Finite Group Databasebeta

← #13151281

Subgroups — #13151281

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D4×C9C211yesmaximal, characteristic, complemented
2C2×D3×#611C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#11721288C211yesmaximal, characteristic, complemented
8#11721287C211yesmaximal, characteristic, complemented
9#11721286C211yesmaximal, characteristic, complemented
10#11721280C211yesmaximal, characteristic, complemented
11C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
12#11721050C211yesmaximal, characteristic, complemented
13#11721032C211yesmaximal, characteristic, complemented
14#11721015C211yesmaximal, characteristic, complemented
15#11720954C211yesmaximal, characteristic, complemented
16#10595302—31nomaximal
17#10589906—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C23×D3×C9C2211yescharacteristic, complemented
20C22×D3×D9C2211yescharacteristic, complemented
21C2×C3×D4×C9C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×#6233C2211yescharacteristic, complemented
24C22×C3⋊Dic9C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic
26C2×C9×#67C2211yescharacteristic, complemented
27C2×C3×#611C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic, complemented
29C22×C3×Dic9C2211yescharacteristic, complemented
30D3×D4×C9—24no—
31C2×C9×D12C2211yescharacteristic
32C2×C4×D3×C9C2211yescharacteristic, complemented
33D3×#611—24no—
34C2×#6195C2211yescharacteristic
35C2×#6195C2211yescharacteristic, complemented
36C2×#6194C2211yescharacteristic
37C2×#6194C2211yescharacteristic, complemented
38C2×D3×Dic9C2211yescharacteristic, complemented
39#88551C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×C3×D3×D4D311yescharacteristic
56C2×D3×#67—31no—
57#64148—31no—
58C3×#939—31no—
59#63983—31no—
60#63980—31no—
61#63978—31no—
62#63977—31no—
63#63976—31no—
64#63969—31no—
65C2×(C2×D3)⋊Dic3—31no—
66#63922—31no—
67#63905—31no—
68#63884—31no—
69#63850—31no—
70C22×D4×C9—31no—
71C22×#611—31no—
72#63515—31no—
73#63515—31no—
74C2×#3676—31no—
75#63501—31no—
76#63501—31no—
77#63501—31no—
78#63501—61no—
79#63501D311yescharacteristic, complemented
80#63499—31no—
81#63499—31no—
82#63497—31no—
83#63497—31no—
84#63491—31no—
85#63491—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9—22no—
90C22×D3×C9—41no—
91C22×D3×C9—41no—
92C22×D3×C9—41no—
93C22×D3×C9—41no—
94C22×D3×C9D414yescomplemented
95C22×D3×C9C2311yescharacteristic
96C22×D3×C9C2311yescharacteristic
97C22×D3×C9C2311yescharacteristic
98C22×C3×D9C2311yescharacteristic
99C2×D3×D9—22no—
100C2×D3×D9—41no—
101C2×D3×D9—41no—
102C3×D4×C9—22no—
103C2×C3×C4×C9C2311yescharacteristic
104#6233—22no—
105#6233—41no—
106C2×C3⋊Dic9—41no—
107C2×C3⋊Dic9C2311yescharacteristic
108C2×C3⋊Dic9C2311yescharacteristic
109C2×C3⋊Dic9C2311yescharacteristic
110C9×#67—22no—
111C9×#67—22no—
112C3×#611—22no—
113C3×#611—41no—
114C2×C9×Dic3C2311yescharacteristic
115C2×C3×Dic9—41no—
116C2×C3×Dic9C2311yescharacteristic
117C2×C3×Dic9C2311yescharacteristic
118C2×C3×Dic9C2311yescharacteristic
119C9×D12—22no—
120C4×D3×C9—22no—
121#6195—22no—
122#6195—41no—
123#6194—22no—
124#6194—41no—
125D3×Dic9—22no—
126#5804—91no—
127#5605—91no—
128C23×C3×D3C2×D311yescharacteristic
129C23×C3×D3C2×D311yescharacteristic
130C22×D32—31no—
131C2×C32×D4C2×D311yescharacteristic
132C2×#638—31no—
133C2×#638—31no—
134C22×C3⋊Dic3—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×#67C2×D311yescharacteristic
139C22×C3×Dic3—31no—
140C3×D3×D4—24no—
141C2×C3×D12C2×D311yescharacteristic
142C2×C3×C4×D3C2×D311yescharacteristic
143D3×#67—64no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#625—31no—
147C2×#625—31no—
148C2×D3×Dic3—31no—
149C24×C9—31no—
150C24×C9—31no—
151C23×D9—31no—
152#3757—31no—
153#3752—31no—
154#3750—31no—
155C3×#217—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×Dic3⋊C4—31no—
158#3724—31no—
159Dic3⋊Dic3—31no—
160#3722—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166(C2×D3)⋊Dic3—31no—
167(C2×D3)⋊Dic3—31no—
168C2×D4×C9—21no—
169C2×D4×C9—31no—
170C2×D4×C9—31no—
171C2×D4×C9—31no—
172C2×D4×C9—64no—
173C2×D4×C9C2×D311yescharacteristic, complemented
174C22×C4×C9—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—31no—
178C2×#611—31no—
179C2×#611—31no—
180C2×#611—31no—
181C2×#611—64no—
182C2×#611—61no—
183C2×#611—61no—
184C2×#611C2×D311yescharacteristic, complemented
185C2×#611C2×D311yescharacteristic, complemented
186C22×Dic9—31no—
187C22×Dic9—31no—
188C22×Dic9—61no—
189C22×Dic9C2×D311yescharacteristic, complemented
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—31no—
194#3676—31no—
195#3676—31no—
196#3676—31no—
197#3676—61no—
198#3676C2×D311yescharacteristic, complemented
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, complemented
204Dic9⋊C4—31no—
205Dic9⋊C4—31no—
206Dic9⋊C4—31no—
207Dic9⋊C4—61no—
208Dic9⋊C4C2×D311yescharacteristic, complemented
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9—21no—
214C22×C3×C9C2×D412yes—
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×D3×C9—21no—
226C2×D3×C9—44no—
227C2×D3×C9—44no—
228C2×D3×C9C2×D412yes—
229C2×D3×C9C2×D412yes—
230C2×C3×D9—21no—
231C2×C3×D9—21no—
232C2×C3×D9—21no—
233D3×D9—44no—
234C3×C4×C9—21no—
235C3⋊Dic9—21no—
236C3⋊Dic9—21no—
237C3⋊Dic9—21no—
238C9×Dic3—21no—
239C3×Dic9—21no—
240C3×Dic9—21no—
241C3×Dic9—21no—
242C22×C3×D4—31no—
243C22×#67—91no—
244C2×D3×D4—91no—
245C2×D3×D4D911yescharacteristic, complemented
246C3×#121—91no—
247#953—91no—
248#953—91no—
249C2×#217—91no—
250#939—31no—
251#939—91no—
252#939—91no—
253#939—91no—
254#939—91no—
255#939—91no—
256#939—181no—
257#937—91no—
258#937—91no—
259#937—91no—
260#937—91no—
261#935—91no—
262#935—91no—
263#930—91no—
264#929—91no—
265#929—91no—
266C2×(C2×D3)⋊C4—91no—
267#894—91no—
268#894—91no—
269#883—91no—
270#883—91no—
271#882—91no—
272#882—91no—
273C23×C32C22×D311yescharacteristic
274C23×C32C22×D311yescharacteristic
275C22×C3⋊D3—31no—
276C22×C3×D3—22no—
277C22×C3×D3—31no—
278C22×C3×D3—41no—
279C22×C3×D3—41no—
280C22×C3×D3—41no—
281C22×C3×D3—41no—
282C22×C3×D3#6714yes—
283C22×C3×D3C22×D311yescharacteristic
284C22×C3×D3C22×D311yescharacteristic
285C22×C3×D3C22×D311yescharacteristic
286C2×D32—62no—
287C2×D32—121no—
288C2×D32—121no—
289C32×D4—22no—
290C2×C32×C4C22×D311yescharacteristic
291#638—62no—
292#638—121no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—31no—
296C2×C3⋊Dic3—121no—
297C3×#67—22no—
298C3×#67—22no—
299C3×#67—62no—
300C3×#67—121no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—121no—
305C2×C3×Dic3C22×D311yescharacteristic
306C3×D12—22no—
307C3×C4×D3—22no—
308#626—62no—
309#626—121no—
310#625—62no—
311#625—121no—
312D3×Dic3—62no—
313C23×C9—21no—
314C23×C9—21no—
315C23×C9—31no—
316C23×C9—31no—
317C23×C9—34no—
318C23×C9—31no—
319C23×C9—62no—
320C23×C9—121no—
321C23×C9—121no—
322C23×C9—121no—
323C23×C9—121no—
324C23×C9C22×D311yescharacteristic
325C23×C9C22×D311yescharacteristic
326C22×D9—31no—
327C22×D9—61no—
328C22×D9—62no—
329C22×D9—121no—
330C22×D9—121no—
331C22×D9C22×D311yescharacteristic
332D4×C9—22no—
333D4×C9—42no—
334D4×C9—62no—
335D4×C9—62no—
336D4×C9—62no—
337C2×C4×C9—21no—
338C2×C4×C9—31no—
339C2×C4×C9—62no—
340C2×C4×C9C22×D311yescharacteristic
341#611—22no—
342#611—41no—
343#611—62no—
344#611—62no—
345#611—62no—
346#611—122no—
347#611—121no—
348#611—121no—
349#611—121no—
350#611—122no—
351C2×Dic9—31no—
352C2×Dic9—31no—
353C2×Dic9—31no—
354C2×Dic9—41no—
355C2×Dic9—61no—
356C2×Dic9—61no—
357C2×Dic9—61no—
358C2×Dic9—62no—
359C2×Dic9—121no—
360C2×Dic9—122no—
361C2×Dic9C22×D311yescharacteristic
362C2×Dic9C22×D311yescharacteristic
363C2×Dic9C22×D311yescharacteristic
364#534—271noSylow
365C2×C3×C9—22no—
366C2×C3×C9—41no—
367C2×C3×C9C22×D411yescharacteristic
368C2×C3×C9H(5,𝔽2)11yescharacteristic
369C2×C3×C9H(5,𝔽2)11yescharacteristic
370C3⋊D9—41no—
371D3×C9—22no—
372D3×C9—22no—
373D3×C9—41no—
374C3×D9—41no—
375C24×C3—31no—
376C24×C3—31no—
377C23×D3—91no—
378C23×D3—91no—
379C23×D3C2×D911yescharacteristic
380C23×D3C2×D911yescharacteristic, complemented
381C2×C3×D4—21no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—64no—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C2×C3×D4C2×D911yescharacteristic, complemented
389C2×C3×D4D3211yescharacteristic
390C22×C3×C4—31no—
391C22×C3×C4—91no—
392C2×#67—31no—
393C2×#67—31no—
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—31no—
410C22×Dic3—91no—
411C22×Dic3—91no—
412C22×Dic3—91no—
413C22×Dic3—181no—
414D3×D4—24no—
415D3×D4—184no—
416C2×D12—91no—
417C2×D12—91no—
418C2×D12C2×D911yescharacteristic
419C2×C4×D3—91no—
420C2×C4×D3C2×D911yescharacteristic, complemented
421C3×C4⋊C4—91no—
422C3×C22⋊C4—91no—
423C3×C22⋊C4—91no—
424#217—31no—
425#217—91no—
426#217—91no—
427#217—91no—
428#217—91no—
429#217—91no—
430#217—91no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—181no—
435(C2×D3)⋊C4—31no—
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—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—181no—
448C4⋊Dic3—91no—
449Dic3⋊C4—31no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454Dic3⋊C4—91no—
455Dic3⋊C4—181no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32C2×#6712yes—
462C22×C32C23×D311yescharacteristic
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—44no—
474C2×C3×D3—44no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3C2×#6712yes—
479C2×C3×D3C2×#6712yes—
480D32—124no—
481C32×C4—21no—
482C3⋊Dic3—61no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3×Dic3—21no—
486C3×Dic3—61no—
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—22no—
496C22×C9—32no—
497C22×C9—32no—
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—61no—
509C22×C9—61no—
510C22×C9—124no—
511C22×C9—124no—
512C22×C9D3×D412yes—
513C22×C9C23×D311yescharacteristic
514C2×D9—21no—
515C2×D9—21no—
516C2×D9—21no—
517C2×D9—61no—
518C2×D9—61no—
519C2×D9—61no—
520C2×D9—121no—
521C2×D9—121no—
522C2×D9—121no—
523C2×D9—124no—
524C4×C9—21no—
525C4×C9—41no—
526C4×C9—61no—
527Dic9—21no—
528Dic9—21no—
529Dic9—21no—
530Dic9—62no—
531Dic9—61no—
532Dic9—61no—
533Dic9—61no—
534Dic9—121no—
535Dic9—121no—
536C22×D4—31no—
537C22×D4—271no—
538#123—271no—
539#123—271no—
540#123—271no—
541#123—271no—
542#121—91no—
543#121—271no—
544#121—271no—
545#121—271no—
546#120—271no—
547#120—271no—
548#120—271no—
549#120—271no—
550C2×C22⋊C4—271no—
551C3×C9#53411yescharacteristic, complemented, Sylow
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—31no—
555C23×C3—31no—
556C23×C3—34no—
557C23×C3—31no—
558C23×C3—62no—
559C23×C3—91no—
560C23×C3—121no—
561C23×C3—121no—
562C23×C3—121no—
563C23×C3—121no—
564C23×C3C22×D911yescharacteristic
565C23×C3C22×D911yescharacteristic
566C23×C3C2×D3211yescharacteristic
567C23×C3C2×D3211yescharacteristic
568C22×D3—22no—
569C22×D3—31no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—91no—
575C22×D3—91no—
576C22×D3—181no—
577C22×D3—182no—
578C22×D3—182no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3#61114yescomplemented
584C22×D3C22×D911yescharacteristic
585C22×D3C22×D911yescharacteristic
586C22×D3C22×D911yescharacteristic
587C3×D4—22no—
588C3×D4—22no—
589C3×D4—42no—
590C3×D4—62no—
591C3×D4—62no—
592C3×D4—62no—
593C3×D4—182no—
594C3×D4—361no—
595C2×C3×C4—21no—
596C2×C3×C4—31no—
597C2×C3×C4—62no—
598C2×C3×C4—91no—
599C2×C3×C4—91no—
600C2×C3×C4—91no—
601C2×C3×C4—361no—
602C2×C3×C4C22×D911yescharacteristic
603C2×C3×C4C2×D3211yescharacteristic
604#67—22no—
605#67—22no—
606#67—62no—
607#67—121no—
608#67—182no—
609#67—182no—
610#67—182no—
611#67—182no—
612#67—182no—
613#67—362no—
614#67—361no—
615#67—361no—
616#67—361no—
617#67—361no—
618#67—361no—
619#67—362no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—91no—
624C2×Dic3—91no—
625C2×Dic3—91no—
626C2×Dic3—91no—
627C2×Dic3—91no—
628C2×Dic3—91no—
629C2×Dic3—121no—
630C2×Dic3—181no—
631C2×Dic3—181no—
632C2×Dic3—181no—
633C2×Dic3—182no—
634C2×Dic3—361no—
635C2×Dic3—361no—
636C2×Dic3—362no—
637C2×Dic3C22×D911yescharacteristic
638D12—22no—
639D12—182no—
640D12—361no—
641C4×D3—22no—
642C4×D3—182no—
643C2×C32—22no—
644C2×C32—41no—
645C2×C32#100411yescharacteristic
646C2×C32#100411yescharacteristic
647C2×C32C22×#6711yescharacteristic
648C3⋊D3—121no—
649C3×D3—22no—
650C3×D3—22no—
651C3×D3—41no—
652C3×D3—121no—
653C2×C9—22no—
654C2×C9—21no—
655C2×C9—21no—
656C2×C9—21no—
657C2×C9—42no—
658C2×C9—41no—
659C2×C9—62no—
660C2×C9—62no—
661C2×C9—81no—
662C2×C9—121no—
663C2×C9C2×D3×D411yescharacteristic
664C2×C9#100411yescharacteristic
665C2×C9#100911yescharacteristic
666D9—41no—
667D9—121no—
668D9—241no—
669C24—31no—
670C24—31no—
671C24—271no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—64no—
676C2×D4—91no—
677C2×D4—91no—
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—31no—
687C22×C4—91no—
688C22×C4—271no—
689C22×C4—271no—
690C4⋊C4—91no—
691C4⋊C4—271no—
692C4⋊C4—271no—
693C4⋊C4—271no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
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—22no—
718C22×C3—32no—
719C22×C3—32no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—124no—
733C22×C3—124no—
734C22×C3—181no—
735C22×C3—181no—
736C22×C3—181no—
737C22×C3C2×#61112yes—
738C22×C3C23×D911yescharacteristic
739C22×C3D3×#6712yes—
740C22×C3C22×D3211yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—44no—
749C2×D3—44no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—361no—
760C2×D3—361no—
761C2×D3—361no—
762C2×D3—364no—
763C2×D3—364no—
764C2×D3C2×#61112yes—
765C2×D3C2×#61112yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—41no—
769C3×C4—61no—
770C3×C4—181no—
771C3×C4—181no—
772C3×C4—181no—
773Dic3—21no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—182no—
778Dic3—181no—
779Dic3—181no—
780Dic3—181no—
781Dic3—181no—
782Dic3—181no—
783Dic3—181no—
784Dic3—361no—
785Dic3—361no—
786C32#580411yescharacteristic
787C9—21no—
788C9#560511yescharacteristic, complemented
789C23—31no—
790C23—31no—
791C23—34no—
792C23—31no—
793C23—62no—
794C23—91no—
795C23—121no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—271no—
800C23—542no—
801C23—1081no—
802C23—1081no—
803C23C2×D3×D911yescharacteristic
804C23C2×D3×D911yescharacteristic
805D4—22no—
806D4—62no—
807D4—62no—
808D4—62no—
809D4—182no—
810D4—361no—
811D4—542no—
812D4—542no—
813D4—542no—
814D4—1081no—
815D4—1081no—
816D4—1081no—
817C2×C4—31no—
818C2×C4—62no—
819C2×C4—91no—
820C2×C4—91no—
821C2×C4—91no—
822C2×C4—271no—
823C2×C4—271no—
824C2×C4—271no—
825C2×C4—361no—
826C2×C4—542no—
827C2×C4—1081no—
828C2×C4C2×D3×D911yescharacteristic
829C2×C3—22no—
830C2×C3—22no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—62no—
838C2×C3—62no—
839C2×C3—81no—
840C2×C3—121no—
841C2×C3—361no—
842C2×C3#6371011yescharacteristic
843C2×C3#6371011yescharacteristic
844C2×C3C22×#61111yescharacteristic
845C2×C3#6431311yescharacteristic
846C2×C3#6431411yescharacteristic
847C2×C3C2×D3×#6711yescharacteristic
848D3—22no—
849D3—22no—
850D3—41no—
851D3—121no—
852D3—361no—
853D3—361no—
854D3—721no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—32no—
861C22—32no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—61no—
868C22—61no—
869C22—124no—
870C22—124no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22—541no—
875C22—541no—
876C22—541no—
877C22—1084no—
878C22D3×#61112yes—
879C22C22×D3×D911yescharacteristic
880C4—21no—
881C4—61no—
882C4—181no—
883C4—181no—
884C4—181no—
885C4—541no—
886C4—541no—
887C4—541no—
888C3—21no—
889C3#1058990611yescharacteristic, complemented
890C3#1059530211yescharacteristic
891C2—22no—
892C2—41no—
893C2—62no—
894C2—62no—
895C2—121no—
896C2—361no—
897C2—1081no—
898C2#1172249911yescharacteristic
899C2#1172250011yescharacteristic
900C2C2×D3×#61111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#534
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×D4×C9C2semidirect
2. C2×D3×#611C2semidirect
3. #11721839C2semidirect
4. C3×#63501C2semidirect
5. #11721292C2semidirect
6. #11721290C2semidirect
7. #11721288C2semidirect
8. #11721287C2semidirect
9. #11721286C2semidirect
10. #11721280C2semidirect
11. C2×(C2×D3)⋊Dic9C2semidirect
12. #11721050C2semidirect
13. #11721032C2semidirect
14. #11721015C2semidirect
15. #11720954C2semidirect
19. C23×D3×C9C22semidirect
20. C22×D3×D9C22semidirect
21. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C2×#6233C22semidirect
24. C22×C3⋊Dic9C22semidirect
26. C2×C9×#67C22semidirect
27. C2×C3×#611C22semidirect
28. C2×C3×#611C22semidirect
29. C22×C3×Dic9C22semidirect
32. C2×C4×D3×C9C22semidirect
35. C2×#6195C22semidirect
37. C2×#6194C22semidirect
38. C2×D3×Dic9C22semidirect
39. #88551C22semidirect
40. #88536C22semidirect
41. #88534C22semidirect
42. C3×#3676C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×Dic9⋊C4C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. #88445C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. #88442C22semidirect
54. Dic9⋊Dic3C22semidirect
79. #63501D3semidirect
94. C22×D3×C9D4semidirect
173. C2×D4×C9C2×D3semidirect
184. C2×#611C2×D3semidirect
185. C2×#611C2×D3semidirect
189. C22×Dic9C2×D3semidirect
198. #3676C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
208. Dic9⋊C4C2×D3semidirect
245. C2×D3×D4D9semidirect
380. C23×D3C2×D9semidirect
388. C2×C3×D4C2×D9semidirect
408. C2×#67C2×D9semidirect
420. C2×C4×D3C2×D9semidirect
551. C3×C9#534semidirect
583. C22×D3#611semidirect
685. C2×D4D3×D9semidirect
788. C9#5605semidirect
889. C3#10589906semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D4×C92
C2×D3×#6112
#117218392
C3×#635012
#117212922
#117212902
#117212882
#117212872
#117212862
#117212802
C2×(C2×D3)⋊Dic92
#117210502
#117210322
#117210152
#117209542
#105953023
#105899063