Finite Group Databasebeta

← C2×#10595017 #11900784

Subgroups — C2×#10595017 #11900784

Order 1152.

3901 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C212yesmaximal, complemented
4C2×#63979C211yesmaximal, characteristic, complemented
5C2×#63958C212yesmaximal, complemented
6C2×#63953C211yesmaximal, characteristic, complemented
7#10595017C2116yesmaximal, direct product factor
8C2×#63913C211yesmaximal, characteristic, complemented
9C2×#63910C212yesmaximal, complemented
10C2×C4×#626C212yesmaximal, complemented
11C2×C4×#624C211yesmaximal, characteristic, complemented
12C2×#63840C211yesmaximal, characteristic, complemented
13C2×#5548—32nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C2×#3828—28no—
18C2×#3828C2218yescomplemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#634C2211yescharacteristic
23C22×C3×#67C2212yes—
24C22×C3×C4×D3C2212yes—
25C22×#627C2211yescharacteristic
26C22×#626C2212yes—
27C22×#626C2212yes—
28C22×#625C2211yescharacteristic
29C22×#624C2212yes—
30C2×#3798—28no—
31C2×#3798C2218yescomplemented
32C2×C3×#217C2212yes—
33C3×C4×#67C22116yescomplemented
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2212yes—
37#63979C2218yescomplemented
38C2×Dic3⋊Dic3C2212yes—
39C2×#3722C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63958C22116yescomplemented
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63953C2218yescomplemented
45#63913C2218yescomplemented
46#63910C22116yescomplemented
47C4×#626C22116yescomplemented
48C4×#624C2218yescomplemented
49#63840C2218yescomplemented
50C22×#235—32no—
51C22×#235—32no—
52C22×#235—61no—
53C2×C3×C4×D4—32no—
54C2×#940—32no—
55C2×#938—32no—
56C2×C4×#67—32no—
57C2×C4×#67D312yescomplemented
58#5548—332no—
59C2×#895—32no—
60C2×#888—32no—
61C2×#885—32no—
62C2×#885—32no—
63C2×#884—32no—
64C2×#884—32no—
65C2×C4×D12—32no—
66C2×C42×D3—32no—
67C24×C32C2311yescharacteristic
68C23×C3⋊D3C2311yescharacteristic
69C23×C3⋊D3C2311yescharacteristic
70C23×C3×D3C2312yes—
71C22×C32×C4—24no—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2314yes—
74C22×C32×C4C2311yescharacteristic
75C2×#638—24no—
76C2×#638—24no—
77C2×#638C2314yes—
78C2×#638C2314yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81#3828—232no—
82C2×C4⋊(C3⋊D3)—24no—
83C2×C4⋊(C3⋊D3)C2314yes—
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3D418yescomplemented
86C2×C4×C3⋊D3C2314yes—
87C2×C4×C3⋊D3C2314yes—
88C2×#634—24no—
89C2×#634C2314yes—
90C2×C3×#67—28no—
91C2×C3×#67C2318yes—
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C2×C3×C4×D3—28no—
96C2×C3×C4×D3C2318yes—
97C2×#627—24no—
98C2×#627C2314yes—
99C2×#626—28no—
100C2×#626—28no—
101C2×#626C2318yes—
102C2×#626C2318yes—
103C2×#625—24no—
104C2×#625C2314yes—
105C2×#624—28no—
106C2×#624C2318yes—
107#3798—232no—
108C3×#217C2318yes—
109C3×(C2×D3)⋊C4C2318yes—
110C3×Dic3⋊C4C2318yes—
111C3×C4×Dic3C2318yes—
112Dic3⋊Dic3C2318yes—
113#3722C2318yes—
114(C2×D3)⋊Dic3C2318yes—
115Dic32C2314yes—
116Dic32C2314yes—
117C2×#532—91noSylow
118C22×C3×D4—32no—
119C23×C3×C4—21no—
120C23×C3×C4—32no—
121C23×C3×C4C2×D312yes—
122C22×#67—32no—
123C22×#67—32no—
124C22×#67—32no—
125C22×#67—32no—
126C22×#67—32no—
127C22×#67—61no—
128C22×#67—61no—
129C22×#67C2×D312yes—
130C2×#235—316no—
131C2×#235—316no—
132C2×#235—68no—
133C2×#235—616no—
134C2×#235—616no—
135C2×#235—616no—
136C22×D12—32no—
137C22×D12—32no—
138C22×D12—32no—
139C22×D12—61no—
140C22×C4×D3—32no—
141C22×C4×D3—32no—
142C22×C4×D3—32no—
143C22×C4×D3—32no—
144C22×C4×D3—61no—
145C22×C4×D3—61no—
146C22×C4×D3C2×D312yes—
147C22×Dic6—32no—
148C22×Dic6—32no—
149C22×Dic6—61no—
150C3×C4×D4—316no—
151C2×C3×C4⋊C4—32no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—32no—
154C2×C3×C42—32no—
155C2×#217—32no—
156C2×#217C2×D312yes—
157#940—316no—
158#938—316no—
159C4×#67—316no—
160C4×#67C2×D3116yescomplemented
161C2×(C2×D3)⋊C4—32no—
162C2×(C2×D3)⋊C4—32no—
163C2×(C2×D3)⋊C4—32no—
164C2×(C2×D3)⋊C4C2×D312yes—
165C2×C4⋊Dic3—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4C2×D312yes—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3C2×D312yes—
171#895—316no—
172#888—316no—
173#885—316no—
174#885—316no—
175#884—316no—
176#884—316no—
177C4×D12—316no—
178C42×D3—316no—
179C23×C32—22no—
180C23×C32—24no—
181C23×C32C2412yes—
182C23×C32C2411yescharacteristic
183C22×C3⋊D3—22no—
184C22×C3⋊D3—24no—
185C22×C3⋊D3—24no—
186C22×C3⋊D3C2×D414yes—
187C22×C3⋊D3C2412yes—
188C22×C3⋊D3C2412yes—
189C22×C3×D3—24no—
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2414yes—
193C2×C32×C4—22no—
194C2×C32×C4—28no—
195C2×C32×C4C2×D414yes—
196C2×C32×C4C2412yes—
197C2×C32×C4C2412yes—
198#638—28no—
199#638—28no—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3C2×D414yes—
202C2×C3⋊Dic3C2412yes—
203C2×C3⋊Dic3C2412yes—
204C4⋊(C3⋊D3)—28no—
205C4×C3⋊D3—28no—
206C4×C3⋊D3C2×D4116yescomplemented
207#634—28no—
208C3×#67—216no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3#4118yescomplemented
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2414yes—
215C3×C4×D3—216no—
216#627—28no—
217#626—216no—
218#626—216no—
219#625—28no—
220#624—216no—
221C22×#41—91no—
222C22×#41—91no—
223#532—916no—
224C2×C4⋊Q8—91no—
225C2×#127—91no—
226C2×#124—91no—
227C2×#124—91no—
228C2×#121—92no—
229C2×#121—92no—
230C2×C4×D4—32no—
231C2×C4×D4—92no—
232C22×C42—91no—
233C24×C3—21no—
234C24×C3—32no—
235C24×C3C22×D312yes—
236C23×D3—32no—
237C23×D3—32no—
238C23×D3—61no—
239C23×D3—61no—
240C23×D3C22×D312yes—
241C2×C3×D4—38no—
242C2×C3×D4—68no—
243C22×C3×C4—28no—
244C22×C3×C4—28no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—21no—
248C22×C3×C4—32no—
249C22×C3×C4—32no—
250C22×C3×C4—32no—
251C22×C3×C4—38no—
252C22×C3×C4—68no—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D318yes—
255C22×C3×C4C22×D312yes—
256C2×#67—28no—
257C2×#67—38no—
258C2×#67—38no—
259C2×#67—38no—
260C2×#67—38no—
261C2×#67—38no—
262C2×#67—64no—
263C2×#67—64no—
264C2×#67—68no—
265C2×#67—68no—
266C2×#67—68no—
267C2×#67—68no—
268C2×#67—68no—
269C2×#67—68no—
270C2×#67—68no—
271C2×#67C22×D318yes—
272C22×Dic3—32no—
273C22×Dic3—32no—
274C22×Dic3—61no—
275C22×Dic3—61no—
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D312yes—
278C22×Dic3C22×D312yes—
279#235—664no—
280#235—664no—
281#235—664no—
282C2×D12—38no—
283C2×D12—38no—
284C2×D12—38no—
285C2×D12—64no—
286C2×D12—68no—
287C2×D12—68no—
288C2×D12—68no—
289C2×D12—68no—
290C2×C4×D3—28no—
291C2×C4×D3—316no—
292C2×C4×D3—38no—
293C2×C4×D3—38no—
294C2×C4×D3—38no—
295C2×C4×D3—38no—
296C2×C4×D3—68no—
297C2×C4×D3—64no—
298C2×C4×D3—64no—
299C2×C4×D3—68no—
300C2×C4×D3—68no—
301C2×C4×D3—68no—
302C2×C4×D3—68no—
303C2×C4×D3C22×D318yes—
304C2×Dic6—38no—
305C2×Dic6—38no—
306C2×Dic6—64no—
307C2×Dic6—68no—
308C2×Dic6—68no—
309C2×Dic6—68no—
310C3×C4⋊C4—38no—
311C3×C22⋊C4—38no—
312C3×C22⋊C4—38no—
313C3×C42—38no—
314#217—38no—
315#217C22×D318yes—
316(C2×D3)⋊C4—38no—
317(C2×D3)⋊C4—38no—
318(C2×D3)⋊C4—38no—
319(C2×D3)⋊C4C22×D318yes—
320C4⋊Dic3—38no—
321Dic3⋊C4—38no—
322Dic3⋊C4C22×D318yes—
323C4×Dic3—38no—
324C4×Dic3—38no—
325C4×Dic3C22×D318yes—
326C22×C32—22no—
327C22×C32—24no—
328C22×C32—44no—
329C22×C32C22×D412yes—
330C22×C32C2×#4114yes—
331C22×C32C2511yescharacteristic
332C2×C3⋊D3—22no—
333C2×C3⋊D3—28no—
334C2×C3⋊D3—24no—
335C2×C3⋊D3—24no—
336C2×C3⋊D3—44no—
337C2×C3⋊D3C22×D414yes—
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—48no—
342C32×C4—22no—
343C32×C4C22×D414yes—
344C3⋊Dic3—22no—
345C3⋊Dic3C22×D414yes—
346C3×Dic3—24no—
347C3×Dic3—24no—
348C3×Dic3C2×#4118yescomplemented
349C2×#41—98no—
350C2×#41—98no—
351C2×#41—188no—
352C2×#41—188no—
353C22×Q8—91no—
354C22×Q8—91no—
355C22×D4—32no—
356C22×D4—92no—
357C22×D4—92no—
358C22×D4—91no—
359C22×D4—91no—
360C22×D4—91no—
361C22×D4—91no—
362C23×C4—32no—
363C23×C4—92no—
364C23×C4—91no—
365C23×C4—91no—
366C23×C4D3211yescharacteristic
367C4⋊Q8—98no—
368#127—98no—
369#124—98no—
370#124—98no—
371#121—916no—
372#121—916no—
373C4×D4—316no—
374C4×D4—916no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—92no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C42—32no—
382C2×C42—98no—
383C2×C42—91no—
384C2×C42—91no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—21no—
390C23×C3—22no—
391C23×C3—34no—
392C23×C3—44no—
393C23×C3—64no—
394C23×C3—64no—
395C23×C3—64no—
396C23×C3C23×D314yes—
397C23×C3C23×D312yes—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—24no—
401C22×D3—38no—
402C22×D3—34no—
403C22×D3—34no—
404C22×D3—64no—
405C22×D3—62no—
406C22×D3—62no—
407C22×D3—64no—
408C22×D3—64no—
409C22×D3—64no—
410C22×D3—64no—
411C22×D3—64no—
412C22×D3—64no—
413C22×D3—124no—
414C22×D3—124no—
415C22×D3C23×D314yes—
416C3×D4—616no—
417C2×C3×C4—24no—
418C2×C3×C4—216no—
419C2×C3×C4—24no—
420C2×C3×C4—216no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—38no—
425C2×C3×C4—34no—
426C2×C3×C4—34no—
427C2×C3×C4—34no—
428C2×C3×C4—64no—
429C2×C3×C4—64no—
430C2×C3×C4—616no—
431C2×C3×C4D3×D418yes—
432C2×C3×C4C23×D314yes—
433C2×C3×C4C23×D314yes—
434#67—216no—
435#67—616no—
436#67—616no—
437#67—616no—
438#67—616no—
439#67—616no—
440#67—616no—
441#67—616no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—38no—
445C2×Dic3—34no—
446C2×Dic3—34no—
447C2×Dic3—64no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—64no—
451C2×Dic3—64no—
452C2×Dic3#23518yescomplemented
453C2×Dic3C23×D314yes—
454C2×Dic3C23×D314yes—
455C2×Dic3C23×D314yes—
456D12—616no—
457D12—616no—
458D12—616no—
459D12—616no—
460C4×D3—216no—
461C4×D3—332no—
462C4×D3—616no—
463C4×D3—616no—
464C4×D3—616no—
465C4×D3—616no—
466C4×D3—616no—
467Dic6—616no—
468Dic6—616no—
469Dic6—616no—
470C2×C32—42no—
471C2×C32#53214yescomplemented
472C2×C32C23×D411yescharacteristic
473C2×C32C22×#4112yes—
474C3⋊D3—24no—
475C3⋊D3—42no—
476C3×D3—44no—
477C24—32no—
478C24—91no—
479C24—91no—
480C24C2×D3211yescharacteristic
481#41—1832no—
482#41—1832no—
483C2×Q8—94no—
484C2×Q8—94no—
485C2×Q8—184no—
486C2×Q8—184no—
487C2×D4—38no—
488C2×D4—68no—
489C2×D4—98no—
490C2×D4—98no—
491C2×D4—94no—
492C2×D4—94no—
493C2×D4—94no—
494C2×D4—94no—
495C2×D4—184no—
496C2×D4—188no—
497C2×D4—188no—
498C2×D4—184no—
499C2×D4—184no—
500C2×D4—184no—
501C22×C4—24no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—38no—
506C22×C4—68no—
507C22×C4—98no—
508C22×C4—91no—
509C22×C4—94no—
510C22×C4—98no—
511C22×C4—91no—
512C22×C4—94no—
513C22×C4—188no—
514C22×C4—184no—
515C22×C4C2×D3211yescharacteristic
516C22×C4C2×D3214yes—
517C22×C4C2×D3211yescharacteristic
518C4⋊C4—38no—
519C4⋊C4—98no—
520C22⋊C4—38no—
521C22⋊C4—38no—
522C22⋊C4—98no—
523C22⋊C4—98no—
524C42—38no—
525C42—94no—
526C42—94no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3—24no—
531C22×C3—24no—
532C22×C3—22no—
533C22×C3—21no—
534C22×C3—44no—
535C22×C3—48no—
536C22×C3—48no—
537C22×C3—64no—
538C22×C3—64no—
539C22×C3—64no—
540C22×C3—128no—
541C22×C3C2×#23514yes—
542C22×C3C2×D3×D414yes—
543C22×C3D3×#4114yes—
544C22×C3C24×D312yes—
545C2×D3—24no—
546C2×D3—24no—
547C2×D3—24no—
548C2×D3—38no—
549C2×D3—48no—
550C2×D3—64no—
551C2×D3—64no—
552C2×D3—64no—
553C2×D3—616no—
554C2×D3—64no—
555C2×D3—64no—
556C2×D3—64no—
557C2×D3—64no—
558C2×D3—124no—
559C2×D3—128no—
560C2×D3—124no—
561C2×D3—128no—
562C2×D3—128no—
563C3×C4—24no—
564C3×C4—24no—
565C3×C4—24no—
566C3×C4—38no—
567C3×C4—64no—
568C3×C4—64no—
569C3×C4C2×D3×D418yes—
570Dic3—24no—
571Dic3—24no—
572Dic3—38no—
573Dic3—64no—
574Dic3—64no—
575Dic3—64no—
576Dic3C2×#23518yescomplemented
577C32C2×#53211yescharacteristic, complemented, Sylow
578C23—24no—
579C23—22no—
580C23—34no—
581C23—64no—
582C23—64no—
583C23—64no—
584C23—94no—
585C23—92no—
586C23—92no—
587C23—184no—
588C23—184no—
589C23—182no—
590C23C22×D3212yes—
591C23C22×D3211yescharacteristic
592Q8—188no—
593Q8—188no—
594D4—616no—
595D4—188no—
596D4—1816no—
597D4—1816no—
598D4—188no—
599D4—188no—
600D4—188no—
601C2×C4—22no—
602C2×C4—28no—
603C2×C4—38no—
604C2×C4—34no—
605C2×C4—34no—
606C2×C4—34no—
607C2×C4—64no—
608C2×C4—64no—
609C2×C4—616no—
610C2×C4—94no—
611C2×C4—92no—
612C2×C4—916no—
613C2×C4—92no—
614C2×C4—1816no—
615C2×C4—182no—
616C2×C4—188no—
617C2×C4#381114yes—
618C2×C4C22×D3212yes—
619C2×C4C22×D3212yes—
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—24no—
623C2×C3—44no—
624C2×C3—44no—
625C2×C3—124no—
626C2×C3#554818yescomplemented
627C2×C3C22×#23512yes—
628C2×C3C22×D3×D412yes—
629C2×C3C2×D3×#4112yes—
630D3—44no—
631D3—68no—
632D3—124no—
633D3—124no—
634D3—124no—
635C22—24no—
636C22—22no—
637C22—44no—
638C22—64no—
639C22—64no—
640C22—64no—
641C22—94no—
642C22—128no—
643C22—184no—
644C22—188no—
645C22—184no—
646C22—182no—
647C22—364no—
648C22D3×#23514yes—
649C22C2×#381112yes—
650C22C23×D3211yescharacteristic
651C4—22no—
652C4—38no—
653C4—64no—
654C4—64no—
655C4—94no—
656C4—182no—
657C4C2×#381114yes—
658C3—21no—
659C3C2×#554812yescomplemented
660C2—42no—
661C2—124no—
662C2—184no—
663C2—362no—
664C2#1059501714yesdirect product factor
665C2C2×D3×#23512yes—
666C2C22×#381111yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C22×#3798C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×#63979C2semidirect
5. C2×#63958C2semidirect
6. C2×#63953C2semidirect
7. #10595017C2direct (N × H)
8. C2×#63913C2semidirect
9. C2×#63910C2semidirect
10. C2×C4×#626C2semidirect
11. C2×C4×#624C2semidirect
12. C2×#63840C2semidirect
18. C2×#3828C22semidirect
31. C2×#3798C22semidirect
33. C3×C4×#67C22semidirect
37. #63979C22semidirect
41. #63958C22semidirect
44. #63953C22semidirect
45. #63913C22semidirect
46. #63910C22semidirect
47. C4×#626C22semidirect
48. C4×#624C22semidirect
49. #63840C22semidirect
57. C2×C4×#67D3semidirect
85. C2×C4×C3⋊D3D4semidirect
160. C4×#67C2×D3semidirect
206. C4×C3⋊D3C2×D4semidirect
211. C2×C3×Dic3#41semidirect
348. C3×Dic3C2×#41semidirect
452. C2×Dic3#235semidirect
471. C2×C32#532semidirect
576. Dic3C2×#235semidirect
577. C32C2×#532semidirect
626. C2×C3#5548semidirect
659. C3C2×#5548semidirect
664. C2#10595017direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×#37982
C2×C3×C4×#672
C2×#639792
C2×#639582
C2×#639532
#105950172
C2×#639132
C2×#639102
C2×C4×#6262
C2×C4×#6242
C2×#638402
C2×#55483