Finite Group Databasebeta

← C2×#10595273 #11903427

Subgroups — C2×#10595273 #11903427

Order 1152.

2389 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64145C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic
4C2×#63964C212yesmaximal, complemented
5C2×#63956C212yesmaximal, complemented
6C2×#63956C212yesmaximal, complemented
7C2×#63955C212yesmaximal, complemented
8#10595273C2116yesmaximal, direct product factor
9C2×C4×#627C211yesmaximal, characteristic, complemented
10C2×#63866C211yesmaximal, characteristic, complemented
11C2×#63844C211yesmaximal, characteristic, complemented
12C2×#63843C211yesmaximal, characteristic, complemented
13C2×#5671—31nomaximal
14C2×#5542—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C22×C3×Dic6C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C2×#3757C2212yes—
21C2×#3757C2212yes—
22#64145C2218yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C3×#936C2218yes—
28C3×D4×Dic3C2218yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2212yes—
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39#63964C22116yescomplemented
40#63956C22116yescomplemented
41#63956C22116yescomplemented
42#63955C22116yescomplemented
43C2×Dic32C2212yes—
44C2×Dic32C2212yes—
45C4×#627C2218yescomplemented
46#63866C2218yescomplemented
47#63844C2218yescomplemented
48#63843C2218yescomplemented
49C2×C3×#124—31no—
50C2×C3×C4×D4—31no—
51C2×Q8×Dic3—31no—
52C2×#944—31no—
53C2×#936—31no—
54C2×#936—31no—
55C2×#936—61no—
56C2×#936D311yescharacteristic
57C2×D4×Dic3D311yescharacteristic
58C2×#926—32no—
59C2×#924—32no—
60#5671—316no—
61#5542—316no—
62C2×#887—31no—
63C2×#887—31no—
64C2×#879—32no—
65C2×#879—32no—
66C2×#879—32no—
67C2×#879—32no—
68C2×#878—32no—
69C2×#877—32no—
70C2×#869—31no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C24×C32C2312yes—
75C2×C32×D4—24no—
76C2×C32×D4C2314yes—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2311yescharacteristic
81C2×#634—24no—
82C2×#634C2314yes—
83C22×C3×Dic3—28no—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2318yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#627—24no—
94C2×#627C2314yes—
95#3757C2318yes—
96#3757C2318yes—
97C4×C3⋊Dic3C2314yes—
98C3×#217C2318yes—
99C3×#217C2318yes—
100C3×#217C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×C4×Dic3C2314yes—
103C3×C4×Dic3C2314yes—
104#3724C2318yes—
105#3724C2314yes—
106Dic3⋊Dic3C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2314yes—
110Dic3⋊Dic3C2314yes—
111Dic32C2318yes—
112Dic32C2318yes—
113C2×#556—91noSylow
114C22×C3×Q8—31no—
115C22×C3×D4—21no—
116C22×C3×D4C2×D311yescharacteristic
117C22×C3×D4C2×D311yescharacteristic
118C23×C3×C4—32no—
119C23×Dic3C2×D312yes—
120C22×Dic6—31no—
121C22×Dic6—31no—
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—61no—
125C22×Dic6C2×D311yescharacteristic
126C3×#124—38no—
127C3×C4×D4—38no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C42—31no—
133C2×C3×C42—31no—
134C2×#217—32no—
135C2×#217—32no—
136C2×#217—32no—
137C2×#217—32no—
138C2×#217—62no—
139C2×#217—62no—
140C2×#217C2×D312yes—
141C2×#217C2×D312yes—
142C2×#217C2×D312yes—
143Q8×Dic3—38no—
144#944—38no—
145#936—38no—
146#936—38no—
147#936—68no—
148#936C2×D318yes—
149D4×Dic3C2×D318yes—
150#926—316no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—32no—
156C2×C4⋊Dic3C2×D311yescharacteristic
157#924—316no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—32no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3—61no—
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176#887—38no—
177#887—38no—
178#879—316no—
179#879—316no—
180#879—316no—
181#879—316no—
182#878—316no—
183#877—316no—
184#869—38no—
185C4×Dic6—38no—
186C4×Dic6—38no—
187C4×Dic6—38no—
188C23×C32—24no—
189C23×C32—24no—
190C23×C32—24no—
191C23×C32C2414yes—
192C23×C32C2411yescharacteristic
193C32×D4—28no—
194C2×C32×C4#4114yes—
195C2×C32×C4C2412yes—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—24no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3C2412yes—
200C2×C3⋊Dic3C2414yes—
201C2×C3⋊Dic3C2412yes—
202#634—28no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—216no—
209C2×C3×Dic3#4114yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C3×Dic6—28no—
217#627—28no—
218#556—916no—
219C2×C4⋊Q8—91no—
220C2×#126—92no—
221C2×#126—92no—
222C2×#124—31no—
223C2×#124—91no—
224C2×C22⋊Q8—92no—
225C2×C4×Q8—91no—
226C2×C4×Q8—91no—
227C2×C4×Q8—91no—
228C2×C4×D4—31no—
229C2×#117—92no—
230C24×C3—22no—
231C24×C3C22×D312yes—
232C24×C3C22×D312yes—
233C2×C3×Q8—34no—
234C2×C3×Q8—64no—
235C2×C3×D4—24no—
236C2×C3×D4—24no—
237C2×C3×D4—24no—
238C2×C3×D4—44no—
239C2×C3×D4C22×D314yes—
240C2×C3×D4C22×D314yes—
241C22×C3×C4—21no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—38no—
249C22×C3×C4—68no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×Dic3—28no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—32no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—32no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261C22×Dic3—62no—
262C22×Dic3C22×D318yes—
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D312yes—
266C22×Dic3C22×D311yescharacteristic
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D311yescharacteristic
269C2×Dic6—24no—
270C2×Dic6—34no—
271C2×Dic6—34no—
272C2×Dic6—34no—
273C2×Dic6—34no—
274C2×Dic6—64no—
275C2×Dic6—64no—
276C2×Dic6—64no—
277C2×Dic6—64no—
278C2×Dic6—64no—
279C2×Dic6—124no—
280C2×Dic6C22×D314yes—
281C3×C4⋊C4—34no—
282C3×C22⋊C4—38no—
283C3×C22⋊C4—38no—
284C3×C22⋊C4—38no—
285C3×C42—34no—
286C3×C42—34no—
287#217—38no—
288#217—38no—
289#217—38no—
290#217—38no—
291#217—68no—
292#217—68no—
293#217C22×D318yes—
294#217C22×D318yes—
295#217C22×D318yes—
296C4⋊Dic3—34no—
297C4⋊Dic3—34no—
298C4⋊Dic3—38no—
299C4⋊Dic3—38no—
300C4⋊Dic3—38no—
301C4⋊Dic3C22×D314yes—
302Dic3⋊C4—34no—
303Dic3⋊C4—38no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311C4×Dic3—34no—
312C4×Dic3—34no—
313C4×Dic3—38no—
314C4×Dic3—38no—
315C4×Dic3—38no—
316C4×Dic3—38no—
317C4×Dic3—64no—
318C4×Dic3C22×D314yes—
319C4×Dic3C22×D314yes—
320C22×C32—24no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—48no—
324C22×C32C2×#4112yes—
325C22×C32C2×#4112yes—
326C22×C322−1+412yes—
327C22×C32C2511yescharacteristic
328C32×C4C2×#4114yes—
329C3⋊Dic3—22no—
330C3⋊Dic3—24no—
331C3⋊Dic3—22no—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—24no—
335C3×Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3C2×#4114yes—
338C22×Q8—31no—
339C22×Q8—91no—
340C22×Q8—91no—
341C22×D4D3211yescharacteristic
342C23×C4—32no—
343C4⋊Q8—98no—
344#126—916no—
345#126—916no—
346#124—38no—
347#124—98no—
348C22⋊Q8—916no—
349C4×Q8—98no—
350C4×Q8—98no—
351C4×Q8—98no—
352C4×D4—38no—
353#117—916no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—92no—
357C2×C4⋊C4—92no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—91no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—92no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—32no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C42—31no—
368C2×C42—31no—
369C2×C42—92no—
370C2×C42—92no—
371C2×C42—91no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—21no—
380C23×C3—44no—
381C23×C3—44no—
382C23×C3—44no—
383C23×C3C23×D314yes—
384C23×C3C23×D314yes—
385C23×C3C23×D311yescharacteristic
386C23×C3C23×D311yescharacteristic
387C3×Q8—68no—
388C3×D4—28no—
389C3×D4—28no—
390C3×D4—48no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—34no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—34no—
397C2×C3×C4—34no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—616no—
401C2×C3×C4—64no—
402C2×C3×C4—62no—
403C2×C3×C4—64no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4#23514yes—
407C2×C3×C4#23714yes—
408C2×C3×C4C23×D312yes—
409C2×C3×C4C23×D312yes—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—216no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—34no—
419C2×Dic3—32no—
420C2×Dic3—32no—
421C2×Dic3—34no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—62no—
427C2×Dic3—64no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—124no—
432C2×Dic3—122no—
433C2×Dic3—122no—
434C2×Dic3#23714yes—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D314yes—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D312yes—
439C2×Dic3C23×D312yes—
440C2×Dic3C23×D312yes—
441Dic6—28no—
442Dic6—68no—
443Dic6—68no—
444Dic6—68no—
445Dic6—68no—
446Dic6—128no—
447C2×C32—44no—
448C2×C32#55614yescomplemented
449C2×C32C22×#4111yescharacteristic
450C2×C32C22×#4111yescharacteristic
451C2×C32C2×2−1+411yescharacteristic
452C24C2×D3212yes—
453C2×Q8—34no—
454C2×Q8—64no—
455C2×Q8—94no—
456C2×Q8—94no—
457C2×Q8—184no—
458C2×Q8—184no—
459C2×D4—24no—
460C2×D4C2×D3214yes—
461C22×C4—31no—
462C22×C4—38no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—31no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—68no—
469C22×C4—91no—
470C22×C4—91no—
471C22×C4—92no—
472C22×C4C2×D3211yescharacteristic
473C4⋊C4—34no—
474C4⋊C4—94no—
475C4⋊C4—98no—
476C4⋊C4—98no—
477C4⋊C4—98no—
478C4⋊C4—94no—
479C4⋊C4—94no—
480C4⋊C4—98no—
481C22⋊C4—38no—
482C22⋊C4—38no—
483C22⋊C4—38no—
484C22⋊C4—98no—
485C22⋊C4—98no—
486C42—34no—
487C42—34no—
488C42—98no—
489C42—98no—
490C42—94no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—24no—
495C22×C3—24no—
496C22×C3—24no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—44no—
502C22×C3—44no—
503C22×C3—44no—
504C22×C3—48no—
505C22×C3—48no—
506C22×C3—88no—
507C22×C3C2×#23512yes—
508C22×C3C2×#23712yes—
509C22×C3C2×#23712yes—
510C22×C3D3×#4112yes—
511C22×C3#101012yes—
512C22×C3#101012yes—
513C22×C3C24×D311yescharacteristic
514C22×C3C24×D311yescharacteristic
515C3×C4—24no—
516C3×C4—34no—
517C3×C4—64no—
518C3×C4—62no—
519C3×C4—64no—
520C3×C4—62no—
521C3×C4—62no—
522C3×C4C2×#23514yes—
523C3×C4C2×#23714yes—
524Dic3—24no—
525Dic3—24no—
526Dic3—22no—
527Dic3—22no—
528Dic3—22no—
529Dic3—64no—
530Dic3—62no—
531Dic3—64no—
532Dic3—62no—
533Dic3—62no—
534Dic3—62no—
535Dic3—124no—
536Dic3—122no—
537Dic3—122no—
538Dic3C2×#23714yes—
539C32C2×#55611yescharacteristic, complemented, Sylow
540C23—24no—
541C23—24no—
542C23—24no—
543C23C22×D3214yes—
544C23C22×D3211yescharacteristic
545Q8—68no—
546Q8—188no—
547Q8—188no—
548D4—28no—
549C2×C4—34no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—34no—
555C2×C4—34no—
556C2×C4—616no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—64no—
560C2×C4—62no—
561C2×C4—64no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—94no—
565C2×C4—182no—
566C2×C4—182no—
567C2×C4—184no—
568C2×C4#380414yes—
569C2×C4C22×D3212yes—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—24no—
574C2×C3—44no—
575C2×C3—44no—
576C2×C3—84no—
577C2×C3#554214yescomplemented
578C2×C3#567114yescomplemented
579C2×C3C22×#23511yescharacteristic
580C2×C3C22×#23711yescharacteristic
581C2×C3C22×#23711yescharacteristic
582C2×C3C2×D3×#4111yescharacteristic
583C2×C3C2×#101011yescharacteristic
584C2×C3C2×#101011yescharacteristic
585C22—24no—
586C22—24no—
587C22—24no—
588C22—48no—
589C22#6430912yes—
590C22D3×#23712yes—
591C22C2×#380412yes—
592C22C23×D3211yescharacteristic
593C4—34no—
594C4—62no—
595C4—62no—
596C4—64no—
597C4—62no—
598C4—64no—
599C4—182no—
600C4—182no—
601C4—184no—
602C4C2×#380414yes—
603C3—21no—
604C3C2×#554211yescharacteristic, complemented
605C3C2×#567111yescharacteristic, complemented
606C2—44no—
607C2#1059527314yesdirect product factor
608C2C2×#6430911yescharacteristic
609C2C2×D3×#23711yescharacteristic
610C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. C2×#63964C2semidirect
5. C2×#63956C2semidirect
6. C2×#63956C2semidirect
7. C2×#63955C2semidirect
8. #10595273C2direct (N × H)
9. C2×C4×#627C2semidirect
10. C2×#63866C2semidirect
11. C2×#63844C2semidirect
12. C2×#63843C2semidirect
39. #63964C22semidirect
40. #63956C22semidirect
41. #63956C22semidirect
42. #63955C22semidirect
45. C4×#627C22semidirect
46. #63866C22semidirect
47. #63844C22semidirect
48. #63843C22semidirect
448. C2×C32#556semidirect
539. C32C2×#556semidirect
577. C2×C3#5542semidirect
578. C2×C3#5671semidirect
604. C3C2×#5542semidirect
605. C3C2×#5671semidirect
607. C2#10595273direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C2×C3×#9362
C2×C3×D4×Dic32
C2×#639642
C2×#639562
C2×#639552
#105952732
C2×C4×#6272
C2×#638662
C2×#638442
C2×#638432
C2×#56713
C2×#55423