Finite Group Databasebeta

← #13148294

Subgroups — #13148294

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×D3×#611C211yesmaximal, characteristic, complemented
2C2×#88642C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#63447C211yesmaximal, characteristic, complemented
6#11721287C211yesmaximal, characteristic, complemented
7#11721275C211yesmaximal, characteristic, complemented
8#11721256C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721048C211yesmaximal, characteristic, complemented
11#11721034C211yesmaximal, characteristic, complemented
12#11721032C211yesmaximal, characteristic, complemented
13C4×#6195C211yesmaximal, characteristic, complemented
14#11721018C211yesmaximal, characteristic, complemented
15#11721013C211yesmaximal, characteristic, complemented
16#10594280—31nomaximal
17#10589592—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C4×C3⋊D9C2211yescharacteristic, complemented
24C2×C3×#611C2211yescharacteristic
25C2×C4×D3×C9C2211yescharacteristic, complemented
26C2×C4×D3×C9C2211yescharacteristic, complemented
27C2×C3×Dic18C2211yescharacteristic, complemented
28D3×#611—24no—
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic, complemented
32C2×#6194C2211yescharacteristic
33C2×D3×Dic9C2211yescharacteristic
34C2×#6192C2211yescharacteristic, complemented
35C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37#88642—24no—
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×C4×Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3799—31no—
57#64093—31no—
58C3×#885—31no—
59C3×D3×C22⋊C4D311yescharacteristic
60#63977—31no—
61#63975—31no—
62#63958—31no—
63#63923—31no—
64#63921—31no—
65#63906—31no—
66#63905—31no—
67C4×#626—31no—
68#63887—31no—
69#63880—31no—
70C22×#611—31no—
71C2×#3697—31no—
72C2×C9×C22⋊C4—31no—
73#63515—31no—
74#63492—31no—
75#63491—31no—
76C4×#611—31no—
77#63447D311yescharacteristic, complemented
78#63446—31no—
79#63446—31no—
80#63446—61no—
81#63445—31no—
82#63444—31no—
83#611⋊C4—31no—
84C22⋊C4×D9—31no—
85#63440—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
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—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101#6233—41no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C4⋊(C3⋊D9)—22no—
105C4×C3⋊D9—41no—
106C3×#611—22no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C4×D3×C9—22no—
113C4×D3×C9—41no—
114C3×Dic18—22no—
115#6195—22no—
116#6195—22no—
117#6195D414yescomplemented
118#6194—22no—
119D3×Dic9—22no—
120#6192—41no—
121(C3⋊D9)⋊C4—22no—
122(C3⋊D9)⋊C4—22no—
123#5676—91no—
124#5490—91no—
125C23×C3×D3C2×D311yescharacteristic
126C22×D32—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4×C3⋊D3—31no—
131C2×C3×#67—31no—
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×Dic6—31no—
135D3×#67—64no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#624—31no—
142C2×#624—31no—
143C2×D3×Dic3—31no—
144#3799—64no—
145C24×C9—31no—
146C23×D9—31no—
147C32×C22⋊C4C2×D311yescharacteristic
148#3752—31no—
149#3750—31no—
150C3×#217—31no—
151C3×#217C2×D311yescharacteristic
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×C4×Dic3—31no—
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—31no—
159Dic3⋊Dic3—31no—
160#3722—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164C22×C4×C9—31no—
165C22×C4×C9—31no—
166C2×#611—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—64no—
173C2×#611—61no—
174C2×#611—61no—
175C2×#611C2×D311yescharacteristic
176C22×Dic9—31no—
177#3697—64no—
178C2×D36—31no—
179C2×D36—31no—
180C2×D36—61no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9—61no—
185C2×Dic18C2×D311yescharacteristic, complemented
186C9×C22⋊C4—21no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4C2×D311yescharacteristic, complemented
191#3676—31no—
192#3676—31no—
193#3676C2×D311yescharacteristic, complemented
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—61no—
198(C2×D9)⋊C4C2×D311yescharacteristic, complemented
199(C2×D9)⋊C4C2×D311yescharacteristic, complemented
200C4⋊Dic9—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—61no—
205C4×Dic9C2×D311yescharacteristic, complemented
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9C2×D412yes—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—44no—
221C2×D3×C9C2×D412yes—
222C2×D3×C9#4112yescomplemented
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C22×#67—91no—
237C2×#239—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#124—91no—
241C2×C3×C22⋊C4—31no—
242#953—91no—
243#946—91no—
244#938—91no—
245#930—91no—
246#929—91no—
247C4×#67—91no—
248#885—31no—
249#884—91no—
250#884—91no—
251#884—91no—
252#884—91no—
253#884—181no—
254#883—91no—
255#883—91no—
256#883—91no—
257#882—91no—
258#882—91no—
259#882—91no—
260#67⋊C4—91no—
261D3×C22⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4D911yescharacteristic, complemented
264#878—91no—
265C4×D12—91no—
266C4×D12—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
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—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—121no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C4⋊(C3⋊D3)—62no—
286C4×C3⋊D3—121no—
287C3×#67—62no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C3×C4×D3—22no—
294C3×C4×D3—41no—
295C3×Dic6—62no—
296#626—34no—
297#626—62no—
298#626—62no—
299#626—121no—
300#625—62no—
301#624—62no—
302#624—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9—31no—
307C23×C9—62no—
308C23×C9—62no—
309C23×C9—121no—
310C23×C9C22×D311yescharacteristic
311C22×D9—31no—
312C22×D9—31no—
313C22×D9—61no—
314C22×D9—61no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—121no—
318C22×D9C22×D311yescharacteristic
319C2×C4×C9—21no—
320C2×C4×C9—21no—
321C2×C4×C9—31no—
322C2×C4×C9—31no—
323C2×C4×C9—62no—
324C2×C4×C9—121no—
325C2×C4×C9C22×D311yescharacteristic
326C2×C4×C9C22×D311yescharacteristic
327#611—22no—
328#611—34no—
329#611—62no—
330#611—62no—
331#611—62no—
332#611—62no—
333#611—122no—
334#611—121no—
335#611—122no—
336C2×Dic9—31no—
337C2×Dic9—31no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—62no—
341C2×Dic9C22×D311yescharacteristic
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344D36—62no—
345D36—122no—
346D36—121no—
347C4×D9—62no—
348C4×D9—62no—
349C4×D9—121no—
350C4×D9—122no—
351Dic18—22no—
352#546—271noSylow
353C2×C3×C9—41no—
354C2×C3×C9C22×D411yescharacteristic
355C2×C3×C9C2×#4111yescharacteristic
356C2×C3×C9H(5,𝔽2)11yescharacteristic
357C3⋊D9—22no—
358C3⋊D9—41no—
359D3×C9—22no—
360D3×C9—22no—
361C3×D9—41no—
362C24×C3—31no—
363C23×D3—91no—
364C23×D3—91no—
365C23×D3C2×D911yescharacteristic
366C2×C3×Q8—91no—
367C2×C3×D4—91no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C2×#67—31no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—181no—
382C2×#67—181no—
383C2×#67—184no—
384C22×Dic3—91no—
385#239—184no—
386D3×D4—184no—
387#235—184no—
388C2×D12—91no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12—181no—
395C2×C4×D3—91no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—181no—
403C2×C4×D3C2×D911yescharacteristic, complemented
404C2×C4×D3C2×D911yescharacteristic, complemented
405C2×Dic6—31no—
406C3×C22⋊C4—21no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4C2×D911yescharacteristic, complemented
414C3×C22⋊C4D3211yescharacteristic
415C3×C42—91no—
416#217—31no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217C2×D911yescharacteristic, complemented
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
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—91no—
430(C2×D3)⋊C4—181no—
431(C2×D3)⋊C4C2×D911yescharacteristic
432(C2×D3)⋊C4C2×D911yescharacteristic
433C4⋊Dic3—91no—
434C4⋊Dic3—91no—
435C4⋊Dic3—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—181no—
442C4×Dic3—31no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—32no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—61no—
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—44no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3#23512yes—
462C2×C3×D3D3×D412yes—
463D32—124no—
464C32×C4—21no—
465C32×C4—21no—
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—32no—
478C22×C9—32no—
479C22×C9—41no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9—61no—
485C22×C9—61no—
486C22×C9—124no—
487C22×C9C23×D311yescharacteristic
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—32no—
492C2×D9—62no—
493C2×D9—61no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—121no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—124no—
504C4×C9—21no—
505C4×C9—21no—
506C4×C9—41no—
507C4×C9—41no—
508C4×C9—61no—
509C4×C9—61no—
510Dic9—21no—
511Dic9—21no—
512Dic9—62no—
513Dic9—61no—
514Dic9—61no—
515Dic9—121no—
516Dic9D3×D412yes—
517C2×#41—271no—
518C22×D4—271no—
519#124—91no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—271no—
524#121—271no—
525#121—271no—
526#120—271no—
527#120—271no—
528C4×D4—271no—
529C4×D4—271no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—271no—
532C3×C9#54611yescharacteristic, complemented, Sylow
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—31no—
536C23×C3—62no—
537C23×C3—62no—
538C23×C3—91no—
539C23×C3—121no—
540C23×C3C22×D911yescharacteristic
541C23×C3C2×D3211yescharacteristic
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—31no—
545C22×D3—41no—
546C22×D3—91no—
547C22×D3—91no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—181no—
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—182no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—62no—
567C2×C3×C4—91no—
568C2×C3×C4—91no—
569C2×C3×C4—91no—
570C2×C3×C4—121no—
571C2×C3×C4C22×D911yescharacteristic
572C2×C3×C4C22×D911yescharacteristic
573C2×C3×C4C2×D3211yescharacteristic
574C2×C3×C4C2×D3211yescharacteristic
575#67—62no—
576#67—94no—
577#67—182no—
578#67—182no—
579#67—182no—
580#67—182no—
581#67—182no—
582#67—182no—
583#67—362no—
584#67—361no—
585#67—361no—
586#67—361no—
587#67—362no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—181no—
596C2×Dic3—181no—
597C2×Dic3—182no—
598C2×Dic3C22×D911yescharacteristic
599C2×Dic3C22×D911yescharacteristic
600D12—94no—
601D12—182no—
602D12—182no—
603D12—182no—
604D12—182no—
605D12—362no—
606D12—361no—
607C4×D3—22no—
608C4×D3—41no—
609C4×D3—182no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—361no—
615C4×D3—361no—
616C4×D3—362no—
617Dic6—62no—
618C2×C32—41no—
619C2×C32C2×#23511yescharacteristic
620C2×C32C2×D3×D411yescharacteristic
621C2×C32#100411yescharacteristic
622C3⋊D3—62no—
623C3⋊D3—121no—
624C3×D3—22no—
625C3×D3—22no—
626C3×D3—121no—
627C2×C9—21no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—41no—
631C2×C9—62no—
632C2×C9—62no—
633C2×C9—81no—
634C2×C9C2×D3×D411yescharacteristic
635C2×C9D3×#4111yescharacteristic
636C2×C9#100911yescharacteristic
637D9—41no—
638D9—62no—
639D9—122no—
640D9—121no—
641D9—241no—
642C24—31no—
643C24—271no—
644#41—544no—
645C2×Q8—91no—
646C2×D4—91no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—544no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—271no—
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—91no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4D3×D911yescharacteristic, complemented
678C42—91no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—32no—
687C22×C3—32no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—124no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3C23×D911yescharacteristic
700C22×C3C22×D3211yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—44no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—92no—
710C2×D3—92no—
711C2×D3—182no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—361no—
723C2×D3—361no—
724C2×D3—361no—
725C2×D3—361no—
726C2×D3—361no—
727C2×D3—364no—
728C2×D3—364no—
729C2×D3#369712yescomplemented
730C2×D3D4×D912yes—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—61no—
738C3×C4—61no—
739C3×C4—92no—
740C3×C4—181no—
741C3×C4—181no—
742Dic3—21no—
743Dic3—21no—
744Dic3—32no—
745Dic3—61no—
746Dic3—61no—
747Dic3—182no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—181no—
752Dic3—361no—
753C32#549011yescharacteristic
754C9—21no—
755C9#567611yescharacteristic, complemented
756C23—31no—
757C23—31no—
758C23—62no—
759C23—62no—
760C23—91no—
761C23—121no—
762C23—271no—
763C23—271no—
764C23—542no—
765C23—542no—
766C23—1081no—
767C23C2×D3×D911yescharacteristic
768Q8—182no—
769D4—182no—
770D4—274no—
771D4—542no—
772D4—542no—
773D4—542no—
774D4—542no—
775D4—542no—
776D4—1081no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—62no—
781C2×C4—91no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—121no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—542no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—1081no—
791C2×C4C2×D3×D911yescharacteristic
792C2×C4C2×D3×D911yescharacteristic
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—41no—
797C2×C3—41no—
798C2×C3—62no—
799C2×C3—62no—
800C2×C3—81no—
801C2×C3—361no—
802C2×C3C2×#369711yescharacteristic
803C2×C3C2×D4×D911yescharacteristic
804C2×C3#6371011yescharacteristic
805C2×C3D3×#23511yescharacteristic
806C2×C3D32×D411yescharacteristic
807C2×C3#6431411yescharacteristic
808D3—22no—
809D3—22no—
810D3—121no—
811D3—182no—
812D3—182no—
813D3—362no—
814D3—361no—
815D3—361no—
816D3—721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—32no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—124no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—272no—
831C22—541no—
832C22—541no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22—1084no—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—21no—
840C4—61no—
841C4—61no—
842C4—92no—
843C4—181no—
844C4—181no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058959211yescharacteristic, complemented
849C3#1059428011yescharacteristic
850C2—41no—
851C2—62no—
852C2—62no—
853C2—361no—
854C2—542no—
855C2—1081no—
856C2D3×#369711yescharacteristic
857C2D3×D4×D911yescharacteristic
858C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D3×#611C2semidirect
2. C2×#88642C2semidirect
3. #11721730C2semidirect
4. D3×C9×C22⋊C4C2semidirect
5. C3×#63447C2semidirect
6. #11721287C2semidirect
7. #11721275C2semidirect
8. #11721256C2semidirect
9. #11721051C2semidirect
10. #11721048C2semidirect
11. #11721034C2semidirect
12. #11721032C2semidirect
13. C4×#6195C2semidirect
14. #11721018C2semidirect
15. #11721013C2semidirect
21. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
23. C2×C4×C3⋊D9C22semidirect
25. C2×C4×D3×C9C22semidirect
26. C2×C4×D3×C9C22semidirect
27. C2×C3×Dic18C22semidirect
31. C2×#6195C22semidirect
34. C2×#6192C22semidirect
35. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C9×#217C22semidirect
42. C3×#3676C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×C4×Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic9⋊Dic3C22semidirect
77. #63447D3semidirect
117. #6195D4semidirect
185. C2×Dic18C2×D3semidirect
190. C9×C22⋊C4C2×D3semidirect
193. #3676C2×D3semidirect
198. (C2×D9)⋊C4C2×D3semidirect
199. (C2×D9)⋊C4C2×D3semidirect
205. C4×Dic9C2×D3semidirect
222. C2×D3×C9#41semidirect
263. D3×C22⋊C4D9semidirect
403. C2×C4×D3C2×D9semidirect
404. C2×C4×D3C2×D9semidirect
413. C3×C22⋊C4C2×D9semidirect
420. #217C2×D9semidirect
532. C3×C9#546semidirect
677. C22⋊C4D3×D9semidirect
729. C2×D3#3697semidirect
755. C9#5676semidirect
848. C3#10589592semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×#886422
#117217302
D3×C9×C22⋊C42
C3×#634472
#117212872
#117212752
#117212562
#117210512
#117210482
#117210342
#117210322
C4×#61952
#117210182
#117210132
#105942803
#105895923