Finite Group Databasebeta

← #13151143

Subgroups — #13151143

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×D3×D4×C9C211yesmaximal, characteristic, complemented
2C2×#88662C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C3×#63497C211yesmaximal, characteristic, complemented
5#11721287C211yesmaximal, characteristic, complemented
6#11721287C211yesmaximal, characteristic, complemented
7#67⋊Dic9C211yesmaximal, characteristic, complemented
8D3×#3676C211yesmaximal, characteristic, complemented
9C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
10#11721263C211yesmaximal, characteristic, complemented
11#11721262C211yesmaximal, characteristic, complemented
12#11721030C211yesmaximal, characteristic, complemented
13#11721017C211yesmaximal, characteristic, complemented
14#11721015C211yesmaximal, characteristic, complemented
15#11720955C211yesmaximal, characteristic, complemented
16#10595148—31nomaximal
17#10589908—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C23×D3×C9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C22×C3⋊Dic9C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic
25C2×C9×#67C2211yescharacteristic
26C22×C3×Dic9C2211yescharacteristic, complemented
27D3×D4×C9—24no—
28C2×C9×D12C2211yescharacteristic
29C2×C4×D3×C9C2211yescharacteristic
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic, complemented
32C2×#6195C2211yescharacteristic, complemented
33#88662—24no—
34C2×D3×Dic9C2211yescharacteristic, complemented
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38#88551C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic, complemented
43C3×#3676C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52(C2×D3)⋊Dic9C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C3×D3×D4D311yescharacteristic
56C2×#3804—31no—
57#64148—31no—
58C3×#935—31no—
59#63977—31no—
60#63977—31no—
61#67⋊Dic3—31no—
62D3×#217—31no—
63C2×(C2×D3)⋊Dic3—31no—
64#63959—31no—
65#63958—31no—
66#63904—31no—
67#63886—31no—
68#63884—31no—
69#63851—31no—
70C22×D4×C9—31no—
71C2×#3699—31no—
72#63515—31no—
73#63515—31no—
74C2×#3676—31no—
75C2×#3676—31no—
76#63501—31no—
77#63501—31no—
78#63501—61no—
79#63500—31no—
80#63498—31no—
81#63497—31no—
82#63497D311yescharacteristic, complemented
83D4×Dic9—31no—
84C4×#611—31no—
85#63486—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9—22no—
90C22×D3×C9—22no—
91C22×D3×C9—22no—
92C22×D3×C9—22no—
93C22×D3×C9—41no—
94C22×D3×C9—41no—
95C22×D3×C9C2311yescharacteristic
96C22×D3×C9C2311yescharacteristic
97C22×D3×C9C2311yescharacteristic
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
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9—22no—
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C9×D12—22no—
115C4×D3×C9—22no—
116#6195—22no—
117#6195—22no—
118#6195—41no—
119D3×Dic9—22no—
120D3×Dic9—41no—
121(C3⋊D9)⋊C4—22no—
122#6189—22no—
123#5806—91no—
124#5654—91no—
125C23×C3×D3C2×D311yescharacteristic
126C23×C3×D3C2×D311yescharacteristic
127C2×C32×D4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130C22×C3⋊Dic3—31no—
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×#67C2×D311yescharacteristic
133C22×C3×Dic3—31no—
134C3×D3×D4—24no—
135C2×C3×D12C2×D311yescharacteristic
136C2×C3×C4×D3C2×D311yescharacteristic
137C2×#627—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#624—31no—
142#3804—64no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C24×C9—31no—
146C24×C9—31no—
147#3757—31no—
148#3752—31no—
149#3750—31no—
150C3×#217—31no—
151C3×#217—31no—
152C3×#217—31no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—31no—
155Dic3⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—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—
164C2×D4×C9—21no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C2×D4×C9—31no—
168C2×D4×C9—64no—
169C2×D4×C9C2×D311yescharacteristic
170C22×C4×C9—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—61no—
177C2×#611—61no—
178C22×Dic9—31no—
179C22×Dic9—31no—
180C22×Dic9—31no—
181C22×Dic9—61no—
182C22×Dic9C2×D311yescharacteristic, complemented
183#3699—64no—
184C2×C4×D9—31no—
185C2×Dic18—31no—
186#3676—31no—
187#3676—31no—
188#3676—31no—
189#3676—31no—
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—31no—
194#3676—61no—
195#3676C2×D311yescharacteristic, complemented
196#3676C2×D311yescharacteristic, complemented
197#3676C2×D311yescharacteristic, complemented
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—61no—
200C4⋊Dic9—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4—61no—
203Dic9⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4C2×D311yescharacteristic, complemented
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×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9—21no—
223C2×D3×C9—44no—
224C2×D3×C9—44no—
225C2×D3×C9C2×D412yes—
226C2×D3×C9#4112yescomplemented
227C3×C4×C9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3C2×D412yes—
232C3×Dic9—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C22×C3×D4—31no—
237C2×#237—91no—
238C2×D3×D4D911yescharacteristic, complemented
239C2×#235—91no—
240C3×#123—91no—
241#953—91no—
242#953—91no—
243C2×#217—91no—
244C2×#217—91no—
245#939—91no—
246#939—91no—
247#939—91no—
248#939—181no—
249#938—91no—
250#936—91no—
251#935—31no—
252#935—91no—
253D4×Dic3—91no—
254C4×#67—91no—
255C2×(C2×D3)⋊C4—91no—
256#924—91no—
257#896—91no—
258#895—91no—
259#894—91no—
260#893—91no—
261#885—91no—
262#884—91no—
263#882—91no—
264#882—91no—
265#67⋊C4—91no—
266D3×C22⋊C4—91no—
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C22×C3⋊D3—31no—
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—41no—
275C22×C3×D3—41no—
276C22×C3×D3C22×D311yescharacteristic
277C22×C3×D3C22×D311yescharacteristic
278C22×C3×D3C22×D311yescharacteristic
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#6714yes—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3C22×D311yescharacteristic
295C3×D12—22no—
296C3×C4×D3—22no—
297#627—62no—
298#626—62no—
299#626—62no—
300#626—121no—
301#624—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—21no—
306C23×C9—31no—
307C23×C9—31no—
308C23×C9—31no—
309C23×C9—62no—
310C23×C9—62no—
311C23×C9—62no—
312C23×C9—62no—
313C23×C9—121no—
314C23×C9—121no—
315C23×C9C22×D311yescharacteristic
316C23×C9C22×D311yescharacteristic
317C22×D9—31no—
318C22×D9—61no—
319D4×C9—22no—
320D4×C9—34no—
321D4×C9—42no—
322D4×C9—62no—
323D4×C9—62no—
324C2×C4×C9—21no—
325C2×C4×C9—31no—
326C2×C4×C9—62no—
327C2×C4×C9C22×D311yescharacteristic
328#611—62no—
329#611—62no—
330#611—62no—
331#611—122no—
332#611—121no—
333#611—121no—
334#611—122no—
335C2×Dic9—22no—
336C2×Dic9—31no—
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—61no—
342C2×Dic9—62no—
343C2×Dic9—121no—
344C2×Dic9—121no—
345C2×Dic9—122no—
346C2×Dic9C22×D311yescharacteristic
347C2×Dic9C22×D311yescharacteristic
348C2×Dic9C22×D311yescharacteristic
349C2×Dic9C22×D311yescharacteristic
350C4×D9—62no—
351Dic18—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—
360D3×C9—22no—
361D3×C9—41no—
362C24×C3—31no—
363C24×C3—31no—
364C23×D3C2×D911yescharacteristic
365C23×D3C2×D911yescharacteristic
366C2×C3×D4—21no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—64no—
371C2×C3×D4C2×D911yescharacteristic
372C2×C3×D4D3211yescharacteristic
373C22×C3×C4—31no—
374C22×C3×C4—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—181no—
383C2×#67—181no—
384C2×#67C2×D911yescharacteristic
385C2×#67C2×D911yescharacteristic
386C22×Dic3—31no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—181no—
392#237—184no—
393D3×D4—24no—
394#235—184no—
395C2×D12—91no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12C2×D911yescharacteristic
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3C2×D911yescharacteristic
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C4⋊C4—91no—
407C3×C4⋊C4—91no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411#217—31no—
412#217—31no—
413#217—31no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—91no—
421#217—91no—
422#217—91no—
423#217—181no—
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—
434C4⋊Dic3—91no—
435Dic3⋊C4—31no—
436Dic3⋊C4—31no—
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—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—44no—
461C2×C3×D3—44no—
462C2×C3×D3#23712yes—
463C2×C3×D3C2×#6712yes—
464C32×C4—21no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—61no—
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—32no—
482C22×C9—41no—
483C22×C9—41no—
484C22×C9—41no—
485C22×C9—41no—
486C22×C9—41no—
487C22×C9—61no—
488C22×C9—61no—
489C22×C9—61no—
490C22×C9—61no—
491C22×C9—61no—
492C22×C9—61no—
493C22×C9—61no—
494C22×C9—124no—
495C22×C9—124no—
496C22×C9D3×D412yes—
497C22×C9C23×D311yescharacteristic
498C2×D9—61no—
499C2×D9—61no—
500C2×D9—61no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—121no—
504C4×C9—21no—
505C4×C9—32no—
506C4×C9—41no—
507Dic9—21no—
508Dic9—21no—
509Dic9—21no—
510Dic9—21no—
511Dic9—62no—
512Dic9—61no—
513Dic9—61no—
514Dic9—61no—
515Dic9—121no—
516Dic9—121no—
517C2×#41—271no—
518C22×D4—31no—
519#124—271no—
520#123—91no—
521#123—271no—
522C22⋊Q8—271no—
523#121—271no—
524#121—271no—
525#121—271no—
526#120—271no—
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—31no—
537C23×C3—31no—
538C23×C3—62no—
539C23×C3—62no—
540C23×C3—62no—
541C23×C3—62no—
542C23×C3—121no—
543C23×C3—121no—
544C23×C3C22×D911yescharacteristic
545C23×C3C22×D911yescharacteristic
546C23×C3C2×D3211yescharacteristic
547C23×C3C2×D3211yescharacteristic
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—91no—
555C22×D3—91no—
556C22×D3—181no—
557C22×D3C22×D911yescharacteristic
558C22×D3C22×D911yescharacteristic
559C22×D3C22×D911yescharacteristic
560C3×D4—22no—
561C3×D4—22no—
562C3×D4—34no—
563C3×D4—42no—
564C3×D4—62no—
565C3×D4—62no—
566C2×C3×C4—21no—
567C2×C3×C4—31no—
568C2×C3×C4—62no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—182no—
574C2×C3×C4C22×D911yescharacteristic
575C2×C3×C4C2×D3211yescharacteristic
576#67—22no—
577#67—182no—
578#67—182no—
579#67—182no—
580#67—182no—
581#67—362no—
582#67—361no—
583#67—361no—
584#67—361no—
585#67—362no—
586#67#61114yescomplemented
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—62no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—181no—
599C2×Dic3—181no—
600C2×Dic3—181no—
601C2×Dic3—182no—
602C2×Dic3—361no—
603C2×Dic3—361no—
604C2×Dic3—361no—
605C2×Dic3—362no—
606C2×Dic3C22×D911yescharacteristic
607D12—22no—
608D12—182no—
609D12—182no—
610D12—361no—
611C4×D3—22no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—361no—
616Dic6—182no—
617Dic6—182no—
618C2×C32—22no—
619C2×C32—41no—
620C2×C32C2×#23711yescharacteristic
621C2×C32#100411yescharacteristic
622C2×C32C22×#6711yescharacteristic
623C3⋊D3—121no—
624C3×D3—22no—
625C3×D3—22no—
626C3×D3—41no—
627C2×C9—22no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—21no—
631C2×C9—42no—
632C2×C9—41no—
633C2×C9—62no—
634C2×C9—62no—
635C2×C9—81no—
636C2×C9—121no—
637C2×C9C2×D3×D411yescharacteristic
638C2×C9D3×#4111yescharacteristic
639C2×C9#100911yescharacteristic
640D9—121no—
641D9—241no—
642C24—31no—
643C24—31no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—64no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4D3×D911yescharacteristic
656C22×C4—31no—
657C22×C4—91no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—91no—
663C4⋊C4—91no—
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—32no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—124no—
706C22×C3—124no—
707C22×C3C2×#61112yes—
708C22×C3C23×D911yescharacteristic
709C22×C3D3×#6712yes—
710C22×C3C22×D3211yescharacteristic
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—44no—
719C2×D3—44no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—361no—
727C2×D3—361no—
728C2×D3—361no—
729C2×D3#369912yescomplemented
730C2×D3C2×#61112yes—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—32no—
734C3×C4—41no—
735C3×C4—181no—
736C3×C4—181no—
737C3×C4—181no—
738C3×C4—181no—
739Dic3—61no—
740Dic3—61no—
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#580611yescharacteristic
754C9—21no—
755C9#565411yescharacteristic, complemented
756C23—31no—
757C23—31no—
758C23—31no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—121no—
764C23—121no—
765C23—271no—
766C23C2×D3×D911yescharacteristic
767C23C2×D3×D911yescharacteristic
768Q8—542no—
769D4—22no—
770D4—34no—
771D4—62no—
772D4—62no—
773D4—542no—
774D4—542no—
775D4—542no—
776D4—1081no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—62no—
780C2×C4—91no—
781C2×C4—91no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—182no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—271no—
788C2×C4—542no—
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—62no—
803C2×C3—81no—
804C2×C3—121no—
805C2×C3C2×#369911yescharacteristic
806C2×C3#6371011yescharacteristic
807C2×C3C22×#61111yescharacteristic
808C2×C3D3×#23711yescharacteristic
809C2×C3#6431411yescharacteristic
810C2×C3C2×D3×#6711yescharacteristic
811D3—22no—
812D3—22no—
813D3—41no—
814D3—361no—
815D3—361no—
816D3—721no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—32no—
823C22—32no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—124no—
832C22—124no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22D3×#61112yes—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—32no—
840C4—181no—
841C4—181no—
842C4—181no—
843C4—181no—
844C4—541no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058990811yescharacteristic, complemented
849C3#1059514811yescharacteristic
850C2—22no—
851C2—41no—
852C2—62no—
853C2—62no—
854C2—121no—
855C2—1081no—
856C2D3×#369911yescharacteristic
857C2#1172250011yescharacteristic
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×D3×D4×C9C2semidirect
2. C2×#88662C2semidirect
3. #11721839C2semidirect
4. C3×#63497C2semidirect
5. #11721287C2semidirect
6. #11721287C2semidirect
7. #67⋊Dic9C2semidirect
8. D3×#3676C2semidirect
9. C2×(C2×D3)⋊Dic9C2semidirect
10. #11721263C2semidirect
11. #11721262C2semidirect
12. #11721030C2semidirect
13. #11721017C2semidirect
14. #11721015C2semidirect
15. #11720955C2semidirect
21. C2×#6233C22semidirect
22. C2×#6233C22semidirect
23. C22×C3⋊Dic9C22semidirect
26. C22×C3×Dic9C22semidirect
31. C2×#6195C22semidirect
32. C2×#6195C22semidirect
34. C2×D3×Dic9C22semidirect
35. C2×D3×Dic9C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
37. C2×#6189C22semidirect
38. #88551C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C3×#3676C22semidirect
42. C3×#3676C22semidirect
43. C3×#3676C22semidirect
44. C3×Dic9⋊C4C22semidirect
45. C3×Dic9⋊C4C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. (C2×D3)⋊Dic9C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic3×Dic9C22semidirect
82. #63497D3semidirect
107. C9×#67D4semidirect
182. C22×Dic9C2×D3semidirect
195. #3676C2×D3semidirect
196. #3676C2×D3semidirect
197. #3676C2×D3semidirect
203. Dic9⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
226. C2×D3×C9#41semidirect
238. C2×D3×D4D9semidirect
532. C3×C9#546semidirect
586. #67#611semidirect
729. C2×D3#3699semidirect
755. C9#5654semidirect
848. C3#10589908semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D4×C92
C2×#886622
#117218392
C3×#634972
#117212872
#67⋊Dic92
D3×#36762
C2×(C2×D3)⋊Dic92
#117212632
#117212622
#117210302
#117210172
#117210152
#117209552
#105951483
#105899083