Finite Group Databasebeta

← #13148142

Subgroups — #13148142

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×#88658C211yesmaximal, characteristic, complemented
2C2×D3×D36C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C9×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#63446C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721292C211yesmaximal, characteristic, complemented
8#11721277C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C4×#6192C211yesmaximal, characteristic, complemented
12#11720997C211yesmaximal, characteristic, complemented
13#11720981C211yesmaximal, characteristic, complemented
14#11720955C211yesmaximal, characteristic, complemented
15#11720940C211yesmaximal, characteristic, complemented
16#10594283—31nomaximal
17#10589652—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
25C2×C3×#611C2211yescharacteristic, complemented
26C2×C3×#611C2211yescharacteristic, complemented
27C22×C9×Dic3C2211yescharacteristic, complemented
28C2×C4×D3×C9C2211yescharacteristic
29C2×C3×D36C2211yescharacteristic
30C2×C3×C4×D9C2211yescharacteristic, complemented
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34#88658—24no—
35C2×Dic3×D9C2211yescharacteristic, complemented
36C2×#6189C2211yescharacteristic, complemented
37D3×D36—24no—
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C4×C9×Dic3C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54Dic3⋊Dic9C2211yescharacteristic, complemented
55C2×#3804—31no—
56C2×D3×D12—31no—
57#64093—31no—
58C3×#884—31no—
59C3×#67⋊C4D311yescharacteristic
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×#3697—31no—
71C22×D36—31no—
72C4×D4×C9—31no—
73#63499—31no—
74#63499—31no—
75#63492—31no—
76#63486—31no—
77#63456—31no—
78#63456—31no—
79#63446—31no—
80#63446—61no—
81#63446D311yescharacteristic, complemented
82C22⋊C4×D9—31no—
83C22⋊C4×D9—31no—
84#63437—31no—
85C4×D36—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
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—
107C3×#611—22no—
108C3×#611—41no—
109C2×C9×Dic3—22no—
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C4×D3×C9—22no—
116C3×D36—22no—
117C3×C4×D9—41no—
118#6192—22no—
119#6192D414yescomplemented
120(C3⋊D9)⋊C4—22no—
121Dic3×D9—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×#67—31no—
133C2×C3×#67C2×D311yescharacteristic
134C22×C3×Dic3C2×D311yescharacteristic
135C2×C3×D12—31no—
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×Dic3C2×D311yescharacteristic
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—
165C22×C4×C9—31no—
166C22×C4×C9—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—61no—
170C2×#611—61no—
171C2×#611C2×D311yescharacteristic, complemented
172C2×#611C2×D311yescharacteristic, complemented
173#3697—64no—
174C2×D36—31no—
175C2×D36—31no—
176C2×D36—31no—
177C2×D36—64no—
178C2×D36—61no—
179C2×D36C2×D311yescharacteristic
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—61no—
184C2×C4×D9C2×D311yescharacteristic, complemented
185C2×Dic18—31no—
186C9×C4⋊C4—31no—
187C9×C22⋊C4—21no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4C2×D311yescharacteristic, complemented
190C42×C9—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—31no—
200(C2×D9)⋊C4—61no—
201(C2×D9)⋊C4C2×D311yescharacteristic, complemented
202C4⋊Dic9—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—61no—
205Dic9⋊C4C2×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#4112yescomplemented
219C2×C3×D9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9C2×D412yes—
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—
233C9×Dic3C2×D412yes—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C2×#237—91no—
237C2×D3×D4—91no—
238C2×#235—91no—
239C22×D12—91no—
240C3×#121—91no—
241C3×C4×D4—31no—
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—31no—
258#884—91no—
259#884—91no—
260#884—181no—
261#67⋊C4D911yescharacteristic, complemented
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×D3—31no—
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—62no—
289C3×#67—121no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C3×D12—62no—
297C3×C4×D3—22no—
298C3×C4×D3—121no—
299#627—62no—
300#626—34no—
301#626—62no—
302#624—62no—
303D3×Dic3—62no—
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—121no—
316C22×D9—121no—
317C22×D9C22×D311yescharacteristic
318C22×D9C22×D311yescharacteristic
319D4×C9—62no—
320C2×C4×C9—21no—
321C2×C4×C9—21no—
322C2×C4×C9—31no—
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9—62no—
326C2×C4×C9—62no—
327C2×C4×C9C22×D311yescharacteristic
328C2×C4×C9C22×D311yescharacteristic
329#611—22no—
330#611—41no—
331#611—62no—
332#611—122no—
333#611—121no—
334#611—122no—
335C2×Dic9—31no—
336C2×Dic9—31no—
337C2×Dic9—61no—
338C2×Dic9—61no—
339C2×Dic9C22×D311yescharacteristic
340C2×Dic9C22×D311yescharacteristic
341D36—22no—
342D36—34no—
343D36—62no—
344D36—62no—
345D36—122no—
346C4×D9—41no—
347C4×D9—62no—
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—
360C3×D9—22no—
361C3×D9—41no—
362C23×D3—91no—
363C23×D3—91no—
364C23×D3—91no—
365C23×D3—91no—
366C2×C3×D4—31no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C2×C3×D4—91no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—91no—
373C2×#67—31no—
374C2×#67—31no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—181no—
382C2×#67—181no—
383C2×#67C2×D911yescharacteristic
384C22×Dic3—91no—
385C22×Dic3C2×D911yescharacteristic, complemented
386#237—184no—
387D3×D4—184no—
388#235—184no—
389C2×D12—31no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12—181no—
395C2×D12—184no—
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
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—31no—
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
435C4⋊Dic3—91no—
436Dic3⋊C4—31no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—181no—
441Dic3⋊C4C2×D911yescharacteristic, complemented
442C4×Dic3C2×D911yescharacteristic, complemented
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—32no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3#23512yes—
462D32—124no—
463D32—124no—
464C32×C4—21no—
465C32×C4—21no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3D3×D412yes—
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×C9C23×D311yescharacteristic
484C2×D9—21no—
485C2×D9—21no—
486C2×D9—21no—
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×D9D3×D412yes—
504C4×C9—21no—
505C4×C9—21no—
506C4×C9—32no—
507C4×C9—41no—
508C4×C9—41no—
509C4×C9—61no—
510C4×C9—61no—
511Dic9—21no—
512Dic9—21no—
513Dic9—62no—
514Dic9—61no—
515Dic9—61no—
516Dic9—121no—
517C2×#41—271no—
518C22×D4—271no—
519#124—271no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—91no—
524#121—271no—
525#121—271no—
526#120—271no—
527#120—271no—
528C4×D4—31no—
529C4×D4—271no—
530C2×C22⋊C4—271no—
531C2×C22⋊C4—271no—
532C3×C9#54611yescharacteristic, complemented, Sylow
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—91no—
536C23×C3—91no—
537C23×C3C22×D911yescharacteristic
538C23×C3C2×D3211yescharacteristic
539C22×D3—31no—
540C22×D3—31no—
541C22×D3—91no—
542C22×D3—91no—
543C22×D3—91no—
544C22×D3—91no—
545C22×D3—181no—
546C22×D3—181no—
547C22×D3—182no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—361no—
556C22×D3—361no—
557C22×D3—361no—
558C22×D3—361no—
559C22×D3C22×D911yescharacteristic
560C3×D4—62no—
561C3×D4—182no—
562C3×D4—182no—
563C3×D4—361no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—361no—
574C2×C3×C4C22×D911yescharacteristic
575C2×C3×C4C22×D911yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577C2×C3×C4C2×D3211yescharacteristic
578#67—22no—
579#67—62no—
580#67—94no—
581#67—121no—
582#67—182no—
583#67—182no—
584#67—182no—
585#67—362no—
586#67—361no—
587#67—361no—
588#67—362no—
589C2×Dic3—22no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—181no—
597C2×Dic3—181no—
598C2×Dic3—182no—
599C2×Dic3C22×D911yescharacteristic
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602D12—62no—
603D12—94no—
604D12—182no—
605D12—182no—
606D12—182no—
607D12—362no—
608C4×D3—22no—
609C4×D3—121no—
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×#23511yescharacteristic
620C2×C32C2×D3×D411yescharacteristic
621C2×C32#100911yescharacteristic
622C3⋊D3—62no—
623C3⋊D3—121no—
624C3×D3—22no—
625C3×D3—62no—
626C3×D3—121no—
627C2×C9—21no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—41no—
631C2×C9—62no—
632C2×C9—81no—
633C2×C9C2×D3×D411yescharacteristic
634C2×C9#100411yescharacteristic
635C2×C9D3×#4111yescharacteristic
636D9—22no—
637D9—41no—
638D9—62no—
639D9—122no—
640D9—121no—
641D9—241no—
642C24—271no—
643C24—271no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—31no—
647C2×D4—91no—
648C2×D4—91no—
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—31no—
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—31no—
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—92no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3C23×D911yescharacteristic
699C22×C3C22×D3211yescharacteristic
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—32no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
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×D3#369712yescomplemented
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—32no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4—181no—
741C3×C4—181no—
742Dic3—21no—
743Dic3—21no—
744Dic3—61no—
745Dic3—61no—
746Dic3—182no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—361no—
752Dic3D4×D912yes—
753C32#555011yescharacteristic
754C9—21no—
755C9#561011yescharacteristic, complemented
756C23—31no—
757C23—91no—
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—182no—
771D4—182no—
772D4—274no—
773D4—361no—
774D4—542no—
775D4—542no—
776D4—542no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—91no—
784C2×C4—91no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—361no—
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—182no—
801C2×C3—361no—
802C2×C3C2×#369711yescharacteristic
803C2×C3C2×D4×D911yescharacteristic
804C2×C3#6371511yescharacteristic
805C2×C3D3×#23511yescharacteristic
806C2×C3D32×D411yescharacteristic
807C2×C3#6431411yescharacteristic
808D3—22no—
809D3—62no—
810D3—121no—
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—92no—
824C22—181no—
825C22—181no—
826C22—181no—
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—32no—
841C4—61no—
842C4—61no—
843C4—181no—
844C4—181no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058965211yescharacteristic, complemented
849C3#1059428311yescharacteristic
850C2—41no—
851C2—62no—
852C2—182no—
853C2—361no—
854C2—542no—
855C2—1081no—
856C2D3×#369711yescharacteristic
857C2D3×D4×D911yescharacteristic
858C2#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×#88658C2semidirect
2. C2×D3×D36C2semidirect
3. #11721730C2semidirect
4. C9×#67⋊C4C2semidirect
5. C3×#63446C2semidirect
6. #11721292C2semidirect
7. #11721292C2semidirect
8. #11721277C2semidirect
9. #11721048C2semidirect
10. D9×(C2×D3)⋊C4C2semidirect
11. C4×#6192C2semidirect
12. #11720997C2semidirect
13. #11720981C2semidirect
14. #11720955C2semidirect
15. #11720940C2semidirect
20. C2×#6233C22semidirect
21. C2×#6233C22semidirect
23. C2×C4×C3⋊D9C22semidirect
25. C2×C3×#611C22semidirect
26. C2×C3×#611C22semidirect
27. C22×C9×Dic3C22semidirect
30. C2×C3×C4×D9C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×Dic3×D9C22semidirect
36. C2×#6189C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C4×C9×Dic3C22semidirect
45. C3×Dic9⋊C4C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. Dic3⋊Dic9C22semidirect
81. #63446D3semidirect
119. #6192D4semidirect
171. C2×#611C2×D3semidirect
172. C2×#611C2×D3semidirect
184. C2×C4×D9C2×D3semidirect
189. C9×C22⋊C4C2×D3semidirect
201. (C2×D9)⋊C4C2×D3semidirect
205. Dic9⋊C4C2×D3semidirect
218. C2×D3×C9#41semidirect
261. #67⋊C4D9semidirect
385. C22×Dic3C2×D9semidirect
411. C3×C22⋊C4C2×D9semidirect
441. Dic3⋊C4C2×D9semidirect
442. C4×Dic3C2×D9semidirect
532. C3×C9#546semidirect
677. C22⋊C4D3×D9semidirect
730. C2×D3#3697semidirect
755. C9#5610semidirect
848. C3#10589652semidirect

Maximal subgroups

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

subgroupindex
C2×#886582
C2×D3×D362
#117217302
C9×#67⋊C42
C3×#634462
#117212922
#117212772
#117210482
D9×(C2×D3)⋊C42
C4×#61922
#117209972
#117209812
#117209552
#117209402
#105942833
#105896523