Finite Group Databasebeta

← C2×#10594557 #11903411

Subgroups — C2×#10594557 #11903411

Order 1152.

2389 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63907C212yesmaximal
5C2×C4×#626C211yesmaximal, characteristic
6C2×#63871C211yesmaximal, characteristic, complemented
7C2×#63862C212yesmaximal, complemented
8C2×#63848C212yesmaximal, complemented
9C2×#63843C212yesmaximal, complemented
10C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
11C2×#63841C211yesmaximal, characteristic, complemented
12#10594557C2116yesmaximal, direct product factor
13C2×#5732—31nomaximal
14C2×#5641—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C22×C3×Dic6C2212yes—
19C22×#626C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2212yes—
24#64101C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#897C2218yescomplemented
31C3×#888C2218yescomplemented
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×#3722C2211yescharacteristic
36C2×#3722C2212yes—
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×Dic32C2212yes—
40C2×Dic32C2212yes—
41#63907C22116yes—
42C4×#626C2218yes—
43#63871C2218yescomplemented
44#63862C22116yescomplemented
45#63848C22116yescomplemented
46#63843C22116yescomplemented
47Dic3×Dic6C2218yescomplemented
48#63841C2218yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×C22⋊Q8—31no—
51C2×#947—32no—
52C2×#946—31no—
53C2×Q8×Dic3—32no—
54C2×Q8×Dic3—31no—
55C2×C4×#67—31no—
56C2×#926—31no—
57#5732—316no—
58#5641—316no—
59C2×#898—32no—
60C2×#898—32no—
61C2×#898—32no—
62C2×#897—31no—
63C2×#897D311yescharacteristic, complemented
64C2×#892—31no—
65C2×#892—31no—
66C2×#892—31no—
67C2×#892—61no—
68C2×#888D311yescharacteristic, complemented
69C2×#887—32no—
70C2×#885—32no—
71C2×#879—32no—
72C2×C4×D12—31no—
73C2×C4×Dic6—31no—
74C23×C3⋊D3C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C2×C4×C3⋊D3—24no—
81C2×C4×C3⋊D3C2314yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3C2314yes—
89C2×C3×Dic6—24no—
90C2×C3×Dic6—28no—
91C2×C3×Dic6C2318yes—
92C2×C3×Dic6C2314yes—
93C2×#626—24no—
94C2×#626C2314yes—
95C32×C4⋊C4C2314yes—
96#3752C2318yes—
97C4⋊(C3⋊Dic3)C2314yes—
98C4×C3⋊Dic3C2318yes—
99C3×(C2×D3)⋊C4C2318yes—
100C3×C4⋊Dic3C2314yes—
101C3×C4⋊Dic3C2318yes—
102C3×Dic3⋊C4C2318yes—
103C3×C4×Dic3C2314yes—
104Dic3⋊Dic3C2318yes—
105Dic3⋊Dic3C2314yes—
106Dic3⋊Dic3C2318yes—
107#3722C2314yes—
108#3722C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2314yes—
111Dic32C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116C23×C3×C4—31no—
117C22×#67—31no—
118C22×D12—31no—
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—61no—
122C22×C4×D3C2×D311yescharacteristic
123C22×Dic6C2×D311yescharacteristic
124C22×Dic6C2×D312yes—
125C3×C4⋊Q8—38no—
126C3×C22⋊Q8—38no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C22⋊C4—32no—
134C2×C3×C42—31no—
135C2×#217—31no—
136C2×#217—32no—
137#947—316no—
138#946—38no—
139Q8×Dic3—316no—
140Q8×Dic3—38no—
141C4×#67—38no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—62no—
151C2×(C2×D3)⋊C4C2×D312yes—
152#926—38no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—32no—
157C2×C4⋊Dic3—32no—
158C2×C4⋊Dic3—61no—
159C2×C4⋊Dic3C2×D311yescharacteristic
160C2×C4⋊Dic3C2×D312yes—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4C2×D312yes—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—62no—
172C2×C4×Dic3C2×D311yescharacteristic
173#898—316no—
174#898—316no—
175#898—316no—
176#897—38no—
177#897C2×D318yescomplemented
178#892—38no—
179#892—38no—
180#892—38no—
181#892—68no—
182#888C2×D318yescomplemented
183#887—316no—
184#885—316no—
185#879—316no—
186C4×D12—38no—
187C4×Dic6—38no—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3C2412yes—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3C2412yes—
197C2×C32×C4—24no—
198C2×C32×C4#4114yes—
199C2×C32×C4C2414yes—
200C2×C32×C4C2412yes—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—24no—
203C2×C3⋊Dic3C2414yes—
204C2×C3⋊Dic3C2412yes—
205C4×C3⋊D3—28no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3#4114yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C3×C4×D3—28no—
217C3×Dic6—28no—
218C3×Dic6—216no—
219#626—28no—
220#556—916no—
221C2×C4⋊Q8—31no—
222C2×#126—92no—
223C2×#126—92no—
224C2×#124—92no—
225C2×C22⋊Q8—31no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×Q8—92no—
229C2×C4×D4—91no—
230C2×#117—91no—
231C2×#117—91no—
232C24×C3—31no—
233C23×D3—31no—
234C23×D3—31no—
235C23×D3—61no—
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—34no—
238C2×C3×Q8—38no—
239C2×C3×Q8—68no—
240C2×C3×Q8—64no—
241C22×C3×C4—21no—
242C22×C3×C4—22no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—32no—
246C22×C3×C4—32no—
247C22×C3×C4—31no—
248C22×C3×C4—34no—
249C22×C3×C4—64no—
250C22×C3×C4C22×D312yes—
251C22×C3×C4C22×D312yes—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—34no—
255C2×#67—64no—
256C22×Dic3—32no—
257C22×Dic3—32no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—61no—
261C22×Dic3—62no—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D311yescharacteristic
267C2×D12—34no—
268C2×D12—64no—
269C2×C4×D3—24no—
270C2×C4×D3—34no—
271C2×C4×D3—34no—
272C2×C4×D3—64no—
273C2×C4×D3—68no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3C22×D314yes—
277C2×Dic6—24no—
278C2×Dic6—28no—
279C2×Dic6C22×D314yes—
280C2×Dic6C22×D318yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—34no—
284C3×C4⋊C4—38no—
285C3×C4⋊C4C22×D314yes—
286C3×C4⋊C4C22×D314yes—
287C3×C22⋊C4—38no—
288C3×C42—34no—
289#217—34no—
290#217—38no—
291(C2×D3)⋊C4—34no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—34no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—68no—
300(C2×D3)⋊C4C22×D318yes—
301C4⋊Dic3—34no—
302C4⋊Dic3—34no—
303C4⋊Dic3—34no—
304C4⋊Dic3—38no—
305C4⋊Dic3—38no—
306C4⋊Dic3—64no—
307C4⋊Dic3C22×D314yes—
308C4⋊Dic3C22×D318yes—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—34no—
312Dic3⋊C4C22×D318yes—
313C4×Dic3—38no—
314C4×Dic3—38no—
315C4×Dic3—38no—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—38no—
319C4×Dic3—68no—
320C4×Dic3C22×D314yes—
321C22×C32C2×#4112yes—
322C22×C32C2×#4112yes—
323C22×C322−1+412yes—
324C22×C32C2511yescharacteristic
325C2×C3⋊D3—22no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—44no—
329C2×C3×D3—22no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—44no—
333C32×C4—24no—
334C32×C4C2×#4114yes—
335C3⋊Dic3—22no—
336C3⋊Dic3—24no—
337C3×Dic3—24no—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—22no—
341C3×Dic3C2×#4114yes—
342C22×Q8—31no—
343C22×Q8—32no—
344C22×D4—91no—
345C23×C4—31no—
346C23×C4—91no—
347C4⋊Q8—38no—
348#126—916no—
349#126—916no—
350#124—916no—
351C22⋊Q8—38no—
352C22⋊Q8—98no—
353C4×Q8—98no—
354C4×Q8—916no—
355C4×D4—98no—
356#117—98no—
357#117—98no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4D3211yescharacteristic
366C2×C22⋊C4—32no—
367C2×C22⋊C4—91no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—92no—
372C2×C42—31no—
373C2×C42—92no—
374C2×C42—92no—
375C2×C42—92no—
376C23×C3—21no—
377C23×C3—32no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3C23×D311yescharacteristic
382C23×C3C23×D311yescharacteristic
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—32no—
387C22×D3—32no—
388C22×D3—62no—
389C22×D3—64no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—122no—
397C22×D3—122no—
398C22×D3C23×D312yes—
399C3×Q8—616no—
400C3×Q8—68no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—34no—
407C2×C3×C4—32no—
408C2×C3×C4—32no—
409C2×C3×C4—34no—
410C2×C3×C4—34no—
411C2×C3×C4—32no—
412C2×C3×C4—44no—
413C2×C3×C4—62no—
414C2×C3×C4—64no—
415C2×C3×C4—62no—
416C2×C3×C4—64no—
417C2×C3×C4—68no—
418C2×C3×C4#23714yes—
419C2×C3×C4#23914yes—
420C2×C3×C4C23×D314yes—
421C2×C3×C4C23×D314yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D312yes—
424#67—68no—
425C2×Dic3—24no—
426C2×Dic3—24no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—34no—
430C2×Dic3—34no—
431C2×Dic3—32no—
432C2×Dic3—32no—
433C2×Dic3—62no—
434C2×Dic3—64no—
435C2×Dic3—64no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—64no—
439C2×Dic3—64no—
440C2×Dic3—124no—
441C2×Dic3#23714yes—
442C2×Dic3C23×D312yes—
443C2×Dic3C23×D314yes—
444C2×Dic3C23×D314yes—
445C2×Dic3C23×D312yes—
446C2×Dic3C23×D312yes—
447D12—68no—
448C4×D3—28no—
449C4×D3—616no—
450C4×D3—68no—
451C4×D3—68no—
452Dic6—28no—
453Dic6—216no—
454C2×C32#55614yescomplemented
455C2×C32C22×#4111yescharacteristic
456C2×C32C22×#4111yescharacteristic
457C2×C32C2×2−1+411yescharacteristic
458C3⋊D3—42no—
459C3×D3—42no—
460C24—31no—
461C24—91no—
462C2×Q8—34no—
463C2×Q8—38no—
464C2×Q8—68no—
465C2×Q8—64no—
466C2×D4—94no—
467C2×D4—184no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—34no—
474C22×C4—64no—
475C22×C4—92no—
476C22×C4—91no—
477C22×C4—94no—
478C22×C4—184no—
479C22×C4C2×D3212yes—
480C22×C4C2×D3211yescharacteristic
481C4⋊C4—34no—
482C4⋊C4—38no—
483C4⋊C4—38no—
484C4⋊C4—94no—
485C4⋊C4—98no—
486C4⋊C4—98no—
487C4⋊C4—94no—
488C4⋊C4C2×D3214yes—
489C22⋊C4—38no—
490C22⋊C4—94no—
491C22⋊C4—98no—
492C22⋊C4—98no—
493C22⋊C4—94no—
494C22⋊C4—98no—
495C42—34no—
496C42—98no—
497C42—98no—
498C42—98no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—62no—
504C22×C3—62no—
505C22×C3—62no—
506C22×C3—124no—
507C22×C3C2×#23712yes—
508C22×C3C2×#23712yes—
509C22×C3C2×#23912yes—
510C22×C3#100712yes—
511C22×C3#100712yes—
512C22×C3D3×#4112yes—
513C22×C3C24×D311yescharacteristic
514C22×C3C24×D311yescharacteristic
515C2×D3—22no—
516C2×D3—22no—
517C2×D3—22no—
518C2×D3—44no—
519C2×D3—64no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—128no—
529C2×D3—124no—
530C2×D3—124no—
531C3×C4—24no—
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—34no—
535C3×C4—44no—
536C3×C4—62no—
537C3×C4—64no—
538C3×C4—62no—
539C3×C4—64no—
540C3×C4C2×#23714yes—
541C3×C4C2×#23914yes—
542Dic3—24no—
543Dic3—24no—
544Dic3—22no—
545Dic3—22no—
546Dic3—64no—
547Dic3—62no—
548Dic3—62no—
549Dic3—64no—
550Dic3—64no—
551Dic3—124no—
552Dic3C2×#23714yes—
553C32C2×#55611yescharacteristic, complemented, Sylow
554C23—32no—
555C23—62no—
556C23—62no—
557C23—62no—
558C23—92no—
559C23—182no—
560C23—182no—
561C23—182no—
562C23C22×D3211yescharacteristic
563Q8—616no—
564Q8—68no—
565D4—188no—
566C2×C4—24no—
567C2×C4—34no—
568C2×C4—32no—
569C2×C4—32no—
570C2×C4—32no—
571C2×C4—34no—
572C2×C4—34no—
573C2×C4—62no—
574C2×C4—64no—
575C2×C4—64no—
576C2×C4—62no—
577C2×C4—68no—
578C2×C4—94no—
579C2×C4—92no—
580C2×C4—182no—
581C2×C4—184no—
582C2×C4—188no—
583C2×C4#379614yes—
584C2×C4C22×D3214yes—
585C2×C4C22×D3212yes—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—24no—
590C2×C3—122no—
591C2×C3#564114yescomplemented
592C2×C3#573214yescomplemented
593C2×C3C22×#23711yescharacteristic
594C2×C3C22×#23711yescharacteristic
595C2×C3C22×#23911yescharacteristic
596C2×C3C2×#100711yescharacteristic
597C2×C3C2×#100711yescharacteristic
598C2×C3C2×D3×#4111yescharacteristic
599D3—42no—
600D3—124no—
601D3—122no—
602D3—122no—
603C22—62no—
604C22—62no—
605C22—62no—
606C22—124no—
607C22—182no—
608C22—182no—
609C22—182no—
610C22—364no—
611C22C2×#379612yes—
612C22D3×#23712yes—
613C22#6431612yes—
614C22C23×D3211yescharacteristic
615C4—24no—
616C4—34no—
617C4—62no—
618C4—64no—
619C4—64no—
620C4—62no—
621C4—182no—
622C4—184no—
623C4C2×#379614yes—
624C3—21no—
625C3C2×#564111yescharacteristic, complemented
626C3C2×#573211yescharacteristic, complemented
627C2—122no—
628C2—362no—
629C2#1059455714yesdirect product factor
630C2C22×#379611yescharacteristic
631C2C2×D3×#23711yescharacteristic
632C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
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×#64101C2semidirect
2. C2×C3×#897C2semidirect
3. C2×C3×#888C2semidirect
6. C2×#63871C2semidirect
7. C2×#63862C2semidirect
8. C2×#63848C2semidirect
9. C2×#63843C2semidirect
10. C2×Dic3×Dic6C2semidirect
11. C2×#63841C2semidirect
12. #10594557C2direct (N × H)
24. #64101C22semidirect
30. C3×#897C22semidirect
31. C3×#888C22semidirect
43. #63871C22semidirect
44. #63862C22semidirect
45. #63848C22semidirect
46. #63843C22semidirect
47. Dic3×Dic6C22semidirect
48. #63841C22semidirect
63. C2×#897D3semidirect
68. C2×#888D3semidirect
177. #897C2×D3semidirect
182. #888C2×D3semidirect
454. C2×C32#556semidirect
553. C32C2×#556semidirect
591. C2×C3#5641semidirect
592. C2×C3#5732semidirect
625. C3C2×#5641semidirect
626. C3C2×#5732semidirect
629. C2#10594557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641012
C2×C3×#8972
C2×C3×#8882
C2×#639072
C2×C4×#6262
C2×#638712
C2×#638622
C2×#638482
C2×#638432
C2×Dic3×Dic62
C2×#638412
#105945572
C2×#57323
C2×#56413