Finite Group Databasebeta

← #13148133

Subgroups — #13148133

Order 1728.

1414 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic, complemented
2C2×D9×#67C211yesmaximal, characteristic, complemented
3C22×#6192C211yesmaximal, characteristic, complemented
4C2×D3×D36C211yesmaximal, characteristic, complemented
5#11721728C211yesmaximal, characteristic, complemented
6C9×#67⋊C4C211yesmaximal, characteristic, complemented
7C3×#63444C211yesmaximal, characteristic, complemented
8#11721277C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721049C211yesmaximal, characteristic, complemented
11#11721034C211yesmaximal, characteristic, complemented
12#11721006C211yesmaximal, characteristic, complemented
13#11721005C211yesmaximal, characteristic, complemented
14#11720983C211yesmaximal, characteristic, complemented
15#11720977C211yesmaximal, characteristic, complemented
16#10594277—31nomaximal
17D4×D36—31nomaximal
18C23×C3⋊D9C2211yescharacteristic, complemented
19C23×C3×D9C2211yescharacteristic, complemented
20C22×D3×D9C2211yescharacteristic, complemented
21C22×D3×D9C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
24C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic, complemented
27C22×C9×Dic3C2211yescharacteristic, complemented
28C2×C4×D3×C9C2211yescharacteristic, complemented
29C2×C3×D36C2211yescharacteristic, complemented
30C2×C3×D36C2211yescharacteristic, complemented
31#88668—24no—
32D9×#67—24no—
33C2×#6195C2211yescharacteristic, complemented
34C2×#6194C2211yescharacteristic, complemented
35C2×#6192—24no—
36C2×#6192C2211yescharacteristic
37C2×#6192C2211yescharacteristic, complemented
38C2×#6192C2211yescharacteristic, complemented
39C2×#6192C2211yescharacteristic, complemented
40C2×#6192C2211yescharacteristic, complemented
41C2×#6192C2211yescharacteristic, complemented
42C2×#6192C2211yescharacteristic, complemented
43C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
44C2×Dic3×D9C2211yescharacteristic, complemented
45D3×D36—24no—
46C3×C9×C22⋊C4C2211yescharacteristic, complemented
47#88536C2211yescharacteristic, complemented
48#88536C2211yescharacteristic, complemented
49C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
51C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
52C9×Dic3⋊C4C2211yescharacteristic, complemented
53C4×C9×Dic3C2211yescharacteristic, complemented
54#88445C2211yescharacteristic, complemented
55(C2×D9)⋊Dic3C2211yescharacteristic, complemented
56Dic3⋊Dic9C2211yescharacteristic, complemented
57C2×#3811—31no—
58C2×D3×#67—31no—
59C22×#626—31no—
60C2×D3×D12—31no—
61#64091—31no—
62C3×#882—31no—
63C3×#67⋊C4D311yescharacteristic
64#63978—31no—
65#63923—31no—
66#63922—31no—
67#63911—31no—
68#63910—31no—
69#63906—31no—
70#63886—31no—
71#63880—31no—
72C2×D4×D9—31no—
73C2×D4×D9—31no—
74C22×D36—31no—
75C22×D36—31no—
76C4×D4×C9—31no—
77#63492—31no—
78#63492—31no—
79#63457—31no—
80#63457—31no—
81#63444—31no—
82#63444—31no—
83#63444—31no—
84#63444—61no—
85#63444D311yescharacteristic, complemented
86#63436—31no—
87C4×D36—31no—
88C23×C3×C9C2311yescharacteristic
89C22×C3⋊D9—22no—
90C22×C3⋊D9—22no—
91C22×C3⋊D9—41no—
92C22×C3⋊D9C2311yescharacteristic
93C22×C3⋊D9C2311yescharacteristic
94C22×C3⋊D9C2311yescharacteristic
95C22×D3×C9C2311yescharacteristic
96C22×C3×D9—22no—
97C22×C3×D9—22no—
98C22×C3×D9—41no—
99C22×C3×D9C2311yescharacteristic
100C22×C3×D9C2311yescharacteristic
101C22×C3×D9C2311yescharacteristic
102C2×D3×D9—22no—
103C2×D3×D9—22no—
104C2×D3×D9—22no—
105C2×D3×D9—22no—
106C2×D3×D9—41no—
107C2×D3×D9—41no—
108C2×C3×C4×C9C2311yescharacteristic
109C2×C3×C4×C9C2311yescharacteristic
110#6233—22no—
111C2×C3⋊Dic9C2311yescharacteristic
112C4⋊(C3⋊D9)—22no—
113C4⋊(C3⋊D9)—41no—
114C9×#67D414yescomplemented
115C3×#611—22no—
116C2×C9×Dic3—22no—
117C2×C9×Dic3C2311yescharacteristic
118C2×C9×Dic3C2311yescharacteristic
119C2×C9×Dic3C2311yescharacteristic
120C2×C3×Dic9C2311yescharacteristic
121C4×D3×C9—22no—
122C3×D36—22no—
123C3×D36—41no—
124#6195—22no—
125#6194—22no—
126#6192—22no—
127#6192—22no—
128#6192—22no—
129#6192—22no—
130#6192—22no—
131#6192—22no—
132#6192D414yescomplemented
133(C3⋊D9)⋊C4—22no—
134Dic3×D9—22no—
135#5590—91no—
136D4×D12—91no—
137C23×C3⋊D3—31no—
138C23×C3×D3—31no—
139C22×D32—31no—
140C22×D32—31no—
141C2×#638—31no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C3×#67—31no—
145C2×C3×#67C2×D311yescharacteristic
146C22×C3×Dic3C2×D311yescharacteristic
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×C4×D3C2×D311yescharacteristic
150#3811—64no—
151D3×#67—64no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—64no—
161C2×#625—31no—
162C2×#624—31no—
163C2×D3×Dic3—31no—
164D3×D12—64no—
165C23×D9—31no—
166C23×D9—31no—
167C23×D9—31no—
168C23×D9—61no—
169C23×D9C2×D311yescharacteristic, complemented
170C32×C22⋊C4C2×D311yescharacteristic
171#3752—31no—
172#3752—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4C2×D311yescharacteristic
176C3×Dic3⋊C4C2×D311yescharacteristic
177C3×C4×Dic3C2×D311yescharacteristic
178Dic3⋊Dic3—31no—
179#3722—31no—
180(C2×D3)⋊Dic3—31no—
181C2×D4×C9—31no—
182C22×C4×C9—31no—
183C22×C4×C9—31no—
184C2×#611—31no—
185C2×#611—31no—
186C2×#611—31no—
187C2×#611—61no—
188C2×#611C2×D311yescharacteristic, complemented
189D4×D9—64no—
190D4×D9—64no—
191C2×D36—31no—
192C2×D36—31no—
193C2×D36—31no—
194C2×D36—31no—
195C2×D36—31no—
196C2×D36—31no—
197C2×D36—31no—
198C2×D36—31no—
199C2×D36—31no—
200C2×D36—64no—
201C2×D36—64no—
202C2×D36—61no—
203C2×D36—61no—
204C2×D36C2×D311yescharacteristic, complemented
205C2×D36C2×D311yescharacteristic, complemented
206C2×C4×D9—31no—
207C2×C4×D9—31no—
208C9×C4⋊C4—31no—
209C9×C22⋊C4—21no—
210C9×C22⋊C4—31no—
211C9×C22⋊C4C2×D311yescharacteristic, complemented
212C42×C9—31no—
213(C2×D9)⋊C4—31no—
214(C2×D9)⋊C4—31no—
215(C2×D9)⋊C4—31no—
216(C2×D9)⋊C4—31no—
217(C2×D9)⋊C4—61no—
218(C2×D9)⋊C4—61no—
219(C2×D9)⋊C4C2×D311yescharacteristic, complemented
220(C2×D9)⋊C4C2×D311yescharacteristic, complemented
221C4⋊Dic9—31no—
222C22×C3×C9—21no—
223C22×C3×C9—21no—
224C22×C3×C9C2×D412yescomplemented
225C22×C3×C9C2411yescharacteristic
226C2×C3⋊D9—21no—
227C2×C3⋊D9—21no—
228C2×C3⋊D9—21no—
229C2×C3⋊D9—21no—
230C2×C3⋊D9—21no—
231C2×C3⋊D9—21no—
232C2×C3⋊D9—21no—
233C2×C3⋊D9—21no—
234C2×C3⋊D9—44no—
235C2×C3⋊D9C2×D412yescomplemented
236C2×D3×C9—21no—
237C2×D3×C9—21no—
238C2×D3×C9C2×D412yescomplemented
239C2×C3×D9—21no—
240C2×C3×D9—21no—
241C2×C3×D9—21no—
242C2×C3×D9—21no—
243C2×C3×D9—21no—
244C2×C3×D9—21no—
245C2×C3×D9—21no—
246C2×C3×D9—21no—
247C2×C3×D9—44no—
248C2×C3×D9C2×D412yescomplemented
249D3×D9—44no—
250D3×D9—44no—
251C3×C4×C9—21no—
252C3×C4×C9—21no—
253C3⋊Dic9—21no—
254C9×Dic3—21no—
255C9×Dic3C2×D412yescomplemented
256C9×Dic3C2×D412yescomplemented
257C3×Dic9—21no—
258C22×#67—91no—
259C22×#67—91no—
260C2×D3×D4—91no—
261C2×D3×D4—91no—
262C2×D3×D4—91no—
263C2×D3×D4—91no—
264C22×D12—91no—
265C22×D12—91no—
266C3×#120—91no—
267C3×C4×D4—31no—
268#940—91no—
269#939—91no—
270#939—91no—
271#937—91no—
272#930—91no—
273#930—91no—
274#895—91no—
275#895—91no—
276#884—91no—
277#884—91no—
278#882—31no—
279#882—91no—
280#882—91no—
281#882—91no—
282#882—91no—
283#882—91no—
284#882—181no—
285#67⋊C4—91no—
286#67⋊C4D911yescharacteristic, complemented
287#874—91no—
288C4×D12—91no—
289C23×C32C22×D311yescharacteristic
290C22×C3⋊D3—31no—
291C22×C3⋊D3—31no—
292C22×C3⋊D3—31no—
293C22×C3⋊D3—62no—
294C22×C3⋊D3—62no—
295C22×C3⋊D3—121no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—31no—
299C22×C3×D3—62no—
300C22×C3×D3—62no—
301C22×C3×D3—121no—
302C22×C3×D3C22×D311yescharacteristic
303C2×D32—62no—
304C2×D32—62no—
305C2×D32—62no—
306C2×D32—62no—
307C2×D32—121no—
308C2×D32—121no—
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C22×D311yescharacteristic
311#638—62no—
312C2×C3⋊Dic3—31no—
313C4⋊(C3⋊D3)—62no—
314C4⋊(C3⋊D3)—121no—
315C3×#67—62no—
316C3×#67D1214yes—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3C22×D311yescharacteristic
320C2×C3×Dic3C22×D311yescharacteristic
321C2×C3×Dic3C22×D311yescharacteristic
322C3×D12—62no—
323C3×D12—121no—
324C3×C4×D3—22no—
325#626—34no—
326#626—62no—
327#626—62no—
328#626—62no—
329#626—62no—
330#626—62no—
331#626—62no—
332#626—62no—
333#625—62no—
334#624—62no—
335D3×Dic3—62no—
336C23×C9—21no—
337C23×C9—31no—
338C23×C9C22×D311yescharacteristic
339C22×D9—22no—
340C22×D9—22no—
341C22×D9—31no—
342C22×D9—31no—
343C22×D9—31no—
344C22×D9—41no—
345C22×D9—61no—
346C22×D9—61no—
347C22×D9—61no—
348C22×D9—62no—
349C22×D9—62no—
350C22×D9—62no—
351C22×D9—62no—
352C22×D9—62no—
353C22×D9—62no—
354C22×D9—122no—
355C22×D9—122no—
356C22×D9—121no—
357C22×D9—121no—
358C22×D9—121no—
359C22×D9—122no—
360C22×D9C22×D311yescharacteristic
361C22×D9C22×D311yescharacteristic
362C22×D9C22×D311yescharacteristic
363D4×C9—34no—
364C2×C4×C9—21no—
365C2×C4×C9—21no—
366C2×C4×C9—31no—
367C2×C4×C9—31no—
368C2×C4×C9—31no—
369C2×C4×C9—62no—
370C2×C4×C9—62no—
371C2×C4×C9C22×D311yescharacteristic
372C2×C4×C9C22×D311yescharacteristic
373#611—22no—
374#611—62no—
375#611—62no—
376#611—62no—
377#611—122no—
378C2×Dic9—31no—
379C2×Dic9—61no—
380C2×Dic9C22×D311yescharacteristic
381D36—22no—
382D36—34no—
383D36—41no—
384D36—62no—
385D36—62no—
386D36—62no—
387D36—62no—
388D36—62no—
389D36—62no—
390D36—62no—
391D36—122no—
392D36—121no—
393D36—122no—
394C4×D9—62no—
395C4×D9—62no—
396D42—271noSylow
397C2×C3×C9—22no—
398C2×C3×C9C22×D411yescharacteristic
399C2×C3×C9C22×D411yescharacteristic
400C2×C3×C9H(5,𝔽2)11yescharacteristic
401C3⋊D9—22no—
402C3⋊D9—41no—
403C3⋊D9—41no—
404D3×C9—22no—
405C3×D9—22no—
406C3×D9—41no—
407C3×D9—41no—
408C24×C3—91no—
409C23×D3—31no—
410C23×D3—91no—
411C23×D3—91no—
412C23×D3—91no—
413C23×D3—91no—
414C23×D3—91no—
415C23×D3—91no—
416C23×D3—181no—
417C2×C3×D4—31no—
418C2×C3×D4—91no—
419C2×C3×D4—91no—
420C2×C3×D4—91no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C2×#67—31no—
424C2×#67—91no—
425C2×#67—91no—
426C2×#67—91no—
427C2×#67—91no—
428C2×#67—91no—
429C2×#67—91no—
430C2×#67—91no—
431C2×#67—91no—
432C2×#67—91no—
433C2×#67—91no—
434C2×#67—91no—
435C2×#67—91no—
436C2×#67—181no—
437C2×#67—184no—
438C2×#67—184no—
439C2×#67C2×D911yescharacteristic
440C22×Dic3—91no—
441C22×Dic3C2×D911yescharacteristic, complemented
442D3×D4—184no—
443D3×D4—184no—
444D3×D4—184no—
445D3×D4—184no—
446C2×D12—31no—
447C2×D12—31no—
448C2×D12—91no—
449C2×D12—91no—
450C2×D12—91no—
451C2×D12—91no—
452C2×D12—91no—
453C2×D12—91no—
454C2×D12—91no—
455C2×D12—91no—
456C2×D12—91no—
457C2×D12—91no—
458C2×D12—91no—
459C2×D12—91no—
460C2×D12—181no—
461C2×D12—181no—
462C2×D12—184no—
463C2×D12—184no—
464C2×C4×D3—91no—
465C2×C4×D3—91no—
466C2×C4×D3—91no—
467C2×C4×D3C2×D911yescharacteristic, complemented
468C3×C4⋊C4—31no—
469C3×C22⋊C4—21no—
470C3×C22⋊C4—31no—
471C3×C22⋊C4—91no—
472C3×C22⋊C4—91no—
473C3×C22⋊C4C2×D911yescharacteristic, complemented
474C3×C22⋊C4D3211yescharacteristic
475C3×C42—31no—
476#217—91no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—31no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—181no—
487(C2×D3)⋊C4—181no—
488(C2×D3)⋊C4C2×D911yescharacteristic, complemented
489C4⋊Dic3—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4C2×D911yescharacteristic, complemented
492C4×Dic3C2×D911yescharacteristic, complemented
493C22×C32—21no—
494C22×C32—21no—
495C22×C32C2×D1212yes—
496C22×C32C23×D311yescharacteristic
497C2×C3⋊D3—32no—
498C2×C3⋊D3—61no—
499C2×C3⋊D3—61no—
500C2×C3⋊D3—61no—
501C2×C3⋊D3—61no—
502C2×C3⋊D3—61no—
503C2×C3⋊D3—61no—
504C2×C3⋊D3—61no—
505C2×C3⋊D3—61no—
506C2×C3⋊D3—124no—
507C2×C3×D3—21no—
508C2×C3×D3—21no—
509C2×C3×D3—32no—
510C2×C3×D3—61no—
511C2×C3×D3—61no—
512C2×C3×D3—61no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—61no—
517C2×C3×D3—61no—
518C2×C3×D3—124no—
519C2×C3×D3C2×D1212yes—
520D32—124no—
521D32—124no—
522C32×C4—21no—
523C32×C4—21no—
524C3⋊Dic3—61no—
525C3×Dic3—21no—
526C3×Dic3—61no—
527C3×Dic3C2×D1212yes—
528C3×Dic3D3×D412yes—
529C22×C9—21no—
530C22×C9—21no—
531C22×C9—21no—
532C22×C9—22no—
533C22×C9—32no—
534C22×C9—41no—
535C22×C9—41no—
536C22×C9—61no—
537C22×C9—61no—
538C22×C9D3×D412yescomplemented
539C22×C9C23×D311yescharacteristic
540C2×D9—21no—
541C2×D9—21no—
542C2×D9—21no—
543C2×D9—21no—
544C2×D9—21no—
545C2×D9—21no—
546C2×D9—21no—
547C2×D9—21no—
548C2×D9—32no—
549C2×D9—44no—
550C2×D9—62no—
551C2×D9—61no—
552C2×D9—61no—
553C2×D9—62no—
554C2×D9—61no—
555C2×D9—61no—
556C2×D9—61no—
557C2×D9—61no—
558C2×D9—61no—
559C2×D9—61no—
560C2×D9—121no—
561C2×D9—121no—
562C2×D9—121no—
563C2×D9—121no—
564C2×D9—121no—
565C2×D9—121no—
566C2×D9—121no—
567C2×D9—124no—
568C2×D9—124no—
569C2×D9—124no—
570C2×D9—128no—
571C2×D9D3×D412yescomplemented
572C4×C9—21no—
573C4×C9—21no—
574C4×C9—32no—
575C4×C9—32no—
576C4×C9—41no—
577C4×C9—41no—
578C4×C9—61no—
579Dic9—21no—
580Dic9—61no—
581Dic9—121no—
582C22×D4—271no—
583C22×D4—271no—
584C22×D4—271no—
585C22×D4—271no—
586#127—271no—
587#121—271no—
588#121—271no—
589#121—271no—
590#121—271no—
591#120—91no—
592#120—271no—
593#120—271no—
594#120—271no—
595C4×D4—31no—
596C4×D4—271no—
597C3×C9D4211yescharacteristic, complemented, Sylow
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—91no—
601C23×C3—91no—
602C23×C3—91no—
603C23×C3—182no—
604C23×C3—182no—
605C23×C3—361no—
606C23×C3C22×D911yescharacteristic
607C23×C3C2×D3211yescharacteristic
608C22×D3—31no—
609C22×D3—31no—
610C22×D3—31no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—91no—
614C22×D3—91no—
615C22×D3—91no—
616C22×D3—91no—
617C22×D3—91no—
618C22×D3—91no—
619C22×D3—121no—
620C22×D3—181no—
621C22×D3—181no—
622C22×D3—181no—
623C22×D3—182no—
624C22×D3—182no—
625C22×D3—182no—
626C22×D3—182no—
627C22×D3—182no—
628C22×D3—182no—
629C22×D3—182no—
630C22×D3—182no—
631C22×D3—182no—
632C22×D3—182no—
633C22×D3—182no—
634C22×D3—182no—
635C22×D3—362no—
636C22×D3—362no—
637C22×D3—361no—
638C22×D3—361no—
639C22×D3—361no—
640C22×D3—361no—
641C22×D3—361no—
642C22×D3—361no—
643C22×D3—362no—
644C22×D3C22×D911yescharacteristic
645C3×D4—34no—
646C3×D4—182no—
647C3×D4—182no—
648C3×D4—361no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—31no—
652C2×C3×C4—31no—
653C2×C3×C4—31no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—91no—
657C2×C3×C4C22×D911yescharacteristic
658C2×C3×C4C22×D911yescharacteristic
659C2×C3×C4C2×D3211yescharacteristic
660C2×C3×C4C2×D3211yescharacteristic
661#67—62no—
662#67—94no—
663#67—182no—
664#67—182no—
665#67—182no—
666#67—182no—
667#67—182no—
668#67—182no—
669#67—182no—
670#67—182no—
671#67—182no—
672#67—182no—
673#67—182no—
674#67—362no—
675#67D3614yescomplemented
676C2×Dic3—22no—
677C2×Dic3—31no—
678C2×Dic3—91no—
679C2×Dic3—91no—
680C2×Dic3—181no—
681C2×Dic3—182no—
682C2×Dic3C22×D911yescharacteristic
683C2×Dic3C22×D911yescharacteristic
684C2×Dic3C22×D911yescharacteristic
685D12—62no—
686D12—94no—
687D12—121no—
688D12—182no—
689D12—182no—
690D12—182no—
691D12—182no—
692D12—182no—
693D12—182no—
694D12—182no—
695D12—182no—
696D12—182no—
697D12—362no—
698D12—361no—
699D12—361no—
700D12—362no—
701C4×D3—22no—
702C4×D3—182no—
703C4×D3—182no—
704C4×D3—182no—
705C2×C32—22no—
706C2×C32C22×D1211yescharacteristic
707C2×C32C2×D3×D411yescharacteristic
708C2×C32#100911yescharacteristic
709C3⋊D3—62no—
710C3⋊D3—121no—
711C3⋊D3—121no—
712C3×D3—22no—
713C3×D3—62no—
714C3×D3—121no—
715C3×D3—121no—
716C2×C9—22no—
717C2×C9—21no—
718C2×C9—21no—
719C2×C9—21no—
720C2×C9—42no—
721C2×C9—62no—
722C2×C9C2×D3×D411yescharacteristic
723C2×C9C2×D3×D411yescharacteristic
724C2×C9#100411yescharacteristic
725D9—22no—
726D9—41no—
727D9—41no—
728D9—62no—
729D9—122no—
730D9—122no—
731D9—121no—
732D9—121no—
733D9—241no—
734C24—91no—
735C24—271no—
736C24—271no—
737C24—271no—
738C2×D4—31no—
739C2×D4—91no—
740C2×D4—91no—
741C2×D4—91no—
742C2×D4—271no—
743C2×D4—271no—
744C2×D4—271no—
745C2×D4—271no—
746C2×D4—271no—
747C2×D4—271no—
748C2×D4—271no—
749C2×D4—271no—
750C2×D4—271no—
751C2×D4—271no—
752C2×D4—271no—
753C2×D4—271no—
754C2×D4—544no—
755C2×D4—544no—
756C2×D4—544no—
757C2×D4—544no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—271no—
761C22×C4—271no—
762C4⋊C4—31no—
763C4⋊C4—271no—
764C22⋊C4—31no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—271no—
768C22⋊C4—271no—
769C22⋊C4—271no—
770C22⋊C4—271no—
771C22⋊C4D3×D911yescharacteristic, complemented
772C42—31no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—22no—
779C22×C3—32no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3—92no—
785C22×C3—181no—
786C22×C3—181no—
787C22×C3—181no—
788C22×C3—181no—
789C22×C3—181no—
790C22×C3—181no—
791C22×C3—181no—
792C22×C3—181no—
793C22×C3—364no—
794C22×C3C2×D3612yescomplemented
795C22×C3C23×D911yescharacteristic
796C22×C3D3×D1212yes—
797C22×C3C22×D3211yescharacteristic
798C2×D3—21no—
799C2×D3—21no—
800C2×D3—32no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—92no—
810C2×D3—92no—
811C2×D3—124no—
812C2×D3—182no—
813C2×D3—181no—
814C2×D3—181no—
815C2×D3—181no—
816C2×D3—181no—
817C2×D3—182no—
818C2×D3—181no—
819C2×D3—181no—
820C2×D3—181no—
821C2×D3—181no—
822C2×D3—181no—
823C2×D3—181no—
824C2×D3—181no—
825C2×D3—181no—
826C2×D3—181no—
827C2×D3—181no—
828C2×D3—181no—
829C2×D3—181no—
830C2×D3—361no—
831C2×D3—361no—
832C2×D3—361no—
833C2×D3—361no—
834C2×D3—361no—
835C2×D3—361no—
836C2×D3—361no—
837C2×D3—364no—
838C2×D3—364no—
839C2×D3—364no—
840C2×D3—364no—
841C2×D3—364no—
842C2×D3—364no—
843C2×D3—368no—
844C2×D3C2×D3612yescomplemented
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—32no—
850C3×C4—32no—
851C3×C4—41no—
852C3×C4—41no—
853C3×C4—61no—
854C3×C4—181no—
855Dic3—21no—
856Dic3—61no—
857Dic3—181no—
858Dic3—181no—
859Dic3—361no—
860Dic3C2×D3612yescomplemented
861Dic3D4×D912yescomplemented
862C32D4×D1211yescharacteristic
863C9—21no—
864C9#559011yescharacteristic, complemented
865C23—31no—
866C23—91no—
867C23—91no—
868C23—91no—
869C23—182no—
870C23—182no—
871C23—271no—
872C23—271no—
873C23—271no—
874C23—361no—
875C23—542no—
876C23—542no—
877C23—542no—
878C23—542no—
879C23—542no—
880C23—542no—
881C23—1081no—
882C23—1081no—
883C23—1081no—
884C23C2×D3×D911yescharacteristic
885D4—34no—
886D4—182no—
887D4—182no—
888D4—274no—
889D4—361no—
890D4—542no—
891D4—542no—
892D4—542no—
893D4—542no—
894D4—542no—
895D4—542no—
896D4—542no—
897D4—542no—
898D4—542no—
899D4—542no—
900D4—1081no—
901C2×C4—31no—
902C2×C4—31no—
903C2×C4—31no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—91no—
907C2×C4—271no—
908C2×C4—542no—
909C2×C4—542no—
910C2×C4C2×D3×D911yescharacteristic
911C2×C4C2×D3×D911yescharacteristic
912C2×C3—22no—
913C2×C3—22no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—42no—
918C2×C3—62no—
919C2×C3—182no—
920C2×C3—361no—
921C2×C3—361no—
922C2×C3C22×D3611yescharacteristic
923C2×C3C2×D4×D911yescharacteristic
924C2×C3#6371511yescharacteristic
925C2×C3C2×D3×D1211yescharacteristic
926C2×C3D32×D411yescharacteristic
927C2×C3#6431411yescharacteristic
928D3—22no—
929D3—62no—
930D3—121no—
931D3—121no—
932D3—182no—
933D3—182no—
934D3—362no—
935D3—362no—
936D3—361no—
937D3—361no—
938D3—361no—
939D3—361no—
940D3—721no—
941C22—21no—
942C22—21no—
943C22—32no—
944C22—61no—
945C22—61no—
946C22—92no—
947C22—181no—
948C22—181no—
949C22—181no—
950C22—181no—
951C22—181no—
952C22—181no—
953C22—181no—
954C22—181no—
955C22—272no—
956C22—364no—
957C22—541no—
958C22—541no—
959C22—541no—
960C22—541no—
961C22—541no—
962C22—541no—
963C22—541no—
964C22—541no—
965C22—1084no—
966C22—1084no—
967C22—1084no—
968C22D3×D3612yescomplemented
969C22C22×D3×D911yescharacteristic
970C4—21no—
971C4—21no—
972C4—32no—
973C4—32no—
974C4—61no—
975C4—181no—
976C4—541no—
977C3—21no—
978C3D4×D3611yescharacteristic, complemented
979C3#1059427711yescharacteristic
980C2—22no—
981C2—62no—
982C2—182no—
983C2—361no—
984C2—361no—
985C2—542no—
986C2—1081no—
987C2—1081no—
988C2C2×D3×D3611yescharacteristic
989C2D3×D4×D911yescharacteristic
990C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9D42
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×#88668C2semidirect
2. C2×D9×#67C2semidirect
3. C22×#6192C2semidirect
4. C2×D3×D36C2semidirect
5. #11721728C2semidirect
6. C9×#67⋊C4C2semidirect
7. C3×#63444C2semidirect
8. #11721277C2semidirect
9. #11721051C2semidirect
10. #11721049C2semidirect
11. #11721034C2semidirect
12. #11721006C2semidirect
13. #11721005C2semidirect
14. #11720983C2semidirect
15. #11720977C2semidirect
18. C23×C3⋊D9C22semidirect
19. C23×C3×D9C22semidirect
20. C22×D3×D9C22semidirect
21. C22×D3×D9C22semidirect
22. C2×#6233C22semidirect
23. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C4⋊(C3⋊D9)C22semidirect
26. C2×C3×#611C22semidirect
27. C22×C9×Dic3C22semidirect
28. C2×C4×D3×C9C22semidirect
29. C2×C3×D36C22semidirect
30. C2×C3×D36C22semidirect
33. C2×#6195C22semidirect
34. C2×#6194C22semidirect
37. C2×#6192C22semidirect
38. C2×#6192C22semidirect
39. C2×#6192C22semidirect
40. C2×#6192C22semidirect
41. C2×#6192C22semidirect
42. C2×#6192C22semidirect
43. C2×(C3⋊D9)⋊C4C22semidirect
44. C2×Dic3×D9C22semidirect
46. C3×C9×C22⋊C4C22semidirect
47. #88536C22semidirect
48. #88536C22semidirect
49. C9×(C2×D3)⋊C4C22semidirect
50. C3×(C2×D9)⋊C4C22semidirect
51. C3×(C2×D9)⋊C4C22semidirect
52. C9×Dic3⋊C4C22semidirect
53. C4×C9×Dic3C22semidirect
54. #88445C22semidirect
55. (C2×D9)⋊Dic3C22semidirect
56. Dic3⋊Dic9C22semidirect
85. #63444D3semidirect
114. C9×#67D4semidirect
132. #6192D4semidirect
169. C23×D9C2×D3semidirect
188. C2×#611C2×D3semidirect
204. C2×D36C2×D3semidirect
205. C2×D36C2×D3semidirect
211. C9×C22⋊C4C2×D3semidirect
219. (C2×D9)⋊C4C2×D3semidirect
220. (C2×D9)⋊C4C2×D3semidirect
224. C22×C3×C9C2×D4semidirect
235. C2×C3⋊D9C2×D4semidirect
238. C2×D3×C9C2×D4semidirect
248. C2×C3×D9C2×D4semidirect
255. C9×Dic3C2×D4semidirect
256. C9×Dic3C2×D4semidirect
286. #67⋊C4D9semidirect
441. C22×Dic3C2×D9semidirect
467. C2×C4×D3C2×D9semidirect
473. C3×C22⋊C4C2×D9semidirect
488. (C2×D3)⋊C4C2×D9semidirect
491. Dic3⋊C4C2×D9semidirect
492. C4×Dic3C2×D9semidirect
538. C22×C9D3×D4semidirect
571. C2×D9D3×D4semidirect
597. C3×C9D42semidirect
675. #67D36semidirect
771. C22⋊C4D3×D9semidirect
794. C22×C3C2×D36semidirect
844. C2×D3C2×D36semidirect
860. Dic3C2×D36semidirect
861. Dic3D4×D9semidirect
864. C9#5590semidirect
968. C22D3×D36semidirect
978. C3D4×D36semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×D9×#672
C22×#61922
C2×D3×D362
#117217282
C9×#67⋊C42
C3×#634442
#117212772
#117210512
#117210492
#117210342
#117210062
#117210052
#117209832
#117209772
#105942773
D4×D363