Finite Group Databasebeta

← #13150963

Subgroups — #13150963

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×D9×#67C211yesmaximal, characteristic, complemented
2C2×#88663C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C9×#940C211yesmaximal, characteristic, complemented
5C3×#63499C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721290C211yesmaximal, characteristic, complemented
8#11721289C211yesmaximal, characteristic, complemented
9#11721285C211yesmaximal, characteristic, complemented
10#11721282C211yesmaximal, characteristic, complemented
11#11721263C211yesmaximal, characteristic, complemented
12#11721050C211yesmaximal, characteristic, complemented
13#11721016C211yesmaximal, characteristic, complemented
14#11720974C211yesmaximal, characteristic, complemented
15#11720940C211yesmaximal, characteristic, complemented
16#10595286—31nomaximal
17#10589817—31nomaximal
18C23×C3×D9C2211yescharacteristic
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×C9×#67C2211yescharacteristic, complemented
27C2×C9×#67C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic
29C2×C3×#611C2211yescharacteristic, complemented
30C2×C9×D12C2211yescharacteristic, complemented
31D9×#67—24no—
32C2×#6195C2211yescharacteristic, complemented
33C2×#6194C2211yescharacteristic
34C2×#6194C2211yescharacteristic
35C2×#6194C2211yescharacteristic, complemented
36#88663—24no—
37C2×D3×Dic9C2211yescharacteristic, complemented
38C2×#6192C2211yescharacteristic
39C2×Dic3×D9C2211yescharacteristic
40C2×#6189C2211yescharacteristic, complemented
41#88551C2211yescharacteristic, complemented
42#88536C2211yescharacteristic, complemented
43#88534C2211yescharacteristic, complemented
44C3×#3676C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C4×C9×Dic3C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3805—31no—
57#64148—31no—
58C3×#940D311yescharacteristic
59C3×#937—31no—
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—
70C2×#3699—31no—
71C2×D4×D9—31no—
72C9×#127—31no—
73#63502—31no—
74#63501—31no—
75#63501—31no—
76#63501—31no—
77#63501—31no—
78#63501—61no—
79#63499—31no—
80#63499—31no—
81#63499—31no—
82#63499D311yescharacteristic, complemented
83#63498—31no—
84#63437—31no—
85#63434—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×C3×D9—22no—
92C22×C3×D9—41no—
93C22×C3×D9—41no—
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—22no—
109C9×#67—41no—
110C9×#67—41no—
111C3×#611—22no—
112C3×#611—41no—
113C2×C9×Dic3C2311yescharacteristic
114C2×C9×Dic3C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C9×D12—41no—
118#6195—41no—
119#6194—22no—
120#6194—22no—
121#6194—41no—
122D3×Dic9—22no—
123#6192—22no—
124Dic3×D9D414yescomplemented
125#6189—22no—
126#5715—91no—
127#5592—91no—
128C23×C3×D3—31no—
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×#67C2×D311yescharacteristic
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×#67C2×D311yescharacteristic
139C2×C3×#67C2×D311yescharacteristic
140C2×C3×D12C2×D311yescharacteristic
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—
151C23×D9—31no—
152C23×D9C2×D311yescharacteristic
153#3757—31no—
154#3752—31no—
155#3750—31no—
156C3×#217—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×C4×Dic3C2×D311yescharacteristic
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×C9—31no—
171C2×D4×C9—31no—
172C2×D4×C9—31no—
173C2×D4×C9C2×D311yescharacteristic, complemented
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—31no—
178C2×#611—31no—
179C2×#611—31no—
180C2×#611—61no—
181C2×#611—61no—
182C2×#611C2×D311yescharacteristic
183C2×#611C2×D311yescharacteristic, complemented
184C22×Dic9—31no—
185C22×Dic9—31no—
186C22×Dic9—61no—
187#3699—64no—
188D4×D9—64no—
189C2×D36—31no—
190C2×C4×D9—31no—
191C2×Dic18—31no—
192C42×C9—31no—
193#3676—31no—
194#3676—31no—
195#3676—31no—
196#3676—61no—
197#3676C2×D311yescharacteristic, complemented
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—61no—
203(C2×D9)⋊C4C2×D311yescharacteristic
204(C2×D9)⋊C4C2×D311yescharacteristic, complemented
205Dic9⋊C4—31no—
206Dic9⋊C4—31no—
207Dic9⋊C4—61no—
208C4×Dic9—31no—
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—21no—
225C2×C3×D9—21no—
226C2×C3×D9—21no—
227C2×C3×D9—21no—
228C2×C3×D9—21no—
229C2×C3×D9—21no—
230C2×C3×D9—44no—
231C2×C3×D9C2×D412yes—
232D3×D9—44no—
233C3×C4×C9—21no—
234C3⋊Dic9—21no—
235C3⋊Dic9—21no—
236C3⋊Dic9C2×D412yes—
237C9×Dic3—21no—
238C9×Dic3C2×D412yes—
239C3×Dic9—21no—
240C3×Dic9—21no—
241C22×#67—91no—
242C2×#237—91no—
243C2×#237—91no—
244C2×D3×D4—91no—
245C3×#127—31no—
246C3×#120—91no—
247#953—91no—
248#940—91no—
249#940—91no—
250#940D911yescharacteristic, complemented
251#939—91no—
252#939—91no—
253#939—91no—
254#939—91no—
255#939—91no—
256#939—91no—
257#939—181no—
258#937—31no—
259#937—91no—
260#937—91no—
261#937—91no—
262#937—91no—
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—31no—
276C22×C3×D3—31no—
277C22×C3×D3—62no—
278C22×C3×D3—121no—
279C22×C3×D3—121no—
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—22no—
295C3×#67—41no—
296C3×#67—41no—
297C3×#67—62no—
298C3×#67—121no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C3×D12—41no—
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×C9C22×D311yescharacteristic
317C23×C9C22×D311yescharacteristic
318C22×D9—22no—
319C22×D9—31no—
320C22×D9—41no—
321C22×D9—41no—
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—62no—
332D4×C9—121no—
333D4×C9—121no—
334D4×C9—121no—
335C2×C4×C9—21no—
336C2×C4×C9—31no—
337C2×C4×C9—31no—
338C2×C4×C9C22×D311yescharacteristic
339#611—22no—
340#611—41no—
341#611—62no—
342#611—62no—
343#611—62no—
344#611—122no—
345#611—121no—
346#611—121no—
347#611—121no—
348#611—122no—
349C2×Dic9—31no—
350C2×Dic9—31no—
351C2×Dic9—31no—
352C2×Dic9—61no—
353C2×Dic9—61no—
354C2×Dic9—61no—
355C2×Dic9—62no—
356C2×Dic9—62no—
357C2×Dic9—122no—
358C2×Dic9C22×D311yescharacteristic
359C2×Dic9C22×D311yescharacteristic
360D36—62no—
361C4×D9—34no—
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—41no—
371D3×C9—41no—
372C3×D9—22no—
373C3×D9—41no—
374C24×C3—91no—
375C23×D3—31no—
376C23×D3—91no—
377C23×D3—91no—
378C2×C3×D4—21no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—31no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C2×C3×D4C2×D911yescharacteristic, complemented
387C2×C3×D4D3211yescharacteristic
388C2×#67—31no—
389C2×#67—31no—
390C2×#67—91no—
391C2×#67—91no—
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—181no—
403C2×#67—181no—
404C2×#67—184no—
405C2×#67C2×D911yescharacteristic
406C2×#67C2×D911yescharacteristic, complemented
407C2×#67C2×D911yescharacteristic, complemented
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—91no—
418C2×D12—91no—
419C2×D12C2×D911yescharacteristic, complemented
420C2×C4×D3—91no—
421C2×C4×D3—91no—
422C2×Dic6—91no—
423C2×Dic6—91no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4—91no—
426C3×C22⋊C4—91no—
427C3×C42—31no—
428#217—31no—
429#217—91no—
430#217—91no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—91no—
435#217—181no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—31no—
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—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—181no—
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—181no—
452C4×Dic3—91no—
453C4×Dic3—91no—
454C4×Dic3C2×D911yescharacteristic, complemented
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—21no—
471C2×C3×D3—32no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—124no—
478D32—124no—
479C32×C4—21no—
480C3⋊Dic3—32no—
481C3⋊Dic3—61no—
482C3⋊Dic3—61no—
483C3×Dic3—21no—
484C3×Dic3—61no—
485C3×Dic3—61no—
486C3×Dic3D3×D412yes—
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—41no—
496C22×C9—41no—
497C22×C9—41no—
498C22×C9—41no—
499C22×C9—41no—
500C22×C9—61no—
501C22×C9—61no—
502C22×C9—61no—
503C22×C9—61no—
504C22×C9—61no—
505C22×C9—61no—
506C22×C9C23×D311yescharacteristic
507C2×D9—21no—
508C2×D9—21no—
509C2×D9—21no—
510C2×D9—21no—
511C2×D9—21no—
512C2×D9—44no—
513C2×D9—61no—
514C2×D9—61no—
515C2×D9—61no—
516C2×D9—121no—
517C2×D9—121no—
518C2×D9—121no—
519C2×D9—124no—
520C2×D9D3×D412yes—
521C4×C9—21no—
522C4×C9—32no—
523C4×C9—41no—
524C4×C9—61no—
525Dic9—21no—
526Dic9—21no—
527Dic9—32no—
528Dic9—62no—
529Dic9—61no—
530Dic9—61no—
531Dic9—121no—
532Dic9—121no—
533C2×#41—271no—
534C22×D4—271no—
535#127—31no—
536#127—271no—
537#124—271no—
538#124—271no—
539#121—271no—
540#121—271no—
541#121—271no—
542#121—271no—
543#120—91no—
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—91no—
554C23×C3—91no—
555C23×C3—182no—
556C23×C3—361no—
557C23×C3—361no—
558C23×C3C22×D911yescharacteristic
559C23×C3C22×D911yescharacteristic
560C23×C3C2×D3211yescharacteristic
561C23×C3C2×D3211yescharacteristic
562C22×D3—31no—
563C22×D3—31no—
564C22×D3—62no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—121no—
568C22×D3—121no—
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—62no—
583C3×D4—121no—
584C3×D4—121no—
585C3×D4—121no—
586C3×D4—182no—
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—22no—
597#67—41no—
598#67—41no—
599#67—62no—
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—91no—
618C2×Dic3—91no—
619C2×Dic3—94no—
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—41no—
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—41no—
647C3×D3—41no—
648C3×D3—62no—
649C3×D3—121no—
650C2×C9—21no—
651C2×C9—21no—
652C2×C9—21no—
653C2×C9—42no—
654C2×C9—41no—
655C2×C9—41no—
656C2×C9—81no—
657C2×C9—121no—
658C2×C9—121no—
659C2×C9C2×D3×D411yescharacteristic
660C2×C9#100411yescharacteristic
661C2×C9#100411yescharacteristic
662D9—22no—
663D9—41no—
664D9—121no—
665D9—241no—
666C24—91no—
667C24—271no—
668#41—544no—
669C2×Q8—271no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
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—91no—
692C22⋊C4—91no—
693C22⋊C4—91no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C42—31no—
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—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—92no—
729C22×C3—181no—
730C22×C3—181no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3—181no—
734C22×C3—364no—
735C22×C3C23×D911yescharacteristic
736C22×C3C22×D3211yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—32no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—124no—
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—364no—
760C2×D3—364no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—32no—
764C3×C4—41no—
765C3×C4—61no—
766C3×C4—181no—
767C3×C4—181no—
768Dic3—21no—
769Dic3—61no—
770Dic3—61no—
771Dic3—92no—
772Dic3—92no—
773Dic3—182no—
774Dic3—181no—
775Dic3—181no—
776Dic3—181no—
777Dic3—181no—
778Dic3—361no—
779Dic3—361no—
780Dic3D4×D912yes—
781C32#571511yescharacteristic
782C9—21no—
783C9#559211yescharacteristic, complemented
784C23—31no—
785C23—31no—
786C23—91no—
787C23—91no—
788C23—182no—
789C23—271no—
790C23—361no—
791C23—361no—
792C23—542no—
793C23—1081no—
794C23—1081no—
795C23C2×D3×D911yescharacteristic
796C23C2×D3×D911yescharacteristic
797Q8—542no—
798D4—41no—
799D4—62no—
800D4—62no—
801D4—121no—
802D4—121no—
803D4—121no—
804D4—182no—
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—81no—
833C2×C3—121no—
834C2×C3—121no—
835C2×C3—182no—
836C2×C3—361no—
837C2×C3C2×D4×D911yescharacteristic
838C2×C3#6371011yescharacteristic
839C2×C3#6371011yescharacteristic
840C2×C3D32×D411yescharacteristic
841C2×C3#6431311yescharacteristic
842C2×C3#6433011yescharacteristic
843D3—41no—
844D3—41no—
845D3—62no—
846D3—121no—
847D3—361no—
848D3—361no—
849D3—721no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—92no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—181no—
868C22—364no—
869C22—541no—
870C22—541no—
871C22—541no—
872C22—1084no—
873C22C22×D3×D911yescharacteristic
874C4—21no—
875C4—32no—
876C4—61no—
877C4—181no—
878C4—181no—
879C4—272no—
880C4—541no—
881C4—541no—
882C3—21no—
883C3#1058981711yescharacteristic, complemented
884C3#1059528611yescharacteristic
885C2—41no—
886C2—41no—
887C2—121no—
888C2—121no—
889C2—182no—
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×D9×#67C2semidirect
2. C2×#88663C2semidirect
3. #11721839C2semidirect
4. C9×#940C2semidirect
5. C3×#63499C2semidirect
6. #11721292C2semidirect
7. #11721290C2semidirect
8. #11721289C2semidirect
9. #11721285C2semidirect
10. #11721282C2semidirect
11. #11721263C2semidirect
12. #11721050C2semidirect
13. #11721016C2semidirect
14. #11720974C2semidirect
15. #11720940C2semidirect
20. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C22×C3⋊Dic9C22semidirect
25. C2×C9×#67C22semidirect
26. C2×C9×#67C22semidirect
27. C2×C9×#67C22semidirect
29. C2×C3×#611C22semidirect
30. C2×C9×D12C22semidirect
32. C2×#6195C22semidirect
35. C2×#6194C22semidirect
37. C2×D3×Dic9C22semidirect
40. C2×#6189C22semidirect
41. #88551C22semidirect
42. #88536C22semidirect
43. #88534C22semidirect
44. C3×#3676C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C4×C9×Dic3C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
82. #63499D3semidirect
124. Dic3×D9D4semidirect
173. C2×D4×C9C2×D3semidirect
183. C2×#611C2×D3semidirect
197. #3676C2×D3semidirect
204. (C2×D9)⋊C4C2×D3semidirect
250. #940D9semidirect
386. C2×C3×D4C2×D9semidirect
406. C2×#67C2×D9semidirect
407. C2×#67C2×D9semidirect
408. C2×#67C2×D9semidirect
419. C2×D12C2×D9semidirect
454. C4×Dic3C2×D9semidirect
548. C3×C9#535semidirect
685. C2×D4D3×D9semidirect
783. C9#5592semidirect
883. C3#10589817semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×#886632
#117218392
C9×#9402
C3×#634992
#117212922
#117212902
#117212892
#117212852
#117212822
#117212632
#117210502
#117210162
#117209742
#117209402
#105952863
#105898173