Finite Group Databasebeta

← #13148293

Subgroups — #13148293

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×#88668C211yesmaximal, characteristic, complemented
2C2×#88640C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
4C9×#883C211yesmaximal, characteristic, complemented
5C3×#63446C211yesmaximal, characteristic, complemented
6#11721281C211yesmaximal, characteristic, complemented
7#11721278C211yesmaximal, characteristic, complemented
8#11721257C211yesmaximal, characteristic, complemented
9#11721049C211yesmaximal, characteristic, complemented
10D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
11#11721014C211yesmaximal, characteristic, complemented
12#11721007C211yesmaximal, characteristic, complemented
13#11721002C211yesmaximal, characteristic, complemented
14#11720994C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10594279—31nomaximal
17#10589756—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic, complemented
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic, complemented
25C2×C4×D3×C9C2211yescharacteristic, complemented
26C2×C3×D36C2211yescharacteristic, complemented
27C2×C3×C4×D9C2211yescharacteristic, complemented
28#88668—24no—
29C2×#6195C2211yescharacteristic
30C2×#6194C2211yescharacteristic, complemented
31C2×D3×Dic9C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic, complemented
35C2×(C3⋊D9)⋊C4C2211yescharacteristic
36C2×#6189C2211yescharacteristic, complemented
37#88640—24no—
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88551C2211yescharacteristic, complemented
40#88536C2211yescharacteristic
41#88536C2211yescharacteristic
42C9×#217C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C9×C4⋊Dic3C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3798—31no—
57C22⋊C4×C3⋊D3—31no—
58C3×#884—31no—
59C3×#883D311yescharacteristic
60#63981—31no—
61#63970—31no—
62#63959—31no—
63#63922—31no—
64D3×(C2×D3)⋊C4—31no—
65#63916—31no—
66#63904—31no—
67#63895—31no—
68#63881—31no—
69#63853—31no—
70C2×D4×D9—31no—
71C2×#3697—31no—
72C9×#123—31no—
73#63501—31no—
74C2×(C2×D9)⋊C4—31no—
75#63458—31no—
76#63457—31no—
77#63456—31no—
78#63455—31no—
79#63447—31no—
80#63446D311yescharacteristic, complemented
81#63444—31no—
82#63444—31no—
83#611⋊C4—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×D3×C9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C4×C3⋊D9—22no—
103C4×C3⋊D9—41no—
104C9×#67—22no—
105C3×#611—22no—
106C3×#611—41no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C4×D3×C9—22no—
113C3×D36—41no—
114C3×C4×D9—22no—
115#6195D414yescomplemented
116#6194—22no—
117D3×Dic9—41no—
118#6192—22no—
119#6192—22no—
120#6192—22no—
121(C3⋊D9)⋊C4—22no—
122#6189—22no—
123#5654—91no—
124#5612—91no—
125C23×C3⋊D3—31no—
126C22×D32—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×D12—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3C2×D311yescharacteristic
135#3811—64no—
136C2×#627—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#625—31no—
142C2×#624—31no—
143C2×D3×Dic3—31no—
144#3798—64no—
145C23×D9—31no—
146C23×D9—31no—
147C23×D9—61no—
148C32×C22⋊C4C2×D311yescharacteristic
149#3757—31no—
150#3752—31no—
151#3752—31no—
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×C4⋊Dic3C2×D311yescharacteristic
156C3×Dic3⋊C4—31no—
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×D4×C9—31no—
166C22×C4×C9—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611C2×D311yescharacteristic
170C2×#611C2×D311yescharacteristic, complemented
171C22×Dic9—31no—
172D4×D9—64no—
173#3697—64no—
174C2×D36—31no—
175C2×D36—31no—
176C2×D36—31no—
177C2×D36C2×D311yescharacteristic, complemented
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—61no—
182C2×C4×D9—61no—
183C2×C4×D9C2×D311yescharacteristic, complemented
184C2×Dic18—31no—
185C9×C4⋊C4—31no—
186C9×C4⋊C4—31no—
187C9×C22⋊C4—21no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4C2×D311yescharacteristic, complemented
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
203Dic9⋊C4—31no—
204Dic9⋊C4C2×D311yescharacteristic, complemented
205C4×Dic9—31no—
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—44no—
215C2×C3⋊D9C2×D412yes—
216C2×C3⋊D9#4112yescomplemented
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9C2×D412yes—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
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—
233C9×Dic3—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C2×D3×D4—91no—
237C2×D3×D4—91no—
238C2×#235—91no—
239C2×#235—91no—
240C3×#123—31no—
241C3×#121—91no—
242#939—91no—
243#938—91no—
244#938—91no—
245#937—91no—
246#937—91no—
247#936—91no—
248C4×#67—91no—
249C2×(C2×D3)⋊C4—91no—
250#897—91no—
251#896—91no—
252#895—91no—
253#894—91no—
254#893—91no—
255#893—91no—
256#885—91no—
257#884—31no—
258#883—91no—
259#883D911yescharacteristic, complemented
260#882—91no—
261#882—91no—
262#67⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—181no—
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×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C4×C3⋊D3—62no—
284C4×C3⋊D3—121no—
285C3×#67—22no—
286C3×#67—62no—
287C3×#67—121no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C3×D12—121no—
294C3×C4×D3—22no—
295C3×C4×D3—62no—
296#627—62no—
297#626—34no—
298#626—62no—
299#626—62no—
300#626—62no—
301#625—62no—
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—62no—
314C22×D9—62no—
315C22×D9—64no—
316C22×D9—122no—
317C22×D9—121no—
318C22×D9—121no—
319C22×D9—122no—
320C22×D9C22×D311yescharacteristic
321C22×D9C22×D311yescharacteristic
322D4×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—62no—
329C2×C4×C9C22×D311yescharacteristic
330C2×C4×C9C22×D311yescharacteristic
331#611—22no—
332#611—34no—
333#611—41no—
334#611—62no—
335C2×Dic9—31no—
336C2×Dic9—31no—
337C2×Dic9—61no—
338C2×Dic9—61no—
339C2×Dic9—121no—
340C2×Dic9C22×D311yescharacteristic
341C2×Dic9C22×D311yescharacteristic
342D36—41no—
343D36—62no—
344D36—62no—
345D36—62no—
346C4×D9—22no—
347C4×D9—62no—
348C4×D9—62no—
349C4×D9—122no—
350C4×D9—121no—
351C4×D9—122no—
352Dic18—62no—
353#546—271noSylow
354C2×C3×C9—41no—
355C2×C3×C9C22×D411yescharacteristic
356C2×C3×C9C2×#4111yescharacteristic
357C2×C3×C9H(5,𝔽2)11yescharacteristic
358C3⋊D9—22no—
359C3⋊D9—22no—
360D3×C9—22no—
361C3×D9—41no—
362C3×D9—41no—
363C23×D3—91no—
364C23×D3—91no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—181no—
368C2×C3×D4—31no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C2×C3×D4—91no—
372C22×C3×C4—31no—
373C22×C3×C4—91no—
374C2×#67—31no—
375C2×#67—31no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67C2×D911yescharacteristic
383C22×Dic3—91no—
384D3×D4—184no—
385D3×D4—184no—
386#235—184no—
387#235—184no—
388C2×D12—31no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×C4×D3—31no—
394C2×C4×D3—91no—
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—181no—
402C2×C4×D3—181no—
403C2×C4×D3C2×D911yescharacteristic, complemented
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—91no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—31no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4C2×D911yescharacteristic, complemented
414C3×C22⋊C4D3211yescharacteristic
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—181no—
421#217C2×D911yescharacteristic, complemented
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—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—181no—
435(C2×D3)⋊C4—181no—
436(C2×D3)⋊C4C2×D911yescharacteristic, complemented
437C4⋊Dic3—91no—
438C4⋊Dic3C2×D911yescharacteristic, complemented
439Dic3⋊C4—31no—
440Dic3⋊C4—91no—
441Dic3⋊C4C2×D911yescharacteristic, complemented
442C4×Dic3—91no—
443C4×Dic3—91no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32C23×D311yescharacteristic
448C2×C3⋊D3—32no—
449C2×C3⋊D3—32no—
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—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3D3×D412yes—
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—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—32no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9C23×D311yescharacteristic
485C2×D9—21no—
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—32no—
492C2×D9—32no—
493C2×D9—62no—
494C2×D9—62no—
495C2×D9—62no—
496C2×D9—62no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—61no—
500C2×D9—61no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—124no—
504C2×D9—124no—
505C2×D9—128no—
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—
518Dic9D3×D412yes—
519C2×#41—271no—
520C22×D4—271no—
521#124—271no—
522#123—31no—
523#123—271no—
524C22⋊Q8—271no—
525#121—91no—
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—182no—
556C22×D3—184no—
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×D4—62no—
566C3×D4—182no—
567C3×D4—361no—
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—62no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4—182no—
578C2×C3×C4C22×D911yescharacteristic
579C2×C3×C4C22×D911yescharacteristic
580C2×C3×C4C2×D3211yescharacteristic
581C2×C3×C4C2×D3211yescharacteristic
582#67—22no—
583#67—62no—
584#67—94no—
585#67—121no—
586#67—182no—
587#67—182no—
588#67—182no—
589#67—182no—
590#67—182no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—181no—
598C2×Dic3—181no—
599C2×Dic3—361no—
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602C2×Dic3C22×D911yescharacteristic
603D12—94no—
604D12—121no—
605D12—182no—
606D12—182no—
607D12—182no—
608C4×D3—22no—
609C4×D3—62no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—362no—
615C4×D3—361no—
616C4×D3—361no—
617C4×D3—361no—
618C4×D3—362no—
619Dic6—182no—
620Dic6—182no—
621C2×C32—41no—
622C2×C32C2×D3×D411yescharacteristic
623C2×C32D3×#4111yescharacteristic
624C2×C32#100911yescharacteristic
625C3⋊D3—62no—
626C3⋊D3—62no—
627C3×D3—22no—
628C3×D3—121no—
629C3×D3—121no—
630C2×C9—21no—
631C2×C9—21no—
632C2×C9—21no—
633C2×C9—42no—
634C2×C9—41no—
635C2×C9—62no—
636C2×C9C2×D3×D411yescharacteristic
637C2×C9#100411yescharacteristic
638C2×C9D3×#4111yescharacteristic
639D9—41no—
640D9—41no—
641D9—64no—
642D9—62no—
643D9—62no—
644D9—122no—
645C24—271no—
646C24—271no—
647#41—544no—
648C2×Q8—271no—
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—31no—
660C22×C4—91no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4—271no—
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—91no—
668C4⋊C4—271no—
669C22⋊C4—31no—
670C22⋊C4—31no—
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, complemented
681C42—271no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—32no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3C23×D911yescharacteristic
702C22×C3C22×D3211yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—92no—
712C2×D3—92no—
713C2×D3—92no—
714C2×D3—92no—
715C2×D3—182no—
716C2×D3—182no—
717C2×D3—182no—
718C2×D3—182no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—361no—
728C2×D3—361no—
729C2×D3—364no—
730C2×D3—364no—
731C2×D3—364no—
732C2×D3—364no—
733C2×D3—368no—
734C2×D3D4×D912yes—
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#561211yescharacteristic, 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—542no—
773D4—62no—
774D4—182no—
775D4—274no—
776D4—361no—
777D4—361no—
778D4—542no—
779D4—542no—
780D4—542no—
781D4—542no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—62no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—182no—
789C2×C4—271no—
790C2×C4—271no—
791C2×C4—542no—
792C2×C4—542no—
793C2×C4—1081no—
794C2×C4—1081no—
795C2×C4C2×D3×D911yescharacteristic
796C2×C4C2×D3×D911yescharacteristic
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—42no—
801C2×C3—41no—
802C2×C3—41no—
803C2×C3—62no—
804C2×C3—361no—
805C2×C3—361no—
806C2×C3C2×D4×D911yescharacteristic
807C2×C3#41×D911yescharacteristic
808C2×C3#6371511yescharacteristic
809C2×C3#6430611yescharacteristic
810C2×C3D32×D411yescharacteristic
811C2×C3#6431411yescharacteristic
812D3—22no—
813D3—121no—
814D3—121no—
815D3—184no—
816D3—182no—
817D3—182no—
818D3—182no—
819D3—182no—
820D3—362no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—32no—
825C22—61no—
826C22—61no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—272no—
834C22—272no—
835C22—541no—
836C22—541no—
837C22—541no—
838C22—541no—
839C22—1084no—
840C22—1084no—
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#1059427911yescharacteristic
854C2—41no—
855C2—62no—
856C2—361no—
857C2—361no—
858C2—542no—
859C2—542no—
860C2#1172247511yescharacteristic
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. C2×#88668C2semidirect
2. C2×#88640C2semidirect
3. C22⋊C4×C3⋊D9C2semidirect
4. C9×#883C2semidirect
5. C3×#63446C2semidirect
6. #11721281C2semidirect
7. #11721278C2semidirect
8. #11721257C2semidirect
9. #11721049C2semidirect
10. D3×(C2×D9)⋊C4C2semidirect
11. #11721014C2semidirect
12. #11721007C2semidirect
13. #11721002C2semidirect
14. #11720994C2semidirect
15. #11720941C2semidirect
20. C2×C4×C3⋊D9C22semidirect
21. C2×C4×C3⋊D9C22semidirect
24. C2×C3×#611C22semidirect
25. C2×C4×D3×C9C22semidirect
26. C2×C3×D36C22semidirect
27. C2×C3×C4×D9C22semidirect
30. C2×#6194C22semidirect
31. C2×D3×Dic9C22semidirect
34. C2×#6192C22semidirect
36. C2×#6189C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88551C22semidirect
42. C9×#217C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C9×C4⋊Dic3C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. C3×Dic9⋊C4C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
80. #63446D3semidirect
115. #6195D4semidirect
170. C2×#611C2×D3semidirect
177. C2×D36C2×D3semidirect
183. C2×C4×D9C2×D3semidirect
190. C9×C22⋊C4C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
216. C2×C3⋊D9#41semidirect
259. #883D9semidirect
403. C2×C4×D3C2×D9semidirect
413. C3×C22⋊C4C2×D9semidirect
421. #217C2×D9semidirect
436. (C2×D3)⋊C4C2×D9semidirect
438. C4⋊Dic3C2×D9semidirect
441. Dic3⋊C4C2×D9semidirect
534. C3×C9#546semidirect
680. C22⋊C4D3×D9semidirect
759. C9#5612semidirect
852. C3#10589756semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886402
C22⋊C4×C3⋊D92
C9×#8832
C3×#634462
#117212812
#117212782
#117212572
#117210492
D3×(C2×D9)⋊C42
#117210142
#117210072
#117210022
#117209942
#117209412
#105942793
#105897563