Finite Group Databasebeta

← #13151135

Subgroups — #13151135

Order 1728.

1110 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic, complemented
2C2×#88662C211yesmaximal, characteristic, complemented
3#11721840C211yesmaximal, characteristic, complemented
4C9×#937C211yesmaximal, characteristic, complemented
5C3×#63501C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721289C211yesmaximal, characteristic, complemented
8#11721288C211yesmaximal, characteristic, complemented
9#11721287C211yesmaximal, characteristic, complemented
10#11721256C211yesmaximal, characteristic, complemented
11#11721242C211yesmaximal, characteristic, complemented
12#11721051C211yesmaximal, characteristic, complemented
13#11721044C211yesmaximal, characteristic, complemented
14#11721039C211yesmaximal, characteristic, complemented
15#11721011C211yesmaximal, characteristic, complemented
16#10595285—31nomaximal
17#10589694—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic, complemented
23C2×#6233C2211yescharacteristic, complemented
24C2×#6233C2211yescharacteristic, complemented
25C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
26C2×C9×#67C2211yescharacteristic
27C2×C9×#67C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic
29C2×C3×#611C2211yescharacteristic, complemented
30C22×C3×Dic9C2211yescharacteristic, complemented
31D3×#611—24no—
32C2×#6195C2211yescharacteristic
33C2×#6195C2211yescharacteristic
34C2×#6195C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic
36#88662—24no—
37C2×D3×Dic9C2211yescharacteristic
38C2×#6192C2211yescharacteristic, complemented
39C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
40C2×#6189C2211yescharacteristic, complemented
41C4×C3⋊Dic9C2211yescharacteristic, complemented
42C9×#217C2211yescharacteristic, complemented
43C3×#3676C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3804—31no—
57#64149—31no—
58C3×#939—31no—
59C3×#937D311yescharacteristic
60#63983—31no—
61#63979—31no—
62#63978—31no—
63#63977—31no—
64#63958—31no—
65#63953—31no—
66#63923—31no—
67#63915—31no—
68#63910—31no—
69#63878—31no—
70C22×#611—31no—
71C2×#3699—31no—
72C9×#120—31no—
73#63515—31no—
74#63502—31no—
75#63502—31no—
76#63502—61no—
77#63501—31no—
78#63501D311yescharacteristic, complemented
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×C3⋊D9C2311yescharacteristic
90C22×D3×C9—22no—
91C22×D3×C9—41no—
92C22×D3×C9—41no—
93C22×D3×C9C2311yescharacteristic
94C22×D3×C9C2311yescharacteristic
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—22no—
103#6233—41no—
104#6233—41no—
105C2×C3⋊Dic9C2311yescharacteristic
106C2×C3⋊Dic9C2311yescharacteristic
107C4⋊(C3⋊D9)—41no—
108C9×#67—22no—
109C9×#67—41no—
110C3×#611—22no—
111C3×#611—41no—
112C2×C9×Dic3C2311yescharacteristic
113C2×C9×Dic3C2311yescharacteristic
114C2×C3×Dic9—22no—
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C2×C3×Dic9C2311yescharacteristic
118#6195—22no—
119#6195—22no—
120#6195—41no—
121#6194—22no—
122D3×Dic9D414yescomplemented
123#6192—41no—
124(C3⋊D9)⋊C4—22no—
125#6189—22no—
126#5607—91no—
127#5592—91no—
128C23×C3×D3C2×D311yescharacteristic
129C22×D32—31no—
130C2×C32×D4C2×D311yescharacteristic
131C2×#638—31no—
132C2×#638—31no—
133C2×#638—31no—
134C2×#638—31no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67C2×D311yescharacteristic
139C2×C3×#67C2×D311yescharacteristic
140C22×C3×Dic3—31no—
141D3×#67—64no—
142C2×#627—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#625—31no—
148C2×#624—31no—
149#3804—64no—
150C2×D3×Dic3—31no—
151C24×C9—31no—
152C23×D9—31no—
153C4×C3⋊Dic3—31no—
154C3×#217—31no—
155C3×#217C2×D311yescharacteristic
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4C2×D311yescharacteristic
158C3×(C2×D3)⋊C4C2×D311yescharacteristic
159C3×Dic3⋊C4—31no—
160Dic3⋊Dic3—31no—
161#3722—31no—
162#3722—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—31no—
178C2×#611—31no—
179C2×#611—64no—
180C2×#611—61no—
181C2×#611—61no—
182C2×#611—61no—
183C2×#611—61no—
184C2×#611C2×D311yescharacteristic
185C2×#611C2×D311yescharacteristic, complemented
186C22×Dic9—31no—
187C22×Dic9C2×D311yescharacteristic, complemented
188#3699—64no—
189C2×D36—31no—
190C2×D36—31no—
191C2×D36—61no—
192C2×C4×D9—31no—
193C2×Dic18—31no—
194C9×C22⋊C4—31no—
195C9×C22⋊C4—31no—
196C9×C22⋊C4—31no—
197#3676—31no—
198#3676—31no—
199#3676C2×D311yescharacteristic, complemented
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—31no—
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4—31no—
205Dic9⋊C4C2×D311yescharacteristic, complemented
206C4×Dic9—31no—
207C4×Dic9—31no—
208C4×Dic9—61no—
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×C3⋊D9—21no—
220C2×C3⋊D9—21no—
221C2×C3⋊D9—21no—
222C2×D3×C9—21no—
223C2×D3×C9—21no—
224C2×D3×C9—21no—
225C2×D3×C9—21no—
226C2×D3×C9—21no—
227C2×D3×C9—44no—
228C2×D3×C9C2×D412yes—
229C2×C3×D9—21no—
230C2×C3×D9—21no—
231C2×C3×D9—21no—
232D3×D9—44no—
233C3×C4×C9—21no—
234C3⋊Dic9—21no—
235C3⋊Dic9C2×D412yes—
236C9×Dic3—21no—
237C9×Dic3—21no—
238C3×Dic9—21no—
239C3×Dic9—21no—
240C3×Dic9C2×D412yes—
241C22×#67—91no—
242C2×#237—91no—
243C2×D3×D4—91no—
244C2×#235—91no—
245C3×#121—91no—
246C3×#120—31no—
247#953—91no—
248#940—91no—
249#940—91no—
250#940—91no—
251#940—91no—
252#940—181no—
253#939—31no—
254#939—91no—
255#938—91no—
256#937—91no—
257#937—91no—
258#937D911yescharacteristic, complemented
259#930—91no—
260#895—91no—
261#892—91no—
262#885—91no—
263#885—91no—
264#885—91no—
265#885—91no—
266#884—91no—
267#884—91no—
268#882—91no—
269#882—91no—
270#882—91no—
271#877—91no—
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3×D3—22no—
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—62no—
289#638—121no—
290#638—121no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—31no—
293C4⋊(C3⋊D3)—121no—
294C3×#67—22no—
295C3×#67—41no—
296C3×#67—62no—
297C3×#67—121no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—62no—
302C2×C3×Dic3C22×D311yescharacteristic
303C2×C3×Dic3C22×D311yescharacteristic
304#627—62no—
305#626—62no—
306#626—62no—
307#626—121no—
308#626—121no—
309#625—62no—
310#624—62no—
311D3×Dic3—34no—
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—31no—
323C22×D9—61no—
324C22×D9—61no—
325C22×D9—62no—
326C22×D9—121no—
327C22×D9—121no—
328C22×D9C22×D311yescharacteristic
329D4×C9—41no—
330D4×C9—42no—
331D4×C9—62no—
332D4×C9—121no—
333C2×C4×C9—21no—
334C2×C4×C9—31no—
335C2×C4×C9—31no—
336C2×C4×C9C22×D311yescharacteristic
337#611—22no—
338#611—41no—
339#611—62no—
340#611—62no—
341#611—62no—
342#611—62no—
343#611—62no—
344#611—122no—
345#611—122no—
346#611—121no—
347#611—121no—
348#611—121no—
349#611—122no—
350#611—122no—
351C2×Dic9—22no—
352C2×Dic9—31no—
353C2×Dic9—34no—
354C2×Dic9—31no—
355C2×Dic9—61no—
356C2×Dic9—61no—
357C2×Dic9C22×D311yescharacteristic
358C2×Dic9C22×D311yescharacteristic
359C2×Dic9C22×D311yescharacteristic
360D36—121no—
361D36—122no—
362D36—121no—
363C4×D9—62no—
364Dic18—62no—
365#535—271noSylow
366C2×C3×C9—41no—
367C2×C3×C9—41no—
368C2×C3×C9C22×D411yescharacteristic
369C2×C3×C9H(5,𝔽2)11yescharacteristic
370C2×C3×C9H(5,𝔽2)11yescharacteristic
371C3⋊D9—41no—
372C3⋊D9—41no—
373D3×C9—22no—
374D3×C9—41no—
375C3×D9—41no—
376C24×C3—31no—
377C23×D3—91no—
378C23×D3—91no—
379C23×D3C2×D911yescharacteristic
380C2×C3×D4—21no—
381C2×C3×D4—31no—
382C2×C3×D4—31no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4C2×D911yescharacteristic, complemented
386C2×C3×D4D3211yescharacteristic
387C22×C3×C4—91no—
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—91no—
403C2×#67—91no—
404C2×#67—181no—
405C2×#67—181no—
406C2×#67—181no—
407C2×#67—181no—
408C2×#67—184no—
409C2×#67C2×D911yescharacteristic
410C2×#67C2×D911yescharacteristic, complemented
411C22×Dic3—31no—
412C22×Dic3—91no—
413#237—184no—
414D3×D4—184no—
415#235—184no—
416C2×D12—91no—
417C2×D12—91no—
418C2×D12—91no—
419C2×D12—91no—
420C2×D12—91no—
421C2×D12—91no—
422C2×D12—181no—
423C2×C4×D3—91no—
424C2×C4×D3—91no—
425C2×C4×D3—91no—
426C2×Dic6—91no—
427C2×Dic6—91no—
428C3×C4⋊C4—91no—
429C3×C22⋊C4—31no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—31no—
432C3×C22⋊C4—91no—
433C3×C22⋊C4—91no—
434#217—31no—
435#217—91no—
436#217—91no—
437#217—91no—
438#217C2×D911yescharacteristic, complemented
439(C2×D3)⋊C4—31no—
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—91no—
447(C2×D3)⋊C4C2×D911yescharacteristic
448(C2×D3)⋊C4C2×D911yescharacteristic, complemented
449C4⋊Dic3—91no—
450Dic3⋊C4—31no—
451Dic3⋊C4—91no—
452C4×Dic3—91no—
453C4×Dic3—91no—
454C4×Dic3—91no—
455C4×Dic3—91no—
456C4×Dic3—181no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32C23×D311yescharacteristic
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—61no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—44no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3D3×D412yes—
480D32—124no—
481C32×C4—21no—
482C3⋊Dic3—32no—
483C3⋊Dic3—61no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—32no—
487C3×Dic3—61no—
488C3×Dic3—61no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—21no—
492C22×C9—21no—
493C22×C9—21no—
494C22×C9—21no—
495C22×C9—21no—
496C22×C9—32no—
497C22×C9—41no—
498C22×C9—41no—
499C22×C9—41no—
500C22×C9—41no—
501C22×C9—41no—
502C22×C9—41no—
503C22×C9—61no—
504C22×C9—61no—
505C22×C9—61no—
506C22×C9—61no—
507C22×C9—61no—
508C22×C9—124no—
509C22×C9C23×D311yescharacteristic
510C2×D9—21no—
511C2×D9—21no—
512C2×D9—21no—
513C2×D9—61no—
514C2×D9—61no—
515C2×D9—61no—
516C2×D9—61no—
517C2×D9—61no—
518C2×D9—61no—
519C2×D9—121no—
520C2×D9—121no—
521C2×D9—121no—
522C2×D9—121no—
523C2×D9—121no—
524C2×D9—121no—
525C2×D9—124no—
526C4×C9—22no—
527C4×C9—21no—
528C4×C9—61no—
529C4×C9—61no—
530Dic9—21no—
531Dic9—21no—
532Dic9—32no—
533Dic9—62no—
534Dic9—62no—
535Dic9—61no—
536Dic9D3×D412yes—
537C2×#41—271no—
538C22×D4—271no—
539#127—271no—
540#127—271no—
541#124—271no—
542#124—271no—
543#121—91no—
544#121—271no—
545#121—271no—
546#121—271no—
547#120—31no—
548#120—271no—
549#120—271no—
550#120—271no—
551#117—271no—
552C3×C9#53511yescharacteristic, complemented, Sylow
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—31no—
556C23×C3—31no—
557C23×C3—62no—
558C23×C3—91no—
559C23×C3—121no—
560C23×C3—121no—
561C23×C3C22×D911yescharacteristic
562C23×C3C22×D911yescharacteristic
563C23×C3C2×D3211yescharacteristic
564C23×C3C2×D3211yescharacteristic
565C22×D3—22no—
566C22×D3—31no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—91no—
570C22×D3—91no—
571C22×D3—91no—
572C22×D3—91no—
573C22×D3—181no—
574C22×D3—181no—
575C22×D3—182no—
576C22×D3—182no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3C22×D911yescharacteristic
582C22×D3C22×D911yescharacteristic
583C3×D4—41no—
584C3×D4—41no—
585C3×D4—42no—
586C3×D4—62no—
587C3×D4—121no—
588C3×D4—182no—
589C3×D4—361no—
590C2×C3×C4—21no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—91no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—182no—
597C2×C3×C4C22×D911yescharacteristic
598C2×C3×C4C2×D3211yescharacteristic
599#67—22no—
600#67—41no—
601#67—62no—
602#67—121no—
603#67—182no—
604#67—182no—
605#67—182no—
606#67—182no—
607#67—182no—
608#67—182no—
609#67—182no—
610#67—182no—
611#67—362no—
612#67—362no—
613#67—361no—
614#67—361no—
615#67—361no—
616#67—361no—
617#67—361no—
618#67—361no—
619#67—362no—
620#67—362no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—62no—
625C2×Dic3—94no—
626C2×Dic3—91no—
627C2×Dic3—91no—
628C2×Dic3—91no—
629C2×Dic3—91no—
630C2×Dic3—181no—
631C2×Dic3—181no—
632C2×Dic3C22×D911yescharacteristic
633C2×Dic3C22×D911yescharacteristic
634D12—182no—
635D12—182no—
636D12—361no—
637D12—361no—
638D12—362no—
639D12—361no—
640D12—361no—
641C4×D3—94no—
642C4×D3—182no—
643C4×D3—182no—
644Dic6—182no—
645Dic6—182no—
646C2×C32—41no—
647C2×C32—41no—
648C2×C32C2×D3×D411yescharacteristic
649C2×C32#100411yescharacteristic
650C2×C32#100411yescharacteristic
651C3⋊D3—121no—
652C3⋊D3—121no—
653C3×D3—22no—
654C3×D3—41no—
655C3×D3—121no—
656C2×C9—21no—
657C2×C9—21no—
658C2×C9—21no—
659C2×C9—41no—
660C2×C9—41no—
661C2×C9—62no—
662C2×C9—81no—
663C2×C9—81no—
664C2×C9—121no—
665C2×C9C2×D3×D411yescharacteristic
666C2×C9#100411yescharacteristic
667C2×C9#100911yescharacteristic
668D9—41no—
669D9—121no—
670D9—121no—
671D9—241no—
672D9—241no—
673C24—31no—
674C24—271no—
675#41—544no—
676C2×Q8—271no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—91no—
680C2×D4—91no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—271no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—271no—
689C2×D4—271no—
690C2×D4—271no—
691C2×D4—544no—
692C2×D4D3×D911yescharacteristic, complemented
693C22×C4—91no—
694C22×C4—271no—
695C22×C4—271no—
696C4⋊C4—91no—
697C4⋊C4—271no—
698C22⋊C4—31no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—91no—
702C22⋊C4—91no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C42—271no—
709C42—271no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—32no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—124no—
736C22×C3—181no—
737C22×C3—181no—
738C22×C3—181no—
739C22×C3C23×D911yescharacteristic
740C22×C3C22×D3211yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—44no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—181no—
760C2×D3—181no—
761C2×D3—181no—
762C2×D3—361no—
763C2×D3—361no—
764C2×D3—361no—
765C2×D3—361no—
766C2×D3—361no—
767C2×D3—361no—
768C2×D3—364no—
769C2×D3—364no—
770C2×D3D4×D912yes—
771C3×C4—22no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—61no—
775C3×C4—61no—
776C3×C4—92no—
777C3×C4—181no—
778C3×C4—181no—
779Dic3—21no—
780Dic3—21no—
781Dic3—32no—
782Dic3—61no—
783Dic3—61no—
784Dic3—92no—
785Dic3—92no—
786Dic3—182no—
787Dic3—182no—
788Dic3—181no—
789Dic3—181no—
790C32#559211yescharacteristic
791C9—21no—
792C9#560711yescharacteristic, complemented
793C23—31no—
794C23—31no—
795C23—62no—
796C23—91no—
797C23—121no—
798C23—121no—
799C23—271no—
800C23—271no—
801C23—542no—
802C23—1081no—
803C23—1081no—
804C23C2×D3×D911yescharacteristic
805C23C2×D3×D911yescharacteristic
806Q8—542no—
807D4—41no—
808D4—62no—
809D4—121no—
810D4—182no—
811D4—361no—
812D4—542no—
813D4—542no—
814D4—542no—
815D4—542no—
816D4—542no—
817D4—1081no—
818D4—1081no—
819D4—1081no—
820D4—1081no—
821D4—1081no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—91no—
825C2×C4—91no—
826C2×C4—91no—
827C2×C4—182no—
828C2×C4—274no—
829C2×C4—271no—
830C2×C4—271no—
831C2×C4—542no—
832C2×C4C2×D3×D911yescharacteristic
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—41no—
837C2×C3—41no—
838C2×C3—41no—
839C2×C3—41no—
840C2×C3—62no—
841C2×C3—81no—
842C2×C3—81no—
843C2×C3—121no—
844C2×C3—361no—
845C2×C3C2×D4×D911yescharacteristic
846C2×C3#6371011yescharacteristic
847C2×C3#6371011yescharacteristic
848C2×C3D32×D411yescharacteristic
849C2×C3#6431411yescharacteristic
850C2×C3#6433011yescharacteristic
851D3—22no—
852D3—41no—
853D3—121no—
854D3—361no—
855D3—361no—
856D3—361no—
857D3—361no—
858D3—721no—
859D3—721no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—32no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—124no—
873C22—181no—
874C22—181no—
875C22—181no—
876C22—541no—
877C22—541no—
878C22—541no—
879C22—541no—
880C22—541no—
881C22—541no—
882C22—1084no—
883C22C22×D3×D911yescharacteristic
884C4—21no—
885C4—61no—
886C4—61no—
887C4—92no—
888C4—181no—
889C4—181no—
890C4—272no—
891C4—541no—
892C3—21no—
893C3#1058969411yescharacteristic, complemented
894C3#1059528511yescharacteristic
895C2—41no—
896C2—41no—
897C2—62no—
898C2—121no—
899C2—361no—
900C2—1081no—
901C2—1081no—
902C2D3×D4×D911yescharacteristic
903C2#1172250011yescharacteristic
904C2#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×#88662C2semidirect
3. #11721840C2semidirect
4. C9×#937C2semidirect
5. C3×#63501C2semidirect
6. #11721292C2semidirect
7. #11721289C2semidirect
8. #11721288C2semidirect
9. #11721287C2semidirect
10. #11721256C2semidirect
11. #11721242C2semidirect
12. #11721051C2semidirect
13. #11721044C2semidirect
14. #11721039C2semidirect
15. #11721011C2semidirect
20. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C2×#6233C22semidirect
24. C2×#6233C22semidirect
25. C2×C4⋊(C3⋊D9)C22semidirect
27. C2×C9×#67C22semidirect
29. C2×C3×#611C22semidirect
30. C22×C3×Dic9C22semidirect
34. C2×#6195C22semidirect
38. C2×#6192C22semidirect
39. C2×(C3⋊D9)⋊C4C22semidirect
40. C2×#6189C22semidirect
41. C4×C3⋊Dic9C22semidirect
42. C9×#217C22semidirect
43. C3×#3676C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×Dic9⋊C4C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. #88445C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
78. #63501D3semidirect
122. D3×Dic9D4semidirect
170. C2×D4×C9C2×D3semidirect
185. C2×#611C2×D3semidirect
187. C22×Dic9C2×D3semidirect
199. #3676C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
205. Dic9⋊C4C2×D3semidirect
258. #937D9semidirect
385. C2×C3×D4C2×D9semidirect
410. C2×#67C2×D9semidirect
438. #217C2×D9semidirect
448. (C2×D3)⋊C4C2×D9semidirect
552. C3×C9#535semidirect
692. C2×D4D3×D9semidirect
792. C9#5607semidirect
893. 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×#886622
#117218402
C9×#9372
C3×#635012
#117212922
#117212892
#117212882
#117212872
#117212562
#117212422
#117210512
#117210442
#117210392
#117210112
#105952853
#105896943