Finite Group Databasebeta

← C3×#83322 #11864949

Subgroups — C3×#83322 #11864949

Order 1152.

1603 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2C32×#532C211yesmaximal, characteristic, complemented
3C3×#5822C212yesmaximal, complemented
4C3×#5237C211yesmaximal, characteristic, complemented
5C3×#5095C212yesmaximal, complemented
6C3×#5077C212yesmaximal, complemented
7C3×#5062C212yesmaximal, complemented
8C3×#5061C212yesmaximal, complemented
9C2×C3×#805C212yesmaximal, complemented
10C3×#3018—31nomaximal
11#83322C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C2×C32×#41C2211yescharacteristic, complemented
14C3×#1010—22no—
15C3×#1009—22no—
16C3×D3×#41—24no—
17C3×#1007C2212yes—
18C3×#1004—22no—
19C3×#1004C2212yes—
20C2×C3×#235—22no—
21C2×C3×#235C2212yes—
22C32×C4⋊Q8C2211yescharacteristic, complemented
23C32×#127C2211yescharacteristic, complemented
24C32×#124C2211yescharacteristic, complemented
25C32×#124C2211yescharacteristic, complemented
26C32×#121—22no—
27C32×C4×D4—22no—
28C2×C32×C42C2211yescharacteristic, complemented
29C3×#951—22no—
30C3×#950—24no—
31C3×#949—22no—
32C3×#942C2214yescomplemented
33C3×#932C2214yescomplemented
34C2×C3×#208C2212yescomplemented
35C3×#836C2212yescomplemented
36C3×#833C2212yescomplemented
37C3×#805C2214yescomplemented
38C3×#805C2214yescomplemented
39C3×#585—31no—
40#5964C2×C311yescharacteristic, complemented
41C3×#575—32no—
42C3×#532—21no—
43C3×#532D311yescharacteristic, complemented
44C3×#532C2×C311yescharacteristic, complemented
45#5822C2×C312yescomplemented
46C3×#456—32no—
47C3×#455—32no—
48C3×#454—32no—
49C3×#453—32no—
50C2×C3×#104—32no—
51C3×#413—31no—
52#5237C2×C311yescharacteristic, complemented
53#5095C2×C312yescomplemented
54#5077C2×C312yescomplemented
55#5062C2×C312yescomplemented
56#5061C2×C312yescomplemented
57C2×#805C2×C312yescomplemented
58C32×#41—22no—
59C32×#41—22no—
60C32×#41—22no—
61C32×#41—22no—
62C2×C32×Q8C2311yescharacteristic
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4—22no—
66C2×C32×D4D412yes—
67C2×C32×D4C2311yescharacteristic
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4D412yes—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—24no—
74C2×C3×#67—22no—
75C3×#239—24no—
76C3×D3×Q8—24no—
77C3×#237—28no—
78C3×#237—24no—
79C3×D3×D4—28no—
80C3×D3×D4—24no—
81C3×#235—24no—
82C3×#235—24no—
83C3×#235—22no—
84C3×#235—24no—
85C3×#235—22no—
86C3×#235D414yescomplemented
87C3×#235C2314yes—
88C2×C3×D12—22no—
89C2×C3×D12D412yescomplemented
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—22no—
92C2×C3×Dic6—22no—
93C2×C3×Dic6D412yescomplemented
94C32×C4⋊C4—22no—
95C32×C22⋊C4—22no—
96C32×C22⋊C4—22no—
97C32×C42—21no—
98C32×C42C2311yescharacteristic
99C32×C42C2311yescharacteristic
100C3×#216—24no—
101C3×#215—24no—
102C3×#214—24no—
103C3×#213—24no—
104C3×#208—22no—
105C3×#208C2314yes—
106C2×C3×C3⋊C8—22no—
107#3018—31noSylow
108C3×2−1+4—32no—
109C3×2−1+4—62no—
110C3×H(5,𝔽2)—32no—
111C3×H(5,𝔽2)—62no—
112C3×H(5,𝔽2)—62no—
113C2×C3×#41—21no—
114C2×C3×#41—21no—
115C2×C3×#41—32no—
116C2×C3×#41—64no—
117C2×C3×#41—62no—
118C2×C3×#41C2×D311yescharacteristic
119C2×C3×#41C2×D311yescharacteristic, complemented
120C2×C3×#41C22×C311yescharacteristic
121C2×C3×#41C22×C311yescharacteristic, complemented
122#1010—22no—
123#1009—22no—
124D3×#41—24no—
125#1007C22×C312yes—
126#1004—22no—
127#1004C22×C312yes—
128C2×#235—22no—
129C2×#235C22×C312yes—
130C3×#137—34no—
131C3×#137—62no—
132C3×AGL(1,ℤ/8)—34no—
133C3×AGL(1,ℤ/8)—62no—
134C3×#135—64no—
135C2×C3×M16—32no—
136C3×C4⋊Q8—21no—
137C3×C4⋊Q8C2×D311yescharacteristic, complemented
138C3×C4⋊Q8C22×C311yescharacteristic, complemented
139C3×#127—21no—
140C3×#127C2×D311yescharacteristic, complemented
141C3×#127C22×C311yescharacteristic, complemented
142C3×#124—21no—
143C3×#124—21no—
144C3×#124C2×D311yescharacteristic, complemented
145C3×#124C2×D311yescharacteristic, complemented
146C3×#124C22×C311yescharacteristic, complemented
147C3×#124C22×C311yescharacteristic, complemented
148C3×#121—24no—
149C3×#121—22no—
150C3×#121—22no—
151C3×C4×D4—24no—
152C3×C4×D4—22no—
153C3×C4×D4—22no—
154C2×C3×C42—21no—
155C2×C3×C42C2×D311yescharacteristic, complemented
156C2×C3×C42C22×C311yescharacteristic, complemented
157#951—22no—
158#950—24no—
159#949—22no—
160#942C22×C314yescomplemented
161#932C22×C314yescomplemented
162C2×#208C22×C312yescomplemented
163C3×#104—34no—
164C3×#104—34no—
165C3×#101—32no—
166C3×#100—32no—
167#836C22×C312yescomplemented
168#833C22×C312yescomplemented
169#805C22×C314yescomplemented
170#805C22×C314yescomplemented
171C23×C32—21no—
172C23×C32C2×D412yes—
173C23×C32C2×D411yescharacteristic
174C22×C3×D3—24no—
175C22×C3×D3—22no—
176C32×Q8—22no—
177C32×Q8—22no—
178C32×D4—24no—
179C32×D4—22no—
180C32×D4—22no—
181C32×D4—44no—
182C32×D4—42no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—42no—
189C2×C32×C4—41no—
190C2×C32×C4—41no—
191C2×C32×C4C2×D412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D412yes—
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2411yescharacteristic
196C3×#67—28no—
197C3×#67—24no—
198C3×#67—24no—
199C2×C3×Dic3—24no—
200C2×C3×Dic3—22no—
201C3×D12—24no—
202C3×D12—22no—
203C3×D12C2×D414yes—
204C3×C4×D3—28no—
205C3×C4×D3—24no—
206C3×C4×D3—24no—
207C3×Dic6—24no—
208C3×Dic6—22no—
209C3×Dic6C2×D414yes—
210C3×C3⋊C8—24no—
211#585—31no—
212#575—32no—
213#532C3×D311yescharacteristic, complemented
214#456—32no—
215#455—32no—
216#454—32no—
217#453—32no—
218C2×#104—32no—
219#413—31no—
220C3×#41—22no—
221C3×#41—22no—
222C3×#41—22no—
223C3×#41—22no—
224C3×#41—22no—
225C3×#41—22no—
226C3×#41—22no—
227C3×#41—22no—
228C3×#41—34no—
229C3×#41—34no—
230C3×#41—42no—
231C3×#41—42no—
232C3×#41—42no—
233C3×#41—42no—
234C3×#41—64no—
235C3×#41—64no—
236C3×#41—64no—
237C3×#41—68no—
238C3×#41—64no—
239C3×#41—62no—
240C3×#41—62no—
241C3×#41—64no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—32no—
245C2×C3×Q8—62no—
246C2×C3×Q8—64no—
247C2×C3×Q8C22×D311yescharacteristic
248C2×C3×Q8C22×D311yescharacteristic
249C2×C3×Q8C23×C311yescharacteristic
250C2×C3×Q8C23×C311yescharacteristic
251C2×C3×D4—24no—
252C2×C3×D4—22no—
253C2×C3×D4—22no—
254C2×C3×D4—21no—
255C2×C3×D4—22no—
256C2×C3×D4—21no—
257C2×C3×D4—22no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—32no—
261C2×C3×D4—62no—
262C2×C3×D4—64no—
263C2×C3×D4—68no—
264C2×C3×D4—62no—
265C2×C3×D4—64no—
266C2×C3×D4#6712yes—
267C2×C3×D4C3×D412yes—
268C2×C3×D4C22×D311yescharacteristic
269C2×C3×D4C22×D311yescharacteristic
270C2×C3×D4C23×C311yescharacteristic
271C2×C3×D4C23×C311yescharacteristic
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—22no—
279C22×C3×C4—21no—
280C22×C3×C4—64no—
281C22×C3×C4—62no—
282C22×C3×C4#6712yes—
283C22×C3×C4C3×D412yes—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C23×C311yescharacteristic
286C2×#67—24no—
287C2×#67—22no—
288#239—24no—
289D3×Q8—24no—
290#237—28no—
291#237—24no—
292D3×D4—28no—
293D3×D4—24no—
294#235—24no—
295#235—24no—
296#235—22no—
297#235—24no—
298#235—22no—
299#235C3×D414yescomplemented
300#235C23×C314yes—
301C2×D12—22no—
302C2×D12C3×D412yescomplemented
303C2×C4×D3—24no—
304C2×C4×D3—22no—
305C2×Dic6—22no—
306C2×Dic6C3×D412yescomplemented
307C3×Q16—64no—
308C3×SD16—64no—
309C3×SD16—64no—
310C3×D8—64no—
311C3×M16—34no—
312C3×M16—62no—
313C2×C3×C8—62no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—22no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—22no—
321C3×C22⋊C4—22no—
322C3×C22⋊C4—22no—
323C3×C42—22no—
324C3×C42—21no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42—21no—
328C3×C42C22×D311yescharacteristic
329C3×C42C22×D311yescharacteristic
330C3×C42C23×C311yescharacteristic
331C3×C42C23×C311yescharacteristic
332#216—24no—
333#215—24no—
334#214—24no—
335#213—24no—
336#208—22no—
337#208C23×C314yes—
338C2×C3⋊C8—22no—
339C22×C32—22no—
340C22×C32—41no—
341C22×C32—42no—
342C22×C32—42no—
343C22×C32—41no—
344C22×C32#12012yes—
345C22×C32C22×D411yescharacteristic
346C2×C3×D3—24no—
347C2×C3×D3—82no—
348C2×C3×D3—84no—
349C32×C4—22no—
350C32×C4—22no—
351C32×C4—41no—
352C32×C4—41no—
353C32×C4#12011yescharacteristic
354C32×C4#12011yescharacteristic
355C32×C4C22×D412yes—
356C3×Dic3—24no—
3572−1+4—32no—
3582−1+4—62no—
359H(5,𝔽2)—32no—
360H(5,𝔽2)—62no—
361H(5,𝔽2)—62no—
362C2×#41—32no—
363C2×#41—64no—
364C2×#41—62no—
365C2×#41C2×C3×D311yescharacteristic
366C2×#41C2×C3×D311yescharacteristic, complemented
367#137—34no—
368#137—62no—
369AGL(1,ℤ/8)—34no—
370AGL(1,ℤ/8)—62no—
371#135—64no—
372C2×M16—32no—
373C4⋊Q8C2×C3×D311yescharacteristic, complemented
374#127C2×C3×D311yescharacteristic, complemented
375#124C2×C3×D311yescharacteristic, complemented
376#124C2×C3×D311yescharacteristic, complemented
377#121—22no—
378C4×D4—22no—
379C2×C42C2×C3×D311yescharacteristic, complemented
380#104—34no—
381#104—34no—
382#101—32no—
383#100—32no—
384C23×C3—22no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—22no—
389C23×C3—64no—
390C23×C3—62no—
391C23×C3C2×#6712yes—
392C23×C3C2×#6711yescharacteristic
393C23×C3C2×C3×D412yes—
394C23×C3C2×C3×D411yescharacteristic
395C22×D3—24no—
396C22×D3—22no—
397C3×Q8—22no—
398C3×Q8—22no—
399C3×Q8—22no—
400C3×Q8—22no—
401C3×Q8—34no—
402C3×Q8—42no—
403C3×Q8—42no—
404C3×Q8—64no—
405C3×Q8—62no—
406C3×D4—24no—
407C3×D4—24no—
408C3×D4—22no—
409C3×D4—22no—
410C3×D4—22no—
411C3×D4—22no—
412C3×D4—34no—
413C3×D4—42no—
414C3×D4—42no—
415C3×D4—44no—
416C3×D4—44no—
417C3×D4—44no—
418C3×D4—48no—
419C3×D4—44no—
420C3×D4—42no—
421C3×D4—42no—
422C3×D4—64no—
423C3×D4—68no—
424C3×D4—64no—
425C3×D4—64no—
426C3×D4—62no—
427C2×C3×C4—22no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—44no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—68no—
457C2×C3×C4—64no—
458C2×C3×C4—62no—
459C2×C3×C4—64no—
460C2×C3×C4—64no—
461C2×C3×C4D3×D412yes—
462C2×C3×C4D3×D412yes—
463C2×C3×C4C2×#6712yes—
464C2×C3×C4C2×#6711yescharacteristic
465C2×C3×C4C2×C3×D412yes—
466C2×C3×C4C2×C3×D412yes—
467C2×C3×C4C2×C3×D412yes—
468C2×C3×C4C2×C3×D411yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470C2×C3×C4C24×C311yescharacteristic
471#67—28no—
472#67—24no—
473#67—24no—
474C2×Dic3—24no—
475C2×Dic3—22no—
476D12—24no—
477D12—22no—
478D12C2×C3×D414yes—
479C4×D3—28no—
480C4×D3—24no—
481C4×D3—24no—
482Dic6—24no—
483Dic6—22no—
484Dic6C2×C3×D414yes—
485C3×C8—64no—
486C3⋊C8—24no—
487C2×C32—21no—
488C2×C32—22no—
489C2×C32—42no—
490C2×C32—81no—
491C2×C32C2×#12011yescharacteristic
492C3×D3—44no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—34no—
498#41—34no—
499#41—64no—
500#41—64no—
501#41—64no—
502#41—68no—
503#41—64no—
504#41—62no—
505#41—62no—
506#41—64no—
507C2×Q8—32no—
508C2×Q8—62no—
509C2×Q8—64no—
510C2×Q8C22×C3×D311yescharacteristic
511C2×Q8C22×C3×D311yescharacteristic
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—32no—
515C2×D4—62no—
516C2×D4—64no—
517C2×D4—68no—
518C2×D4—62no—
519C2×D4—64no—
520C2×D4C3×#6712yes—
521C2×D4C22×C3×D311yescharacteristic
522C2×D4C22×C3×D311yescharacteristic
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—64no—
526C22×C4—62no—
527C22×C4C3×#6712yes—
528C22×C4C22×C3×D311yescharacteristic
529Q16—64no—
530SD16—64no—
531SD16—64no—
532D8—64no—
533M16—34no—
534M16—62no—
535C2×C8—62no—
536C4⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C42—21no—
540C42C22×C3×D311yescharacteristic
541C42C22×C3×D311yescharacteristic
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—21no—
546C22×C3—42no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—64no—
560C22×C3—242no—
561C22×C3—244no—
562C22×C3#93712yes—
563C22×C3C3×#12012yes—
564C22×C3C22×#6711yescharacteristic
565C22×C3C22×C3×D411yescharacteristic
566C2×D3—24no—
567C2×D3—82no—
568C2×D3—84no—
569C3×C4—24no—
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—22no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—22no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—42no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—64no—
585C3×C4#93711yescharacteristic
586C3×C4#93711yescharacteristic
587C3×C4C3×#12011yescharacteristic
588C3×C4C3×#12011yescharacteristic
589C3×C4C2×D3×D412yes—
590C3×C4C22×C3×D412yes—
591Dic3—24no—
592C32#301811yescharacteristic, complemented, Sylow
593C23—21no—
594C23—64no—
595C23—62no—
596C23C2×C3×#6712yes—
597C23C2×C3×#6711yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—34no—
601Q8—64no—
602Q8—62no—
603D4—24no—
604D4—22no—
605D4—22no—
606D4—34no—
607D4—44no—
608D4—42no—
609D4—64no—
610D4—68no—
611D4—64no—
612D4—64no—
613D4—62no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—68no—
623C2×C4—64no—
624C2×C4—62no—
625C2×C4—64no—
626C2×C4—64no—
627C2×C4C3×D3×D412yes—
628C2×C4C3×D3×D412yes—
629C2×C4C2×C3×#6712yes—
630C2×C4C2×C3×#6711yescharacteristic
631C2×C4C23×C3×D311yescharacteristic
632C8—64no—
633C2×C3—22no—
634C2×C3—21no—
635C2×C3—22no—
636C2×C3—21no—
637C2×C3—22no—
638C2×C3—21no—
639C2×C3—42no—
640C2×C3—42no—
641C2×C3—42no—
642C2×C3—82no—
643C2×C3—82no—
644C2×C3—81no—
645C2×C3—81no—
646C2×C3—124no—
647C2×C3C2×#93711yescharacteristic
648C2×C3C2×C3×#12011yescharacteristic
649D3—44no—
650C22—22no—
651C22—41no—
652C22—42no—
653C22—42no—
654C22—41no—
655C22—64no—
656C22—242no—
657C22—244no—
658C22C3×#93712yes—
659C22C22×C3×#6711yescharacteristic
660C4—22no—
661C4—22no—
662C4—41no—
663C4—41no—
664C4—64no—
665C4C3×#93711yescharacteristic
666C4C3×#93711yescharacteristic
667C4C2×C3×D3×D412yes—
668C3—21no—
669C3#8332211yescharacteristic, direct product factor
670C3C3×#301811yescharacteristic, complemented
671C2—21no—
672C2—22no—
673C2—42no—
674C2—81no—
675C2—124no—
676C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC3×C4#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#532C2
socleC2×C32C2×#120
hypercenterC3×#532D3
hypocenterC3C3×#3018
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#532

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. C32×#532C2semidirect
3. C3×#5822C2semidirect
4. C3×#5237C2semidirect
5. C3×#5095C2semidirect
6. C3×#5077C2semidirect
7. C3×#5062C2semidirect
8. C3×#5061C2semidirect
9. C2×C3×#805C2semidirect
11. #83322C3direct (N × H)
13. C2×C32×#41C22semidirect
22. C32×C4⋊Q8C22semidirect
23. C32×#127C22semidirect
24. C32×#124C22semidirect
25. C32×#124C22semidirect
28. C2×C32×C42C22semidirect
32. C3×#942C22semidirect
33. C3×#932C22semidirect
34. C2×C3×#208C22semidirect
35. C3×#836C22semidirect
36. C3×#833C22semidirect
37. C3×#805C22semidirect
38. C3×#805C22semidirect
40. #5964C2×C3semidirect
43. C3×#532D3semidirect
44. C3×#532C2×C3semidirect
45. #5822C2×C3semidirect
52. #5237C2×C3semidirect
53. #5095C2×C3semidirect
54. #5077C2×C3semidirect
55. #5062C2×C3semidirect
56. #5061C2×C3semidirect
57. C2×#805C2×C3semidirect
86. C3×#235D4semidirect
89. C2×C3×D12D4semidirect
93. C2×C3×Dic6D4semidirect
119. C2×C3×#41C2×D3semidirect
121. C2×C3×#41C22×C3semidirect
137. C3×C4⋊Q8C2×D3semidirect
138. C3×C4⋊Q8C22×C3semidirect
140. C3×#127C2×D3semidirect
141. C3×#127C22×C3semidirect
144. C3×#124C2×D3semidirect
145. C3×#124C2×D3semidirect
146. C3×#124C22×C3semidirect
147. C3×#124C22×C3semidirect
155. C2×C3×C42C2×D3semidirect
156. C2×C3×C42C22×C3semidirect
160. #942C22×C3semidirect
161. #932C22×C3semidirect
162. C2×#208C22×C3semidirect
167. #836C22×C3semidirect
168. #833C22×C3semidirect
169. #805C22×C3semidirect
170. #805C22×C3semidirect
213. #532C3×D3semidirect
299. #235C3×D4semidirect
302. C2×D12C3×D4semidirect
306. C2×Dic6C3×D4semidirect
366. C2×#41C2×C3×D3semidirect
373. C4⋊Q8C2×C3×D3semidirect
374. #127C2×C3×D3semidirect
375. #124C2×C3×D3semidirect
376. #124C2×C3×D3semidirect
379. C2×C42C2×C3×D3semidirect
592. C32#3018semidirect
669. C3#83322direct (N × H)
670. C3C3×#3018semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C32×#5322
C3×#58222
C3×#52372
C3×#50952
C3×#50772
C3×#50622
C3×#50612
C2×C3×#8052
C3×#30183
#833223