Finite Group Databasebeta

← C2×#10595272 #11903268

Subgroups — C2×#10595272 #11903268

Order 1152.

2613 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic
4C2×#63982C212yesmaximal, complemented
5C22×Dic3⋊Dic3C212yesmaximal, complemented
6C2×#63964C212yesmaximal, complemented
7C2×#63964C212yesmaximal, complemented
8#10595272C2116yesmaximal, direct product factor
9C2×#63918C211yesmaximal, characteristic, complemented
10C2×C4×#627C211yesmaximal, characteristic, complemented
11C2×#63872C211yesmaximal, characteristic, complemented
12C2×#63869C211yesmaximal, characteristic, complemented
13C2×#5539—31nomaximal
14C2×#5543—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C23×C3×Dic3C2212yes—
18C23×C3×Dic3C2212yes—
19C22×#627C2211yescharacteristic
20C22×#627C2212yes—
21C2×#3757C2212yes—
22D4×C3⋊Dic3C2218yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C3×D4×Dic3C2218yes—
28C3×D4×Dic3C2218yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33#63982C22116yescomplemented
34C2×#3724C2212yes—
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C22116yescomplemented
43#63964C22116yescomplemented
44#63964C22116yescomplemented
45#63918C2218yescomplemented
46C4×#627C2218yescomplemented
47#63872C2218yescomplemented
48#63869C2218yescomplemented
49C2×C3×C4×D4—31no—
50C2×C3×C4×D4—31no—
51C2×D4×Dic3—31no—
52C2×D4×Dic3—31no—
53C2×D4×Dic3—61no—
54C2×D4×Dic3D311yescharacteristic
55C2×D4×Dic3D311yescharacteristic
56C22×C4⋊Dic3—32no—
57C2×#924—32no—
58C2×#924—32no—
59C22×Dic3⋊C4—32no—
60#5543—316no—
61#5539—316no—
62C2×#890—31no—
63C2×#890—31no—
64C2×#890—31no—
65C2×#888—31no—
66C2×#878—32no—
67C2×#878—32no—
68C2×#878—32no—
69C2×#878—32no—
70C2×#870—31no—
71C2×#869—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C24×C32C2312yes—
75C2×C32×D4Q818yescomplemented
76C2×C32×D4C2314yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3—44no—
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2318yes—
83C22×C3×Dic3—28no—
84C22×C3×Dic3—44no—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2318yes—
91C22×C3×Dic3C2318yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×#627—24no—
94C2×#627—44no—
95C2×#627C2314yes—
96C2×#627C2318yes—
97#3757C2318yes—
98C4⋊(C3⋊Dic3)C2314yes—
99C4×C3⋊Dic3C2314yes—
100C3×#217C2318yes—
101C3×#217C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106#3724C2318yes—
107#3724C2314yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2318yes—
111Dic3⋊Dic3C2314yes—
112Dic3⋊Dic3C2314yes—
113Dic3⋊Dic3C2318yes—
114C2×#554—91noSylow
115C22×C3×D4—21no—
116C22×C3×D4C2×D311yescharacteristic
117C22×C3×D4C2×D311yescharacteristic
118C23×C3×C4—32no—
119C23×C3×C4—32no—
120C23×Dic3—32no—
121C23×Dic3—32no—
122C23×Dic3—62no—
123C23×Dic3C2×D312yes—
124C23×Dic3C2×D312yes—
125C22×Dic6—31no—
126C22×Dic6—31no—
127C22×Dic6—32no—
128C22×Dic6—32no—
129C3×C4×D4—38no—
130C3×C4×D4—38no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×#217—32no—
138C2×#217—32no—
139C2×#217—62no—
140C2×#217C2×D312yes—
141C2×#217C2×D312yes—
142D4×Dic3—38no—
143D4×Dic3—38no—
144D4×Dic3—68no—
145D4×Dic3C2×D318yes—
146D4×Dic3C2×D318yes—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—316no—
156C2×C4⋊Dic3—61no—
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×C4⋊Dic3C2×D311yescharacteristic
159#924—316no—
160#924—316no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4—32no—
168C2×Dic3⋊C4—32no—
169C2×Dic3⋊C4—32no—
170C2×Dic3⋊C4—32no—
171C2×Dic3⋊C4—316no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—61no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#890—38no—
178#890—38no—
179#890—38no—
180#888—38no—
181#878—316no—
182#878—316no—
183#878—316no—
184#878—316no—
185#870—38no—
186#869—38no—
187C4×Dic6—38no—
188C4×Dic6—38no—
189C23×C32—24no—
190C23×C32—24no—
191C23×C32C2×Q818yes—
192C23×C32C2414yes—
193C23×C32C2411yescharacteristic
194C32×D4C2×Q8116yescomplemented
195C2×C32×C4C2×Q814yes—
196C2×C32×C4C2412yes—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3—48no—
201C2×C3⋊Dic3C2412yes—
202C2×C3⋊Dic3C2412yes—
203C2×C3⋊Dic3C2414yes—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—216no—
210C2×C3×Dic3—48no—
211C2×C3×Dic3#4114yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218#627—28no—
219#627—48no—
220#554—916no—
221C2×C4⋊Q8—91no—
222C2×#125—91no—
223C2×#125—91no—
224C2×C22⋊Q8—92no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—92no—
227C2×C4×Q8—91no—
228C2×C4×D4—31no—
229C2×C4×D4—31no—
230C2×C4×D4—91no—
231C22×C4⋊C4—92no—
232C24×C3—22no—
233C24×C3C22×D312yes—
234C24×C3C22×D312yes—
235C2×C3×D4—28no—
236C2×C3×D4—24no—
237C2×C3×D4Dic618yescomplemented
238C2×C3×D4Dic618yescomplemented
239C2×C3×D4C22×D314yes—
240C2×C3×D4C22×D314yes—
241C22×C3×C4—21no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—31no—
246C22×C3×C4—32no—
247C22×C3×C4—31no—
248C22×C3×C4—38no—
249C22×C3×C4—38no—
250C22×C3×C4—68no—
251C22×C3×C4—124no—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×Dic3—28no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—32no—
260C22×Dic3—32no—
261C22×Dic3—38no—
262C22×Dic3—38no—
263C22×Dic3—44no—
264C22×Dic3—61no—
265C22×Dic3—61no—
266C22×Dic3—62no—
267C22×Dic3—68no—
268C22×Dic3—124no—
269C22×Dic3—124no—
270C22×Dic3—128no—
271C22×Dic3C22×D318yes—
272C22×Dic3C22×D311yescharacteristic
273C22×Dic3C22×D311yescharacteristic
274C22×Dic3C22×D311yescharacteristic
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D318yes—
278C22×Dic3C22×D311yescharacteristic
279C2×Dic6—34no—
280C2×Dic6—34no—
281C2×Dic6—38no—
282C2×Dic6—38no—
283C2×Dic6—64no—
284C2×Dic6—64no—
285C2×Dic6—124no—
286C2×Dic6—124no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—34no—
289C3×C22⋊C4—38no—
290C3×C22⋊C4—38no—
291C3×C42—34no—
292C3×C42—34no—
293#217—38no—
294#217—38no—
295#217—68no—
296#217C22×D318yes—
297#217C22×D318yes—
298C4⋊Dic3—34no—
299C4⋊Dic3—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304C4⋊Dic3—38no—
305C4⋊Dic3—38no—
306C4⋊Dic3—64no—
307C4⋊Dic3C22×D314yes—
308C4⋊Dic3C22×D314yes—
309Dic3⋊C4—34no—
310Dic3⋊C4—34no—
311Dic3⋊C4—34no—
312Dic3⋊C4—34no—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—38no—
319C4×Dic3—34no—
320C4×Dic3—34no—
321C4×Dic3—64no—
322C4×Dic3C22×D314yes—
323C4×Dic3C22×D314yes—
324C22×C32—216no—
325C22×C32—24no—
326C22×C32—24no—
327C22×C32C22×Q818yes—
328C22×C32C22×Q812yes—
329C22×C32C2×#4112yes—
330C22×C32H(5,𝔽2)12yes—
331C22×C32C2511yescharacteristic
332C32×C4C22×Q814yes—
333C3⋊Dic3—22no—
334C3⋊Dic3—22no—
335C3⋊Dic3—24no—
336C3×Dic3—22no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3—24no—
340C3×Dic3—22no—
341C3×Dic3C2×#4114yes—
342C22×Q8—91no—
343C22×Q8—92no—
344C22×D4D3211yescharacteristic
345C23×C4—32no—
346C23×C4—32no—
347C23×C4—92no—
348C4⋊Q8—98no—
349#125—98no—
350#125—98no—
351C22⋊Q8—916no—
352C22⋊Q8—916no—
353C22⋊Q8—916no—
354C4×Q8—98no—
355C4×D4—38no—
356C4×D4—38no—
357C4×D4—98no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—916no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—92no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4—91no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—92no—
373C2×C42—31no—
374C2×C42—31no—
375C2×C42—91no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—21no—
382C23×C3—28no—
383C23×C3—44no—
384C23×C3—44no—
385C23×C3C2×Dic618yes—
386C23×C3C2×Dic618yes—
387C23×C3C23×D314yes—
388C23×C3C23×D314yes—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C3×D4—216no—
392C3×D4C2×Dic6116yescomplemented
393C3×D4C2×Dic6116yescomplemented
394C2×C3×C4—22no—
395C2×C3×C4—24no—
396C2×C3×C4—34no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—34no—
400C2×C3×C4—32no—
401C2×C3×C4—34no—
402C2×C3×C4—32no—
403C2×C3×C4—616no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—64no—
407C2×C3×C4—64no—
408C2×C3×C4—62no—
409C2×C3×C4—128no—
410C2×C3×C4C2×Dic614yes—
411C2×C3×C4C2×Dic614yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414C2×Dic3—24no—
415C2×Dic3—24no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—216no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—34no—
425C2×Dic3—34no—
426C2×Dic3—48no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—64no—
430C2×Dic3—64no—
431C2×Dic3—62no—
432C2×Dic3—64no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—64no—
436C2×Dic3—62no—
437C2×Dic3—122no—
438C2×Dic3—124no—
439C2×Dic3—128no—
440C2×Dic3—128no—
441C2×Dic3—1216no—
442C2×Dic3#23714yes—
443C2×Dic3C23×D312yes—
444C2×Dic3C23×D312yes—
445C2×Dic3C23×D312yes—
446C2×Dic3C23×D314yes—
447C2×Dic3C23×D314yes—
448C2×Dic3C23×D312yes—
449Dic6—68no—
450Dic6—68no—
451Dic6—128no—
452Dic6—128no—
453C2×C32—28no—
454C2×C32#55414yescomplemented
455C2×C32C23×Q811yescharacteristic
456C2×C32C22×#4111yescharacteristic
457C2×C32C2×H(5,𝔽2)11yescharacteristic
458C24C2×D3212yes—
459C2×Q8—94no—
460C2×Q8—98no—
461C2×Q8—184no—
462C2×Q8—364no—
463C2×D4#62718yescomplemented
464C2×D4C2×D3214yes—
465C22×C4—31no—
466C22×C4—38no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—38no—
473C22×C4—68no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—92no—
477C22×C4—98no—
478C22×C4—124no—
479C22×C4—364no—
480C22×C4C2×D3211yescharacteristic
481C4⋊C4—34no—
482C4⋊C4—34no—
483C4⋊C4—94no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C4⋊C4—98no—
487C4⋊C4—94no—
488C4⋊C4—94no—
489C4⋊C4—98no—
490C4⋊C4—98no—
491C4⋊C4—94no—
492C22⋊C4—38no—
493C22⋊C4—38no—
494C22⋊C4—98no—
495C42—34no—
496C42—34no—
497C42—94no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—216no—
503C22×C3—216no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—28no—
508C22×C3—21no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—416no—
512C22×C3C22×Dic618yes—
513C22×C3C22×Dic618yes—
514C22×C3C22×Dic612yes—
515C22×C3C22×Dic612yes—
516C22×C3C2×#23712yes—
517C22×C3#100412yes—
518C22×C3D3×#4112yes—
519C22×C3#100912yes—
520C22×C3C24×D311yescharacteristic
521C22×C3C24×D311yescharacteristic
522C3×C4—24no—
523C3×C4—34no—
524C3×C4—62no—
525C3×C4—62no—
526C3×C4—64no—
527C3×C4—64no—
528C3×C4—62no—
529C3×C4C22×Dic614yes—
530C3×C4C22×Dic614yes—
531Dic3—24no—
532Dic3—24no—
533Dic3—22no—
534Dic3—22no—
535Dic3—22no—
536Dic3—64no—
537Dic3—62no—
538Dic3—64no—
539Dic3—62no—
540Dic3—62no—
541Dic3—64no—
542Dic3—62no—
543Dic3—124no—
544Dic3—122no—
545Dic3C2×#23714yes—
546C32C2×#55411yescharacteristic, complemented, Sylow
547C23—24no—
548C23—24no—
549C23C2×#62718yes—
550C23C22×D3214yes—
551C23C22×D3211yescharacteristic
552Q8—188no—
553Q8—368no—
554D4C2×#627116yescomplemented
555C2×C4—34no—
556C2×C4—32no—
557C2×C4—32no—
558C2×C4—32no—
559C2×C4—32no—
560C2×C4—34no—
561C2×C4—34no—
562C2×C4—616no—
563C2×C4—64no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—64no—
567C2×C4—62no—
568C2×C4—92no—
569C2×C4—92no—
570C2×C4—94no—
571C2×C4—128no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4—184no—
575C2×C4—368no—
576C2×C4C2×#62714yes—
577C2×C4C22×D3212yes—
578C2×C3—28no—
579C2×C3—28no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—24no—
584C2×C3—48no—
585C2×C3#553914yescomplemented
586C2×C3#554314yescomplemented
587C2×C3C23×Dic611yescharacteristic
588C2×C3C23×Dic611yescharacteristic
589C2×C3C22×#23711yescharacteristic
590C2×C3C2×#100411yescharacteristic
591C2×C3C2×D3×#4111yescharacteristic
592C2×C3C2×#100911yescharacteristic
593C22—24no—
594C22—24no—
595C22—216no—
596C22D3×#23712yes—
597C22#6431412yes—
598C22C22×#62718yes—
599C22C22×#62712yes—
600C22C23×D3211yescharacteristic
601C4—34no—
602C4—64no—
603C4—62no—
604C4—62no—
605C4—64no—
606C4—62no—
607C4—182no—
608C4—182no—
609C4—184no—
610C4C22×#62714yes—
611C3—21no—
612C3C2×#554311yescharacteristic, complemented
613C3C2×#553911yescharacteristic, complemented
614C2—28no—
615C2#1059527214yesdirect product factor
616C2C2×D3×#23711yescharacteristic
617C2C2×#6431411yescharacteristic
618C2C23×#62711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. C2×#63982C2semidirect
5. C22×Dic3⋊Dic3C2semidirect
6. C2×#63964C2semidirect
7. C2×#63964C2semidirect
8. #10595272C2direct (N × H)
9. C2×#63918C2semidirect
10. C2×C4×#627C2semidirect
11. C2×#63872C2semidirect
12. C2×#63869C2semidirect
33. #63982C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. #63964C22semidirect
44. #63964C22semidirect
45. #63918C22semidirect
46. C4×#627C22semidirect
47. #63872C22semidirect
48. #63869C22semidirect
75. C2×C32×D4Q8semidirect
194. C32×D4C2×Q8semidirect
237. C2×C3×D4Dic6semidirect
238. C2×C3×D4Dic6semidirect
392. C3×D4C2×Dic6semidirect
393. C3×D4C2×Dic6semidirect
454. C2×C32#554semidirect
463. C2×D4#627semidirect
546. C32C2×#554semidirect
554. D4C2×#627semidirect
585. C2×C3#5539semidirect
586. C2×C3#5543semidirect
612. C3C2×#5543semidirect
613. C3C2×#5539semidirect
615. C2#10595272direct (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×D4×Dic32
C2×#639822
C22×Dic3⋊Dic32
C2×#639642
#105952722
C2×#639182
C2×C4×#6272
C2×#638722
C2×#638692
C2×#55393
C2×#55433