Finite Group Databasebeta

← C2×#10593932 #11903396

Subgroups — C2×#10593932 #11903396

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×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×Dic3×D12C211yesmaximal, characteristic
5C2×#63887C212yesmaximal, complemented
6C2×#63878C212yesmaximal, complemented
7C2×#63866C211yesmaximal, characteristic, complemented
8C2×#63862C212yesmaximal, complemented
9C2×#63860C211yesmaximal, characteristic
10C2×#63858C212yesmaximal, complemented
11C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
12#10593932C2116yesmaximal, direct product factor
13C2×#5671—31nomaximal
14C2×#5584—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C2×C4×C3⋊Dic3C2212yes—
24C4×#634C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#875C2218yes—
33C3×C4×Dic6C2218yescomplemented
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×Dic32C2212yes—
41Dic3×D12C2218yes—
42#63887C22116yescomplemented
43#63878C22116yescomplemented
44#63866C2218yescomplemented
45#63862C22116yescomplemented
46#63860C2218yes—
47#63858C22116yescomplemented
48Dic3×Dic6C2218yescomplemented
49C2×C3×#124—31no—
50C2×C3×C4×Q8—31no—
51C2×#946—32no—
52C2×Q8×Dic3—31no—
53C2×#944—31no—
54C2×#936—31no—
55C2×D4×Dic3—31no—
56#5671—316no—
57#5584—316no—
58C2×#898—32no—
59C2×#898—32no—
60C2×#892—32no—
61C2×#879—32no—
62C2×#879—32no—
63C2×#878—32no—
64C2×#877—32no—
65C2×#875—31no—
66C2×#875D311yescharacteristic
67C2×C4×D12—31no—
68C2×#869—31no—
69C2×C4×Dic6—31no—
70C2×C4×Dic6—31no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6—61no—
73C2×C4×Dic6D311yescharacteristic, complemented
74C23×C3×D3C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2312yes—
80C2×#634—24no—
81C2×#634C2314yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×D12—24no—
88C2×C3×D12C2314yes—
89C2×C3×Dic6—24no—
90C2×C3×Dic6—24no—
91C2×C3×Dic6C2314yes—
92C2×C3×Dic6C2314yes—
93C2×D3×Dic3—28no—
94C2×D3×Dic3C2318yes—
95C32×C42C2314yes—
96C4⋊(C3⋊Dic3)C2314yes—
97#3750C2318yes—
98C4×C3⋊Dic3C2318yes—
99C3×(C2×D3)⋊C4C2318yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×Dic3⋊C4C2314yes—
103C3×Dic3⋊C4C2314yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106Dic3⋊Dic3C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—31no—
115C22×C3×Q8—31no—
116C22×C3×D4—31no—
117C23×Dic3—32no—
118C22×D12C2×D311yescharacteristic
119C22×C4×D3—32no—
120C22×Dic6—31no—
121C22×Dic6—31no—
122C22×Dic6—61no—
123C22×Dic6C2×D311yescharacteristic
124C22×Dic6C2×D311yescharacteristic
125C3×#124—38no—
126C3×C4×Q8—38no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C42—21no—
133C2×C3×C42—31no—
134C2×C3×C42—31no—
135C2×C3×C42C2×D311yescharacteristic
136C2×C3×C42C2×D311yescharacteristic
137C2×#217—32no—
138C2×#217—32no—
139C2×#217—32no—
140#946—316no—
141Q8×Dic3—38no—
142#944—38no—
143#936—38no—
144D4×Dic3—38no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4C2×D312yes—
149C2×(C2×D3)⋊C4C2×D312yes—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—61no—
156C2×C4⋊Dic3C2×D311yescharacteristic
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—62no—
163C2×Dic3⋊C4C2×D311yescharacteristic
164C2×Dic3⋊C4C2×D311yescharacteristic
165C2×C4×Dic3—32no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—62no—
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D311yescharacteristic
172#898—316no—
173#898—316no—
174#892—316no—
175#879—316no—
176#879—316no—
177#878—316no—
178#877—316no—
179#875—38no—
180#875C2×D318yes—
181C4×D12—38no—
182#869—38no—
183C4×Dic6—38no—
184C4×Dic6—38no—
185C4×Dic6—38no—
186C4×Dic6—68no—
187C4×Dic6C2×D318yescomplemented
188C23×C32C2411yescharacteristic
189C22×C3×D3—24no—
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2414yes—
193C2×C32×C4—22no—
194C2×C32×C4—22no—
195C2×C32×C4#4114yes—
196C2×C32×C4C2412yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3—24no—
201C2×C3⋊Dic3C2414yes—
202C2×C3⋊Dic3C2414yes—
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×Dic3C2412yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C3×D12—28no—
215C3×Dic6—28no—
216C3×Dic6—28no—
217D3×Dic3—216no—
218#556—916no—
219C2×C4⋊Q8—91no—
220C2×#126—92no—
221C2×#126—92no—
222C2×#124—31no—
223C2×#124—91no—
224C2×C22⋊Q8—92no—
225C2×C4×Q8—31no—
226C2×C4×Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×D4—91no—
229C2×#117—92no—
230C24×C3—32no—
231C23×D3C22×D312yes—
232C2×C3×Q8—34no—
233C2×C3×Q8—34no—
234C2×C3×Q8—64no—
235C2×C3×Q8—64no—
236C2×C3×D4—34no—
237C2×C3×D4—64no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—32no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—32no—
256C22×Dic3—38no—
257C22×Dic3—62no—
258C22×Dic3—62no—
259C22×Dic3—68no—
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C2×D12—24no—
266C2×D12C22×D314yes—
267C2×C4×D3—38no—
268C2×C4×D3—68no—
269C2×Dic6—24no—
270C2×Dic6—24no—
271C2×Dic6—34no—
272C2×Dic6—34no—
273C2×Dic6—64no—
274C2×Dic6—68no—
275C2×Dic6—64no—
276C2×Dic6—64no—
277C2×Dic6C22×D314yes—
278C2×Dic6C22×D314yes—
279C3×C4⋊C4—34no—
280C3×C4⋊C4—34no—
281C3×C4⋊C4—34no—
282C3×C22⋊C4—38no—
283C3×C22⋊C4—38no—
284C3×C42—24no—
285C3×C42—34no—
286C3×C42—34no—
287C3×C42C22×D314yes—
288C3×C42C22×D314yes—
289#217—38no—
290#217—38no—
291#217—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4C22×D318yes—
296(C2×D3)⋊C4C22×D318yes—
297C4⋊Dic3—34no—
298C4⋊Dic3—34no—
299C4⋊Dic3—38no—
300C4⋊Dic3—38no—
301C4⋊Dic3—38no—
302C4⋊Dic3—64no—
303C4⋊Dic3C22×D314yes—
304Dic3⋊C4—38no—
305Dic3⋊C4—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—68no—
310Dic3⋊C4C22×D314yes—
311Dic3⋊C4C22×D314yes—
312C4×Dic3—38no—
313C4×Dic3—38no—
314C4×Dic3—38no—
315C4×Dic3—38no—
316C4×Dic3—68no—
317C4×Dic3C22×D314yes—
318C4×Dic3C22×D314yes—
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—22no—
328C32×C4—22no—
329C32×C4C2×#4114yes—
330C3⋊Dic3—24no—
331C3⋊Dic3—24no—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3C2×#4114yes—
337C22×Q8—31no—
338C22×Q8—31no—
339C22×Q8—91no—
340C22×D4—31no—
341C23×C4—92no—
342C4⋊Q8—98no—
343#126—916no—
344#126—916no—
345#124—38no—
346#124—98no—
347C22⋊Q8—916no—
348C4×Q8—38no—
349C4×Q8—98no—
350C4×Q8—98no—
351C4×D4—98no—
352#117—916no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—92no—
357C2×C4⋊C4—92no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—91no—
360C2×C4⋊C4—92no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C42—31no—
367C2×C42—31no—
368C2×C42—92no—
369C2×C42—92no—
370C2×C42D3211yescharacteristic
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×Q8—68no—
384C3×D4—68no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—34no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—34no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—42no—
401C2×C3×C4—64no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4#23714yes—
406C2×C3×C4#23914yes—
407C2×C3×C4C23×D312yes—
408C2×C3×C4C23×D312yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D312yes—
412C2×C3×C4C23×D312yes—
413C2×Dic3—22no—
414C2×Dic3—24no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—34no—
418C2×Dic3—34no—
419C2×Dic3—34no—
420C2×Dic3—34no—
421C2×Dic3—64no—
422C2×Dic3—64no—
423C2×Dic3—68no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—64no—
427C2×Dic3—64no—
428C2×Dic3—616no—
429C2×Dic3—124no—
430C2×Dic3#23514yes—
431C2×Dic3C23×D312yes—
432C2×Dic3C23×D314yes—
433C2×Dic3C23×D312yes—
434C2×Dic3C23×D312yes—
435C2×Dic3C23×D312yes—
436D12—28no—
437C4×D3—616no—
438Dic6—28no—
439Dic6—28no—
440Dic6—616no—
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—34no—
451C2×Q8—64no—
452C2×Q8—64no—
453C2×Q8—94no—
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—98no—
463C22×C4—92no—
464C22×C4—92no—
465C22×C4—188no—
466C22×C4C2×D3211yescharacteristic
467C22×C4C2×D3211yescharacteristic
468C22×C4C2×D3211yescharacteristic
469C4⋊C4—34no—
470C4⋊C4—34no—
471C4⋊C4—34no—
472C4⋊C4—98no—
473C4⋊C4—98no—
474C4⋊C4—98no—
475C4⋊C4—94no—
476C4⋊C4—98no—
477C22⋊C4—38no—
478C22⋊C4—38no—
479C22⋊C4—98no—
480C22⋊C4—98no—
481C22⋊C4—98no—
482C42—34no—
483C42—34no—
484C42—98no—
485C42—98no—
486C42C2×D3214yes—
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×#23712yes—
497C22×C3C2×#23912yes—
498C22×C3D3×#4112yes—
499C22×C3#101012yes—
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—22no—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—24no—
513C3×C4—34no—
514C3×C4—42no—
515C3×C4—64no—
516C3×C4—62no—
517C3×C4—62no—
518C3×C4—62no—
519C3×C4C2×#23714yes—
520C3×C4C2×#23914yes—
521Dic3—22no—
522Dic3—24no—
523Dic3—22no—
524Dic3—22no—
525Dic3—68no—
526Dic3—64no—
527Dic3—64no—
528Dic3—64no—
529Dic3—64no—
530Dic3—124no—
531Dic3C2×#23514yes—
532C32C2×#55611yescharacteristic, complemented, Sylow
533C23—34no—
534C23—64no—
535C23—64no—
536C23—64no—
537C23C22×D3211yescharacteristic
538Q8—68no—
539Q8—68no—
540Q8—188no—
541D4—68no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—34no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—32no—
548C2×C4—32no—
549C2×C4—34no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—94no—
555C2×C4—94no—
556C2×C4—1816no—
557C2×C4—184no—
558C2×C4—184no—
559C2×C4#379614yes—
560C2×C4C22×D3212yes—
561C2×C4C22×D3212yes—
562C2×C4C22×D3212yes—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—24no—
567C2×C3—124no—
568C2×C3#558414yescomplemented
569C2×C3#567114yescomplemented
570C2×C3C22×#23511yescharacteristic
571C2×C3C22×#23711yescharacteristic
572C2×C3C22×#23911yescharacteristic
573C2×C3C2×D3×#4111yescharacteristic
574C2×C3C2×#101011yescharacteristic
575C2×C3C2×#101011yescharacteristic
576D3—44no—
577C22—64no—
578C22—64no—
579C22—64no—
580C22—128no—
581C22C2×#379612yes—
582C22#6429812yes—
583C22D3×#23512yes—
584C22C23×D3211yescharacteristic
585C4—22no—
586C4—22no—
587C4—34no—
588C4—64no—
589C4—62no—
590C4—62no—
591C4—62no—
592C4—184no—
593C4—184no—
594C4C2×#379614yes—
595C3—21no—
596C3C2×#558411yescharacteristic, complemented
597C3C2×#567111yescharacteristic, complemented
598C2—124no—
599C2#1059393214yesdirect product factor
600C2C22×#379611yescharacteristic
601C2C2×#6429811yescharacteristic
602C2C2×D3×#23511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C2×C3×C4×Dic6C2semidirect
5. C2×#63887C2semidirect
6. C2×#63878C2semidirect
7. C2×#63866C2semidirect
8. C2×#63862C2semidirect
10. C2×#63858C2semidirect
11. C2×Dic3×Dic6C2semidirect
12. #10593932C2direct (N × H)
24. C4×#634C22semidirect
33. C3×C4×Dic6C22semidirect
42. #63887C22semidirect
43. #63878C22semidirect
44. #63866C22semidirect
45. #63862C22semidirect
47. #63858C22semidirect
48. Dic3×Dic6C22semidirect
73. C2×C4×Dic6D3semidirect
187. C4×Dic6C2×D3semidirect
443. C2×C32#556semidirect
532. C32C2×#556semidirect
568. C2×C3#5584semidirect
569. C2×C3#5671semidirect
596. C3C2×#5584semidirect
597. C3C2×#5671semidirect
599. C2#10593932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×#8752
C2×C3×C4×Dic62
C2×Dic3×D122
C2×#638872
C2×#638782
C2×#638662
C2×#638622
C2×#638602
C2×#638582
C2×Dic3×Dic62
#105939322
C2×#56713
C2×#55843