Finite Group Databasebeta

← C2×C3×#5533 #11903355

Subgroups — C2×C3×#5533 #11903355

Order 1152.

2389 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C3×#5533C2116yesmaximal, direct product factor
5C2×C3×#897C211yesmaximal, characteristic, complemented
6C2×C3×#892C211yesmaximal, characteristic, complemented
7C2×C3×#888C211yesmaximal, characteristic, complemented
8C2×C3×#887C211yesmaximal, characteristic, complemented
9C2×C3×#885C212yesmaximal
10C2×C3×#879C212yesmaximal, complemented
11C2×C3×#876C212yesmaximal, complemented
12C2×C3×C4×Dic6C212yesmaximal, complemented
13C2×C3×#556—31nomaximal
14C2×#5533C311yesmaximal, characteristic, direct product factor
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2212yes—
19C22×C3×Dic6C2211yescharacteristic
20C32×#117C2218yescomplemented
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2212yes—
24C2×C32×C42C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2211yescharacteristic
27C3×C4×#67C2218yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2212yes—
33C3×#924C2218yescomplemented
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2212yes—
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2212yes—
41C3×#897C2218yescomplemented
42C3×#892C2218yescomplemented
43C3×#888C2218yescomplemented
44C3×#887C2218yescomplemented
45C3×#885C22116yes—
46C3×#879C22116yescomplemented
47C3×#876C22116yescomplemented
48C3×C4×Dic6C22116yescomplemented
49C3×#556—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#126—32no—
52C2×C3×#126—32no—
53C2×C3×#124—32no—
54C2×C3×C22⋊Q8—31no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C4×Q8—31no—
57C2×C3×C4×Q8—32no—
58C2×C3×C4×D4—31no—
59C2×C3×#117—21no—
60C2×C3×#117—31no—
61C2×C3×#117D311yescharacteristic, complemented
62C2×C3×#117C2×C311yescharacteristic, complemented
63C2×C4×#67C2×C311yescharacteristic
64C2×#924C2×C311yescharacteristic, complemented
65#5533C2×C3116yesdirect product factor
66C2×#897C2×C311yescharacteristic, complemented
67C2×#892C2×C311yescharacteristic, complemented
68C2×#888C2×C311yescharacteristic, complemented
69C2×#887C2×C311yescharacteristic, complemented
70C2×#885C2×C312yes—
71C2×#879C2×C312yescomplemented
72C2×#876C2×C312yescomplemented
73C2×C4×Dic6C2×C312yescomplemented
74C24×C32C2311yescharacteristic
75C23×C3×D3C2311yescharacteristic
76C22×C32×C4—24no—
77C22×C32×C4C2312yes—
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2312yes—
80C22×C32×C4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C2×C3×#67—24no—
83C2×C3×#67C2314yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3C2314yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6—28no—
93C2×C3×Dic6C2318yes—
94C2×C3×Dic6C2314yes—
95C32×C4⋊C4C2314yes—
96C32×C4⋊C4C2314yes—
97C32×C22⋊C4C2318yes—
98C32×C42C2318yes—
99C3×#217C2314yes—
100C3×#217C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×(C2×D3)⋊C4C2314yes—
104C3×C4⋊Dic3C2318yes—
105C3×C4⋊Dic3C2314yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2318yes—
109C3×Dic3⋊C4C2314yes—
110C3×C4×Dic3C2318yes—
111C3×C4×Dic3C2318yes—
112C3×C4×Dic3C2314yes—
113C2×#556—31noSylow
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116C22×C3×D4—31no—
117C23×C3×C4—21no—
118C23×C3×C4—31no—
119C23×C3×C4C2×D311yescharacteristic
120C23×C3×C4C22×C311yescharacteristic
121C22×#67C22×C311yescharacteristic
122C22×C4×D3C22×C311yescharacteristic
123C22×Dic6C22×C312yes—
124C22×Dic6C22×C311yescharacteristic
125C3×C4⋊Q8—38no—
126C3×#126—316no—
127C3×#126—316no—
128C3×#124—316no—
129C3×C22⋊Q8—38no—
130C3×C22⋊Q8—38no—
131C3×C4×Q8—38no—
132C3×C4×Q8—316no—
133C3×C4×D4—38no—
134C3×#117—28no—
135C3×#117—38no—
136C3×#117C2×D318yescomplemented
137C3×#117C22×C318yescomplemented
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—32no—
142C2×C3×C4⋊C4—32no—
143C2×C3×C4⋊C4—32no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4C2×D311yescharacteristic
147C2×C3×C4⋊C4C2×D311yescharacteristic
148C2×C3×C4⋊C4C22×C311yescharacteristic
149C2×C3×C4⋊C4C22×C311yescharacteristic
150C2×C3×C22⋊C4—22no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—32no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—32no—
156C2×C3×C22⋊C4C2×D312yes—
157C2×C3×C22⋊C4C22×C312yes—
158C2×C3×C42—22no—
159C2×C3×C42—32no—
160C2×C3×C42—31no—
161C2×C3×C42—32no—
162C2×C3×C42C2×D312yes—
163C2×C3×C42C22×C312yes—
164C2×#217C22×C311yescharacteristic
165C2×#217C22×C312yes—
166C4×#67C22×C318yes—
167C2×(C2×D3)⋊C4C22×C311yescharacteristic
168C2×(C2×D3)⋊C4C22×C312yes—
169C2×(C2×D3)⋊C4C22×C312yes—
170C2×C4⋊Dic3C22×C312yes—
171C2×C4⋊Dic3C22×C311yescharacteristic
172#924C22×C318yescomplemented
173C2×Dic3⋊C4C22×C311yescharacteristic
174C2×Dic3⋊C4C22×C312yes—
175C2×Dic3⋊C4C22×C312yes—
176C2×Dic3⋊C4C22×C312yes—
177C2×C4×Dic3C22×C312yes—
178C2×C4×Dic3C22×C312yes—
179C2×C4×Dic3C22×C311yescharacteristic
180#897C22×C318yescomplemented
181#892C22×C318yescomplemented
182#888C22×C318yescomplemented
183#887C22×C318yescomplemented
184#885C22×C3116yes—
185#879C22×C3116yescomplemented
186#876C22×C3116yescomplemented
187C4×Dic6C22×C3116yescomplemented
188C23×C32—22no—
189C23×C32—22no—
190C23×C32—22no—
191C23×C32C2412yes—
192C23×C32C2411yescharacteristic
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3C2412yes—
197C2×C32×C4—22no—
198C2×C32×C4—28no—
199C2×C32×C4—24no—
200C2×C32×C4—24no—
201C2×C32×C4#4114yes—
202C2×C32×C4C2414yes—
203C2×C32×C4C2412yes—
204C2×C32×C4C2414yes—
205C2×C32×C4C2412yes—
206C3×#67—28no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—24no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3#4114yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2412yes—
217C3×C4×D3—28no—
218C3×Dic6—28no—
219C3×Dic6—216no—
220#556—316no—
221C2×C4⋊Q8—31no—
222C2×#126—32no—
223C2×#126—32no—
224C2×#124—32no—
225C2×C22⋊Q8—31no—
226C2×C22⋊Q8—31no—
227C2×C4×Q8—31no—
228C2×C4×Q8—32no—
229C2×C4×D4—31no—
230C2×#117—31no—
231C2×#117C3×D311yescharacteristic, complemented
232C24×C3—21no—
233C24×C3—31no—
234C24×C3C22×D311yescharacteristic
235C24×C3C23×C311yescharacteristic
236C23×D3C23×C311yescharacteristic
237C2×C3×Q8—34no—
238C2×C3×Q8—38no—
239C2×C3×Q8—68no—
240C2×C3×Q8—64no—
241C2×C3×D4—34no—
242C2×C3×D4—64no—
243C22×C3×C4—28no—
244C22×C3×C4—24no—
245C22×C3×C4—24no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—24no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4—34no—
257C22×C3×C4—64no—
258C22×C3×C4C22×D314yes—
259C22×C3×C4C22×D312yes—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D312yes—
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C23×C312yes—
264C22×C3×C4C23×C311yescharacteristic
265C22×C3×C4C23×C312yes—
266C22×C3×C4C23×C314yes—
267C22×C3×C4C23×C311yescharacteristic
268C2×#67—24no—
269C2×#67C23×C314yes—
270C22×Dic3C23×C311yescharacteristic
271C22×Dic3C23×C311yescharacteristic
272C22×Dic3C23×C312yes—
273C22×Dic3C23×C312yes—
274C22×Dic3C23×C311yescharacteristic
275C2×C4×D3—24no—
276C2×C4×D3C23×C314yes—
277C2×Dic6—24no—
278C2×Dic6—28no—
279C2×Dic6C23×C318yes—
280C2×Dic6C23×C314yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—24no—
283C3×C4⋊C4—34no—
284C3×C4⋊C4—38no—
285C3×C4⋊C4—38no—
286C3×C4⋊C4—38no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4C22×D314yes—
290C3×C4⋊C4C22×D314yes—
291C3×C4⋊C4C23×C314yes—
292C3×C4⋊C4C23×C314yes—
293C3×C22⋊C4—28no—
294C3×C22⋊C4—34no—
295C3×C22⋊C4—38no—
296C3×C22⋊C4—38no—
297C3×C22⋊C4—34no—
298C3×C22⋊C4—38no—
299C3×C22⋊C4C22×D318yes—
300C3×C22⋊C4C23×C318yes—
301C3×C42—28no—
302C3×C42—38no—
303C3×C42—34no—
304C3×C42—38no—
305C3×C42C22×D318yes—
306C3×C42C23×C318yes—
307#217C23×C314yes—
308#217C23×C318yes—
309(C2×D3)⋊C4C23×C314yes—
310(C2×D3)⋊C4C23×C318yes—
311(C2×D3)⋊C4C23×C318yes—
312C4⋊Dic3C23×C318yes—
313C4⋊Dic3C23×C314yes—
314Dic3⋊C4C23×C314yes—
315Dic3⋊C4C23×C318yes—
316Dic3⋊C4C23×C318yes—
317Dic3⋊C4C23×C318yes—
318C4×Dic3C23×C318yes—
319C4×Dic3C23×C318yes—
320C4×Dic3C23×C314yes—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—44no—
325C22×C32C2×#4112yes—
326C22×C32C2×#4112yes—
327C22×C322−1+412yes—
328C22×C32C2511yescharacteristic
329C2×C3×D3—22no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—44no—
333C32×C4—22no—
334C32×C4—24no—
335C32×C4—24no—
336C32×C4C2×#4114yes—
337C3×Dic3—24no—
338C3×Dic3—24no—
339C3×Dic3—22no—
340C3×Dic3—22no—
341C3×Dic3C2×#4114yes—
342C22×Q8—31no—
343C22×Q8—32no—
344C22×D4—31no—
345C23×C4—31no—
346C23×C4C2×C3×D311yescharacteristic
347C4⋊Q8—38no—
348#126—316no—
349#126—316no—
350#124—316no—
351C22⋊Q8—38no—
352C22⋊Q8—38no—
353C4×Q8—38no—
354C4×Q8—316no—
355C4×D4—38no—
356#117—38no—
357#117C2×C3×D318yescomplemented
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—32no—
364C2×C4⋊C4C2×C3×D311yescharacteristic
365C2×C4⋊C4C2×C3×D311yescharacteristic
366C2×C22⋊C4—31no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—32no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4C2×C3×D312yes—
372C2×C42—32no—
373C2×C42—31no—
374C2×C42—32no—
375C2×C42C2×C3×D312yes—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—21no—
384C23×C3—22no—
385C23×C3—32no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—62no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3C23×D312yes—
392C23×C3C23×D311yescharacteristic
393C23×C3C24×C312yes—
394C23×C3C24×C311yescharacteristic
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3C24×C312yes—
399C3×Q8—616no—
400C3×Q8—68no—
401C3×D4—68no—
402C2×C3×C4—24no—
403C2×C3×C4—216no—
404C2×C3×C4—22no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—24no—
410C2×C3×C4—28no—
411C2×C3×C4—28no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—34no—
418C2×C3×C4—32no—
419C2×C3×C4—32no—
420C2×C3×C4—32no—
421C2×C3×C4—34no—
422C2×C3×C4—34no—
423C2×C3×C4—44no—
424C2×C3×C4—44no—
425C2×C3×C4—62no—
426C2×C3×C4—64no—
427C2×C3×C4—64no—
428C2×C3×C4—62no—
429C2×C3×C4—68no—
430C2×C3×C4#23514yes—
431C2×C3×C4C3×#4114yes—
432C2×C3×C4C23×D314yes—
433C2×C3×C4C23×D312yes—
434C2×C3×C4C23×D314yes—
435C2×C3×C4C23×D312yes—
436C2×C3×C4C24×C314yes—
437C2×C3×C4C24×C312yes—
438C2×C3×C4C24×C314yes—
439C2×C3×C4C24×C312yes—
440#67—28no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3C3×#4114yes—
446C2×Dic3C24×C312yes—
447C2×Dic3C24×C312yes—
448C2×Dic3C24×C314yes—
449C2×Dic3C24×C314yes—
450C2×Dic3C24×C312yes—
451C4×D3—28no—
452Dic6—28no—
453Dic6—216no—
454C2×C32—42no—
455C2×C32#55614yescomplemented
456C2×C32C22×#4111yescharacteristic
457C2×C32C22×#4111yescharacteristic
458C2×C32C2×2−1+411yescharacteristic
459C3×D3—42no—
460C24—31no—
461C24C22×C3×D311yescharacteristic
462C2×Q8—34no—
463C2×Q8—38no—
464C2×Q8—68no—
465C2×Q8—64no—
466C2×D4—34no—
467C2×D4—64no—
468C22×C4—24no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—31no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—34no—
475C22×C4—64no—
476C22×C4C22×C3×D312yes—
477C22×C4C22×C3×D311yescharacteristic
478C22×C4C22×C3×D312yes—
479C22×C4C22×C3×D314yes—
480C22×C4C22×C3×D311yescharacteristic
481C4⋊C4—34no—
482C4⋊C4—34no—
483C4⋊C4—38no—
484C4⋊C4—38no—
485C4⋊C4—38no—
486C4⋊C4—38no—
487C4⋊C4C22×C3×D314yes—
488C4⋊C4C22×C3×D314yes—
489C22⋊C4—34no—
490C22⋊C4—38no—
491C22⋊C4—38no—
492C22⋊C4—34no—
493C22⋊C4—38no—
494C22⋊C4C22×C3×D318yes—
495C42—38no—
496C42—34no—
497C42—38no—
498C42C22×C3×D318yes—
499C22×C3—24no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—48no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—124no—
519C22×C3C2×#23512yes—
520C22×C3D3×#4112yes—
521C22×C3#101012yes—
522C22×C3C2×C3×#4112yes—
523C22×C3C2×C3×#4112yes—
524C22×C3C3×2−1+412yes—
525C22×C3C24×D311yescharacteristic
526C22×C3C25×C311yescharacteristic
527C2×D3—22no—
528C2×D3—22no—
529C2×D3—22no—
530C2×D3—44no—
531C3×C4—24no—
532C3×C4—22no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—22no—
537C3×C4—24no—
538C3×C4—24no—
539C3×C4—34no—
540C3×C4—44no—
541C3×C4—44no—
542C3×C4—62no—
543C3×C4—64no—
544C3×C4—64no—
545C3×C4—62no—
546C3×C4C2×#23514yes—
547C3×C4C2×C3×#4114yes—
548Dic3—24no—
549Dic3—24no—
550Dic3—22no—
551Dic3—22no—
552Dic3C2×C3×#4114yes—
553C32C2×#55611yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—32no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23C23×C3×D312yes—
562C23C23×C3×D311yescharacteristic
563Q8—616no—
564Q8—68no—
565D4—68no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—28no—
570C2×C4—34no—
571C2×C4—32no—
572C2×C4—32no—
573C2×C4—32no—
574C2×C4—34no—
575C2×C4—34no—
576C2×C4—62no—
577C2×C4—64no—
578C2×C4—64no—
579C2×C4—62no—
580C2×C4—68no—
581C2×C4C3×#23514yes—
582C2×C4C23×C3×D314yes—
583C2×C4C23×C3×D312yes—
584C2×C4C23×C3×D314yes—
585C2×C4C23×C3×D312yes—
586C2×C3—24no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—44no—
591C2×C3—42no—
592C2×C3—42no—
593C2×C3—122no—
594C2×C3#553314yesdirect product factor
595C2×C3C3×#55614yescomplemented
596C2×C3C22×#23511yescharacteristic
597C2×C3C2×D3×#4111yescharacteristic
598C2×C3C2×#101011yescharacteristic
599C2×C3C22×C3×#4111yescharacteristic
600C2×C3C22×C3×#4111yescharacteristic
601C2×C3C2×C3×2−1+411yescharacteristic
602D3—42no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—44no—
607C22—62no—
608C22—62no—
609C22—62no—
610C22—124no—
611C22C2×C3×#23512yes—
612C22C3×D3×#4112yes—
613C22C3×#101012yes—
614C22C24×C3×D311yescharacteristic
615C4—22no—
616C4—24no—
617C4—24no—
618C4—34no—
619C4—62no—
620C4—64no—
621C4—64no—
622C4—62no—
623C4C2×C3×#23514yes—
624C3—21no—
625C3C2×#553311yescharacteristic, direct product factor
626C3C2×C3×#55611yescharacteristic, complemented
627C2—42no—
628C2—122no—
629C2C3×#553314yesdirect product factor
630C2C22×C3×#23511yescharacteristic
631C2C2×C3×D3×#4111yescharacteristic
632C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C3×#117D3
hypocenterC3C2×C3×#556
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
3. C2×C3×#924C2semidirect
4. C3×#5533C2direct (N × H)
5. C2×C3×#897C2semidirect
6. C2×C3×#892C2semidirect
7. C2×C3×#888C2semidirect
8. C2×C3×#887C2semidirect
10. C2×C3×#879C2semidirect
11. C2×C3×#876C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5533C3direct (N × H)
20. C32×#117C22semidirect
33. C3×#924C22semidirect
41. C3×#897C22semidirect
42. C3×#892C22semidirect
43. C3×#888C22semidirect
44. C3×#887C22semidirect
46. C3×#879C22semidirect
47. C3×#876C22semidirect
48. C3×C4×Dic6C22semidirect
61. C2×C3×#117D3semidirect
62. C2×C3×#117C2×C3semidirect
64. C2×#924C2×C3semidirect
65. #5533C2×C3direct (N × H)
66. C2×#897C2×C3semidirect
67. C2×#892C2×C3semidirect
68. C2×#888C2×C3semidirect
69. C2×#887C2×C3semidirect
71. C2×#879C2×C3semidirect
72. C2×#876C2×C3semidirect
73. C2×C4×Dic6C2×C3semidirect
136. C3×#117C2×D3semidirect
137. C3×#117C22×C3semidirect
172. #924C22×C3semidirect
180. #897C22×C3semidirect
181. #892C22×C3semidirect
182. #888C22×C3semidirect
183. #887C22×C3semidirect
185. #879C22×C3semidirect
186. #876C22×C3semidirect
187. C4×Dic6C22×C3semidirect
231. C2×#117C3×D3semidirect
357. #117C2×C3×D3semidirect
455. C2×C32#556semidirect
553. C32C2×#556semidirect
594. C2×C3#5533direct (N × H)
595. C2×C3C3×#556semidirect
625. C3C2×#5533direct (N × H)
626. C3C2×C3×#556semidirect
629. C2C3×#5533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×C3×C4×#672
C2×C3×#9242
C3×#55332
C2×C3×#8972
C2×C3×#8922
C2×C3×#8882
C2×C3×#8872
C2×C3×#8852
C2×C3×#8792
C2×C3×#8762
C2×C3×C4×Dic62
C2×C3×#5563
C2×#55333