Finite Group Databasebeta

← #13148819

Subgroups — #13148819

Order 1728.

1068 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D9C211yesmaximal, characteristic, complemented
2C2×#88642C211yesmaximal, characteristic, complemented
3#11721750C211yesmaximal, characteristic, complemented
4C9×#893C211yesmaximal, characteristic, complemented
5C3×#63458C211yesmaximal, characteristic, complemented
6#11721051C211yesmaximal, characteristic, complemented
7#11721050C211yesmaximal, characteristic, complemented
8#11721033C211yesmaximal, characteristic, complemented
9#11721030C211yesmaximal, characteristic, complemented
10#11721018C211yesmaximal, characteristic, complemented
11#11721017C211yesmaximal, characteristic, complemented
12#11720977C211yesmaximal, characteristic, complemented
13#11720976C211yesmaximal, characteristic, complemented
14#11720957C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10594623—31nomaximal
17#10589649—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×D12C2211yescharacteristic
22C2×C4×D3×C9C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic, complemented
24C2×C3×C4×D9C2211yescharacteristic
25C2×C3×Dic18C2211yescharacteristic, complemented
26C2×#6195C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic, complemented
29C2×#6194C2211yescharacteristic
30C2×D3×Dic9C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C2×Dic3×D9C2211yescharacteristic
35C4×D3×D9—24no—
36#88642—24no—
37C3×C9×C4⋊C4C2211yescharacteristic, complemented
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C4×C9×Dic3C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51#88445C2211yescharacteristic
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C4×D32—31no—
56C2×#3799—31no—
57#64103—31no—
58C3×#896—31no—
59C3×#893D311yescharacteristic
60#63923—31no—
61#63922—31no—
62#63906—31no—
63#63904—31no—
64#63887—31no—
65#63886—31no—
66#63880—31no—
67#63879—31no—
68#63853—31no—
69#63836—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#63458D311yescharacteristic, complemented
78#63456—31no—
79#63456—61no—
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#63440—31no—
84C4×D36—31no—
85#63434—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
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
99C4⋊(C3⋊D9)—22no—
100C4×C3⋊D9—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C9×D12—22no—
107C4×D3×C9—22no—
108C4×D3×C9—22no—
109C3×C4×D9—22no—
110C3×Dic18—22no—
111#6195—22no—
112#6195—22no—
113#6195—22no—
114#6194—22no—
115D3×Dic9—22no—
116#6192—22no—
117(C3⋊D9)⋊C4—22no—
118(C3⋊D9)⋊C4D414yescomplemented
119Dic3×D9—22no—
120#5627—91no—
121#5547—91no—
122C22×D32—31no—
123C2×C4⋊(C3⋊D3)—31no—
124C2×C4×C3⋊D3—31no—
125C2×C3×D12C2×D311yescharacteristic
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3C2×D311yescharacteristic
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×Dic6—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×#625—31no—
135C2×#624—31no—
136C2×#624—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C4×D32—64no—
140#3799—64no—
141C23×D9—31no—
142C32×C4⋊C4C2×D311yescharacteristic
143#3752—31no—
144#3752—31no—
145#3752—31no—
146#3750—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×Dic3⋊C4—31no—
152C3×Dic3⋊C4—31no—
153C3×C4×Dic3C2×D311yescharacteristic
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156#3722—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159Dic32—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×D36—31no—
171C2×D36—61no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—64no—
177C2×C4×D9—61no—
178C2×C4×D9C2×D311yescharacteristic
179C2×Dic18C2×D311yescharacteristic, complemented
180C9×C4⋊C4—21no—
181C9×C4⋊C4C2×D311yescharacteristic, complemented
182C9×C22⋊C4—31no—
183C9×C22⋊C4—31no—
184C42×C9—31no—
185#3676—31no—
186#3676—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—61no—
192(C2×D9)⋊C4—61no—
193(C2×D9)⋊C4—61no—
194(C2×D9)⋊C4C2×D311yescharacteristic
195(C2×D9)⋊C4C2×D311yescharacteristic
196C4⋊Dic9—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—61no—
200Dic9⋊C4C2×D311yescharacteristic, complemented
201Dic9⋊C4C2×D311yescharacteristic, complemented
202C4×Dic9—31no—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9C2×D412yes—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9#4112yescomplemented
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×C9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C9×Dic3—21no—
226C9×Dic3C2×D412yes—
227C3×Dic9—21no—
228C3×Dic9—21no—
229C3×Dic9C2×D412yes—
230C2×#239—91no—
231C2×#235—91no—
232C22×C4×D3—91no—
233C22×C4×D3—91no—
234C3×C22⋊Q8—91no—
235C3×C4×D4—31no—
236#946—91no—
237#939—91no—
238#937—91no—
239#930—91no—
240C4×#67—91no—
241C4×#67—91no—
242#896—31no—
243#895—91no—
244#894—91no—
245#894—91no—
246#894—91no—
247#894—181no—
248#893—91no—
249#893D911yescharacteristic, complemented
250#892—91no—
251#884—91no—
252#883—91no—
253#882—91no—
254#882—91no—
255#882—91no—
256#67⋊C4—91no—
257#67⋊C4—91no—
258#878—91no—
259C4×D12—91no—
260#872—91no—
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—
274C4⋊(C3⋊D3)—62no—
275C4×C3⋊D3—62no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C3×D12—22no—
282C3×C4×D3—22no—
283C3×C4×D3—22no—
284C3×C4×D3—62no—
285C3×Dic6—62no—
286#626—62no—
287#626—62no—
288#626—62no—
289#626—62no—
290#625—62no—
291#624—34no—
292#624—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—31no—
296C23×C9—31no—
297C22×D9—31no—
298C22×D9—31no—
299C22×D9—61no—
300C22×D9—61no—
301C22×D9—62no—
302C22×D9—62no—
303C22×D9—62no—
304C22×D9C22×D311yescharacteristic
305D4×C9—62no—
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—21no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311C2×C4×C9—62no—
312C2×C4×C9—62no—
313C2×C4×C9C22×D311yescharacteristic
314C2×C4×C9C22×D311yescharacteristic
315C2×C4×C9C22×D311yescharacteristic
316#611—62no—
317#611—62no—
318#611—62no—
319#611—62no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—62no—
325C2×Dic9C22×D311yescharacteristic
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328D36—62no—
329D36—62no—
330D36—122no—
331C4×D9—22no—
332C4×D9—34no—
333C4×D9—62no—
334C4×D9—62no—
335C4×D9—62no—
336C4×D9—122no—
337Dic18—22no—
338#525—271noSylow
339C2×C3×C9C22×D411yescharacteristic
340C2×C3×C9C2×#4111yescharacteristic
341C2×C3×C9C2×#4111yescharacteristic
342C3⋊D9—22no—
343C3⋊D9—41no—
344D3×C9—22no—
345D3×C9—41no—
346C3×D9—22no—
347C23×D3—91no—
348C23×D3—91no—
349C2×C3×Q8—91no—
350C2×C3×D4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C22×Dic3—91no—
361C22×Dic3—91no—
362#239—184no—
363#235—184no—
364C2×D12—91no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12—181no—
371C2×D12C2×D911yescharacteristic
372C2×C4×D3—31no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—181no—
382C2×C4×D3—184no—
383C2×C4×D3—184no—
384C2×C4×D3C2×D911yescharacteristic
385C2×C4×D3C2×D911yescharacteristic, complemented
386C2×Dic6—31no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—91no—
389C3×C4⋊C4—91no—
390C3×C4⋊C4C2×D911yescharacteristic, complemented
391C3×C4⋊C4D3211yescharacteristic
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C42—31no—
397#217—91no—
398#217—91no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
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—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—181no—
412(C2×D3)⋊C4—181no—
413(C2×D3)⋊C4—181no—
414(C2×D3)⋊C4C2×D911yescharacteristic
415(C2×D3)⋊C4C2×D911yescharacteristic, complemented
416C4⋊Dic3—91no—
417C4⋊Dic3—91no—
418Dic3⋊C4—31no—
419Dic3⋊C4—31no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—181no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3C2×D911yescharacteristic, complemented
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—32no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—32no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3#23512yes—
444D32—68no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C3⋊Dic3—61no—
449C3⋊Dic3—61no—
450C3×Dic3—21no—
451C3×Dic3—32no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3D3×D412yes—
455C22×C9—21no—
456C22×C9—32no—
457C22×C9—61no—
458C22×C9—61no—
459C22×C9—61no—
460C22×C9—61no—
461C22×C9—61no—
462C22×C9C23×D311yescharacteristic
463C2×D9—21no—
464C2×D9—21no—
465C2×D9—32no—
466C2×D9—62no—
467C2×D9—68no—
468C2×D9—61no—
469C2×D9—61no—
470C2×D9—61no—
471C2×D9—61no—
472C2×D9—61no—
473C2×D9—121no—
474C2×D9—121no—
475C2×D9—121no—
476C2×D9—121no—
477C2×D9—121no—
478C2×D9#23912yescomplemented
479C4×C9—21no—
480C4×C9—21no—
481C4×C9—21no—
482C4×C9—32no—
483C4×C9—41no—
484C4×C9—41no—
485C4×C9—41no—
486C4×C9—61no—
487Dic9—21no—
488Dic9—21no—
489Dic9—61no—
490Dic9—61no—
491Dic9—121no—
492Dic9—121no—
493Dic9D3×D412yes—
494C2×#41—271no—
495C23×C4—271no—
496#123—271no—
497#123—271no—
498C22⋊Q8—91no—
499C22⋊Q8—271no—
500#121—271no—
501#121—271no—
502#120—271no—
503#120—271no—
504C4×D4—31no—
505C4×D4—271no—
506C4×D4—271no—
507C4×D4—271no—
508#117—271no—
509C3×C9#52511yescharacteristic, complemented, Sylow
510C23×C3—31no—
511C23×C3—31no—
512C23×C3—91no—
513C22×D3—31no—
514C22×D3—91no—
515C22×D3—91no—
516C22×D3—91no—
517C22×D3—91no—
518C22×D3—181no—
519C22×D3—181no—
520C22×D3—182no—
521C22×D3—182no—
522C22×D3—182no—
523C22×D3—182no—
524C22×D3—182no—
525C22×D3—182no—
526C22×D3C22×D911yescharacteristic
527C22×D3C22×D911yescharacteristic
528C3×Q8—182no—
529C3×D4—62no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—62no—
536C2×C3×C4—62no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—182no—
541C2×C3×C4C22×D911yescharacteristic
542C2×C3×C4C22×D911yescharacteristic
543C2×C3×C4C22×D911yescharacteristic
544C2×C3×C4C2×D3211yescharacteristic
545C2×C3×C4C2×D3211yescharacteristic
546C2×C3×C4C2×D3211yescharacteristic
547#67—182no—
548#67—182no—
549#67—182no—
550#67—182no—
551#67—182no—
552#67—182no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—91no—
560C2×Dic3—181no—
561C2×Dic3—181no—
562C2×Dic3—182no—
563C2×Dic3—182no—
564C2×Dic3C22×D911yescharacteristic
565C2×Dic3C22×D911yescharacteristic
566D12—22no—
567D12—182no—
568D12—182no—
569D12—182no—
570D12—182no—
571D12—182no—
572D12—182no—
573D12—362no—
574C4×D3—22no—
575C4×D3—22no—
576C4×D3—62no—
577C4×D3—94no—
578C4×D3—94no—
579C4×D3—182no—
580C4×D3—182no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—362no—
586Dic6—62no—
587C2×C32C2×#23511yescharacteristic
588C2×C32C2×D3×D411yescharacteristic
589C2×C32D3×#4111yescharacteristic
590C3⋊D3—62no—
591C3⋊D3—121no—
592C3×D3—22no—
593C3×D3—41no—
594C3×D3—62no—
595C2×C9—21no—
596C2×C9—21no—
597C2×C9—21no—
598C2×C9—62no—
599C2×C9—121no—
600C2×C9C2×D3×D411yescharacteristic
601C2×C9C2×#23911yescharacteristic
602C2×C9D3×#4111yescharacteristic
603D9—22no—
604D9—62no—
605D9—122no—
606D9—121no—
607D9—241no—
608C24—271no—
609#41—544no—
610C2×Q8—91no—
611C2×D4—31no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—91no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—544no—
627C4⋊C4—91no—
628C4⋊C4—91no—
629C4⋊C4—271no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4D3×D911yescharacteristic, complemented
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C42—31no—
644C42—271no—
645C22×C3—21no—
646C22×C3—32no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—92no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3C23×D911yescharacteristic
656C22×C3C22×D3211yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—32no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—92no—
666C2×D3—92no—
667C2×D3—182no—
668C2×D3—188no—
669C2×D3—188no—
670C2×D3—181no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—361no—
681C2×D3—361no—
682C2×D3—361no—
683C2×D3—361no—
684C2×D3—361no—
685C2×D3#369712yescomplemented
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—32no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—92no—
698C3×C4—181no—
699C3×C4—181no—
700Dic3—21no—
701Dic3—32no—
702Dic3—61no—
703Dic3—61no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—181no—
708Dic3—361no—
709Dic3—361no—
710Dic3D4×D912yes—
711C32#554711yescharacteristic
712C9—21no—
713C9#562711yescharacteristic, complemented
714C23—31no—
715C23—31no—
716C23—91no—
717C23—271no—
718C23—271no—
719C23—542no—
720C23—542no—
721C23—542no—
722Q8—182no—
723D4—62no—
724D4—542no—
725D4—542no—
726D4—542no—
727D4—542no—
728D4—542no—
729D4—542no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—182no—
738C2×C4—274no—
739C2×C4—271no—
740C2×C4—271no—
741C2×C4—542no—
742C2×C4—542no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4C2×D3×D911yescharacteristic
746C2×C4C2×D3×D911yescharacteristic
747C2×C4C2×D3×D911yescharacteristic
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—62no—
752C2×C3—121no—
753C2×C3—182no—
754C2×C3C2×#369711yescharacteristic
755C2×C3C2×D4×D911yescharacteristic
756C2×C3#41×D911yescharacteristic
757C2×C3D3×#23511yescharacteristic
758C2×C3D32×D411yescharacteristic
759C2×C3D3×#23911yescharacteristic
760D3—22no—
761D3—41no—
762D3—62no—
763D3—182no—
764D3—182no—
765D3—362no—
766D3—361no—
767D3—361no—
768D3—721no—
769C22—32no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—92no—
776C22—181no—
777C22—181no—
778C22—272no—
779C22—548no—
780C22—541no—
781C22—541no—
782C22—541no—
783C22—541no—
784C22—541no—
785C22C22×D3×D911yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—32no—
790C4—61no—
791C4—92no—
792C4—181no—
793C4—181no—
794C4—541no—
795C4—541no—
796C3—21no—
797C3#1058964911yescharacteristic, complemented
798C3#1059462311yescharacteristic
799C2—62no—
800C2—121no—
801C2—182no—
802C2—542no—
803C2—1081no—
804C2D3×#369711yescharacteristic
805C2D3×D4×D911yescharacteristic
806C2D9×#23911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#525
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×C4×D3×D9C2semidirect
2. C2×#88642C2semidirect
3. #11721750C2semidirect
4. C9×#893C2semidirect
5. C3×#63458C2semidirect
6. #11721051C2semidirect
7. #11721050C2semidirect
8. #11721033C2semidirect
9. #11721030C2semidirect
10. #11721018C2semidirect
11. #11721017C2semidirect
12. #11720977C2semidirect
13. #11720976C2semidirect
14. #11720957C2semidirect
15. #11720898C2semidirect
23. C2×C4×D3×C9C22semidirect
25. C2×C3×Dic18C22semidirect
28. C2×#6195C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
37. C3×C9×C4⋊C4C22semidirect
39. #88536C22semidirect
40. #88536C22semidirect
41. #88534C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
46. C4×C9×Dic3C22semidirect
47. C3×Dic9⋊C4C22semidirect
48. C3×Dic9⋊C4C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
77. #63458D3semidirect
118. (C3⋊D9)⋊C4D4semidirect
179. C2×Dic18C2×D3semidirect
181. C9×C4⋊C4C2×D3semidirect
200. Dic9⋊C4C2×D3semidirect
201. Dic9⋊C4C2×D3semidirect
215. C2×D3×C9#41semidirect
218. C2×C3×D9#41semidirect
249. #893D9semidirect
385. C2×C4×D3C2×D9semidirect
390. C3×C4⋊C4C2×D9semidirect
415. (C2×D3)⋊C4C2×D9semidirect
427. C4×Dic3C2×D9semidirect
478. C2×D9#239semidirect
509. C3×C9#525semidirect
632. C4⋊C4D3×D9semidirect
685. C2×D3#3697semidirect
713. C9#5627semidirect
797. 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×#886422
#117217502
C9×#8932
C3×#634582
#117210512
#117210502
#117210332
#117210302
#117210182
#117210172
#117209772
#117209762
#117209572
#117208982
#105946233
#105896493