Finite Group Databasebeta

← #13148981

Subgroups — #13148981

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×D36C211yesmaximal, characteristic, complemented
2C2×#88635C211yesmaximal, characteristic, complemented
3#11721751C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×#63456C211yesmaximal, characteristic, complemented
6#11721051C211yesmaximal, characteristic, complemented
7#11721051C211yesmaximal, characteristic, complemented
8#11721048C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721030C211yesmaximal, characteristic, complemented
11#11721005C211yesmaximal, characteristic, complemented
12#11721003C211yesmaximal, characteristic, complemented
13#11720997C211yesmaximal, characteristic, complemented
14#11720983C211yesmaximal, characteristic, complemented
15#11720978C211yesmaximal, characteristic, complemented
16#10594620—31nomaximal
17#10589732—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C4×C3⋊D9C2211yescharacteristic, complemented
24C2×C4×D3×C9C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic, complemented
27C2×C9×Dic6C2211yescharacteristic, complemented
28C2×#6195C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35C2×Dic3×D9C2211yescharacteristic, complemented
36D3×D36—24no—
37#88635—24no—
38C3×C9×C4⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47C9×Dic3⋊C4C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×D12—31no—
56C2×#3799—31no—
57#64104—31no—
58C3×#896D311yescharacteristic
59C3×#894—31no—
60#63923—31no—
61#63923—31no—
62#63921—31no—
63D3×(C2×D3)⋊C4—31no—
64#63910—31no—
65#63907—31no—
66#63904—31no—
67#63897—31no—
68#63886—31no—
69#63881—31no—
70C2×#3701—31no—
71C22×D36—31no—
72C9×C22⋊Q8—31no—
73#63509—31no—
74C4×#611—31no—
75#63457—31no—
76#63457—31no—
77#63457—31no—
78#63457—61no—
79#63456—31no—
80#63456D311yescharacteristic, complemented
81#63455—31no—
82#63444—31no—
83#63444—31no—
84C22⋊C4×D9—31no—
85C22⋊C4×D9—31no—
86C22×C3⋊D9C2311yescharacteristic
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
100C2×C3×C4×C9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C4⋊(C3⋊D9)—22no—
103C4⋊(C3⋊D9)—22no—
104C4⋊(C3⋊D9)—41no—
105C4×C3⋊D9—41no—
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C4×D3×C9—22no—
112C3×D36—22no—
113C3×C4×D9—22no—
114C9×Dic6—22no—
115#6195—22no—
116#6192—22no—
117#6192—22no—
118#6192—41no—
119#6192D414yescomplemented
120(C3⋊D9)⋊C4—22no—
121(C3⋊D9)⋊C4—22no—
122Dic3×D9—41no—
123#5654—91no—
124#5630—91no—
125C22×D32—31no—
126C22×D32—31no—
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4×C3⋊D3—31no—
131C2×C3×D12—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×Dic6C2×D311yescharacteristic
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#624—31no—
141C2×#624—31no—
142C2×D3×Dic3—31no—
143D3×D12—64no—
144#3799—64no—
145C23×D9—31no—
146C23×D9—31no—
147C32×C4⋊C4C2×D311yescharacteristic
148#3752—31no—
149#3752—31no—
150C3×(C2×D3)⋊C4—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×Dic3⋊C4—31no—
156C3×Dic3⋊C4C2×D311yescharacteristic
157C3×Dic3⋊C4C2×D311yescharacteristic
158#3722—31no—
159#3722—31no—
160#3722—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163Dic32—31no—
164C2×Q8×C9—31no—
165C22×C4×C9—31no—
166C2×#611—31no—
167#3701—64no—
168C2×D36—31no—
169C2×D36—31no—
170C2×D36—31no—
171C2×D36—31no—
172C2×D36—31no—
173C2×D36—31no—
174C2×D36—31no—
175C2×D36—64no—
176C2×D36—61no—
177C2×D36—61no—
178C2×D36—61no—
179C2×D36C2×D311yescharacteristic
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9—61no—
185C2×C4×D9C2×D311yescharacteristic, complemented
186C9×C4⋊C4—21no—
187C9×C4⋊C4—31no—
188C9×C4⋊C4—31no—
189C9×C4⋊C4C2×D311yescharacteristic, complemented
190C9×C22⋊C4—31no—
191C9×C22⋊C4—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)⋊C4—61no—
201(C2×D9)⋊C4C2×D311yescharacteristic, complemented
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4C2×D311yescharacteristic, complemented
205C4×Dic9—31no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
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×C4×C9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3C2×D412yes—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C2×#239—91no—
237C2×D3×D4—91no—
238C2×#235—91no—
239C22×D12—91no—
240C3×#123—91no—
241C3×C22⋊Q8—31no—
242#947—91no—
243#939—91no—
244C4×#67—91no—
245C2×(C2×D3)⋊C4—91no—
246#896D911yescharacteristic, complemented
247#895—91no—
248#895—91no—
249#895—91no—
250#895—91no—
251#895—181no—
252#894—31no—
253#894—91no—
254#894—91no—
255#893—91no—
256#893—91no—
257#885—91no—
258#884—91no—
259#882—91no—
260#882—91no—
261#882—91no—
262#882—91no—
263#67⋊C4—91no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—91no—
267C22×C3⋊D3—31no—
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
281C2×C32×C4C22×D311yescharacteristic
282C2×C3⋊Dic3—31no—
283C4⋊(C3⋊D3)—62no—
284C4⋊(C3⋊D3)—62no—
285C4⋊(C3⋊D3)—121no—
286C4×C3⋊D3—121no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C3×D12—62no—
293C3×C4×D3—22no—
294C3×C4×D3—62no—
295C3×Dic6—22no—
296#626—34no—
297#626—62no—
298#626—62no—
299#626—62no—
300#626—121no—
301#624—62no—
302#624—62no—
303D3×Dic3—121no—
304C23×C9—31no—
305C22×D9—31no—
306C22×D9—31no—
307C22×D9—31no—
308C22×D9—61no—
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
319Q8×C9—62no—
320C2×C4×C9—21no—
321C2×C4×C9—21no—
322C2×C4×C9—21no—
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9—31no—
326C2×C4×C9—62no—
327C2×C4×C9C22×D311yescharacteristic
328C2×C4×C9C22×D311yescharacteristic
329C2×C4×C9C22×D311yescharacteristic
330#611—62no—
331C2×Dic9—31no—
332C2×Dic9—61no—
333C2×Dic9C22×D311yescharacteristic
334C2×Dic9C22×D311yescharacteristic
335D36—22no—
336D36—34no—
337D36—62no—
338D36—62no—
339D36—62no—
340D36—62no—
341D36—122no—
342D36—122no—
343D36—121no—
344D36—122no—
345D36—121no—
346C4×D9—22no—
347C4×D9—62no—
348C4×D9—62no—
349C4×D9—121no—
350C4×D9—121no—
351C4×D9—122no—
352#546—271noSylow
353C2×C3×C9C22×D411yescharacteristic
354C2×C3×C9C2×#4111yescharacteristic
355C2×C3×C9H(5,𝔽2)11yescharacteristic
356C3⋊D9—22no—
357C3⋊D9—41no—
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×Q8—31no—
367C2×C3×D4—91no—
368C22×C3×C4—31no—
369C22×C3×C4—91no—
370C2×#67—91no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C22×Dic3—91no—
376#239—184no—
377D3×D4—184no—
378#235—184no—
379C2×D12—31no—
380C2×D12—91no—
381C2×D12—91no—
382C2×D12—91no—
383C2×D12—91no—
384C2×D12—91no—
385C2×D12—91no—
386C2×D12—91no—
387C2×D12—91no—
388C2×D12—91no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—181no—
392C2×D12—181no—
393C2×D12—181no—
394C2×D12—184no—
395C2×C4×D3—31no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—181no—
404C2×C4×D3C2×D911yescharacteristic
405C2×Dic6C2×D911yescharacteristic, complemented
406C3×C4⋊C4—21no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—91no—
410C3×C4⋊C4C2×D911yescharacteristic, complemented
411C3×C4⋊C4D3211yescharacteristic
412C3×C22⋊C4—31no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4—91no—
417#217—91no—
418#217—91no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
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—91no—
434(C2×D3)⋊C4—181no—
435(C2×D3)⋊C4—181no—
436(C2×D3)⋊C4C2×D911yescharacteristic
437(C2×D3)⋊C4C2×D911yescharacteristic
438Dic3⋊C4—31no—
439Dic3⋊C4C2×D911yescharacteristic, complemented
440Dic3⋊C4C2×D911yescharacteristic, complemented
441C4×Dic3—91no—
442C4×Dic3—91no—
443C22×C32C23×D311yescharacteristic
444C2×C3⋊D3—32no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
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#23912yes—
462D32—124no—
463D32—124no—
464C32×C4—21no—
465C32×C4—21no—
466C32×C4—21no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3D3×D412yes—
473C22×C9—21no—
474C22×C9—32no—
475C22×C9—61no—
476C22×C9—61no—
477C22×C9C23×D311yescharacteristic
478C2×D9—21no—
479C2×D9—21no—
480C2×D9—21no—
481C2×D9—21no—
482C2×D9—21no—
483C2×D9—32no—
484C2×D9—62no—
485C2×D9—61no—
486C2×D9—61no—
487C2×D9—61no—
488C2×D9—61no—
489C2×D9—61no—
490C2×D9—61no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—121no—
494C2×D9—121no—
495C2×D9—121no—
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—22no—
505C4×C9—21no—
506C4×C9—21no—
507C4×C9—21no—
508C4×C9—32no—
509C4×C9—41no—
510C4×C9—41no—
511C4×C9—61no—
512C4×C9—61no—
513Dic9—21no—
514Dic9—21no—
515Dic9—61no—
516Dic9—121no—
517C2×#41—271no—
518C22×D4—271no—
519#124—271no—
520#123—91no—
521#123—271no—
522C22⋊Q8—31no—
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—31no—
534C23×C3—91no—
535C23×C3—91no—
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—91no—
539C22×D3—91no—
540C22×D3—91no—
541C22×D3—91no—
542C22×D3—91no—
543C22×D3—91no—
544C22×D3—181no—
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×Q8—62no—
561C3×D4—182no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—31no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—62no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—182no—
572C2×C3×C4C22×D911yescharacteristic
573C2×C3×C4C22×D911yescharacteristic
574C2×C3×C4C22×D911yescharacteristic
575C2×C3×C4C2×D3211yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577C2×C3×C4C2×D3211yescharacteristic
578#67—94no—
579#67—182no—
580#67—182no—
581#67—182no—
582#67—361no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—91no—
586C2×Dic3—91no—
587C2×Dic3—181no—
588C2×Dic3—361no—
589C2×Dic3C22×D911yescharacteristic
590C2×Dic3C22×D911yescharacteristic
591C2×Dic3C22×D911yescharacteristic
592D12—62no—
593D12—94no—
594D12—182no—
595D12—182no—
596D12—182no—
597D12—182no—
598D12—182no—
599D12—182no—
600D12—182no—
601D12—362no—
602D12—362no—
603D12—361no—
604D12—361no—
605D12—362no—
606D12—361no—
607C4×D3—22no—
608C4×D3—62no—
609C4×D3—182no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—361no—
614C4×D3—361no—
615C4×D3—361no—
616C4×D3—362no—
617Dic6—22no—
618C2×C32C2×D3×D411yescharacteristic
619C2×C32C2×#23911yescharacteristic
620C2×C32#100911yescharacteristic
621C3⋊D3—62no—
622C3⋊D3—121no—
623C3⋊D3—121no—
624C3×D3—22no—
625C3×D3—62no—
626C3×D3—121no—
627C2×C9—21no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—62no—
631C2×C9C2×D3×D411yescharacteristic
632C2×C9D3×#4111yescharacteristic
633C2×C9#100911yescharacteristic
634D9—22no—
635D9—41no—
636D9—62no—
637D9—122no—
638D9—121no—
639D9—121no—
640D9—241no—
641D9—241no—
642C24—271no—
643C24—271no—
644#41—544no—
645C2×Q8—31no—
646C2×D4—91no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
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—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—91no—
665C4⋊C4D3×D911yescharacteristic, complemented
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—91no—
669C22⋊C4—91no—
670C22⋊C4—91no—
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—32no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—92no—
684C22×C3—181no—
685C22×C3—181no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3C23×D911yescharacteristic
690C22×C3C22×D3211yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—32no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—92no—
700C2×D3—92no—
701C2×D3—182no—
702C2×D3—181no—
703C2×D3—181no—
704C2×D3—181no—
705C2×D3—181no—
706C2×D3—181no—
707C2×D3—181no—
708C2×D3—181no—
709C2×D3—181no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—361no—
719C2×D3—361no—
720C2×D3—361no—
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#370112yescomplemented
731C3×C4—22no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—32no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—61no—
742C3×C4—61no—
743C3×C4—181no—
744C3×C4—181no—
745Dic3—21no—
746Dic3—21no—
747Dic3—61no—
748Dic3—61no—
749Dic3—181no—
750Dic3—181no—
751Dic3—361no—
752Dic3D4×D912yes—
753C32#563011yescharacteristic
754C9—21no—
755C9#565411yescharacteristic, complemented
756C23—31no—
757C23—91no—
758C23—91no—
759C23—271no—
760C23—271no—
761C23—271no—
762C23—542no—
763C23—542no—
764C23—542no—
765C23—542no—
766C23—1081no—
767C23—1081no—
768Q8—62no—
769D4—182no—
770D4—274no—
771D4—542no—
772D4—542no—
773D4—542no—
774D4—542no—
775D4—542no—
776D4—1081no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—62no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—182no—
785C2×C4—271no—
786C2×C4—542no—
787C2×C4—542no—
788C2×C4—1081no—
789C2×C4—1081no—
790C2×C4C2×D3×D911yescharacteristic
791C2×C4C2×D3×D911yescharacteristic
792C2×C4C2×D3×D911yescharacteristic
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—62no—
797C2×C3—182no—
798C2×C3—361no—
799C2×C3C2×D4×D911yescharacteristic
800C2×C3C2×#370111yescharacteristic
801C2×C3#6371511yescharacteristic
802C2×C3#6430811yescharacteristic
803C2×C3D32×D411yescharacteristic
804C2×C3D3×#23911yescharacteristic
805D3—22no—
806D3—62no—
807D3—121no—
808D3—182no—
809D3—182no—
810D3—362no—
811D3—361no—
812D3—361no—
813D3—361no—
814D3—361no—
815D3—721no—
816D3—721no—
817C22—32no—
818C22—61no—
819C22—61no—
820C22—92no—
821C22—181no—
822C22—181no—
823C22—181no—
824C22—181no—
825C22—181no—
826C22—272no—
827C22—541no—
828C22—541no—
829C22—541no—
830C22—541no—
831C22—541no—
832C22—541no—
833C22—541no—
834C22—541no—
835C22—1084no—
836C22—1084no—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—32no—
842C4—61no—
843C4—61no—
844C4—181no—
845C4—181no—
846C4—541no—
847C3—21no—
848C3#1058973211yescharacteristic, complemented
849C3#1059462011yescharacteristic
850C2—62no—
851C2—182no—
852C2—361no—
853C2—542no—
854C2—1081no—
855C2—1081no—
856C2#1172247811yescharacteristic
857C2D3×D4×D911yescharacteristic
858C2D3×#370111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×D36C2semidirect
2. C2×#88635C2semidirect
3. #11721751C2semidirect
4. C9×#896C2semidirect
5. C3×#63456C2semidirect
6. #11721051C2semidirect
7. #11721051C2semidirect
8. #11721048C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721030C2semidirect
11. #11721005C2semidirect
12. #11721003C2semidirect
13. #11720997C2semidirect
14. #11720983C2semidirect
15. #11720978C2semidirect
21. C2×C4⋊(C3⋊D9)C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
23. C2×C4×C3⋊D9C22semidirect
26. C2×C3×C4×D9C22semidirect
27. C2×C9×Dic6C22semidirect
31. C2×#6192C22semidirect
32. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×Dic3×D9C22semidirect
38. C3×C9×C4⋊C4C22semidirect
39. #88536C22semidirect
40. #88536C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. C9×Dic3⋊C4C22semidirect
48. C3×Dic9⋊C4C22semidirect
50. #88445C22semidirect
51. #88445C22semidirect
52. #88445C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
80. #63456D3semidirect
119. #6192D4semidirect
185. C2×C4×D9C2×D3semidirect
189. C9×C4⋊C4C2×D3semidirect
201. (C2×D9)⋊C4C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
218. C2×D3×C9#41semidirect
246. #896D9semidirect
405. C2×Dic6C2×D9semidirect
410. C3×C4⋊C4C2×D9semidirect
439. Dic3⋊C4C2×D9semidirect
440. Dic3⋊C4C2×D9semidirect
532. C3×C9#546semidirect
665. C4⋊C4D3×D9semidirect
730. C2×D3#3701semidirect
755. C9#5654semidirect
848. C3#10589732semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D362
C2×#886352
#117217512
C9×#8962
C3×#634562
#117210512
#117210482
D9×(C2×D3)⋊C42
#117210302
#117210052
#117210032
#117209972
#117209832
#117209782
#105946203
#105897323