Finite Group Databasebeta

← #13151136

Subgroups — #13151136

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic, complemented
2C2×#88663C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C9×#937C211yesmaximal, characteristic, complemented
5C3×#63502C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721290C211yesmaximal, characteristic, complemented
8#11721289C211yesmaximal, characteristic, complemented
9#11721286C211yesmaximal, characteristic, complemented
10#11721271C211yesmaximal, characteristic, complemented
11#11721257C211yesmaximal, characteristic, complemented
12#11721049C211yesmaximal, characteristic, complemented
13#11721010C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15#11720956C211yesmaximal, characteristic, complemented
16#10595286—31nomaximal
17#10589694—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic, complemented
23C22×C3⋊Dic9C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic
25C2×C9×#67C2211yescharacteristic, complemented
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic, complemented
29C2×C3×#611C2211yescharacteristic, complemented
30C2×C3×D36C2211yescharacteristic, complemented
31D3×#611—24no—
32C2×#6195C2211yescharacteristic
33C2×#6194C2211yescharacteristic
34C2×#6194C2211yescharacteristic
35C2×#6194C2211yescharacteristic, complemented
36#88663—24no—
37C2×D3×Dic9C2211yescharacteristic
38C2×#6192C2211yescharacteristic, complemented
39C2×Dic3×D9C2211yescharacteristic, complemented
40C2×#6189C2211yescharacteristic, complemented
41#88551C2211yescharacteristic, complemented
42#88536C2211yescharacteristic, complemented
43#88534C2211yescharacteristic, complemented
44C9×#217C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic
46C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C3×C4×Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3805—31no—
57#64148—31no—
58C3×#940—31no—
59C3×#937D311yescharacteristic
60#63983—31no—
61#63980—31no—
62#63979—31no—
63#63976—31no—
64#63971—31no—
65#63959—31no—
66#63922—31no—
67#63885—31no—
68#63877—31no—
69#63852—31no—
70C22×#611—31no—
71C2×#3699—31no—
72C9×#120—31no—
73#63515—31no—
74#63502—31no—
75#63502D311yescharacteristic, complemented
76#63501—31no—
77#63501—31no—
78#63501—61no—
79#63499—31no—
80#63447—31no—
81#63447—31no—
82#63446—31no—
83#63446—31no—
84#63444—31no—
85#63439—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9—22no—
90C22×D3×C9—41no—
91C22×D3×C9—41no—
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C22×C3×D9C2311yescharacteristic
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×D3×D9—41no—
99C3×D4×C9—41no—
100C2×C3×C4×C9C2311yescharacteristic
101#6233—22no—
102#6233—41no—
103C2×C3⋊Dic9—22no—
104C2×C3⋊Dic9C2311yescharacteristic
105C2×C3⋊Dic9C2311yescharacteristic
106C2×C3⋊Dic9C2311yescharacteristic
107C9×#67—22no—
108C9×#67—41no—
109C3×#611—22no—
110C3×#611—22no—
111C3×#611—41no—
112C3×#611—41no—
113C2×C9×Dic3C2311yescharacteristic
114C2×C9×Dic3C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C3×D36—41no—
118#6195—22no—
119#6194—22no—
120#6194—22no—
121#6194—41no—
122D3×Dic9D414yescomplemented
123#6192—41no—
124Dic3×D9—22no—
125#6189—22no—
126#5715—91no—
127#5592—91no—
128C23×C3×D3C2×D311yescharacteristic
129C22×D32—31no—
130C2×C32×D4C2×D311yescharacteristic
131C2×#638—31no—
132C2×#638—31no—
133C22×C3⋊Dic3—31no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67C2×D311yescharacteristic
139C2×C3×#67C2×D311yescharacteristic
140C2×C3×D12—31no—
141D3×#67—64no—
142C2×#627—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#625—31no—
146C2×#625—31no—
147C2×#625—31no—
148#3805—64no—
149C2×D3×Dic3—31no—
150C2×D3×Dic3—31no—
151C24×C9—31no—
152C23×D9—31no—
153#3757—31no—
154#3752—31no—
155#3750—31no—
156C3×#217C2×D311yescharacteristic
157C3×(C2×D3)⋊C4C2×D311yescharacteristic
158C3×(C2×D3)⋊C4C2×D311yescharacteristic
159C3×C4×Dic3—31no—
160#3724—31no—
161#3722—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166Dic32—31no—
167C2×D4×C9—21no—
168C2×D4×C9—31no—
169C2×D4×C9—31no—
170C2×D4×C9C2×D311yescharacteristic, complemented
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—64no—
178C2×#611—61no—
179C2×#611—61no—
180C2×#611C2×D311yescharacteristic
181C2×#611C2×D311yescharacteristic, complemented
182C2×#611C2×D311yescharacteristic, complemented
183C2×#611C2×D311yescharacteristic, complemented
184C22×Dic9—31no—
185C22×Dic9—31no—
186C22×Dic9—61no—
187#3699—64no—
188C2×D36—31no—
189C2×D36C2×D311yescharacteristic, complemented
190C2×C4×D9—31no—
191C2×Dic18—31no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4—31no—
194C9×C22⋊C4—31no—
195#3676—31no—
196#3676—31no—
197#3676—31no—
198#3676—61no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—31no—
203(C2×D9)⋊C4—61no—
204Dic9⋊C4—31no—
205Dic9⋊C4—31no—
206Dic9⋊C4—61no—
207C4×Dic9—31no—
208C4×Dic9C2×D311yescharacteristic, complemented
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9—21no—
214C22×C3×C9—21no—
215C22×C3×C9C2411yescharacteristic
216C2×C3⋊D9—21no—
217C2×C3⋊D9—21no—
218C2×C3⋊D9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9—21no—
223C2×D3×C9—21no—
224C2×D3×C9—44no—
225C2×D3×C9C2×D412yes—
226C2×C3×D9—21no—
227C2×C3×D9—21no—
228C2×C3×D9—21no—
229C2×C3×D9—21no—
230C2×C3×D9—21no—
231C2×C3×D9—21no—
232D3×D9—44no—
233C3×C4×C9—21no—
234C3⋊Dic9—21no—
235C3⋊Dic9—21no—
236C3⋊Dic9C2×D412yes—
237C9×Dic3—21no—
238C9×Dic3—21no—
239C3×Dic9—21no—
240C3×Dic9C2×D412yes—
241C22×#67—91no—
242C2×#237—91no—
243C2×#237—91no—
244C2×D3×D4—91no—
245C3×#127—91no—
246C3×#120—31no—
247#953—91no—
248#940—31no—
249#940—91no—
250#940—91no—
251#939—91no—
252#939—91no—
253#939—91no—
254#939—91no—
255#939—91no—
256#939—91no—
257#939—181no—
258#937—91no—
259#937—91no—
260#937—91no—
261#937—91no—
262#937D911yescharacteristic, complemented
263#936—91no—
264#885—91no—
265#885—91no—
266#884—91no—
267#884—91no—
268#882—91no—
269#877—91no—
270#875—91no—
271#872—91no—
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3×D3—22no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—41no—
279C22×C3×D3—41no—
280C22×C3×D3C22×D311yescharacteristic
281C22×C3×D3C22×D311yescharacteristic
282C2×D32—62no—
283C2×D32—121no—
284C2×D32—121no—
285C32×D4—41no—
286C2×C32×C4C22×D311yescharacteristic
287#638—62no—
288#638—121no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—62no—
293C3×#67—22no—
294C3×#67—41no—
295C3×#67—62no—
296C3×#67—62no—
297C3×#67—121no—
298C3×#67—121no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C3×D12—121no—
304#627—62no—
305#626—62no—
306#626—121no—
307#625—62no—
308#625—62no—
309#625—121no—
310D3×Dic3—34no—
311D3×Dic3—62no—
312C23×C9—21no—
313C23×C9—21no—
314C23×C9—31no—
315C23×C9—31no—
316C23×C9—62no—
317C23×C9—121no—
318C23×C9—121no—
319C23×C9C22×D311yescharacteristic
320C23×C9C22×D311yescharacteristic
321C22×D9—31no—
322C22×D9—61no—
323C22×D9—62no—
324C22×D9—121no—
325C22×D9—121no—
326C22×D9C22×D311yescharacteristic
327C22×D9C22×D311yescharacteristic
328D4×C9—41no—
329D4×C9—42no—
330D4×C9—62no—
331D4×C9—121no—
332C2×C4×C9—21no—
333C2×C4×C9—31no—
334C2×C4×C9—31no—
335C2×C4×C9C22×D311yescharacteristic
336#611—22no—
337#611—22no—
338#611—41no—
339#611—41no—
340#611—62no—
341#611—62no—
342#611—62no—
343#611—62no—
344#611—122no—
345#611—121no—
346#611—121no—
347#611—122no—
348C2×Dic9—31no—
349C2×Dic9—34no—
350C2×Dic9—31no—
351C2×Dic9—31no—
352C2×Dic9—61no—
353C2×Dic9—61no—
354C2×Dic9—61no—
355C2×Dic9—62no—
356C2×Dic9—122no—
357C2×Dic9C22×D311yescharacteristic
358C2×Dic9C22×D311yescharacteristic
359D36—41no—
360D36—121no—
361C4×D9—62no—
362Dic18—62no—
363#535—271noSylow
364C2×C3×C9—41no—
365C2×C3×C9—41no—
366C2×C3×C9C22×D411yescharacteristic
367C2×C3×C9H(5,𝔽2)11yescharacteristic
368C2×C3×C9H(5,𝔽2)11yescharacteristic
369C3⋊D9—41no—
370D3×C9—22no—
371D3×C9—41no—
372C3×D9—41no—
373C3×D9—41no—
374C24×C3—31no—
375C23×D3—91no—
376C23×D3—91no—
377C23×D3C2×D911yescharacteristic
378C2×C3×D4—21no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—91no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C2×C3×D4C2×D911yescharacteristic, complemented
387C2×C3×D4D3211yescharacteristic
388C2×#67—31no—
389C2×#67—31no—
390C2×#67—31no—
391C2×#67—31no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—91no—
400C2×#67—91no—
401C2×#67—91no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—181no—
405C2×#67—181no—
406C2×#67—184no—
407C2×#67C2×D911yescharacteristic
408C2×#67C2×D911yescharacteristic, complemented
409C22×Dic3—91no—
410C22×Dic3—91no—
411C22×Dic3—91no—
412C22×Dic3—91no—
413C22×Dic3—181no—
414#237—184no—
415#237—184no—
416D3×D4—184no—
417C2×D12—31no—
418C2×D12—91no—
419C2×D12—91no—
420C2×C4×D3—91no—
421C2×C4×D3—91no—
422C2×Dic6—91no—
423C2×Dic6—91no—
424C3×C22⋊C4—31no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C42—91no—
428#217—91no—
429#217—91no—
430#217—91no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—181no—
435#217C2×D911yescharacteristic, complemented
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—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—181no—
445(C2×D3)⋊C4C2×D911yescharacteristic
446(C2×D3)⋊C4C2×D911yescharacteristic, complemented
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—181no—
452C4×Dic3—31no—
453C4×Dic3—91no—
454C4×Dic3—91no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32C23×D311yescharacteristic
462C2×C3⋊D3—61no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—44no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3D3×D412yes—
478D32—124no—
479C32×C4—21no—
480C3⋊Dic3—32no—
481C3⋊Dic3—61no—
482C3⋊Dic3—61no—
483C3×Dic3—21no—
484C3×Dic3—21no—
485C3×Dic3—32no—
486C3×Dic3—61no—
487C22×C9—22no—
488C22×C9—21no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—21no—
492C22×C9—21no—
493C22×C9—21no—
494C22×C9—21no—
495C22×C9—32no—
496C22×C9—41no—
497C22×C9—41no—
498C22×C9—41no—
499C22×C9—41no—
500C22×C9—41no—
501C22×C9—61no—
502C22×C9—61no—
503C22×C9—61no—
504C22×C9—61no—
505C22×C9—61no—
506C22×C9—124no—
507C22×C9C23×D311yescharacteristic
508C2×D9—21no—
509C2×D9—21no—
510C2×D9—21no—
511C2×D9—21no—
512C2×D9—21no—
513C2×D9—21no—
514C2×D9—61no—
515C2×D9—61no—
516C2×D9—61no—
517C2×D9—121no—
518C2×D9—121no—
519C2×D9—121no—
520C2×D9—124no—
521C4×C9—21no—
522C4×C9—41no—
523C4×C9—61no—
524C4×C9—61no—
525Dic9—21no—
526Dic9—32no—
527Dic9—62no—
528Dic9—61no—
529Dic9—61no—
530Dic9—121no—
531Dic9—121no—
532Dic9D3×D412yes—
533C2×#41—271no—
534C22×D4—271no—
535#127—91no—
536#127—271no—
537#124—271no—
538#124—271no—
539#121—271no—
540#121—271no—
541#121—271no—
542#121—271no—
543#120—31no—
544#120—271no—
545#120—271no—
546#120—271no—
547#117—271no—
548C3×C9#53511yescharacteristic, complemented, Sylow
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—31no—
552C23×C3—31no—
553C23×C3—62no—
554C23×C3—91no—
555C23×C3—91no—
556C23×C3—121no—
557C23×C3—121no—
558C23×C3C22×D911yescharacteristic
559C23×C3C22×D911yescharacteristic
560C23×C3C2×D3211yescharacteristic
561C23×C3C2×D3211yescharacteristic
562C22×D3—22no—
563C22×D3—31no—
564C22×D3—31no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—91no—
568C22×D3—91no—
569C22×D3—181no—
570C22×D3—182no—
571C22×D3—182no—
572C22×D3—361no—
573C22×D3—361no—
574C22×D3—361no—
575C22×D3—361no—
576C22×D3C22×D911yescharacteristic
577C22×D3C22×D911yescharacteristic
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—42no—
581C3×D4—62no—
582C3×D4—121no—
583C3×D4—182no—
584C3×D4—182no—
585C3×D4—361no—
586C3×D4—361no—
587C3×D4—361no—
588C2×C3×C4—21no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4C22×D911yescharacteristic
594C2×C3×C4C2×D3211yescharacteristic
595#67—22no—
596#67—41no—
597#67—62no—
598#67—62no—
599#67—121no—
600#67—121no—
601#67—182no—
602#67—182no—
603#67—182no—
604#67—182no—
605#67—182no—
606#67—182no—
607#67—182no—
608#67—362no—
609#67—361no—
610#67—361no—
611#67—361no—
612#67—361no—
613#67—361no—
614#67—362no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—94no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—91no—
621C2×Dic3—91no—
622C2×Dic3—91no—
623C2×Dic3—91no—
624C2×Dic3—181no—
625C2×Dic3—181no—
626C2×Dic3—181no—
627C2×Dic3—182no—
628C2×Dic3—182no—
629C2×Dic3—182no—
630C2×Dic3—362no—
631C2×Dic3C22×D911yescharacteristic
632C2×Dic3C22×D911yescharacteristic
633D12—121no—
634D12—182no—
635D12—361no—
636C4×D3—94no—
637C4×D3—182no—
638Dic6—182no—
639Dic6—182no—
640C2×C32—41no—
641C2×C32—41no—
642C2×C32C2×D3×D411yescharacteristic
643C2×C32#100411yescharacteristic
644C2×C32#100411yescharacteristic
645C3⋊D3—121no—
646C3×D3—22no—
647C3×D3—41no—
648C3×D3—121no—
649C3×D3—121no—
650C2×C9—21no—
651C2×C9—21no—
652C2×C9—21no—
653C2×C9—42no—
654C2×C9—41no—
655C2×C9—41no—
656C2×C9—62no—
657C2×C9—81no—
658C2×C9—121no—
659C2×C9C2×D3×D411yescharacteristic
660C2×C9#100411yescharacteristic
661C2×C9#100411yescharacteristic
662D9—41no—
663D9—41no—
664D9—121no—
665D9—241no—
666C24—31no—
667C24—271no—
668#41—544no—
669C2×Q8—271no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—91no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—544no—
685C2×D4D3×D911yescharacteristic, complemented
686C22×C4—271no—
687C22×C4—271no—
688C22×C4—271no—
689C4⋊C4—271no—
690C4⋊C4—271no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C42—91no—
702C42—271no—
703C22×C3—22no—
704C22×C3—21no—
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—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—32no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—124no—
729C22×C3—181no—
730C22×C3—181no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3—181no—
734C22×C3—181no—
735C22×C3C23×D911yescharacteristic
736C22×C3C22×D3211yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—44no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—361no—
756C2×D3—361no—
757C2×D3—361no—
758C2×D3—364no—
759C2×D3—364no—
760C2×D3D4×D912yes—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—92no—
767C3×C4—181no—
768Dic3—21no—
769Dic3—21no—
770Dic3—32no—
771Dic3—61no—
772Dic3—92no—
773Dic3—92no—
774Dic3—182no—
775Dic3—181no—
776Dic3—181no—
777Dic3—181no—
778Dic3—181no—
779Dic3—361no—
780Dic3—361no—
781C32#559211yescharacteristic
782C9—21no—
783C9#571511yescharacteristic, complemented
784C23—31no—
785C23—31no—
786C23—62no—
787C23—91no—
788C23—91no—
789C23—121no—
790C23—121no—
791C23—271no—
792C23—542no—
793C23—1081no—
794C23—1081no—
795C23C2×D3×D911yescharacteristic
796C23C2×D3×D911yescharacteristic
797Q8—542no—
798D4—41no—
799D4—62no—
800D4—121no—
801D4—182no—
802D4—182no—
803D4—361no—
804D4—361no—
805D4—361no—
806D4—542no—
807D4—542no—
808D4—542no—
809D4—542no—
810D4—1081no—
811D4—1081no—
812D4—1081no—
813C2×C4—31no—
814C2×C4—31no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—274no—
818C2×C4—271no—
819C2×C4—271no—
820C2×C4—271no—
821C2×C4—542no—
822C2×C4—542no—
823C2×C4C2×D3×D911yescharacteristic
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—42no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—62no—
833C2×C3—81no—
834C2×C3—121no—
835C2×C3—361no—
836C2×C3—361no—
837C2×C3C2×D4×D911yescharacteristic
838C2×C3#6371011yescharacteristic
839C2×C3#6371011yescharacteristic
840C2×C3D32×D411yescharacteristic
841C2×C3#6431311yescharacteristic
842C2×C3#6433011yescharacteristic
843D3—22no—
844D3—41no—
845D3—121no—
846D3—121no—
847D3—361no—
848D3—361no—
849D3—721no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—32no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—124no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—181no—
868C22—181no—
869C22—541no—
870C22—541no—
871C22—541no—
872C22—1084no—
873C22C22×D3×D911yescharacteristic
874C4—21no—
875C4—61no—
876C4—61no—
877C4—92no—
878C4—181no—
879C4—272no—
880C4—541no—
881C4—541no—
882C3—21no—
883C3#1058969411yescharacteristic, complemented
884C3#1059528611yescharacteristic
885C2—41no—
886C2—41no—
887C2—62no—
888C2—121no—
889C2—361no—
890C2—361no—
891C2—1081no—
892C2D3×D4×D911yescharacteristic
893C2#1172249911yescharacteristic
894C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#535
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#611C2semidirect
2. C2×#88663C2semidirect
3. #11721839C2semidirect
4. C9×#937C2semidirect
5. C3×#63502C2semidirect
6. #11721292C2semidirect
7. #11721290C2semidirect
8. #11721289C2semidirect
9. #11721286C2semidirect
10. #11721271C2semidirect
11. #11721257C2semidirect
12. #11721049C2semidirect
13. #11721010C2semidirect
14. #11720982C2semidirect
15. #11720956C2semidirect
20. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C22×C3⋊Dic9C22semidirect
25. C2×C9×#67C22semidirect
27. C2×C3×#611C22semidirect
28. C2×C3×#611C22semidirect
29. C2×C3×#611C22semidirect
30. C2×C3×D36C22semidirect
35. C2×#6194C22semidirect
38. C2×#6192C22semidirect
39. C2×Dic3×D9C22semidirect
40. C2×#6189C22semidirect
41. #88551C22semidirect
42. #88536C22semidirect
43. #88534C22semidirect
44. C9×#217C22semidirect
46. C9×(C2×D3)⋊C4C22semidirect
47. C3×C4×Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
75. #63502D3semidirect
122. D3×Dic9D4semidirect
170. C2×D4×C9C2×D3semidirect
181. C2×#611C2×D3semidirect
182. C2×#611C2×D3semidirect
183. C2×#611C2×D3semidirect
189. C2×D36C2×D3semidirect
208. C4×Dic9C2×D3semidirect
262. #937D9semidirect
386. C2×C3×D4C2×D9semidirect
408. C2×#67C2×D9semidirect
435. #217C2×D9semidirect
446. (C2×D3)⋊C4C2×D9semidirect
548. C3×C9#535semidirect
685. C2×D4D3×D9semidirect
783. C9#5715semidirect
883. C3#10589694semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×#886632
#117218392
C9×#9372
C3×#635022
#117212922
#117212902
#117212892
#117212862
#117212712
#117212572
#117210492
#117210102
#117209822
#117209562
#105952863
#105896943