Finite Group Databasebeta

← #13151992

Subgroups — #13151992

Order 1728.

1238 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6233C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3C3×#63515C211yesmaximal, characteristic, complemented
4C2×C9×#217C211yesmaximal, characteristic, complemented
5#11721278C211yesmaximal, characteristic, complemented
6#11721277C211yesmaximal, characteristic, complemented
7#11721275C211yesmaximal, characteristic, complemented
8#11721274C211yesmaximal, characteristic, complemented
9#611⋊Dic3C211yesmaximal, characteristic, complemented
10#11721271C211yesmaximal, characteristic, complemented
11#11721267C211yesmaximal, characteristic, complemented
12#11721256C211yesmaximal, characteristic, complemented
13#11721251C211yesmaximal, characteristic, complemented
14#11721242C211yesmaximal, characteristic, complemented
15#11721240C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10589592—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C23×C3⋊D9C2211yescharacteristic
20C2×#6233—24no—
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic
23C2×#6233C2211yescharacteristic
24C2×#6233C2211yescharacteristic
25C22×C3⋊Dic9C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic, complemented
29C22×C9×Dic3C2211yescharacteristic, complemented
30C22×C9×Dic3C2211yescharacteristic, complemented
31C2×#6192C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35#88658—24no—
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38C9×#217C2211yescharacteristic
39C9×#217C2211yescharacteristic
40C9×#217C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic
43C3×#3676C2211yescharacteristic, complemented
44C3×#3676C2211yescharacteristic, complemented
45#88445C2211yescharacteristic, complemented
46#88445C2211yescharacteristic, complemented
47#88445C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3804—31no—
57C3×#953—31no—
58C2×C3×#217D311yescharacteristic
59#63982—31no—
60#63981—31no—
61#63978—31no—
62#63975—31no—
63#63974—31no—
64#67⋊Dic3—31no—
65#63971—31no—
66#63966—31no—
67#63958—31no—
68#63953—31no—
69#63952—31no—
70C22×#611—31no—
71C22×#611—61no—
72C2×#3697—31no—
73C2×C9×C22⋊C4—31no—
74#63515D311yescharacteristic, complemented
75#63492—31no—
76#63491—31no—
77C4×#611—31no—
78#63447—31no—
79#63446—31no—
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#611⋊C4—31no—
84C22⋊C4×D9—31no—
85#63440—31no—
86C23×C3×C9—22no—
87C23×C3×C9—22no—
88C23×C3×C9—41no—
89C23×C3×C9C2311yescharacteristic
90C23×C3×C9C2311yescharacteristic
91C23×C3×C9C2311yescharacteristic
92C22×C3⋊D9—22no—
93C22×C3⋊D9—22no—
94C22×C3⋊D9—41no—
95C22×C3⋊D9C2311yescharacteristic
96C22×C3⋊D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98#6233—22no—
99#6233—22no—
100#6233—22no—
101#6233D414yescomplemented
102C2×C3⋊Dic9—22no—
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C3×#611—22no—
106C3×#611—22no—
107C3×#611—41no—
108C2×C9×Dic3—22no—
109C2×C9×Dic3—41no—
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C9×Dic3C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117#6192—22no—
118#6192—41no—
119(C3⋊D9)⋊C4—22no—
120(C3⋊D9)⋊C4—41no—
121Dic3×D9—22no—
122#6189—22no—
123#5591—91no—
124#5490—91no—
125C24×C32C2×D311yescharacteristic
126C23×C3⋊D3—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—31no—
131C2×#638—64no—
132C22×C3⋊Dic3—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C22×C3×Dic3C2×D311yescharacteristic
137C22×C3×Dic3C2×D311yescharacteristic
138C2×#627—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#624—31no—
142C2×#624—31no—
143#3804—64no—
144C2×D3×Dic3—31no—
145C24×C9—21no—
146C24×C9C2×D311yescharacteristic
147C23×D9—31no—
148C23×D9—61no—
149C3×#217—31no—
150C3×#217—31no—
151C3×#217—31no—
152C3×#217C2×D311yescharacteristic
153C3×#217C2×D311yescharacteristic
154C3×#217C2×D311yescharacteristic
155C3×#217C2×D311yescharacteristic
156#3724—31no—
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—31no—
159Dic3⋊Dic3—31no—
160#3722—31no—
161#3722—31no—
162#3722—31no—
163#3722—31no—
164(C2×D3)⋊Dic3—31no—
165Dic32—31no—
166C22×C4×C9—31no—
167C22×C4×C9—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—64no—
173C2×#611—61no—
174C2×#611—61no—
175C2×#611—61no—
176C2×#611—61no—
177C2×#611—68no—
178C2×#611C2×D311yescharacteristic
179C2×#611C2×D311yescharacteristic, complemented
180C2×#611C2×D311yescharacteristic, complemented
181C22×Dic9—31no—
182C22×Dic9—61no—
183#3697—64no—
184C2×D36—31no—
185C2×D36—31no—
186C2×C4×D9—31no—
187C2×C4×D9—31no—
188C2×C4×D9—31no—
189C2×Dic18—31no—
190C9×C22⋊C4—31no—
191C9×C22⋊C4—31no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4—31no—
194#3676C2×D311yescharacteristic
195#3676C2×D311yescharacteristic, complemented
196#3676C2×D311yescharacteristic, complemented
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202C4⋊Dic9—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
205Dic9⋊C4—31no—
206C4×Dic9—31no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9—21no—
214C22×C3×C9—44no—
215C22×C3×C9C2×D412yes—
216C22×C3×C9#4112yescomplemented
217C22×C3×C9C2411yescharacteristic
218C2×C3⋊D9—21no—
219C2×C3⋊D9—21no—
220C2×C3⋊D9—21no—
221C2×C3⋊D9—21no—
222C2×C3⋊D9—21no—
223C2×C3⋊D9—44no—
224C2×C3⋊D9C2×D412yes—
225C2×C3×D9—21no—
226C2×C3×D9—21no—
227C2×C3×D9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9C2×D412yes—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C3×Dic9—21no—
237C22×#67—91no—
238C22×#67—91no—
239C22×#67—181no—
240C2×#237—91no—
241C2×#235—91no—
242C3×#120—91no—
243C2×C3×C22⋊C4—31no—
244#953—31no—
245C2×#217D911yescharacteristic, complemented
246#939—91no—
247#939—91no—
248#938—91no—
249#937—91no—
250D4×Dic3—91no—
251#930—91no—
252#929—91no—
253C4×#67—91no—
254#886—91no—
255#885—91no—
256#885—91no—
257#884—91no—
258#884—91no—
259#883—91no—
260#883—91no—
261#882—91no—
262#67⋊C4—91no—
263#67⋊C4—91no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—91no—
267#878—91no—
268C23×C32—22no—
269C23×C32—22no—
270C23×C32—41no—
271C23×C32C22×D311yescharacteristic
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—62no—
277C22×C3⋊D3—62no—
278C22×C3⋊D3—121no—
279C22×C3×D3—31no—
280#638—34no—
281#638—62no—
282#638—62no—
283#638—62no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—62no—
287C3×#67—62no—
288C3×#67—62no—
289C3×#67—121no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—41no—
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299#627—62no—
300#626—62no—
301#626—121no—
302#624—62no—
303#624—121no—
304D3×Dic3—62no—
305C23×C9—24no—
306C23×C9—22no—
307C23×C9—22no—
308C23×C9—21no—
309C23×C9—21no—
310C23×C9—21no—
311C23×C9—42no—
312C23×C9—41no—
313C23×C9—42no—
314C23×C9C22×D311yescharacteristic
315C23×C9C22×D311yescharacteristic
316C23×C9C22×D311yescharacteristic
317C22×D9—31no—
318C22×D9—31no—
319C22×D9—61no—
320C22×D9—61no—
321C22×D9—62no—
322C22×D9—64no—
323C22×D9—62no—
324C22×D9—122no—
325C22×D9—121no—
326C22×D9—122no—
327C22×D9C22×D311yescharacteristic
328C2×C4×C9—31no—
329C2×C4×C9—31no—
330C2×C4×C9—31no—
331C2×C4×C9—31no—
332C2×C4×C9—62no—
333C2×C4×C9—121no—
334#611—22no—
335#611—22no—
336#611—34no—
337#611—41no—
338#611—64no—
339#611—62no—
340#611—62no—
341#611—64no—
342#611—64no—
343#611—64no—
344#611—62no—
345C2×Dic9—31no—
346C2×Dic9—31no—
347C2×Dic9—61no—
348C2×Dic9—61no—
349C2×Dic9—62no—
350C2×Dic9—64no—
351C2×Dic9C22×D311yescharacteristic
352C2×Dic9C22×D311yescharacteristic
353C2×Dic9C22×D311yescharacteristic
354D36—62no—
355D36—121no—
356C4×D9—62no—
357C4×D9—62no—
358C4×D9—121no—
359Dic18—62no—
360#546—271noSylow
361C2×C3×C9—22no—
362C2×C3×C9—22no—
363C2×C3×C9—41no—
364C2×C3×C9C22×D411yescharacteristic
365C2×C3×C9C2×#4111yescharacteristic
366C2×C3×C9H(5,𝔽2)11yescharacteristic
367C3⋊D9—22no—
368C3⋊D9—41no—
369C3×D9—41no—
370C24×C3—21no—
371C24×C3C2×D911yescharacteristic
372C24×C3D3211yescharacteristic
373C23×D3—91no—
374C23×D3—91no—
375C23×D3—181no—
376C2×C3×D4—91no—
377C2×C3×D4—91no—
378C2×C3×D4—91no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C2×#67—31no—
382C2×#67—31no—
383C2×#67—31no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—181no—
395C2×#67—181no—
396C2×#67—181no—
397C2×#67—181no—
398C2×#67—184no—
399C2×#67—184no—
400C2×#67—188no—
401C22×Dic3—91no—
402C22×Dic3—91no—
403C22×Dic3—91no—
404C22×Dic3—181no—
405C22×Dic3C2×D911yescharacteristic, complemented
406C22×Dic3C2×D911yescharacteristic, complemented
407#237—184no—
408#235—184no—
409C2×D12—91no—
410C2×D12—91no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C2×C4×D3—91no—
414C2×C4×D3—91no—
415C2×C4×D3—91no—
416C2×Dic6—91no—
417C2×Dic6—91no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—91no—
423C3×C22⋊C4—91no—
424C3×C22⋊C4—91no—
425#217—31no—
426#217—31no—
427#217—31no—
428#217—91no—
429#217C2×D911yescharacteristic
430#217C2×D911yescharacteristic
431#217C2×D911yescharacteristic, complemented
432#217C2×D911yescharacteristic, complemented
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442C4⋊Dic3—91no—
443C4⋊Dic3—91no—
444C4⋊Dic3—91no—
445Dic3⋊C4—91no—
446Dic3⋊C4—91no—
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450C4×Dic3—91no—
451C4×Dic3—91no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—44no—
460C22×C32#23512yes—
461C22×C32D3×D412yes—
462C22×C32C23×D311yescharacteristic
463C2×C3⋊D3—32no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—124no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C3⋊Dic3—32no—
474C3⋊Dic3—61no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C22×C9—22no—
483C22×C9—22no—
484C22×C9—21no—
485C22×C9—21no—
486C22×C9—21no—
487C22×C9—21no—
488C22×C9—22no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—21no—
492C22×C9—21no—
493C22×C9—22no—
494C22×C9—22no—
495C22×C9—41no—
496C22×C9—41no—
497C22×C9—41no—
498C22×C9—41no—
499C22×C9—44no—
500C22×C9—48no—
501C22×C9D3×D412yes—
502C22×C9#23712yescomplemented
503C22×C9C23×D311yescharacteristic
504C2×D9—21no—
505C2×D9—21no—
506C2×D9—21no—
507C2×D9—32no—
508C2×D9—62no—
509C2×D9—61no—
510C2×D9—61no—
511C2×D9—62no—
512C2×D9—61no—
513C2×D9—61no—
514C2×D9—61no—
515C2×D9—121no—
516C2×D9—121no—
517C2×D9—121no—
518C2×D9—121no—
519C2×D9—124no—
520C2×D9—128no—
521C4×C9—61no—
522C4×C9—61no—
523C4×C9—61no—
524C4×C9—61no—
525Dic9—21no—
526Dic9—21no—
527Dic9—21no—
528Dic9—32no—
529Dic9—62no—
530Dic9—62no—
531Dic9—61no—
532C2×#41—271no—
533C22×D4—271no—
534#124—271no—
535#123—271no—
536#123—271no—
537C22⋊Q8—271no—
538#121—271no—
539#121—271no—
540#121—271no—
541#120—91no—
542#120—271no—
543C4×D4—271no—
544C4×D4—271no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—271no—
547C3×C9#54611yescharacteristic, complemented, Sylow
548C23×C3—24no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—42no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—42no—
560C23×C3—91no—
561C23×C3C22×D911yescharacteristic
562C23×C3C22×D911yescharacteristic
563C23×C3C22×D911yescharacteristic
564C23×C3C2×D3211yescharacteristic
565C23×C3C2×D3211yescharacteristic
566C23×C3C2×D3211yescharacteristic
567C22×D3—31no—
568C22×D3—91no—
569C22×D3—91no—
570C22×D3—91no—
571C22×D3—91no—
572C22×D3—181no—
573C22×D3—181no—
574C22×D3—182no—
575C22×D3—182no—
576C22×D3—184no—
577C22×D3—182no—
578C22×D3—182no—
579C22×D3—362no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—362no—
583C3×D4—182no—
584C3×D4—182no—
585C3×D4—361no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—62no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—91no—
594C2×C3×C4—121no—
595#67—62no—
596#67—62no—
597#67—94no—
598#67—94no—
599#67—121no—
600#67—184no—
601#67—182no—
602#67—182no—
603#67—182no—
604#67—182no—
605#67—182no—
606#67—184no—
607#67—184no—
608#67—184no—
609#67—182no—
610#67—182no—
611#67—361no—
612C2×Dic3—22no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—41no—
617C2×Dic3—91no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—91no—
621C2×Dic3—181no—
622C2×Dic3—181no—
623C2×Dic3—182no—
624C2×Dic3—182no—
625C2×Dic3—182no—
626C2×Dic3—184no—
627C2×Dic3C22×D911yescharacteristic
628C2×Dic3C22×D911yescharacteristic
629C2×Dic3C22×D911yescharacteristic
630C2×Dic3C22×D911yescharacteristic
631D12—182no—
632D12—361no—
633C4×D3—182no—
634C4×D3—182no—
635C4×D3—182no—
636C4×D3—361no—
637C4×D3—361no—
638Dic6—182no—
639Dic6—182no—
640C2×C32—22no—
641C2×C32—22no—
642C2×C32—41no—
643C2×C32C2×#23511yescharacteristic
644C2×C32C2×D3×D411yescharacteristic
645C2×C32#100411yescharacteristic
646C3⋊D3—62no—
647C3⋊D3—121no—
648C3×D3—121no—
649C2×C9—24no—
650C2×C9—22no—
651C2×C9—22no—
652C2×C9—21no—
653C2×C9—21no—
654C2×C9—21no—
655C2×C9—42no—
656C2×C9—42no—
657C2×C9—41no—
658C2×C9C2×D3×D411yescharacteristic
659C2×C9C2×#23711yescharacteristic
660C2×C9#100411yescharacteristic
661D9—41no—
662D9—62no—
663D9—122no—
664D9—122no—
665D9—121no—
666C24—271no—
667C24D3×D911yescharacteristic
668#41—544no—
669C2×Q8—271no—
670C2×D4—91no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—544no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—271no—
683C22×C4—271no—
684C22×C4—271no—
685C22×C4—271no—
686C4⋊C4—271no—
687C4⋊C4—271no—
688C4⋊C4—271no—
689C4⋊C4—271no—
690C22⋊C4—31no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—91no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C42—271no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—44no—
728C22×C3—44no—
729C22×C3—48no—
730C22×C3—181no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3#369712yescomplemented
734C22×C3D4×D912yes—
735C22×C3C23×D911yescharacteristic
736C22×C3#380412yes—
737C22×C3#381112yes—
738C22×C3C22×D3211yescharacteristic
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—92no—
743C2×D3—92no—
744C2×D3—182no—
745C2×D3—181no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—182no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—361no—
757C2×D3—361no—
758C2×D3—361no—
759C2×D3—361no—
760C2×D3—364no—
761C2×D3—364no—
762C2×D3—368no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—61no—
767C3×C4—181no—
768C3×C4—181no—
769C3×C4—181no—
770Dic3—21no—
771Dic3—21no—
772Dic3—21no—
773Dic3—21no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—92no—
778Dic3—92no—
779Dic3—182no—
780Dic3—182no—
781Dic3—181no—
782Dic3—181no—
783C32#549011yescharacteristic
784C9—21no—
785C9#559111yescharacteristic, complemented
786C23—22no—
787C23—22no—
788C23—41no—
789C23—91no—
790C23—271no—
791C23—271no—
792C23—542no—
793C23—542no—
794C23—1081no—
795C23C2×D3×D911yescharacteristic
796C23C2×D3×D911yescharacteristic
797C23C2×D3×D911yescharacteristic
798Q8—542no—
799D4—182no—
800D4—182no—
801D4—274no—
802D4—361no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—62no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—121no—
817C2×C4—271no—
818C2×C4—271no—
819C2×C4—542no—
820C2×C4—542no—
821C2×C4—542no—
822C2×C4—1081no—
823C2×C3—24no—
824C2×C3—22no—
825C2×C3—22no—
826C2×C3—22no—
827C2×C3—22no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—42no—
832C2×C3—42no—
833C2×C3—41no—
834C2×C3—41no—
835C2×C3—361no—
836C2×C3C2×#369711yescharacteristic
837C2×C3C2×D4×D911yescharacteristic
838C2×C3#6371011yescharacteristic
839C2×C3C2×#380411yescharacteristic
840C2×C3C2×#381111yescharacteristic
841C2×C3#6433011yescharacteristic
842D3—121no—
843D3—182no—
844D3—182no—
845D3—362no—
846D3—362no—
847D3—361no—
848D3—361no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—44no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—272no—
861C22—541no—
862C22—541no—
863C22—541no—
864C22—541no—
865C22—541no—
866C22—1084no—
867C22#8865812yescomplemented
868C22#8866812yes—
869C22C22×D3×D911yescharacteristic
870C4—61no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—181no—
875C4—181no—
876C4—181no—
877C4—272no—
878C4—541no—
879C3—21no—
880C3#1058959211yescharacteristic, complemented
881C3#1059550011yescharacteristic
882C2—22no—
883C2—22no—
884C2—41no—
885C2—361no—
886C2—542no—
887C2—1081no—
888C2C2×#8865811yescharacteristic
889C2C2×#8866811yescharacteristic
890C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC24×C3×C9C22
socleC22×C32C23×D3
hypercenterC24D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#6233C2semidirect
2. C2×#88658C2semidirect
3. C3×#63515C2semidirect
4. C2×C9×#217C2semidirect
5. #11721278C2semidirect
6. #11721277C2semidirect
7. #11721275C2semidirect
8. #11721274C2semidirect
9. #611⋊Dic3C2semidirect
10. #11721271C2semidirect
11. #11721267C2semidirect
12. #11721256C2semidirect
13. #11721251C2semidirect
14. #11721242C2semidirect
15. #11721240C2semidirect
27. C2×C3×#611C22semidirect
28. C2×C3×#611C22semidirect
29. C22×C9×Dic3C22semidirect
30. C22×C9×Dic3C22semidirect
31. C2×#6192C22semidirect
32. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
40. C9×#217C22semidirect
41. C9×#217C22semidirect
43. C3×#3676C22semidirect
44. C3×#3676C22semidirect
45. #88445C22semidirect
46. #88445C22semidirect
47. #88445C22semidirect
48. #88445C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
74. #63515D3semidirect
101. #6233D4semidirect
179. C2×#611C2×D3semidirect
180. C2×#611C2×D3semidirect
195. #3676C2×D3semidirect
196. #3676C2×D3semidirect
216. C22×C3×C9#41semidirect
245. C2×#217D9semidirect
405. C22×Dic3C2×D9semidirect
406. C22×Dic3C2×D9semidirect
431. #217C2×D9semidirect
432. #217C2×D9semidirect
502. C22×C9#237semidirect
547. C3×C9#546semidirect
733. C22×C3#3697semidirect
785. C9#5591semidirect
867. C22#88658semidirect
880. C3#10589592semidirect

Maximal subgroups

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

subgroupindex
C22×#62332
C2×#886582
C3×#635152
C2×C9×#2172
#117212782
#117212772
#117212752
#117212742
#611⋊Dic32
#117212712
#117212672
#117212562
#117212512
#117212422
#117212402
#105955003
#105895923