Finite Group Databasebeta

← C2×#10590618 #11863793

Subgroups — C2×#10590618 #11863793

Order 1152.

1681 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×#64106C211yesmaximal, characteristic, complemented
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×#63557C211yesmaximal, characteristic, complemented
8#10590618C218yesmaximal, direct product factor
9C2×#4808—31nomaximal
10C2×#4783—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×D3×Dic3—21no—
17C2×#3796—22no—
18C2×#3796—24no—
19C2×#3796—24no—
20C2×#3796C2214yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×#3752—21no—
23C2×C4⋊(C3⋊Dic3)—21no—
24#64106—22no—
25#64106C2214yescomplemented
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32C3×#810C2214yescomplemented
33C3×#809C2214yescomplemented
34#63557C2214yescomplemented
35C22×#239—31no—
36C22×#237—31no—
37C22×#216—31no—
38C22×#214—31no—
39C22×Dic12—31no—
40C22×#204—31no—
41C2×#897—31no—
42C2×#897—31no—
43C2×#897—61no—
44C2×C3×#103—31no—
45C2×C3×#102—31no—
46C2×(C2×D3)⋊C8—31no—
47C2×(C2×D3)⋊C8—31no—
48C2×#810D311yescharacteristic, complemented
49C2×#809D311yescharacteristic, complemented
50#4808—38no—
51#4783—38no—
52C23×C3⋊D3D411yescharacteristic
53C23×C3×D3—21no—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3D411yescharacteristic
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3D412yes—
61C2×C4×C3⋊D3C2312yes—
62C2×#634—22no—
63C2×#634—22no—
64C2×#634—21no—
65C2×#634C2312yes—
66C22×C3×Dic3—21no—
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12D414yes—
70C2×C3×D12C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yes—
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×D3×Dic3—28no—
78C2×D3×Dic3—24no—
79#3796—216no—
80#3796—28no—
81#3796—28no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2312yes—
84#3752—24no—
85C4⋊(C3⋊Dic3)—24no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89C2×C3×C3⋊C8C2312yes—
90#3719—28no—
91#3716—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C22×C3×D4—31no—
95C22×#67—61no—
96C23×Dic3—61no—
97C2×#239—34no—
98C2×#239—62no—
99C2×#239—64no—
100C2×#239—64no—
101C2×#237—34no—
102C2×#237—62no—
103C2×#237—64no—
104C2×#237—64no—
105C22×D12—61no—
106C22×D12C2×D311yescharacteristic
107C22×C4×D3—31no—
108C22×C4×D3—31no—
109C22×C4×D3—61no—
110C22×C4×D3—61no—
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C22×Dic6C2×D311yescharacteristic
115C22×C3×C8—31no—
116C22×C3×C8—31no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×#216—34no—
121C2×#216—64no—
122C2×#214—34no—
123C2×#214—64no—
124C2×(C2×D3)⋊C4—61no—
125C2×(C2×D3)⋊C4—61no—
126C2×(C2×D3)⋊C4—62no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3—61no—
129C2×C4⋊Dic3—62no—
130C22×C3⋊C8C2×D311yescharacteristic
131C22×C3⋊C8C2×D311yescharacteristic
132C2×Dic12—34no—
133C2×Dic12—64no—
134C2×#204—34no—
135C2×#204—64no—
136#897—34no—
137#897—34no—
138#897—64no—
139#897—62no—
140#897—62no—
141#897—64no—
142C3×#103—34no—
143C3×#102—34no—
144(C2×D3)⋊C8—34no—
145(C2×D3)⋊C8—34no—
146#810C2×D314yescomplemented
147#809C2×D314yescomplemented
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—22no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3C2×D412yes—
153C22×C3×D3—24no—
154C22×C3×D3—22no—
155C22×C3×D3—42no—
156C22×C3×D3—42no—
157C2×C32×C4—22no—
158C2×C32×C4—42no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—42no—
166C2×C3⋊Dic3C2×D412yes—
167C4×C3⋊D3—24no—
168C4×C3⋊D3—22no—
169C4×C3⋊D3—22no—
170#634—22no—
171#634—22no—
172#634—42no—
173C2×C3×Dic3—24no—
174C2×C3×Dic3—22no—
175C3×D12—24no—
176C3×D12—22no—
177C3×D12C2×D414yes—
178C3×Dic6—24no—
179C3×Dic6—22no—
180C3×Dic6C2×D414yes—
181#626—216no—
182D3×Dic3—216no—
183C3×C3⋊C8—22no—
184C3×C3⋊C8—22no—
185C22×#41—91no—
186C22×Q16—91no—
187C22×SD16—91no—
188C2×C22⋊Q8—91no—
189#452—98no—
190C2×#103—31no—
191C2×#102—31no—
192C2×C22⋊C8—91no—
193C24×C3—61no—
194C23×D3—21no—
195C23×D3—31no—
196C23×D3—31no—
197C23×D3—61no—
198C2×C3×Q8—34no—
199C2×C3×Q8—32no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×D4—34no—
203C2×C3×D4—32no—
204C2×C3×D4—62no—
205C2×C3×D4—61no—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—64no—
214C2×#67—68no—
215C22×Dic3—21no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—61no—
219C22×Dic3—64no—
220C22×Dic3—68no—
221C22×Dic3—62no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224#239—68no—
225#239—616no—
226#239—68no—
227#237—68no—
228#237—616no—
229#237—68no—
230C2×D12—22no—
231C2×D12—21no—
232C2×D12—64no—
233C2×D12—68no—
234C2×D12D1214yes—
235C2×D12C22×D312yes—
236C2×C4×D3—32no—
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3—32no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—64no—
243C2×C4×D3—68no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—122no—
249C2×C4×D3—122no—
250C2×Dic6—22no—
251C2×Dic6—21no—
252C2×Dic6—32no—
253C2×Dic6—32no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—62no—
257C2×Dic6—62no—
258C2×Dic6—62no—
259C2×Dic6—62no—
260C2×Dic6—61no—
261C2×Dic6—61no—
262C2×Dic6—122no—
263C2×Dic6—122no—
264C2×Dic6D1214yes—
265C2×Dic6C22×D312yes—
266C2×C3×C8—32no—
267C2×C3×C8—32no—
268C2×C3×C8—62no—
269C2×C3×C8—62no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—22no—
274C3×C4⋊C4C22×D312yes—
275C3×C4⋊C4C22×D312yes—
276#216—68no—
277#214—68no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—68no—
281C4⋊Dic3—64no—
282C4⋊Dic3—64no—
283C4⋊Dic3—68no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8C22×D312yes—
287C2×C3⋊C8C22×D312yes—
288Dic12—68no—
289#204—68no—
290C22×C32#12012yes—
291C22×C32#13512yes—
292C22×C32#13712yes—
293C22×C32C22×D411yescharacteristic
294C2×C3⋊D3—22no—
295C2×C3⋊D3—22no—
296C2×C3⋊D3—22no—
297C2×C3⋊D3—44no—
298C2×C3×D3—24no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—48no—
302C32×C4—42no—
303C32×C4#12012yes—
304C32×C4C22×D411yescharacteristic
305C32×C4C22×D411yescharacteristic
306C3⋊Dic3—22no—
307C3⋊Dic3—42no—
308C3×Dic3—24no—
309C2×#41—94no—
310C2×#41—182no—
311C2×#41—184no—
312C2×#41—184no—
313C22×Q8—31no—
314C22×Q8—91no—
315C22×D4—31no—
316C22×D4—181no—
317C23×C4—91no—
318C23×C4—181no—
319C2×Q16—94no—
320C2×Q16—184no—
321C2×SD16—94no—
322C2×SD16—184no—
323C22×C8—31no—
324C22×C8—31no—
325C22⋊Q8—94no—
326C22⋊Q8—182no—
327C2×C4⋊C4—181no—
328C2×C4⋊C4D3211yescharacteristic
329C2×C22⋊C4—181no—
330#103—34no—
331#102—34no—
332C22⋊C8—94no—
333C23×C3—21no—
334C23×C3—64no—
335C23×C3—62no—
336C23×C3—122no—
337C23×C3—122no—
338C23×C3D3×D411yescharacteristic
339C23×C3D3×D411yescharacteristic
340C22×D3—24no—
341C22×D3—22no—
342C22×D3—32no—
343C22×D3—32no—
344C22×D3—42no—
345C22×D3—42no—
346C22×D3—62no—
347C22×D3—64no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—122no—
355C22×D3—122no—
356C3×Q8—34no—
357C3×Q8—64no—
358C3×Q8—62no—
359C3×D4—34no—
360C3×D4—64no—
361C3×D4—62no—
362C2×C3×C4—24no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—44no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—64no—
373C2×C3×C4—62no—
374C2×C3×C4C2×D1212yes—
375C2×C3×C4C2×D1212yes—
376C2×C3×C4D3×D412yes—
377C2×C3×C4D3×D412yes—
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382#67—616no—
383C2×Dic3—24no—
384C2×Dic3—22no—
385C2×Dic3—32no—
386C2×Dic3—32no—
387C2×Dic3—62no—
388C2×Dic3—616no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—64no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—122no—
395C2×Dic3—124no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398D12—24no—
399D12—22no—
400D12—616no—
401D12C2×D1214yes—
402C4×D3—616no—
403C4×D3—64no—
404C4×D3—64no—
405C4×D3—62no—
406C4×D3—62no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—122no—
410C4×D3—122no—
411C4×D3—124no—
412Dic6—24no—
413Dic6—22no—
414Dic6—62no—
415Dic6—62no—
416Dic6—62no—
417Dic6—62no—
418Dic6—122no—
419Dic6—122no—
420Dic6—124no—
421Dic6—122no—
422Dic6—122no—
423Dic6C2×D1214yes—
424C3×C8—62no—
425C3×C8—62no—
426C3⋊C8—22no—
427C3⋊C8—22no—
428C2×C32#45214yescomplemented
429C2×C32C2×#12011yescharacteristic
430C2×C32C2×#13511yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C3⋊D3—42no—
433C3×D3—44no—
434C24—61no—
435C24—91no—
436#41—188no—
437#41—188no—
438#41—1816no—
439C2×Q8—32no—
440C2×Q8—34no—
441C2×Q8—62no—
442C2×Q8—61no—
443C2×Q8—92no—
444C2×Q8—181no—
445C2×Q8—182no—
446C2×Q8—182no—
447C2×D4—32no—
448C2×D4—34no—
449C2×D4—62no—
450C2×D4—61no—
451C2×D4—184no—
452C2×D4—188no—
453C22×C4—21no—
454C22×C4—61no—
455C22×C4—91no—
456C22×C4—92no—
457C22×C4—92no—
458C22×C4—184no—
459C22×C4—188no—
460C22×C4—182no—
461C22×C4—182no—
462C22×C4—181no—
463C22×C4C2×D3211yescharacteristic
464Q16—188no—
465SD16—188no—
466C2×C8—32no—
467C2×C8—32no—
468C2×C8—62no—
469C2×C8—62no—
470C4⋊C4—21no—
471C4⋊C4—184no—
472C4⋊C4C2×D3212yes—
473C22⋊C4—184no—
474C22×C3—21no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—64no—
479C22×C3—122no—
480C22×C3—122no—
481C22×C3—128no—
482C22×C3#88212yes—
483C22×C3#88212yes—
484C22×C3#91212yes—
485C22×C3#91512yes—
486C22×C3#91612yes—
487C22×C3#91812yes—
488C22×C3C2×D3×D411yescharacteristic
489C22×C3C2×D3×D411yescharacteristic
490C2×D3—24no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—48no—
494C2×D3—64no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—128no—
504C2×D3—124no—
505C2×D3—124no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—44no—
510C3×C4—42no—
511C3×C4—42no—
512C3×C4—64no—
513C3×C4#88212yes—
514C3×C4#88212yes—
515C3×C4C22×D1211yescharacteristic
516C3×C4C22×D1211yescharacteristic
517C3×C4C2×D3×D411yescharacteristic
518C3×C4C2×D3×D411yescharacteristic
519Dic3—24no—
520Dic3—62no—
521Dic3—62no—
522Dic3—122no—
523Dic3—124no—
524Dic3—122no—
525Dic3—122no—
526C32C2×#45211yescharacteristic, complemented, Sylow
527C23—62no—
528C23—64no—
529C23—92no—
530C23—122no—
531C23—122no—
532C23—182no—
533C23—182no—
534C23—182no—
535C23#381111yescharacteristic
536Q8—34no—
537Q8—62no—
538Q8—64no—
539Q8—182no—
540Q8—182no—
541Q8—362no—
542D4—34no—
543D4—62no—
544D4—64no—
545D4—1816no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—62no—
549C2×C4—64no—
550C2×C4—92no—
551C2×C4—1816no—
552C2×C4—182no—
553C2×C4—182no—
554C2×C4—182no—
555C2×C4—184no—
556C2×C4—182no—
557C2×C4—362no—
558C2×C4D3×D1212yes—
559C2×C4D3×D1212yes—
560C2×C4#381111yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—62no—
563C8—62no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—24no—
567C2×C3—21no—
568C2×C3—124no—
569C2×C3#478314yescomplemented
570C2×C3#480814yescomplemented
571C2×C3C2×#88211yescharacteristic
572C2×C3C2×#88211yescharacteristic
573C2×C3C2×#91211yescharacteristic
574C2×C3C2×#91511yescharacteristic
575C2×C3C2×#91611yescharacteristic
576C2×C3C2×#91811yescharacteristic
577D3—44no—
578D3—124no—
579D3—122no—
580D3—122no—
581C22—64no—
582C22—122no—
583C22—122no—
584C22—128no—
585C22—182no—
586C22—182no—
587C22—182no—
588C22—364no—
589C22#6392312yes—
590C22#6393612yes—
591C22#6395112yes—
592C22C2×#381111yescharacteristic
593C4—42no—
594C4—64no—
595C4—182no—
596C4—362no—
597C4#6392312yes—
598C4C2×D3×D1211yescharacteristic
599C4C2×D3×D1211yescharacteristic
600C3—21no—
601C3C2×#478311yescharacteristic, complemented
602C3C2×#480811yescharacteristic, complemented
603C2—124no—
604C2—362no—
605C2#1059061814yesdirect product factor
606C2C2×#6392311yescharacteristic
607C2C2×#6393611yescharacteristic
608C2C2×#6395111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3796C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64106C2semidirect
3. C22×#3719C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#810C2semidirect
6. C2×C3×#809C2semidirect
7. C2×#63557C2semidirect
8. #10590618C2direct (N × H)
25. #64106C22semidirect
29. C2×#3719C22semidirect
31. C2×#3716C22semidirect
32. C3×#810C22semidirect
33. C3×#809C22semidirect
34. #63557C22semidirect
48. C2×#810D3semidirect
49. C2×#809D3semidirect
146. #810C2×D3semidirect
147. #809C2×D3semidirect
428. C2×C32#452semidirect
526. C32C2×#452semidirect
569. C2×C3#4783semidirect
570. C2×C3#4808semidirect
601. C3C2×#4783semidirect
602. C3C2×#4808semidirect
605. C2#10590618direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×#641062
C22×#37192
C22×#37162
C2×C3×#8102
C2×C3×#8092
C2×#635572
#105906182
C2×#48083
C2×#47833