Finite Group Databasebeta

← C2×#10594629 #11902461

Subgroups — C2×#10594629 #11902461

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×D3×D12C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×#64104C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×#893C211yesmaximal, characteristic, complemented
6C2×#63923C212yesmaximal, complemented
7C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
8C2×#63909C212yesmaximal, complemented
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×#63890C212yesmaximal, complemented
11C2×#63864C211yesmaximal, characteristic, complemented
12#10594629C2116yesmaximal, direct product factor
13C2×#5630—31nomaximal
14C2×#5554—31nomaximal
15C23×D32C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4⋊(C3⋊D3)C2212yescomplemented
18C22×C4×C3⋊D3C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2212yescomplemented
22C22×C3×Dic6C2211yescharacteristic, complemented
23C22×#626C2212yes—
24C22×#626C2211yescharacteristic
25C22×#626C2212yescomplemented
26C22×D3×Dic3C2212yescomplemented
27C2×D3×D12—28no—
28C2×D3×D12C2218yescomplemented
29C2×#3796—28no—
30C2×#3796C2218yescomplemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×#3752C2212yescomplemented
33#64104C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×(C2×D3)⋊C4C2212yescomplemented
36C2×C3×C4⋊Dic3C2212yescomplemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38C3×#897C2218yescomplemented
39C3×#893C2218yescomplemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2212yescomplemented
42C2×#3722C2212yescomplemented
43C2×#3722C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45#63923C22116yescomplemented
46D3×(C2×D3)⋊C4C22116yescomplemented
47#63909C22116yescomplemented
48C4×#626C2218yescomplemented
49#63890C22116yescomplemented
50#63864C2218yescomplemented
51C22×#239—31no—
52C22×#237—31no—
53C22×D3×D4—31no—
54C23×D12—31no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C4×D4—31no—
57C2×#947—31no—
58C2×#930—32no—
59C2×C4×#67—31no—
60C22×(C2×D3)⋊C4—32no—
61#5630—316no—
62#5554—316no—
63C2×#897D311yescharacteristic, complemented
64C2×#895—32no—
65C2×#895—31no—
66C2×#895—31no—
67C2×#895—61no—
68C2×#894—32no—
69C2×#893D311yescharacteristic, complemented
70C2×#886—32no—
71C2×#882—32no—
72C2×#882—32no—
73C2×D3×C22⋊C4—32no—
74C2×#875—31no—
75C2×C4×D12—31no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3⋊D3C2312yes—
78C23×C3×D3C2312yes—
79C23×C3×D3C2311yescharacteristic
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C2×C4⋊(C3⋊D3)—24no—
88C2×C4⋊(C3⋊D3)—44no—
89C2×C4⋊(C3⋊D3)C2314yes—
90C2×C4⋊(C3⋊D3)C2318yescomplemented
91C2×C4×C3⋊D3—24no—
92C2×C4×C3⋊D3C2314yescomplemented
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2312yes—
97C2×C3×D12D418yescomplemented
98C2×C3×D12C2314yes—
99C2×C3×C4×D3—24no—
100C2×C3×C4×D3—44no—
101C2×C3×C4×D3C2314yes—
102C2×C3×C4×D3C2318yescomplemented
103C2×C3×Dic6—24no—
104C2×C3×Dic6C2314yescomplemented
105C2×#626—28no—
106C2×#626—28no—
107C2×#626—24no—
108C2×#626C2318yes—
109C2×#626C2314yes—
110C2×#626C2318yescomplemented
111C2×D3×Dic3—28no—
112C2×D3×Dic3C2318yescomplemented
113D3×D12—232no—
114#3796—232no—
115C32×C4⋊C4C2314yescomplemented
116#3752C2318yescomplemented
117C3×(C2×D3)⋊C4C2318yes—
118C3×(C2×D3)⋊C4C2318yescomplemented
119C3×C4⋊Dic3C2318yescomplemented
120C3×C4×Dic3C2314yescomplemented
121Dic3⋊Dic3C2314yescomplemented
122#3722C2318yescomplemented
123#3722C2318yescomplemented
124#3722C2314yescomplemented
125(C2×D3)⋊Dic3C2314yes—
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C22×C3×Q8—31no—
130C22×C3×D4—31no—
131C23×C3×C4—31no—
132C23×C3×C4—32no—
133C22×#67—32no—
134C22×#67—32no—
135C22×#67—31no—
136C23×Dic3—32no—
137C2×#239—38no—
138C2×#239—68no—
139C2×#237—38no—
140C2×#237—68no—
141C2×D3×D4—38no—
142C2×D3×D4—68no—
143C22×D12—32no—
144C22×D12—31no—
145C22×D12—32no—
146C22×D12—31no—
147C22×D12—31no—
148C22×D12—32no—
149C22×D12—32no—
150C22×D12—38no—
151C22×D12—61no—
152C22×D12—62no—
153C22×D12—68no—
154C22×D12C2×D311yescharacteristic
155C22×C4×D3—32no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C22×C4×D3C2×D311yescharacteristic
160C22×C4×D3C2×D312yescomplemented
161C22×Dic6C2×D311yescharacteristic, complemented
162C3×C22⋊Q8—38no—
163C3×C4×D4—38no—
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4—32no—
166C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
167C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
168C2×C3×C22⋊C4—32no—
169C2×C3×C22⋊C4—32no—
170C2×C3×C42—31no—
171C2×#217—31no—
172#947—38no—
173#930—316no—
174C4×#67—38no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—316no—
185C2×(C2×D3)⋊C4—62no—
186C2×(C2×D3)⋊C4C2×D312yes—
187C2×(C2×D3)⋊C4C2×D312yescomplemented
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3C2×D312yescomplemented
190C2×Dic3⋊C4—31no—
191C2×C4×Dic3C2×D311yescharacteristic, complemented
192#897C2×D318yescomplemented
193#895—316no—
194#895—38no—
195#895—38no—
196#895—68no—
197#894—316no—
198#893C2×D318yescomplemented
199#886—316no—
200#882—316no—
201#882—316no—
202D3×C22⋊C4—316no—
203#875—38no—
204C4×D12—38no—
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—22no—
207C22×C3⋊D3—24no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3—24no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—24no—
212C22×C3⋊D3C2414yes—
213C22×C3⋊D3C2412yes—
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—24no—
227C2×C32×C4C2×D414yes—
228C2×C32×C4C2414yes—
229C2×C32×C4C2412yes—
230C2×C3⋊Dic3—22no—
231C2×C3⋊Dic3C2412yes—
232C4⋊(C3⋊D3)—28no—
233C4⋊(C3⋊D3)—48no—
234C4×C3⋊D3—28no—
235C2×C3×Dic3—24no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3C2412yes—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2414yes—
242C2×C3×Dic3C2412yes—
243C3×D12C2×D4116yescomplemented
244C3×C4×D3—28no—
245C3×C4×D3—48no—
246C3×Dic6—28no—
247#626—216no—
248#626—216no—
249#626—28no—
250D3×Dic3—216no—
251C22×#41—91no—
252C23×D4—91no—
253#546—916no—
254C2×#124—91no—
255C2×#123—92no—
256C2×C22⋊Q8—31no—
257C2×#121—92no—
258C2×#121—91no—
259C2×#120—92no—
260C2×C4×D4—31no—
261C2×C4×D4—91no—
262C22×C22⋊C4—92no—
263C24×C3—31no—
264C24×C3—32no—
265C23×D3—32no—
266C23×D3—32no—
267C23×D3—31no—
268C23×D3—31no—
269C23×D3—38no—
270C23×D3—38no—
271C23×D3—61no—
272C23×D3—62no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—68no—
276C23×D3—68no—
277C23×D3—124no—
278C23×D3—124no—
279C23×D3C22×D312yes—
280C23×D3C22×D311yescharacteristic
281C2×C3×Q8—34no—
282C2×C3×Q8—64no—
283C2×C3×D4—38no—
284C2×C3×D4—34no—
285C22×C3×C4—21no—
286C22×C3×C4—22no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—32no—
291C22×C3×C4—34no—
292C22×C3×C4—38no—
293C22×C3×C4—64no—
294C22×C3×C4—124no—
295C22×C3×C4C22×D312yes—
296C22×C3×C4C22×D312yes—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C2×#67—34no—
300C2×#67—38no—
301C2×#67—38no—
302C2×#67—68no—
303C2×#67—68no—
304C2×#67—64no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—38no—
308C22×Dic3—61no—
309C22×Dic3—68no—
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D312yes—
314#239—632no—
315#237—632no—
316D3×D4—632no—
317C2×D12—34no—
318C2×D12—38no—
319C2×D12—38no—
320C2×D12—34no—
321C2×D12—34no—
322C2×D12—38no—
323C2×D12—38no—
324C2×D12—64no—
325C2×D12—68no—
326C2×D12—68no—
327C2×D12—68no—
328C2×D12—64no—
329C2×D12—64no—
330C2×D12—64no—
331C2×D12—632no—
332C2×D12—124no—
333C2×D12—124no—
334C2×D12—124no—
335C2×D12—128no—
336C2×D12D1218yescomplemented
337C2×D12C22×D314yes—
338C2×C4×D3—24no—
339C2×C4×D3—38no—
340C2×C4×D3—34no—
341C2×C4×D3—34no—
342C2×C4×D3—44no—
343C2×C4×D3—64no—
344C2×C4×D3—68no—
345C2×C4×D3—64no—
346C2×C4×D3—64no—
347C2×C4×D3—124no—
348C2×C4×D3C22×D314yes—
349C2×C4×D3C22×D318yescomplemented
350C2×Dic6—24no—
351C2×Dic6C22×D314yescomplemented
352C3×C4⋊C4—24no—
353C3×C4⋊C4—38no—
354C3×C4⋊C4C22×D314yescomplemented
355C3×C4⋊C4C22×D314yescomplemented
356C3×C22⋊C4—38no—
357C3×C22⋊C4—38no—
358C3×C42—34no—
359#217—34no—
360(C2×D3)⋊C4—34no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—34no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—38no—
367(C2×D3)⋊C4—38no—
368(C2×D3)⋊C4—34no—
369(C2×D3)⋊C4—68no—
370(C2×D3)⋊C4C22×D318yes—
371(C2×D3)⋊C4C22×D318yescomplemented
372C4⋊Dic3—34no—
373C4⋊Dic3C22×D318yescomplemented
374Dic3⋊C4—34no—
375C4×Dic3C22×D314yescomplemented
376C22×C32C22×D412yes—
377C22×C32C2×#4112yes—
378C22×C32H(5,𝔽2)12yes—
379C22×C32C2511yescharacteristic
380C2×C3⋊D3—22no—
381C2×C3⋊D3—22no—
382C2×C3⋊D3—24no—
383C2×C3⋊D3—22no—
384C2×C3⋊D3—24no—
385C2×C3⋊D3—24no—
386C2×C3⋊D3—44no—
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—24no—
398C32×C4C22×D414yes—
399C3⋊Dic3—22no—
400C3×Dic3—24no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C25—92no—
405C2×#41—98no—
406C2×#41—188no—
407C22×Q8—31no—
408C22×D4—31no—
409C22×D4—98no—
410C22×D4—91no—
411C22×D4—92no—
412C22×D4—92no—
413C22×D4—91no—
414C22×D4—92no—
415C22×D4—188no—
416C23×C4—31no—
417C23×C4—32no—
418C23×C4—92no—
419C23×C4—91no—
420#124—98no—
421#123—916no—
422C22⋊Q8—38no—
423#121—916no—
424#121—98no—
425#120—916no—
426C4×D4—38no—
427C4×D4—98no—
428C2×C4⋊C4—32no—
429C2×C4⋊C4—91no—
430C2×C4⋊C4D3211yescharacteristic, complemented
431C2×C22⋊C4—32no—
432C2×C22⋊C4—32no—
433C2×C22⋊C4—916no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—92no—
439C2×C42—31no—
440C23×C3—21no—
441C23×C3—38no—
442C23×C3—34no—
443C23×C3—32no—
444C23×C3—34no—
445C23×C3—62no—
446C23×C3—62no—
447C23×C3—64no—
448C23×C3—64no—
449C23×C3C23×D311yescharacteristic
450C23×C3C23×D311yescharacteristic
451C22×D3—22no—
452C22×D3—24no—
453C22×D3—24no—
454C22×D3—22no—
455C22×D3—34no—
456C22×D3—34no—
457C22×D3—32no—
458C22×D3—32no—
459C22×D3—62no—
460C22×D3—64no—
461C22×D3—616no—
462C22×D3—616no—
463C22×D3—64no—
464C22×D3—62no—
465C22×D3—64no—
466C22×D3—62no—
467C22×D3—64no—
468C22×D3—62no—
469C22×D3—64no—
470C22×D3—62no—
471C22×D3—64no—
472C22×D3—62no—
473C22×D3—64no—
474C22×D3—62no—
475C22×D3—64no—
476C22×D3—616no—
477C22×D3—616no—
478C22×D3—122no—
479C22×D3—122no—
480C22×D3—124no—
481C22×D3—124no—
482C22×D3—124no—
483C22×D3—128no—
484C22×D3—128no—
485C22×D3—1232no—
486C22×D3—1232no—
487C22×D3C2×D1218yes—
488C22×D3#23914yescomplemented
489C22×D3C23×D314yes—
490C22×D3C23×D312yes—
491C3×Q8—68no—
492C3×D4—316no—
493C2×C3×C4—24no—
494C2×C3×C4—24no—
495C2×C3×C4—22no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—34no—
502C2×C3×C4—44no—
503C2×C3×C4—64no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—68no—
508C2×C3×C4—128no—
509C2×C3×C4C2×D1214yes—
510C2×C3×C4D3×D414yes—
511C2×C3×C4C23×D314yes—
512C2×C3×C4C23×D314yes—
513C2×C3×C4C23×D312yes—
514C2×C3×C4C23×D312yes—
515#67—616no—
516#67—616no—
517#67—68no—
518C2×Dic3—24no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—32no—
523C2×Dic3—32no—
524C2×Dic3—62no—
525C2×Dic3—616no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—122no—
529C2×Dic3C23×D312yes—
530C2×Dic3C23×D312yes—
531C2×Dic3C23×D312yes—
532C2×Dic3C23×D314yes—
533D12—616no—
534D12—616no—
535D12—68no—
536D12—68no—
537D12—68no—
538D12—128no—
539D12—128no—
540D12—128no—
541D12—1216no—
542D12C2×D12116yescomplemented
543C4×D3—28no—
544C4×D3—48no—
545C4×D3—616no—
546C4×D3—68no—
547C4×D3—68no—
548C4×D3—128no—
549Dic6—28no—
550C2×C32#54614yescomplemented
551C2×C32C23×D411yescharacteristic
552C2×C32C22×#4111yescharacteristic
553C2×C32C2×H(5,𝔽2)11yescharacteristic
554C3⋊D3—42no—
555C3⋊D3—44no—
556C3×D3—24no—
557C3×D3—28no—
558C24—31no—
559C24—32no—
560C24—98no—
561C24—92no—
562C24—91no—
563C24—188no—
564C24—188no—
565C24—364no—
566#41—1832no—
567C2×Q8—34no—
568C2×Q8—64no—
569C2×D4—34no—
570C2×D4—38no—
571C2×D4—94no—
572C2×D4—98no—
573C2×D4—98no—
574C2×D4—94no—
575C2×D4—98no—
576C2×D4—1832no—
577C2×D4—188no—
578C2×D4—188no—
579C2×D4—184no—
580C2×D4—184no—
581C2×D4—364no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—32no—
585C22×C4—31no—
586C22×C4—34no—
587C22×C4—38no—
588C22×C4—64no—
589C22×C4—98no—
590C22×C4—91no—
591C22×C4—94no—
592C22×C4—124no—
593C22×C4—188no—
594C22×C4—184no—
595C22×C4C2×D3212yes—
596C22×C4C2×D3211yescharacteristic
597C4⋊C4—38no—
598C4⋊C4—94no—
599C4⋊C4C2×D3214yescomplemented
600C22⋊C4—38no—
601C22⋊C4—38no—
602C22⋊C4—98no—
603C22⋊C4—94no—
604C22⋊C4—98no—
605C22⋊C4—94no—
606C22⋊C4—98no—
607C42—34no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—21no—
612C22×C3—38no—
613C22×C3—34no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—64no—
617C22×C3—64no—
618C22×C3—68no—
619C22×C3—616no—
620C22×C3C22×D1212yes—
621C22×C3C2×D3×D412yes—
622C22×C3#100412yes—
623C22×C3C2×#23912yes—
624C22×C3D3×#4112yes—
625C22×C3#100912yes—
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—64no—
635C2×D3—62no—
636C2×D3—64no—
637C2×D3—62no—
638C2×D3—64no—
639C2×D3—62no—
640C2×D3—64no—
641C2×D3—62no—
642C2×D3—64no—
643C2×D3—62no—
644C2×D3—64no—
645C2×D3—62no—
646C2×D3—64no—
647C2×D3—122no—
648C2×D3—122no—
649C2×D3—124no—
650C2×D3—124no—
651C2×D3—124no—
652C2×D3—1232no—
653C2×D3—1232no—
654C2×D3—128no—
655C2×D3—128no—
656C2×D3—124no—
657C2×D3—128no—
658C2×D3—124no—
659C2×D3—248no—
660C2×D3C22×D1218yes—
661C2×D3C2×#23914yescomplemented
662C3×C4—24no—
663C3×C4—24no—
664C3×C4—24no—
665C3×C4—44no—
666C3×C4—64no—
667C3×C4—62no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4C22×D1214yes—
671C3×C4C2×D3×D414yes—
672Dic3—24no—
673Dic3—22no—
674Dic3—22no—
675Dic3—22no—
676Dic3—62no—
677Dic3—62no—
678Dic3—122no—
679C32C2×#54611yescharacteristic, complemented, Sylow
680C23—38no—
681C23—34no—
682C23—32no—
683C23—34no—
684C23—62no—
685C23—64no—
686C23—62no—
687C23—64no—
688C23—94no—
689C23—92no—
690C23—1816no—
691C23—1816no—
692C23—182no—
693C23—184no—
694C23—182no—
695C23—184no—
696C23—182no—
697C23—184no—
698C23—368no—
699C23—3632no—
700C23C22×D3211yescharacteristic
701Q8—68no—
702D4—316no—
703D4—1816no—
704D4—1816no—
705D4—188no—
706D4—188no—
707D4—368no—
708C2×C4—24no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—34no—
712C2×C4—32no—
713C2×C4—62no—
714C2×C4—64no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—68no—
718C2×C4—92no—
719C2×C4—128no—
720C2×C4—1816no—
721C2×C4—182no—
722C2×C4—188no—
723C2×C4D3×D1214yes—
724C2×C4C22×D3214yes—
725C2×C4C22×D3212yes—
726C2×C3—21no—
727C2×C3—24no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—64no—
731C2×C3—68no—
732C2×C3#555414yescomplemented
733C2×C3#563014yescomplemented
734C2×C3C23×D1211yescharacteristic
735C2×C3C22×D3×D411yescharacteristic
736C2×C3C2×#100411yescharacteristic
737C2×C3C22×#23911yescharacteristic
738C2×C3C2×D3×#4111yescharacteristic
739C2×C3C2×#100911yescharacteristic
740D3—28no—
741D3—24no—
742D3—124no—
743D3—124no—
744D3—122no—
745D3—124no—
746D3—122no—
747D3—244no—
748C22—38no—
749C22—34no—
750C22—62no—
751C22—68no—
752C22—616no—
753C22—64no—
754C22—62no—
755C22—64no—
756C22—182no—
757C22—184no—
758C22—182no—
759C22—184no—
760C22—182no—
761C22—184no—
762C22—3632no—
763C22—368no—
764C22—364no—
765C22C2×D3×D1212yes—
766C22#6431412yes—
767C22D3×#23912yes—
768C22C23×D3211yescharacteristic
769C4—24no—
770C4—62no—
771C4—64no—
772C4—62no—
773C4—62no—
774C4—182no—
775C4C2×D3×D1214yes—
776C3—21no—
777C3C2×#555411yescharacteristic, complemented
778C3C2×#563011yescharacteristic, complemented
779C2—64no—
780C2—68no—
781C2—364no—
782C2—362no—
783C2#1059462914yesdirect product factor
784C2C22×D3×D1211yescharacteristic
785C2C2×#6431411yescharacteristic
786C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D12C2semidirect
2. C22×#3796C2semidirect
3. C2×#64104C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×#893C2semidirect
6. C2×#63923C2semidirect
7. C2×D3×(C2×D3)⋊C4C2semidirect
8. C2×#63909C2semidirect
9. C2×C4×#626C2semidirect
10. C2×#63890C2semidirect
11. C2×#63864C2semidirect
12. #10594629C2direct (N × H)
17. C22×C4⋊(C3⋊D3)C22semidirect
18. C22×C4×C3⋊D3C22semidirect
21. C22×C3×C4×D3C22semidirect
22. C22×C3×Dic6C22semidirect
25. C22×#626C22semidirect
26. C22×D3×Dic3C22semidirect
28. C2×D3×D12C22semidirect
30. C2×#3796C22semidirect
31. C2×C32×C4⋊C4C22semidirect
32. C2×#3752C22semidirect
33. #64104C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. C3×#897C22semidirect
39. C3×#893C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×#3722C22semidirect
42. C2×#3722C22semidirect
43. C2×#3722C22semidirect
45. #63923C22semidirect
46. D3×(C2×D3)⋊C4C22semidirect
47. #63909C22semidirect
48. C4×#626C22semidirect
49. #63890C22semidirect
50. #63864C22semidirect
63. C2×#897D3semidirect
69. C2×#893D3semidirect
90. C2×C4⋊(C3⋊D3)C23semidirect
92. C2×C4×C3⋊D3C23semidirect
97. C2×C3×D12D4semidirect
102. C2×C3×C4×D3C23semidirect
104. C2×C3×Dic6C23semidirect
110. C2×#626C23semidirect
112. C2×D3×Dic3C23semidirect
115. C32×C4⋊C4C23semidirect
116. #3752C23semidirect
118. C3×(C2×D3)⋊C4C23semidirect
119. C3×C4⋊Dic3C23semidirect
120. C3×C4×Dic3C23semidirect
121. Dic3⋊Dic3C23semidirect
122. #3722C23semidirect
123. #3722C23semidirect
124. #3722C23semidirect
160. C22×C4×D3C2×D3semidirect
161. C22×Dic6C2×D3semidirect
166. C2×C3×C4⋊C4C2×D3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
187. C2×(C2×D3)⋊C4C2×D3semidirect
189. C2×C4⋊Dic3C2×D3semidirect
191. C2×C4×Dic3C2×D3semidirect
192. #897C2×D3semidirect
198. #893C2×D3semidirect
219. C22×C3×D3#41semidirect
243. C3×D12C2×D4semidirect
336. C2×D12D12semidirect
349. C2×C4×D3C22×D3semidirect
351. C2×Dic6C22×D3semidirect
354. C3×C4⋊C4C22×D3semidirect
355. C3×C4⋊C4C22×D3semidirect
371. (C2×D3)⋊C4C22×D3semidirect
373. C4⋊Dic3C22×D3semidirect
375. C4×Dic3C22×D3semidirect
395. C2×C3×D3C2×#41semidirect
430. C2×C4⋊C4D32semidirect
488. C22×D3#239semidirect
542. D12C2×D12semidirect
550. C2×C32#546semidirect
599. C4⋊C4C2×D32semidirect
661. C2×D3C2×#239semidirect
679. C32C2×#546semidirect
732. C2×C3#5554semidirect
733. C2×C3#5630semidirect
777. C3C2×#5554semidirect
778. C3C2×#5630semidirect
783. C2#10594629direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D122
C22×#37962
C2×#641042
C2×C3×#8972
C2×C3×#8932
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639092
C2×C4×#6262
C2×#638902
C2×#638642
#105946292
C2×#56303
C2×#55543