Finite Group Databasebeta

← #13151285

Subgroups — #13151285

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×C9×#237C211yesmaximal, characteristic, complemented
2C2×D9×#67C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C3×#63499C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#67⋊Dic9C211yesmaximal, characteristic, complemented
7#11721281C211yesmaximal, characteristic, complemented
8#11721277C211yesmaximal, characteristic, complemented
9Dic3×#611C211yesmaximal, characteristic, complemented
10C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
11#11721251C211yesmaximal, characteristic, complemented
12D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
13#11721032C211yesmaximal, characteristic, complemented
14#11721003C211yesmaximal, characteristic, complemented
15#11720984C211yesmaximal, characteristic, complemented
16#10595304—31nomaximal
17#10589931—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic, complemented
23C22×C3⋊Dic9C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic
25C2×C9×#67C2211yescharacteristic, complemented
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic, complemented
28C22×C9×Dic3C2211yescharacteristic, complemented
29C22×C9×Dic3C2211yescharacteristic, complemented
30C9×#237—24no—
31C2×C4×D3×C9C2211yescharacteristic, complemented
32C2×C9×Dic6C2211yescharacteristic, complemented
33D9×#67—24no—
34C2×#6194C2211yescharacteristic
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic
37C2×Dic3×D9C2211yescharacteristic
38#88551C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic, complemented
45#88445C2211yescharacteristic, complemented
46#88445C2211yescharacteristic, complemented
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C3×#237D311yescharacteristic
56C2×D3×#67—31no—
57#64148—31no—
58C3×#937—31no—
59#63983—31no—
60#63978—31no—
61#67⋊Dic3—31no—
62Dic3×#67—31no—
63#63970—31no—
64#63966—31no—
65C2×(C2×D3)⋊Dic3—31no—
66D3×(C2×D3)⋊C4—31no—
67#63907—31no—
68#63905—31no—
69#63887—31no—
70C2×C9×#41—31no—
71C2×D4×D9—31no—
72#63509—31no—
73#63508—31no—
74#63501—31no—
75#63501—31no—
76#63501—61no—
77#63499—31no—
78#63499D311yescharacteristic, complemented
79D4×Dic9—31no—
80#63492—31no—
81#63491—31no—
82#63491—31no—
83C4×#611—31no—
84C2×(C2×D9)⋊C4—31no—
85C2×(C2×D9)⋊C4—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9—22no—
91C22×C3×D9—22no—
92C22×C3×D9—41no—
93C22×C3×D9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C3×D4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101#6233—41no—
102C2×C3⋊Dic9—41no—
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C2×C3⋊Dic9C2311yescharacteristic
106C9×#67—22no—
107C9×#67D414yescomplemented
108C3×#611—22no—
109C3×#611—41no—
110C2×C9×Dic3—22no—
111C2×C9×Dic3—22no—
112C2×C9×Dic3C2311yescharacteristic
113C2×C9×Dic3C2311yescharacteristic
114C2×C9×Dic3C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C4×D3×C9—22no—
118C9×Dic6—22no—
119#6194—22no—
120D3×Dic9—41no—
121#6192—22no—
122Dic3×D9—22no—
123#5829—91no—
124#5591—91no—
125C23×C3×D3—31no—
126C22×D32—31no—
127C2×C32×D4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130C22×C3⋊Dic3—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67C2×D311yescharacteristic
134C2×C3×#67C2×D311yescharacteristic
135C22×C3×Dic3C2×D311yescharacteristic
136C22×C3×Dic3C2×D311yescharacteristic
137C3×#237—24no—
138C2×C3×C4×D3C2×D311yescharacteristic
139C2×C3×Dic6C2×D311yescharacteristic
140D3×#67—64no—
141C2×#626—31no—
142C2×#625—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C23×D9—31no—
146C23×D9C2×D311yescharacteristic
147#3757—31no—
148#3752—31no—
149#3750—31no—
150C3×#217—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156#3722—31no—
157#3722—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163Dic32—31no—
164C9×#41—64no—
165C2×Q8×C9—31no—
166C2×D4×C9—21no—
167C2×D4×C9—31no—
168C2×D4×C9—31no—
169C2×D4×C9C2×D311yescharacteristic, complemented
170C22×C4×C9—31no—
171C22×C4×C9—31no—
172C22×C4×C9—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—61no—
177C2×#611—61no—
178C2×#611C2×D311yescharacteristic
179C2×#611C2×D311yescharacteristic, complemented
180C22×Dic9—31no—
181C22×Dic9—31no—
182C22×Dic9—61no—
183D4×D9—64no—
184C2×D36—31no—
185C2×C4×D9—31no—
186#3676—31no—
187#3676—31no—
188#3676—61no—
189#3676C2×D311yescharacteristic, complemented
190(C2×D9)⋊C4—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—61no—
198(C2×D9)⋊C4C2×D311yescharacteristic
199(C2×D9)⋊C4C2×D311yescharacteristic, complemented
200C4⋊Dic9—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—61no—
205C4×Dic9—31no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9C2×D412yes—
212C22×C3×C9C2411yescharacteristic
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9C2×D412yes—
219C2×C3×D9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—44no—
225C2×C3×D9#4112yescomplemented
226D3×D9—44no—
227C3×C4×C9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3C2×D412yes—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C2×C3×#41—31no—
237C22×#67—91no—
238C2×#237D911yescharacteristic, complemented
239C2×D3×D4—91no—
240C3×#120—91no—
241C2×#217—91no—
242#947—91no—
243#946—91no—
244#939—91no—
245#939—91no—
246#939—91no—
247#939—91no—
248#939—181no—
249#938—91no—
250#937—31no—
251#937—91no—
252#937—91no—
253D4×Dic3—91no—
254D4×Dic3—91no—
255#930—91no—
256#929—91no—
257#929—91no—
258C4×#67—91no—
259C2×(C2×D3)⋊C4—91no—
260C2×(C2×D3)⋊C4—91no—
261#886—91no—
262#885—91no—
263#883—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C22×C3⋊D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—62no—
273C22×C3×D3—62no—
274C22×C3×D3—121no—
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C32×D4—22no—
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—121no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—121no—
287C3×#67—22no—
288C3×#67—62no—
289C3×#67—121no—
290C3×#67#6714yes—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C3×C4×D3—22no—
299C3×Dic6—22no—
300#626—62no—
301#625—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—21no—
306C23×C9—31no—
307C23×C9C22×D311yescharacteristic
308C23×C9C22×D311yescharacteristic
309C22×D9—22no—
310C22×D9—22no—
311C22×D9—31no—
312C22×D9—41no—
313C22×D9—61no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—121no—
317C22×D9C22×D311yescharacteristic
318C22×D9C22×D311yescharacteristic
319Q8×C9—62no—
320D4×C9—22no—
321D4×C9—34no—
322D4×C9—42no—
323D4×C9—62no—
324C2×C4×C9—21no—
325C2×C4×C9—31no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9—62no—
329C2×C4×C9—62no—
330C2×C4×C9—62no—
331C2×C4×C9C22×D311yescharacteristic
332#611—22no—
333#611—41no—
334#611—62no—
335#611—62no—
336#611—122no—
337#611—121no—
338#611—122no—
339C2×Dic9—31no—
340C2×Dic9—31no—
341C2×Dic9—31no—
342C2×Dic9—61no—
343C2×Dic9—61no—
344C2×Dic9—61no—
345C2×Dic9—121no—
346C2×Dic9—121no—
347C2×Dic9—122no—
348C2×Dic9C22×D311yescharacteristic
349C2×Dic9C22×D311yescharacteristic
350D36—62no—
351C4×D9—62no—
352#546—271noSylow
353C2×C3×C9—22no—
354C2×C3×C9—41no—
355C2×C3×C9C22×D411yescharacteristic
356C2×C3×C9C2×#4111yescharacteristic
357C2×C3×C9H(5,𝔽2)11yescharacteristic
358C3⋊D9—41no—
359D3×C9—22no—
360C3×D9—22no—
361C3×D9—41no—
362C24×C3—91no—
363C23×D3—31no—
364C23×D3—91no—
365C23×D3—91no—
366C3×#41—64no—
367C2×C3×Q8—31no—
368C2×C3×D4—21no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—91no—
372C2×C3×D4—91no—
373C2×C3×D4C2×D911yescharacteristic, complemented
374C2×C3×D4D3211yescharacteristic
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—181no—
388C2×#67—181no—
389C2×#67—184no—
390C2×#67C2×D911yescharacteristic
391C2×#67C2×D911yescharacteristic, complemented
392C22×Dic3—91no—
393C22×Dic3—91no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3—181no—
397C22×Dic3C2×D911yescharacteristic, complemented
398C22×Dic3C2×D911yescharacteristic, complemented
399#237—24no—
400D3×D4—184no—
401C2×D12—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3C2×D911yescharacteristic, complemented
405C2×Dic6C2×D911yescharacteristic, complemented
406C3×C22⋊C4—91no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4—91no—
409#217—31no—
410#217—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—181no—
418(C2×D3)⋊C4—31no—
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—181no—
432C4⋊Dic3—91no—
433C4⋊Dic3—91no—
434C4⋊Dic3—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—181no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32C2×#6712yes—
449C22×C32C23×D311yescharacteristic
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—124no—
462C2×C3×D3C2×#6712yes—
463D32—124no—
464C32×C4—21no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3C2×#6712yes—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—22no—
480C22×C9—32no—
481C22×C9—41no—
482C22×C9—41no—
483C22×C9—41no—
484C22×C9—41no—
485C22×C9—41no—
486C22×C9—61no—
487C22×C9—61no—
488C22×C9D3×D412yes—
489C22×C9C23×D311yescharacteristic
490C2×D9—21no—
491C2×D9—21no—
492C2×D9—21no—
493C2×D9—21no—
494C2×D9—21no—
495C2×D9—44no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—124no—
503C2×D9#23712yescomplemented
504C4×C9—21no—
505C4×C9—32no—
506C4×C9—41no—
507C4×C9—61no—
508C4×C9—61no—
509Dic9—21no—
510Dic9—21no—
511Dic9—62no—
512Dic9—61no—
513Dic9—61no—
514Dic9—61no—
515Dic9—121no—
516Dic9—121no—
517C2×#41—31no—
518C22×D4—271no—
519#124—271no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—271no—
524#121—271no—
525#121—271no—
526#120—91no—
527#120—271no—
528C4×D4—271no—
529C4×D4—271no—
530C2×C22⋊C4—271no—
531C2×C22⋊C4—271no—
532C3×C9#54611yescharacteristic, complemented, Sylow
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—91no—
537C23×C3—91no—
538C23×C3—182no—
539C23×C3—182no—
540C23×C3—361no—
541C23×C3C22×D911yescharacteristic
542C23×C3C22×D911yescharacteristic
543C23×C3C2×D3211yescharacteristic
544C23×C3C2×D3211yescharacteristic
545C22×D3—31no—
546C22×D3—31no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—91no—
550C22×D3—91no—
551C22×D3—121no—
552C22×D3—181no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—361no—
558C22×D3—361no—
559C22×D3C22×D911yescharacteristic
560C3×Q8—62no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—34no—
564C3×D4—42no—
565C3×D4—62no—
566C3×D4—182no—
567C3×D4—361no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4C22×D911yescharacteristic
578C2×C3×C4C2×D3211yescharacteristic
579#67—22no—
580#67—62no—
581#67—121no—
582#67—182no—
583#67—182no—
584#67—182no—
585#67—182no—
586#67—182no—
587#67—362no—
588#67—361no—
589#67—361no—
590#67—362no—
591#67#61114yescomplemented
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—181no—
603C2×Dic3—181no—
604C2×Dic3—181no—
605C2×Dic3—182no—
606C2×Dic3—361no—
607C2×Dic3—361no—
608C2×Dic3—361no—
609C2×Dic3—362no—
610C2×Dic3C22×D911yescharacteristic
611C2×Dic3C22×D911yescharacteristic
612C2×Dic3C22×D911yescharacteristic
613D12—182no—
614C4×D3—22no—
615C4×D3—182no—
616C4×D3—361no—
617Dic6—22no—
618C2×C32—22no—
619C2×C32—41no—
620C2×C32D3×#4111yescharacteristic
621C2×C32#100911yescharacteristic
622C2×C32C22×#6711yescharacteristic
623C3⋊D3—121no—
624C3×D3—22no—
625C3×D3—62no—
626C3×D3—121no—
627C2×C9—22no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—21no—
631C2×C9—42no—
632C2×C9—41no—
633C2×C9—62no—
634C2×C9—81no—
635C2×C9C2×D3×D411yescharacteristic
636C2×C9C2×#23711yescharacteristic
637C2×C9#100411yescharacteristic
638D9—22no—
639D9—41no—
640D9—121no—
641D9—241no—
642C24—91no—
643C24—271no—
644#41—64no—
645C2×Q8—31no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—91no—
649C2×D4—91no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—544no—
655C2×D4D3×D911yescharacteristic, complemented
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—91no—
667C22⋊C4—91no—
668C22⋊C4—91no—
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⋊C4—271no—
678C42—271no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—22no—
691C22×C3—32no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—92no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3—181no—
704C22×C3—181no—
705C22×C3—364no—
706C22×C3C2×#61112yes—
707C22×C3C23×D911yescharacteristic
708C22×C3D3×#6712yes—
709C22×C3C22×D3211yescharacteristic
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—32no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—124no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—361no—
726C2×D3—361no—
727C2×D3—361no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3C2×#61112yes—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—32no—
734C3×C4—41no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—181no—
738C3×C4—181no—
739Dic3—21no—
740Dic3—21no—
741Dic3—61no—
742Dic3—61no—
743Dic3—182no—
744Dic3—181no—
745Dic3—181no—
746Dic3—181no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—361no—
751Dic3—361no—
752Dic3C2×#61112yes—
753C32#582911yescharacteristic
754C9—21no—
755C9#559111yescharacteristic, complemented
756C23—31no—
757C23—91no—
758C23—91no—
759C23—182no—
760C23—182no—
761C23—271no—
762C23—361no—
763C23—542no—
764C23—542no—
765C23—1081no—
766C23C2×D3×D911yescharacteristic
767C23C2×D3×D911yescharacteristic
768Q8—62no—
769D4—22no—
770D4—34no—
771D4—62no—
772D4—182no—
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—62no—
784C2×C4—91no—
785C2×C4—91no—
786C2×C4—271no—
787C2×C4—271no—
788C2×C4—271no—
789C2×C4—542no—
790C2×C4—1081no—
791C2×C4—1081no—
792C2×C4C2×D3×D911yescharacteristic
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—42no—
799C2×C3—41no—
800C2×C3—41no—
801C2×C3—62no—
802C2×C3—81no—
803C2×C3—182no—
804C2×C3—361no—
805C2×C3#41×D911yescharacteristic
806C2×C3#6371511yescharacteristic
807C2×C3C22×#61111yescharacteristic
808C2×C3D3×#23711yescharacteristic
809C2×C3#6431411yescharacteristic
810C2×C3C2×D3×#6711yescharacteristic
811D3—22no—
812D3—62no—
813D3—121no—
814D3—361no—
815D3—361no—
816D3—721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—32no—
823C22—61no—
824C22—61no—
825C22—92no—
826C22—181no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—364no—
832C22—541no—
833C22—541no—
834C22—541no—
835C22—1084no—
836C22D3×#61112yes—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—32no—
840C4—61no—
841C4—61no—
842C4—181no—
843C4—181no—
844C4—541no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058993111yescharacteristic, complemented
849C3#1059530411yescharacteristic
850C2—22no—
851C2—41no—
852C2—62no—
853C2—182no—
854C2—361no—
855C2—1081no—
856C2D9×#23711yescharacteristic
857C2#1172250111yescharacteristic
858C2C2×D3×#61111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C9×#237C2semidirect
2. C2×D9×#67C2semidirect
3. #11721839C2semidirect
4. C3×#63499C2semidirect
5. #11721292C2semidirect
6. #67⋊Dic9C2semidirect
7. #11721281C2semidirect
8. #11721277C2semidirect
9. Dic3×#611C2semidirect
10. C2×(C2×D9)⋊Dic3C2semidirect
11. #11721251C2semidirect
12. D3×(C2×D9)⋊C4C2semidirect
13. #11721032C2semidirect
14. #11721003C2semidirect
15. #11720984C2semidirect
20. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C22×C3⋊Dic9C22semidirect
25. C2×C9×#67C22semidirect
27. C2×C3×#611C22semidirect
28. C22×C9×Dic3C22semidirect
29. C22×C9×Dic3C22semidirect
31. C2×C4×D3×C9C22semidirect
32. C2×C9×Dic6C22semidirect
35. C2×D3×Dic9C22semidirect
38. #88551C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C3×#3676C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. (C2×D3)⋊Dic9C22semidirect
45. #88445C22semidirect
46. #88445C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. Dic9⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
78. #63499D3semidirect
107. C9×#67D4semidirect
169. C2×D4×C9C2×D3semidirect
179. C2×#611C2×D3semidirect
189. #3676C2×D3semidirect
199. (C2×D9)⋊C4C2×D3semidirect
225. C2×C3×D9#41semidirect
238. C2×#237D9semidirect
373. C2×C3×D4C2×D9semidirect
391. C2×#67C2×D9semidirect
397. C22×Dic3C2×D9semidirect
398. C22×Dic3C2×D9semidirect
404. C2×C4×D3C2×D9semidirect
405. C2×Dic6C2×D9semidirect
503. C2×D9#237semidirect
532. C3×C9#546semidirect
591. #67#611semidirect
655. C2×D4D3×D9semidirect
755. C9#5591semidirect
848. C3#10589931semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#2372
C2×D9×#672
#117218392
C3×#634992
#117212922
#67⋊Dic92
#117212812
#117212772
Dic3×#6112
C2×(C2×D9)⋊Dic32
#117212512
D3×(C2×D9)⋊C42
#117210322
#117210032
#117209842
#105953043
#105899313