Finite Group Databasebeta

← #13151983

Subgroups — #13151983

Order 1728.

1134 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#611C211yesmaximal, characteristic, complemented
2C2×#88663C211yesmaximal, characteristic, complemented
3C2×#88551C211yesmaximal, characteristic, complemented
4C9×#953C211yesmaximal, characteristic, complemented
5#11721290C211yesmaximal, characteristic, complemented
6#11721285C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8#11721281C211yesmaximal, characteristic, complemented
9#611⋊Dic3C211yesmaximal, characteristic, complemented
10#11721270C211yesmaximal, characteristic, complemented
11#11721269C211yesmaximal, characteristic, complemented
12D9×#217C211yesmaximal, characteristic, complemented
13#11721260C211yesmaximal, characteristic, complemented
14#11721257C211yesmaximal, characteristic, complemented
15#11721253C211yesmaximal, characteristic, complemented
16#10595494—31nomaximal
17#10589693—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic, complemented
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic, complemented
25C2×C3×#611—24no—
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C2×C3×#611C2211yescharacteristic
29C2×C3×#611C2211yescharacteristic
30C22×C3×Dic9C2211yescharacteristic
31C2×#6194C2211yescharacteristic, complemented
32C2×#6194C2211yescharacteristic, complemented
33#88663—24no—
34C2×D3×Dic9C2211yescharacteristic, complemented
35C2×Dic3×D9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38#88551C2211yescharacteristic
39#88551C2211yescharacteristic
40#88551C2211yescharacteristic, complemented
41#88551C2211yescharacteristic, complemented
42C9×#217C2211yescharacteristic
43C9×#217C2211yescharacteristic, complemented
44C9×#217C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46(C2×D9)⋊Dic3C2211yescharacteristic, complemented
47(C2×D9)⋊Dic3C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×C3×#67—31no—
56C2×#3805—31no—
57C2×#3757—31no—
58C3×#953D311yescharacteristic
59#63980—31no—
60#63976—31no—
61#67⋊Dic3—31no—
62Dic3×#67—31no—
63#63970—31no—
64#63970—31no—
65#63969—31no—
66D3×#217—31no—
67#63964—31no—
68#63962—31no—
69#63959—31no—
70C22×#611D311yescharacteristic, complemented
71C2×#3699—31no—
72C9×#120—31no—
73C2×#3676—31no—
74C2×#3676—61no—
75#63501—31no—
76#63501—31no—
77#63500—31no—
78#63499—31no—
79D4×Dic9—31no—
80#63448—31no—
81#63447—31no—
82#63445—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×D3×C9C2311yescharacteristic
93C22×C3×D9—22no—
94C22×C3×D9—22no—
95C22×C3×D9—41no—
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C2×C3⋊Dic9—22no—
99C2×C3⋊Dic9—41no—
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C9×#67—22no—
105C9×#67—22no—
106C9×#67—41no—
107C3×#611—22no—
108C3×#611—22no—
109C3×#611—22no—
110C3×#611D414yescomplemented
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C9×Dic3C2311yescharacteristic
114C2×C3×Dic9—22no—
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117#6194—22no—
118#6194—41no—
119D3×Dic9—22no—
120Dic3×D9—22no—
121Dic3×D9—41no—
122#6189—22no—
123#5806—91no—
124#5591—91no—
125C24×C32C2×D311yescharacteristic
126C23×C3×D3—31no—
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—64no—
134C2×C3×#67C2×D311yescharacteristic
135C2×C3×#67C2×D311yescharacteristic
136C2×C3×#67C2×D311yescharacteristic
137C22×C3×Dic3—31no—
138C2×#627—31no—
139C2×#625—31no—
140C2×#625—31no—
141#3805—64no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C24×C9—21no—
146C24×C9C2×D311yescharacteristic
147C23×D9C2×D311yescharacteristic
148#3757—31no—
149#3757—31no—
150#3757—31no—
151#3757—31no—
152C3×#217C2×D311yescharacteristic
153C3×#217C2×D311yescharacteristic
154C3×#217C2×D311yescharacteristic
155#3724—31no—
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164Dic32—31no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C2×D4×C9—31no—
168C2×#611—24no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611C2×D311yescharacteristic
172C2×#611C2×D311yescharacteristic
173C2×#611C2×D311yescharacteristic
174C2×#611C2×D311yescharacteristic
175C22×Dic9—31no—
176C22×Dic9—31no—
177C22×Dic9—31no—
178C22×Dic9—61no—
179C22×Dic9—61no—
180C22×Dic9C2×D311yescharacteristic
181#3699—64no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×Dic18—31no—
185C9×C22⋊C4—31no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188#3676—31no—
189#3676—31no—
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—61no—
194#3676—61no—
195#3676—61no—
196#3676—61no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201C4⋊Dic9—31no—
202C4⋊Dic9—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
205C4×Dic9—31no—
206C22×C3×C9—21no—
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—44no—
214C22×C3×C9C2×D412yes—
215C22×C3×C9#4112yescomplemented
216C22×C3×C9C2411yescharacteristic
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—44no—
226C2×C3×D9C2×D412yes—
227C3⋊Dic9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C22×C3×D4—91no—
237C22×#67—31no—
238C2×#237—91no—
239C2×#237—91no—
240C3×#120—31no—
241#953—91no—
242#953D911yescharacteristic, complemented
243C2×#217—91no—
244C2×#217—91no—
245C2×#217—91no—
246C2×#217—181no—
247#939—91no—
248#939—91no—
249#939—91no—
250#939—91no—
251#938—91no—
252#938—91no—
253#937—91no—
254#936—91no—
255#935—91no—
256#935—91no—
257D4×Dic3—91no—
258D4×Dic3—91no—
259C4×#67—91no—
260#924—91no—
261#886—91no—
262#885—91no—
263#883—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32—41no—
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C23×C32C22×D311yescharacteristic
273C22×C3×D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—62no—
276C22×C3×D3—62no—
277C22×C3×D3—121no—
278C22×C3×D3C22×D311yescharacteristic
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—31no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—62no—
284C2×C3⋊Dic3—121no—
285C3×#67—22no—
286C3×#67—22no—
287C3×#67—34no—
288C3×#67—41no—
289C3×#67—62no—
290C3×#67—62no—
291C3×#67—62no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298#627—62no—
299#625—62no—
300#625—121no—
301D3×Dic3—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—24no—
305C23×C9—22no—
306C23×C9—22no—
307C23×C9—21no—
308C23×C9—21no—
309C23×C9—21no—
310C23×C9—31no—
311C23×C9—42no—
312C23×C9—41no—
313C23×C9—42no—
314C23×C9C22×D311yescharacteristic
315C23×C9C22×D311yescharacteristic
316C23×C9C22×D311yescharacteristic
317C22×D9—22no—
318C22×D9—22no—
319C22×D9—41no—
320C22×D9C22×D311yescharacteristic
321C22×D9C22×D311yescharacteristic
322D4×C9—62no—
323D4×C9—62no—
324D4×C9—121no—
325C2×C4×C9—31no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328#611—22no—
329#611—22no—
330#611—22no—
331#611—62no—
332#611—121no—
333#611#6714yescomplemented
334C2×Dic9—22no—
335C2×Dic9—31no—
336C2×Dic9—31no—
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—61no—
342C2×Dic9—61no—
343C2×Dic9—62no—
344C2×Dic9—62no—
345C2×Dic9—122no—
346C2×Dic9—121no—
347C2×Dic9—122no—
348C2×Dic9C22×D311yescharacteristic
349C2×Dic9C22×D311yescharacteristic
350C4×D9—62no—
351C4×D9—121no—
352Dic18—62no—
353#546—271noSylow
354C2×C3×C9—22no—
355C2×C3×C9—22no—
356C2×C3×C9—41no—
357C2×C3×C9C22×D411yescharacteristic
358C2×C3×C9C2×#4111yescharacteristic
359C2×C3×C9H(5,𝔽2)11yescharacteristic
360D3×C9—41no—
361C3×D9—22no—
362C3×D9—41no—
363C24×C3—21no—
364C24×C3—91no—
365C24×C3C2×D911yescharacteristic
366C24×C3D3211yescharacteristic
367C23×D3—31no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—91no—
372C2×C3×D4—91no—
373C2×C3×D4—91no—
374C2×C3×D4—91no—
375C2×C3×D4—184no—
376C22×C3×C4—91no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—31no—
381C2×#67—64no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67C2×D911yescharacteristic
387C2×#67C2×D911yescharacteristic, complemented
388C2×#67C2×D911yescharacteristic, complemented
389C22×Dic3—31no—
390C22×Dic3—91no—
391C22×Dic3—91no—
392C22×Dic3—91no—
393C22×Dic3—91no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3—91no—
397C22×Dic3—181no—
398C22×Dic3—181no—
399#237—184no—
400#237—184no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409#217—91no—
410#217—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—91no—
421#217—91no—
422#217—181no—
423#217—181no—
424#217—181no—
425#217—181no—
426#217C2×D911yescharacteristic
427#217C2×D911yescharacteristic, complemented
428#217C2×D911yescharacteristic, complemented
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434C4⋊Dic3—91no—
435C4⋊Dic3—91no—
436C4⋊Dic3—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—44no—
452C22×C32D3×D412yes—
453C22×C32#23712yes—
454C22×C32C23×D311yescharacteristic
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—32no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—124no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—32no—
473C3×Dic3—61no—
474C22×C9—22no—
475C22×C9—22no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—21no—
480C22×C9—22no—
481C22×C9—21no—
482C22×C9—21no—
483C22×C9—21no—
484C22×C9—21no—
485C22×C9—22no—
486C22×C9—22no—
487C22×C9—41no—
488C22×C9—41no—
489C22×C9—41no—
490C22×C9—41no—
491C22×C9—44no—
492C22×C9—48no—
493C22×C9—61no—
494C22×C9—61no—
495C22×C9—61no—
496C22×C9#23712yescomplemented
497C22×C9C2×#6712yes—
498C22×C9C23×D311yescharacteristic
499C2×D9—21no—
500C2×D9—21no—
501C2×D9—21no—
502C2×D9—21no—
503C2×D9—21no—
504C2×D9—44no—
505C2×D9C2×#6712yes—
506C4×C9—61no—
507C4×C9—61no—
508C4×C9—61no—
509Dic9—21no—
510Dic9—61no—
511Dic9—61no—
512Dic9—61no—
513Dic9—61no—
514Dic9—121no—
515Dic9—121no—
516Dic9—121no—
517Dic9—121no—
518Dic9C2×#6712yes—
519C2×#41—271no—
520C22×D4—91no—
521#124—271no—
522#123—271no—
523#123—271no—
524C22⋊Q8—271no—
525#121—271no—
526#121—271no—
527#121—271no—
528#120—31no—
529#120—271no—
530C4×D4—271no—
531C4×D4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C3×C9#54611yescharacteristic, complemented, Sylow
535C23×C3—24no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—42no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—42no—
548C23×C3—91no—
549C23×C3—91no—
550C23×C3—182no—
551C23×C3—182no—
552C23×C3—361no—
553C23×C3C22×D911yescharacteristic
554C23×C3C22×D911yescharacteristic
555C23×C3C22×D911yescharacteristic
556C23×C3C2×D3211yescharacteristic
557C23×C3C2×D3211yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—121no—
564C22×D3C22×D911yescharacteristic
565C3×D4—62no—
566C3×D4—62no—
567C3×D4—94no—
568C3×D4—121no—
569C3×D4—182no—
570C3×D4—182no—
571C3×D4—182no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4—182no—
578#67—22no—
579#67—22no—
580#67—34no—
581#67—41no—
582#67—62no—
583#67—62no—
584#67—62no—
585#67—182no—
586#67—182no—
587#67—361no—
588#67—361no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—62no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—181no—
601C2×Dic3—181no—
602C2×Dic3—181no—
603C2×Dic3—181no—
604C2×Dic3—182no—
605C2×Dic3—182no—
606C2×Dic3—182no—
607C2×Dic3—182no—
608C2×Dic3—362no—
609C2×Dic3—361no—
610C2×Dic3—361no—
611C2×Dic3—361no—
612C2×Dic3—362no—
613C2×Dic3C22×D911yescharacteristic
614C2×Dic3C22×D911yescharacteristic
615C2×Dic3C22×D911yescharacteristic
616C4×D3—182no—
617C4×D3—182no—
618C4×D3—361no—
619Dic6—182no—
620Dic6—182no—
621C2×C32—22no—
622C2×C32—22no—
623C2×C32—41no—
624C2×C32C2×D3×D411yescharacteristic
625C2×C32C2×#23711yescharacteristic
626C2×C32#100411yescharacteristic
627C3×D3—41no—
628C3×D3—62no—
629C3×D3—121no—
630C2×C9—24no—
631C2×C9—22no—
632C2×C9—22no—
633C2×C9—21no—
634C2×C9—21no—
635C2×C9—21no—
636C2×C9—42no—
637C2×C9—42no—
638C2×C9—41no—
639C2×C9—121no—
640C2×C9C2×#23711yescharacteristic
641C2×C9#100411yescharacteristic
642C2×C9C22×#6711yescharacteristic
643D9—22no—
644D9—41no—
645C24—91no—
646C24D3×D911yescharacteristic
647#41—544no—
648C2×Q8—271no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—91no—
653C2×D4—91no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—184no—
657C2×D4—271no—
658C2×D4—271no—
659C22×C4—91no—
660C22×C4—271no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4—271no—
665C4⋊C4—271no—
666C4⋊C4—271no—
667C4⋊C4—271no—
668C4⋊C4—271no—
669C22⋊C4—31no—
670C22⋊C4—31no—
671C22⋊C4—31no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C42—271no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—22no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—44no—
707C22×C3—44no—
708C22×C3—48no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—92no—
713C22×C3—181no—
714C22×C3—181no—
715C22×C3—181no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—364no—
719C22×C3D4×D912yes—
720C22×C3#369912yescomplemented
721C22×C3C23×D911yescharacteristic
722C22×C3#380512yes—
723C22×C3D3×#6712yes—
724C22×C3C22×D3211yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—32no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—124no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—61no—
738C3×C4—92no—
739C3×C4—181no—
740Dic3—21no—
741Dic3—21no—
742Dic3—21no—
743Dic3—32no—
744Dic3—61no—
745Dic3—181no—
746Dic3—181no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—181no—
752Dic3—181no—
753Dic3—361no—
754Dic3—361no—
755Dic3—361no—
756Dic3—361no—
757C32#559111yescharacteristic
758C9—21no—
759C9#580611yescharacteristic, complemented
760C23—22no—
761C23—22no—
762C23—31no—
763C23—41no—
764C23—91no—
765C23—91no—
766C23—182no—
767C23—182no—
768C23—361no—
769C23C2×D3×D911yescharacteristic
770C23C2×D3×D911yescharacteristic
771C23C2×D3×D911yescharacteristic
772Q8—542no—
773D4—62no—
774D4—62no—
775D4—94no—
776D4—121no—
777D4—182no—
778D4—182no—
779D4—182no—
780D4—542no—
781D4—1081no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—182no—
788C2×C4—271no—
789C2×C4—271no—
790C2×C4—271no—
791C2×C4—271no—
792C2×C4—542no—
793C2×C4—542no—
794C2×C4—542no—
795C2×C4—1081no—
796C2×C4—1081no—
797C2×C3—24no—
798C2×C3—22no—
799C2×C3—22no—
800C2×C3—22no—
801C2×C3—22no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—42no—
806C2×C3—42no—
807C2×C3—41no—
808C2×C3—41no—
809C2×C3—121no—
810C2×C3—182no—
811C2×C3—361no—
812C2×C3C2×D4×D911yescharacteristic
813C2×C3C2×#369911yescharacteristic
814C2×C3#6371011yescharacteristic
815C2×C3C2×#380511yescharacteristic
816C2×C3C2×D3×#6711yescharacteristic
817C2×C3#6433011yescharacteristic
818D3—41no—
819D3—62no—
820D3—121no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—44no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—92no—
833C22—181no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—181no—
838C22—364no—
839C22#8866312yescomplemented
840C22D9×#6712yes—
841C22C22×D3×D911yescharacteristic
842C4—61no—
843C4—61no—
844C4—61no—
845C4—92no—
846C4—181no—
847C4—541no—
848C4—541no—
849C4—541no—
850C4—541no—
851C3—21no—
852C3#1058969311yescharacteristic, complemented
853C3#1059549411yescharacteristic
854C2—22no—
855C2—22no—
856C2—41no—
857C2—121no—
858C2—182no—
859C2—361no—
860C2C2×#8866311yescharacteristic
861C2C2×D9×#6711yescharacteristic
862C2#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×C3×#611C2semidirect
2. C2×#88663C2semidirect
3. C2×#88551C2semidirect
4. C9×#953C2semidirect
5. #11721290C2semidirect
6. #11721285C2semidirect
7. #67×Dic9C2semidirect
8. #11721281C2semidirect
9. #611⋊Dic3C2semidirect
10. #11721270C2semidirect
11. #11721269C2semidirect
12. D9×#217C2semidirect
13. #11721260C2semidirect
14. #11721257C2semidirect
15. #11721253C2semidirect
20. C22×C3⋊Dic9C22semidirect
21. C22×C3⋊Dic9C22semidirect
23. C2×C9×#67C22semidirect
24. C2×C9×#67C22semidirect
31. C2×#6194C22semidirect
32. C2×#6194C22semidirect
34. C2×D3×Dic9C22semidirect
35. C2×Dic3×D9C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
40. #88551C22semidirect
41. #88551C22semidirect
43. C9×#217C22semidirect
44. C9×#217C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
46. (C2×D9)⋊Dic3C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
70. C22×#611D3semidirect
110. C3×#611D4semidirect
215. C22×C3×C9#41semidirect
242. #953D9semidirect
333. #611#67semidirect
387. C2×#67C2×D9semidirect
388. C2×#67C2×D9semidirect
427. #217C2×D9semidirect
428. #217C2×D9semidirect
496. C22×C9#237semidirect
534. C3×C9#546semidirect
720. C22×C3#3699semidirect
759. C9#5806semidirect
839. C22#88663semidirect
852. C3#10589693semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6112
C2×#886632
C2×#885512
C9×#9532
#117212902
#117212852
#67×Dic92
#117212812
#611⋊Dic32
#117212702
#117212692
D9×#2172
#117212602
#117212572
#117212532
#105954943
#105896933