Finite Group Databasebeta

← C2×#10594335 #11903404

Subgroups — C2×#10594335 #11903404

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×C4×#627C211yesmaximal, characteristic, complemented
5C2×#63866C211yesmaximal, characteristic, complemented
6C2×#63863C211yesmaximal, characteristic
7C2×#63862C212yesmaximal, complemented
8C2×#63860C211yesmaximal, characteristic
9C2×#63859C212yesmaximal, complemented
10C2×#63855C212yesmaximal, complemented
11C2×#63851C212yesmaximal, complemented
12#10594335C2116yesmaximal, direct product factor
13C2×#5568—31nomaximal
14C2×#5542—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×C3×Dic6C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3750C2212yes—
22C2×C4×C3⋊Dic3C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24#64096C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#893C2218yes—
31C3×#887C2218yescomplemented
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2212yes—
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C4×#627C2218yescomplemented
42#63866C2218yescomplemented
43#63863C2218yes—
44#63862C22116yescomplemented
45#63860C2218yes—
46#63859C22116yescomplemented
47#63855C22116yescomplemented
48#63851C22116yescomplemented
49C2×C3×C4×Q8—31no—
50C2×C3×C4×D4—31no—
51C2×#947—31no—
52C2×#944—31no—
53C2×#936—31no—
54C2×#936—31no—
55C2×#926—32no—
56C2×#924—32no—
57#5568—316no—
58#5542—316no—
59C2×#898—32no—
60C2×#896—32no—
61C2×#893D311yescharacteristic
62C2×#887—31no—
63C2×#887—31no—
64C2×#887—61no—
65C2×#887D311yescharacteristic, complemented
66C2×#879—32no—
67C2×#879—32no—
68C2×#876—32no—
69C2×#875—31no—
70C2×#872—32no—
71C2×#869—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C23×C3×D3C2312yes—
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C2×#634—24no—
81C2×#634C2314yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×D12—24no—
88C2×C3×D12C2314yes—
89C2×C3×C4×D3—28no—
90C2×C3×C4×D3C2318yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#627—24no—
94C2×#627C2314yes—
95C32×C4⋊C4C2314yes—
96#3750C2318yes—
97C4×C3⋊Dic3C2318yes—
98C4×C3⋊Dic3C2314yes—
99C3×(C2×D3)⋊C4C2318yes—
100C3×Dic3⋊C4C2318yes—
101C3×C4×Dic3C2318yes—
102C3×C4×Dic3C2314yes—
103C3×C4×Dic3C2314yes—
104#3724C2314yes—
105Dic3⋊Dic3C2318yes—
106Dic3⋊Dic3C2314yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2314yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—31no—
115C22×C3×D4—31no—
116C23×C3×C4—32no—
117C22×D12C2×D311yescharacteristic
118C22×C4×D3C2×D312yes—
119C22×Dic6—31no—
120C22×Dic6—31no—
121C22×Dic6—31no—
122C22×Dic6—31no—
123C22×Dic6—61no—
124C22×Dic6C2×D311yescharacteristic
125C3×C4×Q8—38no—
126C3×C4×D4—38no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4C2×D311yescharacteristic
130C2×C3×C4⋊C4C2×D311yescharacteristic
131C2×C3×C22⋊C4—32no—
132C2×C3×C42—31no—
133C2×C3×C42—31no—
134C2×C3×C42—32no—
135C2×#217—32no—
136C2×#217—32no—
137C2×#217—32no—
138C2×#217—32no—
139#947—38no—
140#944—38no—
141#936—38no—
142#936—38no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4C2×D312yes—
148#926—316no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—32no—
153#924—316no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—62no—
163C2×Dic3⋊C4C2×D312yes—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—62no—
169C2×C4×Dic3—61no—
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D312yes—
173#898—316no—
174#896—316no—
175#893C2×D318yes—
176#887—38no—
177#887—38no—
178#887—68no—
179#887C2×D318yescomplemented
180#879—316no—
181#879—316no—
182#876—316no—
183#875—38no—
184#872—316no—
185#869—38no—
186C4×Dic6—38no—
187C4×Dic6—38no—
188C23×C32C2411yescharacteristic
189C22×C3×D3—24no—
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2414yes—
193C2×C32×C4—24no—
194C2×C32×C4#4114yes—
195C2×C32×C4C2414yes—
196C2×C32×C4C2412yes—
197C2×C3⋊Dic3—24no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3C2412yes—
201C2×C3⋊Dic3C2414yes—
202C2×C3⋊Dic3C2412yes—
203#634—28no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3#4114yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C3×D12—28no—
215C3×C4×D3—216no—
216C3×Dic6—28no—
217#627—28no—
218#556—916no—
219C2×C4⋊Q8—91no—
220C2×#126—92no—
221C2×#126—92no—
222C2×#124—91no—
223C2×#124—91no—
224C2×C22⋊Q8—92no—
225C2×C4×Q8—31no—
226C2×C4×Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×D4—31no—
229C2×#117—92no—
230C24×C3—32no—
231C23×D3C22×D312yes—
232C2×C3×Q8—34no—
233C2×C3×Q8—64no—
234C2×C3×D4—34no—
235C2×C3×D4—64no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—31no—
243C22×C3×C4—38no—
244C22×C3×C4—68no—
245C22×C3×C4C22×D312yes—
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—32no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—32no—
255C22×Dic3—61no—
256C22×Dic3—62no—
257C22×Dic3—61no—
258C22×Dic3C22×D311yescharacteristic
259C22×Dic3C22×D311yescharacteristic
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D311yescharacteristic
263C2×D12—24no—
264C2×D12C22×D314yes—
265C2×C4×D3—28no—
266C2×C4×D3C22×D318yes—
267C2×Dic6—24no—
268C2×Dic6—34no—
269C2×Dic6—34no—
270C2×Dic6—34no—
271C2×Dic6—34no—
272C2×Dic6—64no—
273C2×Dic6—64no—
274C2×Dic6—68no—
275C2×Dic6—64no—
276C2×Dic6—64no—
277C2×Dic6—64no—
278C2×Dic6C22×D314yes—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—38no—
281C3×C4⋊C4C22×D314yes—
282C3×C4⋊C4C22×D314yes—
283C3×C22⋊C4—38no—
284C3×C42—34no—
285C3×C42—34no—
286C3×C42—38no—
287#217—38no—
288#217—38no—
289#217—38no—
290#217—38no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4C22×D318yes—
296C4⋊Dic3—34no—
297C4⋊Dic3—34no—
298C4⋊Dic3—38no—
299C4⋊Dic3—38no—
300Dic3⋊C4—38no—
301Dic3⋊C4—38no—
302Dic3⋊C4—34no—
303Dic3⋊C4—34no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—68no—
309Dic3⋊C4C22×D318yes—
310C4×Dic3—34no—
311C4×Dic3—34no—
312C4×Dic3—38no—
313C4×Dic3—38no—
314C4×Dic3—68no—
315C4×Dic3—64no—
316C4×Dic3C22×D314yes—
317C4×Dic3C22×D314yes—
318C4×Dic3C22×D318yes—
319C22×C32C2×#4112yes—
320C22×C32C2×#4112yes—
321C22×C322−1+412yes—
322C22×C32C2511yescharacteristic
323C2×C3×D3—24no—
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—48no—
327C32×C4—24no—
328C32×C4C2×#4114yes—
329C3⋊Dic3—24no—
330C3⋊Dic3—22no—
331C3⋊Dic3—22no—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3C2×#4114yes—
337C22×Q8—31no—
338C22×Q8—91no—
339C22×Q8—91no—
340C22×D4—31no—
341C23×C4—32no—
342C4⋊Q8—98no—
343#126—916no—
344#126—916no—
345#124—98no—
346#124—98no—
347C22⋊Q8—916no—
348C4×Q8—38no—
349C4×Q8—98no—
350C4×Q8—98no—
351C4×D4—38no—
352#117—916no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—92no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—91no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—92no—
360C2×C4⋊C4D3211yescharacteristic
361C2×C22⋊C4—32no—
362C2×C22⋊C4—92no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C42—32no—
367C2×C42—31no—
368C2×C42—31no—
369C2×C42—92no—
370C2×C42—91no—
371C23×C3—21no—
372C23×C3—34no—
373C23×C3—64no—
374C23×C3—64no—
375C23×C3—64no—
376C23×C3C23×D311yescharacteristic
377C23×C3C23×D311yescharacteristic
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3C23×D314yes—
382C3×Q8—68no—
383C3×D4—68no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—34no—
390C2×C3×C4—32no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—34no—
394C2×C3×C4—32no—
395C2×C3×C4—44no—
396C2×C3×C4—616no—
397C2×C3×C4—64no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4#23514yes—
402C2×C3×C4#23514yes—
403C2×C3×C4C23×D314yes—
404C2×C3×C4C23×D314yes—
405C2×C3×C4C23×D312yes—
406C2×C3×C4C23×D312yes—
407C2×Dic3—24no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—32no—
412C2×Dic3—32no—
413C2×Dic3—34no—
414C2×Dic3—32no—
415C2×Dic3—32no—
416C2×Dic3—34no—
417C2×Dic3—62no—
418C2×Dic3—64no—
419C2×Dic3—62no—
420C2×Dic3—68no—
421C2×Dic3—64no—
422C2×Dic3—64no—
423C2×Dic3—64no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—122no—
429C2×Dic3#23714yes—
430C2×Dic3C23×D312yes—
431C2×Dic3C23×D312yes—
432C2×Dic3C23×D312yes—
433C2×Dic3C23×D314yes—
434C2×Dic3C23×D312yes—
435D12—28no—
436C4×D3—216no—
437Dic6—28no—
438Dic6—68no—
439Dic6—616no—
440Dic6—68no—
441Dic6—68no—
442Dic6—68no—
443C2×C32#55614yescomplemented
444C2×C32C22×#4111yescharacteristic
445C2×C32C22×#4111yescharacteristic
446C2×C32C2×2−1+411yescharacteristic
447C3×D3—44no—
448C24—32no—
449C2×Q8—34no—
450C2×Q8—64no—
451C2×Q8—94no—
452C2×Q8—94no—
453C2×Q8—184no—
454C2×Q8—184no—
455C2×D4—34no—
456C2×D4—64no—
457C22×C4—31no—
458C22×C4—31no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—32no—
462C22×C4—38no—
463C22×C4—68no—
464C22×C4—91no—
465C22×C4—92no—
466C22×C4—91no—
467C22×C4C2×D3212yes—
468C22×C4C2×D3211yescharacteristic
469C4⋊C4—38no—
470C4⋊C4—94no—
471C4⋊C4—98no—
472C4⋊C4—94no—
473C4⋊C4—94no—
474C4⋊C4—98no—
475C4⋊C4—98no—
476C4⋊C4C2×D3214yes—
477C22⋊C4—38no—
478C22⋊C4—98no—
479C22⋊C4—98no—
480C22⋊C4—98no—
481C22⋊C4—98no—
482C42—38no—
483C42—34no—
484C42—34no—
485C42—98no—
486C42—94no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—21no—
491C22×C3—64no—
492C22×C3—64no—
493C22×C3—64no—
494C22×C3—128no—
495C22×C3C2×#23512yes—
496C22×C3C2×#23512yes—
497C22×C3C2×#23712yes—
498C22×C3#100712yes—
499C22×C3D3×#4112yes—
500C22×C3#101012yes—
501C22×C3C24×D311yescharacteristic
502C22×C3C24×D311yescharacteristic
503C2×D3—24no—
504C2×D3—24no—
505C2×D3—24no—
506C2×D3—48no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—34no—
511C3×C4—44no—
512C3×C4—64no—
513C3×C4—62no—
514C3×C4—62no—
515C3×C4—62no—
516C3×C4C2×#23514yes—
517C3×C4C2×#23514yes—
518Dic3—24no—
519Dic3—22no—
520Dic3—22no—
521Dic3—22no—
522Dic3—68no—
523Dic3—64no—
524Dic3—64no—
525Dic3—64no—
526Dic3—62no—
527Dic3—62no—
528Dic3—62no—
529Dic3—62no—
530Dic3—122no—
531Dic3C2×#23714yes—
532C32C2×#55611yescharacteristic, complemented, Sylow
533C23—34no—
534C23—64no—
535C23—64no—
536C23—64no—
537C23C22×D3211yescharacteristic
538Q8—68no—
539Q8—188no—
540Q8—188no—
541D4—68no—
542C2×C4—24no—
543C2×C4—34no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—32no—
548C2×C4—34no—
549C2×C4—616no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—92no—
555C2×C4—94no—
556C2×C4—92no—
557C2×C4—184no—
558C2×C4—182no—
559C2×C4—182no—
560C2×C4#379814yes—
561C2×C4C22×D3214yes—
562C2×C4C22×D3212yes—
563C2×C3—24no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—124no—
568C2×C3#554214yescomplemented
569C2×C3#556814yescomplemented
570C2×C3C22×#23511yescharacteristic
571C2×C3C22×#23511yescharacteristic
572C2×C3C22×#23711yescharacteristic
573C2×C3C2×#100711yescharacteristic
574C2×C3C2×D3×#4111yescharacteristic
575C2×C3C2×#101011yescharacteristic
576D3—44no—
577C22—64no—
578C22—64no—
579C22—64no—
580C22—128no—
581C22C2×#379812yes—
582C22D3×#23712yes—
583C22#6431512yes—
584C22C23×D3211yescharacteristic
585C4—24no—
586C4—34no—
587C4—64no—
588C4—62no—
589C4—62no—
590C4—62no—
591C4—184no—
592C4—182no—
593C4—182no—
594C4C2×#379814yes—
595C3—21no—
596C3C2×#554211yescharacteristic, complemented
597C3C2×#556811yescharacteristic, complemented
598C2—124no—
599C2#1059433514yesdirect product factor
600C2C22×#379811yescharacteristic
601C2C2×D3×#23711yescharacteristic
602C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#556
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×#64096C2semidirect
3. C2×C3×#887C2semidirect
4. C2×C4×#627C2semidirect
5. C2×#63866C2semidirect
7. C2×#63862C2semidirect
9. C2×#63859C2semidirect
10. C2×#63855C2semidirect
11. C2×#63851C2semidirect
12. #10594335C2direct (N × H)
24. #64096C22semidirect
31. C3×#887C22semidirect
41. C4×#627C22semidirect
42. #63866C22semidirect
44. #63862C22semidirect
46. #63859C22semidirect
47. #63855C22semidirect
48. #63851C22semidirect
65. C2×#887D3semidirect
179. #887C2×D3semidirect
443. C2×C32#556semidirect
532. C32C2×#556semidirect
568. C2×C3#5542semidirect
569. C2×C3#5568semidirect
596. C3C2×#5542semidirect
597. C3C2×#5568semidirect
599. C2#10594335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C3×#8932
C2×C3×#8872
C2×C4×#6272
C2×#638662
C2×#638632
C2×#638622
C2×#638602
C2×#638592
C2×#638552
C2×#638512
#105943352
C2×#55683
C2×#55423