Finite Group Databasebeta

← C2×#10594983 #11901683

Subgroups — C2×#10594983 #11901683

Order 1152.

2425 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#63969C212yesmaximal, complemented
5C2×#63959C212yesmaximal, complemented
6C2×#63918C211yesmaximal, characteristic, complemented
7#10594983C2116yesmaximal, direct product factor
8C2×#63899C212yesmaximal, complemented
9C2×Dic3×D12C211yesmaximal, characteristic, complemented
10C2×#63860C211yesmaximal, characteristic, complemented
11C2×#63858C212yesmaximal, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×#5603—31nomaximal
14C2×#5534—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×D12C2211yescharacteristic
19C22×#627C2212yes—
20C22×D3×Dic3C2212yes—
21C2×#3757C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23#64133C2218yescomplemented
24C2×#3750C2212yes—
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C3×#930C2218yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C3×#926C2218yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35#63969C22116yescomplemented
36C2×#3724C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63959C22116yescomplemented
42C2×Dic32C2212yes—
43#63918C2218yescomplemented
44#63899C22116yescomplemented
45Dic3×D12C2218yescomplemented
46#63860C2218yescomplemented
47#63858C22116yescomplemented
48#63844C2218yescomplemented
49C2×C3×#121—31no—
50C2×C3×#117—31no—
51C2×#936—32no—
52C2×#936—31no—
53C2×#935—32no—
54C2×D4×Dic3—31no—
55C2×#930D311yescharacteristic
56C2×#926D311yescharacteristic, complemented
57C2×#924—31no—
58C2×#924—31no—
59C2×#924—61no—
60#5603—316no—
61#5534—316no—
62C2×#898—32no—
63C2×#896—32no—
64C2×#888—31no—
65C2×#887—31no—
66C2×#885—32no—
67C2×#883—32no—
68C2×#879—32no—
69C2×#878—32no—
70C2×#875—31no—
71C2×C4×D12—31no—
72C2×#869—31no—
73C2×C4×Dic6—31no—
74C24×C32C2311yescharacteristic
75C23×C3×D3C2312yes—
76C22×C32×C4—24no—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2314yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2312yes—
82C2×#634—24no—
83C2×#634C2314yes—
84C2×C3×#67—44no—
85C2×C3×#67C2318yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C2×C3×D12—24no—
92C2×C3×D12C2314yes—
93C2×#627—44no—
94C2×#627C2318yes—
95C2×D3×Dic3—44no—
96C2×D3×Dic3C2318yes—
97#3757C2318yes—
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2318yes—
100C3×#217C2314yes—
101C3×#217C2314yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4⋊Dic3C2314yes—
105C3×C4⋊Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107C3×C4×Dic3C2314yes—
108#3724C2318yes—
109Dic3⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113Dic32C2318yes—
114C2×#542—91noSylow
115C22×C3×D4—32no—
116C22×C3×D4—31no—
117C23×C3×C4—21no—
118C23×C3×C4C2×D311yescharacteristic
119C23×C3×C4C2×D311yescharacteristic
120C22×#67C2×D312yes—
121C23×Dic3—32no—
122C22×D12C2×D311yescharacteristic
123C22×C4×D3—32no—
124C22×Dic6—31no—
125C22×Dic6—31no—
126C22×Dic6—32no—
127C22×Dic6—32no—
128C22×Dic6—61no—
129C3×#121—38no—
130C3×#117—38no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C42—31no—
138C2×C3×C42—31no—
139C2×#217—32no—
140C2×#217—32no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—62no—
145C2×#217C2×D311yescharacteristic
146C2×#217C2×D311yescharacteristic
147#936—316no—
148#936—38no—
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#926C2×D318yescomplemented
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—32no—
160C2×C4⋊Dic3—61no—
161C2×C4⋊Dic3C2×D311yescharacteristic
162C2×C4⋊Dic3C2×D311yescharacteristic
163C2×C4⋊Dic3C2×D311yescharacteristic
164#924—38no—
165#924—38no—
166#924—68no—
167C2×Dic3⋊C4—32no—
168C2×Dic3⋊C4—32no—
169C2×Dic3⋊C4—32no—
170C2×Dic3⋊C4—32no—
171C2×Dic3⋊C4—32no—
172C2×Dic3⋊C4—62no—
173C2×C4×Dic3—32no—
174C2×C4×Dic3—32no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#898—316no—
178#896—316no—
179#888—38no—
180#887—38no—
181#885—316no—
182#883—316no—
183#879—316no—
184#878—316no—
185#875—38no—
186C4×D12—38no—
187#869—38no—
188C4×Dic6—38no—
189C23×C32—22no—
190C23×C32—22no—
191C23×C32—22no—
192C23×C32C2412yes—
193C23×C32C2411yescharacteristic
194C22×C3×D3—24no—
195C22×C3×D3—24no—
196C22×C3×D3—24no—
197C22×C3×D3C2414yes—
198C2×C32×C4—22no—
199C2×C32×C4—28no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2412yes—
202C2×C32×C4C2412yes—
203C2×C3⋊Dic3—24no—
204C2×C3⋊Dic3—24no—
205C2×C3⋊Dic3C2414yes—
206C2×C3⋊Dic3C2414yes—
207#634—28no—
208C3×#67—48no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2412yes—
219C3×D12—28no—
220#627—48no—
221D3×Dic3—48no—
222#542—916no—
223C2×C4⋊Q8—91no—
224C2×#126—92no—
225C2×#124—91no—
226C2×#124—92no—
227C2×#123—92no—
228C2×C22⋊Q8—92no—
229C2×C22⋊Q8—91no—
230C2×#121—31no—
231C2×C4×Q8—91no—
232C2×C4×D4—91no—
233C2×#117—31no—
234C24×C3—21no—
235C24×C3—32no—
236C24×C3C22×D311yescharacteristic
237C24×C3C22×D311yescharacteristic
238C23×D3C22×D312yes—
239C2×C3×D4—38no—
240C2×C3×D4—34no—
241C2×C3×D4—64no—
242C2×C3×D4—124no—
243C22×C3×C4—24no—
244C22×C3×C4—24no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—24no—
248C22×C3×C4—31no—
249C22×C3×C4—32no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—44no—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D314yes—
257C22×C3×C4C22×D314yes—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C2×#67—44no—
261C2×#67C22×D318yes—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—32no—
265C22×Dic3—32no—
266C22×Dic3—38no—
267C22×Dic3—62no—
268C22×Dic3—62no—
269C22×Dic3—124no—
270C22×Dic3C22×D311yescharacteristic
271C22×Dic3C22×D312yes—
272C22×Dic3C22×D311yescharacteristic
273C22×Dic3C22×D311yescharacteristic
274C22×Dic3C22×D311yescharacteristic
275C2×D12—24no—
276C2×D12C22×D314yes—
277C2×C4×D3—38no—
278C2×C4×D3—124no—
279C2×Dic6—34no—
280C2×Dic6—34no—
281C2×Dic6—38no—
282C2×Dic6—38no—
283C2×Dic6—64no—
284C2×Dic6—64no—
285C2×Dic6—64no—
286C2×Dic6—124no—
287C2×Dic6—124no—
288C2×Dic6—124no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—34no—
291C3×C4⋊C4—34no—
292C3×C22⋊C4—34no—
293C3×C22⋊C4—34no—
294C3×C22⋊C4—38no—
295C3×C42—34no—
296C3×C42—34no—
297#217—38no—
298#217—38no—
299#217—38no—
300#217—38no—
301#217—38no—
302#217—68no—
303#217C22×D314yes—
304#217C22×D314yes—
305(C2×D3)⋊C4—38no—
306(C2×D3)⋊C4—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4C22×D318yes—
309C4⋊Dic3—34no—
310C4⋊Dic3—34no—
311C4⋊Dic3—38no—
312C4⋊Dic3—64no—
313C4⋊Dic3C22×D314yes—
314C4⋊Dic3C22×D314yes—
315C4⋊Dic3C22×D314yes—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—38no—
319Dic3⋊C4—38no—
320Dic3⋊C4—38no—
321Dic3⋊C4—68no—
322C4×Dic3—38no—
323C4×Dic3—38no—
324C4×Dic3C22×D314yes—
325C4×Dic3C22×D314yes—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—44no—
330C22×C32C2×#4112yes—
331C22×C32H(5,𝔽2)12yes—
332C22×C322−1+412yes—
333C22×C32C2511yescharacteristic
334C2×C3×D3—24no—
335C2×C3×D3—24no—
336C2×C3×D3—24no—
337C2×C3×D3—48no—
338C32×C4—22no—
339C32×C4C2×#4114yes—
340C3⋊Dic3—24no—
341C3⋊Dic3—24no—
342C3×Dic3—22no—
343C3×Dic3—22no—
344C3×Dic3—24no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C22×Q8—92no—
348C22×Q8—91no—
349C22×D4—32no—
350C22×D4—31no—
351C23×C4—92no—
352C23×C4D3211yescharacteristic
353C4⋊Q8—98no—
354#126—916no—
355#124—98no—
356#124—916no—
357#123—916no—
358C22⋊Q8—916no—
359C22⋊Q8—98no—
360#121—38no—
361C4×Q8—98no—
362C4×D4—98no—
363#117—38no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—92no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—92no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C42—31no—
379C2×C42—31no—
380C2×C42—92no—
381C23×C3—24no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—21no—
390C23×C3—34no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—64no—
394C23×C3—64no—
395C23×C3—64no—
396C23×C3C23×D312yes—
397C23×C3C23×D312yes—
398C23×C3C23×D311yescharacteristic
399C23×C3C23×D311yescharacteristic
400C22×D3—24no—
401C22×D3—24no—
402C22×D3—24no—
403C22×D3C23×D314yes—
404C3×D4—68no—
405C3×D4—128no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—28no—
409C2×C3×C4—28no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—24no—
413C2×C3×C4—32no—
414C2×C3×C4—34no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—48no—
419C2×C3×C4—42no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—64no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4#23514yes—
426C2×C3×C4#23714yes—
427C2×C3×C4C23×D312yes—
428C2×C3×C4C23×D312yes—
429C2×C3×C4C23×D312yes—
430C2×C3×C4C23×D312yes—
431#67—48no—
432C2×Dic3—24no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—34no—
438C2×Dic3—34no—
439C2×Dic3—34no—
440C2×Dic3—34no—
441C2×Dic3—64no—
442C2×Dic3—64no—
443C2×Dic3—64no—
444C2×Dic3—64no—
445C2×Dic3—64no—
446C2×Dic3—64no—
447C2×Dic3—124no—
448C2×Dic3—124no—
449C2×Dic3—128no—
450C2×Dic3C23×D312yes—
451C2×Dic3C23×D314yes—
452C2×Dic3C23×D312yes—
453C2×Dic3C23×D312yes—
454C2×Dic3C23×D312yes—
455D12—28no—
456C4×D3—128no—
457Dic6—68no—
458Dic6—68no—
459Dic6—128no—
460Dic6—128no—
461Dic6—128no—
462C2×C32—42no—
463C2×C32#54214yescomplemented
464C2×C32C22×#4111yescharacteristic
465C2×C32C2×H(5,𝔽2)11yescharacteristic
466C2×C32C2×2−1+411yescharacteristic
467C3×D3—44no—
468C24—32no—
469C24C2×D3211yescharacteristic
470C2×Q8—98no—
471C2×Q8—94no—
472C2×Q8—184no—
473C2×Q8—364no—
474C2×D4—38no—
475C2×D4—34no—
476C2×D4—64no—
477C2×D4—124no—
478C22×C4—24no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—32no—
484C22×C4—98no—
485C22×C4—92no—
486C22×C4—92no—
487C22×C4—364no—
488C22×C4C2×D3214yes—
489C22×C4C2×D3211yescharacteristic
490C22×C4C2×D3211yescharacteristic
491C4⋊C4—34no—
492C4⋊C4—34no—
493C4⋊C4—34no—
494C4⋊C4—98no—
495C4⋊C4—98no—
496C4⋊C4—94no—
497C4⋊C4—98no—
498C22⋊C4—34no—
499C22⋊C4—34no—
500C22⋊C4—38no—
501C22⋊C4—98no—
502C22⋊C4—98no—
503C22⋊C4—98no—
504C22⋊C4—98no—
505C42—34no—
506C42—34no—
507C42—98no—
508C22×C3—24no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—48no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—64no—
525C22×C3—64no—
526C22×C3—64no—
527C22×C3—128no—
528C22×C3C2×#23512yes—
529C22×C3C2×#23712yes—
530C22×C3#100412yes—
531C22×C3#100912yes—
532C22×C3#101012yes—
533C22×C3#101012yes—
534C22×C3C24×D311yescharacteristic
535C22×C3C24×D311yescharacteristic
536C2×D3—24no—
537C2×D3—24no—
538C2×D3—24no—
539C2×D3—48no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—24no—
543C3×C4—42no—
544C3×C4—62no—
545C3×C4—62no—
546C3×C4—64no—
547C3×C4—62no—
548C3×C4—62no—
549C3×C4C2×#23514yes—
550C3×C4C2×#23714yes—
551Dic3—24no—
552Dic3—22no—
553Dic3—22no—
554Dic3—22no—
555Dic3—22no—
556Dic3—64no—
557Dic3—64no—
558Dic3—64no—
559Dic3—64no—
560Dic3—124no—
561Dic3—124no—
562C32C2×#54211yescharacteristic, complemented, Sylow
563C23—22no—
564C23—22no—
565C23—22no—
566C23—34no—
567C23—64no—
568C23—64no—
569C23—64no—
570C23C22×D3212yes—
571C23C22×D3211yescharacteristic
572Q8—188no—
573Q8—368no—
574D4—68no—
575D4—128no—
576C2×C4—22no—
577C2×C4—28no—
578C2×C4—32no—
579C2×C4—32no—
580C2×C4—32no—
581C2×C4—32no—
582C2×C4—34no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—64no—
587C2×C4—62no—
588C2×C4—94no—
589C2×C4—94no—
590C2×C4—184no—
591C2×C4—184no—
592C2×C4—368no—
593C2×C4#380414yes—
594C2×C4C22×D3212yes—
595C2×C4C22×D3212yes—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—24no—
600C2×C3—44no—
601C2×C3—42no—
602C2×C3—42no—
603C2×C3—124no—
604C2×C3#553414yescomplemented
605C2×C3#560314yescomplemented
606C2×C3C22×#23511yescharacteristic
607C2×C3C22×#23711yescharacteristic
608C2×C3C2×#100411yescharacteristic
609C2×C3C2×#100911yescharacteristic
610C2×C3C2×#101011yescharacteristic
611C2×C3C2×#101011yescharacteristic
612D3—44no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—44no—
617C22—64no—
618C22—64no—
619C22—64no—
620C22—128no—
621C22#6429812yes—
622C22#6430712yes—
623C22C2×#380412yes—
624C22C23×D3211yescharacteristic
625C4—22no—
626C4—62no—
627C4—62no—
628C4—62no—
629C4—64no—
630C4—62no—
631C4—184no—
632C4—184no—
633C4C2×#380414yes—
634C3—21no—
635C3C2×#553411yescharacteristic, complemented
636C3C2×#560311yescharacteristic, complemented
637C2—42no—
638C2—124no—
639C2#1059498314yesdirect product factor
640C2C2×#6429811yescharacteristic
641C2C2×#6430711yescharacteristic
642C2C22×#380411yescharacteristic
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×#64133C2semidirect
3. C2×C3×#926C2semidirect
4. C2×#63969C2semidirect
5. C2×#63959C2semidirect
6. C2×#63918C2semidirect
7. #10594983C2direct (N × H)
8. C2×#63899C2semidirect
9. C2×Dic3×D12C2semidirect
10. C2×#63860C2semidirect
11. C2×#63858C2semidirect
12. C2×#63844C2semidirect
23. #64133C22semidirect
29. C3×#926C22semidirect
35. #63969C22semidirect
41. #63959C22semidirect
43. #63918C22semidirect
44. #63899C22semidirect
45. Dic3×D12C22semidirect
46. #63860C22semidirect
47. #63858C22semidirect
48. #63844C22semidirect
56. C2×#926D3semidirect
156. #926C2×D3semidirect
463. C2×C32#542semidirect
562. C32C2×#542semidirect
604. C2×C3#5534semidirect
605. C2×C3#5603semidirect
635. C3C2×#5534semidirect
636. C3C2×#5603semidirect
639. C2#10594983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9302
C2×C3×#9262
C2×#639692
C2×#639592
C2×#639182
#105949832
C2×#638992
C2×Dic3×D122
C2×#638602
C2×#638582
C2×#638442
C2×#56033
C2×#55343