Finite Group Databasebeta

← C2×#10594078 #11900441

Subgroups — C2×#10594078 #11900441

Order 1152.

3931 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C23×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×#64095C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic, complemented
5C2×C3×#877C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63962C211yesmaximal, characteristic, complemented
8C2×#63893C212yesmaximal, complemented
9C2×Dic3×D12C212yesmaximal, complemented
10C2×#63886C212yesmaximal, complemented
11C2×#63880C212yesmaximal, complemented
12#10594078C2116yesmaximal, direct product factor
13C2×#5586—31nomaximal
14C2×#5524—31nomaximal
15C24×C3×D3C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×D12C2212yes—
21C22×#627C2211yescharacteristic, complemented
22C22×#626C2212yes—
23C22×#626C2211yescharacteristic, complemented
24C22×#624C2211yescharacteristic, complemented
25C2×#3804—28no—
26C2×#3804C2218yescomplemented
27C22×D3×Dic3—28no—
28C22×D3×Dic3C2212yes—
29C22×D3×Dic3C2212yes—
30C22×D3×Dic3C2218yescomplemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3752C2212yescomplemented
34C2×C4⋊(C3⋊Dic3)C2212yescomplemented
35#64095C2218yescomplemented
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2212yescomplemented
39C2×C3×C4×Dic3C2212yescomplemented
40C3×#882C2218yescomplemented
41C3×#877C2218yescomplemented
42#63977C2218yescomplemented
43C2×Dic3⋊Dic3C2212yescomplemented
44#63962C2218yescomplemented
45C2×(C2×D3)⋊Dic3C2212yes—
46C2×(C2×D3)⋊Dic3C2212yescomplemented
47#63893C22116yescomplemented
48Dic3×D12C22116yescomplemented
49#63886C22116yescomplemented
50#63880C22116yescomplemented
51C24×Dic3—31no—
52C22×#237—31no—
53C22×#235—31no—
54C23×C4×D3—31no—
55C2×C3×#120—31no—
56C2×C3×#117—31no—
57C2×#953—31no—
58C2×#939—32no—
59C2×#935—31no—
60C2×D4×Dic3—32no—
61#5586—316no—
62#5524—316no—
63C2×#897—32no—
64C2×#895—32no—
65C2×#886—31no—
66C2×#886—31no—
67C2×#886—31no—
68C2×#886—61no—
69C2×#882—31no—
70C2×#882D311yescharacteristic, complemented
71C2×#67⋊C4—32no—
72C2×#878—32no—
73C2×#877D311yescharacteristic, complemented
74C2×C4×D12—32no—
75C2×C4×D12—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3—24no—
79C23×C3×D3—28no—
80C23×C3×D3C2314yes—
81C23×C3×D3C2311yescharacteristic
82C23×C3×D3C2312yes—
83C22×C32×C4C2312yes—
84C2×#638—24no—
85C2×#638C2314yes—
86C22×C3⋊Dic3—24no—
87C22×C3⋊Dic3C2312yes—
88C22×C3⋊Dic3C2314yes—
89C22×C3⋊Dic3C2311yescharacteristic
90C2×C3×#67—24no—
91C2×C3×#67C2314yes—
92C22×C3×Dic3D418yescomplemented
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2314yes—
98C2×C3×D12—28no—
99C2×C3×D12C2318yes—
100C2×#627—24no—
101C2×#627C2314yescomplemented
102C2×#626—28no—
103C2×#626—24no—
104C2×#626C2318yes—
105C2×#626C2314yescomplemented
106C2×#624—24no—
107C2×#624C2314yescomplemented
108#3804—232no—
109C2×D3×Dic3—28no—
110C2×D3×Dic3—28no—
111C2×D3×Dic3—24no—
112C2×D3×Dic3—232no—
113C2×D3×Dic3C2318yes—
114C2×D3×Dic3C2318yes—
115C2×D3×Dic3C2314yescomplemented
116C32×C22⋊C4C2314yes—
117#3752C2318yescomplemented
118C4⋊(C3⋊Dic3)C2318yescomplemented
119C3×#217C2314yes—
120C3×(C2×D3)⋊C4C2318yes—
121C3×Dic3⋊C4C2318yescomplemented
122C3×C4×Dic3C2318yescomplemented
123Dic3⋊Dic3C2318yescomplemented
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#525—91noSylow
127C25×C3—31no—
128C24×D3C2×D311yescharacteristic
129C22×C3×D4—31no—
130C22×C3×D4—32no—
131C23×C3×C4—31no—
132C22×#67—31no—
133C22×#67—31no—
134C22×#67—31no—
135C22×#67—32no—
136C22×#67—61no—
137C22×#67C2×D311yescharacteristic
138C23×Dic3—31no—
139C23×Dic3—31no—
140C23×Dic3—32no—
141C23×Dic3—32no—
142C23×Dic3—31no—
143C23×Dic3—38no—
144C23×Dic3—61no—
145C23×Dic3—68no—
146C23×Dic3C2×D311yescharacteristic
147C2×#237—38no—
148C2×#237—68no—
149C2×#235—38no—
150C2×#235—68no—
151C22×D12—31no—
152C22×D12—32no—
153C22×D12C2×D312yes—
154C22×C4×D3—32no—
155C22×C4×D3—32no—
156C22×C4×D3—38no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—68no—
161C22×Dic6—31no—
162C22×Dic6—31no—
163C3×#120—38no—
164C3×#117—38no—
165C2×C3×C4⋊C4—32no—
166C2×C3×C22⋊C4—21no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—32no—
169C2×C3×C22⋊C4C2×D311yescharacteristic
170C2×C3×C22⋊C4C2×D311yescharacteristic
171C2×C3×C42—32no—
172#953—38no—
173C2×#217—32no—
174C2×#217—32no—
175C2×#217C2×D311yescharacteristic
176#939—316no—
177#935—38no—
178D4×Dic3—316no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—62no—
184C2×(C2×D3)⋊C4C2×D312yes—
185C2×C4⋊Dic3—32no—
186C2×C4⋊Dic3—32no—
187C2×C4⋊Dic3—32no—
188C2×C4⋊Dic3—62no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4C2×D312yescomplemented
191C2×C4×Dic3C2×D312yescomplemented
192#897—316no—
193#895—316no—
194#886—38no—
195#886—38no—
196#886—38no—
197#886—68no—
198#882—38no—
199#882C2×D318yescomplemented
200#67⋊C4—316no—
201#878—316no—
202#877C2×D318yescomplemented
203C4×D12—316no—
204C4×D12—316no—
205C23×C32—24no—
206C23×C32C2×D414yes—
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3⋊D3—22no—
210C22×C3⋊D3—24no—
211C22×C3⋊D3C2412yes—
212C22×C3×D3—232no—
213C22×C3×D3—28no—
214C22×C3×D3—24no—
215C22×C3×D3—24no—
216C22×C3×D3—216no—
217C22×C3×D3—22no—
218C22×C3×D3—24no—
219C22×C3×D3#4118yescomplemented
220C22×C3×D3C2412yes—
221C22×C3×D3C2414yes—
222C2×C32×C4—24no—
223C2×C32×C4C2414yes—
224#638—28no—
225C2×C3⋊Dic3—28no—
226C2×C3⋊Dic3—24no—
227C2×C3⋊Dic3—22no—
228C2×C3⋊Dic3C2412yes—
229C2×C3⋊Dic3C2414yes—
230C3×#67—28no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3C2×D414yes—
234C2×C3×Dic3C2×D414yes—
235C2×C3×Dic3C2×D4116yescomplemented
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2412yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2412yes—
240C3×D12—216no—
241#627—28no—
242#626—216no—
243#626—28no—
244#624—28no—
245D3×Dic3—216no—
246D3×Dic3—216no—
247D3×Dic3—28no—
248C22×#41—91no—
249C24×C4—91no—
250#525—916no—
251C2×#123—91no—
252C2×#123—91no—
253C2×C22⋊Q8—92no—
254C2×#121—92no—
255C2×#120—31no—
256C2×#120—91no—
257C2×C4×D4—92no—
258C2×C4×D4—92no—
259C2×#117—31no—
260C24×C3—21no—
261C24×C3—32no—
262C24×C3—34no—
263C24×C3—31no—
264C24×C3—68no—
265C24×C3—64no—
266C24×C3C22×D311yescharacteristic
267C24×C3C22×D311yescharacteristic
268C23×D3—24no—
269C23×D3—28no—
270C23×D3—31no—
271C23×D3—31no—
272C23×D3—61no—
273C23×D3C22×D314yes—
274C23×D3C22×D311yescharacteristic
275C23×D3C22×D312yes—
276C2×C3×D4—34no—
277C2×C3×D4—38no—
278C2×C3×D4—68no—
279C2×C3×D4—64no—
280C22×C3×C4—22no—
281C22×C3×C4—38no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—34no—
285C22×C3×C4—31no—
286C22×C3×C4—32no—
287C22×C3×C4C22×D312yes—
288C22×C3×C4C22×D312yes—
289C2×#67—24no—
290C2×#67—34no—
291C2×#67—34no—
292C2×#67—38no—
293C2×#67—34no—
294C2×#67—64no—
295C2×#67—68no—
296C2×#67—64no—
297C2×#67—64no—
298C2×#67—64no—
299C2×#67—124no—
300C2×#67C22×D314yes—
301C22×Dic3—34no—
302C22×Dic3—34no—
303C22×Dic3—32no—
304C22×Dic3—31no—
305C22×Dic3—32no—
306C22×Dic3—31no—
307C22×Dic3—38no—
308C22×Dic3—38no—
309C22×Dic3—34no—
310C22×Dic3—64no—
311C22×Dic3—61no—
312C22×Dic3—62no—
313C22×Dic3—64no—
314C22×Dic3—64no—
315C22×Dic3—64no—
316C22×Dic3—68no—
317C22×Dic3—68no—
318C22×Dic3—632no—
319C22×Dic3—124no—
320C22×Dic3D1218yescomplemented
321C22×Dic3C22×D312yes—
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D314yes—
326#237—632no—
327#235—632no—
328C2×D12—28no—
329C2×D12—38no—
330C2×D12—34no—
331C2×D12—64no—
332C2×D12—68no—
333C2×D12C22×D318yes—
334C2×C4×D3—38no—
335C2×C4×D3—34no—
336C2×C4×D3—38no—
337C2×C4×D3—34no—
338C2×C4×D3—34no—
339C2×C4×D3—64no—
340C2×C4×D3—68no—
341C2×C4×D3—68no—
342C2×C4×D3—632no—
343C2×C4×D3—64no—
344C2×C4×D3—64no—
345C2×Dic6—34no—
346C2×Dic6—34no—
347C2×Dic6—64no—
348C2×Dic6—64no—
349C3×C4⋊C4—38no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4—38no—
353C3×C22⋊C4C22×D314yes—
354C3×C22⋊C4C22×D314yes—
355C3×C42—38no—
356#217—38no—
357#217—38no—
358#217C22×D314yes—
359(C2×D3)⋊C4—38no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—68no—
364(C2×D3)⋊C4C22×D318yes—
365C4⋊Dic3—38no—
366C4⋊Dic3—38no—
367C4⋊Dic3—38no—
368C4⋊Dic3—68no—
369Dic3⋊C4—38no—
370Dic3⋊C4C22×D318yescomplemented
371C4×Dic3C22×D318yescomplemented
372C22×C32—28no—
373C22×C32—24no—
374C22×C32C22×D414yes—
375C22×C32C22×D412yes—
376C22×C32C2×#4114yes—
377C22×C32C2511yescharacteristic
378C2×C3⋊D3—22no—
379C2×C3⋊D3—24no—
380C2×C3⋊D3—44no—
381C2×C3×D3—232no—
382C2×C3×D3—216no—
383C2×C3×D3—24no—
384C2×C3×D3—24no—
385C2×C3×D3—22no—
386C2×C3×D3—24no—
387C2×C3×D3—44no—
388C2×C3×D3C2×#4118yescomplemented
389C32×C4—24no—
390C3⋊Dic3—24no—
391C3⋊Dic3—22no—
392C3×Dic3—22no—
393C3×Dic3—24no—
394C3×Dic3C22×D414yes—
395C3×Dic3C22×D414yes—
396C25—31no—
397C2×#41—98no—
398C2×#41—188no—
399C22×Q8—91no—
400C22×D4—31no—
401C22×D4—32no—
402C22×D4—92no—
403C22×D4—91no—
404C22×D4—91no—
405C23×C4—31no—
406C23×C4—91no—
407C23×C4—92no—
408C23×C4—91no—
409C23×C4—92no—
410C23×C4—98no—
411C23×C4—91no—
412C23×C4—188no—
413#123—98no—
414#123—98no—
415C22⋊Q8—916no—
416#121—916no—
417#120—38no—
418#120—98no—
419C4×D4—916no—
420C4×D4—916no—
421#117—38no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—92no—
424C2×C4⋊C4—92no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—32no—
427C2×C22⋊C4—92no—
428C2×C22⋊C4—92no—
429C2×C22⋊C4—92no—
430C2×C22⋊C4D3211yescharacteristic
431C2×C42—32no—
432C23×C3—24no—
433C23×C3—24no—
434C23×C3—22no—
435C23×C3—21no—
436C23×C3—24no—
437C23×C3—38no—
438C23×C3—34no—
439C23×C3—32no—
440C23×C3—44no—
441C23×C3—616no—
442C23×C3—632no—
443C23×C3—68no—
444C23×C3—64no—
445C23×C3—64no—
446C23×C3—62no—
447C23×C3—64no—
448C23×C3C2×D1214yes—
449C23×C3D3×D414yes—
450C23×C3C23×D312yes—
451C23×C3C23×D312yes—
452C23×C3C23×D311yescharacteristic
453C23×C3C23×D311yescharacteristic
454C22×D3—232no—
455C22×D3—28no—
456C22×D3—24no—
457C22×D3—24no—
458C22×D3—216no—
459C22×D3—22no—
460C22×D3—24no—
461C22×D3—32no—
462C22×D3—32no—
463C22×D3—62no—
464C22×D3—62no—
465C22×D3—62no—
466C22×D3—64no—
467C22×D3—64no—
468C22×D3—122no—
469C22×D3—124no—
470C22×D3#23718yescomplemented
471C22×D3C23×D312yes—
472C22×D3C23×D314yes—
473C3×D4—616no—
474C3×D4—68no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—34no—
479C2×C3×C4—34no—
480C2×C3×C4—316no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—34no—
485C2×C3×C4—44no—
486C2×C3×C4—62no—
487C2×C3×C4—64no—
488C2×C3×C4C23×D314yes—
489C2×C3×C4C23×D314yes—
490#67—28no—
491#67—616no—
492#67—68no—
493#67—68no—
494#67—68no—
495#67—128no—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—34no—
499C2×Dic3—32no—
500C2×Dic3—34no—
501C2×Dic3—32no—
502C2×Dic3—62no—
503C2×Dic3—64no—
504C2×Dic3—62no—
505C2×Dic3—68no—
506C2×Dic3—64no—
507C2×Dic3—62no—
508C2×Dic3—68no—
509C2×Dic3—64no—
510C2×Dic3—68no—
511C2×Dic3—616no—
512C2×Dic3—616no—
513C2×Dic3—124no—
514C2×Dic3—128no—
515C2×Dic3—122no—
516C2×Dic3C2×D1214yes—
517C2×Dic3C2×D1214yes—
518C2×Dic3C2×D12116yescomplemented
519C2×Dic3C23×D314yes—
520C2×Dic3C23×D312yes—
521C2×Dic3C23×D312yes—
522C2×Dic3C23×D312yes—
523D12—216no—
524D12—68no—
525D12—616no—
526C4×D3—68no—
527C4×D3—616no—
528C4×D3—616no—
529C4×D3—68no—
530C4×D3—68no—
531Dic6—68no—
532Dic6—68no—
533C2×C32—24no—
534C2×C32#52514yescomplemented
535C2×C32C23×D411yescharacteristic
536C2×C32C22×#4112yes—
537C3⋊D3—42no—
538C3×D3—28no—
539C3×D3—42no—
540C24—32no—
541C24—34no—
542C24—31no—
543C24—68no—
544C24—64no—
545C24—91no—
546C24C2×D3211yescharacteristic
547#41—1832no—
548C2×Q8—94no—
549C2×Q8—184no—
550C2×D4—34no—
551C2×D4—38no—
552C2×D4—68no—
553C2×D4—64no—
554C2×D4—98no—
555C2×D4—94no—
556C2×D4—94no—
557C2×D4—184no—
558C2×D4—188no—
559C2×D4—184no—
560C22×C4—34no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—38no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—94no—
567C22×C4—98no—
568C22×C4—94no—
569C22×C4—98no—
570C22×C4—94no—
571C22×C4—92no—
572C22×C4—91no—
573C22×C4—184no—
574C22×C4—188no—
575C22×C4—188no—
576C22×C4—1832no—
577C22×C4—184no—
578C22×C4—184no—
579C22×C4C2×D3212yes—
580C4⋊C4—38no—
581C4⋊C4—98no—
582C4⋊C4—98no—
583C22⋊C4—34no—
584C22⋊C4—38no—
585C22⋊C4—98no—
586C22⋊C4—98no—
587C22⋊C4—98no—
588C22⋊C4C2×D3214yes—
589C42—38no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—28no—
593C22×C3—28no—
594C22×C3—22no—
595C22×C3—24no—
596C22×C3—24no—
597C22×C3—21no—
598C22×C3—38no—
599C22×C3—48no—
600C22×C3—44no—
601C22×C3—632no—
602C22×C3—64no—
603C22×C3—64no—
604C22×C3—616no—
605C22×C3—62no—
606C22×C3—64no—
607C22×C3—124no—
608C22×C3C22×D1214yes—
609C22×C3C22×D1212yes—
610C22×C3C2×D3×D414yes—
611C22×C3C2×D3×D412yes—
612C22×C3C2×#23714yes—
613C22×C3D3×#4114yes—
614C22×C3C24×D311yescharacteristic
615C22×C3C24×D311yescharacteristic
616C2×D3—232no—
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—216no—
620C2×D3—22no—
621C2×D3—24no—
622C2×D3—44no—
623C2×D3—62no—
624C2×D3—62no—
625C2×D3—64no—
626C2×D3—64no—
627C2×D3—122no—
628C2×D3—124no—
629C2×D3—124no—
630C2×D3—124no—
631C2×D3—244no—
632C2×D3C2×#23718yescomplemented
633C3×C4—24no—
634C3×C4—24no—
635C3×C4—34no—
636C3×C4—34no—
637C3×C4—44no—
638C3×C4—62no—
639C3×C4—64no—
640Dic3—22no—
641Dic3—24no—
642Dic3—62no—
643Dic3—64no—
644Dic3—62no—
645Dic3—64no—
646Dic3—124no—
647Dic3—122no—
648Dic3C22×D1214yes—
649Dic3C22×D1214yes—
650C32C2×#52511yescharacteristic, complemented, Sylow
651C23—24no—
652C23—38no—
653C23—34no—
654C23—32no—
655C23—616no—
656C23—632no—
657C23—68no—
658C23—64no—
659C23—64no—
660C23—62no—
661C23—64no—
662C23—92no—
663C23—182no—
664C23—184no—
665C23D3×D1214yes—
666C23C22×D3212yes—
667C23C22×D3211yescharacteristic
668Q8—188no—
669D4—616no—
670D4—68no—
671D4—188no—
672D4—1816no—
673D4—188no—
674C2×C4—24no—
675C2×C4—34no—
676C2×C4—34no—
677C2×C4—316no—
678C2×C4—32no—
679C2×C4—32no—
680C2×C4—34no—
681C2×C4—32no—
682C2×C4—62no—
683C2×C4—64no—
684C2×C4—94no—
685C2×C4—92no—
686C2×C4—188no—
687C2×C4—1816no—
688C2×C4—1816no—
689C2×C4—188no—
690C2×C4—188no—
691C2×C4—184no—
692C2×C4—182no—
693C2×C4C22×D3214yes—
694C2×C3—24no—
695C2×C3—24no—
696C2×C3—24no—
697C2×C3—21no—
698C2×C3—22no—
699C2×C3—44no—
700C2×C3—68no—
701C2×C3—122no—
702C2×C3#552414yescomplemented
703C2×C3#558614yescomplemented
704C2×C3C23×D1211yescharacteristic
705C2×C3C22×D3×D411yescharacteristic
706C2×C3C22×#23712yes—
707C2×C3C2×D3×#4112yes—
708D3—28no—
709D3—42no—
710D3—122no—
711D3—122no—
712D3—242no—
713C22—28no—
714C22—24no—
715C22—38no—
716C22—632no—
717C22—616no—
718C22—64no—
719C22—64no—
720C22—62no—
721C22—64no—
722C22—124no—
723C22—182no—
724C22—184no—
725C22—364no—
726C22C2×D3×D1214yes—
727C22C2×D3×D1212yes—
728C22D3×#23714yes—
729C22C23×D3211yescharacteristic
730C4—24no—
731C4—34no—
732C4—34no—
733C4—62no—
734C4—64no—
735C4—184no—
736C4—182no—
737C3—21no—
738C3C2×#552411yescharacteristic, complemented
739C3C2×#558611yescharacteristic, complemented
740C2—24no—
741C2—68no—
742C2—122no—
743C2—362no—
744C2#1059407814yesdirect product factor
745C2C22×D3×D1211yescharacteristic
746C2C2×D3×#23712yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#525
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×#3804C2semidirect
2. C23×D3×Dic3C2semidirect
3. C2×#64095C2semidirect
4. C2×C3×#882C2semidirect
5. C2×C3×#877C2semidirect
6. C2×#63977C2semidirect
7. C2×#63962C2semidirect
8. C2×#63893C2semidirect
9. C2×Dic3×D12C2semidirect
10. C2×#63886C2semidirect
11. C2×#63880C2semidirect
12. #10594078C2direct (N × H)
21. C22×#627C22semidirect
23. C22×#626C22semidirect
24. C22×#624C22semidirect
26. C2×#3804C22semidirect
30. C22×D3×Dic3C22semidirect
31. C22×D3×Dic3C22semidirect
33. C2×#3752C22semidirect
34. C2×C4⋊(C3⋊Dic3)C22semidirect
35. #64095C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C3×#882C22semidirect
41. C3×#877C22semidirect
42. #63977C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
44. #63962C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. #63893C22semidirect
48. Dic3×D12C22semidirect
49. #63886C22semidirect
50. #63880C22semidirect
70. C2×#882D3semidirect
73. C2×#877D3semidirect
92. C22×C3×Dic3D4semidirect
101. C2×#627C23semidirect
105. C2×#626C23semidirect
107. C2×#624C23semidirect
115. C2×D3×Dic3C23semidirect
117. #3752C23semidirect
118. C4⋊(C3⋊Dic3)C23semidirect
121. C3×Dic3⋊C4C23semidirect
122. C3×C4×Dic3C23semidirect
123. Dic3⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
190. C2×Dic3⋊C4C2×D3semidirect
191. C2×C4×Dic3C2×D3semidirect
199. #882C2×D3semidirect
202. #877C2×D3semidirect
219. C22×C3×D3#41semidirect
235. C2×C3×Dic3C2×D4semidirect
320. C22×Dic3D12semidirect
370. Dic3⋊C4C22×D3semidirect
371. C4×Dic3C22×D3semidirect
388. C2×C3×D3C2×#41semidirect
470. C22×D3#237semidirect
518. C2×Dic3C2×D12semidirect
534. C2×C32#525semidirect
632. C2×D3C2×#237semidirect
650. C32C2×#525semidirect
702. C2×C3#5524semidirect
703. C2×C3#5586semidirect
738. C3C2×#5524semidirect
739. C3C2×#5586semidirect
744. C2#10594078direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C23×D3×Dic32
C2×#640952
C2×C3×#8822
C2×C3×#8772
C2×#639772
C2×#639622
C2×#638932
C2×Dic3×D122
C2×#638862
C2×#638802
#105940782
C2×#55863
C2×#55243