Finite Group Databasebeta

← C2×#10594079 #11900439

Subgroups — C2×#10594079 #11900439

Order 1152.

4091 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#624C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C2×C3×#886C211yesmaximal, characteristic, complemented
5C2×C3×#877C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63966C211yesmaximal, characteristic, complemented
8C2×#63910C212yesmaximal, complemented
9C2×#63895C212yesmaximal, complemented
10C2×#63894C212yesmaximal, complemented
11C2×#63880C212yesmaximal, complemented
12#10594079C2116yesmaximal, direct product factor
13C2×#5656—31nomaximal
14C2×#5524—31nomaximal
15C24×C3⋊D3C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4⋊(C3⋊D3)C2212yes—
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×#627C2211yescharacteristic, complemented
22C22×#626C2212yes—
23C22×#626C2211yescharacteristic, complemented
24C22×#624—28no—
25C22×#624C2212yes—
26C22×#624C2212yes—
27C22×#624C2218yescomplemented
28C22×#624C2211yescharacteristic, complemented
29C2×#3804—28no—
30C2×#3804C2218yescomplemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3752C2212yes—
34#64091C2218yescomplemented
35C2×C3×#217C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×C4⋊Dic3C2212yescomplemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39C2×C3×C4×Dic3C2212yescomplemented
40C3×#886C2218yescomplemented
41C3×#877C2218yescomplemented
42#63981C2218yescomplemented
43#63966C2218yescomplemented
44C2×Dic3⋊Dic3C2212yescomplemented
45C2×#3722C2212yes—
46C2×#3722C2212yescomplemented
47#63910C22116yescomplemented
48#63895C22116yescomplemented
49#63894C22116yescomplemented
50#63880C22116yescomplemented
51C22×#237—31no—
52C22×#235—31no—
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C2×C3×#123—31no—
56C2×C3×#117—31no—
57C2×#937—31no—
58C2×#929—31no—
59#5656—316no—
60#5524—316no—
61C2×#897—32no—
62C2×#896—32no—
63C2×#895—32no—
64C2×#893—32no—
65C2×#886—31no—
66C2×#886D311yescharacteristic, complemented
67C2×#884—32no—
68C2×#882—31no—
69C2×#882—31no—
70C2×#882—31no—
71C2×#882—61no—
72C2×#67⋊C4—32no—
73C2×#877D311yescharacteristic, complemented
74C2×C4×D12—32no—
75C2×C4×D12—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3—24no—
78C23×C3⋊D3—28no—
79C23×C3⋊D3C2314yes—
80C23×C3⋊D3C2311yescharacteristic
81C23×C3⋊D3C2312yes—
82C23×C3×D3C2311yescharacteristic
83C22×C32×C4C2312yes—
84C2×#638—24no—
85C2×#638C2314yes—
86C22×C3⋊Dic3C2311yescharacteristic
87C2×C4⋊(C3⋊D3)—28no—
88C2×C4⋊(C3⋊D3)C2318yes—
89C2×C3×#67—24no—
90C2×C3×#67C2314yes—
91C22×C3×Dic3—24no—
92C22×C3×Dic3D418yescomplemented
93C22×C3×Dic3C2314yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2314yes—
100C2×#627—24no—
101C2×#627C2314yescomplemented
102C2×#626—28no—
103C2×#626—24no—
104C2×#626C2318yes—
105C2×#626C2314yescomplemented
106C2×#624—24no—
107C2×#624—28no—
108C2×#624—28no—
109C2×#624—232no—
110C2×#624C2318yes—
111C2×#624C2318yes—
112C2×#624C2314yescomplemented
113#3804—232no—
114C2×D3×Dic3—24no—
115C2×D3×Dic3C2314yescomplemented
116C32×C22⋊C4C2314yes—
117#3752C2318yes—
118C3×#217C2314yes—
119C3×(C2×D3)⋊C4C2318yescomplemented
120C3×C4⋊Dic3C2318yescomplemented
121C3×Dic3⋊C4C2318yescomplemented
122C3×C4×Dic3C2318yescomplemented
123Dic3⋊Dic3C2318yescomplemented
124#3722C2318yes—
125#3722C2318yescomplemented
126C2×#525—91noSylow
127C24×D3—31no—
128C24×D3—31no—
129C24×D3—61no—
130C22×C3×D4—31no—
131C23×C3×C4—31no—
132C23×C3×C4—31no—
133C22×#67—31no—
134C22×#67—31no—
135C22×#67—31no—
136C22×#67—32no—
137C22×#67—61no—
138C22×#67C2×D311yescharacteristic
139C23×Dic3—31no—
140C23×Dic3C2×D311yescharacteristic
141C23×Dic3C2×D311yescharacteristic
142C2×#237—38no—
143C2×#237—68no—
144C2×#235—38no—
145C2×#235—68no—
146C22×D12—31no—
147C22×D12—32no—
148C22×D12—32no—
149C22×D12—32no—
150C22×D12—62no—
151C22×C4×D3—31no—
152C22×C4×D3—38no—
153C22×C4×D3—32no—
154C22×C4×D3—32no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3—38no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—68no—
161C22×C4×D3—68no—
162C22×Dic6—31no—
163C22×Dic6—31no—
164C3×#123—38no—
165C3×#117—38no—
166C2×C3×C4⋊C4—32no—
167C2×C3×C4⋊C4—32no—
168C2×C3×C22⋊C4—21no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—32no—
171C2×C3×C22⋊C4C2×D311yescharacteristic
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C42—32no—
174C2×#217C2×D311yescharacteristic
175#937—38no—
176#929—38no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
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×D312yescomplemented
185C2×C4⋊Dic3—32no—
186C2×C4⋊Dic3C2×D312yescomplemented
187C2×Dic3⋊C4—32no—
188C2×Dic3⋊C4C2×D312yescomplemented
189C2×C4×Dic3C2×D312yescomplemented
190#897—316no—
191#896—316no—
192#895—316no—
193#893—316no—
194#886—38no—
195#886C2×D318yescomplemented
196#884—316no—
197#882—38no—
198#882—38no—
199#882—38no—
200#882—68no—
201#67⋊C4—316no—
202#877C2×D318yescomplemented
203C4×D12—316no—
204C4×D12—316no—
205C23×C32—24no—
206C23×C32C2×D414yes—
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3⋊D3—232no—
210C22×C3⋊D3—28no—
211C22×C3⋊D3—24no—
212C22×C3⋊D3—24no—
213C22×C3⋊D3—216no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3—24no—
216C22×C3⋊D3#4118yescomplemented
217C22×C3⋊D3C2412yes—
218C22×C3⋊D3C2414yes—
219C22×C3×D3—22no—
220C22×C3×D3—24no—
221C22×C3×D3C2412yes—
222C2×C32×C4—24no—
223C2×C32×C4C2414yes—
224#638—28no—
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3C2412yes—
227C4⋊(C3⋊D3)—216no—
228C3×#67—28no—
229C2×C3×Dic3—28no—
230C2×C3×Dic3—24no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3C2×D414yes—
234C2×C3×Dic3C2×D414yes—
235C2×C3×Dic3C2×D4116yescomplemented
236C2×C3×Dic3C2412yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2414yes—
239C2×C3×Dic3C2412yes—
240C2×C3×Dic3C2412yes—
241#627—28no—
242#626—216no—
243#626—28no—
244#624—28no—
245#624—216no—
246#624—216no—
247D3×Dic3—28no—
248C22×#41—91no—
249C24×C4—91no—
250#525—916no—
251C2×#123—31no—
252C2×#123—91no—
253C2×C22⋊Q8—92no—
254C2×#121—92no—
255C2×#120—91no—
256C2×#120—91no—
257C2×C4×D4—92no—
258C2×C4×D4—92no—
259C2×#117—31no—
260C24×C3—21no—
261C24×C3—31no—
262C24×C3C22×D311yescharacteristic
263C24×C3C22×D311yescharacteristic
264C23×D3—32no—
265C23×D3—32no—
266C23×D3—34no—
267C23×D3—34no—
268C23×D3—31no—
269C23×D3—31no—
270C23×D3—62no—
271C23×D3—64no—
272C23×D3—61no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—64no—
276C23×D3—64no—
277C23×D3—128no—
278C23×D3—124no—
279C23×D3C22×D311yescharacteristic
280C2×C3×D4—34no—
281C2×C3×D4—64no—
282C22×C3×C4—22no—
283C22×C3×C4—38no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—34no—
287C22×C3×C4—32no—
288C22×C3×C4—32no—
289C22×C3×C4—31no—
290C22×C3×C4—34no—
291C22×C3×C4—64no—
292C22×C3×C4C22×D312yes—
293C22×C3×C4C22×D312yes—
294C2×#67—24no—
295C2×#67—34no—
296C2×#67—34no—
297C2×#67—38no—
298C2×#67—34no—
299C2×#67—64no—
300C2×#67—68no—
301C2×#67—64no—
302C2×#67—64no—
303C2×#67—64no—
304C2×#67—124no—
305C2×#67C22×D314yes—
306C22×Dic3—24no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—34no—
310C22×Dic3—61no—
311C22×Dic3—64no—
312C22×Dic3D1218yescomplemented
313C22×Dic3C22×D314yes—
314C22×Dic3C22×D312yes—
315C22×Dic3C22×D312yes—
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D314yes—
320#237—632no—
321#235—632no—
322C2×D12—38no—
323C2×D12—34no—
324C2×D12—38no—
325C2×D12—38no—
326C2×D12—68no—
327C2×D12—68no—
328C2×D12—68no—
329C2×D12—64no—
330C2×D12—68no—
331C2×D12—128no—
332C2×C4×D3—34no—
333C2×C4×D3—38no—
334C2×C4×D3—34no—
335C2×C4×D3—38no—
336C2×C4×D3—38no—
337C2×C4×D3—34no—
338C2×C4×D3—38no—
339C2×C4×D3—68no—
340C2×C4×D3—68no—
341C2×C4×D3—632no—
342C2×C4×D3—64no—
343C2×C4×D3—64no—
344C2×C4×D3—68no—
345C2×C4×D3—68no—
346C2×C4×D3—64no—
347C2×C4×D3—632no—
348C2×Dic6—34no—
349C2×Dic6—34no—
350C2×Dic6—64no—
351C2×Dic6—64no—
352C3×C4⋊C4—38no—
353C3×C4⋊C4—38no—
354C3×C22⋊C4—24no—
355C3×C22⋊C4—34no—
356C3×C22⋊C4—38no—
357C3×C22⋊C4C22×D314yes—
358C3×C22⋊C4C22×D314yes—
359C3×C42—38no—
360#217C22×D314yes—
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×D318yescomplemented
369C4⋊Dic3—38no—
370C4⋊Dic3C22×D318yescomplemented
371Dic3⋊C4—38no—
372Dic3⋊C4C22×D318yescomplemented
373C4×Dic3C22×D318yescomplemented
374C22×C32—28no—
375C22×C32—24no—
376C22×C32C22×D414yes—
377C22×C32C22×D412yes—
378C22×C32C2×#4114yes—
379C22×C32C2511yescharacteristic
380C2×C3⋊D3—232no—
381C2×C3⋊D3—216no—
382C2×C3⋊D3—24no—
383C2×C3⋊D3—24no—
384C2×C3⋊D3—22no—
385C2×C3⋊D3—24no—
386C2×C3⋊D3—44no—
387C2×C3⋊D3C2×#4118yescomplemented
388C2×C3×D3—22no—
389C2×C3×D3—24no—
390C2×C3×D3—44no—
391C32×C4—24no—
392C3⋊Dic3—22no—
393C3×Dic3—24no—
394C3×Dic3—22no—
395C3×Dic3—24no—
396C3×Dic3C22×D414yes—
397C3×Dic3C22×D414yes—
398C25—91no—
399C2×#41—98no—
400C2×#41—188no—
401C22×Q8—91no—
402C22×D4—31no—
403C22×D4—92no—
404C22×D4—91no—
405C22×D4—91no—
406C22×D4—92no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—92no—
410C23×C4—91no—
411C23×C4—92no—
412C23×C4—98no—
413C23×C4—91no—
414C23×C4—188no—
415#123—38no—
416#123—98no—
417C22⋊Q8—916no—
418#121—916no—
419#120—98no—
420#120—98no—
421C4×D4—916no—
422C4×D4—916no—
423#117—38no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—92no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—92no—
430C2×C22⋊C4—92no—
431C2×C22⋊C4—92no—
432C2×C22⋊C4D3211yescharacteristic
433C2×C42—32no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—22no—
437C23×C3—21no—
438C23×C3—24no—
439C23×C3—32no—
440C23×C3—44no—
441C23×C3—62no—
442C23×C3—64no—
443C23×C3C2×D1214yes—
444C23×C3D3×D414yes—
445C23×C3C23×D312yes—
446C23×C3C23×D312yes—
447C23×C3C23×D311yescharacteristic
448C23×C3C23×D311yescharacteristic
449C22×D3—22no—
450C22×D3—24no—
451C22×D3—38no—
452C22×D3—38no—
453C22×D3—34no—
454C22×D3—34no—
455C22×D3—32no—
456C22×D3—32no—
457C22×D3—68no—
458C22×D3—64no—
459C22×D3—62no—
460C22×D3—616no—
461C22×D3—616no—
462C22×D3—632no—
463C22×D3—632no—
464C22×D3—68no—
465C22×D3—64no—
466C22×D3—68no—
467C22×D3—64no—
468C22×D3—64no—
469C22×D3—64no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—64no—
473C22×D3—64no—
474C22×D3—1216no—
475C22×D3—124no—
476C22×D3—128no—
477C22×D3—124no—
478C22×D3—1232no—
479C22×D3—124no—
480C22×D3—122no—
481C22×D3C23×D312yes—
482C3×D4—68no—
483C2×C3×C4—24no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—34no—
487C2×C3×C4—34no—
488C2×C3×C4—316no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—34no—
492C2×C3×C4—34no—
493C2×C3×C4—32no—
494C2×C3×C4—44no—
495C2×C3×C4—62no—
496C2×C3×C4—68no—
497C2×C3×C4—64no—
498C2×C3×C4—64no—
499C2×C3×C4C23×D314yes—
500C2×C3×C4C23×D314yes—
501#67—28no—
502#67—616no—
503#67—68no—
504#67—68no—
505#67—68no—
506#67—128no—
507C2×Dic3—22no—
508C2×Dic3—28no—
509C2×Dic3—24no—
510C2×Dic3—24no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—62no—
516C2×Dic3—68no—
517C2×Dic3—122no—
518C2×Dic3C2×D1214yes—
519C2×Dic3C2×D1214yes—
520C2×Dic3C2×D12116yescomplemented
521C2×Dic3C23×D314yes—
522C2×Dic3C23×D314yes—
523C2×Dic3C23×D312yes—
524C2×Dic3C23×D312yes—
525C2×Dic3C23×D312yes—
526D12—616no—
527D12—616no—
528D12—68no—
529D12—616no—
530D12—1216no—
531C4×D3—616no—
532C4×D3—616no—
533C4×D3—68no—
534C4×D3—68no—
535C4×D3—616no—
536C4×D3—616no—
537C4×D3—68no—
538Dic6—68no—
539Dic6—68no—
540C2×C32—24no—
541C2×C32#52514yescomplemented
542C2×C32C23×D411yescharacteristic
543C2×C32C22×#4112yes—
544C3⋊D3—28no—
545C3⋊D3—42no—
546C3×D3—42no—
547C24—31no—
548C24—92no—
549C24—94no—
550C24—91no—
551C24—188no—
552C24—184no—
553C24C2×D3211yescharacteristic
554#41—1832no—
555C2×Q8—94no—
556C2×Q8—184no—
557C2×D4—34no—
558C2×D4—64no—
559C2×D4—98no—
560C2×D4—94no—
561C2×D4—94no—
562C2×D4—98no—
563C2×D4—188no—
564C2×D4—184no—
565C2×D4—188no—
566C2×D4—184no—
567C22×C4—34no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—38no—
571C22×C4—34no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—31no—
575C22×C4—64no—
576C22×C4—98no—
577C22×C4—94no—
578C22×C4—98no—
579C22×C4—94no—
580C22×C4—91no—
581C22×C4—188no—
582C22×C4—188no—
583C22×C4—1832no—
584C22×C4—184no—
585C22×C4—184no—
586C22×C4C2×D3212yes—
587C4⋊C4—38no—
588C4⋊C4—38no—
589C4⋊C4—98no—
590C22⋊C4—34no—
591C22⋊C4—38no—
592C22⋊C4—98no—
593C22⋊C4—98no—
594C22⋊C4—98no—
595C22⋊C4C2×D3214yes—
596C42—38no—
597C22×C3—28no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—28no—
601C22×C3—22no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—21no—
605C22×C3—48no—
606C22×C3—44no—
607C22×C3—62no—
608C22×C3—64no—
609C22×C3—124no—
610C22×C3C22×D1214yes—
611C22×C3C22×D1212yes—
612C22×C3C2×D3×D414yes—
613C22×C3C2×D3×D412yes—
614C22×C3D3×#4114yes—
615C22×C3D3×#4114yes—
616C22×C3C24×D311yescharacteristic
617C22×C3C24×D311yescharacteristic
618C2×D3—22no—
619C2×D3—24no—
620C2×D3—38no—
621C2×D3—38no—
622C2×D3—44no—
623C2×D3—68no—
624C2×D3—632no—
625C2×D3—632no—
626C2×D3—616no—
627C2×D3—64no—
628C2×D3—64no—
629C2×D3—64no—
630C2×D3—64no—
631C2×D3—616no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—64no—
635C2×D3—64no—
636C2×D3—1216no—
637C2×D3—124no—
638C2×D3—124no—
639C2×D3—1232no—
640C2×D3—124no—
641C2×D3—122no—
642C2×D3—124no—
643C2×D3—124no—
644C2×D3—244no—
645C3×C4—24no—
646C3×C4—24no—
647C3×C4—34no—
648C3×C4—34no—
649C3×C4—44no—
650C3×C4—62no—
651C3×C4—64no—
652C3×C4—64no—
653Dic3—22no—
654Dic3—24no—
655Dic3—24no—
656Dic3—62no—
657Dic3—62no—
658Dic3—122no—
659Dic3C22×D1214yes—
660Dic3C22×D1214yes—
661C32C2×#52511yescharacteristic, complemented, Sylow
662C23—24no—
663C23—32no—
664C23—62no—
665C23—64no—
666C23—98no—
667C23—94no—
668C23—92no—
669C23—1816no—
670C23—1832no—
671C23—188no—
672C23—184no—
673C23—184no—
674C23—182no—
675C23—184no—
676C23D3×D1214yes—
677C23C22×D3212yes—
678C23C22×D3211yescharacteristic
679Q8—188no—
680D4—68no—
681D4—1816no—
682D4—188no—
683D4—1816no—
684D4—188no—
685C2×C4—24no—
686C2×C4—34no—
687C2×C4—34no—
688C2×C4—316no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—34no—
692C2×C4—34no—
693C2×C4—32no—
694C2×C4—68no—
695C2×C4—64no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—92no—
699C2×C4—1816no—
700C2×C4—1816no—
701C2×C4—188no—
702C2×C4—188no—
703C2×C4—182no—
704C2×C4C22×D3214yes—
705C2×C3—24no—
706C2×C3—24no—
707C2×C3—24no—
708C2×C3—21no—
709C2×C3—22no—
710C2×C3—44no—
711C2×C3—122no—
712C2×C3#552414yescomplemented
713C2×C3#565614yescomplemented
714C2×C3C23×D1211yescharacteristic
715C2×C3C22×D3×D411yescharacteristic
716C2×C3C2×D3×#4112yes—
717C2×C3C2×D3×#4112yes—
718D3—42no—
719D3—68no—
720D3—68no—
721D3—128no—
722D3—122no—
723D3—122no—
724D3—242no—
725C22—28no—
726C22—24no—
727C22—62no—
728C22—64no—
729C22—98no—
730C22—124no—
731C22—1832no—
732C22—1816no—
733C22—184no—
734C22—184no—
735C22—182no—
736C22—184no—
737C22—364no—
738C22C2×D3×D1214yes—
739C22C2×D3×D1212yes—
740C22#6431214yes—
741C22C23×D3211yescharacteristic
742C4—24no—
743C4—34no—
744C4—34no—
745C4—64no—
746C4—62no—
747C4—64no—
748C4—182no—
749C3—21no—
750C3C2×#552411yescharacteristic, complemented
751C3C2×#565611yescharacteristic, complemented
752C2—24no—
753C2—122no—
754C2—188no—
755C2—362no—
756C2#1059407914yesdirect product factor
757C2C22×D3×D1211yescharacteristic
758C2C2×#6431212yes—
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. C23×#624C2semidirect
2. C22×#3804C2semidirect
3. C2×#64091C2semidirect
4. C2×C3×#886C2semidirect
5. C2×C3×#877C2semidirect
6. C2×#63981C2semidirect
7. C2×#63966C2semidirect
8. C2×#63910C2semidirect
9. C2×#63895C2semidirect
10. C2×#63894C2semidirect
11. C2×#63880C2semidirect
12. #10594079C2direct (N × H)
21. C22×#627C22semidirect
23. C22×#626C22semidirect
27. C22×#624C22semidirect
28. C22×#624C22semidirect
30. C2×#3804C22semidirect
31. C22×D3×Dic3C22semidirect
34. #64091C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C3×#886C22semidirect
41. C3×#877C22semidirect
42. #63981C22semidirect
43. #63966C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
46. C2×#3722C22semidirect
47. #63910C22semidirect
48. #63895C22semidirect
49. #63894C22semidirect
50. #63880C22semidirect
66. C2×#886D3semidirect
73. C2×#877D3semidirect
92. C22×C3×Dic3D4semidirect
101. C2×#627C23semidirect
105. C2×#626C23semidirect
112. C2×#624C23semidirect
115. C2×D3×Dic3C23semidirect
119. C3×(C2×D3)⋊C4C23semidirect
120. C3×C4⋊Dic3C23semidirect
121. C3×Dic3⋊C4C23semidirect
122. C3×C4×Dic3C23semidirect
123. Dic3⋊Dic3C23semidirect
125. #3722C23semidirect
184. C2×(C2×D3)⋊C4C2×D3semidirect
186. C2×C4⋊Dic3C2×D3semidirect
188. C2×Dic3⋊C4C2×D3semidirect
189. C2×C4×Dic3C2×D3semidirect
195. #886C2×D3semidirect
202. #877C2×D3semidirect
216. C22×C3⋊D3#41semidirect
235. C2×C3×Dic3C2×D4semidirect
312. C22×Dic3D12semidirect
368. (C2×D3)⋊C4C22×D3semidirect
370. C4⋊Dic3C22×D3semidirect
372. Dic3⋊C4C22×D3semidirect
373. C4×Dic3C22×D3semidirect
387. C2×C3⋊D3C2×#41semidirect
520. C2×Dic3C2×D12semidirect
541. C2×C32#525semidirect
661. C32C2×#525semidirect
712. C2×C3#5524semidirect
713. C2×C3#5656semidirect
750. C3C2×#5524semidirect
751. C3C2×#5656semidirect
756. C2#10594079direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6242
C22×#38042
C2×#640912
C2×C3×#8862
C2×C3×#8772
C2×#639812
C2×#639662
C2×#639102
C2×#638952
C2×#638942
C2×#638802
#105940792
C2×#56563
C2×#55243