Finite Group Databasebeta

← C3×#10595153 #13174800

Subgroups — C3×#10595153 #13174800

Order 1728.

1642 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3C3×#64149C211yesmaximal, characteristic, complemented
4C32×#936C211yesmaximal, characteristic, complemented
5C3×#63971C214yesmaximal, complemented
6C3×#63952C214yesmaximal, complemented
7C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
8C3×#63873C211yesmaximal, characteristic, complemented
9C3×#63864C211yesmaximal, characteristic, complemented
10C3×#5832—31nomaximal
11C3×#5668—31nomaximal
12#10595153C311yesmaximal, characteristic, direct product factor
13C2×C33×D4C2211yescharacteristic
14C2×C3×#638C2214yes—
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C32×#67C2212yes—
17C22×C32×Dic3C2212yes—
18C32×#237—24no—
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic
22C2×C3×#626C2212yes—
23C2×C3×#624C2212yes—
24C2×C3×D3×Dic3C2212yes—
25C3×#3799—24no—
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C32×#217C2214yes—
28C32×C4×Dic3C2211yescharacteristic
29C3×#3724C2214yes—
30C3×#3722C2214yes—
31C3×Dic32C2212yes—
32C2×C32×#41—31no—
33C2×C3×#239—31no—
34C2×C3×#237—21no—
35C2×C3×#237D311yescharacteristic, complemented
36C2×C3×#237C2×C311yescharacteristic, complemented
37C2×C3×#235—31no—
38C2×#3799C2×C311yescharacteristic, complemented
39C32×#124—31no—
40#64149C2×C311yescharacteristic, complemented
41C3×#947—31no—
42C3×#944—31no—
43C3×#944—31no—
44C3×#940—31no—
45C3×#940—31no—
46C3×#940—61no—
47C3×#939—34no—
48C3×#936—21no—
49C3×#936D311yescharacteristic, complemented
50C3×#936C2×C311yescharacteristic, complemented
51C3×C4×#67—34no—
52C2×C3×C4×Dic3—31no—
53C3×#884—34no—
54C3×#67⋊C4—34no—
55C3×#875—31no—
56C3×C42×D3—31no—
57#63971C2×C314yescomplemented
58#63952C2×C314yescomplemented
59C4×D3×Dic3C2×C311yescharacteristic, complemented
60#63873C2×C311yescharacteristic, complemented
61#63864C2×C311yescharacteristic, complemented
62C23×C33C2312yes—
63C22×C3×C3⋊D3C2312yes—
64C22×C32×D3C2311yescharacteristic
65C33×D4—22no—
66C2×C33×C4C2311yescharacteristic
67C3×#638—28no—
68C2×C3×C3⋊Dic3C2312yes—
69C3×C4⋊(C3⋊D3)—22no—
70C32×#67—24no—
71C2×C32×Dic3—24no—
72C2×C32×Dic3C2312yes—
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2311yescharacteristic
76C32×C4×D3D414yescomplemented
77C32×Dic6—22no—
78C32×Dic6—22no—
79C3×#626—24no—
80C3×#624—24no—
81C3×D3×Dic3—24no—
82C3×#532—91no—
83#5832—31no—
84#5668—31no—
85C32×#41—64no—
86C2×C32×Q8—31no—
87C2×C32×Q8—31no—
88C2×C32×D4—21no—
89C2×C32×D4—21no—
90C2×C32×D4—21no—
91C2×C32×D4—32no—
92C2×C32×D4—41no—
93C2×C32×D4C2×D311yescharacteristic
94C2×C32×D4C2×D311yescharacteristic
95C2×C32×D4C22×C311yescharacteristic
96C22×C32×C4—31no—
97C22×C32×C4—32no—
98C2×#638C22×C314yes—
99C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
100C2×C3×#67—22no—
101C2×C3×#67—34no—
102C2×C3×#67—34no—
103C2×C3×#67—32no—
104C2×C3×#67—64no—
105C2×C3×#67C2×D312yes—
106C2×C3×#67C22×C312yes—
107C22×C3×Dic3—22no—
108C22×C3×Dic3—32no—
109C22×C3×Dic3C2×D312yes—
110C22×C3×Dic3C22×C312yes—
111C3×#239—64no—
112C3×#237—28no—
113C3×#237—24no—
114C3×#237—24no—
115C3×#235—64no—
116C2×C3×D12—32no—
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×D12—61no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—32no—
122C2×C3×C4×D3—32no—
123C2×C3×C4×D3—32no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×C3×C4×D3C22×C311yescharacteristic
126C2×C3×Dic6—21no—
127C2×C3×Dic6—21no—
128C2×C3×Dic6C2×D311yescharacteristic
129C2×C3×Dic6C2×D311yescharacteristic
130C2×C3×Dic6C22×C311yescharacteristic
131C2×C3×Dic6C22×C311yescharacteristic
132C2×#626C22×C312yes—
133C2×#624C22×C312yes—
134C2×D3×Dic3C22×C312yes—
135#3799—24no—
136C32×C22⋊C4—34no—
137C32×C42—31no—
138C4×C3⋊Dic3C22×C311yescharacteristic
139C3×#217—24no—
140C3×#217C2×D314yes—
141C3×#217C22×C314yes—
142C3×(C2×D3)⋊C4—34no—
143C3×(C2×D3)⋊C4—34no—
144C3×Dic3⋊C4—34no—
145C3×Dic3⋊C4—34no—
146C3×C4×Dic3—21no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—32no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—61no—
152C3×C4×Dic3C2×D311yescharacteristic
153C3×C4×Dic3C22×C311yescharacteristic
154#3724C22×C314yes—
155#3722C22×C314yes—
156Dic32C22×C312yes—
157C22×C33—22no—
158C22×C33—24no—
159C22×C33C2411yescharacteristic
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3—24no—
162C2×C32×D3—22no—
163C2×C32×D3C2×D412yes—
164C33×C4C2×D412yes—
165C3×C3⋊Dic3#4114yescomplemented
166C32×Dic3—22no—
167C32×Dic3—22no—
168C32×Dic3—22no—
169C32×Dic3C2×D412yes—
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C2×C3×#41—61no—
173C2×C3×#41—91no—
174C2×#239—31no—
175C2×#237C3×D311yescharacteristic, complemented
176C2×#235—31no—
177C3×C4⋊Q8—91no—
178C3×#127—91no—
179C3×#124—31no—
180C3×#124—31no—
181C3×#124—61no—
182C3×#124—91no—
183C3×#121—94no—
184C3×C4×D4—94no—
185C2×C3×C42—91no—
186#947—31no—
187#944—31no—
188#944—31no—
189#940—31no—
190#940—31no—
191#940—61no—
192#939—34no—
193#936C3×D311yescharacteristic, complemented
194C4×#67—34no—
195C2×C4×Dic3—31no—
196#884—34no—
197#67⋊C4—34no—
198#875—31no—
199C42×D3—31no—
200C23×C32—22no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—31no—
204C23×C32—42no—
205C23×C32C22×D312yes—
206C23×C32C22×D312yes—
207C23×C32C23×C312yes—
208C22×C3⋊D3C23×C312yes—
209C22×C3×D3—21no—
210C22×C3×D3—32no—
211C22×C3×D3—32no—
212C22×C3×D3—62no—
213C22×C3×D3C22×D311yescharacteristic
214C22×C3×D3C23×C311yescharacteristic
215C32×Q8—62no—
216C32×Q8—62no—
217C32×D4—22no—
218C32×D4—24no—
219C32×D4—22no—
220C32×D4—22no—
221C32×D4—42no—
222C32×D4—42no—
223C32×D4—44no—
224C32×D4—64no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—31no—
229C2×C32×C4—34no—
230C2×C32×C4—32no—
231C2×C32×C4—32no—
232C2×C32×C4—32no—
233C2×C32×C4—41no—
234C2×C32×C4—64no—
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C22×D311yescharacteristic
237C2×C32×C4C23×C311yescharacteristic
238#638—28no—
239C2×C3⋊Dic3C23×C312yes—
240C4⋊(C3⋊D3)—22no—
241C3×#67—28no—
242C3×#67—24no—
243C3×#67—24no—
244C3×#67—64no—
245C3×#67—68no—
246C3×#67—68no—
247C3×#67—128no—
248C2×C3×Dic3—28no—
249C2×C3×Dic3—24no—
250C2×C3×Dic3—24no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—32no—
256C2×C3×Dic3—32no—
257C2×C3×Dic3—62no—
258C2×C3×Dic3—64no—
259C2×C3×Dic3C22×D312yes—
260C2×C3×Dic3C22×D312yes—
261C2×C3×Dic3C22×D312yes—
262C2×C3×Dic3C22×D311yescharacteristic
263C2×C3×Dic3C23×C312yes—
264C2×C3×Dic3C23×C312yes—
265C2×C3×Dic3C23×C312yes—
266C2×C3×Dic3C23×C311yescharacteristic
267C3×D12—64no—
268C3×D12—62no—
269C3×D12—62no—
270C3×D12—122no—
271C3×C4×D3—24no—
272C3×C4×D3—64no—
273C3×C4×D3—64no—
274C3×C4×D3—64no—
275C3×C4×D3#6714yescomplemented
276C3×C4×D3C3×D414yescomplemented
277C3×Dic6—24no—
278C3×Dic6—22no—
279C3×Dic6—22no—
280C3×Dic6—22no—
281C3×Dic6—22no—
282C3×Dic6—42no—
283#626—24no—
284#624—24no—
285D3×Dic3—24no—
286#532—91noSylow
287C2×C33—42no—
288C2×C33C22×D411yescharacteristic
289C2×C33C2×#4112yes—
290C3×C3⋊D3—42no—
291C32×D3—22no—
292C3×#41—64no—
293C3×#41—64no—
294C3×#41—68no—
295C3×#41—184no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×Q8—61no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—32no—
306C2×C3×D4—32no—
307C2×C3×D4—41no—
308C2×C3×D4—62no—
309C2×C3×D4—92no—
310C2×C3×D4—94no—
311C2×C3×D4—91no—
312C2×C3×D4D3211yescharacteristic
313C2×C3×D4C2×C3×D311yescharacteristic
314C2×C3×D4C2×C3×D311yescharacteristic
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—32no—
318C22×C3×C4—32no—
319C22×C3×C4—61no—
320C22×C3×C4—62no—
321C22×C3×C4—92no—
322C22×C3×C4—92no—
323C2×#67—34no—
324C2×#67—34no—
325C2×#67—32no—
326C2×#67—64no—
327C2×#67C2×C3×D312yes—
328C22×Dic3—32no—
329C22×Dic3C2×C3×D312yes—
330#239—64no—
331#237—24no—
332#235—64no—
333C2×D12—32no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×C4×D3—32no—
338C2×C4×D3—32no—
339C2×C4×D3—32no—
340C2×C4×D3C2×C3×D311yescharacteristic
341C2×Dic6C2×C3×D311yescharacteristic
342C2×Dic6C2×C3×D311yescharacteristic
343C3×C4⋊C4—94no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—64no—
347C3×C22⋊C4—94no—
348C3×C42—31no—
349C3×C42—31no—
350C3×C42—61no—
351C3×C42—92no—
352C3×C42—91no—
353#217C2×C3×D314yes—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356Dic3⋊C4—34no—
357Dic3⋊C4—34no—
358C4×Dic3—31no—
359C4×Dic3—31no—
360C4×Dic3—32no—
361C4×Dic3—32no—
362C4×Dic3—61no—
363C4×Dic3C2×C3×D311yescharacteristic
364C22×C32—22no—
365C22×C32—24no—
366C22×C32—24no—
367C22×C32—24no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—24no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—32no—
375C22×C32—41no—
376C22×C32—42no—
377C22×C32—42no—
378C22×C32—44no—
379C22×C32—44no—
380C22×C32—44no—
381C22×C32—44no—
382C22×C32—62no—
383C22×C32—84no—
384C22×C32C23×D311yescharacteristic
385C22×C32C23×D311yescharacteristic
386C22×C32C24×C311yescharacteristic
387C2×C3⋊D3—22no—
388C2×C3⋊D3—24no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—42no—
393C2×C3×D3—62no—
394C2×C3×D3—64no—
395C2×C3×D3—64no—
396C2×C3×D3—62no—
397C2×C3×D3—122no—
398C2×C3×D3—124no—
399C2×C3×D3C2×#6712yes—
400C2×C3×D3C2×C3×D412yes—
401C32×C4—22no—
402C32×C4—22no—
403C32×C4—22no—
404C32×C4—32no—
405C32×C4—42no—
406C32×C4—62no—
407C32×C4—62no—
408C32×C4—62no—
409C32×C4D3×D412yes—
410C32×C4C2×#6712yes—
411C32×C4C2×C3×D412yes—
412C3⋊Dic3C3×#4114yescomplemented
413C3×Dic3—24no—
414C3×Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—34no—
422C3×Dic3—34no—
423C3×Dic3—42no—
424C3×Dic3—42no—
425C3×Dic3—64no—
426C3×Dic3C2×#6712yes—
427C3×Dic3C2×C3×D412yes—
428C2×#41—31no—
429C2×#41—91no—
430C4⋊Q8—91no—
431#127—91no—
432#124—31no—
433#124—91no—
434#121—94no—
435C4×D4—94no—
436C2×C42—91no—
437C33#53211yescharacteristic, complemented, Sylow
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—31no—
442C23×C3—31no—
443C23×C3—42no—
444C23×C3—61no—
445C23×C3—92no—
446C23×C3C2×D3212yes—
447C23×C3C22×C3×D312yes—
448C23×C3C22×C3×D312yes—
449C22×D3—32no—
450C22×D3—32no—
451C22×D3—62no—
452C22×D3C22×C3×D311yescharacteristic
453C3×Q8—64no—
454C3×Q8—62no—
455C3×Q8—62no—
456C3×Q8—62no—
457C3×Q8—62no—
458C3×Q8—122no—
459C3×D4—24no—
460C3×D4—22no—
461C3×D4—22no—
462C3×D4—22no—
463C3×D4—42no—
464C3×D4—42no—
465C3×D4—44no—
466C3×D4—64no—
467C3×D4—64no—
468C3×D4—68no—
469C3×D4—184no—
470C3×D4—188no—
471C3×D4—182no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—34no—
478C2×C3×C4—34no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—41no—
486C2×C3×C4—64no—
487C2×C3×C4—61no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—64no—
492C2×C3×C4—64no—
493C2×C3×C4—68no—
494C2×C3×C4—92no—
495C2×C3×C4—184no—
496C2×C3×C4—184no—
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C22×C3×D311yescharacteristic
499C2×C3×C4C22×C3×D311yescharacteristic
500#67—24no—
501#67—64no—
502#67—68no—
503#67—68no—
504#67—128no—
505C2×Dic3—24no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—62no—
509C2×Dic3—64no—
510C2×Dic3C22×C3×D312yes—
511C2×Dic3C22×C3×D312yes—
512C2×Dic3C22×C3×D312yes—
513C2×Dic3C22×C3×D311yescharacteristic
514D12—64no—
515D12—62no—
516D12—62no—
517D12—122no—
518C4×D3—64no—
519C4×D3—64no—
520C4×D3—64no—
521C4×D3C3×#6714yescomplemented
522Dic6—22no—
523Dic6—22no—
524C2×C32—22no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—22no—
528C2×C32—22no—
529C2×C32—21no—
530C2×C32—41no—
531C2×C32—42no—
532C2×C32—42no—
533C2×C32—44no—
534C2×C32—42no—
535C2×C32—42no—
536C2×C32—62no—
537C2×C32—82no—
538C2×C32—82no—
539C2×C32—84no—
540C2×C32C2×D3×D411yescharacteristic
541C2×C32D3×#4112yes—
542C2×C32D3×#4112yes—
543C2×C32C22×#6711yescharacteristic
544C2×C32C22×C3×D411yescharacteristic
545C2×C32C2×C3×#4112yes—
546C3⋊D3—42no—
547C3×D3—22no—
548C3×D3—22no—
549C3×D3—42no—
550C3×D3—122no—
551C3×D3—122no—
552C3×D3—242no—
553#41—64no—
554#41—184no—
555C2×Q8—31no—
556C2×Q8—31no—
557C2×D4—32no—
558C2×D4—92no—
559C2×D4—94no—
560C2×D4—91no—
561C2×D4C3×D3211yescharacteristic
562C22×C4—31no—
563C22×C4—32no—
564C22×C4—92no—
565C22×C4—92no—
566C4⋊C4—94no—
567C22⋊C4—34no—
568C22⋊C4—94no—
569C42—31no—
570C42—92no—
571C42—91no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—24no—
577C22×C3—24no—
578C22×C3—22no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—32no—
583C22×C3—32no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—44no—
590C22×C3—41no—
591C22×C3—62no—
592C22×C3—62no—
593C22×C3—62no—
594C22×C3—84no—
595C22×C3—122no—
596C22×C3—184no—
597C22×C3—182no—
598C22×C3C22×D3211yescharacteristic
599C22×C3C23×C3×D311yescharacteristic
600C22×C3C23×C3×D311yescharacteristic
601C2×D3—22no—
602C2×D3—62no—
603C2×D3—64no—
604C2×D3—64no—
605C2×D3—62no—
606C2×D3—122no—
607C2×D3—124no—
608C2×D3C2×C3×#6712yes—
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—32no—
613C3×C4—32no—
614C3×C4—42no—
615C3×C4—62no—
616C3×C4—64no—
617C3×C4—62no—
618C3×C4—62no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—62no—
622C3×C4—62no—
623C3×C4—94no—
624C3×C4—122no—
625C3×C4—122no—
626C3×C4D3×#6712yes—
627C3×C4C3×D3×D412yes—
628C3×C4C2×C3×#6712yes—
629Dic3—22no—
630Dic3—22no—
631Dic3—22no—
632Dic3—34no—
633Dic3—34no—
634Dic3—64no—
635Dic3C2×C3×#6712yes—
636C32—21no—
637C32—21no—
638C32—21no—
639C32—41no—
640C32#566811yescharacteristic, complemented
641C32#583211yescharacteristic, complemented
642C32C3×#53211yescharacteristic, complemented
643C23—31no—
644C23—92no—
645C23C2×C3×D3212yes—
646Q8—62no—
647Q8—62no—
648D4—22no—
649D4—64no—
650D4—184no—
651D4—188no—
652D4—182no—
653C2×C4—31no—
654C2×C4—34no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—64no—
659C2×C4—92no—
660C2×C4—184no—
661C2×C4—184no—
662C2×C4C2×C3×D3211yescharacteristic
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—22no—
667C2×C3—22no—
668C2×C3—22no—
669C2×C3—44no—
670C2×C3—42no—
671C2×C3—42no—
672C2×C3—42no—
673C2×C3—41no—
674C2×C3—42no—
675C2×C3—62no—
676C2×C3—62no—
677C2×C3—82no—
678C2×C3—82no—
679C2×C3—84no—
680C2×C3—122no—
681C2×C3—362no—
682C2×C3#6431212yes—
683C2×C3C2×D3×#6711yescharacteristic
684C2×C3C2×C3×D3×D411yescharacteristic
685C2×C3C3×D3×#4112yes—
686C2×C3C3×D3×#4112yes—
687C2×C3C22×C3×#6711yescharacteristic
688D3—22no—
689D3—122no—
690D3—122no—
691D3—242no—
692C22—22no—
693C22—24no—
694C22—32no—
695C22—62no—
696C22—182no—
697C22—184no—
698C22C22×C3×D3211yescharacteristic
699C4—32no—
700C4—62no—
701C4—62no—
702C4—62no—
703C4—94no—
704C4C3×D3×#6712yes—
705C3—21no—
706C3—21no—
707C3—21no—
708C3—41no—
709C3#1059515311yescharacteristic, direct product factor
710C3C3×#566811yescharacteristic, complemented
711C3C3×#583211yescharacteristic, complemented
712C2—42no—
713C2—62no—
714C2—362no—
715C2C3×#6431212yes—
716C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×C3×#3799C2semidirect
3. C3×#64149C2semidirect
4. C32×#936C2semidirect
5. C3×#63971C2semidirect
6. C3×#63952C2semidirect
7. C3×C4×D3×Dic3C2semidirect
8. C3×#63873C2semidirect
9. C3×#63864C2semidirect
12. #10595153C3direct (N × H)
35. C2×C3×#237D3semidirect
36. C2×C3×#237C2×C3semidirect
38. C2×#3799C2×C3semidirect
40. #64149C2×C3semidirect
49. C3×#936D3semidirect
50. C3×#936C2×C3semidirect
57. #63971C2×C3semidirect
58. #63952C2×C3semidirect
59. C4×D3×Dic3C2×C3semidirect
60. #63873C2×C3semidirect
61. #63864C2×C3semidirect
76. C32×C4×D3D4semidirect
165. C3×C3⋊Dic3#41semidirect
175. C2×#237C3×D3semidirect
193. #936C3×D3semidirect
275. C3×C4×D3#67semidirect
276. C3×C4×D3C3×D4semidirect
412. C3⋊Dic3C3×#41semidirect
437. C33#532semidirect
521. C4×D3C3×#67semidirect
640. C32#5668semidirect
641. C32#5832semidirect
642. C32C3×#532semidirect
709. C3#10595153direct (N × H)
710. C3C3×#5668semidirect
711. C3C3×#5832semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C3×#37992
C3×#641492
C32×#9362
C3×#639712
C3×#639522
C3×C4×D3×Dic32
C3×#638732
C3×#638642
C3×#58323
C3×#56683
#105951533