Finite Group Databasebeta

← C2×#10595126 #11901675

Subgroups — C2×#10595126 #11901675

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic
3C2×C3×#936C211yesmaximal, characteristic, complemented
4C2×#63982C212yesmaximal, complemented
5C2×#63962C212yesmaximal, complemented
6C2×#63959C212yesmaximal, complemented
7C2×#63956C212yesmaximal, complemented
8#10595126C2116yesmaximal, direct product factor
9C2×#63918C211yesmaximal, characteristic, complemented
10C2×#63856C211yesmaximal, characteristic, complemented
11C2×#63855C211yesmaximal, characteristic, complemented
12C2×#63843C211yesmaximal, characteristic, complemented
13C2×#5682—31nomaximal
14C2×#5603—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2212yes—
21C2×#3757C2212yes—
22D4×C3⋊Dic3C2218yescomplemented
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28C3×#938C2218yes—
29C3×#936C2218yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32#63982C22116yescomplemented
33C2×#3724C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2212yes—
38#63962C22116yescomplemented
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2212yes—
42#63959C22116yescomplemented
43#63956C22116yescomplemented
44C2×Dic32C2212yes—
45#63918C2218yescomplemented
46#63856C2218yescomplemented
47#63855C2218yescomplemented
48#63843C2218yescomplemented
49C2×C3×#124—31no—
50C2×C3×#121—31no—
51C2×#946—31no—
52C2×Q8×Dic3—31no—
53C2×#938D311yescharacteristic
54C2×#936—32no—
55C2×#936D311yescharacteristic, complemented
56C2×#935—32no—
57C2×D4×Dic3—31no—
58C2×D4×Dic3—31no—
59C2×D4×Dic3—61no—
60C2×#926—31no—
61C2×#924—31no—
62#5682—316no—
63#5603—316no—
64C2×#888—31no—
65C2×#887—31no—
66C2×#886—32no—
67C2×#885—32no—
68C2×#879—32no—
69C2×#879—32no—
70C2×#878—32no—
71C2×#878—32no—
72C2×#872—31no—
73C2×#869—31no—
74C24×C32C2312yes—
75C23×C3×D3C2311yescharacteristic
76C2×C32×D4—24no—
77C2×C32×D4C2314yes—
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3—44no—
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2318yes—
84C2×C3×#67—44no—
85C2×C3×#67C2318yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6C2314yes—
95C2×#627—44no—
96C2×#627C2318yes—
97#3757C2318yes—
98C4⋊(C3⋊Dic3)C2314yes—
99C4×C3⋊Dic3C2314yes—
100C3×#217C2318yes—
101C3×#217C2318yes—
102C3×#217C2318yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4×Dic3C2314yes—
105#3724C2318yes—
106Dic3⋊Dic3C2318yes—
107Dic3⋊Dic3C2314yes—
108Dic3⋊Dic3C2314yes—
109Dic3⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2314yes—
111(C2×D3)⋊Dic3C2314yes—
112(C2×D3)⋊Dic3C2318yes—
113Dic32C2318yes—
114C2×#542—91noSylow
115C22×C3×Q8—31no—
116C22×C3×D4—21no—
117C22×C3×D4—32no—
118C22×C3×D4C2×D311yescharacteristic
119C22×C3×D4C2×D311yescharacteristic
120C23×C3×C4—31no—
121C22×#67C2×D312yes—
122C23×Dic3—32no—
123C23×Dic3—32no—
124C23×Dic3—62no—
125C22×C4×D3C2×D311yescharacteristic
126C22×Dic6—32no—
127C22×Dic6—32no—
128C22×Dic6C2×D311yescharacteristic
129C3×#124—38no—
130C3×#121—38no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C42—31no—
136C2×#217—32no—
137C2×#217—32no—
138C2×#217—32no—
139C2×#217—31no—
140C2×#217—31no—
141C2×#217—62no—
142C2×#217C2×D312yes—
143C2×#217C2×D312yes—
144C2×#217C2×D312yes—
145#946—38no—
146Q8×Dic3—38no—
147#938C2×D318yes—
148#936—316no—
149#936C2×D318yescomplemented
150#935—316no—
151D4×Dic3—38no—
152D4×Dic3—38no—
153D4×Dic3—68no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—32no—
157#926—38no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—32no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—32no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—61no—
165C2×C4⋊Dic3C2×D311yescharacteristic
166#924—38no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—32no—
170C2×Dic3⋊C4—32no—
171C2×Dic3⋊C4—32no—
172C2×Dic3⋊C4—32no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—32no—
176C2×C4×Dic3—32no—
177C2×C4×Dic3—61no—
178C2×C4×Dic3C2×D311yescharacteristic
179#888—38no—
180#887—38no—
181#886—316no—
182#885—316no—
183#879—316no—
184#879—316no—
185#878—316no—
186#878—316no—
187#872—38no—
188#869—38no—
189C23×C32—24no—
190C23×C32—24no—
191C23×C32—24no—
192C23×C32C2414yes—
193C23×C32C2411yescharacteristic
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3C2412yes—
198C32×D4—28no—
199C2×C32×C4#4114yes—
200C2×C32×C4C2412yes—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—24no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—48no—
205C2×C3⋊Dic3C2412yes—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2414yes—
208C3×#67—48no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2412yes—
219C3×C4×D3—28no—
220C3×Dic6—28no—
221#627—48no—
222#542—916no—
223C2×C4⋊Q8—91no—
224C2×#126—92no—
225C2×#124—31no—
226C2×#124—92no—
227C2×#123—92no—
228C2×C22⋊Q8—92no—
229C2×C22⋊Q8—91no—
230C2×#121—31no—
231C2×C4×Q8—91no—
232C2×C4×D4—91no—
233C2×#117—91no—
234C24×C3—22no—
235C24×C3—31no—
236C24×C3C22×D312yes—
237C24×C3C22×D312yes—
238C23×D3C22×D311yescharacteristic
239C2×C3×Q8—34no—
240C2×C3×Q8—64no—
241C2×C3×D4—28no—
242C2×C3×D4—24no—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4—38no—
246C2×C3×D4—124no—
247C2×C3×D4C22×D314yes—
248C2×C3×D4C22×D314yes—
249C22×C3×C4—21no—
250C22×C3×C4—32no—
251C22×C3×C4—32no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—34no—
256C22×C3×C4—64no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C2×#67—44no—
260C2×#67C22×D318yes—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—31no—
265C22×Dic3—32no—
266C22×Dic3—32no—
267C22×Dic3—38no—
268C22×Dic3—38no—
269C22×Dic3—61no—
270C22×Dic3—61no—
271C22×Dic3—62no—
272C22×Dic3—68no—
273C22×Dic3—124no—
274C22×Dic3—124no—
275C22×Dic3—128no—
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D312yes—
278C22×Dic3C22×D311yescharacteristic
279C22×Dic3C22×D311yescharacteristic
280C22×Dic3C22×D311yescharacteristic
281C2×C4×D3—24no—
282C2×C4×D3C22×D314yes—
283C2×Dic6—24no—
284C2×Dic6—38no—
285C2×Dic6—38no—
286C2×Dic6—124no—
287C2×Dic6—124no—
288C2×Dic6C22×D314yes—
289C3×C4⋊C4—34no—
290C3×C22⋊C4—38no—
291C3×C22⋊C4—38no—
292C3×C22⋊C4—38no—
293C3×C42—34no—
294#217—38no—
295#217—38no—
296#217—38no—
297#217—34no—
298#217—34no—
299#217—68no—
300#217C22×D318yes—
301#217C22×D318yes—
302#217C22×D318yes—
303(C2×D3)⋊C4—34no—
304(C2×D3)⋊C4—34no—
305(C2×D3)⋊C4—38no—
306C4⋊Dic3—34no—
307C4⋊Dic3—34no—
308C4⋊Dic3—38no—
309C4⋊Dic3—34no—
310C4⋊Dic3—38no—
311C4⋊Dic3—34no—
312C4⋊Dic3—64no—
313C4⋊Dic3C22×D314yes—
314Dic3⋊C4—34no—
315Dic3⋊C4—34no—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—38no—
319Dic3⋊C4—38no—
320C4×Dic3—34no—
321C4×Dic3—34no—
322C4×Dic3—38no—
323C4×Dic3—38no—
324C4×Dic3—64no—
325C4×Dic3C22×D314yes—
326C22×C32—24no—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—48no—
330C22×C32C2×#4112yes—
331C22×C32H(5,𝔽2)12yes—
332C22×C322−1+412yes—
333C22×C32C2511yescharacteristic
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3—22no—
337C2×C3×D3—44no—
338C32×C4C2×#4114yes—
339C3⋊Dic3—22no—
340C3⋊Dic3—24no—
341C3⋊Dic3—22no—
342C3×Dic3—24no—
343C3×Dic3—22no—
344C3×Dic3—22no—
345C3×Dic3—24no—
346C3×Dic3—22no—
347C22×Q8—31no—
348C22×Q8—92no—
349C22×D4—32no—
350C22×D4D3211yescharacteristic
351C23×C4—31no—
352C23×C4—92no—
353C4⋊Q8—98no—
354#126—916no—
355#124—38no—
356#124—916no—
357#123—916no—
358C22⋊Q8—916no—
359C22⋊Q8—98no—
360#121—38no—
361C4×Q8—98no—
362C4×D4—98no—
363#117—98no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—92no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4—92no—
370C2×C4⋊C4—91no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—91no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C42—31no—
379C2×C42—92no—
380C2×C42—91no—
381C23×C3—28no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—21no—
390C23×C3—32no—
391C23×C3—44no—
392C23×C3—44no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3C23×D314yes—
397C23×C3C23×D314yes—
398C23×C3C23×D311yescharacteristic
399C23×C3C23×D311yescharacteristic
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—22no—
403C22×D3C23×D312yes—
404C3×Q8—68no—
405C3×D4—216no—
406C3×D4—28no—
407C3×D4—28no—
408C3×D4—128no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4—34no—
412C2×C3×C4—34no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—32no—
416C2×C3×C4—62no—
417C2×C3×C4—64no—
418C2×C3×C4—62no—
419C2×C3×C4—64no—
420C2×C3×C4—62no—
421C2×C3×C4—68no—
422C2×C3×C4#23714yes—
423C2×C3×C4#23714yes—
424C2×C3×C4C23×D312yes—
425C2×C3×C4C23×D312yes—
426#67—48no—
427C2×Dic3—24no—
428C2×Dic3—22no—
429C2×Dic3—24no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—32no—
433C2×Dic3—32no—
434C2×Dic3—32no—
435C2×Dic3—32no—
436C2×Dic3—34no—
437C2×Dic3—34no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—64no—
441C2×Dic3—64no—
442C2×Dic3—64no—
443C2×Dic3—62no—
444C2×Dic3—64no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—122no—
449C2×Dic3—124no—
450C2×Dic3—128no—
451C2×Dic3—128no—
452C2×Dic3—1216no—
453C2×Dic3C23×D314yes—
454C2×Dic3C23×D314yes—
455C2×Dic3C23×D312yes—
456C2×Dic3C23×D312yes—
457C2×Dic3C23×D312yes—
458C4×D3—28no—
459Dic6—28no—
460Dic6—128no—
461Dic6—128no—
462C2×C32—44no—
463C2×C32#54214yescomplemented
464C2×C32C22×#4111yescharacteristic
465C2×C32C2×H(5,𝔽2)11yescharacteristic
466C2×C32C2×2−1+411yescharacteristic
467C3×D3—42no—
468C24—31no—
469C24C2×D3212yes—
470C2×Q8—34no—
471C2×Q8—64no—
472C2×Q8—98no—
473C2×Q8—364no—
474C2×D4—24no—
475C2×D4—38no—
476C2×D4—124no—
477C2×D4C2×D3214yes—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—32no—
481C22×C4—32no—
482C22×C4—31no—
483C22×C4—34no—
484C22×C4—64no—
485C22×C4—91no—
486C22×C4—91no—
487C22×C4—92no—
488C22×C4—98no—
489C22×C4—364no—
490C22×C4C2×D3211yescharacteristic
491C4⋊C4—34no—
492C4⋊C4—94no—
493C4⋊C4—94no—
494C4⋊C4—98no—
495C4⋊C4—98no—
496C4⋊C4—98no—
497C4⋊C4—94no—
498C22⋊C4—38no—
499C22⋊C4—38no—
500C22⋊C4—38no—
501C22⋊C4—94no—
502C22⋊C4—94no—
503C22⋊C4—98no—
504C22⋊C4—98no—
505C42—34no—
506C42—98no—
507C42—94no—
508C22×C3—28no—
509C22×C3—24no—
510C22×C3—24no—
511C22×C3—24no—
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—416no—
522C22×C3—48no—
523C22×C3—48no—
524C22×C3—62no—
525C22×C3—62no—
526C22×C3—62no—
527C22×C3—124no—
528C22×C3C2×#23712yes—
529C22×C3C2×#23712yes—
530C22×C3#100412yes—
531C22×C3#100912yes—
532C22×C3#101012yes—
533C22×C3#101012yes—
534C22×C3C24×D311yescharacteristic
535C22×C3C24×D311yescharacteristic
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—22no—
539C2×D3—44no—
540C3×C4—24no—
541C3×C4—62no—
542C3×C4—64no—
543C3×C4—62no—
544C3×C4—64no—
545C3×C4—62no—
546C3×C4C2×#23714yes—
547C3×C4C2×#23714yes—
548Dic3—24no—
549Dic3—22no—
550Dic3—24no—
551Dic3—22no—
552Dic3—22no—
553Dic3—64no—
554Dic3—64no—
555Dic3—62no—
556Dic3—64no—
557Dic3—62no—
558Dic3—62no—
559Dic3—62no—
560Dic3—124no—
561Dic3—122no—
562C32C2×#54211yescharacteristic, complemented, Sylow
563C23—24no—
564C23—24no—
565C23—24no—
566C23—32no—
567C23—62no—
568C23—62no—
569C23—62no—
570C23C22×D3214yes—
571C23C22×D3211yescharacteristic
572Q8—68no—
573Q8—368no—
574D4—28no—
575D4—128no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—34no—
579C2×C4—34no—
580C2×C4—32no—
581C2×C4—62no—
582C2×C4—64no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—64no—
586C2×C4—68no—
587C2×C4—92no—
588C2×C4—92no—
589C2×C4—94no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4—184no—
593C2×C4—368no—
594C2×C4#380514yes—
595C2×C4C22×D3212yes—
596C2×C3—24no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—48no—
601C2×C3—44no—
602C2×C3—44no—
603C2×C3—122no—
604C2×C3#560314yescomplemented
605C2×C3#568214yescomplemented
606C2×C3C22×#23711yescharacteristic
607C2×C3C22×#23711yescharacteristic
608C2×C3C2×#100411yescharacteristic
609C2×C3C2×#100911yescharacteristic
610C2×C3C2×#101011yescharacteristic
611C2×C3C2×#101011yescharacteristic
612D3—42no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—48no—
617C22—62no—
618C22—62no—
619C22—62no—
620C22—124no—
621C22#6430912yes—
622C22#6431412yes—
623C22C2×#380512yes—
624C22C23×D3211yescharacteristic
625C4—62no—
626C4—64no—
627C4—62no—
628C4—62no—
629C4—64no—
630C4—182no—
631C4—182no—
632C4—184no—
633C4C2×#380514yes—
634C3—21no—
635C3C2×#560311yescharacteristic, complemented
636C3C2×#568211yescharacteristic, complemented
637C2—44no—
638C2—122no—
639C2#1059512614yesdirect product factor
640C2C2×#6430911yescharacteristic
641C2C2×#6431411yescharacteristic
642C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
3. C2×C3×#936C2semidirect
4. C2×#63982C2semidirect
5. C2×#63962C2semidirect
6. C2×#63959C2semidirect
7. C2×#63956C2semidirect
8. #10595126C2direct (N × H)
9. C2×#63918C2semidirect
10. C2×#63856C2semidirect
11. C2×#63855C2semidirect
12. C2×#63843C2semidirect
22. D4×C3⋊Dic3C22semidirect
29. C3×#936C22semidirect
32. #63982C22semidirect
38. #63962C22semidirect
42. #63959C22semidirect
43. #63956C22semidirect
45. #63918C22semidirect
46. #63856C22semidirect
47. #63855C22semidirect
48. #63843C22semidirect
55. C2×#936D3semidirect
149. #936C2×D3semidirect
463. C2×C32#542semidirect
562. C32C2×#542semidirect
604. C2×C3#5603semidirect
605. C2×C3#5682semidirect
635. C3C2×#5603semidirect
636. C3C2×#5682semidirect
639. C2#10595126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9382
C2×C3×#9362
C2×#639822
C2×#639622
C2×#639592
C2×#639562
#105951262
C2×#639182
C2×#638562
C2×#638552
C2×#638432
C2×#56823
C2×#56033