Finite Group Databasebeta

← C2×#10594579 #11903076

Subgroups — C2×#10594579 #11903076

Order 1152.

2457 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C3×#890C211yesmaximal, characteristic, complemented
4C2×C4×#626C211yesmaximal, characteristic
5C2×#63871C211yesmaximal, characteristic, complemented
6C2×#63858C212yesmaximal, complemented
7C2×#63853C212yesmaximal
8C2×#63849C212yesmaximal, complemented
9C2×#63846C212yesmaximal, complemented
10C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
11C2×#63841C211yesmaximal, characteristic, complemented
12#10594579C2116yesmaximal, direct product factor
13C2×#5694—31nomaximal
14C2×#5639—31nomaximal
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#626C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C4⋊C4×C3⋊D3C2218yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#897C2218yescomplemented
31C3×#890C2218yescomplemented
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×#3722C2211yescharacteristic
36C2×#3722C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×Dic32C2212yes—
40C2×Dic32C2212yes—
41C4×#626C2218yes—
42#63871C2218yescomplemented
43#63858C22116yescomplemented
44#63853C22116yes—
45#63849C22116yescomplemented
46#63846C22116yescomplemented
47Dic3×Dic6C2218yescomplemented
48#63841C2218yescomplemented
49C2×C3×#125—31no—
50C2×C3×C22⋊Q8—31no—
51C2×#946—31no—
52C2×Q8×Dic3—31no—
53C2×C4×#67—31no—
54C2×#926—31no—
55#5694—316no—
56#5639—316no—
57C2×#898—32no—
58C2×#897—31no—
59C2×#897D311yescharacteristic, complemented
60C2×#894—32no—
61C2×#892—31no—
62C2×#892—32no—
63C2×#892—32no—
64C2×D3×C4⋊C4—31no—
65C2×D3×C4⋊C4—31no—
66C2×D3×C4⋊C4—61no—
67C2×#890—32no—
68C2×#890D311yescharacteristic, complemented
69C2×#889—32no—
70C2×#883—32no—
71C2×#879—32no—
72C2×C4×D12—31no—
73C2×C4×Dic6—31no—
74C23×C3⋊D3C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C2×C4×C3⋊D3—28no—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3C2318yes—
83C2×C4×C3⋊D3C2314yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3C2314yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#626—24no—
94C2×#626C2314yes—
95C32×C4⋊C4C2314yes—
96C4⋊(C3⋊Dic3)C2314yes—
97#3750C2318yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×C4⋊Dic3C2314yes—
100C3×C4⋊Dic3C2318yes—
101C3×C4⋊Dic3C2318yes—
102C3×Dic3⋊C4C2318yes—
103C3×C4×Dic3C2314yes—
104Dic3⋊Dic3C2318yes—
105Dic3⋊Dic3C2314yes—
106Dic3⋊Dic3C2318yes—
107#3722C2314yes—
108#3722C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2314yes—
111Dic32C2318yes—
112Dic32C2318yes—
113C2×#552—91noSylow
114C22×C3×Q8—31no—
115C23×C3×C4—31no—
116C22×#67—31no—
117C22×D12—31no—
118C22×C4×D3—31no—
119C22×C4×D3—32no—
120C22×C4×D3—32no—
121C22×C4×D3—31no—
122C22×C4×D3—61no—
123C22×C4×D3—62no—
124C22×C4×D3C2×D311yescharacteristic
125C22×Dic6C2×D311yescharacteristic
126C3×#125—38no—
127C3×C22⋊Q8—38no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C22⋊C4—32no—
136C2×C3×C42—31no—
137C2×#217—31no—
138C2×#217—32no—
139#946—38no—
140Q8×Dic3—38no—
141C4×#67—38no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4C2×D312yes—
149#926—38no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—61no—
156C2×C4⋊Dic3C2×D312yes—
157C2×C4⋊Dic3C2×D312yes—
158C2×C4⋊Dic3C2×D311yescharacteristic
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—62no—
165C2×Dic3⋊C4C2×D312yes—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3C2×D311yescharacteristic
171#898—316no—
172#897—38no—
173#897C2×D318yescomplemented
174#894—316no—
175#892—38no—
176#892—316no—
177#892—316no—
178D3×C4⋊C4—38no—
179D3×C4⋊C4—38no—
180D3×C4⋊C4—68no—
181#890—316no—
182#890C2×D318yescomplemented
183#889—316no—
184#883—316no—
185#879—316no—
186C4×D12—38no—
187C4×Dic6—38no—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3#4114yes—
192C22×C3⋊D3C2412yes—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3C2412yes—
197C2×C32×C4—24no—
198C2×C32×C4#4114yes—
199C2×C32×C4C2414yes—
200C2×C32×C4C2412yes—
201C2×C3⋊Dic3—22no—
202C2×C3⋊Dic3—24no—
203C2×C3⋊Dic3C2414yes—
204C2×C3⋊Dic3C2412yes—
205C4×C3⋊D3—28no—
206C4×C3⋊D3—216no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C3×C4×D3—28no—
218C3×Dic6—28no—
219#626—28no—
220#552—916no—
221C2×#126—92no—
222C2×#125—31no—
223C2×#125—92no—
224C2×#123—92no—
225C2×C22⋊Q8—31no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×D4—91no—
229C2×#117—92no—
230C2×#117—91no—
231C22×C4⋊C4—91no—
232C24×C3—31no—
233C23×D3—31no—
234C23×D3—31no—
235C23×D3—61no—
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—34no—
238C2×C3×Q8—64no—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—31no—
246C22×C3×C4—34no—
247C22×C3×C4—64no—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D312yes—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—34no—
253C2×#67—64no—
254C22×Dic3—32no—
255C22×Dic3—32no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—61no—
259C22×Dic3—62no—
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D311yescharacteristic
265C2×D12—34no—
266C2×D12—64no—
267C2×C4×D3—24no—
268C2×C4×D3—34no—
269C2×C4×D3—38no—
270C2×C4×D3—38no—
271C2×C4×D3—34no—
272C2×C4×D3—64no—
273C2×C4×D3—68no—
274C2×C4×D3—68no—
275C2×C4×D3—68no—
276C2×C4×D3—68no—
277C2×C4×D3—64no—
278C2×C4×D3—64no—
279C2×C4×D3—128no—
280C2×C4×D3C22×D314yes—
281C2×Dic6—24no—
282C2×Dic6C22×D314yes—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—38no—
285C3×C4⋊C4—38no—
286C3×C4⋊C4—34no—
287C3×C4⋊C4—38no—
288C3×C4⋊C4C22×D314yes—
289C3×C4⋊C4C22×D314yes—
290C3×C22⋊C4—38no—
291C3×C42—34no—
292#217—34no—
293#217—38no—
294(C2×D3)⋊C4—34no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—34no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4C22×D318yes—
301C4⋊Dic3—34no—
302C4⋊Dic3—34no—
303C4⋊Dic3—34no—
304C4⋊Dic3—38no—
305C4⋊Dic3—38no—
306C4⋊Dic3—64no—
307C4⋊Dic3C22×D318yes—
308C4⋊Dic3C22×D318yes—
309C4⋊Dic3C22×D314yes—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4—38no—
314Dic3⋊C4—34no—
315Dic3⋊C4—68no—
316Dic3⋊C4C22×D318yes—
317C4×Dic3—38no—
318C4×Dic3—38no—
319C4×Dic3—38no—
320C4×Dic3—38no—
321C4×Dic3C22×D314yes—
322C22×C32C2×#4112yes—
323C22×C32C2×#4112yes—
324C22×C322−1+412yes—
325C22×C32C2511yescharacteristic
326C2×C3⋊D3—28no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3C2×#4114yes—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C2×C3×D3—44no—
334C32×C4—24no—
335C32×C4C2×#4114yes—
336C3⋊Dic3—22no—
337C3⋊Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3—24no—
340C3×Dic3—22no—
341C3×Dic3—22no—
342C3×Dic3—24no—
343C22×Q8—31no—
344C22×D4—91no—
345C23×C4—31no—
346C23×C4—92no—
347C23×C4—91no—
348#126—916no—
349#125—38no—
350#125—916no—
351#123—916no—
352C22⋊Q8—38no—
353C22⋊Q8—98no—
354C4×Q8—98no—
355C4×D4—98no—
356#117—916no—
357#117—98no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—92no—
367C2×C4⋊C4—98no—
368C2×C4⋊C4D3211yescharacteristic
369C2×C22⋊C4—32no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—91no—
374C2×C42—31no—
375C2×C42—92no—
376C2×C42—92no—
377C23×C3—21no—
378C23×C3—32no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3C23×D311yescharacteristic
383C23×C3C23×D311yescharacteristic
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—34no—
388C22×D3—34no—
389C22×D3—32no—
390C22×D3—32no—
391C22×D3—64no—
392C22×D3—62no—
393C22×D3—64no—
394C22×D3—64no—
395C22×D3—62no—
396C22×D3—62no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3C23×D312yes—
400C3×Q8—68no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—34no—
409C2×C3×C4—34no—
410C2×C3×C4—32no—
411C2×C3×C4—44no—
412C2×C3×C4—62no—
413C2×C3×C4—64no—
414C2×C3×C4—62no—
415C2×C3×C4—64no—
416C2×C3×C4—62no—
417C2×C3×C4—68no—
418C2×C3×C4#23714yes—
419C2×C3×C4#23914yes—
420C2×C3×C4C23×D314yes—
421C2×C3×C4C23×D314yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D312yes—
424#67—68no—
425C2×Dic3—24no—
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—62no—
435C2×Dic3—64no—
436C2×Dic3—64no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—64no—
440C2×Dic3—64no—
441C2×Dic3—124no—
442C2×Dic3C23×D312yes—
443C2×Dic3C23×D312yes—
444C2×Dic3C23×D314yes—
445C2×Dic3C23×D314yes—
446C2×Dic3C23×D312yes—
447D12—68no—
448C4×D3—28no—
449C4×D3—616no—
450C4×D3—616no—
451C4×D3—616no—
452C4×D3—68no—
453C4×D3—68no—
454C4×D3—1216no—
455Dic6—28no—
456C2×C32#55214yescomplemented
457C2×C32C22×#4111yescharacteristic
458C2×C32C22×#4111yescharacteristic
459C2×C32C2×2−1+411yescharacteristic
460C3⋊D3—24no—
461C3×D3—42no—
462C24—31no—
463C24—91no—
464C2×Q8—34no—
465C2×Q8—64no—
466C2×D4—94no—
467C2×D4—184no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—34no—
474C22×C4—64no—
475C22×C4—92no—
476C22×C4—91no—
477C22×C4—98no—
478C22×C4—94no—
479C22×C4—188no—
480C22×C4—184no—
481C22×C4C2×D3212yes—
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—38no—
484C4⋊C4—34no—
485C4⋊C4—38no—
486C4⋊C4—38no—
487C4⋊C4—94no—
488C4⋊C4—98no—
489C4⋊C4—98no—
490C4⋊C4—94no—
491C4⋊C4—98no—
492C4⋊C4C2×D3214yes—
493C22⋊C4—38no—
494C22⋊C4—94no—
495C22⋊C4—98no—
496C22⋊C4—98no—
497C22⋊C4—94no—
498C42—34no—
499C42—98no—
500C42—98no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—62no—
508C22×C3—124no—
509C22×C3C2×#23712yes—
510C22×C3C2×#23912yes—
511C22×C3#100712yes—
512C22×C3D3×#4112yes—
513C22×C3D3×#4112yes—
514C22×C3#101012yes—
515C22×C3C24×D311yescharacteristic
516C22×C3C24×D311yescharacteristic
517C2×D3—22no—
518C2×D3—22no—
519C2×D3—22no—
520C2×D3—34no—
521C2×D3—34no—
522C2×D3—44no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—616no—
526C2×D3—64no—
527C2×D3—68no—
528C2×D3—68no—
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—44no—
537C3×C4—62no—
538C3×C4—64no—
539C3×C4—62no—
540C3×C4—64no—
541C3×C4—62no—
542C3×C4C2×#23714yes—
543C3×C4C2×#23914yes—
544Dic3—24no—
545Dic3—22no—
546Dic3—22no—
547Dic3—22no—
548Dic3—24no—
549Dic3—64no—
550Dic3—62no—
551Dic3—62no—
552Dic3—64no—
553Dic3—64no—
554Dic3—124no—
555C32C2×#55211yescharacteristic, complemented, Sylow
556C23—32no—
557C23—62no—
558C23—62no—
559C23—62no—
560C23—94no—
561C23—92no—
562C23—182no—
563C23—182no—
564C23C22×D3211yescharacteristic
565Q8—68no—
566D4—188no—
567C2×C4—24no—
568C2×C4—32no—
569C2×C4—32no—
570C2×C4—32no—
571C2×C4—34no—
572C2×C4—34no—
573C2×C4—62no—
574C2×C4—64no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—64no—
578C2×C4—68no—
579C2×C4—94no—
580C2×C4—92no—
581C2×C4—1816no—
582C2×C4—182no—
583C2×C4—184no—
584C2×C4—188no—
585C2×C4#379614yes—
586C2×C4C22×D3214yes—
587C2×C4C22×D3212yes—
588C2×C3—24no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—122no—
593C2×C3#563914yescomplemented
594C2×C3#569414yescomplemented
595C2×C3C22×#23711yescharacteristic
596C2×C3C22×#23911yescharacteristic
597C2×C3C2×#100711yescharacteristic
598C2×C3C2×D3×#4111yescharacteristic
599C2×C3C2×D3×#4111yescharacteristic
600C2×C3C2×#101011yescharacteristic
601D3—42no—
602D3—68no—
603D3—64no—
604D3—64no—
605C22—62no—
606C22—62no—
607C22—62no—
608C22—94no—
609C22—124no—
610C22—188no—
611C22—182no—
612C22—182no—
613C22C2×#379612yes—
614C22#6431212yes—
615C22#6431512yes—
616C22C23×D3211yescharacteristic
617C4—24no—
618C4—62no—
619C4—64no—
620C4—62no—
621C4—62no—
622C4—64no—
623C4—182no—
624C4—184no—
625C4C2×#379614yes—
626C3—21no—
627C3C2×#563911yescharacteristic, complemented
628C3C2×#569411yescharacteristic, complemented
629C2—122no—
630C2—184no—
631C2#1059457914yesdirect product factor
632C2C22×#379611yescharacteristic
633C2C2×#6431211yescharacteristic
634C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#552
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×C4⋊C4×C3⋊D3C2semidirect
2. C2×C3×#897C2semidirect
3. C2×C3×#890C2semidirect
5. C2×#63871C2semidirect
6. C2×#63858C2semidirect
8. C2×#63849C2semidirect
9. C2×#63846C2semidirect
10. C2×Dic3×Dic6C2semidirect
11. C2×#63841C2semidirect
12. #10594579C2direct (N × H)
23. C4⋊C4×C3⋊D3C22semidirect
30. C3×#897C22semidirect
31. C3×#890C22semidirect
42. #63871C22semidirect
43. #63858C22semidirect
45. #63849C22semidirect
46. #63846C22semidirect
47. Dic3×Dic6C22semidirect
48. #63841C22semidirect
59. C2×#897D3semidirect
68. C2×#890D3semidirect
173. #897C2×D3semidirect
182. #890C2×D3semidirect
456. C2×C32#552semidirect
555. C32C2×#552semidirect
593. C2×C3#5639semidirect
594. C2×C3#5694semidirect
627. C3C2×#5639semidirect
628. C3C2×#5694semidirect
631. C2#10594579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C3×#8972
C2×C3×#8902
C2×C4×#6262
C2×#638712
C2×#638582
C2×#638532
C2×#638492
C2×#638462
C2×Dic3×Dic62
C2×#638412
#105945792
C2×#56943
C2×#56393