Finite Group Databasebeta

← C2×#10594949 #11900635

Subgroups — C2×#10594949 #11900635

Order 1152.

2625 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×#64133C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
4C2×Dic3×#67C212yesmaximal, complemented
5C2×#63961C212yesmaximal, complemented
6#10594949C2116yesmaximal, direct product factor
7C2×Dic3×D12C211yesmaximal, characteristic, complemented
8C2×#63877C212yesmaximal, complemented
9C2×#63869C211yesmaximal, characteristic, complemented
10C2×#63860C211yesmaximal, characteristic, complemented
11C2×#63859C212yesmaximal, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×#5600—31nomaximal
14C2×#5479—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×#3757C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24#64133C2218yescomplemented
25C2×#3750C2212yes—
26C3×#930C2218yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2218yescomplemented
34Dic3×#67C22116yescomplemented
35C2×#3724C2212yes—
36C2×#3724C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38#63961C22116yescomplemented
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42C2×Dic32C2212yes—
43Dic3×D12C2218yescomplemented
44#63877C22116yescomplemented
45#63869C2218yescomplemented
46#63860C2218yescomplemented
47#63859C22116yescomplemented
48#63844C2218yescomplemented
49C2×C3×#121—31no—
50C22×C3×C42—31no—
51C2×#936—31no—
52C2×#935—32no—
53C2×D4×Dic3—32no—
54C2×D4×Dic3—31no—
55C2×#930D311yescharacteristic
56C2×#929—32no—
57C2×C4×#67—32no—
58C2×#924—31no—
59C2×#924—31no—
60C2×#924—61no—
61C22×C4×Dic3D311yescharacteristic, complemented
62#5600—316no—
63C2×#890—31no—
64C2×#887—31no—
65C2×#879—32no—
66C2×#877—32no—
67#5479—316no—
68C2×#876—32no—
69C2×#875—31no—
70C2×C4×D12—31no—
71C2×#872—32no—
72C2×#870—31no—
73C2×C4×Dic6—31no—
74C24×C32C2311yescharacteristic
75C23×C3×D3C2312yes—
76C22×C32×C4—24no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2314yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2312yes—
82C2×#634—24no—
83C2×#634C2314yes—
84C2×C3×#67—28no—
85C2×C3×#67C2318yes—
86C22×C3×Dic3—24no—
87C22×C3×Dic3—24no—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2314yes—
92C22×C3×Dic3C2314yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C2×C3×D12—24no—
96C2×C3×D12C2314yes—
97C2×D3×Dic3—28no—
98C2×D3×Dic3C2318yes—
99#3757C2318yes—
100C4⋊(C3⋊Dic3)C2314yes—
101#3750C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107C3×C4×Dic3C2314yes—
108#3724C2318yes—
109#3724C2318yes—
110Dic3⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114Dic32C2318yes—
115C2×#529—91noSylow
116C22×C3×D4—32no—
117C22×C3×D4—31no—
118C23×C3×C4—21no—
119C23×C3×C4—31no—
120C23×C3×C4—31no—
121C23×C3×C4C2×D311yescharacteristic
122C23×C3×C4C2×D311yescharacteristic
123C22×#67C2×D312yes—
124C23×Dic3—32no—
125C23×Dic3C2×D311yescharacteristic
126C23×Dic3C2×D311yescharacteristic
127C22×D12C2×D311yescharacteristic
128C22×C4×D3—32no—
129C22×Dic6—31no—
130C22×Dic6—31no—
131C22×Dic6—61no—
132C3×#121—38no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×C3×C42—31no—
139C2×C3×C42—38no—
140C2×#217—32no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—32no—
145C2×#217—62no—
146#936—38no—
147#935—316no—
148D4×Dic3—316no—
149D4×Dic3—38no—
150#930C2×D318yes—
151#929—316no—
152C4×#67—316no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4C2×D312yes—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—32no—
160C2×C4⋊Dic3—61no—
161C2×C4⋊Dic3C2×D311yescharacteristic
162#924—38no—
163#924—38no—
164#924—68no—
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—32no—
172C2×Dic3⋊C4—62no—
173C2×C4×Dic3—32no—
174C2×C4×Dic3—32no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177C2×C4×Dic3C2×D311yescharacteristic
178C2×C4×Dic3C2×D311yescharacteristic
179C2×C4×Dic3C2×D318yescomplemented
180#890—38no—
181#887—38no—
182#879—316no—
183#877—316no—
184#876—316no—
185#875—38no—
186C4×D12—38no—
187#872—316no—
188#870—38no—
189C4×Dic6—38no—
190C23×C32—22no—
191C23×C32—22no—
192C23×C32#4114yes—
193C23×C32C2412yes—
194C23×C32C2411yescharacteristic
195C22×C3×D3—24no—
196C22×C3×D3—24no—
197C22×C3×D3—24no—
198C22×C3×D3C2414yes—
199C2×C32×C4—22no—
200C2×C32×C4—28no—
201C2×C32×C4#4114yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2412yes—
204C2×C3⋊Dic3—24no—
205C2×C3⋊Dic3—24no—
206C2×C3⋊Dic3C2414yes—
207C2×C3⋊Dic3C2414yes—
208#634—28no—
209C3×#67—216no—
210C2×C3×Dic3—28no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—28no—
216C2×C3×Dic3#4114yes—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2412yes—
219C2×C3×Dic3C2412yes—
220C2×C3×Dic3C2412yes—
221C2×C3×Dic3C2412yes—
222C3×D12—28no—
223D3×Dic3—216no—
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—91no—
233C2×C4×D4—92no—
234C2×#117—92no—
235C22×C42—31no—
236C24×C3—21no—
237C24×C3—32no—
238C24×C3C22×D311yescharacteristic
239C24×C3C22×D311yescharacteristic
240C23×D3C22×D312yes—
241C2×C3×D4—38no—
242C2×C3×D4—34no—
243C2×C3×D4—68no—
244C2×C3×D4—64no—
245C22×C3×C4—24no—
246C22×C3×C4—24no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—24no—
250C22×C3×C4—31no—
251C22×C3×C4—32no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—34no—
256C22×C3×C4—34no—
257C22×C3×C4—44no—
258C22×C3×C4—64no—
259C22×C3×C4—64no—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D314yes—
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D314yes—
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C2×#67—28no—
267C2×#67C22×D318yes—
268C22×Dic3—24no—
269C22×Dic3—24no—
270C22×Dic3—32no—
271C22×Dic3—32no—
272C22×Dic3—32no—
273C22×Dic3—32no—
274C22×Dic3—38no—
275C22×Dic3—62no—
276C22×Dic3—62no—
277C22×Dic3—68no—
278C22×Dic3C22×D312yes—
279C22×Dic3C22×D311yescharacteristic
280C22×Dic3C22×D311yescharacteristic
281C22×Dic3C22×D311yescharacteristic
282C22×Dic3C22×D314yes—
283C22×Dic3C22×D314yes—
284C22×Dic3C22×D311yescharacteristic
285C2×D12—24no—
286C2×D12C22×D314yes—
287C2×C4×D3—38no—
288C2×C4×D3—68no—
289C2×Dic6—34no—
290C2×Dic6—34no—
291C2×Dic6—64no—
292C2×Dic6—64no—
293C2×Dic6—64no—
294C2×Dic6—124no—
295C3×C4⋊C4—34no—
296C3×C22⋊C4—38no—
297C3×C42—34no—
298C3×C42—34no—
299C3×C42—34no—
300C3×C42—34no—
301#217—38no—
302#217—38no—
303#217—38no—
304#217—38no—
305#217—38no—
306#217—68no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—38no—
309(C2×D3)⋊C4—38no—
310(C2×D3)⋊C4C22×D318yes—
311C4⋊Dic3—34no—
312C4⋊Dic3—34no—
313C4⋊Dic3—38no—
314C4⋊Dic3—64no—
315C4⋊Dic3C22×D314yes—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—38no—
319Dic3⋊C4—38no—
320Dic3⋊C4—38no—
321Dic3⋊C4—38no—
322Dic3⋊C4—38no—
323Dic3⋊C4—68no—
324C4×Dic3—38no—
325C4×Dic3—38no—
326C4×Dic3C22×D314yes—
327C4×Dic3C22×D314yes—
328C4×Dic3C22×D314yes—
329C4×Dic3C22×D314yes—
330C22×C32—28no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32C2×#4114yes—
334C22×C32C2×#4112yes—
335C22×C32C2×#4112yes—
336C22×C32C2×#4112yes—
337C22×C32C2511yescharacteristic
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—48no—
342C32×C4—22no—
343C32×C4C2×#4114yes—
344C3⋊Dic3—24no—
345C3⋊Dic3—24no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—24no—
350C3×Dic3C2×#4114yes—
351C22×Q8—91no—
352C22×D4—32no—
353C22×D4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—92no—
357C23×C4D3211yescharacteristic
358#126—916no—
359#125—98no—
360#124—98no—
361#123—916no—
362C22⋊Q8—98no—
363#121—38no—
364C4×Q8—98no—
365C4×D4—98no—
366C4×D4—916no—
367#117—916no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—92no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—92no—
372C2×C4⋊C4—92no—
373C2×C4⋊C4—91no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C22⋊C4—92no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—31no—
382C2×C42—31no—
383C2×C42—38no—
384C2×C42—92no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—24no—
392C23×C3—34no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—64no—
396C23×C3—64no—
397C23×C3—64no—
398C23×C3#23514yes—
399C23×C3#23714yes—
400C23×C3C23×D312yes—
401C23×C3C23×D312yes—
402C23×C3C23×D311yescharacteristic
403C23×C3C23×D311yescharacteristic
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—24no—
407C22×D3C23×D314yes—
408C3×D4—616no—
409C3×D4—68no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—28no—
413C2×C3×C4—28no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—24no—
417C2×C3×C4—34no—
418C2×C3×C4—32no—
419C2×C3×C4—34no—
420C2×C3×C4—32no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—48no—
424C2×C3×C4—42no—
425C2×C3×C4—68no—
426C2×C3×C4—64no—
427C2×C3×C4—68no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4#23514yes—
432C2×C3×C4#23714yes—
433C2×C3×C4C23×D312yes—
434C2×C3×C4C23×D312yes—
435C2×C3×C4C23×D312yes—
436C2×C3×C4C23×D312yes—
437#67—216no—
438C2×Dic3—28no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—24no—
443C2×Dic3—28no—
444C2×Dic3—34no—
445C2×Dic3—34no—
446C2×Dic3—34no—
447C2×Dic3—34no—
448C2×Dic3—64no—
449C2×Dic3—64no—
450C2×Dic3—64no—
451C2×Dic3—64no—
452C2×Dic3—64no—
453C2×Dic3—64no—
454C2×Dic3—616no—
455C2×Dic3—124no—
456C2×Dic3—124no—
457C2×Dic3#23514yes—
458C2×Dic3C23×D314yes—
459C2×Dic3C23×D312yes—
460C2×Dic3C23×D312yes—
461C2×Dic3C23×D312yes—
462C2×Dic3C23×D312yes—
463D12—28no—
464C4×D3—616no—
465Dic6—68no—
466Dic6—68no—
467Dic6—128no—
468C2×C32—24no—
469C2×C32#52914yescomplemented
470C2×C32C22×#4111yescharacteristic
471C2×C32C22×#4111yescharacteristic
472C2×C32C22×#4111yescharacteristic
473C3×D3—44no—
474C24—32no—
475C24C2×D3211yescharacteristic
476C2×Q8—94no—
477C2×Q8—184no—
478C2×D4—38no—
479C2×D4—34no—
480C2×D4—68no—
481C2×D4—64no—
482C22×C4—24no—
483C22×C4—31no—
484C22×C4—34no—
485C22×C4—34no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—31no—
489C22×C4—32no—
490C22×C4—64no—
491C22×C4—64no—
492C22×C4—98no—
493C22×C4—92no—
494C22×C4—92no—
495C22×C4—188no—
496C22×C4C2×D3214yes—
497C22×C4C2×D3211yescharacteristic
498C22×C4C2×D3211yescharacteristic
499C4⋊C4—34no—
500C4⋊C4—98no—
501C4⋊C4—98no—
502C4⋊C4—98no—
503C4⋊C4—98no—
504C4⋊C4—94no—
505C22⋊C4—38no—
506C22⋊C4—98no—
507C22⋊C4—98no—
508C22⋊C4—98no—
509C22⋊C4—98no—
510C42—34no—
511C42—34no—
512C42—34no—
513C42—34no—
514C42—98no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—28no—
520C22×C3—28no—
521C22×C3—22no—
522C22×C3—24no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—48no—
529C22×C3—64no—
530C22×C3—64no—
531C22×C3—64no—
532C22×C3—128no—
533C22×C3C2×#23514yes—
534C22×C3C2×#23512yes—
535C22×C3C2×#23512yes—
536C22×C3C2×#23512yes—
537C22×C3C2×#23714yes—
538C22×C3C2×#23712yes—
539C22×C3C2×#23712yes—
540C22×C3D3×#4112yes—
541C22×C3C24×D311yescharacteristic
542C22×C3C24×D311yescharacteristic
543C2×D3—24no—
544C2×D3—24no—
545C2×D3—24no—
546C2×D3—48no—
547C3×C4—22no—
548C3×C4—22no—
549C3×C4—24no—
550C3×C4—34no—
551C3×C4—42no—
552C3×C4—64no—
553C3×C4—62no—
554C3×C4—62no—
555C3×C4—62no—
556C3×C4C2×#23514yes—
557C3×C4C2×#23714yes—
558Dic3—22no—
559Dic3—22no—
560Dic3—22no—
561Dic3—24no—
562Dic3—64no—
563Dic3—64no—
564Dic3—64no—
565Dic3—64no—
566Dic3—124no—
567Dic3—124no—
568Dic3C2×#23514yes—
569C32C2×#52911yescharacteristic, complemented, Sylow
570C23—22no—
571C23—22no—
572C23—34no—
573C23—64no—
574C23—64no—
575C23—64no—
576C23#379514yes—
577C23C22×D3212yes—
578C23C22×D3211yescharacteristic
579Q8—188no—
580D4—616no—
581D4—68no—
582C2×C4—22no—
583C2×C4—28no—
584C2×C4—34no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—32no—
588C2×C4—32no—
589C2×C4—34no—
590C2×C4—68no—
591C2×C4—68no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—64no—
595C2×C4—62no—
596C2×C4—94no—
597C2×C4—94no—
598C2×C4—1816no—
599C2×C4—184no—
600C2×C4—184no—
601C2×C4#380414yes—
602C2×C4C22×D3212yes—
603C2×C4C22×D3212yes—
604C2×C3—24no—
605C2×C3—24no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—24no—
610C2×C3—44no—
611C2×C3—124no—
612C2×C3#547914yescomplemented
613C2×C3#560014yescomplemented
614C2×C3C22×#23511yescharacteristic
615C2×C3C22×#23511yescharacteristic
616C2×C3C22×#23511yescharacteristic
617C2×C3C22×#23711yescharacteristic
618C2×C3C22×#23711yescharacteristic
619C2×C3C2×D3×#4111yescharacteristic
620D3—44no—
621C22—22no—
622C22—22no—
623C22—28no—
624C22—64no—
625C22—64no—
626C22—64no—
627C22—128no—
628C22C2×#379514yes—
629C22C2×#379512yes—
630C22D3×#23512yes—
631C22C2×#380412yes—
632C22C23×D3211yescharacteristic
633C4—22no—
634C4—34no—
635C4—62no—
636C4—62no—
637C4—64no—
638C4—62no—
639C4—184no—
640C4—184no—
641C4C2×#380414yes—
642C3—21no—
643C3C2×#547911yescharacteristic, complemented
644C3C2×#560011yescharacteristic, complemented
645C2—24no—
646C2—124no—
647C2#1059494914yesdirect product factor
648C2C22×#379511yescharacteristic
649C2C2×D3×#23511yescharacteristic
650C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64133C2semidirect
3. C22×C3×C4×Dic3C2semidirect
4. C2×Dic3×#67C2semidirect
5. C2×#63961C2semidirect
6. #10594949C2direct (N × H)
7. C2×Dic3×D12C2semidirect
8. C2×#63877C2semidirect
9. C2×#63869C2semidirect
10. C2×#63860C2semidirect
11. C2×#63859C2semidirect
12. C2×#63844C2semidirect
24. #64133C22semidirect
33. C2×C3×C4×Dic3C22semidirect
34. Dic3×#67C22semidirect
38. #63961C22semidirect
43. Dic3×D12C22semidirect
44. #63877C22semidirect
45. #63869C22semidirect
46. #63860C22semidirect
47. #63859C22semidirect
48. #63844C22semidirect
61. C22×C4×Dic3D3semidirect
179. C2×C4×Dic3C2×D3semidirect
469. C2×C32#529semidirect
569. C32C2×#529semidirect
612. C2×C3#5479semidirect
613. C2×C3#5600semidirect
643. C3C2×#5479semidirect
644. C3C2×#5600semidirect
647. C2#10594949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9302
C22×C3×C4×Dic32
C2×Dic3×#672
C2×#639612
#105949492
C2×Dic3×D122
C2×#638772
C2×#638692
C2×#638602
C2×#638592
C2×#638442
C2×#56003
C2×#54793