Finite Group Databasebeta

← C2×#10594291 #11900971

Subgroups — C2×#10594291 #11900971

Order 1152.

4299 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C23×#626C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C2×C3×#886C211yesmaximal, characteristic, complemented
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63966C211yesmaximal, characteristic, complemented
8C2×#63923C212yesmaximal, complemented
9C2×#63909C212yesmaximal, complemented
10C2×#63906C212yesmaximal, complemented
11C2×#63890C212yesmaximal, complemented
12#10594291C2116yesmaximal, direct product factor
13C2×#5653—31nomaximal
14C2×#5493—31nomaximal
15C24×C3⋊D3C2211yescharacteristic, complemented
16C24×C3×D3C2211yescharacteristic
17C23×D32C2211yescharacteristic, complemented
18C22×#638C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2212yescomplemented
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic, complemented
22C22×C3×C4×D3C2212yescomplemented
23C2×D3×#67—28no—
24C2×D3×#67C2218yescomplemented
25C22×#626—28no—
26C22×#626C2212yes—
27C22×#626C2212yescomplemented
28C22×#626C2211yescharacteristic, complemented
29C22×#626C2212yescomplemented
30C22×#626C2218yescomplemented
31C22×#625C2211yescharacteristic, complemented
32C22×D3×Dic3C2211yescharacteristic, complemented
33C2×C32×C22⋊C4C2211yescharacteristic, complemented
34C2×#3752C2212yescomplemented
35#64091C2218yescomplemented
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×C4⋊Dic3C2212yescomplemented
40C3×#886C2218yescomplemented
41C3×D3×C22⋊C4C2218yescomplemented
42#63981C2218yescomplemented
43#63966C2218yescomplemented
44C2×Dic3⋊Dic3C2212yescomplemented
45C2×#3722C2212yescomplemented
46C2×#3722C2212yescomplemented
47#63923C22116yescomplemented
48#63909C22116yescomplemented
49#63906C22116yescomplemented
50#63890C22116yescomplemented
51C23×#67—31no—
52C23×#67—31no—
53C22×D3×D4—31no—
54C23×D12—31no—
55C2×C3×#123—31no—
56C22×C3×C22⋊C4—31no—
57C2×#937—31no—
58C2×#930—32no—
59C2×#930—32no—
60C2×#929—31no—
61#5653—316no—
62C2×#895—32no—
63C2×#894—32no—
64#5493—316no—
65C2×#886—31no—
66C2×#886—32no—
67C2×#886D311yescharacteristic, complemented
68C2×#884—32no—
69C2×#882—31no—
70C2×#882—31no—
71C2×#882—31no—
72C2×#882—32no—
73C2×#882—32no—
74C2×#882—61no—
75C2×D3×C22⋊C4D311yescharacteristic, complemented
76C24×C32C2311yescharacteristic
77C23×C3⋊D3—24no—
78C23×C3⋊D3—44no—
79C23×C3⋊D3C2312yes—
80C23×C3⋊D3C2311yescharacteristic
81C23×C3⋊D3C2314yescomplemented
82C23×C3×D3—44no—
83C23×C3×D3D418yescomplemented
84C23×C3×D3C2311yescharacteristic
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2314yes—
88C22×D32—24no—
89C22×D32—44no—
90C22×D32C2314yescomplemented
91C22×C32×C4C2312yes—
92C2×#638—24no—
93C2×#638C2314yes—
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—44no—
96C2×C4⋊(C3⋊D3)C2318yescomplemented
97C2×C3×#67—24no—
98C2×C3×#67C2314yes—
99C22×C3×Dic3—24no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2312yes—
102C22×C3×Dic3C2312yes—
103C22×C3×Dic3C2314yescomplemented
104C2×C3×C4×D3—44no—
105C2×C3×C4×D3C2318yescomplemented
106D3×#67—232no—
107C2×#626—28no—
108C2×#626—28no—
109C2×#626—24no—
110C2×#626—232no—
111C2×#626—44no—
112C2×#626C2318yes—
113C2×#626C2318yescomplemented
114C2×#626C2314yescomplemented
115C2×#626C2318yescomplemented
116C2×#625—24no—
117C2×#625C2314yescomplemented
118C2×D3×Dic3—24no—
119C2×D3×Dic3C2314yescomplemented
120C32×C22⋊C4C2314yescomplemented
121#3752C2318yescomplemented
122C3×#217C2314yescomplemented
123C3×(C2×D3)⋊C4C2318yescomplemented
124C3×(C2×D3)⋊C4C2318yescomplemented
125C3×C4⋊Dic3C2318yescomplemented
126Dic3⋊Dic3C2318yescomplemented
127#3722C2318yescomplemented
128#3722C2318yescomplemented
129C2×#534—91noSylow
130C25×C3—31no—
131C24×D3—31no—
132C24×D3—31no—
133C24×D3—31no—
134C24×D3—31no—
135C24×D3—61no—
136C24×D3C2×D311yescharacteristic
137C22×C3×D4—31no—
138C23×C3×C4—31no—
139C23×C3×C4—32no—
140C22×#67—31no—
141C22×#67—31no—
142C22×#67—31no—
143C22×#67—31no—
144C22×#67—38no—
145C22×#67—32no—
146C22×#67—32no—
147C22×#67—31no—
148C22×#67—32no—
149C22×#67—38no—
150C22×#67—61no—
151C22×#67—68no—
152C22×#67—68no—
153C22×#67C2×D311yescharacteristic
154C23×Dic3—31no—
155C23×Dic3C2×D311yescharacteristic, complemented
156C2×D3×D4—38no—
157C2×D3×D4—68no—
158C22×D12—38no—
159C22×D12—32no—
160C22×D12—32no—
161C22×D12—31no—
162C22×D12—32no—
163C22×D12—32no—
164C22×D12—32no—
165C22×D12—62no—
166C22×D12—68no—
167C22×C4×D3—31no—
168C22×C4×D3C2×D312yescomplemented
169C3×#123—38no—
170C2×C3×C4⋊C4—32no—
171C2×C3×C22⋊C4—21no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—32no—
174C2×C3×C22⋊C4—32no—
175C2×C3×C22⋊C4—38no—
176C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
177C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
178C2×#217C2×D311yescharacteristic, complemented
179#937—38no—
180#930—316no—
181#930—316no—
182#929—38no—
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—62no—
190C2×(C2×D3)⋊C4C2×D312yescomplemented
191C2×(C2×D3)⋊C4C2×D312yescomplemented
192C2×C4⋊Dic3—32no—
193C2×C4⋊Dic3C2×D312yescomplemented
194C2×Dic3⋊C4—32no—
195#895—316no—
196#894—316no—
197#886—38no—
198#886—316no—
199#886C2×D318yescomplemented
200#884—316no—
201#882—38no—
202#882—38no—
203#882—38no—
204#882—316no—
205#882—316no—
206#882—68no—
207D3×C22⋊C4C2×D318yescomplemented
208C23×C32—24no—
209C23×C32C2×D414yes—
210C23×C32C2412yes—
211C23×C32C2411yescharacteristic
212C22×C3⋊D3—24no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3—24no—
215C22×C3⋊D3—28no—
216C22×C3⋊D3—24no—
217C22×C3⋊D3—24no—
218C22×C3⋊D3—48no—
219C22×C3⋊D3—416no—
220C22×C3⋊D3C2412yes—
221C22×C3⋊D3C2414yes—
222C22×C3×D3—24no—
223C22×C3×D3—24no—
224C22×C3×D3—22no—
225C22×C3×D3—24no—
226C22×C3×D3—416no—
227C22×C3×D3—48no—
228C22×C3×D3C2×D414yes—
229C22×C3×D3C2×D414yes—
230C22×C3×D3C2×D4116yescomplemented
231C22×C3×D3C2412yes—
232C22×C3×D3C2412yes—
233C22×C3×D3C2412yes—
234C2×D32—28no—
235C2×D32—48no—
236C2×D32—416no—
237C2×C32×C4—24no—
238C2×C32×C4C2414yes—
239#638—28no—
240C2×C3⋊Dic3—22no—
241C2×C3⋊Dic3C2412yes—
242C4⋊(C3⋊D3)—48no—
243C3×#67—28no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—24no—
246C2×C3×Dic3—28no—
247C2×C3×Dic3—24no—
248C2×C3×Dic3C2414yes—
249C2×C3×Dic3C2412yes—
250C2×C3×Dic3C2414yes—
251C3×C4×D3—48no—
252#626—216no—
253#626—216no—
254#626—28no—
255#626—48no—
256#625—28no—
257D3×Dic3—28no—
258C23×D4—91no—
259C23×D4—91no—
260#534—916no—
261C2×#123—31no—
262C2×#123—92no—
263C2×#123—91no—
264C2×#121—92no—
265C2×#121—92no—
266C2×#120—92no—
267C2×#120—91no—
268C2×#120—91no—
269C22×C22⋊C4—31no—
270C24×C3—21no—
271C24×C3—31no—
272C24×C3—31no—
273C24×C3—38no—
274C24×C3—34no—
275C24×C3—31no—
276C24×C3—124no—
277C24×C3C22×D311yescharacteristic
278C24×C3C22×D311yescharacteristic
279C23×D3—32no—
280C23×D3—31no—
281C23×D3—32no—
282C23×D3—31no—
283C23×D3—34no—
284C23×D3—34no—
285C23×D3—34no—
286C23×D3—34no—
287C23×D3—44no—
288C23×D3—62no—
289C23×D3—61no—
290C23×D3—64no—
291C23×D3—64no—
292C23×D3—64no—
293C23×D3—64no—
294C23×D3—64no—
295C23×D3—124no—
296C23×D3—124no—
297C23×D3—124no—
298C23×D3—124no—
299C23×D3—124no—
300C23×D3—128no—
301C23×D3D1218yescomplemented
302C23×D3C22×D311yescharacteristic
303C23×D3C22×D311yescharacteristic
304C23×D3C22×D311yescharacteristic
305C23×D3C22×D314yes—
306C2×C3×D4—34no—
307C2×C3×D4—64no—
308C22×C3×C4—22no—
309C22×C3×C4—32no—
310C22×C3×C4—32no—
311C22×C3×C4—31no—
312C22×C3×C4—34no—
313C22×C3×C4—38no—
314C22×C3×C4—64no—
315C22×C3×C4—124no—
316C22×C3×C4C22×D312yes—
317C22×C3×C4C22×D312yes—
318C2×#67—24no—
319C2×#67—34no—
320C2×#67—34no—
321C2×#67—34no—
322C2×#67—34no—
323C2×#67—38no—
324C2×#67—38no—
325C2×#67—34no—
326C2×#67—38no—
327C2×#67—64no—
328C2×#67—68no—
329C2×#67—68no—
330C2×#67—632no—
331C2×#67—64no—
332C2×#67—632no—
333C2×#67—64no—
334C2×#67—64no—
335C2×#67—64no—
336C2×#67—64no—
337C2×#67—124no—
338C2×#67—124no—
339C2×#67C22×D314yes—
340C22×Dic3—24no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—34no—
344C22×Dic3—61no—
345C22×Dic3—64no—
346C22×Dic3C22×D312yes—
347C22×Dic3C22×D312yes—
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D314yescomplemented
350D3×D4—632no—
351C2×D12—38no—
352C2×D12—38no—
353C2×D12—34no—
354C2×D12—38no—
355C2×D12—38no—
356C2×D12—38no—
357C2×D12—68no—
358C2×D12—68no—
359C2×D12—68no—
360C2×D12—64no—
361C2×D12—632no—
362C2×D12—124no—
363C2×D12—124no—
364C2×D12—128no—
365C2×D12—124no—
366C2×C4×D3—34no—
367C2×C4×D3—44no—
368C2×C4×D3—64no—
369C2×C4×D3C22×D318yescomplemented
370C3×C4⋊C4—38no—
371C3×C22⋊C4—24no—
372C3×C22⋊C4—34no—
373C3×C22⋊C4—38no—
374C3×C22⋊C4—38no—
375C3×C22⋊C4C22×D314yescomplemented
376C3×C22⋊C4C22×D314yescomplemented
377#217C22×D314yescomplemented
378(C2×D3)⋊C4—38no—
379(C2×D3)⋊C4—38no—
380(C2×D3)⋊C4—38no—
381(C2×D3)⋊C4—38no—
382(C2×D3)⋊C4—38no—
383(C2×D3)⋊C4—38no—
384(C2×D3)⋊C4—68no—
385(C2×D3)⋊C4C22×D318yescomplemented
386(C2×D3)⋊C4C22×D318yescomplemented
387C4⋊Dic3—38no—
388C4⋊Dic3C22×D318yescomplemented
389Dic3⋊C4—38no—
390C22×C32—28no—
391C22×C32—24no—
392C22×C32C22×D414yes—
393C22×C32C22×D412yes—
394C22×C32H(5,𝔽2)14yes—
395C22×C32C2511yescharacteristic
396C2×C3⋊D3—24no—
397C2×C3⋊D3—24no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3—24no—
400C2×C3⋊D3—24no—
401C2×C3⋊D3—416no—
402C2×C3⋊D3—48no—
403C2×C3⋊D3—44no—
404C2×C3×D3—28no—
405C2×C3×D3—28no—
406C2×C3×D3—24no—
407C2×C3×D3—24no—
408C2×C3×D3—22no—
409C2×C3×D3—24no—
410C2×C3×D3—416no—
411C2×C3×D3—44no—
412C2×C3×D3C22×D414yes—
413C2×C3×D3C22×D414yes—
414D32—416no—
415C32×C4—24no—
416C3⋊Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—24no—
419C3×Dic3—24no—
420C25—31no—
421C25—91no—
422C25—91no—
423C22×D4—31no—
424C22×D4—92no—
425C22×D4—92no—
426C22×D4—91no—
427C22×D4—98no—
428C22×D4—92no—
429C22×D4—98no—
430C22×D4—91no—
431C22×D4—91no—
432C22×D4—92no—
433C22×D4—188no—
434C22×D4—188no—
435C23×C4—31no—
436C23×C4—32no—
437C23×C4—91no—
438#123—38no—
439#123—916no—
440#123—98no—
441#121—916no—
442#121—916no—
443#120—916no—
444#120—98no—
445#120—98no—
446C2×C4⋊C4—32no—
447C2×C4⋊C4—92no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4—32no—
450C2×C22⋊C4—32no—
451C2×C22⋊C4—38no—
452C2×C22⋊C4—92no—
453C2×C22⋊C4—92no—
454C2×C22⋊C4—92no—
455C2×C22⋊C4D3211yescharacteristic, complemented
456C23×C3—24no—
457C23×C3—24no—
458C23×C3—22no—
459C23×C3—21no—
460C23×C3—24no—
461C23×C3—34no—
462C23×C3—34no—
463C23×C3—32no—
464C23×C3—32no—
465C23×C3—316no—
466C23×C3—32no—
467C23×C3—44no—
468C23×C3—64no—
469C23×C3—64no—
470C23×C3—62no—
471C23×C3—64no—
472C23×C3—1216no—
473C23×C3—128no—
474C23×C3C2×D1214yes—
475C23×C3D3×D414yes—
476C23×C3C23×D312yes—
477C23×C3C23×D312yes—
478C23×C3C23×D311yescharacteristic
479C23×C3C23×D311yescharacteristic
480C22×D3—24no—
481C22×D3—24no—
482C22×D3—22no—
483C22×D3—24no—
484C22×D3—34no—
485C22×D3—32no—
486C22×D3—32no—
487C22×D3—34no—
488C22×D3—416no—
489C22×D3—48no—
490C22×D3—64no—
491C22×D3—62no—
492C22×D3—68no—
493C22×D3—68no—
494C22×D3—68no—
495C22×D3—64no—
496C22×D3—62no—
497C22×D3—68no—
498C22×D3—62no—
499C22×D3—64no—
500C22×D3—64no—
501C22×D3—64no—
502C22×D3—64no—
503C22×D3—64no—
504C22×D3—64no—
505C22×D3—64no—
506C22×D3—68no—
507C22×D3—124no—
508C22×D3—128no—
509C22×D3—124no—
510C22×D3—124no—
511C22×D3—122no—
512C22×D3—128no—
513C22×D3—128no—
514C22×D3—1216no—
515C22×D3—1216no—
516C22×D3—128no—
517C22×D3—128no—
518C22×D3—1216no—
519C22×D3—1216no—
520C22×D3—1216no—
521C22×D3—1232no—
522C22×D3C2×D1214yes—
523C22×D3C2×D1214yes—
524C22×D3C2×D12116yescomplemented
525C22×D3C23×D312yes—
526C22×D3C23×D312yes—
527C22×D3C23×D312yes—
528C3×D4—68no—
529C2×C3×C4—24no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—34no—
533C2×C3×C4—34no—
534C2×C3×C4—32no—
535C2×C3×C4—44no—
536C2×C3×C4—62no—
537C2×C3×C4—68no—
538C2×C3×C4—64no—
539C2×C3×C4—64no—
540C2×C3×C4—128no—
541C2×C3×C4C23×D314yes—
542C2×C3×C4C23×D314yes—
543#67—28no—
544#67—616no—
545#67—616no—
546#67—68no—
547#67—68no—
548#67—68no—
549#67—68no—
550#67—68no—
551#67—128no—
552#67—128no—
553C2×Dic3—24no—
554C2×Dic3—28no—
555C2×Dic3—22no—
556C2×Dic3—24no—
557C2×Dic3—32no—
558C2×Dic3—32no—
559C2×Dic3—62no—
560C2×Dic3—68no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3—122no—
564C2×Dic3C23×D314yes—
565C2×Dic3C23×D314yes—
566C2×Dic3C23×D312yes—
567D12—616no—
568D12—616no—
569D12—68no—
570D12—128no—
571D12—128no—
572D12—1216no—
573D12—128no—
574C4×D3—48no—
575C4×D3—68no—
576C2×C32—24no—
577C2×C32#53414yescomplemented
578C2×C32C23×D411yescharacteristic
579C2×C32C2×H(5,𝔽2)12yes—
580C3⋊D3—44no—
581C3⋊D3—42no—
582C3×D3—24no—
583C3×D3—24no—
584C3×D3—42no—
585C24—31no—
586C24—31no—
587C24—34no—
588C24—38no—
589C24—31no—
590C24—94no—
591C24—92no—
592C24—91no—
593C24—94no—
594C24—124no—
595C24—184no—
596C24—184no—
597C24—364no—
598C24—364no—
599C24C2×D3211yescharacteristic
600C2×D4—34no—
601C2×D4—64no—
602C2×D4—98no—
603C2×D4—98no—
604C2×D4—94no—
605C2×D4—98no—
606C2×D4—94no—
607C2×D4—94no—
608C2×D4—98no—
609C2×D4—188no—
610C2×D4—188no—
611C2×D4—1832no—
612C2×D4—184no—
613C2×D4—1832no—
614C2×D4—184no—
615C2×D4—184no—
616C2×D4—364no—
617C2×D4—364no—
618C22×C4—34no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—31no—
622C22×C4—38no—
623C22×C4—64no—
624C22×C4—94no—
625C22×C4—91no—
626C22×C4—124no—
627C22×C4—184no—
628C22×C4C2×D3212yes—
629C4⋊C4—38no—
630C4⋊C4—98no—
631C22⋊C4—34no—
632C22⋊C4—38no—
633C22⋊C4—38no—
634C22⋊C4—98no—
635C22⋊C4—98no—
636C22⋊C4—98no—
637C22⋊C4C2×D3214yescomplemented
638C22×C3—28no—
639C22×C3—24no—
640C22×C3—24no—
641C22×C3—28no—
642C22×C3—22no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—21no—
646C22×C3—34no—
647C22×C3—34no—
648C22×C3—44no—
649C22×C3—48no—
650C22×C3—68no—
651C22×C3—68no—
652C22×C3—64no—
653C22×C3—64no—
654C22×C3—62no—
655C22×C3—64no—
656C22×C3—1216no—
657C22×C3—124no—
658C22×C3C22×D1214yes—
659C22×C3C22×D1212yes—
660C22×C3C2×D3×D414yes—
661C22×C3C2×D3×D412yes—
662C22×C3#100414yes—
663C22×C3#100914yes—
664C22×C3C24×D311yescharacteristic
665C22×C3C24×D311yescharacteristic
666C2×D3—24no—
667C2×D3—24no—
668C2×D3—28no—
669C2×D3—28no—
670C2×D3—22no—
671C2×D3—24no—
672C2×D3—416no—
673C2×D3—44no—
674C2×D3—68no—
675C2×D3—64no—
676C2×D3—62no—
677C2×D3—64no—
678C2×D3—62no—
679C2×D3—64no—
680C2×D3—64no—
681C2×D3—64no—
682C2×D3—64no—
683C2×D3—64no—
684C2×D3—64no—
685C2×D3—124no—
686C2×D3—124no—
687C2×D3—124no—
688C2×D3—122no—
689C2×D3—1216no—
690C2×D3—1216no—
691C2×D3—1216no—
692C2×D3—1216no—
693C2×D3—1216no—
694C2×D3—1232no—
695C2×D3—128no—
696C2×D3—124no—
697C2×D3—128no—
698C2×D3—124no—
699C2×D3—244no—
700C2×D3C22×D1214yes—
701C2×D3C22×D1214yes—
702C3×C4—24no—
703C3×C4—24no—
704C3×C4—44no—
705C3×C4—62no—
706C3×C4—64no—
707C3×C4—64no—
708Dic3—24no—
709Dic3—22no—
710Dic3—24no—
711Dic3—62no—
712Dic3—62no—
713Dic3—122no—
714C32C2×#53411yescharacteristic, complemented, Sylow
715C23—24no—
716C23—34no—
717C23—34no—
718C23—32no—
719C23—32no—
720C23—316no—
721C23—32no—
722C23—64no—
723C23—64no—
724C23—62no—
725C23—64no—
726C23—94no—
727C23—92no—
728C23—128no—
729C23—1216no—
730C23—188no—
731C23—188no—
732C23—184no—
733C23—182no—
734C23—184no—
735C23—184no—
736C23—184no—
737C23—368no—
738C23—3616no—
739C23—368no—
740C23—3616no—
741C23D3×D1214yes—
742C23C22×D3212yes—
743C23C22×D3211yescharacteristic
744D4—68no—
745D4—1816no—
746D4—1816no—
747D4—188no—
748D4—188no—
749D4—188no—
750D4—368no—
751D4—368no—
752C2×C4—24no—
753C2×C4—34no—
754C2×C4—34no—
755C2×C4—32no—
756C2×C4—68no—
757C2×C4—64no—
758C2×C4—62no—
759C2×C4—64no—
760C2×C4—92no—
761C2×C4—128no—
762C2×C4—188no—
763C2×C4—182no—
764C2×C4C22×D3214yes—
765C2×C3—24no—
766C2×C3—24no—
767C2×C3—21no—
768C2×C3—22no—
769C2×C3—24no—
770C2×C3—44no—
771C2×C3—64no—
772C2×C3—64no—
773C2×C3—122no—
774C2×C3#549314yescomplemented
775C2×C3#565314yescomplemented
776C2×C3C23×D1211yescharacteristic
777C2×C3C22×D3×D411yescharacteristic
778C2×C3C2×#100412yes—
779C2×C3C2×#100912yes—
780D3—24no—
781D3—24no—
782D3—42no—
783D3—128no—
784D3—124no—
785D3—122no—
786D3—124no—
787D3—122no—
788D3—242no—
789C22—24no—
790C22—28no—
791C22—34no—
792C22—34no—
793C22—64no—
794C22—64no—
795C22—68no—
796C22—68no—
797C22—62no—
798C22—64no—
799C22—1216no—
800C22—124no—
801C22—184no—
802C22—182no—
803C22—184no—
804C22—184no—
805C22—184no—
806C22—3616no—
807C22—3616no—
808C22—368no—
809C22—364no—
810C22C2×D3×D1214yes—
811C22C2×D3×D1212yes—
812C22#6431414yes—
813C22C23×D3211yescharacteristic
814C4—24no—
815C4—64no—
816C4—62no—
817C4—64no—
818C4—182no—
819C3—21no—
820C3C2×#549311yescharacteristic, complemented
821C3C2×#565311yescharacteristic, complemented
822C2—24no—
823C2—64no—
824C2—64no—
825C2—122no—
826C2—364no—
827C2—362no—
828C2#1059429114yesdirect product factor
829C2C22×D3×D1211yescharacteristic
830C2C2×#6431412yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C23×#626C2semidirect
3. C2×#64091C2semidirect
4. C2×C3×#886C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C2×#63981C2semidirect
7. C2×#63966C2semidirect
8. C2×#63923C2semidirect
9. C2×#63909C2semidirect
10. C2×#63906C2semidirect
11. C2×#63890C2semidirect
12. #10594291C2direct (N × H)
15. C24×C3⋊D3C22semidirect
17. C23×D32C22semidirect
19. C22×C4⋊(C3⋊D3)C22semidirect
21. C23×C3×Dic3C22semidirect
22. C22×C3×C4×D3C22semidirect
24. C2×D3×#67C22semidirect
27. C22×#626C22semidirect
28. C22×#626C22semidirect
29. C22×#626C22semidirect
30. C22×#626C22semidirect
31. C22×#625C22semidirect
32. C22×D3×Dic3C22semidirect
33. C2×C32×C22⋊C4C22semidirect
34. C2×#3752C22semidirect
35. #64091C22semidirect
36. C2×C3×#217C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C3×#886C22semidirect
41. C3×D3×C22⋊C4C22semidirect
42. #63981C22semidirect
43. #63966C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
45. C2×#3722C22semidirect
46. C2×#3722C22semidirect
47. #63923C22semidirect
48. #63909C22semidirect
49. #63906C22semidirect
50. #63890C22semidirect
67. C2×#886D3semidirect
75. C2×D3×C22⋊C4D3semidirect
81. C23×C3⋊D3C23semidirect
83. C23×C3×D3D4semidirect
90. C22×D32C23semidirect
96. C2×C4⋊(C3⋊D3)C23semidirect
103. C22×C3×Dic3C23semidirect
105. C2×C3×C4×D3C23semidirect
113. C2×#626C23semidirect
114. C2×#626C23semidirect
115. C2×#626C23semidirect
117. C2×#625C23semidirect
119. C2×D3×Dic3C23semidirect
120. C32×C22⋊C4C23semidirect
121. #3752C23semidirect
122. C3×#217C23semidirect
123. C3×(C2×D3)⋊C4C23semidirect
124. C3×(C2×D3)⋊C4C23semidirect
125. C3×C4⋊Dic3C23semidirect
126. Dic3⋊Dic3C23semidirect
127. #3722C23semidirect
128. #3722C23semidirect
155. C23×Dic3C2×D3semidirect
168. C22×C4×D3C2×D3semidirect
176. C2×C3×C22⋊C4C2×D3semidirect
177. C2×C3×C22⋊C4C2×D3semidirect
178. C2×#217C2×D3semidirect
190. C2×(C2×D3)⋊C4C2×D3semidirect
191. C2×(C2×D3)⋊C4C2×D3semidirect
193. C2×C4⋊Dic3C2×D3semidirect
199. #886C2×D3semidirect
207. D3×C22⋊C4C2×D3semidirect
230. C22×C3×D3C2×D4semidirect
301. C23×D3D12semidirect
349. C22×Dic3C22×D3semidirect
369. C2×C4×D3C22×D3semidirect
375. C3×C22⋊C4C22×D3semidirect
376. C3×C22⋊C4C22×D3semidirect
377. #217C22×D3semidirect
385. (C2×D3)⋊C4C22×D3semidirect
386. (C2×D3)⋊C4C22×D3semidirect
388. C4⋊Dic3C22×D3semidirect
455. C2×C22⋊C4D32semidirect
524. C22×D3C2×D12semidirect
577. C2×C32#534semidirect
637. C22⋊C4C2×D32semidirect
714. C32C2×#534semidirect
774. C2×C3#5493semidirect
775. C2×C3#5653semidirect
820. C3C2×#5493semidirect
821. C3C2×#5653semidirect
828. C2#10594291direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C23×#6262
C2×#640912
C2×C3×#8862
C2×C3×D3×C22⋊C42
C2×#639812
C2×#639662
C2×#639232
C2×#639092
C2×#639062
C2×#638902
#105942912
C2×#56533
C2×#54933