Finite Group Databasebeta

← C2×#10595363 #11900797

Subgroups — C2×#10595363 #11900797

Order 1152.

3901 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3832C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C3×#947C211yesmaximal, characteristic, complemented
4C2×C3×#944C211yesmaximal, characteristic, complemented
5#10595363C2116yesmaximal, direct product factor
6C2×#63911C211yesmaximal, characteristic, complemented
7C2×#63910C214yesmaximal, complemented
8C2×C4×#624C211yesmaximal, characteristic, complemented
9C2×#63881C214yesmaximal, complemented
10C2×#63864C211yesmaximal, characteristic, complemented
11C2×#5725—31nomaximal
12C2×#5668—31nomaximal
13C22×C32×Q8C2211yescharacteristic
14C2×#3832—28no—
15C2×#3832C2218yescomplemented
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4⋊(C3⋊D3)C2212yes—
18C22×C4×C3⋊D3C2212yes—
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×#626C2212yes—
23C22×#626C2214yes—
24C22×#624C2212yes—
25C22×D3×Dic3C2212yes—
26C2×#3796—28no—
27C2×#3796C2218yescomplemented
28C3×#947C2218yescomplemented
29C3×#944C2218yescomplemented
30C2×C3×(C2×D3)⋊C4C2214yes—
31C2×C3×Dic3⋊C4C2214yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3722C2214yes—
35C2×Dic32C2212yes—
36#63911C2218yescomplemented
37#63910C22132yescomplemented
38C4×#624C2218yescomplemented
39#63881C22132yescomplemented
40#63864C2218yescomplemented
41C22×#239—31no—
42C22×#239—31no—
43C22×#239—31no—
44C22×#239—61no—
45C22×#237—31no—
46C2×C3×C4⋊Q8—31no—
47C2×C3×#124—31no—
48C2×#947—31no—
49C2×#947D311yescharacteristic, complemented
50C2×#944D311yescharacteristic, complemented
51C2×#940—31no—
52#5725—316no—
53#5668—316no—
54C2×#895—34no—
55C2×#893—34no—
56C2×#884—34no—
57C2×#67⋊C4—34no—
58C2×#875—31no—
59C2×#874—31no—
60C2×C42×D3—31no—
61C2×C42×D3—31no—
62C23×C3⋊D3C2312yes—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2312yes—
65C2×C32×Q8—24no—
66C2×C32×Q8C2314yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70#3832—232no—
71C2×C4⋊(C3⋊D3)—28no—
72C2×C4⋊(C3⋊D3)—24no—
73C2×C4⋊(C3⋊D3)C2314yes—
74C2×C4⋊(C3⋊D3)C2318yes—
75C2×C4×C3⋊D3—28no—
76C2×C4×C3⋊D3D418yescomplemented
77C2×C4×C3⋊D3C2318yes—
78C2×C4×C3⋊D3C2314yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×C3×D12—24no—
83C2×C3×D12C2314yes—
84C2×C3×Dic6—24no—
85C2×C3×Dic6C2314yes—
86C2×#626—28no—
87C2×#626—216no—
88C2×#626C2318yes—
89C2×#626C23116yes—
90C2×#624—28no—
91C2×#624C2318yes—
92C2×D3×Dic3—28no—
93C2×D3×Dic3C2318yes—
94#3796—232no—
95C3×(C2×D3)⋊C4C23116yes—
96C3×Dic3⋊C4C23116yes—
97C3×C4×Dic3C2314yes—
98C3×C4×Dic3C2314yes—
99#3722C23116yes—
100Dic32C2318yes—
101C2×#532—91noSylow
102C22×C3×Q8—21no—
103C22×C3×Q8—31no—
104C22×C3×Q8C2×D311yescharacteristic
105C22×C3×Q8C2×D311yescharacteristic
106C22×C3×D4—31no—
107C22×#67—32no—
108C22×#67—34no—
109C23×Dic3—32no—
110C2×#239—38no—
111C2×#239—38no—
112C2×#239—38no—
113C2×#239—68no—
114C2×#239—68no—
115C2×#239—68no—
116C2×#239—68no—
117C2×#239—616no—
118C2×#237—38no—
119C2×#237—68no—
120C22×D12—32no—
121C22×D12—34no—
122C22×D12—31no—
123C22×D12—31no—
124C22×D12—32no—
125C22×D12—32no—
126C22×D12—62no—
127C22×D12—61no—
128C22×D12C2×D311yescharacteristic
129C22×C4×D3—31no—
130C22×C4×D3—31no—
131C22×C4×D3—32no—
132C22×C4×D3—32no—
133C22×C4×D3—32no—
134C22×C4×D3—32no—
135C22×C4×D3—32no—
136C22×C4×D3—61no—
137C22×C4×D3—62no—
138C22×Dic6C2×D311yescharacteristic
139C3×C4⋊Q8—38no—
140C3×#124—38no—
141C2×C3×C4⋊C4—34no—
142C2×C3×C22⋊C4—34no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145#947—38no—
146#947C2×D318yescomplemented
147#944C2×D318yescomplemented
148#940—38no—
149C2×(C2×D3)⋊C4—34no—
150C2×(C2×D3)⋊C4—34no—
151C2×(C2×D3)⋊C4C2×D314yes—
152C2×Dic3⋊C4C2×D314yes—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3C2×D311yescharacteristic
156C2×C4×Dic3C2×D311yescharacteristic
157#895—332no—
158#893—332no—
159#884—332no—
160#67⋊C4—332no—
161#875—38no—
162#874—38no—
163C42×D3—38no—
164C42×D3—38no—
165C23×C32C2411yescharacteristic
166C22×C3⋊D3—24no—
167C22×C3⋊D3—24no—
168C22×C3⋊D3—28no—
169C22×C3⋊D3C2×D414yes—
170C22×C3⋊D3C2414yes—
171C22×C3⋊D3C2412yes—
172C22×C3×D3—24no—
173C22×C3×D3—28no—
174C22×C3×D3C2414yes—
175C32×Q8—28no—
176C2×C32×C4—24no—
177C2×C32×C4C2×D414yes—
178C2×C32×C4C2414yes—
179C2×C32×C4C2412yes—
180C2×C3⋊Dic3C2×D414yes—
181C2×C3⋊Dic3C2412yes—
182C4⋊(C3⋊D3)—216no—
183C4⋊(C3⋊D3)—28no—
184C4×C3⋊D3—216no—
185C4×C3⋊D3C2×D4116yescomplemented
186C2×C3×Dic3—24no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3#4118yescomplemented
189C2×C3×Dic3C2414yes—
190C2×C3×Dic3C2414yes—
191C2×C3×Dic3C2414yes—
192C3×D12—28no—
193C3×Dic6—28no—
194#626—216no—
195#626—232no—
196#624—216no—
197D3×Dic3—216no—
198C22×#41—91no—
199C22×#41—91no—
200#532—916no—
201C2×C4⋊Q8—31no—
202C2×#127—91no—
203C2×#124—31no—
204C2×#124—91no—
205C2×#121—94no—
206C2×C4×D4—94no—
207C22×C42—91no—
208C24×C3—32no—
209C23×D3—31no—
210C23×D3—31no—
211C23×D3—32no—
212C23×D3—32no—
213C23×D3—61no—
214C23×D3—62no—
215C23×D3C22×D312yes—
216C2×C3×Q8—28no—
217C2×C3×Q8—24no—
218C2×C3×Q8—24no—
219C2×C3×Q8—24no—
220C2×C3×Q8—34no—
221C2×C3×Q8—64no—
222C2×C3×Q8C22×D314yes—
223C2×C3×Q8C22×D314yes—
224C2×C3×D4—34no—
225C2×C3×D4—64no—
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—316no—
236C2×#67—38no—
237C2×#67—68no—
238C2×#67—616no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—38no—
242C22×Dic3—61no—
243C22×Dic3—68no—
244C22×Dic3C22×D312yes—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D312yes—
247#239—632no—
248#239—632no—
249#239—632no—
250#239—664no—
251#237—632no—
252C2×D12—24no—
253C2×D12—316no—
254C2×D12—38no—
255C2×D12—34no—
256C2×D12—34no—
257C2×D12—38no—
258C2×D12—38no—
259C2×D12—68no—
260C2×D12—64no—
261C2×D12—68no—
262C2×D12—68no—
263C2×D12—616no—
264C2×D12—68no—
265C2×D12—616no—
266C2×D12—68no—
267C2×D12—64no—
268C2×D12—64no—
269C2×D12C22×D314yes—
270C2×C4×D3—38no—
271C2×C4×D3—38no—
272C2×C4×D3—34no—
273C2×C4×D3—34no—
274C2×C4×D3—38no—
275C2×C4×D3—38no—
276C2×C4×D3—38no—
277C2×C4×D3—38no—
278C2×C4×D3—38no—
279C2×C4×D3—68no—
280C2×C4×D3—64no—
281C2×C4×D3—68no—
282C2×C4×D3—68no—
283C2×C4×D3—68no—
284C2×C4×D3—68no—
285C2×C4×D3—68no—
286C2×C4×D3—616no—
287C2×C4×D3—68no—
288C2×Dic6—24no—
289C2×Dic6C22×D314yes—
290C3×C4⋊C4—316no—
291C3×C22⋊C4—316no—
292C3×C42—34no—
293C3×C42—34no—
294(C2×D3)⋊C4—316no—
295(C2×D3)⋊C4—316no—
296(C2×D3)⋊C4C22×D3116yes—
297Dic3⋊C4C22×D3116yes—
298C4×Dic3—38no—
299C4×Dic3—38no—
300C4×Dic3C22×D314yes—
301C4×Dic3C22×D314yes—
302C22×C32C22×D412yes—
303C22×C32C2×#4114yes—
304C22×C32C2511yescharacteristic
305C2×C3⋊D3—24no—
306C2×C3⋊D3—28no—
307C2×C3⋊D3—24no—
308C2×C3⋊D3—28no—
309C2×C3⋊D3—48no—
310C2×C3⋊D3C22×D414yes—
311C2×C3×D3—24no—
312C2×C3×D3—28no—
313C2×C3×D3—48no—
314C32×C4—24no—
315C32×C4C22×D414yes—
316C3⋊Dic3C22×D414yes—
317C3×Dic3—24no—
318C3×Dic3—24no—
319C3×Dic3C2×#4118yescomplemented
320C2×#41—98no—
321C2×#41—98no—
322C2×#41—188no—
323C2×#41—188no—
324C22×Q8—31no—
325C22×Q8D3211yescharacteristic
326C22×D4—31no—
327C22×D4—94no—
328C22×D4—92no—
329C22×D4—92no—
330C22×D4—91no—
331C23×C4—92no—
332C23×C4—92no—
333C23×C4—91no—
334C23×C4—92no—
335C4⋊Q8—38no—
336#127—98no—
337#124—38no—
338#124—98no—
339#121—932no—
340C4×D4—932no—
341C2×C4⋊C4—34no—
342C2×C22⋊C4—34no—
343C2×C22⋊C4—94no—
344C2×C42—31no—
345C2×C42—31no—
346C2×C42—98no—
347C2×C42—92no—
348C23×C3—21no—
349C23×C3—34no—
350C23×C3—64no—
351C23×C3—68no—
352C23×C3C23×D311yescharacteristic
353C23×C3C23×D311yescharacteristic
354C22×D3—24no—
355C22×D3—28no—
356C22×D3—34no—
357C22×D3—34no—
358C22×D3—32no—
359C22×D3—32no—
360C22×D3—34no—
361C22×D3—34no—
362C22×D3—64no—
363C22×D3—62no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—68no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—68no—
371C22×D3—68no—
372C22×D3—124no—
373C22×D3—128no—
374C22×D3C23×D314yes—
375C3×Q8—216no—
376C3×Q8—28no—
377C3×Q8—28no—
378C3×Q8—68no—
379C3×D4—68no—
380C2×C3×C4—28no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—38no—
387C2×C3×C4—34no—
388C2×C3×C4—34no—
389C2×C3×C4—34no—
390C2×C3×C4—64no—
391C2×C3×C4—64no—
392C2×C3×C4D3×D414yes—
393C2×C3×C4D3×D414yes—
394C2×C3×C4C23×D314yes—
395C2×C3×C4C23×D314yes—
396C2×C3×C4C23×D312yes—
397C2×C3×C4C23×D312yes—
398#67—616no—
399#67—632no—
400C2×Dic3—24no—
401C2×Dic3—24no—
402C2×Dic3—34no—
403C2×Dic3—34no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—64no—
407C2×Dic3—62no—
408C2×Dic3—616no—
409C2×Dic3#23918yescomplemented
410C2×Dic3C23×D314yes—
411C2×Dic3C23×D314yes—
412C2×Dic3C23×D314yes—
413D12—28no—
414D12—616no—
415D12—616no—
416D12—632no—
417D12—616no—
418D12—632no—
419D12—616no—
420D12—68no—
421D12—68no—
422C4×D3—316no—
423C4×D3—316no—
424C4×D3—616no—
425C4×D3—616no—
426C4×D3—616no—
427C4×D3—616no—
428C4×D3—616no—
429C4×D3—632no—
430C4×D3—616no—
431Dic6—28no—
432C2×C32#53214yescomplemented
433C2×C32C23×D411yescharacteristic
434C2×C32C22×#4112yes—
435C3⋊D3—24no—
436C3⋊D3—44no—
437C3×D3—44no—
438C24—32no—
439C24—91no—
440C24—92no—
441#41—1832no—
442#41—1832no—
443C2×Q8—24no—
444C2×Q8—34no—
445C2×Q8—64no—
446C2×Q8C2×D3214yes—
447C2×D4—34no—
448C2×D4—64no—
449C2×D4—916no—
450C2×D4—98no—
451C2×D4—98no—
452C2×D4—94no—
453C2×D4—188no—
454C2×D4—1816no—
455C2×D4—188no—
456C2×D4—184no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—98no—
461C22×C4—98no—
462C22×C4—91no—
463C22×C4—94no—
464C22×C4—98no—
465C22×C4—98no—
466C22×C4—188no—
467C22×C4—188no—
468C22×C4—188no—
469C22×C4C2×D3212yes—
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—316no—
472C22⋊C4—316no—
473C22⋊C4—916no—
474C42—34no—
475C42—34no—
476C42—98no—
477C22×C3—24no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—64no—
481C22×C3—68no—
482C22×C3—128no—
483C22×C3C2×D3×D412yes—
484C22×C3C2×D3×D412yes—
485C22×C3C2×#23914yes—
486C22×C3D3×#4114yes—
487C22×C3C24×D311yescharacteristic
488C22×C3C24×D311yescharacteristic
489C2×D3—24no—
490C2×D3—28no—
491C2×D3—34no—
492C2×D3—34no—
493C2×D3—48no—
494C2×D3—64no—
495C2×D3—68no—
496C2×D3—64no—
497C2×D3—64no—
498C2×D3—68no—
499C2×D3—68no—
500C2×D3—64no—
501C2×D3—64no—
502C2×D3—68no—
503C2×D3—68no—
504C2×D3—128no—
505C2×D3—124no—
506C2×D3—128no—
507C2×D3—1216no—
508C2×D3—128no—
509C2×D3—128no—
510C3×C4—28no—
511C3×C4—24no—
512C3×C4—24no—
513C3×C4—24no—
514C3×C4—38no—
515C3×C4—64no—
516C3×C4—64no—
517C3×C4C2×D3×D414yes—
518C3×C4C2×D3×D414yes—
519Dic3—24no—
520Dic3—24no—
521Dic3—34no—
522Dic3—34no—
523Dic3—64no—
524Dic3C2×#23918yescomplemented
525C32C2×#53211yescharacteristic, complemented, Sylow
526C23—34no—
527C23—68no—
528C23—64no—
529C23—94no—
530C23—92no—
531C23—94no—
532C23—184no—
533C23—188no—
534C23—184no—
535C23C22×D3211yescharacteristic
536Q8—28no—
537Q8—68no—
538D4—68no—
539D4—1816no—
540D4—1832no—
541D4—1816no—
542D4—188no—
543C2×C4—24no—
544C2×C4—38no—
545C2×C4—34no—
546C2×C4—34no—
547C2×C4—34no—
548C2×C4—64no—
549C2×C4—64no—
550C2×C4—94no—
551C2×C4—92no—
552C2×C4—916no—
553C2×C4—1816no—
554C2×C4—1816no—
555C2×C4—1816no—
556C2×C4#381114yes—
557C2×C4C22×D3214yes—
558C2×C4C22×D3212yes—
559C2×C3—24no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—124no—
563C2×C3#566814yescomplemented
564C2×C3#572514yescomplemented
565C2×C3C22×D3×D411yescharacteristic
566C2×C3C22×D3×D411yescharacteristic
567C2×C3C22×#23912yes—
568C2×C3C2×D3×#4112yes—
569D3—44no—
570D3—64no—
571D3—64no—
572D3—124no—
573D3—128no—
574D3—124no—
575D3—124no—
576C22—68no—
577C22—64no—
578C22—94no—
579C22—128no—
580C22—188no—
581C22—184no—
582C22—188no—
583C22—184no—
584C22—368no—
585C22D3×#23914yes—
586C22C2×#381112yes—
587C22C23×D3211yescharacteristic
588C4—24no—
589C4—38no—
590C4—64no—
591C4—64no—
592C4—94no—
593C4C2×#381114yes—
594C3—21no—
595C3C2×#566811yescharacteristic, complemented
596C3C2×#572511yescharacteristic, complemented
597C2—124no—
598C2—184no—
599C2—364no—
600C2#1059536314yesdirect product factor
601C2C2×D3×#23912yes—
602C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C22×#3796C2semidirect
3. C2×C3×#947C2semidirect
4. C2×C3×#944C2semidirect
5. #10595363C2direct (N × H)
6. C2×#63911C2semidirect
7. C2×#63910C2semidirect
8. C2×C4×#624C2semidirect
9. C2×#63881C2semidirect
10. C2×#63864C2semidirect
15. C2×#3832C22semidirect
27. C2×#3796C22semidirect
28. C3×#947C22semidirect
29. C3×#944C22semidirect
36. #63911C22semidirect
37. #63910C22semidirect
38. C4×#624C22semidirect
39. #63881C22semidirect
40. #63864C22semidirect
49. C2×#947D3semidirect
50. C2×#944D3semidirect
76. C2×C4×C3⋊D3D4semidirect
146. #947C2×D3semidirect
147. #944C2×D3semidirect
185. C4×C3⋊D3C2×D4semidirect
188. C2×C3×Dic3#41semidirect
319. C3×Dic3C2×#41semidirect
409. C2×Dic3#239semidirect
432. C2×C32#532semidirect
524. Dic3C2×#239semidirect
525. C32C2×#532semidirect
563. C2×C3#5668semidirect
564. C2×C3#5725semidirect
595. C3C2×#5668semidirect
596. C3C2×#5725semidirect
600. C2#10595363direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38322
C22×#37962
C2×C3×#9472
C2×C3×#9442
#105953632
C2×#639112
C2×#639102
C2×C4×#6242
C2×#638812
C2×#638642
C2×#57253
C2×#56683