Finite Group Databasebeta

← C2×#11724611 #13181663

Subgroups — C2×#11724611 #13181663

Order 1728.

6332 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6312C211yesmaximal, characteristic, complemented
2C22×C3×#638C211yesmaximal, characteristic, complemented
3C22×C32×#67C211yesmaximal, characteristic, complemented
4#11724611C2116yesmaximal, direct product factor
5C2×#89039C212yesmaximal, complemented
6C2×C3⋊D3×#67C212yesmaximal, complemented
7C2×D3×#638C212yesmaximal, complemented
8C2×#89031C212yesmaximal, complemented
9C2×#89029C212yesmaximal, complemented
10C2×#89028C212yesmaximal, complemented
11C2×#64361—31nomaximal
12C2×#64330—34nomaximal
13C24×C33C2211yescharacteristic, complemented
14C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
15C23×C3×C3⋊D3C2211yescharacteristic, complemented
16C23×C32×D3C2211yescharacteristic, complemented
17C22×D3×C3⋊D3C2212yescomplemented
18C2×#6312C2212yescomplemented
19C2×#6312C2212yescomplemented
20C2×#6312C2218yescomplemented
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2212yescomplemented
23C2×C3×#638C2212yescomplemented
24C2×C3×#638C2218yescomplemented
25C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
26C2×C32×#67C2212yescomplemented
27C2×C32×#67C2212yescomplemented
28C2×C32×#67C2218yescomplemented
29C22×C32×Dic3C2211yescharacteristic, complemented
30#89039C22116yescomplemented
31C3⋊D3×#67C22116yescomplemented
32D3×#638C22116yescomplemented
33C2×#6293C2212yescomplemented
34C2×#6292C2212yescomplemented
35C2×#6291C2212yescomplemented
36C2×#6290C2212yescomplemented
37C2×#6289C2212yescomplemented
38#89031C22116yescomplemented
39C2×Dic3×C3⋊D3C2212yescomplemented
40#89029C22116yescomplemented
41#89028C22116yescomplemented
42C2×D3×C3⋊Dic3C2212yescomplemented
43C22×C32×D4—31no—
44C22×#638—32no—
45C22×#638—31no—
46C22×#638—34no—
47C22×#638—64no—
48C22×#638D311yescharacteristic, complemented
49#64361—316no—
50C2×#3830—32no—
51C2×#3830—32no—
52C2×D4×C3⋊D3—32no—
53C2×D4×C3⋊D3—32no—
54C2×#3828—32no—
55C22×C3×#67—34no—
56C22×C3×#67D314yescomplemented
57#64330—364no—
58C2×#3811—38no—
59C2×D3×#67—38no—
60C2×D3×#67—38no—
61C2×#3805—38no—
62C2×#3804—38no—
63C2×#3804—38no—
64C23×C33—42no—
65C23×C33C2311yescharacteristic
66C23×C33C2311yescharacteristic
67C23×C33C2311yescharacteristic
68C23×C33C2314yescomplemented
69C22×C3⋊(C3⋊D3)—42no—
70C22×C3⋊(C3⋊D3)C2312yes—
71C22×C3⋊(C3⋊D3)C2314yescomplemented
72C22×C3×C3⋊D3—42no—
73C22×C3×C3⋊D3C2312yes—
74C22×C3×C3⋊D3C2314yescomplemented
75C22×C32×D3—42no—
76C22×C32×D3C2312yes—
77C22×C32×D3C2314yescomplemented
78C2×D3×C3⋊D3—44no—
79C2×D3×C3⋊D3C2318yescomplemented
80#6312C2318yescomplemented
81#6312C2318yescomplemented
82C2×C3⋊(C3⋊Dic3)C2312yes—
83C2×C3⋊(C3⋊Dic3)C2314yescomplemented
84C3×#638C2318yescomplemented
85C3×#638C2318yescomplemented
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2314yescomplemented
88C32×#67C2318yescomplemented
89C32×#67C2318yescomplemented
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2314yescomplemented
92#6293C2318yescomplemented
93#6292C2318yescomplemented
94#6291C2318yescomplemented
95#6290C2318yescomplemented
96#6289C2318yescomplemented
97Dic3×C3⋊D3C2318yescomplemented
98D3×C3⋊Dic3C2318yescomplemented
99C2×#1004—94no—
100C2×#1004—91no—
101C24×C32—24no—
102C24×C32—31no—
103C24×C32C2×D314yescomplemented
104C24×C32C2×D311yescharacteristic, complemented
105C23×C3⋊D3—31no—
106C23×C3⋊D3—34no—
107C23×C3⋊D3—32no—
108C23×C3⋊D3—64no—
109C23×C3⋊D3C2×D311yescharacteristic, complemented
110C23×C3×D3—34no—
111C23×C3×D3C2×D314yescomplemented
112C22×D32—38no—
113C2×C32×D4—32no—
114C2×C32×D4—32no—
115C2×C32×D4—38no—
116C22×C32×C4—31no—
117C2×#638—32no—
118C2×#638—32no—
119C2×#638—38no—
120C2×#638—38no—
121C2×#638—38no—
122C2×#638—332no—
123C2×#638—32no—
124C2×#638—316no—
125C2×#638—32no—
126C2×#638—68no—
127C2×#638—68no—
128C2×#638—632no—
129C2×#638C2×D312yescomplemented
130C2×#638C2×D312yescomplemented
131C2×#638C2×D318yescomplemented
132C22×C3⋊Dic3—31no—
133C22×C3⋊Dic3—34no—
134C22×C3⋊Dic3—32no—
135C22×C3⋊Dic3—64no—
136C22×C3⋊Dic3C2×D311yescharacteristic, complemented
137#3830—316no—
138#3830—316no—
139D4×C3⋊D3—316no—
140D4×C3⋊D3—316no—
141#3828—316no—
142C2×C4⋊(C3⋊D3)—32no—
143C2×C4×C3⋊D3—32no—
144C2×C4×C3⋊D3—32no—
145C2×#634—32no—
146C2×C3×#67—38no—
147C2×C3×#67—38no—
148C2×C3×#67—332no—
149C2×C3×#67C2×D318yescomplemented
150C2×C3×#67C2×D318yescomplemented
151C2×C3×#67C2×D3132yescomplemented
152C22×C3×Dic3—34no—
153C22×C3×Dic3C2×D314yescomplemented
154#3811—364no—
155D3×#67—364no—
156D3×#67—364no—
157C2×#627—38no—
158C2×#626—38no—
159C2×#626—38no—
160C2×#625—38no—
161C2×#624—38no—
162#3805—364no—
163#3804—364no—
164#3804—364no—
165C2×D3×Dic3—38no—
166C2×D3×Dic3—38no—
167C22×C33—22no—
168C22×C33—22no—
169C22×C33—22no—
170C22×C33—44no—
171C22×C33C2412yes—
172C22×C33C2412yes—
173C22×C33C2412yes—
174C22×C33C2411yescharacteristic
175C2×C3⋊(C3⋊D3)—24no—
176C2×C3⋊(C3⋊D3)—44no—
177C2×C3⋊(C3⋊D3)C2414yes—
178C2×C3×C3⋊D3—24no—
179C2×C3×C3⋊D3—44no—
180C2×C3×C3⋊D3C2414yes—
181C2×C32×D3—24no—
182C2×C32×D3—44no—
183C2×C32×D3C2414yes—
184D3×C3⋊D3—48no—
185C3⋊(C3⋊Dic3)C2414yes—
186C3×C3⋊Dic3C2414yes—
187C32×Dic3C2414yes—
188C22×C3×D4—34no—
189C22×C3×D4—91no—
190C22×#67—34no—
191C22×#67—98no—
192C22×#67—94no—
193C22×#67—91no—
194C22×#67—92no—
195C22×#67—184no—
196C22×#67C3⋊D311yescharacteristic, complemented
197#1004—964no—
198#1004—916no—
199C2×#237—98no—
200C2×#237—98no—
201C2×#237—92no—
202C2×#237—92no—
203C2×D3×D4—98no—
204C2×D3×D4—98no—
205C2×D3×D4—92no—
206C2×D3×D4—92no—
207C2×#235—98no—
208C2×#235—92no—
209C23×C32—24no—
210C23×C32—24no—
211C23×C32—24no—
212C23×C32—216no—
213C23×C32—32no—
214C23×C32—34no—
215C23×C32—42no—
216C23×C32—48no—
217C23×C32—416no—
218C23×C32—122no—
219C23×C32C22×D314yes—
220C23×C32C22×D314yes—
221C23×C32C22×D314yes—
222C23×C32C22×D311yescharacteristic
223C23×C32C22×D311yescharacteristic
224C23×C32C22×D311yescharacteristic
225C23×C32C22×D3116yescomplemented
226C23×C32C22×D314yescomplemented
227C22×C3⋊D3—32no—
228C22×C3⋊D3—34no—
229C22×C3⋊D3—38no—
230C22×C3⋊D3—38no—
231C22×C3⋊D3—316no—
232C22×C3⋊D3—42no—
233C22×C3⋊D3—68no—
234C22×C3⋊D3—616no—
235C22×C3⋊D3—124no—
236C22×C3⋊D3—122no—
237C22×C3⋊D3—128no—
238C22×C3⋊D3—1216no—
239C22×C3⋊D3C22×D312yes—
240C22×C3⋊D3C22×D314yescomplemented
241C22×C3×D3—38no—
242C22×C3×D3—316no—
243C22×C3×D3—48no—
244C22×C3×D3—128no—
245C22×C3×D3C22×D318yes—
246C22×C3×D3C22×D3116yescomplemented
247C2×D32—332no—
248C2×D32—1216no—
249C32×D4—38no—
250C32×D4—38no—
251C2×C32×C4—32no—
252C2×C32×C4—34no—
253#638—38no—
254#638—38no—
255#638—38no—
256#638—38no—
257#638—332no—
258#638—332no—
259#638—632no—
260#638—632no—
261#638C22×D318yescomplemented
262#638C22×D318yescomplemented
263C2×C3⋊Dic3—32no—
264C2×C3⋊Dic3—34no—
265C2×C3⋊Dic3—38no—
266C2×C3⋊Dic3—38no—
267C2×C3⋊Dic3—316no—
268C2×C3⋊Dic3—68no—
269C2×C3⋊Dic3—616no—
270C2×C3⋊Dic3C22×D312yes—
271C2×C3⋊Dic3C22×D314yescomplemented
272C4⋊(C3⋊D3)—38no—
273C4×C3⋊D3—38no—
274C4×C3⋊D3—38no—
275#634—38no—
276C3×#67—332no—
277C3×#67—332no—
278C3×#67C22×D3132yescomplemented
279C3×#67C22×D3132yescomplemented
280C2×C3×Dic3—38no—
281C2×C3×Dic3—316no—
282C2×C3×Dic3C22×D318yes—
283C2×C3×Dic3C22×D3116yescomplemented
284#627—332no—
285#626—332no—
286#626—332no—
287#625—332no—
288#624—332no—
289D3×Dic3—332no—
290D3×Dic3—332no—
291C2×H(5,𝔽2)—271noSylow
292C2×C33—22no—
293C2×C33—22no—
294C2×C33—22no—
295C2×C33H(5,𝔽2)12yescomplemented
296C2×C33C2511yescharacteristic
297C3⋊(C3⋊D3)—24no—
298C3×C3⋊D3—24no—
299C32×D3—24no—
300C24×C3—24no—
301C24×C3—34no—
302C24×C3—91no—
303C24×C3D3214yescomplemented
304C24×C3C2×C3⋊D311yescharacteristic, complemented
305C23×D3—34no—
306C23×D3—98no—
307C23×D3—94no—
308C23×D3—91no—
309C23×D3—92no—
310C23×D3—184no—
311C23×D3C2×C3⋊D311yescharacteristic, complemented
312C2×C3×D4—38no—
313C2×C3×D4—38no—
314C2×C3×D4—332no—
315C2×C3×D4—92no—
316C2×C3×D4—92no—
317C2×C3×D4—98no—
318C22×C3×C4—34no—
319C22×C3×C4—91no—
320C2×#67—38no—
321C2×#67—38no—
322C2×#67—332no—
323C2×#67—98no—
324C2×#67—964no—
325C2×#67—98no—
326C2×#67—98no—
327C2×#67—98no—
328C2×#67—932no—
329C2×#67—92no—
330C2×#67—92no—
331C2×#67—98no—
332C2×#67—92no—
333C2×#67—916no—
334C2×#67—92no—
335C2×#67—188no—
336C2×#67—188no—
337C2×#67—1832no—
338C2×#67C2×C3⋊D312yescomplemented
339C2×#67C2×C3⋊D312yescomplemented
340C2×#67C2×C3⋊D318yescomplemented
341C22×Dic3—34no—
342C22×Dic3—98no—
343C22×Dic3—94no—
344C22×Dic3—91no—
345C22×Dic3—92no—
346C22×Dic3—184no—
347C22×Dic3C2×C3⋊D311yescharacteristic, complemented
348#237—964no—
349#237—964no—
350#237—916no—
351#237—916no—
352D3×D4—964no—
353D3×D4—964no—
354D3×D4—916no—
355D3×D4—916no—
356#235—964no—
357#235—916no—
358C2×D12—98no—
359C2×D12—92no—
360C2×C4×D3—98no—
361C2×C4×D3—98no—
362C2×C4×D3—92no—
363C2×C4×D3—92no—
364C2×Dic6—98no—
365C2×Dic6—92no—
366C22×C32—216no—
367C22×C32—22no—
368C22×C32—28no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—28no—
372C22×C32—24no—
373C22×C32—28no—
374C22×C32—28no—
375C22×C32—28no—
376C22×C32—28no—
377C22×C32—34no—
378C22×C32—48no—
379C22×C32—48no—
380C22×C32—44no—
381C22×C32—416no—
382C22×C32—432no—
383C22×C32—64no—
384C22×C32—124no—
385C22×C32C23×D318yes—
386C22×C32C23×D318yes—
387C22×C32C23×D318yes—
388C22×C32C23×D314yes—
389C22×C32C23×D312yes—
390C22×C32C23×D312yes—
391C22×C32C23×D312yes—
392C22×C32C23×D311yescharacteristic
393C2×C3⋊D3—24no—
394C2×C3⋊D3—34no—
395C2×C3⋊D3—316no—
396C2×C3⋊D3—44no—
397C2×C3⋊D3—616no—
398C2×C3⋊D3—64no—
399C2×C3⋊D3—616no—
400C2×C3⋊D3—1216no—
401C2×C3⋊D3—128no—
402C2×C3⋊D3—124no—
403C2×C3⋊D3—1216no—
404C2×C3⋊D3—1232no—
405C2×C3⋊D3C23×D314yes—
406C2×C3×D3—216no—
407C2×C3×D3—316no—
408C2×C3×D3—416no—
409C2×C3×D3—616no—
410C2×C3×D3—1216no—
411C2×C3×D3C23×D3116yes—
412D32—1232no—
413C32×C4—34no—
414C3⋊Dic3—34no—
415C3⋊Dic3—316no—
416C3⋊Dic3—616no—
417C3⋊Dic3C23×D314yes—
418C3×Dic3—316no—
419C3×Dic3C23×D3116yes—
420H(5,𝔽2)—2716no—
421C2×#41—272no—
422C2×#41—272no—
423C2×#41—272no—
424C22×D4—31no—
425C22×D4—91no—
426C22×D4—272no—
427C22×D4—272no—
428C22×D4—272no—
429C22×D4—271no—
430C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
431C23×C3—24no—
432C23×C3—24no—
433C23×C3—24no—
434C23×C3—216no—
435C23×C3—38no—
436C23×C3—316no—
437C23×C3—48no—
438C23×C3—42no—
439C23×C3—416no—
440C23×C3—92no—
441C23×C3—94no—
442C23×C3—128no—
443C23×C3—362no—
444C23×C3C2×D3214yes—
445C23×C3C2×D3214yes—
446C23×C3C2×D3214yes—
447C23×C3C2×D32116yescomplemented
448C23×C3C22×C3⋊D311yescharacteristic
449C23×C3C22×C3⋊D311yescharacteristic
450C23×C3C22×C3⋊D311yescharacteristic
451C23×C3C22×C3⋊D314yescomplemented
452C22×D3—38no—
453C22×D3—316no—
454C22×D3—42no—
455C22×D3—932no—
456C22×D3—98no—
457C22×D3—92no—
458C22×D3—916no—
459C22×D3—94no—
460C22×D3—98no—
461C22×D3—128no—
462C22×D3—188no—
463C22×D3—1816no—
464C22×D3—364no—
465C22×D3—3616no—
466C22×D3—368no—
467C22×D3—362no—
468C22×D3—3616no—
469C22×D3C22×C3⋊D312yes—
470C22×D3C22×C3⋊D314yescomplemented
471C3×D4—332no—
472C3×D4—332no—
473C3×D4—98no—
474C3×D4—98no—
475C2×C3×C4—38no—
476C2×C3×C4—316no—
477C2×C3×C4—92no—
478C2×C3×C4—94no—
479#67—332no—
480#67—332no—
481#67—932no—
482#67—932no—
483#67—932no—
484#67—932no—
485#67—98no—
486#67—98no—
487#67—98no—
488#67—98no—
489#67—1832no—
490#67—1832no—
491#67C22×C3⋊D318yescomplemented
492#67C22×C3⋊D318yescomplemented
493C2×Dic3—38no—
494C2×Dic3—316no—
495C2×Dic3—932no—
496C2×Dic3—98no—
497C2×Dic3—916no—
498C2×Dic3—92no—
499C2×Dic3—94no—
500C2×Dic3—98no—
501C2×Dic3—1816no—
502C2×Dic3—188no—
503C2×Dic3C22×C3⋊D312yes—
504C2×Dic3C22×C3⋊D314yescomplemented
505D12—932no—
506D12—98no—
507C4×D3—932no—
508C4×D3—932no—
509C4×D3—98no—
510C4×D3—98no—
511Dic6—932no—
512Dic6—98no—
513C2×C32—216no—
514C2×C32—22no—
515C2×C32—28no—
516C2×C32—22no—
517C2×C32—22no—
518C2×C32—28no—
519C2×C32—24no—
520C2×C32—28no—
521C2×C32—28no—
522C2×C32—48no—
523C2×C32—48no—
524C2×C32—64no—
525C2×C32#100418yescomplemented
526C2×C32#100412yescomplemented
527C2×C32C24×D314yes—
528C2×C32C24×D311yescharacteristic
529C3⋊D3—24no—
530C3⋊D3—64no—
531C3⋊D3—616no—
532C3⋊D3—1216no—
533C3×D3—216no—
534C3×D3—616no—
535C24—31no—
536C24—91no—
537C24—272no—
538C24—271no—
539C24D3×C3⋊D311yescharacteristic, complemented
540#41—2716no—
541#41—2716no—
542#41—2716no—
543C2×Q8—272no—
544C2×D4—32no—
545C2×D4—32no—
546C2×D4—38no—
547C2×D4—92no—
548C2×D4—92no—
549C2×D4—98no—
550C2×D4—272no—
551C2×D4—272no—
552C2×D4—2716no—
553C2×D4—2716no—
554C2×D4—2716no—
555C2×D4—272no—
556C2×D4—272no—
557C2×D4—272no—
558C2×D4—278no—
559C22×C4—31no—
560C22×C4—91no—
561C22×C4—272no—
562C22×C4—272no—
563C22×C4—272no—
564C22×C4—271no—
565C22×C3—216no—
566C22×C3—28no—
567C22×C3—28no—
568C22×C3—28no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—28no—
573C22×C3—28no—
574C22×C3—28no—
575C22×C3—24no—
576C22×C3—316no—
577C22×C3—48no—
578C22×C3—48no—
579C22×C3—416no—
580C22×C3—44no—
581C22×C3—432no—
582C22×C3—616no—
583C22×C3—94no—
584C22×C3—1216no—
585C22×C3—184no—
586C22×C3—364no—
587C22×C3C22×D3218yes—
588C22×C3C22×D3218yes—
589C22×C3C22×D3218yes—
590C22×C3C22×D3214yes—
591C22×C3C23×C3⋊D312yes—
592C22×C3C23×C3⋊D312yes—
593C22×C3C23×C3⋊D312yes—
594C22×C3C23×C3⋊D311yescharacteristic
595C2×D3—24no—
596C2×D3—316no—
597C2×D3—44no—
598C2×D3—616no—
599C2×D3—916no—
600C2×D3—94no—
601C2×D3—1216no—
602C2×D3—1816no—
603C2×D3—1816no—
604C2×D3—184no—
605C2×D3—3616no—
606C2×D3—368no—
607C2×D3—3632no—
608C2×D3—3616no—
609C2×D3—364no—
610C2×D3—3632no—
611C2×D3C23×C3⋊D314yes—
612C3×C4—316no—
613C3×C4—94no—
614Dic3—316no—
615Dic3—916no—
616Dic3—94no—
617Dic3—1816no—
618Dic3C23×C3⋊D314yes—
619C32—24no—
620C32C2×#100414yescomplemented
621C32C2×#100411yescharacteristic, complemented
622C23—32no—
623C23—34no—
624C23—42no—
625C23—92no—
626C23—94no—
627C23—122no—
628C23—278no—
629C23—272no—
630C23—274no—
631C23—362no—
632C23—1082no—
633C23—1084no—
634C23C2×D3×C3⋊D311yescharacteristic
635C23C2×D3×C3⋊D311yescharacteristic
636C23C2×D3×C3⋊D311yescharacteristic
637C23C2×D3×C3⋊D314yescomplemented
638Q8—278no—
639D4—38no—
640D4—38no—
641D4—98no—
642D4—98no—
643D4—278no—
644D4—278no—
645D4—278no—
646D4—278no—
647D4—278no—
648C2×C4—34no—
649C2×C4—32no—
650C2×C4—94no—
651C2×C4—92no—
652C2×C4—278no—
653C2×C4—278no—
654C2×C4—278no—
655C2×C4—274no—
656C2×C4—272no—
657C2×C3—216no—
658C2×C3—28no—
659C2×C3—28no—
660C2×C3—28no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—22no—
664C2×C3—28no—
665C2×C3—24no—
666C2×C3—48no—
667C2×C3—48no—
668C2×C3—616no—
669C2×C3—184no—
670C2×C3#6433018yescomplemented
671C2×C3#6436112yescomplemented
672C2×C3C23×D3214yes—
673C2×C3C24×C3⋊D311yescharacteristic
674D3—24no—
675D3—616no—
676D3—1816no—
677D3—184no—
678D3—3616no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—34no—
683C22—44no—
684C22—64no—
685C22—94no—
686C22—124no—
687C22—184no—
688C22—274no—
689C22—364no—
690C22—544no—
691C22—1084no—
692C22—1088no—
693C22C22×D3×C3⋊D312yes—
694C22C22×D3×C3⋊D312yes—
695C22C22×D3×C3⋊D312yes—
696C22C22×D3×C3⋊D311yescharacteristic
697C4—34no—
698C4—94no—
699C4—274no—
700C3—24no—
701C3C2×#6433014yescomplemented
702C3C2×#6436111yescharacteristic, complemented
703C2—22no—
704C2—22no—
705C2—22no—
706C2—64no—
707C2—184no—
708C2—544no—
709C2#1172461112yesdirect product factor
710C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC22C22×D3×C3⋊D3
commutator, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC24×C33C22
socleC22×C33C24
hypercenterC24D3×C3⋊D3
hypocenterC33C2×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#6312C2semidirect
2. C22×C3×#638C2semidirect
3. C22×C32×#67C2semidirect
4. #11724611C2direct (N × H)
5. C2×#89039C2semidirect
6. C2×C3⋊D3×#67C2semidirect
7. C2×D3×#638C2semidirect
8. C2×#89031C2semidirect
9. C2×#89029C2semidirect
10. C2×#89028C2semidirect
13. C24×C33C22semidirect
14. C23×C3⋊(C3⋊D3)C22semidirect
15. C23×C3×C3⋊D3C22semidirect
16. C23×C32×D3C22semidirect
17. C22×D3×C3⋊D3C22semidirect
18. C2×#6312C22semidirect
19. C2×#6312C22semidirect
20. C2×#6312C22semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C22×C3×C3⋊Dic3C22semidirect
26. C2×C32×#67C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×#67C22semidirect
29. C22×C32×Dic3C22semidirect
30. #89039C22semidirect
31. C3⋊D3×#67C22semidirect
32. D3×#638C22semidirect
33. C2×#6293C22semidirect
34. C2×#6292C22semidirect
35. C2×#6291C22semidirect
36. C2×#6290C22semidirect
37. C2×#6289C22semidirect
38. #89031C22semidirect
39. C2×Dic3×C3⋊D3C22semidirect
40. #89029C22semidirect
41. #89028C22semidirect
42. C2×D3×C3⋊Dic3C22semidirect
48. C22×#638D3semidirect
56. C22×C3×#67D3semidirect
68. C23×C33C23semidirect
71. C22×C3⋊(C3⋊D3)C23semidirect
74. C22×C3×C3⋊D3C23semidirect
77. C22×C32×D3C23semidirect
79. C2×D3×C3⋊D3C23semidirect
80. #6312C23semidirect
81. #6312C23semidirect
83. C2×C3⋊(C3⋊Dic3)C23semidirect
84. C3×#638C23semidirect
85. C3×#638C23semidirect
87. C2×C3×C3⋊Dic3C23semidirect
88. C32×#67C23semidirect
89. C32×#67C23semidirect
91. C2×C32×Dic3C23semidirect
92. #6293C23semidirect
93. #6292C23semidirect
94. #6291C23semidirect
95. #6290C23semidirect
96. #6289C23semidirect
97. Dic3×C3⋊D3C23semidirect
98. D3×C3⋊Dic3C23semidirect
103. C24×C32C2×D3semidirect
104. C24×C32C2×D3semidirect
109. C23×C3⋊D3C2×D3semidirect
111. C23×C3×D3C2×D3semidirect
129. C2×#638C2×D3semidirect
130. C2×#638C2×D3semidirect
131. C2×#638C2×D3semidirect
136. C22×C3⋊Dic3C2×D3semidirect
149. C2×C3×#67C2×D3semidirect
150. C2×C3×#67C2×D3semidirect
151. C2×C3×#67C2×D3semidirect
153. C22×C3×Dic3C2×D3semidirect
196. C22×#67C3⋊D3semidirect
225. C23×C32C22×D3semidirect
226. C23×C32C22×D3semidirect
240. C22×C3⋊D3C22×D3semidirect
246. C22×C3×D3C22×D3semidirect
261. #638C22×D3semidirect
262. #638C22×D3semidirect
271. C2×C3⋊Dic3C22×D3semidirect
278. C3×#67C22×D3semidirect
279. C3×#67C22×D3semidirect
283. C2×C3×Dic3C22×D3semidirect
295. C2×C33H(5,𝔽2)semidirect
303. C24×C3D32semidirect
304. C24×C3C2×C3⋊D3semidirect
311. C23×D3C2×C3⋊D3semidirect
338. C2×#67C2×C3⋊D3semidirect
339. C2×#67C2×C3⋊D3semidirect
340. C2×#67C2×C3⋊D3semidirect
347. C22×Dic3C2×C3⋊D3semidirect
430. C33C2×H(5,𝔽2)semidirect
447. C23×C3C2×D32semidirect
451. C23×C3C22×C3⋊D3semidirect
470. C22×D3C22×C3⋊D3semidirect
491. #67C22×C3⋊D3semidirect
492. #67C22×C3⋊D3semidirect
504. C2×Dic3C22×C3⋊D3semidirect
525. C2×C32#1004semidirect
526. C2×C32#1004semidirect
539. C24D3×C3⋊D3semidirect
620. C32C2×#1004semidirect
621. C32C2×#1004semidirect
637. C23C2×D3×C3⋊D3semidirect
670. C2×C3#64330semidirect
671. C2×C3#64361semidirect
701. C3C2×#64330semidirect
702. C3C2×#64361semidirect
709. C2#11724611direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#63122
C22×C3×#6382
C22×C32×#672
#117246112
C2×#890392
C2×C3⋊D3×#672
C2×D3×#6382
C2×#890312
C2×#890292
C2×#890282
C2×#643613
C2×#643303