Finite Group Databasebeta

← #13178654

Subgroups — #13178654

Order 1728.

1744 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6295C211yesmaximal, characteristic, complemented
2C2×#89046C211yesmaximal, characteristic, complemented
3C3×#64146C212yesmaximal, complemented
4C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#11723725C212yesmaximal, complemented
6#11723723C212yesmaximal, complemented
7#11723721C211yesmaximal, characteristic, complemented
8#11723717C211yesmaximal, characteristic, complemented
9#11723690C212yesmaximal, complemented
10#11723685C211yesmaximal, characteristic, complemented
11#11723672C211yesmaximal, characteristic, complemented
12#10595225—31nomaximal
13#10595135—32nomaximal
14C23×C3×C3⋊D3C2212yes—
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yescomplemented
17C2×C3×#638C2212yescomplemented
18C22×C3×C3⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×#6296C2211yescharacteristic, complemented
21C2×#6295—24no—
22C2×#6295C2211yescharacteristic
23C2×#6295C2212yes—
24C2×#6295C2211yescharacteristic
25#89046—24no—
26C2×#6294C2212yescomplemented
27C2×#6294C2212yescomplemented
28C3×#3757C2211yescharacteristic
29C3×#3757C2212yes—
30C3×#3757C2211yescharacteristic, complemented
31C3×#3752C2212yescomplemented
32C3×#3752C2212yescomplemented
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88815C2212yescomplemented
37#88814C2212yescomplemented
38#88814C2212yescomplemented
39C22×#626—32no—
40C22×#625—31no—
41C2×#3805—31no—
42C2×#3804—32no—
43#64146D312yescomplemented
44D4×C3⋊Dic3D311yescharacteristic, complemented
45C3×#937—32no—
46C3×#937—32no—
47C3×#937—62no—
48C3×D4×Dic3—32no—
49C3×D4×Dic3—61no—
50#63982—31no—
51#63980—31no—
52#63978—32no—
53#63974—32no—
54#63971—32no—
55#63970—32no—
56D3×#217—32no—
57D3×#217—32no—
58#63964—32no—
59#63958—32no—
60#63915—31no—
61#63902—31no—
62#63891—32no—
63#63890—32no—
64#63880—32no—
65#63854—32no—
66#63852—32no—
67C23×C33C2311yescharacteristic
68C23×C33C2311yescharacteristic
69C22×C3×C3⋊D3—24no—
70C22×C3×C3⋊D3—24no—
71C22×C3×C3⋊D3—42no—
72C22×C3×C3⋊D3C2312yes—
73C22×C3×C3⋊D3C2312yes—
74C33×D4—22no—
75C2×C33×C4C2311yescharacteristic
76C3×#638—24no—
77C3×#638—42no—
78C2×C3×C3⋊Dic3—22no—
79C2×C3×C3⋊Dic3—22no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86#6296—22no—
87#6295—24no—
88#6295—22no—
89#6295D414yescomplemented
90#6294—24no—
91#6294—42no—
92#5591—92no—
93#5550—91no—
94C23×C3⋊D3C2×D312yes—
95C23×C3×D3—32no—
96C23×C3×D3—32no—
97C23×C3×D3—62no—
98C2×C32×D4—21no—
99C2×C32×D4—22no—
100C2×C32×D4—41no—
101C2×C32×D4C2×D312yes—
102C2×C32×D4C2×D311yescharacteristic
103C2×#638C2×D312yescomplemented
104C2×#638C2×D312yescomplemented
105C22×C3⋊Dic3C2×D311yescharacteristic
106C22×C3⋊Dic3C2×D311yescharacteristic, complemented
107C2×C3×#67—32no—
108C2×C3×#67—32no—
109C2×C3×#67—32no—
110C2×C3×#67—32no—
111C2×C3×#67—62no—
112C2×C3×#67—62no—
113C22×C3×Dic3—32no—
114C22×C3×Dic3—32no—
115C22×C3×Dic3—61no—
116C22×C3×Dic3—61no—
117C2×#627—32no—
118C2×#627—31no—
119C2×#626—32no—
120C2×#626—32no—
121C2×#626—32no—
122C2×#626—32no—
123C2×#626—68no—
124C2×#625—31no—
125C2×#625—32no—
126C2×#625—31no—
127C2×#625—64no—
128C2×#624—32no—
129C2×#624—32no—
130#3805—64no—
131#3804—68no—
132C2×D3×Dic3—32no—
133C2×D3×Dic3—32no—
134C2×D3×Dic3—32no—
135C2×D3×Dic3—32no—
136#3757C2×D311yescharacteristic
137#3757C2×D312yes—
138#3757C2×D311yescharacteristic, complemented
139#3752C2×D312yescomplemented
140#3752C2×D312yescomplemented
141C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
142C4×C3⋊Dic3C2×D311yescharacteristic, complemented
143C3×#217—32no—
144C3×#217—32no—
145C3×#217—32no—
146C3×#217—32no—
147C3×#217—61no—
148C3×#217—62no—
149C3×#217—61no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—62no—
155C3×(C2×D3)⋊C4—62no—
156C3×C4⋊Dic3—32no—
157C3×C4⋊Dic3—61no—
158C3×C4×Dic3—32no—
159C3×C4×Dic3—61no—
160#3724—32no—
161#3724—31no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165#3722—32no—
166#3722—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171C22×C33—21no—
172C22×C33—21no—
173C22×C33—21no—
174C22×C33—21no—
175C22×C33—21no—
176C22×C33#4112yescomplemented
177C22×C33C2411yescharacteristic
178C2×C3×C3⋊D3—22no—
179C2×C3×C3⋊D3—22no—
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—48no—
184C2×C3×C3⋊D3C2×D414yes—
185C33×C4—21no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3C2×D412yes—
192C22×#67—92no—
193C2×#237—92no—
194C2×#235—91no—
195C22×D12—91no—
196C3×#120—92no—
197C3×C4×D4—91no—
198C2×#217—92no—
199#939—92no—
200#939—92no—
201#938—92no—
202#937—32no—
203#937—32no—
204#937—62no—
205D4×Dic3—32no—
206D4×Dic3—61no—
207#930—91no—
208#924—91no—
209#894—92no—
210#886—92no—
211#885—92no—
212#884—92no—
213#883—92no—
214#67⋊C4—92no—
215D3×C22⋊C4—92no—
216D3×C22⋊C4—92no—
217#878—92no—
218#875—91no—
219C4×D12—91no—
220C23×C32—22no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—22no—
224C23×C32—41no—
225C23×C32—41no—
226C23×C32C22×D312yes—
227C23×C32C22×D311yescharacteristic
228C23×C32C22×D311yescharacteristic
229C23×C32C22×D312yes—
230C22×C3⋊D3—24no—
231C22×C3⋊D3—24no—
232C22×C3⋊D3—42no—
233C22×C3⋊D3C22×D312yes—
234C22×C3⋊D3C22×D312yes—
235C22×C3×D3—32no—
236C22×C3×D3—32no—
237C22×C3×D3—32no—
238C22×C3×D3—32no—
239C22×C3×D3—62no—
240C22×C3×D3—62no—
241C22×C3×D3—64no—
242C22×C3×D3—64no—
243C22×C3×D3—64no—
244C22×C3×D3—64no—
245C22×C3×D3—124no—
246C22×C3×D3—124no—
247C22×C3×D3—122no—
248C22×C3×D3—122no—
249C22×C3×D3—124no—
250C32×D4—22no—
251C32×D4—24no—
252C32×D4—24no—
253C32×D4—44no—
254C32×D4—44no—
255C2×C32×C4—21no—
256C2×C32×C4—22no—
257C2×C32×C4—41no—
258C2×C32×C4C22×D312yes—
259C2×C32×C4C22×D311yescharacteristic
260#638—24no—
261#638—42no—
262C2×C3⋊Dic3—22no—
263C2×C3⋊Dic3—22no—
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D312yes—
267C2×C3⋊Dic3C22×D312yes—
268C2×C3⋊Dic3C22×D311yescharacteristic
269C2×C3⋊Dic3C22×D311yescharacteristic
270C3×#67—64no—
271C3×#67—64no—
272C3×#67—124no—
273C3×#67—122no—
274C3×#67—122no—
275C3×#67—124no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3—64no—
291C2×C3×Dic3—64no—
292C2×C3×Dic3—122no—
293C2×C3×Dic3—122no—
294#627—64no—
295#627—62no—
296#626—38no—
297#626—64no—
298#626—64no—
299#626—64no—
300#625—34no—
301#625—64no—
302#625—62no—
303#624—64no—
304#624—122no—
305D3×Dic3—64no—
306D3×Dic3—64no—
307D3×Dic3—122no—
308D3×Dic3—122no—
309#546—271noSylow
310C2×C33—22no—
311C2×C33—41no—
312C2×C33C22×D411yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33H(5,𝔽2)11yescharacteristic
315C3×C3⋊D3—24no—
316C3×C3⋊D3—42no—
317C24×C3—92no—
318C23×D3—32no—
319C23×D3—32no—
320C23×D3—62no—
321C2×C3×D4—21no—
322C2×C3×D4—22no—
323C2×C3×D4—41no—
324C2×C3×D4—92no—
325C2×C3×D4—92no—
326C2×C3×D4D3212yes—
327C2×C3×D4D3211yescharacteristic
328C22×C3×C4—91no—
329C22×C3×C4—91no—
330C2×#67—32no—
331C2×#67—32no—
332C2×#67—32no—
333C2×#67—32no—
334C2×#67—62no—
335C2×#67—62no—
336C2×#67—92no—
337C2×#67—92no—
338C2×#67—92no—
339C2×#67—92no—
340C2×#67—188no—
341C22×Dic3—32no—
342C22×Dic3—32no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—92no—
346C22×Dic3—92no—
347#237—188no—
348#235—184no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—92no—
352C2×D12—184no—
353C2×C4×D3—92no—
354C2×C4×D3—92no—
355C2×C4×D3—92no—
356C2×C4×D3—92no—
357C2×Dic6—91no—
358C2×Dic6—92no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—92no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—92no—
364C3×C22⋊C4—92no—
365C3×C42—91no—
366#217—32no—
367#217—32no—
368#217—32no—
369#217—32no—
370#217—61no—
371#217—61no—
372#217—62no—
373#217—92no—
374#217—92no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—32no—
377(C2×D3)⋊C4—32no—
378(C2×D3)⋊C4—32no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4—92no—
382(C2×D3)⋊C4—92no—
383(C2×D3)⋊C4—92no—
384(C2×D3)⋊C4—92no—
385C4⋊Dic3—32no—
386C4⋊Dic3—61no—
387C4⋊Dic3—91no—
388C4⋊Dic3—92no—
389Dic3⋊C4—92no—
390Dic3⋊C4—92no—
391Dic3⋊C4—92no—
392C4×Dic3—32no—
393C4×Dic3—61no—
394C22×C32—21no—
395C22×C32—22no—
396C22×C32—21no—
397C22×C32—22no—
398C22×C32—21no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—21no—
402C22×C32—22no—
403C22×C32—22no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—22no—
407C22×C32—24no—
408C22×C32—22no—
409C22×C32—41no—
410C22×C32—42no—
411C22×C32—42no—
412C22×C32—42no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—42no—
416C22×C32—42no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—42no—
420C22×C32—42no—
421C22×C32—81no—
422C22×C32—81no—
423C22×C32—81no—
424C22×C32—81no—
425C22×C32#23512yescomplemented
426C22×C32#23714yescomplemented
427C22×C32C23×D311yescharacteristic
428C22×C32C23×D312yes—
429C2×C3⋊D3—22no—
430C2×C3⋊D3—22no—
431C2×C3⋊D3—22no—
432C2×C3⋊D3—22no—
433C2×C3⋊D3—22no—
434C2×C3⋊D3—48no—
435C2×C3⋊D3D3×D414yes—
436C2×C3×D3—34no—
437C2×C3×D3—34no—
438C2×C3×D3—64no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—62no—
442C2×C3×D3—62no—
443C2×C3×D3—64no—
444C2×C3×D3—62no—
445C2×C3×D3—62no—
446C2×C3×D3—62no—
447C2×C3×D3—62no—
448C2×C3×D3—62no—
449C2×C3×D3—62no—
450C2×C3×D3—122no—
451C2×C3×D3—122no—
452C2×C3×D3—122no—
453C2×C3×D3—122no—
454C2×C3×D3—128no—
455C2×C3×D3—128no—
456C2×C3×D3—1216no—
457C32×C4—21no—
458C32×C4—22no—
459C32×C4—22no—
460C32×C4—42no—
461C32×C4—42no—
462C3⋊Dic3—21no—
463C3⋊Dic3—22no—
464C3⋊Dic3—21no—
465C3⋊Dic3—22no—
466C3⋊Dic3—21no—
467C3⋊Dic3D3×D412yes—
468C3×Dic3—34no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—62no—
472C3×Dic3—62no—
473C3×Dic3—62no—
474C3×Dic3—62no—
475C3×Dic3—62no—
476C3×Dic3—62no—
477C3×Dic3—121no—
478C3×Dic3—121no—
479C3×Dic3—121no—
480C3×Dic3—122no—
481C3×Dic3—122no—
482C2×#41—271no—
483C22×D4—271no—
484#124—271no—
485#123—272no—
486C22⋊Q8—271no—
487#121—272no—
488#121—271no—
489#120—92no—
490C4×D4—91no—
491C4×D4—271no—
492C2×C22⋊C4—272no—
493C33#54611yescharacteristic, complemented, Sylow
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—92no—
501C23×C3—92no—
502C23×C3—184no—
503C23×C3—184no—
504C23×C3—362no—
505C23×C3C2×D3212yes—
506C23×C3C2×D3211yescharacteristic
507C23×C3C2×D3212yes—
508C23×C3C2×D3211yescharacteristic
509C22×D3—32no—
510C22×D3—32no—
511C22×D3—32no—
512C22×D3—32no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—64no—
516C22×D3—64no—
517C22×D3—64no—
518C22×D3—64no—
519C22×D3—124no—
520C22×D3—124no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—124no—
524C3×D4—24no—
525C3×D4—24no—
526C3×D4—22no—
527C3×D4—44no—
528C3×D4—44no—
529C3×D4—184no—
530C3×D4—362no—
531C2×C3×C4—21no—
532C2×C3×C4—22no—
533C2×C3×C4—41no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—92no—
537C2×C3×C4—92no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—182no—
541C2×C3×C4—182no—
542C2×C3×C4C2×D3212yes—
543C2×C3×C4C2×D3211yescharacteristic
544#67—64no—
545#67—64no—
546#67—98no—
547#67—124no—
548#67—122no—
549#67—122no—
550#67—124no—
551#67—184no—
552#67—184no—
553#67—184no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—32no—
559C2×Dic3—32no—
560C2×Dic3—32no—
561C2×Dic3—32no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—62no—
567C2×Dic3—62no—
568C2×Dic3—64no—
569C2×Dic3—64no—
570C2×Dic3—122no—
571C2×Dic3—122no—
572C2×Dic3—184no—
573C2×Dic3—362no—
574D12—94no—
575D12—182no—
576D12—184no—
577C4×D3—184no—
578C4×D3—184no—
579C4×D3—362no—
580C4×D3—362no—
581Dic6—184no—
582Dic6—182no—
583C2×C32—22no—
584C2×C32—24no—
585C2×C32—21no—
586C2×C32—22no—
587C2×C32—21no—
588C2×C32—22no—
589C2×C32—22no—
590C2×C32—21no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—44no—
595C2×C32—42no—
596C2×C32—41no—
597C2×C32—42no—
598C2×C32—42no—
599C2×C32—82no—
600C2×C32—82no—
601C2×C32—82no—
602C2×C32C2×#23511yescharacteristic
603C2×C32C2×D3×D411yescharacteristic
604C2×C32C2×D3×D412yes—
605C2×C32C2×#23712yes—
606C2×C32#100412yes—
607C2×C32#100911yescharacteristic
608C3⋊D3—24no—
609C3⋊D3—42no—
610C3×D3—64no—
611C3×D3—64no—
612C3×D3—124no—
613C3×D3—124no—
614C3×D3—122no—
615C3×D3—122no—
616C24—92no—
617#41—544no—
618C2×Q8—271no—
619C2×D4—92no—
620C2×D4—92no—
621C2×D4—271no—
622C2×D4—272no—
623C2×D4—271no—
624C2×D4—544no—
625C2×D4#111311yescharacteristic
626C22×C4—91no—
627C22×C4—91no—
628C22×C4—272no—
629C22×C4—272no—
630C4⋊C4—91no—
631C4⋊C4—271no—
632C4⋊C4—272no—
633C22⋊C4—91no—
634C22⋊C4—92no—
635C22⋊C4—91no—
636C22⋊C4—92no—
637C22⋊C4—92no—
638C22⋊C4—272no—
639C22⋊C4—272no—
640C42—91no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—24no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—41no—
667C22×C3—42no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—94no—
673C22×C3—182no—
674C22×C3—182no—
675C22×C3—182no—
676C22×C3—182no—
677C22×C3—182no—
678C22×C3—368no—
679C22×C3#380414yescomplemented
680C22×C3#380512yescomplemented
681C22×C3C22×D3211yescharacteristic
682C22×C3C22×D3212yes—
683C2×D3—34no—
684C2×D3—34no—
685C2×D3—64no—
686C2×D3—62no—
687C2×D3—62no—
688C2×D3—62no—
689C2×D3—62no—
690C2×D3—64no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—122no—
698C2×D3—122no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—128no—
702C2×D3—128no—
703C2×D3—1216no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—21no—
707C3×C4—42no—
708C3×C4—42no—
709C3×C4—92no—
710C3×C4—182no—
711C3×C4—181no—
712C3×C4—181no—
713C3×C4—181no—
714C3×C4—182no—
715Dic3—34no—
716Dic3—62no—
717Dic3—62no—
718Dic3—62no—
719Dic3—62no—
720Dic3—62no—
721Dic3—62no—
722Dic3—62no—
723Dic3—62no—
724Dic3—121no—
725Dic3—121no—
726Dic3—122no—
727Dic3—122no—
728Dic3—121no—
729C32—22no—
730C32—21no—
731C32—41no—
732C32#555011yescharacteristic, complemented
733C32#559112yescomplemented
734C23—92no—
735C23—92no—
736C23—184no—
737C23—184no—
738C23—362no—
739C23C2×#111311yescharacteristic
740C23C2×#111311yescharacteristic
741Q8—542no—
742D4—22no—
743D4—184no—
744D4—274no—
745D4—362no—
746D4—542no—
747D4—544no—
748C2×C4—91no—
749C2×C4—91no—
750C2×C4—92no—
751C2×C4—92no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—182no—
755C2×C4—182no—
756C2×C4—544no—
757C2×C4—1082no—
758C2×C4C2×#111311yescharacteristic
759C2×C3—24no—
760C2×C3—22no—
761C2×C3—21no—
762C2×C3—22no—
763C2×C3—22no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—22no—
767C2×C3—44no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—42no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—82no—
776C2×C3—82no—
777C2×C3—82no—
778C2×C3—184no—
779C2×C3—362no—
780C2×C3D32×D412yes—
781C2×C3D32×D411yescharacteristic
782C2×C3#6431311yescharacteristic
783C2×C3#6431412yes—
784C2×C3C2×#380412yes—
785C2×C3C2×#380511yescharacteristic
786D3—64no—
787D3—64no—
788D3—124no—
789D3—124no—
790D3—122no—
791D3—122no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—94no—
798C22—182no—
799C22—182no—
800C22—182no—
801C22—182no—
802C22—182no—
803C22—368no—
804C22#8904612yescomplemented
805C22C22×#111311yescharacteristic
806C4—21no—
807C4—92no—
808C4—181no—
809C4—181no—
810C4—182no—
811C4—181no—
812C4—182no—
813C3—22no—
814C3—21no—
815C3—41no—
816C3#1059513512yescomplemented
817C3#1059522511yescharacteristic, complemented
818C2—22no—
819C2—41no—
820C2—184no—
821C2—362no—
822C2D4×#111311yescharacteristic
823C2#1172462311yescharacteristic
824C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6295C2semidirect
2. C2×#89046C2semidirect
3. C3×#64146C2semidirect
4. C3×D4×C3⋊Dic3C2semidirect
5. #11723725C2semidirect
6. #11723723C2semidirect
7. #11723721C2semidirect
8. #11723717C2semidirect
9. #11723690C2semidirect
10. #11723685C2semidirect
11. #11723672C2semidirect
16. C2×C3×#638C22semidirect
17. C2×C3×#638C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
20. C2×#6296C22semidirect
26. C2×#6294C22semidirect
27. C2×#6294C22semidirect
30. C3×#3757C22semidirect
31. C3×#3752C22semidirect
32. C3×#3752C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C3×C4×C3⋊Dic3C22semidirect
35. #88815C22semidirect
36. #88815C22semidirect
37. #88814C22semidirect
38. #88814C22semidirect
43. #64146D3semidirect
44. D4×C3⋊Dic3D3semidirect
89. #6295D4semidirect
103. C2×#638C2×D3semidirect
104. C2×#638C2×D3semidirect
106. C22×C3⋊Dic3C2×D3semidirect
138. #3757C2×D3semidirect
139. #3752C2×D3semidirect
140. #3752C2×D3semidirect
141. C4⋊(C3⋊Dic3)C2×D3semidirect
142. C4×C3⋊Dic3C2×D3semidirect
176. C22×C33#41semidirect
425. C22×C32#235semidirect
426. C22×C32#237semidirect
493. C33#546semidirect
679. C22×C3#3804semidirect
680. C22×C3#3805semidirect
732. C32#5550semidirect
733. C32#5591semidirect
804. C22#89046semidirect
816. C3#10595135semidirect
817. C3#10595225semidirect

Maximal subgroups

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

subgroupindex
C22×#62952
C2×#890462
C3×#641462
C3×D4×C3⋊Dic32
#117237252
#117237232
#117237212
#117237172
#117236902
#117236852
#117236722
#105952253
#105951353