Finite Group Databasebeta

← C2×#10594984 #11901682

Subgroups — C2×#10594984 #11901682

Order 1152.

2429 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C2×#63969C212yesmaximal, complemented
5C2×#63959C212yesmaximal, complemented
6C2×#63919C211yesmaximal, characteristic, complemented
7#10594984C2116yesmaximal, direct product factor
8C2×#63898C211yesmaximal, characteristic, complemented
9C2×#63893C212yesmaximal, complemented
10C2×#63863C211yesmaximal, characteristic, complemented
11C2×#63861C212yesmaximal, complemented
12C2×#63843C211yesmaximal, characteristic, complemented
13C2×#5643—31nomaximal
14C2×#5603—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×D12C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#627C2212yes—
20C22×D3×Dic3C2212yes—
21C2×#3757C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23#64135C2218yescomplemented
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×#217C2212yes—
29C3×#930C2218yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C3×#924C2218yescomplemented
34C2×C3×Dic3⋊C4C2212yes—
35#63969C22116yescomplemented
36C2×#3724C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63959C22116yescomplemented
42C2×Dic32C2212yes—
43#63919C2218yescomplemented
44#63898C2218yescomplemented
45#63893C22116yescomplemented
46#63863C2218yescomplemented
47#63861C22116yescomplemented
48#63843C2218yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×#121—31no—
51C2×#947—31no—
52C2×Q8×Dic3—31no—
53C2×#936—31no—
54C2×#936—32no—
55C2×#935—32no—
56C2×D4×Dic3—31no—
57C2×#930D311yescharacteristic
58C2×#926—31no—
59C2×#926—31no—
60C2×#926—61no—
61C2×#924D311yescharacteristic, complemented
62#5643—316no—
63#5603—316no—
64C2×#898—32no—
65C2×#897—32no—
66C2×#893—31no—
67C2×#888—31no—
68C2×#888—31no—
69C2×#887—31no—
70C2×#885—32no—
71C2×#883—32no—
72C2×#879—32no—
73C2×#878—32no—
74C24×C32C2311yescharacteristic
75C23×C3×D3C2312yes—
76C22×C32×C4—24no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2314yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C2×C3×#67—44no—
85C2×C3×#67C2318yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C2×C3×D12—24no—
90C2×C3×D12C2314yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#627—44no—
94C2×#627C2318yes—
95C2×D3×Dic3—44no—
96C2×D3×Dic3C2318yes—
97#3757C2314yes—
98#3757C2314yes—
99C4⋊(C3⋊Dic3)C2314yes—
100C4⋊(C3⋊Dic3)C2314yes—
101C4×C3⋊Dic3C2314yes—
102C4×C3⋊Dic3C2314yes—
103C3×#217C2318yes—
104C3×(C2×D3)⋊C4C2318yes—
105C3×C4⋊Dic3C2314yes—
106C3×C4⋊Dic3C2314yes—
107C3×Dic3⋊C4C2318yes—
108#3724C2318yes—
109Dic3⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113Dic32C2318yes—
114C2×#542—91noSylow
115C22×C3×Q8—31no—
116C22×C3×D4—32no—
117C22×C3×D4—31no—
118C23×C3×C4—21no—
119C23×C3×C4C2×D311yescharacteristic
120C23×C3×C4C2×D311yescharacteristic
121C22×#67C2×D312yes—
122C23×Dic3—32no—
123C22×D12C2×D311yescharacteristic
124C22×C4×D3—32no—
125C22×Dic6—32no—
126C22×Dic6—32no—
127C22×Dic6C2×D311yescharacteristic
128C3×C22⋊Q8—38no—
129C3×#121—38no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×#217—31no—
136C2×#217—31no—
137C2×#217—31no—
138C2×#217—31no—
139C2×#217—32no—
140C2×#217—32no—
141C2×#217—32no—
142C2×#217—61no—
143C2×#217—61no—
144C2×#217C2×D312yes—
145#947—38no—
146Q8×Dic3—38no—
147#936—38no—
148#936—316no—
149#935—316no—
150D4×Dic3—38no—
151#930C2×D318yes—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4C2×D312yes—
156#926—38no—
157#926—38no—
158#926—68no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—32no—
164C2×C4⋊Dic3—61no—
165C2×C4⋊Dic3—61no—
166C2×C4⋊Dic3C2×D311yescharacteristic
167C2×C4⋊Dic3C2×D311yescharacteristic
168#924C2×D318yescomplemented
169C2×Dic3⋊C4—32no—
170C2×Dic3⋊C4—32no—
171C2×Dic3⋊C4—32no—
172C2×Dic3⋊C4C2×D312yes—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—32no—
178C2×C4×Dic3—32no—
179C2×C4×Dic3—61no—
180C2×C4×Dic3—61no—
181#898—316no—
182#897—316no—
183#893—38no—
184#888—38no—
185#888—38no—
186#887—38no—
187#885—316no—
188#883—316no—
189#879—316no—
190#878—316no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—22no—
194C23×C32C2412yes—
195C23×C32C2411yescharacteristic
196C22×C3×D3—24no—
197C22×C3×D3—24no—
198C22×C3×D3—24no—
199C22×C3×D3C2414yes—
200C2×C32×C4—22no—
201C2×C32×C4—28no—
202C2×C32×C4#4114yes—
203C2×C32×C4C2412yes—
204C2×C32×C4C2412yes—
205C2×C3⋊Dic3—22no—
206C2×C3⋊Dic3—22no—
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3C2412yes—
210C2×C3⋊Dic3C2412yes—
211C2×C3⋊Dic3C2412yes—
212C2×C3⋊Dic3C2412yes—
213C3×#67—48no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—24no—
216C2×C3×Dic3—24no—
217C2×C3×Dic3C2414yes—
218C2×C3×Dic3C2414yes—
219C2×C3×Dic3C2414yes—
220C3×D12—28no—
221C3×Dic6—28no—
222#627—48no—
223D3×Dic3—48no—
224#542—916no—
225C2×C4⋊Q8—91no—
226C2×#126—92no—
227C2×#124—92no—
228C2×#124—91no—
229C2×#123—92no—
230C2×C22⋊Q8—31no—
231C2×C22⋊Q8—92no—
232C2×#121—31no—
233C2×C4×Q8—91no—
234C2×C4×D4—91no—
235C2×#117—91no—
236C24×C3—21no—
237C24×C3—32no—
238C24×C3C22×D311yescharacteristic
239C24×C3C22×D311yescharacteristic
240C23×D3C22×D312yes—
241C2×C3×Q8—34no—
242C2×C3×Q8—64no—
243C2×C3×D4—38no—
244C2×C3×D4—34no—
245C2×C3×D4—64no—
246C2×C3×D4—124no—
247C22×C3×C4—28no—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—24no—
253C22×C3×C4—32no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D314yes—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D314yes—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D311yescharacteristic
262C2×#67—44no—
263C2×#67C22×D318yes—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—38no—
273C22×Dic3—61no—
274C22×Dic3—61no—
275C22×Dic3—61no—
276C22×Dic3—61no—
277C22×Dic3—124no—
278C22×Dic3C22×D312yes—
279C22×Dic3C22×D312yes—
280C22×Dic3C22×D312yes—
281C2×D12—24no—
282C2×D12C22×D314yes—
283C2×C4×D3—38no—
284C2×C4×D3—124no—
285C2×Dic6—24no—
286C2×Dic6—38no—
287C2×Dic6—38no—
288C2×Dic6—124no—
289C2×Dic6—124no—
290C2×Dic6C22×D314yes—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4—38no—
294C3×C22⋊C4—38no—
295C3×C22⋊C4—38no—
296#217—34no—
297#217—34no—
298#217—34no—
299#217—34no—
300#217—38no—
301#217—38no—
302#217—38no—
303#217—64no—
304#217—64no—
305#217C22×D318yes—
306(C2×D3)⋊C4—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—38no—
309(C2×D3)⋊C4C22×D318yes—
310C4⋊Dic3—34no—
311C4⋊Dic3—34no—
312C4⋊Dic3—34no—
313C4⋊Dic3—34no—
314C4⋊Dic3—38no—
315C4⋊Dic3—64no—
316C4⋊Dic3—64no—
317C4⋊Dic3C22×D314yes—
318C4⋊Dic3C22×D314yes—
319Dic3⋊C4—38no—
320Dic3⋊C4—38no—
321Dic3⋊C4—38no—
322Dic3⋊C4C22×D318yes—
323C4×Dic3—34no—
324C4×Dic3—34no—
325C4×Dic3—34no—
326C4×Dic3—34no—
327C4×Dic3—38no—
328C4×Dic3—38no—
329C4×Dic3—64no—
330C4×Dic3—64no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—44no—
335C22×C32C2×#4112yes—
336C22×C32H(5,𝔽2)12yes—
337C22×C322−1+412yes—
338C22×C32C2511yescharacteristic
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—24no—
342C2×C3×D3—48no—
343C32×C4—22no—
344C32×C4C2×#4114yes—
345C3⋊Dic3—22no—
346C3⋊Dic3—22no—
347C3⋊Dic3—22no—
348C3⋊Dic3—22no—
349C3×Dic3—24no—
350C3×Dic3—24no—
351C3×Dic3—24no—
352C22×Q8—31no—
353C22×Q8—92no—
354C22×D4—32no—
355C22×D4—31no—
356C23×C4—92no—
357C23×C4D3211yescharacteristic
358C4⋊Q8—98no—
359#126—916no—
360#124—916no—
361#124—98no—
362#123—916no—
363C22⋊Q8—38no—
364C22⋊Q8—916no—
365#121—38no—
366C4×Q8—98no—
367C4×D4—98no—
368#117—98no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—92no—
373C2×C4⋊C4—92no—
374C2×C4⋊C4—91no—
375C2×C4⋊C4—91no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—92no—
379C2×C22⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C22⋊C4—91no—
382C2×C22⋊C4—91no—
383C2×C42—92no—
384C2×C42—91no—
385C2×C42—91no—
386C23×C3—24no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—34no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—64no—
399C23×C3—64no—
400C23×C3—64no—
401C23×C3C23×D312yes—
402C23×C3C23×D312yes—
403C23×C3C23×D311yescharacteristic
404C23×C3C23×D311yescharacteristic
405C22×D3—24no—
406C22×D3—24no—
407C22×D3—24no—
408C22×D3C23×D314yes—
409C3×Q8—68no—
410C3×D4—68no—
411C3×D4—128no—
412C2×C3×C4—24no—
413C2×C3×C4—216no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—28no—
417C2×C3×C4—28no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—24no—
421C2×C3×C4—34no—
422C2×C3×C4—34no—
423C2×C3×C4—34no—
424C2×C3×C4—64no—
425C2×C3×C4—64no—
426C2×C3×C4—64no—
427C2×C3×C4#23714yes—
428C2×C3×C4#23714yes—
429C2×C3×C4C23×D312yes—
430C2×C3×C4C23×D312yes—
431C2×C3×C4C23×D312yes—
432C2×C3×C4C23×D312yes—
433#67—48no—
434C2×Dic3—24no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—32no—
440C2×Dic3—32no—
441C2×Dic3—32no—
442C2×Dic3—32no—
443C2×Dic3—32no—
444C2×Dic3—32no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—122no—
458C2×Dic3—122no—
459C2×Dic3—122no—
460C2×Dic3—122no—
461C2×Dic3—128no—
462C2×Dic3C23×D314yes—
463C2×Dic3C23×D314yes—
464C2×Dic3C23×D314yes—
465D12—28no—
466C4×D3—128no—
467Dic6—28no—
468Dic6—128no—
469Dic6—128no—
470C2×C32—42no—
471C2×C32#54214yescomplemented
472C2×C32C22×#4111yescharacteristic
473C2×C32C2×H(5,𝔽2)11yescharacteristic
474C2×C32C2×2−1+411yescharacteristic
475C3×D3—44no—
476C24—32no—
477C24C2×D3211yescharacteristic
478C2×Q8—34no—
479C2×Q8—64no—
480C2×Q8—98no—
481C2×Q8—364no—
482C2×D4—38no—
483C2×D4—34no—
484C2×D4—64no—
485C2×D4—124no—
486C22×C4—24no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—32no—
490C22×C4—98no—
491C22×C4—91no—
492C22×C4—91no—
493C22×C4—91no—
494C22×C4—91no—
495C22×C4—364no—
496C22×C4C2×D3214yes—
497C22×C4C2×D3211yescharacteristic
498C22×C4C2×D3211yescharacteristic
499C4⋊C4—34no—
500C4⋊C4—34no—
501C4⋊C4—38no—
502C4⋊C4—98no—
503C4⋊C4—98no—
504C4⋊C4—94no—
505C4⋊C4—94no—
506C22⋊C4—38no—
507C22⋊C4—38no—
508C22⋊C4—98no—
509C22⋊C4—98no—
510C22⋊C4—98no—
511C22⋊C4—94no—
512C22⋊C4—94no—
513C42—98no—
514C42—94no—
515C42—94no—
516C22×C3—24no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—21no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—48no—
530C22×C3—44no—
531C22×C3—44no—
532C22×C3—64no—
533C22×C3—64no—
534C22×C3—64no—
535C22×C3—128no—
536C22×C3C2×#23712yes—
537C22×C3C2×#23712yes—
538C22×C3#100412yes—
539C22×C3#100712yes—
540C22×C3#100912yes—
541C22×C3#101012yes—
542C22×C3C24×D311yescharacteristic
543C22×C3C24×D311yescharacteristic
544C2×D3—24no—
545C2×D3—24no—
546C2×D3—24no—
547C2×D3—48no—
548C3×C4—24no—
549C3×C4—22no—
550C3×C4—22no—
551C3×C4—24no—
552C3×C4—64no—
553C3×C4—64no—
554C3×C4—64no—
555C3×C4C2×#23714yes—
556C3×C4C2×#23714yes—
557Dic3—24no—
558Dic3—24no—
559Dic3—24no—
560Dic3—62no—
561Dic3—62no—
562Dic3—62no—
563Dic3—62no—
564Dic3—62no—
565Dic3—62no—
566Dic3—62no—
567Dic3—62no—
568Dic3—122no—
569Dic3—122no—
570Dic3—122no—
571Dic3—122no—
572C32C2×#54211yescharacteristic, complemented, Sylow
573C23—22no—
574C23—22no—
575C23—22no—
576C23—34no—
577C23—64no—
578C23—64no—
579C23—64no—
580C23C22×D3212yes—
581C23C22×D3211yescharacteristic
582Q8—68no—
583Q8—368no—
584D4—68no—
585D4—128no—
586C2×C4—22no—
587C2×C4—28no—
588C2×C4—34no—
589C2×C4—34no—
590C2×C4—34no—
591C2×C4—64no—
592C2×C4—64no—
593C2×C4—64no—
594C2×C4—92no—
595C2×C4—92no—
596C2×C4—92no—
597C2×C4—92no—
598C2×C4—182no—
599C2×C4—182no—
600C2×C4—182no—
601C2×C4—182no—
602C2×C4—368no—
603C2×C4#380514yes—
604C2×C4C22×D3212yes—
605C2×C4C22×D3212yes—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—24no—
610C2×C3—44no—
611C2×C3—42no—
612C2×C3—42no—
613C2×C3—124no—
614C2×C3#560314yescomplemented
615C2×C3#564314yescomplemented
616C2×C3C22×#23711yescharacteristic
617C2×C3C22×#23711yescharacteristic
618C2×C3C2×#100411yescharacteristic
619C2×C3C2×#100711yescharacteristic
620C2×C3C2×#100911yescharacteristic
621C2×C3C2×#101011yescharacteristic
622D3—44no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—44no—
627C22—64no—
628C22—64no—
629C22—64no—
630C22—128no—
631C22#6429712yes—
632C22#6430712yes—
633C22C2×#380512yes—
634C22C23×D3211yescharacteristic
635C4—22no—
636C4—64no—
637C4—64no—
638C4—64no—
639C4—182no—
640C4—182no—
641C4—182no—
642C4—182no—
643C4C2×#380514yes—
644C3—21no—
645C3C2×#560311yescharacteristic, complemented
646C3C2×#564311yescharacteristic, complemented
647C2—42no—
648C2—124no—
649C2#1059498414yesdirect product factor
650C2C2×#6429711yescharacteristic
651C2C2×#6430711yescharacteristic
652C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
3. C2×C3×#924C2semidirect
4. C2×#63969C2semidirect
5. C2×#63959C2semidirect
6. C2×#63919C2semidirect
7. #10594984C2direct (N × H)
8. C2×#63898C2semidirect
9. C2×#63893C2semidirect
10. C2×#63863C2semidirect
11. C2×#63861C2semidirect
12. C2×#63843C2semidirect
23. #64135C22semidirect
33. C3×#924C22semidirect
35. #63969C22semidirect
41. #63959C22semidirect
43. #63919C22semidirect
44. #63898C22semidirect
45. #63893C22semidirect
46. #63863C22semidirect
47. #63861C22semidirect
48. #63843C22semidirect
61. C2×#924D3semidirect
168. #924C2×D3semidirect
471. C2×C32#542semidirect
572. C32C2×#542semidirect
614. C2×C3#5603semidirect
615. C2×C3#5643semidirect
645. C3C2×#5603semidirect
646. C3C2×#5643semidirect
649. C2#10594984direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×#9302
C2×C3×#9242
C2×#639692
C2×#639592
C2×#639192
#105949842
C2×#638982
C2×#638932
C2×#638632
C2×#638612
C2×#638432
C2×#56433
C2×#56033