Finite Group Databasebeta

← C2×#10593855 #11901909

Subgroups — C2×#10593855 #11901909

Order 1152.

2325 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×C3×#870C211yesmaximal, characteristic, complemented
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×#63919C211yesmaximal, characteristic, complemented
5C2×#63900C211yesmaximal, characteristic
6C2×#63895C212yesmaximal
7C2×#63888C212yesmaximal
8C2×#63872C211yesmaximal, characteristic, complemented
9C2×#63849C211yesmaximal, characteristic
10C2×#63847C212yesmaximal, complemented
11C2×#63839C212yesmaximal, complemented
12#10593855C2116yesmaximal, direct product factor
13C2×#5729—31nomaximal
14C2×#5689—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C22×#627C2212yes—
18C22×#624C2212yes—
19C2×C32×C42C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64081C2218yes—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×Dic3⋊C4C2212yes—
33C3×#870C2218yescomplemented
34C3×#869C2218yescomplemented
35C2×#3724C2212yes—
36C2×#3724C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×#3722C2212yes—
40C2×Dic32C2212yes—
41#63919C2218yescomplemented
42#63900C2218yes—
43#63895C22116yes—
44#63888C22116yes—
45#63872C2218yescomplemented
46#63849C2218yes—
47#63847C22116yescomplemented
48#63839C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×#125—31no—
51C2×#946—32no—
52C2×#944—32no—
53#5729—316no—
54#5689—316no—
55C2×#897—32no—
56C2×#896—32no—
57C2×#896—32no—
58C2×#892—31no—
59C2×#892—31no—
60C2×D3×C4⋊C4—31no—
61C2×D3×C4⋊C4—31no—
62C2×#890—31no—
63C2×#890—31no—
64C2×#889—32no—
65C2×#889—32no—
66C2×#888—32no—
67C2×#888—31no—
68C2×#888—31no—
69C2×#872—31no—
70C2×#872—31no—
71C2×#872—61no—
72C2×#870D311yescharacteristic, complemented
73C2×#869D311yescharacteristic, complemented
74C23×C3⋊D3C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C2×C4×C3⋊D3Q818yescomplemented
82C2×C4×C3⋊D3C2314yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C2×C3×Dic6—44no—
88C2×C3×Dic6C2318yes—
89C2×#627—44no—
90C2×#627C2318yes—
91C2×#624—44no—
92C2×#624C2318yes—
93C32×C42C2314yes—
94#3752C2314yes—
95#3752C2314yes—
96#3750C2314yes—
97#3750C2314yes—
98C4×C3⋊Dic3C2314yes—
99C3×C4⋊Dic3C2318yes—
100C3×C4⋊Dic3C2314yes—
101C3×C4⋊Dic3C2314yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2314yes—
104C3×Dic3⋊C4C2318yes—
105C3×Dic3⋊C4C2318yes—
106#3724C2318yes—
107#3724C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110#3722C2318yes—
111Dic32C2318yes—
112C2×#544—91noSylow
113C22×C3×Q8—32no—
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×C4×D3—32no—
117C22×C4×D3—32no—
118C22×C4×D3—61no—
119C22×Dic6—32no—
120C22×Dic6—32no—
121C22×Dic6C2×D312yes—
122C3×C4⋊Q8—38no—
123C3×#125—38no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4—32no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—32no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C42—21no—
132C2×C3×C42C2×D311yescharacteristic
133C2×C3×C42C2×D311yescharacteristic
134#946—316no—
135#944—316no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—61no—
143C2×(C2×D3)⋊C4—61no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×C4⋊Dic3C2×D312yes—
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—61no—
162C2×Dic3⋊C4—61no—
163C2×Dic3⋊C4C2×D312yes—
164C2×Dic3⋊C4C2×D312yes—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—61no—
170#897—316no—
171#896—316no—
172#896—316no—
173#892—38no—
174#892—38no—
175D3×C4⋊C4—38no—
176D3×C4⋊C4—38no—
177#890—38no—
178#890—38no—
179#889—316no—
180#889—316no—
181#888—316no—
182#888—38no—
183#888—38no—
184#872—38no—
185#872—38no—
186#872—68no—
187#870C2×D318yescomplemented
188#869C2×D318yescomplemented
189C23×C32C2411yescharacteristic
190C22×C3⋊D3—22no—
191C22×C3⋊D3—22no—
192C22×C3⋊D3C2×Q814yes—
193C22×C3⋊D3C2412yes—
194C2×C32×C4—22no—
195C2×C32×C4—22no—
196C2×C32×C4C2×Q814yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199C2×C32×C4C2412yes—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3C2×Q814yes—
203C2×C3⋊Dic3C2412yes—
204C2×C3⋊Dic3C2412yes—
205C2×C3⋊Dic3C2412yes—
206C4×C3⋊D3C2×Q8116yescomplemented
207C2×C3×Dic3—24no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2414yes—
215C3×Dic6—48no—
216#627—48no—
217#624—48no—
218#544—916no—
219C2×C4⋊Q8—31no—
220C2×C4⋊Q8—91no—
221C2×C4⋊Q8—92no—
222C2×#125—31no—
223C2×#125—92no—
224C2×#125—91no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—92no—
227C2×#117—91no—
228C2×#117—91no—
229C22×C4⋊C4—91no—
230C23×D3—31no—
231C23×D3—31no—
232C23×D3—61no—
233C2×C3×Q8—38no—
234C2×C3×Q8—124no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—32no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×Dic3—31no—
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256C22×Dic3—61no—
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261C2×C4×D3—38no—
262C2×C4×D3—38no—
263C2×C4×D3—34no—
264C2×C4×D3—34no—
265C2×C4×D3—38no—
266C2×C4×D3—38no—
267C2×C4×D3—64no—
268C2×C4×D3—68no—
269C2×C4×D3—124no—
270C2×C4×D3—124no—
271C2×Dic6—38no—
272C2×Dic6—38no—
273C2×Dic6—44no—
274C2×Dic6—124no—
275C2×Dic6—124no—
276C2×Dic6C22×D318yes—
277C3×C4⋊C4—34no—
278C3×C4⋊C4—34no—
279C3×C4⋊C4—38no—
280C3×C4⋊C4—38no—
281C3×C4⋊C4—38no—
282C3×C4⋊C4—34no—
283C3×C4⋊C4—34no—
284C3×C42—24no—
285C3×C42C22×D314yes—
286C3×C42C22×D314yes—
287(C2×D3)⋊C4—34no—
288(C2×D3)⋊C4—34no—
289(C2×D3)⋊C4—34no—
290(C2×D3)⋊C4—34no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295C4⋊Dic3—38no—
296C4⋊Dic3—38no—
297C4⋊Dic3C22×D314yes—
298C4⋊Dic3C22×D318yes—
299C4⋊Dic3C22×D314yes—
300C4⋊Dic3C22×D314yes—
301C4⋊Dic3C22×D314yes—
302Dic3⋊C4—34no—
303Dic3⋊C4—34no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—64no—
313Dic3⋊C4—64no—
314Dic3⋊C4C22×D318yes—
315Dic3⋊C4C22×D318yes—
316C4×Dic3—34no—
317C4×Dic3—34no—
318C4×Dic3—38no—
319C4×Dic3—38no—
320C4×Dic3—64no—
321C22×C32C22×Q812yes—
322C22×C32H(5,𝔽2)12yes—
323C22×C322−1+412yes—
324C22×C32C2511yescharacteristic
325C2×C3⋊D3—28no—
326C2×C3⋊D3—22no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3C22×Q814yes—
329C32×C4—22no—
330C32×C4—22no—
331C32×C4C22×Q814yes—
332C3⋊Dic3—22no—
333C3⋊Dic3—22no—
334C3⋊Dic3C22×Q814yes—
335C3×Dic3—24no—
336C3×Dic3—24no—
337C3×Dic3—24no—
338C3×Dic3—24no—
339C22×Q8—32no—
340C22×Q8—92no—
341C23×C4—92no—
342C23×C4—91no—
343C4⋊Q8—38no—
344C4⋊Q8—98no—
345C4⋊Q8—916no—
346#125—38no—
347#125—916no—
348#125—98no—
349C22⋊Q8—916no—
350C22⋊Q8—916no—
351#117—98no—
352#117—98no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—98no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4—91no—
370C2×C42—92no—
371C2×C42—91no—
372C2×C42D3211yescharacteristic
373C23×C3—21no—
374C23×C3C23×D311yescharacteristic
375C23×C3C23×D311yescharacteristic
376C22×D3—34no—
377C22×D3—34no—
378C22×D3—32no—
379C22×D3—32no—
380C22×D3—64no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—122no—
387C22×D3—122no—
388C3×Q8—128no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—34no—
398C2×C3×C4—34no—
399C2×C3×C4—34no—
400C2×C3×C4—34no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—64no—
404C2×C3×C4—64no—
405C2×C3×C4—64no—
406C2×C3×C4—64no—
407C2×C3×C4D3×Q814yes—
408C2×C3×C4D3×Q814yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D312yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—24no—
419C2×Dic3—34no—
420C2×Dic3—34no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—64no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—122no—
436C2×Dic3—122no—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D314yes—
439C2×Dic3C23×D314yes—
440C2×Dic3C23×D314yes—
441C4×D3—316no—
442C4×D3—316no—
443C4×D3—616no—
444C4×D3—128no—
445C4×D3—128no—
446Dic6—48no—
447Dic6—128no—
448Dic6—128no—
449C2×C32#54414yescomplemented
450C2×C32C23×Q811yescharacteristic
451C2×C32C2×H(5,𝔽2)11yescharacteristic
452C2×C32C2×2−1+411yescharacteristic
453C3⋊D3—24no—
454C24—91no—
455C2×Q8—38no—
456C2×Q8—98no—
457C2×Q8—124no—
458C2×Q8—364no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—32no—
463C22×C4—98no—
464C22×C4—91no—
465C22×C4—94no—
466C22×C4—98no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—364no—
470C22×C4C2×D3211yescharacteristic
471C22×C4C2×D3211yescharacteristic
472C22×C4C2×D3211yescharacteristic
473C4⋊C4—34no—
474C4⋊C4—34no—
475C4⋊C4—34no—
476C4⋊C4—34no—
477C4⋊C4—38no—
478C4⋊C4—38no—
479C4⋊C4—38no—
480C4⋊C4—98no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—98no—
484C4⋊C4—94no—
485C4⋊C4—94no—
486C22⋊C4—98no—
487C22⋊C4—94no—
488C22⋊C4—94no—
489C42—98no—
490C42—94no—
491C42C2×D3214yes—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—21no—
496C22×C3#100412yes—
497C22×C3C2×D3×Q812yes—
498C22×C3C2×D3×Q812yes—
499C22×C3#100712yes—
500C22×C3#100912yes—
501C22×C3#101012yes—
502C22×C3C24×D311yescharacteristic
503C22×C3C24×D311yescharacteristic
504C2×D3—34no—
505C2×D3—34no—
506C2×D3—64no—
507C2×D3—68no—
508C2×D3—62no—
509C2×D3—62no—
510C2×D3—62no—
511C2×D3—62no—
512C2×D3—68no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—128no—
516C3×C4—22no—
517C3×C4—22no—
518C3×C4—22no—
519C3×C4—22no—
520C3×C4—24no—
521C3×C4—42no—
522C3×C4—42no—
523C3×C4—64no—
524C3×C4—64no—
525C3×C4—64no—
526C3×C4—64no—
527C3×C4C2×D3×Q814yes—
528C3×C4C2×D3×Q814yes—
529Dic3—24no—
530Dic3—24no—
531Dic3—24no—
532Dic3—24no—
533Dic3—34no—
534Dic3—34no—
535Dic3—64no—
536Dic3—62no—
537Dic3—62no—
538Dic3—62no—
539Dic3—62no—
540Dic3—122no—
541Dic3—122no—
542C32C2×#54411yescharacteristic, complemented, Sylow
543C23—94no—
544C23—92no—
545C23—182no—
546C23—182no—
547C23C22×D3211yescharacteristic
548Q8—128no—
549Q8—368no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—34no—
553C2×C4—34no—
554C2×C4—34no—
555C2×C4—34no—
556C2×C4—64no—
557C2×C4—64no—
558C2×C4—64no—
559C2×C4—64no—
560C2×C4—94no—
561C2×C4—92no—
562C2×C4—916no—
563C2×C4—92no—
564C2×C4—92no—
565C2×C4—182no—
566C2×C4—182no—
567C2×C4—368no—
568C2×C4#379714yes—
569C2×C4C22×D3212yes—
570C2×C4C22×D3212yes—
571C2×C4C22×D3212yes—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—24no—
576C2×C3#568914yescomplemented
577C2×C3#572914yescomplemented
578C2×C3C2×#100411yescharacteristic
579C2×C3C22×D3×Q811yescharacteristic
580C2×C3C22×D3×Q811yescharacteristic
581C2×C3C2×#100711yescharacteristic
582C2×C3C2×#100911yescharacteristic
583C2×C3C2×#101011yescharacteristic
584D3—64no—
585D3—64no—
586D3—124no—
587C22—94no—
588C22—182no—
589C22—182no—
590C22—188no—
591C22#6429712yes—
592C22C2×#379712yes—
593C22#6430712yes—
594C22C23×D3211yescharacteristic
595C4—22no—
596C4—22no—
597C4—64no—
598C4—64no—
599C4—64no—
600C4—64no—
601C4—94no—
602C4—182no—
603C4—182no—
604C4C2×#379714yes—
605C3—21no—
606C3C2×#568911yescharacteristic, complemented
607C3C2×#572911yescharacteristic, complemented
608C2—184no—
609C2#1059385514yesdirect product factor
610C2C2×#6429711yescharacteristic
611C2C22×#379711yescharacteristic
612C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#870C2semidirect
3. C2×C3×#869C2semidirect
4. C2×#63919C2semidirect
8. C2×#63872C2semidirect
10. C2×#63847C2semidirect
11. C2×#63839C2semidirect
12. #10593855C2direct (N × H)
33. C3×#870C22semidirect
34. C3×#869C22semidirect
41. #63919C22semidirect
45. #63872C22semidirect
47. #63847C22semidirect
48. #63839C22semidirect
72. C2×#870D3semidirect
73. C2×#869D3semidirect
81. C2×C4×C3⋊D3Q8semidirect
187. #870C2×D3semidirect
188. #869C2×D3semidirect
206. C4×C3⋊D3C2×Q8semidirect
449. C2×C32#544semidirect
542. C32C2×#544semidirect
576. C2×C3#5689semidirect
577. C2×C3#5729semidirect
606. C3C2×#5689semidirect
607. C3C2×#5729semidirect
609. C2#10593855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C3×#8702
C2×C3×#8692
C2×#639192
C2×#639002
C2×#638952
C2×#638882
C2×#638722
C2×#638492
C2×#638472
C2×#638392
#105938552
C2×#57293
C2×#56893