Finite Group Databasebeta

← #13151284

Subgroups — #13151284

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3699C211yesmaximal, characteristic, complemented
2C2×D3×#611C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C9×#937C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721288C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8#611⋊Dic3C211yesmaximal, characteristic, complemented
9#11721270C211yesmaximal, characteristic, complemented
10C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
11#11721255C211yesmaximal, characteristic, complemented
12D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#11721035C211yesmaximal, characteristic, complemented
14#11721031C211yesmaximal, characteristic, complemented
15#11721018C211yesmaximal, characteristic, complemented
16#10595304—31nomaximal
17#10589693—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
28C22×C3×Dic9C2211yescharacteristic, complemented
29C22×C3×Dic9C2211yescharacteristic, complemented
30C3×#3699—24no—
31C2×C3×C4×D9C2211yescharacteristic, complemented
32C2×C3×Dic18C2211yescharacteristic, complemented
33D3×#611—24no—
34C2×#6195C2211yescharacteristic
35C2×#6194C2211yescharacteristic
36C2×D3×Dic9C2211yescharacteristic
37C2×Dic3×D9C2211yescharacteristic, complemented
38#88551C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C3×#237—31no—
56C2×D3×#67—31no—
57#64148—31no—
58C3×#937D311yescharacteristic
59#63983—31no—
60#63978—31no—
61#67⋊Dic3—31no—
62Dic3×#67—31no—
63#63970—31no—
64#63966—31no—
65C2×(C2×D3)⋊Dic3—31no—
66D3×(C2×D3)⋊C4—31no—
67#63907—31no—
68#63905—31no—
69#63887—31no—
70C22×#611—31no—
71C2×#3699D311yescharacteristic, complemented
72C9×#120—31no—
73C2×#3676—31no—
74#63501—31no—
75#63501—31no—
76#63501—61no—
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×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9—22no—
90C22×D3×C9—22no—
91C22×D3×C9—41no—
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C3×D4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101#6233—41no—
102C2×C3⋊Dic9—41no—
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C2×C3⋊Dic9C2311yescharacteristic
106C9×#67—22no—
107C9×#67—41no—
108C3×#611—22no—
109C3×#611D414yescomplemented
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C3×Dic9—22no—
113C2×C3×Dic9—22no—
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C3×C4×D9—22no—
118C3×Dic18—22no—
119#6195—22no—
120#6194—22no—
121D3×Dic9—22no—
122Dic3×D9—41no—
123#5829—91no—
124#5591—91no—
125C23×C3×D3C2×D311yescharacteristic
126C22×D32—31no—
127C2×C32×D4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130C22×C3⋊Dic3—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67C2×D311yescharacteristic
134C2×C3×#67C2×D311yescharacteristic
135C22×C3×Dic3—31no—
136C22×C3×Dic3—31no—
137C3×#237—64no—
138C2×C3×C4×D3—31no—
139C2×C3×Dic6—31no—
140D3×#67—64no—
141C2×#626—31no—
142C2×#625—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C24×C9—31no—
146C23×D9—31no—
147#3757—31no—
148#3752—31no—
149#3750—31no—
150C3×#217C2×D311yescharacteristic
151C3×(C2×D3)⋊C4C2×D311yescharacteristic
152C3×(C2×D3)⋊C4C2×D311yescharacteristic
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156#3722—31no—
157#3722—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163Dic32—31no—
164C2×D4×C9—21no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C2×D4×C9C2×D311yescharacteristic, complemented
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—64no—
173C2×#611—61no—
174C2×#611—61no—
175C2×#611C2×D311yescharacteristic
176C2×#611C2×D311yescharacteristic, complemented
177C22×Dic9—31no—
178C22×Dic9—31no—
179C22×Dic9—61no—
180C22×Dic9C2×D311yescharacteristic, complemented
181C22×Dic9C2×D311yescharacteristic, complemented
182#3699—24no—
183C2×C4×D9—31no—
184C2×C4×D9C2×D311yescharacteristic, complemented
185C2×Dic18C2×D311yescharacteristic, complemented
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189#3676—31no—
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—31no—
194#3676—61no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—61no—
200C4⋊Dic9—31no—
201C4⋊Dic9—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—61no—
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×C9C2×D412yes—
212C22×C3×C9C2411yescharacteristic
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—44no—
222C2×D3×C9#4112yescomplemented
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9C2×D412yes—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C2×C3×#41—91no—
237C22×#67—91no—
238C2×#237—31no—
239C2×D3×D4—91no—
240C3×#120—31no—
241C2×#217—91no—
242#947—91no—
243#946—91no—
244#939—91no—
245#939—91no—
246#939—91no—
247#939—91no—
248#939—181no—
249#938—91no—
250#937—91no—
251#937—91no—
252#937D911yescharacteristic, complemented
253D4×Dic3—91no—
254D4×Dic3—91no—
255#930—91no—
256#929—91no—
257#929—91no—
258C4×#67—91no—
259C2×(C2×D3)⋊C4—91no—
260C2×(C2×D3)⋊C4—91no—
261#886—91no—
262#885—91no—
263#883—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C22×C3⋊D3—31no—
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—31no—
273C22×C3×D3—41no—
274C22×C3×D3C22×D311yescharacteristic
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C32×D4—22no—
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—121no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—121no—
287C3×#67—22no—
288C3×#67—34no—
289C3×#67—41no—
290C3×#67—62no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C3×C4×D3—62no—
299C3×Dic6—62no—
300#626—62no—
301#625—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—21no—
306C23×C9—31no—
307C23×C9—31no—
308C23×C9—62no—
309C23×C9—62no—
310C23×C9—121no—
311C23×C9C22×D311yescharacteristic
312C23×C9C22×D311yescharacteristic
313C22×D9—31no—
314C22×D9—61no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—121no—
318C22×D9C22×D311yescharacteristic
319D4×C9—22no—
320D4×C9—42no—
321D4×C9—62no—
322D4×C9—121no—
323C2×C4×C9—21no—
324C2×C4×C9—31no—
325C2×C4×C9—31no—
326C2×C4×C9C22×D311yescharacteristic
327#611—22no—
328#611—62no—
329#611—62no—
330#611—62no—
331#611—122no—
332#611—121no—
333#611—122no—
334#611#6714yescomplemented
335C2×Dic9—22no—
336C2×Dic9—22no—
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—31no—
340C2×Dic9—61no—
341C2×Dic9—61no—
342C2×Dic9—61no—
343C2×Dic9—62no—
344C2×Dic9—121no—
345C2×Dic9—122no—
346C2×Dic9C22×D311yescharacteristic
347C2×Dic9C22×D311yescharacteristic
348C2×Dic9C22×D311yescharacteristic
349C4×D9—22no—
350C4×D9—121no—
351Dic18—22no—
352#546—271noSylow
353C2×C3×C9—22no—
354C2×C3×C9—41no—
355C2×C3×C9C22×D411yescharacteristic
356C2×C3×C9C2×#4111yescharacteristic
357C2×C3×C9H(5,𝔽2)11yescharacteristic
358C3⋊D9—41no—
359D3×C9—22no—
360D3×C9—41no—
361C3×D9—22no—
362C24×C3—31no—
363C23×D3—91no—
364C23×D3—91no—
365C23×D3C2×D911yescharacteristic
366C3×#41—184no—
367C2×C3×Q8—91no—
368C2×C3×D4—21no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—91no—
372C2×C3×D4—91no—
373C2×C3×D4C2×D911yescharacteristic, complemented
374C2×C3×D4D3211yescharacteristic
375C22×C3×C4—91no—
376C22×C3×C4—91no—
377C22×C3×C4—91no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—181no—
388C2×#67—181no—
389C2×#67—184no—
390C2×#67C2×D911yescharacteristic
391C2×#67C2×D911yescharacteristic, complemented
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3—91no—
397C22×Dic3—91no—
398C22×Dic3—181no—
399#237—64no—
400D3×D4—184no—
401C2×D12—91no—
402C2×C4×D3—31no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×Dic6—31no—
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—181no—
417#217C2×D911yescharacteristic, complemented
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—181no—
430(C2×D3)⋊C4C2×D911yescharacteristic
431(C2×D3)⋊C4C2×D911yescharacteristic, complemented
432C4⋊Dic3—91no—
433C4⋊Dic3—91no—
434C4⋊Dic3—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—181no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32D3×D412yes—
449C22×C32C23×D311yescharacteristic
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—32no—
459C2×C3×D3—44no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3#23712yes—
463D32—124no—
464C32×C4—21no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—32no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—22no—
480C22×C9—32no—
481C22×C9—41no—
482C22×C9—41no—
483C22×C9—41no—
484C22×C9—41no—
485C22×C9—41no—
486C22×C9—61no—
487C22×C9—61no—
488C22×C9—61no—
489C22×C9—61no—
490C22×C9—61no—
491C22×C9—124no—
492C22×C9C2×#6712yes—
493C22×C9C23×D311yescharacteristic
494C2×D9—21no—
495C2×D9—21no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—124no—
503C2×D9C2×#6712yes—
504C4×C9—21no—
505C4×C9—41no—
506C4×C9—61no—
507C4×C9—61no—
508Dic9—21no—
509Dic9—21no—
510Dic9—62no—
511Dic9—61no—
512Dic9—61no—
513Dic9—61no—
514Dic9—121no—
515Dic9—121no—
516Dic9C2×#6712yes—
517C2×#41—91no—
518C22×D4—271no—
519#124—271no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—271no—
524#121—271no—
525#121—271no—
526#120—31no—
527#120—271no—
528C4×D4—271no—
529C4×D4—271no—
530C2×C22⋊C4—271no—
531C2×C22⋊C4—271no—
532C3×C9#54611yescharacteristic, complemented, Sylow
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—62no—
538C23×C3—62no—
539C23×C3—91no—
540C23×C3—121no—
541C23×C3C22×D911yescharacteristic
542C23×C3C22×D911yescharacteristic
543C23×C3C2×D3211yescharacteristic
544C23×C3C2×D3211yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—31no—
548C22×D3—41no—
549C22×D3—91no—
550C22×D3—91no—
551C22×D3—181no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—361no—
557C22×D3—361no—
558C22×D3C22×D911yescharacteristic
559C22×D3C22×D911yescharacteristic
560C3×Q8—182no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—42no—
564C3×D4—62no—
565C3×D4—94no—
566C3×D4—121no—
567C3×D4—182no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—91no—
574C2×C3×C4—182no—
575C2×C3×C4—182no—
576C2×C3×C4—182no—
577C2×C3×C4C22×D911yescharacteristic
578C2×C3×C4C2×D3211yescharacteristic
579#67—22no—
580#67—34no—
581#67—41no—
582#67—62no—
583#67—182no—
584#67—182no—
585#67—182no—
586#67—182no—
587#67—182no—
588#67—362no—
589#67—361no—
590#67—361no—
591#67—362no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—91no—
603C2×Dic3—181no—
604C2×Dic3—181no—
605C2×Dic3—181no—
606C2×Dic3—182no—
607C2×Dic3—361no—
608C2×Dic3—361no—
609C2×Dic3—361no—
610C2×Dic3—362no—
611C2×Dic3C22×D911yescharacteristic
612C2×Dic3C22×D911yescharacteristic
613D12—182no—
614C4×D3—62no—
615C4×D3—182no—
616C4×D3—361no—
617Dic6—62no—
618C2×C32—22no—
619C2×C32—41no—
620C2×C32C2×D3×D411yescharacteristic
621C2×C32C2×#23711yescharacteristic
622C2×C32#100411yescharacteristic
623C3⋊D3—121no—
624C3×D3—22no—
625C3×D3—41no—
626C3×D3—62no—
627C2×C9—22no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—21no—
631C2×C9—42no—
632C2×C9—41no—
633C2×C9—62no—
634C2×C9—81no—
635C2×C9—121no—
636C2×C9D3×#4111yescharacteristic
637C2×C9#100911yescharacteristic
638C2×C9C22×#6711yescharacteristic
639D9—22no—
640D9—121no—
641D9—241no—
642C24—31no—
643C24—271no—
644#41—184no—
645C2×Q8—91no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—91no—
649C2×D4—91no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—544no—
655C2×D4D3×D911yescharacteristic, complemented
656C22×C4—91no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C42—271no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—22no—
691C22×C3—32no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—92no—
703C22×C3—124no—
704C22×C3—181no—
705C22×C3—181no—
706C22×C3D4×D912yes—
707C22×C3C23×D911yescharacteristic
708C22×C3D3×#6712yes—
709C22×C3C22×D3211yescharacteristic
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—32no—
716C2×D3—44no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—361no—
726C2×D3—361no—
727C2×D3—361no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3#369912yescomplemented
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—41no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—92no—
737C3×C4—181no—
738C3×C4—181no—
739Dic3—21no—
740Dic3—21no—
741Dic3—32no—
742Dic3—61no—
743Dic3—61no—
744Dic3—182no—
745Dic3—181no—
746Dic3—181no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—361no—
752Dic3—361no—
753C32#559111yescharacteristic
754C9—21no—
755C9#582911yescharacteristic, complemented
756C23—31no—
757C23—31no—
758C23—62no—
759C23—62no—
760C23—91no—
761C23—121no—
762C23—271no—
763C23—542no—
764C23—542no—
765C23—1081no—
766C23C2×D3×D911yescharacteristic
767C23C2×D3×D911yescharacteristic
768Q8—182no—
769D4—22no—
770D4—62no—
771D4—94no—
772D4—121no—
773D4—182no—
774D4—542no—
775D4—542no—
776D4—542no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—91no—
781C2×C4—91no—
782C2×C4—91no—
783C2×C4—182no—
784C2×C4—182no—
785C2×C4—182no—
786C2×C4—271no—
787C2×C4—271no—
788C2×C4—271no—
789C2×C4—542no—
790C2×C4—1081no—
791C2×C4—1081no—
792C2×C4C2×D3×D911yescharacteristic
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—42no—
799C2×C3—41no—
800C2×C3—41no—
801C2×C3—62no—
802C2×C3—81no—
803C2×C3—121no—
804C2×C3—182no—
805C2×C3C2×D4×D911yescharacteristic
806C2×C3C2×#369911yescharacteristic
807C2×C3#6371011yescharacteristic
808C2×C3D3×#23711yescharacteristic
809C2×C3#6431411yescharacteristic
810C2×C3C2×D3×#6711yescharacteristic
811D3—22no—
812D3—41no—
813D3—62no—
814D3—361no—
815D3—361no—
816D3—721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—32no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—92no—
829C22—124no—
830C22—181no—
831C22—181no—
832C22—541no—
833C22—541no—
834C22—541no—
835C22—1084no—
836C22D9×#6712yes—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—61no—
840C4—61no—
841C4—92no—
842C4—181no—
843C4—181no—
844C4—541no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058969311yescharacteristic, complemented
849C3#1059530411yescharacteristic
850C2—22no—
851C2—41no—
852C2—62no—
853C2—121no—
854C2—182no—
855C2—1081no—
856C2D3×#369911yescharacteristic
857C2#1172250011yescharacteristic
858C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#546
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×C3×#3699C2semidirect
2. C2×D3×#611C2semidirect
3. #11721839C2semidirect
4. C9×#937C2semidirect
5. #11721292C2semidirect
6. #11721288C2semidirect
7. #67×Dic9C2semidirect
8. #611⋊Dic3C2semidirect
9. #11721270C2semidirect
10. C2×(C2×D3)⋊Dic9C2semidirect
11. #11721255C2semidirect
12. D9×(C2×D3)⋊C4C2semidirect
13. #11721035C2semidirect
14. #11721031C2semidirect
15. #11721018C2semidirect
20. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C22×C3⋊Dic9C22semidirect
25. C2×C9×#67C22semidirect
27. C2×C3×#611C22semidirect
28. C22×C3×Dic9C22semidirect
29. C22×C3×Dic9C22semidirect
31. C2×C3×C4×D9C22semidirect
32. C2×C3×Dic18C22semidirect
37. C2×Dic3×D9C22semidirect
38. #88551C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C9×#217C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
71. C2×#3699D3semidirect
109. C3×#611D4semidirect
167. C2×D4×C9C2×D3semidirect
176. C2×#611C2×D3semidirect
180. C22×Dic9C2×D3semidirect
181. C22×Dic9C2×D3semidirect
184. C2×C4×D9C2×D3semidirect
185. C2×Dic18C2×D3semidirect
222. C2×D3×C9#41semidirect
252. #937D9semidirect
334. #611#67semidirect
373. C2×C3×D4C2×D9semidirect
391. C2×#67C2×D9semidirect
417. #217C2×D9semidirect
431. (C2×D3)⋊C4C2×D9semidirect
532. C3×C9#546semidirect
655. C2×D4D3×D9semidirect
730. C2×D3#3699semidirect
755. C9#5829semidirect
848. C3#10589693semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#36992
C2×D3×#6112
#117218392
C9×#9372
#117212922
#117212882
#67×Dic92
#611⋊Dic32
#117212702
C2×(C2×D3)⋊Dic92
#117212552
D9×(C2×D3)⋊C42
#117210352
#117210312
#117210182
#105953043
#105896933