Finite Group Databasebeta

← C2×C3×#5597 #11901123

Subgroups — C2×C3×#5597 #11901123

Order 1152.

3493 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C212yesmaximal, complemented
2C2×C32×#121C211yesmaximal, characteristic, complemented
3C2×C3×#939C212yesmaximal, complemented
4C2×C3×#939C212yesmaximal, complemented
5C2×C3×#930C211yesmaximal, characteristic, complemented
6C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C3×#5597C2116yesmaximal, direct product factor
8C2×C3×#896C212yesmaximal, complemented
9C2×C3×#884C212yesmaximal, complemented
10C2×C3×#878C212yesmaximal, complemented
11C2×C3×#537—31nomaximal
12C2×#5597C311yesmaximal, characteristic, direct product factor
13C22×C32×D4C2212yes—
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yes—
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C2×C3×#237—216no—
23C2×C3×#237C22116yescomplemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2212yes—
26C22×C3×Dic6C2212yes—
27C32×#121C2218yescomplemented
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2212yes—
30C2×C3×#217C2212yes—
31C3×#939C22116yescomplemented
32C3×#939C22116yescomplemented
33C3×#930C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×Dic3⋊C4C2212yes—
40C2×C3×Dic3⋊C4C2218yescomplemented
41C3×#896C22116yescomplemented
42C3×#884C22116yescomplemented
43C3×#878C22116yescomplemented
44C22×C3×#41—32no—
45C22×#237C2×C312yescomplemented
46C3×#537—316no—
47C2×C3×C22⋊Q8—32no—
48C2×C3×C22⋊Q8—32no—
49C2×C3×#121—21no—
50C2×C3×#121—32no—
51C2×C3×#121—32no—
52C2×C3×#121—31no—
53C2×C3×#121—32no—
54C2×C3×#121D311yescharacteristic, complemented
55C2×C3×#121C2×C311yescharacteristic, complemented
56C22×C3×C4⋊C4—31no—
57C2×#939C2×C312yescomplemented
58C2×#939C2×C312yescomplemented
59C2×#930C2×C311yescharacteristic, complemented
60C22×Dic3⋊C4C2×C311yescharacteristic, complemented
61#5597C2×C3116yesdirect product factor
62C2×#896C2×C312yescomplemented
63C2×#884C2×C312yescomplemented
64C2×#878C2×C312yescomplemented
65C24×C32C2312yes—
66C24×C32C2311yescharacteristic
67C23×C3×D3C2312yes—
68C2×C32×D4—28no—
69C2×C32×D4—42no—
70C2×C32×D4C2318yes—
71C2×C32×D4C2314yes—
72C22×C32×C4—42no—
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2314yes—
77C2×C3×#67—28no—
78C2×C3×#67—28no—
79C2×C3×#67—44no—
80C2×C3×#67C2318yes—
81C2×C3×#67C2318yes—
82C2×C3×#67C2318yes—
83C22×C3×Dic3—28no—
84C22×C3×Dic3—42no—
85C22×C3×Dic3D418yescomplemented
86C22×C3×Dic3C2318yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2314yes—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2314yes—
92C3×#237—264no—
93C2×C3×D12—42no—
94C2×C3×D12C2314yes—
95C2×C3×C4×D3—28no—
96C2×C3×C4×D3C2318yes—
97C2×C3×Dic6—28no—
98C2×C3×Dic6C2318yes—
99C32×C4⋊C4C2314yes—
100C32×C22⋊C4C2318yes—
101C3×#217C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2318yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C2×#537—31noSylow
109C2×C3×#41—316no—
110C2×C3×#41—616no—
111C22×C3×Q8—32no—
112C22×C3×D4—22no—
113C22×C3×D4—21no—
114C22×C3×D4—32no—
115C22×C3×D4—32no—
116C22×C3×D4—32no—
117C22×C3×D4—31no—
118C22×C3×D4C2×D312yes—
119C22×C3×D4C2×D311yescharacteristic
120C22×C3×D4C22×C312yes—
121C22×C3×D4C22×C311yescharacteristic
122C23×C3×C4—21no—
123C23×C3×C4—31no—
124C23×C3×C4—32no—
125C23×C3×C4—31no—
126C23×C3×C4—32no—
127C23×C3×C4C2×D311yescharacteristic
128C23×C3×C4C22×C311yescharacteristic
129C22×#67C22×C312yes—
130C22×#67C22×C312yes—
131C22×#67C22×C312yes—
132C23×Dic3C22×C312yes—
133C23×Dic3C22×C311yescharacteristic
134C23×Dic3C22×C311yescharacteristic
135C2×#237—216no—
136C2×#237C22×C3116yescomplemented
137C22×D12C22×C311yescharacteristic
138C22×C4×D3C22×C312yes—
139C22×Dic6C22×C312yes—
140C3×C22⋊Q8—316no—
141C3×C22⋊Q8—316no—
142C3×#121—28no—
143C3×#121—316no—
144C3×#121—316no—
145C3×#121—38no—
146C3×#121—316no—
147C3×#121C2×D318yescomplemented
148C3×#121C22×C318yescomplemented
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—32no—
152C2×C3×C4⋊C4—32no—
153C2×C3×C4⋊C4—38no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C22×C311yescharacteristic
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—32no—
159C2×C3×C22⋊C4—32no—
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4C2×D312yes—
162C2×C3×C22⋊C4C22×C312yes—
163C2×#217C22×C312yes—
164#939C22×C3116yescomplemented
165#939C22×C3116yescomplemented
166#930C22×C318yescomplemented
167C2×(C2×D3)⋊C4C22×C312yes—
168C2×(C2×D3)⋊C4C22×C312yes—
169C2×C4⋊Dic3C22×C311yescharacteristic
170C2×Dic3⋊C4C22×C312yes—
171C2×Dic3⋊C4C22×C312yes—
172C2×Dic3⋊C4C22×C312yes—
173C2×Dic3⋊C4C22×C318yescomplemented
174#896C22×C3116yescomplemented
175#884C22×C3116yescomplemented
176#878C22×C3116yescomplemented
177C23×C32—22no—
178C23×C32—22no—
179C23×C32—24no—
180C23×C32—24no—
181C23×C32—24no—
182C23×C32C2×D414yes—
183C23×C32C2414yes—
184C23×C32C2412yes—
185C23×C32C2411yescharacteristic
186C22×C3×D3—24no—
187C22×C3×D3—24no—
188C22×C3×D3—24no—
189C22×C3×D3C2414yes—
190C32×D4—216no—
191C32×D4—44no—
192C2×C32×C4—22no—
193C2×C32×C4—24no—
194C2×C32×C4—22no—
195C2×C32×C4—44no—
196C2×C32×C4C2412yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2414yes—
199C3×#67—216no—
200C3×#67—216no—
201C3×#67—48no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—216no—
205C2×C3×Dic3—44no—
206C2×C3×Dic3C2×D418yes—
207C2×C3×Dic3C2×D4116yescomplemented
208C2×C3×Dic3C2414yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2414yes—
211C3×D12—44no—
212C3×C4×D3—216no—
213C3×Dic6—216no—
214C22×#41—32no—
215#537—316no—
216C2×C22⋊Q8—32no—
217C2×C22⋊Q8—32no—
218C2×#121—32no—
219C2×#121—32no—
220C2×#121—31no—
221C2×#121—32no—
222C2×#121C3×D311yescharacteristic, complemented
223C22×C4⋊C4—31no—
224C24×C3—21no—
225C24×C3—22no—
226C24×C3—32no—
227C24×C3C22×D312yes—
228C24×C3C22×D311yescharacteristic
229C24×C3C23×C312yes—
230C24×C3C23×C311yescharacteristic
231C23×D3C23×C312yes—
232C3×#41—664no—
233C2×C3×Q8—38no—
234C2×C3×Q8—68no—
235C2×C3×D4—28no—
236C2×C3×D4—28no—
237C2×C3×D4—28no—
238C2×C3×D4—24no—
239C2×C3×D4—38no—
240C2×C3×D4—38no—
241C2×C3×D4—38no—
242C2×C3×D4—34no—
243C2×C3×D4—48no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—44no—
247C2×C3×D4—68no—
248C2×C3×D4—68no—
249C2×C3×D4—122no—
250C2×C3×D4—124no—
251C2×C3×D4C22×D318yes—
252C2×C3×D4C22×D314yes—
253C2×C3×D4C23×C318yes—
254C2×C3×D4C23×C314yes—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—24no—
259C22×C3×C4—38no—
260C22×C3×C4—34no—
261C22×C3×C4—32no—
262C22×C3×C4—38no—
263C22×C3×C4—32no—
264C22×C3×C4—32no—
265C22×C3×C4—34no—
266C22×C3×C4—38no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—44no—
270C22×C3×C4—68no—
271C22×C3×C4—68no—
272C22×C3×C4—122no—
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D312yes—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D314yes—
277C22×C3×C4C23×C311yescharacteristic
278C22×C3×C4C23×C311yescharacteristic
279C22×C3×C4C23×C312yes—
280C22×C3×C4C23×C314yes—
281C2×#67—28no—
282C2×#67—28no—
283C2×#67—44no—
284C2×#67C23×C318yes—
285C2×#67C23×C318yes—
286C2×#67C23×C318yes—
287C22×Dic3—28no—
288C22×Dic3—42no—
289C22×Dic3C3×D418yescomplemented
290C22×Dic3C23×C318yes—
291C22×Dic3C23×C312yes—
292C22×Dic3C23×C312yes—
293C22×Dic3C23×C314yes—
294C22×Dic3C23×C312yes—
295C22×Dic3C23×C314yes—
296#237—264no—
297C2×D12—42no—
298C2×D12C23×C314yes—
299C2×C4×D3—28no—
300C2×C4×D3C23×C318yes—
301C2×Dic6—28no—
302C2×Dic6C23×C318yes—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—38no—
305C3×C4⋊C4—38no—
306C3×C4⋊C4—38no—
307C3×C4⋊C4—34no—
308C3×C4⋊C4C22×D314yes—
309C3×C4⋊C4C23×C314yes—
310C3×C22⋊C4—28no—
311C3×C22⋊C4—38no—
312C3×C22⋊C4—38no—
313C3×C22⋊C4—38no—
314C3×C22⋊C4C22×D318yes—
315C3×C22⋊C4C23×C318yes—
316#217C23×C318yes—
317(C2×D3)⋊C4C23×C318yes—
318(C2×D3)⋊C4C23×C318yes—
319C4⋊Dic3C23×C314yes—
320Dic3⋊C4C23×C318yes—
321Dic3⋊C4C23×C318yes—
322Dic3⋊C4C23×C318yes—
323C22×C32—28no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—24no—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—48no—
330C22×C32C22×D414yes—
331C22×C32C22×D412yes—
332C22×C32H(5,𝔽2)12yes—
333C22×C322−1+412yes—
334C22×C32C2511yescharacteristic
335C2×C3×D3—24no—
336C2×C3×D3—24no—
337C2×C3×D3—24no—
338C2×C3×D3—48no—
339C32×C4—22no—
340C32×C4—24no—
341C32×C4—22no—
342C3×Dic3—24no—
343C3×Dic3—24no—
344C3×Dic3C22×D418yes—
345C2×#41—316no—
346C2×#41—616no—
347C22×Q8—32no—
348C22×D4—32no—
349C22×D4—32no—
350C22×D4—32no—
351C22×D4—31no—
352C22×D4C2×C3×D312yes—
353C22×D4C2×C3×D311yescharacteristic
354C23×C4—31no—
355C23×C4—32no—
356C23×C4—31no—
357C23×C4—32no—
358C23×C4C2×C3×D311yescharacteristic
359C22⋊Q8—316no—
360C22⋊Q8—316no—
361#121—316no—
362#121—316no—
363#121—38no—
364#121—316no—
365#121C2×C3×D318yescomplemented
366C2×C4⋊C4—32no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—38no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4C2×C3×D311yescharacteristic
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4C2×C3×D312yes—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—21no—
387C23×C3—22no—
388C23×C3—24no—
389C23×C3—24no—
390C23×C3—34no—
391C23×C3—42no—
392C23×C3—42no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3—64no—
397C23×C3—64no—
398C23×C3—64no—
399C23×C3D3×D414yes—
400C23×C3C2×C3×D414yes—
401C23×C3C23×D314yes—
402C23×C3C23×D312yes—
403C23×C3C23×D311yescharacteristic
404C23×C3C24×C314yes—
405C23×C3C24×C312yes—
406C23×C3C24×C311yescharacteristic
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3C24×C314yes—
411C3×Q8—616no—
412C3×D4—216no—
413C3×D4—216no—
414C3×D4—416no—
415C3×D4—44no—
416C3×D4—44no—
417C3×D4—48no—
418C3×D4—616no—
419C3×D4—616no—
420C3×D4—124no—
421C3×D4—128no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—24no—
432C2×C3×C4—38no—
433C2×C3×C4—316no—
434C2×C3×C4—34no—
435C2×C3×C4—34no—
436C2×C3×C4—34no—
437C2×C3×C4—42no—
438C2×C3×C4—44no—
439C2×C3×C4—44no—
440C2×C3×C4—44no—
441C2×C3×C4—48no—
442C2×C3×C4—616no—
443C2×C3×C4—616no—
444C2×C3×C4—64no—
445C2×C3×C4—64no—
446C2×C3×C4—124no—
447C2×C3×C4C23×D312yes—
448C2×C3×C4C23×D314yes—
449C2×C3×C4C23×D312yes—
450C2×C3×C4C24×C312yes—
451C2×C3×C4C24×C312yes—
452C2×C3×C4C24×C314yes—
453#67—216no—
454#67—216no—
455#67—48no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—216no—
459C2×Dic3—44no—
460C2×Dic3C2×C3×D418yes—
461C2×Dic3C2×C3×D4116yescomplemented
462C2×Dic3C24×C314yes—
463C2×Dic3C24×C314yes—
464C2×Dic3C24×C314yes—
465D12—44no—
466C4×D3—216no—
467Dic6—216no—
468C2×C32—24no—
469C2×C32—44no—
470C2×C32#53714yescomplemented
471C2×C32C23×D411yescharacteristic
472C2×C32C2×H(5,𝔽2)11yescharacteristic
473C2×C32C2×2−1+411yescharacteristic
474C3×D3—44no—
475C24—32no—
476C24C22×C3×D312yes—
477C24C22×C3×D311yescharacteristic
478#41—664no—
479C2×Q8—38no—
480C2×Q8—68no—
481C2×D4—28no—
482C2×D4—38no—
483C2×D4—38no—
484C2×D4—38no—
485C2×D4—34no—
486C2×D4—42no—
487C2×D4—68no—
488C2×D4—68no—
489C2×D4—122no—
490C2×D4—124no—
491C2×D4C22×C3×D318yes—
492C2×D4C22×C3×D314yes—
493C22×C4—32no—
494C22×C4—34no—
495C22×C4—38no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—38no—
499C22×C4—34no—
500C22×C4—38no—
501C22×C4—42no—
502C22×C4—68no—
503C22×C4—68no—
504C22×C4—122no—
505C22×C4C22×C3×D311yescharacteristic
506C22×C4C22×C3×D312yes—
507C22×C4C22×C3×D311yescharacteristic
508C22×C4C22×C3×D314yes—
509C4⋊C4—38no—
510C4⋊C4—38no—
511C4⋊C4—38no—
512C4⋊C4—34no—
513C4⋊C4C22×C3×D314yes—
514C22⋊C4—38no—
515C22⋊C4—38no—
516C22⋊C4—38no—
517C22⋊C4C22×C3×D318yes—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—28no—
523C22×C3—28no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3—22no—
531C22×C3—24no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—21no—
535C22×C3—42no—
536C22×C3—48no—
537C22×C3—42no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—48no—
542C22×C3—48no—
543C22×C3—64no—
544C22×C3—64no—
545C22×C3—64no—
546C22×C3—88no—
547C22×C3—128no—
548C22×C3C2×D3×D414yes—
549C22×C3C2×D3×D412yes—
550C22×C3#100412yes—
551C22×C3#101012yes—
552C22×C3C22×C3×D414yes—
553C22×C3C22×C3×D412yes—
554C22×C3C3×H(5,𝔽2)12yes—
555C22×C3C3×2−1+412yes—
556C22×C3C24×D311yescharacteristic
557C22×C3C25×C311yescharacteristic
558C2×D3—24no—
559C2×D3—24no—
560C2×D3—24no—
561C2×D3—48no—
562C3×C4—24no—
563C3×C4—24no—
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—24no—
567C3×C4—22no—
568C3×C4—22no—
569C3×C4—38no—
570C3×C4—42no—
571C3×C4—44no—
572C3×C4—64no—
573C3×C4—64no—
574Dic3—24no—
575Dic3—24no—
576Dic3C22×C3×D418yes—
577C32C2×#53711yescharacteristic, complemented, Sylow
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—34no—
584C23—64no—
585C23—64no—
586C23—64no—
587C23C3×D3×D414yes—
588C23C23×C3×D314yes—
589C23C23×C3×D312yes—
590C23C23×C3×D311yescharacteristic
591Q8—616no—
592D4—216no—
593D4—44no—
594D4—616no—
595D4—616no—
596D4—124no—
597D4—128no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—38no—
602C2×C4—316no—
603C2×C4—34no—
604C2×C4—34no—
605C2×C4—34no—
606C2×C4—44no—
607C2×C4—616no—
608C2×C4—616no—
609C2×C4—64no—
610C2×C4—64no—
611C2×C4—124no—
612C2×C4C23×C3×D312yes—
613C2×C4C23×C3×D314yes—
614C2×C4C23×C3×D312yes—
615C2×C3—24no—
616C2×C3—24no—
617C2×C3—24no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—44no—
622C2×C3—44no—
623C2×C3—44no—
624C2×C3—84no—
625C2×C3—124no—
626C2×C3#559714yesdirect product factor
627C2×C3C3×#53714yescomplemented
628C2×C3C22×D3×D411yescharacteristic
629C2×C3C2×#100411yescharacteristic
630C2×C3C2×#101011yescharacteristic
631C2×C3C23×C3×D411yescharacteristic
632C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
633C2×C3C2×C3×2−1+411yescharacteristic
634D3—44no—
635C22—28no—
636C22—22no—
637C22—22no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—48no—
642C22—64no—
643C22—64no—
644C22—64no—
645C22—128no—
646C22C2×C3×D3×D414yes—
647C22C2×C3×D3×D412yes—
648C22C3×#100412yes—
649C22C3×#101012yes—
650C22C24×C3×D311yescharacteristic
651C4—24no—
652C4—22no—
653C4—22no—
654C4—38no—
655C4—64no—
656C4—64no—
657C3—21no—
658C3C2×#559711yescharacteristic, direct product factor
659C3C2×C3×#53711yescharacteristic, complemented
660C2—24no—
661C2—44no—
662C2—124no—
663C2C3×#559714yesdirect product factor
664C2C22×C3×D3×D411yescharacteristic
665C2C2×C3×#100411yescharacteristic
666C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#537
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×C32×#121C2semidirect
3. C2×C3×#939C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#930C2semidirect
6. C22×C3×Dic3⋊C4C2semidirect
7. C3×#5597C2direct (N × H)
8. C2×C3×#896C2semidirect
9. C2×C3×#884C2semidirect
10. C2×C3×#878C2semidirect
12. C2×#5597C3direct (N × H)
23. C2×C3×#237C22semidirect
27. C32×#121C22semidirect
31. C3×#939C22semidirect
32. C3×#939C22semidirect
33. C3×#930C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C3×#896C22semidirect
42. C3×#884C22semidirect
43. C3×#878C22semidirect
45. C22×#237C2×C3semidirect
54. C2×C3×#121D3semidirect
55. C2×C3×#121C2×C3semidirect
57. C2×#939C2×C3semidirect
58. C2×#939C2×C3semidirect
59. C2×#930C2×C3semidirect
60. C22×Dic3⋊C4C2×C3semidirect
61. #5597C2×C3direct (N × H)
62. C2×#896C2×C3semidirect
63. C2×#884C2×C3semidirect
64. C2×#878C2×C3semidirect
85. C22×C3×Dic3D4semidirect
136. C2×#237C22×C3semidirect
147. C3×#121C2×D3semidirect
148. C3×#121C22×C3semidirect
164. #939C22×C3semidirect
165. #939C22×C3semidirect
166. #930C22×C3semidirect
173. C2×Dic3⋊C4C22×C3semidirect
174. #896C22×C3semidirect
175. #884C22×C3semidirect
176. #878C22×C3semidirect
207. C2×C3×Dic3C2×D4semidirect
222. C2×#121C3×D3semidirect
289. C22×Dic3C3×D4semidirect
365. #121C2×C3×D3semidirect
461. C2×Dic3C2×C3×D4semidirect
470. C2×C32#537semidirect
577. C32C2×#537semidirect
626. C2×C3#5597direct (N × H)
627. C2×C3C3×#537semidirect
658. C3C2×#5597direct (N × H)
659. C3C2×C3×#537semidirect
663. C2C3×#5597direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×C32×#1212
C2×C3×#9392
C2×C3×#9302
C22×C3×Dic3⋊C42
C3×#55972
C2×C3×#8962
C2×C3×#8842
C2×C3×#8782
C2×C3×#5373
C2×#55973