Finite Group Databasebeta

← C2×#10594444 #11900680

Subgroups — C2×#10594444 #11900680

Order 1152.

2577 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×#893C211yesmaximal, characteristic, complemented
4C2×#63908C211yesmaximal, characteristic
5C2×#63891C212yesmaximal, complemented
6C2×#63879C212yesmaximal, complemented
7C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
8C2×#63863C211yesmaximal, characteristic, complemented
9C2×#63858C212yesmaximal, complemented
10C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
11C2×#63841C212yesmaximal, complemented
12#10594444C2116yesmaximal, direct product factor
13C2×#5624—31nomaximal
14C2×#5557—31nomaximal
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#625C2212yes—
20C22×D3×Dic3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2212yes—
25C2×#3750C2212yes—
26C2×C4×C3⋊Dic3C2211yescharacteristic
27#64099C2218yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4⋊Dic3C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#897C2218yescomplemented
33C3×#893C2218yescomplemented
34C2×Dic3⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yes—
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63908C2218yes—
42#63891C22116yescomplemented
43#63879C22116yescomplemented
44C4×D3×Dic3C2218yescomplemented
45#63863C2218yescomplemented
46#63858C22116yescomplemented
47Dic3×Dic6C2218yescomplemented
48#63841C22116yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×C4×D4—31no—
51C2×#947—31no—
52C2×Q8×Dic3—31no—
53C2×#938—31no—
54C2×#936—31no—
55C2×#930—31no—
56C2×C4×#67—32no—
57C2×#926—32no—
58C22×C4×Dic3—31no—
59#5624—316no—
60#5557—316no—
61C2×#898—32no—
62C2×#897D311yescharacteristic, complemented
63C2×#893D311yescharacteristic, complemented
64C2×#892—32no—
65C2×#890—31no—
66C2×#890—31no—
67C2×#890—61no—
68C2×#886—32no—
69C2×#883—32no—
70C2×#67⋊C4—32no—
71C2×#879—32no—
72C2×C42×D3—31no—
73C2×C4×Dic6—31no—
74C23×C3×D3C2312yes—
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C2×C3×D12—24no—
86C2×C3×D12C2314yes—
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3—28no—
89C2×C3×C4×D3C2318yes—
90C2×C3×C4×D3C2314yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#625—28no—
94C2×#625C2318yes—
95C2×D3×Dic3—24no—
96C2×D3×Dic3—24no—
97C2×D3×Dic3C2314yes—
98C2×D3×Dic3C2314yes—
99C32×C4⋊C4C2314yes—
100C4⋊(C3⋊Dic3)C2318yes—
101C4⋊(C3⋊Dic3)C2314yes—
102#3750C2318yes—
103C4×C3⋊Dic3C2314yes—
104C3×(C2×D3)⋊C4C2318yes—
105C3×(C2×D3)⋊C4C2318yes—
106C3×C4⋊Dic3C2318yes—
107C3×C4×Dic3C2314yes—
108Dic3⋊Dic3C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2314yes—
113Dic32C2318yes—
114Dic32C2314yes—
115C2×#529—91noSylow
116C22×C3×Q8—31no—
117C22×C3×D4—31no—
118C23×C3×C4—31no—
119C23×C3×C4—32no—
120C22×#67—32no—
121C22×#67—32no—
122C23×Dic3—31no—
123C23×Dic3—31no—
124C22×D12C2×D311yescharacteristic
125C22×C4×D3—31no—
126C22×C4×D3—31no—
127C22×C4×D3C2×D311yescharacteristic
128C22×C4×D3C2×D312yes—
129C22×Dic6C2×D311yescharacteristic
130C3×C22⋊Q8—38no—
131C3×C4×D4—38no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—32no—
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C42—31no—
139C2×#217—32no—
140C2×#217—32no—
141C2×#217—32no—
142#947—38no—
143Q8×Dic3—38no—
144#938—38no—
145#936—38no—
146#930—38no—
147C4×#67—316no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4C2×D312yes—
152C2×(C2×D3)⋊C4C2×D312yes—
153#926—316no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—32no—
156C2×C4⋊Dic3—32no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—32no—
159C2×C4⋊Dic3—62no—
160C2×C4⋊Dic3—61no—
161C2×C4⋊Dic3C2×D312yes—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—62no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—38no—
175C2×C4×Dic3—61no—
176C2×C4×Dic3C2×D311yescharacteristic
177#898—316no—
178#897C2×D318yescomplemented
179#893C2×D318yescomplemented
180#892—316no—
181#890—38no—
182#890—38no—
183#890—68no—
184#886—316no—
185#883—316no—
186#67⋊C4—316no—
187#879—316no—
188C42×D3—38no—
189C4×Dic6—38no—
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—24no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2414yes—
202C2×C32×C4C2412yes—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—24no—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208C2×C3⋊Dic3C2414yes—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3#4114yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C3×D12—28no—
218C3×C4×D3—28no—
219C3×C4×D3—216no—
220C3×Dic6—28no—
221#625—216no—
222D3×Dic3—28no—
223D3×Dic3—28no—
224#529—916no—
225C2×#126—92no—
226C2×#125—91no—
227C2×#124—91no—
228C2×#123—92no—
229C2×C22⋊Q8—31no—
230C2×#121—91no—
231C2×C4×Q8—91no—
232C2×C4×D4—31no—
233C2×C4×D4—92no—
234C2×#117—92no—
235C22×C42—91no—
236C24×C3—31no—
237C24×C3—32no—
238C23×D3C22×D312yes—
239C23×D3C22×D311yescharacteristic
240C2×C3×Q8—34no—
241C2×C3×Q8—64no—
242C2×C3×D4—34no—
243C2×C3×D4—64no—
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—32no—
250C22×C3×C4—34no—
251C22×C3×C4—38no—
252C22×C3×C4—68no—
253C22×C3×C4—64no—
254C22×C3×C4C22×D312yes—
255C22×C3×C4C22×D312yes—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—38no—
259C2×#67—38no—
260C2×#67—68no—
261C2×#67—68no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—32no—
267C22×Dic3—32no—
268C22×Dic3—34no—
269C22×Dic3—34no—
270C22×Dic3—61no—
271C22×Dic3—61no—
272C22×Dic3—62no—
273C22×Dic3—64no—
274C22×Dic3—64no—
275C22×Dic3C22×D311yescharacteristic
276C22×Dic3C22×D311yescharacteristic
277C22×Dic3C22×D312yes—
278C22×Dic3C22×D311yescharacteristic
279C2×D12—24no—
280C2×D12C22×D314yes—
281C2×C4×D3—24no—
282C2×C4×D3—28no—
283C2×C4×D3—34no—
284C2×C4×D3—34no—
285C2×C4×D3—64no—
286C2×C4×D3—64no—
287C2×C4×D3C22×D314yes—
288C2×C4×D3C22×D318yes—
289C2×Dic6—24no—
290C2×Dic6C22×D314yes—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—38no—
293C3×C4⋊C4C22×D314yes—
294C3×C4⋊C4C22×D314yes—
295C3×C22⋊C4—38no—
296C3×C22⋊C4—38no—
297C3×C42—34no—
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)⋊C4C22×D318yes—
305(C2×D3)⋊C4C22×D318yes—
306C4⋊Dic3—34no—
307C4⋊Dic3—38no—
308C4⋊Dic3—38no—
309C4⋊Dic3—34no—
310C4⋊Dic3—38no—
311C4⋊Dic3—68no—
312C4⋊Dic3—64no—
313C4⋊Dic3C22×D318yes—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—68no—
318C4×Dic3—34no—
319C4×Dic3—34no—
320C4×Dic3—38no—
321C4×Dic3—34no—
322C4×Dic3—34no—
323C4×Dic3—38no—
324C4×Dic3—34no—
325C4×Dic3—34no—
326C4×Dic3—64no—
327C4×Dic3C22×D314yes—
328C22×C32C2×#4112yes—
329C22×C32C2×#4112yes—
330C22×C32C2×#4112yes—
331C22×C32C2511yescharacteristic
332C2×C3×D3—28no—
333C2×C3×D3—22no—
334C2×C3×D3—22no—
335C2×C3×D3—24no—
336C2×C3×D3—24no—
337C2×C3×D3—24no—
338C2×C3×D3—48no—
339C2×C3×D3C2×#4114yes—
340C32×C4—24no—
341C32×C4C2×#4114yes—
342C3⋊Dic3—22no—
343C3⋊Dic3—22no—
344C3⋊Dic3—24no—
345C3×Dic3—22no—
346C3×Dic3—24no—
347C3×Dic3—22no—
348C3×Dic3C2×#4114yes—
349C22×Q8—31no—
350C22×D4—31no—
351C22×D4—92no—
352C23×C4—32no—
353C23×C4—31no—
354C23×C4—91no—
355C23×C4—91no—
356#126—916no—
357#125—98no—
358#124—98no—
359#123—916no—
360C22⋊Q8—38no—
361#121—98no—
362C4×Q8—98no—
363C4×D4—38no—
364C4×D4—916no—
365#117—916no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—92no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4—92no—
370C2×C4⋊C4—91no—
371C2×C4⋊C4D3211yescharacteristic
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C42—31no—
378C2×C42—98no—
379C2×C42—91no—
380C2×C42—92no—
381C2×C42—91no—
382C2×C42—91no—
383C23×C3—21no—
384C23×C3—34no—
385C23×C3—32no—
386C23×C3—34no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3—64no—
390C23×C3—64no—
391C23×C3—64no—
392C23×C3C23×D311yescharacteristic
393C23×C3C23×D311yescharacteristic
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3#23914yes—
400C22×D3C23×D314yes—
401C22×D3C23×D312yes—
402C3×Q8—68no—
403C3×D4—68no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—34no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—34no—
414C2×C3×C4—44no—
415C2×C3×C4—616no—
416C2×C3×C4—62no—
417C2×C3×C4—64no—
418C2×C3×C4—62no—
419C2×C3×C4—68no—
420C2×C3×C4#23514yes—
421C2×C3×C4#23714yes—
422C2×C3×C4C23×D314yes—
423C2×C3×C4C23×D314yes—
424C2×C3×C4C23×D312yes—
425C2×C3×C4C23×D312yes—
426#67—616no—
427#67—616no—
428C2×Dic3—24no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—32no—
432C2×Dic3—32no—
433C2×Dic3—32no—
434C2×Dic3—32no—
435C2×Dic3—34no—
436C2×Dic3—34no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—64no—
440C2×Dic3—68no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—64no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—64no—
447C2×Dic3—68no—
448C2×Dic3—122no—
449C2×Dic3—122no—
450C2×Dic3—124no—
451C2×Dic3#23714yes—
452C2×Dic3C23×D312yes—
453C2×Dic3C23×D312yes—
454C2×Dic3C23×D314yes—
455C2×Dic3C23×D312yes—
456D12—28no—
457C4×D3—28no—
458C4×D3—216no—
459C4×D3—68no—
460C4×D3—68no—
461Dic6—28no—
462C2×C32#52914yescomplemented
463C2×C32C22×#4111yescharacteristic
464C2×C32C22×#4111yescharacteristic
465C2×C32C22×#4111yescharacteristic
466C3×D3—24no—
467C3×D3—44no—
468C24—31no—
469C24—32no—
470C2×Q8—34no—
471C2×Q8—64no—
472C2×D4—34no—
473C2×D4—64no—
474C2×D4—98no—
475C2×D4—188no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—32no—
480C22×C4—34no—
481C22×C4—38no—
482C22×C4—68no—
483C22×C4—64no—
484C22×C4—94no—
485C22×C4—94no—
486C22×C4—91no—
487C22×C4—91no—
488C22×C4—92no—
489C22×C4—184no—
490C22×C4—184no—
491C22×C4C2×D3212yes—
492C22×C4C2×D3211yescharacteristic
493C4⋊C4—38no—
494C4⋊C4—98no—
495C4⋊C4—98no—
496C4⋊C4—98no—
497C4⋊C4—94no—
498C4⋊C4C2×D3214yes—
499C22⋊C4—38no—
500C22⋊C4—38no—
501C22⋊C4—98no—
502C22⋊C4—98no—
503C22⋊C4—98no—
504C42—34no—
505C42—94no—
506C42—94no—
507C42—98no—
508C42—94no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—34no—
514C22×C3—62no—
515C22×C3—62no—
516C22×C3—68no—
517C22×C3—64no—
518C22×C3—64no—
519C22×C3—64no—
520C22×C3—128no—
521C22×C3C2×#23512yes—
522C22×C3C2×#23712yes—
523C22×C3C2×#23712yes—
524C22×C3C2×#23912yes—
525C22×C3D3×#4112yes—
526C22×C3D3×#4112yes—
527C22×C3C24×D311yescharacteristic
528C22×C3C24×D311yescharacteristic
529C2×D3—22no—
530C2×D3—22no—
531C2×D3—28no—
532C2×D3—24no—
533C2×D3—24no—
534C2×D3—24no—
535C2×D3—48no—
536C2×D3C2×#23914yes—
537C3×C4—24no—
538C3×C4—24no—
539C3×C4—24no—
540C3×C4—34no—
541C3×C4—44no—
542C3×C4—62no—
543C3×C4—64no—
544C3×C4—62no—
545C3×C4C2×#23514yes—
546C3×C4C2×#23714yes—
547Dic3—24no—
548Dic3—22no—
549Dic3—22no—
550Dic3—62no—
551Dic3—62no—
552Dic3—64no—
553Dic3—62no—
554Dic3—62no—
555Dic3—64no—
556Dic3—122no—
557Dic3—122no—
558Dic3—124no—
559Dic3C2×#23714yes—
560C32C2×#52911yescharacteristic, complemented, Sylow
561C23—34no—
562C23—32no—
563C23—34no—
564C23—62no—
565C23—62no—
566C23—64no—
567C23—64no—
568C23—64no—
569C23C22×D3211yescharacteristic
570Q8—68no—
571D4—68no—
572D4—1816no—
573C2×C4—24no—
574C2×C4—34no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—34no—
579C2×C4—616no—
580C2×C4—62no—
581C2×C4—64no—
582C2×C4—62no—
583C2×C4—68no—
584C2×C4—92no—
585C2×C4—92no—
586C2×C4—94no—
587C2×C4—188no—
588C2×C4—188no—
589C2×C4—182no—
590C2×C4—182no—
591C2×C4—184no—
592C2×C4#379514yes—
593C2×C4C22×D3214yes—
594C2×C4C22×D3212yes—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—24no—
599C2×C3—64no—
600C2×C3—124no—
601C2×C3#555714yescomplemented
602C2×C3#562414yescomplemented
603C2×C3C22×#23511yescharacteristic
604C2×C3C22×#23711yescharacteristic
605C2×C3C22×#23711yescharacteristic
606C2×C3C22×#23911yescharacteristic
607C2×C3C2×D3×#4111yescharacteristic
608C2×C3C2×D3×#4111yescharacteristic
609D3—24no—
610D3—44no—
611C22—34no—
612C22—62no—
613C22—62no—
614C22—68no—
615C22—64no—
616C22—64no—
617C22—64no—
618C22—128no—
619C22C2×#379512yes—
620C22D3×#23712yes—
621C22D3×#23912yes—
622C22C23×D3211yescharacteristic
623C4—24no—
624C4—34no—
625C4—62no—
626C4—64no—
627C4—62no—
628C4—182no—
629C4—182no—
630C4—184no—
631C4C2×#379514yes—
632C3—21no—
633C3C2×#555711yescharacteristic, complemented
634C3C2×#562411yescharacteristic, complemented
635C2—64no—
636C2—124no—
637C2#1059444414yesdirect product factor
638C2C22×#379511yescharacteristic
639C2C2×D3×#23711yescharacteristic
640C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63908C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64099C2semidirect
2. C2×C3×#897C2semidirect
3. C2×C3×#893C2semidirect
5. C2×#63891C2semidirect
6. C2×#63879C2semidirect
7. C2×C4×D3×Dic3C2semidirect
8. C2×#63863C2semidirect
9. C2×#63858C2semidirect
10. C2×Dic3×Dic6C2semidirect
11. C2×#63841C2semidirect
12. #10594444C2direct (N × H)
27. #64099C22semidirect
32. C3×#897C22semidirect
33. C3×#893C22semidirect
42. #63891C22semidirect
43. #63879C22semidirect
44. C4×D3×Dic3C22semidirect
45. #63863C22semidirect
46. #63858C22semidirect
47. Dic3×Dic6C22semidirect
48. #63841C22semidirect
62. C2×#897D3semidirect
63. C2×#893D3semidirect
178. #897C2×D3semidirect
179. #893C2×D3semidirect
462. C2×C32#529semidirect
560. C32C2×#529semidirect
601. C2×C3#5557semidirect
602. C2×C3#5624semidirect
633. C3C2×#5557semidirect
634. C3C2×#5624semidirect
637. C2#10594444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×C3×#8972
C2×C3×#8932
C2×#639082
C2×#638912
C2×#638792
C2×C4×D3×Dic32
C2×#638632
C2×#638582
C2×Dic3×Dic62
C2×#638412
#105944442
C2×#56243
C2×#55573