Finite Group Databasebeta

← C2×#10593873 #11900851

Subgroups — C2×#10593873 #11900851

Order 1152.

2485 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×C42×D3C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×C4×#627C212yesmaximal, complemented
6C2×#63867C212yesmaximal, complemented
7C2×#63866C211yesmaximal, characteristic, complemented
8C2×#63857C211yesmaximal, characteristic
9C2×#63856C211yesmaximal, characteristic
10C2×#63855C212yesmaximal
11C2×#63851C212yesmaximal
12#10593873C2116yesmaximal, direct product factor
13C2×#5578—31nomaximal
14C2×#5470—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2212yes—
25C4×#634C2218yescomplemented
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×C42×D3C2218yes—
33C3×C4×Dic6C2218yescomplemented
34C2×#3724C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63918C2218yescomplemented
42C4×#627C22116yescomplemented
43#63867C22116yescomplemented
44#63866C2218yescomplemented
45#63857C2218yes—
46#63856C2218yes—
47#63855C22116yes—
48#63851C22116yes—
49C2×C3×C4×Q8—31no—
50C22×C3×C42—31no—
51C2×#946—31no—
52C2×#944—31no—
53C2×#926—32no—
54C2×#924—31no—
55C2×#924—31no—
56C2×#924—32no—
57#5578—316no—
58C2×#897—31no—
59C2×#896—32no—
60C2×#889—32no—
61C2×#888—31no—
62C2×#872—32no—
63C2×C42×D3D311yescharacteristic
64#5470—316no—
65C2×#870—32no—
66C2×#869—31no—
67C2×#869—31no—
68C2×C4×Dic6—31no—
69C2×C4×Dic6—31no—
70C2×C4×Dic6—32no—
71C2×C4×Dic6—32no—
72C2×C4×Dic6—61no—
73C2×C4×Dic6D311yescharacteristic, complemented
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2312yes—
80C2×#634—24no—
81C2×#634C2314yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3Q818yescomplemented
90C2×C3×C4×D3C2314yes—
91C2×C3×C4×D3C2314yes—
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6C2314yes—
95C2×#627—28no—
96C2×#627C2318yes—
97C32×C42C2314yes—
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2318yes—
100C4×C3⋊Dic3C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×Dic3⋊C4C2318yes—
103C3×C4×Dic3C2318yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107#3724C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2318yes—
111Dic3⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#533—91noSylow
115C22×C3×Q8—31no—
116C23×C3×C4—31no—
117C23×C3×C4—31no—
118C23×C3×C4—31no—
119C22×C4×D3C2×D311yescharacteristic
120C22×C4×D3C2×D311yescharacteristic
121C22×C4×D3C2×D311yescharacteristic
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—32no—
125C22×Dic6—32no—
126C22×Dic6—61no—
127C22×Dic6C2×D311yescharacteristic
128C3×C4×Q8—38no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C42—21no—
132C2×C3×C42—31no—
133C2×C3×C42—32no—
134C2×C3×C42—31no—
135C2×C3×C42—31no—
136C2×C3×C42—38no—
137C2×C3×C42C2×D311yescharacteristic
138C2×C3×C42C2×D311yescharacteristic
139C2×#217—32no—
140C2×#217—32no—
141#946—38no—
142#944—38no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145#926—316no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—32no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—32no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—61no—
153C2×C4⋊Dic3C2×D311yescharacteristic
154#924—38no—
155#924—38no—
156#924—316no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—62no—
166C2×Dic3⋊C4C2×D312yes—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—62no—
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D312yes—
172C2×C4×Dic3C2×D311yescharacteristic
173C2×C4×Dic3C2×D311yescharacteristic
174#897—38no—
175#896—316no—
176#889—316no—
177#888—38no—
178#872—316no—
179C42×D3C2×D318yes—
180#870—316no—
181#869—38no—
182#869—38no—
183C4×Dic6—38no—
184C4×Dic6—38no—
185C4×Dic6—316no—
186C4×Dic6—316no—
187C4×Dic6—68no—
188C4×Dic6C2×D318yescomplemented
189C23×C32C2411yescharacteristic
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3C2×Q814yes—
193C22×C3×D3C2412yes—
194C2×C32×C4—22no—
195C2×C32×C4C2×Q814yes—
196C2×C32×C4#4114yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199C2×C32×C4C2412yes—
200C2×C3⋊Dic3—24no—
201C2×C3⋊Dic3—24no—
202C2×C3⋊Dic3C2414yes—
203C2×C3⋊Dic3C2414yes—
204#634—28no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3C2×Q814yes—
209C2×C3×Dic3#4114yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C3×C4×D3—28no—
216C3×C4×D3—28no—
217C3×C4×D3C2×Q8116yescomplemented
218C3×Dic6—28no—
219#627—216no—
220#533—916no—
221C2×C4⋊Q8—91no—
222C2×C4⋊Q8—91no—
223C2×#125—92no—
224C2×C22⋊Q8—92no—
225C2×C22⋊Q8—91no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—31no—
228C2×C4×Q8—92no—
229C2×C4×Q8—91no—
230C2×#117—92no—
231C22×C42—31no—
232C24×C3—31no—
233C23×D3C22×D311yescharacteristic
234C2×C3×Q8—34no—
235C2×C3×Q8—64no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—38no—
242C22×C3×C4—34no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—34no—
247C22×C3×C4—34no—
248C22×C3×C4—64no—
249C22×C3×C4—64no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×Dic3—32no—
257C22×Dic3—32no—
258C22×Dic3—32no—
259C22×Dic3—32no—
260C22×Dic3—62no—
261C22×Dic3—62no—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D311yescharacteristic
267C2×C4×D3—24no—
268C2×C4×D3—24no—
269C2×C4×D3Dic618yescomplemented
270C2×C4×D3C22×D314yes—
271C2×C4×D3C22×D314yes—
272C2×C4×D3C22×D314yes—
273C2×Dic6—24no—
274C2×Dic6—34no—
275C2×Dic6—34no—
276C2×Dic6—38no—
277C2×Dic6—38no—
278C2×Dic6—64no—
279C2×Dic6—68no—
280C2×Dic6—68no—
281C2×Dic6—64no—
282C2×Dic6—64no—
283C2×Dic6—68no—
284C2×Dic6C22×D314yes—
285C3×C4⋊C4—34no—
286C3×C4⋊C4—38no—
287C3×C42—24no—
288C3×C42—34no—
289C3×C42—38no—
290C3×C42—34no—
291C3×C42—34no—
292C3×C42C22×D314yes—
293C3×C42C22×D314yes—
294#217—38no—
295#217—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298C4⋊Dic3—34no—
299C4⋊Dic3—34no—
300C4⋊Dic3—38no—
301C4⋊Dic3—38no—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304C4⋊Dic3—64no—
305C4⋊Dic3C22×D314yes—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4—38no—
314Dic3⋊C4—68no—
315Dic3⋊C4C22×D318yes—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—68no—
319C4×Dic3C22×D314yes—
320C4×Dic3C22×D318yes—
321C4×Dic3C22×D314yes—
322C4×Dic3C22×D314yes—
323C22×C32C22×Q812yes—
324C22×C32C2×#4112yes—
325C22×C32C2×#4112yes—
326C22×C32C2511yescharacteristic
327C2×C3×D3—28no—
328C2×C3×D3—22no—
329C2×C3×D3—22no—
330C2×C3×D3C22×Q814yes—
331C32×C4—22no—
332C32×C4C22×Q814yes—
333C32×C4C2×#4114yes—
334C3⋊Dic3—24no—
335C3⋊Dic3—24no—
336C3×Dic3—24no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3C22×Q814yes—
340C3×Dic3C2×#4114yes—
341C22×Q8—31no—
342C22×Q8—92no—
343C22×Q8—91no—
344C23×C4—31no—
345C23×C4—31no—
346C23×C4—31no—
347C4⋊Q8—98no—
348C4⋊Q8—98no—
349#125—916no—
350C22⋊Q8—916no—
351C22⋊Q8—98no—
352C22⋊Q8—98no—
353C4×Q8—38no—
354C4×Q8—916no—
355C4×Q8—98no—
356#117—916no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—92no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—91no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—32no—
371C2×C42—31no—
372C2×C42—38no—
373C2×C42—92no—
374C2×C42D3211yescharacteristic
375C23×C3—21no—
376C23×C3—34no—
377C23×C3—32no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3C23×D311yescharacteristic
381C23×C3C23×D311yescharacteristic
382C22×D3—22no—
383C22×D3—22no—
384C22×D3C2×Dic614yes—
385C22×D3C23×D312yes—
386C3×Q8—68no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—34no—
395C2×C3×C4—34no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—316no—
399C2×C3×C4—32no—
400C2×C3×C4—34no—
401C2×C3×C4—34no—
402C2×C3×C4—42no—
403C2×C3×C4—68no—
404C2×C3×C4—64no—
405C2×C3×C4—62no—
406C2×C3×C4—64no—
407C2×C3×C4—68no—
408C2×C3×C4C2×Dic614yes—
409C2×C3×C4#23514yes—
410C2×C3×C4#23514yes—
411C2×C3×C4D3×Q814yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×C3×C4C23×D312yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D312yes—
418C2×Dic3—24no—
419C2×Dic3—22no—
420C2×Dic3—24no—
421C2×Dic3—34no—
422C2×Dic3—34no—
423C2×Dic3—34no—
424C2×Dic3—34no—
425C2×Dic3—64no—
426C2×Dic3—64no—
427C2×Dic3—68no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430C2×Dic3—64no—
431C2×Dic3—64no—
432C2×Dic3—124no—
433C2×Dic3C2×Dic614yes—
434C2×Dic3#23514yes—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D314yes—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D312yes—
439C2×Dic3C23×D312yes—
440C4×D3—28no—
441C4×D3—28no—
442C4×D3C2×Dic6116yescomplemented
443Dic6—28no—
444Dic6—616no—
445Dic6—616no—
446Dic6—68no—
447Dic6—68no—
448Dic6—616no—
449C2×C32#53314yescomplemented
450C2×C32C23×Q811yescharacteristic
451C2×C32C22×#4111yescharacteristic
452C2×C32C22×#4111yescharacteristic
453C3×D3—24no—
454C24—31no—
455C2×Q8—34no—
456C2×Q8—64no—
457C2×Q8—98no—
458C2×Q8—94no—
459C2×Q8—188no—
460C2×Q8—184no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—34no—
464C22×C4—38no—
465C22×C4—31no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—34no—
469C22×C4—34no—
470C22×C4—64no—
471C22×C4—64no—
472C22×C4—92no—
473C22×C4—92no—
474C22×C4C2×D3211yescharacteristic
475C22×C4C2×D3211yescharacteristic
476C22×C4C2×D3211yescharacteristic
477C4⋊C4—38no—
478C4⋊C4—34no—
479C4⋊C4—98no—
480C4⋊C4—98no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—98no—
484C4⋊C4—98no—
485C4⋊C4—94no—
486C22⋊C4—98no—
487C22⋊C4—98no—
488C42—34no—
489C42—34no—
490C42—34no—
491C42—38no—
492C42—98no—
493C42C2×D3214yes—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3—34no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—68no—
502C22×C3C22×Dic612yes—
503C22×C3C2×#23512yes—
504C22×C3C2×#23512yes—
505C22×C3C2×#23512yes—
506C22×C3C2×D3×Q812yes—
507C22×C3D3×#4112yes—
508C22×C3C24×D311yescharacteristic
509C22×C3C24×D311yescharacteristic
510C2×D3—22no—
511C2×D3—22no—
512C2×D3—28no—
513C2×D3C22×Dic614yes—
514C3×C4—22no—
515C3×C4—22no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—34no—
519C3×C4—34no—
520C3×C4—42no—
521C3×C4—64no—
522C3×C4—62no—
523C3×C4—64no—
524C3×C4C22×Dic614yes—
525C3×C4C2×#23514yes—
526C3×C4C2×#23514yes—
527C3×C4C2×D3×Q814yes—
528Dic3—24no—
529Dic3—22no—
530Dic3—24no—
531Dic3—68no—
532Dic3—64no—
533Dic3—64no—
534Dic3—64no—
535Dic3—64no—
536Dic3—124no—
537Dic3C22×Dic614yes—
538Dic3C2×#23514yes—
539C32C2×#53311yescharacteristic, complemented, Sylow
540C23—34no—
541C23—32no—
542C23—62no—
543C23—62no—
544C23C22×D3211yescharacteristic
545Q8—68no—
546Q8—1816no—
547Q8—188no—
548C2×C4—22no—
549C2×C4—34no—
550C2×C4—34no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—316no—
554C2×C4—32no—
555C2×C4—34no—
556C2×C4—34no—
557C2×C4—68no—
558C2×C4—62no—
559C2×C4—64no—
560C2×C4—64no—
561C2×C4—68no—
562C2×C4—94no—
563C2×C4—94no—
564C2×C4—184no—
565C2×C4—184no—
566C2×C4D3×Dic614yes—
567C2×C4#379814yes—
568C2×C4C22×D3212yes—
569C2×C4C22×D3212yes—
570C2×C4C22×D3212yes—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—24no—
575C2×C3—64no—
576C2×C3#547014yescomplemented
577C2×C3#557814yescomplemented
578C2×C3C23×Dic611yescharacteristic
579C2×C3C22×#23511yescharacteristic
580C2×C3C22×#23511yescharacteristic
581C2×C3C22×#23511yescharacteristic
582C2×C3C22×D3×Q811yescharacteristic
583C2×C3C2×D3×#4111yescharacteristic
584D3—24no—
585C22—34no—
586C22—62no—
587C22—62no—
588C22—68no—
589C22C2×D3×Dic612yes—
590C22C2×#379812yes—
591C22D3×#23512yes—
592C22C23×D3211yescharacteristic
593C4—22no—
594C4—34no—
595C4—34no—
596C4—62no—
597C4—64no—
598C4—64no—
599C4—184no—
600C4—184no—
601C4C2×D3×Dic614yes—
602C4C2×#379814yes—
603C3—21no—
604C3C2×#547011yescharacteristic, complemented
605C3C2×#557811yescharacteristic, complemented
606C2—64no—
607C2#1059387314yesdirect product factor
608C2C22×D3×Dic611yescharacteristic
609C2C22×#379811yescharacteristic
610C2C2×D3×#23511yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. C2×#63918C2semidirect
5. C2×C4×#627C2semidirect
6. C2×#63867C2semidirect
7. C2×#63866C2semidirect
12. #10593873C2direct (N × H)
25. C4×#634C22semidirect
33. C3×C4×Dic6C22semidirect
41. #63918C22semidirect
42. C4×#627C22semidirect
43. #63867C22semidirect
44. #63866C22semidirect
73. C2×C4×Dic6D3semidirect
89. C2×C3×C4×D3Q8semidirect
188. C4×Dic6C2×D3semidirect
217. C3×C4×D3C2×Q8semidirect
269. C2×C4×D3Dic6semidirect
442. C4×D3C2×Dic6semidirect
449. C2×C32#533semidirect
539. C32C2×#533semidirect
576. C2×C3#5470semidirect
577. C2×C3#5578semidirect
604. C3C2×#5470semidirect
605. C3C2×#5578semidirect
607. C2#10593873direct (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×C42×D32
C2×C3×C4×Dic62
C2×#639182
C2×C4×#6272
C2×#638672
C2×#638662
C2×#638572
C2×#638562
C2×#638552
C2×#638512
#105938732
C2×#55783
C2×#54703