Finite Group Databasebeta

← C2×#10594223 #11901505

Subgroups — C2×#10594223 #11901505

Order 1152.

2685 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic, complemented
2C2×C3×#884C212yesmaximal, complemented
3C2×#63980C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C2×#63970C212yesmaximal, complemented
6C2×#63914C211yesmaximal, characteristic, complemented
7C2×#63905C212yesmaximal, complemented
8C2×#63902C211yesmaximal, characteristic, complemented
9C2×C4×#625C211yesmaximal, characteristic, complemented
10C2×#63884C212yesmaximal, complemented
11C2×#63870C211yesmaximal, characteristic, complemented
12#10594223C2116yesmaximal, direct product factor
13C2×#5615—32nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×D12C2212yes—
18C22×C3×C4×D3C2212yes—
19C22×#625C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×#625C2212yes—
22C22×D3×Dic3C2212yes—
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29#64086C2218yescomplemented
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yes—
32C3×#884C22116yescomplemented
33#63980C2218yescomplemented
34#63980C2218yescomplemented
35#63970C22116yescomplemented
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2212yes—
42#63914C2218yescomplemented
43#63905C22116yescomplemented
44#63902C2218yescomplemented
45C4×#625C2218yescomplemented
46#63884C22116yescomplemented
47#63870C2218yescomplemented
48C2×C3×#121—32no—
49C2×#940—32no—
50C2×#939—32no—
51C2×#939—32no—
52C2×#939—32no—
53C2×#938—32no—
54C2×#935—32no—
55C2×#929—32no—
56C2×C4×#67—32no—
57#5615—332no—
58C2×#894—32no—
59C2×#889—32no—
60C2×#884D312yescomplemented
61C2×#883—32no—
62C2×#67⋊C4—32no—
63C2×#877—32no—
64C2×#877—61no—
65C24×C32C2311yescharacteristic
66C23×C3×D3C2312yes—
67C23×C3×D3C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—24no—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2314yes—
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C3×#67—44no—
77C2×C3×#67—44no—
78C2×C3×#67C2318yes—
79C2×C3×#67C2318yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×C3×D12—44no—
83C2×C3×D12C2318yes—
84C2×C3×C4×D3—44no—
85C2×C3×C4×D3C2318yes—
86C2×#625—24no—
87C2×#625—24no—
88C2×#625—44no—
89C2×#625C2314yes—
90C2×#625C2314yes—
91C2×#625C2318yes—
92C2×D3×Dic3—44no—
93C2×D3×Dic3C2318yes—
94C32×C22⋊C4C2314yes—
95#3757C2314yes—
96#3750C2314yes—
97#3750C2314yes—
98C4×C3⋊Dic3C2314yes—
99C4×C3⋊Dic3C2314yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×Dic3⋊C4C2318yes—
102#3724C2314yes—
103#3724C2314yes—
104Dic3⋊Dic3C2318yes—
105(C2×D3)⋊Dic3C2318yes—
106(C2×D3)⋊Dic3C2318yes—
107(C2×D3)⋊Dic3C2318yes—
108C2×#540—91noSylow
109C22×C3×D4—32no—
110C22×C3×D4—32no—
111C22×C3×D4—32no—
112C23×C3×C4—32no—
113C22×#67—32no—
114C22×#67—32no—
115C22×#67—32no—
116C22×#67—32no—
117C22×#67C2×D312yes—
118C22×#67C2×D312yes—
119C23×Dic3—32no—
120C23×Dic3—32no—
121C23×Dic3—61no—
122C22×D12C2×D312yes—
123C22×C4×D3—32no—
124C22×C4×D3C2×D312yes—
125C3×#121—316no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4C2×D312yes—
130C2×#217—32no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—32no—
134C2×#217—61no—
135#940—316no—
136#939—316no—
137#939—316no—
138#939—316no—
139#938—316no—
140#935—316no—
141#929—316no—
142C4×#67—316no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4C2×D312yes—
147C2×C4⋊Dic3—32no—
148C2×Dic3⋊C4—32no—
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—61no—
154C2×Dic3⋊C4—61no—
155C2×Dic3⋊C4C2×D312yes—
156C2×C4×Dic3—32no—
157C2×C4×Dic3—32no—
158C2×C4×Dic3—61no—
159C2×C4×Dic3—61no—
160#894—316no—
161#889—316no—
162#884C2×D3116yescomplemented
163#883—316no—
164#67⋊C4—316no—
165#877—316no—
166#877—68no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32C2412yes—
171C23×C32C2411yescharacteristic
172C22×C3×D3—24no—
173C22×C3×D3—24no—
174C22×C3×D3—24no—
175C22×C3×D3—24no—
176C22×C3×D3—24no—
177C22×C3×D3—24no—
178C22×C3×D3C2414yes—
179C22×C3×D3C2414yes—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4C2412yes—
183C2×C32×C4C2412yes—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—28no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3#4114yes—
189C2×C3⋊Dic3C2412yes—
190C2×C3⋊Dic3C2412yes—
191C2×C3⋊Dic3C2412yes—
192C2×C3⋊Dic3C2412yes—
193C3×#67—48no—
194C3×#67—48no—
195C2×C3×Dic3—24no—
196C2×C3×Dic3—24no—
197C2×C3×Dic3C2414yes—
198C2×C3×Dic3C2414yes—
199C3×D12—48no—
200C3×C4×D3—48no—
201#625—28no—
202#625—28no—
203#625—48no—
204D3×Dic3—48no—
205#540—916no—
206C2×#127—91no—
207C2×#125—91no—
208C2×#123—92no—
209C2×#123—92no—
210C2×#121—32no—
211C2×#121—92no—
212C2×#121—91no—
213C2×#121—91no—
214C2×C4×D4—91no—
215C2×C4×D4—91no—
216C2×#117—91no—
217C24×C3—21no—
218C24×C3—32no—
219C24×C3—32no—
220C24×C3C22×D312yes—
221C23×D3C22×D312yes—
222C23×D3C22×D312yes—
223C2×C3×D4—38no—
224C2×C3×D4—38no—
225C2×C3×D4—38no—
226C2×C3×D4—124no—
227C2×C3×D4—124no—
228C2×C3×D4—124no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—38no—
234C22×C3×C4—124no—
235C22×C3×C4C22×D312yes—
236C22×C3×C4C22×D312yes—
237C2×#67—38no—
238C2×#67—38no—
239C2×#67—38no—
240C2×#67—38no—
241C2×#67—44no—
242C2×#67—44no—
243C2×#67—68no—
244C2×#67—68no—
245C2×#67—124no—
246C2×#67—124no—
247C2×#67C22×D318yes—
248C2×#67C22×D318yes—
249C22×Dic3—32no—
250C22×Dic3—38no—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—38no—
255C22×Dic3—64no—
256C22×Dic3—61no—
257C22×Dic3—61no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—68no—
261C22×Dic3—68no—
262C22×Dic3—124no—
263C22×Dic3C22×D312yes—
264C22×Dic3C22×D312yes—
265C2×D12—44no—
266C2×D12C22×D318yes—
267C2×C4×D3—38no—
268C2×C4×D3—44no—
269C2×C4×D3—124no—
270C2×C4×D3C22×D318yes—
271C3×C4⋊C4—38no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—38no—
274C3×C22⋊C4C22×D318yes—
275#217—38no—
276#217—38no—
277#217—38no—
278#217—38no—
279#217—64no—
280(C2×D3)⋊C4—38no—
281(C2×D3)⋊C4—38no—
282(C2×D3)⋊C4—38no—
283(C2×D3)⋊C4C22×D318yes—
284C4⋊Dic3—38no—
285Dic3⋊C4—38no—
286Dic3⋊C4—38no—
287Dic3⋊C4—38no—
288Dic3⋊C4—38no—
289Dic3⋊C4—38no—
290Dic3⋊C4—64no—
291Dic3⋊C4—64no—
292Dic3⋊C4C22×D318yes—
293C4×Dic3—38no—
294C4×Dic3—38no—
295C4×Dic3—64no—
296C4×Dic3—64no—
297C22×C32—22no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—44no—
301C22×C32C2×#4112yes—
302C22×C32H(5,𝔽2)12yes—
303C22×C32H(5,𝔽2)12yes—
304C22×C32C2511yescharacteristic
305C2×C3×D3—24no—
306C2×C3×D3—24no—
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—24no—
310C2×C3×D3—24no—
311C2×C3×D3—48no—
312C2×C3×D3—48no—
313C32×C4—22no—
314C32×C4—22no—
315C3⋊Dic3—22no—
316C3⋊Dic3—22no—
317C3⋊Dic3—22no—
318C3⋊Dic3C2×#4114yes—
319C3×Dic3—24no—
320C3×Dic3—24no—
321C22×D4—32no—
322C22×D4—32no—
323C22×D4—32no—
324C22×D4—91no—
325C22×D4—91no—
326C22×D4—92no—
327C23×C4—32no—
328C23×C4—92no—
329C23×C4—91no—
330#127—98no—
331#125—98no—
332#123—916no—
333#123—916no—
334#121—316no—
335#121—916no—
336#121—98no—
337#121—98no—
338C4×D4—98no—
339C4×D4—98no—
340#117—98no—
341C2×C4⋊C4—32no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—91no—
344C2×C4⋊C4—92no—
345C2×C4⋊C4—91no—
346C2×C4⋊C4—91no—
347C2×C22⋊C4—32no—
348C2×C22⋊C4—92no—
349C2×C22⋊C4—92no—
350C2×C22⋊C4—92no—
351C2×C22⋊C4—91no—
352C2×C22⋊C4D3211yescharacteristic
353C2×C42—91no—
354C2×C42—91no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—34no—
362C23×C3—34no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—64no—
366C23×C3—64no—
367C23×C3—64no—
368C23×C3—64no—
369C23×C3—64no—
370C23×C3—64no—
371C23×C3C23×D314yes—
372C23×C3C23×D312yes—
373C22×D3—24no—
374C22×D3—24no—
375C22×D3—24no—
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3C23×D314yes—
380C22×D3C23×D314yes—
381C3×D4—128no—
382C3×D4—128no—
383C3×D4—128no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—34no—
389C2×C3×C4—34no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—64no—
393C2×C3×C4—64no—
394C2×C3×C4—128no—
395C2×C3×C4C23×D314yes—
396C2×C3×C4C23×D314yes—
397#67—48no—
398#67—48no—
399#67—616no—
400#67—616no—
401#67—128no—
402#67—128no—
403C2×Dic3—24no—
404C2×Dic3—24no—
405C2×Dic3—38no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—34no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—616no—
416C2×Dic3—616no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—122no—
422C2×Dic3—122no—
423C2×Dic3—128no—
424C2×Dic3C23×D314yes—
425C2×Dic3C23×D314yes—
426D12—48no—
427C4×D3—48no—
428C4×D3—128no—
429C2×C32—42no—
430C2×C32#54014yescomplemented
431C2×C32C22×#4111yescharacteristic
432C2×C32C2×H(5,𝔽2)11yescharacteristic
433C2×C32C2×H(5,𝔽2)11yescharacteristic
434C3×D3—44no—
435C3×D3—44no—
436C24—32no—
437C24—32no—
438C24C2×D3211yescharacteristic
439C2×D4—38no—
440C2×D4—38no—
441C2×D4—38no—
442C2×D4—94no—
443C2×D4—94no—
444C2×D4—98no—
445C2×D4—124no—
446C2×D4—124no—
447C2×D4—124no—
448C2×D4—184no—
449C2×D4—184no—
450C2×D4—364no—
451C22×C4—32no—
452C22×C4—32no—
453C22×C4—38no—
454C22×C4—98no—
455C22×C4—91no—
456C22×C4—94no—
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—124no—
461C22×C4—184no—
462C22×C4—364no—
463C22×C4C2×D3211yescharacteristic
464C22×C4C2×D3211yescharacteristic
465C4⋊C4—38no—
466C4⋊C4—94no—
467C4⋊C4—94no—
468C4⋊C4—98no—
469C4⋊C4—94no—
470C4⋊C4—94no—
471C22⋊C4—38no—
472C22⋊C4—98no—
473C22⋊C4—98no—
474C22⋊C4—98no—
475C22⋊C4—94no—
476C22⋊C4C2×D3214yes—
477C42—94no—
478C42—94no—
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—24no—
482C22×C3—24no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—48no—
490C22×C3—48no—
491C22×C3—64no—
492C22×C3—64no—
493C22×C3—64no—
494C22×C3—64no—
495C22×C3—64no—
496C22×C3—64no—
497C22×C3—128no—
498C22×C3—128no—
499C22×C3#100414yes—
500C22×C3#100414yes—
501C22×C3D3×#4114yes—
502C22×C3C24×D312yes—
503C2×D3—24no—
504C2×D3—24no—
505C2×D3—24no—
506C2×D3—24no—
507C2×D3—24no—
508C2×D3—24no—
509C2×D3—48no—
510C2×D3—48no—
511C3×C4—24no—
512C3×C4—24no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—64no—
516C3×C4—64no—
517Dic3—24no—
518Dic3—24no—
519Dic3—38no—
520Dic3—64no—
521Dic3—64no—
522Dic3—64no—
523Dic3—64no—
524Dic3—64no—
525Dic3—122no—
526Dic3—122no—
527C32C2×#54011yescharacteristic, complemented, Sylow
528C23—22no—
529C23—22no—
530C23—22no—
531C23—34no—
532C23—34no—
533C23—64no—
534C23—64no—
535C23—64no—
536C23—64no—
537C23—64no—
538C23—64no—
539C23C22×D3212yes—
540C23C22×D3211yescharacteristic
541D4—128no—
542D4—128no—
543D4—128no—
544D4—188no—
545D4—188no—
546D4—368no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—34no—
550C2×C4—34no—
551C2×C4—64no—
552C2×C4—64no—
553C2×C4—94no—
554C2×C4—92no—
555C2×C4—92no—
556C2×C4—92no—
557C2×C4—92no—
558C2×C4—128no—
559C2×C4—188no—
560C2×C4—182no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4—368no—
564C2×C4C22×D3212yes—
565C2×C4C22×D3212yes—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—24no—
570C2×C3—44no—
571C2×C3—44no—
572C2×C3—124no—
573C2×C3—124no—
574C2×C3#561518yescomplemented
575C2×C3C2×#100412yes—
576C2×C3C2×#100412yes—
577C2×C3C2×D3×#4112yes—
578D3—44no—
579D3—44no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—44no—
584C22—64no—
585C22—64no—
586C22—64no—
587C22—64no—
588C22—64no—
589C22—64no—
590C22—128no—
591C22—128no—
592C22#6430612yes—
593C22#6431312yes—
594C22#6431312yes—
595C22C23×D3211yescharacteristic
596C4—22no—
597C4—22no—
598C4—64no—
599C4—64no—
600C4—94no—
601C4—182no—
602C4—182no—
603C4—182no—
604C3—21no—
605C3C2×#561512yescomplemented
606C2—42no—
607C2—124no—
608C2—124no—
609C2#1059422314yesdirect product factor
610C2C2×#6430611yescharacteristic
611C2C2×#6431311yescharacteristic
612C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#540
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×#64086C2semidirect
2. C2×C3×#884C2semidirect
3. C2×#63980C2semidirect
4. C2×#63980C2semidirect
5. C2×#63970C2semidirect
6. C2×#63914C2semidirect
7. C2×#63905C2semidirect
8. C2×#63902C2semidirect
9. C2×C4×#625C2semidirect
10. C2×#63884C2semidirect
11. C2×#63870C2semidirect
12. #10594223C2direct (N × H)
29. #64086C22semidirect
32. C3×#884C22semidirect
33. #63980C22semidirect
34. #63980C22semidirect
35. #63970C22semidirect
42. #63914C22semidirect
43. #63905C22semidirect
44. #63902C22semidirect
45. C4×#625C22semidirect
46. #63884C22semidirect
47. #63870C22semidirect
60. C2×#884D3semidirect
162. #884C2×D3semidirect
430. C2×C32#540semidirect
527. C32C2×#540semidirect
574. C2×C3#5615semidirect
605. C3C2×#5615semidirect
609. C2#10594223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640862
C2×C3×#8842
C2×#639802
C2×#639702
C2×#639142
C2×#639052
C2×#639022
C2×C4×#6252
C2×#638842
C2×#638702
#105942232
C2×#56153