Finite Group Databasebeta

← #13148144

Subgroups — #13148144

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×#88668C211yesmaximal, characteristic, complemented
3C2×D9×D12C211yesmaximal, characteristic, complemented
4C2×D3×D36C211yesmaximal, characteristic, complemented
5#11721728C211yesmaximal, characteristic, complemented
6C9×#884C211yesmaximal, characteristic, complemented
7C3×#63446C211yesmaximal, characteristic, complemented
8#11721292C211yesmaximal, characteristic, complemented
9#11721289C211yesmaximal, characteristic, complemented
10#11721050C211yesmaximal, characteristic, complemented
11#11721049C211yesmaximal, characteristic, complemented
12#11721039C211yesmaximal, characteristic, complemented
13#11721030C211yesmaximal, characteristic, complemented
14#11721005C211yesmaximal, characteristic, complemented
15#11721002C211yesmaximal, characteristic, complemented
16#10594284—31nomaximal
17#10589711—31nomaximal
18C23×C3⋊D9C2211yescharacteristic, complemented
19C22×D3×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, complemented
26C2×C9×#67C2211yescharacteristic, complemented
27C2×C3×#611C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic, complemented
29C2×C9×D12C2211yescharacteristic, complemented
30C2×C4×D3×C9C2211yescharacteristic, complemented
31C2×C3×D36C2211yescharacteristic, complemented
32C2×C3×C4×D9C2211yescharacteristic, complemented
33#88668—24no—
34#88668—24no—
35C2×#6195C2211yescharacteristic
36C2×#6195C2211yescharacteristic, complemented
37C2×#6195C2211yescharacteristic, complemented
38C2×#6194C2211yescharacteristic, complemented
39C2×#6192C2211yescharacteristic
40C2×#6192C2211yescharacteristic, complemented
41C2×#6192C2211yescharacteristic, complemented
42C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
43C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
44D9×D12—24no—
45D3×D36—24no—
46C3×C9×C22⋊C4C2211yescharacteristic, complemented
47#88536C2211yescharacteristic, complemented
48#88536C2211yescharacteristic, complemented
49C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
51C9×Dic3⋊C4C2211yescharacteristic, complemented
52C3×Dic9⋊C4C2211yescharacteristic, complemented
53(C2×D3)⋊Dic9C2211yescharacteristic, complemented
54#88445C2211yescharacteristic, complemented
55(C2×D9)⋊Dic3C2211yescharacteristic, complemented
56Dic3×Dic9C2211yescharacteristic, complemented
57C2×#3811—31no—
58C2×#3811—31no—
59C2×D3×D12—31no—
60C2×D3×D12—31no—
61#64091—31no—
62C3×#884—31no—
63C3×#884D311yescharacteristic
64#63983—31no—
65#63979—31no—
66#63922—31no—
67#63922—31no—
68#63910—31no—
69#63910—31no—
70#63904—31no—
71#63904—31no—
72C2×D4×D9—31no—
73C2×D4×D9—31no—
74C2×D4×D9—31no—
75C22×D36—31no—
76C9×#121—31no—
77#63502—31no—
78#63499—31no—
79#63499—31no—
80C4×#611—31no—
81#63457—31no—
82#63455—31no—
83#63446—31no—
84#63446D311yescharacteristic, complemented
85#63444—31no—
86#63444—31no—
87#63444—61no—
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×D3×C9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C22×C3×D9C2311yescharacteristic
99C2×D3×D9—22no—
100C2×D3×D9—22no—
101C2×D3×D9—22no—
102C2×D3×D9—22no—
103C2×D3×D9—22no—
104C2×D3×D9—22no—
105C2×D3×D9—41no—
106C2×D3×D9—41no—
107C2×D3×D9—41no—
108C2×C3×C4×C9C2311yescharacteristic
109C2×C3×C4×C9C2311yescharacteristic
110#6233—41no—
111C2×C3⋊Dic9C2311yescharacteristic
112C4⋊(C3⋊D9)—22no—
113C4⋊(C3⋊D9)—22no—
114C9×#67—22no—
115C9×#67—22no—
116C3×#611—22no—
117C3×#611—22no—
118C2×C9×Dic3C2311yescharacteristic
119C2×C9×Dic3C2311yescharacteristic
120C2×C3×Dic9C2311yescharacteristic
121C2×C3×Dic9C2311yescharacteristic
122C9×D12—22no—
123C4×D3×C9—22no—
124C3×D36—22no—
125C3×C4×D9—22no—
126#6195—22no—
127#6195—22no—
128#6195D414yescomplemented
129#6194—41no—
130#6192—22no—
131#6192—22no—
132#6192D414yescomplemented
133(C3⋊D9)⋊C4—22no—
134(C3⋊D9)⋊C4—22no—
135#5609—91no—
136#5609—91no—
137C23×C3⋊D3—31no—
138C22×D32—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×#67—31no—
146C2×C3×#67C2×D311yescharacteristic
147C2×C3×#67C2×D311yescharacteristic
148C2×C3×D12—31no—
149C2×C3×D12C2×D311yescharacteristic
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3C2×D311yescharacteristic
152#3811—64no—
153#3811—64no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#625—31no—
161C2×#624—31no—
162C2×#624—31no—
163D3×D12—64no—
164D3×D12—64no—
165C23×D9—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×Dic3⋊C4—31no—
176C3×Dic3⋊C4C2×D311yescharacteristic
177#3722—31no—
178(C2×D3)⋊Dic3—31no—
179(C2×D3)⋊Dic3—31no—
180Dic32—31no—
181C2×D4×C9—31no—
182C2×D4×C9—31no—
183C2×D4×C9—31no—
184C22×C4×C9—31no—
185C2×#611—31no—
186C2×#611—31no—
187C2×#611—31no—
188C2×#611—31no—
189C2×#611—31no—
190C2×#611—61no—
191C2×#611C2×D311yescharacteristic, complemented
192C2×#611C2×D311yescharacteristic, complemented
193D4×D9—64no—
194D4×D9—64no—
195D4×D9—64no—
196C2×D36—31no—
197C2×D36—31no—
198C2×D36—31no—
199C2×D36—31no—
200C2×D36—31no—
201C2×D36—64no—
202C2×D36—61no—
203C2×D36—61no—
204C2×D36C2×D311yescharacteristic, complemented
205C2×C4×D9—31no—
206C2×C4×D9—31no—
207C2×C4×D9C2×D311yescharacteristic, complemented
208C9×C4⋊C4—31no—
209C9×C22⋊C4—21no—
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—31no—
217(C2×D9)⋊C4—61no—
218(C2×D9)⋊C4—61no—
219(C2×D9)⋊C4C2×D311yescharacteristic, complemented
220Dic9⋊C4C2×D311yescharacteristic, complemented
221C4×Dic9—31no—
222C22×C3×C9—21no—
223C22×C3×C9—21no—
224C22×C3×C9—21no—
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—44no—
234C2×C3⋊D9C2×D412yescomplemented
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×C9C2×D412yescomplemented
242C2×C3×D9—21no—
243C2×C3×D9—21no—
244C2×C3×D9—21no—
245C2×C3×D9—21no—
246C2×C3×D9—21no—
247C2×C3×D9C2×D412yescomplemented
248D3×D9—44no—
249D3×D9—44no—
250D3×D9—44no—
251C3×C4×C9—21no—
252C3×C4×C9—21no—
253C3⋊Dic9—21no—
254C9×Dic3—21no—
255C9×Dic3C2×D412yescomplemented
256C3×Dic9—21no—
257C3×Dic9C2×D412yescomplemented
258C2×D3×D4—91no—
259C2×D3×D4—91no—
260C2×D3×D4—91no—
261C2×D3×D4—91no—
262C2×D3×D4—91no—
263C2×D3×D4—91no—
264C22×D12—91no—
265C22×D12—91no—
266C3×#121—31no—
267C3×#121—91no—
268#940—91no—
269#940—91no—
270#937—91no—
271#937—91no—
272#937—91no—
273#937—91no—
274C4×#67—91no—
275C4×#67—91no—
276#895—91no—
277#895—91no—
278#893—91no—
279#893—91no—
280#884—31no—
281#884—91no—
282#884—91no—
283#884D911yescharacteristic, complemented
284#882—91no—
285#882—91no—
286#882—91no—
287#882—91no—
288#882—181no—
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×D3C22×D311yescharacteristic
299C22×C3×D3C22×D311yescharacteristic
300C2×D32—62no—
301C2×D32—62no—
302C2×D32—62no—
303C2×D32—62no—
304C2×D32—62no—
305C2×D32—62no—
306C2×D32—121no—
307C2×D32—121no—
308C2×D32—121no—
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C22×D311yescharacteristic
311#638—121no—
312C2×C3⋊Dic3—31no—
313C4⋊(C3⋊D3)—62no—
314C4⋊(C3⋊D3)—62no—
315C3×#67—22no—
316C3×#67—22no—
317C3×#67—62no—
318C3×#67—62no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3C22×D311yescharacteristic
322C2×C3×Dic3C22×D311yescharacteristic
323C3×D12—22no—
324C3×D12—62no—
325C3×C4×D3—22no—
326C3×C4×D3—62no—
327#626—34no—
328#626—34no—
329#626—62no—
330#626—62no—
331#626—62no—
332#626—62no—
333#625—121no—
334#624—62no—
335#624—62no—
336C23×C9—21no—
337C23×C9—31no—
338C23×C9—31no—
339C23×C9C22×D311yescharacteristic
340C22×D9—31no—
341C22×D9—31no—
342C22×D9—31no—
343C22×D9—61no—
344C22×D9—61no—
345C22×D9—61no—
346C22×D9—62no—
347C22×D9—62no—
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—121no—
360C22×D9—122no—
361C22×D9C22×D311yescharacteristic
362C22×D9C22×D311yescharacteristic
363D4×C9—62no—
364D4×C9—62no—
365D4×C9—62no—
366C2×C4×C9—21no—
367C2×C4×C9—21no—
368C2×C4×C9—31no—
369C2×C4×C9—31no—
370C2×C4×C9—62no—
371C2×C4×C9C22×D311yescharacteristic
372C2×C4×C9C22×D311yescharacteristic
373#611—22no—
374#611—22no—
375#611—34no—
376#611—62no—
377#611—62no—
378#611—121no—
379#611—121no—
380#611—122no—
381C2×Dic9—31no—
382C2×Dic9—61no—
383C2×Dic9C22×D311yescharacteristic
384C2×Dic9C22×D311yescharacteristic
385D36—22no—
386D36—34no—
387D36—62no—
388D36—62no—
389D36—62no—
390D36—62no—
391D36—122no—
392D36—122no—
393C4×D9—22no—
394C4×D9—62no—
395C4×D9—62no—
396D42—271noSylow
397C2×C3×C9—41no—
398C2×C3×C9C22×D411yescharacteristic
399C2×C3×C9C22×D411yescharacteristic
400C2×C3×C9H(5,𝔽2)11yescharacteristic
401C3⋊D9—22no—
402C3⋊D9—22no—
403C3⋊D9—41no—
404D3×C9—22no—
405D3×C9—41no—
406C3×D9—22no—
407C3×D9—41no—
408C23×D3—91no—
409C23×D3—91no—
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—31no—
419C2×C3×D4—31no—
420C2×C3×D4—91no—
421C2×C3×D4—91no—
422C2×C3×D4—91no—
423C22×C3×C4—31no—
424C22×C3×C4—91no—
425C2×#67—31no—
426C2×#67—31no—
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—91no—
437C2×#67—181no—
438C2×#67C2×D911yescharacteristic, complemented
439C2×#67C2×D911yescharacteristic, complemented
440D3×D4—184no—
441D3×D4—184no—
442D3×D4—184no—
443D3×D4—184no—
444D3×D4—184no—
445D3×D4—184no—
446C2×D12—31no—
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—181no—
458C2×D12—181no—
459C2×D12—184no—
460C2×D12—184no—
461C2×D12C2×D911yescharacteristic, complemented
462C2×C4×D3—31no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×C4×D3—91no—
466C2×C4×D3—91no—
467C2×C4×D3C2×D911yescharacteristic, complemented
468C3×C4⋊C4—31no—
469C3×C4⋊C4—91no—
470C3×C22⋊C4—21no—
471C3×C22⋊C4—31no—
472C3×C22⋊C4—91no—
473C3×C22⋊C4C2×D911yescharacteristic, complemented
474C3×C22⋊C4D3211yescharacteristic
475#217—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—91no—
486(C2×D3)⋊C4—181no—
487(C2×D3)⋊C4—181no—
488(C2×D3)⋊C4C2×D911yescharacteristic, complemented
489Dic3⋊C4—31no—
490Dic3⋊C4C2×D911yescharacteristic, complemented
491C4×Dic3—91no—
492C4×Dic3—91no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32C23×D311yescharacteristic
497C2×C3⋊D3—32no—
498C2×C3⋊D3—32no—
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—32no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—61no—
517C2×C3×D3—61no—
518C2×C3×D3D3×D412yes—
519D32—124no—
520D32—124no—
521D32—124no—
522C32×C4—21no—
523C32×C4—21no—
524C3⋊Dic3—61no—
525C3×Dic3—21no—
526C3×Dic3—32no—
527C3×Dic3—61no—
528C3×Dic3D3×D412yes—
529C22×C9—22no—
530C22×C9—21no—
531C22×C9—21no—
532C22×C9—21no—
533C22×C9—21no—
534C22×C9—32no—
535C22×C9—41no—
536C22×C9—41no—
537C22×C9—61no—
538C22×C9—61no—
539C22×C9—61no—
540C22×C9—61no—
541C22×C9—61no—
542C22×C9C23×D311yescharacteristic
543C2×D9—21no—
544C2×D9—21no—
545C2×D9—21no—
546C2×D9—21no—
547C2×D9—21no—
548C2×D9—32no—
549C2×D9—32no—
550C2×D9—62no—
551C2×D9—62no—
552C2×D9—61no—
553C2×D9—61no—
554C2×D9—61no—
555C2×D9—61no—
556C2×D9—61no—
557C2×D9—61no—
558C2×D9—61no—
559C2×D9—121no—
560C2×D9—121no—
561C2×D9—121no—
562C2×D9—121no—
563C2×D9—121no—
564C2×D9—121no—
565C2×D9—121no—
566C2×D9—124no—
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—41no—
576C4×C9—41no—
577C4×C9—61no—
578Dic9—21no—
579Dic9—61no—
580Dic9—121no—
581Dic9D3×D412yescomplemented
582C22×D4—271no—
583C22×D4—271no—
584C22×D4—271no—
585C22×D4—271no—
586#127—271no—
587#121—31no—
588#121—91no—
589#121—271no—
590#121—271no—
591#120—271no—
592#120—271no—
593#120—271no—
594#120—271no—
595C4×D4—271no—
596C4×D4—271no—
597C3×C9D4211yescharacteristic, complemented, Sylow
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—91no—
602C23×C3—91no—
603C23×C3C22×D911yescharacteristic
604C23×C3C2×D3211yescharacteristic
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—91no—
608C22×D3—91no—
609C22×D3—91no—
610C22×D3—91no—
611C22×D3—91no—
612C22×D3—91no—
613C22×D3—181no—
614C22×D3—181no—
615C22×D3—181no—
616C22×D3—182no—
617C22×D3—182no—
618C22×D3—182no—
619C22×D3—182no—
620C22×D3—182no—
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—362no—
633C22×D3—362no—
634C22×D3—361no—
635C22×D3—361no—
636C22×D3—361no—
637C22×D3—361no—
638C22×D3—361no—
639C22×D3—361no—
640C22×D3—361no—
641C22×D3—361no—
642C22×D3—362no—
643C22×D3C22×D911yescharacteristic
644C22×D3C22×D911yescharacteristic
645C3×D4—62no—
646C3×D4—62no—
647C3×D4—62no—
648C3×D4—182no—
649C3×D4—182no—
650C3×D4—182no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—31no—
654C2×C3×C4—31no—
655C2×C3×C4—62no—
656C2×C3×C4—91no—
657C2×C3×C4—91no—
658C2×C3×C4—182no—
659C2×C3×C4C22×D911yescharacteristic
660C2×C3×C4C22×D911yescharacteristic
661C2×C3×C4C2×D3211yescharacteristic
662C2×C3×C4C2×D3211yescharacteristic
663#67—22no—
664#67—22no—
665#67—62no—
666#67—62no—
667#67—94no—
668#67—94no—
669#67—182no—
670#67—182no—
671#67—182no—
672#67—182no—
673#67—361no—
674#67—361no—
675#67—361no—
676#67—361no—
677#67—362no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—91no—
681C2×Dic3—91no—
682C2×Dic3—181no—
683C2×Dic3C22×D911yescharacteristic
684C2×Dic3C22×D911yescharacteristic
685D12—22no—
686D12—62no—
687D12—94no—
688D12—94no—
689D12—182no—
690D12—182no—
691D12—182no—
692D12—182no—
693D12—182no—
694D12—182no—
695D12—182no—
696D12—182no—
697D12—362no—
698D12—362no—
699C4×D3—22no—
700C4×D3—62no—
701C4×D3—182no—
702C4×D3—182no—
703C4×D3—182no—
704C4×D3—182no—
705C2×C32—41no—
706C2×C32C2×D3×D411yescharacteristic
707C2×C32C2×D3×D411yescharacteristic
708C2×C32#100911yescharacteristic
709C3⋊D3—62no—
710C3⋊D3—62no—
711C3⋊D3—121no—
712C3×D3—22no—
713C3×D3—41no—
714C3×D3—62no—
715C3×D3—121no—
716C2×C9—21no—
717C2×C9—21no—
718C2×C9—21no—
719C2×C9—42no—
720C2×C9—41no—
721C2×C9—62no—
722C2×C9—121no—
723C2×C9C2×D3×D411yescharacteristic
724C2×C9C2×D3×D411yescharacteristic
725C2×C9#100911yescharacteristic
726D9—22no—
727D9—41no—
728D9—62no—
729D9—62no—
730D9—122no—
731D9—122no—
732D9—121no—
733D9—241no—
734C24—271no—
735C24—271no—
736C24—271no—
737C24—271no—
738C2×D4—31no—
739C2×D4—31no—
740C2×D4—31no—
741C2×D4—91no—
742C2×D4—91no—
743C2×D4—91no—
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—91no—
760C22×C4—271no—
761C22×C4—271no—
762C4⋊C4—31no—
763C4⋊C4—91no—
764C22⋊C4—31no—
765C22⋊C4—91no—
766C22⋊C4—271no—
767C22⋊C4—271no—
768C22⋊C4—271no—
769C22⋊C4—271no—
770C22⋊C4—271no—
771C22⋊C4D3×D911yescharacteristic, complemented
772C42—271no—
773C22×C3—22no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—32no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—61no—
789C22×C3—92no—
790C22×C3—181no—
791C22×C3—181no—
792C22×C3—181no—
793C22×C3—181no—
794C22×C3—181no—
795C22×C3C23×D911yescharacteristic
796C22×C3C22×D3211yescharacteristic
797C2×D3—21no—
798C2×D3—21no—
799C2×D3—21no—
800C2×D3—21no—
801C2×D3—21no—
802C2×D3—32no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—92no—
809C2×D3—92no—
810C2×D3—92no—
811C2×D3—92no—
812C2×D3—182no—
813C2×D3—182no—
814C2×D3—181no—
815C2×D3—181no—
816C2×D3—181no—
817C2×D3—181no—
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—361no—
829C2×D3—361no—
830C2×D3—361no—
831C2×D3—361no—
832C2×D3—361no—
833C2×D3—361no—
834C2×D3—361no—
835C2×D3—364no—
836C2×D3—364no—
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—32no—
850C3×C4—41no—
851C3×C4—41no—
852C3×C4—61no—
853C3×C4—92no—
854C3×C4—181no—
855Dic3—21no—
856Dic3—32no—
857Dic3—61no—
858Dic3—181no—
859Dic3—181no—
860Dic3—361no—
861Dic3D4×D912yescomplemented
862C32#560911yescharacteristic
863C9—21no—
864C9#560911yescharacteristic, complemented
865C23—31no—
866C23—31no—
867C23—91no—
868C23—91no—
869C23—271no—
870C23—271no—
871C23—271no—
872C23—542no—
873C23—542no—
874C23—542no—
875C23—542no—
876C23—542no—
877C23—542no—
878C23—542no—
879C23—542no—
880C23—1081no—
881C23—1081no—
882C23—1081no—
883C23—1081no—
884C23C2×D3×D911yescharacteristic
885D4—62no—
886D4—62no—
887D4—62no—
888D4—182no—
889D4—182no—
890D4—182no—
891D4—274no—
892D4—274no—
893D4—542no—
894D4—542no—
895D4—542no—
896D4—542no—
897D4—542no—
898D4—542no—
899D4—1081no—
900D4—1081no—
901C2×C4—31no—
902C2×C4—31no—
903C2×C4—62no—
904C2×C4—91no—
905C2×C4—91no—
906C2×C4—182no—
907C2×C4—271no—
908C2×C4—542no—
909C2×C4—542no—
910C2×C4C2×D3×D911yescharacteristic
911C2×C4C2×D3×D911yescharacteristic
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—42no—
916C2×C3—41no—
917C2×C3—41no—
918C2×C3—62no—
919C2×C3—121no—
920C2×C3—182no—
921C2×C3—361no—
922C2×C3C2×D4×D911yescharacteristic
923C2×C3C2×D4×D911yescharacteristic
924C2×C3#6371511yescharacteristic
925C2×C3#6430811yescharacteristic
926C2×C3D32×D411yescharacteristic
927C2×C3D32×D411yescharacteristic
928D3—22no—
929D3—41no—
930D3—62no—
931D3—121no—
932D3—182no—
933D3—182no—
934D3—182no—
935D3—182no—
936D3—362no—
937D3—362no—
938D3—361no—
939D3—361no—
940D3—721no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—32no—
945C22—61no—
946C22—61no—
947C22—61no—
948C22—61no—
949C22—61no—
950C22—92no—
951C22—181no—
952C22—181no—
953C22—181no—
954C22—181no—
955C22—181no—
956C22—272no—
957C22—272no—
958C22—541no—
959C22—541no—
960C22—541no—
961C22—541no—
962C22—541no—
963C22—541no—
964C22—541no—
965C22—1084no—
966C22—1084no—
967C22—1084no—
968C22—1084no—
969C22C22×D3×D911yescharacteristic
970C4—21no—
971C4—21no—
972C4—32no—
973C4—61no—
974C4—92no—
975C4—181no—
976C4—541no—
977C3—21no—
978C3#1058971111yescharacteristic, complemented
979C3#1059428411yescharacteristic
980C2—41no—
981C2—62no—
982C2—121no—
983C2—182no—
984C2—361no—
985C2—542no—
986C2—542no—
987C2—1081no—
988C2#1172247811yescharacteristic
989C2D3×D4×D911yescharacteristic
990C2D3×D4×D911yescharacteristic
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×#88668C2semidirect
3. C2×D9×D12C2semidirect
4. C2×D3×D36C2semidirect
5. #11721728C2semidirect
6. C9×#884C2semidirect
7. C3×#63446C2semidirect
8. #11721292C2semidirect
9. #11721289C2semidirect
10. #11721050C2semidirect
11. #11721049C2semidirect
12. #11721039C2semidirect
13. #11721030C2semidirect
14. #11721005C2semidirect
15. #11721002C2semidirect
18. C23×C3⋊D9C22semidirect
19. C22×D3×D9C22semidirect
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
26. C2×C9×#67C22semidirect
27. C2×C3×#611C22semidirect
28. C2×C3×#611C22semidirect
29. C2×C9×D12C22semidirect
30. C2×C4×D3×C9C22semidirect
31. C2×C3×D36C22semidirect
32. C2×C3×C4×D9C22semidirect
36. C2×#6195C22semidirect
37. C2×#6195C22semidirect
38. C2×#6194C22semidirect
40. C2×#6192C22semidirect
41. C2×#6192C22semidirect
42. C2×(C3⋊D9)⋊C4C22semidirect
43. C2×(C3⋊D9)⋊C4C22semidirect
46. C3×C9×C22⋊C4C22semidirect
47. #88536C22semidirect
48. #88536C22semidirect
49. C9×(C2×D3)⋊C4C22semidirect
50. C3×(C2×D9)⋊C4C22semidirect
51. C9×Dic3⋊C4C22semidirect
52. C3×Dic9⋊C4C22semidirect
53. (C2×D3)⋊Dic9C22semidirect
54. #88445C22semidirect
55. (C2×D9)⋊Dic3C22semidirect
56. Dic3×Dic9C22semidirect
84. #63446D3semidirect
128. #6195D4semidirect
132. #6192D4semidirect
191. C2×#611C2×D3semidirect
192. C2×#611C2×D3semidirect
204. C2×D36C2×D3semidirect
207. C2×C4×D9C2×D3semidirect
211. C9×C22⋊C4C2×D3semidirect
219. (C2×D9)⋊C4C2×D3semidirect
220. Dic9⋊C4C2×D3semidirect
234. C2×C3⋊D9C2×D4semidirect
235. C2×C3⋊D9C2×D4semidirect
241. C2×D3×C9C2×D4semidirect
247. C2×C3×D9C2×D4semidirect
255. C9×Dic3C2×D4semidirect
257. C3×Dic9C2×D4semidirect
283. #884D9semidirect
438. C2×#67C2×D9semidirect
439. C2×#67C2×D9semidirect
461. C2×D12C2×D9semidirect
467. C2×C4×D3C2×D9semidirect
473. C3×C22⋊C4C2×D9semidirect
488. (C2×D3)⋊C4C2×D9semidirect
490. Dic3⋊C4C2×D9semidirect
571. C2×D9D3×D4semidirect
581. Dic9D3×D4semidirect
597. C3×C9D42semidirect
771. C22⋊C4D3×D9semidirect
844. C2×D3D4×D9semidirect
861. Dic3D4×D9semidirect
864. C9#5609semidirect
978. C3#10589711semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×D9×D122
C2×D3×D362
#117217282
C9×#8842
C3×#634462
#117212922
#117212892
#117210502
#117210492
#117210392
#117210302
#117210052
#117210022
#105942843
#105897113