Finite Group Databasebeta

← C2×#10593983 #11901680

Subgroups — C2×#10593983 #11901680

Order 1152.

2413 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×#63915C212yesmaximal, complemented
6C2×#63908C211yesmaximal, characteristic
7C2×#63905C212yesmaximal, complemented
8C2×#63862C212yesmaximal, complemented
9C2×#63860C211yesmaximal, characteristic, complemented
10C2×#63857C211yesmaximal, characteristic, complemented
11C2×#63851C212yesmaximal, complemented
12#10593983C2116yesmaximal, direct product factor
13C2×#5561—31nomaximal
14C2×#5534—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×#627C2212yes—
20C22×#625C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2212yes—
25C4×#634C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×C4×D12C2218yescomplemented
34C3×#872C2218yescomplemented
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63918C2218yescomplemented
42#63915C22116yescomplemented
43#63908C2218yes—
44#63905C22116yescomplemented
45#63862C22116yescomplemented
46#63860C2218yescomplemented
47#63857C2218yescomplemented
48#63851C22116yescomplemented
49C2×C3×C4×D4—31no—
50C2×C3×#117—31no—
51C2×#938—31no—
52C2×#936—31no—
53C2×#930—31no—
54C2×#929—32no—
55C2×#924—31no—
56C2×#924—32no—
57#5561—316no—
58#5534—316no—
59C2×#898—32no—
60C2×#897—31no—
61C2×#896—32no—
62C2×#888—31no—
63C2×#885—32no—
64C2×#885—32no—
65C2×#883—32no—
66C2×#879—32no—
67C2×#875—31no—
68C2×C4×D12D311yescharacteristic, complemented
69C2×#872D311yescharacteristic, complemented
70C2×#869—31no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—61no—
74C23×C3×D3C2311yescharacteristic
75C23×C3×D3C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2312yes—
81C2×#634—24no—
82C2×#634C2314yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×D12—24no—
88C2×C3×D12C2314yes—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—44no—
91C2×C3×C4×D3C2314yes—
92C2×C3×C4×D3C2318yes—
93C2×#627—44no—
94C2×#627C2318yes—
95C2×#625—44no—
96C2×#625C2318yes—
97C32×C42C2314yes—
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2318yes—
100C4×C3⋊Dic3C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2314yes—
103C3×(C2×D3)⋊C4C2314yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2314yes—
106C3×Dic3⋊C4C2314yes—
107C3×C4×Dic3C2314yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#542—91noSylow
115C22×C3×D4—31no—
116C23×C3×C4—31no—
117C23×C3×C4—32no—
118C22×#67—32no—
119C22×#67—32no—
120C22×D12C2×D311yescharacteristic
121C22×C4×D3C2×D311yescharacteristic
122C22×C4×D3C2×D312yes—
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—32no—
126C22×Dic6—32no—
127C22×Dic6—61no—
128C3×C4×D4—38no—
129C3×#117—38no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C42—21no—
137C2×C3×C42—31no—
138C2×C3×C42C2×D311yescharacteristic
139C2×C3×C42C2×D311yescharacteristic
140C2×#217—32no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144#938—38no—
145#936—38no—
146#930—38no—
147#929—316no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4C2×D311yescharacteristic
153C2×(C2×D3)⋊C4C2×D311yescharacteristic
154C2×(C2×D3)⋊C4C2×D312yes—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—32no—
158C2×C4⋊Dic3—32no—
159C2×C4⋊Dic3—61no—
160C2×C4⋊Dic3C2×D311yescharacteristic
161#924—38no—
162#924—316no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4—62no—
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—62no—
173C2×C4×Dic3C2×D311yescharacteristic
174#898—316no—
175#897—38no—
176#896—316no—
177#888—38no—
178#885—316no—
179#885—316no—
180#883—316no—
181#879—316no—
182#875—38no—
183C4×D12C2×D318yescomplemented
184#872C2×D318yescomplemented
185#869—38no—
186C4×Dic6—38no—
187C4×Dic6—38no—
188C4×Dic6—68no—
189C23×C32C2411yescharacteristic
190C22×C3×D3—22no—
191C22×C3×D3—24no—
192C22×C3×D3—22no—
193C22×C3×D3—24no—
194C22×C3×D3—22no—
195C22×C3×D3—24no—
196C22×C3×D3C2414yes—
197C22×C3×D3C2412yes—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2412yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2412yes—
204C2×C3⋊Dic3—24no—
205C2×C3⋊Dic3—24no—
206C2×C3⋊Dic3C2414yes—
207C2×C3⋊Dic3C2414yes—
208#634—28no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2414yes—
217C3×D12—28no—
218C3×C4×D3—28no—
219C3×C4×D3—48no—
220#627—48no—
221#625—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—91no—
231C2×C4×Q8—91no—
232C2×C4×D4—31no—
233C2×#117—31no—
234C24×C3—32no—
235C24×C3—31no—
236C23×D3C22×D312yes—
237C23×D3C22×D311yescharacteristic
238C2×C3×D4—34no—
239C2×C3×D4—64no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—34no—
248C22×C3×C4—38no—
249C22×C3×C4—64no—
250C22×C3×C4—124no—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C2×#67—38no—
258C2×#67—38no—
259C2×#67—124no—
260C2×#67—124no—
261C22×Dic3—32no—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—32no—
265C22×Dic3—62no—
266C22×Dic3—62no—
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D311yescharacteristic
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D311yescharacteristic
271C2×D12—24no—
272C2×D12C22×D314yes—
273C2×C4×D3—24no—
274C2×C4×D3—44no—
275C2×C4×D3C22×D314yes—
276C2×C4×D3C22×D318yes—
277C2×Dic6—34no—
278C2×Dic6—34no—
279C2×Dic6—38no—
280C2×Dic6—38no—
281C2×Dic6—64no—
282C2×Dic6—68no—
283C2×Dic6—64no—
284C2×Dic6—64no—
285C2×Dic6—124no—
286C2×Dic6—124no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—34no—
289C3×C4⋊C4—34no—
290C3×C22⋊C4—38no—
291C3×C22⋊C4—34no—
292C3×C22⋊C4—34no—
293C3×C42—24no—
294C3×C42—34no—
295C3×C42C22×D314yes—
296C3×C42C22×D314yes—
297#217—38no—
298#217—38no—
299#217—38no—
300#217—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4C22×D314yes—
306(C2×D3)⋊C4C22×D314yes—
307(C2×D3)⋊C4C22×D318yes—
308C4⋊Dic3—34no—
309C4⋊Dic3—34no—
310C4⋊Dic3—38no—
311C4⋊Dic3—38no—
312C4⋊Dic3—64no—
313C4⋊Dic3C22×D314yes—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—68no—
319Dic3⋊C4C22×D314yes—
320Dic3⋊C4C22×D314yes—
321C4×Dic3—38no—
322C4×Dic3—38no—
323C4×Dic3—68no—
324C4×Dic3C22×D314yes—
325C22×C32C2×#4112yes—
326C22×C32H(5,𝔽2)12yes—
327C22×C322−1+412yes—
328C22×C32C2511yescharacteristic
329C2×C3×D3—22no—
330C2×C3×D3—24no—
331C2×C3×D3—22no—
332C2×C3×D3—24no—
333C2×C3×D3—24no—
334C2×C3×D3—22no—
335C2×C3×D3—44no—
336C2×C3×D3—48no—
337C32×C4—22no—
338C32×C4—22no—
339C32×C4C2×#4114yes—
340C3⋊Dic3—24no—
341C3⋊Dic3—24no—
342C3×Dic3—22no—
343C3×Dic3—22no—
344C3×Dic3—24no—
345C3×Dic3—22no—
346C22×Q8—92no—
347C22×Q8—91no—
348C22×D4—31no—
349C22×D4—92no—
350C23×C4—31no—
351C23×C4—32no—
352C4⋊Q8—98no—
353#126—916no—
354#124—98no—
355#124—916no—
356#123—916no—
357C22⋊Q8—916no—
358C22⋊Q8—98no—
359#121—98no—
360C4×Q8—98no—
361C4×D4—38no—
362#117—38no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—92no—
367C2×C4⋊C4—92no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—92no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C42—31no—
378C2×C42—92no—
379C2×C42D3211yescharacteristic
380C23×C3—21no—
381C23×C3—34no—
382C23×C3—32no—
383C23×C3—62no—
384C23×C3—64no—
385C23×C3—62no—
386C23×C3—64no—
387C23×C3—64no—
388C23×C3—62no—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—22no—
392C22×D3—24no—
393C22×D3—24no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—24no—
397C22×D3C23×D314yes—
398C22×D3C23×D312yes—
399C3×D4—68no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—24no—
409C2×C3×C4—32no—
410C2×C3×C4—34no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—42no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—64no—
417C2×C3×C4—62no—
418C2×C3×C4—68no—
419C2×C3×C4—128no—
420C2×C3×C4#23514yes—
421C2×C3×C4#23514yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D312yes—
424C2×C3×C4C23×D312yes—
425C2×C3×C4C23×D312yes—
426C2×C3×C4C23×D312yes—
427C2×C3×C4C23×D312yes—
428#67—128no—
429#67—128no—
430C2×Dic3—22no—
431C2×Dic3—24no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—34no—
435C2×Dic3—34no—
436C2×Dic3—34no—
437C2×Dic3—34no—
438C2×Dic3—64no—
439C2×Dic3—64no—
440C2×Dic3—68no—
441C2×Dic3—64no—
442C2×Dic3—64no—
443C2×Dic3—64no—
444C2×Dic3—64no—
445C2×Dic3—124no—
446C2×Dic3C23×D312yes—
447C2×Dic3C23×D312yes—
448C2×Dic3C23×D314yes—
449C2×Dic3C23×D312yes—
450D12—28no—
451C4×D3—28no—
452C4×D3—48no—
453Dic6—616no—
454Dic6—68no—
455Dic6—68no—
456Dic6—128no—
457Dic6—128no—
458C2×C32#54214yescomplemented
459C2×C32C22×#4111yescharacteristic
460C2×C32C2×H(5,𝔽2)11yescharacteristic
461C2×C32C2×2−1+411yescharacteristic
462C3×D3—44no—
463C3×D3—42no—
464C24—31no—
465C24—32no—
466C2×Q8—98no—
467C2×Q8—94no—
468C2×Q8—184no—
469C2×Q8—364no—
470C2×D4—34no—
471C2×D4—64no—
472C2×D4—98no—
473C2×D4—364no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—32no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—38no—
480C22×C4—64no—
481C22×C4—92no—
482C22×C4—92no—
483C22×C4—124no—
484C22×C4C2×D3211yescharacteristic
485C22×C4C2×D3211yescharacteristic
486C22×C4C2×D3211yescharacteristic
487C4⋊C4—34no—
488C4⋊C4—34no—
489C4⋊C4—34no—
490C4⋊C4—98no—
491C4⋊C4—98no—
492C4⋊C4—94no—
493C4⋊C4—98no—
494C22⋊C4—34no—
495C22⋊C4—34no—
496C22⋊C4—38no—
497C22⋊C4—98no—
498C22⋊C4—98no—
499C22⋊C4—98no—
500C22⋊C4—98no—
501C42—34no—
502C42—98no—
503C42C2×D3214yes—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—62no—
509C22×C3—64no—
510C22×C3—62no—
511C22×C3—64no—
512C22×C3—62no—
513C22×C3—64no—
514C22×C3—128no—
515C22×C3—124no—
516C22×C3C2×#23512yes—
517C22×C3C2×#23512yes—
518C22×C3#100412yes—
519C22×C3#100912yes—
520C22×C3#101012yes—
521C22×C3#101012yes—
522C22×C3C24×D311yescharacteristic
523C22×C3C24×D311yescharacteristic
524C2×D3—22no—
525C2×D3—24no—
526C2×D3—24no—
527C2×D3—22no—
528C2×D3—24no—
529C2×D3—22no—
530C2×D3—44no—
531C2×D3—48no—
532C3×C4—24no—
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—24no—
538C3×C4—42no—
539C3×C4—62no—
540C3×C4—62no—
541C3×C4—64no—
542C3×C4—62no—
543C3×C4C2×#23514yes—
544C3×C4C2×#23514yes—
545Dic3—22no—
546Dic3—24no—
547Dic3—22no—
548Dic3—22no—
549Dic3—68no—
550Dic3—64no—
551Dic3—64no—
552Dic3—64no—
553Dic3—64no—
554Dic3—124no—
555C32C2×#54211yescharacteristic, complemented, Sylow
556C23—32no—
557C23—34no—
558C23—62no—
559C23—64no—
560C23—62no—
561C23—64no—
562C23—64no—
563C23—62no—
564C23C22×D3211yescharacteristic
565Q8—188no—
566Q8—368no—
567D4—68no—
568D4—368no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—32no—
572C2×C4—32no—
573C2×C4—34no—
574C2×C4—32no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—64no—
578C2×C4—62no—
579C2×C4—68no—
580C2×C4—94no—
581C2×C4—94no—
582C2×C4—128no—
583C2×C4—184no—
584C2×C4—184no—
585C2×C4#379814yes—
586C2×C4C22×D3212yes—
587C2×C4C22×D3212yes—
588C2×C4C22×D3212yes—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—24no—
593C2×C3—122no—
594C2×C3—124no—
595C2×C3#553414yescomplemented
596C2×C3#556114yescomplemented
597C2×C3C22×#23511yescharacteristic
598C2×C3C22×#23511yescharacteristic
599C2×C3C2×#100411yescharacteristic
600C2×C3C2×#100911yescharacteristic
601C2×C3C2×#101011yescharacteristic
602C2×C3C2×#101011yescharacteristic
603D3—44no—
604D3—42no—
605C22—62no—
606C22—64no—
607C22—62no—
608C22—64no—
609C22—64no—
610C22—62no—
611C22—124no—
612C22—128no—
613C22#6429812yes—
614C22C2×#379812yes—
615C22#6430712yes—
616C22C23×D3211yescharacteristic
617C4—22no—
618C4—22no—
619C4—62no—
620C4—62no—
621C4—64no—
622C4—62no—
623C4—184no—
624C4—184no—
625C4C2×#379814yes—
626C3—21no—
627C3C2×#553411yescharacteristic, complemented
628C3C2×#556111yescharacteristic, complemented
629C2—122no—
630C2—124no—
631C2#1059398314yesdirect product factor
632C2C2×#6429811yescharacteristic
633C2C22×#379811yescharacteristic
634C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×#63908C2
hypercenterC2×C42D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×C3×#872C2semidirect
4. C2×#63918C2semidirect
5. C2×#63915C2semidirect
7. C2×#63905C2semidirect
8. C2×#63862C2semidirect
9. C2×#63860C2semidirect
10. C2×#63857C2semidirect
11. C2×#63851C2semidirect
12. #10593983C2direct (N × H)
25. C4×#634C22semidirect
33. C3×C4×D12C22semidirect
34. C3×#872C22semidirect
41. #63918C22semidirect
42. #63915C22semidirect
44. #63905C22semidirect
45. #63862C22semidirect
46. #63860C22semidirect
47. #63857C22semidirect
48. #63851C22semidirect
68. C2×C4×D12D3semidirect
69. C2×#872D3semidirect
183. C4×D12C2×D3semidirect
184. #872C2×D3semidirect
458. C2×C32#542semidirect
555. C32C2×#542semidirect
595. C2×C3#5534semidirect
596. C2×C3#5561semidirect
627. C3C2×#5534semidirect
628. C3C2×#5561semidirect
631. C2#10593983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×C4×D122
C2×C3×#8722
C2×#639182
C2×#639152
C2×#639082
C2×#639052
C2×#638622
C2×#638602
C2×#638572
C2×#638512
#105939832
C2×#55613
C2×#55343