Finite Group Databasebeta

← C2×C3×#5689 #11901892

Subgroups — C2×C3×#5689 #11901892

Order 1152.

2273 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#125C211yesmaximal, characteristic, complemented
2C3×#5689C2116yesmaximal, direct product factor
3C2×C3×#897C212yesmaximal
4C2×C3×#896C212yesmaximal
5C2×C3×#892C211yesmaximal, characteristic
6C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
7C2×C3×#890C211yesmaximal, characteristic, complemented
8C2×C3×#889C212yesmaximal, complemented
9C2×C3×#888C212yesmaximal, complemented
10C2×C3×#888C211yesmaximal, characteristic, complemented
11C2×C3×#872C211yesmaximal, characteristic
12C2×C3×#869C211yesmaximal, characteristic, complemented
13C2×C3×#544—31nomaximal
14C2×#5689C311yesmaximal, characteristic, direct product factor
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6C2212yes—
18C22×C3×Dic6C2212yes—
19C32×#125C2218yescomplemented
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2212yes—
22C2×C32×C4⋊C4C2212yes—
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×C4×Dic3C2212yes—
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#897C22116yes—
40C3×#896C22116yes—
41C3×#892C2218yes—
42C3×D3×C4⋊C4C2218yes—
43C3×#890C2218yescomplemented
44C3×#889C22116yescomplemented
45C3×#888C22116yescomplemented
46C3×#888C2218yescomplemented
47C3×#872C2218yes—
48C3×#869C2218yescomplemented
49C3×#544—316no—
50C2×C3×C4⋊Q8—32no—
51C2×C3×C4⋊Q8—31no—
52C2×C3×C4⋊Q8—31no—
53C2×C3×#125—21no—
54C2×C3×#125—32no—
55C2×C3×#125—31no—
56C2×C3×#125D311yescharacteristic, complemented
57C2×C3×#125C2×C311yescharacteristic, complemented
58C2×C3×C22⋊Q8—32no—
59C2×C3×C22⋊Q8—32no—
60C2×C3×#117—31no—
61C2×C3×#117—31no—
62C22×C3×C4⋊C4—31no—
63#5689C2×C3116yesdirect product factor
64C2×#897C2×C312yes—
65C2×#896C2×C312yes—
66C2×#892C2×C311yescharacteristic
67C2×D3×C4⋊C4C2×C311yescharacteristic
68C2×#890C2×C311yescharacteristic, complemented
69C2×#889C2×C312yescomplemented
70C2×#888C2×C311yescharacteristic, complemented
71C2×#888C2×C312yescomplemented
72C2×#872C2×C311yescharacteristic
73C2×#869C2×C311yescharacteristic, complemented
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C2×C3×C4×D3—44no—
86C2×C3×C4×D3Q818yescomplemented
87C2×C3×C4×D3C2318yes—
88C2×C3×C4×D3C2314yes—
89C2×C3×Dic6—44no—
90C2×C3×Dic6—44no—
91C2×C3×Dic6C2318yes—
92C2×C3×Dic6C2318yes—
93C32×C4⋊C4C2314yes—
94C32×C4⋊C4C2318yes—
95C32×C4⋊C4C2318yes—
96C32×C4⋊C4C2314yes—
97C32×C42C2314yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×(C2×D3)⋊C4C2314yes—
100C3×(C2×D3)⋊C4C2314yes—
101C3×C4⋊Dic3C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2314yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2314yes—
109C3×Dic3⋊C4C2318yes—
110C3×C4×Dic3C2318yes—
111C3×C4×Dic3C2314yes—
112C2×#544—31noSylow
113C22×C3×Q8—32no—
114C22×C3×Q8—32no—
115C23×C3×C4—31no—
116C23×C3×C4—32no—
117C22×C4×D3C22×C312yes—
118C22×C4×D3C22×C311yescharacteristic
119C22×Dic6C22×C312yes—
120C22×Dic6C22×C312yes—
121C3×C4⋊Q8—316no—
122C3×C4⋊Q8—38no—
123C3×C4⋊Q8—38no—
124C3×#125—28no—
125C3×#125—316no—
126C3×#125—38no—
127C3×#125C2×D318yescomplemented
128C3×#125C22×C318yescomplemented
129C3×C22⋊Q8—316no—
130C3×C22⋊Q8—316no—
131C3×#117—38no—
132C3×#117—38no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—22no—
136C2×C3×C4⋊C4—22no—
137C2×C3×C4⋊C4—32no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—32no—
141C2×C3×C4⋊C4—32no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—32no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4—38no—
147C2×C3×C4⋊C4C2×D311yescharacteristic
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D312yes—
150C2×C3×C4⋊C4C2×D312yes—
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C4⋊C4C22×C312yes—
153C2×C3×C4⋊C4C22×C312yes—
154C2×C3×C4⋊C4C22×C311yescharacteristic
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C42—21no—
159C2×C3×C42—32no—
160C2×C3×C42—31no—
161C2×C3×C42C2×D311yescharacteristic
162C2×C3×C42C22×C311yescharacteristic
163C2×(C2×D3)⋊C4C22×C311yescharacteristic
164C2×(C2×D3)⋊C4C22×C311yescharacteristic
165C2×(C2×D3)⋊C4C22×C312yes—
166C2×C4⋊Dic3C22×C311yescharacteristic
167C2×C4⋊Dic3C22×C312yes—
168C2×C4⋊Dic3C22×C311yescharacteristic
169C2×C4⋊Dic3C22×C312yes—
170C2×Dic3⋊C4C22×C311yescharacteristic
171C2×Dic3⋊C4C22×C311yescharacteristic
172C2×Dic3⋊C4C22×C312yes—
173C2×Dic3⋊C4C22×C312yes—
174C2×Dic3⋊C4C22×C312yes—
175C2×C4×Dic3C22×C311yescharacteristic
176C2×C4×Dic3C22×C312yes—
177#897C22×C3116yes—
178#896C22×C3116yes—
179#892C22×C318yes—
180D3×C4⋊C4C22×C318yes—
181#890C22×C318yescomplemented
182#889C22×C3116yescomplemented
183#888C22×C318yescomplemented
184#888C22×C3116yescomplemented
185#872C22×C318yes—
186#869C22×C318yescomplemented
187C23×C32C2411yescharacteristic
188C22×C3×D3—22no—
189C22×C3×D3—22no—
190C22×C3×D3C2×Q814yes—
191C22×C3×D3C2412yes—
192C2×C32×C4—22no—
193C2×C32×C4—24no—
194C2×C32×C4—24no—
195C2×C32×C4—22no—
196C2×C32×C4C2×Q814yes—
197C2×C32×C4C2414yes—
198C2×C32×C4C2414yes—
199C2×C32×C4C2412yes—
200C2×C32×C4C2412yes—
201C2×C32×C4C2412yes—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3C2×Q814yes—
207C2×C3×Dic3C2412yes—
208C2×C3×Dic3C2414yes—
209C2×C3×Dic3C2412yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2412yes—
212C3×C4×D3—48no—
213C3×C4×D3C2×Q8116yescomplemented
214C3×Dic6—48no—
215C3×Dic6—48no—
216#544—316no—
217C2×C4⋊Q8—32no—
218C2×C4⋊Q8—31no—
219C2×C4⋊Q8—31no—
220C2×#125—32no—
221C2×#125—31no—
222C2×#125C3×D311yescharacteristic, complemented
223C2×C22⋊Q8—32no—
224C2×C22⋊Q8—32no—
225C2×#117—31no—
226C2×#117—31no—
227C22×C4⋊C4—31no—
228C24×C3—31no—
229C23×D3C23×C311yescharacteristic
230C2×C3×Q8—38no—
231C2×C3×Q8—38no—
232C2×C3×Q8—124no—
233C2×C3×Q8—124no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—31no—
240C22×C3×C4—38no—
241C22×C3×C4—34no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—38no—
247C22×C3×C4—124no—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D312yes—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C23×C312yes—
254C22×C3×C4C23×C312yes—
255C22×C3×C4C23×C311yescharacteristic
256C22×C3×C4C23×C311yescharacteristic
257C22×C3×C4C23×C311yescharacteristic
258C22×Dic3C23×C311yescharacteristic
259C22×Dic3C23×C311yescharacteristic
260C22×Dic3C23×C312yes—
261C22×Dic3C23×C312yes—
262C22×Dic3C23×C311yescharacteristic
263C2×C4×D3—44no—
264C2×C4×D3C3×Q818yescomplemented
265C2×C4×D3C23×C318yes—
266C2×C4×D3C23×C314yes—
267C2×Dic6—44no—
268C2×Dic6—44no—
269C2×Dic6C23×C318yes—
270C2×Dic6C23×C318yes—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—28no—
274C3×C4⋊C4—28no—
275C3×C4⋊C4—38no—
276C3×C4⋊C4—34no—
277C3×C4⋊C4—34no—
278C3×C4⋊C4—38no—
279C3×C4⋊C4—38no—
280C3×C4⋊C4—34no—
281C3×C4⋊C4—34no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—38no—
284C3×C4⋊C4C22×D314yes—
285C3×C4⋊C4C22×D314yes—
286C3×C4⋊C4C22×D318yes—
287C3×C4⋊C4C22×D318yes—
288C3×C4⋊C4C23×C314yes—
289C3×C4⋊C4C23×C318yes—
290C3×C4⋊C4C23×C318yes—
291C3×C4⋊C4C23×C314yes—
292C3×C22⋊C4—34no—
293C3×C22⋊C4—38no—
294C3×C22⋊C4—34no—
295C3×C42—24no—
296C3×C42—38no—
297C3×C42—34no—
298C3×C42C22×D314yes—
299C3×C42C23×C314yes—
300(C2×D3)⋊C4C23×C314yes—
301(C2×D3)⋊C4C23×C314yes—
302(C2×D3)⋊C4C23×C318yes—
303C4⋊Dic3C23×C314yes—
304C4⋊Dic3C23×C318yes—
305C4⋊Dic3C23×C314yes—
306C4⋊Dic3C23×C318yes—
307Dic3⋊C4C23×C314yes—
308Dic3⋊C4C23×C314yes—
309Dic3⋊C4C23×C318yes—
310Dic3⋊C4C23×C318yes—
311Dic3⋊C4C23×C318yes—
312C4×Dic3C23×C314yes—
313C4×Dic3C23×C318yes—
314C22×C32C22×Q812yes—
315C22×C32H(5,𝔽2)12yes—
316C22×C322−1+412yes—
317C22×C32C2511yescharacteristic
318C2×C3×D3—28no—
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3C22×Q814yes—
322C32×C4—22no—
323C32×C4—24no—
324C32×C4—24no—
325C32×C4—22no—
326C32×C4C22×Q814yes—
327C3×Dic3—22no—
328C3×Dic3—24no—
329C3×Dic3—24no—
330C3×Dic3—22no—
331C3×Dic3C22×Q814yes—
332C22×Q8—32no—
333C22×Q8—32no—
334C23×C4—31no—
335C23×C4—32no—
336C4⋊Q8—316no—
337C4⋊Q8—38no—
338C4⋊Q8—38no—
339#125—316no—
340#125—38no—
341#125C2×C3×D318yescomplemented
342C22⋊Q8—316no—
343C22⋊Q8—316no—
344#117—38no—
345#117—38no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—32no—
352C2×C4⋊C4—32no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4—38no—
356C2×C4⋊C4C2×C3×D311yescharacteristic
357C2×C4⋊C4C2×C3×D311yescharacteristic
358C2×C4⋊C4C2×C3×D312yes—
359C2×C4⋊C4C2×C3×D312yes—
360C2×C22⋊C4—31no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—31no—
363C2×C42—32no—
364C2×C42—31no—
365C2×C42C2×C3×D311yescharacteristic
366C23×C3—21no—
367C23×C3—34no—
368C23×C3—32no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3C23×D311yescharacteristic
372C23×C3C24×C311yescharacteristic
373C22×D3—22no—
374C22×D3—22no—
375C22×D3C2×C3×Q814yes—
376C22×D3C24×C312yes—
377C3×Q8—128no—
378C3×Q8—128no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—34no—
394C2×C3×C4—32no—
395C2×C3×C4—316no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—34no—
399C2×C3×C4—34no—
400C2×C3×C4—44no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—44no—
404C2×C3×C4—64no—
405C2×C3×C4—62no—
406C2×C3×C4—64no—
407C2×C3×C4—62no—
408C2×C3×C4—128no—
409C2×C3×C4D3×Q814yes—
410C2×C3×C4C2×C3×Q814yes—
411C2×C3×C4C23×D314yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D314yes—
415C2×C3×C4C23×D312yes—
416C2×C3×C4C24×C314yes—
417C2×C3×C4C24×C314yes—
418C2×C3×C4C24×C312yes—
419C2×C3×C4C24×C312yes—
420C2×C3×C4C24×C312yes—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—22no—
425C2×Dic3C2×C3×Q814yes—
426C2×Dic3C24×C312yes—
427C2×Dic3C24×C312yes—
428C2×Dic3C24×C314yes—
429C2×Dic3C24×C314yes—
430C2×Dic3C24×C312yes—
431C4×D3—48no—
432C4×D3C2×C3×Q8116yescomplemented
433Dic6—48no—
434Dic6—48no—
435C2×C32#54414yescomplemented
436C2×C32C23×Q811yescharacteristic
437C2×C32C2×H(5,𝔽2)11yescharacteristic
438C2×C32C2×2−1+411yescharacteristic
439C3×D3—24no—
440C24—31no—
441C2×Q8—38no—
442C2×Q8—38no—
443C2×Q8—124no—
444C2×Q8—124no—
445C22×C4—31no—
446C22×C4—34no—
447C22×C4—38no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—32no—
451C22×C4—32no—
452C22×C4—38no—
453C22×C4—124no—
454C22×C4C22×C3×D312yes—
455C22×C4C22×C3×D311yescharacteristic
456C22×C4C22×C3×D311yescharacteristic
457C22×C4C22×C3×D312yes—
458C22×C4C22×C3×D311yescharacteristic
459C4⋊C4—38no—
460C4⋊C4—34no—
461C4⋊C4—34no—
462C4⋊C4—34no—
463C4⋊C4—34no—
464C4⋊C4—38no—
465C4⋊C4—38no—
466C4⋊C4—38no—
467C4⋊C4—38no—
468C4⋊C4C22×C3×D314yes—
469C4⋊C4C22×C3×D314yes—
470C4⋊C4C22×C3×D318yes—
471C4⋊C4C22×C3×D318yes—
472C22⋊C4—34no—
473C22⋊C4—38no—
474C22⋊C4—34no—
475C42—38no—
476C42—34no—
477C42C22×C3×D314yes—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—34no—
483C22×C3—68no—
484C22×C3—62no—
485C22×C3—62no—
486C22×C3C2×D3×Q812yes—
487C22×C3#100912yes—
488C22×C3#101012yes—
489C22×C3C22×C3×Q812yes—
490C22×C3C3×H(5,𝔽2)12yes—
491C22×C3C3×2−1+412yes—
492C22×C3C24×D311yescharacteristic
493C22×C3C25×C311yescharacteristic
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—28no—
497C2×D3C22×C3×Q814yes—
498C3×C4—24no—
499C3×C4—22no—
500C3×C4—24no—
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—24no—
504C3×C4—24no—
505C3×C4—22no—
506C3×C4—24no—
507C3×C4—34no—
508C3×C4—44no—
509C3×C4—42no—
510C3×C4—42no—
511C3×C4—44no—
512C3×C4—64no—
513C3×C4—62no—
514C3×C4—64no—
515C3×C4—62no—
516C3×C4C2×D3×Q814yes—
517C3×C4C22×C3×Q814yes—
518Dic3—22no—
519Dic3—24no—
520Dic3—24no—
521Dic3—22no—
522Dic3C22×C3×Q814yes—
523C32C2×#54411yescharacteristic, complemented, Sylow
524C23—34no—
525C23—32no—
526C23—62no—
527C23—62no—
528C23C23×C3×D311yescharacteristic
529Q8—128no—
530Q8—128no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—34no—
536C2×C4—32no—
537C2×C4—316no—
538C2×C4—32no—
539C2×C4—32no—
540C2×C4—34no—
541C2×C4—34no—
542C2×C4—64no—
543C2×C4—62no—
544C2×C4—64no—
545C2×C4—62no—
546C2×C4—128no—
547C2×C4C3×D3×Q814yes—
548C2×C4C23×C3×D314yes—
549C2×C4C23×C3×D312yes—
550C2×C4C23×C3×D312yes—
551C2×C4C23×C3×D314yes—
552C2×C4C23×C3×D312yes—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—24no—
557C2×C3—64no—
558C2×C3#568914yesdirect product factor
559C2×C3C3×#54414yescomplemented
560C2×C3C22×D3×Q811yescharacteristic
561C2×C3C2×#100911yescharacteristic
562C2×C3C2×#101011yescharacteristic
563C2×C3C23×C3×Q811yescharacteristic
564C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
565C2×C3C2×C3×2−1+411yescharacteristic
566D3—24no—
567C22—34no—
568C22—62no—
569C22—62no—
570C22—68no—
571C22C2×C3×D3×Q812yes—
572C22C3×#100912yes—
573C22C3×#101012yes—
574C22C24×C3×D311yescharacteristic
575C4—24no—
576C4—22no—
577C4—24no—
578C4—22no—
579C4—34no—
580C4—64no—
581C4—62no—
582C4—64no—
583C4—62no—
584C4C2×C3×D3×Q814yes—
585C3—21no—
586C3C2×#568911yescharacteristic, direct product factor
587C3C2×C3×#54411yescharacteristic, complemented
588C2—64no—
589C2C3×#568914yesdirect product factor
590C2C22×C3×D3×Q811yescharacteristic
591C2C2×C3×#100911yescharacteristic
592C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#125C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C3×#125D3
hypocenterC3C2×C3×#544
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#125

Complements

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

NH ≅ G/Ntype
1. C2×C32×#125C2semidirect
2. C3×#5689C2direct (N × H)
7. C2×C3×#890C2semidirect
8. C2×C3×#889C2semidirect
9. C2×C3×#888C2semidirect
10. C2×C3×#888C2semidirect
12. C2×C3×#869C2semidirect
14. C2×#5689C3direct (N × H)
19. C32×#125C22semidirect
43. C3×#890C22semidirect
44. C3×#889C22semidirect
45. C3×#888C22semidirect
46. C3×#888C22semidirect
48. C3×#869C22semidirect
56. C2×C3×#125D3semidirect
57. C2×C3×#125C2×C3semidirect
63. #5689C2×C3direct (N × H)
68. C2×#890C2×C3semidirect
69. C2×#889C2×C3semidirect
70. C2×#888C2×C3semidirect
71. C2×#888C2×C3semidirect
73. C2×#869C2×C3semidirect
86. C2×C3×C4×D3Q8semidirect
127. C3×#125C2×D3semidirect
128. C3×#125C22×C3semidirect
181. #890C22×C3semidirect
182. #889C22×C3semidirect
183. #888C22×C3semidirect
184. #888C22×C3semidirect
186. #869C22×C3semidirect
213. C3×C4×D3C2×Q8semidirect
222. C2×#125C3×D3semidirect
264. C2×C4×D3C3×Q8semidirect
341. #125C2×C3×D3semidirect
432. C4×D3C2×C3×Q8semidirect
435. C2×C32#544semidirect
523. C32C2×#544semidirect
558. C2×C3#5689direct (N × H)
559. C2×C3C3×#544semidirect
586. C3C2×#5689direct (N × H)
587. C3C2×C3×#544semidirect
589. C2C3×#5689direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1252
C3×#56892
C2×C3×#8972
C2×C3×#8962
C2×C3×#8922
C2×C3×D3×C4⋊C42
C2×C3×#8902
C2×C3×#8892
C2×C3×#8882
C2×C3×#8722
C2×C3×#8692
C2×C3×#5443
C2×#56893