Finite Group Databasebeta

← C2×#10594447 #11900678

Subgroups — C2×#10594447 #11900678

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×#64106C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic, complemented
3C2×C3×#890C211yesmaximal, characteristic, complemented
4C2×#63916C211yesmaximal, characteristic
5C2×#63904C212yesmaximal, complemented
6C2×C4×#624C211yesmaximal, characteristic, complemented
7C2×#63861C212yesmaximal, complemented
8C2×#63860C211yesmaximal, characteristic, complemented
9C2×#63854C212yesmaximal, complemented
10C2×#63844C211yesmaximal, characteristic, complemented
11C2×#63841C212yesmaximal, complemented
12#10594447C2116yesmaximal, direct product factor
13C2×#5691—31nomaximal
14C2×#5557—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×#626C2212yes—
20C22×#624C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3752C2212yes—
24C2×C4⋊(C3⋊Dic3)C2212yes—
25#64106C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#893C2218yescomplemented
33C3×#890C2218yescomplemented
34C2×#3724C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yes—
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63916C2218yes—
42#63904C22116yescomplemented
43C4×#624C2218yescomplemented
44#63861C22116yescomplemented
45#63860C2218yescomplemented
46#63854C22116yescomplemented
47#63844C2218yescomplemented
48#63841C22116yescomplemented
49C2×C3×#125—31no—
50C2×C3×C4×D4—31no—
51C2×#938—31no—
52C2×#936—31no—
53C2×C4×#67—32no—
54C2×#926—32no—
55#5691—316no—
56#5557—316no—
57C2×#898—32no—
58C2×#897—31no—
59C2×#897—31no—
60C2×#897—61no—
61C2×#895—31no—
62C2×#894—32no—
63C2×#893—32no—
64C2×#893D311yescharacteristic, complemented
65C2×#892—32no—
66C2×#890D311yescharacteristic, complemented
67C2×#887—31no—
68C2×#883—32no—
69C2×#879—32no—
70C2×#875—31no—
71C2×C42×D3—31no—
72C2×C42×D3—31no—
73C2×C4×Dic6—31no—
74C23×C3⋊D3C2311yescharacteristic
75C23×C3×D3C2312yes—
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C2×C4×C3⋊D3—24no—
81C2×C4×C3⋊D3C2314yes—
82C2×#634—24no—
83C2×#634C2314yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×D12—24no—
90C2×C3×D12C2314yes—
91C2×C3×C4×D3—28no—
92C2×C3×C4×D3C2318yes—
93C2×#626—28no—
94C2×#626C2318yes—
95C2×#624—24no—
96C2×#624—24no—
97C2×#624C2314yes—
98C2×#624C2314yes—
99C32×C4⋊C4C2314yes—
100#3752C2318yes—
101C4⋊(C3⋊Dic3)C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×C4⋊Dic3C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2318yes—
106C3×C4×Dic3C2314yes—
107C3×C4×Dic3C2314yes—
108#3724C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2314yes—
113Dic32C2318yes—
114Dic32C2314yes—
115C2×#529—91noSylow
116C22×C3×D4—31no—
117C23×C3×C4—32no—
118C22×#67—32no—
119C22×D12—32no—
120C22×D12C2×D311yescharacteristic
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—31no—
126C22×C4×D3—31no—
127C22×C4×D3—61no—
128C22×C4×D3C2×D312yes—
129C22×Dic6—31no—
130C22×Dic6—31no—
131C22×Dic6—61no—
132C3×#125—38no—
133C3×C4×D4—38no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—32no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—32no—
138C2×C3×C4⋊C4C2×D311yescharacteristic
139C2×C3×C4⋊C4C2×D311yescharacteristic
140C2×C3×C22⋊C4—32no—
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×#217—32no—
144C2×#217—32no—
145C2×#217—32no—
146#938—38no—
147#936—38no—
148C4×#67—316no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—62no—
155C2×(C2×D3)⋊C4C2×D312yes—
156#926—316no—
157C2×C4⋊Dic3—32no—
158C2×C4⋊Dic3—32no—
159C2×C4⋊Dic3—62no—
160C2×C4⋊Dic3C2×D311yescharacteristic
161C2×C4⋊Dic3C2×D312yes—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4C2×D312yes—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D311yescharacteristic
173#898—316no—
174#897—38no—
175#897—38no—
176#897—68no—
177#895—38no—
178#894—316no—
179#893—316no—
180#893C2×D318yescomplemented
181#892—316no—
182#890C2×D318yescomplemented
183#887—38no—
184#883—316no—
185#879—316no—
186#875—38no—
187C42×D3—38no—
188C42×D3—38no—
189C4×Dic6—38no—
190C23×C32C2411yescharacteristic
191C22×C3⋊D3—22no—
192C22×C3⋊D3—22no—
193C22×C3⋊D3#4114yes—
194C22×C3⋊D3C2412yes—
195C22×C3×D3—24no—
196C22×C3×D3—24no—
197C22×C3×D3—24no—
198C22×C3×D3C2414yes—
199C2×C32×C4—24no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2414yes—
202C2×C32×C4C2412yes—
203C2×C3⋊Dic3—24no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3C2412yes—
206C2×C3⋊Dic3C2414yes—
207C4×C3⋊D3—28no—
208#634—28no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3#4114yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2414yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2412yes—
219C3×D12—28no—
220C3×C4×D3—216no—
221#626—216no—
222#624—28no—
223#624—28no—
224#529—916no—
225C2×#126—92no—
226C2×#125—31no—
227C2×#124—91no—
228C2×#123—92no—
229C2×C22⋊Q8—91no—
230C2×#121—91no—
231C2×C4×Q8—91no—
232C2×C4×D4—31no—
233C2×C4×D4—92no—
234C2×#117—92no—
235C22×C42—91no—
236C24×C3—32no—
237C23×D3—31no—
238C23×D3—31no—
239C23×D3—61no—
240C23×D3C22×D312yes—
241C2×C3×D4—34no—
242C2×C3×D4—64no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—32no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—38no—
251C22×C3×C4—68no—
252C22×C3×C4C22×D312yes—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—38no—
257C2×#67—68no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—61no—
263C22×Dic3—62no—
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D311yescharacteristic
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D311yescharacteristic
269C2×D12—24no—
270C2×D12—38no—
271C2×D12—68no—
272C2×D12C22×D314yes—
273C2×C4×D3—28no—
274C2×C4×D3—34no—
275C2×C4×D3—34no—
276C2×C4×D3—34no—
277C2×C4×D3—34no—
278C2×C4×D3—34no—
279C2×C4×D3—34no—
280C2×C4×D3—64no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—64no—
284C2×C4×D3—64no—
285C2×C4×D3—64no—
286C2×C4×D3—64no—
287C2×C4×D3—124no—
288C2×C4×D3C22×D318yes—
289C2×Dic6—34no—
290C2×Dic6—34no—
291C2×Dic6—64no—
292C2×Dic6—64no—
293C2×Dic6—64no—
294C2×Dic6—124no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—34no—
297C3×C4⋊C4—38no—
298C3×C4⋊C4—38no—
299C3×C4⋊C4C22×D314yes—
300C3×C4⋊C4C22×D314yes—
301C3×C22⋊C4—38no—
302C3×C42—34no—
303C3×C42—34no—
304#217—38no—
305#217—38no—
306#217—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—38no—
309(C2×D3)⋊C4—38no—
310(C2×D3)⋊C4—38no—
311(C2×D3)⋊C4—38no—
312(C2×D3)⋊C4—68no—
313(C2×D3)⋊C4C22×D318yes—
314C4⋊Dic3—38no—
315C4⋊Dic3—38no—
316C4⋊Dic3—68no—
317C4⋊Dic3C22×D314yes—
318C4⋊Dic3C22×D318yes—
319Dic3⋊C4—38no—
320Dic3⋊C4—38no—
321Dic3⋊C4C22×D318yes—
322C4×Dic3—38no—
323C4×Dic3—34no—
324C4×Dic3—34no—
325C4×Dic3—34no—
326C4×Dic3—34no—
327C4×Dic3—38no—
328C4×Dic3C22×D314yes—
329C4×Dic3C22×D314yes—
330C22×C32C2×#4112yes—
331C22×C32C2×#4112yes—
332C22×C32C2×#4112yes—
333C22×C32C2511yescharacteristic
334C2×C3⋊D3—28no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3C2×#4114yes—
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—48no—
342C32×C4—24no—
343C32×C4C2×#4114yes—
344C3⋊Dic3—24no—
345C3⋊Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—24no—
350C3×Dic3C2×#4114yes—
351C22×Q8—91no—
352C22×D4—31no—
353C22×D4—92no—
354C23×C4—32no—
355C23×C4—91no—
356C23×C4—91no—
357C23×C4—91no—
358#126—916no—
359#125—38no—
360#124—98no—
361#123—916no—
362C22⋊Q8—98no—
363#121—98no—
364C4×Q8—98no—
365C4×D4—38no—
366C4×D4—916no—
367#117—916no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—92no—
372C2×C4⋊C4—92no—
373C2×C4⋊C4D3211yescharacteristic
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—98no—
382C2×C42—91no—
383C2×C42—92no—
384C2×C42—91no—
385C23×C3—21no—
386C23×C3—34no—
387C23×C3—64no—
388C23×C3—64no—
389C23×C3—64no—
390C23×C3C23×D311yescharacteristic
391C23×C3C23×D311yescharacteristic
392C22×D3—24no—
393C22×D3—24no—
394C22×D3—24no—
395C22×D3—34no—
396C22×D3—34no—
397C22×D3—32no—
398C22×D3—32no—
399C22×D3—64no—
400C22×D3—62no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—122no—
406C22×D3—122no—
407C22×D3C23×D314yes—
408C3×D4—68no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
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—32no—
420C2×C3×C4—44no—
421C2×C3×C4—616no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—64no—
426C2×C3×C4#23514yes—
427C2×C3×C4#23914yes—
428C2×C3×C4C23×D314yes—
429C2×C3×C4C23×D314yes—
430C2×C3×C4C23×D312yes—
431C2×C3×C4C23×D312yes—
432#67—616no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—24no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—34no—
440C2×Dic3—34no—
441C2×Dic3—62no—
442C2×Dic3—64no—
443C2×Dic3—64no—
444C2×Dic3—62no—
445C2×Dic3—64no—
446C2×Dic3—62no—
447C2×Dic3—124no—
448C2×Dic3—122no—
449C2×Dic3#23714yes—
450C2×Dic3C23×D312yes—
451C2×Dic3C23×D312yes—
452C2×Dic3C23×D312yes—
453C2×Dic3C23×D314yes—
454C2×Dic3C23×D312yes—
455D12—28no—
456D12—616no—
457C4×D3—216no—
458C4×D3—68no—
459C4×D3—68no—
460C4×D3—68no—
461C4×D3—68no—
462C4×D3—68no—
463C4×D3—68no—
464C4×D3—128no—
465Dic6—68no—
466Dic6—68no—
467Dic6—128no—
468C2×C32#52914yescomplemented
469C2×C32C22×#4111yescharacteristic
470C2×C32C22×#4111yescharacteristic
471C2×C32C22×#4111yescharacteristic
472C3⋊D3—24no—
473C3×D3—44no—
474C24—32no—
475C24—91no—
476C2×Q8—94no—
477C2×Q8—184no—
478C2×D4—34no—
479C2×D4—64no—
480C2×D4—98no—
481C2×D4—188no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—38no—
488C22×C4—68no—
489C22×C4—94no—
490C22×C4—94no—
491C22×C4—91no—
492C22×C4—92no—
493C22×C4—94no—
494C22×C4—184no—
495C22×C4—184no—
496C22×C4—184no—
497C22×C4C2×D3212yes—
498C22×C4C2×D3211yescharacteristic
499C4⋊C4—38no—
500C4⋊C4—38no—
501C4⋊C4—34no—
502C4⋊C4—98no—
503C4⋊C4—98no—
504C4⋊C4C2×D3214yes—
505C22⋊C4—38no—
506C22⋊C4—98no—
507C22⋊C4—98no—
508C22⋊C4—98no—
509C22⋊C4—98no—
510C42—34no—
511C42—34no—
512C42—94no—
513C42—94no—
514C42—98no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—64no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—128no—
523C22×C3C2×#23512yes—
524C22×C3C2×#23712yes—
525C22×C3C2×#23912yes—
526C22×C3D3×#4112yes—
527C22×C3D3×#4112yes—
528C22×C3D3×#4112yes—
529C22×C3C24×D311yescharacteristic
530C22×C3C24×D311yescharacteristic
531C2×D3—24no—
532C2×D3—24no—
533C2×D3—24no—
534C2×D3—34no—
535C2×D3—34no—
536C2×D3—48no—
537C2×D3—64no—
538C2×D3—68no—
539C2×D3—62no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—68no—
544C2×D3—122no—
545C2×D3—122no—
546C2×D3—128no—
547C3×C4—24no—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—34no—
551C3×C4—44no—
552C3×C4—62no—
553C3×C4—62no—
554C3×C4—62no—
555C3×C4—64no—
556C3×C4C2×#23514yes—
557C3×C4C2×#23914yes—
558Dic3—22no—
559Dic3—22no—
560Dic3—22no—
561Dic3—24no—
562Dic3—64no—
563Dic3—62no—
564Dic3—64no—
565Dic3—62no—
566Dic3—124no—
567Dic3—122no—
568Dic3C2×#23714yes—
569C32C2×#52911yescharacteristic, complemented, Sylow
570C23—34no—
571C23—64no—
572C23—64no—
573C23—64no—
574C23—94no—
575C23—92no—
576C23—182no—
577C23—182no—
578C23C22×D3211yescharacteristic
579Q8—188no—
580D4—68no—
581D4—1816no—
582C2×C4—24no—
583C2×C4—34no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—32no—
588C2×C4—34no—
589C2×C4—616no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—64no—
594C2×C4—92no—
595C2×C4—94no—
596C2×C4—188no—
597C2×C4—188no—
598C2×C4—182no—
599C2×C4—184no—
600C2×C4—188no—
601C2×C4#379914yes—
602C2×C4C22×D3214yes—
603C2×C4C22×D3212yes—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—24no—
608C2×C3—124no—
609C2×C3#555714yescomplemented
610C2×C3#569114yescomplemented
611C2×C3C22×#23511yescharacteristic
612C2×C3C22×#23711yescharacteristic
613C2×C3C22×#23911yescharacteristic
614C2×C3C2×D3×#4111yescharacteristic
615C2×C3C2×D3×#4111yescharacteristic
616C2×C3C2×D3×#4111yescharacteristic
617D3—44no—
618D3—64no—
619D3—64no—
620D3—124no—
621C22—64no—
622C22—64no—
623C22—64no—
624C22—94no—
625C22—128no—
626C22—182no—
627C22—182no—
628C22—188no—
629C22C2×#379912yes—
630C22D3×#23712yes—
631C22#6431912yes—
632C22C23×D3211yescharacteristic
633C4—24no—
634C4—34no—
635C4—62no—
636C4—62no—
637C4—62no—
638C4—64no—
639C4—182no—
640C4—184no—
641C4C2×#379914yes—
642C3—21no—
643C3C2×#555711yescharacteristic, complemented
644C3C2×#569111yescharacteristic, complemented
645C2—124no—
646C2—184no—
647C2#1059444714yesdirect product factor
648C2C22×#379911yescharacteristic
649C2C2×D3×#23711yescharacteristic
650C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63916C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64106C2semidirect
2. C2×C3×#893C2semidirect
3. C2×C3×#890C2semidirect
5. C2×#63904C2semidirect
6. C2×C4×#624C2semidirect
7. C2×#63861C2semidirect
8. C2×#63860C2semidirect
9. C2×#63854C2semidirect
10. C2×#63844C2semidirect
11. C2×#63841C2semidirect
12. #10594447C2direct (N × H)
25. #64106C22semidirect
32. C3×#893C22semidirect
33. C3×#890C22semidirect
42. #63904C22semidirect
43. C4×#624C22semidirect
44. #63861C22semidirect
45. #63860C22semidirect
46. #63854C22semidirect
47. #63844C22semidirect
48. #63841C22semidirect
64. C2×#893D3semidirect
66. C2×#890D3semidirect
180. #893C2×D3semidirect
182. #890C2×D3semidirect
468. C2×C32#529semidirect
569. C32C2×#529semidirect
609. C2×C3#5557semidirect
610. C2×C3#5691semidirect
643. C3C2×#5557semidirect
644. C3C2×#5691semidirect
647. C2#10594447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×C3×#8932
C2×C3×#8902
C2×#639162
C2×#639042
C2×C4×#6242
C2×#638612
C2×#638602
C2×#638542
C2×#638442
C2×#638412
#105944472
C2×#56913
C2×#55573