Finite Group Databasebeta

← C2×#10595172 #11900674

Subgroups — C2×#10595172 #11900674

Order 1152.

2629 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64145C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×Dic3×#67C212yesmaximal, complemented
5C2×#63969C212yesmaximal, complemented
6C2×#63956C212yesmaximal, complemented
7C2×#63955C212yesmaximal, complemented
8#10595172C2116yesmaximal, direct product factor
9C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
10C2×#63872C211yesmaximal, characteristic, complemented
11C2×#63857C211yesmaximal, characteristic, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×#5600—31nomaximal
14C2×#5557—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×#3757C2212yes—
23C2×#3757C2212yes—
24#64145C2218yescomplemented
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28C3×#938C2218yes—
29C3×D4×Dic3C2218yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33Dic3×#67C22116yescomplemented
34#63969C22116yescomplemented
35C2×#3724C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40#63956C22116yescomplemented
41#63955C22116yescomplemented
42C2×Dic32C2212yes—
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C4×D3×Dic3C2218yescomplemented
46#63872C2218yescomplemented
47#63857C2218yescomplemented
48#63844C2218yescomplemented
49C2×C3×#121—31no—
50C2×C3×C4×D4—31no—
51C2×#938D311yescharacteristic
52C2×#936—31no—
53C2×#936—31no—
54C2×#936—61no—
55C2×#935—32no—
56C2×D4×Dic3—32no—
57C2×D4×Dic3D311yescharacteristic, complemented
58C2×C4×#67—32no—
59C2×#926—32no—
60C2×#924—31no—
61C22×C4×Dic3—31no—
62#5600—316no—
63#5557—316no—
64C2×#897—31no—
65C2×#890—31no—
66C2×#890—31no—
67C2×#887—31no—
68C2×#883—32no—
69C2×#879—32no—
70C2×#879—32no—
71C2×#877—32no—
72C2×C42×D3—31no—
73C2×C4×Dic6—31no—
74C24×C32C2312yes—
75C23×C3×D3C2311yescharacteristic
76C2×C32×D4—24no—
77C2×C32×D4C2314yes—
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2312yes—
82C2×#634—24no—
83C2×#634C2314yes—
84C2×C3×#67—28no—
85C2×C3×#67C2318yes—
86C22×C3×Dic3—28no—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2318yes—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3C2314yes—
95C2×D3×Dic3—24no—
96C2×D3×Dic3—24no—
97C2×D3×Dic3C2314yes—
98C2×D3×Dic3C2314yes—
99#3757C2318yes—
100#3757C2318yes—
101C4×C3⋊Dic3C2314yes—
102C3×#217C2318yes—
103C3×#217C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×C4⋊Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107#3724C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2318yes—
113Dic32C2314yes—
114Dic32C2314yes—
115C2×#529—91noSylow
116C22×C3×D4—21no—
117C22×C3×D4—32no—
118C22×C3×D4C2×D311yescharacteristic
119C22×C3×D4C2×D311yescharacteristic
120C23×C3×C4—32no—
121C23×C3×C4—31no—
122C22×#67C2×D312yes—
123C23×Dic3—31no—
124C23×Dic3—31no—
125C23×Dic3C2×D312yes—
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C22×C4×D3C2×D311yescharacteristic
129C22×Dic6—31no—
130C22×Dic6—31no—
131C22×Dic6—61no—
132C3×#121—38no—
133C3×C4×D4—38no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C42—31no—
139C2×#217—32no—
140C2×#217—32no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—62no—
145C2×#217—62no—
146C2×#217C2×D312yes—
147C2×#217C2×D312yes—
148#938C2×D318yes—
149#936—38no—
150#936—38no—
151#936—68no—
152#935—316no—
153D4×Dic3—316no—
154D4×Dic3C2×D318yescomplemented
155C4×#67—316no—
156C2×(C2×D3)⋊C4—32no—
157#926—316no—
158C2×C4⋊Dic3—32no—
159C2×C4⋊Dic3—32no—
160C2×C4⋊Dic3—32no—
161C2×C4⋊Dic3C2×D311yescharacteristic
162C2×C4⋊Dic3C2×D311yescharacteristic
163#924—38no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4—32no—
168C2×Dic3⋊C4—32no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—32no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—38no—
178C2×C4×Dic3—61no—
179C2×C4×Dic3C2×D311yescharacteristic
180#897—38no—
181#890—38no—
182#890—38no—
183#887—38no—
184#883—316no—
185#879—316no—
186#879—316no—
187#877—316no—
188C42×D3—38no—
189C4×Dic6—38no—
190C23×C32—24no—
191C23×C32—24no—
192C23×C32—24no—
193C23×C32C2414yes—
194C23×C32C2411yescharacteristic
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3#4114yes—
198C22×C3×D3C2412yes—
199C32×D4—28no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2412yes—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—24no—
205C2×C3⋊Dic3C2414yes—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208#634—28no—
209C3×#67—216no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3—216no—
215C2×C3×Dic3#4114yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2412yes—
219C2×C3×Dic3C2414yes—
220C2×C3×Dic3C2412yes—
221C3×C4×D3—28no—
222D3×Dic3—28no—
223D3×Dic3—28no—
224#529—916no—
225C2×#126—92no—
226C2×#125—91no—
227C2×#124—91no—
228C2×#123—92no—
229C2×C22⋊Q8—91no—
230C2×#121—31no—
231C2×C4×Q8—91no—
232C2×C4×D4—31no—
233C2×C4×D4—92no—
234C2×#117—92no—
235C22×C42—91no—
236C24×C3—22no—
237C24×C3—31no—
238C24×C3C22×D312yes—
239C24×C3C22×D312yes—
240C23×D3C22×D311yescharacteristic
241C2×C3×D4—24no—
242C2×C3×D4—24no—
243C2×C3×D4—24no—
244C2×C3×D4—38no—
245C2×C3×D4—44no—
246C2×C3×D4—68no—
247C2×C3×D4C22×D314yes—
248C2×C3×D4C22×D314yes—
249C22×C3×C4—21no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—32no—
253C22×C3×C4—31no—
254C22×C3×C4—32no—
255C22×C3×C4—38no—
256C22×C3×C4—34no—
257C22×C3×C4—68no—
258C22×C3×C4—64no—
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C2×#67—28no—
262C2×#67C22×D318yes—
263C22×Dic3—28no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—32no—
269C22×Dic3—32no—
270C22×Dic3—34no—
271C22×Dic3—34no—
272C22×Dic3—61no—
273C22×Dic3—61no—
274C22×Dic3—62no—
275C22×Dic3—64no—
276C22×Dic3—64no—
277C22×Dic3C22×D318yes—
278C22×Dic3C22×D311yescharacteristic
279C22×Dic3C22×D311yescharacteristic
280C22×Dic3C22×D312yes—
281C22×Dic3C22×D312yes—
282C22×Dic3C22×D311yescharacteristic
283C2×C4×D3—24no—
284C2×C4×D3—34no—
285C2×C4×D3—34no—
286C2×C4×D3—64no—
287C2×C4×D3—64no—
288C2×C4×D3C22×D314yes—
289C2×Dic6—34no—
290C2×Dic6—34no—
291C2×Dic6—64no—
292C2×Dic6—64no—
293C2×Dic6—64no—
294C2×Dic6—124no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—34no—
297C3×C22⋊C4—38no—
298C3×C22⋊C4—38no—
299C3×C42—34no—
300#217—38no—
301#217—38no—
302#217—38no—
303#217—38no—
304#217—38no—
305#217—68no—
306#217—68no—
307#217C22×D318yes—
308#217C22×D318yes—
309(C2×D3)⋊C4—38no—
310C4⋊Dic3—38no—
311C4⋊Dic3—38no—
312C4⋊Dic3—38no—
313C4⋊Dic3C22×D314yes—
314C4⋊Dic3C22×D314yes—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—38no—
319Dic3⋊C4—38no—
320C4×Dic3—34no—
321C4×Dic3—34no—
322C4×Dic3—38no—
323C4×Dic3—34no—
324C4×Dic3—34no—
325C4×Dic3—34no—
326C4×Dic3—38no—
327C4×Dic3—34no—
328C4×Dic3—64no—
329C4×Dic3C22×D314yes—
330C22×C32—24no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—48no—
334C22×C32C2×#4112yes—
335C22×C32C2×#4112yes—
336C22×C32C2×#4112yes—
337C22×C32C2511yescharacteristic
338C2×C3×D3—28no—
339C2×C3×D3—22no—
340C2×C3×D3—22no—
341C2×C3×D3C2×#4114yes—
342C32×C4C2×#4114yes—
343C3⋊Dic3—22no—
344C3⋊Dic3—22no—
345C3⋊Dic3—24no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C3×Dic3—24no—
349C3×Dic3—24no—
350C3×Dic3C2×#4114yes—
351C22×Q8—91no—
352C22×D4—32no—
353C22×D4D3211yescharacteristic
354C23×C4—32no—
355C23×C4—31no—
356C23×C4—91no—
357C23×C4—91no—
358#126—916no—
359#125—98no—
360#124—98no—
361#123—916no—
362C22⋊Q8—98no—
363#121—38no—
364C4×Q8—98no—
365C4×D4—38no—
366C4×D4—916no—
367#117—916no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—92no—
372C2×C4⋊C4—92no—
373C2×C4⋊C4—92no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C22⋊C4—92no—
379C2×C42—31no—
380C2×C42—98no—
381C2×C42—91no—
382C2×C42—92no—
383C2×C42—91no—
384C2×C42—91no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—21no—
393C23×C3—34no—
394C23×C3—32no—
395C23×C3—44no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3C23×D314yes—
401C23×C3C23×D314yes—
402C23×C3C23×D311yescharacteristic
403C23×C3C23×D311yescharacteristic
404C22×D3—22no—
405C22×D3—22no—
406C22×D3#23714yes—
407C22×D3C23×D312yes—
408C3×D4—28no—
409C3×D4—28no—
410C3×D4—48no—
411C3×D4—616no—
412C2×C3×C4—22no—
413C2×C3×C4—24no—
414C2×C3×C4—34no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—34no—
418C2×C3×C4—32no—
419C2×C3×C4—34no—
420C2×C3×C4—616no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—64no—
424C2×C3×C4—64no—
425C2×C3×C4—68no—
426C2×C3×C4#23514yes—
427C2×C3×C4#23714yes—
428C2×C3×C4C23×D312yes—
429C2×C3×C4C23×D312yes—
430#67—216no—
431C2×Dic3—22no—
432C2×Dic3—24no—
433C2×Dic3—24no—
434C2×Dic3—22no—
435C2×Dic3—216no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—32no—
440C2×Dic3—34no—
441C2×Dic3—34no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—64no—
445C2×Dic3—68no—
446C2×Dic3—64no—
447C2×Dic3—64no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—68no—
453C2×Dic3—124no—
454C2×Dic3—122no—
455C2×Dic3—122no—
456C2×Dic3#23714yes—
457C2×Dic3C23×D312yes—
458C2×Dic3C23×D312yes—
459C2×Dic3C23×D314yes—
460C2×Dic3C23×D314yes—
461C2×Dic3C23×D312yes—
462C4×D3—28no—
463C4×D3—68no—
464C4×D3—68no—
465Dic6—68no—
466Dic6—68no—
467Dic6—128no—
468C2×C32—44no—
469C2×C32#52914yescomplemented
470C2×C32C22×#4111yescharacteristic
471C2×C32C22×#4111yescharacteristic
472C2×C32C22×#4111yescharacteristic
473C3×D3—24no—
474C24—31no—
475C24C2×D3212yes—
476C2×Q8—94no—
477C2×Q8—184no—
478C2×D4—24no—
479C2×D4—38no—
480C2×D4—68no—
481C2×D4C2×D3214yes—
482C22×C4—31no—
483C22×C4—38no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—32no—
488C22×C4—34no—
489C22×C4—68no—
490C22×C4—64no—
491C22×C4—94no—
492C22×C4—94no—
493C22×C4—91no—
494C22×C4—91no—
495C22×C4—92no—
496C22×C4—184no—
497C22×C4—184no—
498C22×C4C2×D3211yescharacteristic
499C4⋊C4—34no—
500C4⋊C4—34no—
501C4⋊C4—98no—
502C4⋊C4—98no—
503C4⋊C4—98no—
504C4⋊C4—98no—
505C22⋊C4—38no—
506C22⋊C4—38no—
507C22⋊C4—98no—
508C22⋊C4—98no—
509C22⋊C4—98no—
510C42—34no—
511C42—94no—
512C42—94no—
513C42—98no—
514C42—94no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—21no—
525C22×C3—34no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—48no—
530C22×C3—48no—
531C22×C3—62no—
532C22×C3—62no—
533C22×C3—68no—
534C22×C3—88no—
535C22×C3C2×#23512yes—
536C22×C3C2×#23712yes—
537C22×C3C2×#23712yes—
538C22×C3C2×#23712yes—
539C22×C3D3×#4112yes—
540C22×C3D3×#4112yes—
541C22×C3C24×D311yescharacteristic
542C22×C3C24×D311yescharacteristic
543C2×D3—22no—
544C2×D3—22no—
545C2×D3—28no—
546C2×D3C2×#23714yes—
547C3×C4—24no—
548C3×C4—34no—
549C3×C4—62no—
550C3×C4—62no—
551C3×C4—64no—
552C3×C4—64no—
553C3×C4C2×#23514yes—
554C3×C4C2×#23714yes—
555Dic3—22no—
556Dic3—24no—
557Dic3—24no—
558Dic3—22no—
559Dic3—64no—
560Dic3—64no—
561Dic3—62no—
562Dic3—62no—
563Dic3—62no—
564Dic3—62no—
565Dic3—124no—
566Dic3—122no—
567Dic3—122no—
568Dic3C2×#23714yes—
569C32C2×#52911yescharacteristic, complemented, Sylow
570C23—24no—
571C23—24no—
572C23—24no—
573C23—34no—
574C23—32no—
575C23—62no—
576C23—62no—
577C23C22×D3214yes—
578C23C22×D3211yescharacteristic
579Q8—188no—
580D4—28no—
581D4—616no—
582C2×C4—34no—
583C2×C4—32no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—34no—
587C2×C4—34no—
588C2×C4—616no—
589C2×C4—64no—
590C2×C4—62no—
591C2×C4—64no—
592C2×C4—62no—
593C2×C4—68no—
594C2×C4—92no—
595C2×C4—92no—
596C2×C4—94no—
597C2×C4—188no—
598C2×C4—188no—
599C2×C4—182no—
600C2×C4—182no—
601C2×C4—184no—
602C2×C4#380414yes—
603C2×C4C22×D3212yes—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—24no—
608C2×C3—44no—
609C2×C3—44no—
610C2×C3—64no—
611C2×C3—84no—
612C2×C3#555714yescomplemented
613C2×C3#560014yescomplemented
614C2×C3C22×#23511yescharacteristic
615C2×C3C22×#23711yescharacteristic
616C2×C3C22×#23711yescharacteristic
617C2×C3C22×#23711yescharacteristic
618C2×C3C2×D3×#4111yescharacteristic
619C2×C3C2×D3×#4111yescharacteristic
620D3—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—34no—
625C22—48no—
626C22—62no—
627C22—62no—
628C22—68no—
629C22D3×#23712yes—
630C22D3×#23712yes—
631C22C2×#380412yes—
632C22C23×D3211yescharacteristic
633C4—34no—
634C4—64no—
635C4—62no—
636C4—64no—
637C4—62no—
638C4—182no—
639C4—182no—
640C4—184no—
641C4C2×#380414yes—
642C3—21no—
643C3C2×#555711yescharacteristic, complemented
644C3C2×#560011yescharacteristic, complemented
645C2—44no—
646C2—64no—
647C2#1059517214yesdirect product factor
648C2C2×D3×#23711yescharacteristic
649C2C2×D3×#23711yescharacteristic
650C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64145C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×Dic3×#67C2semidirect
5. C2×#63969C2semidirect
6. C2×#63956C2semidirect
7. C2×#63955C2semidirect
8. #10595172C2direct (N × H)
9. C2×C4×D3×Dic3C2semidirect
10. C2×#63872C2semidirect
11. C2×#63857C2semidirect
12. C2×#63844C2semidirect
24. #64145C22semidirect
29. C3×D4×Dic3C22semidirect
33. Dic3×#67C22semidirect
34. #63969C22semidirect
40. #63956C22semidirect
41. #63955C22semidirect
45. C4×D3×Dic3C22semidirect
46. #63872C22semidirect
47. #63857C22semidirect
48. #63844C22semidirect
57. C2×D4×Dic3D3semidirect
154. D4×Dic3C2×D3semidirect
469. C2×C32#529semidirect
569. C32C2×#529semidirect
612. C2×C3#5557semidirect
613. C2×C3#5600semidirect
643. C3C2×#5557semidirect
644. C3C2×#5600semidirect
647. C2#10595172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C2×C3×#9382
C2×C3×D4×Dic32
C2×Dic3×#672
C2×#639692
C2×#639562
C2×#639552
#105951722
C2×C4×D3×Dic32
C2×#638722
C2×#638572
C2×#638442
C2×#56003
C2×#55573