Finite Group Databasebeta

← #13148273

Subgroups — #13148273

Order 1728.

1076 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6194C211yesmaximal, characteristic, complemented
2C2×#88641C211yesmaximal, characteristic, complemented
3#11721724C211yesmaximal, characteristic, complemented
4D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#63444C211yesmaximal, characteristic, complemented
6#11721286C211yesmaximal, characteristic, complemented
7#611⋊Dic3C211yesmaximal, characteristic, complemented
8D9×#217C211yesmaximal, characteristic, complemented
9#11721042C211yesmaximal, characteristic, complemented
10#11721037C211yesmaximal, characteristic, complemented
11#11721032C211yesmaximal, characteristic, complemented
12#11720989C211yesmaximal, characteristic, complemented
13#11720982C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15#11720976C211yesmaximal, characteristic, complemented
16#10594184—31nomaximal
17#10589592—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×#6226C2211yescharacteristic, complemented
22C2×C3×#611C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic, complemented
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×C3×D36C2211yescharacteristic, complemented
26C2×C3×D36C2211yescharacteristic, complemented
27C2×#6194—24no—
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31C2×#6194C2211yescharacteristic
32C2×#6194C2211yescharacteristic, complemented
33C2×#6194C2211yescharacteristic, complemented
34C2×Dic3×D9C2211yescharacteristic, complemented
35C2×Dic3×D9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37#88641—24no—
38C3×C9×C22⋊C4C2211yescharacteristic
39#88551C2211yescharacteristic
40C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42#88534C2211yescharacteristic, complemented
43C9×#217C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×#625—31no—
56C2×#3795—31no—
57#64087—31no—
58C3×#882—31no—
59C3×D3×C22⋊C4D311yescharacteristic
60#63976—31no—
61#67⋊Dic3—31no—
62D3×#217—31no—
63#63913—31no—
64#63908—31no—
65#63905—31no—
66#63891—31no—
67#63885—31no—
68#63885—31no—
69#63879—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#63447—31no—
78#63446—31no—
79#63446—31no—
80#63445—31no—
81#63444D311yescharacteristic, complemented
82#611⋊C4—31no—
83C22⋊C4×D9—31no—
84#63440—31no—
85#63440—61no—
86C23×C3×C9C2311yescharacteristic
87C22×D3×C9—22no—
88C22×D3×C9—22no—
89C22×D3×C9—41no—
90C22×D3×C9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×C3×D9—22no—
93C22×C3×D9—22no—
94C22×C3×D9—41no—
95C22×C3×D9C2311yescharacteristic
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3⋊Dic9—22no—
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105#6226—22no—
106C3×#611—22no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C4×D3×C9—22no—
111C4×D3×C9—41no—
112C3×D36—22no—
113C3×D36—41no—
114#6194—22no—
115#6194—22no—
116#6194—22no—
117#6194—22no—
118#6194—41no—
119#6194D414yescomplemented
120Dic3×D9—22no—
121Dic3×D9—22no—
122Dic3×D9—41no—
123#5591—91no—
124#5490—91no—
125C23×C3×D3—31no—
126C23×C3×D3C2×D311yescharacteristic
127C22×C3⋊Dic3—31no—
128C2×#634—31no—
129C2×C3×#67—31no—
130C2×C3×D12—31no—
131C2×C3×D12—31no—
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×#625—31no—
135C2×#625—31no—
136C2×#625—31no—
137C2×#625—31no—
138C2×#625—31no—
139C2×#625—31no—
140C2×#625—64no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144#3795—64no—
145C24×C9—31no—
146C23×D9C2×D311yescharacteristic
147C32×C22⋊C4C2×D311yescharacteristic
148#3757—31no—
149C4⋊(C3⋊Dic3)—31no—
150#3750—31no—
151#3750—31no—
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×(C2×D3)⋊C4C2×D311yescharacteristic
157Dic3⋊Dic3—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—
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×#611C2×D311yescharacteristic
174C22×Dic9—31no—
175C22×Dic9—61no—
176#3697—64no—
177C2×D36C2×D311yescharacteristic, complemented
178C2×D36C2×D311yescharacteristic, complemented
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×Dic18—31no—
183C2×Dic18—61no—
184C9×C22⋊C4—21no—
185C9×C22⋊C4—31no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4C2×D311yescharacteristic
189#3676—31no—
190#3676—31no—
191#3676—31no—
192#3676—61no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4C2×D311yescharacteristic, complemented
197(C2×D9)⋊C4C2×D311yescharacteristic, complemented
198C4⋊Dic9—31no—
199C4⋊Dic9—61no—
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×C9#4112yescomplemented
209C22×C3×C9C2411yescharacteristic
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—44no—
216C2×D3×C9C2×D412yes—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—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×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9—21no—
232C3⋊Dic9C2×D412yes—
233C9×Dic3—21no—
234C9×Dic3—21no—
235C3×Dic9—21no—
236C22×#67—91no—
237C22×#67—91no—
238C2×#237—91no—
239C2×#235—91no—
240C3×#120—91no—
241C2×C3×C22⋊C4—31no—
242#953—91no—
243C2×#217—91no—
244#939—91no—
245#939—91no—
246#938—91no—
247#937—91no—
248D4×Dic3—91no—
249#930—91no—
250#929—91no—
251C4×#67—91no—
252#886—91no—
253#885—91no—
254#885—91no—
255#884—91no—
256#884—91no—
257#883—91no—
258#883—91no—
259#882—31no—
260#67⋊C4—91no—
261#67⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4D911yescharacteristic, complemented
264#878—91no—
265#878—91no—
266#878—181no—
267C23×C32C22×D311yescharacteristic
268C22×C3×D3—22no—
269C22×C3×D3—22no—
270C22×C3×D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—41no—
274C22×C3×D3—62no—
275C22×C3×D3—62no—
276C22×C3×D3—121no—
277C22×C3×D3C22×D311yescharacteristic
278C22×C3×D3C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—62no—
286#634—62no—
287C3×#67—62no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C3×D12—62no—
292C3×D12—121no—
293C3×C4×D3—22no—
294C3×C4×D3—41no—
295#625—34no—
296#625—62no—
297#625—62no—
298#625—62no—
299#625—62no—
300#625—121no—
301D3×Dic3—62no—
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—22no—
312C22×D9—22no—
313C22×D9—41no—
314C22×D9C22×D311yescharacteristic
315C22×D9C22×D311yescharacteristic
316C22×D9C22×D311yescharacteristic
317C2×C4×C9—21no—
318C2×C4×C9—21no—
319C2×C4×C9—31no—
320C2×C4×C9—31no—
321C2×C4×C9—62no—
322C2×C4×C9—121no—
323C2×C4×C9C22×D311yescharacteristic
324C2×C4×C9C22×D311yescharacteristic
325#611—22no—
326#611—34no—
327#611—62no—
328#611—62no—
329#611—62no—
330#611—62no—
331#611—121no—
332C2×Dic9—31no—
333C2×Dic9—31no—
334C2×Dic9—31no—
335C2×Dic9—31no—
336C2×Dic9—61no—
337C2×Dic9—61no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—62no—
341C2×Dic9—122no—
342C2×Dic9C22×D311yescharacteristic
343D36—22no—
344D36—41no—
345C4×D9—62no—
346C4×D9—62no—
347C4×D9—121no—
348Dic18—62no—
349Dic18—122no—
350#546—271noSylow
351C2×C3×C9—22no—
352C2×C3×C9C22×D411yescharacteristic
353C2×C3×C9C2×#4111yescharacteristic
354C2×C3×C9H(5,𝔽2)11yescharacteristic
355D3×C9—22no—
356D3×C9—41no—
357C3×D9—22no—
358C3×D9—41no—
359C3×D9—41no—
360C24×C3—31no—
361C24×C3—91no—
362C23×D3—31no—
363C23×D3C2×D911yescharacteristic
364C2×C3×D4—91no—
365C2×C3×D4—91no—
366C2×C3×D4—91no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C2×#67—31no—
370C2×#67—91no—
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—91no—
382C2×#67—184no—
383C2×#67—184no—
384C22×Dic3—91no—
385C22×Dic3—91no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—181no—
390#237—184no—
391#235—184no—
392C2×D12—31no—
393C2×D12—31no—
394C2×C4×D3—91no—
395C2×C4×D3—91no—
396C2×C4×D3—91no—
397C2×C4×D3C2×D911yescharacteristic, complemented
398C2×C4×D3C2×D911yescharacteristic, complemented
399C2×Dic6—91no—
400C2×Dic6—91no—
401C2×Dic6—181no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—91no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4C2×D911yescharacteristic
409C3×C22⋊C4D3211yescharacteristic
410#217—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—181no—
418#217C2×D911yescharacteristic
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
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)⋊C4C2×D911yescharacteristic, complemented
427(C2×D3)⋊C4C2×D911yescharacteristic, complemented
428C4⋊Dic3—91no—
429C4⋊Dic3—91no—
430C4⋊Dic3—91no—
431C4⋊Dic3—181no—
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×C32#23512yes—
444C22×C32C23×D311yescharacteristic
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—32no—
451C2×C3×D3—44no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—124no—
461C2×C3×D3D3×D412yes—
462C32×C4—21no—
463C32×C4—21no—
464C3⋊Dic3—32no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
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×C9#23712yescomplemented
485C22×C9C23×D311yescharacteristic
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—21no—
492C2×D9—21no—
493C2×D9—21no—
494C2×D9—44no—
495C2×D9D3×D412yes—
496C4×C9—21no—
497C4×C9—21no—
498C4×C9—41no—
499C4×C9—41no—
500C4×C9—61no—
501C4×C9—61no—
502Dic9—21no—
503Dic9—32no—
504Dic9—62no—
505Dic9—61no—
506Dic9—61no—
507Dic9—61no—
508Dic9—121no—
509Dic9—121no—
510Dic9—121no—
511C2×#41—271no—
512C22×D4—271no—
513#124—271no—
514#123—271no—
515#123—271no—
516C22⋊Q8—271no—
517#121—271no—
518#121—271no—
519#121—271no—
520#120—91no—
521#120—271no—
522C4×D4—271no—
523C4×D4—271no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—271no—
526C3×C9#54611yescharacteristic, complemented, Sylow
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3—91no—
533C23×C3—91no—
534C23×C3—91no—
535C23×C3—121no—
536C23×C3—182no—
537C23×C3—182no—
538C23×C3—361no—
539C23×C3C22×D911yescharacteristic
540C23×C3C2×D3211yescharacteristic
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—31no—
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—41no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—121no—
550C22×D3C22×D911yescharacteristic
551C22×D3C22×D911yescharacteristic
552C3×D4—182no—
553C3×D4—182no—
554C3×D4—361no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—62no—
560C2×C3×C4—91no—
561C2×C3×C4—121no—
562C2×C3×C4C22×D911yescharacteristic
563C2×C3×C4C22×D911yescharacteristic
564C2×C3×C4C2×D3211yescharacteristic
565C2×C3×C4C2×D3211yescharacteristic
566#67—62no—
567#67—94no—
568#67—94no—
569#67—182no—
570#67—182no—
571#67—182no—
572#67—182no—
573#67—182no—
574#67—182no—
575#67—182no—
576#67—182no—
577#67—361no—
578#67—361no—
579C2×Dic3—31no—
580C2×Dic3—91no—
581C2×Dic3—91no—
582C2×Dic3—91no—
583C2×Dic3—91no—
584C2×Dic3—91no—
585C2×Dic3—91no—
586C2×Dic3—91no—
587C2×Dic3—91no—
588C2×Dic3—181no—
589C2×Dic3—181no—
590C2×Dic3—181no—
591C2×Dic3—181no—
592C2×Dic3—182no—
593C2×Dic3—182no—
594C2×Dic3—182no—
595C2×Dic3—182no—
596C2×Dic3—362no—
597C2×Dic3—361no—
598C2×Dic3C22×D911yescharacteristic
599C2×Dic3C22×D911yescharacteristic
600D12—62no—
601D12—121no—
602C4×D3—22no—
603C4×D3—41no—
604C4×D3—182no—
605C4×D3—182no—
606C4×D3—361no—
607Dic6—182no—
608Dic6—182no—
609Dic6—362no—
610C2×C32—22no—
611C2×C32C2×#23511yescharacteristic
612C2×C32C2×D3×D411yescharacteristic
613C2×C32#100411yescharacteristic
614C3×D3—22no—
615C3×D3—41no—
616C3×D3—62no—
617C3×D3—121no—
618C3×D3—121no—
619C2×C9—22no—
620C2×C9—21no—
621C2×C9—21no—
622C2×C9—21no—
623C2×C9—42no—
624C2×C9—62no—
625C2×C9—121no—
626C2×C9C2×D3×D411yescharacteristic
627C2×C9C2×#23711yescharacteristic
628C2×C9#100411yescharacteristic
629D9—22no—
630D9—41no—
631D9—41no—
632C24—31no—
633C24—91no—
634#41—544no—
635C2×Q8—271no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4—91no—
639C2×D4—271no—
640C2×D4—271no—
641C2×D4—271no—
642C2×D4—271no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—544no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—271no—
649C22×C4—271no—
650C22×C4—271no—
651C22×C4—271no—
652C4⋊C4—271no—
653C4⋊C4—271no—
654C4⋊C4—271no—
655C4⋊C4—271no—
656C22⋊C4—31no—
657C22⋊C4—31no—
658C22⋊C4—31no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4D3×D911yescharacteristic
668C42—271no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—22no—
674C22×C3—21no—
675C22×C3—32no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—92no—
684C22×C3—124no—
685C22×C3—181no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3—364no—
694C22×C3#369712yescomplemented
695C22×C3C23×D911yescharacteristic
696C22×C3#379512yes—
697C22×C3C22×D3211yescharacteristic
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—32no—
704C2×D3—44no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—124no—
714C2×D3D4×D912yes—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—181no—
724Dic3—21no—
725Dic3—21no—
726Dic3—61no—
727Dic3—92no—
728Dic3—92no—
729Dic3—182no—
730Dic3—181no—
731Dic3—181no—
732Dic3—181no—
733Dic3—181no—
734Dic3—181no—
735Dic3—181no—
736Dic3—361no—
737Dic3—361no—
738Dic3—361no—
739C32#549011yescharacteristic
740C9—21no—
741C9#559111yescharacteristic, complemented
742C23—31no—
743C23—31no—
744C23—62no—
745C23—62no—
746C23—91no—
747C23—91no—
748C23—91no—
749C23—121no—
750C23—182no—
751C23—182no—
752C23—361no—
753C23C2×D3×D911yescharacteristic
754Q8—542no—
755D4—182no—
756D4—182no—
757D4—274no—
758D4—361no—
759D4—542no—
760D4—542no—
761D4—542no—
762D4—542no—
763D4—1081no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—62no—
767C2×C4—91no—
768C2×C4—121no—
769C2×C4—271no—
770C2×C4—271no—
771C2×C4—271no—
772C2×C4—271no—
773C2×C4—542no—
774C2×C4—542no—
775C2×C4—542no—
776C2×C4—1081no—
777C2×C4C2×D3×D911yescharacteristic
778C2×C4C2×D3×D911yescharacteristic
779C2×C3—22no—
780C2×C3—22no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—42no—
785C2×C3—62no—
786C2×C3—121no—
787C2×C3—182no—
788C2×C3—361no—
789C2×C3—361no—
790C2×C3C2×#369711yescharacteristic
791C2×C3C2×D4×D911yescharacteristic
792C2×C3#6371011yescharacteristic
793C2×C3C2×#379511yescharacteristic
794C2×C3D32×D411yescharacteristic
795C2×C3#6431311yescharacteristic
796D3—22no—
797D3—41no—
798D3—62no—
799D3—121no—
800D3—121no—
801C22—21no—
802C22—21no—
803C22—32no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—92no—
810C22—124no—
811C22—181no—
812C22—181no—
813C22—181no—
814C22—181no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—364no—
820C22#8864112yescomplemented
821C22C22×D3×D911yescharacteristic
822C4—21no—
823C4—21no—
824C4—61no—
825C4—61no—
826C4—181no—
827C4—272no—
828C4—541no—
829C4—541no—
830C4—541no—
831C3—21no—
832C3#1058959211yescharacteristic, complemented
833C3#1059418411yescharacteristic
834C2—22no—
835C2—62no—
836C2—121no—
837C2—182no—
838C2—361no—
839C2—361no—
840C2C2×#8864111yescharacteristic
841C2D3×D4×D911yescharacteristic
842C2#1172249911yescharacteristic
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. C22×#6194C2semidirect
2. C2×#88641C2semidirect
3. #11721724C2semidirect
4. D3×C9×C22⋊C4C2semidirect
5. C3×#63444C2semidirect
6. #11721286C2semidirect
7. #611⋊Dic3C2semidirect
8. D9×#217C2semidirect
9. #11721042C2semidirect
10. #11721037C2semidirect
11. #11721032C2semidirect
12. #11720989C2semidirect
13. #11720982C2semidirect
14. #11720982C2semidirect
15. #11720976C2semidirect
21. C2×#6226C22semidirect
23. C2×C4×D3×C9C22semidirect
24. C2×C4×D3×C9C22semidirect
25. C2×C3×D36C22semidirect
26. C2×C3×D36C22semidirect
32. C2×#6194C22semidirect
33. C2×#6194C22semidirect
34. C2×Dic3×D9C22semidirect
35. C2×Dic3×D9C22semidirect
36. C2×Dic3×D9C22semidirect
40. C4⋊(C3⋊Dic9)C22semidirect
41. #88534C22semidirect
42. #88534C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
81. #63444D3semidirect
119. #6194D4semidirect
177. C2×D36C2×D3semidirect
178. C2×D36C2×D3semidirect
196. (C2×D9)⋊C4C2×D3semidirect
197. (C2×D9)⋊C4C2×D3semidirect
208. C22×C3×C9#41semidirect
263. D3×C22⋊C4D9semidirect
397. C2×C4×D3C2×D9semidirect
398. C2×C4×D3C2×D9semidirect
426. (C2×D3)⋊C4C2×D9semidirect
427. (C2×D3)⋊C4C2×D9semidirect
484. C22×C9#237semidirect
526. C3×C9#546semidirect
694. C22×C3#3697semidirect
741. C9#5591semidirect
820. C22#88641semidirect
832. C3#10589592semidirect

Maximal subgroups

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

subgroupindex
C22×#61942
C2×#886412
#117217242
D3×C9×C22⋊C42
C3×#634442
#117212862
#611⋊Dic32
D9×#2172
#117210422
#117210372
#117210322
#117209892
#117209822
#117209762
#105941843
#105895923