Finite Group Databasebeta

← C2×#10590824 #11863628

Subgroups — C2×#10590824 #11863628

Order 1152.

1685 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590824C218yesmaximal, direct product factor
9C2×#5170—31nomaximal
10C2×#4806—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627—21no—
16C22×#626—21no—
17C22×#624—21no—
18C2×#3797—22no—
19C2×#3797—24no—
20C2×#3797—24no—
21C2×#3797C2214yescomplemented
22C22×C32×C8C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×#204—24no—
26C2×C3×#204C2214yescomplemented
27C2×(C2×D3)⋊Dic3—21no—
28#63916—22no—
29#63916C2214yes—
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63647C2214yescomplemented
33C3×#816C2214yescomplemented
34#63565C2214yescomplemented
35C22×D3×Q8—31no—
36C22×D3×Q8—31no—
37C22×C3×SD16—31no—
38C22×#215—31no—
39C2×#938—31no—
40C22×#214—31no—
41C22×#204D311yescharacteristic, complemented
42C2×#895—31no—
43C2×C3×#103—31no—
44C2×#835—31no—
45#5170—38no—
46C2×(C2×D3)⋊C8—31no—
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—61no—
49C2×#816D311yescharacteristic, complemented
50C2×#810—31no—
51#4806—38no—
52C23×C3⋊D3D411yescharacteristic
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3D411yescharacteristic
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3D412yes—
59C2×C4×C3⋊D3C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6D414yescomplemented
72C2×C3×Dic6D414yescomplemented
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2312yes—
75C2×#627—28no—
76C2×#627—24no—
77C2×#626—24no—
78C2×#626—44no—
79C2×#624—28no—
80C2×#624—24no—
81#3797—216no—
82#3797—28no—
83#3797—28no—
84C2×C32×C8—22no—
85C2×C32×C8C2312yes—
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×#204—28no—
91(C2×D3)⋊Dic3—24no—
92#3715—28no—
93C2×#448—91noSylow
94C22×C3×Q8—31no—
95C22×C3×Q8—31no—
96C22×C3×D4—31no—
97C22×#67—61no—
98C2×D3×Q8—34no—
99C2×D3×Q8—34no—
100C2×D3×Q8—62no—
101C2×D3×Q8—62no—
102C2×D3×Q8—64no—
103C2×D3×Q8—64no—
104C2×D3×Q8—64no—
105C2×D3×Q8—64no—
106C22×D12—61no—
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—31no—
109C22×C4×D3—31no—
110C22×C4×D3—61no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C22×Dic6—61no—
114C22×Dic6—61no—
115C22×Dic6C2×D311yescharacteristic
116C22×Dic6C2×D311yescharacteristic
117C2×C3×SD16—34no—
118C2×C3×SD16—64no—
119C22×C3×C8—21no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C2×D311yescharacteristic
122C2×C3×C4⋊C4—31no—
123C2×#217—61no—
124C2×#215—34no—
125C2×#215—64no—
126#938—34no—
127#938—62no—
128C2×#214—34no—
129C2×#214—64no—
130C2×(C2×D3)⋊C4—61no—
131C2×C4⋊Dic3C2×D311yescharacteristic
132C22×C3⋊C8—31no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—61no—
135C2×#204—24no—
136C2×#204C2×D314yescomplemented
137#895—34no—
138#895—62no—
139C3×#103—34no—
140#835—34no—
141(C2×D3)⋊C8—34no—
142(C2×D3)⋊C8—34no—
143(C2×D3)⋊C8—64no—
144#816C2×D314yescomplemented
145#810—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3SD1614yescomplemented
150C22×C3⋊D3C2×D412yes—
151C22×C3×D3—22no—
152C22×C3×D3—42no—
153C22×C3×D3—42no—
154C22×C3×D3—42no—
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C2×D412yes—
161C4×C3⋊D3—24no—
162C4×C3⋊D3—22no—
163C4×C3⋊D3—22no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—24no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—42no—
170C3×D12—22no—
171C3×D12—22no—
172C3×D12—42no—
173C3×Dic6—24no—
174C3×Dic6—24no—
175C3×Dic6—22no—
176C3×Dic6—22no—
177C3×Dic6C2×D414yescomplemented
178C3×Dic6C2×D414yescomplemented
179#627—216no—
180#626—48no—
181#624—216no—
182C32×C8—22no—
183C3⋊(C3⋊C8)—22no—
184C23×Q8—91no—
185C22×SD16—31no—
186C22×SD16—91no—
187C2×#121—91no—
188#448—98no—
189C2×#103—31no—
190C2×#103—91no—
191C2×C22⋊C8—91no—
192C24×C3—61no—
193C23×D3—21no—
194C23×D3—31no—
195C23×D3—31no—
196C23×D3—61no—
197C2×C3×Q8—34no—
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×D4—32no—
206C2×C3×D4—62no—
207C2×C3×D4—62no—
208C2×C3×D4—61no—
209C22×C3×C4—21no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—64no—
216C2×#67—124no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—61no—
223D3×Q8—68no—
224D3×Q8—68no—
225D3×Q8—616no—
226D3×Q8—616no—
227D3×Q8—68no—
228D3×Q8—68no—
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—21no—
232C2×D12—64no—
233C2×D12—124no—
234C2×D12C22×D312yes—
235C2×C4×D3—32no—
236C2×C4×D3—32no—
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3—68no—
244C2×C4×D3—68no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—122no—
250C2×C4×D3—122no—
251C2×Dic6—22no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—22no—
255C2×Dic6—64no—
256C2×Dic6—64no—
257C2×Dic6—68no—
258C2×Dic6—68no—
259C2×Dic6D1214yescomplemented
260C2×Dic6#6714yescomplemented
261C2×Dic6C22×D312yes—
262C2×Dic6C22×D312yes—
263C3×SD16—68no—
264C2×C3×C8—22no—
265C2×C3×C8—22no—
266C2×C3×C8—22no—
267C2×C3×C8—42no—
268C2×C3×C8C22×D312yes—
269C2×C3×C8C22×D312yes—
270C3×C4⋊C4—32no—
271C3×C4⋊C4—61no—
272#217—64no—
273#215—68no—
274#214—68no—
275(C2×D3)⋊C4—64no—
276C4⋊Dic3—21no—
277C4⋊Dic3C22×D312yes—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—32no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8—122no—
284#204—28no—
285C22×C32#12012yes—
286C22×C32C2×SD1612yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—28no—
292C2×C3⋊D3C2×SD1614yescomplemented
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C2×C3×D3—42no—
296C2×C3×D3—84no—
297C32×C4#12012yes—
298C32×C4C22×D411yescharacteristic
299C32×C4C22×D411yescharacteristic
300C3⋊Dic3—22no—
301C3×Dic3—24no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C22×Q8—31no—
305C22×Q8—31no—
306C22×Q8—94no—
307C22×Q8—181no—
308C22×Q8—182no—
309C22×Q8—184no—
310C22×Q8—184no—
311C22×D4—31no—
312C22×D4—181no—
313C23×C4—91no—
314C23×C4—181no—
315C2×SD16—34no—
316C2×SD16—64no—
317C2×SD16—94no—
318C2×SD16—184no—
319C22×C8—91no—
320C22×C8D3211yescharacteristic
321#121—94no—
322#121—182no—
323C2×C4⋊C4—31no—
324C2×C22⋊C4—181no—
325#103—34no—
326#103—94no—
327C22⋊C8—94no—
328C23×C3—21no—
329C23×C3—62no—
330C23×C3—122no—
331C23×C3—122no—
332C23×C3—122no—
333C23×C3D3×D411yescharacteristic
334C23×C3D3×D411yescharacteristic
335C22×D3—22no—
336C22×D3—34no—
337C22×D3—34no—
338C22×D3—32no—
339C22×D3—32no—
340C22×D3—42no—
341C22×D3—42no—
342C22×D3—42no—
343C22×D3—64no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—122no—
350C22×D3—122no—
351C3×Q8—34no—
352C3×Q8—34no—
353C3×Q8—64no—
354C3×Q8—64no—
355C3×Q8—62no—
356C3×Q8—62no—
357C3×D4—62no—
358C3×D4—62no—
359C3×D4—122no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—64no—
365C2×C3×C4—64no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—122no—
370C2×C3×C4C2×D1212yes—
371C2×C3×C4D3×D412yes—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D412yes—
375C2×C3×C4C2×#6712yes—
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378#67—128no—
379C2×Dic3—24no—
380C2×Dic3—24no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—32no—
385C2×Dic3—32no—
386C2×Dic3—42no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—122no—
391D12—22no—
392D12—22no—
393D12—42no—
394D12—128no—
395C4×D3—616no—
396C4×D3—616no—
397C4×D3—64no—
398C4×D3—64no—
399C4×D3—62no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—62no—
403C4×D3—122no—
404C4×D3—122no—
405C4×D3—124no—
406Dic6—24no—
407Dic6—24no—
408Dic6—22no—
409Dic6—22no—
410Dic6—616no—
411Dic6—616no—
412Dic6C2×D1214yescomplemented
413Dic6C2×#6714yescomplemented
414C3×C8—22no—
415C3×C8—22no—
416C3×C8—42no—
417C3⋊C8—62no—
418C3⋊C8—62no—
419C3⋊C8—122no—
420C2×C32#44814yescomplemented
421C2×C32C2×#12011yescharacteristic
422C2×C32C22×SD1611yescharacteristic
423C2×C32C2×#13711yescharacteristic
424C3⋊D3—24no—
425C3×D3—82no—
426C24—61no—
427C24—91no—
428C2×Q8—32no—
429C2×Q8—32no—
430C2×Q8—34no—
431C2×Q8—34no—
432C2×Q8—62no—
433C2×Q8—61no—
434C2×Q8—61no—
435C2×Q8—62no—
436C2×Q8—184no—
437C2×Q8—188no—
438C2×Q8—188no—
439C2×Q8—188no—
440C2×Q8—1816no—
441C2×D4—32no—
442C2×D4—62no—
443C2×D4—61no—
444C2×D4—62no—
445C2×D4—184no—
446C2×D4—364no—
447C22×C4—61no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—91no—
451C22×C4—92no—
452C22×C4—92no—
453C22×C4—184no—
454C22×C4—188no—
455C22×C4—182no—
456C22×C4—182no—
457C22×C4C2×D3211yescharacteristic
458SD16—68no—
459SD16—188no—
460C2×C8—22no—
461C2×C8—92no—
462C2×C8—182no—
463C2×C8C2×D3212yes—
464C4⋊C4—32no—
465C4⋊C4—61no—
466C22⋊C4—184no—
467C22×C3—21no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—244no—
475C22×C3#88212yes—
476C22×C3D3×SD1612yes—
477C22×C3D3×SD1612yes—
478C22×C3#91512yes—
479C22×C3#91812yes—
480C22×C3#93712yes—
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×D3×D411yescharacteristic
483C2×D3—34no—
484C2×D3—34no—
485C2×D3—42no—
486C2×D3—42no—
487C2×D3—42no—
488C2×D3—64no—
489C2×D3—68no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—68no—
495C2×D3—84no—
496C2×D3—122no—
497C2×D3—128no—
498C2×D3—122no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—22no—
502C3×C4—64no—
503C3×C4—64no—
504C3×C4—122no—
505C3×C4#88212yes—
506C3×C4#93712yes—
507C3×C4C22×D1211yescharacteristic
508C3×C4C2×D3×D411yescharacteristic
509C3×C4C2×D3×D411yescharacteristic
510C3×C4C22×#6711yescharacteristic
511Dic3—24no—
512Dic3—24no—
513Dic3—42no—
514Dic3—62no—
515Dic3—62no—
516Dic3—122no—
517C32C2×#44811yescharacteristic, complemented, Sylow
518C23—62no—
519C23—92no—
520C23—94no—
521C23—122no—
522C23—122no—
523C23—122no—
524C23—182no—
525C23—182no—
526C23#380211yescharacteristic
527Q8—34no—
528Q8—34no—
529Q8—62no—
530Q8—62no—
531Q8—64no—
532Q8—64no—
533Q8—1816no—
534D4—62no—
535D4—62no—
536D4—122no—
537D4—368no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—64no—
541C2×C4—64no—
542C2×C4—62no—
543C2×C4—92no—
544C2×C4—122no—
545C2×C4—1816no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4—184no—
550C2×C4D3×D1212yes—
551C2×C4#380211yescharacteristic
552C2×C4D3×#6712yes—
553C2×C4C22×D3211yescharacteristic
554C8—22no—
555C8—182no—
556C2×C3—24no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—242no—
561C2×C3#480614yescomplemented
562C2×C3#517014yescomplemented
563C2×C3C2×#88211yescharacteristic
564C2×C3C2×D3×SD1611yescharacteristic
565C2×C3C2×D3×SD1611yescharacteristic
566C2×C3C2×#91511yescharacteristic
567C2×C3C2×#91811yescharacteristic
568C2×C3C2×#93711yescharacteristic
569D3—64no—
570D3—64no—
571D3—82no—
572D3—124no—
573C22—94no—
574C22—122no—
575C22—122no—
576C22—122no—
577C22—188no—
578C22—182no—
579C22—182no—
580C22—244no—
581C22#6379612yes—
582C22#6381112yes—
583C22#6392212yes—
584C22C2×#380211yescharacteristic
585C4—64no—
586C4—64no—
587C4—122no—
588C4—182no—
589C4#6392212yes—
590C4C2×D3×D1211yescharacteristic
591C4C2×D3×#6711yescharacteristic
592C3—21no—
593C3C2×#480611yescharacteristic, complemented
594C3C2×#517011yescharacteristic, complemented
595C2—184no—
596C2—242no—
597C2#1059082414yesdirect product factor
598C2C2×#6379611yescharacteristic
599C2C2×#6381111yescharacteristic
600C2C2×#6392211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
hypercenterC22×C8D32
hypocenterC32C2×#448
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3797C2semidirect
2. C22×C3×#204C2semidirect
4. C22×#3715C2semidirect
5. C2×#63647C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63565C2semidirect
8. #10590824C2direct (N × H)
21. C2×#3797C22semidirect
26. C2×C3×#204C22semidirect
31. C2×#3715C22semidirect
32. #63647C22semidirect
33. C3×#816C22semidirect
34. #63565C22semidirect
41. C22×#204D3semidirect
49. C2×#816D3semidirect
71. C2×C3×Dic6D4semidirect
72. C2×C3×Dic6D4semidirect
136. C2×#204C2×D3semidirect
144. #816C2×D3semidirect
149. C22×C3⋊D3SD16semidirect
177. C3×Dic6C2×D4semidirect
178. C3×Dic6C2×D4semidirect
259. C2×Dic6D12semidirect
260. C2×Dic6#67semidirect
292. C2×C3⋊D3C2×SD16semidirect
412. Dic6C2×D12semidirect
413. Dic6C2×#67semidirect
420. C2×C32#448semidirect
517. C32C2×#448semidirect
561. C2×C3#4806semidirect
562. C2×C3#5170semidirect
593. C3C2×#4806semidirect
594. C3C2×#5170semidirect
597. C2#10590824direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×C3×#2042
C2×#639162
C22×#37152
C2×#636472
C2×C3×#8162
C2×#635652
#105908242
C2×#51703
C2×#48063