Finite Group Databasebeta

← #13172930

Subgroups — #13172930

Order 1728.

1728 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6295C211yesmaximal, characteristic, complemented
2C2×#88964C211yesmaximal, characteristic, complemented
3C3⋊D3×#217C212yesmaximal, complemented
4#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#63982C211yesmaximal, characteristic, complemented
6C3×#63981C212yesmaximal, complemented
7#11723007C211yesmaximal, characteristic, complemented
8#11722997C212yesmaximal, complemented
9#11722962C212yesmaximal, complemented
10#11722955C211yesmaximal, characteristic, complemented
11#11722938C211yesmaximal, characteristic, complemented
12#10595225—31nomaximal
13#10594063—32nomaximal
14C23×C3×C3⋊D3C2212yes—
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C2×C32×#67C2211yescharacteristic
17C2×#6295—24no—
18C2×#6295C2211yescharacteristic
19C2×#6295C2212yes—
20C2×#6295C2211yescharacteristic
21C2×Dic3×C3⋊D3C2212yescomplemented
22C2×Dic3×C3⋊D3C2212yescomplemented
23C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C3×#627C2211yescharacteristic, complemented
25C2×C3×#626C2212yescomplemented
26C2×C3×#626C2212yescomplemented
27#88964—24no—
28#88864C2211yescharacteristic
29C32×#217C2212yes—
30Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31#88803C2212yescomplemented
32#88803C2212yescomplemented
33(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34Dic3×C3⋊Dic3C2211yescharacteristic, complemented
35C3×#3724C2211yescharacteristic, complemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×#3722C2212yescomplemented
38C3×#3722C2212yescomplemented
39C22×#626—32no—
40C22×#625—31no—
41C2×#3805—31no—
42C2×#3796—32no—
43D4×C3⋊Dic3—31no—
44C22⋊C4×C3⋊D3—32no—
45C3×#937—32no—
46C3×#882—32no—
47C3×#878—32no—
48#63982D311yescharacteristic, complemented
49#63981D312yescomplemented
50#63980—31no—
51Dic3×#67—32no—
52Dic3×#67—61no—
53#63970—32no—
54D3×#217—32no—
55D3×#217—32no—
56D3×#217—62no—
57#63916—32no—
58#63915—31no—
59#63907—32no—
60#63902—31no—
61#63891—32no—
62#63890—32no—
63#63886—32no—
64#63886—32no—
65#63881—32no—
66#63853—32no—
67C23×C33C2311yescharacteristic
68C22×C3×C3⋊D3—24no—
69C22×C3×C3⋊D3—24no—
70C22×C3×C3⋊D3—42no—
71C22×C3×C3⋊D3C2312yes—
72C22×C3×C3⋊D3C2312yes—
73C22×C32×D3C2311yescharacteristic
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
76C2×C3×C3⋊Dic3—22no—
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C32×#67—22no—
80C2×C32×Dic3C2312yes—
81C2×C32×Dic3C2312yes—
82C2×C32×Dic3C2311yescharacteristic
83#6295—24no—
84#6295—22no—
85#6295D414yescomplemented
86Dic3×C3⋊D3—24no—
87Dic3×C3⋊D3—42no—
88D3×C3⋊Dic3—22no—
89C3×#627—22no—
90C3×#626—24no—
91C3×#626—42no—
92#5630—91no—
93#5591—92no—
94C23×C3⋊D3C2×D312yes—
95C23×C3×D3—32no—
96C23×C3×D3—32no—
97C23×C3×D3—62no—
98C2×C32×D4—31no—
99C22×C3⋊Dic3—31no—
100C22×C3⋊Dic3C2×D311yescharacteristic
101C2×C4×C3⋊D3—32no—
102C2×C4×C3⋊D3—32no—
103C2×C3×#67—21no—
104C2×C3×#67—32no—
105C2×C3×#67—32no—
106C2×C3×#67C2×D312yes—
107C22×C3×Dic3—32no—
108C22×C3×Dic3—61no—
109C2×C3×D12—32no—
110C2×C3×D12—32no—
111C2×C3×Dic6—32no—
112C2×#627C2×D311yescharacteristic, complemented
113C2×#626—32no—
114C2×#626—32no—
115C2×#626—32no—
116C2×#626—32no—
117C2×#626—68no—
118C2×#626C2×D312yescomplemented
119C2×#626C2×D312yescomplemented
120C2×#625—31no—
121C2×#625—32no—
122C2×#625—31no—
123C2×#625—64no—
124#3805—64no—
125C2×D3×Dic3—32no—
126C2×D3×Dic3—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—32no—
129C2×D3×Dic3—32no—
130C2×D3×Dic3—62no—
131C2×D3×Dic3—62no—
132C2×D3×Dic3—61no—
133#3796—68no—
134C32×C22⋊C4—32no—
135#3757—32no—
136#3757—31no—
137#3757—31no—
138#3757—62no—
139#3757—61no—
140#3757—121no—
141#3752—32no—
142#3752—32no—
143C4⋊(C3⋊Dic3)—31no—
144C4×C3⋊Dic3—31no—
145C3×#217—22no—
146C3×#217C2×D312yes—
147C3×#217C2×D312yes—
148C3×(C2×D3)⋊C4—32no—
149C3×(C2×D3)⋊C4—32no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—32no—
152C3×C4⋊Dic3—32no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155#3724C2×D311yescharacteristic, complemented
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—61no—
158Dic3⋊Dic3C2×D312yescomplemented
159#3722C2×D312yescomplemented
160#3722C2×D312yescomplemented
161(C2×D3)⋊Dic3—32no—
162(C2×D3)⋊Dic3—32no—
163(C2×D3)⋊Dic3—32no—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—62no—
167(C2×D3)⋊Dic3—62no—
168(C2×D3)⋊Dic3—61no—
169Dic32—32no—
170Dic32—61no—
171C22×C33—21no—
172C22×C33—21no—
173C22×C33#4112yescomplemented
174C22×C33C2411yescharacteristic
175C2×C3×C3⋊D3—22no—
176C2×C3×C3⋊D3—22no—
177C2×C3×C3⋊D3—22no—
178C2×C3×C3⋊D3—22no—
179C2×C3×C3⋊D3—22no—
180C2×C3×C3⋊D3—48no—
181C2×C3×C3⋊D3C2×D414yes—
182C2×C32×D3—21no—
183C2×C32×D3—21no—
184C2×C32×D3—21no—
185C3⋊(C3⋊Dic3)—21no—
186C3⋊(C3⋊Dic3)—21no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3C2×D412yes—
189C32×Dic3—22no—
190C32×Dic3—21no—
191C32×Dic3—22no—
192C22×#67—92no—
193C2×#239—91no—
194C2×#237—92no—
195C22×D12—91no—
196C3×C22⋊Q8—91no—
197C3×#120—92no—
198C2×#217—92no—
199#947—91no—
200#939—92no—
201#939—92no—
202#938—92no—
203#937—32no—
204D4×Dic3—92no—
205D4×Dic3—181no—
206C4×#67—91no—
207#895—91no—
208#895—92no—
209#894—92no—
210#893—91no—
211#886—92no—
212#885—92no—
213#883—92no—
214#882—32no—
215#67⋊C4—92no—
216D3×C22⋊C4—92no—
217D3×C22⋊C4—92no—
218D3×C22⋊C4—182no—
219#878—32no—
220C23×C32—22no—
221C23×C32—21no—
222C23×C32—31no—
223C23×C32—41no—
224C23×C32C22×D312yes—
225C23×C32C22×D311yescharacteristic
226C22×C3⋊D3—24no—
227C22×C3⋊D3—24no—
228C22×C3⋊D3—42no—
229C22×C3⋊D3C22×D312yes—
230C22×C3⋊D3C22×D312yes—
231C22×C3×D3—21no—
232C22×C3×D3—32no—
233C22×C3×D3—32no—
234C22×C3×D3—32no—
235C22×C3×D3—32no—
236C22×C3×D3—62no—
237C22×C3×D3—62no—
238C22×C3×D3—64no—
239C22×C3×D3—64no—
240C22×C3×D3—68no—
241C22×C3×D3—64no—
242C22×C3×D3—64no—
243C22×C3×D3—124no—
244C22×C3×D3—122no—
245C22×C3×D3—122no—
246C22×C3×D3—124no—
247C22×C3×D3C22×D312yes—
248C32×D4—62no—
249C2×C32×C4—32no—
250C2×C32×C4—32no—
251C2×C32×C4—31no—
252C2×C3⋊Dic3—22no—
253C2×C3⋊Dic3—32no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—32no—
257C2×C3⋊Dic3—61no—
258C2×C3⋊Dic3—62no—
259C2×C3⋊Dic3—62no—
260C2×C3⋊Dic3—61no—
261C2×C3⋊Dic3—62no—
262C2×C3⋊Dic3—121no—
263C2×C3⋊Dic3—121no—
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C4×C3⋊D3—64no—
267C4×C3⋊D3—122no—
268C3×#67—24no—
269C3×#67—24no—
270C3×#67—64no—
271C3×#67—122no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—64no—
280C2×C3×Dic3—122no—
281C2×C3×Dic3C22×D312yes—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C3×D12—64no—
287C3×D12—122no—
288C3×Dic6—64no—
289#627—22no—
290#626—24no—
291#626—38no—
292#626—42no—
293#626—64no—
294#626—64no—
295#626—64no—
296#625—34no—
297#625—64no—
298#625—62no—
299D3×Dic3—64no—
300D3×Dic3—64no—
301D3×Dic3—64no—
302D3×Dic3—122no—
303D3×Dic3—124no—
304D3×Dic3—122no—
305D3×Dic3—122no—
306D3×Dic3—124no—
307#546—271noSylow
308C2×C33—22no—
309C2×C33C22×D411yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C2×C33H(5,𝔽2)11yescharacteristic
312C3×C3⋊D3—24no—
313C3×C3⋊D3—42no—
314C32×D3—41no—
315C24×C3—92no—
316C23×D3—32no—
317C23×D3—32no—
318C23×D3—62no—
319C2×C3×Q8—91no—
320C2×C3×D4—32no—
321C2×C3×D4—61no—
322C2×C3×D4—92no—
323C2×C3×D4—92no—
324C22×C3×C4—91no—
325C2×#67—32no—
326C2×#67—32no—
327C2×#67—92no—
328C2×#67—92no—
329C2×#67—92no—
330C2×#67—92no—
331C2×#67—188no—
332C2×#67D3211yescharacteristic
333C22×Dic3—32no—
334C22×Dic3—61no—
335C22×Dic3—92no—
336C22×Dic3—92no—
337C22×Dic3—92no—
338C22×Dic3—181no—
339#239—184no—
340#237—188no—
341C2×D12—32no—
342C2×D12—32no—
343C2×D12—91no—
344C2×D12—92no—
345C2×D12—91no—
346C2×D12—184no—
347C2×C4×D3—92no—
348C2×C4×D3—92no—
349C2×C4×D3—91no—
350C2×C4×D3—92no—
351C2×C4×D3—92no—
352C2×C4×D3—182no—
353C2×C4×D3—182no—
354C2×Dic6—32no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—92no—
357C3×C22⋊C4—32no—
358C3×C22⋊C4—32no—
359C3×C22⋊C4—62no—
360C3×C22⋊C4—92no—
361C3×C22⋊C4—92no—
362#217—92no—
363#217—91no—
364#217—92no—
365#217—92no—
366#217—92no—
367#217—181no—
368#217—182no—
369#217—181no—
370#217—361no—
371#217D3212yes—
372(C2×D3)⋊C4—32no—
373(C2×D3)⋊C4—32no—
374(C2×D3)⋊C4—32no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—92no—
377(C2×D3)⋊C4—92no—
378(C2×D3)⋊C4—92no—
379(C2×D3)⋊C4—92no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—182no—
382(C2×D3)⋊C4—182no—
383C4⋊Dic3—32no—
384C4⋊Dic3—92no—
385C4⋊Dic3—181no—
386Dic3⋊C4—32no—
387Dic3⋊C4—32no—
388Dic3⋊C4—91no—
389C4×Dic3—92no—
390C4×Dic3—91no—
391C4×Dic3—181no—
392C22×C32—22no—
393C22×C32—21no—
394C22×C32—22no—
395C22×C32—21no—
396C22×C32—22no—
397C22×C32—21no—
398C22×C32—24no—
399C22×C32—22no—
400C22×C32—41no—
401C22×C32—42no—
402C22×C32—41no—
403C22×C32—42no—
404C22×C32—42no—
405C22×C32—41no—
406C22×C32—61no—
407C22×C32—61no—
408C22×C32—61no—
409C22×C32—81no—
410C22×C32—81no—
411C22×C32#23714yescomplemented
412C22×C32#23912yescomplemented
413C22×C32C23×D312yes—
414C22×C32C23×D311yescharacteristic
415C2×C3⋊D3—22no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—48no—
421C2×C3⋊D3D3×D414yes—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—34no—
427C2×C3×D3—34no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—64no—
431C2×C3×D3—64no—
432C2×C3×D3—64no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—64no—
438C2×C3×D3—62no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—62no—
442C2×C3×D3—62no—
443C2×C3×D3—62no—
444C2×C3×D3—122no—
445C2×C3×D3—122no—
446C2×C3×D3—128no—
447C2×C3×D3—128no—
448C2×C3×D3—1216no—
449C32×C4—61no—
450C32×C4—62no—
451C32×C4—62no—
452C3⋊Dic3—21no—
453C3⋊Dic3—62no—
454C3⋊Dic3—61no—
455C3⋊Dic3—62no—
456C3⋊Dic3—61no—
457C3⋊Dic3—121no—
458C3⋊Dic3—122no—
459C3⋊Dic3—122no—
460C3⋊Dic3—121no—
461C3⋊Dic3—241no—
462C3⋊Dic3—241no—
463C3⋊Dic3D3×D412yes—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—34no—
471C3×Dic3—42no—
472C3×Dic3—42no—
473C3×Dic3—62no—
474C3×Dic3—62no—
475C3×Dic3—121no—
476C2×#41—271no—
477C22×D4—271no—
478#124—271no—
479#123—272no—
480C22⋊Q8—91no—
481#121—272no—
482#121—271no—
483#120—92no—
484C4×D4—271no—
485C4×D4—271no—
486C2×C22⋊C4—272no—
487C33#54611yescharacteristic, complemented, Sylow
488C23×C3—22no—
489C23×C3—21no—
490C23×C3—32no—
491C23×C3—41no—
492C23×C3—61no—
493C23×C3—92no—
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—32no—
503C22×D3—32no—
504C22×D3—62no—
505C22×D3—62no—
506C22×D3—64no—
507C22×D3—64no—
508C22×D3—68no—
509C22×D3—64no—
510C22×D3—64no—
511C22×D3—124no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—124no—
515C22×D3C2×D3211yescharacteristic
516C3×Q8—182no—
517C3×D4—64no—
518C3×D4—64no—
519C3×D4—184no—
520C3×D4—362no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—61no—
527C2×C3×C4—62no—
528C2×C3×C4—62no—
529C2×C3×C4—91no—
530C2×C3×C4—91no—
531C2×C3×C4—182no—
532#67—22no—
533#67—64no—
534#67—98no—
535#67—122no—
536#67—184no—
537#67—184no—
538#67—184no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—64no—
544C2×Dic3—91no—
545C2×Dic3—92no—
546C2×Dic3—91no—
547C2×Dic3—92no—
548C2×Dic3—122no—
549C2×Dic3—181no—
550C2×Dic3—181no—
551C2×Dic3—182no—
552C2×Dic3—182no—
553C2×Dic3—184no—
554C2×Dic3—184no—
555C2×Dic3—361no—
556C2×Dic3—361no—
557C2×Dic3—362no—
558C2×Dic3—362no—
559C2×Dic3C2×D3211yescharacteristic
560C2×Dic3C2×D3212yes—
561C2×Dic3C2×D3212yes—
562D12—64no—
563D12—94no—
564D12—122no—
565D12—182no—
566D12—184no—
567C4×D3—184no—
568C4×D3—184no—
569C4×D3—182no—
570C4×D3—364no—
571C4×D3—362no—
572C4×D3—362no—
573C4×D3—364no—
574Dic6—64no—
575C2×C32—24no—
576C2×C32—22no—
577C2×C32—22no—
578C2×C32—22no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—22no—
582C2×C32—21no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32—41no—
586C2×C32—44no—
587C2×C32—42no—
588C2×C32—82no—
589C2×C32—121no—
590C2×C32C2×D3×D412yes—
591C2×C32C2×D3×D411yescharacteristic
592C2×C32C2×#23712yes—
593C2×C32#100412yes—
594C2×C32C2×#23911yescharacteristic
595C2×C32#100911yescharacteristic
596C3⋊D3—24no—
597C3⋊D3—42no—
598C3×D3—42no—
599C3×D3—42no—
600C3×D3—68no—
601C3×D3—64no—
602C3×D3—64no—
603C3×D3—124no—
604C3×D3—122no—
605C3×D3—122no—
606C24—92no—
607#41—544no—
608C2×Q8—91no—
609C2×D4—31no—
610C2×D4—92no—
611C2×D4—92no—
612C2×D4—271no—
613C2×D4—272no—
614C2×D4—271no—
615C2×D4—544no—
616C22×C4—91no—
617C22×C4—272no—
618C22×C4—272no—
619C22×C4—271no—
620C4⋊C4—91no—
621C4⋊C4—92no—
622C4⋊C4—271no—
623C22⋊C4—32no—
624C22⋊C4—92no—
625C22⋊C4—92no—
626C22⋊C4—272no—
627C22⋊C4—272no—
628C22⋊C4—271no—
629C22⋊C4—271no—
630C42—271no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—24no—
639C22×C3—41no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—42no—
645C22×C3—62no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—62no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—94no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—182no—
655C22×C3—182no—
656C22×C3—182no—
657C22×C3—182no—
658C22×C3—182no—
659C22×C3—368no—
660C22×C3#379614yescomplemented
661C22×C3#380512yescomplemented
662C22×C3C22×D3212yes—
663C22×C3C22×D3211yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—34no—
668C2×D3—34no—
669C2×D3—64no—
670C2×D3—64no—
671C2×D3—64no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—62no—
675C2×D3—62no—
676C2×D3—64no—
677C2×D3—62no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—62no—
683C2×D3—122no—
684C2×D3—122no—
685C2×D3—128no—
686C2×D3—128no—
687C2×D3—1216no—
688C3×C4—62no—
689C3×C4—62no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—62no—
693C3×C4—62no—
694C3×C4—92no—
695C3×C4—122no—
696C3×C4—122no—
697C3×C4—181no—
698Dic3—22no—
699Dic3—22no—
700Dic3—21no—
701Dic3—34no—
702Dic3—62no—
703Dic3—62no—
704Dic3—121no—
705Dic3—181no—
706Dic3—182no—
707Dic3—181no—
708Dic3—182no—
709Dic3—362no—
710Dic3—362no—
711Dic3—361no—
712Dic3—361no—
713Dic3—721no—
714Dic3—721no—
715C32—22no—
716C32—21no—
717C32—41no—
718C32#559112yescomplemented
719C32#563011yescharacteristic, complemented
720C23—31no—
721C23—92no—
722C23—92no—
723C23—184no—
724C23—184no—
725C23—362no—
726C23D3311yescharacteristic
727Q8—182no—
728D4—62no—
729D4—184no—
730D4—274no—
731D4—362no—
732D4—542no—
733D4—544no—
734C2×C4—31no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—91no—
738C2×C4—91no—
739C2×C4—182no—
740C2×C4—271no—
741C2×C4—271no—
742C2×C4—544no—
743C2×C4—542no—
744C2×C4—1082no—
745C2×C3—24no—
746C2×C3—22no—
747C2×C3—22no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—22no—
751C2×C3—21no—
752C2×C3—22no—
753C2×C3—44no—
754C2×C3—42no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—82no—
759C2×C3—122no—
760C2×C3—122no—
761C2×C3—184no—
762C2×C3—362no—
763C2×C3C2×#379612yes—
764C2×C3D32×D412yes—
765C2×C3D32×D411yescharacteristic
766C2×C3#6431311yescharacteristic
767C2×C3#6431412yes—
768C2×C3C2×#380511yescharacteristic
769D3—41no—
770D3—68no—
771D3—64no—
772D3—64no—
773D3—124no—
774D3—122no—
775D3—122no—
776C22—21no—
777C22—21no—
778C22—61no—
779C22—61no—
780C22—61no—
781C22—94no—
782C22—182no—
783C22—182no—
784C22—182no—
785C22—182no—
786C22—182no—
787C22—368no—
788C22#8896412yescomplemented
789C22C2×D3311yescharacteristic
790C4—62no—
791C4—61no—
792C4—62no—
793C4—92no—
794C4—181no—
795C4—541no—
796C4—541no—
797C3—22no—
798C3—21no—
799C3—41no—
800C3#1059406312yescomplemented
801C3#1059522511yescharacteristic, complemented
802C2—22no—
803C2—121no—
804C2—184no—
805C2—362no—
806C2#1172441611yescharacteristic
807C2C2×#8896411yescharacteristic
808C2#1172444011yescharacteristic
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. C22×#6295C2semidirect
2. C2×#88964C2semidirect
3. C3⋊D3×#217C2semidirect
4. #67×C3⋊Dic3C2semidirect
5. C3×#63982C2semidirect
6. C3×#63981C2semidirect
7. #11723007C2semidirect
8. #11722997C2semidirect
9. #11722962C2semidirect
10. #11722955C2semidirect
11. #11722938C2semidirect
21. C2×Dic3×C3⋊D3C22semidirect
22. C2×Dic3×C3⋊D3C22semidirect
23. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×#627C22semidirect
25. C2×C3×#626C22semidirect
26. C2×C3×#626C22semidirect
30. Dic3⋊(C3⋊Dic3)C22semidirect
31. #88803C22semidirect
32. #88803C22semidirect
33. (C2×D3)⋊(C3⋊Dic3)C22semidirect
34. Dic3×C3⋊Dic3C22semidirect
35. C3×#3724C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×#3722C22semidirect
48. #63982D3semidirect
49. #63981D3semidirect
85. #6295D4semidirect
112. C2×#627C2×D3semidirect
118. C2×#626C2×D3semidirect
119. C2×#626C2×D3semidirect
155. #3724C2×D3semidirect
158. Dic3⋊Dic3C2×D3semidirect
159. #3722C2×D3semidirect
160. #3722C2×D3semidirect
173. C22×C33#41semidirect
411. C22×C32#237semidirect
412. C22×C32#239semidirect
487. C33#546semidirect
660. C22×C3#3796semidirect
661. C22×C3#3805semidirect
718. C32#5591semidirect
719. C32#5630semidirect
788. C22#88964semidirect
800. C3#10594063semidirect
801. 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×#889642
C3⋊D3×#2172
#67×C3⋊Dic32
C3×#639822
C3×#639812
#117230072
#117229972
#117229622
#117229552
#117229382
#105952253
#105940633