Finite Group Databasebeta

← C3×#87239 #11904290

Subgroups — C3×#87239 #11904290

Order 1152.

4481 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×D4C211yesmaximal, characteristic, complemented
2C2×C3×#1004C211yesmaximal, characteristic, complemented
3C2×C3×#953C214yesmaximal, complemented
4C3×#5806C218yesmaximal, complemented
5C3×#5805C212yesmaximal, complemented
6C3×#5804C214yesmaximal, complemented
7C3×D4×#67C218yesmaximal, complemented
8C3×#5798C211yesmaximal, characteristic, complemented
9C3×#5791C212yesmaximal, complemented
10C3×#3484—31nomaximal
11#87239C311yesmaximal, characteristic, direct product factor
12C25×C32C2212yescomplemented
13C22×C32×D4—28no—
14C22×C32×D4C2211yescharacteristic
15C22×C32×D4C2218yescomplemented
16C22×C32×D4C2212yescomplemented
17C22×C32×D4C2211yescharacteristic, complemented
18C23×C32×C4C2211yescharacteristic, complemented
19C22×C3×#67C2214yescomplemented
20C22×C3×#67C2218yescomplemented
21C3×#1004—28no—
22C2×C3×#237C2214yescomplemented
23C2×C3×D3×D4C2214yescomplemented
24C2×C3×#235C2212yescomplemented
25C3×#953C2214yescomplemented
26C3×#953C22116yescomplemented
27C3×#953C2218yescomplemented
28C2×C3×#217C2214yescomplemented
29C2×C3×#217C2218yescomplemented
30C3×#940C2214yescomplemented
31C3×#939C22116yescomplemented
32C3×#938C2218yescomplemented
33C3×#937C2218yescomplemented
34C3×#936C2214yescomplemented
35C3×#935C2218yescomplemented
36C3×D4×Dic3C2218yescomplemented
37C3×#930C2214yescomplemented
38C3×#929C2214yescomplemented
39C3×C4×#67C2218yescomplemented
40C3×#926C2212yescomplemented
41C3×#924C2214yescomplemented
42C2×C3×H(5,𝔽2)—31no—
43C23×C3×D4—21no—
44C23×C3×D4D311yescharacteristic, complemented
45C23×C3×D4C2×C311yescharacteristic, complemented
46C2×#1004C2×C311yescharacteristic, complemented
47C3×#546—38no—
48C3×D42—38no—
49C3×#535—32no—
50C3×#534—34no—
51C3×#525—32no—
52C2×C3×#120—34no—
53C3×#518—31no—
54C2×#953C2×C314yescomplemented
55#5806C2×C318yescomplemented
56#5805C2×C312yescomplemented
57#5804C2×C314yescomplemented
58D4×#67C2×C318yescomplemented
59#5798C2×C311yescharacteristic, complemented
60#5791C2×C312yescomplemented
61C24×C32—28no—
62C24×C32—48no—
63C24×C32C2311yescharacteristic
64C24×C32C2318yes—
65C24×C32C2312yes—
66C24×C32C2312yes—
67C23×C3×D3C2314yescomplemented
68C2×C32×D4—28no—
69C2×C32×D4—232no—
70C2×C32×D4—24no—
71C2×C32×D4D418yescomplemented
72C2×C32×D4C2318yes—
73C2×C32×D4C2314yes—
74C2×C32×D4C2314yes—
75C22×C32×C4—24no—
76C22×C32×C4C2314yes—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C2×C3×#67—216no—
80C2×C3×#67—416no—
81C2×C3×#67C2318yes—
82C2×C3×#67C2314yes—
83C2×C3×#67C2318yescomplemented
84C2×C3×#67C23116yescomplemented
85C22×C3×Dic3C2314yescomplemented
86C22×C3×Dic3C2318yescomplemented
87C3×#237—216no—
88C3×D3×D4—216no—
89C3×#235—28no—
90C2×C3×D12C2312yescomplemented
91C2×C3×C4×D3C2314yescomplemented
92C2×C3×Dic6C2312yescomplemented
93C3×#217C2318yes—
94C3×#217C2314yes—
95C3×#217C2318yescomplemented
96C3×#217C23116yescomplemented
97C3×(C2×D3)⋊C4C2318yescomplemented
98C3×C4⋊Dic3C2314yescomplemented
99C3×Dic3⋊C4C2318yescomplemented
100C3×C4×Dic3C2314yescomplemented
101#3484—31noSylow
102C25×C3—22no—
103C25×C3C2×D312yescomplemented
104C25×C3C22×C312yescomplemented
105C3×H(5,𝔽2)—68no—
106C2×C3×#41—34no—
107C2×C3×#41—32no—
108C22×C3×D4—216no—
109C22×C3×D4—28no—
110C22×C3×D4—28no—
111C22×C3×D4—21no—
112C22×C3×D4—22no—
113C22×C3×D4—21no—
114C22×C3×D4—28no—
115C22×C3×D4—34no—
116C22×C3×D4—38no—
117C22×C3×D4—34no—
118C22×C3×D4C2×D311yescharacteristic
119C22×C3×D4C2×D312yescomplemented
120C22×C3×D4C2×D311yescharacteristic, complemented
121C22×C3×D4C2×D318yescomplemented
122C22×C3×D4C22×C311yescharacteristic
123C22×C3×D4C22×C318yescomplemented
124C22×C3×D4C22×C312yescomplemented
125C22×C3×D4C22×C311yescharacteristic, complemented
126C23×C3×C4—21no—
127C23×C3×C4C2×D311yescharacteristic, complemented
128C23×C3×C4C22×C311yescharacteristic, complemented
129C22×#67C22×C314yescomplemented
130C22×#67C22×C318yescomplemented
131#1004—28no—
132C2×#237C22×C314yescomplemented
133C2×D3×D4C22×C314yescomplemented
134C2×#235C22×C312yescomplemented
135C3×#127—34no—
136C3×#124—34no—
137C3×#123—38no—
138C3×#123—34no—
139C3×C22⋊Q8—34no—
140C3×#121—38no—
141C3×#121—316no—
142C3×#121—34no—
143C3×#120—34no—
144C3×#120—38no—
145C3×#120—316no—
146C3×#120—38no—
147C3×C4×D4—38no—
148C3×C4×D4—38no—
149C3×#117—32no—
150C2×C3×C22⋊C4—34no—
151C2×C3×C22⋊C4—38no—
152#953C22×C314yescomplemented
153#953C22×C3116yescomplemented
154#953C22×C318yescomplemented
155C2×#217C22×C314yescomplemented
156C2×#217C22×C318yescomplemented
157#940C22×C314yescomplemented
158#939C22×C3116yescomplemented
159#938C22×C318yescomplemented
160#937C22×C318yescomplemented
161#936C22×C314yescomplemented
162#935C22×C318yescomplemented
163D4×Dic3C22×C318yescomplemented
164#930C22×C314yescomplemented
165#929C22×C314yescomplemented
166C4×#67C22×C318yescomplemented
167#926C22×C312yescomplemented
168#924C22×C314yescomplemented
169C23×C32—22no—
170C23×C32—24no—
171C23×C32—216no—
172C23×C32—24no—
173C23×C32—216no—
174C23×C32—44no—
175C23×C32—48no—
176C23×C32—44no—
177C23×C32—432no—
178C23×C32C2×D418yescomplemented
179C23×C32C2414yes—
180C23×C32C2414yes—
181C23×C32C2411yescharacteristic
182C23×C32C2412yes—
183C22×C3×D3—28no—
184C22×C3×D3—48no—
185C22×C3×D3C2414yes—
186C32×D4—216no—
187C32×D4—28no—
188C32×D4C2×D4116yescomplemented
189C2×C32×C4—22no—
190C2×C32×C4—28no—
191C2×C32×C4C2×D414yescomplemented
192C2×C32×C4C2412yes—
193C2×C32×C4C2412yes—
194C3×#67—28no—
195C3×#67—216no—
196C3×#67—216no—
197C3×#67—416no—
198C2×C3×Dic3—28no—
199C2×C3×Dic3—48no—
200C2×C3×Dic3C2418yes—
201C2×C3×Dic3C2414yes—
202C3×D12—24no—
203C3×C4×D3—28no—
204C3×Dic6—24no—
205C2×H(5,𝔽2)—31no—
206C23×D4C3×D311yescharacteristic, complemented
207#546—38no—
208D42—38no—
209#535—32no—
210#534—34no—
211#525—32no—
212C2×#120—34no—
213#518—31no—
214C24×C3—216no—
215C24×C3—28no—
216C24×C3—28no—
217C24×C3—21no—
218C24×C3—28no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—34no—
222C24×C3—48no—
223C24×C3—48no—
224C24×C3—416no—
225C24×C3C22×D311yescharacteristic
226C24×C3C22×D318yes—
227C24×C3C22×D312yes—
228C24×C3C22×D312yes—
229C24×C3C23×C311yescharacteristic
230C24×C3C23×C318yes—
231C24×C3C23×C312yes—
232C24×C3C23×C312yes—
233C23×D3C23×C314yescomplemented
234C3×#41—616no—
235C3×#41—68no—
236C2×C3×Q8—32no—
237C2×C3×D4—216no—
238C2×C3×D4—264no—
239C2×C3×D4—28no—
240C2×C3×D4—28no—
241C2×C3×D4—28no—
242C2×C3×D4—232no—
243C2×C3×D4—232no—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—28no—
247C2×C3×D4—28no—
248C2×C3×D4—24no—
249C2×C3×D4—24no—
250C2×C3×D4—38no—
251C2×C3×D4—34no—
252C2×C3×D4—38no—
253C2×C3×D4—316no—
254C2×C3×D4—32no—
255C2×C3×D4—616no—
256C2×C3×D4—616no—
257C2×C3×D4—1216no—
258C2×C3×D4#6718yescomplemented
259C2×C3×D4C3×D418yescomplemented
260C2×C3×D4C22×D318yes—
261C2×C3×D4C22×D314yes—
262C2×C3×D4C22×D314yes—
263C2×C3×D4C23×C318yes—
264C2×C3×D4C23×C314yes—
265C2×C3×D4C23×C314yes—
266C22×C3×C4—28no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—34no—
273C22×C3×C4—38no—
274C22×C3×C4—34no—
275C22×C3×C4C22×D314yes—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C23×C314yes—
279C22×C3×C4C23×C311yescharacteristic
280C22×C3×C4C23×C311yescharacteristic
281C2×#67—216no—
282C2×#67—416no—
283C2×#67C23×C318yes—
284C2×#67C23×C314yes—
285C2×#67C23×C318yescomplemented
286C2×#67C23×C3116yescomplemented
287C22×Dic3C23×C314yescomplemented
288C22×Dic3C23×C318yescomplemented
289#237—216no—
290D3×D4—216no—
291#235—28no—
292C2×D12C23×C312yescomplemented
293C2×C4×D3C23×C314yescomplemented
294C2×Dic6C23×C312yescomplemented
295C3×C4⋊C4—38no—
296C3×C4⋊C4—34no—
297C3×C22⋊C4—34no—
298C3×C22⋊C4—38no—
299C3×C22⋊C4—38no—
300C3×C22⋊C4—316no—
301C3×C22⋊C4—38no—
302C3×C42—34no—
303#217C23×C318yes—
304#217C23×C314yes—
305#217C23×C318yescomplemented
306#217C23×C3116yescomplemented
307(C2×D3)⋊C4C23×C318yescomplemented
308C4⋊Dic3C23×C314yescomplemented
309Dic3⋊C4C23×C318yescomplemented
310C4×Dic3C23×C314yescomplemented
311C22×C32—28no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—24no—
316C22×C32—28no—
317C22×C32—28no—
318C22×C32—48no—
319C22×C32—432no—
320C22×C32—48no—
321C22×C32C22×D418yes—
322C22×C32C22×D412yes—
323C22×C32H(5,𝔽2)14yescomplemented
324C22×C32C2511yescharacteristic
325C2×C3×D3—24no—
326C2×C3×D3—28no—
327C2×C3×D3—88no—
328C32×C4—22no—
329C32×C4C22×D414yes—
330C3×Dic3—24no—
331C3×Dic3—28no—
332C25C2×C3×D312yescomplemented
333H(5,𝔽2)—68no—
334C2×#41—34no—
335C2×#41—32no—
336C22×D4—28no—
337C22×D4—34no—
338C22×D4—38no—
339C22×D4—34no—
340C22×D4C2×C3×D311yescharacteristic
341C22×D4C2×C3×D312yescomplemented
342C22×D4C2×C3×D311yescharacteristic, complemented
343C22×D4C2×C3×D318yescomplemented
344C23×C4C2×C3×D311yescharacteristic, complemented
345#127—34no—
346#124—34no—
347#123—38no—
348#123—34no—
349C22⋊Q8—34no—
350#121—316no—
351#121—38no—
352#121—34no—
353#120—34no—
354#120—38no—
355#120—316no—
356#120—38no—
357C4×D4—38no—
358C4×D4—38no—
359#117—32no—
360C2×C22⋊C4—34no—
361C2×C22⋊C4—38no—
362C23×C3—24no—
363C23×C3—28no—
364C23×C3—24no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—24no—
368C23×C3—232no—
369C23×C3—28no—
370C23×C3—216no—
371C23×C3—216no—
372C23×C3—24no—
373C23×C3—216no—
374C23×C3—24no—
375C23×C3—216no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—28no—
381C23×C3—34no—
382C23×C3—416no—
383C23×C3—44no—
384C23×C3—48no—
385C23×C3—44no—
386C23×C3—44no—
387C23×C3—48no—
388C23×C3—44no—
389C23×C3—48no—
390C23×C3—416no—
391C23×C3—48no—
392C23×C3—432no—
393C23×C3—432no—
394C23×C3—464no—
395C23×C3—68no—
396C23×C3—128no—
397C23×C3C2×#6718yescomplemented
398C23×C3C2×C3×D418yescomplemented
399C23×C3C23×D314yes—
400C23×C3C23×D312yes—
401C23×C3C23×D311yescharacteristic
402C23×C3C23×D314yes—
403C23×C3C24×C314yes—
404C23×C3C24×C311yescharacteristic
405C23×C3C24×C314yes—
406C23×C3C24×C312yes—
407C22×D3—28no—
408C22×D3—48no—
409C22×D3C24×C314yes—
410C3×Q8—64no—
411C3×D4—232no—
412C3×D4—216no—
413C3×D4—216no—
414C3×D4—216no—
415C3×D4—28no—
416C3×D4—28no—
417C3×D4—216no—
418C3×D4—616no—
419C3×D4—68no—
420C3×D4—616no—
421C3×D4—64no—
422C3×D4—1216no—
423C3×D4C2×#67116yescomplemented
424C3×D4C2×C3×D4116yescomplemented
425C2×C3×C4—24no—
426C2×C3×C4—216no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—28no—
430C2×C3×C4—28no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—38no—
435C2×C3×C4—34no—
436C2×C3×C4—68no—
437C2×C3×C4—68no—
438C2×C3×C4—128no—
439C2×C3×C4C2×#6714yescomplemented
440C2×C3×C4C2×C3×D414yescomplemented
441C2×C3×C4C23×D312yes—
442C2×C3×C4C23×D312yes—
443C2×C3×C4C24×C312yes—
444C2×C3×C4C24×C312yes—
445#67—28no—
446#67—216no—
447#67—216no—
448#67—416no—
449C2×Dic3—28no—
450C2×Dic3—48no—
451C2×Dic3C24×C318yes—
452C2×Dic3C24×C314yes—
453D12—24no—
454C4×D3—28no—
455Dic6—24no—
456C2×C32—22no—
457C2×C32—24no—
458C2×C32—28no—
459C2×C32—44no—
460C2×C32C23×D411yescharacteristic
461C2×C32C2×H(5,𝔽2)12yes—
462C3×D3—44no—
463C24—28no—
464C24—34no—
465C24—48no—
466C24C22×C3×D311yescharacteristic
467C24C22×C3×D318yes—
468C24C22×C3×D312yes—
469C24C22×C3×D312yes—
470#41—616no—
471#41—68no—
472C2×Q8—32no—
473C2×D4—28no—
474C2×D4—232no—
475C2×D4—24no—
476C2×D4—38no—
477C2×D4—34no—
478C2×D4—38no—
479C2×D4—316no—
480C2×D4—32no—
481C2×D4—616no—
482C2×D4—616no—
483C2×D4—1216no—
484C2×D4C3×#6718yescomplemented
485C2×D4C22×C3×D318yes—
486C2×D4C22×C3×D314yes—
487C2×D4C22×C3×D314yes—
488C22×C4—24no—
489C22×C4—34no—
490C22×C4—38no—
491C22×C4—34no—
492C22×C4C22×C3×D314yes—
493C22×C4C22×C3×D311yescharacteristic
494C22×C4C22×C3×D311yescharacteristic
495C4⋊C4—34no—
496C4⋊C4—38no—
497C22⋊C4—34no—
498C22⋊C4—38no—
499C22⋊C4—38no—
500C22⋊C4—316no—
501C22⋊C4—38no—
502C42—34no—
503C22×C3—24no—
504C22×C3—216no—
505C22×C3—28no—
506C22×C3—28no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—28no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—28no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—28no—
518C22×C3—28no—
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—28no—
522C22×C3—24no—
523C22×C3—22no—
524C22×C3—28no—
525C22×C3—21no—
526C22×C3—48no—
527C22×C3—48no—
528C22×C3—48no—
529C22×C3—48no—
530C22×C3—432no—
531C22×C3—432no—
532C22×C3—416no—
533C22×C3—464no—
534C22×C3—416no—
535C22×C3—48no—
536C22×C3—48no—
537C22×C3—68no—
538C22×C3—64no—
539C22×C3—248no—
540C22×C3#100414yescomplemented
541C22×C3C22×#6712yes—
542C22×C3C22×#6718yes—
543C22×C3C22×C3×D418yes—
544C22×C3C22×C3×D412yes—
545C22×C3C3×H(5,𝔽2)14yescomplemented
546C22×C3C24×D311yescharacteristic
547C22×C3C25×C311yescharacteristic
548C2×D3—24no—
549C2×D3—28no—
550C2×D3—88no—
551C3×C4—24no—
552C3×C4—22no—
553C3×C4—22no—
554C3×C4—24no—
555C3×C4—68no—
556C3×C4—64no—
557C3×C4C22×#6714yes—
558C3×C4C22×C3×D414yes—
559Dic3—24no—
560Dic3—28no—
561C32#348411yescharacteristic, complemented, Sylow
562C23—24no—
563C23—22no—
564C23—216no—
565C23—216no—
566C23—24no—
567C23—34no—
568C23—44no—
569C23—48no—
570C23—44no—
571C23—432no—
572C23—68no—
573C23—128no—
574C23C2×C3×#6718yescomplemented
575C23C23×C3×D314yes—
576C23C23×C3×D312yes—
577C23C23×C3×D311yescharacteristic
578C23C23×C3×D314yes—
579Q8—64no—
580D4—216no—
581D4—28no—
582D4—616no—
583D4—68no—
584D4—616no—
585D4—64no—
586D4—1216no—
587D4C2×C3×#67116yescomplemented
588C2×C4—22no—
589C2×C4—28no—
590C2×C4—38no—
591C2×C4—34no—
592C2×C4—68no—
593C2×C4—68no—
594C2×C4—128no—
595C2×C4C2×C3×#6714yescomplemented
596C2×C4C23×C3×D312yes—
597C2×C4C23×C3×D312yes—
598C2×C3—28no—
599C2×C3—24no—
600C2×C3—28no—
601C2×C3—22no—
602C2×C3—24no—
603C2×C3—24no—
604C2×C3—22no—
605C2×C3—28no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—48no—
609C2×C3—48no—
610C2×C3—44no—
611C2×C3—44no—
612C2×C3—124no—
613C2×C3C2×#100412yes—
614C2×C3C23×#6711yescharacteristic
615C2×C3C23×C3×D411yescharacteristic
616C2×C3C2×C3×H(5,𝔽2)12yes—
617D3—44no—
618C22—28no—
619C22—28no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—28no—
624C22—24no—
625C22—48no—
626C22—432no—
627C22—48no—
628C22—68no—
629C22—64no—
630C22—248no—
631C22C3×#100414yescomplemented
632C22C22×C3×#6712yes—
633C22C22×C3×#6718yes—
634C22C24×C3×D311yescharacteristic
635C4—22no—
636C4—68no—
637C4—64no—
638C4C22×C3×#6714yes—
639C3—21no—
640C3#8723911yescharacteristic, direct product factor
641C3C3×#348411yescharacteristic, complemented
642C2—24no—
643C2—22no—
644C2—28no—
645C2—44no—
646C2—124no—
647C2C2×C3×#100412yes—
648C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC23×C32×D4C2
socleC22×C32C25
hypercenterC23×C3×D4D3
hypocenterC3C3×#3484
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C32×D4C2semidirect
2. C2×C3×#1004C2semidirect
3. C2×C3×#953C2semidirect
4. C3×#5806C2semidirect
5. C3×#5805C2semidirect
6. C3×#5804C2semidirect
7. C3×D4×#67C2semidirect
8. C3×#5798C2semidirect
9. C3×#5791C2semidirect
11. #87239C3direct (N × H)
12. C25×C32C22semidirect
15. C22×C32×D4C22semidirect
16. C22×C32×D4C22semidirect
17. C22×C32×D4C22semidirect
18. C23×C32×C4C22semidirect
19. C22×C3×#67C22semidirect
20. C22×C3×#67C22semidirect
22. C2×C3×#237C22semidirect
23. C2×C3×D3×D4C22semidirect
24. C2×C3×#235C22semidirect
25. C3×#953C22semidirect
26. C3×#953C22semidirect
27. C3×#953C22semidirect
28. C2×C3×#217C22semidirect
29. C2×C3×#217C22semidirect
30. C3×#940C22semidirect
31. C3×#939C22semidirect
32. C3×#938C22semidirect
33. C3×#937C22semidirect
34. C3×#936C22semidirect
35. C3×#935C22semidirect
36. C3×D4×Dic3C22semidirect
37. C3×#930C22semidirect
38. C3×#929C22semidirect
39. C3×C4×#67C22semidirect
40. C3×#926C22semidirect
41. C3×#924C22semidirect
44. C23×C3×D4D3semidirect
45. C23×C3×D4C2×C3semidirect
46. C2×#1004C2×C3semidirect
54. C2×#953C2×C3semidirect
55. #5806C2×C3semidirect
56. #5805C2×C3semidirect
57. #5804C2×C3semidirect
58. D4×#67C2×C3semidirect
59. #5798C2×C3semidirect
60. #5791C2×C3semidirect
67. C23×C3×D3C23semidirect
71. C2×C32×D4D4semidirect
83. C2×C3×#67C23semidirect
84. C2×C3×#67C23semidirect
85. C22×C3×Dic3C23semidirect
86. C22×C3×Dic3C23semidirect
90. C2×C3×D12C23semidirect
91. C2×C3×C4×D3C23semidirect
92. C2×C3×Dic6C23semidirect
95. C3×#217C23semidirect
96. C3×#217C23semidirect
97. C3×(C2×D3)⋊C4C23semidirect
98. C3×C4⋊Dic3C23semidirect
99. C3×Dic3⋊C4C23semidirect
100. C3×C4×Dic3C23semidirect
103. C25×C3C2×D3semidirect
104. C25×C3C22×C3semidirect
119. C22×C3×D4C2×D3semidirect
120. C22×C3×D4C2×D3semidirect
121. C22×C3×D4C2×D3semidirect
123. C22×C3×D4C22×C3semidirect
124. C22×C3×D4C22×C3semidirect
125. C22×C3×D4C22×C3semidirect
127. C23×C3×C4C2×D3semidirect
128. C23×C3×C4C22×C3semidirect
129. C22×#67C22×C3semidirect
130. C22×#67C22×C3semidirect
132. C2×#237C22×C3semidirect
133. C2×D3×D4C22×C3semidirect
134. C2×#235C22×C3semidirect
152. #953C22×C3semidirect
153. #953C22×C3semidirect
154. #953C22×C3semidirect
155. C2×#217C22×C3semidirect
156. C2×#217C22×C3semidirect
157. #940C22×C3semidirect
158. #939C22×C3semidirect
159. #938C22×C3semidirect
160. #937C22×C3semidirect
161. #936C22×C3semidirect
162. #935C22×C3semidirect
163. D4×Dic3C22×C3semidirect
164. #930C22×C3semidirect
165. #929C22×C3semidirect
166. C4×#67C22×C3semidirect
167. #926C22×C3semidirect
168. #924C22×C3semidirect
178. C23×C32C2×D4semidirect
188. C32×D4C2×D4semidirect
191. C2×C32×C4C2×D4semidirect
206. C23×D4C3×D3semidirect
233. C23×D3C23×C3semidirect
258. C2×C3×D4#67semidirect
259. C2×C3×D4C3×D4semidirect
285. C2×#67C23×C3semidirect
286. C2×#67C23×C3semidirect
287. C22×Dic3C23×C3semidirect
288. C22×Dic3C23×C3semidirect
292. C2×D12C23×C3semidirect
293. C2×C4×D3C23×C3semidirect
294. C2×Dic6C23×C3semidirect
305. #217C23×C3semidirect
306. #217C23×C3semidirect
307. (C2×D3)⋊C4C23×C3semidirect
308. C4⋊Dic3C23×C3semidirect
309. Dic3⋊C4C23×C3semidirect
310. C4×Dic3C23×C3semidirect
323. C22×C32H(5,𝔽2)semidirect
332. C25C2×C3×D3semidirect
341. C22×D4C2×C3×D3semidirect
342. C22×D4C2×C3×D3semidirect
343. C22×D4C2×C3×D3semidirect
344. C23×C4C2×C3×D3semidirect
397. C23×C3C2×#67semidirect
398. C23×C3C2×C3×D4semidirect
423. C3×D4C2×#67semidirect
424. C3×D4C2×C3×D4semidirect
439. C2×C3×C4C2×#67semidirect
440. C2×C3×C4C2×C3×D4semidirect
484. C2×D4C3×#67semidirect
540. C22×C3#1004semidirect
545. C22×C3C3×H(5,𝔽2)semidirect
561. C32#3484semidirect
574. C23C2×C3×#67semidirect
587. D4C2×C3×#67semidirect
595. C2×C4C2×C3×#67semidirect
631. C22C3×#1004semidirect
640. C3#87239direct (N × H)
641. C3C3×#3484semidirect

Maximal subgroups

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

subgroupindex
C23×C32×D42
C2×C3×#10042
C2×C3×#9532
C3×#58062
C3×#58052
C3×#58042
C3×D4×#672
C3×#57982
C3×#57912
C3×#34843
#872393