Finite Group Databasebeta

← #13150540

Subgroups — #13150540

Order 1728.

1080 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3697C211yesmaximal, characteristic, complemented
2C2×D3×#611C211yesmaximal, characteristic, complemented
3#11721818C211yesmaximal, characteristic, complemented
4C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#11721286C211yesmaximal, characteristic, complemented
6#11721277C211yesmaximal, characteristic, complemented
7Dic3×#611C211yesmaximal, characteristic, complemented
8#11721049C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721035C211yesmaximal, characteristic, complemented
11#11721033C211yesmaximal, characteristic, complemented
12#11721031C211yesmaximal, characteristic, complemented
13#11721018C211yesmaximal, characteristic, complemented
14#11721012C211yesmaximal, characteristic, complemented
15#11720982C211yesmaximal, characteristic, complemented
16#10595065—31nomaximal
17#10589592—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic, complemented
24C22×C9×Dic3C2211yescharacteristic, complemented
25C3×#3697—24no—
26C2×C3×D36C2211yescharacteristic, complemented
27C2×C3×C4×D9C2211yescharacteristic, complemented
28C2×C3×C4×D9C2211yescharacteristic, complemented
29C2×C3×Dic18C2211yescharacteristic, complemented
30D3×#611—24no—
31C2×#6195C2211yescharacteristic
32C2×#6194C2211yescharacteristic
33C2×#6194C2211yescharacteristic
34C2×#6194C2211yescharacteristic, complemented
35C2×D3×Dic9C2211yescharacteristic
36C2×#6192C2211yescharacteristic, complemented
37C2×Dic3×D9C2211yescharacteristic, complemented
38#88551C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42#88534C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C3×#235—31no—
56C2×D3×#67—31no—
57#64138—31no—
58C2×C3×(C2×D3)⋊C4D311yescharacteristic
59#63978—31no—
60#63976—31no—
61Dic3×#67—31no—
62#63922—31no—
63D3×(C2×D3)⋊C4—31no—
64#63907—31no—
65#63906—31no—
66#63905—31no—
67#63887—31no—
68#63885—31no—
69#63879—31no—
70C22×#611—31no—
71C2×#3697D311yescharacteristic, complemented
72C2×C9×C22⋊C4—31no—
73#63515—31no—
74#63492—31no—
75#63491—31no—
76#63491—61no—
77C4×#611—31no—
78#63447—31no—
79#63446—31no—
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#611⋊C4—31no—
84C22⋊C4×D9—31no—
85#63440—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9—22no—
89C22×D3×C9—22no—
90C22×D3×C9—41no—
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233—22no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C3×#611—22no—
106C3×#611D414yescomplemented
107C2×C9×Dic3—41no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C3×D36—22no—
113C3×C4×D9—22no—
114C3×C4×D9—22no—
115C3×Dic18—22no—
116#6195—22no—
117#6194—22no—
118#6194—22no—
119#6194—41no—
120D3×Dic9—22no—
121#6192—41no—
122Dic3×D9—41no—
123#5829—91no—
124#5490—91no—
125C23×C3×D3C2×D311yescharacteristic
126C22×D32—31no—
127C22×C32×C4C2×D311yescharacteristic
128C2×#638—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C22×C3×Dic3C2×D311yescharacteristic
132C3×#235—64no—
133C2×C3×D12—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×Dic6—31no—
137D3×#67—64no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#625—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#3752—31no—
150#3750—31no—
151#3750—31no—
152C3×(C2×D3)⋊C4C2×D311yescharacteristic
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—31no—
158#3722—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163Dic32—31no—
164C22×C4×C9—21no—
165C22×C4×C9—31no—
166C22×C4×C9C2×D311yescharacteristic, complemented
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—64no—
173C2×#611—61no—
174C2×#611C2×D311yescharacteristic
175C2×#611C2×D311yescharacteristic, complemented
176C22×Dic9—31no—
177#3697—24no—
178C2×D36—31no—
179C2×D36C2×D311yescharacteristic, complemented
180C2×C4×D9—31no—
181C2×C4×D9C2×D311yescharacteristic, complemented
182C2×C4×D9C2×D311yescharacteristic, complemented
183C2×Dic18C2×D311yescharacteristic, complemented
184C9×C22⋊C4—31no—
185C9×C22⋊C4—31no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188#3676—31no—
189#3676—31no—
190#3676—31no—
191#3676—61no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—61no—
198(C2×D9)⋊C4—61no—
199C4⋊Dic9—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—61no—
204Dic9⋊C4—61no—
205C4×Dic9—31no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9C2×D412yes—
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—44no—
219C2×D3×C9#4112yescomplemented
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9C2×D412yes—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C2×C3×#41—91no—
237C22×#67—91no—
238C2×D3×D4—91no—
239C2×#235—31no—
240C2×C3×C22⋊C4—31no—
241#953—91no—
242#947—91no—
243#946—91no—
244#939—91no—
245#939—91no—
246#937—91no—
247#937—91no—
248D4×Dic3—91no—
249#930—91no—
250#930—91no—
251#929—91no—
252#929—91no—
253#929—91no—
254#929—181no—
255C4×#67—91no—
256C4×#67—91no—
257C2×(C2×D3)⋊C4—91no—
258C2×(C2×D3)⋊C4D911yescharacteristic, complemented
259#885—91no—
260#884—91no—
261#884—91no—
262#883—91no—
263#882—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3—31no—
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×C4—22no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282#638—62no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C3×#67—34no—
287C3×#67—62no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—41no—
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C3×D12—62no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×Dic6—62no—
297#626—62no—
298#626—121no—
299#625—62no—
300#625—62no—
301#625—121no—
302D3×Dic3—62no—
303D3×Dic3—121no—
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—61no—
313C22×D9—62no—
314C22×D9—62no—
315C22×D9—121no—
316C22×D9C22×D311yescharacteristic
317C22×D9C22×D311yescharacteristic
318C2×C4×C9—22no—
319C2×C4×C9—21no—
320C2×C4×C9—21no—
321C2×C4×C9—31no—
322C2×C4×C9—31no—
323C2×C4×C9—42no—
324C2×C4×C9—121no—
325C2×C4×C9C22×D311yescharacteristic
326C2×C4×C9C22×D311yescharacteristic
327#611—22no—
328#611—62no—
329#611—62no—
330#611—62no—
331#611—62no—
332#611—122no—
333#611—121no—
334#611#6714yescomplemented
335C2×Dic9—31no—
336C2×Dic9—31no—
337C2×Dic9—31no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—62no—
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344D36—22no—
345D36—121no—
346C4×D9—22no—
347C4×D9—22no—
348C4×D9—121no—
349Dic18—22no—
350#546—271noSylow
351C2×C3×C9—22no—
352C2×C3×C9C22×D411yescharacteristic
353C2×C3×C9C2×#4111yescharacteristic
354C2×C3×C9H(5,𝔽2)11yescharacteristic
355C3⋊D9—41no—
356D3×C9—22no—
357D3×C9—41no—
358C3×D9—22no—
359C3×D9—41no—
360C24×C3—31no—
361C23×D3—91no—
362C23×D3—91no—
363C23×D3C2×D911yescharacteristic
364C3×#41—184no—
365C2×C3×Q8—91no—
366C2×C3×D4—91no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C22×C3×C4C2×D911yescharacteristic, complemented
374C22×C3×C4D3211yescharacteristic
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
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—184no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3C2×D911yescharacteristic, complemented
392D3×D4—184no—
393#235—64no—
394C2×D12—31no—
395C2×D12—91no—
396C2×D12—91no—
397C2×C4×D3—31no—
398C2×C4×D3—31no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×Dic6—31no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—31no—
406#217—91no—
407#217—91no—
408#217—91no—
409#217—91no—
410#217—91no—
411#217—91no—
412#217—181no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—91no—
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—181no—
424(C2×D3)⋊C4—181no—
425(C2×D3)⋊C4C2×D911yescharacteristic
426(C2×D3)⋊C4C2×D911yescharacteristic
427(C2×D3)⋊C4C2×D911yescharacteristic, complemented
428(C2×D3)⋊C4C2×D911yescharacteristic, complemented
429C4⋊Dic3—91no—
430C4⋊Dic3—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—181no—
438Dic3⋊C4—181no—
439C4×Dic3—91no—
440C4×Dic3—91no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32D3×D412yes—
444C22×C32C23×D311yescharacteristic
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—32no—
454C2×C3×D3—44no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3#23512yes—
461D32—124no—
462C32×C4—21no—
463C32×C4—21no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—32no—
470C3×Dic3—61no—
471C22×C9—21no—
472C22×C9—21no—
473C22×C9—21no—
474C22×C9—22no—
475C22×C9—32no—
476C22×C9—41no—
477C22×C9—41no—
478C22×C9—61no—
479C22×C9—61no—
480C22×C9—61no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9—124no—
484C22×C9C2×#6712yes—
485C22×C9C23×D311yescharacteristic
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—121no—
495C2×D9—121no—
496C2×D9—121no—
497C2×D9—124no—
498C2×D9C2×#6712yes—
499C4×C9—21no—
500C4×C9—21no—
501C4×C9—41no—
502C4×C9—41no—
503C4×C9—61no—
504C4×C9—61no—
505Dic9—21no—
506Dic9—61no—
507Dic9—61no—
508Dic9—61no—
509Dic9—121no—
510Dic9—121no—
511Dic9—121no—
512Dic9C2×#6712yes—
513C2×#41—91no—
514C22×D4—271no—
515#124—271no—
516#123—271no—
517#123—271no—
518C22⋊Q8—271no—
519#121—271no—
520#121—271no—
521#121—271no—
522#120—271no—
523#120—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—271no—
528C3×C9#54611yescharacteristic, complemented, Sylow
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—62no—
533C23×C3—62no—
534C23×C3—91no—
535C23×C3—91no—
536C23×C3—121no—
537C23×C3C22×D911yescharacteristic
538C23×C3C2×D3211yescharacteristic
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—31no—
542C22×D3—31no—
543C22×D3—41no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—181no—
547C22×D3—182no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—361no—
552C22×D3—361no—
553C22×D3C22×D911yescharacteristic
554C22×D3C22×D911yescharacteristic
555C3×Q8—182no—
556C3×D4—94no—
557C3×D4—182no—
558C3×D4—182no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—42no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—121no—
569C2×C3×C4—182no—
570C2×C3×C4—182no—
571C2×C3×C4C22×D911yescharacteristic
572C2×C3×C4C22×D911yescharacteristic
573C2×C3×C4C2×D3211yescharacteristic
574C2×C3×C4C2×D3211yescharacteristic
575#67—34no—
576#67—62no—
577#67—182no—
578#67—182no—
579#67—182no—
580#67—182no—
581#67—182no—
582#67—182no—
583#67—182no—
584#67—362no—
585#67—361no—
586#67—361no—
587#67—361no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—41no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—181no—
598C2×Dic3—181no—
599C2×Dic3—181no—
600C2×Dic3—182no—
601C2×Dic3—361no—
602C2×Dic3C22×D911yescharacteristic
603C2×Dic3C22×D911yescharacteristic
604D12—62no—
605D12—182no—
606D12—361no—
607C4×D3—62no—
608C4×D3—62no—
609C4×D3—182no—
610C4×D3—361no—
611Dic6—62no—
612C2×C32—22no—
613C2×C32C2×#23511yescharacteristic
614C2×C32C2×D3×D411yescharacteristic
615C2×C32#100411yescharacteristic
616C3⋊D3—121no—
617C3×D3—22no—
618C3×D3—41no—
619C3×D3—62no—
620C3×D3—121no—
621C2×C9—22no—
622C2×C9—21no—
623C2×C9—21no—
624C2×C9—21no—
625C2×C9—42no—
626C2×C9—62no—
627C2×C9—121no—
628C2×C9D3×#4111yescharacteristic
629C2×C9#100911yescharacteristic
630C2×C9C22×#6711yescharacteristic
631D9—22no—
632D9—41no—
633D9—121no—
634D9—241no—
635C24—31no—
636C24—271no—
637#41—184no—
638C2×Q8—91no—
639C2×D4—91no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—271no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—544no—
649C22×C4—31no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4D3×D911yescharacteristic, complemented
655C4⋊C4—271no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C42—271no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—32no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—92no—
687C22×C3—124no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3D4×D912yes—
694C22×C3C23×D911yescharacteristic
695C22×C3D3×#6712yes—
696C22×C3C22×D3211yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—32no—
703C2×D3—44no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—181no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—361no—
716C2×D3—361no—
717C2×D3—361no—
718C2×D3—364no—
719C2×D3—364no—
720C2×D3#369712yescomplemented
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—92no—
730C3×C4—181no—
731Dic3—21no—
732Dic3—21no—
733Dic3—32no—
734Dic3—61no—
735Dic3—181no—
736Dic3—181no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740Dic3—181no—
741Dic3—361no—
742Dic3—361no—
743Dic3—361no—
744C32#549011yescharacteristic
745C9—21no—
746C9#582911yescharacteristic, complemented
747C23—31no—
748C23—31no—
749C23—62no—
750C23—62no—
751C23—91no—
752C23—91no—
753C23—121no—
754C23—271no—
755C23—542no—
756C23—542no—
757C23—1081no—
758C23C2×D3×D911yescharacteristic
759Q8—182no—
760D4—94no—
761D4—182no—
762D4—182no—
763D4—542no—
764D4—542no—
765D4—542no—
766D4—542no—
767D4—1081no—
768D4—1081no—
769C2×C4—22no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—121no—
775C2×C4—182no—
776C2×C4—182no—
777C2×C4—271no—
778C2×C4—271no—
779C2×C4—271no—
780C2×C4—542no—
781C2×C4—1081no—
782C2×C4C2×D3×D911yescharacteristic
783C2×C4C2×D3×D911yescharacteristic
784C2×C3—22no—
785C2×C3—22no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—42no—
790C2×C3—62no—
791C2×C3—121no—
792C2×C3—182no—
793C2×C3—361no—
794C2×C3C2×#369711yescharacteristic
795C2×C3C2×D4×D911yescharacteristic
796C2×C3#6371011yescharacteristic
797C2×C3D3×#23511yescharacteristic
798C2×C3#6430711yescharacteristic
799C2×C3C2×D3×#6711yescharacteristic
800D3—22no—
801D3—41no—
802D3—62no—
803D3—121no—
804D3—361no—
805D3—361no—
806D3—721no—
807C22—21no—
808C22—21no—
809C22—32no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—92no—
816C22—124no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—541no—
823C22—541no—
824C22—541no—
825C22—1084no—
826C22D9×#6712yes—
827C22C22×D3×D911yescharacteristic
828C4—21no—
829C4—21no—
830C4—61no—
831C4—61no—
832C4—92no—
833C4—181no—
834C4—541no—
835C4—541no—
836C4—541no—
837C3—21no—
838C3#1058959211yescharacteristic, complemented
839C3#1059506511yescharacteristic
840C2—22no—
841C2—62no—
842C2—121no—
843C2—182no—
844C2—361no—
845C2—1081no—
846C2D3×#369711yescharacteristic
847C2#1172247611yescharacteristic
848C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
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×C3×#3697C2semidirect
2. C2×D3×#611C2semidirect
3. #11721818C2semidirect
4. C2×C9×(C2×D3)⋊C4C2semidirect
5. #11721286C2semidirect
6. #11721277C2semidirect
7. Dic3×#611C2semidirect
8. #11721049C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721035C2semidirect
11. #11721033C2semidirect
12. #11721031C2semidirect
13. #11721018C2semidirect
14. #11721012C2semidirect
15. #11720982C2semidirect
20. C22×C3×C4×C9C22semidirect
23. C2×C3×#611C22semidirect
24. C22×C9×Dic3C22semidirect
26. C2×C3×D36C22semidirect
27. C2×C3×C4×D9C22semidirect
28. C2×C3×C4×D9C22semidirect
29. C2×C3×Dic18C22semidirect
34. C2×#6194C22semidirect
36. C2×#6192C22semidirect
37. C2×Dic3×D9C22semidirect
38. #88551C22semidirect
39. #88536C22semidirect
40. #88536C22semidirect
41. #88534C22semidirect
42. #88534C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C9×(C2×D3)⋊C4C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
71. C2×#3697D3semidirect
106. C3×#611D4semidirect
166. C22×C4×C9C2×D3semidirect
175. C2×#611C2×D3semidirect
179. C2×D36C2×D3semidirect
181. C2×C4×D9C2×D3semidirect
182. C2×C4×D9C2×D3semidirect
183. C2×Dic18C2×D3semidirect
219. C2×D3×C9#41semidirect
258. C2×(C2×D3)⋊C4D9semidirect
334. #611#67semidirect
373. C22×C3×C4C2×D9semidirect
391. C22×Dic3C2×D9semidirect
427. (C2×D3)⋊C4C2×D9semidirect
428. (C2×D3)⋊C4C2×D9semidirect
528. C3×C9#546semidirect
654. C22×C4D3×D9semidirect
720. C2×D3#3697semidirect
746. C9#5829semidirect
838. C3#10589592semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#36972
C2×D3×#6112
#117218182
C2×C9×(C2×D3)⋊C42
#117212862
#117212772
Dic3×#6112
#117210492
D9×(C2×D3)⋊C42
#117210352
#117210332
#117210312
#117210182
#117210122
#117209822
#105950653
#105895923