×D3semidirect
139. C23×C3×C4C2×D3semidirect
145. C22×#67C2×D3semidirect
150. C2×#235C2×D3semidirect
160. C22×C4×D3C2×D3semidirect
161. C22×Dic6C2×D3semidirect
169. C2×#217C2×D3semidirect
180. C4×#67C2×D3semidirect
198. C2×Dic3⋊C4C2×D3semidirect
199. C2×C4×Dic3C2×D3semidirect
219. C22×C3×D3#41semidirect
245. C3×D12C2×D4semidirect
308. C22×C3×C4C22×D3semidirect
309. C22×C3×C4C22×D3semidirect
321. C2×#67C22×D3semidirect
342. C2×D12#67semidirect
349. C2×C4×D3C22×D3semidirect
351. C2×Dic6C22×D3semidirect
358. #217C22×D3semidirect
374. Dic3⋊C4C22×D3semidirect
375. C4×Dic3C22×D3semidirect
395. C2×C3×D3C2×#41semidirect
419. C23×C4D32semidirect
487. C22×D3#235semidirect
545. D12C2×#67semidirect
551. C2×C32#546semidirect
596. C22×C4C2×D32semidirect
660. C2×D3C2×#235semidirect
679. C32C2×#546semidirect
735. C2×C3#5550semidirect
736. C2×C3#5829semidirect
777. C3C2×#5550semidirect
778. C3C2×#5829semidirect
783. C2#10595067direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×D3×D122
C2×#641392
C2×C3×C4×#672
C2×#639832
C2×#639712
#105950672
C2×D3×(C2×D3)⋊C42
C2×Dic3×D122
C2×#638642
C2×#638562
C2×#638502
C2×#58293
C2×#55503