Finite Group Databasebeta

← #13172665

Subgroups — #13172665

Order 1728.

1652 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3805C211yesmaximal, characteristic, complemented
2C2×D3×#625C211yesmaximal, characteristic, complemented
3#11723717C211yesmaximal, characteristic, complemented
4#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#11723615C212yesmaximal, complemented
6C3×#63983C212yesmaximal, complemented
7#11723007C211yesmaximal, characteristic, complemented
8#11722988C212yesmaximal, complemented
9#11722976C211yesmaximal, characteristic, complemented
10#11722925C211yesmaximal, characteristic, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12#10595304—32nomaximal
13#10595225—31nomaximal
14C22×C3×D32C2212yes—
15C2×C3×#638C2212yescomplemented
16C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
17C2×C32×#67C2211yescharacteristic
18C2×C32×#67C2212yescomplemented
19C2×#6295C2211yescharacteristic
20C2×#6290C2212yes—
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×D3×C3⋊Dic3C2212yescomplemented
23C2×C3×#627C2211yescharacteristic, complemented
24C2×C3×#625C2211yescharacteristic
25C3×#3805—24no—
26C2×C3×D3×Dic3C2212yescomplemented
27D3×#625—24no—
28#88864C2211yescharacteristic, complemented
29#88815C2211yescharacteristic, complemented
30#88814C2212yescomplemented
31#88807C2212yescomplemented
32Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33#88803C2212yescomplemented
34(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
35Dic3×C3⋊Dic3C2211yescharacteristic, complemented
36C3×#3722C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C2×C3×#237—32no—
40C2×D3×#67—32no—
41C22×#625—31no—
42C2×#3805D311yescharacteristic, complemented
43#64148—32no—
44D4×C3⋊Dic3—31no—
45C3×#937—32no—
46C3×#937—32no—
47#63983D312yescomplemented
48#63982—31no—
49#63980—31no—
50#63978—32no—
51#67⋊Dic3—32no—
52Dic3×#67—32no—
53Dic3×#67—61no—
54#63970—32no—
55#63970—32no—
56#63970—62no—
57D3×#217—32no—
58#63966—32no—
59C2×(C2×D3)⋊Dic3—32no—
60D3×(C2×D3)⋊C4—32no—
61#63915—31no—
62#63907—32no—
63#63905—32no—
64#63902—31no—
65#63891—32no—
66#63887—32no—
67C23×C33C2311yescharacteristic
68C22×C3×C3⋊D3C2312yes—
69C22×C32×D3C2312yes—
70C22×C32×D3C2311yescharacteristic
71C2×C3×D32—24no—
72C2×C3×D32—24no—
73C2×C3×D32—42no—
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
76C3×#638—42no—
77C2×C3×C3⋊Dic3—22no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C32×#67—24no—
82C32×#67—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85#6295—22no—
86#6290—24no—
87D3×C3⋊Dic3—22no—
88D3×C3⋊Dic3—42no—
89C3×#627—22no—
90C3×#625D414yescomplemented
91C3×D3×Dic3—24no—
92#5829—91no—
93#5591—92no—
94C23×C3×D3—32no—
95C23×C3×D3—32no—
96C22×D32C2×D312yes—
97C2×C32×D4—31no—
98C2×C32×D4—32no—
99C2×#638—32no—
100C2×#638C2×D312yescomplemented
101C22×C3⋊Dic3—31no—
102C22×C3⋊Dic3—32no—
103C22×C3⋊Dic3C2×D311yescharacteristic, complemented
104C2×C3×#67—21no—
105C2×C3×#67—22no—
106C2×C3×#67—32no—
107C2×C3×#67—32no—
108C2×C3×#67—32no—
109C2×C3×#67—62no—
110C2×C3×#67C2×D312yes—
111C2×C3×#67C2×D312yescomplemented
112C2×C3×#67C2×D312yescomplemented
113C22×C3×Dic3—32no—
114C22×C3×Dic3—32no—
115C22×C3×Dic3—61no—
116C3×#237—68no—
117C2×C3×C4×D3—32no—
118C2×C3×Dic6—32no—
119D3×#67—68no—
120C2×#627C2×D311yescharacteristic, complemented
121C2×#626—32no—
122C2×#625—32no—
123C2×#625—32no—
124C2×#625—31no—
125C2×#625—64no—
126C2×#625—62no—
127C2×#625C2×D311yescharacteristic
128#3805—24no—
129C2×D3×Dic3—32no—
130C2×D3×Dic3—32no—
131C2×D3×Dic3—32no—
132C2×D3×Dic3—61no—
133C2×D3×Dic3—62no—
134C2×D3×Dic3C2×D312yescomplemented
135#3757—31no—
136#3757—32no—
137#3757—31no—
138#3757—62no—
139#3757—61no—
140#3757—121no—
141#3752—32no—
142C4⋊(C3⋊Dic3)—31no—
143#3750—32no—
144C4×C3⋊Dic3—31no—
145C3×#217—32no—
146C3×#217—32no—
147C3×(C2×D3)⋊C4—32no—
148C3×(C2×D3)⋊C4—32no—
149C3×(C2×D3)⋊C4—32no—
150C3×(C2×D3)⋊C4—32no—
151#3724—31no—
152Dic3⋊Dic3—32no—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—61no—
157Dic3⋊Dic3—62no—
158#3722—32no—
159#3722C2×D312yescomplemented
160(C2×D3)⋊Dic3—32no—
161(C2×D3)⋊Dic3—32no—
162(C2×D3)⋊Dic3—32no—
163(C2×D3)⋊Dic3—32no—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—62no—
166(C2×D3)⋊Dic3—61no—
167(C2×D3)⋊Dic3C2×D312yes—
168(C2×D3)⋊Dic3C2×D312yescomplemented
169Dic32—32no—
170Dic32—61no—
171C22×C33—21no—
172C22×C33—21no—
173C22×C33—21no—
174C22×C33C2411yescharacteristic
175C2×C3×C3⋊D3—22no—
176C2×C3×C3⋊D3—22no—
177C2×C3×C3⋊D3—22no—
178C2×C32×D3—21no—
179C2×C32×D3—22no—
180C2×C32×D3—22no—
181C2×C32×D3—21no—
182C2×C32×D3C2×D414yes—
183C2×C32×D3#4112yescomplemented
184C3×D32—48no—
185C3⋊(C3⋊Dic3)—21no—
186C3⋊(C3⋊Dic3)—21no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3C2×D412yes—
190C32×Dic3—22no—
191C32×Dic3—21no—
192C2×C3×#41—91no—
193C22×#67—92no—
194C2×#237—32no—
195C2×D3×D4—91no—
196C3×#120—92no—
197C2×#217—92no—
198#947—91no—
199#946—91no—
200#939—92no—
201#939—92no—
202#939—92no—
203#939—182no—
204#938—92no—
205#937—32no—
206#937—32no—
207D4×Dic3—91no—
208D4×Dic3—92no—
209D4×Dic3—181no—
210#930—91no—
211#929—92no—
212C4×#67—91no—
213C2×(C2×D3)⋊C4—92no—
214#886—92no—
215#885—92no—
216#883—92no—
217#67⋊C4—92no—
218D3×C22⋊C4—92no—
219#878—92no—
220C23×C32—21no—
221C23×C32—22no—
222C23×C32—31no—
223C23×C32—32no—
224C23×C32—41no—
225C23×C32C22×D312yes—
226C23×C32C22×D311yescharacteristic
227C22×C3⋊D3C22×D312yes—
228C22×C3×D3—21no—
229C22×C3×D3—22no—
230C22×C3×D3—32no—
231C22×C3×D3—32no—
232C22×C3×D3—62no—
233C22×C3×D3—64no—
234C22×C3×D3—64no—
235C22×C3×D3—64no—
236C22×C3×D3—64no—
237C22×C3×D3—122no—
238C22×C3×D3—122no—
239C22×C3×D3C22×D312yes—
240C22×C3×D3C22×D312yes—
241C22×C3×D3C22×D312yes—
242C2×D32—24no—
243C2×D32—24no—
244C2×D32—42no—
245C32×D4—62no—
246C32×D4—64no—
247C2×C32×C4—31no—
248C2×C32×C4—32no—
249#638—42no—
250#638—64no—
251C2×C3⋊Dic3—22no—
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—32no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—61no—
257C2×C3⋊Dic3—62no—
258C2×C3⋊Dic3—61no—
259C2×C3⋊Dic3—62no—
260C2×C3⋊Dic3—62no—
261C2×C3⋊Dic3—121no—
262C2×C3⋊Dic3—121no—
263C2×C3⋊Dic3—122no—
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D312yes—
266C2×C3⋊Dic3C22×D311yescharacteristic
267C3×#67—24no—
268C3×#67—24no—
269C3×#67—24no—
270C3×#67—24no—
271C3×#67—38no—
272C3×#67—44no—
273C3×#67—122no—
274C3×#67—122no—
275C3×#67—124no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—64no—
286C2×C3×Dic3—64no—
287C2×C3×Dic3—122no—
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D312yes—
291C3×C4×D3—64no—
292C3×Dic6—64no—
293#627—22no—
294#626—64no—
295#625—64no—
296#625—64no—
297#625—62no—
298#625—124no—
299#625#6714yescomplemented
300D3×Dic3—24no—
301D3×Dic3—64no—
302D3×Dic3—122no—
303D3×Dic3—122no—
304D3×Dic3—122no—
305D3×Dic3—124no—
306#546—271noSylow
307C2×C33—41no—
308C2×C33C22×D411yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33H(5,𝔽2)11yescharacteristic
311C3×C3⋊D3—42no—
312C32×D3—22no—
313C32×D3—24no—
314C24×C3—92no—
315C23×D3—32no—
316C23×D3—32no—
317C3×#41—184no—
318C2×C3×Q8—91no—
319C2×C3×D4—32no—
320C2×C3×D4—32no—
321C2×C3×D4—32no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4—91no—
325C2×C3×D4—92no—
326C22×C3×C4—92no—
327C22×C3×C4—91no—
328C2×#67—32no—
329C2×#67—32no—
330C2×#67—32no—
331C2×#67—62no—
332C2×#67—92no—
333C2×#67—92no—
334C2×#67—92no—
335C2×#67—92no—
336C2×#67—182no—
337C2×#67—188no—
338C2×#67D3211yescharacteristic
339C2×#67D3212yescomplemented
340C22×Dic3—32no—
341C22×Dic3—32no—
342C22×Dic3—61no—
343C22×Dic3—92no—
344C22×Dic3—92no—
345C22×Dic3—92no—
346C22×Dic3—181no—
347C22×Dic3—182no—
348#237—68no—
349D3×D4—184no—
350C2×D12—91no—
351C2×C4×D3—32no—
352C2×C4×D3—91no—
353C2×C4×D3—92no—
354C2×Dic6—32no—
355C3×C22⋊C4—92no—
356C3×C22⋊C4—92no—
357C3×C22⋊C4—92no—
358#217—32no—
359#217—32no—
360#217—92no—
361#217—92no—
362#217—91no—
363#217—92no—
364#217—92no—
365#217—181no—
366#217—181no—
367#217—182no—
368#217—361no—
369(C2×D3)⋊C4—32no—
370(C2×D3)⋊C4—32no—
371(C2×D3)⋊C4—32no—
372(C2×D3)⋊C4—32no—
373(C2×D3)⋊C4—92no—
374(C2×D3)⋊C4—92no—
375(C2×D3)⋊C4—92no—
376(C2×D3)⋊C4—92no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—182no—
379C4⋊Dic3—91no—
380C4⋊Dic3—92no—
381C4⋊Dic3—92no—
382C4⋊Dic3—181no—
383Dic3⋊C4—92no—
384Dic3⋊C4—92no—
385Dic3⋊C4—92no—
386Dic3⋊C4—91no—
387Dic3⋊C4—182no—
388C4×Dic3—92no—
389C4×Dic3—91no—
390C4×Dic3—181no—
391C22×C32—21no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—22no—
400C22×C32—34no—
401C22×C32—32no—
402C22×C32—41no—
403C22×C32—42no—
404C22×C32—42no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—42no—
408C22×C32—42no—
409C22×C32—62no—
410C22×C32—62no—
411C22×C32—61no—
412C22×C32—61no—
413C22×C32—81no—
414C22×C32—81no—
415C22×C32C23×D312yes—
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—24no—
428C2×C3×D3—41no—
429C2×C3×D3—42no—
430C2×C3×D3—42no—
431C2×C3×D3—41no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—62no—
438C2×C3×D3—122no—
439C2×C3×D3—122no—
440C2×C3×D3—122no—
441C2×C3×D3—128no—
442C2×C3×D3—128no—
443C2×C3×D3D3×D414yes—
444C2×C3×D3#23714yescomplemented
445C2×C3×D3C2×#6714yes—
446D32—48no—
447C32×C4—61no—
448C32×C4—62no—
449C3⋊Dic3—22no—
450C3⋊Dic3—21no—
451C3⋊Dic3—62no—
452C3⋊Dic3—62no—
453C3⋊Dic3—61no—
454C3⋊Dic3—61no—
455C3⋊Dic3—121no—
456C3⋊Dic3—122no—
457C3⋊Dic3—122no—
458C3⋊Dic3—121no—
459C3⋊Dic3—241no—
460C3⋊Dic3—241no—
461C3⋊Dic3C2×#6712yes—
462C3×Dic3—22no—
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—34no—
467C3×Dic3—42no—
468C3×Dic3—62no—
469C3×Dic3—64no—
470C3×Dic3—62no—
471C3×Dic3—62no—
472C3×Dic3—62no—
473C3×Dic3—121no—
474C2×#41—91no—
475C22×D4—271no—
476#124—271no—
477#123—272no—
478C22⋊Q8—271no—
479#121—271no—
480#121—272no—
481#120—92no—
482C4×D4—271no—
483C4×D4—271no—
484C2×C22⋊C4—272no—
485C33#54611yescharacteristic, complemented, Sylow
486C23×C3—21no—
487C23×C3—22no—
488C23×C3—32no—
489C23×C3—32no—
490C23×C3—32no—
491C23×C3—41no—
492C23×C3—61no—
493C23×C3—62no—
494C23×C3—92no—
495C23×C3—184no—
496C23×C3—184no—
497C23×C3—362no—
498C23×C3C2×D3212yes—
499C23×C3C2×D3211yescharacteristic
500C22×D3—32no—
501C22×D3—32no—
502C22×D3—62no—
503C22×D3—64no—
504C22×D3—64no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3C2×D3211yescharacteristic
510C22×D3C2×D3212yes—
511C3×Q8—182no—
512C3×D4—64no—
513C3×D4—64no—
514C3×D4—64no—
515C3×D4—64no—
516C3×D4—94no—
517C3×D4—124no—
518C3×D4—362no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—61no—
523C2×C3×C4—62no—
524C2×C3×C4—91no—
525C2×C3×C4—92no—
526C2×C3×C4—91no—
527C2×C3×C4—184no—
528C2×C3×C4—182no—
529#67—22no—
530#67—24no—
531#67—38no—
532#67—122no—
533#67—122no—
534#67—124no—
535#67—184no—
536#67—184no—
537#67—184no—
538#67—184no—
539#67—364no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—61no—
545C2×Dic3—62no—
546C2×Dic3—61no—
547C2×Dic3—64no—
548C2×Dic3—64no—
549C2×Dic3—91no—
550C2×Dic3—92no—
551C2×Dic3—91no—
552C2×Dic3—92no—
553C2×Dic3—122no—
554C2×Dic3—181no—
555C2×Dic3—182no—
556C2×Dic3—181no—
557C2×Dic3—182no—
558C2×Dic3—184no—
559C2×Dic3—361no—
560C2×Dic3—361no—
561C2×Dic3—362no—
562C2×Dic3—362no—
563C2×Dic3—362no—
564C2×Dic3—364no—
565C2×Dic3C2×D3211yescharacteristic
566C2×Dic3C2×D3212yes—
567D12—182no—
568C4×D3—64no—
569C4×D3—182no—
570C4×D3—362no—
571Dic6—64no—
572C2×C32—21no—
573C2×C32—22no—
574C2×C32—21no—
575C2×C32—22no—
576C2×C32—21no—
577C2×C32—22no—
578C2×C32—41no—
579C2×C32—41no—
580C2×C32—41no—
581C2×C32—41no—
582C2×C32—42no—
583C2×C32—42no—
584C2×C32—62no—
585C2×C32—64no—
586C2×C32—82no—
587C2×C32—82no—
588C2×C32C2×D3×D412yes—
589C2×C32C2×#23712yes—
590C2×C32#100412yes—
591C2×C32D3×#4111yescharacteristic
592C2×C32#100911yescharacteristic
593C2×C32C22×#6711yescharacteristic
594C3⋊D3—42no—
595C3×D3—24no—
596C3×D3—24no—
597C3×D3—24no—
598C3×D3—42no—
599C3×D3—44no—
600C3×D3—122no—
601C3×D3—122no—
602C3×D3—242no—
603C24—92no—
604#41—184no—
605C2×Q8—91no—
606C2×D4—31no—
607C2×D4—32no—
608C2×D4—91no—
609C2×D4—92no—
610C2×D4—271no—
611C2×D4—272no—
612C2×D4—544no—
613C22×C4—92no—
614C22×C4—91no—
615C22×C4—271no—
616C22×C4—272no—
617C4⋊C4—271no—
618C4⋊C4—272no—
619C4⋊C4—271no—
620C22⋊C4—92no—
621C22⋊C4—92no—
622C22⋊C4—92no—
623C22⋊C4—272no—
624C22⋊C4—272no—
625C22⋊C4—271no—
626C22⋊C4—271no—
627C42—271no—
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—22no—
637C22×C3—34no—
638C22×C3—34no—
639C22×C3—34no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—64no—
648C22×C3—62no—
649C22×C3—62no—
650C22×C3—62no—
651C22×C3—62no—
652C22×C3—62no—
653C22×C3—62no—
654C22×C3—62no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—122no—
658C22×C3—121no—
659C22×C3—122no—
660C22×C3—121no—
661C22×C3—182no—
662C22×C3—182no—
663C22×C3—182no—
664C22×C3—368no—
665C22×C3C22×D3211yescharacteristic
666C22×C3C22×D3212yes—
667C2×D3—21no—
668C2×D3—22no—
669C2×D3—21no—
670C2×D3—22no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—62no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—122no—
678C2×D3—122no—
679C2×D3—122no—
680C2×D3—128no—
681C2×D3—128no—
682C2×D3#380512yescomplemented
683C2×D3D3×#6714yes—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—92no—
689C3×C4—122no—
690C3×C4—181no—
691C3×C4—182no—
692Dic3—21no—
693Dic3—22no—
694Dic3—34no—
695Dic3—62no—
696Dic3—64no—
697Dic3—62no—
698Dic3—62no—
699Dic3—62no—
700Dic3—121no—
701Dic3—181no—
702Dic3—181no—
703Dic3—182no—
704Dic3—182no—
705Dic3—362no—
706Dic3—361no—
707Dic3—362no—
708Dic3—361no—
709Dic3—721no—
710Dic3—721no—
711C32—21no—
712C32—22no—
713C32—41no—
714C32#559112yescomplemented
715C32#582911yescharacteristic, complemented
716C23—31no—
717C23—32no—
718C23—92no—
719C23—184no—
720C23—184no—
721C23—362no—
722C23D3311yescharacteristic
723Q8—182no—
724D4—64no—
725D4—62no—
726D4—94no—
727D4—362no—
728D4—542no—
729D4—544no—
730C2×C4—31no—
731C2×C4—32no—
732C2×C4—91no—
733C2×C4—92no—
734C2×C4—91no—
735C2×C4—184no—
736C2×C4—182no—
737C2×C4—271no—
738C2×C4—271no—
739C2×C4—542no—
740C2×C4—1082no—
741C2×C3—21no—
742C2×C3—22no—
743C2×C3—22no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—22no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—42no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—64no—
754C2×C3—64no—
755C2×C3—64no—
756C2×C3—82no—
757C2×C3—82no—
758C2×C3—122no—
759C2×C3—124no—
760C2×C3—362no—
761C2×C3D32×D411yescharacteristic
762C2×C3D3×#23712yes—
763C2×C3#6431311yescharacteristic
764C2×C3#6431412yes—
765C2×C3C2×#380511yescharacteristic
766C2×C3C2×D3×#6712yes—
767D3—22no—
768D3—24no—
769D3—122no—
770D3—122no—
771D3—242no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—32no—
776C22—34no—
777C22—62no—
778C22—62no—
779C22—61no—
780C22—61no—
781C22—182no—
782C22—182no—
783C22—182no—
784C22—368no—
785C22C2×D3311yescharacteristic
786C4—61no—
787C4—62no—
788C4—92no—
789C4—182no—
790C4—181no—
791C4—541no—
792C4—541no—
793C3—22no—
794C3—21no—
795C3—41no—
796C3#1059522511yescharacteristic, complemented
797C3#1059530412yescomplemented
798C2—41no—
799C2—62no—
800C2—64no—
801C2—362no—
802C2D3×#380511yescharacteristic
803C2#1172441611yescharacteristic
804C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3805C2semidirect
2. C2×D3×#625C2semidirect
3. #11723717C2semidirect
4. #67×C3⋊Dic3C2semidirect
5. #11723615C2semidirect
6. C3×#63983C2semidirect
7. #11723007C2semidirect
8. #11722988C2semidirect
9. #11722976C2semidirect
10. #11722925C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
15. C2×C3×#638C22semidirect
16. C22×C3×C3⋊Dic3C22semidirect
18. C2×C32×#67C22semidirect
22. C2×D3×C3⋊Dic3C22semidirect
23. C2×C3×#627C22semidirect
26. C2×C3×D3×Dic3C22semidirect
28. #88864C22semidirect
29. #88815C22semidirect
30. #88814C22semidirect
31. #88807C22semidirect
32. Dic3⋊(C3⋊Dic3)C22semidirect
33. #88803C22semidirect
35. Dic3×C3⋊Dic3C22semidirect
36. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
42. C2×#3805D3semidirect
47. #63983D3semidirect
90. C3×#625D4semidirect
100. C2×#638C2×D3semidirect
103. C22×C3⋊Dic3C2×D3semidirect
111. C2×C3×#67C2×D3semidirect
112. C2×C3×#67C2×D3semidirect
120. C2×#627C2×D3semidirect
134. C2×D3×Dic3C2×D3semidirect
159. #3722C2×D3semidirect
168. (C2×D3)⋊Dic3C2×D3semidirect
183. C2×C32×D3#41semidirect
299. #625#67semidirect
339. C2×#67D32semidirect
444. C2×C3×D3#237semidirect
485. C33#546semidirect
682. C2×D3#3805semidirect
714. C32#5591semidirect
715. C32#5829semidirect
796. C3#10595225semidirect
797. C3#10595304semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38052
C2×D3×#6252
#117237172
#67×C3⋊Dic32
#117236152
C3×#639832
#117230072
#117229882
#117229762
#117229252
D3×(C2×D3)⋊Dic32
#105953043
#105952253