Finite Group Databasebeta

← #13148289

Subgroups — #13148289

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×D3×#611C211yesmaximal, characteristic, complemented
3C22×#6195C211yesmaximal, characteristic, complemented
4C2×D9×D12C211yesmaximal, characteristic, complemented
5#11721728C211yesmaximal, characteristic, complemented
6C9×#882C211yesmaximal, characteristic, complemented
7C3×#611⋊C4C211yesmaximal, characteristic, complemented
8#11721288C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721050C211yesmaximal, characteristic, complemented
11#11721040C211yesmaximal, characteristic, complemented
12#11721039C211yesmaximal, characteristic, complemented
13#11721033C211yesmaximal, characteristic, complemented
14#11721017C211yesmaximal, characteristic, complemented
15#11721013C211yesmaximal, characteristic, complemented
16#10594277—31nomaximal
17#10589692—31nomaximal
18C23×C3⋊D9C2211yescharacteristic, complemented
19C23×D3×C9C2211yescharacteristic, 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, complemented
26C2×C3×#611C2211yescharacteristic
27C22×C3×Dic9C2211yescharacteristic, complemented
28C2×C9×D12C2211yescharacteristic, complemented
29C2×C9×D12C2211yescharacteristic, complemented
30C2×C3×C4×D9C2211yescharacteristic, complemented
31#88668—24no—
32D3×#611—24no—
33C2×#6195—24no—
34C2×#6195C2211yescharacteristic
35C2×#6195C2211yescharacteristic, complemented
36C2×#6195C2211yescharacteristic, complemented
37C2×#6195C2211yescharacteristic, complemented
38C2×#6195C2211yescharacteristic, complemented
39C2×#6195C2211yescharacteristic, complemented
40C2×#6195C2211yescharacteristic, complemented
41C2×#6194C2211yescharacteristic, complemented
42C2×D3×Dic9C2211yescharacteristic, complemented
43C2×#6192C2211yescharacteristic, complemented
44C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
45D9×D12—24no—
46C3×C9×C22⋊C4C2211yescharacteristic, complemented
47#88536C2211yescharacteristic, complemented
48#88536C2211yescharacteristic, complemented
49C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
52C3×Dic9⋊C4C2211yescharacteristic, complemented
53C3×C4×Dic9C2211yescharacteristic, complemented
54(C2×D3)⋊Dic9C2211yescharacteristic, complemented
55#88445C2211yescharacteristic, complemented
56Dic9⋊Dic3C2211yescharacteristic, complemented
57C2×#3811—31no—
58C2×D3×#67—31no—
59C22×#626—31no—
60C2×D3×D12—31no—
61#64091—31no—
62C3×#882D311yescharacteristic
63C3×#67⋊C4—31no—
64#63978—31no—
65#63923—31no—
66#63922—31no—
67#63911—31no—
68#63910—31no—
69#63906—31no—
70#63886—31no—
71#63880—31no—
72C22×#611—31no—
73C22×#611—31no—
74C2×D4×D9—31no—
75C2×D4×D9—31no—
76C9×#120—31no—
77#63502—31no—
78#63501—31no—
79#63501—31no—
80#63499—31no—
81#63446—31no—
82#63446—31no—
83#63444—31no—
84#63444—31no—
85#63444—61no—
86#611⋊C4—31no—
87#611⋊C4D311yescharacteristic, complemented
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×C9—22no—
96C22×D3×C9—22no—
97C22×D3×C9—41no—
98C22×D3×C9C2311yescharacteristic
99C22×D3×C9C2311yescharacteristic
100C22×D3×C9C2311yescharacteristic
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×#67—22no—
115C3×#611D414yescomplemented
116C2×C9×Dic3C2311yescharacteristic
117C2×C3×Dic9—22no—
118C2×C3×Dic9C2311yescharacteristic
119C2×C3×Dic9C2311yescharacteristic
120C2×C3×Dic9C2311yescharacteristic
121C9×D12—22no—
122C9×D12—41no—
123C3×C4×D9—22no—
124#6195—22no—
125#6195—22no—
126#6195—22no—
127#6195—22no—
128#6195—22no—
129#6195—22no—
130#6195D414yescomplemented
131#6194—22no—
132D3×Dic9—22no—
133#6192—22no—
134(C3⋊D9)⋊C4—22no—
135#5590—91no—
136D4×D12—91no—
137C23×C3⋊D3—31no—
138C23×C3×D3C2×D311yescharacteristic
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×Dic3—31no—
147C2×C3×D12C2×D311yescharacteristic
148C2×C3×D12C2×D311yescharacteristic
149C2×C3×C4×D3—31no—
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—
165C24×C9—31no—
166C23×D9—31no—
167C23×D9—31no—
168C23×D9—31no—
169C23×D9—61no—
170C32×C22⋊C4C2×D311yescharacteristic
171#3752—31no—
172#3752—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4C2×D311yescharacteristic
175C3×(C2×D3)⋊C4C2×D311yescharacteristic
176C3×Dic3⋊C4—31no—
177C3×C4×Dic3—31no—
178Dic3⋊Dic3—31no—
179#3722—31no—
180(C2×D3)⋊Dic3—31no—
181C2×D4×C9—31no—
182C2×D4×C9—31no—
183C2×D4×C9—31no—
184C2×#611—31no—
185C2×#611—31no—
186C2×#611—31no—
187C2×#611—31no—
188C2×#611—31no—
189C2×#611—31no—
190C2×#611—31no—
191C2×#611—31no—
192C2×#611—31no—
193C2×#611—64no—
194C2×#611—64no—
195C2×#611—61no—
196C2×#611C2×D311yescharacteristic
197C22×Dic9—31no—
198C22×Dic9C2×D311yescharacteristic, complemented
199D4×D9—64no—
200D4×D9—64no—
201C2×D36—31no—
202C2×D36—31no—
203C2×D36—31no—
204C2×D36—61no—
205C2×D36—61no—
206C2×C4×D9—31no—
207C2×C4×D9C2×D311yescharacteristic, complemented
208C9×C22⋊C4—21no—
209C9×C22⋊C4—31no—
210C9×C22⋊C4—31no—
211C9×C22⋊C4C2×D311yescharacteristic, complemented
212#3676—31no—
213(C2×D9)⋊C4—31no—
214(C2×D9)⋊C4—31no—
215(C2×D9)⋊C4—31no—
216(C2×D9)⋊C4—61no—
217(C2×D9)⋊C4—61no—
218(C2×D9)⋊C4C2×D311yescharacteristic, complemented
219Dic9⋊C4—31no—
220Dic9⋊C4C2×D311yescharacteristic, complemented
221C4×Dic9C2×D311yescharacteristic, complemented
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×C9—21no—
239C2×D3×C9—21no—
240C2×D3×C9—21no—
241C2×D3×C9—21no—
242C2×D3×C9—21no—
243C2×D3×C9—21no—
244C2×D3×C9—44no—
245C2×D3×C9C2×D412yescomplemented
246C2×C3×D9—21no—
247C2×C3×D9—21no—
248C2×C3×D9C2×D412yescomplemented
249D3×D9—44no—
250D3×D9—44no—
251C3×C4×C9—21no—
252C3×C4×C9—21no—
253C3⋊Dic9—21no—
254C9×Dic3—21no—
255C3×Dic9—21no—
256C3×Dic9C2×D412yescomplemented
257C3×Dic9C2×D412yescomplemented
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—31no—
267C3×C4×D4—91no—
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—91no—
279#882—91no—
280#882—91no—
281#882—91no—
282#882—91no—
283#882—181no—
284#882D911yescharacteristic, complemented
285#67⋊C4—31no—
286#67⋊C4—91no—
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—22no—
297C22×C3×D3—22no—
298C22×C3×D3—31no—
299C22×C3×D3—41no—
300C22×C3×D3C22×D311yescharacteristic
301C22×C3×D3C22×D311yescharacteristic
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—22no—
316C3×#67—34no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—62no—
321C2×C3×Dic3C22×D311yescharacteristic
322C3×D12—22no—
323C3×D12—41no—
324C3×C4×D3—62no—
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×C9—31no—
339C23×C9—31no—
340C23×C9—62no—
341C23×C9—62no—
342C23×C9—121no—
343C23×C9C22×D311yescharacteristic
344C22×D9—31no—
345C22×D9—31no—
346C22×D9—31no—
347C22×D9—61no—
348C22×D9—61no—
349C22×D9—61no—
350C22×D9—62no—
351C22×D9—62no—
352C22×D9—62no—
353C22×D9—62no—
354C22×D9—62no—
355C22×D9—62no—
356C22×D9—122no—
357C22×D9—122no—
358C22×D9—121no—
359C22×D9—121no—
360C22×D9—121no—
361C22×D9—122no—
362C22×D9C22×D311yescharacteristic
363D4×C9—62no—
364D4×C9—62no—
365D4×C9—121no—
366C2×C4×C9—21no—
367C2×C4×C9—21no—
368C2×C4×C9—31no—
369C2×C4×C9C22×D311yescharacteristic
370C2×C4×C9C22×D311yescharacteristic
371#611—34no—
372#611—62no—
373#611—62no—
374#611—62no—
375#611—62no—
376#611—62no—
377#611—62no—
378#611—62no—
379#611—62no—
380#611—122no—
381#611D1214yescomplemented
382C2×Dic9—22no—
383C2×Dic9—31no—
384C2×Dic9—61no—
385C2×Dic9—62no—
386C2×Dic9C22×D311yescharacteristic
387C2×Dic9C22×D311yescharacteristic
388C2×Dic9C22×D311yescharacteristic
389D36—62no—
390D36—62no—
391D36—122no—
392D36—121no—
393D36—122no—
394C4×D9—22no—
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—
405D3×C9—41no—
406D3×C9—41no—
407C3×D9—22no—
408C24×C3—31no—
409C23×D3—91no—
410C23×D3—91no—
411C23×D3—91no—
412C23×D3—91no—
413C23×D3—91no—
414C23×D3—91no—
415C23×D3—181no—
416C23×D3C2×D911yescharacteristic, complemented
417C2×C3×D4—31no—
418C2×C3×D4—31no—
419C2×C3×D4—31no—
420C2×C3×D4—91no—
421C22×C3×C4—91no—
422C22×C3×C4—91no—
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, complemented
440C22×Dic3—31no—
441C22×Dic3—91no—
442D3×D4—184no—
443D3×D4—184no—
444D3×D4—184no—
445D3×D4—184no—
446C2×D12—91no—
447C2×D12—91no—
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—181no—
459C2×D12—181no—
460C2×D12—184no—
461C2×D12—184no—
462C2×D12C2×D911yescharacteristic, complemented
463C2×D12C2×D911yescharacteristic, complemented
464C2×C4×D3—31no—
465C2×C4×D3—91no—
466C2×C4×D3—91no—
467C2×C4×D3—91no—
468C3×C4⋊C4—91no—
469C3×C22⋊C4—21no—
470C3×C22⋊C4—31no—
471C3×C22⋊C4—31no—
472C3×C22⋊C4—91no—
473C3×C22⋊C4C2×D911yescharacteristic, complemented
474C3×C22⋊C4D3211yescharacteristic
475C3×C42—91no—
476#217—91no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—91no—
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—181no—
486(C2×D3)⋊C4—181no—
487(C2×D3)⋊C4C2×D911yescharacteristic, complemented
488(C2×D3)⋊C4C2×D911yescharacteristic, complemented
489C4⋊Dic3—91no—
490Dic3⋊C4—31no—
491Dic3⋊C4—91no—
492C4×Dic3—31no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32D3×D412yes—
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—21no—
510C2×C3×D3—21no—
511C2×C3×D3—21no—
512C2×C3×D3—21no—
513C2×C3×D3—21no—
514C2×C3×D3—21no—
515C2×C3×D3—32no—
516C2×C3×D3—44no—
517C2×C3×D3—61no—
518C2×C3×D3—61no—
519C2×C3×D3D3×D412yes—
520D32—124no—
521D32—124no—
522C32×C4—21no—
523C32×C4—21no—
524C3⋊Dic3—61no—
525C3×Dic3—21no—
526C3×Dic3—32no—
527C3×Dic3—32no—
528C3×Dic3—61no—
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×C9—61no—
539C22×C9—61no—
540C22×C9—61no—
541C22×C9—61no—
542C22×C9—61no—
543C22×C9—61no—
544C22×C9—124no—
545C22×C9C2×D1212yescomplemented
546C22×C9C23×D311yescharacteristic
547C2×D9—21no—
548C2×D9—21no—
549C2×D9—32no—
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×D9C2×D1212yescomplemented
572C4×C9—21no—
573C4×C9—21no—
574C4×C9—41no—
575C4×C9—41no—
576C4×C9—61no—
577Dic9—21no—
578Dic9—61no—
579Dic9—121no—
580Dic9C2×D1212yescomplemented
581Dic9D3×D412yescomplemented
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—31no—
592#120—271no—
593#120—271no—
594#120—271no—
595C4×D4—91no—
596C4×D4—271no—
597C3×C9D4211yescharacteristic, complemented, Sylow
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—31no—
602C23×C3—62no—
603C23×C3—62no—
604C23×C3—91no—
605C23×C3—121no—
606C23×C3C22×D911yescharacteristic
607C23×C3C2×D3211yescharacteristic
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—31no—
611C22×D3—41no—
612C22×D3—91no—
613C22×D3—91no—
614C22×D3—91no—
615C22×D3—91no—
616C22×D3—91no—
617C22×D3—91no—
618C22×D3—181no—
619C22×D3—181no—
620C22×D3—181no—
621C22×D3—182no—
622C22×D3—182no—
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—362no—
634C22×D3—362no—
635C22×D3—361no—
636C22×D3—361no—
637C22×D3—361no—
638C22×D3—361no—
639C22×D3—361no—
640C22×D3—361no—
641C22×D3—362no—
642C22×D3C22×D911yescharacteristic
643C22×D3C22×D911yescharacteristic
644C22×D3C22×D911yescharacteristic
645C3×D4—62no—
646C3×D4—62no—
647C3×D4—94no—
648C3×D4—121no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—31no—
652C2×C3×C4—91no—
653C2×C3×C4—91no—
654C2×C3×C4—91no—
655C2×C3×C4—182no—
656C2×C3×C4—182no—
657C2×C3×C4C22×D911yescharacteristic
658C2×C3×C4C22×D911yescharacteristic
659C2×C3×C4C2×D3211yescharacteristic
660C2×C3×C4C2×D3211yescharacteristic
661#67—22no—
662#67—34no—
663#67—94no—
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—182no—
675#67—362no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—62no—
680C2×Dic3—91no—
681C2×Dic3—91no—
682C2×Dic3—181no—
683C2×Dic3—182no—
684C2×Dic3C22×D911yescharacteristic
685D12—22no—
686D12—41no—
687D12—94no—
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—62no—
702C4×D3—182no—
703C4×D3—182no—
704C4×D3—182no—
705C2×C32—22no—
706C2×C32C2×D3×D411yescharacteristic
707C2×C32C2×D3×D411yescharacteristic
708C2×C32#100411yescharacteristic
709C3⋊D3—62no—
710C3⋊D3—121no—
711C3⋊D3—121no—
712C3×D3—22no—
713C3×D3—41no—
714C3×D3—41no—
715C3×D3—62no—
716C2×C9—22no—
717C2×C9—21no—
718C2×C9—21no—
719C2×C9—21no—
720C2×C9—42no—
721C2×C9—62no—
722C2×C9—121no—
723C2×C9—121no—
724C2×C9C22×D1211yescharacteristic
725C2×C9C2×D3×D411yescharacteristic
726C2×C9#100911yescharacteristic
727D9—22no—
728D9—62no—
729D9—122no—
730D9—122no—
731D9—121no—
732D9—121no—
733D9—241no—
734C24—31no—
735C24—271no—
736C24—271no—
737C24—271no—
738C2×D4—31no—
739C2×D4—31no—
740C2×D4—31no—
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—91no—
759C22×C4—91no—
760C22×C4—271no—
761C22×C4—271no—
762C4⋊C4—91no—
763C4⋊C4—271no—
764C22⋊C4—31no—
765C22⋊C4—31no—
766C22⋊C4—91no—
767C22⋊C4—271no—
768C22⋊C4—271no—
769C22⋊C4—271no—
770C22⋊C4—271no—
771C22⋊C4D3×D911yescharacteristic, complemented
772C42—91no—
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—61no—
785C22×C3—61no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—61no—
789C22×C3—61no—
790C22×C3—92no—
791C22×C3—124no—
792C22×C3—181no—
793C22×C3—181no—
794C22×C3D4×D912yescomplemented
795C22×C3C23×D911yescharacteristic
796C22×C3D3×D1212yes—
797C22×C3C22×D3211yescharacteristic
798C2×D3—21no—
799C2×D3—21no—
800C2×D3—21no—
801C2×D3—21no—
802C2×D3—21no—
803C2×D3—21no—
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—32no—
807C2×D3—44no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—92no—
811C2×D3—92no—
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×D3D4×D912yescomplemented
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—61no—
852C3×C4—92no—
853C3×C4—92no—
854C3×C4—181no—
855Dic3—21no—
856Dic3—32no—
857Dic3—32no—
858Dic3—61no—
859Dic3—181no—
860Dic3—181no—
861Dic3—361no—
862C32#559011yescharacteristic
863C9—21no—
864C9D4×D1211yescharacteristic, complemented
865C23—31no—
866C23—31no—
867C23—31no—
868C23—62no—
869C23—62no—
870C23—91no—
871C23—121no—
872C23—271no—
873C23—271no—
874C23—271no—
875C23—542no—
876C23—542no—
877C23—542no—
878C23—542no—
879C23—542no—
880C23—542no—
881C23—1081no—
882C23—1081no—
883C23—1081no—
884C23C2×D3×D911yescharacteristic
885D4—62no—
886D4—62no—
887D4—94no—
888D4—121no—
889D4—274no—
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—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—182no—
906C2×C4—182no—
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—121no—
920C2×C3—121no—
921C2×C3—182no—
922C2×C3C2×D4×D911yescharacteristic
923C2×C3C2×D4×D911yescharacteristic
924C2×C3#6371011yescharacteristic
925C2×C3C2×D3×D1211yescharacteristic
926C2×C3D32×D411yescharacteristic
927C2×C3#6431411yescharacteristic
928D3—22no—
929D3—41no—
930D3—41no—
931D3—62no—
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—61no—
947C22—61no—
948C22—61no—
949C22—61no—
950C22—61no—
951C22—61no—
952C22—92no—
953C22—124no—
954C22—181no—
955C22—181no—
956C22—272no—
957C22—541no—
958C22—541no—
959C22—541no—
960C22—541no—
961C22—541no—
962C22—541no—
963C22—541no—
964C22—541no—
965C22—1084no—
966C22—1084no—
967C22—1084no—
968C22D9×D1212yescomplemented
969C22C22×D3×D911yescharacteristic
970C4—21no—
971C4—21no—
972C4—61no—
973C4—92no—
974C4—92no—
975C4—181no—
976C4—541no—
977C3—21no—
978C3#1058969211yescharacteristic, complemented
979C3#1059427711yescharacteristic
980C2—22no—
981C2—62no—
982C2—121no—
983C2—121no—
984C2—182no—
985C2—542no—
986C2—1081no—
987C2—1081no—
988C2C2×D9×D1211yescharacteristic
989C2D3×D4×D911yescharacteristic
990C2#1172250011yescharacteristic
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×D3×#611C2semidirect
3. C22×#6195C2semidirect
4. C2×D9×D12C2semidirect
5. #11721728C2semidirect
6. C9×#882C2semidirect
7. C3×#611⋊C4C2semidirect
8. #11721288C2semidirect
9. #11721051C2semidirect
10. #11721050C2semidirect
11. #11721040C2semidirect
12. #11721039C2semidirect
13. #11721033C2semidirect
14. #11721017C2semidirect
15. #11721013C2semidirect
18. C23×C3⋊D9C22semidirect
19. C23×D3×C9C22semidirect
20. C22×D3×D9C22semidirect
21. C22×D3×D9C22semidirect
22. C2×#6233C22semidirect
23. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C4⋊(C3⋊D9)C22semidirect
25. C2×C9×#67C22semidirect
27. C22×C3×Dic9C22semidirect
28. C2×C9×D12C22semidirect
29. C2×C9×D12C22semidirect
30. C2×C3×C4×D9C22semidirect
35. C2×#6195C22semidirect
36. C2×#6195C22semidirect
37. C2×#6195C22semidirect
38. C2×#6195C22semidirect
39. C2×#6195C22semidirect
40. C2×#6195C22semidirect
41. C2×#6194C22semidirect
42. C2×D3×Dic9C22semidirect
43. C2×#6192C22semidirect
44. C2×(C3⋊D9)⋊C4C22semidirect
46. C3×C9×C22⋊C4C22semidirect
47. #88536C22semidirect
48. #88536C22semidirect
49. C9×(C2×D3)⋊C4C22semidirect
50. C9×(C2×D3)⋊C4C22semidirect
51. C3×(C2×D9)⋊C4C22semidirect
52. C3×Dic9⋊C4C22semidirect
53. C3×C4×Dic9C22semidirect
54. (C2×D3)⋊Dic9C22semidirect
55. #88445C22semidirect
56. Dic9⋊Dic3C22semidirect
87. #611⋊C4D3semidirect
115. C3×#611D4semidirect
130. #6195D4semidirect
198. C22×Dic9C2×D3semidirect
207. C2×C4×D9C2×D3semidirect
211. C9×C22⋊C4C2×D3semidirect
218. (C2×D9)⋊C4C2×D3semidirect
220. Dic9⋊C4C2×D3semidirect
221. C4×Dic9C2×D3semidirect
224. C22×C3×C9C2×D4semidirect
235. C2×C3⋊D9C2×D4semidirect
245. C2×D3×C9C2×D4semidirect
248. C2×C3×D9C2×D4semidirect
256. C3×Dic9C2×D4semidirect
257. C3×Dic9C2×D4semidirect
284. #882D9semidirect
381. #611D12semidirect
416. C23×D3C2×D9semidirect
439. C2×#67C2×D9semidirect
462. C2×D12C2×D9semidirect
463. C2×D12C2×D9semidirect
473. C3×C22⋊C4C2×D9semidirect
487. (C2×D3)⋊C4C2×D9semidirect
488. (C2×D3)⋊C4C2×D9semidirect
545. C22×C9C2×D12semidirect
571. C2×D9C2×D12semidirect
580. Dic9C2×D12semidirect
581. Dic9D3×D4semidirect
597. C3×C9D42semidirect
771. C22⋊C4D3×D9semidirect
794. C22×C3D4×D9semidirect
844. C2×D3D4×D9semidirect
864. C9D4×D12semidirect
968. C22D9×D12semidirect
978. C3#10589692semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×D3×#6112
C22×#61952
C2×D9×D122
#117217282
C9×#8822
C3×#611⋊C42
#117212882
#117210512
#117210502
#117210402
#117210392
#117210332
#117210172
#117210132
#105942773
#105896923