Finite Group Databasebeta

← #13147721

Subgroups — #13147721

Order 1728.

1066 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D9C211yesmaximal, characteristic, complemented
2C2×#88640C211yesmaximal, characteristic, complemented
3#11721709C211yesmaximal, characteristic, complemented
4C4×C9×D12C211yesmaximal, characteristic, complemented
5C3×C4×D36C211yesmaximal, characteristic, complemented
6#11721050C211yesmaximal, characteristic, complemented
7#11721049C211yesmaximal, characteristic, complemented
8C4×#6194C211yesmaximal, characteristic, complemented
9C4×#6194C211yesmaximal, characteristic, complemented
10#11721026C211yesmaximal, characteristic, complemented
11#11721016C211yesmaximal, characteristic, complemented
12#11720999C211yesmaximal, characteristic, complemented
13#11720982C211yesmaximal, characteristic, complemented
14#11720958C211yesmaximal, characteristic, complemented
15#11720942C211yesmaximal, characteristic, complemented
16#10594006—31nomaximal
17#10589649—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C9×D12C2211yescharacteristic
21C2×C4×D3×C9C2211yescharacteristic
22C2×C4×D3×C9C2211yescharacteristic, complemented
23C2×C3×D36C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic, complemented
30C2×D3×Dic9C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C2×#6189C2211yescharacteristic, complemented
35C4×D3×D9—24no—
36#88640—24no—
37C3×C42×C9C2211yescharacteristic, complemented
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic
40#88534C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C4×C3⋊Dic9C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C9×C4⋊Dic3C2211yescharacteristic, complemented
48C3×C4⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54#88442C2211yescharacteristic, complemented
55C2×C4×D32—31no—
56C2×#3798—31no—
57#64081—31no—
58C3×C4×D12—31no—
59C3×C4×D12D311yescharacteristic
60#63922—31no—
61#63922—31no—
62C4×#625—31no—
63C4×#625—31no—
64#63899—31no—
65#63899—31no—
66#63885—31no—
67#63885—31no—
68#63854—31no—
69#63854—31no—
70C2×#3697—31no—
71C22×C4×D9—31no—
72C4×D4×C9—31no—
73#63501—31no—
74#63499—31no—
75C4×#611—31no—
76C4×#611—31no—
77#63458—31no—
78#63456—31no—
79#63446—31no—
80#63445—31no—
81#63444—31no—
82#63440—31no—
83C4×D36D311yescharacteristic, complemented
84#63434—31no—
85#63434—61no—
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×D3×D9—22no—
92C2×D3×D9—22no—
93C2×D3×D9—22no—
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C4×C3⋊D9D414yescomplemented
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C9×D12—22no—
106C4×D3×C9—22no—
107C4×D3×C9—22no—
108C3×D36—22no—
109C3×C4×D9—22no—
110C3×C4×D9—22no—
111#6195—22no—
112#6194—22no—
113#6194—22no—
114#6194—22no—
115D3×Dic9—22no—
116#6192—22no—
117(C3⋊D9)⋊C4—22no—
118Dic3×D9—22no—
119#6189—22no—
120#5547—91no—
121#5547—91no—
122C22×D32—31no—
123C2×C4×C3⋊D3—31no—
124C2×C3×D12—31no—
125C2×C3×D12C2×D311yescharacteristic
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×#627—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#625—31no—
134C2×#625—31no—
135C2×#625—31no—
136C2×#624—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C4×D32—64no—
140#3798—64no—
141C23×D9—31no—
142C32×C42C2×D311yescharacteristic
143#3752—31no—
144#3752—31no—
145#3750—31no—
146#3750—31no—
147C4×C3⋊Dic3—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×(C2×D3)⋊C4C2×D311yescharacteristic
152C3×C4⋊Dic3—31no—
153C3×C4⋊Dic3C2×D311yescharacteristic
154#3724—31no—
155#3724—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160C2×D4×C9—31no—
161C22×C4×C9—31no—
162C22×C4×C9—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—31no—
167C22×Dic9—31no—
168#3697—64no—
169C2×D36—31no—
170C2×D36C2×D311yescharacteristic
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—64no—
175C2×C4×D9—61no—
176C2×C4×D9C2×D311yescharacteristic
177C2×C4×D9C2×D311yescharacteristic, complemented
178C2×Dic18—31no—
179C9×C4⋊C4—31no—
180C9×C22⋊C4—31no—
181C9×C22⋊C4—31no—
182C42×C9—21no—
183C42×C9C2×D311yescharacteristic, complemented
184#3676—31no—
185#3676—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—61no—
191(C2×D9)⋊C4—61no—
192(C2×D9)⋊C4C2×D311yescharacteristic
193(C2×D9)⋊C4C2×D311yescharacteristic, complemented
194C4⋊Dic9C2×D311yescharacteristic, complemented
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—61no—
200Dic9⋊C4—61no—
201C4×Dic9—31no—
202C4×Dic9—61no—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9C2×D412yes—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9#4112yescomplemented
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9#4112yescomplemented
219D3×D9—28no—
220C3×C4×C9—21no—
221C3×C4×C9—21no—
222C3×C4×C9C2×D412yes—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C3⋊Dic9C2×D412yes—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C2×#235—91no—
231C2×#235—91no—
232C22×C4×D3—91no—
233C22×C4×D3—91no—
234C3×C4×D4—31no—
235C3×C4×D4—91no—
236#939—91no—
237#939—91no—
238#937—91no—
239#937—91no—
240C4×#67—91no—
241C4×#67—91no—
242C4×#67—91no—
243C4×#67—91no—
244#896—91no—
245#896—91no—
246#894—91no—
247#894—91no—
248#884—91no—
249#884—91no—
250#883—91no—
251#883—91no—
252#882—91no—
253#882—91no—
254#878—91no—
255#878—91no—
256C4×D12—31no—
257C4×D12D911yescharacteristic, complemented
258#872—91no—
259#872—91no—
260#872—181no—
261C22×C3⋊D3—31no—
262C22×C3×D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3C22×D311yescharacteristic
265C22×C3×D3C22×D311yescharacteristic
266C2×D32—62no—
267C2×D32—62no—
268C2×D32—62no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C4×C3⋊D3—34no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C3×D12—22no—
281C3×D12—62no—
282C3×C4×D3—22no—
283C3×C4×D3—22no—
284C3×C4×D3—62no—
285C3×C4×D3—62no—
286#627—62no—
287#626—62no—
288#626—62no—
289#625—62no—
290#625—62no—
291#625—62no—
292#624—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—31no—
296C23×C9—31no—
297C22×D9—31no—
298C22×D9—61no—
299C22×D9—62no—
300C22×D9—62no—
301C22×D9—62no—
302C22×D9C22×D311yescharacteristic
303C22×D9C22×D311yescharacteristic
304D4×C9—62no—
305C2×C4×C9—21no—
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—62no—
311C2×C4×C9—62no—
312C2×C4×C9C22×D311yescharacteristic
313C2×C4×C9C22×D311yescharacteristic
314C2×C4×C9C22×D311yescharacteristic
315#611—62no—
316#611—62no—
317#611—62no—
318#611—62no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9—62no—
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328D36—22no—
329D36—62no—
330C4×D9—22no—
331C4×D9—22no—
332C4×D9—34no—
333C4×D9—64no—
334C4×D9—62no—
335C4×D9—62no—
336Dic18—62no—
337#525—271noSylow
338C2×C3×C9C22×D411yescharacteristic
339C2×C3×C9C2×#4111yescharacteristic
340C2×C3×C9C2×#4111yescharacteristic
341C3⋊D9—22no—
342D3×C9—22no—
343D3×C9—41no—
344C3×D9—22no—
345C3×D9—41no—
346C23×D3—91no—
347C23×D3—91no—
348C2×C3×D4—31no—
349C2×C3×D4—91no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—91no—
353C22×C3×C4—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C22×Dic3—91no—
363C22×Dic3—91no—
364#235—184no—
365#235—184no—
366C2×D12—31no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12C2×D911yescharacteristic
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—181no—
379C2×C4×D3—184no—
380C2×C4×D3—184no—
381C2×C4×D3C2×D911yescharacteristic
382C2×C4×D3C2×D911yescharacteristic, complemented
383C2×Dic6—91no—
384C2×Dic6—91no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—91no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C42—21no—
392C3×C42C2×D911yescharacteristic, complemented
393C3×C42D3211yescharacteristic
394#217—91no—
395#217—91no—
396#217—91no—
397#217—91no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—181no—
409(C2×D3)⋊C4—181no—
410(C2×D3)⋊C4C2×D911yescharacteristic
411(C2×D3)⋊C4C2×D911yescharacteristic, complemented
412C4⋊Dic3—31no—
413C4⋊Dic3C2×D911yescharacteristic, complemented
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—181no—
423Dic3⋊C4—181no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3—181no—
427C22×C32C23×D311yescharacteristic
428C2×C3⋊D3—32no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—32no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3#23512yes—
443D32—68no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4D3×D412yes—
447C3⋊Dic3—32no—
448C3⋊Dic3—61no—
449C3⋊Dic3—61no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C22×C9—21no—
455C22×C9—32no—
456C22×C9—61no—
457C22×C9—61no—
458C22×C9—61no—
459C22×C9—61no—
460C22×C9—61no—
461C22×C9C23×D311yescharacteristic
462C2×D9—21no—
463C2×D9—21no—
464C2×D9—21no—
465C2×D9—21no—
466C2×D9—21no—
467C2×D9—32no—
468C2×D9—62no—
469C2×D9—68no—
470C2×D9—61no—
471C2×D9—61no—
472C2×D9—121no—
473C2×D9—121no—
474C2×D9#23512yescomplemented
475C4×C9—21no—
476C4×C9—21no—
477C4×C9—22no—
478C4×C9—41no—
479C4×C9—41no—
480C4×C9—61no—
481C4×C9—61no—
482C4×C9D3×D412yes—
483Dic9—21no—
484Dic9—21no—
485Dic9—32no—
486Dic9—62no—
487Dic9—61no—
488Dic9—61no—
489Dic9—121no—
490Dic9—121no—
491C2×#41—271no—
492C23×C4—271no—
493#123—271no—
494#123—271no—
495C22⋊Q8—271no—
496C22⋊Q8—271no—
497#121—271no—
498#121—271no—
499#120—271no—
500#120—271no—
501C4×D4—31no—
502C4×D4—91no—
503C4×D4—271no—
504C4×D4—271no—
505#117—271no—
506C3×C9#52511yescharacteristic, complemented, Sylow
507C23×C3—31no—
508C23×C3—31no—
509C23×C3—91no—
510C23×C3—91no—
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—91no—
514C22×D3—91no—
515C22×D3—181no—
516C22×D3—182no—
517C22×D3—182no—
518C22×D3—182no—
519C22×D3—182no—
520C22×D3—182no—
521C22×D3—182no—
522C22×D3C22×D911yescharacteristic
523C22×D3C22×D911yescharacteristic
524C3×D4—62no—
525C3×D4—182no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—62no—
532C2×C3×C4—62no—
533C2×C3×C4—91no—
534C2×C3×C4—91no—
535C2×C3×C4—182no—
536C2×C3×C4—182no—
537C2×C3×C4C22×D911yescharacteristic
538C2×C3×C4C22×D911yescharacteristic
539C2×C3×C4C22×D911yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541C2×C3×C4C2×D3211yescharacteristic
542C2×C3×C4C2×D3211yescharacteristic
543#67—182no—
544#67—182no—
545#67—182no—
546#67—182no—
547#67—182no—
548#67—182no—
549#67—182no—
550#67—182no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—181no—
560C2×Dic3—181no—
561C2×Dic3—181no—
562C2×Dic3—182no—
563C2×Dic3—182no—
564C2×Dic3C22×D911yescharacteristic
565C2×Dic3C22×D911yescharacteristic
566D12—22no—
567D12—62no—
568D12—182no—
569D12—182no—
570C4×D3—22no—
571C4×D3—22no—
572C4×D3—62no—
573C4×D3—62no—
574C4×D3—94no—
575C4×D3—94no—
576C4×D3—184no—
577C4×D3—182no—
578C4×D3—182no—
579C4×D3—182no—
580C4×D3—182no—
581Dic6—182no—
582Dic6—182no—
583C2×C32C2×#23511yescharacteristic
584C2×C32C2×D3×D411yescharacteristic
585C2×C32D3×#4111yescharacteristic
586C3⋊D3—62no—
587C3×D3—22no—
588C3×D3—41no—
589C3×D3—62no—
590C3×D3—121no—
591C2×C9—21no—
592C2×C9—21no—
593C2×C9—21no—
594C2×C9—62no—
595C2×C9—121no—
596C2×C9C2×#23511yescharacteristic
597C2×C9C2×D3×D411yescharacteristic
598C2×C9D3×#4111yescharacteristic
599D9—22no—
600D9—41no—
601D9—62no—
602D9—122no—
603C24—271no—
604#41—544no—
605C2×Q8—271no—
606C2×D4—31no—
607C2×D4—91no—
608C2×D4—271no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—271no—
618C22×C4—271no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—544no—
622C4⋊C4—31no—
623C4⋊C4—91no—
624C4⋊C4—271no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C42—271no—
639C42D3×D911yescharacteristic, complemented
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—92no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3C23×D911yescharacteristic
654C22×C3C22×D3211yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—32no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—92no—
667C2×D3—92no—
668C2×D3—182no—
669C2×D3—188no—
670C2×D3—188no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—361no—
676C2×D3—361no—
677C2×D3#369712yescomplemented
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—22no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—181no—
688C3×C4—181no—
689C3×C4D4×D912yes—
690C3×C4#380212yes—
691Dic3—21no—
692Dic3—21no—
693Dic3—61no—
694Dic3—61no—
695Dic3—92no—
696Dic3—92no—
697Dic3—182no—
698Dic3—181no—
699Dic3—181no—
700Dic3—181no—
701Dic3—181no—
702Dic3—361no—
703Dic3—361no—
704C32#554711yescharacteristic
705C9—21no—
706C9#554711yescharacteristic, complemented
707C23—31no—
708C23—31no—
709C23—91no—
710C23—91no—
711C23—271no—
712C23—542no—
713C23—542no—
714C23—542no—
715Q8—542no—
716D4—62no—
717D4—182no—
718D4—542no—
719D4—542no—
720D4—542no—
721D4—542no—
722D4—542no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—182no—
730C2×C4—182no—
731C2×C4—271no—
732C2×C4—274no—
733C2×C4—271no—
734C2×C4—271no—
735C2×C4—542no—
736C2×C4—542no—
737C2×C4—542no—
738C2×C4C2×D3×D911yescharacteristic
739C2×C4C2×D3×D911yescharacteristic
740C2×C4C2×D3×D911yescharacteristic
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—62no—
745C2×C3—121no—
746C2×C3—182no—
747C2×C3—361no—
748C2×C3C2×#369711yescharacteristic
749C2×C3C2×D4×D911yescharacteristic
750C2×C3#41×D911yescharacteristic
751C2×C3C2×#380211yescharacteristic
752C2×C3D3×#23511yescharacteristic
753C2×C3D3×#23511yescharacteristic
754D3—22no—
755D3—41no—
756D3—62no—
757D3—121no—
758D3—182no—
759D3—182no—
760D3—362no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—92no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—272no—
774C22—548no—
775C22—541no—
776C22—541no—
777C22C22×D3×D911yescharacteristic
778C4—21no—
779C4—21no—
780C4—61no—
781C4—61no—
782C4—181no—
783C4—181no—
784C4—272no—
785C4—541no—
786C4—541no—
787C4#8864612yes—
788C3—21no—
789C3#1058964911yescharacteristic, complemented
790C3#1059400611yescharacteristic
791C2—62no—
792C2—121no—
793C2—182no—
794C2—361no—
795C2—542no—
796C2C2×#8864611yescharacteristic
797C2D3×#369711yescharacteristic
798C2D9×#23511yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C42×C9C22
socleC22×C32C23×D3
hypercenterC42D3×D9
hypocenterC3×C9#525
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D9C2semidirect
2. C2×#88640C2semidirect
3. #11721709C2semidirect
4. C4×C9×D12C2semidirect
5. C3×C4×D36C2semidirect
6. #11721050C2semidirect
7. #11721049C2semidirect
8. C4×#6194C2semidirect
9. C4×#6194C2semidirect
10. #11721026C2semidirect
11. #11721016C2semidirect
12. #11720999C2semidirect
13. #11720982C2semidirect
14. #11720958C2semidirect
15. #11720942C2semidirect
22. C2×C4×D3×C9C22semidirect
25. C2×C3×C4×D9C22semidirect
29. C2×#6194C22semidirect
34. C2×#6189C22semidirect
37. C3×C42×C9C22semidirect
40. #88534C22semidirect
41. #88534C22semidirect
42. C4×C3⋊Dic9C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C9×C4⋊Dic3C22semidirect
48. C3×C4⋊Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. #88442C22semidirect
54. #88442C22semidirect
83. C4×D36D3semidirect
100. C4×C3⋊D9D4semidirect
177. C2×C4×D9C2×D3semidirect
183. C42×C9C2×D3semidirect
193. (C2×D9)⋊C4C2×D3semidirect
194. C4⋊Dic9C2×D3semidirect
212. C2×D3×C9#41semidirect
218. C2×C3×D9#41semidirect
257. C4×D12D9semidirect
382. C2×C4×D3C2×D9semidirect
392. C3×C42C2×D9semidirect
411. (C2×D3)⋊C4C2×D9semidirect
413. C4⋊Dic3C2×D9semidirect
474. C2×D9#235semidirect
506. C3×C9#525semidirect
639. C42D3×D9semidirect
677. C2×D3#3697semidirect
706. C9#5547semidirect
789. C3#10589649semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D92
C2×#886402
#117217092
C4×C9×D122
C3×C4×D362
#117210502
#117210492
C4×#61942
#117210262
#117210162
#117209992
#117209822
#117209582
#117209422
#105940063
#105896493