Finite Group Databasebeta

← C2×#10595424 #11900467

Subgroups — C2×#10595424 #11900467

Order 1152.

3921 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×#239C211yesmaximal, characteristic, complemented
2C22×C4×D32C211yesmaximal, characteristic, complemented
3C2×#64155C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5#10595424C2116yesmaximal, direct product factor
6C2×#63922C212yesmaximal, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63908C211yesmaximal, characteristic, complemented
9C2×#63904C212yesmaximal, complemented
10C2×#63884C212yesmaximal, complemented
11C2×#63879C212yesmaximal, complemented
12C2×#63841C211yesmaximal, characteristic, complemented
13C2×#5828—31nomaximal
14C2×#5627—31nomaximal
15C23×D32C2211yescharacteristic
16C22×C32×Q8C2211yescharacteristic, complemented
17C22×C4×C3⋊D3C2211yescharacteristic
18C2×C3×#239—28no—
19C2×C3×#239C2218yescomplemented
20C22×C3×D12C2212yes—
21C22×C3×D12C2211yescharacteristic, complemented
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2212yescomplemented
25C22×#626C2212yes—
26C22×#625C2212yes—
27C22×#624C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C2×C4×D32—28no—
31C2×C4×D32C2218yescomplemented
32#64155C2218yescomplemented
33C2×#3752C2212yes—
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C2×#3750C2212yescomplemented
36C3×#946C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4C2212yescomplemented
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2212yescomplemented
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43C2×Dic32C2212yescomplemented
44#63922C22116yescomplemented
45#63916C2218yescomplemented
46#63908C2218yescomplemented
47#63904C22116yescomplemented
48#63884C22116yescomplemented
49#63879C22116yescomplemented
50#63841C2218yescomplemented
51C22×C3×#41—31no—
52C22×#239D311yescharacteristic, complemented
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C2×C3×C22⋊Q8—31no—
56#5828—316no—
57C2×#946—31no—
58C2×#946—31no—
59C2×#946—61no—
60C2×#946D311yescharacteristic, complemented
61C2×#938—31no—
62C2×#938—31no—
63C2×#937—32no—
64C2×#935—32no—
65C2×#930—31no—
66C2×C4×#67—32no—
67C2×C4×#67—32no—
68C2×#926—31no—
69#5627—316no—
70C2×#895—31no—
71C2×#894—32no—
72C2×#893—32no—
73C2×#892—31no—
74C2×#882—32no—
75C2×#67⋊C4—32no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×D32—24no—
81C22×D32—24no—
82C22×D32—24no—
83C22×D32C2314yes—
84C2×C32×Q8—24no—
85C2×C32×Q8C2314yescomplemented
86C22×C32×C4C2312yes—
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2312yes—
90C2×C4×C3⋊D3—24no—
91C2×C4×C3⋊D3C2314yes—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C3×#239—232no—
96C2×C3×D12—28no—
97C2×C3×D12—24no—
98C2×C3×D12C2318yes—
99C2×C3×D12C2314yescomplemented
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3—28no—
102C2×C3×C4×D3D418yescomplemented
103C2×C3×C4×D3C2314yes—
104C2×C3×C4×D3C2314yes—
105C2×C3×C4×D3C2318yescomplemented
106C2×#626—28no—
107C2×#626C2318yes—
108C2×#625—28no—
109C2×#625C2318yes—
110C2×#624—24no—
111C2×#624C2314yes—
112C2×D3×Dic3—24no—
113C2×D3×Dic3—24no—
114C2×D3×Dic3C2314yes—
115C2×D3×Dic3C2314yes—
116C4×D32—232no—
117#3752C2318yes—
118C4⋊(C3⋊Dic3)C2314yescomplemented
119#3750C2318yescomplemented
120C3×(C2×D3)⋊C4C2318yes—
121C3×C4⋊Dic3C2314yescomplemented
122C3×Dic3⋊C4C2318yescomplemented
123(C2×D3)⋊Dic3C2318yes—
124(C2×D3)⋊Dic3C2318yescomplemented
125(C2×D3)⋊Dic3C2318yescomplemented
126Dic32C2318yescomplemented
127C2×#525—91noSylow
128C24×D3—31no—
129C24×D3—31no—
130C2×C3×#41—38no—
131C2×C3×#41—68no—
132C22×C3×Q8—21no—
133C22×C3×Q8C2×D311yescharacteristic, complemented
134C22×C3×Q8C2×D311yescharacteristic, complemented
135C22×C3×D4—32no—
136C22×C3×D4—31no—
137C23×C3×C4—31no—
138C23×C3×C4—31no—
139C23×C3×C4—32no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—32no—
143C23×Dic3—31no—
144C23×Dic3—31no—
145C2×#239—28no—
146C2×#239C2×D318yescomplemented
147C22×D12—32no—
148C22×D12C2×D312yes—
149C22×D12C2×D311yescharacteristic, complemented
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—38no—
157C22×C4×D3—38no—
158C22×C4×D3—61no—
159C22×C4×D3—68no—
160C22×C4×D3—68no—
161C22×C4×D3C2×D311yescharacteristic
162C22×C4×D3C2×D311yescharacteristic
163C22×C4×D3C2×D312yescomplemented
164C3×C22⋊Q8—38no—
165C2×C3×C4⋊C4—32no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—32no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—32no—
171#946—38no—
172#946—38no—
173#946—68no—
174#946C2×D318yescomplemented
175#938—38no—
176#938—38no—
177#937—316no—
178#935—316no—
179#930—38no—
180C4×#67—316no—
181C4×#67—316no—
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—62no—
188C2×(C2×D3)⋊C4C2×D312yes—
189#926—38no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—61no—
193C2×C4⋊Dic3C2×D311yescharacteristic, complemented
194C2×Dic3⋊C4—32no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—62no—
197C2×Dic3⋊C4C2×D312yescomplemented
198C2×C4×Dic3—32no—
199C2×C4×Dic3—32no—
200#895—38no—
201#894—316no—
202#893—316no—
203#892—38no—
204#882—316no—
205#67⋊C4—316no—
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—22no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3#4114yescomplemented
210C22×C3⋊D3C2412yes—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—24no—
217C22×C3×D3—24no—
218C22×C3×D3C2×D414yes—
219C22×C3×D3#4114yescomplemented
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C22×C3×D3C2412yes—
223C2×D32—232no—
224C2×D32—28no—
225C2×D32—28no—
226C2×D32—28no—
227C32×Q8—28no—
228C2×C32×C4—24no—
229C2×C32×C4C2×D414yes—
230C2×C32×C4C2414yes—
231C2×C32×C4C2412yes—
232C2×C3⋊Dic3—22no—
233C2×C3⋊Dic3—24no—
234C2×C3⋊Dic3C2414yes—
235C2×C3⋊Dic3C2412yes—
236C4×C3⋊D3—28no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3C2×D414yes—
240C2×C3×Dic3C2414yes—
241C2×C3×Dic3C2412yes—
242C2×C3×Dic3C2412yes—
243C3×D12—216no—
244C3×D12—28no—
245C3×C4×D3—28no—
246C3×C4×D3—216no—
247C3×C4×D3C2×D4116yescomplemented
248#626—216no—
249#625—216no—
250#624—28no—
251D3×Dic3—28no—
252D3×Dic3—28no—
253C22×#41—31no—
254C24×C4—91no—
255#525—916no—
256C2×#123—92no—
257C2×C22⋊Q8—31no—
258C2×C22⋊Q8—91no—
259C2×#121—91no—
260C2×#121—91no—
261C2×#120—92no—
262C2×C4×D4—92no—
263C2×C4×D4—92no—
264C2×#117—91no—
265C24×C3—31no—
266C24×C3—31no—
267C24×C3—32no—
268C23×D3—31no—
269C23×D3—31no—
270C23×D3—34no—
271C23×D3—34no—
272C23×D3—61no—
273C23×D3—64no—
274C23×D3—64no—
275C23×D3—64no—
276C23×D3—64no—
277C23×D3—64no—
278C23×D3—64no—
279C23×D3C22×D312yes—
280C23×D3C22×D311yescharacteristic
281C23×D3C22×D311yescharacteristic
282C3×#41—632no—
283C2×C3×Q8—24no—
284C2×C3×Q8—24no—
285C2×C3×Q8—24no—
286C2×C3×Q8—44no—
287C2×C3×Q8C22×D314yescomplemented
288C2×C3×Q8C22×D314yescomplemented
289C2×C3×D4—38no—
290C2×C3×D4—34no—
291C2×C3×D4—68no—
292C2×C3×D4—64no—
293C22×C3×C4—21no—
294C22×C3×C4—22no—
295C22×C3×C4—31no—
296C22×C3×C4—38no—
297C22×C3×C4—34no—
298C22×C3×C4—32no—
299C22×C3×C4—31no—
300C22×C3×C4—38no—
301C22×C3×C4—34no—
302C22×C3×C4—68no—
303C22×C3×C4—64no—
304C22×C3×C4C22×D312yes—
305C22×C3×C4C22×D312yes—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—38no—
309C2×#67—38no—
310C2×#67—38no—
311C2×#67—68no—
312C2×#67—68no—
313C2×#67—68no—
314C22×Dic3—32no—
315C22×Dic3—32no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—34no—
319C22×Dic3—34no—
320C22×Dic3—61no—
321C22×Dic3—62no—
322C22×Dic3—64no—
323C22×Dic3—64no—
324C22×Dic3C22×D312yes—
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327#239—232no—
328C2×D12—28no—
329C2×D12—24no—
330C2×D12—38no—
331C2×D12—68no—
332C2×D12C22×D318yes—
333C2×D12C22×D314yescomplemented
334C2×C4×D3—24no—
335C2×C4×D3—28no—
336C2×C4×D3—34no—
337C2×C4×D3—34no—
338C2×C4×D3—34no—
339C2×C4×D3—34no—
340C2×C4×D3—34no—
341C2×C4×D3—34no—
342C2×C4×D3—64no—
343C2×C4×D3—632no—
344C2×C4×D3—64no—
345C2×C4×D3—64no—
346C2×C4×D3—64no—
347C2×C4×D3—64no—
348C2×C4×D3—64no—
349C2×C4×D3—64no—
350C2×C4×D3—632no—
351C2×C4×D3—124no—
352C2×C4×D3#6718yescomplemented
353C2×C4×D3C22×D314yes—
354C2×C4×D3C22×D314yes—
355C2×C4×D3C22×D318yescomplemented
356C3×C4⋊C4—34no—
357C3×C4⋊C4—38no—
358C3×C22⋊C4—38no—
359#217—38no—
360#217—38no—
361#217—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×D318yes—
369C4⋊Dic3—34no—
370C4⋊Dic3—34no—
371C4⋊Dic3—64no—
372C4⋊Dic3C22×D314yescomplemented
373Dic3⋊C4—38no—
374Dic3⋊C4—38no—
375Dic3⋊C4—68no—
376Dic3⋊C4C22×D318yescomplemented
377C4×Dic3—38no—
378C4×Dic3—38no—
379C22×C32C22×D412yes—
380C22×C32C2×#4112yes—
381C22×C32C2×#4112yes—
382C22×C32C2511yescharacteristic
383C2×C3⋊D3—28no—
384C2×C3⋊D3—22no—
385C2×C3⋊D3—22no—
386C2×C3⋊D3C2×#4114yescomplemented
387C2×C3×D3—28no—
388C2×C3×D3—28no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—22no—
393C2×C3×D3—24no—
394C2×C3×D3—24no—
395C2×C3×D3—24no—
396C2×C3×D3—48no—
397C2×C3×D3C22×D414yes—
398C2×C3×D3C2×#4114yescomplemented
399D32—232no—
400C32×C4—24no—
401C32×C4C22×D414yes—
402C3⋊Dic3—22no—
403C3⋊Dic3—24no—
404C3×Dic3—22no—
405C3×Dic3—24no—
406C3×Dic3C22×D414yes—
407C25—91no—
408C2×#41—38no—
409C2×#41—68no—
410C22×Q8D3211yescharacteristic, complemented
411C22×D4—32no—
412C22×D4—31no—
413C22×D4—92no—
414C22×D4—92no—
415C23×C4—31no—
416C23×C4—32no—
417C23×C4—31no—
418C23×C4—91no—
419C23×C4—98no—
420C23×C4—91no—
421C23×C4—91no—
422C23×C4—91no—
423C23×C4—188no—
424#123—916no—
425C22⋊Q8—38no—
426C22⋊Q8—98no—
427#121—98no—
428#121—98no—
429#120—916no—
430C4×D4—916no—
431C4×D4—916no—
432#117—98no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—32no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—92no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—92no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—92no—
442C2×C42—92no—
443C23×C3—21no—
444C23×C3—34no—
445C23×C3—34no—
446C23×C3—32no—
447C23×C3—32no—
448C23×C3—34no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3—62no—
453C23×C3—64no—
454C23×C3—64no—
455C23×C3—64no—
456C23×C3C23×D311yescharacteristic
457C23×C3C23×D311yescharacteristic
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—24no—
465C22×D3—34no—
466C22×D3—34no—
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—64no—
470C22×D3—62no—
471C22×D3—68no—
472C22×D3—68no—
473C22×D3—68no—
474C22×D3—68no—
475C22×D3—632no—
476C22×D3—632no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—68no—
482C22×D3—68no—
483C22×D3—122no—
484C22×D3—122no—
485C22×D3#23914yescomplemented
486C22×D3C2×#6714yes—
487C22×D3C23×D314yes—
488C22×D3C23×D312yes—
489C22×D3C23×D312yes—
490C3×Q8—28no—
491C3×Q8—28no—
492C3×Q8—48no—
493C3×D4—616no—
494C3×D4—68no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—22no—
498C2×C3×C4—24no—
499C2×C3×C4—24no—
500C2×C3×C4—34no—
501C2×C3×C4—32no—
502C2×C3×C4—316no—
503C2×C3×C4—34no—
504C2×C3×C4—32no—
505C2×C3×C4—44no—
506C2×C3×C4—616no—
507C2×C3×C4—64no—
508C2×C3×C4—62no—
509C2×C3×C4—68no—
510C2×C3×C4D3×D414yes—
511C2×C3×C4C2×#6714yes—
512C2×C3×C4C23×D314yes—
513C2×C3×C4C23×D314yes—
514C2×C3×C4C23×D312yes—
515C2×C3×C4C23×D312yes—
516#67—616no—
517#67—616no—
518#67—616no—
519C2×Dic3—22no—
520C2×Dic3—24no—
521C2×Dic3—34no—
522C2×Dic3—34no—
523C2×Dic3—32no—
524C2×Dic3—32no—
525C2×Dic3—62no—
526C2×Dic3—64no—
527C2×Dic3—68no—
528C2×Dic3—62no—
529C2×Dic3—64no—
530C2×Dic3—64no—
531C2×Dic3—62no—
532C2×Dic3—68no—
533C2×Dic3—122no—
534C2×Dic3—124no—
535C2×Dic3C2×#6714yes—
536C2×Dic3C23×D314yes—
537C2×Dic3C23×D312yes—
538C2×Dic3C23×D312yes—
539D12—216no—
540D12—28no—
541D12—616no—
542C4×D3—28no—
543C4×D3—216no—
544C4×D3—68no—
545C4×D3—68no—
546C4×D3—68no—
547C4×D3—68no—
548C4×D3—68no—
549C4×D3—68no—
550C4×D3—128no—
551C4×D3C2×#67116yescomplemented
552C2×C32#52514yescomplemented
553C2×C32C23×D411yescharacteristic
554C2×C32C22×#4111yescharacteristic
555C2×C32C22×#4111yescharacteristic
556C3⋊D3—24no—
557C3×D3—24no—
558C3×D3—24no—
559C3×D3—44no—
560C24—31no—
561C24—31no—
562C24—32no—
563C24—94no—
564C24—91no—
565C24—184no—
566C24—184no—
567C24—184no—
568#41—632no—
569C2×Q8—24no—
570C2×Q8C2×D3214yescomplemented
571C2×D4—38no—
572C2×D4—34no—
573C2×D4—68no—
574C2×D4—64no—
575C2×D4—98no—
576C2×D4—98no—
577C2×D4—188no—
578C2×D4—188no—
579C22×C4—31no—
580C22×C4—34no—
581C22×C4—38no—
582C22×C4—32no—
583C22×C4—31no—
584C22×C4—38no—
585C22×C4—34no—
586C22×C4—68no—
587C22×C4—64no—
588C22×C4—94no—
589C22×C4—94no—
590C22×C4—94no—
591C22×C4—92no—
592C22×C4—91no—
593C22×C4—94no—
594C22×C4—184no—
595C22×C4—1832no—
596C22×C4—184no—
597C22×C4—184no—
598C22×C4—184no—
599C22×C4C2×D3212yes—
600C22×C4C2×D3211yescharacteristic
601C4⋊C4—34no—
602C4⋊C4—38no—
603C4⋊C4—94no—
604C4⋊C4—98no—
605C22⋊C4—38no—
606C22⋊C4—98no—
607C22⋊C4—98no—
608C22⋊C4—98no—
609C22⋊C4—98no—
610C42—98no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—21no—
615C22×C3—34no—
616C22×C3—34no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—62no—
620C22×C3—62no—
621C22×C3—68no—
622C22×C3—68no—
623C22×C3—64no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—128no—
627C22×C3C2×D3×D412yes—
628C22×C3C2×#23912yes—
629C22×C3D3×#4112yes—
630C22×C3D3×#4112yes—
631C22×C3D3×#4112yes—
632C22×C3C22×#6712yes—
633C22×C3C24×D311yescharacteristic
634C22×C3C24×D311yescharacteristic
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—28no—
640C2×D3—28no—
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—24no—
644C2×D3—34no—
645C2×D3—34no—
646C2×D3—48no—
647C2×D3—64no—
648C2×D3—632no—
649C2×D3—632no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—68no—
655C2×D3—68no—
656C2×D3—122no—
657C2×D3—122no—
658C2×D3—128no—
659C2×D3C2×#23914yescomplemented
660C2×D3C22×#6714yes—
661C3×C4—24no—
662C3×C4—24no—
663C3×C4—24no—
664C3×C4—34no—
665C3×C4—44no—
666C3×C4—64no—
667C3×C4—62no—
668C3×C4C2×D3×D414yes—
669C3×C4C22×#6714yes—
670Dic3—22no—
671Dic3—24no—
672Dic3—62no—
673Dic3—64no—
674Dic3—64no—
675Dic3—62no—
676Dic3—122no—
677Dic3—124no—
678Dic3C22×#6714yes—
679C32C2×#52511yescharacteristic, complemented, Sylow
680C23—34no—
681C23—34no—
682C23—32no—
683C23—32no—
684C23—34no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—64no—
690C23—64no—
691C23—64no—
692C23—94no—
693C23—92no—
694C23—188no—
695C23—188no—
696C23—188no—
697C23—1832no—
698C23—182no—
699C23—182no—
700C23C22×D3211yescharacteristic
701Q8—28no—
702D4—616no—
703D4—68no—
704D4—1816no—
705D4—1816no—
706C2×C4—24no—
707C2×C4—34no—
708C2×C4—32no—
709C2×C4—316no—
710C2×C4—34no—
711C2×C4—32no—
712C2×C4—616no—
713C2×C4—64no—
714C2×C4—62no—
715C2×C4—68no—
716C2×C4—94no—
717C2×C4—92no—
718C2×C4—188no—
719C2×C4—188no—
720C2×C4—188no—
721C2×C4—184no—
722C2×C4—182no—
723C2×C4—188no—
724C2×C4D3×#6714yes—
725C2×C4C22×D3214yes—
726C2×C4C22×D3212yes—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—24no—
730C2×C3—21no—
731C2×C3—64no—
732C2×C3—64no—
733C2×C3—124no—
734C2×C3#562714yescomplemented
735C2×C3#582814yescomplemented
736C2×C3C22×D3×D411yescharacteristic
737C2×C3C22×#23911yescharacteristic
738C2×C3C2×D3×#4111yescharacteristic
739C2×C3C2×D3×#4111yescharacteristic
740C2×C3C2×D3×#4111yescharacteristic
741C2×C3C23×#6711yescharacteristic
742D3—24no—
743D3—24no—
744D3—44no—
745D3—64no—
746D3—64no—
747D3—124no—
748C22—34no—
749C22—34no—
750C22—62no—
751C22—62no—
752C22—62no—
753C22—68no—
754C22—68no—
755C22—62no—
756C22—64no—
757C22—64no—
758C22—64no—
759C22—94no—
760C22—128no—
761C22—1832no—
762C22—182no—
763C22—188no—
764C22—182no—
765C22D3×#23912yes—
766C22#6431912yes—
767C22C2×D3×#6712yes—
768C22C23×D3211yescharacteristic
769C4—24no—
770C4—34no—
771C4—64no—
772C4—62no—
773C4—184no—
774C4—182no—
775C4C2×D3×#6714yes—
776C3—21no—
777C3C2×#562711yescharacteristic, complemented
778C3C2×#582811yescharacteristic, complemented
779C2—64no—
780C2—64no—
781C2—124no—
782C2—184no—
783C2#1059542414yesdirect product factor
784C2C2×D3×#23911yescharacteristic
785C2C2×#6431911yescharacteristic
786C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#525
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×C4×D32C2semidirect
3. C2×#64155C2semidirect
4. C2×C3×#946C2semidirect
5. #10595424C2direct (N × H)
6. C2×#63922C2semidirect
7. C2×#63916C2semidirect
8. C2×#63908C2semidirect
9. C2×#63904C2semidirect
10. C2×#63884C2semidirect
11. C2×#63879C2semidirect
12. C2×#63841C2semidirect
16. C22×C32×Q8C22semidirect
19. C2×C3×#239C22semidirect
21. C22×C3×D12C22semidirect
24. C22×C3×C4×D3C22semidirect
31. C2×C4×D32C22semidirect
32. #64155C22semidirect
34. C2×C4⋊(C3⋊Dic3)C22semidirect
35. C2×#3750C22semidirect
36. C3×#946C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
41. C2×(C2×D3)⋊Dic3C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C2×Dic32C22semidirect
44. #63922C22semidirect
45. #63916C22semidirect
46. #63908C22semidirect
47. #63904C22semidirect
48. #63884C22semidirect
49. #63879C22semidirect
50. #63841C22semidirect
52. C22×#239D3semidirect
60. C2×#946D3semidirect
85. C2×C32×Q8C23semidirect
99. C2×C3×D12C23semidirect
102. C2×C3×C4×D3D4semidirect
105. C2×C3×C4×D3C23semidirect
118. C4⋊(C3⋊Dic3)C23semidirect
119. #3750C23semidirect
121. C3×C4⋊Dic3C23semidirect
122. C3×Dic3⋊C4C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
126. Dic32C23semidirect
133. C22×C3×Q8C2×D3semidirect
134. C22×C3×Q8C2×D3semidirect
146. C2×#239C2×D3semidirect
149. C22×D12C2×D3semidirect
163. C22×C4×D3C2×D3semidirect
174. #946C2×D3semidirect
193. C2×C4⋊Dic3C2×D3semidirect
197. C2×Dic3⋊C4C2×D3semidirect
209. C22×C3⋊D3#41semidirect
219. C22×C3×D3#41semidirect
247. C3×C4×D3C2×D4semidirect
287. C2×C3×Q8C22×D3semidirect
288. C2×C3×Q8C22×D3semidirect
333. C2×D12C22×D3semidirect
352. C2×C4×D3#67semidirect
355. C2×C4×D3C22×D3semidirect
372. C4⋊Dic3C22×D3semidirect
376. Dic3⋊C4C22×D3semidirect
386. C2×C3⋊D3C2×#41semidirect
398. C2×C3×D3C2×#41semidirect
410. C22×Q8D32semidirect
485. C22×D3#239semidirect
551. C4×D3C2×#67semidirect
552. C2×C32#525semidirect
570. C2×Q8C2×D32semidirect
659. C2×D3C2×#239semidirect
679. C32C2×#525semidirect
734. C2×C3#5627semidirect
735. C2×C3#5828semidirect
777. C3C2×#5627semidirect
778. C3C2×#5828semidirect
783. C2#10595424direct (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×C4×D322
C2×#641552
C2×C3×#9462
#105954242
C2×#639222
C2×#639162
C2×#639082
C2×#639042
C2×#638842
C2×#638792
C2×#638412
C2×#58283
C2×#56273