Finite Group Databasebeta

← #13148978

Subgroups — #13148978

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×D36C211yesmaximal, characteristic, complemented
2C2×#88640C211yesmaximal, characteristic, complemented
3#11721750C211yesmaximal, characteristic, complemented
4C9×#893C211yesmaximal, characteristic, complemented
5C3×#63456C211yesmaximal, characteristic, complemented
6#11721050C211yesmaximal, characteristic, complemented
7#11721050C211yesmaximal, characteristic, complemented
8#11721048C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721039C211yesmaximal, characteristic, complemented
11#11721034C211yesmaximal, characteristic, complemented
12#11720982C211yesmaximal, characteristic, complemented
13#11720977C211yesmaximal, characteristic, complemented
14#11720955C211yesmaximal, characteristic, complemented
15#11720940C211yesmaximal, characteristic, complemented
16#10594619—31nomaximal
17#10589652—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C9×D12C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×C3×D36C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic, complemented
27C2×#6195C2211yescharacteristic, complemented
28C2×#6195C2211yescharacteristic, complemented
29C2×#6194C2211yescharacteristic, complemented
30C2×#6194C2211yescharacteristic, complemented
31C2×#6192C2211yescharacteristic
32C2×#6192C2211yescharacteristic
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C2×Dic3×D9C2211yescharacteristic, complemented
35C2×#6189C2211yescharacteristic, complemented
36D3×D36—24no—
37#88640—24no—
38C3×C9×C4⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88536C2211yescharacteristic, complemented
42#88534C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C4×C9×Dic3C2211yescharacteristic, complemented
49C3×Dic9⋊C4C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic
51(C2×D3)⋊Dic9C2211yescharacteristic
52#88445C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54Dic3⋊Dic9C2211yescharacteristic, complemented
55C2×D3×D12—31no—
56C2×#3798—31no—
57#64103—31no—
58C3×#894—31no—
59C3×#893D311yescharacteristic
60#63922—31no—
61#63922—31no—
62#63921—31no—
63D3×(C2×D3)⋊C4—31no—
64#63910—31no—
65#63906—31no—
66#63885—31no—
67#63880—31no—
68#63852—31no—
69#63851—31no—
70C2×#3697—31no—
71C22×D36—31no—
72C4×D4×C9—31no—
73#63499—31no—
74#63499—31no—
75#63492—31no—
76#63486—31no—
77#63456—31no—
78#63456—61no—
79#63456D311yescharacteristic, complemented
80#63446—31no—
81#63446—31no—
82C22⋊C4×D9—31no—
83C22⋊C4×D9—31no—
84#63437—31no—
85C4×D36—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
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
102C2×C3⋊Dic9C2311yescharacteristic
103C4⋊(C3⋊D9)—22no—
104C4×C3⋊D9—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C9×D12—22no—
110C4×D3×C9—22no—
111C4×D3×C9—22no—
112C3×D36—22no—
113C3×C4×D9—22no—
114#6195—22no—
115#6195—41no—
116#6194—22no—
117#6194—41no—
118#6192—22no—
119#6192D414yescomplemented
120(C3⋊D9)⋊C4—41no—
121Dic3×D9—41no—
122#6189—22no—
123#5654—91no—
124#5550—91no—
125C22×D32—31no—
126C22×D32—31no—
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4×C3⋊D3—31no—
129C2×C3×D12—31no—
130C2×C3×D12C2×D311yescharacteristic
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×#627—31no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#625—31no—
140C2×#625—31no—
141C2×#624—31no—
142C2×D3×Dic3—31no—
143D3×D12—64no—
144#3798—64no—
145C23×D9—31no—
146C23×D9—31no—
147C32×C4⋊C4C2×D311yescharacteristic
148#3752—31no—
149#3752—31no—
150#3752—31no—
151#3750—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×(C2×D3)⋊C4C2×D311yescharacteristic
157C3×Dic3⋊C4—31no—
158C3×C4×Dic3C2×D311yescharacteristic
159Dic3⋊Dic3—31no—
160#3722—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164C2×D4×C9—31no—
165C22×C4×C9—31no—
166C22×C4×C9—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171#3697—64no—
172C2×D36—31no—
173C2×D36—31no—
174C2×D36—31no—
175C2×D36—64no—
176C2×D36—61no—
177C2×D36C2×D311yescharacteristic
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—61no—
182C2×C4×D9C2×D311yescharacteristic, complemented
183C2×Dic18—31no—
184C9×C4⋊C4—21no—
185C9×C4⋊C4C2×D311yescharacteristic, complemented
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188C42×C9—31no—
189#3676—31no—
190#3676—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—61no—
197(C2×D9)⋊C4—61no—
198(C2×D9)⋊C4—61no—
199(C2×D9)⋊C4C2×D311yescharacteristic, complemented
200(C2×D9)⋊C4C2×D311yescharacteristic, complemented
201(C2×D9)⋊C4C2×D311yescharacteristic, complemented
202C4⋊Dic9—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—61no—
205Dic9⋊C4C2×D311yescharacteristic, complemented
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⋊D9C2×D412yes—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
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—
231C3⋊Dic9—21no—
232C9×Dic3—21no—
233C9×Dic3C2×D412yes—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C2×D3×D4—91no—
237C2×#235—91no—
238C2×#235—91no—
239C22×D12—91no—
240C3×#123—91no—
241C3×C4×D4—31no—
242#939—91no—
243#937—91no—
244#937—91no—
245#930—91no—
246C2×(C2×D3)⋊C4—91no—
247#924—91no—
248#896—91no—
249#895—91no—
250#894—31no—
251#894—91no—
252#894—91no—
253#894—181no—
254#893D911yescharacteristic, complemented
255#885—91no—
256#884—91no—
257#884—91no—
258#884—91no—
259#882—91no—
260#882—91no—
261#67⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—91no—
265#875—91no—
266C4×D12—91no—
267C22×C3⋊D3—31no—
268C22×C3⋊D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3C22×D311yescharacteristic
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—
283C2×C3⋊Dic3—31no—
284C4⋊(C3⋊D3)—62no—
285C4×C3⋊D3—62no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C3×D12—22no—
291C3×D12—62no—
292C3×C4×D3—22no—
293C3×C4×D3—22no—
294C3×C4×D3—62no—
295#627—62no—
296#626—34no—
297#626—62no—
298#626—62no—
299#626—121no—
300#625—62no—
301#625—121no—
302#624—121no—
303D3×Dic3—121no—
304C23×C9—31no—
305C23×C9—31no—
306C22×D9—31no—
307C22×D9—31no—
308C22×D9—61no—
309C22×D9—61no—
310C22×D9—62no—
311C22×D9—62no—
312C22×D9—62no—
313C22×D9—62no—
314C22×D9—121no—
315C22×D9—121no—
316C22×D9C22×D311yescharacteristic
317C22×D9C22×D311yescharacteristic
318D4×C9—62no—
319C2×C4×C9—21no—
320C2×C4×C9—21no—
321C2×C4×C9—21no—
322C2×C4×C9—31no—
323C2×C4×C9—31no—
324C2×C4×C9—62no—
325C2×C4×C9—62no—
326C2×C4×C9C22×D311yescharacteristic
327C2×C4×C9C22×D311yescharacteristic
328C2×C4×C9C22×D311yescharacteristic
329#611—62no—
330#611—62no—
331#611—121no—
332#611—121no—
333C2×Dic9—31no—
334C2×Dic9—31no—
335C2×Dic9—61no—
336C2×Dic9—61no—
337C2×Dic9C22×D311yescharacteristic
338C2×Dic9C22×D311yescharacteristic
339D36—22no—
340D36—34no—
341D36—62no—
342D36—62no—
343D36—122no—
344C4×D9—22no—
345C4×D9—62no—
346C4×D9—122no—
347C4×D9—121no—
348C4×D9—121no—
349Dic18—62no—
350#546—271noSylow
351C2×C3×C9C22×D411yescharacteristic
352C2×C3×C9C2×#4111yescharacteristic
353C2×C3×C9H(5,𝔽2)11yescharacteristic
354C3⋊D9—22no—
355C3⋊D9—41no—
356D3×C9—22no—
357D3×C9—41no—
358C3×D9—22no—
359C3×D9—41no—
360C23×D3—91no—
361C23×D3—91no—
362C23×D3—91no—
363C23×D3—91no—
364C2×C3×D4—31no—
365C2×C3×D4—91no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C22×Dic3—91no—
378D3×D4—184no—
379#235—184no—
380#235—184no—
381C2×D12—31no—
382C2×D12—91no—
383C2×D12—91no—
384C2×D12—91no—
385C2×D12—91no—
386C2×D12—91no—
387C2×D12—91no—
388C2×D12—181no—
389C2×D12—184no—
390C2×D12C2×D911yescharacteristic
391C2×C4×D3—31no—
392C2×C4×D3—91no—
393C2×C4×D3—91no—
394C2×C4×D3—91no—
395C2×C4×D3—91no—
396C2×C4×D3—91no—
397C2×C4×D3—181no—
398C2×C4×D3C2×D911yescharacteristic
399C2×C4×D3C2×D911yescharacteristic, complemented
400C2×Dic6—91no—
401C2×Dic6—91no—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—91no—
404C3×C4⋊C4C2×D911yescharacteristic, complemented
405C3×C4⋊C4D3211yescharacteristic
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C42—31no—
412#217—91no—
413#217—91no—
414#217—91no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
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—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—181no—
430(C2×D3)⋊C4—181no—
431(C2×D3)⋊C4—181no—
432(C2×D3)⋊C4C2×D911yescharacteristic
433(C2×D3)⋊C4C2×D911yescharacteristic, complemented
434C4⋊Dic3—91no—
435Dic3⋊C4—31no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—181no—
440C4×Dic3C2×D911yescharacteristic, complemented
441C22×C32C23×D311yescharacteristic
442C2×C3⋊D3—32no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
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—32no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3#23512yes—
460D32—124no—
461D32—124no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3×Dic3—21no—
468C3×Dic3—61no—
469C3×Dic3—61no—
470C3×Dic3D3×D412yes—
471C22×C9—21no—
472C22×C9—32no—
473C22×C9—61no—
474C22×C9—61no—
475C22×C9—61no—
476C22×C9—61no—
477C22×C9—61no—
478C22×C9C23×D311yescharacteristic
479C2×D9—21no—
480C2×D9—21no—
481C2×D9—21no—
482C2×D9—21no—
483C2×D9—21no—
484C2×D9—32no—
485C2×D9—62no—
486C2×D9—61no—
487C2×D9—61no—
488C2×D9—61no—
489C2×D9—61no—
490C2×D9—61no—
491C2×D9—121no—
492C2×D9—121no—
493C2×D9—121no—
494C2×D9—121no—
495C2×D9—121no—
496C2×D9—124no—
497C2×D9—124no—
498C2×D9D3×D412yes—
499C4×C9—21no—
500C4×C9—21no—
501C4×C9—21no—
502C4×C9—32no—
503C4×C9—41no—
504C4×C9—41no—
505C4×C9—41no—
506C4×C9—61no—
507Dic9—21no—
508Dic9—21no—
509Dic9—61no—
510Dic9—61no—
511Dic9—121no—
512Dic9—121no—
513C2×#41—271no—
514C22×D4—271no—
515#124—271no—
516#123—91no—
517#123—271no—
518C22⋊Q8—271no—
519#121—271no—
520#121—271no—
521#121—271no—
522#120—271no—
523#120—271no—
524C4×D4—31no—
525C4×D4—271no—
526C2×C22⋊C4—271no—
527C2×C22⋊C4—271no—
528C3×C9#54611yescharacteristic, complemented, Sylow
529C23×C3—31no—
530C23×C3—31no—
531C23×C3—91no—
532C23×C3—91no—
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—91no—
536C22×D3—91no—
537C22×D3—91no—
538C22×D3—91no—
539C22×D3—181no—
540C22×D3—181no—
541C22×D3—182no—
542C22×D3—182no—
543C22×D3—182no—
544C22×D3—182no—
545C22×D3—182no—
546C22×D3—182no—
547C22×D3—182no—
548C22×D3—182no—
549C22×D3—361no—
550C22×D3—361no—
551C22×D3—361no—
552C22×D3—361no—
553C22×D3C22×D911yescharacteristic
554C22×D3C22×D911yescharacteristic
555C3×D4—62no—
556C3×D4—182no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—91no—
565C2×C3×C4—91no—
566C2×C3×C4—182no—
567C2×C3×C4C22×D911yescharacteristic
568C2×C3×C4C22×D911yescharacteristic
569C2×C3×C4C22×D911yescharacteristic
570C2×C3×C4C2×D3211yescharacteristic
571C2×C3×C4C2×D3211yescharacteristic
572C2×C3×C4C2×D3211yescharacteristic
573#67—94no—
574#67—182no—
575#67—182no—
576#67—182no—
577#67—182no—
578#67—361no—
579#67—361no—
580#67—361no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—91no—
584C2×Dic3—91no—
585C2×Dic3—91no—
586C2×Dic3—91no—
587C2×Dic3—181no—
588C2×Dic3—181no—
589C2×Dic3—361no—
590C2×Dic3C22×D911yescharacteristic
591C2×Dic3C22×D911yescharacteristic
592D12—22no—
593D12—62no—
594D12—94no—
595D12—182no—
596D12—182no—
597D12—182no—
598D12—182no—
599D12—362no—
600D12—361no—
601C4×D3—22no—
602C4×D3—22no—
603C4×D3—62no—
604C4×D3—182no—
605C4×D3—182no—
606C4×D3—362no—
607C4×D3—361no—
608C4×D3—361no—
609C4×D3—361no—
610Dic6—182no—
611Dic6—182no—
612C2×C32C2×#23511yescharacteristic
613C2×C32C2×D3×D411yescharacteristic
614C2×C32#100911yescharacteristic
615C3⋊D3—62no—
616C3⋊D3—121no—
617C3×D3—22no—
618C3×D3—41no—
619C3×D3—62no—
620C3×D3—121no—
621C2×C9—21no—
622C2×C9—21no—
623C2×C9—21no—
624C2×C9—62no—
625C2×C9—121no—
626C2×C9C2×D3×D411yescharacteristic
627C2×C9D3×#4111yescharacteristic
628C2×C9#100911yescharacteristic
629D9—22no—
630D9—41no—
631D9—62no—
632D9—122no—
633D9—121no—
634D9—241no—
635C24—271no—
636C24—271no—
637#41—544no—
638C2×Q8—271no—
639C2×D4—31no—
640C2×D4—91no—
641C2×D4—271no—
642C2×D4—271no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—544no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C4⋊C4—91no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4D3×D911yescharacteristic, complemented
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—91no—
662C22⋊C4—91no—
663C22⋊C4—91no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C42—31no—
672C22×C3—21no—
673C22×C3—32no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—92no—
680C22×C3—181no—
681C22×C3—181no—
682C22×C3—181no—
683C22×C3—181no—
684C22×C3—181no—
685C22×C3C23×D911yescharacteristic
686C22×C3C22×D3211yescharacteristic
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—32no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—92no—
699C2×D3—92no—
700C2×D3—182no—
701C2×D3—181no—
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—361no—
712C2×D3—361no—
713C2×D3—361no—
714C2×D3—361no—
715C2×D3—361no—
716C2×D3—364no—
717C2×D3—364no—
718C2×D3—364no—
719C2×D3—364no—
720C2×D3#369712yescomplemented
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—32no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—61no—
732C3×C4—181no—
733C3×C4—181no—
734Dic3—21no—
735Dic3—61no—
736Dic3—61no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740Dic3—181no—
741Dic3—361no—
742Dic3—361no—
743Dic3D4×D912yes—
744C32#555011yescharacteristic
745C9—21no—
746C9#565411yescharacteristic, complemented
747C23—31no—
748C23—31no—
749C23—91no—
750C23—91no—
751C23—271no—
752C23—271no—
753C23—542no—
754C23—542no—
755C23—542no—
756C23—542no—
757C23—1081no—
758C23—1081no—
759Q8—542no—
760D4—62no—
761D4—182no—
762D4—274no—
763D4—542no—
764D4—542no—
765D4—542no—
766D4—542no—
767D4—1081no—
768D4—1081no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—182no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—542no—
779C2×C4—1081no—
780C2×C4—1081no—
781C2×C4C2×D3×D911yescharacteristic
782C2×C4C2×D3×D911yescharacteristic
783C2×C4C2×D3×D911yescharacteristic
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—62no—
788C2×C3—121no—
789C2×C3—182no—
790C2×C3—361no—
791C2×C3C2×#369711yescharacteristic
792C2×C3C2×D4×D911yescharacteristic
793C2×C3#6371511yescharacteristic
794C2×C3D3×#23511yescharacteristic
795C2×C3D32×D411yescharacteristic
796C2×C3#6432011yescharacteristic
797D3—22no—
798D3—41no—
799D3—62no—
800D3—121no—
801D3—182no—
802D3—182no—
803D3—362no—
804D3—361no—
805D3—361no—
806D3—721no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—92no—
814C22—181no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—272no—
820C22—541no—
821C22—541no—
822C22—541no—
823C22—541no—
824C22—541no—
825C22—1084no—
826C22—1084no—
827C22C22×D3×D911yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—32no—
832C4—61no—
833C4—181no—
834C4—181no—
835C4—541no—
836C4—541no—
837C3—21no—
838C3#1058965211yescharacteristic, complemented
839C3#1059461911yescharacteristic
840C2—62no—
841C2—121no—
842C2—182no—
843C2—361no—
844C2—542no—
845C2—1081no—
846C2D3×#369711yescharacteristic
847C2D3×D4×D911yescharacteristic
848C2#1172251511yescharacteristic
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×#88640C2semidirect
3. #11721750C2semidirect
4. C9×#893C2semidirect
5. C3×#63456C2semidirect
6. #11721050C2semidirect
7. #11721050C2semidirect
8. #11721048C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721039C2semidirect
11. #11721034C2semidirect
12. #11720982C2semidirect
13. #11720977C2semidirect
14. #11720955C2semidirect
15. #11720940C2semidirect
21. C2×C4×C3⋊D9C22semidirect
24. C2×C4×D3×C9C22semidirect
26. C2×C3×C4×D9C22semidirect
27. C2×#6195C22semidirect
28. C2×#6195C22semidirect
29. C2×#6194C22semidirect
30. C2×#6194C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C2×Dic3×D9C22semidirect
35. C2×#6189C22semidirect
38. C3×C9×C4⋊C4C22semidirect
39. #88536C22semidirect
40. #88536C22semidirect
41. #88536C22semidirect
42. #88534C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C4×C9×Dic3C22semidirect
49. C3×Dic9⋊C4C22semidirect
52. #88445C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. Dic3⋊Dic9C22semidirect
79. #63456D3semidirect
119. #6192D4semidirect
182. C2×C4×D9C2×D3semidirect
185. C9×C4⋊C4C2×D3semidirect
199. (C2×D9)⋊C4C2×D3semidirect
200. (C2×D9)⋊C4C2×D3semidirect
201. (C2×D9)⋊C4C2×D3semidirect
205. Dic9⋊C4C2×D3semidirect
218. C2×D3×C9#41semidirect
254. #893D9semidirect
399. C2×C4×D3C2×D9semidirect
404. C3×C4⋊C4C2×D9semidirect
433. (C2×D3)⋊C4C2×D9semidirect
440. C4×Dic3C2×D9semidirect
528. C3×C9#546semidirect
658. C4⋊C4D3×D9semidirect
720. C2×D3#3697semidirect
746. C9#5654semidirect
838. C3#10589652semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D362
C2×#886402
#117217502
C9×#8932
C3×#634562
#117210502
#117210482
D9×(C2×D3)⋊C42
#117210392
#117210342
#117209822
#117209772
#117209552
#117209402
#105946193
#105896523