Finite Group Databasebeta

← C2×#10593974 #11900648

Subgroups — C2×#10593974 #11900648

Order 1152.

2613 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×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×C3×C42×D3C211yesmaximal, characteristic, complemented
4C2×#63908C211yesmaximal, characteristic
5C2×#63905C212yesmaximal, complemented
6C2×C4×#625C212yesmaximal, complemented
7C2×#63869C211yesmaximal, characteristic, complemented
8C2×#63860C211yesmaximal, characteristic, complemented
9C2×#63859C212yesmaximal, complemented
10C2×#63857C211yesmaximal, characteristic, complemented
11C2×#63855C212yesmaximal, complemented
12#10593974C2116yesmaximal, direct product factor
13C2×#5557—31nomaximal
14C2×#5479—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#625C2212yes—
22C2×C32×C42C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2212yes—
25C2×C4×C3⋊Dic3C2212yes—
26C4×#634C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×C4×D12C2218yescomplemented
33C3×C42×D3C2218yescomplemented
34C2×#3724C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63908C2218yes—
42#63905C22116yescomplemented
43C4×#625C22116yescomplemented
44#63869C2218yescomplemented
45#63860C2218yescomplemented
46#63859C22116yescomplemented
47#63857C2218yescomplemented
48#63855C22116yescomplemented
49C2×C3×C4×D4—31no—
50C22×C3×C42—31no—
51C2×#938—31no—
52C2×#936—31no—
53C2×#930—31no—
54C2×#929—32no—
55C2×C4×#67—32no—
56C2×C4×#67—32no—
57C2×#926—32no—
58C2×#924—31no—
59#5557—316no—
60C2×#897—31no—
61C2×#890—31no—
62C2×#883—32no—
63C2×#879—32no—
64#5479—316no—
65C2×#876—32no—
66C2×#875—31no—
67C2×C4×D12D311yescharacteristic, complemented
68C2×#872—32no—
69C2×C42×D3D311yescharacteristic, complemented
70C2×#870—31no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—61no—
74C23×C3×D3C2312yes—
75C23×C3×D3C2311yescharacteristic
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—24no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—28no—
93C2×C3×C4×D3C2318yes—
94C2×C3×C4×D3C2314yes—
95C2×C3×C4×D3C2314yes—
96C2×C3×C4×D3C2314yes—
97C2×#625—28no—
98C2×#625C2318yes—
99C32×C42C2314yes—
100C4⋊(C3⋊Dic3)C2314yes—
101#3750C2318yes—
102C4×C3⋊Dic3C2318yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107C3×C4×Dic3C2314yes—
108#3724C2318yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114(C2×D3)⋊Dic3C2318yes—
115C2×#529—91noSylow
116C22×C3×D4—31no—
117C23×C3×C4—31no—
118C23×C3×C4—32no—
119C23×C3×C4—31no—
120C23×C3×C4—31no—
121C22×#67—32no—
122C22×#67—32no—
123C22×D12C2×D311yescharacteristic
124C22×C4×D3C2×D311yescharacteristic
125C22×C4×D3C2×D311yescharacteristic
126C22×C4×D3C2×D311yescharacteristic
127C22×C4×D3C2×D312yes—
128C22×Dic6—31no—
129C22×Dic6—31no—
130C22×Dic6—61no—
131C3×C4×D4—38no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C42—21no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×C3×C42—38no—
139C2×C3×C42C2×D311yescharacteristic
140C2×C3×C42C2×D311yescharacteristic
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—32no—
145#938—38no—
146#936—38no—
147#930—38no—
148#929—316no—
149C4×#67—316no—
150C4×#67—316no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4C2×D312yes—
156#926—316no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—32no—
160C2×C4⋊Dic3—32no—
161C2×C4⋊Dic3—61no—
162C2×C4⋊Dic3C2×D311yescharacteristic
163#924—38no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4—32no—
168C2×Dic3⋊C4—32no—
169C2×Dic3⋊C4—32no—
170C2×Dic3⋊C4—62no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3—62no—
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#897—38no—
178#890—38no—
179#883—316no—
180#879—316no—
181#876—316no—
182#875—38no—
183C4×D12C2×D318yescomplemented
184#872—316no—
185C42×D3C2×D318yescomplemented
186#870—38no—
187C4×Dic6—38no—
188C4×Dic6—38no—
189C4×Dic6—68no—
190C23×C32C2411yescharacteristic
191C22×C3×D3—22no—
192C22×C3×D3—22no—
193C22×C3×D3—24no—
194C22×C3×D3—24no—
195C22×C3×D3—24no—
196C22×C3×D3#4114yes—
197C22×C3×D3C2414yes—
198C22×C3×D3C2412yes—
199C2×C32×C4—22no—
200C2×C32×C4#4114yes—
201C2×C32×C4#4114yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2412yes—
204C2×C32×C4C2412yes—
205C2×C3⋊Dic3—24no—
206C2×C3⋊Dic3—24no—
207C2×C3⋊Dic3C2414yes—
208C2×C3⋊Dic3C2414yes—
209#634—28no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2414yes—
218C3×D12—28no—
219C3×C4×D3—28no—
220C3×C4×D3—28no—
221C3×C4×D3—28no—
222C3×C4×D3—216no—
223#625—216no—
224#529—916no—
225C2×#126—92no—
226C2×#125—91no—
227C2×#124—91no—
228C2×#123—92no—
229C2×C22⋊Q8—91no—
230C2×#121—91no—
231C2×C4×Q8—91no—
232C2×C4×D4—31no—
233C2×C4×D4—92no—
234C2×#117—92no—
235C22×C42—31no—
236C24×C3—31no—
237C24×C3—32no—
238C23×D3C22×D312yes—
239C23×D3C22×D311yescharacteristic
240C2×C3×D4—34no—
241C2×C3×D4—64no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—32no—
249C22×C3×C4—34no—
250C22×C3×C4—38no—
251C22×C3×C4—34no—
252C22×C3×C4—34no—
253C22×C3×C4—64no—
254C22×C3×C4—68no—
255C22×C3×C4—64no—
256C22×C3×C4—64no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C2×#67—38no—
264C2×#67—38no—
265C2×#67—68no—
266C2×#67—68no—
267C22×Dic3—32no—
268C22×Dic3—32no—
269C22×Dic3—32no—
270C22×Dic3—32no—
271C22×Dic3—62no—
272C22×Dic3—62no—
273C22×Dic3C22×D311yescharacteristic
274C22×Dic3C22×D311yescharacteristic
275C22×Dic3C22×D311yescharacteristic
276C22×Dic3C22×D312yes—
277C2×D12—24no—
278C2×D12C22×D314yes—
279C2×C4×D3—24no—
280C2×C4×D3—24no—
281C2×C4×D3—24no—
282C2×C4×D3—28no—
283C2×C4×D3C22×D314yes—
284C2×C4×D3C22×D314yes—
285C2×C4×D3C22×D314yes—
286C2×C4×D3C22×D318yes—
287C2×Dic6—34no—
288C2×Dic6—34no—
289C2×Dic6—64no—
290C2×Dic6—68no—
291C2×Dic6—64no—
292C2×Dic6—64no—
293C3×C4⋊C4—34no—
294C3×C22⋊C4—38no—
295C3×C42—24no—
296C3×C42—34no—
297C3×C42—34no—
298C3×C42—34no—
299C3×C42C22×D314yes—
300C3×C42C22×D314yes—
301#217—38no—
302#217—38no—
303#217—38no—
304#217—38no—
305(C2×D3)⋊C4—38no—
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—38no—
313C4⋊Dic3—38no—
314C4⋊Dic3—64no—
315C4⋊Dic3C22×D314yes—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—38no—
319Dic3⋊C4—38no—
320Dic3⋊C4—38no—
321Dic3⋊C4—38no—
322Dic3⋊C4—68no—
323C4×Dic3—38no—
324C4×Dic3—38no—
325C4×Dic3—68no—
326C4×Dic3C22×D314yes—
327C4×Dic3C22×D314yes—
328C4×Dic3C22×D314yes—
329C22×C32C2×#4112yes—
330C22×C32C2×#4112yes—
331C22×C32C2×#4112yes—
332C22×C32C2511yescharacteristic
333C2×C3×D3—28no—
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3—24no—
337C2×C3×D3—24no—
338C2×C3×D3—24no—
339C2×C3×D3—48no—
340C2×C3×D3C2×#4114yes—
341C32×C4—22no—
342C32×C4C2×#4114yes—
343C32×C4C2×#4114yes—
344C3⋊Dic3—24no—
345C3⋊Dic3—24no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C3×Dic3—22no—
349C3×Dic3—24no—
350C22×Q8—91no—
351C22×D4—31no—
352C22×D4—92no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—32no—
356C23×C4—31no—
357#126—916no—
358#125—98no—
359#124—98no—
360#123—916no—
361C22⋊Q8—98no—
362#121—98no—
363C4×Q8—98no—
364C4×D4—38no—
365C4×D4—916no—
366#117—916no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4—92no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—91no—
372C2×C4⋊C4—92no—
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—31no—
381C2×C42—38no—
382C2×C42—92no—
383C2×C42D3211yescharacteristic
384C23×C3—21no—
385C23×C3—34no—
386C23×C3—32no—
387C23×C3—34no—
388C23×C3—62no—
389C23×C3—62no—
390C23×C3—64no—
391C23×C3—64no—
392C23×C3—64no—
393C23×C3C23×D311yescharacteristic
394C23×C3C23×D311yescharacteristic
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3#23514yes—
401C22×D3C23×D314yes—
402C22×D3C23×D312yes—
403C3×D4—68no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—32no—
414C2×C3×C4—34no—
415C2×C3×C4—42no—
416C2×C3×C4—68no—
417C2×C3×C4—64no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—616no—
422C2×C3×C4—68no—
423C2×C3×C4—68no—
424C2×C3×C4#23514yes—
425C2×C3×C4#23514yes—
426C2×C3×C4#23514yes—
427C2×C3×C4#23714yes—
428C2×C3×C4C23×D312yes—
429C2×C3×C4C23×D312yes—
430C2×C3×C4C23×D312yes—
431C2×C3×C4C23×D312yes—
432C2×C3×C4C23×D312yes—
433C2×C3×C4C23×D312yes—
434#67—616no—
435#67—616no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—24no—
440C2×Dic3—34no—
441C2×Dic3—34no—
442C2×Dic3—34no—
443C2×Dic3—34no—
444C2×Dic3—64no—
445C2×Dic3—64no—
446C2×Dic3—68no—
447C2×Dic3—64no—
448C2×Dic3—64no—
449C2×Dic3—64no—
450C2×Dic3—64no—
451C2×Dic3—124no—
452C2×Dic3C23×D312yes—
453C2×Dic3C23×D312yes—
454C2×Dic3C23×D312yes—
455C2×Dic3C23×D314yes—
456D12—28no—
457C4×D3—28no—
458C4×D3—28no—
459C4×D3—28no—
460C4×D3—216no—
461Dic6—616no—
462Dic6—68no—
463Dic6—68no—
464C2×C32#52914yescomplemented
465C2×C32C22×#4111yescharacteristic
466C2×C32C22×#4111yescharacteristic
467C2×C32C22×#4111yescharacteristic
468C3×D3—24no—
469C3×D3—44no—
470C24—31no—
471C24—32no—
472C2×Q8—94no—
473C2×Q8—184no—
474C2×D4—34no—
475C2×D4—64no—
476C2×D4—98no—
477C2×D4—188no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—32no—
482C22×C4—34no—
483C22×C4—34no—
484C22×C4—34no—
485C22×C4—38no—
486C22×C4—64no—
487C22×C4—64no—
488C22×C4—68no—
489C22×C4—64no—
490C22×C4—92no—
491C22×C4—92no—
492C22×C4C2×D3211yescharacteristic
493C22×C4C2×D3211yescharacteristic
494C22×C4C2×D3211yescharacteristic
495C4⋊C4—34no—
496C4⋊C4—98no—
497C4⋊C4—98no—
498C4⋊C4—98no—
499C4⋊C4—94no—
500C4⋊C4—98no—
501C22⋊C4—38no—
502C22⋊C4—98no—
503C22⋊C4—98no—
504C22⋊C4—98no—
505C22⋊C4—98no—
506C42—34no—
507C42—34no—
508C42—34no—
509C42—98no—
510C42C2×D3214yes—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—34no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—68no—
519C22×C3—64no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—128no—
523C22×C3C2×#23512yes—
524C22×C3C2×#23512yes—
525C22×C3C2×#23512yes—
526C22×C3C2×#23512yes—
527C22×C3C2×#23712yes—
528C22×C3D3×#4112yes—
529C22×C3C24×D311yescharacteristic
530C22×C3C24×D311yescharacteristic
531C2×D3—22no—
532C2×D3—22no—
533C2×D3—28no—
534C2×D3—24no—
535C2×D3—24no—
536C2×D3—24no—
537C2×D3—48no—
538C2×D3C2×#23514yes—
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—24no—
542C3×C4—24no—
543C3×C4—42no—
544C3×C4—64no—
545C3×C4—62no—
546C3×C4—62no—
547C3×C4—62no—
548C3×C4C2×#23514yes—
549C3×C4C2×#23514yes—
550C3×C4C2×#23514yes—
551C3×C4C2×#23714yes—
552Dic3—22no—
553Dic3—22no—
554Dic3—22no—
555Dic3—24no—
556Dic3—68no—
557Dic3—64no—
558Dic3—64no—
559Dic3—64no—
560Dic3—64no—
561Dic3—124no—
562C32C2×#52911yescharacteristic, complemented, Sylow
563C23—34no—
564C23—32no—
565C23—34no—
566C23—62no—
567C23—62no—
568C23—64no—
569C23—64no—
570C23—64no—
571C23C22×D3211yescharacteristic
572Q8—188no—
573D4—68no—
574D4—1816no—
575C2×C4—22no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—34no—
580C2×C4—68no—
581C2×C4—62no—
582C2×C4—64no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—68no—
586C2×C4—616no—
587C2×C4—68no—
588C2×C4—94no—
589C2×C4—94no—
590C2×C4—184no—
591C2×C4—184no—
592C2×C4#379514yes—
593C2×C4#379814yes—
594C2×C4C22×D3212yes—
595C2×C4C22×D3212yes—
596C2×C4C22×D3212yes—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—24no—
601C2×C3—64no—
602C2×C3—124no—
603C2×C3#547914yescomplemented
604C2×C3#555714yescomplemented
605C2×C3C22×#23511yescharacteristic
606C2×C3C22×#23511yescharacteristic
607C2×C3C22×#23511yescharacteristic
608C2×C3C22×#23511yescharacteristic
609C2×C3C22×#23711yescharacteristic
610C2×C3C2×D3×#4111yescharacteristic
611D3—24no—
612D3—44no—
613C22—34no—
614C22—62no—
615C22—62no—
616C22—68no—
617C22—64no—
618C22—64no—
619C22—64no—
620C22—128no—
621C22C2×#379512yes—
622C22C2×#379812yes—
623C22D3×#23512yes—
624C22C23×D3211yescharacteristic
625C4—22no—
626C4—62no—
627C4—64no—
628C4—62no—
629C4—62no—
630C4—184no—
631C4—184no—
632C4C2×#379514yes—
633C4C2×#379814yes—
634C3—21no—
635C3C2×#547911yescharacteristic, complemented
636C3C2×#555711yescharacteristic, complemented
637C2—64no—
638C2—124no—
639C2#1059397414yesdirect product factor
640C2C22×#379511yescharacteristic
641C2C22×#379811yescharacteristic
642C2C2×D3×#23511yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×#63908C2
hypercenterC2×C42D32
hypocenterC32C2×#529
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
2. C2×C3×C4×D12C2semidirect
3. C2×C3×C42×D3C2semidirect
5. C2×#63905C2semidirect
6. C2×C4×#625C2semidirect
7. C2×#63869C2semidirect
8. C2×#63860C2semidirect
9. C2×#63859C2semidirect
10. C2×#63857C2semidirect
11. C2×#63855C2semidirect
12. #10593974C2direct (N × H)
26. C4×#634C22semidirect
32. C3×C4×D12C22semidirect
33. C3×C42×D3C22semidirect
42. #63905C22semidirect
43. C4×#625C22semidirect
44. #63869C22semidirect
45. #63860C22semidirect
46. #63859C22semidirect
47. #63857C22semidirect
48. #63855C22semidirect
67. C2×C4×D12D3semidirect
69. C2×C42×D3D3semidirect
183. C4×D12C2×D3semidirect
185. C42×D3C2×D3semidirect
464. C2×C32#529semidirect
562. C32C2×#529semidirect
603. C2×C3#5479semidirect
604. C2×C3#5557semidirect
635. C3C2×#5479semidirect
636. C3C2×#5557semidirect
639. C2#10593974direct (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×C42×D32
C2×#639082
C2×#639052
C2×C4×#6252
C2×#638692
C2×#638602
C2×#638592
C2×#638572
C2×#638552
#105939742
C2×#55573
C2×#54793