Finite Group Databasebeta

← #13148134

Subgroups — #13148134

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×#6192C211yesmaximal, characteristic, complemented
2C2×#88634C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
4C3×#63444C211yesmaximal, characteristic, complemented
5C9×#878C211yesmaximal, characteristic, complemented
6#11721278C211yesmaximal, characteristic, complemented
7Dic3×#611C211yesmaximal, characteristic, complemented
8D9×#217C211yesmaximal, characteristic, complemented
9#11721007C211yesmaximal, characteristic, complemented
10#11721003C211yesmaximal, characteristic, complemented
11#11720988C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720983C211yesmaximal, characteristic, complemented
14#11720978C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10594063—31nomaximal
17#10589732—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic, complemented
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic, complemented
25C2×C3×D36C2211yescharacteristic, complemented
26C2×C9×Dic6C2211yescharacteristic, complemented
27C2×#6192—24no—
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic, complemented
34C2×Dic3×D9C2211yescharacteristic, complemented
35C2×Dic3×D9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37#88634—24no—
38C3×C9×C22⋊C4C2211yescharacteristic
39#88551C2211yescharacteristic
40#88536C2211yescharacteristic, complemented
41#88536C2211yescharacteristic, complemented
42C9×#217C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C9×C4⋊Dic3C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47C9×Dic3⋊C4C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×#626—31no—
56C2×#3796—31no—
57C22⋊C4×C3⋊D3—31no—
58C3×#882—31no—
59C3×#878D311yescharacteristic
60#63981—31no—
61Dic3×#67—31no—
62D3×#217—31no—
63#63916—31no—
64#63907—31no—
65#63890—31no—
66#63886—31no—
67#63886—31no—
68#63881—31no—
69#63853—31no—
70C2×#3701—31no—
71C22×D36—31no—
72C9×C22⋊Q8—31no—
73#63509—31no—
74C4×#611—31no—
75#63457—31no—
76#63457—31no—
77#63457—31no—
78#63456—31no—
79#63456—31no—
80#63455—31no—
81#63444—31no—
82#63444D311yescharacteristic, complemented
83C22⋊C4×D9—31no—
84C22⋊C4×D9—31no—
85C22⋊C4×D9—61no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
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⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C4×C3⋊D9—22no—
103C4×C3⋊D9—41no—
104C3×#611—22no—
105C2×C9×Dic3—22no—
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C3×D36—22no—
112C3×D36—41no—
113C9×Dic6—22no—
114#6192—22no—
115#6192—22no—
116#6192—22no—
117#6192—22no—
118#6192—41no—
119#6192D414yescomplemented
120Dic3×D9—22no—
121Dic3×D9—22no—
122Dic3×D9—41no—
123#5630—91no—
124#5591—91no—
125C23×C3⋊D3—31no—
126C23×C3×D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C3×#67—31no—
130C22×C3×Dic3C2×D311yescharacteristic
131C2×C3×D12—31no—
132C2×C3×D12—31no—
133C2×C3×Dic6C2×D311yescharacteristic
134C2×#626—31no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—64no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144#3796—64no—
145C23×D9—31no—
146C23×D9—61no—
147C23×D9C2×D311yescharacteristic
148C32×C22⋊C4C2×D311yescharacteristic
149#3757—31no—
150#3752—31no—
151#3752—31no—
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×C4⋊Dic3C2×D311yescharacteristic
156C3×Dic3⋊C4C2×D311yescharacteristic
157C3×Dic3⋊C4C2×D311yescharacteristic
158Dic3⋊Dic3—31no—
159#3722—31no—
160#3722—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164Dic32—31no—
165C2×Q8×C9—31no—
166C22×C4×C9—31no—
167C2×#611C2×D311yescharacteristic
168#3701—64no—
169C2×D36—31no—
170C2×D36—31no—
171C2×D36—31no—
172C2×D36—31no—
173C2×D36—31no—
174C2×D36—31no—
175C2×D36—64no—
176C2×D36C2×D311yescharacteristic, complemented
177C2×D36C2×D311yescharacteristic, complemented
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—61no—
184C2×C4×D9—61no—
185C9×C4⋊C4—31no—
186C9×C4⋊C4—31no—
187C9×C4⋊C4—31no—
188C9×C22⋊C4—21no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4C2×D311yescharacteristic
191#3676—31no—
192#3676—61no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—61no—
201(C2×D9)⋊C4—61no—
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4—31no—
205C4×Dic9—31no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9#4112yescomplemented
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⋊D9—44no—
216C2×C3⋊D9C2×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—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C9×Dic3C2×D412yes—
235C3×Dic9—21no—
236C22×#67—91no—
237C2×#239—91no—
238C2×#237—91no—
239C22×D12—91no—
240C3×C22⋊Q8—31no—
241C3×#120—91no—
242C2×#217—91no—
243#947—91no—
244#939—91no—
245#939—91no—
246#938—91no—
247#937—91no—
248D4×Dic3—91no—
249C4×#67—91no—
250#895—91no—
251#895—91no—
252#895—91no—
253#894—91no—
254#894—91no—
255#893—91no—
256#886—91no—
257#885—91no—
258#883—91no—
259#882—31no—
260#882—91no—
261#67⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—181no—
266#878D911yescharacteristic, complemented
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—121no—
273C22×C3×D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—62no—
277C22×C3×D3—62no—
278C22×C3×D3—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C4×C3⋊D3—62no—
284C4×C3⋊D3—121no—
285C3×#67—62no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C3×D12—62no—
293C3×D12—121no—
294C3×Dic6—22no—
295#626—34no—
296#626—62no—
297#626—62no—
298#626—62no—
299#626—62no—
300#626—121no—
301D3×Dic3—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9C22×D311yescharacteristic
306C22×D9—22no—
307C22×D9—22no—
308C22×D9—31no—
309C22×D9—31no—
310C22×D9—41no—
311C22×D9—61no—
312C22×D9—61no—
313C22×D9—62no—
314C22×D9—64no—
315C22×D9—62no—
316C22×D9—122no—
317C22×D9—121no—
318C22×D9—122no—
319C22×D9C22×D311yescharacteristic
320C22×D9C22×D311yescharacteristic
321C22×D9C22×D311yescharacteristic
322Q8×C9—62no—
323C2×C4×C9—21no—
324C2×C4×C9—21no—
325C2×C4×C9—31no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—62no—
330C2×C4×C9C22×D311yescharacteristic
331C2×C4×C9C22×D311yescharacteristic
332#611—22no—
333C2×Dic9—31no—
334C2×Dic9—31no—
335C2×Dic9—61no—
336C2×Dic9—61no—
337C2×Dic9C22×D311yescharacteristic
338D36—22no—
339D36—34no—
340D36—41no—
341D36—62no—
342D36—62no—
343D36—62no—
344D36—62no—
345D36—121no—
346C4×D9—62no—
347C4×D9—62no—
348C4×D9—62no—
349C4×D9—122no—
350C4×D9—121no—
351C4×D9—121no—
352C4×D9—122no—
353#546—271noSylow
354C2×C3×C9—22no—
355C2×C3×C9C22×D411yescharacteristic
356C2×C3×C9C2×#4111yescharacteristic
357C2×C3×C9H(5,𝔽2)11yescharacteristic
358C3⋊D9—22no—
359C3⋊D9—41no—
360C3×D9—22no—
361C3×D9—41no—
362C3×D9—41no—
363C24×C3—91no—
364C23×D3—31no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—181no—
368C2×C3×Q8—31no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C2×C3×D4—91no—
372C22×C3×C4—31no—
373C2×#67—31no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—184no—
381C22×Dic3—91no—
382C22×Dic3—91no—
383C22×Dic3—91no—
384C22×Dic3C2×D911yescharacteristic
385#239—184no—
386#237—184no—
387C2×D12—31no—
388C2×D12—31no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12—91no—
395C2×D12—184no—
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—91no—
403C2×C4×D3—181no—
404C2×C4×D3—181no—
405C2×Dic6C2×D911yescharacteristic, complemented
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4C2×D911yescharacteristic
414C3×C22⋊C4D3211yescharacteristic
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—181no—
421#217C2×D911yescharacteristic
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
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—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—181no—
436(C2×D3)⋊C4—181no—
437C4⋊Dic3—91no—
438C4⋊Dic3C2×D911yescharacteristic, complemented
439Dic3⋊C4—91no—
440Dic3⋊C4C2×D911yescharacteristic, complemented
441Dic3⋊C4C2×D911yescharacteristic, complemented
442C4×Dic3—91no—
443C4×Dic3—91no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32#23912yes—
447C22×C32C23×D311yescharacteristic
448C2×C3⋊D3—32no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—124no—
455C2×C3×D3—32no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—124no—
465C32×C4—21no—
466C32×C4—21no—
467C3⋊Dic3—61no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—61no—
473C3×Dic3D3×D412yes—
474C22×C9—21no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—22no—
478C22×C9—41no—
479C22×C9—41no—
480C22×C9#23712yescomplemented
481C22×C9C23×D311yescharacteristic
482C2×D9—21no—
483C2×D9—21no—
484C2×D9—21no—
485C2×D9—21no—
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—32no—
491C2×D9—44no—
492C2×D9—62no—
493C2×D9—62no—
494C2×D9—62no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—62no—
498C2×D9—61no—
499C2×D9—61no—
500C2×D9—61no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—124no—
504C2×D9—128no—
505C2×D9D3×D412yes—
506C4×C9—21no—
507C4×C9—21no—
508C4×C9—32no—
509C4×C9—41no—
510C4×C9—41no—
511C4×C9—61no—
512C4×C9—61no—
513C4×C9—61no—
514Dic9—21no—
515Dic9—61no—
516Dic9—61no—
517Dic9—121no—
518Dic9—121no—
519C2×#41—271no—
520C22×D4—271no—
521#124—271no—
522#123—271no—
523#123—271no—
524C22⋊Q8—31no—
525#121—271no—
526#121—271no—
527#121—271no—
528#120—91no—
529#120—271no—
530C4×D4—271no—
531C4×D4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C3×C9#54611yescharacteristic, complemented, Sylow
535C23×C3—21no—
536C23×C3—91no—
537C23×C3—91no—
538C23×C3—91no—
539C23×C3—182no—
540C23×C3—182no—
541C23×C3—361no—
542C23×C3C22×D911yescharacteristic
543C23×C3C2×D3211yescharacteristic
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—31no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—91no—
550C22×D3—91no—
551C22×D3—91no—
552C22×D3—91no—
553C22×D3—121no—
554C22×D3—181no—
555C22×D3—181no—
556C22×D3—182no—
557C22×D3—182no—
558C22×D3—184no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—362no—
562C22×D3—361no—
563C22×D3—361no—
564C22×D3—362no—
565C3×Q8—62no—
566C3×D4—182no—
567C3×D4—182no—
568C3×D4—361no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—62no—
576C2×C3×C4—91no—
577C2×C3×C4C22×D911yescharacteristic
578C2×C3×C4C22×D911yescharacteristic
579C2×C3×C4C2×D3211yescharacteristic
580C2×C3×C4C2×D3211yescharacteristic
581#67—62no—
582#67—94no—
583#67—182no—
584#67—182no—
585#67—182no—
586#67—182no—
587#67—361no—
588C2×Dic3—22no—
589C2×Dic3—31no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—181no—
595C2×Dic3—181no—
596C2×Dic3—182no—
597C2×Dic3—182no—
598C2×Dic3—361no—
599C2×Dic3C22×D911yescharacteristic
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602C2×Dic3C22×D911yescharacteristic
603D12—62no—
604D12—94no—
605D12—121no—
606D12—182no—
607D12—182no—
608D12—182no—
609D12—182no—
610D12—361no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—362no—
616C4×D3—361no—
617C4×D3—361no—
618C4×D3—361no—
619C4×D3—362no—
620Dic6—22no—
621C2×C32—22no—
622C2×C32C2×D3×D411yescharacteristic
623C2×C32C2×#23911yescharacteristic
624C2×C32#100911yescharacteristic
625C3⋊D3—62no—
626C3⋊D3—121no—
627C3×D3—62no—
628C3×D3—121no—
629C3×D3—121no—
630C2×C9—22no—
631C2×C9—21no—
632C2×C9—21no—
633C2×C9—21no—
634C2×C9—42no—
635C2×C9C2×D3×D411yescharacteristic
636C2×C9C2×#23711yescharacteristic
637C2×C9#100411yescharacteristic
638D9—22no—
639D9—41no—
640D9—41no—
641D9—64no—
642D9—62no—
643D9—122no—
644D9—121no—
645C24—91no—
646C24—271no—
647#41—544no—
648C2×Q8—31no—
649C2×D4—91no—
650C2×D4—91no—
651C2×D4—91no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—544no—
659C22×C4—31no—
660C22×C4—271no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4—271no—
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—271no—
669C22⋊C4—31no—
670C22⋊C4—91no—
671C22⋊C4—91no—
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⋊C4D3×D911yescharacteristic
681C42—271no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—22no—
687C22×C3—21no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—92no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—364no—
700C22×C3#370112yescomplemented
701C22×C3C23×D911yescharacteristic
702C22×C3#379612yes—
703C22×C3C22×D3211yescharacteristic
704C2×D3—32no—
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—92no—
714C2×D3—92no—
715C2×D3—124no—
716C2×D3—182no—
717C2×D3—182no—
718C2×D3—182no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—182no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—361no—
731C2×D3—361no—
732C2×D3—364no—
733C2×D3—364no—
734C2×D3—368no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—32no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—181no—
746Dic3—21no—
747Dic3—21no—
748Dic3—21no—
749Dic3—61no—
750Dic3—181no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754Dic3—361no—
755Dic3—361no—
756Dic3D4×D912yes—
757C32#563011yescharacteristic
758C9—21no—
759C9#559111yescharacteristic, complemented
760C23—91no—
761C23—91no—
762C23—91no—
763C23—182no—
764C23—182no—
765C23—271no—
766C23—271no—
767C23—361no—
768C23—542no—
769C23—542no—
770C23—1081no—
771C23C2×D3×D911yescharacteristic
772Q8—62no—
773D4—182no—
774D4—182no—
775D4—274no—
776D4—361no—
777D4—542no—
778D4—542no—
779D4—542no—
780D4—542no—
781D4—1081no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—62no—
787C2×C4—91no—
788C2×C4—271no—
789C2×C4—271no—
790C2×C4—542no—
791C2×C4—542no—
792C2×C4—542no—
793C2×C4—1081no—
794C2×C4—1081no—
795C2×C4C2×D3×D911yescharacteristic
796C2×C4C2×D3×D911yescharacteristic
797C2×C3—22no—
798C2×C3—22no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—42no—
803C2×C3—182no—
804C2×C3—361no—
805C2×C3—361no—
806C2×C3C2×D4×D911yescharacteristic
807C2×C3C2×#370111yescharacteristic
808C2×C3#6371511yescharacteristic
809C2×C3C2×#379611yescharacteristic
810C2×C3D32×D411yescharacteristic
811C2×C3#6431411yescharacteristic
812D3—62no—
813D3—121no—
814D3—121no—
815D3—184no—
816D3—182no—
817D3—182no—
818D3—362no—
819D3—361no—
820D3—361no—
821C22—21no—
822C22—21no—
823C22—92no—
824C22—181no—
825C22—181no—
826C22—181no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—272no—
833C22—364no—
834C22—541no—
835C22—541no—
836C22—541no—
837C22—541no—
838C22—541no—
839C22—1084no—
840C22#8863412yescomplemented
841C22C22×D3×D911yescharacteristic
842C4—21no—
843C4—21no—
844C4—32no—
845C4—61no—
846C4—61no—
847C4—61no—
848C4—181no—
849C4—541no—
850C4—541no—
851C3—21no—
852C3#1058973211yescharacteristic, complemented
853C3#1059406311yescharacteristic
854C2—22no—
855C2—182no—
856C2—361no—
857C2—361no—
858C2—542no—
859C2—1081no—
860C2C2×#8863411yescharacteristic
861C2D3×D4×D911yescharacteristic
862C2#1172250111yescharacteristic
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×#6192C2semidirect
2. C2×#88634C2semidirect
3. C22⋊C4×C3⋊D9C2semidirect
4. C3×#63444C2semidirect
5. C9×#878C2semidirect
6. #11721278C2semidirect
7. Dic3×#611C2semidirect
8. D9×#217C2semidirect
9. #11721007C2semidirect
10. #11721003C2semidirect
11. #11720988C2semidirect
12. #11720983C2semidirect
13. #11720983C2semidirect
14. #11720978C2semidirect
15. #11720941C2semidirect
20. C2×C4×C3⋊D9C22semidirect
21. C2×C4×C3⋊D9C22semidirect
24. C2×C3×D36C22semidirect
25. C2×C3×D36C22semidirect
26. C2×C9×Dic6C22semidirect
32. C2×#6192C22semidirect
33. C2×#6192C22semidirect
34. C2×Dic3×D9C22semidirect
35. C2×Dic3×D9C22semidirect
36. C2×Dic3×D9C22semidirect
40. #88536C22semidirect
41. #88536C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C9×C4⋊Dic3C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. C9×Dic3⋊C4C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
82. #63444D3semidirect
119. #6192D4semidirect
176. C2×D36C2×D3semidirect
177. C2×D36C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
208. C22×C3×C9#41semidirect
266. #878D9semidirect
405. C2×Dic6C2×D9semidirect
438. C4⋊Dic3C2×D9semidirect
440. Dic3⋊C4C2×D9semidirect
441. Dic3⋊C4C2×D9semidirect
480. C22×C9#237semidirect
534. C3×C9#546semidirect
700. C22×C3#3701semidirect
759. C9#5591semidirect
840. C22#88634semidirect
852. C3#10589732semidirect

Maximal subgroups

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

subgroupindex
C22×#61922
C2×#886342
C22⋊C4×C3⋊D92
C3×#634442
C9×#8782
#117212782
Dic3×#6112
D9×#2172
#117210072
#117210032
#117209882
#117209832
#117209782
#117209412
#105940633
#105897323