Finite Group Databasebeta

← C2×#10594265 #11900292

Subgroups — C2×#10594265 #11900292

Order 1152.

5393 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C22×#3811C211yesmaximal, characteristic, complemented
3C22×#3802C211yesmaximal, characteristic, complemented
4C22×C4×D32C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
6C2×C3×#884C212yesmaximal, complemented
7C2×#63970C212yesmaximal, complemented
8C2×#63921C211yesmaximal, characteristic, complemented
9C2×#63906C212yesmaximal, complemented
10C2×#63886C212yesmaximal, complemented
11C2×#63883C211yesmaximal, characteristic, complemented
12#10594265C2116yesmaximal, direct product factor
13C2×D3×#121—32nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C23×D32C2211yescharacteristic
16C23×D32C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×#67C2212yescomplemented
20C22×C3×#67C2212yescomplemented
21C22×C3×D12C2212yescomplemented
22C22×C3×C4×D3C2212yescomplemented
23C2×#3811—28no—
24C2×#3811—28no—
25C2×#3811C2218yescomplemented
26C2×#3811C2218yescomplemented
27C22×#626C2212yescomplemented
28C22×#626C2212yescomplemented
29C22×#625C2212yescomplemented
30C22×#624C2211yescharacteristic
31C22×#624C2211yescharacteristic
32C22×D3×Dic3C2212yescomplemented
33C2×#3802—28no—
34C2×#3802C2218yescomplemented
35C2×C4×D32—28no—
36C2×C4×D32C2218yescomplemented
37C2×C32×C22⋊C4C2211yescharacteristic, complemented
38C2×#3757C2211yescharacteristic, complemented
39C2×#3752C2211yescharacteristic, complemented
40C2×#3752C2211yescharacteristic, complemented
41C22⋊C4×C3⋊D3C2218yescomplemented
42C2×C3×(C2×D3)⋊C4C2212yescomplemented
43C2×C3×Dic3⋊C4C2212yescomplemented
44C3×#884C22116yescomplemented
45#63970C22116yescomplemented
46C2×Dic3⋊Dic3C2212yescomplemented
47C2×(C2×D3)⋊Dic3C2212yescomplemented
48#63921C2218yescomplemented
49#63906C22116yescomplemented
50#63886C22116yescomplemented
51#63883C2218yescomplemented
52C22×D3×D4—32no—
53C22×D3×D4—32no—
54C22×D3×D4—32no—
55C23×C4×D3—32no—
56C2×C3×#121—32no—
57C2×#939—32no—
58C2×#939—32no—
59C2×#938—32no—
60C2×#930—32no—
61D3×#121—332no—
62C2×#895—32no—
63C2×D3×C4⋊C4—32no—
64C2×#884—32no—
65C2×#884D312yescomplemented
66C2×D3×C22⋊C4—32no—
67C2×D3×C22⋊C4—32no—
68C2×D3×C22⋊C4—61no—
69C24×C32C2311yescharacteristic
70C23×C3⋊D3—24no—
71C23×C3⋊D3—24no—
72C23×C3⋊D3—24no—
73C23×C3⋊D3C2311yescharacteristic
74C23×C3⋊D3C2314yes—
75C23×C3⋊D3C2311yescharacteristic
76C23×C3×D3C2312yes—
77C23×C3×D3C2312yes—
78C22×D32—24no—
79C22×D32—24no—
80C22×D32—24no—
81C22×D32—24no—
82C22×D32—24no—
83C22×D32D418yescomplemented
84C22×D32C2314yes—
85C22×D32C2314yes—
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C2×C4×C3⋊D3—24no—
91C2×C4×C3⋊D3—24no—
92C2×C4×C3⋊D3C2314yes—
93C2×C4×C3⋊D3C2314yes—
94C2×C3×#67—28no—
95C2×C3×#67—28no—
96C2×C3×#67C2318yescomplemented
97C2×C3×#67C2318yescomplemented
98C22×C3×Dic3C2312yes—
99C22×C3×Dic3C2312yes—
100C2×C3×D12—28no—
101C2×C3×D12C2318yescomplemented
102C2×C3×C4×D3—28no—
103C2×C3×C4×D3C2318yescomplemented
104#3811—232no—
105#3811—232no—
106C2×#626—28no—
107C2×#626—28no—
108C2×#626C2318yescomplemented
109C2×#626C2318yescomplemented
110C2×#625—28no—
111C2×#625C2318yescomplemented
112C2×#624—24no—
113C2×#624D418yescomplemented
114C2×#624C2314yes—
115C2×#624C2314yes—
116C2×D3×Dic3—28no—
117C2×D3×Dic3C2318yescomplemented
118#3802—232no—
119C4×D32—232no—
120C32×C22⋊C4C2314yescomplemented
121#3757C2314yescomplemented
122#3752C2314yescomplemented
123#3752C2314yescomplemented
124C3×(C2×D3)⋊C4C2318yescomplemented
125C3×Dic3⋊C4C2318yescomplemented
126Dic3⋊Dic3C2318yescomplemented
127(C2×D3)⋊Dic3C2318yescomplemented
128C22×#121—91noSylow
129C24×D3—32no—
130C24×D3—32no—
131C24×D3—32no—
132C24×D3—61no—
133C22×C3×D4—32no—
134C22×C3×D4—32no—
135C22×C3×D4—32no—
136C23×C3×C4—32no—
137C22×#67—32no—
138C22×#67—32no—
139C22×#67—32no—
140C22×#67—32no—
141C22×#67C2×D312yescomplemented
142C22×#67C2×D312yescomplemented
143C23×Dic3—32no—
144C2×D3×D4—316no—
145C2×D3×D4—316no—
146C2×D3×D4—316no—
147C2×D3×D4—616no—
148C2×D3×D4—616no—
149C2×D3×D4—616no—
150C22×D12—32no—
151C22×D12—32no—
152C22×D12C2×D312yescomplemented
153C22×C4×D3—32no—
154C22×C4×D3—32no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3—32no—
158C22×C4×D3—316no—
159C22×C4×D3—61no—
160C22×C4×D3—61no—
161C22×C4×D3—616no—
162C22×C4×D3C2×D312yescomplemented
163C3×#121—316no—
164C2×C3×C4⋊C4—32no—
165C2×C3×C22⋊C4—21no—
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4C2×D312yescomplemented
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—61no—
171#939—316no—
172#939—316no—
173#938—316no—
174#930—316no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—61no—
179C2×(C2×D3)⋊C4—61no—
180C2×(C2×D3)⋊C4C2×D312yescomplemented
181C2×C4⋊Dic3—32no—
182C2×Dic3⋊C4—32no—
183C2×Dic3⋊C4C2×D312yescomplemented
184#895—316no—
185D3×C4⋊C4—316no—
186#884—316no—
187#884C2×D3116yescomplemented
188D3×C22⋊C4—316no—
189D3×C22⋊C4—316no—
190D3×C22⋊C4—68no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—22no—
194C23×C32C2412yes—
195C23×C32C2411yescharacteristic
196C22×C3⋊D3—22no—
197C22×C3⋊D3—28no—
198C22×C3⋊D3—22no—
199C22×C3⋊D3—22no—
200C22×C3⋊D3—28no—
201C22×C3⋊D3—28no—
202C22×C3⋊D3—416no—
203C22×C3⋊D3C2×D414yes—
204C22×C3⋊D3C2×D414yes—
205C22×C3⋊D3#4114yes—
206C22×C3⋊D3C2412yes—
207C22×C3⋊D3C2412yes—
208C22×C3×D3—24no—
209C22×C3×D3—24no—
210C22×C3×D3—24no—
211C22×C3×D3—24no—
212C22×C3×D3—24no—
213C22×C3×D3C2×D418yescomplemented
214C22×C3×D3C2414yes—
215C22×C3×D3C2414yes—
216C2×D32—232no—
217C2×D32—28no—
218C2×D32—28no—
219C2×D32—28no—
220C2×D32—28no—
221C2×D32—28no—
222C2×D32—416no—
223C2×D32C2×D4116yescomplemented
224C2×C32×C4—22no—
225C2×C32×C4—22no—
226C2×C32×C4C2412yes—
227C2×C32×C4C2412yes—
228C2×C3⋊Dic3—22no—
229C2×C3⋊Dic3—22no—
230C2×C3⋊Dic3C2412yes—
231C2×C3⋊Dic3C2412yes—
232C4×C3⋊D3—28no—
233C4×C3⋊D3—28no—
234C3×#67—216no—
235C3×#67—216no—
236C2×C3×Dic3—24no—
237C2×C3×Dic3C2×D418yescomplemented
238C2×C3×Dic3C2414yes—
239C2×C3×Dic3C2414yes—
240C3×D12—216no—
241C3×C4×D3—216no—
242#626—216no—
243#626—216no—
244#625—216no—
245#624—28no—
246#624C2×D4116yescomplemented
247D3×Dic3—216no—
248C23×D4—91no—
249C23×D4—91no—
250C23×D4—91no—
251C24×C4—91no—
252C2×#121—32no—
253C2×#121—92no—
254C2×#121—92no—
255C2×#121—916no—
256C2×#121—92no—
257C22×C4⋊C4—91no—
258C22×C22⋊C4—91no—
259C22×C22⋊C4—91no—
260C24×C3—21no—
261C24×C3—32no—
262C24×C3—32no—
263C24×C3C22×D312yes—
264C23×D3—32no—
265C23×D3—316no—
266C23×D3—38no—
267C23×D3—38no—
268C23×D3—32no—
269C23×D3—38no—
270C23×D3—61no—
271C23×D3—64no—
272C23×D3—61no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—68no—
276C23×D3—68no—
277C23×D3—68no—
278C23×D3—68no—
279C23×D3—68no—
280C23×D3—68no—
281C23×D3—68no—
282C23×D3—124no—
283C23×D3—124no—
284C23×D3C22×D312yes—
285C23×D3C22×D312yes—
286C2×C3×D4—38no—
287C2×C3×D4—38no—
288C2×C3×D4—38no—
289C2×C3×D4—68no—
290C2×C3×D4—68no—
291C2×C3×D4—68no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—32no—
295C22×C3×C4—32no—
296C22×C3×C4—38no—
297C22×C3×C4—68no—
298C22×C3×C4C22×D312yes—
299C22×C3×C4C22×D312yes—
300C2×#67—28no—
301C2×#67—28no—
302C2×#67—38no—
303C2×#67—38no—
304C2×#67—38no—
305C2×#67—38no—
306C2×#67—68no—
307C2×#67—68no—
308C2×#67—68no—
309C2×#67—68no—
310C2×#67C22×D318yescomplemented
311C2×#67C22×D318yescomplemented
312C22×Dic3—32no—
313C22×Dic3—32no—
314C22×Dic3—38no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—68no—
318C22×Dic3C22×D312yes—
319C22×Dic3C22×D312yes—
320D3×D4—664no—
321D3×D4—664no—
322D3×D4—664no—
323C2×D12—28no—
324C2×D12—38no—
325C2×D12—38no—
326C2×D12—68no—
327C2×D12—68no—
328C2×D12C22×D318yescomplemented
329C2×C4×D3—28no—
330C2×C4×D3—316no—
331C2×C4×D3—38no—
332C2×C4×D3—38no—
333C2×C4×D3—38no—
334C2×C4×D3—38no—
335C2×C4×D3—38no—
336C2×C4×D3—64no—
337C2×C4×D3—64no—
338C2×C4×D3—664no—
339C2×C4×D3—68no—
340C2×C4×D3—68no—
341C2×C4×D3—68no—
342C2×C4×D3—68no—
343C2×C4×D3—124no—
344C2×C4×D3—124no—
345C2×C4×D3C22×D318yescomplemented
346C3×C4⋊C4—38no—
347C3×C22⋊C4—24no—
348C3×C22⋊C4—38no—
349C3×C22⋊C4C22×D318yescomplemented
350#217—38no—
351#217—38no—
352#217—64no—
353(C2×D3)⋊C4—38no—
354(C2×D3)⋊C4—38no—
355(C2×D3)⋊C4—38no—
356(C2×D3)⋊C4—64no—
357(C2×D3)⋊C4—64no—
358(C2×D3)⋊C4C22×D318yescomplemented
359C4⋊Dic3—38no—
360Dic3⋊C4—38no—
361Dic3⋊C4C22×D318yescomplemented
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—44no—
366C22×C32C22×D412yes—
367C22×C32C22×D412yes—
368C22×C32C2×#4112yes—
369C22×C32C2511yescharacteristic
370C2×C3⋊D3—22no—
371C2×C3⋊D3—22no—
372C2×C3⋊D3—22no—
373C2×C3⋊D3—44no—
374C2×C3⋊D3—416no—
375C2×C3⋊D3#121116yescomplemented
376C2×C3⋊D3C22×D414yes—
377C2×C3⋊D3C22×D414yes—
378C2×C3⋊D3C2×#4114yes—
379C2×C3×D3—216no—
380C2×C3×D3—24no—
381C2×C3×D3—24no—
382C2×C3×D3—24no—
383C2×C3×D3—24no—
384C2×C3×D3—24no—
385C2×C3×D3—48no—
386C2×C3×D3C22×D418yescomplemented
387D32—232no—
388D32—416no—
389C32×C4—22no—
390C32×C4—22no—
391C3⋊Dic3—22no—
392C3⋊Dic3—22no—
393C3×Dic3—24no—
394C3×Dic3C22×D418yescomplemented
395C25—91no—
396C25—91no—
397C25—91no—
398C22×D4—32no—
399C22×D4—32no—
400C22×D4—32no—
401C22×D4—92no—
402C22×D4—92no—
403C22×D4—98no—
404C22×D4—98no—
405C22×D4—98no—
406C22×D4—92no—
407C22×D4—188no—
408C22×D4—188no—
409C22×D4—188no—
410C23×C4—32no—
411C23×C4—91no—
412C23×C4—91no—
413C23×C4—98no—
414C23×C4—92no—
415C23×C4—91no—
416C23×C4—91no—
417C23×C4—188no—
418#121—316no—
419#121—916no—
420#121—916no—
421#121—916no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—98no—
424C2×C4⋊C4—92no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—98no—
427C2×C22⋊C4—92no—
428C2×C22⋊C4—91no—
429C2×C22⋊C4—91no—
430C2×C22⋊C4—91no—
431C2×C22⋊C4—98no—
432C2×C22⋊C4D3211yescharacteristic, complemented
433C23×C3—24no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—38no—
440C23×C3—34no—
441C23×C3—34no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3—64no—
445C23×C3—64no—
446C23×C3—64no—
447C23×C3—64no—
448C23×C3—64no—
449C23×C3C23×D314yes—
450C23×C3C23×D312yes—
451C22×D3—24no—
452C22×D3—24no—
453C22×D3—24no—
454C22×D3—24no—
455C22×D3—24no—
456C22×D3—38no—
457C22×D3—38no—
458C22×D3—38no—
459C22×D3—34no—
460C22×D3—332no—
461C22×D3—34no—
462C22×D3—64no—
463C22×D3—64no—
464C22×D3—64no—
465C22×D3—62no—
466C22×D3—62no—
467C22×D3—616no—
468C22×D3—616no—
469C22×D3—664no—
470C22×D3—616no—
471C22×D3—616no—
472C22×D3—616no—
473C22×D3—616no—
474C22×D3—616no—
475C22×D3—616no—
476C22×D3—616no—
477C22×D3—64no—
478C22×D3—64no—
479C22×D3—64no—
480C22×D3—64no—
481C22×D3—128no—
482C22×D3—128no—
483C22×D3—122no—
484C22×D3—122no—
485C22×D3—1232no—
486C22×D3—1232no—
487C22×D3—1232no—
488C22×D3D3×D418yescomplemented
489C22×D3C23×D314yes—
490C22×D3C23×D314yes—
491C3×D4—616no—
492C3×D4—616no—
493C3×D4—616no—
494C2×C3×C4—24no—
495C2×C3×C4—24no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—38no—
499C2×C3×C4—34no—
500C2×C3×C4—34no—
501C2×C3×C4—42no—
502C2×C3×C4—42no—
503C2×C3×C4—616no—
504C2×C3×C4—64no—
505C2×C3×C4C23×D314yes—
506C2×C3×C4C23×D314yes—
507#67—216no—
508#67—216no—
509#67—616no—
510#67—616no—
511#67—616no—
512#67—616no—
513C2×Dic3—24no—
514C2×Dic3—34no—
515C2×Dic3—34no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—64no—
519C2×Dic3—64no—
520C2×Dic3—616no—
521C2×Dic3—122no—
522C2×Dic3—122no—
523C2×Dic3D3×D418yescomplemented
524C2×Dic3C23×D314yes—
525C2×Dic3C23×D314yes—
526D12—216no—
527D12—616no—
528D12—616no—
529C4×D3—216no—
530C4×D3—332no—
531C4×D3—616no—
532C4×D3—616no—
533C4×D3—616no—
534C4×D3—616no—
535C4×D3—128no—
536C4×D3—128no—
537C2×C32—42no—
538C2×C32C2×#12114yescomplemented
539C2×C32C23×D411yescharacteristic
540C2×C32C23×D411yescharacteristic
541C2×C32C22×#4111yescharacteristic
542C3⋊D3—42no—
543C3⋊D3C2×#12118yescomplemented
544C3×D3—28no—
545C3×D3—44no—
546C24—32no—
547C24—32no—
548C24—94no—
549C24—98no—
550C24—94no—
551C24—91no—
552C24—94no—
553C24—91no—
554C24—184no—
555C24—184no—
556C24—184no—
557C24—184no—
558C24—184no—
559C24—184no—
560C24—184no—
561C24—184no—
562C24C2×D3211yescharacteristic
563C2×D4—38no—
564C2×D4—38no—
565C2×D4—38no—
566C2×D4—68no—
567C2×D4—68no—
568C2×D4—68no—
569C2×D4—98no—
570C2×D4—98no—
571C2×D4—98no—
572C2×D4—188no—
573C2×D4—188no—
574C2×D4—1832no—
575C2×D4—1832no—
576C2×D4—1832no—
577C2×D4—188no—
578C22×C4—32no—
579C22×C4—32no—
580C22×C4—38no—
581C22×C4—68no—
582C22×C4—94no—
583C22×C4—98no—
584C22×C4—94no—
585C22×C4—98no—
586C22×C4—91no—
587C22×C4—91no—
588C22×C4—94no—
589C22×C4—94no—
590C22×C4—184no—
591C22×C4—184no—
592C22×C4—188no—
593C22×C4—1832no—
594C22×C4—184no—
595C22×C4C2×D3211yescharacteristic
596C22×C4C2×D3211yescharacteristic
597C4⋊C4—38no—
598C4⋊C4—98no—
599C22⋊C4—38no—
600C22⋊C4—98no—
601C22⋊C4—94no—
602C22⋊C4—94no—
603C22⋊C4—94no—
604C22⋊C4C2×D3214yescomplemented
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—38no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—48no—
617C22×C3—48no—
618C22×C3—64no—
619C22×C3—64no—
620C22×C3—616no—
621C22×C3—64no—
622C22×C3—64no—
623C22×C3—64no—
624C22×C3—128no—
625C22×C3C2×D3×D414yes—
626C22×C3C2×D3×D414yes—
627C22×C3D3×#4114yes—
628C22×C3C24×D312yes—
629C2×D3—24no—
630C2×D3—24no—
631C2×D3—216no—
632C2×D3—24no—
633C2×D3—24no—
634C2×D3—24no—
635C2×D3—38no—
636C2×D3—38no—
637C2×D3—38no—
638C2×D3—332no—
639C2×D3—48no—
640C2×D3—64no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—616no—
644C2×D3—664no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—122no—
650C2×D3—122no—
651C2×D3—1232no—
652C2×D3—1232no—
653C2×D3—1232no—
654C2×D3—128no—
655C2×D3—128no—
656C2×D3C2×D3×D418yescomplemented
657C3×C4—24no—
658C3×C4—24no—
659C3×C4—38no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—64no—
663Dic3—24no—
664Dic3—64no—
665Dic3—64no—
666Dic3—122no—
667Dic3—122no—
668Dic3C2×D3×D418yescomplemented
669C32C22×#12111yescharacteristic, complemented, Sylow
670C23—22no—
671C23—22no—
672C23—22no—
673C23—38no—
674C23—34no—
675C23—34no—
676C23—64no—
677C23—64no—
678C23—64no—
679C23—64no—
680C23—64no—
681C23—916no—
682C23—94no—
683C23—94no—
684C23—94no—
685C23—92no—
686C23—92no—
687C23—188no—
688C23—188no—
689C23—188no—
690C23—188no—
691C23—188no—
692C23—1832no—
693C23—188no—
694C23—188no—
695C23—188no—
696C23—182no—
697C23—182no—
698C23—182no—
699C23—3616no—
700C23—3616no—
701C23C22×D3212yes—
702C23C22×D3211yescharacteristic
703D4—616no—
704D4—616no—
705D4—616no—
706D4—1816no—
707D4—1816no—
708D4—1816no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—38no—
712C2×C4—34no—
713C2×C4—34no—
714C2×C4—616no—
715C2×C4—64no—
716C2×C4—916no—
717C2×C4—92no—
718C2×C4—92no—
719C2×C4—188no—
720C2×C4—188no—
721C2×C4—1816no—
722C2×C4—188no—
723C2×C4—182no—
724C2×C4—182no—
725C2×C4C22×D3212yes—
726C2×C4C22×D3212yes—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—24no—
731C2×C3—44no—
732C2×C3—44no—
733C2×C3—68no—
734C2×C3—124no—
735C2×C3D3×#12118yescomplemented
736C2×C3C22×D3×D412yes—
737C2×C3C22×D3×D412yes—
738C2×C3C2×D3×#4112yes—
739D3—28no—
740D3—316no—
741D3—44no—
742D3—68no—
743D3—124no—
744D3—124no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—38no—
749C22—44no—
750C22—64no—
751C22—64no—
752C22—616no—
753C22—64no—
754C22—64no—
755C22—64no—
756C22—94no—
757C22—94no—
758C22—94no—
759C22—916no—
760C22—128no—
761C22—1832no—
762C22—182no—
763C22—182no—
764C22—182no—
765C22—3616no—
766C22—3616no—
767C22—364no—
768C22#6430612yes—
769C22D32×D412yes—
770C22D32×D412yes—
771C22C23×D3211yescharacteristic
772C4—22no—
773C4—22no—
774C4—38no—
775C4—64no—
776C4—182no—
777C4—182no—
778C3—21no—
779C3C2×D3×#12112yescomplemented
780C2—42no—
781C2—68no—
782C2—98no—
783C2—124no—
784C2—362no—
785C2#1059426514yesdirect product factor
786C2C2×#6430611yescharacteristic
787C2C2×D32×D411yescharacteristic
788C2C2×D32×D411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C22×#121
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×#3811C2semidirect
2. C22×#3811C2semidirect
3. C22×#3802C2semidirect
4. C22×C4×D32C2semidirect
5. C2×C22⋊C4×C3⋊D3C2semidirect
6. C2×C3×#884C2semidirect
7. C2×#63970C2semidirect
8. C2×#63921C2semidirect
9. C2×#63906C2semidirect
10. C2×#63886C2semidirect
11. C2×#63883C2semidirect
12. #10594265C2direct (N × H)
19. C22×C3×#67C22semidirect
20. C22×C3×#67C22semidirect
21. C22×C3×D12C22semidirect
22. C22×C3×C4×D3C22semidirect
25. C2×#3811C22semidirect
26. C2×#3811C22semidirect
27. C22×#626C22semidirect
28. C22×#626C22semidirect
29. C22×#625C22semidirect
32. C22×D3×Dic3C22semidirect
34. C2×#3802C22semidirect
36. C2×C4×D32C22semidirect
37. C2×C32×C22⋊C4C22semidirect
38. C2×#3757C22semidirect
39. C2×#3752C22semidirect
40. C2×#3752C22semidirect
41. C22⋊C4×C3⋊D3C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C3×#884C22semidirect
45. #63970C22semidirect
46. C2×Dic3⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. #63921C22semidirect
49. #63906C22semidirect
50. #63886C22semidirect
51. #63883C22semidirect
65. C2×#884D3semidirect
83. C22×D32D4semidirect
96. C2×C3×#67C23semidirect
97. C2×C3×#67C23semidirect
101. C2×C3×D12C23semidirect
103. C2×C3×C4×D3C23semidirect
108. C2×#626C23semidirect
109. C2×#626C23semidirect
111. C2×#625C23semidirect
113. C2×#624D4semidirect
117. C2×D3×Dic3C23semidirect
120. C32×C22⋊C4C23semidirect
121. #3757C23semidirect
122. #3752C23semidirect
123. #3752C23semidirect
124. C3×(C2×D3)⋊C4C23semidirect
125. C3×Dic3⋊C4C23semidirect
126. Dic3⋊Dic3C23semidirect
127. (C2×D3)⋊Dic3C23semidirect
141. C22×#67C2×D3semidirect
142. C22×#67C2×D3semidirect
152. C22×D12C2×D3semidirect
162. C22×C4×D3C2×D3semidirect
167. C2×C3×C22⋊C4C2×D3semidirect
180. C2×(C2×D3)⋊C4C2×D3semidirect
183. C2×Dic3⋊C4C2×D3semidirect
187. #884C2×D3semidirect
213. C22×C3×D3C2×D4semidirect
223. C2×D32C2×D4semidirect
237. C2×C3×Dic3C2×D4semidirect
246. #624C2×D4semidirect
310. C2×#67C22×D3semidirect
311. C2×#67C22×D3semidirect
328. C2×D12C22×D3semidirect
345. C2×C4×D3C22×D3semidirect
349. C3×C22⋊C4C22×D3semidirect
358. (C2×D3)⋊C4C22×D3semidirect
361. Dic3⋊C4C22×D3semidirect
375. C2×C3⋊D3#121semidirect
386. C2×C3×D3C22×D4semidirect
394. C3×Dic3C22×D4semidirect
432. C2×C22⋊C4D32semidirect
488. C22×D3D3×D4semidirect
523. C2×Dic3D3×D4semidirect
538. C2×C32C2×#121semidirect
543. C3⋊D3C2×#121semidirect
604. C22⋊C4C2×D32semidirect
656. C2×D3C2×D3×D4semidirect
668. Dic3C2×D3×D4semidirect
669. C32C22×#121semidirect
735. C2×C3D3×#121semidirect
779. C3C2×D3×#121semidirect
785. C2#10594265direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38112
C22×#38022
C22×C4×D322
C2×C22⋊C4×C3⋊D32
C2×C3×#8842
C2×#639702
C2×#639212
C2×#639062
C2×#638862
C2×#638832
#105942652
C2×D3×#1213