Finite Group Databasebeta

← C2×#10594325 #11901916

Subgroups — C2×#10594325 #11901916

Order 1152.

2369 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#890C211yesmaximal, characteristic, complemented
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×#63874C211yesmaximal, characteristic
6C2×#63871C212yesmaximal
7C2×#63869C211yesmaximal, characteristic, complemented
8C2×#63865C212yesmaximal
9C2×#63849C211yesmaximal, characteristic
10C2×#63847C212yesmaximal, complemented
11C2×#63839C212yesmaximal, complemented
12#10594325C2116yesmaximal, direct product factor
13C2×#5729—31nomaximal
14C2×#5689—31nomaximal
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×Dic6C2212yes—
18C22×#627C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750C2212yes—
22C4⋊C4×C3⋊D3C2218yes—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#890C2218yescomplemented
31C3×#888C2218yescomplemented
32C2×#3724C2211yescharacteristic
33C2×#3724C2212yes—
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×#3722C2212yes—
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×Dic32C2212yes—
41#63918C2218yescomplemented
42#63874C2218yes—
43#63871C22116yes—
44#63869C2218yescomplemented
45#63865C22116yes—
46#63849C2218yes—
47#63847C22116yescomplemented
48#63839C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×#125—31no—
51C2×#946—32no—
52C2×#944—32no—
53#5729—316no—
54#5689—316no—
55C2×#897—32no—
56C2×#896—32no—
57C2×#896—32no—
58C2×#892—31no—
59C2×#892—31no—
60C2×D3×C4⋊C4—31no—
61C2×D3×C4⋊C4—31no—
62C2×D3×C4⋊C4—61no—
63C2×#890—31no—
64C2×#890D311yescharacteristic, complemented
65C2×#889—32no—
66C2×#889—32no—
67C2×#888—32no—
68C2×#888—31no—
69C2×#888D311yescharacteristic, complemented
70C2×#872—31no—
71C2×#872—31no—
72C2×#870—31no—
73C2×#869—31no—
74C23×C3⋊D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C4×C3⋊D3—44no—
80C2×C4×C3⋊D3Q818yescomplemented
81C2×C4×C3⋊D3C2318yes—
82C2×C4×C3⋊D3C2314yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C2×C3×Dic6—44no—
90C2×C3×Dic6C2318yes—
91C2×#627—44no—
92C2×#627C2318yes—
93C32×C4⋊C4C2314yes—
94C4⋊(C3⋊Dic3)C2314yes—
95#3750C2318yes—
96C3×C4⋊Dic3C2314yes—
97C3×C4⋊Dic3C2318yes—
98C3×C4⋊Dic3C2314yes—
99C3×Dic3⋊C4C2318yes—
100C3×Dic3⋊C4C2318yes—
101C3×C4×Dic3C2314yes—
102C3×C4×Dic3C2314yes—
103#3724C2314yes—
104#3724C2314yes—
105#3724C2318yes—
106Dic3⋊Dic3C2318yes—
107Dic3⋊Dic3C2318yes—
108#3722C2318yes—
109#3722C2314yes—
110#3722C2314yes—
111Dic32C2318yes—
112C2×#544—91noSylow
113C22×C3×Q8—32no—
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×C4×D3—32no—
117C22×C4×D3—32no—
118C22×C4×D3—61no—
119C22×C4×D3—62no—
120C22×Dic6—32no—
121C22×Dic6—32no—
122C22×Dic6C2×D312yes—
123C3×C4⋊Q8—38no—
124C3×#125—38no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C42—31no—
134C2×C3×C42—31no—
135#946—316no—
136#944—316no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—61no—
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×C4⋊Dic3C2×D312yes—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—62no—
162C2×Dic3⋊C4C2×D312yes—
163C2×Dic3⋊C4C2×D312yes—
164C2×C4×Dic3—32no—
165C2×C4×Dic3—32no—
166C2×C4×Dic3C2×D311yescharacteristic
167C2×C4×Dic3C2×D311yescharacteristic
168#897—316no—
169#896—316no—
170#896—316no—
171#892—38no—
172#892—38no—
173D3×C4⋊C4—38no—
174D3×C4⋊C4—38no—
175D3×C4⋊C4—68no—
176#890—38no—
177#890C2×D318yescomplemented
178#889—316no—
179#889—316no—
180#888—316no—
181#888—38no—
182#888C2×D318yescomplemented
183#872—38no—
184#872—38no—
185#870—38no—
186#869—38no—
187C23×C32C2411yescharacteristic
188C22×C3⋊D3—22no—
189C22×C3⋊D3—22no—
190C22×C3⋊D3C2×Q814yes—
191C22×C3⋊D3C2412yes—
192C2×C32×C4—24no—
193C2×C32×C4C2×Q814yes—
194C2×C32×C4C2414yes—
195C2×C32×C4C2412yes—
196C2×C3⋊Dic3—24no—
197C2×C3⋊Dic3C2×Q814yes—
198C2×C3⋊Dic3C2414yes—
199C2×C3⋊Dic3C2412yes—
200C4×C3⋊D3—48no—
201C4×C3⋊D3C2×Q8116yescomplemented
202C2×C3×Dic3—22no—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3C2414yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C3×Dic6—48no—
215#627—48no—
216#544—916no—
217C2×C4⋊Q8—31no—
218C2×C4⋊Q8—91no—
219C2×C4⋊Q8—92no—
220C2×#125—31no—
221C2×#125—91no—
222C2×#125—92no—
223C2×C22⋊Q8—92no—
224C2×C22⋊Q8—92no—
225C2×#117—91no—
226C2×#117—91no—
227C22×C4⋊C4—91no—
228C23×D3—31no—
229C23×D3—31no—
230C23×D3—61no—
231C2×C3×Q8—38no—
232C2×C3×Q8—124no—
233C22×C3×C4—21no—
234C22×C3×C4—22no—
235C22×C3×C4—32no—
236C22×C3×C4—32no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4C22×D312yes—
242C22×C3×C4C22×D312yes—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—32no—
248C22×Dic3—32no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D311yescharacteristic
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D311yescharacteristic
256C22×Dic3C22×D311yescharacteristic
257C2×C4×D3—38no—
258C2×C4×D3—38no—
259C2×C4×D3—34no—
260C2×C4×D3—34no—
261C2×C4×D3—38no—
262C2×C4×D3—38no—
263C2×C4×D3—64no—
264C2×C4×D3—68no—
265C2×C4×D3—68no—
266C2×C4×D3—124no—
267C2×C4×D3—124no—
268C2×C4×D3—128no—
269C2×Dic6—38no—
270C2×Dic6—38no—
271C2×Dic6—44no—
272C2×Dic6—124no—
273C2×Dic6—124no—
274C2×Dic6C22×D318yes—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—34no—
277C3×C4⋊C4—38no—
278C3×C4⋊C4—38no—
279C3×C4⋊C4—38no—
280C3×C4⋊C4—34no—
281C3×C4⋊C4C22×D314yes—
282C3×C4⋊C4C22×D314yes—
283C3×C42—34no—
284C3×C42—34no—
285(C2×D3)⋊C4—34no—
286(C2×D3)⋊C4—34no—
287(C2×D3)⋊C4—34no—
288(C2×D3)⋊C4—34no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—38no—
291C4⋊Dic3—34no—
292C4⋊Dic3—34no—
293C4⋊Dic3—38no—
294C4⋊Dic3—38no—
295C4⋊Dic3—64no—
296C4⋊Dic3C22×D314yes—
297C4⋊Dic3C22×D314yes—
298C4⋊Dic3C22×D318yes—
299Dic3⋊C4—38no—
300Dic3⋊C4—38no—
301Dic3⋊C4—38no—
302Dic3⋊C4—38no—
303Dic3⋊C4—34no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—68no—
310Dic3⋊C4C22×D318yes—
311Dic3⋊C4C22×D318yes—
312C4×Dic3—38no—
313C4×Dic3—38no—
314C4×Dic3C22×D314yes—
315C4×Dic3C22×D314yes—
316C22×C32C22×Q812yes—
317C22×C32H(5,𝔽2)12yes—
318C22×C322−1+412yes—
319C22×C32C2511yescharacteristic
320C2×C3⋊D3—28no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3C22×Q814yes—
324C32×C4—24no—
325C32×C4C22×Q814yes—
326C3⋊Dic3—24no—
327C3⋊Dic3C22×Q814yes—
328C3×Dic3—22no—
329C3×Dic3—24no—
330C3×Dic3—22no—
331C3×Dic3—22no—
332C3×Dic3—24no—
333C3×Dic3—22no—
334C22×Q8—32no—
335C22×Q8—92no—
336C23×C4—91no—
337C23×C4—92no—
338C4⋊Q8—38no—
339C4⋊Q8—98no—
340C4⋊Q8—916no—
341#125—38no—
342#125—98no—
343#125—916no—
344C22⋊Q8—916no—
345C22⋊Q8—916no—
346#117—98no—
347#117—98no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—32no—
351C2×C4⋊C4—32no—
352C2×C4⋊C4—32no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—92no—
356C2×C4⋊C4—92no—
357C2×C4⋊C4—92no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—91no—
360C2×C4⋊C4—98no—
361C2×C4⋊C4D3211yescharacteristic
362C2×C22⋊C4—91no—
363C2×C22⋊C4—91no—
364C2×C22⋊C4—92no—
365C2×C42—31no—
366C2×C42—31no—
367C2×C42—92no—
368C23×C3—21no—
369C23×C3C23×D311yescharacteristic
370C23×C3C23×D311yescharacteristic
371C22×D3—34no—
372C22×D3—34no—
373C22×D3—32no—
374C22×D3—32no—
375C22×D3—64no—
376C22×D3—62no—
377C22×D3—64no—
378C22×D3—64no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—62no—
383C3×Q8—128no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—34no—
390C2×C3×C4—34no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—44no—
396C2×C3×C4—62no—
397C2×C3×C4—64no—
398C2×C3×C4—62no—
399C2×C3×C4—64no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4D3×Q814yes—
403C2×C3×C4D3×Q814yes—
404C2×C3×C4C23×D314yes—
405C2×C3×C4C23×D314yes—
406C2×C3×C4C23×D312yes—
407C2×C3×C4C23×D312yes—
408C2×Dic3—22no—
409C2×Dic3—24no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—34no—
419C2×Dic3—34no—
420C2×Dic3—64no—
421C2×Dic3—62no—
422C2×Dic3—64no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—124no—
426C2×Dic3C23×D314yes—
427C2×Dic3C23×D314yes—
428C2×Dic3C23×D312yes—
429C2×Dic3C23×D312yes—
430C2×Dic3C23×D312yes—
431C2×Dic3C23×D312yes—
432C4×D3—316no—
433C4×D3—316no—
434C4×D3—616no—
435C4×D3—128no—
436C4×D3—128no—
437C4×D3—1216no—
438Dic6—48no—
439Dic6—128no—
440Dic6—128no—
441C2×C32#54414yescomplemented
442C2×C32C23×Q811yescharacteristic
443C2×C32C2×H(5,𝔽2)11yescharacteristic
444C2×C32C2×2−1+411yescharacteristic
445C3⋊D3—24no—
446C24—91no—
447C2×Q8—38no—
448C2×Q8—98no—
449C2×Q8—124no—
450C2×Q8—364no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—91no—
458C22×C4—94no—
459C22×C4—98no—
460C22×C4—92no—
461C22×C4—98no—
462C22×C4—364no—
463C22×C4C2×D3212yes—
464C22×C4C2×D3211yescharacteristic
465C4⋊C4—34no—
466C4⋊C4—34no—
467C4⋊C4—38no—
468C4⋊C4—38no—
469C4⋊C4—38no—
470C4⋊C4—94no—
471C4⋊C4—94no—
472C4⋊C4—98no—
473C4⋊C4—98no—
474C4⋊C4—98no—
475C4⋊C4—98no—
476C4⋊C4—94no—
477C4⋊C4C2×D3214yes—
478C22⋊C4—94no—
479C22⋊C4—94no—
480C22⋊C4—98no—
481C42—34no—
482C42—34no—
483C42—98no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3#100412yes—
489C22×C3C2×D3×Q812yes—
490C22×C3C2×D3×Q812yes—
491C22×C3#100712yes—
492C22×C3#100912yes—
493C22×C3#101012yes—
494C22×C3C24×D311yescharacteristic
495C22×C3C24×D311yescharacteristic
496C2×D3—34no—
497C2×D3—34no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—616no—
501C2×D3—64no—
502C2×D3—68no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—68no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—24no—
511C3×C4—44no—
512C3×C4—62no—
513C3×C4—64no—
514C3×C4—62no—
515C3×C4—64no—
516C3×C4—62no—
517C3×C4—62no—
518C3×C4C2×D3×Q814yes—
519C3×C4C2×D3×Q814yes—
520Dic3—22no—
521Dic3—24no—
522Dic3—22no—
523Dic3—22no—
524Dic3—24no—
525Dic3—22no—
526Dic3—34no—
527Dic3—34no—
528Dic3—64no—
529Dic3—64no—
530Dic3—64no—
531Dic3—124no—
532C32C2×#54411yescharacteristic, complemented, Sylow
533C23—94no—
534C23—92no—
535C23—182no—
536C23—182no—
537C23C22×D3211yescharacteristic
538Q8—128no—
539Q8—368no—
540C2×C4—24no—
541C2×C4—32no—
542C2×C4—32no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—34no—
546C2×C4—34no—
547C2×C4—62no—
548C2×C4—64no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—64no—
553C2×C4—94no—
554C2×C4—92no—
555C2×C4—916no—
556C2×C4—94no—
557C2×C4—184no—
558C2×C4—368no—
559C2×C4#379714yes—
560C2×C4C22×D3214yes—
561C2×C4C22×D3212yes—
562C2×C3—24no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3#568914yescomplemented
567C2×C3#572914yescomplemented
568C2×C3C2×#100411yescharacteristic
569C2×C3C22×D3×Q811yescharacteristic
570C2×C3C22×D3×Q811yescharacteristic
571C2×C3C2×#100711yescharacteristic
572C2×C3C2×#100911yescharacteristic
573C2×C3C2×#101011yescharacteristic
574D3—68no—
575D3—64no—
576D3—64no—
577C22—94no—
578C22—188no—
579C22—182no—
580C22—182no—
581C22C2×#379712yes—
582C22#6431412yes—
583C22#6431512yes—
584C22C23×D3211yescharacteristic
585C4—24no—
586C4—62no—
587C4—64no—
588C4—62no—
589C4—62no—
590C4—62no—
591C4—64no—
592C4—94no—
593C4—184no—
594C4C2×#379714yes—
595C3—21no—
596C3C2×#568911yescharacteristic, complemented
597C3C2×#572911yescharacteristic, complemented
598C2—184no—
599C2#1059432514yesdirect product factor
600C2C22×#379711yescharacteristic
601C2C2×#6431411yescharacteristic
602C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#890C2semidirect
3. C2×C3×#888C2semidirect
4. C2×#63918C2semidirect
7. C2×#63869C2semidirect
10. C2×#63847C2semidirect
11. C2×#63839C2semidirect
12. #10594325C2direct (N × H)
30. C3×#890C22semidirect
31. C3×#888C22semidirect
41. #63918C22semidirect
44. #63869C22semidirect
47. #63847C22semidirect
48. #63839C22semidirect
64. C2×#890D3semidirect
69. C2×#888D3semidirect
80. C2×C4×C3⋊D3Q8semidirect
177. #890C2×D3semidirect
182. #888C2×D3semidirect
201. C4×C3⋊D3C2×Q8semidirect
441. C2×C32#544semidirect
532. C32C2×#544semidirect
566. C2×C3#5689semidirect
567. C2×C3#5729semidirect
596. C3C2×#5689semidirect
597. C3C2×#5729semidirect
599. C2#10594325direct (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×#8902
C2×C3×#8882
C2×#639182
C2×#638742
C2×#638712
C2×#638692
C2×#638652
C2×#638492
C2×#638472
C2×#638392
#105943252
C2×#57293
C2×#56893