Finite Group Databasebeta

← C2×#10594427 #11900676

Subgroups — C2×#10594427 #11900676

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×#64096C211yesmaximal, characteristic, complemented
2C2×C3×#895C211yesmaximal, characteristic
3C2×C3×#890C211yesmaximal, characteristic, complemented
4C2×#63898C211yesmaximal, characteristic, complemented
5C2×#63898C212yesmaximal, complemented
6C2×#63884C212yesmaximal, complemented
7C2×#63878C212yesmaximal, complemented
8C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
9C2×#63860C211yesmaximal, characteristic, complemented
10C2×#63858C212yesmaximal, complemented
11C2×#63857C211yesmaximal, characteristic, complemented
12#10594427C2116yesmaximal, direct product factor
13C2×#5691—31nomaximal
14C2×#5600—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×D12C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2212yes—
26#64096C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#895C2218yes—
33C3×#890C2218yescomplemented
34C2×Dic3⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63898C22116yescomplemented
42#63898C2218yescomplemented
43#63884C22116yescomplemented
44#63878C22116yescomplemented
45C4×D3×Dic3C2218yescomplemented
46#63860C2218yescomplemented
47#63858C22116yescomplemented
48#63857C2218yescomplemented
49C2×C3×#125—31no—
50C2×C3×#121—31no—
51C2×#936—31no—
52C2×#935—32no—
53C2×D4×Dic3—32no—
54C2×D4×Dic3—31no—
55C2×#924—31no—
56C22×C4×Dic3—31no—
57#5691—316no—
58#5600—316no—
59C2×#898—32no—
60C2×#897—31no—
61C2×#895D311yescharacteristic
62C2×#894—32no—
63C2×#893—31no—
64C2×#893—32no—
65C2×#892—32no—
66C2×#890D311yescharacteristic, complemented
67C2×#887—31no—
68C2×#887—31no—
69C2×#887—61no—
70C2×#879—32no—
71C2×#877—32no—
72C2×#875—31no—
73C2×C42×D3—31no—
74C23×C3×D3C2312yes—
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2311yescharacteristic
81C2×#634—24no—
82C2×#634C2314yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×D12—28no—
88C2×C3×D12—24no—
89C2×C3×D12C2314yes—
90C2×C3×D12C2318yes—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3C2314yes—
93C2×D3×Dic3—24no—
94C2×D3×Dic3—24no—
95C2×D3×Dic3—28no—
96C2×D3×Dic3C2314yes—
97C2×D3×Dic3C2314yes—
98C2×D3×Dic3C2318yes—
99C32×C4⋊C4C2314yes—
100#3750C2318yes—
101C4×C3⋊Dic3C2314yes—
102C4×C3⋊Dic3C2318yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×C4⋊Dic3C2318yes—
106C3×Dic3⋊C4C2318yes—
107C3×C4×Dic3C2314yes—
108Dic3⋊Dic3C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113Dic32C2314yes—
114Dic32C2314yes—
115C2×#529—91noSylow
116C22×C3×D4—32no—
117C22×C3×D4—31no—
118C23×C3×C4—31no—
119C23×Dic3—32no—
120C23×Dic3—31no—
121C23×Dic3—31no—
122C22×D12C2×D311yescharacteristic
123C22×D12C2×D312yes—
124C22×C4×D3—31no—
125C22×C4×D3—31no—
126C22×C4×D3—32no—
127C22×C4×D3C2×D311yescharacteristic
128C22×Dic6—31no—
129C22×Dic6—31no—
130C22×Dic6—61no—
131C3×#125—38no—
132C3×#121—38no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4—32no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C4⋊C4C2×D311yescharacteristic
138C2×C3×C4⋊C4C2×D311yescharacteristic
139C2×C3×C22⋊C4—32no—
140C2×C3×C42—31no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—32no—
145#936—38no—
146#935—316no—
147D4×Dic3—316no—
148D4×Dic3—38no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4C2×D312yes—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3C2×D312yes—
156C2×C4⋊Dic3C2×D311yescharacteristic
157#924—38no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—62no—
162C2×Dic3⋊C4C2×D312yes—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—32no—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—38no—
172C2×C4×Dic3—62no—
173C2×C4×Dic3—61no—
174C2×C4×Dic3C2×D311yescharacteristic
175#898—316no—
176#897—38no—
177#895C2×D318yes—
178#894—316no—
179#893—38no—
180#893—316no—
181#892—316no—
182#890C2×D318yescomplemented
183#887—38no—
184#887—38no—
185#887—68no—
186#879—316no—
187#877—316no—
188#875—38no—
189C42×D3—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—24no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3#4114yes—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2414yes—
208C2×C3⋊Dic3C2412yes—
209#634—28no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2414yes—
218C3×D12—216no—
219C3×D12—28no—
220C3×C4×D3—28no—
221D3×Dic3—28no—
222D3×Dic3—28no—
223D3×Dic3—216no—
224#529—916no—
225C2×#126—92no—
226C2×#125—31no—
227C2×#124—91no—
228C2×#123—92no—
229C2×C22⋊Q8—91no—
230C2×#121—31no—
231C2×C4×Q8—91no—
232C2×C4×D4—92no—
233C2×C4×D4—91no—
234C2×#117—92no—
235C22×C42—91no—
236C24×C3—31no—
237C24×C3—32no—
238C23×D3C22×D312yes—
239C23×D3C22×D311yescharacteristic
240C2×C3×D4—38no—
241C2×C3×D4—34no—
242C2×C3×D4—68no—
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—64no—
252C22×C3×C4C22×D312yes—
253C22×C3×C4C22×D312yes—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—38no—
263C22×Dic3—34no—
264C22×Dic3—34no—
265C22×Dic3—61no—
266C22×Dic3—62no—
267C22×Dic3—61no—
268C22×Dic3—64no—
269C22×Dic3—68no—
270C22×Dic3—64no—
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D311yescharacteristic
273C22×Dic3C22×D311yescharacteristic
274C22×Dic3C22×D312yes—
275C2×D12—28no—
276C2×D12—24no—
277C2×D12C22×D314yes—
278C2×D12C22×D318yes—
279C2×C4×D3—24no—
280C2×C4×D3—34no—
281C2×C4×D3—34no—
282C2×C4×D3—38no—
283C2×C4×D3—64no—
284C2×C4×D3—68no—
285C2×C4×D3—64no—
286C2×C4×D3C22×D314yes—
287C2×Dic6—34no—
288C2×Dic6—34no—
289C2×Dic6—64no—
290C2×Dic6—68no—
291C2×Dic6—64no—
292C2×Dic6—64no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—38no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—38no—
297C3×C4⋊C4C22×D314yes—
298C3×C4⋊C4C22×D314yes—
299C3×C22⋊C4—38no—
300C3×C42—34no—
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—38no—
311C4⋊Dic3C22×D318yes—
312C4⋊Dic3C22×D314yes—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—68no—
317Dic3⋊C4C22×D318yes—
318C4×Dic3—34no—
319C4×Dic3—38no—
320C4×Dic3—38no—
321C4×Dic3—34no—
322C4×Dic3—34no—
323C4×Dic3—34no—
324C4×Dic3—34no—
325C4×Dic3—34no—
326C4×Dic3—64no—
327C4×Dic3—68no—
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—24no—
342C32×C4C2×#4114yes—
343C3⋊Dic3—24no—
344C3⋊Dic3—22no—
345C3⋊Dic3C2×#4114yes—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C3×Dic3—24no—
349C3×Dic3—22no—
350C22×Q8—91no—
351C22×D4—32no—
352C22×D4—31no—
353C23×C4—31no—
354C23×C4—92no—
355C23×C4—91no—
356C23×C4—91no—
357#126—916no—
358#125—38no—
359#124—98no—
360#123—916no—
361C22⋊Q8—98no—
362#121—38no—
363C4×Q8—98no—
364C4×D4—98no—
365C4×D4—916no—
366#117—916no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—92no—
372C2×C4⋊C4D3211yescharacteristic
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—98no—
380C2×C42—91no—
381C2×C42—91no—
382C2×C42—92no—
383C2×C42—91no—
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#23714yes—
401C22×D3C23×D314yes—
402C22×D3C23×D312yes—
403C3×D4—616no—
404C3×D4—68no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—22no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—34no—
414C2×C3×C4—44no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—64no—
419C2×C3×C4—68no—
420C2×C3×C4#23714yes—
421C2×C3×C4#23914yes—
422C2×C3×C4C23×D314yes—
423C2×C3×C4C23×D314yes—
424C2×C3×C4C23×D312yes—
425C2×C3×C4C23×D312yes—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—24no—
430C2×Dic3—34no—
431C2×Dic3—34no—
432C2×Dic3—32no—
433C2×Dic3—32no—
434C2×Dic3—32no—
435C2×Dic3—32no—
436C2×Dic3—34no—
437C2×Dic3—34no—
438C2×Dic3—64no—
439C2×Dic3—62no—
440C2×Dic3—64no—
441C2×Dic3—62no—
442C2×Dic3—68no—
443C2×Dic3—616no—
444C2×Dic3—68no—
445C2×Dic3—68no—
446C2×Dic3—64no—
447C2×Dic3—62no—
448C2×Dic3—64no—
449C2×Dic3—62no—
450C2×Dic3—122no—
451C2×Dic3C23×D312yes—
452C2×Dic3C23×D312yes—
453C2×Dic3C23×D312yes—
454C2×Dic3C23×D314yes—
455D12—216no—
456D12—28no—
457C4×D3—28no—
458C4×D3—68no—
459C4×D3—616no—
460C4×D3—68no—
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—38no—
475C2×D4—34no—
476C2×D4—68no—
477C2×D4—64no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—32no—
482C22×C4—34no—
483C22×C4—64no—
484C22×C4—94no—
485C22×C4—94no—
486C22×C4—98no—
487C22×C4—91no—
488C22×C4—91no—
489C22×C4—92no—
490C22×C4—184no—
491C22×C4—188no—
492C22×C4—184no—
493C22×C4C2×D3212yes—
494C22×C4C2×D3211yescharacteristic
495C4⋊C4—38no—
496C4⋊C4—34no—
497C4⋊C4—38no—
498C4⋊C4—98no—
499C4⋊C4—98no—
500C4⋊C4C2×D3214yes—
501C22⋊C4—38no—
502C22⋊C4—98no—
503C22⋊C4—98no—
504C22⋊C4—98no—
505C22⋊C4—98no—
506C42—34no—
507C42—94no—
508C42—94no—
509C42—94no—
510C42—98no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—34no—
516C22×C3—68no—
517C22×C3—62no—
518C22×C3—62no—
519C22×C3—64no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—128no—
523C22×C3C2×#23712yes—
524C22×C3C2×#23712yes—
525C22×C3C2×#23912yes—
526C22×C3D3×#4112yes—
527C22×C3D3×#4112yes—
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×#23714yes—
539C3×C4—24no—
540C3×C4—24no—
541C3×C4—24no—
542C3×C4—44no—
543C3×C4—62no—
544C3×C4—62no—
545C3×C4—62no—
546C3×C4—64no—
547C3×C4C2×#23714yes—
548C3×C4C2×#23914yes—
549Dic3—22no—
550Dic3—22no—
551Dic3—22no—
552Dic3—24no—
553Dic3—34no—
554Dic3—34no—
555Dic3—64no—
556Dic3—68no—
557Dic3—64no—
558Dic3—62no—
559Dic3—64no—
560Dic3—62no—
561Dic3—122no—
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—616no—
574D4—68no—
575C2×C4—24no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—34no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—64no—
584C2×C4—68no—
585C2×C4—94no—
586C2×C4—92no—
587C2×C4—92no—
588C2×C4—94no—
589C2×C4—188no—
590C2×C4—1816no—
591C2×C4—188no—
592C2×C4—184no—
593C2×C4—182no—
594C2×C4#379614yes—
595C2×C4C22×D3214yes—
596C2×C4C22×D3212yes—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—24no—
601C2×C3—64no—
602C2×C3—124no—
603C2×C3#560014yescomplemented
604C2×C3#569114yescomplemented
605C2×C3C22×#23711yescharacteristic
606C2×C3C22×#23711yescharacteristic
607C2×C3C22×#23911yescharacteristic
608C2×C3C2×D3×#4111yescharacteristic
609C2×C3C2×D3×#4111yescharacteristic
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×#379612yes—
622C22D3×#23712yes—
623C22#6431912yes—
624C22C23×D3211yescharacteristic
625C4—24no—
626C4—62no—
627C4—62no—
628C4—62no—
629C4—64no—
630C4—94no—
631C4—184no—
632C4—182no—
633C4C2×#379614yes—
634C3—21no—
635C3C2×#560011yescharacteristic, complemented
636C3C2×#569111yescharacteristic, complemented
637C2—64no—
638C2—124no—
639C2#1059442714yesdirect product factor
640C2C22×#379611yescharacteristic
641C2C2×D3×#23711yescharacteristic
642C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×C3×#895C2
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×#64096C2semidirect
3. C2×C3×#890C2semidirect
4. C2×#63898C2semidirect
5. C2×#63898C2semidirect
6. C2×#63884C2semidirect
7. C2×#63878C2semidirect
8. C2×C4×D3×Dic3C2semidirect
9. C2×#63860C2semidirect
10. C2×#63858C2semidirect
11. C2×#63857C2semidirect
12. #10594427C2direct (N × H)
26. #64096C22semidirect
33. C3×#890C22semidirect
41. #63898C22semidirect
42. #63898C22semidirect
43. #63884C22semidirect
44. #63878C22semidirect
45. C4×D3×Dic3C22semidirect
46. #63860C22semidirect
47. #63858C22semidirect
48. #63857C22semidirect
66. C2×#890D3semidirect
182. #890C2×D3semidirect
464. C2×C32#529semidirect
562. C32C2×#529semidirect
603. C2×C3#5600semidirect
604. C2×C3#5691semidirect
635. C3C2×#5600semidirect
636. C3C2×#5691semidirect
639. C2#10594427direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C3×#8952
C2×C3×#8902
C2×#638982
C2×#638842
C2×#638782
C2×C4×D3×Dic32
C2×#638602
C2×#638582
C2×#638572
#105944272
C2×#56913
C2×#56003