Finite Group Databasebeta

← #13150562

Subgroups — #13150562

Order 1728.

1166 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88736C211yesmaximal, characteristic, complemented
2C2×D9×#67C211yesmaximal, characteristic, complemented
3C9×#929C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
5#11721288C211yesmaximal, characteristic, complemented
6#11721276C211yesmaximal, characteristic, complemented
7#11721241C211yesmaximal, characteristic, complemented
8#11721051C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10#11721042C211yesmaximal, characteristic, complemented
11#11721041C211yesmaximal, characteristic, complemented
12#11721005C211yesmaximal, characteristic, complemented
13#11720996C211yesmaximal, characteristic, complemented
14#11720978C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10595077—31nomaximal
17#10589756—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic, complemented
23#88736—24no—
24C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
25C2×C4×C3⋊D9C2211yescharacteristic, complemented
26C2×C4×C3⋊D9C2211yescharacteristic, complemented
27C2×#6226C2211yescharacteristic, complemented
28C2×C9×#67C2211yescharacteristic
29C22×C3×Dic9C2211yescharacteristic, complemented
30D9×#67—24no—
31C2×#6195C2211yescharacteristic, complemented
32C2×#6194C2211yescharacteristic
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic
35C2×#6192C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37C2×Dic3×D9C2211yescharacteristic
38C9×#217C2211yescharacteristic, complemented
39C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C9×Dic3⋊C4C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3828—31no—
56C2×D3×#67—31no—
57C3×#929D311yescharacteristic
58C2×C3×(C2×D3)⋊C4—31no—
59#63978—31no—
60#63977—31no—
61#63952—31no—
62#63923—31no—
63#63921—31no—
64#63913—31no—
65#63912—31no—
66#63910—31no—
67#63896—31no—
68#63881—31no—
69#63853—31no—
70C2×D4×D9—31no—
71C2×#3697—31no—
72C2×#3697—61no—
73C9×#123—31no—
74#63501—31no—
75C2×(C2×D9)⋊C4D311yescharacteristic, complemented
76#63458—31no—
77#63457—31no—
78#63456—31no—
79#63455—31no—
80#63447—31no—
81#63446—31no—
82#63444—31no—
83#63444—31no—
84#611⋊C4—31no—
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
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—
98C2×C3×C4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233—22no—
102#6233D414yescomplemented
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C4⋊(C3⋊D9)—22no—
106C4×C3⋊D9—22no—
107C4×C3⋊D9—22no—
108#6226—22no—
109C9×#67—22no—
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C3×Dic9—41no—
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116#6195—41no—
117#6194—22no—
118#6192—22no—
119#6192—22no—
120#6192—41no—
121(C3⋊D9)⋊C4—41no—
122Dic3×D9—22no—
123#5654—91no—
124#5490—91no—
125C23×C3×D3—31no—
126C22×D32—31no—
127C22×C32×C4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130#3828—64no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×#634—31no—
135C2×C3×#67C2×D311yescharacteristic
136C22×C3×Dic3—31no—
137D3×#67—64no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#625—31no—
143C2×#624—31no—
144C2×D3×Dic3—31no—
145C23×D9—31no—
146C23×D9C2×D311yescharacteristic
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4C2×D311yescharacteristic
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×Dic3⋊C4C2×D311yescharacteristic
155C3×Dic3⋊C4C2×D311yescharacteristic
156#3724—31no—
157Dic3⋊Dic3—31no—
158#3722—31no—
159#3722—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163Dic32—31no—
164C2×D4×C9—31no—
165C22×C4×C9—21no—
166C22×C4×C9C2×D311yescharacteristic, complemented
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—61no—
172C2×#611—61no—
173C22×Dic9C2×D311yescharacteristic, complemented
174D4×D9—64no—
175#3697—64no—
176#3697—68no—
177C2×D36—31no—
178C2×D36—31no—
179C2×D36—31no—
180C2×D36—31no—
181C2×D36—61no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9—31no—
185C2×C4×D9—31no—
186C2×C4×D9—61no—
187C2×C4×D9—61no—
188C2×Dic18—31no—
189C2×Dic18—61no—
190C9×C4⋊C4—31no—
191C9×C4⋊C4—31no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4—31no—
194C9×C22⋊C4—31no—
195#3676—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4C2×D311yescharacteristic
201(C2×D9)⋊C4C2×D311yescharacteristic
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4—31no—
205Dic9⋊C4—31no—
206C4×Dic9—31no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9C2×D412yes—
210C22×C3×C9C2411yescharacteristic
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3⋊D9C2×D412yes—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—44no—
226C2×C3×D9#4112yescomplemented
227D3×D9—44no—
228C3×C4×C9—21no—
229C3×C4×C9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9C2×D412yes—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C9×Dic3—21no—
235C3×Dic9—21no—
236C3×Dic9—21no—
237C22×#67—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C2×#235—91no—
241C2×#235—181no—
242C3×#123—31no—
243C2×C3×C22⋊C4—91no—
244#953—91no—
245#939—91no—
246#930—91no—
247#929D911yescharacteristic, complemented
248C4×#67—91no—
249C2×(C2×D3)⋊C4—31no—
250#896—91no—
251#895—91no—
252#894—91no—
253#893—91no—
254#885—91no—
255#885—91no—
256#884—91no—
257#884—91no—
258#884—91no—
259#883—91no—
260#882—91no—
261#882—91no—
262#882—91no—
263#67⋊C4—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—91no—
267#878—91no—
268C23×C32C22×D311yescharacteristic
269C22×C3⋊D3—31no—
270C22×C3⋊D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—62no—
274C22×C3×D3—62no—
275C22×C3×D3—121no—
276C22×C3×D3C22×D311yescharacteristic
277C2×D32—62no—
278C2×D32—62no—
279C2×D32—121no—
280C2×C32×C4—22no—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283#638—34no—
284#638—62no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C4⋊(C3⋊D3)—62no—
288C4×C3⋊D3—62no—
289C4×C3⋊D3—62no—
290#634—62no—
291C3×#67—22no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—121no—
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298#626—62no—
299#626—62no—
300#626—121no—
301#626—121no—
302#625—62no—
303#624—121no—
304D3×Dic3—62no—
305C23×C9—21no—
306C23×C9—31no—
307C23×C9C22×D311yescharacteristic
308C22×D9—22no—
309C22×D9—22no—
310C22×D9—31no—
311C22×D9—31no—
312C22×D9—41no—
313C22×D9—61no—
314C22×D9—61no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—121no—
318C22×D9C22×D311yescharacteristic
319C22×D9C22×D311yescharacteristic
320D4×C9—62no—
321C2×C4×C9—24no—
322C2×C4×C9—22no—
323C2×C4×C9—21no—
324C2×C4×C9—21no—
325C2×C4×C9—31no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9C22×D311yescharacteristic
329C2×C4×C9C22×D311yescharacteristic
330#611—34no—
331#611—64no—
332#611—62no—
333#611—64no—
334#611—62no—
335#611—121no—
336C2×Dic9—31no—
337C2×Dic9—31no—
338C2×Dic9—41no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9C22×D311yescharacteristic
342C2×Dic9C22×D311yescharacteristic
343D36—62no—
344D36—64no—
345D36—62no—
346D36—62no—
347D36—121no—
348C4×D9—62no—
349C4×D9—62no—
350C4×D9—62no—
351C4×D9—64no—
352C4×D9—64no—
353C4×D9—121no—
354Dic18—62no—
355Dic18—64no—
356#546—271noSylow
357C2×C3×C9—22no—
358C2×C3×C9C22×D411yescharacteristic
359C2×C3×C9C2×#4111yescharacteristic
360C2×C3×C9H(5,𝔽2)11yescharacteristic
361C3⋊D9—22no—
362C3⋊D9—41no—
363D3×C9—41no—
364C3×D9—22no—
365C3×D9—41no—
366C24×C3—91no—
367C23×D3—31no—
368C23×D3—91no—
369C23×D3—91no—
370C2×C3×D4—31no—
371C22×C3×C4—21no—
372C22×C3×C4—91no—
373C22×C3×C4C2×D911yescharacteristic, complemented
374C22×C3×C4D3211yescharacteristic
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—181no—
386C2×#67—181no—
387C2×#67—184no—
388C2×#67C2×D911yescharacteristic
389C22×Dic3—31no—
390C22×Dic3—91no—
391D3×D4—184no—
392#235—184no—
393#235—184no—
394#235—188no—
395C2×D12—91no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12—91no—
399C2×D12—91no—
400C2×D12—91no—
401C2×D12—181no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×C4×D3—91no—
408C2×C4×D3—91no—
409C2×C4×D3—181no—
410C2×C4×D3—181no—
411C2×Dic6—91no—
412C2×Dic6—91no—
413C2×Dic6—181no—
414C3×C4⋊C4—31no—
415C3×C4⋊C4—31no—
416C3×C22⋊C4—31no—
417C3×C22⋊C4—31no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—91no—
420C3×C22⋊C4—91no—
421C3×C22⋊C4—91no—
422C3×C22⋊C4—91no—
423#217—91no—
424#217—91no—
425#217—91no—
426#217C2×D911yescharacteristic, complemented
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4C2×D911yescharacteristic, complemented
439(C2×D3)⋊C4C2×D911yescharacteristic, complemented
440C4⋊Dic3—91no—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443Dic3⋊C4—91no—
444Dic3⋊C4C2×D911yescharacteristic, complemented
445Dic3⋊C4C2×D911yescharacteristic, complemented
446C4×Dic3—91no—
447C4×Dic3—91no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32D3×D412yes—
451C22×C32C23×D311yescharacteristic
452C2×C3⋊D3—32no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—32no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—124no—
468D32—124no—
469C32×C4—21no—
470C32×C4—21no—
471C3⋊Dic3—32no—
472C3⋊Dic3—61no—
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—61no—
477C3×Dic3—61no—
478C22×C9—21no—
479C22×C9—21no—
480C22×C9—21no—
481C22×C9—22no—
482C22×C9—41no—
483C22×C9—41no—
484C22×C9—61no—
485C22×C9—61no—
486C22×C9—61no—
487C22×C9D3×D412yes—
488C22×C9C23×D311yescharacteristic
489C2×D9—21no—
490C2×D9—21no—
491C2×D9—21no—
492C2×D9—21no—
493C2×D9—21no—
494C2×D9—32no—
495C2×D9—44no—
496C2×D9—62no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—62no—
500C2×D9—61no—
501C2×D9—61no—
502C2×D9—61no—
503C2×D9—121no—
504C2×D9—121no—
505C2×D9—121no—
506C2×D9—121no—
507C2×D9—124no—
508C2×D9#23512yescomplemented
509C4×C9—22no—
510C4×C9—22no—
511C4×C9—21no—
512C4×C9—21no—
513C4×C9—61no—
514C4×C9—61no—
515C4×C9—61no—
516Dic9—21no—
517Dic9—21no—
518Dic9—32no—
519Dic9—62no—
520Dic9—62no—
521Dic9—61no—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—31no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—271no—
537C3×C9#54611yescharacteristic, complemented, Sylow
538C23×C3—21no—
539C23×C3—31no—
540C23×C3—91no—
541C23×C3—91no—
542C23×C3—182no—
543C23×C3—182no—
544C23×C3—361no—
545C23×C3C22×D911yescharacteristic
546C23×C3C2×D3211yescharacteristic
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—91no—
552C22×D3—91no—
553C22×D3—91no—
554C22×D3—91no—
555C22×D3—121no—
556C22×D3—181no—
557C22×D3—181no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—182no—
562C22×D3—361no—
563C22×D3—361no—
564C22×D3C22×D911yescharacteristic
565C3×D4—62no—
566C2×C3×C4—24no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—91no—
575C2×C3×C4—91no—
576C2×C3×C4—361no—
577C2×C3×C4C22×D911yescharacteristic
578C2×C3×C4C22×D911yescharacteristic
579C2×C3×C4C2×D3211yescharacteristic
580C2×C3×C4C2×D3211yescharacteristic
581#67—22no—
582#67—94no—
583#67—94no—
584#67—184no—
585#67—182no—
586#67—182no—
587#67—182no—
588#67—182no—
589#67—184no—
590#67—182no—
591#67—182no—
592#67—361no—
593#67—361no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—121no—
601C2×Dic3—181no—
602C2×Dic3—181no—
603C2×Dic3—182no—
604C2×Dic3C22×D911yescharacteristic
605C2×Dic3C22×D911yescharacteristic
606C2×Dic3C22×D911yescharacteristic
607D12—182no—
608D12—182no—
609D12—184no—
610D12—182no—
611D12—182no—
612D12—361no—
613D12—361no—
614C4×D3—182no—
615C4×D3—182no—
616C4×D3—182no—
617C4×D3—182no—
618C4×D3—182no—
619C4×D3—184no—
620C4×D3—184no—
621C4×D3—361no—
622C4×D3—361no—
623Dic6—182no—
624Dic6—182no—
625Dic6—184no—
626C2×C32—22no—
627C2×C32C2×D3×D411yescharacteristic
628C2×C32D3×#4111yescharacteristic
629C2×C32#100911yescharacteristic
630C3⋊D3—62no—
631C3⋊D3—121no—
632C3×D3—41no—
633C3×D3—62no—
634C3×D3—121no—
635C2×C9—22no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—21no—
639C2×C9—42no—
640C2×C9—121no—
641C2×C9C2×#23511yescharacteristic
642C2×C9C2×D3×D411yescharacteristic
643C2×C9#100411yescharacteristic
644D9—22no—
645D9—41no—
646D9—62no—
647D9—122no—
648D9—122no—
649D9—121no—
650C24—91no—
651C24—271no—
652#41—544no—
653C2×Q8—271no—
654C2×D4—31no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—544no—
664C22×C4—91no—
665C22×C4—271no—
666C22×C4—271no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4D3×D911yescharacteristic, complemented
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—91no—
680C22⋊C4—91no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4—271no—
686C42—271no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—22no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—92no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3—181no—
704C22×C3—364no—
705C22×C3D4×D912yes—
706C22×C3C23×D911yescharacteristic
707C22×C3#381112yes—
708C22×C3C22×D3211yescharacteristic
709C2×D3—21no—
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—92no—
719C2×D3—92no—
720C2×D3—124no—
721C2×D3—182no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—182no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—181no—
731C2×D3—181no—
732C2×D3—181no—
733C2×D3—361no—
734C2×D3—361no—
735C2×D3—361no—
736C2×D3—361no—
737C2×D3—364no—
738C2×D3—364no—
739C3×C4—22no—
740C3×C4—22no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4—181no—
749C3×C4—181no—
750Dic3—21no—
751Dic3—21no—
752Dic3—21no—
753Dic3—61no—
754Dic3—61no—
755Dic3—92no—
756Dic3—92no—
757Dic3—182no—
758Dic3—182no—
759Dic3—181no—
760Dic3—181no—
761C32#565411yescharacteristic
762C9—21no—
763C9#549011yescharacteristic, complemented
764C23—31no—
765C23—91no—
766C23—91no—
767C23—182no—
768C23—182no—
769C23—271no—
770C23—271no—
771C23—361no—
772C23—542no—
773C23—542no—
774C23—1081no—
775C23C2×D3×D911yescharacteristic
776Q8—542no—
777D4—62no—
778D4—274no—
779D4—542no—
780D4—542no—
781D4—542no—
782D4—542no—
783D4—542no—
784D4—1081no—
785D4—1081no—
786C2×C4—22no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—91no—
791C2×C4—91no—
792C2×C4—271no—
793C2×C4—271no—
794C2×C4—361no—
795C2×C4—542no—
796C2×C4—542no—
797C2×C4—542no—
798C2×C4—1081no—
799C2×C4C2×D3×D911yescharacteristic
800C2×C4C2×D3×D911yescharacteristic
801C2×C3—22no—
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—42no—
807C2×C3—121no—
808C2×C3—182no—
809C2×C3—361no—
810C2×C3C2×D4×D911yescharacteristic
811C2×C3#41×D911yescharacteristic
812C2×C3#6371511yescharacteristic
813C2×C3D3×#23511yescharacteristic
814C2×C3#6430711yescharacteristic
815C2×C3C2×#381111yescharacteristic
816D3—41no—
817D3—62no—
818D3—121no—
819D3—182no—
820D3—182no—
821D3—362no—
822D3—362no—
823D3—361no—
824D3—361no—
825C22—21no—
826C22—21no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—92no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22—181no—
836C22—272no—
837C22—364no—
838C22—541no—
839C22—541no—
840C22—541no—
841C22—541no—
842C22—541no—
843C22—1084no—
844C22#8866812yes—
845C22C22×D3×D911yescharacteristic
846C4—21no—
847C4—21no—
848C4—61no—
849C4—61no—
850C4—61no—
851C4—181no—
852C4—181no—
853C4—272no—
854C4—541no—
855C3—21no—
856C3#1058975611yescharacteristic, complemented
857C3#1059507711yescharacteristic
858C2—22no—
859C2—121no—
860C2—182no—
861C2—361no—
862C2—542no—
863C2—1081no—
864C2D9×#23511yescharacteristic
865C2#1172247711yescharacteristic
866C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
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×#88736C2semidirect
2. C2×D9×#67C2semidirect
3. C9×#929C2semidirect
4. C2×C3×(C2×D9)⋊C4C2semidirect
5. #11721288C2semidirect
6. #11721276C2semidirect
7. #11721241C2semidirect
8. #11721051C2semidirect
9. #11721048C2semidirect
10. #11721042C2semidirect
11. #11721041C2semidirect
12. #11721005C2semidirect
13. #11720996C2semidirect
14. #11720978C2semidirect
15. #11720941C2semidirect
20. C22×C3×C4×C9C22semidirect
22. C2×#6233C22semidirect
24. C2×C4⋊(C3⋊D9)C22semidirect
25. C2×C4×C3⋊D9C22semidirect
26. C2×C4×C3⋊D9C22semidirect
27. C2×#6226C22semidirect
29. C22×C3×Dic9C22semidirect
31. C2×#6195C22semidirect
35. C2×#6192C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
38. C9×#217C22semidirect
39. C9×(C2×D3)⋊C4C22semidirect
40. C9×(C2×D3)⋊C4C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C9×Dic3⋊C4C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
75. C2×(C2×D9)⋊C4D3semidirect
102. #6233D4semidirect
166. C22×C4×C9C2×D3semidirect
173. C22×Dic9C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
226. C2×C3×D9#41semidirect
247. #929D9semidirect
373. C22×C3×C4C2×D9semidirect
426. #217C2×D9semidirect
438. (C2×D3)⋊C4C2×D9semidirect
439. (C2×D3)⋊C4C2×D9semidirect
444. Dic3⋊C4C2×D9semidirect
445. Dic3⋊C4C2×D9semidirect
508. C2×D9#235semidirect
537. C3×C9#546semidirect
669. C22×C4D3×D9semidirect
763. C9#5490semidirect
856. C3#10589756semidirect

Maximal subgroups

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

subgroupindex
C2×#887362
C2×D9×#672
C9×#9292
C2×C3×(C2×D9)⋊C42
#117212882
#117212762
#117212412
#117210512
#117210482
#117210422
#117210412
#117210052
#117209962
#117209782
#117209412
#105950773
#105897563