Finite Group Databasebeta

← C2×#10595121 #11901676

Subgroups — C2×#10595121 #11901676

Order 1152.

2477 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63966C212yesmaximal, complemented
5C2×#63964C212yesmaximal, complemented
6C2×#63956C212yesmaximal, complemented
7C2×#63953C212yesmaximal, complemented
8#10595121C2116yesmaximal, direct product factor
9C2×#63918C211yesmaximal, characteristic, complemented
10C2×#63874C211yesmaximal, characteristic, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5682—31nomaximal
14C2×#5561—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4×C3⋊D3C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2212yes—
21C2×#3757C2212yes—
22#64147C2218yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C3×#936C2218yescomplemented
28C3×D4×Dic3C2218yescomplemented
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34#63966C22116yescomplemented
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38#63964C22116yescomplemented
39C2×#3722C2212yes—
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42#63956C22116yescomplemented
43C2×Dic32C2212yes—
44#63953C22116yescomplemented
45#63918C2218yescomplemented
46#63874C2218yescomplemented
47#63871C2218yescomplemented
48Dic3×Dic6C2218yescomplemented
49C2×C3×#124—31no—
50C2×C3×C4×D4—31no—
51C2×#946—31no—
52C2×Q8×Dic3—31no—
53C2×#938—31no—
54C2×#938—31no—
55C2×#938—61no—
56C2×#936D311yescharacteristic, complemented
57C2×D4×Dic3D311yescharacteristic, complemented
58C2×#929—32no—
59C2×#924—32no—
60#5682—316no—
61#5561—316no—
62C2×#897—31no—
63C2×#888—31no—
64C2×#886—32no—
65C2×#885—32no—
66C2×#885—32no—
67C2×#879—32no—
68C2×#879—32no—
69C2×#878—32no—
70C2×#872—31no—
71C2×#872—31no—
72C2×#869—31no—
73C2×C4×Dic6—31no—
74C24×C32C2312yes—
75C23×C3⋊D3C2311yescharacteristic
76C2×C32×D4—24no—
77C2×C32×D4C2314yes—
78C22×C32×C4C2311yescharacteristic
79C2×#638—44no—
80C2×#638C2318yes—
81C22×C3⋊Dic3C2312yes—
82C22×C3⋊Dic3C2311yescharacteristic
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3C2314yes—
85C22×C3×Dic3—44no—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2318yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6C2314yes—
95C2×#627—44no—
96C2×#627C2318yes—
97#3757C2318yes—
98C4⋊(C3⋊Dic3)C2314yes—
99C3×#217C2318yes—
100C3×#217C2318yes—
101C3×#217C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4×Dic3C2314yes—
104C3×C4×Dic3C2314yes—
105#3724C2314yes—
106#3724C2314yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110#3722C2318yes—
111#3722C2314yes—
112#3722C2314yes—
113Dic32C2318yes—
114C2×#542—91noSylow
115C22×C3×Q8—31no—
116C22×C3×D4—21no—
117C22×C3×D4C2×D311yescharacteristic
118C22×C3×D4C2×D311yescharacteristic
119C23×C3×C4—32no—
120C22×#67—32no—
121C22×#67—32no—
122C22×#67—62no—
123C23×Dic3C2×D312yes—
124C22×C4×D3—31no—
125C22×C4×D3—31no—
126C22×C4×D3—61no—
127C22×Dic6—32no—
128C22×Dic6—32no—
129C22×Dic6C2×D311yescharacteristic
130C3×#124—38no—
131C3×C4×D4—38no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×#217—32no—
139C2×#217—32no—
140C2×#217—62no—
141C2×#217C2×D312yes—
142C2×#217C2×D312yes—
143C2×#217C2×D312yes—
144#946—38no—
145Q8×Dic3—38no—
146#938—38no—
147#938—38no—
148#938—68no—
149#936C2×D318yescomplemented
150D4×Dic3C2×D318yescomplemented
151#929—316no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—32no—
161C2×C4⋊Dic3—32no—
162C2×C4⋊Dic3—32no—
163C2×C4⋊Dic3—61no—
164C2×C4⋊Dic3C2×D311yescharacteristic
165#924—316no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—32no—
172C2×Dic3⋊C4—32no—
173C2×C4×Dic3—32no—
174C2×C4×Dic3—32no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#897—38no—
178#888—38no—
179#886—316no—
180#885—316no—
181#885—316no—
182#879—316no—
183#879—316no—
184#878—316no—
185#872—38no—
186#872—38no—
187#869—38no—
188C4×Dic6—38no—
189C23×C32—24no—
190C23×C32—24no—
191C23×C32—24no—
192C23×C32C2414yes—
193C23×C32C2411yescharacteristic
194C22×C3⋊D3—22no—
195C22×C3⋊D3—22no—
196C22×C3⋊D3—22no—
197C22×C3⋊D3C2412yes—
198C32×D4—28no—
199C2×C32×C4#4114yes—
200C2×C32×C4C2412yes—
201#638—48no—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—24no—
204C2×C3⋊Dic3C2414yes—
205C2×C3⋊Dic3C2412yes—
206C4×C3⋊D3—28no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—48no—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C2×C3×Dic3C2414yes—
219C2×C3×Dic3C2412yes—
220C3×Dic6—28no—
221#627—48no—
222#542—916no—
223C2×C4⋊Q8—91no—
224C2×#126—92no—
225C2×#124—31no—
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—91no—
234C24×C3—22no—
235C24×C3C22×D312yes—
236C24×C3C22×D312yes—
237C23×D3—31no—
238C23×D3—31no—
239C23×D3—61no—
240C2×C3×Q8—34no—
241C2×C3×Q8—64no—
242C2×C3×D4—24no—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4—44no—
246C2×C3×D4C22×D314yes—
247C2×C3×D4C22×D314yes—
248C22×C3×C4—21no—
249C22×C3×C4—31no—
250C22×C3×C4—32no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—31no—
255C22×C3×C4—38no—
256C22×C3×C4—124no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C2×#67—38no—
260C2×#67—38no—
261C2×#67—68no—
262C2×#67—124no—
263C2×#67—124no—
264C2×#67—128no—
265C22×Dic3—32no—
266C22×Dic3—32no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—44no—
270C22×Dic3—62no—
271C22×Dic3—61no—
272C22×Dic3C22×D311yescharacteristic
273C22×Dic3C22×D312yes—
274C22×Dic3C22×D311yescharacteristic
275C22×Dic3C22×D311yescharacteristic
276C22×Dic3C22×D311yescharacteristic
277C22×Dic3C22×D312yes—
278C22×Dic3C22×D318yes—
279C2×C4×D3—34no—
280C2×C4×D3—34no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—64no—
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×C22⋊C4—38no—
293C3×C22⋊C4—38no—
294C3×C22⋊C4—38no—
295C3×C42—34no—
296C3×C42—34no—
297#217—38no—
298#217—38no—
299#217—68no—
300#217C22×D318yes—
301#217C22×D318yes—
302#217C22×D318yes—
303(C2×D3)⋊C4—34no—
304(C2×D3)⋊C4—34no—
305(C2×D3)⋊C4—34no—
306(C2×D3)⋊C4—34no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—38no—
309C4⋊Dic3—34no—
310C4⋊Dic3—34no—
311C4⋊Dic3—38no—
312C4⋊Dic3—38no—
313C4⋊Dic3—38no—
314C4⋊Dic3—64no—
315C4⋊Dic3C22×D314yes—
316Dic3⋊C4—38no—
317Dic3⋊C4—34no—
318Dic3⋊C4—34no—
319Dic3⋊C4—34no—
320Dic3⋊C4—34no—
321Dic3⋊C4—38no—
322Dic3⋊C4—38no—
323C4×Dic3—38no—
324C4×Dic3—38no—
325C4×Dic3C22×D314yes—
326C4×Dic3C22×D314yes—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—48no—
331C22×C32C2×#4112yes—
332C22×C32H(5,𝔽2)12yes—
333C22×C322−1+412yes—
334C22×C32C2511yescharacteristic
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—22no—
338C2×C3⋊D3—44no—
339C32×C4C2×#4114yes—
340C3⋊Dic3—22no—
341C3⋊Dic3—24no—
342C3×Dic3—24no—
343C3×Dic3—22no—
344C3×Dic3—24no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C22×Q8—31no—
349C22×Q8—92no—
350C22×D4—92no—
351C22×D4D3211yescharacteristic
352C23×C4—32no—
353C23×C4—91no—
354C4⋊Q8—98no—
355#126—916no—
356#124—38no—
357#124—916no—
358#123—916no—
359C22⋊Q8—916no—
360C22⋊Q8—98no—
361#121—98no—
362C4×Q8—98no—
363C4×D4—38no—
364#117—98no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4—92no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—91no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—91no—
377C2×C22⋊C4—92no—
378C2×C22⋊C4—92no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—92no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—21no—
390C23×C3—44no—
391C23×C3—44no—
392C23×C3—44no—
393C23×C3C23×D314yes—
394C23×C3C23×D314yes—
395C23×C3C23×D311yescharacteristic
396C23×C3C23×D311yescharacteristic
397C22×D3—32no—
398C22×D3—32no—
399C22×D3—62no—
400C22×D3—64no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—62no—
407C22×D3—122no—
408C22×D3—122no—
409C3×Q8—68no—
410C3×D4—28no—
411C3×D4—28no—
412C3×D4—48no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—32no—
416C2×C3×C4—34no—
417C2×C3×C4—32no—
418C2×C3×C4—32no—
419C2×C3×C4—34no—
420C2×C3×C4—32no—
421C2×C3×C4—64no—
422C2×C3×C4—62no—
423C2×C3×C4—64no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—128no—
428C2×C3×C4#23514yes—
429C2×C3×C4#23714yes—
430C2×C3×C4C23×D312yes—
431C2×C3×C4C23×D312yes—
432#67—128no—
433#67—128no—
434#67—1216no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—34no—
442C2×Dic3—34no—
443C2×Dic3—32no—
444C2×Dic3—32no—
445C2×Dic3—48no—
446C2×Dic3—64no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—64no—
451C2×Dic3—64no—
452C2×Dic3—122no—
453C2×Dic3—124no—
454C2×Dic3C23×D312yes—
455C2×Dic3C23×D314yes—
456C2×Dic3C23×D312yes—
457C2×Dic3C23×D312yes—
458C2×Dic3C23×D312yes—
459C2×Dic3C23×D314yes—
460C4×D3—68no—
461C4×D3—68no—
462C4×D3—128no—
463Dic6—28no—
464Dic6—128no—
465Dic6—128no—
466C2×C32—44no—
467C2×C32#54214yescomplemented
468C2×C32C22×#4111yescharacteristic
469C2×C32C2×H(5,𝔽2)11yescharacteristic
470C2×C32C2×2−1+411yescharacteristic
471C3⋊D3—42no—
472C24—91no—
473C24C2×D3212yes—
474C2×Q8—34no—
475C2×Q8—64no—
476C2×Q8—98no—
477C2×Q8—364no—
478C2×D4—24no—
479C2×D4—98no—
480C2×D4—364no—
481C2×D4C2×D3214yes—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—32no—
488C22×C4—38no—
489C22×C4—92no—
490C22×C4—91no—
491C22×C4—94no—
492C22×C4—124no—
493C22×C4—184no—
494C22×C4C2×D3211yescharacteristic
495C4⋊C4—34no—
496C4⋊C4—94no—
497C4⋊C4—94no—
498C4⋊C4—98no—
499C4⋊C4—98no—
500C4⋊C4—98no—
501C4⋊C4—94no—
502C22⋊C4—38no—
503C22⋊C4—38no—
504C22⋊C4—38no—
505C22⋊C4—94no—
506C22⋊C4—94no—
507C22⋊C4—98no—
508C22⋊C4—98no—
509C42—34no—
510C42—34no—
511C42—98no—
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—21no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—48no—
526C22×C3—48no—
527C22×C3—88no—
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—64no—
537C2×D3—62no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—122no—
544C2×D3—122no—
545C2×D3—128no—
546C2×D3—124no—
547C2×D3—124no—
548C3×C4—24no—
549C3×C4—64no—
550C3×C4—62no—
551C3×C4—64no—
552C3×C4—62no—
553C3×C4—62no—
554C3×C4—62no—
555C3×C4C2×#23514yes—
556C3×C4C2×#23714yes—
557Dic3—24no—
558Dic3—24no—
559Dic3—22no—
560Dic3—22no—
561Dic3—22no—
562Dic3—22no—
563Dic3—62no—
564Dic3—62no—
565Dic3—64no—
566Dic3—64no—
567Dic3—122no—
568Dic3—124no—
569C32C2×#54211yescharacteristic, complemented, Sylow
570C23—24no—
571C23—24no—
572C23—24no—
573C23—92no—
574C23—182no—
575C23—182no—
576C23—182no—
577C23C22×D3214yes—
578C23C22×D3211yescharacteristic
579Q8—68no—
580Q8—368no—
581D4—28no—
582D4—368no—
583C2×C4—32no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—34no—
588C2×C4—34no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—64no—
593C2×C4—62no—
594C2×C4—64no—
595C2×C4—94no—
596C2×C4—92no—
597C2×C4—128no—
598C2×C4—184no—
599C2×C4—182no—
600C2×C4—188no—
601C2×C4#380414yes—
602C2×C4C22×D3212yes—
603C2×C3—24no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—44no—
608C2×C3—44no—
609C2×C3—84no—
610C2×C3#556114yescomplemented
611C2×C3#568214yescomplemented
612C2×C3C22×#23511yescharacteristic
613C2×C3C22×#23711yescharacteristic
614C2×C3C2×#100411yescharacteristic
615C2×C3C2×#100911yescharacteristic
616C2×C3C2×#101011yescharacteristic
617C2×C3C2×#101011yescharacteristic
618D3—124no—
619D3—122no—
620D3—122no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—48no—
625C22—182no—
626C22—182no—
627C22—182no—
628C22—364no—
629C22#6430912yes—
630C22#6431412yes—
631C22C2×#380412yes—
632C22C23×D3211yescharacteristic
633C4—62no—
634C4—62no—
635C4—62no—
636C4—64no—
637C4—62no—
638C4—64no—
639C4—184no—
640C4—182no—
641C4C2×#380414yes—
642C3—21no—
643C3C2×#556111yescharacteristic, complemented
644C3C2×#568211yescharacteristic, complemented
645C2—44no—
646C2—362no—
647C2#1059512114yesdirect product factor
648C2C2×#6430911yescharacteristic
649C2C2×#6431411yescharacteristic
650C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×#64147C2
hypercenterC22×D4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#936C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63966C2semidirect
5. C2×#63964C2semidirect
6. C2×#63956C2semidirect
7. C2×#63953C2semidirect
8. #10595121C2direct (N × H)
9. C2×#63918C2semidirect
10. C2×#63874C2semidirect
11. C2×#63871C2semidirect
12. C2×Dic3×Dic6C2semidirect
27. C3×#936C22semidirect
28. C3×D4×Dic3C22semidirect
34. #63966C22semidirect
38. #63964C22semidirect
42. #63956C22semidirect
44. #63953C22semidirect
45. #63918C22semidirect
46. #63874C22semidirect
47. #63871C22semidirect
48. Dic3×Dic6C22semidirect
56. C2×#936D3semidirect
57. C2×D4×Dic3D3semidirect
149. #936C2×D3semidirect
150. D4×Dic3C2×D3semidirect
467. C2×C32#542semidirect
569. C32C2×#542semidirect
610. C2×C3#5561semidirect
611. C2×C3#5682semidirect
643. C3C2×#5561semidirect
644. C3C2×#5682semidirect
647. C2#10595121direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C3×#9362
C2×C3×D4×Dic32
C2×#639662
C2×#639642
C2×#639562
C2×#639532
#105951212
C2×#639182
C2×#638742
C2×#638712
C2×Dic3×Dic62
C2×#56823
C2×#55613