Finite Group Databasebeta

← C2×#10594824 #11901584

Subgroups — C2×#10594824 #11901584

Order 1152.

2169 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic
4C2×#63956C212yesmaximal
5C2×#63956C212yesmaximal
6C2×#63869C211yesmaximal, characteristic, complemented
7C2×#63866C211yesmaximal, characteristic, complemented
8#10594824C2116yesmaximal, direct product factor
9C2×#63847C212yesmaximal, complemented
10C2×#63846C212yesmaximal, complemented
11C2×#63844C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5625—31nomaximal
14C2×#5518—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C2×#3757C2212yes—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20#64133C2218yes—
21C2×#3750C2212yes—
22C2×C3×#217C2212yes—
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C3×#926C2218yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C3×#924C2218yes—
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2212yes—
34C2×#3724C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39#63956C22116yes—
40#63956C22116yes—
41C2×Dic32C2212yes—
42C2×Dic32C2212yes—
43#63869C2218yescomplemented
44#63866C2218yescomplemented
45#63847C22116yescomplemented
46#63846C22116yescomplemented
47#63844C2218yescomplemented
48Dic3×Dic6C2218yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×#117—31no—
51C2×Q8×Dic3—31no—
52C2×#944—31no—
53C2×#926D311yescharacteristic
54C2×#924—31no—
55C2×#924—31no—
56C2×#924—61no—
57C2×#924D311yescharacteristic
58#5625—316no—
59#5518—316no—
60C2×#890—32no—
61C2×#890—31no—
62C2×#889—32no—
63C2×#889—32no—
64C2×#889—32no—
65C2×#887—31no—
66C2×#879—32no—
67C2×#879—32no—
68C2×#879—32no—
69C2×#879—32no—
70C2×#870—31no—
71C2×#869—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C24×C32C2311yescharacteristic
75C22×C32×C4—24no—
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2314yes—
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×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C2×C3×Dic6—24no—
90C2×C3×Dic6C2314yes—
91#3757C2318yes—
92C4⋊(C3⋊Dic3)C2314yes—
93#3750C2318yes—
94C3×#217C2318yes—
95C3×#217C2314yes—
96C3×#217C2314yes—
97C3×C4⋊Dic3C2314yes—
98C3×C4⋊Dic3C2314yes—
99C3×C4⋊Dic3C2314yes—
100C3×Dic3⋊C4C2318yes—
101C3×C4×Dic3C2314yes—
102C3×C4×Dic3C2314yes—
103#3724C2318yes—
104#3724C2318yes—
105Dic3⋊Dic3C2318yes—
106Dic3⋊Dic3C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic32C2318yes—
110Dic32C2318yes—
111C2×#541—91noSylow
112C22×C3×Q8—31no—
113C23×C3×C4—21no—
114C23×C3×C4C2×D311yescharacteristic
115C23×C3×C4C2×D311yescharacteristic
116C22×Dic6—31no—
117C22×Dic6—31no—
118C22×Dic6—61no—
119C22×Dic6C2×D311yescharacteristic
120C3×C22⋊Q8—38no—
121C3×#117—38no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C42—31no—
130C2×C3×C42—31no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—62no—
134C2×#217C2×D312yes—
135C2×#217C2×D311yescharacteristic
136C2×#217C2×D311yescharacteristic
137Q8×Dic3—38no—
138#944—38no—
139#926C2×D318yes—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—32no—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3—61no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×C4⋊Dic3C2×D311yescharacteristic
150#924—38no—
151#924—38no—
152#924—68no—
153#924C2×D318yes—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
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
171C2×C4×Dic3C2×D311yescharacteristic
172#890—316no—
173#890—38no—
174#889—316no—
175#889—316no—
176#889—316no—
177#887—38no—
178#879—316no—
179#879—316no—
180#879—316no—
181#879—316no—
182#870—38no—
183#869—38no—
184C4×Dic6—38no—
185C4×Dic6—38no—
186C23×C32—22no—
187C23×C32—22no—
188C23×C32—22no—
189C23×C32C2412yes—
190C23×C32C2411yescharacteristic
191C2×C32×C4—22no—
192C2×C32×C4—28no—
193C2×C32×C4#4114yes—
194C2×C32×C4C2412yes—
195C2×C32×C4C2412yes—
196C2×C3⋊Dic3—24no—
197C2×C3⋊Dic3—24no—
198C2×C3⋊Dic3C2414yes—
199C2×C3⋊Dic3C2414yes—
200#634—28no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3C2412yes—
208C2×C3×Dic3C2412yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C3×Dic6—28no—
214#541—916no—
215C2×C4⋊Q8—91no—
216C2×#126—92no—
217C2×#126—92no—
218C2×#125—91no—
219C2×#125—92no—
220C2×#125—92no—
221C2×C22⋊Q8—31no—
222C2×C22⋊Q8—91no—
223C2×C4×Q8—91no—
224C2×C4×Q8—91no—
225C2×#117—31no—
226C24×C3—21no—
227C24×C3C22×D311yescharacteristic
228C24×C3C22×D311yescharacteristic
229C2×C3×Q8—34no—
230C2×C3×Q8—64no—
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—24no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—32no—
239C22×C3×C4—32no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—44no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D314yes—
246C22×C3×C4C22×D314yes—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×Dic3—32no—
250C22×Dic3—32no—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3C22×D311yescharacteristic
256C22×Dic3C22×D311yescharacteristic
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D311yescharacteristic
260C22×Dic3C22×D311yescharacteristic
261C2×Dic6—24no—
262C2×Dic6—34no—
263C2×Dic6—34no—
264C2×Dic6—64no—
265C2×Dic6—64no—
266C2×Dic6—64no—
267C2×Dic6—124no—
268C2×Dic6C22×D314yes—
269C3×C4⋊C4—34no—
270C3×C4⋊C4—34no—
271C3×C4⋊C4—34no—
272C3×C4⋊C4—38no—
273C3×C22⋊C4—34no—
274C3×C22⋊C4—34no—
275C3×C22⋊C4—38no—
276C3×C42—34no—
277C3×C42—34no—
278#217—38no—
279#217—38no—
280#217—68no—
281#217C22×D318yes—
282#217C22×D314yes—
283#217C22×D314yes—
284C4⋊Dic3—34no—
285C4⋊Dic3—34no—
286C4⋊Dic3—38no—
287C4⋊Dic3—38no—
288C4⋊Dic3—38no—
289C4⋊Dic3—38no—
290C4⋊Dic3—64no—
291C4⋊Dic3C22×D314yes—
292C4⋊Dic3C22×D314yes—
293C4⋊Dic3C22×D314yes—
294Dic3⋊C4—38no—
295Dic3⋊C4—38no—
296Dic3⋊C4—38no—
297Dic3⋊C4—38no—
298Dic3⋊C4—38no—
299Dic3⋊C4—38no—
300Dic3⋊C4—38no—
301Dic3⋊C4—38no—
302Dic3⋊C4—38no—
303Dic3⋊C4—38no—
304Dic3⋊C4—68no—
305Dic3⋊C4C22×D318yes—
306C4×Dic3—38no—
307C4×Dic3—38no—
308C4×Dic3—38no—
309C4×Dic3—38no—
310C4×Dic3C22×D314yes—
311C4×Dic3C22×D314yes—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—44no—
316C22×C32C2×#4112yes—
317C22×C322−1+412yes—
318C22×C322−1+412yes—
319C22×C32C2511yescharacteristic
320C32×C4—22no—
321C32×C4C2×#4114yes—
322C3⋊Dic3—24no—
323C3⋊Dic3—24no—
324C3×Dic3—24no—
325C3×Dic3—22no—
326C3×Dic3—22no—
327C3×Dic3—22no—
328C3×Dic3—24no—
329C3×Dic3—22no—
330C22×Q8—31no—
331C22×Q8—91no—
332C23×C4D3211yescharacteristic
333C4⋊Q8—98no—
334#126—916no—
335#126—916no—
336#125—98no—
337#125—916no—
338#125—916no—
339C22⋊Q8—38no—
340C22⋊Q8—98no—
341C4×Q8—98no—
342C4×Q8—98no—
343#117—38no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—32no—
348C2×C4⋊C4—92no—
349C2×C4⋊C4—92no—
350C2×C4⋊C4—92no—
351C2×C4⋊C4—92no—
352C2×C4⋊C4—92no—
353C2×C4⋊C4—92no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—92no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—31no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—92no—
360C2×C42—31no—
361C2×C42—31no—
362C2×C42—92no—
363C2×C42—92no—
364C23×C3—24no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—21no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3C23×D312yes—
376C23×C3C23×D312yes—
377C23×C3C23×D311yescharacteristic
378C23×C3C23×D311yescharacteristic
379C3×Q8—68no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—28no—
383C2×C3×C4—28no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—24no—
387C2×C3×C4—32no—
388C2×C3×C4—32no—
389C2×C3×C4—34no—
390C2×C3×C4—34no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—48no—
394C2×C3×C4—42no—
395C2×C3×C4—64no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—64no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4#23514yes—
402C2×C3×C4#23714yes—
403C2×C3×C4C23×D312yes—
404C2×C3×C4C23×D312yes—
405C2×C3×C4C23×D312yes—
406C2×C3×C4C23×D312yes—
407C2×Dic3—24no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—24no—
413C2×Dic3—34no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—34no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—64no—
422C2×Dic3—64no—
423C2×Dic3—124no—
424C2×Dic3—124no—
425C2×Dic3C23×D312yes—
426C2×Dic3C23×D312yes—
427C2×Dic3C23×D314yes—
428C2×Dic3C23×D314yes—
429C2×Dic3C23×D312yes—
430C2×Dic3C23×D312yes—
431Dic6—28no—
432Dic6—68no—
433Dic6—68no—
434Dic6—128no—
435C2×C32—42no—
436C2×C32#54114yescomplemented
437C2×C32C22×#4111yescharacteristic
438C2×C32C2×2−1+411yescharacteristic
439C2×C32C2×2−1+411yescharacteristic
440C24C2×D3211yescharacteristic
441C2×Q8—34no—
442C2×Q8—64no—
443C2×Q8—94no—
444C2×Q8—184no—
445C22×C4—24no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—32no—
451C22×C4—32no—
452C22×C4—92no—
453C22×C4—92no—
454C22×C4C2×D3214yes—
455C22×C4C2×D3211yescharacteristic
456C22×C4C2×D3211yescharacteristic
457C4⋊C4—34no—
458C4⋊C4—34no—
459C4⋊C4—34no—
460C4⋊C4—38no—
461C4⋊C4—98no—
462C4⋊C4—98no—
463C4⋊C4—98no—
464C4⋊C4—98no—
465C4⋊C4—98no—
466C4⋊C4—98no—
467C4⋊C4—94no—
468C4⋊C4—98no—
469C22⋊C4—34no—
470C22⋊C4—34no—
471C22⋊C4—38no—
472C22⋊C4—98no—
473C42—34no—
474C42—34no—
475C42—98no—
476C42—98no—
477C22×C3—24no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—48no—
491C22×C3—44no—
492C22×C3—44no—
493C22×C3C2×#23512yes—
494C22×C3C2×#23712yes—
495C22×C3#100712yes—
496C22×C3#101012yes—
497C22×C3#101012yes—
498C22×C3#101012yes—
499C22×C3C24×D311yescharacteristic
500C22×C3C24×D311yescharacteristic
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—24no—
504C3×C4—42no—
505C3×C4—64no—
506C3×C4—62no—
507C3×C4—62no—
508C3×C4—62no—
509C3×C4—62no—
510C3×C4—64no—
511C3×C4C2×#23514yes—
512C3×C4C2×#23714yes—
513Dic3—24no—
514Dic3—22no—
515Dic3—22no—
516Dic3—24no—
517Dic3—22no—
518Dic3—22no—
519Dic3—64no—
520Dic3—64no—
521Dic3—64no—
522Dic3—64no—
523Dic3—124no—
524Dic3—124no—
525C32C2×#54111yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—22no—
529C23C22×D3212yes—
530C23C22×D3211yescharacteristic
531Q8—68no—
532Q8—188no—
533C2×C4—22no—
534C2×C4—28no—
535C2×C4—32no—
536C2×C4—32no—
537C2×C4—32no—
538C2×C4—32no—
539C2×C4—34no—
540C2×C4—34no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—64no—
546C2×C4—64no—
547C2×C4—94no—
548C2×C4—94no—
549C2×C4—184no—
550C2×C4—184no—
551C2×C4#380414yes—
552C2×C4C22×D3212yes—
553C2×C4C22×D3212yes—
554C2×C3—24no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—44no—
559C2×C3—42no—
560C2×C3—42no—
561C2×C3#551814yescomplemented
562C2×C3#562514yescomplemented
563C2×C3C22×#23511yescharacteristic
564C2×C3C22×#23711yescharacteristic
565C2×C3C2×#100711yescharacteristic
566C2×C3C2×#101011yescharacteristic
567C2×C3C2×#101011yescharacteristic
568C2×C3C2×#101011yescharacteristic
569C22—22no—
570C22—22no—
571C22—22no—
572C22—44no—
573C22#6429712yes—
574C22#6429812yes—
575C22C2×#380412yes—
576C22C23×D3211yescharacteristic
577C4—22no—
578C4—62no—
579C4—62no—
580C4—62no—
581C4—62no—
582C4—64no—
583C4—64no—
584C4—184no—
585C4—184no—
586C4C2×#380414yes—
587C3—21no—
588C3C2×#551811yescharacteristic, complemented
589C3C2×#562511yescharacteristic, complemented
590C2—42no—
591C2#1059482414yesdirect product factor
592C2C2×#6429711yescharacteristic
593C2C2×#6429811yescharacteristic
594C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. C2×#63869C2semidirect
7. C2×#63866C2semidirect
8. #10594824C2direct (N × H)
9. C2×#63847C2semidirect
10. C2×#63846C2semidirect
11. C2×#63844C2semidirect
12. C2×Dic3×Dic6C2semidirect
43. #63869C22semidirect
44. #63866C22semidirect
45. #63847C22semidirect
46. #63846C22semidirect
47. #63844C22semidirect
48. Dic3×Dic6C22semidirect
436. C2×C32#541semidirect
525. C32C2×#541semidirect
561. C2×C3#5518semidirect
562. C2×C3#5625semidirect
588. C3C2×#5518semidirect
589. C3C2×#5625semidirect
591. C2#10594824direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9262
C2×C3×#9242
C2×#639562
C2×#638692
C2×#638662
#105948242
C2×#638472
C2×#638462
C2×#638442
C2×Dic3×Dic62
C2×#56253
C2×#55183