Finite Group Databasebeta

← C2×#10595072 #11900956

Subgroups — C2×#10595072 #11900956

Order 1152.

4181 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C212yesmaximal, complemented
2C2×#64139C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×#63978C212yesmaximal, complemented
6#10595072C2116yesmaximal, direct product factor
7C2×#63923C212yesmaximal, complemented
8C2×#63922C212yesmaximal, complemented
9C2×#63891C212yesmaximal, complemented
10C2×#63890C212yesmaximal, complemented
11C2×#5605—31nomaximal
12C2×#5493—31nomaximal
13C24×C3×D3C2211yescharacteristic
14C23×D32C2212yescomplemented
15C23×C32×C4C2211yescharacteristic, complemented
16C22×#638C2212yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C22×C3×#67C2212yescomplemented
19C23×C3×Dic3C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic, complemented
21C2×D3×#67—216no—
22C2×D3×#67C22116yescomplemented
23C22×#626C2212yes—
24C22×#626C2212yescomplemented
25C22×#625C2212yes—
26C22×D3×Dic3C2212yescomplemented
27#64139C2218yescomplemented
28C2×#3752C2212yescomplemented
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×#930C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yescomplemented
34C2×C3×(C2×D3)⋊C4C2218yescomplemented
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36#63978C22116yescomplemented
37C2×Dic3⋊Dic3C2212yescomplemented
38C2×#3722C2212yescomplemented
39C2×(C2×D3)⋊Dic3C2212yescomplemented
40#63923C22116yescomplemented
41#63922C22116yescomplemented
42#63891C22116yescomplemented
43#63890C22116yescomplemented
44C23×#67—32no—
45C22×D3×D4—32no—
46C2×C3×#121—31no—
47C22×C3×C22⋊C4—31no—
48C2×#939—32no—
49C2×#937—32no—
50C2×#930—31no—
51C2×#930—31no—
52C2×#930—32no—
53C2×#930—61no—
54C2×#930D311yescharacteristic, complemented
55C22×(C2×D3)⋊C4D311yescharacteristic, complemented
56#5605—316no—
57C2×#894—32no—
58#5493—316no—
59C2×#886—32no—
60C2×#886—32no—
61C2×#883—32no—
62C2×#882—32no—
63C2×#882—32no—
64C2×#882—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2312yes—
67C23×C3×D3—42no—
68C23×C3×D3—42no—
69C23×C3×D3D418yescomplemented
70C23×C3×D3C2312yes—
71C23×C3×D3C2312yes—
72C23×C3×D3C2314yes—
73C22×D32—28no—
74C22×D32—44no—
75C22×D32—44no—
76C22×D32C2318yescomplemented
77C22×C32×C4—42no—
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2314yescomplemented
81C2×#638—28no—
82C2×#638C2318yescomplemented
83C22×C3⋊Dic3C2312yes—
84C2×C4⋊(C3⋊D3)—42no—
85C2×C4⋊(C3⋊D3)C2314yescomplemented
86C2×C3×#67—28no—
87C2×C3×#67C2318yescomplemented
88C22×C3×Dic3—42no—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2314yescomplemented
92C2×C3×D12—42no—
93C2×C3×D12C2314yescomplemented
94D3×#67—264no—
95C2×#626—28no—
96C2×#626—44no—
97C2×#626C2318yes—
98C2×#626C2318yescomplemented
99C2×#625—28no—
100C2×#625C2318yes—
101C2×D3×Dic3—28no—
102C2×D3×Dic3C2318yescomplemented
103#3752C2318yescomplemented
104C4⋊(C3⋊Dic3)C2314yescomplemented
105C3×(C2×D3)⋊C4C2318yescomplemented
106C3×(C2×D3)⋊C4C2318yescomplemented
107C3×(C2×D3)⋊C4C2318yescomplemented
108C3×C4⋊Dic3C2314yescomplemented
109Dic3⋊Dic3C2318yescomplemented
110#3722C2318yescomplemented
111(C2×D3)⋊Dic3C2318yescomplemented
112C2×#534—91noSylow
113C25×C3—31no—
114C24×D3—32no—
115C24×D3—32no—
116C24×D3C2×D311yescharacteristic
117C22×C3×D4—32no—
118C22×C3×D4—31no—
119C23×C3×C4—21no—
120C23×C3×C4—31no—
121C23×C3×C4C2×D311yescharacteristic, complemented
122C23×C3×C4C2×D311yescharacteristic, complemented
123C22×#67—32no—
124C22×#67—32no—
125C22×#67—32no—
126C22×#67—32no—
127C22×#67—316no—
128C22×#67—32no—
129C22×#67—32no—
130C22×#67—62no—
131C22×#67—616no—
132C22×#67C2×D312yescomplemented
133C23×Dic3—32no—
134C23×Dic3C2×D311yescharacteristic, complemented
135C2×D3×D4—316no—
136C2×D3×D4—616no—
137C22×D12—32no—
138C22×D12—32no—
139C22×D12—31no—
140C22×D12—31no—
141C22×D12—61no—
142C22×D12C2×D311yescharacteristic, complemented
143C22×C4×D3—32no—
144C3×#121—38no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C22⋊C4—32no—
147C2×C3×C22⋊C4—32no—
148C2×C3×C22⋊C4—32no—
149C2×C3×C22⋊C4—38no—
150C2×#217—32no—
151#939—316no—
152#937—316no—
153#930—38no—
154#930—38no—
155#930—316no—
156#930—68no—
157#930C2×D318yescomplemented
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—32no—
160C2×(C2×D3)⋊C4—32no—
161C2×(C2×D3)⋊C4—32no—
162C2×(C2×D3)⋊C4—32no—
163C2×(C2×D3)⋊C4—62no—
164C2×(C2×D3)⋊C4C2×D312yescomplemented
165C2×(C2×D3)⋊C4C2×D312yescomplemented
166C2×(C2×D3)⋊C4C2×D312yescomplemented
167C2×(C2×D3)⋊C4C2×D318yescomplemented
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—32no—
171C2×C4⋊Dic3—61no—
172C2×C4⋊Dic3C2×D311yescharacteristic, complemented
173C2×Dic3⋊C4—32no—
174#894—316no—
175#886—316no—
176#886—316no—
177#883—316no—
178#882—316no—
179#882—316no—
180#882—316no—
181C23×C32—22no—
182C23×C32—22no—
183C23×C32C2×D414yes—
184C23×C32C2412yes—
185C23×C32C2411yescharacteristic
186C22×C3⋊D3—24no—
187C22×C3⋊D3—24no—
188C22×C3⋊D3—24no—
189C22×C3⋊D3C2414yes—
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3—24no—
193C22×C3×D3—24no—
194C22×C3×D3—24no—
195C22×C3×D3—416no—
196C22×C3×D3—44no—
197C22×C3×D3—44no—
198C22×C3×D3C2×D418yes—
199C22×C3×D3C2×D4116yescomplemented
200C22×C3×D3C2414yes—
201C22×C3×D3C2414yes—
202C2×D32—216no—
203C2×D32—48no—
204C2×D32—48no—
205C2×D32—432no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—44no—
209C2×C32×C4C2412yes—
210C2×C32×C4C2412yes—
211#638—216no—
212C2×C3⋊Dic3—24no—
213C2×C3⋊Dic3C2414yes—
214C4⋊(C3⋊D3)—44no—
215C3×#67—216no—
216C2×C3×Dic3—24no—
217C2×C3×Dic3—24no—
218C2×C3×Dic3—44no—
219C2×C3×Dic3C2414yes—
220C2×C3×Dic3C2414yes—
221C3×D12—44no—
222#626—216no—
223#626—48no—
224#625—216no—
225D3×Dic3—216no—
226C23×D4—92no—
227#534—916no—
228C2×#123—92no—
229C2×#123—92no—
230C2×#121—31no—
231C2×#121—92no—
232C2×#121—91no—
233C2×#120—92no—
234C2×#120—92no—
235C22×C22⋊C4—31no—
236C24×C3—21no—
237C24×C3—32no—
238C24×C3—38no—
239C24×C3—34no—
240C24×C3—32no—
241C24×C3—122no—
242C24×C3—122no—
243C24×C3C22×D311yescharacteristic
244C24×C3C22×D311yescharacteristic
245C23×D3—32no—
246C23×D3—32no—
247C23×D3—38no—
248C23×D3—38no—
249C23×D3—42no—
250C23×D3—42no—
251C23×D3—62no—
252C23×D3—68no—
253C23×D3—68no—
254C23×D3—124no—
255C23×D3—124no—
256C23×D3—124no—
257C23×D3—124no—
258C23×D3D1218yescomplemented
259C23×D3C22×D312yes—
260C23×D3C22×D312yes—
261C23×D3C22×D314yes—
262C2×C3×D4—38no—
263C2×C3×D4—34no—
264C2×C3×D4—68no—
265C2×C3×D4—122no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—24no—
269C22×C3×C4—32no—
270C22×C3×C4—32no—
271C22×C3×C4—34no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—44no—
275C22×C3×C4—122no—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D314yescomplemented
281C22×C3×C4C22×D314yescomplemented
282C2×#67—28no—
283C2×#67—38no—
284C2×#67—38no—
285C2×#67—38no—
286C2×#67—38no—
287C2×#67—38no—
288C2×#67—38no—
289C2×#67—68no—
290C2×#67—68no—
291C2×#67—664no—
292C2×#67—68no—
293C2×#67—68no—
294C2×#67—68no—
295C2×#67—68no—
296C2×#67—128no—
297C2×#67—124no—
298C2×#67C22×D318yescomplemented
299C22×Dic3—32no—
300C22×Dic3—32no—
301C22×Dic3—38no—
302C22×Dic3—42no—
303C22×Dic3—62no—
304C22×Dic3—68no—
305C22×Dic3C22×D312yes—
306C22×Dic3C22×D312yes—
307C22×Dic3C22×D314yescomplemented
308D3×D4—664no—
309C2×D12—38no—
310C2×D12—38no—
311C2×D12—34no—
312C2×D12—34no—
313C2×D12—42no—
314C2×D12—64no—
315C2×D12—68no—
316C2×D12—122no—
317C2×D12—122no—
318C2×D12—124no—
319C2×D12—124no—
320C2×D12C22×D314yescomplemented
321C2×C4×D3—38no—
322C2×C4×D3—68no—
323C3×C4⋊C4—34no—
324C3×C22⋊C4—38no—
325C3×C22⋊C4—38no—
326C3×C22⋊C4—38no—
327#217—38no—
328(C2×D3)⋊C4—38no—
329(C2×D3)⋊C4—38no—
330(C2×D3)⋊C4—38no—
331(C2×D3)⋊C4—38no—
332(C2×D3)⋊C4—38no—
333(C2×D3)⋊C4—68no—
334(C2×D3)⋊C4C22×D318yescomplemented
335(C2×D3)⋊C4C22×D318yescomplemented
336(C2×D3)⋊C4C22×D318yescomplemented
337C4⋊Dic3—34no—
338C4⋊Dic3—34no—
339C4⋊Dic3—38no—
340C4⋊Dic3—64no—
341C4⋊Dic3C22×D314yescomplemented
342Dic3⋊C4—38no—
343C22×C32—28no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32C22×D414yes—
347C22×C32C22×D412yes—
348C22×C32H(5,𝔽2)12yes—
349C22×C32H(5,𝔽2)12yes—
350C22×C32C2511yescharacteristic
351C2×C3⋊D3—24no—
352C2×C3⋊D3—24no—
353C2×C3⋊D3—24no—
354C2×C3⋊D3—48no—
355C2×C3×D3—216no—
356C2×C3×D3—24no—
357C2×C3×D3—24no—
358C2×C3×D3—24no—
359C2×C3×D3—24no—
360C2×C3×D3—24no—
361C2×C3×D3—416no—
362C2×C3×D3—48no—
363C2×C3×D3C22×D418yes—
364D32—432no—
365C32×C4—22no—
366C32×C4—22no—
367C3⋊Dic3—24no—
368C3×Dic3—24no—
369C3×Dic3—24no—
370C25—31no—
371C25—92no—
372C22×D4—32no—
373C22×D4—31no—
374C22×D4—92no—
375C22×D4—92no—
376C22×D4—916no—
377C22×D4—92no—
378C22×D4—92no—
379C22×D4—91no—
380C22×D4—1816no—
381C23×C4—31no—
382C23×C4—92no—
383C23×C4D3211yescharacteristic, complemented
384#123—916no—
385#123—916no—
386#121—38no—
387#121—916no—
388#121—98no—
389#120—916no—
390#120—916no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—92no—
393C2×C4⋊C4—91no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—38no—
398C2×C22⋊C4—92no—
399C2×C22⋊C4—92no—
400C2×C22⋊C4—92no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—24no—
408C23×C3—38no—
409C23×C3—34no—
410C23×C3—316no—
411C23×C3—34no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3—64no—
415C23×C3—64no—
416C23×C3—64no—
417C23×C3—64no—
418C23×C3—64no—
419C23×C3—124no—
420C23×C3—124no—
421C23×C3—1216no—
422C23×C3C2×D1214yes—
423C23×C3D3×D414yes—
424C23×C3C23×D312yes—
425C23×C3C23×D312yes—
426C23×C3C23×D311yescharacteristic
427C23×C3C23×D311yescharacteristic
428C22×D3—24no—
429C22×D3—24no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—24no—
433C22×D3—34no—
434C22×D3—34no—
435C22×D3—416no—
436C22×D3—44no—
437C22×D3—44no—
438C22×D3—64no—
439C22×D3—616no—
440C22×D3—64no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3—64no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—616no—
447C22×D3—124no—
448C22×D3—124no—
449C22×D3—124no—
450C22×D3—128no—
451C22×D3—128no—
452C22×D3—128no—
453C22×D3—128no—
454C22×D3—1232no—
455C22×D3—1232no—
456C22×D3C2×D1218yes—
457C22×D3C2×D12116yescomplemented
458C22×D3C23×D314yes—
459C22×D3C23×D314yes—
460C3×D4—616no—
461C3×D4—124no—
462C2×C3×C4—24no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—34no—
470C2×C3×C4—34no—
471C2×C3×C4—42no—
472C2×C3×C4—44no—
473C2×C3×C4—44no—
474C2×C3×C4—48no—
475C2×C3×C4—64no—
476C2×C3×C4—64no—
477C2×C3×C4—124no—
478C2×C3×C4C23×D312yes—
479C2×C3×C4C23×D312yes—
480C2×C3×C4C23×D312yes—
481C2×C3×C4C23×D312yes—
482#67—216no—
483#67—616no—
484#67—616no—
485#67—616no—
486#67—616no—
487#67—616no—
488#67—1216no—
489#67—128no—
490C2×Dic3—24no—
491C2×Dic3—24no—
492C2×Dic3—34no—
493C2×Dic3—34no—
494C2×Dic3—44no—
495C2×Dic3—64no—
496C2×Dic3—616no—
497C2×Dic3—64no—
498C2×Dic3—64no—
499C2×Dic3—124no—
500C2×Dic3C23×D314yes—
501C2×Dic3C23×D314yes—
502D12—44no—
503D12—616no—
504D12—124no—
505D12—124no—
506D12—128no—
507D12—128no—
508C4×D3—616no—
509C2×C32—24no—
510C2×C32#53414yescomplemented
511C2×C32C23×D411yescharacteristic
512C2×C32C2×H(5,𝔽2)11yescharacteristic
513C2×C32C2×H(5,𝔽2)11yescharacteristic
514C3⋊D3—44no—
515C3×D3—28no—
516C3×D3—44no—
517C24—32no—
518C24—34no—
519C24—38no—
520C24—32no—
521C24—98no—
522C24—92no—
523C24—122no—
524C24—122no—
525C24—188no—
526C24—364no—
527C24—364no—
528C24C2×D3211yescharacteristic
529C2×D4—38no—
530C2×D4—34no—
531C2×D4—68no—
532C2×D4—98no—
533C2×D4—98no—
534C2×D4—98no—
535C2×D4—98no—
536C2×D4—94no—
537C2×D4—122no—
538C2×D4—188no—
539C2×D4—1864no—
540C2×D4—188no—
541C2×D4—188no—
542C2×D4—362no—
543C2×D4—364no—
544C22×C4—32no—
545C22×C4—32no—
546C22×C4—34no—
547C22×C4—42no—
548C22×C4—98no—
549C22×C4—92no—
550C22×C4—122no—
551C22×C4—188no—
552C22×C4C2×D3211yescharacteristic
553C22×C4C2×D3211yescharacteristic
554C22×C4C2×D3214yescomplemented
555C4⋊C4—34no—
556C4⋊C4—98no—
557C4⋊C4—94no—
558C22⋊C4—38no—
559C22⋊C4—38no—
560C22⋊C4—38no—
561C22⋊C4—98no—
562C22⋊C4—98no—
563C22⋊C4—98no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—22no—
571C22×C3—24no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—21no—
575C22×C3—38no—
576C22×C3—42no—
577C22×C3—48no—
578C22×C3—42no—
579C22×C3—64no—
580C22×C3—64no—
581C22×C3—616no—
582C22×C3—64no—
583C22×C3—64no—
584C22×C3—64no—
585C22×C3—1216no—
586C22×C3—128no—
587C22×C3C22×D1214yes—
588C22×C3C22×D1212yes—
589C22×C3C2×D3×D414yes—
590C22×C3C2×D3×D412yes—
591C22×C3#100412yes—
592C22×C3#100412yes—
593C22×C3#100412yes—
594C22×C3#100912yes—
595C22×C3C24×D311yescharacteristic
596C22×C3C24×D311yescharacteristic
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—216no—
600C2×D3—24no—
601C2×D3—24no—
602C2×D3—24no—
603C2×D3—416no—
604C2×D3—48no—
605C2×D3—64no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—64no—
610C2×D3—64no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—124no—
614C2×D3—1232no—
615C2×D3—1232no—
616C2×D3—128no—
617C2×D3—128no—
618C2×D3—248no—
619C2×D3C22×D1218yes—
620C3×C4—24no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—42no—
626C3×C4—64no—
627C3×C4—64no—
628Dic3—24no—
629Dic3—24no—
630Dic3—64no—
631Dic3—64no—
632Dic3—124no—
633C32C2×#53411yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—38no—
637C23—34no—
638C23—316no—
639C23—34no—
640C23—64no—
641C23—64no—
642C23—64no—
643C23—64no—
644C23—64no—
645C23—94no—
646C23—1216no—
647C23—124no—
648C23—124no—
649C23—1816no—
650C23—184no—
651C23—184no—
652C23—184no—
653C23—368no—
654C23—368no—
655C23—3632no—
656C23D3×D1214yes—
657C23C22×D3212yes—
658C23C22×D3211yescharacteristic
659D4—616no—
660D4—124no—
661D4—1816no—
662D4—1816no—
663D4—1816no—
664D4—364no—
665D4—368no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—34no—
669C2×C4—34no—
670C2×C4—44no—
671C2×C4—64no—
672C2×C4—64no—
673C2×C4—94no—
674C2×C4—124no—
675C2×C4—1816no—
676C2×C4—184no—
677C2×C4C22×D3212yes—
678C2×C4C22×D3212yes—
679C2×C3—24no—
680C2×C3—24no—
681C2×C3—24no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—44no—
686C2×C3—68no—
687C2×C3—124no—
688C2×C3#549314yescomplemented
689C2×C3#560514yescomplemented
690C2×C3C23×D1211yescharacteristic
691C2×C3C22×D3×D411yescharacteristic
692C2×C3C2×#100411yescharacteristic
693C2×C3C2×#100411yescharacteristic
694C2×C3C2×#100411yescharacteristic
695C2×C3C2×#100911yescharacteristic
696D3—28no—
697D3—44no—
698D3—124no—
699D3—124no—
700D3—244no—
701C22—28no—
702C22—22no—
703C22—22no—
704C22—38no—
705C22—616no—
706C22—64no—
707C22—64no—
708C22—64no—
709C22—64no—
710C22—64no—
711C22—1216no—
712C22—128no—
713C22—184no—
714C22—184no—
715C22—184no—
716C22—3632no—
717C22—368no—
718C22C2×D3×D1214yes—
719C22C2×D3×D1212yes—
720C22#6430712yes—
721C22#6433012yes—
722C22C23×D3211yescharacteristic
723C4—22no—
724C4—22no—
725C4—64no—
726C4—64no—
727C4—184no—
728C3—21no—
729C3C2×#549311yescharacteristic, complemented
730C3C2×#560511yescharacteristic, complemented
731C2—24no—
732C2—68no—
733C2—124no—
734C2—364no—
735C2#1059507214yesdirect product factor
736C2C22×D3×D1211yescharacteristic
737C2C2×#6430711yescharacteristic
738C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C2×#64139C2semidirect
3. C2×C3×#930C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C2×#63978C2semidirect
6. #10595072C2direct (N × H)
7. C2×#63923C2semidirect
8. C2×#63922C2semidirect
9. C2×#63891C2semidirect
10. C2×#63890C2semidirect
14. C23×D32C22semidirect
15. C23×C32×C4C22semidirect
16. C22×#638C22semidirect
17. C22×C4⋊(C3⋊D3)C22semidirect
18. C22×C3×#67C22semidirect
19. C23×C3×Dic3C22semidirect
20. C22×C3×D12C22semidirect
22. C2×D3×#67C22semidirect
24. C22×#626C22semidirect
26. C22×D3×Dic3C22semidirect
27. #64139C22semidirect
28. C2×#3752C22semidirect
29. C2×C4⋊(C3⋊Dic3)C22semidirect
30. C3×#930C22semidirect
31. C2×C3×(C2×D3)⋊C4C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. #63978C22semidirect
37. C2×Dic3⋊Dic3C22semidirect
38. C2×#3722C22semidirect
39. C2×(C2×D3)⋊Dic3C22semidirect
40. #63923C22semidirect
41. #63922C22semidirect
42. #63891C22semidirect
43. #63890C22semidirect
54. C2×#930D3semidirect
55. C22×(C2×D3)⋊C4D3semidirect
69. C23×C3×D3D4semidirect
76. C22×D32C23semidirect
80. C22×C32×C4C23semidirect
82. C2×#638C23semidirect
85. C2×C4⋊(C3⋊D3)C23semidirect
87. C2×C3×#67C23semidirect
91. C22×C3×Dic3C23semidirect
93. C2×C3×D12C23semidirect
98. C2×#626C23semidirect
102. C2×D3×Dic3C23semidirect
103. #3752C23semidirect
104. C4⋊(C3⋊Dic3)C23semidirect
105. C3×(C2×D3)⋊C4C23semidirect
106. C3×(C2×D3)⋊C4C23semidirect
107. C3×(C2×D3)⋊C4C23semidirect
108. C3×C4⋊Dic3C23semidirect
109. Dic3⋊Dic3C23semidirect
110. #3722C23semidirect
111. (C2×D3)⋊Dic3C23semidirect
121. C23×C3×C4C2×D3semidirect
122. C23×C3×C4C2×D3semidirect
132. C22×#67C2×D3semidirect
134. C23×Dic3C2×D3semidirect
142. C22×D12C2×D3semidirect
157. #930C2×D3semidirect
164. C2×(C2×D3)⋊C4C2×D3semidirect
165. C2×(C2×D3)⋊C4C2×D3semidirect
166. C2×(C2×D3)⋊C4C2×D3semidirect
167. C2×(C2×D3)⋊C4C2×D3semidirect
172. C2×C4⋊Dic3C2×D3semidirect
199. C22×C3×D3C2×D4semidirect
258. C23×D3D12semidirect
280. C22×C3×C4C22×D3semidirect
281. C22×C3×C4C22×D3semidirect
298. C2×#67C22×D3semidirect
307. C22×Dic3C22×D3semidirect
320. C2×D12C22×D3semidirect
334. (C2×D3)⋊C4C22×D3semidirect
335. (C2×D3)⋊C4C22×D3semidirect
336. (C2×D3)⋊C4C22×D3semidirect
341. C4⋊Dic3C22×D3semidirect
383. C23×C4D32semidirect
457. C22×D3C2×D12semidirect
510. C2×C32#534semidirect
554. C22×C4C2×D32semidirect
633. C32C2×#534semidirect
688. C2×C3#5493semidirect
689. C2×C3#5605semidirect
729. C3C2×#5493semidirect
730. C3C2×#5605semidirect
735. C2#10595072direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C2×#641392
C2×C3×#9302
C22×C3×(C2×D3)⋊C42
C2×#639782
#105950722
C2×#639232
C2×#639222
C2×#638912
C2×#638902
C2×#56053
C2×#54933