Finite Group Databasebeta

← #13150546

Subgroups — #13150546

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
1C2×C3×#3697C211yesmaximal, characteristic, complemented
2C2×#88668C211yesmaximal, characteristic, complemented
3C2×#88536C211yesmaximal, characteristic, complemented
4C9×#929C211yesmaximal, characteristic, complemented
5#11721290C211yesmaximal, characteristic, complemented
6#11721278C211yesmaximal, characteristic, complemented
7#611⋊Dic3C211yesmaximal, characteristic, complemented
8#11721049C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721035C211yesmaximal, characteristic, complemented
11#11721033C211yesmaximal, characteristic, complemented
12#11721002C211yesmaximal, characteristic, complemented
13#11720985C211yesmaximal, characteristic, complemented
14#11720983C211yesmaximal, characteristic, complemented
15#11720938C211yesmaximal, characteristic, complemented
16#10595068—31nomaximal
17#10589756—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic, complemented
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic, complemented
25C3×#3697—24no—
26C2×C3×D36C2211yescharacteristic, complemented
27C2×C3×C4×D9C2211yescharacteristic, complemented
28C2×C3×C4×D9C2211yescharacteristic, complemented
29C2×C3×Dic18C2211yescharacteristic, complemented
30#88668—24no—
31C2×#6195C2211yescharacteristic
32C2×#6194C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic
35C2×#6192C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic
37C2×Dic3×D9C2211yescharacteristic, complemented
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic
40#88536C2211yescharacteristic, complemented
41#88536C2211yescharacteristic, complemented
42C9×#217C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C9×Dic3⋊C4C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C3×#235—31no—
56C2×#3811—31no—
57C2×#3752—31no—
58C3×#929D311yescharacteristic
59#63981—31no—
60#63980—31no—
61#67⋊Dic3—31no—
62#63922—31no—
63D3×(C2×D3)⋊C4—31no—
64#63907—31no—
65#63906—31no—
66#63904—31no—
67#63888—31no—
68#63886—31no—
69#63850—31no—
70C2×D4×D9—31no—
71C2×#3697D311yescharacteristic, complemented
72C9×#123—31no—
73#63501—31no—
74C2×(C2×D9)⋊C4—31no—
75C2×(C2×D9)⋊C4—61no—
76#63458—31no—
77#63457—31no—
78#63456—31no—
79#63455—31no—
80#63447—31no—
81#63446—31no—
82#63444—31no—
83#63444—31no—
84#611⋊C4—31no—
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
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
101C2×C3⋊Dic9—41no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C9×#67—22no—
105C3×#611—22no—
106C3×#611D414yescomplemented
107C2×C9×Dic3C2311yescharacteristic
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—41no—
118#6192—22no—
119#6192—22no—
120#6192—41no—
121(C3⋊D9)⋊C4—22no—
122Dic3×D9—41no—
123#5829—91no—
124#5654—91no—
125C23×C3⋊D3—31no—
126C22×D32—31no—
127C22×C32×C4C2×D311yescharacteristic
128C22×C3⋊Dic3—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C2×C3×#67C2×D311yescharacteristic
132C3×#235—64no—
133C2×C3×D12—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×Dic6—31no—
137#3811—64no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#625—31no—
143C2×#624—31no—
144C2×D3×Dic3—31no—
145C23×D9—31no—
146C23×D9—31no—
147C23×D9—61no—
148#3752—31no—
149#3752—31no—
150#3752—31no—
151#3752—31no—
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×Dic3⋊C4C2×D311yescharacteristic
156C3×Dic3⋊C4C2×D311yescharacteristic
157#3724—31no—
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×D4×C9—31no—
166C22×C4×C9—21no—
167C22×C4×C9C2×D311yescharacteristic, complemented
168C2×#611—31no—
169C2×#611—31no—
170C2×#611C2×D311yescharacteristic
171C2×#611C2×D311yescharacteristic, complemented
172C22×Dic9—31no—
173C22×Dic9—61no—
174D4×D9—64no—
175#3697—24no—
176C2×D36—31no—
177C2×D36—31no—
178C2×D36—31no—
179C2×D36C2×D311yescharacteristic, complemented
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9C2×D311yescharacteristic, complemented
183C2×C4×D9C2×D311yescharacteristic, complemented
184C2×Dic18C2×D311yescharacteristic, complemented
185C9×C4⋊C4—31no—
186C9×C4⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190#3676—31no—
191(C2×D9)⋊C4—31no—
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—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—61no—
200(C2×D9)⋊C4—61no—
201(C2×D9)⋊C4—61no—
202(C2×D9)⋊C4—61no—
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
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×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—44no—
216C2×C3⋊D9#4112yescomplemented
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
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—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C2×C3×#41—91no—
237C2×D3×D4—91no—
238C2×D3×D4—91no—
239C2×#235—31no—
240C3×#123—31no—
241#947—91no—
242#946—91no—
243#939—91no—
244#939—91no—
245#939—91no—
246#937—91no—
247#937—91no—
248D4×Dic3—91no—
249#930—91no—
250#929—91no—
251#929D911yescharacteristic, complemented
252C4×#67—91no—
253C2×(C2×D3)⋊C4—91no—
254C2×(C2×D3)⋊C4—91no—
255C2×(C2×D3)⋊C4—91no—
256C2×(C2×D3)⋊C4—181no—
257#896—91no—
258#895—91no—
259#894—91no—
260#893—91no—
261#885—91no—
262#884—91no—
263#882—91no—
264#882—91no—
265#67⋊C4—91no—
266D3×C22⋊C4—91no—
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×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4—22no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—121no—
285C3×#67—22no—
286C3×#67—34no—
287C3×#67—62no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3C22×D311yescharacteristic
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—62no—
299#626—62no—
300#626—121no—
301#625—121no—
302#624—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9C22×D311yescharacteristic
307C22×D9—31no—
308C22×D9—31no—
309C22×D9—61no—
310C22×D9—61no—
311C22×D9—62no—
312C22×D9—62no—
313C22×D9—64no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—122no—
317C22×D9—121no—
318C22×D9—121no—
319C22×D9—122no—
320C22×D9C22×D311yescharacteristic
321C22×D9C22×D311yescharacteristic
322D4×C9—62no—
323C2×C4×C9—22no—
324C2×C4×C9—21no—
325C2×C4×C9—21no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—42no—
330C2×C4×C9C22×D311yescharacteristic
331C2×C4×C9C22×D311yescharacteristic
332#611—22no—
333#611—62no—
334#611—121no—
335#611#6714yescomplemented
336C2×Dic9—31no—
337C2×Dic9—31no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—121no—
341C2×Dic9—122no—
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344D36—22no—
345D36—62no—
346D36—62no—
347D36—121no—
348C4×D9—22no—
349C4×D9—22no—
350C4×D9—62no—
351C4×D9—121no—
352Dic18—22no—
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—
360D3×C9—41no—
361C3×D9—22no—
362C3×D9—41no—
363C23×D3—91no—
364C23×D3—91no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—181no—
368C3×#41—184no—
369C2×C3×Q8—91no—
370C2×C3×D4—31no—
371C2×C3×D4—91no—
372C2×C3×D4—91no—
373C2×C3×D4—91no—
374C22×C3×C4—21no—
375C22×C3×C4—91no—
376C22×C3×C4—91no—
377C22×C3×C4C2×D911yescharacteristic, complemented
378C22×C3×C4D3211yescharacteristic
379C2×#67—31no—
380C2×#67—31no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67C2×D911yescharacteristic
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—181no—
392D3×D4—184no—
393D3×D4—184no—
394#235—64no—
395C2×D12—31no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12—91no—
399C2×D12—91no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×Dic6—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217C2×D911yescharacteristic, complemented
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—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)⋊C4—181no—
432(C2×D3)⋊C4—181no—
433(C2×D3)⋊C4—181no—
434(C2×D3)⋊C4C2×D911yescharacteristic, complemented
435(C2×D3)⋊C4C2×D911yescharacteristic, complemented
436C4⋊Dic3—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4C2×D911yescharacteristic, complemented
441Dic3⋊C4C2×D911yescharacteristic, complemented
442C4×Dic3—91no—
443C4×Dic3—91no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32D3×D412yes—
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—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—32no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464D32—124no—
465C32×C4—21no—
466C32×C4—21no—
467C3⋊Dic3—61no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—32no—
473C3×Dic3—61no—
474C22×C9—22no—
475C22×C9—22no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—22no—
480C22×C9—61no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9C2×#6712yes—
484C22×C9C23×D311yescharacteristic
485C2×D9—21no—
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—32no—
491C2×D9—62no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—62no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—121no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—124no—
503C2×D9—124no—
504C2×D9—128no—
505C2×D9C2×#6712yes—
506C4×C9—21no—
507C4×C9—21no—
508C4×C9—41no—
509C4×C9—41no—
510C4×C9—61no—
511C4×C9—61no—
512C4×C9—61no—
513Dic9—21no—
514Dic9—61no—
515Dic9—61no—
516Dic9—121no—
517Dic9—121no—
518Dic9C2×#6712yes—
519C2×#41—91no—
520C22×D4—271no—
521#124—271no—
522#123—31no—
523#123—271no—
524C22⋊Q8—271no—
525#121—271no—
526#121—271no—
527#121—271no—
528#120—271no—
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—31no—
537C23×C3—91no—
538C23×C3—91no—
539C23×C3C22×D911yescharacteristic
540C23×C3C2×D3211yescharacteristic
541C22×D3—31no—
542C22×D3—31no—
543C22×D3—91no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—91no—
547C22×D3—181no—
548C22×D3—181no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—184no—
556C22×D3—182no—
557C22×D3—182no—
558C22×D3—362no—
559C22×D3—361no—
560C22×D3—361no—
561C22×D3—361no—
562C22×D3—361no—
563C22×D3—362no—
564C22×D3C22×D911yescharacteristic
565C3×Q8—182no—
566C3×D4—62no—
567C3×D4—94no—
568C3×D4—182no—
569C3×D4—182no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—42no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—182no—
581C2×C3×C4—182no—
582C2×C3×C4C22×D911yescharacteristic
583C2×C3×C4C22×D911yescharacteristic
584C2×C3×C4C2×D3211yescharacteristic
585C2×C3×C4C2×D3211yescharacteristic
586#67—22no—
587#67—34no—
588#67—62no—
589#67—182no—
590#67—182no—
591#67—182no—
592#67—361no—
593#67—361no—
594#67—361no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—181no—
602C2×Dic3—181no—
603C2×Dic3—361no—
604C2×Dic3—361no—
605C2×Dic3—361no—
606C2×Dic3—362no—
607C2×Dic3C22×D911yescharacteristic
608C2×Dic3C22×D911yescharacteristic
609C2×Dic3C22×D911yescharacteristic
610D12—62no—
611D12—182no—
612D12—182no—
613D12—182no—
614D12—361no—
615C4×D3—62no—
616C4×D3—62no—
617C4×D3—182no—
618C4×D3—182no—
619C4×D3—361no—
620Dic6—62no—
621C2×C32—22no—
622C2×C32C2×D3×D411yescharacteristic
623C2×C32D3×#4111yescharacteristic
624C2×C32#100911yescharacteristic
625C3⋊D3—62no—
626C3⋊D3—121no—
627C3×D3—41no—
628C3×D3—62no—
629C3×D3—121no—
630C2×C9—24no—
631C2×C9—22no—
632C2×C9—21no—
633C2×C9—21no—
634C2×C9—21no—
635C2×C9—121no—
636C2×C9D3×#4111yescharacteristic
637C2×C9#100911yescharacteristic
638C2×C9C22×#6711yescharacteristic
639D9—22no—
640D9—41no—
641D9—62no—
642D9—122no—
643D9—122no—
644D9—121no—
645C24—271no—
646C24—271no—
647#41—184no—
648C2×Q8—91no—
649C2×D4—31no—
650C2×D4—91no—
651C2×D4—91no—
652C2×D4—91no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—544no—
659C22×C4—91no—
660C22×C4—91no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4D3×D911yescharacteristic, complemented
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—271no—
668C4⋊C4—271no—
669C22⋊C4—31no—
670C22⋊C4—31no—
671C22⋊C4—31no—
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⋊C4—271no—
681C42—271no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—22no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—92no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3D4×D912yes—
700C22×C3C23×D911yescharacteristic
701C22×C3D3×#6712yes—
702C22×C3C22×D3211yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—32no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—92no—
713C2×D3—92no—
714C2×D3—182no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—182no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—361no—
727C2×D3—361no—
728C2×D3—361no—
729C2×D3—361no—
730C2×D3—364no—
731C2×D3—364no—
732C2×D3—364no—
733C2×D3—364no—
734C2×D3—368no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—92no—
745C3×C4—181no—
746Dic3—21no—
747Dic3—21no—
748Dic3—21no—
749Dic3—32no—
750Dic3—61no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754Dic3—181no—
755Dic3—361no—
756Dic3—361no—
757C32#565411yescharacteristic
758C9—21no—
759C9#582911yescharacteristic, complemented
760C23—31no—
761C23—91no—
762C23—91no—
763C23—271no—
764C23—271no—
765C23—542no—
766C23—542no—
767C23—542no—
768C23—542no—
769C23—1081no—
770C23—1081no—
771C23C2×D3×D911yescharacteristic
772Q8—182no—
773D4—62no—
774D4—94no—
775D4—182no—
776D4—182no—
777D4—542no—
778D4—542no—
779D4—542no—
780D4—1081no—
781D4—1081no—
782C2×C4—22no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—271no—
791C2×C4—271no—
792C2×C4—542no—
793C2×C4—1081no—
794C2×C4—1081no—
795C2×C4C2×D3×D911yescharacteristic
796C2×C4C2×D3×D911yescharacteristic
797C2×C3—24no—
798C2×C3—22no—
799C2×C3—22no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—121no—
804C2×C3—182no—
805C2×C3—361no—
806C2×C3C2×D4×D911yescharacteristic
807C2×C3#41×D911yescharacteristic
808C2×C3#6371511yescharacteristic
809C2×C3#6430611yescharacteristic
810C2×C3#6430811yescharacteristic
811C2×C3C2×D3×#6711yescharacteristic
812D3—41no—
813D3—62no—
814D3—121no—
815D3—182no—
816D3—182no—
817D3—362no—
818D3—362no—
819D3—361no—
820D3—361no—
821C22—21no—
822C22—21no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—92no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—272no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22—541no—
837C22—541no—
838C22—1084no—
839C22—1084no—
840C22D9×#6712yes—
841C22C22×D3×D911yescharacteristic
842C4—21no—
843C4—21no—
844C4—61no—
845C4—61no—
846C4—61no—
847C4—92no—
848C4—181no—
849C4—541no—
850C4—541no—
851C3—21no—
852C3#1058975611yescharacteristic, complemented
853C3#1059506811yescharacteristic
854C2—22no—
855C2—121no—
856C2—182no—
857C2—361no—
858C2—542no—
859C2—1081no—
860C2#1172247511yescharacteristic
861C2#1172247811yescharacteristic
862C2C2×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×#88668C2semidirect
3. C2×#88536C2semidirect
4. C9×#929C2semidirect
5. #11721290C2semidirect
6. #11721278C2semidirect
7. #611⋊Dic3C2semidirect
8. #11721049C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721035C2semidirect
11. #11721033C2semidirect
12. #11721002C2semidirect
13. #11720985C2semidirect
14. #11720983C2semidirect
15. #11720938C2semidirect
20. C22×C3×C4×C9C22semidirect
21. C22×C3⋊Dic9C22semidirect
24. C2×C3×#611C22semidirect
26. C2×C3×D36C22semidirect
27. C2×C3×C4×D9C22semidirect
28. C2×C3×C4×D9C22semidirect
29. C2×C3×Dic18C22semidirect
32. C2×#6194C22semidirect
35. C2×#6192C22semidirect
37. C2×Dic3×D9C22semidirect
40. #88536C22semidirect
41. #88536C22semidirect
42. C9×#217C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C9×Dic3⋊C4C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
71. C2×#3697D3semidirect
106. C3×#611D4semidirect
167. C22×C4×C9C2×D3semidirect
171. C2×#611C2×D3semidirect
179. C2×D36C2×D3semidirect
182. C2×C4×D9C2×D3semidirect
183. C2×C4×D9C2×D3semidirect
184. C2×Dic18C2×D3semidirect
216. C2×C3⋊D9#41semidirect
251. #929D9semidirect
335. #611#67semidirect
377. C22×C3×C4C2×D9semidirect
414. #217C2×D9semidirect
434. (C2×D3)⋊C4C2×D9semidirect
435. (C2×D3)⋊C4C2×D9semidirect
440. Dic3⋊C4C2×D9semidirect
441. Dic3⋊C4C2×D9semidirect
534. C3×C9#546semidirect
664. C22×C4D3×D9semidirect
759. C9#5829semidirect
852. C3#10589756semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#36972
C2×#886682
C2×#885362
C9×#9292
#117212902
#117212782
#611⋊Dic32
#117210492
D9×(C2×D3)⋊C42
#117210352
#117210332
#117210022
#117209852
#117209832
#117209382
#105950683
#105897563