Finite Group Databasebeta

← D9×#884 #13148403

Subgroups — D9×#884 #13148403

Order 1728.

1372 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D9×#67C211yesmaximal, characteristic, complemented
2C2×D9×#67C211yesmaximal, characteristic, complemented
3C2×D9×D12C211yesmaximal, characteristic, complemented
4C2×C4×D3×D9C211yesmaximal, characteristic, complemented
5#11721730C211yesmaximal, characteristic, complemented
6C9×#884C211yesmaximal, characteristic, complemented
7C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
8#11721282C211yesmaximal, characteristic, complemented
9#11721262C211yesmaximal, characteristic, complemented
10D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11721041C211yesmaximal, characteristic, complemented
12#11721034C211yesmaximal, characteristic, complemented
13#11721016C211yesmaximal, characteristic, complemented
14#11721005C211yesmaximal, characteristic, complemented
15D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
16D3×#884—31nomaximal
17D9×#121—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
24C2×C4×C3⋊D9C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic, complemented
26C2×C9×#67C2211yescharacteristic, complemented
27C2×C9×D12C2211yescharacteristic, complemented
28C2×C4×D3×C9C2211yescharacteristic, complemented
29C2×C3×C4×D9C2211yescharacteristic
30C2×C3×C4×D9C2211yescharacteristic
31D9×#67—24no—
32D9×#67—24no—
33C2×#6195C2211yescharacteristic, complemented
34C2×#6195C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic, complemented
36C2×#6194C2211yescharacteristic, complemented
37C2×D3×Dic9C2211yescharacteristic, complemented
38C2×#6192C2211yescharacteristic, complemented
39C2×#6192C2211yescharacteristic, complemented
40C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
41C2×Dic3×D9C2211yescharacteristic
42C2×Dic3×D9C2211yescharacteristic
43D9×D12—24no—
44C4×D3×D9—24no—
45C3×C9×C22⋊C4C2211yescharacteristic, complemented
46#88536C2211yescharacteristic, complemented
47#88534C2211yescharacteristic, complemented
48C3×#3676C2211yescharacteristic, complemented
49C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
51C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
52C9×Dic3⋊C4C2211yescharacteristic, complemented
53(C2×D3)⋊Dic9C2211yescharacteristic, complemented
54#88445C2211yescharacteristic, complemented
55Dic3⋊Dic9C2211yescharacteristic, complemented
56#88442C2211yescharacteristic, complemented
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×D3×D12—31no—
60C2×C4×D32—31no—
61#64093—31no—
62C3×#884D311yescharacteristic
63C3×D3×C22⋊C4—31no—
64#63971—31no—
65#63958—31no—
66D3×(C2×D3)⋊C4—31no—
67#63912—31no—
68#63910—31no—
69#63906—31no—
70#63885—31no—
71D3×Dic3⋊C4—31no—
72C2×D4×D9—31no—
73C2×D4×D9—31no—
74C2×D4×D9—31no—
75C22×C4×D9—31no—
76C9×#121—31no—
77#63501—31no—
78#63501—31no—
79#63500—31no—
80#63492—31no—
81#63457—31no—
82C4⋊C4×D9—31no—
83#63446—31no—
84#63446—31no—
85#63446—61no—
86C22⋊C4×D9—31no—
87C22⋊C4×D9D311yescharacteristic, complemented
88C23×C3×C9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×C3×D9—22no—
94C22×C3×D9—22no—
95C22×C3×D9—22no—
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C2×D3×D9—22no—
99C2×D3×D9—22no—
100C2×D3×D9—22no—
101C2×D3×D9—22no—
102C2×D3×D9—22no—
103C2×D3×D9D414yescomplemented
104C2×C3×C4×C9C2311yescharacteristic
105C2×C3×C4×C9C2311yescharacteristic
106#6233—22no—
107#6233—22no—
108C2×C3⋊Dic9C2311yescharacteristic
109C2×C3⋊Dic9C2311yescharacteristic
110C4⋊(C3⋊D9)—22no—
111C4×C3⋊D9—22no—
112C9×#67—22no—
113C9×#67—22no—
114C2×C9×Dic3C2311yescharacteristic
115C2×C9×Dic3C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C2×C3×Dic9C2311yescharacteristic
118C9×D12—22no—
119C4×D3×C9—22no—
120C3×C4×D9—22no—
121C3×C4×D9—22no—
122#6195—22no—
123#6195—22no—
124#6194—22no—
125#6194—22no—
126D3×Dic9—22no—
127#6192—22no—
128#6192—22no—
129(C3⋊D9)⋊C4—22no—
130Dic3×D9—22no—
131Dic3×D9D414yescomplemented
132D3×#121—91no—
133C2×#884—91no—
134C23×C3×D3—31no—
135C22×D32—31no—
136C22×D32—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4×C3⋊D3—31no—
141C2×C3×#67C2×D311yescharacteristic
142C2×C3×#67C2×D311yescharacteristic
143C2×C3×D12C2×D311yescharacteristic
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3C2×D311yescharacteristic
147D3×#67—64no—
148D3×#67—64no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#625—31no—
154C2×#625—31no—
155C2×#624—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159D3×D12—64no—
160C4×D32—64no—
161C23×D9—31no—
162C23×D9—31no—
163C23×D9C2×D311yescharacteristic
164C32×C22⋊C4C2×D311yescharacteristic
165#3752—31no—
166#3750—31no—
167C3×#217—31no—
168C3×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4C2×D311yescharacteristic
171C3×Dic3⋊C4C2×D311yescharacteristic
172#3724—31no—
173Dic3⋊Dic3—31no—
174#3722—31no—
175(C2×D3)⋊Dic3—31no—
176C2×D4×C9—31no—
177C2×D4×C9—31no—
178C2×D4×C9—31no—
179C22×C4×C9—31no—
180C2×#611—31no—
181C2×#611—31no—
182C2×#611—31no—
183C2×#611—31no—
184C2×#611—31no—
185C2×#611—31no—
186C2×#611—61no—
187C2×#611—61no—
188C22×Dic9—31no—
189D4×D9—64no—
190D4×D9—64no—
191D4×D9—64no—
192C2×D36—31no—
193C2×D36—31no—
194C2×D36—31no—
195C2×D36—61no—
196C2×C4×D9—31no—
197C2×C4×D9—31no—
198C2×C4×D9—31no—
199C2×C4×D9—31no—
200C2×C4×D9—64no—
201C2×C4×D9—61no—
202C2×C4×D9C2×D311yescharacteristic
203C2×C4×D9C2×D311yescharacteristic
204C9×C4⋊C4—31no—
205C9×C22⋊C4—21no—
206C9×C22⋊C4—31no—
207C9×C22⋊C4C2×D311yescharacteristic, complemented
208#3676—31no—
209#3676C2×D311yescharacteristic, complemented
210(C2×D9)⋊C4—31no—
211(C2×D9)⋊C4—31no—
212(C2×D9)⋊C4—61no—
213(C2×D9)⋊C4C2×D311yescharacteristic, complemented
214(C2×D9)⋊C4C2×D311yescharacteristic, complemented
215C4⋊Dic9—31no—
216Dic9⋊C4—31no—
217Dic9⋊C4—31no—
218Dic9⋊C4—61no—
219C22×C3×C9—21no—
220C22×C3×C9—21no—
221C22×C3×C9—21no—
222C22×C3×C9C2411yescharacteristic
223C2×C3⋊D9—21no—
224C2×C3⋊D9—21no—
225C2×C3⋊D9—21no—
226C2×C3⋊D9—21no—
227C2×C3⋊D9—21no—
228C2×C3⋊D9C2×D412yescomplemented
229C2×D3×C9—21no—
230C2×D3×C9—21no—
231C2×D3×C9—21no—
232C2×D3×C9—21no—
233C2×D3×C9—21no—
234C2×D3×C9C2×D412yescomplemented
235C2×C3×D9—21no—
236C2×C3×D9—21no—
237C2×C3×D9—21no—
238C2×C3×D9—44no—
239C2×C3×D9C2×D412yes—
240C2×C3×D9C2×D412yes—
241C2×C3×D9#4112yes—
242D3×D9—28no—
243D3×D9—44no—
244C3×C4×C9—21no—
245C3×C4×C9—21no—
246C3⋊Dic9—21no—
247C3⋊Dic9C2×D412yescomplemented
248C9×Dic3—21no—
249C9×Dic3C2×D412yescomplemented
250C3×Dic9—21no—
251C3×Dic9—21no—
252C22×#67—91no—
253C22×#67—91no—
254C2×D3×D4—91no—
255C2×D3×D4—91no—
256C2×D3×D4—91no—
257C22×D12—91no—
258C22×C4×D3—91no—
259C22×C4×D3—91no—
260C3×#121—31no—
261C2×C3×C22⋊C4—91no—
262#939—91no—
263#939—91no—
264#938—91no—
265#930—91no—
266C2×(C2×D3)⋊C4—91no—
267C2×Dic3⋊C4—91no—
268#895—91no—
269D3×C4⋊C4—91no—
270#884—91no—
271#884—91no—
272#884—91no—
273#884—91no—
274#884—91no—
275#884—91no—
276#884—91no—
277#884—91no—
278#884—91no—
279#884—181no—
280#884D911yescharacteristic, direct product factor
281D3×C22⋊C4—31no—
282D3×C22⋊C4—91no—
283C23×C32C22×D311yescharacteristic
284C22×C3⋊D3—31no—
285C22×C3⋊D3—31no—
286C22×C3×D3—31no—
287C22×C3×D3—31no—
288C22×C3×D3—62no—
289C22×C3×D3—62no—
290C22×C3×D3—62no—
291C22×C3×D3C22×D311yescharacteristic
292C22×C3×D3C22×D311yescharacteristic
293C2×D32—34no—
294C2×D32—62no—
295C2×D32—62no—
296C2×D32—62no—
297C2×D32—62no—
298C2×D32—62no—
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301#638—62no—
302#638—62no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—31no—
305C4⋊(C3⋊D3)—62no—
306C4×C3⋊D3—62no—
307C3×#67—22no—
308C3×#67—22no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3C22×D311yescharacteristic
312C2×C3×Dic3C22×D311yescharacteristic
313C3×D12—22no—
314C3×C4×D3—22no—
315C3×C4×D3—62no—
316C3×C4×D3—62no—
317#626—62no—
318#626—62no—
319#626—62no—
320#626—62no—
321#625—62no—
322#625—62no—
323#624—62no—
324D3×Dic3—34no—
325D3×Dic3—62no—
326D3×Dic3—62no—
327C23×C9—21no—
328C23×C9—31no—
329C23×C9—31no—
330C23×C9C22×D311yescharacteristic
331C22×D9—22no—
332C22×D9—22no—
333C22×D9—22no—
334C22×D9—31no—
335C22×D9—34no—
336C22×D9—31no—
337C22×D9—61no—
338C22×D9—61no—
339C22×D9—62no—
340C22×D9—62no—
341C22×D9—62no—
342C22×D9—62no—
343C22×D9—62no—
344C22×D9C22×D311yescharacteristic
345C22×D9C22×D311yescharacteristic
346D4×C9—62no—
347D4×C9—62no—
348D4×C9—62no—
349C2×C4×C9—21no—
350C2×C4×C9—21no—
351C2×C4×C9—31no—
352C2×C4×C9—31no—
353C2×C4×C9—62no—
354C2×C4×C9C22×D311yescharacteristic
355C2×C4×C9C22×D311yescharacteristic
356#611—62no—
357#611—62no—
358#611—62no—
359#611—62no—
360#611—62no—
361#611—62no—
362#611—122no—
363#611—122no—
364C2×Dic9—31no—
365C2×Dic9—31no—
366C2×Dic9—61no—
367C2×Dic9—61no—
368C2×Dic9—62no—
369C2×Dic9C22×D311yescharacteristic
370C2×Dic9C22×D311yescharacteristic
371D36—62no—
372D36—62no—
373D36—62no—
374D36—122no—
375C4×D9—22no—
376C4×D9—22no—
377C4×D9—34no—
378C4×D9—62no—
379C4×D9—62no—
380C4×D9—62no—
381C4×D9—122no—
382C2×#121—271noSylow
383C2×C3×C9—41no—
384C2×C3×C9C22×D411yescharacteristic
385C2×C3×C9C22×D411yescharacteristic
386C2×C3×C9C2×#4111yescharacteristic
387C3⋊D9—22no—
388C3⋊D9—41no—
389D3×C9—22no—
390D3×C9—41no—
391C3×D9—41no—
392C3×D9#12114yescomplemented
393C24×C3—91no—
394C23×D3—31no—
395C23×D3—91no—
396C23×D3—91no—
397C23×D3—91no—
398C23×D3—91no—
399C2×C3×D4—31no—
400C2×C3×D4—31no—
401C2×C3×D4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—91no—
404C22×C3×C4—91no—
405C2×#67—91no—
406C2×#67—91no—
407C2×#67—91no—
408C2×#67—91no—
409C2×#67—91no—
410C2×#67—91no—
411C2×#67—91no—
412C2×#67—91no—
413C2×#67—91no—
414C2×#67—91no—
415C2×#67—91no—
416C2×#67—91no—
417C2×#67—181no—
418C2×#67—181no—
419C2×#67—184no—
420C2×#67—184no—
421C2×#67C2×D911yescharacteristic, complemented
422C2×#67C2×D911yescharacteristic, complemented
423C22×Dic3—91no—
424C22×Dic3—91no—
425C22×Dic3—91no—
426D3×D4—184no—
427D3×D4—184no—
428D3×D4—184no—
429C2×D12—91no—
430C2×D12—91no—
431C2×D12—91no—
432C2×D12—91no—
433C2×D12—91no—
434C2×D12—91no—
435C2×D12—181no—
436C2×D12—184no—
437C2×D12C2×D911yescharacteristic, complemented
438C2×C4×D3—31no—
439C2×C4×D3—31no—
440C2×C4×D3—91no—
441C2×C4×D3—91no—
442C2×C4×D3—91no—
443C2×C4×D3—91no—
444C2×C4×D3—91no—
445C2×C4×D3—91no—
446C2×C4×D3—91no—
447C2×C4×D3—181no—
448C2×C4×D3—184no—
449C2×C4×D3—184no—
450C2×C4×D3C2×D911yescharacteristic, complemented
451C3×C4⋊C4—31no—
452C3×C22⋊C4—21no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4C2×D911yescharacteristic, complemented
458C3×C22⋊C4D3211yescharacteristic
459#217—31no—
460#217—91no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—91no—
464(C2×D3)⋊C4—91no—
465(C2×D3)⋊C4—91no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—181no—
469(C2×D3)⋊C4C2×D911yescharacteristic, complemented
470C4⋊Dic3—91no—
471Dic3⋊C4—91no—
472Dic3⋊C4—91no—
473Dic3⋊C4—91no—
474Dic3⋊C4—91no—
475Dic3⋊C4—91no—
476Dic3⋊C4—181no—
477Dic3⋊C4C2×D911yescharacteristic, complemented
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32C23×D311yescharacteristic
482C2×C3⋊D3—32no—
483C2×C3⋊D3—61no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—61no—
487C2×C3⋊D3—61no—
488C2×C3×D3—21no—
489C2×C3×D3—21no—
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—21no—
493C2×C3×D3—32no—
494C2×C3×D3—32no—
495C2×C3×D3—32no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—124no—
500C2×C3×D3D3×D412yes—
501D32—68no—
502D32—124no—
503C32×C4—21no—
504C32×C4—21no—
505C3⋊Dic3—32no—
506C3⋊Dic3—61no—
507C3×Dic3—21no—
508C3×Dic3—61no—
509C3×Dic3—61no—
510C3×Dic3D3×D412yes—
511C22×C9—21no—
512C22×C9—21no—
513C22×C9—21no—
514C22×C9—21no—
515C22×C9—32no—
516C22×C9—41no—
517C22×C9—41no—
518C22×C9—41no—
519C22×C9—61no—
520C22×C9—61no—
521C22×C9—61no—
522C22×C9—61no—
523C22×C9—61no—
524C22×C9C23×D311yescharacteristic
525C2×D9—21no—
526C2×D9—21no—
527C2×D9—21no—
528C2×D9—32no—
529C2×D9—44no—
530C2×D9—62no—
531C2×D9—61no—
532C2×D9—61no—
533C2×D9—68no—
534C2×D9—61no—
535C2×D9—61no—
536C2×D9—61no—
537C2×D9—121no—
538C2×D9—121no—
539C2×D9—121no—
540C2×D9—121no—
541C2×D9—121no—
542C2×D9—124no—
543C2×D9#23512yes—
544C2×D9D3×D412yes—
545C2×D9D3×D412yes—
546C4×C9—21no—
547C4×C9—21no—
548C4×C9—32no—
549C4×C9—41no—
550C4×C9—41no—
551C4×C9—61no—
552Dic9—21no—
553Dic9—21no—
554Dic9—32no—
555Dic9—62no—
556Dic9—61no—
557Dic9—121no—
558C22×D4—271no—
559C22×D4—271no—
560C22×D4—271no—
561C23×C4—271no—
562#121—31no—
563#121—271no—
564#121—271no—
565#121—271no—
566#121—271no—
567#121—271no—
568#121—271no—
569#121—271no—
570C2×C4⋊C4—271no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—271no—
573C3×C9C2×#12111yescharacteristic, complemented, Sylow
574C23×C3—21no—
575C23×C3—31no—
576C23×C3—31no—
577C23×C3—91no—
578C23×C3—91no—
579C23×C3—182no—
580C23×C3—182no—
581C23×C3—182no—
582C23×C3C22×D911yescharacteristic
583C23×C3C2×D3211yescharacteristic
584C22×D3—31no—
585C22×D3—31no—
586C22×D3—62no—
587C22×D3—62no—
588C22×D3—62no—
589C22×D3—94no—
590C22×D3—91no—
591C22×D3—91no—
592C22×D3—94no—
593C22×D3—91no—
594C22×D3—91no—
595C22×D3—181no—
596C22×D3—181no—
597C22×D3—182no—
598C22×D3—182no—
599C22×D3—182no—
600C22×D3—182no—
601C22×D3—182no—
602C22×D3—182no—
603C22×D3—182no—
604C22×D3—182no—
605C22×D3—182no—
606C22×D3—182no—
607C22×D3C22×D911yescharacteristic
608C22×D3C22×D911yescharacteristic
609C3×D4—62no—
610C3×D4—62no—
611C3×D4—62no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—31no—
615C2×C3×C4—31no—
616C2×C3×C4—62no—
617C2×C3×C4—91no—
618C2×C3×C4—91no—
619C2×C3×C4—182no—
620C2×C3×C4—182no—
621C2×C3×C4C22×D911yescharacteristic
622C2×C3×C4C22×D911yescharacteristic
623C2×C3×C4C2×D3211yescharacteristic
624C2×C3×C4C2×D3211yescharacteristic
625#67—22no—
626#67—22no—
627#67—182no—
628#67—182no—
629#67—182no—
630#67—182no—
631#67—182no—
632#67—182no—
633#67—182no—
634#67—182no—
635#67—182no—
636#67—182no—
637#67—182no—
638#67—182no—
639#67—362no—
640#67—362no—
641C2×Dic3—31no—
642C2×Dic3—31no—
643C2×Dic3—91no—
644C2×Dic3—91no—
645C2×Dic3—94no—
646C2×Dic3—91no—
647C2×Dic3—91no—
648C2×Dic3—181no—
649C2×Dic3—181no—
650C2×Dic3—182no—
651C2×Dic3—182no—
652C2×Dic3C22×D911yescharacteristic
653C2×Dic3C22×D911yescharacteristic
654D12—22no—
655D12—182no—
656D12—182no—
657D12—182no—
658D12—182no—
659D12—182no—
660D12—182no—
661D12—362no—
662C4×D3—22no—
663C4×D3—62no—
664C4×D3—62no—
665C4×D3—94no—
666C4×D3—182no—
667C4×D3—182no—
668C4×D3—182no—
669C4×D3—182no—
670C4×D3—182no—
671C4×D3—182no—
672C4×D3—362no—
673C2×C32—41no—
674C2×C32C2×D3×D411yescharacteristic
675C2×C32C2×D3×D411yescharacteristic
676C2×C32D3×#4111yescharacteristic
677C3⋊D3—62no—
678C3⋊D3—121no—
679C3×D3—22no—
680C3×D3—34no—
681C3×D3—41no—
682C3×D3—121no—
683C2×C9—21no—
684C2×C9—21no—
685C2×C9—21no—
686C2×C9—41no—
687C2×C9—62no—
688C2×C9—81no—
689C2×C9—121no—
690C2×C9C2×#23511yescharacteristic
691C2×C9C2×D3×D411yescharacteristic
692C2×C9C2×D3×D411yescharacteristic
693D9—41no—
694D9—62no—
695D9—122no—
696D9—121no—
697D9—241no—
698D9#88414yesdirect product factor
699C24—91no—
700C24—271no—
701C24—271no—
702C2×D4—31no—
703C2×D4—31no—
704C2×D4—31no—
705C2×D4—271no—
706C2×D4—271no—
707C2×D4—271no—
708C2×D4—271no—
709C2×D4—271no—
710C2×D4—271no—
711C2×D4—271no—
712C2×D4—271no—
713C2×D4—271no—
714C2×D4—544no—
715C2×D4—544no—
716C2×D4—544no—
717C22×C4—31no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—271no—
721C22×C4—271no—
722C22×C4—271no—
723C22×C4—271no—
724C22×C4—271no—
725C22×C4—544no—
726C4⋊C4—31no—
727C4⋊C4—271no—
728C4⋊C4—271no—
729C4⋊C4—271no—
730C22⋊C4—31no—
731C22⋊C4—91no—
732C22⋊C4—91no—
733C22⋊C4—91no—
734C22⋊C4—271no—
735C22⋊C4—271no—
736C22⋊C4—271no—
737C22⋊C4D3×D911yescharacteristic, complemented
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—32no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—92no—
755C22×C3—92no—
756C22×C3—92no—
757C22×C3—181no—
758C22×C3—181no—
759C22×C3—181no—
760C22×C3—364no—
761C22×C3C23×D911yescharacteristic
762C22×C3C22×D3211yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—32no—
769C2×D3—32no—
770C2×D3—32no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—92no—
775C2×D3—92no—
776C2×D3—124no—
777C2×D3—182no—
778C2×D3—188no—
779C2×D3—188no—
780C2×D3—181no—
781C2×D3—181no—
782C2×D3—181no—
783C2×D3—181no—
784C2×D3—181no—
785C2×D3—181no—
786C2×D3—181no—
787C2×D3—181no—
788C2×D3—181no—
789C2×D3—181no—
790C2×D3—361no—
791C2×D3—361no—
792C2×D3—361no—
793C2×D3—361no—
794C2×D3—361no—
795C2×D3—364no—
796C2×D3—364no—
797C2×D3D4×D912yescomplemented
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—32no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—61no—
806C3×C4—181no—
807C3×C4—181no—
808Dic3—21no—
809Dic3—61no—
810Dic3—61no—
811Dic3—92no—
812Dic3—92no—
813Dic3—182no—
814Dic3—181no—
815Dic3—181no—
816Dic3—361no—
817Dic3D4×D912yescomplemented
818C32D3×#12111yescharacteristic
819C9—21no—
820C9C2×#88411yescharacteristic, complemented
821C23—31no—
822C23—31no—
823C23—91no—
824C23—91no—
825C23—182no—
826C23—182no—
827C23—182no—
828C23—274no—
829C23—271no—
830C23—271no—
831C23—542no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23—542no—
836C23C2×D3×D911yescharacteristic
837D4—62no—
838D4—62no—
839D4—62no—
840D4—542no—
841D4—542no—
842D4—542no—
843D4—542no—
844D4—542no—
845D4—542no—
846D4—542no—
847D4—542no—
848D4—542no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—62no—
852C2×C4—91no—
853C2×C4—91no—
854C2×C4—182no—
855C2×C4—182no—
856C2×C4—274no—
857C2×C4—271no—
858C2×C4—271no—
859C2×C4—542no—
860C2×C4—542no—
861C2×C4—542no—
862C2×C4—542no—
863C2×C4C2×D3×D911yescharacteristic
864C2×C4C2×D3×D911yescharacteristic
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—41no—
869C2×C3—41no—
870C2×C3—62no—
871C2×C3—81no—
872C2×C3—94no—
873C2×C3—121no—
874C2×C3—361no—
875C2×C3C2×D4×D911yescharacteristic
876C2×C3C2×D4×D911yescharacteristic
877C2×C3#41×D911yescharacteristic
878C2×C3D3×#23511yescharacteristic
879C2×C3D32×D411yescharacteristic
880C2×C3D32×D411yescharacteristic
881D3—22no—
882D3—34no—
883D3—41no—
884D3—121no—
885D3—182no—
886D3—182no—
887D3—362no—
888D3—361no—
889D3—361no—
890D3—721no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—32no—
895C22—61no—
896C22—61no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—92no—
901C22—92no—
902C22—92no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—272no—
907C22—364no—
908C22—548no—
909C22—541no—
910C22—541no—
911C22—541no—
912C22—541no—
913C22—541no—
914C22—1084no—
915C22C22×D3×D911yescharacteristic
916C4—21no—
917C4—21no—
918C4—32no—
919C4—61no—
920C4—181no—
921C4—181no—
922C4—272no—
923C4—541no—
924C3—21no—
925C3D9×#12111yescharacteristic, complemented
926C3D3×#88411yescharacteristic
927C2—41no—
928C2—62no—
929C2—94no—
930C2—121no—
931C2—361no—
932C2—542no—
933C2—1081no—
934C2D9×#23511yescharacteristic
935C2D3×D4×D911yescharacteristic
936C2D3×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×C9C2×#121
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×D9×#67C2semidirect
2. C2×D9×#67C2semidirect
3. C2×D9×D12C2semidirect
4. C2×C4×D3×D9C2semidirect
5. #11721730C2semidirect
6. C9×#884C2semidirect
7. C3×C22⋊C4×D9C2semidirect
8. #11721282C2semidirect
9. #11721262C2semidirect
10. D9×(C2×D3)⋊C4C2semidirect
11. #11721041C2semidirect
12. #11721034C2semidirect
13. #11721016C2semidirect
14. #11721005C2semidirect
15. D9×Dic3⋊C4C2semidirect
21. C2×#6233C22semidirect
22. C2×#6233C22semidirect
23. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C4×C3⋊D9C22semidirect
25. C2×C9×#67C22semidirect
26. C2×C9×#67C22semidirect
27. C2×C9×D12C22semidirect
28. C2×C4×D3×C9C22semidirect
33. C2×#6195C22semidirect
34. C2×#6195C22semidirect
35. C2×#6194C22semidirect
36. C2×#6194C22semidirect
37. C2×D3×Dic9C22semidirect
38. C2×#6192C22semidirect
39. C2×#6192C22semidirect
40. C2×(C3⋊D9)⋊C4C22semidirect
45. C3×C9×C22⋊C4C22semidirect
46. #88536C22semidirect
47. #88534C22semidirect
48. C3×#3676C22semidirect
49. C9×(C2×D3)⋊C4C22semidirect
50. C3×(C2×D9)⋊C4C22semidirect
51. C3×(C2×D9)⋊C4C22semidirect
52. C9×Dic3⋊C4C22semidirect
53. (C2×D3)⋊Dic9C22semidirect
54. #88445C22semidirect
55. Dic3⋊Dic9C22semidirect
56. #88442C22semidirect
87. C22⋊C4×D9D3semidirect
103. C2×D3×D9D4semidirect
131. Dic3×D9D4semidirect
207. C9×C22⋊C4C2×D3semidirect
209. #3676C2×D3semidirect
213. (C2×D9)⋊C4C2×D3semidirect
214. (C2×D9)⋊C4C2×D3semidirect
228. C2×C3⋊D9C2×D4semidirect
234. C2×D3×C9C2×D4semidirect
247. C3⋊Dic9C2×D4semidirect
249. C9×Dic3C2×D4semidirect
280. #884D9direct (N × H)
392. C3×D9#121semidirect
421. C2×#67C2×D9semidirect
422. C2×#67C2×D9semidirect
437. C2×D12C2×D9semidirect
450. C2×C4×D3C2×D9semidirect
457. C3×C22⋊C4C2×D9semidirect
469. (C2×D3)⋊C4C2×D9semidirect
477. Dic3⋊C4C2×D9semidirect
573. C3×C9C2×#121semidirect
698. D9#884direct (N × H)
737. C22⋊C4D3×D9semidirect
797. C2×D3D4×D9semidirect
817. Dic3D4×D9semidirect
820. C9C2×#884semidirect
925. C3D9×#121semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×D9×D122
C2×C4×D3×D92
#117217302
C9×#8842
C3×C22⋊C4×D92
#117212822
#117212622
D9×(C2×D3)⋊C42
#117210412
#117210342
#117210162
#117210052
D9×Dic3⋊C42
D3×#8843
D9×#1213