Finite Group Databasebeta

← C3×#87295 #11904714

Subgroups — C3×#87295 #11904714

Order 1152.

3441 conjugacy classes of subgroups.

The subgroup lattice has 675 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×2−1+4C211yesmaximal, characteristic, complemented
2C2×C3×D3×#41C211yesmaximal, characteristic, complemented
3C3×#5833C213yesmaximal, complemented
4C3×#5829C216yesmaximal, complemented
5C3×#5828C213yesmaximal, complemented
6C3×#5827C211yesmaximal, characteristic, complemented
7C3×#5824C216yesmaximal, complemented
8C3×#5817C212yesmaximal, complemented
9C3×#5816C213yesmaximal, complemented
10C3×Q8×#67C212yesmaximal, complemented
11C2×C3×#946C213yesmaximal, complemented
12C3×#3489—31nomaximal
13#87295C311yesmaximal, characteristic, direct product factor
14C32×2−1+4—28no—
15C2×C32×#41C2211yescharacteristic
16C2×C32×#41C2216yescomplemented
17C2×C32×#41C2213yescomplemented
18C22×C32×Q8C2213yescomplemented
19C22×C32×Q8C2212yescomplemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×#237C2213yes—
24C2×C3×D3×D4C2213yes—
25C2×C3×#235C2213yes—
26C22×C3×C4×D3C2213yes—
27C3×#947C2216yescomplemented
28C3×#946C2213yes—
29C3×#946C2216yes—
30C3×#946C2216yescomplemented
31C3×#946C2216yescomplemented
32C3×#946C2213yescomplemented
33C3×Q8×Dic3C2212yescomplemented
34C3×#944C2216yescomplemented
35C3×#939C22112yescomplemented
36C3×#938C2211yescharacteristic
37C3×#938C2213yescomplemented
38C3×#937C2216yes—
39C3×#935C2216yescomplemented
40C3×D4×Dic3C2216yescomplemented
41C3×#930C2216yescomplemented
42C3×#929C22112yescomplemented
43C3×C4×#67C2216yes—
44C3×C4×#67C2216yescomplemented
45C2×C3×(C2×D3)⋊C4C2216yes—
46C3×#926C2213yescomplemented
47C2×C3×C4⋊Dic3C2213yescomplemented
48C3×#924C2216yescomplemented
49C2×C3×Dic3⋊C4C2216yescomplemented
50C2×C3×2−1+4—21no—
51C2×C3×2−1+4D311yescharacteristic, complemented
52C2×C3×2−1+4C2×C311yescharacteristic, complemented
53C22×C3×#41—31no—
54C2×D3×#41C2×C311yescharacteristic, complemented
55C3×D4×Q8—32no—
56C3×#548—32no—
57C3×#547—36no—
58C3×#546—36no—
59C3×#537—33no—
60C3×#536—33no—
61C3×#525—33no—
62C2×C3×C22⋊Q8—33no—
63C3×#520—31no—
64#5833C2×C313yescomplemented
65#5829C2×C316yescomplemented
66#5828C2×C313yescomplemented
67#5827C2×C311yescharacteristic, complemented
68#5824C2×C316yescomplemented
69#5817C2×C312yescomplemented
70#5816C2×C313yescomplemented
71Q8×#67C2×C312yescomplemented
72C2×#946C2×C313yescomplemented
73C23×C3×D3C2313yes—
74C32×#41—224no—
75C32×#41—212no—
76C32×#41D418yescomplemented
77C2×C32×Q8—28no—
78C2×C32×Q8—212no—
79C2×C32×Q8C2316yes—
80C2×C32×Q8C2313yes—
81C2×C32×Q8C2311yescharacteristic
82C2×C32×D4C2316yes—
83C2×C32×D4C2311yescharacteristic
84C2×C32×D4C2313yes—
85C22×C32×C4C2316yes—
86C22×C32×C4C2316yes—
87C22×C32×C4C2313yes—
88C2×C3×#67C2312yes—
89C2×C3×#67C2316yes—
90C2×C3×#67C2316yes—
91C22×C3×Dic3C2313yes—
92C22×C3×Dic3C2316yes—
93C3×#239—24no—
94C3×D3×Q8—24no—
95C3×#237—212no—
96C3×D3×D4—212no—
97C3×#235—212no—
98C2×C3×D12C2313yes—
99C2×C3×C4×D3—212no—
100C2×C3×C4×D3C2313yes—
101C2×C3×C4×D3C2313yes—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2313yes—
104C2×C3×Dic6C2313yes—
105C3×#217C2316yes—
106C3×#217C2316yes—
107C3×#217C2312yes—
108C3×(C2×D3)⋊C4C2316yes—
109C3×(C2×D3)⋊C4C23112yes—
110C3×(C2×D3)⋊C4C2316yes—
111C3×C4⋊Dic3C2316yes—
112C3×C4⋊Dic3C2313yes—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×Dic3⋊C4C2316yes—
115C3×Dic3⋊C4C23112yes—
116C3×Dic3⋊C4C2316yes—
117C3×C4×Dic3C2316yes—
118#3489—31noSylow
119C3×2−1+4—216no—
120C3×2−1+4—28no—
121C3×2−1+4—28no—
122C2×C3×#41—21no—
123C2×C3×#41—23no—
124C2×C3×#41—26no—
125C2×C3×#41—31no—
126C2×C3×#41—33no—
127C2×C3×#41—33no—
128C2×C3×#41—68no—
129C2×C3×#41C2×D311yescharacteristic
130C2×C3×#41C2×D313yescomplemented
131C2×C3×#41C2×D316yescomplemented
132C2×C3×#41C22×C311yescharacteristic
133C2×C3×#41C22×C316yescomplemented
134C2×C3×#41C22×C313yescomplemented
135C22×C3×Q8—23no—
136C22×C3×Q8—22no—
137C22×C3×Q8—31no—
138C22×C3×Q8C2×D313yescomplemented
139C22×C3×Q8C2×D312yescomplemented
140C22×C3×Q8C22×C313yescomplemented
141C22×C3×Q8C22×C312yescomplemented
142C22×C3×D4—33no—
143C23×C3×C4—33no—
144D3×#41—28no—
145C2×#239C22×C311yescharacteristic
146C2×D3×Q8C22×C311yescharacteristic
147C2×#237C22×C313yes—
148C2×D3×D4C22×C313yes—
149C2×#235C22×C313yes—
150C22×C4×D3C22×C313yes—
151C3×C4⋊Q8—36no—
152C3×#124—36no—
153C3×#123—36no—
154C3×#123—312no—
155C3×C22⋊Q8—33no—
156C3×C22⋊Q8—36no—
157C3×C22⋊Q8—36no—
158C3×C22⋊Q8—36no—
159C3×C22⋊Q8—33no—
160C3×C22⋊Q8—36no—
161C3×#121—31no—
162C3×#121—33no—
163C3×#121—312no—
164C3×#121—36no—
165C3×#120—36no—
166C3×C4×Q8—32no—
167C3×C4×D4—36no—
168C3×C4×D4—36no—
169C3×C4×D4—36no—
170C3×#117—33no—
171C2×C3×C4⋊C4—36no—
172C2×C3×C4⋊C4—33no—
173C2×C3×C22⋊C4—36no—
174#947C22×C316yescomplemented
175#946C22×C313yes—
176#946C22×C316yes—
177#946C22×C316yescomplemented
178#946C22×C316yescomplemented
179#946C22×C313yescomplemented
180Q8×Dic3C22×C312yescomplemented
181#944C22×C316yescomplemented
182#939C22×C3112yescomplemented
183#938C22×C311yescharacteristic
184#938C22×C313yescomplemented
185#937C22×C316yes—
186#935C22×C316yescomplemented
187D4×Dic3C22×C316yescomplemented
188#930C22×C316yescomplemented
189#929C22×C3112yescomplemented
190C4×#67C22×C316yes—
191C4×#67C22×C316yescomplemented
192C2×(C2×D3)⋊C4C22×C316yes—
193#926C22×C313yescomplemented
194C2×C4⋊Dic3C22×C313yescomplemented
195#924C22×C316yescomplemented
196C2×Dic3⋊C4C22×C316yescomplemented
197C23×C32C2412yes—
198C23×C32C2413yes—
199C22×C3×D3—26no—
200C22×C3×D3—26no—
201C22×C3×D3—43no—
202C22×C3×D3C2413yes—
203C22×C3×D3C2411yescharacteristic
204C32×Q8—212no—
205C32×Q8—26no—
206C32×Q8C2×D414yes—
207C32×D4—212no—
208C32×D4—22no—
209C32×D4C2×D4112yes—
210C2×C32×C4—212no—
211C2×C32×C4—212no—
212C2×C32×C4C2×D4112yes—
213C2×C32×C4C2416yes—
214C2×C32×C4C2413yes—
215C2×C32×C4C2411yescharacteristic
216C3×#67—212no—
217C3×#67—24no—
218C3×#67—46no—
219C2×C3×Dic3—26no—
220C2×C3×Dic3—46no—
221C2×C3×Dic3C2412yes—
222C2×C3×Dic3C2416yes—
223C2×C3×Dic3C2413yes—
224C2×C3×Dic3C2411yescharacteristic
225C3×D12—26no—
226C3×C4×D3—22no—
227C3×C4×D3—26no—
228C3×C4×D3—26no—
229C3×C4×D3—26no—
230C3×Dic6—26no—
231C2×2−1+4C3×D311yescharacteristic, complemented
232C22×#41—31no—
233D4×Q8—32no—
234#548—32no—
235#547—36no—
236#546—36no—
237#537—33no—
238#536—33no—
239#525—33no—
240C2×C22⋊Q8—33no—
241#520—31no—
242C24×C3—33no—
243C23×D3C23×C313yes—
244C3×#41—248no—
245C3×#41—224no—
246C3×#41—224no—
247C3×#41—224no—
248C3×#41—212no—
249C3×#41—212no—
250C3×#41—28no—
251C3×#41—64no—
252C3×#41—612no—
253C3×#41—612no—
254C3×#41#6718yescomplemented
255C3×#41C3×D418yescomplemented
256C2×C3×Q8—216no—
257C2×C3×Q8—224no—
258C2×C3×Q8—28no—
259C2×C3×Q8—28no—
260C2×C3×Q8—212no—
261C2×C3×Q8—212no—
262C2×C3×Q8—23no—
263C2×C3×Q8—26no—
264C2×C3×Q8—21no—
265C2×C3×Q8—33no—
266C2×C3×Q8—64no—
267C2×C3×Q8C22×D313yes—
268C2×C3×Q8C22×D316yes—
269C2×C3×Q8C22×D311yescharacteristic
270C2×C3×Q8C23×C316yes—
271C2×C3×Q8C23×C313yes—
272C2×C3×Q8C23×C311yescharacteristic
273C2×C3×D4—26no—
274C2×C3×D4—21no—
275C2×C3×D4—23no—
276C2×C3×D4—32no—
277C2×C3×D4—36no—
278C2×C3×D4—36no—
279C2×C3×D4—33no—
280C2×C3×D4—612no—
281C2×C3×D4C22×D316yes—
282C2×C3×D4C22×D311yescharacteristic
283C2×C3×D4C22×D313yes—
284C2×C3×D4C23×C316yes—
285C2×C3×D4C23×C311yescharacteristic
286C2×C3×D4C23×C313yes—
287C22×C3×C4—26no—
288C22×C3×C4—26no—
289C22×C3×C4—23no—
290C22×C3×C4—33no—
291C22×C3×C4—36no—
292C22×C3×C4—33no—
293C22×C3×C4—33no—
294C22×C3×C4—31no—
295C22×C3×C4—33no—
296C22×C3×C4—612no—
297C22×C3×C4C22×D316yes—
298C22×C3×C4C22×D316yes—
299C22×C3×C4C22×D313yes—
300C22×C3×C4C23×C316yes—
301C22×C3×C4C23×C316yes—
302C22×C3×C4C23×C313yes—
303C2×#67C23×C312yes—
304C2×#67C23×C316yes—
305C2×#67C23×C316yes—
306C22×Dic3C23×C313yes—
307C22×Dic3C23×C316yes—
308#239—24no—
309D3×Q8—24no—
310#237—212no—
311D3×D4—212no—
312#235—212no—
313C2×D12C23×C313yes—
314C2×C4×D3—212no—
315C2×C4×D3C23×C313yes—
316C2×C4×D3C23×C313yes—
317C2×C4×D3C23×C311yescharacteristic
318C2×C4×D3C23×C313yes—
319C2×Dic6C23×C313yes—
320C3×C4⋊C4—36no—
321C3×C4⋊C4—312no—
322C3×C4⋊C4—36no—
323C3×C4⋊C4—33no—
324C3×C4⋊C4—36no—
325C3×C4⋊C4—31no—
326C3×C22⋊C4—36no—
327C3×C22⋊C4—32no—
328C3×C22⋊C4—36no—
329C3×C22⋊C4—36no—
330C3×C22⋊C4—312no—
331C3×C22⋊C4—36no—
332C3×C42—36no—
333#217C23×C316yes—
334#217C23×C316yes—
335#217C23×C312yes—
336(C2×D3)⋊C4C23×C316yes—
337(C2×D3)⋊C4C23×C3112yes—
338(C2×D3)⋊C4C23×C316yes—
339C4⋊Dic3C23×C316yes—
340C4⋊Dic3C23×C313yes—
341C4⋊Dic3C23×C311yescharacteristic
342Dic3⋊C4C23×C316yes—
343Dic3⋊C4C23×C3112yes—
344Dic3⋊C4C23×C316yes—
345C4×Dic3C23×C316yes—
346C22×C32—22no—
347C22×C32—23no—
348C22×C32—23no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32C22×D416yes—
352C22×C32C2511yescharacteristic
353C2×C3×D3—21no—
354C2×C3×D3—21no—
355C2×C3×D3—23no—
356C2×C3×D3—23no—
357C2×C3×D3—23no—
358C2×C3×D3—412no—
359C2×C3×D32−1+412yescomplemented
360C32×C4—26no—
361C32×C4C22×D416yes—
362C32×C4C22×D412yes—
363C3×Dic3—23no—
364C3×Dic3—21no—
365C3×Dic3—22no—
366C3×Dic3—26no—
3672−1+4—28no—
368C2×#41—31no—
369C2×#41—33no—
370C2×#41—33no—
371C2×#41—68no—
372C2×#41C2×C3×D311yescharacteristic
373C2×#41C2×C3×D313yescomplemented
374C2×#41C2×C3×D316yescomplemented
375C22×Q8—31no—
376C22×Q8C2×C3×D313yescomplemented
377C22×Q8C2×C3×D312yescomplemented
378C22×D4—33no—
379C23×C4—33no—
380C4⋊Q8—36no—
381#124—36no—
382#123—36no—
383#123—312no—
384C22⋊Q8—33no—
385C22⋊Q8—36no—
386C22⋊Q8—36no—
387C22⋊Q8—36no—
388C22⋊Q8—33no—
389C22⋊Q8—36no—
390#121—31no—
391#121—33no—
392#121—312no—
393#121—36no—
394#120—36no—
395C4×Q8—32no—
396C4×D4—36no—
397C4×D4—36no—
398C4×D4—36no—
399#117—33no—
400C2×C4⋊C4—33no—
401C2×C4⋊C4—36no—
402C2×C22⋊C4—36no—
403C23×C3—22no—
404C23×C3—23no—
405C23×C3—31no—
406C23×C3—33no—
407C23×C3—66no—
408C23×C3—66no—
409C23×C3—123no—
410C23×C3C23×D312yes—
411C23×C3C23×D313yes—
412C23×C3C24×C312yes—
413C23×C3C24×C313yes—
414C22×D3—26no—
415C22×D3—26no—
416C22×D3—43no—
417C22×D3C24×C313yes—
418C22×D3C24×C311yescharacteristic
419C3×Q8—224no—
420C3×Q8—212no—
421C3×Q8—212no—
422C3×Q8—26no—
423C3×Q8—212no—
424C3×Q8—26no—
425C3×Q8—24no—
426C3×Q8—66no—
427C3×Q8C2×#6714yes—
428C3×Q8C2×C3×D414yes—
429C3×D4—224no—
430C3×D4—24no—
431C3×D4—212no—
432C3×D4—212no—
433C3×D4—22no—
434C3×D4—22no—
435C3×D4—212no—
436C3×D4—64no—
437C3×D4—612no—
438C3×D4—66no—
439C3×D4—126no—
440C3×D4C2×#67112yes—
441C3×D4C2×C3×D4112yes—
442C2×C3×C4—224no—
443C2×C3×C4—224no—
444C2×C3×C4—212no—
445C2×C3×C4—212no—
446C2×C3×C4—212no—
447C2×C3×C4—212no—
448C2×C3×C4—26no—
449C2×C3×C4—23no—
450C2×C3×C4—21no—
451C2×C3×C4—212no—
452C2×C3×C4—32no—
453C2×C3×C4—36no—
454C2×C3×C4—31no—
455C2×C3×C4—33no—
456C2×C3×C4—66no—
457C2×C3×C4—62no—
458C2×C3×C4—66no—
459C2×C3×C4—66no—
460C2×C3×C4—66no—
461C2×C3×C4—126no—
462C2×C3×C4C2×#67112yes—
463C2×C3×C4C2×C3×D4112yes—
464C2×C3×C4C23×D316yes—
465C2×C3×C4C23×D313yes—
466C2×C3×C4C23×D311yescharacteristic
467C2×C3×C4C24×C316yes—
468C2×C3×C4C24×C313yes—
469C2×C3×C4C24×C311yescharacteristic
470#67—212no—
471#67—24no—
472#67—46no—
473C2×Dic3—26no—
474C2×Dic3—46no—
475C2×Dic3C24×C312yes—
476C2×Dic3C24×C316yes—
477C2×Dic3C24×C313yes—
478C2×Dic3C24×C311yescharacteristic
479D12—26no—
480C4×D3—22no—
481C4×D3—26no—
482C4×D3—26no—
483C4×D3—26no—
484Dic6—26no—
485C2×C32—26no—
486C2×C32—42no—
487C2×C32C23×D411yescharacteristic
488C2×C32C2×2−1+411yescharacteristic
489C2×C32#58511yescharacteristic
490C3×D3—22no—
491C3×D3—43no—
492C24—33no—
493#41—224no—
494#41—212no—
495#41—64no—
496#41—612no—
497#41—612no—
498#41C3×#6718yescomplemented
499C2×Q8—28no—
500C2×Q8—212no—
501C2×Q8—33no—
502C2×Q8—64no—
503C2×Q8C22×C3×D313yes—
504C2×Q8C22×C3×D316yes—
505C2×Q8C22×C3×D311yescharacteristic
506C2×D4—32no—
507C2×D4—36no—
508C2×D4—36no—
509C2×D4—33no—
510C2×D4—612no—
511C2×D4C22×C3×D316yes—
512C2×D4C22×C3×D311yescharacteristic
513C2×D4C22×C3×D313yes—
514C22×C4—33no—
515C22×C4—36no—
516C22×C4—33no—
517C22×C4—33no—
518C22×C4—31no—
519C22×C4—33no—
520C22×C4—612no—
521C22×C4C22×C3×D316yes—
522C22×C4C22×C3×D316yes—
523C22×C4C22×C3×D313yes—
524C4⋊C4—33no—
525C4⋊C4—36no—
526C4⋊C4—36no—
527C4⋊C4—312no—
528C4⋊C4—31no—
529C4⋊C4—36no—
530C22⋊C4—36no—
531C22⋊C4—32no—
532C22⋊C4—36no—
533C22⋊C4—36no—
534C22⋊C4—312no—
535C22⋊C4—36no—
536C42—36no—
537C22×C3—23no—
538C22×C3—23no—
539C22×C3—23no—
540C22×C3—23no—
541C22×C3—24no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—26no—
549C22×C3—21no—
550C22×C3—32no—
551C22×C3—43no—
552C22×C3—43no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—61no—
556C22×C3—61no—
557C22×C3—63no—
558C22×C3—63no—
559C22×C3—63no—
560C22×C3—1212no—
561C22×C3C22×#6716yes—
562C22×C3C22×C3×D416yes—
563C22×C3C24×D311yescharacteristic
564C22×C3C25×C311yescharacteristic
565C2×D3—21no—
566C2×D3—21no—
567C2×D3—23no—
568C2×D3—23no—
569C2×D3—23no—
570C2×D3—412no—
571C2×D3C3×2−1+412yescomplemented
572C3×C4—212no—
573C3×C4—26no—
574C3×C4—26no—
575C3×C4—26no—
576C3×C4—22no—
577C3×C4—62no—
578C3×C4—66no—
579C3×C4—61no—
580C3×C4—63no—
581C3×C4C22×#6716yes—
582C3×C4C22×#6712yes—
583C3×C4C22×C3×D416yes—
584C3×C4C22×C3×D412yes—
585Dic3—23no—
586Dic3—21no—
587Dic3—22no—
588Dic3—26no—
589C32#348911yescharacteristic, complemented, Sylow
590C23—31no—
591C23—33no—
592C23—66no—
593C23—66no—
594C23—123no—
595C23C23×C3×D312yes—
596C23C23×C3×D313yes—
597Q8—212no—
598Q8—26no—
599Q8—66no—
600Q8C2×C3×#6714yes—
601D4—212no—
602D4—22no—
603D4—64no—
604D4—612no—
605D4—66no—
606D4—126no—
607D4C2×C3×#67112yes—
608C2×C4—212no—
609C2×C4—212no—
610C2×C4—32no—
611C2×C4—36no—
612C2×C4—31no—
613C2×C4—33no—
614C2×C4—66no—
615C2×C4—62no—
616C2×C4—66no—
617C2×C4—66no—
618C2×C4—66no—
619C2×C4—126no—
620C2×C4C2×C3×#67112yes—
621C2×C4C23×C3×D316yes—
622C2×C4C23×C3×D313yes—
623C2×C4C23×C3×D311yescharacteristic
624C2×C3—26no—
625C2×C3—26no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—46no—
630C2×C3—44no—
631C2×C3—42no—
632C2×C3—42no—
633C2×C3—62no—
634C2×C3—123no—
635C2×C3D3×2−1+411yescharacteristic
636C2×C3#596811yescharacteristic
637C2×C3C23×#6711yescharacteristic
638C2×C3C23×C3×D411yescharacteristic
639C2×C3C2×C3×2−1+411yescharacteristic
640C2×C3C3×#58511yescharacteristic
641D3—22no—
642D3—43no—
643C22—23no—
644C22—23no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—32no—
649C22—61no—
650C22—61no—
651C22—63no—
652C22—63no—
653C22—63no—
654C22—1212no—
655C22C22×C3×#6716yes—
656C22C24×C3×D311yescharacteristic
657C4—26no—
658C4—62no—
659C4—66no—
660C4—61no—
661C4—63no—
662C4C22×C3×#6716yes—
663C4C22×C3×#6712yes—
664C3—21no—
665C3#8729511yescharacteristic, direct product factor
666C3C3×#348911yescharacteristic, complemented
667C2—26no—
668C2—42no—
669C2—62no—
670C2—123no—
671C2C3×D3×2−1+411yescharacteristic
672C2C3×#596811yescharacteristic
673C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×2−1+4C2
socleC22×C32C25
hypercenterC2×C3×2−1+4D3
hypocenterC3C3×#3489
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C32×2−1+4C2semidirect
2. C2×C3×D3×#41C2semidirect
3. C3×#5833C2semidirect
4. C3×#5829C2semidirect
5. C3×#5828C2semidirect
6. C3×#5827C2semidirect
7. C3×#5824C2semidirect
8. C3×#5817C2semidirect
9. C3×#5816C2semidirect
10. C3×Q8×#67C2semidirect
11. C2×C3×#946C2semidirect
13. #87295C3direct (N × H)
16. C2×C32×#41C22semidirect
17. C2×C32×#41C22semidirect
18. C22×C32×Q8C22semidirect
19. C22×C32×Q8C22semidirect
27. C3×#947C22semidirect
30. C3×#946C22semidirect
31. C3×#946C22semidirect
32. C3×#946C22semidirect
33. C3×Q8×Dic3C22semidirect
34. C3×#944C22semidirect
35. C3×#939C22semidirect
37. C3×#938C22semidirect
39. C3×#935C22semidirect
40. C3×D4×Dic3C22semidirect
41. C3×#930C22semidirect
42. C3×#929C22semidirect
44. C3×C4×#67C22semidirect
46. C3×#926C22semidirect
47. C2×C3×C4⋊Dic3C22semidirect
48. C3×#924C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×2−1+4D3semidirect
52. C2×C3×2−1+4C2×C3semidirect
54. C2×D3×#41C2×C3semidirect
64. #5833C2×C3semidirect
65. #5829C2×C3semidirect
66. #5828C2×C3semidirect
67. #5827C2×C3semidirect
68. #5824C2×C3semidirect
69. #5817C2×C3semidirect
70. #5816C2×C3semidirect
71. Q8×#67C2×C3semidirect
72. C2×#946C2×C3semidirect
76. C32×#41D4semidirect
130. C2×C3×#41C2×D3semidirect
131. C2×C3×#41C2×D3semidirect
133. C2×C3×#41C22×C3semidirect
134. C2×C3×#41C22×C3semidirect
138. C22×C3×Q8C2×D3semidirect
139. C22×C3×Q8C2×D3semidirect
140. C22×C3×Q8C22×C3semidirect
141. C22×C3×Q8C22×C3semidirect
174. #947C22×C3semidirect
177. #946C22×C3semidirect
178. #946C22×C3semidirect
179. #946C22×C3semidirect
180. Q8×Dic3C22×C3semidirect
181. #944C22×C3semidirect
182. #939C22×C3semidirect
184. #938C22×C3semidirect
186. #935C22×C3semidirect
187. D4×Dic3C22×C3semidirect
188. #930C22×C3semidirect
189. #929C22×C3semidirect
191. C4×#67C22×C3semidirect
193. #926C22×C3semidirect
194. C2×C4⋊Dic3C22×C3semidirect
195. #924C22×C3semidirect
196. C2×Dic3⋊C4C22×C3semidirect
231. C2×2−1+4C3×D3semidirect
254. C3×#41#67semidirect
255. C3×#41C3×D4semidirect
359. C2×C3×D32−1+4semidirect
373. C2×#41C2×C3×D3semidirect
374. C2×#41C2×C3×D3semidirect
376. C22×Q8C2×C3×D3semidirect
377. C22×Q8C2×C3×D3semidirect
498. #41C3×#67semidirect
571. C2×D3C3×2−1+4semidirect
589. C32#3489semidirect
665. C3#87295direct (N × H)
666. C3C3×#3489semidirect

Maximal subgroups

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

subgroupindex
C2×C32×2−1+42
C2×C3×D3×#412
C3×#58332
C3×#58292
C3×#58282
C3×#58272
C3×#58242
C3×#58172
C3×#58162
C3×Q8×#672
C2×C3×#9462
C3×#34893
#872953