Finite Group Databasebeta

← #13148298

Subgroups — #13148298

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88662C211yesmaximal, characteristic, complemented
2C2×D9×D12C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C9×#884C211yesmaximal, characteristic, complemented
5C3×#611⋊C4C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721292C211yesmaximal, characteristic, complemented
8#11721288C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
11C4×#6195C211yesmaximal, characteristic, complemented
12#11721015C211yesmaximal, characteristic, complemented
13#11720997C211yesmaximal, characteristic, complemented
14#11720956C211yesmaximal, characteristic, complemented
15#11720939C211yesmaximal, characteristic, complemented
16#10594283—31nomaximal
17#10589712—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic
23C2×C4×C3⋊D9C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic, complemented
26C2×C3×#611C2211yescharacteristic
27C22×C3×Dic9C2211yescharacteristic, complemented
28C2×C9×D12C2211yescharacteristic
29C2×C4×D3×C9C2211yescharacteristic, complemented
30C2×C3×C4×D9C2211yescharacteristic
31C2×#6195C2211yescharacteristic
32C2×#6195C2211yescharacteristic
33#88662—24no—
34C2×D3×Dic9C2211yescharacteristic, complemented
35C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
36C2×#6189C2211yescharacteristic, complemented
37D9×D12—24no—
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45C3×C4×Dic9C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic
53(C2×D9)⋊Dic3C2211yescharacteristic
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×#3804—31no—
56C2×D3×D12—31no—
57#64093—31no—
58C3×#884D311yescharacteristic
59C3×#67⋊C4—31no—
60#63983—31no—
61#63983—31no—
62#63978—31no—
63#63921—31no—
64D3×(C2×D3)⋊C4—31no—
65C4×#626—31no—
66#63897—31no—
67#63884—31no—
68#63852—31no—
69#63851—31no—
70C2×#3699—31no—
71C2×D4×D9—31no—
72C9×#121—31no—
73#63501—31no—
74#63499—31no—
75#63499—31no—
76#63497—31no—
77C4×#611—31no—
78C2×(C2×D9)⋊C4—31no—
79#63458—31no—
80#63456—31no—
81#63447—31no—
82#63446—31no—
83#63446—61no—
84#611⋊C4D311yescharacteristic, complemented
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×D3×D9—22no—
93C2×D3×D9—22no—
94C2×D3×D9—22no—
95C2×D3×D9—22no—
96C2×D3×D9—41no—
97C2×D3×D9—41no—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101#6233—41no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C4⋊(C3⋊D9)—22no—
105C4×C3⋊D9—41no—
106C9×#67—22no—
107C9×#67—41no—
108C3×#611—22no—
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C3×Dic9—22no—
112C2×C3×Dic9C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C9×D12—22no—
116C4×D3×C9—41no—
117C3×C4×D9—22no—
118#6195—22no—
119#6195D414yescomplemented
120D3×Dic9—22no—
121(C3⋊D9)⋊C4—22no—
122#6189—22no—
123#5610—91no—
124#5550—91no—
125C22×D32—31no—
126C22×D32—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4×C3⋊D3—31no—
131C2×C3×#67—31no—
132C2×C3×#67C2×D311yescharacteristic
133C2×C3×#67C2×D311yescharacteristic
134C22×C3×Dic3—31no—
135C2×C3×D12C2×D311yescharacteristic
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×#627—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#624—31no—
142#3804—64no—
143C2×D3×Dic3—31no—
144D3×D12—64no—
145C23×D9—31no—
146C23×D9—31no—
147C32×C22⋊C4C2×D311yescharacteristic
148#3752—31no—
149#3750—31no—
150C3×(C2×D3)⋊C4—31no—
151C3×(C2×D3)⋊C4C2×D311yescharacteristic
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4C2×D311yescharacteristic
154C3×C4×Dic3—31no—
155Dic3⋊Dic3—31no—
156#3722—31no—
157#3722—31no—
158#3722—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164C2×D4×C9—31no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C22×C4×C9—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—61no—
173C2×#611—61no—
174C2×#611C2×D311yescharacteristic
175C22×Dic9—31no—
176C22×Dic9C2×D311yescharacteristic, complemented
177#3699—64no—
178D4×D9—64no—
179C2×D36—31no—
180C2×D36—61no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—61no—
184C2×C4×D9C2×D311yescharacteristic
185C2×Dic18—31no—
186C9×C4⋊C4—31no—
187C9×C22⋊C4—21no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4C2×D311yescharacteristic, complemented
190#3676—31no—
191#3676—31no—
192#3676—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)⋊C4C2×D311yescharacteristic
201Dic9⋊C4—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—61no—
204Dic9⋊C4C2×D311yescharacteristic, complemented
205C4×Dic9C2×D311yescharacteristic, complemented
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—21no—
215C2×C3⋊D9C2×D412yes—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9C2×D412yes—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9#4112yescomplemented
225D3×D9—44no—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C2×#237—91no—
237C2×D3×D4—91no—
238C2×#235—91no—
239C22×D12—91no—
240C3×#121—31no—
241C3×C4×D4—91no—
242#939—91no—
243#937—91no—
244#937—91no—
245#937—91no—
246#937—91no—
247#935—91no—
248#930—91no—
249C4×#67—91no—
250C2×(C2×D3)⋊C4—91no—
251#924—91no—
252#896—91no—
253#894—91no—
254#894—91no—
255#894—91no—
256#885—91no—
257#884—91no—
258#884—91no—
259#884—181no—
260#884D911yescharacteristic, complemented
261#67⋊C4—31no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—91no—
265#875—91no—
266C4×D12—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3C22×D311yescharacteristic
272C22×C3×D3C22×D311yescharacteristic
273C2×D32—62no—
274C2×D32—62no—
275C2×D32—62no—
276C2×D32—62no—
277C2×D32—121no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—121no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C4⋊(C3⋊D3)—62no—
286C4×C3⋊D3—121no—
287C3×#67—22no—
288C3×#67—41no—
289C3×#67—62no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C3×D12—22no—
297C3×C4×D3—41no—
298C3×C4×D3—62no—
299#627—62no—
300#626—34no—
301#626—62no—
302#624—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9—31no—
307C23×C9C22×D311yescharacteristic
308C22×D9—31no—
309C22×D9—31no—
310C22×D9—61no—
311C22×D9—61no—
312C22×D9—62no—
313C22×D9—62no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—121no—
317C22×D9—121no—
318C22×D9C22×D311yescharacteristic
319D4×C9—62no—
320D4×C9—62no—
321D4×C9—121no—
322C2×C4×C9—21no—
323C2×C4×C9—21no—
324C2×C4×C9—31no—
325C2×C4×C9—31no—
326C2×C4×C9—121no—
327C2×C4×C9C22×D311yescharacteristic
328C2×C4×C9C22×D311yescharacteristic
329#611—22no—
330#611—34no—
331#611—62no—
332#611—62no—
333#611—122no—
334#611—121no—
335#611—122no—
336C2×Dic9—22no—
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—62no—
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344C2×Dic9C22×D311yescharacteristic
345D36—62no—
346D36—122no—
347C4×D9—22no—
348C4×D9—62no—
349C4×D9—121no—
350C4×D9—122no—
351Dic18—62no—
352#546—271noSylow
353C2×C3×C9—41no—
354C2×C3×C9C22×D411yescharacteristic
355C2×C3×C9C2×#4111yescharacteristic
356C2×C3×C9H(5,𝔽2)11yescharacteristic
357C3⋊D9—22no—
358C3⋊D9—41no—
359D3×C9—22no—
360D3×C9—41no—
361C3×D9—22no—
362C23×D3—91no—
363C23×D3—91no—
364C23×D3—91no—
365C23×D3—91no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—91no—
370C22×C3×C4—31no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C2×#67—31no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—181no—
381C2×#67—181no—
382C2×#67C2×D911yescharacteristic, complemented
383C2×#67C2×D911yescharacteristic, complemented
384C22×Dic3—31no—
385C22×Dic3—91no—
386#237—184no—
387D3×D4—184no—
388#235—184no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—181no—
394C2×D12—184no—
395C2×D12C2×D911yescharacteristic
396C2×C4×D3—31no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—181no—
403C2×C4×D3C2×D911yescharacteristic, complemented
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—91no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4C2×D911yescharacteristic, complemented
412C3×C22⋊C4D3211yescharacteristic
413C3×C42—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419(C2×D3)⋊C4—31no—
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—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—181no—
434(C2×D3)⋊C4C2×D911yescharacteristic, complemented
435C4⋊Dic3—91no—
436Dic3⋊C4—31no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—181no—
441Dic3⋊C4C2×D911yescharacteristic, complemented
442C4×Dic3—31no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—32no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
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×D3D3×D412yes—
462D32—124no—
463D32—124no—
464C32×C4—21no—
465C32×C4—21no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—32no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—32no—
478C22×C9—41no—
479C22×C9—41no—
480C22×C9—41no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9—61no—
485C22×C9—61no—
486C22×C9C23×D311yescharacteristic
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—32no—
490C2×D9—62no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—121no—
497C2×D9—121no—
498C2×D9—121no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—124no—
502C2×D9—124no—
503C2×D9#23512yescomplemented
504C4×C9—21no—
505C4×C9—21no—
506C4×C9—41no—
507C4×C9—41no—
508C4×C9—61no—
509C4×C9—61no—
510Dic9—21no—
511Dic9—21no—
512Dic9—62no—
513Dic9—61no—
514Dic9—61no—
515Dic9—121no—
516Dic9D3×D412yes—
517C2×#41—271no—
518C22×D4—271no—
519#124—271no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—31no—
524#121—271no—
525#121—271no—
526#120—271no—
527#120—271no—
528C4×D4—91no—
529C4×D4—271no—
530C2×C22⋊C4—271no—
531C2×C22⋊C4—271no—
532C3×C9#54611yescharacteristic, complemented, Sylow
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—31no—
536C23×C3—91no—
537C23×C3C22×D911yescharacteristic
538C23×C3C2×D3211yescharacteristic
539C22×D3—31no—
540C22×D3—91no—
541C22×D3—91no—
542C22×D3—91no—
543C22×D3—91no—
544C22×D3—181no—
545C22×D3—181no—
546C22×D3—182no—
547C22×D3—182no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—361no—
555C22×D3—361no—
556C22×D3—361no—
557C22×D3—361no—
558C22×D3C22×D911yescharacteristic
559C22×D3C22×D911yescharacteristic
560C3×D4—62no—
561C3×D4—62no—
562C3×D4—121no—
563C3×D4—182no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—91no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—121no—
572C2×C3×C4—182no—
573C2×C3×C4—182no—
574C2×C3×C4C22×D911yescharacteristic
575C2×C3×C4C22×D911yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577C2×C3×C4C2×D3211yescharacteristic
578#67—22no—
579#67—41no—
580#67—62no—
581#67—94no—
582#67—182no—
583#67—182no—
584#67—182no—
585#67—362no—
586#67—361no—
587#67—361no—
588#67—362no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—62no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—181no—
598C2×Dic3—181no—
599C2×Dic3—182no—
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602D12—22no—
603D12—94no—
604D12—182no—
605D12—182no—
606D12—182no—
607D12—362no—
608C4×D3—41no—
609C4×D3—62no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—361no—
614C4×D3—361no—
615C4×D3—362no—
616Dic6—182no—
617Dic6—182no—
618C2×C32—41no—
619C2×C32C2×D3×D411yescharacteristic
620C2×C32#100411yescharacteristic
621C2×C32D3×#4111yescharacteristic
622C3⋊D3—62no—
623C3⋊D3—121no—
624C3×D3—22no—
625C3×D3—41no—
626C3×D3—62no—
627C2×C9—21no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—41no—
631C2×C9—62no—
632C2×C9—81no—
633C2×C9—121no—
634C2×C9C2×#23511yescharacteristic
635C2×C9C2×D3×D411yescharacteristic
636C2×C9#100911yescharacteristic
637D9—22no—
638D9—62no—
639D9—122no—
640D9—121no—
641D9—241no—
642C24—271no—
643C24—271no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—91no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—544no—
656C22×C4—31no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—31no—
663C4⋊C4—91no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—91no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4D3×D911yescharacteristic, complemented
678C42—91no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—32no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—92no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3C23×D911yescharacteristic
699C22×C3C22×D3211yescharacteristic
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—32no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—92no—
709C2×D3—92no—
710C2×D3—182no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—361no—
722C2×D3—361no—
723C2×D3—361no—
724C2×D3—361no—
725C2×D3—361no—
726C2×D3—364no—
727C2×D3—364no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3D4×D912yes—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—61no—
738C3×C4—61no—
739C3×C4—92no—
740C3×C4—181no—
741C3×C4—181no—
742Dic3—21no—
743Dic3—21no—
744Dic3—32no—
745Dic3—61no—
746Dic3—61no—
747Dic3—182no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—181no—
752Dic3—361no—
753C32#561011yescharacteristic
754C9—21no—
755C9#555011yescharacteristic, complemented
756C23—31no—
757C23—31no—
758C23—91no—
759C23—271no—
760C23—271no—
761C23—542no—
762C23—542no—
763C23—542no—
764C23—542no—
765C23—1081no—
766C23—1081no—
767C23C2×D3×D911yescharacteristic
768Q8—542no—
769D4—62no—
770D4—62no—
771D4—121no—
772D4—182no—
773D4—274no—
774D4—542no—
775D4—542no—
776D4—542no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—91no—
781C2×C4—91no—
782C2×C4—91no—
783C2×C4—121no—
784C2×C4—182no—
785C2×C4—182no—
786C2×C4—271no—
787C2×C4—271no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—1081no—
791C2×C4C2×D3×D911yescharacteristic
792C2×C4C2×D3×D911yescharacteristic
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—41no—
797C2×C3—41no—
798C2×C3—62no—
799C2×C3—81no—
800C2×C3—121no—
801C2×C3—182no—
802C2×C3C2×D4×D911yescharacteristic
803C2×C3#6371011yescharacteristic
804C2×C3#41×D911yescharacteristic
805C2×C3D3×#23511yescharacteristic
806C2×C3D32×D411yescharacteristic
807C2×C3#6431411yescharacteristic
808D3—22no—
809D3—41no—
810D3—62no—
811D3—182no—
812D3—182no—
813D3—362no—
814D3—361no—
815D3—361no—
816D3—721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—92no—
827C22—181no—
828C22—181no—
829C22—272no—
830C22—541no—
831C22—541no—
832C22—541no—
833C22—541no—
834C22—541no—
835C22—1084no—
836C22—1084no—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—21no—
840C4—61no—
841C4—61no—
842C4—92no—
843C4—181no—
844C4—181no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058971211yescharacteristic, complemented
849C3#1059428311yescharacteristic
850C2—41no—
851C2—62no—
852C2—121no—
853C2—182no—
854C2—542no—
855C2—1081no—
856C2D9×#23511yescharacteristic
857C2D3×D4×D911yescharacteristic
858C2#1172250011yescharacteristic
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×#88662C2semidirect
2. C2×D9×D12C2semidirect
3. #11721730C2semidirect
4. C9×#884C2semidirect
5. C3×#611⋊C4C2semidirect
6. #11721292C2semidirect
7. #11721292C2semidirect
8. #11721288C2semidirect
9. #11721048C2semidirect
10. D3×(C2×D9)⋊C4C2semidirect
11. C4×#6195C2semidirect
12. #11721015C2semidirect
13. #11720997C2semidirect
14. #11720956C2semidirect
15. #11720939C2semidirect
20. C2×#6233C22semidirect
21. C2×#6233C22semidirect
23. C2×C4×C3⋊D9C22semidirect
24. C2×C9×#67C22semidirect
25. C2×C9×#67C22semidirect
27. C22×C3×Dic9C22semidirect
29. C2×C4×D3×C9C22semidirect
34. C2×D3×Dic9C22semidirect
35. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×#6189C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C9×(C2×D3)⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C3×Dic9⋊C4C22semidirect
45. C3×C4×Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. #88445C22semidirect
54. Dic9⋊Dic3C22semidirect
84. #611⋊C4D3semidirect
119. #6195D4semidirect
176. C22×Dic9C2×D3semidirect
189. C9×C22⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
205. C4×Dic9C2×D3semidirect
224. C2×C3×D9#41semidirect
260. #884D9semidirect
382. C2×#67C2×D9semidirect
383. C2×#67C2×D9semidirect
403. C2×C4×D3C2×D9semidirect
411. C3×C22⋊C4C2×D9semidirect
434. (C2×D3)⋊C4C2×D9semidirect
441. Dic3⋊C4C2×D9semidirect
503. C2×D9#235semidirect
532. C3×C9#546semidirect
677. C22⋊C4D3×D9semidirect
755. C9#5550semidirect
848. C3#10589712semidirect

Maximal subgroups

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

subgroupindex
C2×#886622
C2×D9×D122
#117217302
C9×#8842
C3×#611⋊C42
#117212922
#117212882
#117210482
D3×(C2×D9)⋊C42
C4×#61952
#117210152
#117209972
#117209562
#117209392
#105942833
#105897123