Finite Group Databasebeta

← #13148418

Subgroups — #13148418

Order 1728.

1080 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic, complemented
2C2×#88663C211yesmaximal, characteristic, complemented
3#11721732C211yesmaximal, characteristic, complemented
4C9×#882C211yesmaximal, characteristic, complemented
5C3×#611⋊C4C211yesmaximal, characteristic, complemented
6#11721288C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
8#11721050C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721036C211yesmaximal, characteristic, complemented
11#11721023C211yesmaximal, characteristic, complemented
12D12×Dic9C211yesmaximal, characteristic, complemented
13#11721017C211yesmaximal, characteristic, complemented
14#11720989C211yesmaximal, characteristic, complemented
15#11720956C211yesmaximal, characteristic, complemented
16#10594292—31nomaximal
17#10589693—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic, complemented
23C2×C3×#611C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic, complemented
25C2×C9×D12C2211yescharacteristic
26C2×C9×D12C2211yescharacteristic, complemented
27C2×C3×C4×D9C2211yescharacteristic, complemented
28D3×#611—24no—
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic, complemented
31C2×#6194C2211yescharacteristic
32C2×#6194C2211yescharacteristic, complemented
33#88663—24no—
34C2×D3×Dic9C2211yescharacteristic
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
42C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47C3×C4×Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52(C2×D3)⋊Dic9C2211yescharacteristic, complemented
53#88445C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3805—31no—
57#64095—31no—
58C3×#882D311yescharacteristic
59C3×#67⋊C4—31no—
60#63978—31no—
61C2×(C2×D3)⋊Dic3—31no—
62#63922—31no—
63D3×(C2×D3)⋊C4—31no—
64#63908—31no—
65#63893—31no—
66Dic3×D12—31no—
67#63891—31no—
68#63886—31no—
69#63852—31no—
70C22×#611—31no—
71C2×#3699—31no—
72C9×#120—31no—
73C2×#3676—31no—
74#63501—31no—
75#63501—31no—
76#63500—31no—
77#63499—31no—
78D4×Dic9—31no—
79#63448—31no—
80#63448—61no—
81#63447—31no—
82#63445—31no—
83#611⋊C4D311yescharacteristic, complemented
84C22⋊C4×D9—31no—
85#63440—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9—22no—
89C22×D3×C9—22no—
90C22×D3×C9—41no—
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101C2×C3⋊Dic9—22no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C9×#67—22no—
106C3×#611D414yescomplemented
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9—41no—
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C9×D12—22no—
113C9×D12—41no—
114C3×C4×D9—41no—
115#6195—22no—
116#6195—41no—
117#6194—22no—
118#6194—22no—
119D3×Dic9—22no—
120D3×Dic9—22no—
121Dic3×D9—22no—
122#6189—22no—
123#5591—91no—
124#5554—91no—
125C23×C3×D3C2×D311yescharacteristic
126C22×D32—31no—
127C2×#638—31no—
128C22×C3⋊Dic3—31no—
129C2×C3×#67—31no—
130C2×C3×#67C2×D311yescharacteristic
131C22×C3×Dic3—31no—
132C2×C3×D12C2×D311yescharacteristic
133C2×C3×D12C2×D311yescharacteristic
134C2×C3×C4×D3—31no—
135D3×#67—64no—
136C2×#627—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#625—31no—
140C2×#625—31no—
141#3805—64no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C24×C9—31no—
146C23×D9—31no—
147C32×C22⋊C4C2×D311yescharacteristic
148#3752—31no—
149#3752—31no—
150C4⋊(C3⋊Dic3)—31no—
151C4⋊(C3⋊Dic3)—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×Dic3⋊C4—31no—
156C3×C4×Dic3—31no—
157Dic3⋊Dic3—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—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—64no—
173C2×#611—61no—
174C2×#611C2×D311yescharacteristic
175C22×Dic9—31no—
176C22×Dic9—31no—
177C22×Dic9—31no—
178C22×Dic9—61no—
179C22×Dic9C2×D311yescharacteristic, complemented
180#3699—64no—
181C2×C4×D9—31no—
182C2×C4×D9C2×D311yescharacteristic, complemented
183C2×Dic18—31no—
184C9×C22⋊C4—21no—
185C9×C22⋊C4—31no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4C2×D311yescharacteristic, complemented
188#3676—31no—
189#3676—31no—
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—61no—
197(C2×D9)⋊C4—61no—
198(C2×D9)⋊C4C2×D311yescharacteristic, complemented
199C4⋊Dic9—31no—
200C4⋊Dic9—31no—
201C4⋊Dic9—61no—
202C4⋊Dic9—61no—
203Dic9⋊C4—31no—
204Dic9⋊C4C2×D311yescharacteristic, complemented
205C4×Dic9C2×D311yescharacteristic, complemented
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×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—44no—
222C2×D3×C9#4112yescomplemented
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—
231C3⋊Dic9—21no—
232C9×Dic3—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C22×#67—91no—
237C2×#237—91no—
238C2×#237—91no—
239C2×D3×D4—91no—
240C3×#120—31no—
241C3×C4×D4—91no—
242C2×#217—91no—
243#939—91no—
244#939—91no—
245#938—91no—
246#937—91no—
247D4×Dic3—91no—
248#930—91no—
249#930—91no—
250C2×(C2×D3)⋊C4—91no—
251C2×(C2×D3)⋊C4—91no—
252#897—91no—
253#895—91no—
254#886—91no—
255#886—91no—
256#886—91no—
257#886—181no—
258#885—91no—
259#883—91no—
260#882—91no—
261#882D911yescharacteristic, complemented
262#67⋊C4—31no—
263D3×C22⋊C4—91no—
264#878—91no—
265#875—91no—
266C4×D12—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3—31no—
272C22×C3×D3—41no—
273C22×C3×D3C22×D311yescharacteristic
274C22×C3×D3C22×D311yescharacteristic
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—62no—
286C3×#67—22no—
287C3×#67—34no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—121no—
292C2×C3×Dic3C22×D311yescharacteristic
293C3×D12—22no—
294C3×D12—41no—
295C3×C4×D3—121no—
296#627—62no—
297#626—62no—
298#626—121no—
299#625—62no—
300#625—62no—
301D3×Dic3—62no—
302D3×Dic3—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9—31no—
307C23×C9—31no—
308C23×C9—62no—
309C23×C9—62no—
310C23×C9—121no—
311C23×C9C22×D311yescharacteristic
312C22×D9—31no—
313C22×D9—61no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—121no—
317C22×D9C22×D311yescharacteristic
318D4×C9—62no—
319D4×C9—62no—
320D4×C9—121no—
321C2×C4×C9—21no—
322C2×C4×C9—21no—
323C2×C4×C9—31no—
324C2×C4×C9C22×D311yescharacteristic
325C2×C4×C9C22×D311yescharacteristic
326#611—62no—
327#611—62no—
328#611—62no—
329#611—62no—
330#611—122no—
331#611—121no—
332#611D1214yescomplemented
333C2×Dic9—31no—
334C2×Dic9—31no—
335C2×Dic9—31no—
336C2×Dic9—41no—
337C2×Dic9—61no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—62no—
341C2×Dic9—62no—
342C2×Dic9—62no—
343C2×Dic9—122no—
344C2×Dic9C22×D311yescharacteristic
345C2×Dic9C22×D311yescharacteristic
346C2×Dic9C22×D311yescharacteristic
347C4×D9—41no—
348C4×D9—62no—
349Dic18—62no—
350#546—271noSylow
351C2×C3×C9—22no—
352C2×C3×C9C22×D411yescharacteristic
353C2×C3×C9C2×#4111yescharacteristic
354C2×C3×C9H(5,𝔽2)11yescharacteristic
355C3⋊D9—41no—
356D3×C9—22no—
357D3×C9—41no—
358D3×C9—41no—
359C3×D9—22no—
360C24×C3—31no—
361C23×D3—91no—
362C23×D3—91no—
363C23×D3C2×D911yescharacteristic
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—91no—
368C22×C3×C4—91no—
369C22×C3×C4—91no—
370C2×#67—31no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—181no—
380C2×#67—184no—
381C2×#67C2×D911yescharacteristic, complemented
382C22×Dic3—31no—
383C22×Dic3—91no—
384C22×Dic3—91no—
385C22×Dic3—91no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—181no—
389#237—184no—
390#237—184no—
391D3×D4—184no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12C2×D911yescharacteristic
395C2×D12C2×D911yescharacteristic, complemented
396C2×C4×D3—31no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×Dic6—91no—
401C2×Dic6—91no—
402C3×C4⋊C4—91no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—91no—
407C3×C22⋊C4C2×D911yescharacteristic, complemented
408C3×C22⋊C4D3211yescharacteristic
409C3×C42—91no—
410#217—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415(C2×D3)⋊C4—31no—
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—181no—
428(C2×D3)⋊C4—181no—
429(C2×D3)⋊C4C2×D911yescharacteristic
430(C2×D3)⋊C4C2×D911yescharacteristic, complemented
431C4⋊Dic3—91no—
432C4⋊Dic3—91no—
433C4⋊Dic3—91no—
434C4⋊Dic3—91no—
435C4⋊Dic3—91no—
436C4⋊Dic3—181no—
437C4⋊Dic3—181no—
438Dic3⋊C4—31no—
439Dic3⋊C4—91no—
440C4×Dic3—31no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32D3×D412yes—
444C22×C32C23×D311yescharacteristic
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—32no—
457C2×C3×D3—44no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3#23712yes—
461D32—124no—
462C32×C4—21no—
463C32×C4—21no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3×Dic3—21no—
468C3×Dic3—32no—
469C3×Dic3—61no—
470C3×Dic3—61no—
471C22×C9—21no—
472C22×C9—21no—
473C22×C9—21no—
474C22×C9—22no—
475C22×C9—32no—
476C22×C9—41no—
477C22×C9—41no—
478C22×C9—61no—
479C22×C9—61no—
480C22×C9—61no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9—61no—
485C22×C9—61no—
486C22×C9—124no—
487C22×C9C2×D1212yes—
488C22×C9C23×D311yescharacteristic
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—121no—
495C2×D9—121no—
496C2×D9—121no—
497C2×D9—124no—
498C2×D9C2×D1212yes—
499C4×C9—21no—
500C4×C9—21no—
501C4×C9—41no—
502C4×C9—41no—
503C4×C9—61no—
504Dic9—21no—
505Dic9—21no—
506Dic9—61no—
507Dic9—61no—
508Dic9—61no—
509Dic9—121no—
510Dic9—121no—
511Dic9—121no—
512Dic9C2×D1212yes—
513C2×#41—271no—
514C22×D4—271no—
515#124—271no—
516#123—271no—
517#123—271no—
518C22⋊Q8—271no—
519#121—271no—
520#121—271no—
521#121—271no—
522#120—31no—
523#120—271no—
524C4×D4—91no—
525C4×D4—271no—
526C2×C22⋊C4—271no—
527C2×C22⋊C4—271no—
528C3×C9#54611yescharacteristic, complemented, Sylow
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—62no—
534C23×C3—62no—
535C23×C3—91no—
536C23×C3—121no—
537C23×C3C22×D911yescharacteristic
538C23×C3C2×D3211yescharacteristic
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—31no—
542C22×D3—41no—
543C22×D3—91no—
544C22×D3—91no—
545C22×D3—181no—
546C22×D3—182no—
547C22×D3—182no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—361no—
551C22×D3—361no—
552C22×D3C22×D911yescharacteristic
553C22×D3C22×D911yescharacteristic
554C22×D3C22×D911yescharacteristic
555C3×D4—62no—
556C3×D4—62no—
557C3×D4—94no—
558C3×D4—121no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—91no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—361no—
566C2×C3×C4—361no—
567C2×C3×C4C22×D911yescharacteristic
568C2×C3×C4C22×D911yescharacteristic
569C2×C3×C4C2×D3211yescharacteristic
570C2×C3×C4C2×D3211yescharacteristic
571#67—22no—
572#67—34no—
573#67—182no—
574#67—182no—
575#67—182no—
576#67—182no—
577#67—182no—
578#67—182no—
579#67—182no—
580#67—362no—
581#67—361no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—91no—
586C2×Dic3—91no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—121no—
592C2×Dic3—181no—
593C2×Dic3—181no—
594C2×Dic3—181no—
595C2×Dic3—182no—
596C2×Dic3—182no—
597C2×Dic3—182no—
598C2×Dic3—182no—
599C2×Dic3—182no—
600C2×Dic3—362no—
601C2×Dic3C22×D911yescharacteristic
602D12—22no—
603D12—41no—
604D12—182no—
605D12—361no—
606C4×D3—121no—
607C4×D3—182no—
608C4×D3—182no—
609C4×D3—182no—
610Dic6—182no—
611Dic6—182no—
612C2×C32—22no—
613C2×C32C2×D3×D411yescharacteristic
614C2×C32C2×#23711yescharacteristic
615C2×C32#100411yescharacteristic
616C3⋊D3—121no—
617C3×D3—22no—
618C3×D3—41no—
619C3×D3—41no—
620C3×D3—62no—
621C2×C9—22no—
622C2×C9—21no—
623C2×C9—21no—
624C2×C9—21no—
625C2×C9—42no—
626C2×C9—62no—
627C2×C9—121no—
628C2×C9—121no—
629C2×C9C22×D1211yescharacteristic
630C2×C9#100411yescharacteristic
631C2×C9D3×#4111yescharacteristic
632D9—22no—
633D9—121no—
634D9—241no—
635C24—31no—
636C24—271no—
637#41—544no—
638C2×Q8—271no—
639C2×D4—31no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—91no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—544no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C4⋊C4—91no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—91no—
662C22⋊C4—271no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4D3×D911yescharacteristic, complemented
671C42—91no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—32no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—92no—
690C22×C3—124no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3D4×D912yes—
694C22×C3C23×D911yescharacteristic
695C22×C3D3×D1212yes—
696C22×C3C22×D3211yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—32no—
706C2×D3—44no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—181no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—361no—
716C2×D3—361no—
717C2×D3—361no—
718C2×D3—364no—
719C2×D3—364no—
720C2×D3#369912yescomplemented
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—61no—
728C3×C4—92no—
729C3×C4—181no—
730C3×C4—181no—
731Dic3—21no—
732Dic3—32no—
733Dic3—61no—
734Dic3—61no—
735Dic3—181no—
736Dic3—181no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740Dic3—181no—
741Dic3—361no—
742Dic3—361no—
743Dic3—361no—
744C32#559111yescharacteristic
745C9—21no—
746C9#555411yescharacteristic, complemented
747C23—31no—
748C23—31no—
749C23—31no—
750C23—62no—
751C23—62no—
752C23—91no—
753C23—121no—
754C23—271no—
755C23—542no—
756C23—542no—
757C23—1081no—
758C23C2×D3×D911yescharacteristic
759Q8—542no—
760D4—62no—
761D4—62no—
762D4—94no—
763D4—121no—
764D4—542no—
765D4—542no—
766D4—542no—
767D4—542no—
768D4—1081no—
769C2×C4—31no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—271no—
774C2×C4—271no—
775C2×C4—271no—
776C2×C4—361no—
777C2×C4—361no—
778C2×C4—542no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4C2×D3×D911yescharacteristic
783C2×C4C2×D3×D911yescharacteristic
784C2×C3—22no—
785C2×C3—22no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—42no—
790C2×C3—62no—
791C2×C3—121no—
792C2×C3—121no—
793C2×C3—182no—
794C2×C3C2×D4×D911yescharacteristic
795C2×C3C2×#369911yescharacteristic
796C2×C3#6371011yescharacteristic
797C2×C3C2×D3×D1211yescharacteristic
798C2×C3D3×#23711yescharacteristic
799C2×C3#6431311yescharacteristic
800D3—22no—
801D3—41no—
802D3—41no—
803D3—62no—
804D3—361no—
805D3—361no—
806D3—721no—
807C22—21no—
808C22—21no—
809C22—32no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—92no—
819C22—124no—
820C22—181no—
821C22—181no—
822C22—541no—
823C22—541no—
824C22—541no—
825C22—1084no—
826C22D9×D1212yes—
827C22C22×D3×D911yescharacteristic
828C4—21no—
829C4—21no—
830C4—61no—
831C4—92no—
832C4—181no—
833C4—181no—
834C4—541no—
835C4—541no—
836C4—541no—
837C3—21no—
838C3#1058969311yescharacteristic, complemented
839C3#1059429211yescharacteristic
840C2—22no—
841C2—62no—
842C2—121no—
843C2—121no—
844C2—182no—
845C2—1081no—
846C2C2×D9×D1211yescharacteristic
847C2D3×#369911yescharacteristic
848C2#1172249911yescharacteristic
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×D3×#611C2semidirect
2. C2×#88663C2semidirect
3. #11721732C2semidirect
4. C9×#882C2semidirect
5. C3×#611⋊C4C2semidirect
6. #11721288C2semidirect
7. C2×(C2×D3)⋊Dic9C2semidirect
8. #11721050C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721036C2semidirect
11. #11721023C2semidirect
12. D12×Dic9C2semidirect
13. #11721017C2semidirect
14. #11720989C2semidirect
15. #11720956C2semidirect
21. C22×C3⋊Dic9C22semidirect
22. C2×C9×#67C22semidirect
24. C22×C3×Dic9C22semidirect
26. C2×C9×D12C22semidirect
27. C2×C3×C4×D9C22semidirect
30. C2×#6195C22semidirect
32. C2×#6194C22semidirect
35. C2×D3×Dic9C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88536C22semidirect
40. #88536C22semidirect
41. C4⋊(C3⋊Dic9)C22semidirect
42. C4⋊(C3⋊Dic9)C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×Dic9⋊C4C22semidirect
47. C3×C4×Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. (C2×D3)⋊Dic9C22semidirect
53. #88445C22semidirect
54. Dic9⋊Dic3C22semidirect
83. #611⋊C4D3semidirect
106. C3×#611D4semidirect
179. C22×Dic9C2×D3semidirect
182. C2×C4×D9C2×D3semidirect
187. C9×C22⋊C4C2×D3semidirect
198. (C2×D9)⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
205. C4×Dic9C2×D3semidirect
222. C2×D3×C9#41semidirect
261. #882D9semidirect
332. #611D12semidirect
381. C2×#67C2×D9semidirect
395. C2×D12C2×D9semidirect
407. C3×C22⋊C4C2×D9semidirect
430. (C2×D3)⋊C4C2×D9semidirect
528. C3×C9#546semidirect
670. C22⋊C4D3×D9semidirect
720. C2×D3#3699semidirect
746. C9#5554semidirect
838. C3#10589693semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×#886632
#117217322
C9×#8822
C3×#611⋊C42
#117212882
C2×(C2×D3)⋊Dic92
#117210502
D9×(C2×D3)⋊C42
#117210362
#117210232
D12×Dic92
#117210172
#117209892
#117209562
#105942923
#105896933