Finite Group Databasebeta

← C2×#10594311 #11910216

Subgroups — C2×#10594311 #11910216

Order 1152.

3147 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic, complemented
2C2×C3×#885C212yesmaximal, complemented
3C2×#63983C211yesmaximal, characteristic, complemented
4C2×#63981C212yesmaximal, complemented
5C2×#63953C211yesmaximal, characteristic, complemented
6C2×#63923C212yesmaximal, complemented
7C2×#63907C212yesmaximal, complemented
8C2×#63864C212yesmaximal, complemented
9C2×#63852C212yesmaximal, complemented
10#10594311C2116yesmaximal, direct product factor
11C2×#5683—32nomaximal
12C24×C3⋊D3C2211yescharacteristic, complemented
13C23×D32C2211yescharacteristic, complemented
14C22×#638C2211yescharacteristic
15C22×C4⋊(C3⋊D3)C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×Dic6C2212yescomplemented
18C22×#627C2211yescharacteristic, complemented
19C22×#626C2212yes—
20C22×#626C2212yes—
21C2×C32×C22⋊C4C2211yescharacteristic, complemented
22C2×#3752C2212yescomplemented
23#64091C2218yescomplemented
24C2×C3×#217C2212yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yescomplemented
27C2×C3×C4×Dic3C2212yescomplemented
28C3×#885C22116yescomplemented
29#63983C2218yescomplemented
30#63981C22116yescomplemented
31C2×#3722C2212yescomplemented
32C2×#3722C2211yescharacteristic, complemented
33C2×#3722C2212yescomplemented
34C2×#3722C2212yescomplemented
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36C2×Dic32C2211yescharacteristic, complemented
37#63953C2218yescomplemented
38#63923C22116yescomplemented
39#63907C22116yescomplemented
40#63864C22116yescomplemented
41#63852C22116yescomplemented
42C2×C3×#124—32no—
43C2×#947—32no—
44C2×#947—32no—
45C2×#937—32no—
46C2×#937—32no—
47#5683—332no—
48C2×#885—32no—
49C2×#885—32no—
50C2×#885—32no—
51C2×#885D312yescomplemented
52C2×#882—32no—
53C2×#882—32no—
54C2×#882—32no—
55C2×#882—32no—
56C2×#882—61no—
57C2×#875—32no—
58C2×#875—32no—
59C24×C32C2311yescharacteristic
60C23×C3⋊D3—44no—
61C23×C3⋊D3—42no—
62C23×C3⋊D3C2312yes—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3⋊D3C2314yescomplemented
65C23×C3×D3C2312yes—
66C22×D32—42no—
67C22×D32—44no—
68C22×D32C2314yescomplemented
69C22×C32×C4C2312yes—
70C2×#638—42no—
71C2×#638C2314yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4⋊(C3⋊D3)—44no—
74C2×C4⋊(C3⋊D3)C2318yes—
75C2×C3×#67—44no—
76C2×C3×#67C2318yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×C3×Dic6—44no—
81C2×C3×Dic6C2318yescomplemented
82C2×#627—42no—
83C2×#627C2314yescomplemented
84C2×#626—44no—
85C2×#626—44no—
86C2×#626C2318yes—
87C2×#626C2318yes—
88C32×C22⋊C4C2314yescomplemented
89#3752C2318yescomplemented
90C3×#217C2318yescomplemented
91C3×(C2×D3)⋊C4C2318yescomplemented
92C3×(C2×D3)⋊C4C2318yescomplemented
93C3×C4×Dic3C2318yescomplemented
94#3722C2318yescomplemented
95#3722C2314yescomplemented
96#3722C2318yescomplemented
97#3722C2318yescomplemented
98(C2×D3)⋊Dic3C2318yescomplemented
99Dic32C2314yescomplemented
100C2×H(3,𝔽4)—91noSylow
101C24×D3—32no—
102C24×D3—32no—
103C24×D3—61no—
104C22×C3×Q8—32no—
105C22×C3×D4—32no—
106C22×#67—32no—
107C22×#67—32no—
108C22×#67—32no—
109C22×#67—61no—
110C22×#67C2×D312yes—
111C22×D12—32no—
112C22×D12—32no—
113C22×D12—32no—
114C22×D12—32no—
115C22×D12—62no—
116C22×Dic6—32no—
117C22×Dic6C2×D312yescomplemented
118C3×#124—316no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—32no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4C2×D312yescomplemented
124C2×C3×C42—32no—
125C2×#217—32no—
126C2×#217C2×D312yescomplemented
127#947—316no—
128#947—316no—
129#937—316no—
130#937—316no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—62no—
142C2×(C2×D3)⋊C4C2×D312yescomplemented
143C2×(C2×D3)⋊C4C2×D312yescomplemented
144C2×C4×Dic3—32no—
145C2×C4×Dic3C2×D312yescomplemented
146#885—316no—
147#885—316no—
148#885—316no—
149#885C2×D3116yescomplemented
150#882—316no—
151#882—316no—
152#882—316no—
153#882—316no—
154#882—68no—
155#875—316no—
156#875—316no—
157C23×C32—22no—
158C23×C32—24no—
159C23×C32C2412yes—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—24no—
162C22×C3⋊D3—24no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—24no—
165C22×C3⋊D3—24no—
166C22×C3⋊D3—48no—
167C22×C3⋊D3—44no—
168C22×C3⋊D3—416no—
169C22×C3⋊D3C2412yes—
170C22×C3⋊D3C2414yes—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3—24no—
174C22×C3×D3C2414yes—
175C2×D32—44no—
176C2×D32—48no—
177C2×D32—416no—
178C2×C32×C4—24no—
179C2×C32×C4C2414yes—
180#638—44no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3C2412yes—
183C4⋊(C3⋊D3)—48no—
184C3×#67—48no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3C2414yes—
189C2×C3×Dic3C2414yes—
190C2×C3×Dic3C2414yes—
191C3×Dic6—48no—
192#627—44no—
193#626—48no—
194#626—48no—
195H(3,𝔽4)—916no—
196C2×#124—32no—
197C2×#124—92no—
198C2×#124—92no—
199C2×#124—91no—
200C2×#124—92no—
201C2×#120—92no—
202C2×#120—92no—
203C2×#120—91no—
204C2×#120—91no—
205C24×C3—21no—
206C24×C3—32no—
207C24×C3C22×D312yes—
208C23×D3—32no—
209C23×D3—32no—
210C23×D3—32no—
211C23×D3—38no—
212C23×D3—38no—
213C23×D3—62no—
214C23×D3—61no—
215C23×D3—64no—
216C23×D3—124no—
217C23×D3—124no—
218C23×D3—124no—
219C23×D3—124no—
220C23×D3—124no—
221C23×D3—124no—
222C23×D3—128no—
223C23×D3—124no—
224C23×D3C22×D312yes—
225C2×C3×Q8—38no—
226C2×C3×Q8—124no—
227C2×C3×D4—38no—
228C2×C3×D4—124no—
229C22×C3×C4—22no—
230C22×C3×C4—32no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D312yes—
235C2×#67—38no—
236C2×#67—38no—
237C2×#67—38no—
238C2×#67—44no—
239C2×#67—64no—
240C2×#67—124no—
241C2×#67—124no—
242C2×#67—124no—
243C2×#67—124no—
244C2×#67C22×D318yes—
245C22×Dic3—32no—
246C22×Dic3—61no—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D312yes—
250C2×D12—38no—
251C2×D12—38no—
252C2×D12—38no—
253C2×D12—38no—
254C2×D12—68no—
255C2×D12—124no—
256C2×D12—124no—
257C2×D12—128no—
258C2×D12—124no—
259C2×D12—124no—
260C2×Dic6—38no—
261C2×Dic6—44no—
262C2×Dic6—124no—
263C2×Dic6C22×D318yescomplemented
264C3×C22⋊C4—24no—
265C3×C22⋊C4—38no—
266C3×C22⋊C4—38no—
267C3×C22⋊C4—38no—
268C3×C22⋊C4C22×D318yescomplemented
269C3×C42—38no—
270#217—38no—
271#217C22×D318yescomplemented
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—38no—
276(C2×D3)⋊C4—38no—
277(C2×D3)⋊C4—38no—
278(C2×D3)⋊C4—38no—
279(C2×D3)⋊C4—38no—
280(C2×D3)⋊C4—38no—
281(C2×D3)⋊C4—38no—
282(C2×D3)⋊C4—68no—
283(C2×D3)⋊C4C22×D318yescomplemented
284(C2×D3)⋊C4C22×D318yescomplemented
285C4×Dic3—38no—
286C4×Dic3C22×D318yescomplemented
287C22×C32—22no—
288C22×C32—24no—
289C22×C32—44no—
290C22×C32H(5,𝔽2)14yes—
291C22×C32H(5,𝔽2)12yes—
292C22×C32C2511yescharacteristic
293C2×C3⋊D3—24no—
294C2×C3⋊D3—24no—
295C2×C3⋊D3—24no—
296C2×C3⋊D3—24no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—416no—
299C2×C3⋊D3—48no—
300C2×C3⋊D3—44no—
301C2×C3×D3—24no—
302C2×C3×D3—24no—
303C2×C3×D3—24no—
304C2×C3×D3—48no—
305D32—416no—
306C32×C4—24no—
307C3⋊Dic3—22no—
308C3×Dic3—24no—
309C3×Dic3—24no—
310C3×Dic3—24no—
311C25—91no—
312C25—91no—
313C22×Q8—32no—
314C22×Q8—91no—
315C22×D4—32no—
316C22×D4—92no—
317C22×D4—92no—
318C22×D4—91no—
319C22×D4—92no—
320#124—316no—
321#124—916no—
322#124—916no—
323#124—98no—
324#124—916no—
325#120—916no—
326#120—916no—
327#120—98no—
328#120—98no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—32no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—91no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4D3211yescharacteristic, complemented
339C2×C42—32no—
340C2×C42—91no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—34no—
348C23×C3—44no—
349C23×C3—64no—
350C23×C3—64no—
351C23×C3—64no—
352C23×C3C23×D314yes—
353C23×C3C23×D312yes—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—34no—
358C22×D3—34no—
359C22×D3—34no—
360C22×D3—64no—
361C22×D3—62no—
362C22×D3—68no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—64no—
371C22×D3—64no—
372C22×D3—124no—
373C22×D3—124no—
374C22×D3—124no—
375C22×D3—122no—
376C22×D3—128no—
377C22×D3—128no—
378C22×D3—128no—
379C22×D3—1232no—
380C22×D3—128no—
381C22×D3—128no—
382C22×D3—128no—
383C22×D3—1216no—
384C22×D3—128no—
385C22×D3—1232no—
386C22×D3—1232no—
387C22×D3C23×D314yes—
388C3×Q8—128no—
389C3×D4—128no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—34no—
394C2×C3×C4—34no—
395C2×C3×C4—34no—
396C2×C3×C4—44no—
397C2×C3×C4—64no—
398C2×C3×C4—64no—
399C2×C3×C4—64no—
400C2×C3×C4C23×D314yes—
401C2×C3×C4C23×D314yes—
402#67—48no—
403#67—128no—
404#67—128no—
405#67—128no—
406#67—128no—
407C2×Dic3—24no—
408C2×Dic3—24no—
409C2×Dic3—24no—
410C2×Dic3—34no—
411C2×Dic3—62no—
412C2×Dic3—64no—
413C2×Dic3—122no—
414C2×Dic3C23×D314yes—
415C2×Dic3C23×D314yes—
416C2×Dic3C23×D314yes—
417D12—128no—
418D12—128no—
419D12—1216no—
420D12—128no—
421D12—128no—
422Dic6—48no—
423Dic6—128no—
424C2×C32—42no—
425C2×C32H(3,𝔽4)14yescomplemented
426C2×C32C2×H(5,𝔽2)12yes—
427C2×C32C2×H(5,𝔽2)11yescharacteristic
428C3⋊D3—44no—
429C3⋊D3—42no—
430C3×D3—44no—
431C24—32no—
432C24—94no—
433C24—92no—
434C24—91no—
435C24—94no—
436C24—362no—
437C24—364no—
438C24—362no—
439C24—364no—
440C24C2×D3211yescharacteristic
441C2×Q8—38no—
442C2×Q8—94no—
443C2×Q8—124no—
444C2×Q8—362no—
445C2×D4—38no—
446C2×D4—98no—
447C2×D4—98no—
448C2×D4—94no—
449C2×D4—98no—
450C2×D4—124no—
451C2×D4—364no—
452C2×D4—364no—
453C2×D4—364no—
454C2×D4—362no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—91no—
459C22×C4C2×D3212yes—
460C22⋊C4—38no—
461C22⋊C4—38no—
462C22⋊C4—38no—
463C22⋊C4—98no—
464C22⋊C4—98no—
465C22⋊C4—94no—
466C22⋊C4—98no—
467C22⋊C4—98no—
468C22⋊C4—98no—
469C22⋊C4C2×D3214yescomplemented
470C42—38no—
471C42—94no—
472C22×C3—24no—
473C22×C3—24no—
474C22×C3—24no—
475C22×C3—24no—
476C22×C3—22no—
477C22×C3—24no—
478C22×C3—21no—
479C22×C3—44no—
480C22×C3—48no—
481C22×C3—48no—
482C22×C3—64no—
483C22×C3—64no—
484C22×C3—64no—
485C22×C3—128no—
486C22×C3#100414yes—
487C22×C3#100914yes—
488C22×C3#100914yes—
489C22×C3C24×D312yes—
490C2×D3—24no—
491C2×D3—24no—
492C2×D3—24no—
493C2×D3—48no—
494C2×D3—68no—
495C2×D3—64no—
496C2×D3—64no—
497C2×D3—64no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—64no—
501C2×D3—64no—
502C2×D3—64no—
503C2×D3—64no—
504C2×D3—124no—
505C2×D3—124no—
506C2×D3—124no—
507C2×D3—122no—
508C2×D3—1232no—
509C2×D3—1216no—
510C2×D3—1232no—
511C2×D3—1232no—
512C2×D3—128no—
513C2×D3—128no—
514C2×D3—128no—
515C2×D3—244no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—44no—
519C3×C4—64no—
520C3×C4—64no—
521C3×C4—64no—
522Dic3—24no—
523Dic3—24no—
524Dic3—24no—
525Dic3—64no—
526Dic3—122no—
527C32C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
528C23—22no—
529C23—24no—
530C23—34no—
531C23—64no—
532C23—64no—
533C23—64no—
534C23—94no—
535C23—92no—
536C23—184no—
537C23—182no—
538C23—184no—
539C23—184no—
540C23—184no—
541C23—364no—
542C23—368no—
543C23—3616no—
544C23—364no—
545C23—368no—
546C23—3616no—
547C23C22×D3212yes—
548C23C22×D3211yescharacteristic
549Q8—128no—
550Q8—364no—
551D4—128no—
552D4—368no—
553D4—368no—
554D4—368no—
555D4—364no—
556C2×C4—24no—
557C2×C4—34no—
558C2×C4—34no—
559C2×C4—34no—
560C2×C4—64no—
561C2×C4—64no—
562C2×C4—64no—
563C2×C4—92no—
564C2×C4—182no—
565C2×C4C22×D3214yes—
566C2×C3—24no—
567C2×C3—21no—
568C2×C3—22no—
569C2×C3—44no—
570C2×C3—44no—
571C2×C3—124no—
572C2×C3#568318yescomplemented
573C2×C3C2×#100412yes—
574C2×C3C2×#100912yes—
575C2×C3C2×#100912yes—
576D3—44no—
577D3—128no—
578D3—124no—
579D3—124no—
580D3—124no—
581D3—242no—
582C22—22no—
583C22—24no—
584C22—44no—
585C22—64no—
586C22—64no—
587C22—64no—
588C22—128no—
589C22—184no—
590C22—182no—
591C22—184no—
592C22—184no—
593C22—184no—
594C22—3616no—
595C22—3616no—
596C22—368no—
597C22—364no—
598C22#6430812yes—
599C22#6431414yes—
600C22C23×D3211yescharacteristic
601C4—24no—
602C4—64no—
603C4—64no—
604C4—64no—
605C4—182no—
606C3—21no—
607C3C2×#568312yescomplemented
608C2—42no—
609C2—124no—
610C2—364no—
611C2—362no—
612C2#1059431114yesdirect product factor
613C2C2×#6430811yescharacteristic
614C2C2×#6431412yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×H(3,𝔽4)
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64091C2semidirect
2. C2×C3×#885C2semidirect
3. C2×#63983C2semidirect
4. C2×#63981C2semidirect
5. C2×#63953C2semidirect
6. C2×#63923C2semidirect
7. C2×#63907C2semidirect
8. C2×#63864C2semidirect
9. C2×#63852C2semidirect
10. #10594311C2direct (N × H)
12. C24×C3⋊D3C22semidirect
13. C23×D32C22semidirect
17. C22×C3×Dic6C22semidirect
18. C22×#627C22semidirect
21. C2×C32×C22⋊C4C22semidirect
22. C2×#3752C22semidirect
23. #64091C22semidirect
24. C2×C3×#217C22semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
26. C2×C3×(C2×D3)⋊C4C22semidirect
27. C2×C3×C4×Dic3C22semidirect
28. C3×#885C22semidirect
29. #63983C22semidirect
30. #63981C22semidirect
31. C2×#3722C22semidirect
32. C2×#3722C22semidirect
33. C2×#3722C22semidirect
34. C2×#3722C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. C2×Dic32C22semidirect
37. #63953C22semidirect
38. #63923C22semidirect
39. #63907C22semidirect
40. #63864C22semidirect
41. #63852C22semidirect
51. C2×#885D3semidirect
64. C23×C3⋊D3C23semidirect
68. C22×D32C23semidirect
81. C2×C3×Dic6C23semidirect
83. C2×#627C23semidirect
88. C32×C22⋊C4C23semidirect
89. #3752C23semidirect
90. C3×#217C23semidirect
91. C3×(C2×D3)⋊C4C23semidirect
92. C3×(C2×D3)⋊C4C23semidirect
93. C3×C4×Dic3C23semidirect
94. #3722C23semidirect
95. #3722C23semidirect
96. #3722C23semidirect
97. #3722C23semidirect
98. (C2×D3)⋊Dic3C23semidirect
99. Dic32C23semidirect
117. C22×Dic6C2×D3semidirect
123. C2×C3×C22⋊C4C2×D3semidirect
126. C2×#217C2×D3semidirect
142. C2×(C2×D3)⋊C4C2×D3semidirect
143. C2×(C2×D3)⋊C4C2×D3semidirect
145. C2×C4×Dic3C2×D3semidirect
149. #885C2×D3semidirect
263. C2×Dic6C22×D3semidirect
268. C3×C22⋊C4C22×D3semidirect
271. #217C22×D3semidirect
283. (C2×D3)⋊C4C22×D3semidirect
284. (C2×D3)⋊C4C22×D3semidirect
286. C4×Dic3C22×D3semidirect
338. C2×C22⋊C4D32semidirect
425. C2×C32H(3,𝔽4)semidirect
469. C22⋊C4C2×D32semidirect
527. C32C2×H(3,𝔽4)semidirect
572. C2×C3#5683semidirect
607. C3C2×#5683semidirect
612. C2#10594311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640912
C2×C3×#8852
C2×#639832
C2×#639812
C2×#639532
C2×#639232
C2×#639072
C2×#638642
C2×#638522
#105943112
C2×#56833