Finite Group Databasebeta

← C2×#10591170 #11863788

Subgroups — C2×#10591170 #11863788

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic, complemented
3C22×#3718C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63657C211yesmaximal, characteristic, complemented
6#10591170C218yesmaximal, direct product factor
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5239—31nomaximal
10C2×#5047—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67—21no—
13C2×C3×#235—22no—
14C2×C3×#235—24no—
15C2×C3×#235—24no—
16C2×C3×#235C2214yes—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3—21no—
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×#217—21no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924—22no—
26C3×#924C2214yescomplemented
27C2×C3×Dic3⋊C4—21no—
28C2×#3718—24no—
29C2×#3718C2214yescomplemented
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63657C2214yescomplemented
33#63565C2214yescomplemented
34#63562C2214yescomplemented
35C22×C3×#41—31no—
36C22×#235D311yescharacteristic
37C2×C3×C22⋊Q8—31no—
38C22×#216—31no—
39C22×#216—31no—
40C22×#215—31no—
41C22×#214—31no—
42C2×#924D311yescharacteristic, complemented
43#5239—38no—
44C2×#835—31no—
45C2×#832—31no—
46C2×#830—31no—
47C2×#830—31no—
48C2×#830—61no—
49#5047—38no—
50C2×#810—31no—
51C2×#809—31no—
52C24×C32D411yescharacteristic
53C23×C3×D3—21no—
54C22×C32×C4—22no—
55C22×C32×C4—22no—
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D412yes—
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—28no—
61C2×C3×#67—24no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C3×#235—216no—
66C3×#235—28no—
67C3×#235—28no—
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12D414yes—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—28no—
73C2×C3×C4×D3—24no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D414yes—
80C2×C3×Dic6C2312yes—
81C2×C3×Dic6C2312yes—
82C2×C3⋊(C3⋊C8)—22no—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#217—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—24no—
90#3718—28no—
91#3715—28no—
92C2×#452—91noSylow
93C2×C3×#41—34no—
94C2×C3×#41—64no—
95C2×C3×#41—64no—
96C2×C3×#41—62no—
97C22×C3×Q8—31no—
98C22×C3×Q8—31no—
99C22×C3×D4—31no—
100C22×C3×D4—61no—
101C23×C3×C4—21no—
102C23×C3×C4—61no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C22×#67—21no—
106C2×#235—22no—
107C2×#235—24no—
108C2×#235—24no—
109C2×#235C2×D314yes—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—21no—
112C22×Dic6C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C3×C22⋊Q8—34no—
115C3×C22⋊Q8—62no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—61no—
118C2×C3×C22⋊C4—61no—
119C2×#217—21no—
120C2×#216—34no—
121C2×#216—34no—
122C2×#216—64no—
123C2×#216—64no—
124C2×#215—34no—
125C2×#215—64no—
126C2×#214—34no—
127C2×#214—64no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129#924—22no—
130#924C2×D314yescomplemented
131C2×Dic3⋊C4—21no—
132C22×C3⋊C8—31no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—61no—
137C22×C3⋊C8—61no—
138#835—34no—
139#832—34no—
140#830—34no—
141#830—34no—
142#830—64no—
143#810—34no—
144#809—34no—
145C23×C32—22no—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32C2×D412yes—
149C23×C32C2×D411yescharacteristic
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C22×C3×D3—42no—
153C22×C3×D3—42no—
154C2×C32×C4—22no—
155C2×C32×C4—24no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2411yescharacteristic
163C3×#67—216no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—42no—
169C2×C3×Dic3—42no—
170C3×D12—24no—
171C3×D12—22no—
172C3×D12C2×D414yes—
173C3×C4×D3—216no—
174C3×Dic6—24no—
175C3×Dic6—22no—
176C3×Dic6—22no—
177C3×Dic6—22no—
178C3×Dic6—42no—
179C3×Dic6C2×D414yes—
180C3⋊(C3⋊C8)—22no—
181C3⋊(C3⋊C8)—22no—
182C22×#41—31no—
183C22×Q16—91no—
184C22×SD16—91no—
185C2×C22⋊Q8—31no—
186#452—98no—
187C2×#103—91no—
188C2×#102—91no—
189C2×C22⋊C8—91no—
190C24×C3—21no—
191C24×C3—61no—
192C24×C3#6711yescharacteristic
193C24×C3#6711yescharacteristic
194C23×D3—21no—
195C3×#41—68no—
196C3×#41—68no—
197C3×#41—616no—
198C2×C3×Q8—34no—
199C2×C3×Q8—32no—
200C2×C3×Q8—32no—
201C2×C3×Q8—62no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204C2×C3×Q8—62no—
205C2×C3×Q8—62no—
206C2×C3×D4—34no—
207C2×C3×D4—32no—
208C2×C3×D4—68no—
209C2×C3×D4—64no—
210C2×C3×D4—62no—
211C2×C3×D4—61no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—22no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—68no—
223C22×C3×C4—61no—
224C22×C3×C4—64no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4#6711yescharacteristic
228C22×C3×C4#6712yes—
229C22×C3×C4#6711yescharacteristic
230C22×C3×C4#6712yes—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—28no—
236C2×#67—24no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240#235—216no—
241#235—28no—
242#235—28no—
243C2×D12—21no—
244C2×D12—22no—
245C2×D12#6714yes—
246C2×D12C22×D312yes—
247C2×C4×D3—28no—
248C2×C4×D3—24no—
249C2×Dic6—21no—
250C2×Dic6—22no—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—21no—
254C2×Dic6#6714yes—
255C2×Dic6C22×D312yes—
256C2×Dic6C22×D312yes—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—64no—
259C3×C4⋊C4—61no—
260C3×C22⋊C4—64no—
261#217—24no—
262#216—68no—
263#216—68no—
264#215—68no—
265#214—68no—
266C4⋊Dic3—21no—
267C4⋊Dic3C22×D312yes—
268Dic3⋊C4—24no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—32no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—62no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—122no—
280C2×C3⋊C8—122no—
281C22×C32—22no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—44no—
285C22×C32#12012yes—
286C22×C32#13512yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—24no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—48no—
293C32×C4—22no—
294C32×C4#12012yes—
295C32×C4C22×D411yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3×Dic3—24no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C2×#41—34no—
301C2×#41—64no—
302C2×#41—64no—
303C2×#41—62no—
304C22×Q8—31no—
305C22×Q8—31no—
306C22×D4—31no—
307C22×D4—61no—
308C23×C4—61no—
309C23×C4D3211yescharacteristic
310C2×Q16—94no—
311C2×Q16—184no—
312C2×SD16—94no—
313C2×SD16—184no—
314C22×C8—91no—
315C22×C8—91no—
316C22⋊Q8—34no—
317C22⋊Q8—62no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—61no—
320C2×C22⋊C4—61no—
321#103—94no—
322#102—94no—
323C22⋊C8—94no—
324C23×C3—24no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—64no—
336C23×C3—62no—
337C23×C3—122no—
338C23×C3—122no—
339C23×C3C2×#6712yes—
340C23×C3C2×#6712yes—
341C23×C3C2×#6711yescharacteristic
342C23×C3C2×#6711yescharacteristic
343C22×D3—24no—
344C22×D3—22no—
345C22×D3—42no—
346C22×D3—42no—
347C3×Q8—34no—
348C3×Q8—64no—
349C3×Q8—62no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C3×D4—34no—
354C3×D4—616no—
355C3×D4—64no—
356C3×D4—62no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—44no—
373C2×C3×C4—42no—
374C2×C3×C4—616no—
375C2×C3×C4—64no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—122no—
380C2×C3×C4—122no—
381C2×C3×C4D3×D412yes—
382C2×C3×C4D3×D412yes—
383C2×C3×C4C2×#6712yes—
384C2×C3×C4C2×#6712yes—
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6712yes—
388C2×C3×C4C2×#6712yes—
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391#67—216no—
392C2×Dic3—24no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—42no—
397C2×Dic3—42no—
398D12—24no—
399D12—22no—
400D12C2×#6714yes—
401C4×D3—216no—
402Dic6—24no—
403Dic6—22no—
404Dic6—22no—
405Dic6—22no—
406Dic6—42no—
407Dic6C2×#6714yes—
408C3⋊C8—62no—
409C3⋊C8—62no—
410C3⋊C8—62no—
411C3⋊C8—62no—
412C3⋊C8—122no—
413C3⋊C8—122no—
414C2×C32—42no—
415C2×C32#45214yescomplemented
416C2×C32C2×#12011yescharacteristic
417C2×C32C2×#13511yescharacteristic
418C2×C32C2×#13711yescharacteristic
419C3×D3—44no—
420C24—61no—
421C24#62511yescharacteristic
422#41—68no—
423#41—68no—
424#41—616no—
425C2×Q8—32no—
426C2×Q8—32no—
427C2×Q8—34no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—62no—
431C2×Q8—62no—
432C2×Q8—62no—
433C2×D4—32no—
434C2×D4—34no—
435C2×D4—68no—
436C2×D4—64no—
437C2×D4—61no—
438C2×D4—62no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—68no—
442C22×C4—61no—
443C22×C4—64no—
444C22×C4—61no—
445C22×C4—61no—
446C22×C4#62512yes—
447C22×C4#62511yescharacteristic
448C22×C4C2×D3212yes—
449C22×C4C2×D3211yescharacteristic
450Q16—188no—
451SD16—188no—
452C2×C8—92no—
453C2×C8—92no—
454C2×C8—182no—
455C2×C8—182no—
456C4⋊C4—32no—
457C4⋊C4—61no—
458C4⋊C4—64no—
459C22⋊C4—64no—
460C22×C3—24no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—21no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—48no—
474C22×C3—44no—
475C22×C3—44no—
476C22×C3—64no—
477C22×C3—122no—
478C22×C3—128no—
479C22×C3—122no—
480C22×C3#93712yes—
481C22×C3#94212yes—
482C22×C3#95012yes—
483C22×C3#95012yes—
484C22×C3#95112yes—
485C22×C3#95312yes—
486C22×C3C22×#6711yescharacteristic
487C22×C3C22×#6711yescharacteristic
488C2×D3—24no—
489C2×D3—48no—
490C2×D3—42no—
491C2×D3—42no—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—22no—
497C3×C4—42no—
498C3×C4—64no—
499C3×C4—122no—
500C3×C4—122no—
501C3×C4#93712yes—
502C3×C4#95312yes—
503C3×C4C2×D3×D411yescharacteristic
504C3×C4C2×D3×D411yescharacteristic
505C3×C4C22×#6711yescharacteristic
506C3×C4C22×#6711yescharacteristic
507Dic3—24no—
508Dic3—42no—
509Dic3—42no—
510C32C2×#45211yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—22no—
514C23—62no—
515C23—64no—
516C23—122no—
517C23—122no—
518C23C2×#62512yes—
519C23C2×#62511yescharacteristic
520Q8—34no—
521Q8—62no—
522Q8—64no—
523Q8—62no—
524Q8—62no—
525Q8—122no—
526D4—34no—
527D4—616no—
528D4—62no—
529D4—64no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—616no—
535C2×C4—62no—
536C2×C4—64no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—122no—
540C2×C4—122no—
541C2×C4C2×#62512yes—
542C2×C4C2×#62511yescharacteristic
543C2×C4D3×#6712yes—
544C2×C4D3×#6712yes—
545C2×C4C22×D3211yescharacteristic
546C8—182no—
547C8—182no—
548C2×C3—21no—
549C2×C3—24no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—44no—
553C2×C3—42no—
554C2×C3—42no—
555C2×C3—124no—
556C2×C3#504714yescomplemented
557C2×C3#523914yescomplemented
558C2×C3C2×#93711yescharacteristic
559C2×C3C2×#94211yescharacteristic
560C2×C3C2×#95011yescharacteristic
561C2×C3C2×#95011yescharacteristic
562C2×C3C2×#95111yescharacteristic
563C2×C3C2×#95311yescharacteristic
564D3—44no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—44no—
569C22—64no—
570C22—128no—
571C22—122no—
572C22—122no—
573C22#6382212yes—
574C22#6382712yes—
575C22#6397612yes—
576C22C22×#62511yescharacteristic
577C4—22no—
578C4—64no—
579C4—122no—
580C4—122no—
581C4#6397612yes—
582C4C2×D3×#6711yescharacteristic
583C4C2×D3×#6711yescharacteristic
584C3—21no—
585C3C2×#504711yescharacteristic, complemented
586C3C2×#523911yescharacteristic, complemented
587C2—42no—
588C2—124no—
589C2#1059117014yesdirect product factor
590C2C2×#6382211yescharacteristic
591C2C2×#6382711yescharacteristic
592C2C2×#6397611yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC22×C3×#235C2
hypercenterC23×C4D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#924C2semidirect
3. C22×#3718C2semidirect
4. C22×#3715C2semidirect
5. C2×#63657C2semidirect
6. #10591170C2direct (N × H)
7. C2×#63565C2semidirect
8. C2×#63562C2semidirect
26. C3×#924C22semidirect
29. C2×#3718C22semidirect
31. C2×#3715C22semidirect
32. #63657C22semidirect
33. #63565C22semidirect
34. #63562C22semidirect
42. C2×#924D3semidirect
130. #924C2×D3semidirect
415. C2×C32#452semidirect
510. C32C2×#452semidirect
556. C2×C3#5047semidirect
557. C2×C3#5239semidirect
585. C3C2×#5047semidirect
586. C3C2×#5239semidirect
589. C2#10591170direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×C3×#9242
C22×#37182
C22×#37152
C2×#636572
#105911702
C2×#635652
C2×#635622
C2×#52393
C2×#50473