Finite Group Databasebeta

← C2×#10595043 #11901157

Subgroups — C2×#10595043 #11901157

Order 1152.

3725 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×#3828C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63978C214yesmaximal, complemented
5#10595043C2116yesmaximal, direct product factor
6C2×#63916C212yesmaximal, complemented
7C2×#63909C212yesmaximal, complemented
8C2×#63871C212yesmaximal, complemented
9C2×#63857C212yesmaximal, complemented
10C2×#5833—31nomaximal
11C2×#5510—31nomaximal
12C23×C32×C4C2211yescharacteristic
13C22×#638C2212yes—
14C2×#3828—28no—
15C2×#3828C2218yescomplemented
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4×C3⋊D3C2212yes—
18C22×#634C2211yescharacteristic
19C22×C3×#67C2212yes—
20C23×C3×Dic3C2212yes—
21C2×C3×#235—28no—
22C2×C3×#235C2218yescomplemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2212yes—
25C22×C3×Dic6C2211yescharacteristic
26C22×#626C2214yes—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×C4⋊Dic3C2218yescomplemented
30#63978C22132yescomplemented
31C2×Dic3⋊Dic3C2214yes—
32C2×#3722C2214yes—
33C2×(C2×D3)⋊Dic3C2214yes—
34#63916C22116yescomplemented
35#63909C22116yescomplemented
36#63871C22116yescomplemented
37#63857C22116yescomplemented
38C22×C3×#41—31no—
39C22×#235—31no—
40C22×#235—31no—
41C22×#235—61no—
42C22×#235D311yescharacteristic, complemented
43C22×C3×C4⋊C4—31no—
44#5833—316no—
45C2×#946—32no—
46C2×#939—34no—
47C2×#938—32no—
48C2×#930—34no—
49C2×#930—32no—
50C22×C4⋊Dic3D311yescharacteristic, complemented
51C2×#924—32no—
52#5510—316no—
53C2×#897—32no—
54C2×#897—32no—
55C2×#895—32no—
56C2×#895—32no—
57C24×C32C2311yescharacteristic
58C23×C3⋊D3C2312yes—
59C23×C3×D3C2312yes—
60C22×C32×C4D418yescomplemented
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2314yes—
64C2×#638—28no—
65C2×#638C2318yes—
66C22×C3⋊Dic3C2312yes—
67#3828—232no—
68C2×C4⋊(C3⋊D3)—24no—
69C2×C4⋊(C3⋊D3)C2314yes—
70C2×C4×C3⋊D3—28no—
71C2×C4×C3⋊D3C2318yes—
72C2×#634—24no—
73C2×#634C2314yes—
74C2×C3×#67—28no—
75C2×C3×#67C2318yes—
76C22×C3×Dic3—44no—
77C22×C3×Dic3C2314yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2318yes—
80C3×#235—232no—
81C2×C3×D12—24no—
82C2×C3×D12C2314yes—
83C2×C3×C4×D3—28no—
84C2×C3×C4×D3C2318yes—
85C2×C3×Dic6—24no—
86C2×C3×Dic6C2314yes—
87C2×#626—48no—
88C2×#626C23116yes—
89C3×C4⋊Dic3C2318yes—
90C3×C4⋊Dic3C2318yes—
91Dic3⋊Dic3C23116yes—
92#3722C23116yes—
93(C2×D3)⋊Dic3C23116yes—
94C2×#537—91noSylow
95C2×C3×#41—38no—
96C2×C3×#41—68no—
97C22×C3×Q8—31no—
98C22×C3×D4—32no—
99C22×C3×D4—31no—
100C23×C3×C4—21no—
101C23×C3×C4—32no—
102C23×C3×C4—32no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C22×#67—32no—
106C22×#67—32no—
107C22×#67—34no—
108C22×#67—62no—
109C22×#67C2×D312yes—
110C23×Dic3C2×D312yes—
111C2×#235—28no—
112C2×#235—38no—
113C2×#235—38no—
114C2×#235—68no—
115C2×#235—616no—
116C2×#235—68no—
117C2×#235—68no—
118C2×#235C2×D318yescomplemented
119C22×D12—31no—
120C22×D12—31no—
121C22×D12—34no—
122C22×D12—61no—
123C22×D12C2×D311yescharacteristic
124C22×C4×D3—32no—
125C22×C4×D3—32no—
126C22×C4×D3—62no—
127C22×C4×D3C2×D312yes—
128C22×Dic6—31no—
129C22×Dic6—31no—
130C22×Dic6—61no—
131C22×Dic6C2×D311yescharacteristic
132C2×C3×C4⋊C4—32no—
133C2×C3×C4⋊C4—32no—
134C2×C3×C4⋊C4—38no—
135C2×#217—34no—
136#946—316no—
137#939—332no—
138#938—316no—
139#930—332no—
140#930—316no—
141C2×(C2×D3)⋊C4—34no—
142C2×(C2×D3)⋊C4—34no—
143C2×(C2×D3)⋊C4—34no—
144C2×C4⋊Dic3—34no—
145C2×C4⋊Dic3C2×D312yes—
146C2×C4⋊Dic3C2×D312yes—
147C2×C4⋊Dic3C2×D318yescomplemented
148#924—316no—
149C2×Dic3⋊C4—34no—
150#897—316no—
151#897—316no—
152#895—316no—
153#895—316no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32C2×D414yes—
157C23×C32C2412yes—
158C23×C32C2411yescharacteristic
159C22×C3⋊D3—24no—
160C22×C3⋊D3—24no—
161C22×C3⋊D3—24no—
162C22×C3⋊D3C2414yes—
163C22×C3×D3—24no—
164C22×C3×D3—24no—
165C22×C3×D3—24no—
166C22×C3×D3C2414yes—
167C2×C32×C4C2×D414yes—
168C2×C32×C4C2×D414yes—
169C2×C32×C4C2×D4116yescomplemented
170C2×C32×C4C2412yes—
171C2×C32×C4C2412yes—
172#638—216no—
173C2×C3⋊Dic3—24no—
174C2×C3⋊Dic3C2414yes—
175C4⋊(C3⋊D3)—28no—
176C4×C3⋊D3—216no—
177#634—28no—
178C3×#67—216no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3—28no—
181C2×C3×Dic3—48no—
182C2×C3×Dic3C2418yes—
183C2×C3×Dic3C2414yes—
184C3×D12—28no—
185C3×C4×D3—216no—
186C3×Dic6—28no—
187#626—416no—
188C22×#41—31no—
189C22×#41—91no—
190#537—916no—
191C2×C22⋊Q8—92no—
192C2×C22⋊Q8—92no—
193C2×#121—92no—
194C2×#121—92no—
195C2×#121—94no—
196C22×C4⋊C4—31no—
197C24×C3—21no—
198C24×C3—32no—
199C24×C3C22×D311yescharacteristic
200C24×C3C22×D311yescharacteristic
201C23×D3—32no—
202C23×D3—32no—
203C23×D3—62no—
204C23×D3C22×D312yes—
205C3×#41—632no—
206C2×C3×Q8—34no—
207C2×C3×Q8—64no—
208C2×C3×D4—38no—
209C2×C3×D4—34no—
210C2×C3×D4—68no—
211C2×C3×D4—64no—
212C22×C3×C4—28no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—24no—
216C22×C3×C4—32no—
217C22×C3×C4—34no—
218C22×C3×C4—38no—
219C22×C3×C4—38no—
220C22×C3×C4—68no—
221C22×C3×C4—124no—
222C22×C3×C4D1218yescomplemented
223C22×C3×C4#6718yescomplemented
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D314yes—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D314yes—
230C2×#67—28no—
231C2×#67—38no—
232C2×#67—38no—
233C2×#67—316no—
234C2×#67—68no—
235C2×#67—616no—
236C2×#67—68no—
237C2×#67—68no—
238C2×#67—128no—
239C2×#67C22×D318yes—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—44no—
243C22×Dic3—62no—
244C22×Dic3C22×D314yes—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D318yes—
247#235—232no—
248#235—664no—
249#235—632no—
250#235—632no—
251C2×D12—24no—
252C2×D12—34no—
253C2×D12—34no—
254C2×D12—316no—
255C2×D12—64no—
256C2×D12—68no—
257C2×D12—64no—
258C2×D12—64no—
259C2×D12—128no—
260C2×D12C22×D314yes—
261C2×C4×D3—28no—
262C2×C4×D3—38no—
263C2×C4×D3—38no—
264C2×C4×D3—68no—
265C2×C4×D3—616no—
266C2×C4×D3—68no—
267C2×C4×D3—68no—
268C2×C4×D3C22×D318yes—
269C2×Dic6—24no—
270C2×Dic6—34no—
271C2×Dic6—34no—
272C2×Dic6—64no—
273C2×Dic6—68no—
274C2×Dic6—64no—
275C2×Dic6—64no—
276C2×Dic6C22×D314yes—
277C3×C4⋊C4—38no—
278C3×C4⋊C4—38no—
279#217—316no—
280(C2×D3)⋊C4—316no—
281(C2×D3)⋊C4—316no—
282(C2×D3)⋊C4—316no—
283C4⋊Dic3—316no—
284C4⋊Dic3C22×D318yes—
285C4⋊Dic3C22×D318yes—
286Dic3⋊C4—316no—
287C22×C32—28no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32C22×D414yes—
291C22×C32C22×D412yes—
292C22×C32H(5,𝔽2)12yes—
293C22×C322−1+412yes—
294C22×C32C2511yescharacteristic
295C2×C3⋊D3—24no—
296C2×C3⋊D3—24no—
297C2×C3⋊D3—24no—
298C2×C3⋊D3—48no—
299C2×C3×D3—24no—
300C2×C3×D3—24no—
301C2×C3×D3—24no—
302C2×C3×D3—48no—
303C32×C4C22×D414yes—
304C32×C4C22×D414yes—
305C3⋊Dic3—24no—
306C3×Dic3—24no—
307C3×Dic3—28no—
308C2×#41—38no—
309C2×#41—68no—
310C2×#41—98no—
311C2×#41—188no—
312C22×Q8—31no—
313C22×Q8—91no—
314C22×D4—32no—
315C22×D4—31no—
316C22×D4—94no—
317C22×D4—92no—
318C22×D4—91no—
319C23×C4—32no—
320C23×C4—32no—
321C23×C4—92no—
322C23×C4D3211yescharacteristic
323C22⋊Q8—916no—
324C22⋊Q8—916no—
325#121—916no—
326#121—916no—
327#121—932no—
328C2×C4⋊C4—32no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—38no—
331C2×C4⋊C4—94no—
332C2×C22⋊C4—94no—
333C2×C22⋊C4—94no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—21no—
340C23×C3—24no—
341C23×C3—34no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—64no—
345C23×C3—64no—
346C23×C3—64no—
347C23×C3C2×D1214yes—
348C23×C3C2×#6714yes—
349C23×C3C23×D312yes—
350C23×C3C23×D312yes—
351C23×C3C23×D311yescharacteristic
352C23×C3C23×D311yescharacteristic
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—24no—
356C22×D3—34no—
357C22×D3—34no—
358C22×D3—64no—
359C22×D3—68no—
360C22×D3—64no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—124no—
367C22×D3—124no—
368C22×D3C23×D314yes—
369C3×Q8—68no—
370C3×D4—616no—
371C3×D4—68no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—216no—
377C2×C3×C4—34no—
378C2×C3×C4—38no—
379C2×C3×C4—64no—
380C2×C3×C4—68no—
381C2×C3×C4—616no—
382C2×C3×C4—128no—
383C2×C3×C4C2×D1214yes—
384C2×C3×C4C2×D1214yes—
385C2×C3×C4C2×D12116yescomplemented
386C2×C3×C4C2×#6714yes—
387C2×C3×C4C2×#6714yes—
388C2×C3×C4C2×#67116yescomplemented
389C2×C3×C4C23×D312yes—
390C2×C3×C4C23×D312yes—
391C2×C3×C4C23×D312yes—
392C2×C3×C4C23×D312yes—
393#67—216no—
394#67—632no—
395#67—616no—
396#67—616no—
397#67—1216no—
398C2×Dic3—28no—
399C2×Dic3—24no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—48no—
403C2×Dic3—64no—
404C2×Dic3—68no—
405C2×Dic3—64no—
406C2×Dic3—64no—
407C2×Dic3C23×D318yes—
408C2×Dic3C23×D314yes—
409D12—28no—
410D12—616no—
411D12—68no—
412D12—68no—
413D12—1216no—
414C4×D3—216no—
415C4×D3—632no—
416C4×D3—616no—
417C4×D3—616no—
418Dic6—28no—
419Dic6—616no—
420Dic6—68no—
421Dic6—68no—
422C2×C32—24no—
423C2×C32#53714yescomplemented
424C2×C32C23×D411yescharacteristic
425C2×C32C2×H(5,𝔽2)11yescharacteristic
426C2×C32C2×2−1+411yescharacteristic
427C3⋊D3—44no—
428C3×D3—44no—
429C24—32no—
430C24—92no—
431C24C2×D3211yescharacteristic
432#41—632no—
433#41—1832no—
434C2×Q8—34no—
435C2×Q8—64no—
436C2×Q8—94no—
437C2×Q8—184no—
438C2×D4—38no—
439C2×D4—34no—
440C2×D4—68no—
441C2×D4—64no—
442C2×D4—916no—
443C2×D4—98no—
444C2×D4—94no—
445C2×D4—188no—
446C2×D4—184no—
447C2×D4—368no—
448C22×C4—34no—
449C22×C4—32no—
450C22×C4—38no—
451C22×C4—38no—
452C22×C4—68no—
453C22×C4—92no—
454C22×C4—98no—
455C22×C4—124no—
456C22×C4—188no—
457C22×C4#62618yescomplemented
458C22×C4C2×D3211yescharacteristic
459C22×C4C2×D3211yescharacteristic
460C22×C4C2×D3214yes—
461C4⋊C4—38no—
462C4⋊C4—38no—
463C4⋊C4—916no—
464C22⋊C4—916no—
465C22⋊C4—916no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—28no—
471C22×C3—28no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—24no—
476C22×C3—21no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—48no—
480C22×C3—64no—
481C22×C3—64no—
482C22×C3—64no—
483C22×C3—128no—
484C22×C3C22×D1214yes—
485C22×C3C22×D1212yes—
486C22×C3#100412yes—
487C22×C3#100712yes—
488C22×C3#100912yes—
489C22×C3#101012yes—
490C22×C3C22×#6714yes—
491C22×C3C22×#6712yes—
492C22×C3C24×D311yescharacteristic
493C22×C3C24×D311yescharacteristic
494C2×D3—24no—
495C2×D3—24no—
496C2×D3—24no—
497C2×D3—48no—
498C2×D3—68no—
499C2×D3—64no—
500C2×D3—64no—
501C2×D3—64no—
502C2×D3—64no—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—124no—
506C2×D3—124no—
507C2×D3—1216no—
508C2×D3—128no—
509C2×D3—128no—
510C3×C4—24no—
511C3×C4—24no—
512C3×C4—64no—
513C3×C4—68no—
514C3×C4C22×D1214yes—
515C3×C4C22×D1214yes—
516C3×C4C22×#6714yes—
517C3×C4C22×#6714yes—
518Dic3—28no—
519Dic3—24no—
520Dic3—68no—
521Dic3—64no—
522Dic3—64no—
523C32C2×#53711yescharacteristic, complemented, Sylow
524C23—22no—
525C23—22no—
526C23—34no—
527C23—64no—
528C23—64no—
529C23—64no—
530C23—94no—
531C23—184no—
532C23—184no—
533C23—184no—
534C23C2×#62614yes—
535C23C22×D3212yes—
536C23C22×D3211yescharacteristic
537Q8—68no—
538Q8—188no—
539D4—616no—
540D4—68no—
541D4—1816no—
542D4—188no—
543D4—3616no—
544C2×C4—38no—
545C2×C4—34no—
546C2×C4—68no—
547C2×C4—64no—
548C2×C4—616no—
549C2×C4—94no—
550C2×C4—128no—
551C2×C4—184no—
552C2×C4—1816no—
553C2×C4C2×#62614yes—
554C2×C4C2×#62614yes—
555C2×C4C2×#626116yescomplemented
556C2×C4C22×D3212yes—
557C2×C4C22×D3212yes—
558C2×C3—24no—
559C2×C3—24no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—24no—
564C2×C3—44no—
565C2×C3—124no—
566C2×C3#551014yescomplemented
567C2×C3#583314yescomplemented
568C2×C3C23×D1211yescharacteristic
569C2×C3C2×#100411yescharacteristic
570C2×C3C2×#100711yescharacteristic
571C2×C3C2×#100911yescharacteristic
572C2×C3C2×#101011yescharacteristic
573C2×C3C23×#6711yescharacteristic
574D3—44no—
575D3—128no—
576D3—124no—
577D3—124no—
578C22—22no—
579C22—22no—
580C22—28no—
581C22—64no—
582C22—64no—
583C22—64no—
584C22—128no—
585C22—184no—
586C22—184no—
587C22—184no—
588C22—368no—
589C22#6429712yes—
590C22#6430712yes—
591C22C22×#62614yes—
592C22C22×#62612yes—
593C22C23×D3211yescharacteristic
594C4—68no—
595C4—64no—
596C4—184no—
597C4C22×#62614yes—
598C4C22×#62614yes—
599C3—21no—
600C3C2×#551011yescharacteristic, complemented
601C3C2×#583311yescharacteristic, complemented
602C2—24no—
603C2—124no—
604C2—364no—
605C2#1059504314yesdirect product factor
606C2C2×#6429711yescharacteristic
607C2C2×#6430711yescharacteristic
608C2C23×#62611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C22×C3×#235C2semidirect
3. C22×C3×C4⋊Dic3C2semidirect
4. C2×#63978C2semidirect
5. #10595043C2direct (N × H)
6. C2×#63916C2semidirect
7. C2×#63909C2semidirect
8. C2×#63871C2semidirect
9. C2×#63857C2semidirect
15. C2×#3828C22semidirect
22. C2×C3×#235C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. #63978C22semidirect
34. #63916C22semidirect
35. #63909C22semidirect
36. #63871C22semidirect
37. #63857C22semidirect
42. C22×#235D3semidirect
50. C22×C4⋊Dic3D3semidirect
60. C22×C32×C4D4semidirect
118. C2×#235C2×D3semidirect
147. C2×C4⋊Dic3C2×D3semidirect
169. C2×C32×C4C2×D4semidirect
222. C22×C3×C4D12semidirect
223. C22×C3×C4#67semidirect
385. C2×C3×C4C2×D12semidirect
388. C2×C3×C4C2×#67semidirect
423. C2×C32#537semidirect
457. C22×C4#626semidirect
523. C32C2×#537semidirect
555. C2×C4C2×#626semidirect
566. C2×C3#5510semidirect
567. C2×C3#5833semidirect
600. C3C2×#5510semidirect
601. C3C2×#5833semidirect
605. C2#10595043direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×C3×#2352
C22×C3×C4⋊Dic32
C2×#639782
#105950432
C2×#639162
C2×#639092
C2×#638712
C2×#638572
C2×#58333
C2×#55103