Finite Group Databasebeta

← #13147705

Subgroups — #13147705

Order 1728.

1084 conjugacy classes of subgroups.

The subgroup lattice has 810 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
3C4×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
4C9×#872C211yesmaximal, characteristic, complemented
5C3×C4×D36C211yesmaximal, characteristic, complemented
6#11721051C211yesmaximal, characteristic, complemented
7#11721049C211yesmaximal, characteristic, complemented
8#11721021C211yesmaximal, characteristic, complemented
9#11721020C211yesmaximal, characteristic, complemented
10#11721005C211yesmaximal, characteristic, complemented
11C4×#6192C211yesmaximal, characteristic, complemented
12C4×#6192C211yesmaximal, characteristic, complemented
13#11720995C211yesmaximal, characteristic, complemented
14#11720991C211yesmaximal, characteristic, complemented
15#11720983C211yesmaximal, characteristic, complemented
16#10593997—31nomaximal
17#10589626—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C4×D3×C9C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
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, complemented
40C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C9×Dic3⋊C4C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47C4×C9×Dic3C2211yescharacteristic, complemented
48C3×C4⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic3⋊Dic9C2211yescharacteristic, complemented
55C2×C4×D32—31no—
56C2×#3798—31no—
57C4×C4⋊(C3⋊D3)—31no—
58C3×C4×D12—31no—
59C3×#872D311yescharacteristic
60#63923—31no—
61#63922—31no—
62#63910—31no—
63C4×#626—31no—
64C4×#626—31no—
65#63895—31no—
66#63893—31no—
67#63891—31no—
68#63890—31no—
69#63886—31no—
70C2×#3697—31no—
71C22×C4×D9—31no—
72C9×#117—31no—
73#63459—31no—
74#63459—31no—
75#63457—31no—
76#63457—31no—
77#63448—31no—
78#63448—31no—
79#63444—31no—
80#63444—31no—
81C4×D36—31no—
82C4×D36—31no—
83C4×D36—31no—
84C4×D36—61no—
85C4×D36D311yescharacteristic, complemented
86C22×C3⋊D9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
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
99C4⋊(C3⋊D9)—22no—
100C4×C3⋊D9—22no—
101C4×C3⋊D9—22no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C4×D3×C9D414yescomplemented
108C3×D36—22no—
109C3×C4×D9—22no—
110C3×C4×D9—22no—
111#6195—22no—
112#6194—22no—
113D3×Dic9—22no—
114#6192—22no—
115#6192—22no—
116#6192—22no—
117(C3⋊D9)⋊C4—22no—
118Dic3×D9—22no—
119#6189—22no—
120#5547—91no—
121#5524—91no—
122C22×D32—31no—
123C2×C4⋊(C3⋊D3)—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C3×D12—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×#627—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×#626—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—
145C4⋊(C3⋊Dic3)—31no—
146C3×(C2×D3)⋊C4—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4C2×D311yescharacteristic
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×C4⋊Dic3—31no—
151C3×Dic3⋊C4C2×D311yescharacteristic
152C3×Dic3⋊C4C2×D311yescharacteristic
153C3×C4×Dic3C2×D311yescharacteristic
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156#3722—31no—
157#3722—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160C22×C4×C9—31no—
161C2×#611—31no—
162C2×#611—31no—
163C22×Dic9—31no—
164#3697—64no—
165C2×D36—31no—
166C2×D36—31no—
167C2×D36—31no—
168C2×D36—31no—
169C2×D36—61no—
170C2×D36C2×D311yescharacteristic
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—64no—
176C2×C4×D9—61no—
177C2×C4×D9—61no—
178C2×C4×D9C2×D311yescharacteristic
179C2×C4×D9C2×D311yescharacteristic, complemented
180C2×Dic18—31no—
181C9×C4⋊C4—31no—
182C9×C4⋊C4—31no—
183C9×C22⋊C4—31no—
184C9×C22⋊C4—31no—
185C42×C9—21no—
186C42×C9—31no—
187C42×C9C2×D311yescharacteristic, complemented
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—61no—
195(C2×D9)⋊C4—61no—
196(C2×D9)⋊C4C2×D311yescharacteristic
197(C2×D9)⋊C4C2×D311yescharacteristic, complemented
198C4⋊Dic9—31no—
199C4⋊Dic9—31no—
200C4⋊Dic9—31no—
201C4⋊Dic9—61no—
202C4⋊Dic9C2×D311yescharacteristic, complemented
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⋊D9#4112yescomplemented
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9C2×D412yes—
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—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C9×Dic3C2×D412yes—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C2×#235—91no—
231C2×#235—91no—
232C22×C4×D3—91no—
233C22×C4×D3—91no—
234C3×C4×D4—91no—
235C3×#117—31no—
236#939—91no—
237#937—91no—
238C4×#67—91no—
239C4×#67—91no—
240#897—91no—
241#897—91no—
242#896—91no—
243#895—91no—
244#895—91no—
245#894—91no—
246#886—91no—
247#886—91no—
248#884—91no—
249#883—91no—
250#882—91no—
251#882—91no—
252#882—91no—
253#878—91no—
254C4×D12—31no—
255C4×D12—91no—
256C4×D12—91no—
257C4×D12—91no—
258C4×D12—91no—
259C4×D12—181no—
260#872D911yescharacteristic, complemented
261C22×C3⋊D3—31no—
262C22×C3⋊D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3—31no—
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—
276C4×C3⋊D3—62no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C3×D12—62no—
283C3×C4×D3—62no—
284C3×C4×D3—62no—
285C3×C4×D3D1214yes—
286#627—62no—
287#626—62no—
288#626—62no—
289#626—62no—
290#626—62no—
291#625—62no—
292#624—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—31no—
296C22×D9—31no—
297C22×D9—31no—
298C22×D9—61no—
299C22×D9—61no—
300C22×D9—62no—
301C22×D9—62no—
302C22×D9—62no—
303C22×D9C22×D311yescharacteristic
304C22×D9C22×D311yescharacteristic
305C2×C4×C9—21no—
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—31no—
309C2×C4×C9—34no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9C22×D311yescharacteristic
313C2×C4×C9C22×D311yescharacteristic
314C2×C4×C9C22×D311yescharacteristic
315#611—62no—
316#611—62no—
317C2×Dic9—31no—
318C2×Dic9—31no—
319C2×Dic9—61no—
320C2×Dic9—61no—
321C2×Dic9—62no—
322C2×Dic9C22×D311yescharacteristic
323C2×Dic9C22×D311yescharacteristic
324D36—22no—
325D36—62no—
326D36—64no—
327D36—62no—
328D36—62no—
329D36—62no—
330C4×D9—22no—
331C4×D9—22no—
332C4×D9—62no—
333C4×D9—62no—
334C4×D9—62no—
335C4×D9—62no—
336C4×D9—122no—
337C4×D9—122no—
338Dic18—62no—
339#525—271noSylow
340C2×C3×C9C22×D411yescharacteristic
341C2×C3×C9C2×#4111yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343C3⋊D9—22no—
344C3⋊D9—41no—
345D3×C9—22no—
346C3×D9—22no—
347C3×D9—41no—
348C23×D3—91no—
349C23×D3—91no—
350C2×C3×D4—91no—
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—
360C22×Dic3—91no—
361C22×Dic3—91no—
362#235—184no—
363#235—184no—
364C2×D12—31no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12—91no—
371C2×D12—181no—
372C2×C4×D3—31no—
373C2×C4×D3—31no—
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—91no—
382C2×C4×D3—181no—
383C2×C4×D3—181no—
384C2×C4×D3—184no—
385C2×C4×D3—184no—
386C2×C4×D3C2×D911yescharacteristic
387C2×Dic6—91no—
388C2×Dic6—91no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C42—21no—
397C3×C42—31no—
398C3×C42C2×D911yescharacteristic, complemented
399C3×C42D3211yescharacteristic
400#217—91no—
401#217—91no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
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—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—181no—
415(C2×D3)⋊C4—181no—
416(C2×D3)⋊C4C2×D911yescharacteristic
417(C2×D3)⋊C4C2×D911yescharacteristic
418C4⋊Dic3—31no—
419C4⋊Dic3—91no—
420C4⋊Dic3—91no—
421C4⋊Dic3—91no—
422C4⋊Dic3—91no—
423C4⋊Dic3—181no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4C2×D911yescharacteristic, complemented
427Dic3⋊C4C2×D911yescharacteristic, complemented
428C4×Dic3C2×D911yescharacteristic, complemented
429C22×C32C23×D311yescharacteristic
430C2×C3⋊D3—32no—
431C2×C3⋊D3—61no—
432C2×C3⋊D3—61no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—32no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C2×C3×D3C2×D1212yes—
445D32—68no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4C2×D1212yes—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3×Dic3—21no—
452C3×Dic3—21no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3C2×D1212yes—
456C22×C9—21no—
457C22×C9—32no—
458C22×C9—61no—
459C22×C9—61no—
460C22×C9C23×D311yescharacteristic
461C2×D9—21no—
462C2×D9—21no—
463C2×D9—21no—
464C2×D9—21no—
465C2×D9—21no—
466C2×D9—32no—
467C2×D9—62no—
468C2×D9—68no—
469C2×D9—61no—
470C2×D9—61no—
471C2×D9—62no—
472C2×D9—61no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—121no—
476C2×D9—121no—
477C2×D9—121no—
478C2×D9—121no—
479C2×D9#23512yescomplemented
480C4×C9—22no—
481C4×C9—21no—
482C4×C9—21no—
483C4×C9—22no—
484C4×C9—32no—
485C4×C9—41no—
486C4×C9—61no—
487C4×C9—61no—
488C4×C9D3×D412yes—
489Dic9—21no—
490Dic9—21no—
491Dic9—61no—
492Dic9—61no—
493Dic9—121no—
494Dic9—121no—
495C2×#41—271no—
496C23×C4—271no—
497#123—271no—
498#123—271no—
499C22⋊Q8—271no—
500C22⋊Q8—271no—
501#121—271no—
502#121—271no—
503#120—271no—
504#120—271no—
505C4×D4—91no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509#117—31no—
510C3×C9#52511yescharacteristic, complemented, Sylow
511C23×C3—31no—
512C23×C3—91no—
513C23×C3—91no—
514C22×D3—31no—
515C22×D3—31no—
516C22×D3—91no—
517C22×D3—91no—
518C22×D3—91no—
519C22×D3—91no—
520C22×D3—181no—
521C22×D3—181no—
522C22×D3—182no—
523C22×D3—182no—
524C22×D3—182no—
525C22×D3—182no—
526C22×D3—182no—
527C22×D3—182no—
528C22×D3C22×D911yescharacteristic
529C3×D4—182no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—34no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4—182no—
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—91no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—181no—
560C2×Dic3—181no—
561C2×Dic3—182no—
562C2×Dic3—182no—
563C2×Dic3C22×D911yescharacteristic
564C2×Dic3C22×D911yescharacteristic
565C2×Dic3C22×D911yescharacteristic
566D12—62no—
567D12—182no—
568D12—182no—
569D12—184no—
570D12—182no—
571D12—182no—
572D12—182no—
573D12—182no—
574C4×D3—62no—
575C4×D3—62no—
576C4×D3—182no—
577C4×D3—182no—
578C4×D3—182no—
579C4×D3—182no—
580C4×D3—182no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—182no—
584C4×D3—362no—
585C4×D3—362no—
586C4×D3D3614yescomplemented
587Dic6—182no—
588Dic6—182no—
589C2×C32C22×D1211yescharacteristic
590C2×C32D3×#4111yescharacteristic
591C2×C32D3×#4111yescharacteristic
592C3⋊D3—62no—
593C3⋊D3—121no—
594C3×D3—22no—
595C3×D3—62no—
596C3×D3—121no—
597C2×C9—21no—
598C2×C9—21no—
599C2×C9—21no—
600C2×C9—62no—
601C2×C9C2×#23511yescharacteristic
602C2×C9C2×D3×D411yescharacteristic
603C2×C9D3×#4111yescharacteristic
604D9—22no—
605D9—41no—
606D9—62no—
607D9—122no—
608D9—122no—
609D9—121no—
610C24—271no—
611#41—544no—
612C2×Q8—271no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C22×C4—31no—
621C22×C4—91no—
622C22×C4—91no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—271no—
628C22×C4—544no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—91no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—31no—
646C42D3×D911yescharacteristic, complemented
647C22×C3—21no—
648C22×C3—32no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—92no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3C23×D911yescharacteristic
658C22×C3C22×D3211yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—32no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—92no—
668C2×D3—92no—
669C2×D3—182no—
670C2×D3—188no—
671C2×D3—188no—
672C2×D3—181no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—182no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—361no—
684C2×D3—361no—
685C2×D3—361no—
686C2×D3—361no—
687C2×D3C2×D3612yes—
688C3×C4—22no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—22no—
694C3×C4—32no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—181no—
699C3×C4—181no—
700C3×C4C2×D3612yes—
701C3×C4D3×D1212yes—
702Dic3—21no—
703Dic3—21no—
704Dic3—61no—
705Dic3—61no—
706Dic3—181no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—361no—
711Dic3—361no—
712Dic3C2×D3612yes—
713C32#552411yescharacteristic
714C9—21no—
715C9#554711yescharacteristic, complemented
716C23—31no—
717C23—91no—
718C23—91no—
719C23—271no—
720C23—271no—
721C23—542no—
722C23—542no—
723C23—542no—
724Q8—542no—
725D4—182no—
726D4—542no—
727D4—542no—
728D4—542no—
729D4—542no—
730D4—542no—
731D4—542no—
732C2×C4—31no—
733C2×C4—34no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—182no—
739C2×C4—182no—
740C2×C4—271no—
741C2×C4—271no—
742C2×C4—542no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4C2×D3×D911yescharacteristic
748C2×C4C2×D3×D911yescharacteristic
749C2×C4C2×D3×D911yescharacteristic
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—62no—
754C2×C3—182no—
755C2×C3—361no—
756C2×C3C22×D3611yescharacteristic
757C2×C3#41×D911yescharacteristic
758C2×C3#41×D911yescharacteristic
759C2×C3C2×D3×D1211yescharacteristic
760C2×C3D3×#23511yescharacteristic
761C2×C3#6430611yescharacteristic
762D3—22no—
763D3—62no—
764D3—121no—
765D3—182no—
766D3—182no—
767D3—362no—
768D3—362no—
769D3—361no—
770D3—361no—
771C22—32no—
772C22—61no—
773C22—61no—
774C22—92no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—272no—
781C22—548no—
782C22—541no—
783C22—541no—
784C22—541no—
785C22—541no—
786C22—541no—
787C22C22×D3×D911yescharacteristic
788C4—21no—
789C4—21no—
790C4—32no—
791C4—61no—
792C4—61no—
793C4—181no—
794C4—181no—
795C4—541no—
796C4—541no—
797C4D3×D3612yes—
798C3—21no—
799C3#1058962611yescharacteristic, complemented
800C3#1059399711yescharacteristic
801C2—62no—
802C2—182no—
803C2—361no—
804C2—542no—
805C2—1081no—
806C2C2×D3×D3611yescharacteristic
807C2D9×#23511yescharacteristic
808C2#1172247511yescharacteristic
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. C4×C4⋊(C3⋊D9)C2semidirect
4. C9×#872C2semidirect
5. C3×C4×D36C2semidirect
6. #11721051C2semidirect
7. #11721049C2semidirect
8. #11721021C2semidirect
9. #11721020C2semidirect
10. #11721005C2semidirect
11. C4×#6192C2semidirect
12. C4×#6192C2semidirect
13. #11720995C2semidirect
14. #11720991C2semidirect
15. #11720983C2semidirect
21. C2×C4×C3⋊D9C22semidirect
25. C2×C3×C4×D9C22semidirect
31. C2×#6192C22semidirect
34. C2×#6189C22semidirect
37. C3×C42×C9C22semidirect
39. #88536C22semidirect
40. C4⋊(C3⋊Dic9)C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C9×Dic3⋊C4C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. C4×C9×Dic3C22semidirect
48. C3×C4⋊Dic9C22semidirect
50. #88445C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic3⋊Dic9C22semidirect
85. C4×D36D3semidirect
107. C4×D3×C9D4semidirect
179. C2×C4×D9C2×D3semidirect
187. C42×C9C2×D3semidirect
197. (C2×D9)⋊C4C2×D3semidirect
202. C4⋊Dic9C2×D3semidirect
209. C2×C3⋊D9#41semidirect
218. C2×C3×D9#41semidirect
260. #872D9semidirect
398. C3×C42C2×D9semidirect
426. Dic3⋊C4C2×D9semidirect
427. Dic3⋊C4C2×D9semidirect
428. C4×Dic3C2×D9semidirect
479. C2×D9#235semidirect
510. C3×C9#525semidirect
586. C4×D3D36semidirect
646. C42D3×D9semidirect
715. C9#5547semidirect
799. C3#10589626semidirect

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
C4×C4⋊(C3⋊D9)2
C9×#8722
C3×C4×D362
#117210512
#117210492
#117210212
#117210202
#117210052
C4×#61922
#117209952
#117209912
#117209832
#105939973
#105896263