Finite Group Databasebeta

← C2×#10595389 #11903425

Subgroups — C2×#10595389 #11903425

Order 1152.

2369 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10595389C2116yesmaximal, direct product factor
5C2×C4×#627C211yesmaximal, characteristic, complemented
6C2×#63899C212yesmaximal, complemented
7C2×#63898C211yesmaximal, characteristic
8C2×#63877C212yesmaximal, complemented
9C2×#63860C211yesmaximal, characteristic
10C2×#63859C212yesmaximal, complemented
11C2×#63858C212yesmaximal, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×#5671—31nomaximal
14C2×#5568—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×#627C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20#64153C2218yescomplemented
21C2×#3750C2212yes—
22C2×#3750C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C3×#947C2218yes—
25C3×Q8×Dic3C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2212yes—
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×Dic32C2212yes—
41C4×#627C2218yescomplemented
42#63899C22116yescomplemented
43#63898C2218yes—
44#63877C22116yescomplemented
45#63860C2218yes—
46#63859C22116yescomplemented
47#63858C22116yescomplemented
48#63844C2218yescomplemented
49C2×C3×#124—31no—
50C2×C3×C4×Q8—31no—
51C2×#947D311yescharacteristic
52C2×Q8×Dic3D311yescharacteristic, complemented
53C2×#944—31no—
54C2×#944—31no—
55C2×#944—61no—
56C2×#936—31no—
57C2×D4×Dic3—31no—
58#5671—316no—
59#5568—316no—
60C2×#898—32no—
61C2×#896—32no—
62C2×#893—31no—
63C2×#887—31no—
64C2×#879—32no—
65C2×#879—32no—
66C2×#878—32no—
67C2×#877—32no—
68C2×#876—32no—
69C2×#875—31no—
70C2×#872—32no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C23×C3×D3C2312yes—
75C2×C32×Q8—24no—
76C2×C32×Q8C2314yes—
77C22×C32×C4C2312yes—
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C2×#634—24no—
83C2×#634C2314yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×D12—24no—
90C2×C3×D12C2314yes—
91C2×#627—24no—
92C2×#627C2314yes—
93C2×D3×Dic3—28no—
94C2×D3×Dic3C2318yes—
95#3750C2318yes—
96#3750C2318yes—
97C4×C3⋊Dic3C2314yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×(C2×D3)⋊C4C2318yes—
100C3×C4⋊Dic3C2314yes—
101C3×C4⋊Dic3C2318yes—
102C3×C4×Dic3C2318yes—
103C3×C4×Dic3C2314yes—
104C3×C4×Dic3C2314yes—
105#3724C2318yes—
106#3724C2314yes—
107Dic3⋊Dic3C2314yes—
108Dic3⋊Dic3C2314yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—21no—
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×D4—31no—
118C23×Dic3—32no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—32no—
121C22×Dic6—31no—
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—61no—
126C3×#124—38no—
127C3×C4×Q8—38no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C22⋊C4—32no—
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—
138#947C2×D318yes—
139Q8×Dic3C2×D318yescomplemented
140#944—38no—
141#944—38no—
142#944—68no—
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⋊Dic3C2×D311yescharacteristic
153C2×C4⋊Dic3C2×D312yes—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—62no—
165C2×Dic3⋊C4—62no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—61no—
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D311yescharacteristic
173C2×C4×Dic3C2×D312yes—
174#898—316no—
175#896—316no—
176#893—38no—
177#887—38no—
178#879—316no—
179#879—316no—
180#878—316no—
181#877—316no—
182#876—316no—
183#875—38no—
184#872—316no—
185C4×Dic6—38no—
186C4×Dic6—38no—
187C4×Dic6—38no—
188C23×C32C2411yescharacteristic
189C22×C3×D3—24no—
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2414yes—
193C32×Q8—28no—
194C2×C32×C4—24no—
195C2×C32×C4#4114yes—
196C2×C32×C4C2414yes—
197C2×C32×C4C2412yes—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3#4114yes—
201C2×C3⋊Dic3C2414yes—
202C2×C3⋊Dic3C2412yes—
203C2×C3⋊Dic3C2412yes—
204#634—28no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C3×D12—28no—
216#627—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—24no—
233C2×C3×Q8—24no—
234C2×C3×Q8—24no—
235C2×C3×Q8—44no—
236C2×C3×Q8C22×D314yes—
237C2×C3×Q8C22×D314yes—
238C2×C3×D4—34no—
239C2×C3×D4—64no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—31no—
243C22×C3×C4—32no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—32no—
256C22×Dic3—32no—
257C22×Dic3—38no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—62no—
261C22×Dic3—68no—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D311yescharacteristic
267C2×D12—24no—
268C2×D12C22×D314yes—
269C2×C4×D3—38no—
270C2×C4×D3—68no—
271C2×Dic6—34no—
272C2×Dic6—34no—
273C2×Dic6—34no—
274C2×Dic6—34no—
275C2×Dic6—64no—
276C2×Dic6—64no—
277C2×Dic6—64no—
278C2×Dic6—64no—
279C2×Dic6—64no—
280C2×Dic6—124no—
281C3×C4⋊C4—34no—
282C3×C4⋊C4—38no—
283C3×C22⋊C4—38no—
284C3×C22⋊C4—38no—
285C3×C42—34no—
286C3×C42—34no—
287C3×C42—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)⋊C4C22×D318yes—
295(C2×D3)⋊C4C22×D318yes—
296C4⋊Dic3—34no—
297C4⋊Dic3—34no—
298C4⋊Dic3C22×D314yes—
299C4⋊Dic3C22×D318yes—
300Dic3⋊C4—38no—
301Dic3⋊C4—38no—
302Dic3⋊C4—38no—
303Dic3⋊C4—38no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307Dic3⋊C4—38no—
308Dic3⋊C4—34no—
309Dic3⋊C4—38no—
310Dic3⋊C4—68no—
311Dic3⋊C4—68no—
312C4×Dic3—34no—
313C4×Dic3—34no—
314C4×Dic3—38no—
315C4×Dic3—38no—
316C4×Dic3—64no—
317C4×Dic3C22×D314yes—
318C4×Dic3C22×D314yes—
319C4×Dic3C22×D318yes—
320C22×C32C2×#4112yes—
321C22×C32C2×#4112yes—
322C22×C322−1+412yes—
323C22×C32C2511yescharacteristic
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—24no—
327C2×C3×D3—48no—
328C32×C4—24no—
329C32×C4C2×#4114yes—
330C3⋊Dic3—22no—
331C3⋊Dic3—24no—
332C3⋊Dic3C2×#4114yes—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3—22no—
338C22×Q8—91no—
339C22×Q8—91no—
340C22×Q8D3211yescharacteristic
341C22×D4—31no—
342C23×C4—92no—
343C4⋊Q8—98no—
344#126—916no—
345#126—916no—
346#124—38no—
347#124—98no—
348C22⋊Q8—916no—
349C4×Q8—38no—
350C4×Q8—98no—
351C4×Q8—98no—
352C4×D4—98no—
353#117—916no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—32no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—92no—
358C2×C4⋊C4—91no—
359C2×C4⋊C4—91no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—32no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C42—32no—
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—92no—
371C2×C42—91no—
372C23×C3—21no—
373C23×C3—34no—
374C23×C3—64no—
375C23×C3—64no—
376C23×C3—64no—
377C23×C3C23×D311yescharacteristic
378C23×C3C23×D311yescharacteristic
379C22×D3—24no—
380C22×D3—24no—
381C22×D3—24no—
382C22×D3C23×D314yes—
383C3×Q8—28no—
384C3×Q8—28no—
385C3×Q8—48no—
386C3×D4—68no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—32no—
393C2×C3×C4—34no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—44no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—64no—
402C2×C3×C4—62no—
403C2×C3×C4#23514yes—
404C2×C3×C4#23714yes—
405C2×C3×C4C23×D314yes—
406C2×C3×C4C23×D314yes—
407C2×C3×C4C23×D312yes—
408C2×C3×C4C23×D312yes—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—34no—
421C2×Dic3—34no—
422C2×Dic3—64no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—64no—
426C2×Dic3—616no—
427C2×Dic3—64no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—124no—
433C2×Dic3C23×D312yes—
434C2×Dic3C23×D314yes—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D312yes—
437C2×Dic3C23×D312yes—
438D12—28no—
439C4×D3—616no—
440Dic6—68no—
441Dic6—68no—
442Dic6—68no—
443Dic6—68no—
444Dic6—128no—
445C2×C32#55614yescomplemented
446C2×C32C22×#4111yescharacteristic
447C2×C32C22×#4111yescharacteristic
448C2×C32C2×2−1+411yescharacteristic
449C3×D3—44no—
450C24—32no—
451C2×Q8—24no—
452C2×Q8—94no—
453C2×Q8—94no—
454C2×Q8—184no—
455C2×Q8—184no—
456C2×Q8C2×D3214yes—
457C2×D4—34no—
458C2×D4—64no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—32no—
462C22×C4—31no—
463C22×C4—31no—
464C22×C4—98no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—92no—
468C22×C4—188no—
469C22×C4C2×D3212yes—
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—34no—
472C4⋊C4—38no—
473C4⋊C4—94no—
474C4⋊C4—98no—
475C4⋊C4—94no—
476C4⋊C4—94no—
477C4⋊C4—98no—
478C4⋊C4—98no—
479C22⋊C4—38no—
480C22⋊C4—38no—
481C22⋊C4—98no—
482C22⋊C4—98no—
483C22⋊C4—98no—
484C42—38no—
485C42—34no—
486C42—34no—
487C42—98no—
488C42—94no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—21no—
493C22×C3—64no—
494C22×C3—64no—
495C22×C3—64no—
496C22×C3—128no—
497C22×C3C2×#23512yes—
498C22×C3C2×#23712yes—
499C22×C3#100712yes—
500C22×C3D3×#4112yes—
501C22×C3D3×#4112yes—
502C22×C3#101012yes—
503C22×C3C24×D311yescharacteristic
504C22×C3C24×D311yescharacteristic
505C2×D3—24no—
506C2×D3—24no—
507C2×D3—24no—
508C2×D3—48no—
509C3×C4—24no—
510C3×C4—24no—
511C3×C4—24no—
512C3×C4—44no—
513C3×C4—62no—
514C3×C4—62no—
515C3×C4—62no—
516C3×C4—64no—
517C3×C4—62no—
518C3×C4C2×#23514yes—
519C3×C4C2×#23714yes—
520Dic3—22no—
521Dic3—22no—
522Dic3—22no—
523Dic3—24no—
524Dic3—22no—
525Dic3—34no—
526Dic3—34no—
527Dic3—64no—
528Dic3—64no—
529Dic3—64no—
530Dic3—64no—
531Dic3—62no—
532Dic3—62no—
533Dic3—124no—
534C32C2×#55611yescharacteristic, complemented, Sylow
535C23—34no—
536C23—64no—
537C23—64no—
538C23—64no—
539C23C22×D3211yescharacteristic
540Q8—28no—
541Q8—188no—
542Q8—188no—
543D4—68no—
544C2×C4—24no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—34no—
548C2×C4—32no—
549C2×C4—32no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—64no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—94no—
556C2×C4—92no—
557C2×C4—92no—
558C2×C4—94no—
559C2×C4—1816no—
560C2×C4—182no—
561C2×C4—184no—
562C2×C4#380414yes—
563C2×C4C22×D3214yes—
564C2×C4C22×D3212yes—
565C2×C3—24no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—124no—
570C2×C3#556814yescomplemented
571C2×C3#567114yescomplemented
572C2×C3C22×#23511yescharacteristic
573C2×C3C22×#23711yescharacteristic
574C2×C3C2×#100711yescharacteristic
575C2×C3C2×D3×#4111yescharacteristic
576C2×C3C2×D3×#4111yescharacteristic
577C2×C3C2×#101011yescharacteristic
578D3—44no—
579C22—64no—
580C22—64no—
581C22—64no—
582C22—128no—
583C22#6431512yes—
584C22#6431912yes—
585C22C2×#380412yes—
586C22C23×D3211yescharacteristic
587C4—24no—
588C4—62no—
589C4—62no—
590C4—64no—
591C4—62no—
592C4—62no—
593C4—94no—
594C4—182no—
595C4—184no—
596C4C2×#380414yes—
597C3—21no—
598C3C2×#556811yescharacteristic, complemented
599C3C2×#567111yescharacteristic, complemented
600C2—124no—
601C2#1059538914yesdirect product factor
602C2C2×#6431511yescharacteristic
603C2C2×#6431911yescharacteristic
604C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64153C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. #10595389C2direct (N × H)
5. C2×C4×#627C2semidirect
6. C2×#63899C2semidirect
8. C2×#63877C2semidirect
10. C2×#63859C2semidirect
11. C2×#63858C2semidirect
12. C2×#63844C2semidirect
20. #64153C22semidirect
25. C3×Q8×Dic3C22semidirect
41. C4×#627C22semidirect
42. #63899C22semidirect
44. #63877C22semidirect
46. #63859C22semidirect
47. #63858C22semidirect
48. #63844C22semidirect
52. C2×Q8×Dic3D3semidirect
139. Q8×Dic3C2×D3semidirect
445. C2×C32#556semidirect
534. C32C2×#556semidirect
570. C2×C3#5568semidirect
571. C2×C3#5671semidirect
598. C3C2×#5568semidirect
599. C3C2×#5671semidirect
601. C2#10595389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9472
C2×C3×Q8×Dic32
#105953892
C2×C4×#6272
C2×#638992
C2×#638982
C2×#638772
C2×#638602
C2×#638592
C2×#638582
C2×#638442
C2×#56713
C2×#55683