Finite Group Databasebeta

← #13148283

Subgroups — #13148283

Order 1728.

1378 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic, complemented
2C2×D3×#611C211yesmaximal, characteristic, complemented
3C2×#88646C211yesmaximal, characteristic, complemented
4C2×D9×D12C211yesmaximal, characteristic, complemented
5#11721730C211yesmaximal, characteristic, complemented
6C9×#882C211yesmaximal, characteristic, complemented
7C3×#63446C211yesmaximal, characteristic, complemented
8#11721292C211yesmaximal, characteristic, complemented
9#11721289C211yesmaximal, characteristic, complemented
10#11721051C211yesmaximal, characteristic, complemented
11#11721049C211yesmaximal, characteristic, complemented
12#11721017C211yesmaximal, characteristic, complemented
13#11721016C211yesmaximal, characteristic, complemented
14#11721014C211yesmaximal, characteristic, complemented
15#11721012C211yesmaximal, characteristic, complemented
16#10594275—31nomaximal
17#10589692—31nomaximal
18C23×D3×C9C2211yescharacteristic, complemented
19C22×D3×D9C2211yescharacteristic, complemented
20C22×D3×D9C2211yescharacteristic, complemented
21C22×D3×D9C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×#6233C2211yescharacteristic, complemented
24C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
25C2×C4×C3⋊D9C2211yescharacteristic, complemented
26C2×C9×#67C2211yescharacteristic, complemented
27C2×C3×#611C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic, complemented
29C2×C9×D12C2211yescharacteristic, complemented
30C2×C9×D12C2211yescharacteristic, complemented
31C2×C3×D36C2211yescharacteristic, complemented
32C2×C3×C4×D9C2211yescharacteristic, complemented
33D3×#611—24no—
34D3×#611—24no—
35C2×#6195C2211yescharacteristic
36C2×#6195C2211yescharacteristic, complemented
37C2×#6195C2211yescharacteristic, complemented
38C2×#6194C2211yescharacteristic
39C2×#6194C2211yescharacteristic, complemented
40C2×#6194C2211yescharacteristic, complemented
41C2×D3×Dic9C2211yescharacteristic, complemented
42C2×D3×Dic9C2211yescharacteristic, complemented
43C2×#6192C2211yescharacteristic, complemented
44#88646—24no—
45D9×D12—24no—
46C3×C9×C22⋊C4C2211yescharacteristic, complemented
47#88536C2211yescharacteristic, complemented
48#88534C2211yescharacteristic, complemented
49C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
52C3×Dic9⋊C4C2211yescharacteristic, complemented
53(C2×D3)⋊Dic9C2211yescharacteristic, complemented
54#88445C2211yescharacteristic, complemented
55(C2×D9)⋊Dic3C2211yescharacteristic, complemented
56Dic3×Dic9C2211yescharacteristic, complemented
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3802—31no—
60C2×D3×D12—31no—
61#64093—31no—
62C3×#884—31no—
63C3×#882D311yescharacteristic
64#63983—31no—
65#63979—31no—
66#63923—31no—
67#63922—31no—
68#63886—31no—
69#63885—31no—
70#63881—31no—
71#63879—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—61no—
83#63446D311yescharacteristic, complemented
84#63444—31no—
85#63444—31no—
86#611⋊C4—31no—
87#611⋊C4—31no—
88C23×C3×C9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9—22no—
92C22×D3×C9—22no—
93C22×D3×C9—41no—
94C22×D3×C9C2311yescharacteristic
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—22no—
111#6233—22no—
112C2×C3⋊Dic9C2311yescharacteristic
113C2×C3⋊Dic9C2311yescharacteristic
114C4⋊(C3⋊D9)—22no—
115C4×C3⋊D9—22no—
116C9×#67—41no—
117C3×#611—22no—
118C3×#611—22no—
119C2×C9×Dic3C2311yescharacteristic
120C2×C3×Dic9C2311yescharacteristic
121C2×C3×Dic9C2311yescharacteristic
122C9×D12—22no—
123C9×D12—22no—
124C3×D36—22no—
125C3×C4×D9—22no—
126#6195—22no—
127#6195—22no—
128#6195D414yescomplemented
129#6194—22no—
130#6194—22no—
131#6194D414yescomplemented
132D3×Dic9—22no—
133D3×Dic9—22no—
134#6192—41no—
135#5609—91no—
136#5590—91no—
137C23×C3×D3C2×D311yescharacteristic
138C22×D32—31no—
139C22×D32—31no—
140C22×D32—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4×C3⋊D3—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67C2×D311yescharacteristic
148C2×C3×D12—31no—
149C2×C3×D12C2×D311yescharacteristic
150C2×C3×D12C2×D311yescharacteristic
151C2×C3×C4×D3—31no—
152D3×#67—64no—
153D3×#67—64no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#625—31no—
159C2×#625—31no—
160C2×#625—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163#3802—64no—
164D3×D12—64no—
165C24×C9—31no—
166C23×D9—31no—
167C23×D9—31no—
168C23×D9—31no—
169C32×C22⋊C4C2×D311yescharacteristic
170#3752—31no—
171#3750—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4C2×D311yescharacteristic
174C3×(C2×D3)⋊C4C2×D311yescharacteristic
175C3×Dic3⋊C4—31no—
176#3722—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179Dic32—31no—
180C2×D4×C9—31no—
181C2×D4×C9—31no—
182C2×D4×C9—31no—
183C2×#611—31no—
184C2×#611—31no—
185C2×#611—31no—
186C2×#611—31no—
187C2×#611—31no—
188C2×#611—31no—
189C2×#611—31no—
190C2×#611—31no—
191C2×#611—64no—
192C2×#611—64no—
193C2×#611—61no—
194C2×#611—61no—
195C2×#611C2×D311yescharacteristic, complemented
196C2×#611C2×D311yescharacteristic, complemented
197C22×Dic9—31no—
198C22×Dic9—31no—
199D4×D9—64no—
200D4×D9—64no—
201C2×D36—31no—
202C2×D36—31no—
203C2×D36—61no—
204C2×D36C2×D311yescharacteristic, complemented
205C2×C4×D9—31no—
206C2×C4×D9—61no—
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)⋊C4C2×D311yescharacteristic, complemented
218Dic9⋊C4—31no—
219Dic9⋊C4—61no—
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⋊D9C2×D412yescomplemented
232C2×D3×C9—21no—
233C2×D3×C9—21no—
234C2×D3×C9—21no—
235C2×D3×C9—21no—
236C2×D3×C9—21no—
237C2×D3×C9—21no—
238C2×D3×C9—21no—
239C2×D3×C9—44no—
240C2×D3×C9C2×D412yescomplemented
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—
254C3⋊Dic9C2×D412yescomplemented
255C9×Dic3—21no—
256C3×Dic9—21no—
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—
264C2×D3×D4—91no—
265C22×D12—91no—
266C3×#121—91no—
267C3×#120—31no—
268#940—91no—
269#940—91no—
270#939—91no—
271#939—91no—
272#937—91no—
273#937—91no—
274#937—91no—
275C4×#67—91no—
276#895—91no—
277#893—91no—
278#884—31no—
279#884—91no—
280#884—91no—
281#884—91no—
282#884—181no—
283#882—91no—
284#882—91no—
285#882—91no—
286#882D911yescharacteristic, complemented
287#67⋊C4—91no—
288#67⋊C4—91no—
289C23×C32C22×D311yescharacteristic
290C22×C3⋊D3—31no—
291C22×C3⋊D3—31no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—31no—
295C22×C3×D3—31no—
296C22×C3×D3—41no—
297C22×C3×D3C22×D311yescharacteristic
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—62no—
312#638—62no—
313C2×C3⋊Dic3—31no—
314C2×C3⋊Dic3—31no—
315C4⋊(C3⋊D3)—62no—
316C4×C3⋊D3—62no—
317C3×#67—41no—
318C3×#67—62no—
319C3×#67—62no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3C22×D311yescharacteristic
323C3×D12—22no—
324C3×D12—22no—
325C3×D12—62no—
326C3×C4×D3—62no—
327#626—34no—
328#626—62no—
329#626—62no—
330#626—121no—
331#625—34no—
332#625—62no—
333#625—62no—
334D3×Dic3—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—61no—
347C22×D9—61no—
348C22×D9—62no—
349C22×D9—62no—
350C22×D9—62no—
351C22×D9—62no—
352C22×D9—62no—
353C22×D9—62no—
354C22×D9—121no—
355C22×D9—121no—
356C22×D9—121no—
357C22×D9C22×D311yescharacteristic
358C22×D9C22×D311yescharacteristic
359D4×C9—62no—
360D4×C9—62no—
361D4×C9—121no—
362C2×C4×C9—21no—
363C2×C4×C9—21no—
364C2×C4×C9—31no—
365C2×C4×C9C22×D311yescharacteristic
366C2×C4×C9C22×D311yescharacteristic
367#611—22no—
368#611—22no—
369#611—34no—
370#611—34no—
371#611—62no—
372#611—62no—
373#611—62no—
374#611—62no—
375#611—62no—
376#611—62no—
377#611—122no—
378#611—122no—
379C2×Dic9—31no—
380C2×Dic9—31no—
381C2×Dic9—61no—
382C2×Dic9—61no—
383C2×Dic9—62no—
384C2×Dic9—62no—
385C2×Dic9C22×D311yescharacteristic
386C2×Dic9C22×D311yescharacteristic
387D36—22no—
388D36—62no—
389D36—122no—
390D36—121no—
391C4×D9—22no—
392C4×D9—62no—
393C4×D9—122no—
394D42—271noSylow
395C2×C3×C9—41no—
396C2×C3×C9C22×D411yescharacteristic
397C2×C3×C9C22×D411yescharacteristic
398C2×C3×C9H(5,𝔽2)11yescharacteristic
399C3⋊D9—22no—
400C3⋊D9—41no—
401D3×C9—22no—
402D3×C9—22no—
403D3×C9—41no—
404C3×D9—22no—
405C3×D9—41no—
406C24×C3—31no—
407C23×D3—91no—
408C23×D3—91no—
409C23×D3—91no—
410C23×D3—91no—
411C23×D3—91no—
412C23×D3—91no—
413C23×D3C2×D911yescharacteristic, complemented
414C2×C3×D4—31no—
415C2×C3×D4—31no—
416C2×C3×D4—31no—
417C2×C3×D4—91no—
418C2×C3×D4—91no—
419C2×C3×D4—91no—
420C22×C3×C4—91no—
421C2×#67—31no—
422C2×#67—31no—
423C2×#67—91no—
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—91no—
437C2×#67—181no—
438C2×#67—181no—
439C2×#67—184no—
440C2×#67—184no—
441C2×#67C2×D911yescharacteristic, complemented
442C22×Dic3—91no—
443C22×Dic3—91no—
444D3×D4—184no—
445D3×D4—184no—
446D3×D4—184no—
447D3×D4—184no—
448D3×D4—184no—
449C2×D12—31no—
450C2×D12—91no—
451C2×D12—91no—
452C2×D12—91no—
453C2×D12—91no—
454C2×D12—91no—
455C2×D12—91no—
456C2×D12—181no—
457C2×D12—184no—
458C2×D12C2×D911yescharacteristic, complemented
459C2×D12C2×D911yescharacteristic, complemented
460C2×C4×D3—31no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×C4×D3—181no—
466C3×C4⋊C4—91no—
467C3×C22⋊C4—21no—
468C3×C22⋊C4—31no—
469C3×C22⋊C4—31no—
470C3×C22⋊C4—91no—
471C3×C22⋊C4C2×D911yescharacteristic, complemented
472C3×C22⋊C4D3211yescharacteristic
473#217—91no—
474#217—91no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—181no—
483(C2×D3)⋊C4C2×D911yescharacteristic, complemented
484(C2×D3)⋊C4C2×D911yescharacteristic, complemented
485Dic3⋊C4—31no—
486Dic3⋊C4—91no—
487Dic3⋊C4—91no—
488Dic3⋊C4—181no—
489C4×Dic3—91no—
490C4×Dic3—91no—
491C22×C32—21no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32C23×D311yescharacteristic
495C2×C3⋊D3—32no—
496C2×C3⋊D3—61no—
497C2×C3⋊D3—61no—
498C2×C3⋊D3—61no—
499C2×C3⋊D3—61no—
500C2×C3⋊D3—61no—
501C2×C3×D3—21no—
502C2×C3×D3—21no—
503C2×C3×D3—21no—
504C2×C3×D3—21no—
505C2×C3×D3—21no—
506C2×C3×D3—21no—
507C2×C3×D3—21no—
508C2×C3×D3—32no—
509C2×C3×D3—44no—
510C2×C3×D3—61no—
511C2×C3×D3—61no—
512C2×C3×D3—61no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3D3×D412yes—
516C2×C3×D3D3×D412yes—
517D32—124no—
518D32—124no—
519D32—124no—
520C32×C4—21no—
521C32×C4—21no—
522C3⋊Dic3—32no—
523C3⋊Dic3—61no—
524C3×Dic3—21no—
525C3×Dic3—32no—
526C3×Dic3—61no—
527C22×C9—21no—
528C22×C9—21no—
529C22×C9—21no—
530C22×C9—21no—
531C22×C9—32no—
532C22×C9—32no—
533C22×C9—41no—
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—124no—
544C22×C9C23×D311yescharacteristic
545C2×D9—21no—
546C2×D9—21no—
547C2×D9—21no—
548C2×D9—21no—
549C2×D9—21no—
550C2×D9—32no—
551C2×D9—62no—
552C2×D9—61no—
553C2×D9—61no—
554C2×D9—61no—
555C2×D9—61no—
556C2×D9—61no—
557C2×D9—121no—
558C2×D9—121no—
559C2×D9—121no—
560C2×D9—121no—
561C2×D9—121no—
562C2×D9—124no—
563C2×D9—124no—
564C2×D9—124no—
565C2×D9D3×D412yescomplemented
566C4×C9—21no—
567C4×C9—21no—
568C4×C9—41no—
569C4×C9—41no—
570C4×C9—61no—
571Dic9—21no—
572Dic9—32no—
573Dic9—62no—
574Dic9—61no—
575Dic9—121no—
576Dic9D3×D412yescomplemented
577C22×D4—271no—
578C22×D4—271no—
579C22×D4—271no—
580C22×D4—271no—
581#127—271no—
582#121—91no—
583#121—271no—
584#121—271no—
585#121—271no—
586#120—31no—
587#120—271no—
588#120—271no—
589#120—271no—
590C4×D4—271no—
591C4×D4—271no—
592C3×C9D4211yescharacteristic, complemented, Sylow
593C23×C3—21no—
594C23×C3—31no—
595C23×C3—31no—
596C23×C3—31no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—91no—
600C23×C3—91no—
601C23×C3—121no—
602C23×C3C22×D911yescharacteristic
603C23×C3C2×D3211yescharacteristic
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—31no—
607C22×D3—31no—
608C22×D3—41no—
609C22×D3—91no—
610C22×D3—91no—
611C22×D3—91no—
612C22×D3—91no—
613C22×D3—181no—
614C22×D3—181no—
615C22×D3—182no—
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—361no—
628C22×D3—361no—
629C22×D3—361no—
630C22×D3—361no—
631C22×D3—361no—
632C22×D3—361no—
633C22×D3C22×D911yescharacteristic
634C22×D3C22×D911yescharacteristic
635C22×D3C22×D911yescharacteristic
636C3×D4—62no—
637C3×D4—62no—
638C3×D4—121no—
639C3×D4—182no—
640C3×D4—182no—
641C3×D4—182no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—31no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—182no—
648C2×C3×C4C22×D911yescharacteristic
649C2×C3×C4C22×D911yescharacteristic
650C2×C3×C4C2×D3211yescharacteristic
651C2×C3×C4C2×D3211yescharacteristic
652#67—41no—
653#67—62no—
654#67—62no—
655#67—94no—
656#67—94no—
657#67—94no—
658#67—182no—
659#67—182no—
660#67—182no—
661#67—182no—
662#67—182no—
663#67—182no—
664#67—182no—
665#67—182no—
666#67—182no—
667#67—182no—
668#67—362no—
669#67—362no—
670#67—361no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—91no—
674C2×Dic3—91no—
675C2×Dic3—91no—
676C2×Dic3—91no—
677C2×Dic3—181no—
678C2×Dic3—181no—
679C2×Dic3—182no—
680C2×Dic3—182no—
681C2×Dic3C22×D911yescharacteristic
682D12—22no—
683D12—22no—
684D12—62no—
685D12—94no—
686D12—182no—
687D12—182no—
688D12—182no—
689D12—182no—
690D12—362no—
691D12—361no—
692C4×D3—62no—
693C4×D3—182no—
694C4×D3—182no—
695C4×D3—182no—
696C4×D3—182no—
697C4×D3—362no—
698C2×C32—41no—
699C2×C32C2×D3×D411yescharacteristic
700C2×C32C2×D3×D411yescharacteristic
701C2×C32#100411yescharacteristic
702C3⋊D3—62no—
703C3⋊D3—121no—
704C3×D3—22no—
705C3×D3—22no—
706C3×D3—41no—
707C3×D3—62no—
708C3×D3—121no—
709C2×C9—21no—
710C2×C9—21no—
711C2×C9—21no—
712C2×C9—41no—
713C2×C9—62no—
714C2×C9—62no—
715C2×C9—81no—
716C2×C9—121no—
717C2×C9C2×D3×D411yescharacteristic
718C2×C9C2×D3×D411yescharacteristic
719C2×C9#100911yescharacteristic
720D9—22no—
721D9—41no—
722D9—62no—
723D9—122no—
724D9—121no—
725D9—241no—
726C24—31no—
727C24—271no—
728C24—271no—
729C24—271no—
730C2×D4—31no—
731C2×D4—31no—
732C2×D4—31no—
733C2×D4—91no—
734C2×D4—91no—
735C2×D4—91no—
736C2×D4—271no—
737C2×D4—271no—
738C2×D4—271no—
739C2×D4—271no—
740C2×D4—271no—
741C2×D4—271no—
742C2×D4—271no—
743C2×D4—271no—
744C2×D4—271no—
745C2×D4—271no—
746C2×D4—544no—
747C2×D4—544no—
748C2×D4—544no—
749C2×D4—544no—
750C22×C4—91no—
751C22×C4—271no—
752C22×C4—271no—
753C22×C4—271no—
754C4⋊C4—91no—
755C4⋊C4—271no—
756C22⋊C4—31no—
757C22⋊C4—31no—
758C22⋊C4—91no—
759C22⋊C4—271no—
760C22⋊C4—271no—
761C22⋊C4—271no—
762C22⋊C4—271no—
763C22⋊C4D3×D911yescharacteristic, complemented
764C42—271no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—32no—
773C22×C3—32no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3—61no—
780C22×C3—61no—
781C22×C3—61no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3—92no—
785C22×C3—124no—
786C22×C3—181no—
787C22×C3—181no—
788C22×C3—181no—
789C22×C3—181no—
790C22×C3—181no—
791C22×C3C23×D911yescharacteristic
792C22×C3C22×D3211yescharacteristic
793C2×D3—21no—
794C2×D3—21no—
795C2×D3—21no—
796C2×D3—21no—
797C2×D3—21no—
798C2×D3—21no—
799C2×D3—21no—
800C2×D3—32no—
801C2×D3—44no—
802C2×D3—61no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—92no—
808C2×D3—92no—
809C2×D3—182no—
810C2×D3—181no—
811C2×D3—181no—
812C2×D3—181no—
813C2×D3—181no—
814C2×D3—181no—
815C2×D3—181no—
816C2×D3—181no—
817C2×D3—181no—
818C2×D3—181no—
819C2×D3—181no—
820C2×D3—361no—
821C2×D3—361no—
822C2×D3—361no—
823C2×D3—361no—
824C2×D3—361no—
825C2×D3—364no—
826C2×D3—364no—
827C2×D3—364no—
828C2×D3—364no—
829C2×D3—364no—
830C2×D3—364no—
831C2×D3D4×D912yescomplemented
832C2×D3D4×D912yescomplemented
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—41no—
838C3×C4—41no—
839C3×C4—61no—
840C3×C4—92no—
841C3×C4—181no—
842Dic3—21no—
843Dic3—32no—
844Dic3—61no—
845Dic3—92no—
846Dic3—92no—
847Dic3—182no—
848Dic3—181no—
849Dic3—181no—
850Dic3—361no—
851C32#559011yescharacteristic
852C9—21no—
853C9#560911yescharacteristic, complemented
854C23—31no—
855C23—31no—
856C23—31no—
857C23—62no—
858C23—62no—
859C23—91no—
860C23—91no—
861C23—121no—
862C23—271no—
863C23—271no—
864C23—542no—
865C23—542no—
866C23—542no—
867C23—542no—
868C23—542no—
869C23—542no—
870C23—1081no—
871C23—1081no—
872C23—1081no—
873C23C2×D3×D911yescharacteristic
874D4—62no—
875D4—62no—
876D4—121no—
877D4—182no—
878D4—182no—
879D4—182no—
880D4—274no—
881D4—274no—
882D4—542no—
883D4—542no—
884D4—542no—
885D4—542no—
886D4—542no—
887D4—542no—
888D4—542no—
889D4—1081no—
890C2×C4—31no—
891C2×C4—91no—
892C2×C4—91no—
893C2×C4—182no—
894C2×C4—271no—
895C2×C4—271no—
896C2×C4—542no—
897C2×C4—542no—
898C2×C4—542no—
899C2×C4C2×D3×D911yescharacteristic
900C2×C4C2×D3×D911yescharacteristic
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—62no—
907C2×C3—62no—
908C2×C3—81no—
909C2×C3—121no—
910C2×C3—182no—
911C2×C3—361no—
912C2×C3C2×D4×D911yescharacteristic
913C2×C3C2×D4×D911yescharacteristic
914C2×C3#6371011yescharacteristic
915C2×C3#6430711yescharacteristic
916C2×C3D32×D411yescharacteristic
917C2×C3D32×D411yescharacteristic
918D3—22no—
919D3—22no—
920D3—41no—
921D3—62no—
922D3—121no—
923D3—182no—
924D3—182no—
925D3—362no—
926D3—361no—
927D3—361no—
928D3—721no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—32no—
933C22—32no—
934C22—61no—
935C22—61no—
936C22—61no—
937C22—61no—
938C22—61no—
939C22—61no—
940C22—61no—
941C22—92no—
942C22—124no—
943C22—181no—
944C22—181no—
945C22—181no—
946C22—181no—
947C22—181no—
948C22—272no—
949C22—541no—
950C22—541no—
951C22—541no—
952C22—541no—
953C22—541no—
954C22—1084no—
955C22—1084no—
956C22—1084no—
957C22C22×D3×D911yescharacteristic
958C4—21no—
959C4—21no—
960C4—61no—
961C4—92no—
962C4—181no—
963C4—272no—
964C4—541no—
965C3—21no—
966C3#1058969211yescharacteristic, complemented
967C3#1059427511yescharacteristic
968C2—41no—
969C2—62no—
970C2—62no—
971C2—121no—
972C2—182no—
973C2—361no—
974C2—542no—
975C2—1081no—
976C2#1172247611yescharacteristic
977C2D3×D4×D911yescharacteristic
978C2D3×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×D3×#611C2semidirect
2. C2×D3×#611C2semidirect
3. C2×#88646C2semidirect
4. C2×D9×D12C2semidirect
5. #11721730C2semidirect
6. C9×#882C2semidirect
7. C3×#63446C2semidirect
8. #11721292C2semidirect
9. #11721289C2semidirect
10. #11721051C2semidirect
11. #11721049C2semidirect
12. #11721017C2semidirect
13. #11721016C2semidirect
14. #11721014C2semidirect
15. #11721012C2semidirect
18. C23×D3×C9C22semidirect
19. C22×D3×D9C22semidirect
20. C22×D3×D9C22semidirect
21. C22×D3×D9C22semidirect
22. C2×#6233C22semidirect
23. C2×#6233C22semidirect
24. C2×C4⋊(C3⋊D9)C22semidirect
25. C2×C4×C3⋊D9C22semidirect
26. C2×C9×#67C22semidirect
27. C2×C3×#611C22semidirect
28. C2×C3×#611C22semidirect
29. C2×C9×D12C22semidirect
30. C2×C9×D12C22semidirect
31. C2×C3×D36C22semidirect
32. C2×C3×C4×D9C22semidirect
36. C2×#6195C22semidirect
37. C2×#6195C22semidirect
39. C2×#6194C22semidirect
40. C2×#6194C22semidirect
41. C2×D3×Dic9C22semidirect
42. C2×D3×Dic9C22semidirect
43. C2×#6192C22semidirect
46. C3×C9×C22⋊C4C22semidirect
47. #88536C22semidirect
48. #88534C22semidirect
49. C9×(C2×D3)⋊C4C22semidirect
50. C9×(C2×D3)⋊C4C22semidirect
51. C3×(C2×D9)⋊C4C22semidirect
52. C3×Dic9⋊C4C22semidirect
53. (C2×D3)⋊Dic9C22semidirect
54. #88445C22semidirect
55. (C2×D9)⋊Dic3C22semidirect
56. Dic3×Dic9C22semidirect
83. #63446D3semidirect
128. #6195D4semidirect
131. #6194D4semidirect
195. C2×#611C2×D3semidirect
196. C2×#611C2×D3semidirect
204. C2×D36C2×D3semidirect
207. C2×C4×D9C2×D3semidirect
211. C9×C22⋊C4C2×D3semidirect
217. (C2×D9)⋊C4C2×D3semidirect
220. Dic9⋊C4C2×D3semidirect
231. C2×C3⋊D9C2×D4semidirect
240. C2×D3×C9C2×D4semidirect
241. C2×D3×C9C2×D4semidirect
247. C2×C3×D9C2×D4semidirect
254. C3⋊Dic9C2×D4semidirect
257. C3×Dic9C2×D4semidirect
286. #882D9semidirect
413. C23×D3C2×D9semidirect
441. C2×#67C2×D9semidirect
458. C2×D12C2×D9semidirect
459. C2×D12C2×D9semidirect
471. C3×C22⋊C4C2×D9semidirect
483. (C2×D3)⋊C4C2×D9semidirect
484. (C2×D3)⋊C4C2×D9semidirect
565. C2×D9D3×D4semidirect
576. Dic9D3×D4semidirect
592. C3×C9D42semidirect
763. C22⋊C4D3×D9semidirect
831. C2×D3D4×D9semidirect
832. C2×D3D4×D9semidirect
853. C9#5609semidirect
966. C3#10589692semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×#886462
C2×D9×D122
#117217302
C9×#8822
C3×#634462
#117212922
#117212892
#117210512
#117210492
#117210172
#117210162
#117210142
#117210122
#105942753
#105896923