Finite Group Databasebeta

← C2×#10595298 #11900288

Subgroups — C2×#10595298 #11900288

Order 1152.

5737 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#3811C211yesmaximal, characteristic, complemented
3C22×#3811C211yesmaximal, characteristic, complemented
4C23×#624C211yesmaximal, characteristic, complemented
5C2×C3×#939C212yesmaximal, complemented
6C2×#63978C212yesmaximal, complemented
7C2×#63974C211yesmaximal, characteristic, complemented
8C2×#63958C212yesmaximal, complemented
9#10595298C2116yesmaximal, direct product factor
10C2×#63921C211yesmaximal, characteristic, complemented
11C2×#63910C212yesmaximal, complemented
12C2×#63883C211yesmaximal, characteristic, complemented
13C2×D3×#121—32nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C24×C3⋊D3C2211yescharacteristic
16C23×D32C2211yescharacteristic
17C22×C32×D4C2211yescharacteristic, complemented
18C22×#638C2211yescharacteristic, complemented
19C22×#638C2211yescharacteristic, complemented
20C2×D4×C3⋊D3—28no—
21C2×D4×C3⋊D3C2218yescomplemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic
24C22×C3×#67C2212yescomplemented
25C22×C3×#67C2212yescomplemented
26C23×C3×Dic3C2212yescomplemented
27C2×#3811—28no—
28C2×#3811—28no—
29C2×#3811C2218yescomplemented
30C2×#3811C2218yescomplemented
31C22×#626C2212yescomplemented
32C22×#626C2212yescomplemented
33C22×#624—28no—
34C22×#624C2211yescharacteristic
35C22×#624C2211yescharacteristic
36C22×#624C2211yescharacteristic
37C22×#624C2218yescomplemented
38C22×#624C2212yescomplemented
39C2×C3×#217C2212yescomplemented
40C3×#939C22116yescomplemented
41C2×C3×(C2×D3)⋊C4C2212yescomplemented
42C2×C3×Dic3⋊C4C2212yescomplemented
43#63978C22116yescomplemented
44#63974C2218yescomplemented
45C2×Dic3⋊Dic3C2212yescomplemented
46C2×#3722C2212yescomplemented
47C2×(C2×D3)⋊Dic3C2212yescomplemented
48#63958C22116yescomplemented
49#63921C2218yescomplemented
50#63910C22116yescomplemented
51#63883C2218yescomplemented
52C22×D3×D4—32no—
53C22×D3×D4—32no—
54C22×D3×D4—32no—
55C22×D3×D4—61no—
56C23×C4×D3—32no—
57C2×C3×#121—32no—
58C2×#939—32no—
59C2×#939D312yescomplemented
60C2×#938—32no—
61C2×#930—32no—
62D3×#121—332no—
63C2×#895—32no—
64C2×D3×C4⋊C4—32no—
65C2×#884—32no—
66C2×#884—32no—
67C2×D3×C22⋊C4—32no—
68C2×D3×C22⋊C4—32no—
69C24×C32C2311yescharacteristic
70C24×C32C2311yescharacteristic
71C23×C3⋊D3—24no—
72C23×C3⋊D3—24no—
73C23×C3⋊D3—24no—
74C23×C3⋊D3—24no—
75C23×C3⋊D3—24no—
76C23×C3⋊D3D418yescomplemented
77C23×C3⋊D3C2311yescharacteristic
78C23×C3⋊D3C2314yes—
79C23×C3⋊D3C2311yescharacteristic
80C23×C3⋊D3C2314yes—
81C23×C3⋊D3C2311yescharacteristic
82C23×C3×D3C2312yes—
83C22×D32—24no—
84C22×D32—24no—
85C22×D32—24no—
86C22×D32C2314yes—
87C2×C32×D4—24no—
88C2×C32×D4C2314yescomplemented
89C22×C32×C4C2311yescharacteristic
90C2×#638—24no—
91C2×#638—24no—
92C2×#638C2314yescomplemented
93C2×#638C2314yescomplemented
94C22×C3⋊Dic3C2311yescharacteristic
95D4×C3⋊D3—232no—
96C2×C4⋊(C3⋊D3)—24no—
97C2×C4⋊(C3⋊D3)C2314yescomplemented
98C2×C4×C3⋊D3—24no—
99C2×C4×C3⋊D3C2314yes—
100C2×C3×#67—28no—
101C2×C3×#67—28no—
102C2×C3×#67C2318yescomplemented
103C2×C3×#67C2318yescomplemented
104C22×C3×Dic3—28no—
105C22×C3×Dic3C2312yes—
106C22×C3×Dic3C2312yes—
107C22×C3×Dic3C2312yes—
108C22×C3×Dic3C2318yescomplemented
109#3811—232no—
110#3811—232no—
111C2×#626—28no—
112C2×#626—28no—
113C2×#626C2318yescomplemented
114C2×#626C2318yescomplemented
115C2×#624—24no—
116C2×#624—24no—
117C2×#624—28no—
118C2×#624—232no—
119C2×#624D418yescomplemented
120C2×#624C2314yes—
121C2×#624C2314yes—
122C2×#624C2314yes—
123C2×#624C2318yescomplemented
124C3×#217C2318yescomplemented
125C3×(C2×D3)⋊C4C2318yescomplemented
126C3×Dic3⋊C4C2318yescomplemented
127Dic3⋊Dic3C2318yescomplemented
128#3722C2318yescomplemented
129(C2×D3)⋊Dic3C2318yescomplemented
130C22×#121—91noSylow
131C24×D3—32no—
132C24×D3—32no—
133C24×D3—32no—
134C24×D3—61no—
135C24×D3—61no—
136C22×C3×D4—21no—
137C22×C3×D4—32no—
138C22×C3×D4—32no—
139C22×C3×D4C2×D312yescomplemented
140C23×C3×C4—32no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—32no—
145C22×#67—61no—
146C22×#67—61no—
147C22×#67C2×D312yescomplemented
148C22×#67C2×D312yescomplemented
149C23×Dic3C2×D312yescomplemented
150C2×D3×D4—316no—
151C2×D3×D4—316no—
152C2×D3×D4—316no—
153C2×D3×D4—68no—
154C2×D3×D4—616no—
155C2×D3×D4—616no—
156C2×D3×D4—616no—
157C2×D3×D4—616no—
158C22×D12—32no—
159C22×D12—32no—
160C22×D12—32no—
161C22×D12—61no—
162C22×C4×D3—32no—
163C22×C4×D3—32no—
164C22×C4×D3—32no—
165C22×C4×D3—32no—
166C22×C4×D3—32no—
167C22×C4×D3—32no—
168C22×C4×D3—316no—
169C22×C4×D3—61no—
170C22×C4×D3—616no—
171C3×#121—316no—
172C2×C3×C4⋊C4—32no—
173C2×C3×C22⋊C4—32no—
174C2×C3×C22⋊C4—32no—
175C2×#217—32no—
176C2×#217C2×D312yescomplemented
177#939—316no—
178#939C2×D3116yescomplemented
179#938—316no—
180#930—316no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4C2×D312yescomplemented
185C2×C4⋊Dic3—32no—
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4C2×D312yescomplemented
188#895—316no—
189D3×C4⋊C4—316no—
190#884—316no—
191#884—316no—
192D3×C22⋊C4—316no—
193D3×C22⋊C4—316no—
194C23×C32—22no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32C2×D414yescomplemented
200C23×C32C2412yes—
201C23×C32C2412yes—
202C23×C32C2411yescharacteristic
203C22×C3⋊D3—22no—
204C22×C3⋊D3—28no—
205C22×C3⋊D3—22no—
206C22×C3⋊D3—22no—
207C22×C3⋊D3—232no—
208C22×C3⋊D3—28no—
209C22×C3⋊D3—28no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3—28no—
213C22×C3⋊D3—28no—
214C22×C3⋊D3—416no—
215C22×C3⋊D3C2×D414yes—
216C22×C3⋊D3C2×D414yes—
217C22×C3⋊D3C2×D4116yescomplemented
218C22×C3⋊D3C2×D414yescomplemented
219C22×C3⋊D3#4114yes—
220C22×C3⋊D3C2412yes—
221C22×C3⋊D3C2412yes—
222C22×C3⋊D3C2412yes—
223C22×C3×D3—24no—
224C22×C3×D3—24no—
225C22×C3×D3—24no—
226C22×C3×D3C2414yes—
227C2×D32—28no—
228C2×D32—28no—
229C2×D32—28no—
230C2×D32—416no—
231C32×D4—28no—
232C2×C32×C4—22no—
233C2×C32×C4C2412yes—
234#638—28no—
235#638—28no—
236C2×C3⋊Dic3—22no—
237C2×C3⋊Dic3C2412yes—
238C4⋊(C3⋊D3)—28no—
239C4×C3⋊D3—28no—
240C3×#67—216no—
241C3×#67—216no—
242C2×C3×Dic3—24no—
243C2×C3×Dic3—24no—
244C2×C3×Dic3—216no—
245C2×C3×Dic3C2×D418yescomplemented
246C2×C3×Dic3C2414yes—
247C2×C3×Dic3C2414yes—
248C2×C3×Dic3C2414yes—
249#626—216no—
250#626—216no—
251#624—28no—
252#624—28no—
253#624—216no—
254#624C2×D4116yescomplemented
255C23×D4—91no—
256C23×D4—91no—
257C23×D4—91no—
258C24×C4—91no—
259C2×#121—32no—
260C2×#121—92no—
261C2×#121—92no—
262C2×#121—916no—
263C2×#121—92no—
264C22×C4⋊C4—91no—
265C22×C22⋊C4—91no—
266C22×C22⋊C4—91no—
267C24×C3—21no—
268C24×C3—21no—
269C24×C3—32no—
270C24×C3C22×D312yes—
271C24×C3C22×D312yes—
272C23×D3—32no—
273C23×D3—316no—
274C23×D3—32no—
275C23×D3—38no—
276C23×D3—38no—
277C23×D3—32no—
278C23×D3—38no—
279C23×D3—61no—
280C23×D3—68no—
281C23×D3—61no—
282C23×D3—61no—
283C23×D3—64no—
284C23×D3—64no—
285C23×D3—68no—
286C23×D3—68no—
287C23×D3—68no—
288C23×D3—68no—
289C23×D3—68no—
290C23×D3—68no—
291C23×D3—68no—
292C23×D3—68no—
293C23×D3—68no—
294C23×D3—124no—
295C23×D3—124no—
296C23×D3—124no—
297C23×D3—124no—
298C23×D3C22×D312yes—
299C2×C3×D4—28no—
300C2×C3×D4—28no—
301C2×C3×D4—24no—
302C2×C3×D4—38no—
303C2×C3×D4—38no—
304C2×C3×D4—68no—
305C2×C3×D4—68no—
306C2×C3×D4C22×D318yescomplemented
307C22×C3×C4—21no—
308C22×C3×C4—32no—
309C22×C3×C4—32no—
310C22×C3×C4—32no—
311C22×C3×C4—38no—
312C22×C3×C4—68no—
313C22×C3×C4C22×D312yes—
314C2×#67—28no—
315C2×#67—28no—
316C2×#67—38no—
317C2×#67—38no—
318C2×#67—38no—
319C2×#67—38no—
320C2×#67—64no—
321C2×#67—64no—
322C2×#67—68no—
323C2×#67—68no—
324C2×#67—68no—
325C2×#67—68no—
326C2×#67—68no—
327C2×#67—68no—
328C2×#67C22×D318yescomplemented
329C2×#67C22×D318yescomplemented
330C22×Dic3—28no—
331C22×Dic3—32no—
332C22×Dic3—61no—
333C22×Dic3C22×D312yes—
334C22×Dic3C22×D312yes—
335C22×Dic3C22×D312yes—
336C22×Dic3C22×D318yescomplemented
337D3×D4—664no—
338D3×D4—664no—
339D3×D4—664no—
340D3×D4—664no—
341C2×D12—38no—
342C2×D12—38no—
343C2×D12—38no—
344C2×D12—64no—
345C2×D12—68no—
346C2×D12—68no—
347C2×D12—68no—
348C2×D12—68no—
349C2×C4×D3—316no—
350C2×C4×D3—38no—
351C2×C4×D3—38no—
352C2×C4×D3—38no—
353C2×C4×D3—38no—
354C2×C4×D3—38no—
355C2×C4×D3—38no—
356C2×C4×D3—64no—
357C2×C4×D3—664no—
358C2×C4×D3—68no—
359C2×C4×D3—68no—
360C2×C4×D3—68no—
361C2×C4×D3—68no—
362C2×C4×D3—68no—
363C2×C4×D3—68no—
364C3×C4⋊C4—38no—
365C3×C22⋊C4—38no—
366C3×C22⋊C4—38no—
367#217—38no—
368#217C22×D318yescomplemented
369(C2×D3)⋊C4—38no—
370(C2×D3)⋊C4—38no—
371(C2×D3)⋊C4—38no—
372(C2×D3)⋊C4C22×D318yescomplemented
373C4⋊Dic3—38no—
374Dic3⋊C4—38no—
375Dic3⋊C4C22×D318yescomplemented
376C22×C32—22no—
377C22×C32—28no—
378C22×C32—22no—
379C22×C32—22no—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32—44no—
383C22×C32C22×D412yes—
384C22×C32C22×D412yes—
385C22×C32C22×D414yescomplemented
386C22×C32C2×#4112yes—
387C22×C32C2511yescharacteristic
388C2×C3⋊D3—22no—
389C2×C3⋊D3—28no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—232no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3—22no—
395C2×C3⋊D3—44no—
396C2×C3⋊D3—416no—
397C2×C3⋊D3#121116yescomplemented
398C2×C3⋊D3C22×D414yes—
399C2×C3⋊D3C22×D414yes—
400C2×C3⋊D3C22×D414yescomplemented
401C2×C3⋊D3C2×#4114yes—
402C2×C3×D3—24no—
403C2×C3×D3—24no—
404C2×C3×D3—24no—
405C2×C3×D3—48no—
406D32—416no—
407C32×C4—22no—
408C3⋊Dic3—22no—
409C3×Dic3—24no—
410C3×Dic3—24no—
411C3×Dic3C22×D418yescomplemented
412C25—91no—
413C25—91no—
414C25—91no—
415C22×D4—32no—
416C22×D4—32no—
417C22×D4—92no—
418C22×D4—92no—
419C22×D4—98no—
420C22×D4—98no—
421C22×D4—91no—
422C22×D4—91no—
423C22×D4—98no—
424C22×D4—91no—
425C22×D4—188no—
426C22×D4—188no—
427C22×D4—188no—
428C22×D4D3211yescharacteristic, complemented
429C23×C4—32no—
430C23×C4—91no—
431C23×C4—91no—
432C23×C4—91no—
433C23×C4—92no—
434C23×C4—98no—
435C23×C4—91no—
436C23×C4—188no—
437#121—316no—
438#121—916no—
439#121—916no—
440#121—916no—
441C2×C4⋊C4—32no—
442C2×C4⋊C4—98no—
443C2×C4⋊C4—92no—
444C2×C22⋊C4—32no—
445C2×C22⋊C4—32no—
446C2×C22⋊C4—98no—
447C2×C22⋊C4—98no—
448C2×C22⋊C4—92no—
449C2×C22⋊C4—92no—
450C23×C3—24no—
451C23×C3—24no—
452C23×C3—24no—
453C23×C3—24no—
454C23×C3—24no—
455C23×C3—24no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—21no—
459C23×C3—24no—
460C23×C3—34no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—64no—
466C23×C3—64no—
467C23×C3—64no—
468C23×C3D3×D418yescomplemented
469C23×C3C23×D314yes—
470C23×C3C23×D314yes—
471C23×C3C23×D312yes—
472C22×D3—24no—
473C22×D3—24no—
474C22×D3—24no—
475C22×D3—38no—
476C22×D3—38no—
477C22×D3—38no—
478C22×D3—34no—
479C22×D3—38no—
480C22×D3—332no—
481C22×D3—34no—
482C22×D3—34no—
483C22×D3—64no—
484C22×D3—64no—
485C22×D3—64no—
486C22×D3—62no—
487C22×D3—64no—
488C22×D3—616no—
489C22×D3—62no—
490C22×D3—62no—
491C22×D3—616no—
492C22×D3—616no—
493C22×D3—616no—
494C22×D3—616no—
495C22×D3—616no—
496C22×D3—664no—
497C22×D3—616no—
498C22×D3—616no—
499C22×D3—616no—
500C22×D3—64no—
501C22×D3—64no—
502C22×D3—64no—
503C22×D3—616no—
504C22×D3—64no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—128no—
508C22×D3—1232no—
509C22×D3—128no—
510C22×D3—128no—
511C22×D3—128no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—1232no—
517C22×D3—1232no—
518C22×D3—1232no—
519C22×D3C23×D314yes—
520C3×D4—216no—
521C3×D4—216no—
522C3×D4—616no—
523C3×D4—616no—
524C2×C3×C4—24no—
525C2×C3×C4—24no—
526C2×C3×C4—22no—
527C2×C3×C4—38no—
528C2×C3×C4—34no—
529C2×C3×C4—34no—
530C2×C3×C4—34no—
531C2×C3×C4—616no—
532C2×C3×C4—64no—
533C2×C3×C4—64no—
534C2×C3×C4C23×D314yes—
535#67—216no—
536#67—216no—
537#67—616no—
538#67—616no—
539#67—616no—
540#67—616no—
541#67—616no—
542#67—616no—
543C2×Dic3—24no—
544C2×Dic3—24no—
545C2×Dic3—216no—
546C2×Dic3—34no—
547C2×Dic3—62no—
548C2×Dic3—64no—
549C2×Dic3—64no—
550C2×Dic3D3×D418yescomplemented
551C2×Dic3C23×D314yes—
552C2×Dic3C23×D314yes—
553C2×Dic3C23×D314yes—
554D12—616no—
555D12—616no—
556D12—616no—
557D12—616no—
558C4×D3—332no—
559C4×D3—616no—
560C4×D3—616no—
561C4×D3—616no—
562C4×D3—616no—
563C4×D3—616no—
564C4×D3—616no—
565C2×C32—24no—
566C2×C32—42no—
567C2×C32C2×#12114yescomplemented
568C2×C32C23×D411yescharacteristic
569C2×C32C23×D411yescharacteristic
570C2×C32C22×#4111yescharacteristic
571C3⋊D3—24no—
572C3⋊D3—42no—
573C3⋊D3C2×#12118yescomplemented
574C3×D3—44no—
575C24—32no—
576C24—94no—
577C24—91no—
578C24—94no—
579C24—91no—
580C24—98no—
581C24—94no—
582C24—91no—
583C24—184no—
584C24—184no—
585C24—184no—
586C24—184no—
587C24—184no—
588C24—184no—
589C24—184no—
590C24—184no—
591C24C2×D3211yescharacteristic
592C24C2×D3211yescharacteristic
593C2×D4—24no—
594C2×D4—38no—
595C2×D4—38no—
596C2×D4—68no—
597C2×D4—68no—
598C2×D4—98no—
599C2×D4—98no—
600C2×D4—94no—
601C2×D4—94no—
602C2×D4—94no—
603C2×D4—184no—
604C2×D4—188no—
605C2×D4—188no—
606C2×D4—1832no—
607C2×D4—1832no—
608C2×D4—1832no—
609C2×D4—184no—
610C2×D4—184no—
611C2×D4C2×D3214yescomplemented
612C22×C4—32no—
613C22×C4—38no—
614C22×C4—32no—
615C22×C4—32no—
616C22×C4—68no—
617C22×C4—94no—
618C22×C4—98no—
619C22×C4—94no—
620C22×C4—94no—
621C22×C4—98no—
622C22×C4—91no—
623C22×C4—94no—
624C22×C4—184no—
625C22×C4—188no—
626C22×C4—1832no—
627C22×C4—184no—
628C22×C4—184no—
629C22×C4C2×D3211yescharacteristic
630C4⋊C4—38no—
631C4⋊C4—98no—
632C22⋊C4—38no—
633C22⋊C4—38no—
634C22⋊C4—98no—
635C22⋊C4—98no—
636C22×C3—24no—
637C22×C3—24no—
638C22×C3—216no—
639C22×C3—24no—
640C22×C3—24no—
641C22×C3—24no—
642C22×C3—24no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—24no—
647C22×C3—21no—
648C22×C3—42no—
649C22×C3—42no—
650C22×C3—48no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—48no—
654C22×C3—48no—
655C22×C3—64no—
656C22×C3—64no—
657C22×C3—64no—
658C22×C3—128no—
659C22×C3C2×D3×D414yes—
660C22×C3C2×D3×D414yes—
661C22×C3C2×D3×D418yescomplemented
662C22×C3D3×#4114yes—
663C22×C3C24×D312yes—
664C2×D3—24no—
665C2×D3—24no—
666C2×D3—24no—
667C2×D3—38no—
668C2×D3—38no—
669C2×D3—38no—
670C2×D3—332no—
671C2×D3—38no—
672C2×D3—48no—
673C2×D3—64no—
674C2×D3—616no—
675C2×D3—64no—
676C2×D3—64no—
677C2×D3—64no—
678C2×D3—664no—
679C2×D3—64no—
680C2×D3—64no—
681C2×D3—616no—
682C2×D3—64no—
683C2×D3—64no—
684C2×D3—64no—
685C2×D3—64no—
686C2×D3—1232no—
687C2×D3—122no—
688C2×D3—122no—
689C2×D3—128no—
690C2×D3—122no—
691C2×D3—122no—
692C2×D3—1232no—
693C2×D3—1232no—
694C2×D3—1232no—
695C2×D3—128no—
696C2×D3—128no—
697C3×C4—24no—
698C3×C4—24no—
699C3×C4—38no—
700C3×C4—64no—
701C3×C4—64no—
702Dic3—24no—
703Dic3—24no—
704Dic3—64no—
705Dic3—64no—
706Dic3C2×D3×D418yescomplemented
707C32C22×#12111yescharacteristic, complemented, Sylow
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—34no—
714C23—64no—
715C23—64no—
716C23—64no—
717C23—94no—
718C23—94no—
719C23—94no—
720C23—92no—
721C23—94no—
722C23—916no—
723C23—92no—
724C23—92no—
725C23—188no—
726C23—188no—
727C23—1832no—
728C23—188no—
729C23—188no—
730C23—188no—
731C23—188no—
732C23—188no—
733C23—188no—
734C23—182no—
735C23—182no—
736C23—182no—
737C23—182no—
738C23—182no—
739C23—3616no—
740C23—3616no—
741C23#381114yescomplemented
742C23C22×D3212yes—
743C23C22×D3212yes—
744C23C22×D3211yescharacteristic
745D4—28no—
746D4—616no—
747D4—616no—
748D4—188no—
749D4—1816no—
750D4—1816no—
751D4—188no—
752D4—188no—
753C2×C4—22no—
754C2×C4—38no—
755C2×C4—34no—
756C2×C4—34no—
757C2×C4—34no—
758C2×C4—616no—
759C2×C4—64no—
760C2×C4—64no—
761C2×C4—916no—
762C2×C4—92no—
763C2×C4—188no—
764C2×C4—1816no—
765C2×C4—188no—
766C2×C4—188no—
767C2×C4—182no—
768C2×C4C22×D3212yes—
769C2×C3—28no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—24no—
774C2×C3—44no—
775C2×C3—44no—
776C2×C3—44no—
777C2×C3—124no—
778C2×C3D3×#12118yescomplemented
779C2×C3C22×D3×D412yes—
780C2×C3C22×D3×D412yes—
781C2×C3C2×D3×#4112yes—
782D3—316no—
783D3—44no—
784D3—68no—
785D3—68no—
786D3—124no—
787D3—124no—
788D3—124no—
789C22—22no—
790C22—22no—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—44no—
796C22—64no—
797C22—64no—
798C22—64no—
799C22—94no—
800C22—94no—
801C22—94no—
802C22—916no—
803C22—94no—
804C22—128no—
805C22—1832no—
806C22—182no—
807C22—182no—
808C22—188no—
809C22—182no—
810C22—182no—
811C22—182no—
812C22—3616no—
813C22—3616no—
814C22—364no—
815C22D32×D412yes—
816C22#6431212yes—
817C22C2×#381112yes—
818C22C2×#381114yescomplemented
819C22C23×D3211yescharacteristic
820C4—22no—
821C4—38no—
822C4—64no—
823C4—64no—
824C4—182no—
825C3—21no—
826C3C2×D3×#12112yescomplemented
827C2—24no—
828C2—42no—
829C2—98no—
830C2—124no—
831C2—184no—
832C2—362no—
833C2#1059529814yesdirect product factor
834C2C2×D32×D411yescharacteristic
835C2C2×#6431211yescharacteristic
836C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C22×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C3⋊D3C2semidirect
2. C22×#3811C2semidirect
3. C22×#3811C2semidirect
4. C23×#624C2semidirect
5. C2×C3×#939C2semidirect
6. C2×#63978C2semidirect
7. C2×#63974C2semidirect
8. C2×#63958C2semidirect
9. #10595298C2direct (N × H)
10. C2×#63921C2semidirect
11. C2×#63910C2semidirect
12. C2×#63883C2semidirect
17. C22×C32×D4C22semidirect
18. C22×#638C22semidirect
19. C22×#638C22semidirect
21. C2×D4×C3⋊D3C22semidirect
22. C22×C4⋊(C3⋊D3)C22semidirect
24. C22×C3×#67C22semidirect
25. C22×C3×#67C22semidirect
26. C23×C3×Dic3C22semidirect
29. C2×#3811C22semidirect
30. C2×#3811C22semidirect
31. C22×#626C22semidirect
32. C22×#626C22semidirect
37. C22×#624C22semidirect
38. C22×#624C22semidirect
39. C2×C3×#217C22semidirect
40. C3×#939C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. #63978C22semidirect
44. #63974C22semidirect
45. C2×Dic3⋊Dic3C22semidirect
46. C2×#3722C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. #63958C22semidirect
49. #63921C22semidirect
50. #63910C22semidirect
51. #63883C22semidirect
59. C2×#939D3semidirect
76. C23×C3⋊D3D4semidirect
88. C2×C32×D4C23semidirect
92. C2×#638C23semidirect
93. C2×#638C23semidirect
97. C2×C4⋊(C3⋊D3)C23semidirect
102. C2×C3×#67C23semidirect
103. C2×C3×#67C23semidirect
108. C22×C3×Dic3C23semidirect
113. C2×#626C23semidirect
114. C2×#626C23semidirect
119. C2×#624D4semidirect
123. C2×#624C23semidirect
124. C3×#217C23semidirect
125. C3×(C2×D3)⋊C4C23semidirect
126. C3×Dic3⋊C4C23semidirect
127. Dic3⋊Dic3C23semidirect
128. #3722C23semidirect
129. (C2×D3)⋊Dic3C23semidirect
139. C22×C3×D4C2×D3semidirect
147. C22×#67C2×D3semidirect
148. C22×#67C2×D3semidirect
149. C23×Dic3C2×D3semidirect
176. C2×#217C2×D3semidirect
178. #939C2×D3semidirect
184. C2×(C2×D3)⋊C4C2×D3semidirect
187. C2×Dic3⋊C4C2×D3semidirect
199. C23×C32C2×D4semidirect
217. C22×C3⋊D3C2×D4semidirect
218. C22×C3⋊D3C2×D4semidirect
245. C2×C3×Dic3C2×D4semidirect
254. #624C2×D4semidirect
306. C2×C3×D4C22×D3semidirect
328. C2×#67C22×D3semidirect
329. C2×#67C22×D3semidirect
336. C22×Dic3C22×D3semidirect
368. #217C22×D3semidirect
372. (C2×D3)⋊C4C22×D3semidirect
375. Dic3⋊C4C22×D3semidirect
385. C22×C32C22×D4semidirect
397. C2×C3⋊D3#121semidirect
400. C2×C3⋊D3C22×D4semidirect
411. C3×Dic3C22×D4semidirect
428. C22×D4D32semidirect
468. C23×C3D3×D4semidirect
550. C2×Dic3D3×D4semidirect
567. C2×C32C2×#121semidirect
573. C3⋊D3C2×#121semidirect
611. C2×D4C2×D32semidirect
661. C22×C3C2×D3×D4semidirect
706. Dic3C2×D3×D4semidirect
707. C32C22×#121semidirect
741. C23#3811semidirect
778. C2×C3D3×#121semidirect
818. C22C2×#3811semidirect
826. C3C2×D3×#121semidirect
833. C2#10595298direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C22×#38112
C23×#6242
C2×C3×#9392
C2×#639782
C2×#639742
C2×#639582
#105952982
C2×#639212
C2×#639102
C2×#638832
C2×D3×#1213