Finite Group Databasebeta

← C2×C3×#5595 #11910161

Subgroups — C2×C3×#5595 #11910161

Order 1152.

3019 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#120C211yesmaximal, characteristic, complemented
2C2×C3×#953C212yesmaximal, complemented
3C2×C3×#940C211yesmaximal, characteristic, complemented
4C2×C3×#939C212yesmaximal, complemented
5C2×C3×#938C212yesmaximal, complemented
6C2×C3×#935C211yesmaximal, characteristic, complemented
7C3×#5595C2116yesmaximal, direct product factor
8C2×C3×#884C212yesmaximal, complemented
9C2×C3×#883C212yesmaximal, complemented
10C2×C3×#879C212yesmaximal, complemented
11C2×C3×#560—31nomaximal
12C2×#5595C311yesmaximal, characteristic, direct product factor
13C25×C32C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C22×C32×D4C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yescomplemented
20C23×C3×Dic3C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic, complemented
22C22×C3×C4×D3C2212yescomplemented
23C32×#120C2218yescomplemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2212yes—
26C3×#953C22116yescomplemented
27C2×C3×#217C2212yes—
28C2×C3×#217C2212yes—
29C2×C3×#217C2212yes—
30C2×C3×#217C2211yescharacteristic, complemented
31C3×#940C2218yescomplemented
32C3×#939C22116yescomplemented
33C3×#938C22116yescomplemented
34C3×#935C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yescomplemented
36C2×C3×C4⋊Dic3C2212yescomplemented
37C2×C3×Dic3⋊C4C2212yescomplemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39C2×C3×C4×Dic3C2211yescharacteristic, complemented
40C3×#884C22116yescomplemented
41C3×#883C22116yescomplemented
42C3×#879C22116yescomplemented
43C3×#560—316no—
44C2×C3×#127—31no—
45C2×C3×#126—32no—
46C2×C3×#123—31no—
47C2×C3×#123—32no—
48C2×C3×#121—32no—
49C2×C3×#121—32no—
50C2×C3×#121—32no—
51C2×C3×#120—21no—
52C2×C3×#120—32no—
53C2×C3×#120D311yescharacteristic, complemented
54C2×C3×#120C2×C311yescharacteristic, complemented
55C2×#953C2×C312yescomplemented
56C2×#940C2×C311yescharacteristic, complemented
57C2×#939C2×C312yescomplemented
58C2×#938C2×C312yescomplemented
59C2×#935C2×C311yescharacteristic, complemented
60#5595C2×C3116yesdirect product factor
61C2×#884C2×C312yescomplemented
62C2×#883C2×C312yescomplemented
63C2×#879C2×C312yescomplemented
64C24×C32—44no—
65C24×C32—42no—
66C24×C32C2311yescharacteristic
67C24×C32C2312yes—
68C24×C32C2311yescharacteristic
69C24×C32C2314yes—
70C23×C3×D3C2312yes—
71C2×C32×D4—44no—
72C2×C32×D4—42no—
73C2×C32×D4C2314yes—
74C2×C32×D4C2318yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2312yes—
77C2×C3×#67—44no—
78C2×C3×#67—44no—
79C2×C3×#67—44no—
80C2×C3×#67—44no—
81C2×C3×#67C2318yes—
82C2×C3×#67C2318yes—
83C2×C3×#67C2318yes—
84C2×C3×#67C2318yescomplemented
85C22×C3×Dic3—42no—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2314yescomplemented
90C2×C3×D12—42no—
91C2×C3×D12C2314yescomplemented
92C2×C3×C4×D3—44no—
93C2×C3×C4×D3C2318yescomplemented
94C32×C22⋊C4C2318yes—
95C32×C22⋊C4C2314yes—
96C3×#217C2318yes—
97C3×#217C2318yes—
98C3×#217C2318yes—
99C3×#217C2314yescomplemented
100C3×(C2×D3)⋊C4C2318yescomplemented
101C3×C4⋊Dic3C2318yescomplemented
102C3×Dic3⋊C4C2318yescomplemented
103C3×Dic3⋊C4C2318yescomplemented
104C3×C4×Dic3C2314yescomplemented
105C2×#560—31noSylow
106C25×C3—21no—
107C25×C3C2×D311yescharacteristic
108C25×C3C22×C311yescharacteristic
109C22×C3×D4—22no—
110C22×C3×D4—21no—
111C22×C3×D4—32no—
112C22×C3×D4—32no—
113C22×C3×D4—32no—
114C22×C3×D4—32no—
115C22×C3×D4—31no—
116C22×C3×D4C2×D312yes—
117C22×C3×D4C2×D311yescharacteristic
118C22×C3×D4C22×C311yescharacteristic
119C22×C3×D4C22×C312yes—
120C23×C3×C4—31no—
121C23×C3×C4—32no—
122C22×#67C22×C312yes—
123C22×#67C22×C312yes—
124C22×#67C22×C312yes—
125C22×#67C22×C312yescomplemented
126C23×Dic3C22×C311yescharacteristic, complemented
127C22×D12C22×C311yescharacteristic, complemented
128C22×C4×D3C22×C312yescomplemented
129C3×#127—38no—
130C3×#126—316no—
131C3×#123—38no—
132C3×#123—316no—
133C3×#121—316no—
134C3×#121—316no—
135C3×#121—316no—
136C3×#120—28no—
137C3×#120—316no—
138C3×#120C2×D318yescomplemented
139C3×#120C22×C318yescomplemented
140C2×C3×C4⋊C4—32no—
141C2×C3×C4⋊C4—32no—
142C2×C3×C4⋊C4—32no—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—32no—
146C2×C3×C22⋊C4—32no—
147C2×C3×C22⋊C4—32no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—32no—
150C2×C3×C22⋊C4C2×D312yes—
151C2×C3×C22⋊C4C2×D311yescharacteristic
152C2×C3×C22⋊C4C22×C312yes—
153C2×C3×C22⋊C4C22×C311yescharacteristic
154C2×C3×C42—31no—
155#953C22×C3116yescomplemented
156C2×#217C22×C312yes—
157C2×#217C22×C312yes—
158C2×#217C22×C312yes—
159C2×#217C22×C311yescharacteristic, complemented
160#940C22×C318yescomplemented
161#939C22×C3116yescomplemented
162#938C22×C3116yescomplemented
163#935C22×C318yescomplemented
164C2×(C2×D3)⋊C4C22×C312yescomplemented
165C2×C4⋊Dic3C22×C312yescomplemented
166C2×Dic3⋊C4C22×C312yescomplemented
167C2×Dic3⋊C4C22×C312yescomplemented
168C2×C4×Dic3C22×C311yescharacteristic, complemented
169#884C22×C3116yescomplemented
170#883C22×C3116yescomplemented
171#879C22×C3116yescomplemented
172C23×C32—24no—
173C23×C32—22no—
174C23×C32—24no—
175C23×C32—24no—
176C23×C32—24no—
177C23×C32—22no—
178C23×C32—24no—
179C23×C32—48no—
180C23×C32—44no—
181C23×C32—416no—
182C23×C32C2414yes—
183C23×C32C2412yes—
184C23×C32C2412yes—
185C23×C32C2411yescharacteristic
186C22×C3×D3—24no—
187C22×C3×D3—24no—
188C22×C3×D3—24no—
189C22×C3×D3C2414yes—
190C32×D4—48no—
191C32×D4—44no—
192C2×C32×C4—24no—
193C2×C32×C4—22no—
194C2×C32×C4C2412yes—
195C2×C32×C4C2414yes—
196C3×#67—48no—
197C3×#67—48no—
198C3×#67—48no—
199C3×#67—48no—
200C2×C3×Dic3—24no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3—44no—
204C2×C3×Dic3C2414yes—
205C2×C3×Dic3C2414yes—
206C2×C3×Dic3C2414yes—
207C3×D12—44no—
208C3×C4×D3—48no—
209#560—316no—
210C2×#127—31no—
211C2×#126—32no—
212C2×#123—31no—
213C2×#123—32no—
214C2×#121—32no—
215C2×#121—32no—
216C2×#121—32no—
217C2×#120—32no—
218C2×#120C3×D311yescharacteristic, complemented
219C24×C3—22no—
220C24×C3—21no—
221C24×C3—24no—
222C24×C3—21no—
223C24×C3—32no—
224C24×C3—44no—
225C24×C3—42no—
226C24×C3—44no—
227C24×C3—42no—
228C24×C3—48no—
229C24×C3—44no—
230C24×C3C22×D312yes—
231C24×C3C22×D311yescharacteristic
232C24×C3C22×D311yescharacteristic
233C24×C3C22×D314yes—
234C24×C3C23×C312yes—
235C24×C3C23×C311yescharacteristic
236C24×C3C23×C311yescharacteristic
237C24×C3C23×C314yes—
238C23×D3C23×C312yes—
239C2×C3×D4—28no—
240C2×C3×D4—24no—
241C2×C3×D4—38no—
242C2×C3×D4—38no—
243C2×C3×D4—38no—
244C2×C3×D4—38no—
245C2×C3×D4—34no—
246C2×C3×D4—44no—
247C2×C3×D4—42no—
248C2×C3×D4—44no—
249C2×C3×D4—42no—
250C2×C3×D4—48no—
251C2×C3×D4—44no—
252C2×C3×D4—122no—
253C2×C3×D4—124no—
254C2×C3×D4—124no—
255C2×C3×D4—124no—
256C2×C3×D4—124no—
257C2×C3×D4C22×D318yes—
258C2×C3×D4C22×D314yes—
259C2×C3×D4C23×C314yes—
260C2×C3×D4C23×C318yes—
261C22×C3×C4—21no—
262C22×C3×C4—22no—
263C22×C3×C4—32no—
264C22×C3×C4—32no—
265C22×C3×C4—32no—
266C22×C3×C4—34no—
267C22×C3×C4—38no—
268C22×C3×C4—124no—
269C22×C3×C4—122no—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D312yes—
272C22×C3×C4C23×C311yescharacteristic
273C22×C3×C4C23×C312yes—
274C2×#67—44no—
275C2×#67—44no—
276C2×#67—44no—
277C2×#67—44no—
278C2×#67C23×C318yes—
279C2×#67C23×C318yes—
280C2×#67C23×C318yes—
281C2×#67C23×C318yescomplemented
282C22×Dic3—42no—
283C22×Dic3C23×C312yes—
284C22×Dic3C23×C312yes—
285C22×Dic3C23×C312yes—
286C22×Dic3C23×C314yescomplemented
287C2×D12—42no—
288C2×D12C23×C314yescomplemented
289C2×C4×D3—44no—
290C2×C4×D3C23×C318yescomplemented
291C3×C4⋊C4—38no—
292C3×C4⋊C4—38no—
293C3×C4⋊C4—38no—
294C3×C22⋊C4—28no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—38no—
297C3×C22⋊C4—38no—
298C3×C22⋊C4—38no—
299C3×C22⋊C4—34no—
300C3×C22⋊C4—38no—
301C3×C22⋊C4C22×D318yes—
302C3×C22⋊C4C22×D314yes—
303C3×C22⋊C4C23×C318yes—
304C3×C22⋊C4C23×C314yes—
305C3×C42—34no—
306#217C23×C318yes—
307#217C23×C318yes—
308#217C23×C318yes—
309#217C23×C314yescomplemented
310(C2×D3)⋊C4C23×C318yescomplemented
311C4⋊Dic3C23×C318yescomplemented
312Dic3⋊C4C23×C318yescomplemented
313Dic3⋊C4C23×C318yescomplemented
314C4×Dic3C23×C314yescomplemented
315C22×C32—24no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—24no—
319C22×C32—24no—
320C22×C32—24no—
321C22×C32—24no—
322C22×C32—416no—
323C22×C32—48no—
324C22×C32—44no—
325C22×C32—44no—
326C22×C32H(5,𝔽2)14yes—
327C22×C32H(5,𝔽2)12yes—
328C22×C32C2511yescharacteristic
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—48no—
333C32×C4—24no—
334C32×C4—22no—
335C3×Dic3—24no—
336C3×Dic3—24no—
337C3×Dic3—24no—
338C25C2×C3×D311yescharacteristic
339C22×D4—32no—
340C22×D4—32no—
341C22×D4—32no—
342C22×D4—32no—
343C22×D4—31no—
344C22×D4C2×C3×D312yes—
345C22×D4C2×C3×D311yescharacteristic
346C23×C4—31no—
347C23×C4—32no—
348#127—38no—
349#126—316no—
350#123—38no—
351#123—316no—
352#121—316no—
353#121—316no—
354#121—316no—
355#120—316no—
356#120C2×C3×D318yescomplemented
357C2×C4⋊C4—32no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—32no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—31no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4C2×C3×D312yes—
366C2×C22⋊C4C2×C3×D311yescharacteristic
367C2×C42—31no—
368C23×C3—28no—
369C23×C3—24no—
370C23×C3—22no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—22no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—22no—
384C23×C3—21no—
385C23×C3—24no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—34no—
389C23×C3—44no—
390C23×C3—44no—
391C23×C3—44no—
392C23×C3—42no—
393C23×C3—44no—
394C23×C3—48no—
395C23×C3—44no—
396C23×C3—48no—
397C23×C3—44no—
398C23×C3—416no—
399C23×C3—48no—
400C23×C3—432no—
401C23×C3—416no—
402C23×C3—416no—
403C23×C3—64no—
404C23×C3—64no—
405C23×C3—64no—
406C23×C3C23×D314yes—
407C23×C3C23×D312yes—
408C23×C3C23×D312yes—
409C23×C3C23×D311yescharacteristic
410C23×C3C24×C314yes—
411C23×C3C24×C312yes—
412C23×C3C24×C312yes—
413C23×C3C24×C311yescharacteristic
414C22×D3—24no—
415C22×D3—24no—
416C22×D3—24no—
417C22×D3C24×C314yes—
418C3×D4—48no—
419C3×D4—44no—
420C3×D4—48no—
421C3×D4—44no—
422C3×D4—416no—
423C3×D4—48no—
424C3×D4—124no—
425C3×D4—128no—
426C3×D4—128no—
427C3×D4—128no—
428C3×D4—128no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—24no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—24no—
435C2×C3×C4—34no—
436C2×C3×C4—34no—
437C2×C3×C4—34no—
438C2×C3×C4—44no—
439C2×C3×C4—42no—
440C2×C3×C4—64no—
441C2×C3×C4—64no—
442C2×C3×C4—64no—
443C2×C3×C4—128no—
444C2×C3×C4—124no—
445C2×C3×C4C23×D312yes—
446C2×C3×C4C23×D314yes—
447C2×C3×C4C24×C312yes—
448C2×C3×C4C24×C314yes—
449#67—48no—
450#67—48no—
451#67—48no—
452#67—48no—
453C2×Dic3—24no—
454C2×Dic3—24no—
455C2×Dic3—24no—
456C2×Dic3—44no—
457C2×Dic3C24×C314yes—
458C2×Dic3C24×C314yes—
459C2×Dic3C24×C314yes—
460D12—44no—
461C4×D3—48no—
462C2×C32—44no—
463C2×C32—42no—
464C2×C32—42no—
465C2×C32#56014yescomplemented
466C2×C32C2×H(5,𝔽2)12yes—
467C2×C32C2×H(5,𝔽2)11yescharacteristic
468C3×D3—44no—
469C24—32no—
470C24—44no—
471C24—42no—
472C24C22×C3×D312yes—
473C24C22×C3×D311yescharacteristic
474C24C22×C3×D311yescharacteristic
475C24C22×C3×D314yes—
476C2×D4—38no—
477C2×D4—38no—
478C2×D4—38no—
479C2×D4—38no—
480C2×D4—34no—
481C2×D4—44no—
482C2×D4—42no—
483C2×D4—122no—
484C2×D4—124no—
485C2×D4—124no—
486C2×D4—124no—
487C2×D4—124no—
488C2×D4C22×C3×D318yes—
489C2×D4C22×C3×D314yes—
490C22×C4—32no—
491C22×C4—32no—
492C22×C4—32no—
493C22×C4—34no—
494C22×C4—38no—
495C22×C4—124no—
496C22×C4—122no—
497C22×C4C22×C3×D311yescharacteristic
498C22×C4C22×C3×D312yes—
499C4⋊C4—38no—
500C4⋊C4—38no—
501C4⋊C4—38no—
502C22⋊C4—38no—
503C22⋊C4—38no—
504C22⋊C4—38no—
505C22⋊C4—34no—
506C22⋊C4—38no—
507C22⋊C4C22×C3×D318yes—
508C22⋊C4C22×C3×D314yes—
509C42—34no—
510C22×C3—28no—
511C22×C3—24no—
512C22×C3—22no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—22no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—22no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—24no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—22no—
526C22×C3—24no—
527C22×C3—22no—
528C22×C3—21no—
529C22×C3—44no—
530C22×C3—44no—
531C22×C3—44no—
532C22×C3—42no—
533C22×C3—44no—
534C22×C3—416no—
535C22×C3—48no—
536C22×C3—432no—
537C22×C3—416no—
538C22×C3—416no—
539C22×C3—48no—
540C22×C3—44no—
541C22×C3—44no—
542C22×C3—48no—
543C22×C3—44no—
544C22×C3—44no—
545C22×C3—64no—
546C22×C3—64no—
547C22×C3—64no—
548C22×C3—84no—
549C22×C3—128no—
550C22×C3#100414yes—
551C22×C3#100412yes—
552C22×C3C3×H(5,𝔽2)14yes—
553C22×C3C3×H(5,𝔽2)12yes—
554C22×C3C24×D311yescharacteristic
555C22×C3C25×C311yescharacteristic
556C2×D3—24no—
557C2×D3—24no—
558C2×D3—24no—
559C2×D3—48no—
560C3×C4—24no—
561C3×C4—22no—
562C3×C4—24no—
563C3×C4—22no—
564C3×C4—44no—
565C3×C4—42no—
566C3×C4—64no—
567C3×C4—64no—
568C3×C4—64no—
569Dic3—24no—
570Dic3—24no—
571Dic3—24no—
572C32C2×#56011yescharacteristic, complemented, Sylow
573C23—22no—
574C23—24no—
575C23—24no—
576C23—22no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—34no—
581C23—48no—
582C23—44no—
583C23—416no—
584C23—64no—
585C23—64no—
586C23—64no—
587C23C23×C3×D314yes—
588C23C23×C3×D312yes—
589C23C23×C3×D312yes—
590C23C23×C3×D311yescharacteristic
591D4—48no—
592D4—44no—
593D4—124no—
594D4—128no—
595D4—128no—
596D4—128no—
597D4—128no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—34no—
601C2×C4—34no—
602C2×C4—34no—
603C2×C4—64no—
604C2×C4—64no—
605C2×C4—64no—
606C2×C4—128no—
607C2×C4—124no—
608C2×C4C23×C3×D312yes—
609C2×C4C23×C3×D314yes—
610C2×C3—24no—
611C2×C3—22no—
612C2×C3—21no—
613C2×C3—48no—
614C2×C3—44no—
615C2×C3—44no—
616C2×C3—42no—
617C2×C3—42no—
618C2×C3—44no—
619C2×C3—42no—
620C2×C3—42no—
621C2×C3—82no—
622C2×C3—124no—
623C2×C3#559514yesdirect product factor
624C2×C3C3×#56014yescomplemented
625C2×C3C2×#100412yes—
626C2×C3C2×#100411yescharacteristic
627C2×C3C2×C3×H(5,𝔽2)12yes—
628C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
629D3—44no—
630C22—22no—
631C22—24no—
632C22—24no—
633C22—22no—
634C22—24no—
635C22—24no—
636C22—24no—
637C22—416no—
638C22—48no—
639C22—44no—
640C22—44no—
641C22—64no—
642C22—64no—
643C22—64no—
644C22—128no—
645C22C3×#100414yes—
646C22C3×#100412yes—
647C22C24×C3×D311yescharacteristic
648C4—24no—
649C4—22no—
650C4—64no—
651C4—64no—
652C4—64no—
653C3—21no—
654C3C2×#559511yescharacteristic, direct product factor
655C3C2×C3×#56011yescharacteristic, complemented
656C2—44no—
657C2—42no—
658C2—42no—
659C2—124no—
660C2C3×#559514yesdirect product factor
661C2C2×C3×#100412yes—
662C2C2×C3×#100411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#120C2
socleC23×C32C24
hypercenterC2×C3×#120D3
hypocenterC3C2×C3×#560
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
1. C2×C32×#120C2semidirect
2. C2×C3×#953C2semidirect
3. C2×C3×#940C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#938C2semidirect
6. C2×C3×#935C2semidirect
7. C3×#5595C2direct (N × H)
8. C2×C3×#884C2semidirect
9. C2×C3×#883C2semidirect
10. C2×C3×#879C2semidirect
12. C2×#5595C3direct (N × H)
19. C22×C3×#67C22semidirect
20. C23×C3×Dic3C22semidirect
21. C22×C3×D12C22semidirect
22. C22×C3×C4×D3C22semidirect
23. C32×#120C22semidirect
26. C3×#953C22semidirect
30. C2×C3×#217C22semidirect
31. C3×#940C22semidirect
32. C3×#939C22semidirect
33. C3×#938C22semidirect
34. C3×#935C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C3×#884C22semidirect
41. C3×#883C22semidirect
42. C3×#879C22semidirect
53. C2×C3×#120D3semidirect
54. C2×C3×#120C2×C3semidirect
55. C2×#953C2×C3semidirect
56. C2×#940C2×C3semidirect
57. C2×#939C2×C3semidirect
58. C2×#938C2×C3semidirect
59. C2×#935C2×C3semidirect
60. #5595C2×C3direct (N × H)
61. C2×#884C2×C3semidirect
62. C2×#883C2×C3semidirect
63. C2×#879C2×C3semidirect
84. C2×C3×#67C23semidirect
89. C22×C3×Dic3C23semidirect
91. C2×C3×D12C23semidirect
93. C2×C3×C4×D3C23semidirect
99. C3×#217C23semidirect
100. C3×(C2×D3)⋊C4C23semidirect
101. C3×C4⋊Dic3C23semidirect
102. C3×Dic3⋊C4C23semidirect
103. C3×Dic3⋊C4C23semidirect
104. C3×C4×Dic3C23semidirect
125. C22×#67C22×C3semidirect
126. C23×Dic3C22×C3semidirect
127. C22×D12C22×C3semidirect
128. C22×C4×D3C22×C3semidirect
138. C3×#120C2×D3semidirect
139. C3×#120C22×C3semidirect
155. #953C22×C3semidirect
159. C2×#217C22×C3semidirect
160. #940C22×C3semidirect
161. #939C22×C3semidirect
162. #938C22×C3semidirect
163. #935C22×C3semidirect
164. C2×(C2×D3)⋊C4C22×C3semidirect
165. C2×C4⋊Dic3C22×C3semidirect
166. C2×Dic3⋊C4C22×C3semidirect
167. C2×Dic3⋊C4C22×C3semidirect
168. C2×C4×Dic3C22×C3semidirect
169. #884C22×C3semidirect
170. #883C22×C3semidirect
171. #879C22×C3semidirect
218. C2×#120C3×D3semidirect
281. C2×#67C23×C3semidirect
286. C22×Dic3C23×C3semidirect
288. C2×D12C23×C3semidirect
290. C2×C4×D3C23×C3semidirect
309. #217C23×C3semidirect
310. (C2×D3)⋊C4C23×C3semidirect
311. C4⋊Dic3C23×C3semidirect
312. Dic3⋊C4C23×C3semidirect
313. Dic3⋊C4C23×C3semidirect
314. C4×Dic3C23×C3semidirect
356. #120C2×C3×D3semidirect
465. C2×C32#560semidirect
572. C32C2×#560semidirect
623. C2×C3#5595direct (N × H)
624. C2×C3C3×#560semidirect
654. C3C2×#5595direct (N × H)
655. C3C2×C3×#560semidirect
660. C2C3×#5595direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1202
C2×C3×#9532
C2×C3×#9402
C2×C3×#9392
C2×C3×#9382
C2×C3×#9352
C3×#55952
C2×C3×#8842
C2×C3×#8832
C2×C3×#8792
C2×C3×#5603
C2×#55953