Finite Group Databasebeta

← D9×#939 #13150958

Subgroups — D9×#939 #13150958

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×C3×D4×D9C211yesmaximal, characteristic, complemented
2C2×D9×#67C211yesmaximal, characteristic, complemented
3C2×D9×#67C211yesmaximal, characteristic, complemented
4C22×Dic3×D9C211yesmaximal, characteristic, complemented
5#11721839C211yesmaximal, characteristic, complemented
6C9×#939C211yesmaximal, characteristic, complemented
7#11721290C211yesmaximal, characteristic, complemented
8#11721277C211yesmaximal, characteristic, complemented
9#11721271C211yesmaximal, characteristic, complemented
10#11721270C211yesmaximal, characteristic, complemented
11D9×#217C211yesmaximal, characteristic, complemented
12D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#11720983C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
16D3×#939—31nomaximal
17D9×#121—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic
21C2×C3×D4×C9C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×#6233C2211yescharacteristic, complemented
24C22×C3⋊Dic9C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic, complemented
26C2×C9×#67C2211yescharacteristic, complemented
27C2×C3×#611C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic, complemented
29C22×C9×Dic3C2211yescharacteristic, complemented
30C3×D4×D9—24no—
31C2×C3×D36C2211yescharacteristic, complemented
32C2×C3×C4×D9C2211yescharacteristic
33D9×#67—24no—
34D9×#67—24no—
35C2×#6194C2211yescharacteristic, complemented
36C2×#6194C2211yescharacteristic, complemented
37C2×#6192C2211yescharacteristic, complemented
38C2×#6192C2211yescharacteristic, complemented
39C2×Dic3×D9—24no—
40C2×Dic3×D9C2211yescharacteristic
41C2×Dic3×D9C2211yescharacteristic
42C2×Dic3×D9C2211yescharacteristic
43C2×Dic3×D9C2211yescharacteristic, complemented
44C2×Dic3×D9C2211yescharacteristic, complemented
45#88551C2211yescharacteristic, complemented
46#88536C2211yescharacteristic, complemented
47#88534C2211yescharacteristic, complemented
48C9×#217C2211yescharacteristic, complemented
49C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C9×Dic3⋊C4C2211yescharacteristic, complemented
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54(C2×D9)⋊Dic3C2211yescharacteristic, complemented
55Dic3⋊Dic9C2211yescharacteristic, complemented
56#88442C2211yescharacteristic, complemented
57C2×C3×D3×D4—31no—
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C22×D3×Dic3—31no—
61#64148—31no—
62C3×#939D311yescharacteristic
63#63980—31no—
64#63978—31no—
65#63971—31no—
66#63970—31no—
67D3×#217—31no—
68D3×(C2×D3)⋊C4—31no—
69#63886—31no—
70#63885—31no—
71D3×Dic3⋊C4—31no—
72C2×D4×D9—31no—
73C2×D4×D9—31no—
74C2×D4×D9D311yescharacteristic, complemented
75C22×C4×D9—31no—
76C9×#121—31no—
77#63501—31no—
78#63501—31no—
79#63501—61no—
80#63500—31no—
81#63492—31no—
82#63457—31no—
83C4⋊C4×D9—31no—
84#63446—31no—
85#63446—31no—
86C22⋊C4×D9—31no—
87C22⋊C4×D9—31no—
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×C3×D9—22no—
93C22×C3×D9—22no—
94C22×C3×D9—22no—
95C22×C3×D9—22no—
96C22×C3×D9—22no—
97C22×C3×D9D414yescomplemented
98C22×C3×D9C2311yescharacteristic
99C22×C3×D9C2311yescharacteristic
100C22×C3×D9C2311yescharacteristic
101C2×D3×D9—22no—
102C2×D3×D9—22no—
103C2×D3×D9—22no—
104C3×D4×C9—22no—
105C2×C3×C4×C9C2311yescharacteristic
106#6233—22no—
107#6233—22no—
108C2×C3⋊Dic9—22no—
109C2×C3⋊Dic9C2311yescharacteristic
110C2×C3⋊Dic9C2311yescharacteristic
111C2×C3⋊Dic9C2311yescharacteristic
112C9×#67—22no—
113C9×#67—22no—
114C3×#611—22no—
115C3×#611—22no—
116C2×C9×Dic3—22no—
117C2×C9×Dic3C2311yescharacteristic
118C2×C9×Dic3C2311yescharacteristic
119C2×C9×Dic3C2311yescharacteristic
120C2×C3×Dic9C2311yescharacteristic
121C3×D36—22no—
122C3×C4×D9—22no—
123#6194—22no—
124#6194—22no—
125#6192—22no—
126#6192—22no—
127Dic3×D9—22no—
128Dic3×D9—22no—
129Dic3×D9—22no—
130Dic3×D9—22no—
131Dic3×D9D414yescomplemented
132C2×#939—91no—
133D3×#121—91no—
134C23×C3×D3—31no—
135C23×C3×D3—31no—
136C22×D32—31no—
137C2×C32×D4C2×D311yescharacteristic
138C2×#638—31no—
139C2×#638—31no—
140C22×C3⋊Dic3—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67C2×D311yescharacteristic
144C2×C3×#67C2×D311yescharacteristic
145C22×C3×Dic3C2×D311yescharacteristic
146C3×D3×D4—64no—
147C2×C3×D12—31no—
148C2×C3×C4×D3—31no—
149D3×#67—64no—
150D3×#67—64no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#625—31no—
154C2×#625—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—64no—
161C23×D9—31no—
162C23×D9C2×D311yescharacteristic
163C23×D9C2×D311yescharacteristic
164#3757—31no—
165#3752—31no—
166#3750—31no—
167C3×#217C2×D311yescharacteristic
168C3×(C2×D3)⋊C4C2×D311yescharacteristic
169C3×Dic3⋊C4C2×D311yescharacteristic
170#3724—31no—
171Dic3⋊Dic3—31no—
172#3722—31no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176C2×D4×C9—21no—
177C2×D4×C9—31no—
178C2×D4×C9—31no—
179C2×D4×C9C2×D311yescharacteristic, complemented
180C22×C4×C9—31no—
181C2×#611—31no—
182C2×#611—31no—
183C2×#611—31no—
184C2×#611—31no—
185C2×#611—61no—
186C2×#611—61no—
187C2×#611C2×D311yescharacteristic, complemented
188C2×#611C2×D311yescharacteristic, complemented
189C22×Dic9—31no—
190C22×Dic9—61no—
191D4×D9—24no—
192D4×D9—64no—
193D4×D9—64no—
194C2×D36—31no—
195C2×D36—31no—
196C2×D36C2×D311yescharacteristic, complemented
197C2×C4×D9—31no—
198C2×C4×D9—31no—
199C2×C4×D9—31no—
200C2×C4×D9—31no—
201C2×C4×D9—31no—
202C2×C4×D9—64no—
203C2×C4×D9C2×D311yescharacteristic
204C9×C4⋊C4—31no—
205C9×C22⋊C4—31no—
206C9×C22⋊C4—31no—
207#3676—31no—
208#3676—31no—
209#3676—61no—
210(C2×D9)⋊C4—31no—
211(C2×D9)⋊C4—31no—
212(C2×D9)⋊C4—31no—
213(C2×D9)⋊C4—31no—
214(C2×D9)⋊C4—61no—
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×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×D3×C9—21no—
230C2×D3×C9—21no—
231C2×D3×C9—21no—
232C2×C3×D9—21no—
233C2×C3×D9—21no—
234C2×C3×D9—28no—
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×D9C2×D412yescomplemented
242C2×C3×D9#4112yes—
243D3×D9—44no—
244C3×C4×C9—21no—
245C3⋊Dic9—21no—
246C3⋊Dic9—21no—
247C3⋊Dic9C2×D412yescomplemented
248C9×Dic3—21no—
249C9×Dic3—21no—
250C9×Dic3C2×D412yescomplemented
251C3×Dic9—21no—
252C22×C3×D4—91no—
253C22×#67—91no—
254C22×#67—91no—
255C23×Dic3—91no—
256C2×D3×D4—31no—
257C2×D3×D4—91no—
258C2×D3×D4—91no—
259C22×C4×D3—91no—
260C3×#121—31no—
261C2×#217—91no—
262#939—91no—
263#939—91no—
264#939—91no—
265#939—91no—
266#939—91no—
267#939—91no—
268#939—91no—
269#939—91no—
270#939—91no—
271#939—181no—
272#939D911yescharacteristic, direct product factor
273#938—91no—
274#930—91no—
275C2×(C2×D3)⋊C4—91no—
276C2×Dic3⋊C4—91no—
277#895—91no—
278D3×C4⋊C4—91no—
279#884—91no—
280#884—91no—
281D3×C22⋊C4—91no—
282D3×C22⋊C4—91no—
283C23×C32C22×D311yescharacteristic
284C23×C32C22×D311yescharacteristic
285C22×C3⋊D3—31no—
286C22×C3×D3—31no—
287C22×C3×D3—34no—
288C22×C3×D3—31no—
289C22×C3×D3—31no—
290C22×C3×D3—62no—
291C22×C3×D3—62no—
292C22×C3×D3—62no—
293C22×C3×D3—62no—
294C22×C3×D3—62no—
295C22×C3×D3C22×D311yescharacteristic
296C2×D32—62no—
297C2×D32—62no—
298C2×D32—62no—
299C32×D4—22no—
300C2×C32×C4C22×D311yescharacteristic
301#638—62no—
302#638—62no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—31no—
305C2×C3⋊Dic3—31no—
306C2×C3⋊Dic3—62no—
307C3×#67—22no—
308C3×#67—22no—
309C3×#67—62no—
310C3×#67—62no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3C22×D311yescharacteristic
314C2×C3×Dic3C22×D311yescharacteristic
315C2×C3×Dic3C22×D311yescharacteristic
316C3×D12—62no—
317C3×C4×D3—62no—
318#626—62no—
319#626—62no—
320#625—62no—
321#625—62no—
322D3×Dic3—34no—
323D3×Dic3—62no—
324D3×Dic3—62no—
325D3×Dic3—62no—
326D3×Dic3—62no—
327C23×C9—21no—
328C23×C9—21no—
329C23×C9—31no—
330C23×C9C22×D311yescharacteristic
331C23×C9C22×D311yescharacteristic
332C22×D9—22no—
333C22×D9—22no—
334C22×D9—22no—
335C22×D9—22no—
336C22×D9—22no—
337C22×D9—31no—
338C22×D9—61no—
339C22×D9—62no—
340C22×D9—62no—
341C22×D9—62no—
342C22×D9#6714yescomplemented
343C22×D9C22×D311yescharacteristic
344C22×D9C22×D311yescharacteristic
345C22×D9C22×D311yescharacteristic
346D4×C9—22no—
347D4×C9—42no—
348D4×C9—62no—
349D4×C9—62no—
350C2×C4×C9—21no—
351C2×C4×C9—31no—
352C2×C4×C9—31no—
353C2×C4×C9—31no—
354C2×C4×C9—62no—
355C2×C4×C9C22×D311yescharacteristic
356#611—22no—
357#611—22no—
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—31no—
367C2×Dic9—61no—
368C2×Dic9—61no—
369C2×Dic9—61no—
370C2×Dic9—62no—
371C2×Dic9—122no—
372C2×Dic9C22×D311yescharacteristic
373D36—22no—
374D36—62no—
375D36—62no—
376C4×D9—22no—
377C4×D9—34no—
378C4×D9—62no—
379C4×D9—62no—
380C4×D9—62no—
381C4×D9—62no—
382C2×#121—271noSylow
383C2×C3×C9—22no—
384C2×C3×C9—41no—
385C2×C3×C9C22×D411yescharacteristic
386C2×C3×C9C22×D411yescharacteristic
387C2×C3×C9C2×#4111yescharacteristic
388C3⋊D9—41no—
389D3×C9—41no—
390C3×D9—22no—
391C3×D9—41no—
392C3×D9#12114yescomplemented
393C24×C3—91no—
394C24×C3—91no—
395C23×D3—31no—
396C23×D3—31no—
397C23×D3—91no—
398C23×D3—91no—
399C2×C3×D4—21no—
400C2×C3×D4—31no—
401C2×C3×D4—31no—
402C2×C3×D4—91no—
403C2×C3×D4—91no—
404C2×C3×D4—91no—
405C2×C3×D4—184no—
406C2×C3×D4C2×D911yescharacteristic, complemented
407C2×C3×D4D3211yescharacteristic
408C22×C3×C4—31no—
409C22×C3×C4—91no—
410C2×#67—31no—
411C2×#67—31no—
412C2×#67—91no—
413C2×#67—91no—
414C2×#67—91no—
415C2×#67—91no—
416C2×#67—91no—
417C2×#67—91no—
418C2×#67—91no—
419C2×#67—91no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—181no—
423C2×#67—181no—
424C2×#67—184no—
425C2×#67—184no—
426C2×#67C2×D911yescharacteristic, complemented
427C2×#67C2×D911yescharacteristic, complemented
428C22×Dic3—91no—
429C22×Dic3—91no—
430C22×Dic3—91no—
431C22×Dic3—91no—
432C22×Dic3—91no—
433C22×Dic3—91no—
434C22×Dic3—91no—
435C22×Dic3—181no—
436C22×Dic3—184no—
437C22×Dic3C2×D911yescharacteristic, complemented
438D3×D4—64no—
439D3×D4—184no—
440D3×D4—184no—
441C2×D12—31no—
442C2×D12—91no—
443C2×D12—91no—
444C2×C4×D3—31no—
445C2×C4×D3—91no—
446C2×C4×D3—91no—
447C2×C4×D3—91no—
448C2×C4×D3—91no—
449C2×C4×D3—91no—
450C2×C4×D3—184no—
451C3×C4⋊C4—31no—
452C3×C22⋊C4—31no—
453C3×C22⋊C4—31no—
454#217—91no—
455#217—91no—
456#217—91no—
457#217—91no—
458#217—91no—
459#217—181no—
460#217C2×D911yescharacteristic, complemented
461(C2×D3)⋊C4—91no—
462(C2×D3)⋊C4—91no—
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×C32—21no—
482C22×C32—21no—
483C22×C32D3×D412yes—
484C22×C32C23×D311yescharacteristic
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—32no—
492C2×C3×D3—32no—
493C2×C3×D3—32no—
494C2×C3×D3—32no—
495C2×C3×D3—68no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—61no—
500C2×C3×D3—61no—
501C2×C3×D3—124no—
502D32—124no—
503C32×C4—21no—
504C3⋊Dic3—32no—
505C3⋊Dic3—61no—
506C3⋊Dic3—61no—
507C3×Dic3—21no—
508C3×Dic3—21no—
509C3×Dic3—61no—
510C3×Dic3D3×D412yes—
511C22×C9—21no—
512C22×C9—21no—
513C22×C9—21no—
514C22×C9—21no—
515C22×C9—21no—
516C22×C9—21no—
517C22×C9—22no—
518C22×C9—41no—
519C22×C9—41no—
520C22×C9—41no—
521C22×C9—41no—
522C22×C9—41no—
523C22×C9—61no—
524C22×C9—61no—
525C22×C9—61no—
526C22×C9C2×#6712yescomplemented
527C22×C9C23×D311yescharacteristic
528C2×D9—21no—
529C2×D9—21no—
530C2×D9—28no—
531C2×D9—21no—
532C2×D9—21no—
533C2×D9—21no—
534C2×D9—44no—
535C2×D9—61no—
536C2×D9—61no—
537C2×D9—61no—
538C2×D9—121no—
539C2×D9—121no—
540C2×D9—121no—
541C2×D9—124no—
542C2×D9D3×D412yes—
543C2×D9#23712yes—
544C2×D9C2×#6712yes—
545C2×D9C2×#6712yescomplemented
546C4×C9—21no—
547C4×C9—32no—
548C4×C9—41no—
549C4×C9—61no—
550C4×C9—61no—
551Dic9—21no—
552Dic9—32no—
553Dic9—62no—
554Dic9—61no—
555Dic9—61no—
556Dic9—121no—
557Dic9—121no—
558C22×D4—91no—
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—271no—
572C2×C22⋊C4—271no—
573C3×C9C2×#12111yescharacteristic, complemented, Sylow
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—31no—
577C23×C3—91no—
578C23×C3—94no—
579C23×C3—91no—
580C23×C3—91no—
581C23×C3—182no—
582C23×C3—182no—
583C23×C3—182no—
584C23×C3—182no—
585C23×C3—182no—
586C23×C3C22×D911yescharacteristic
587C23×C3C22×D911yescharacteristic
588C23×C3C2×D3211yescharacteristic
589C23×C3C2×D3211yescharacteristic
590C22×D3—31no—
591C22×D3—31no—
592C22×D3—34no—
593C22×D3—31no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—91no—
600C22×D3—91no—
601C22×D3—181no—
602C22×D3—182no—
603C22×D3—182no—
604C22×D3—182no—
605C22×D3—182no—
606C22×D3—182no—
607C22×D3—182no—
608C22×D3C22×D911yescharacteristic
609C3×D4—22no—
610C3×D4—22no—
611C3×D4—42no—
612C3×D4—62no—
613C3×D4—62no—
614C3×D4—182no—
615C3×D4—182no—
616C3×D4—182no—
617C2×C3×C4—21no—
618C2×C3×C4—31no—
619C2×C3×C4—31no—
620C2×C3×C4—31no—
621C2×C3×C4—62no—
622C2×C3×C4—91no—
623C2×C3×C4—182no—
624C2×C3×C4C22×D911yescharacteristic
625C2×C3×C4C2×D3211yescharacteristic
626#67—22no—
627#67—22no—
628#67—62no—
629#67—62no—
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—182no—
640#67—362no—
641#67—362no—
642C2×Dic3—22no—
643C2×Dic3—31no—
644C2×Dic3—91no—
645C2×Dic3—91no—
646C2×Dic3—94no—
647C2×Dic3—91no—
648C2×Dic3—91no—
649C2×Dic3—91no—
650C2×Dic3—91no—
651C2×Dic3—181no—
652C2×Dic3—181no—
653C2×Dic3—181no—
654C2×Dic3—182no—
655C2×Dic3—182no—
656C2×Dic3—182no—
657C2×Dic3—182no—
658C2×Dic3—182no—
659C2×Dic3—182no—
660C2×Dic3—362no—
661C2×Dic3C22×D911yescharacteristic
662C2×Dic3C22×D911yescharacteristic
663C2×Dic3C22×D911yescharacteristic
664D12—62no—
665D12—182no—
666D12—182no—
667C4×D3—62no—
668C4×D3—94no—
669C4×D3—182no—
670C4×D3—182no—
671C4×D3—182no—
672C4×D3—182no—
673C2×C32—22no—
674C2×C32—41no—
675C2×C32C2×D3×D411yescharacteristic
676C2×C32C2×D3×D411yescharacteristic
677C2×C32D3×#4111yescharacteristic
678C3⋊D3—121no—
679C3×D3—34no—
680C3×D3—41no—
681C3×D3—62no—
682C3×D3—121no—
683C2×C9—22no—
684C2×C9—21no—
685C2×C9—21no—
686C2×C9—21no—
687C2×C9—42no—
688C2×C9—41no—
689C2×C9—81no—
690C2×C9—121no—
691C2×C9C2×D3×D411yescharacteristic
692C2×C9C2×#23711yescharacteristic
693C2×C9C22×#6711yescharacteristic
694D9—22no—
695D9—41no—
696D9—121no—
697D9—241no—
698D9#93914yesdirect product factor
699C24—91no—
700C24—91no—
701C24—271no—
702C2×D4—31no—
703C2×D4—31no—
704C2×D4—91no—
705C2×D4—91no—
706C2×D4—91no—
707C2×D4—184no—
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×D4D3×D911yescharacteristic, complemented
717C22×C4—31no—
718C22×C4—91no—
719C22×C4—271no—
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—31no—
732C22⋊C4—271no—
733C22⋊C4—271no—
734C22⋊C4—271no—
735C22⋊C4—271no—
736C22⋊C4—271no—
737C22⋊C4—271no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—22no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—61no—
756C22×C3—61no—
757C22×C3—61no—
758C22×C3—92no—
759C22×C3—92no—
760C22×C3—92no—
761C22×C3—92no—
762C22×C3—188no—
763C22×C3—181no—
764C22×C3—181no—
765C22×C3—181no—
766C22×C3—181no—
767C22×C3—181no—
768C22×C3—364no—
769C22×C3D4×D912yescomplemented
770C22×C3C23×D911yescharacteristic
771C22×C3D3×#6712yes—
772C22×C3C22×D3211yescharacteristic
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—21no—
776C2×D3—32no—
777C2×D3—32no—
778C2×D3—32no—
779C2×D3—32no—
780C2×D3—68no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—61no—
784C2×D3—61no—
785C2×D3—61no—
786C2×D3—124no—
787C2×D3—181no—
788C2×D3—181no—
789C2×D3—181no—
790C2×D3—181no—
791C2×D3—181no—
792C2×D3—181no—
793C2×D3—361no—
794C2×D3—361no—
795C2×D3—361no—
796C2×D3—364no—
797C2×D3—364no—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—32no—
801C3×C4—41no—
802C3×C4—61no—
803C3×C4—61no—
804C3×C4—181no—
805Dic3—21no—
806Dic3—21no—
807Dic3—61no—
808Dic3—92no—
809Dic3—92no—
810Dic3—182no—
811Dic3—181no—
812Dic3—181no—
813Dic3—181no—
814Dic3—181no—
815Dic3—361no—
816Dic3—361no—
817Dic3D4×D912yescomplemented
818C32D3×#12111yescharacteristic
819C9—21no—
820C9C2×#93911yescharacteristic, complemented
821C23—31no—
822C23—91no—
823C23—91no—
824C23—94no—
825C23—91no—
826C23—182no—
827C23—182no—
828C23—182no—
829C23—182no—
830C23—182no—
831C23—271no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23C2×D3×D911yescharacteristic
836C23C2×D3×D911yescharacteristic
837D4—22no—
838D4—62no—
839D4—62no—
840D4—182no—
841D4—182no—
842D4—182no—
843D4—542no—
844D4—542no—
845D4—542no—
846D4—542no—
847D4—542no—
848D4—542no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—62no—
853C2×C4—91no—
854C2×C4—182no—
855C2×C4—274no—
856C2×C4—271no—
857C2×C4—271no—
858C2×C4—271no—
859C2×C4—542no—
860C2×C4—542no—
861C2×C4—542no—
862C2×C4—542no—
863C2×C4—542no—
864C2×C4C2×D3×D911yescharacteristic
865C2×C3—22no—
866C2×C3—22no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—42no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—81no—
874C2×C3—94no—
875C2×C3—121no—
876C2×C3—182no—
877C2×C3—361no—
878C2×C3C2×D4×D911yescharacteristic
879C2×C3C2×D4×D911yescharacteristic
880C2×C3#41×D911yescharacteristic
881C2×C3D32×D411yescharacteristic
882C2×C3D3×#23711yescharacteristic
883C2×C3C2×D3×#6711yescharacteristic
884D3—34no—
885D3—41no—
886D3—62no—
887D3—121no—
888D3—361no—
889D3—361no—
890D3—721no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—61no—
897C22—61no—
898C22—61no—
899C22—92no—
900C22—92no—
901C22—92no—
902C22—92no—
903C22—188no—
904C22—181no—
905C22—181no—
906C22—181no—
907C22—181no—
908C22—181no—
909C22—364no—
910C22—541no—
911C22—541no—
912C22—541no—
913C22—1084no—
914C22D9×#6712yescomplemented
915C22C22×D3×D911yescharacteristic
916C4—21no—
917C4—32no—
918C4—61no—
919C4—61no—
920C4—181no—
921C4—272no—
922C4—541no—
923C4—541no—
924C3—21no—
925C3D9×#12111yescharacteristic, complemented
926C3D3×#93911yescharacteristic
927C2—22no—
928C2—41no—
929C2—94no—
930C2—121no—
931C2—182no—
932C2—361no—
933C2—1081no—
934C2D3×D4×D911yescharacteristic
935C2D9×#23711yescharacteristic
936C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9C2×#121
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×D4×D9C2semidirect
2. C2×D9×#67C2semidirect
3. C2×D9×#67C2semidirect
4. C22×Dic3×D9C2semidirect
5. #11721839C2semidirect
6. C9×#939C2semidirect
7. #11721290C2semidirect
8. #11721277C2semidirect
9. #11721271C2semidirect
10. #11721270C2semidirect
11. D9×#217C2semidirect
12. D9×(C2×D3)⋊C4C2semidirect
13. #11720983C2semidirect
14. #11720982C2semidirect
15. D9×Dic3⋊C4C2semidirect
21. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C2×#6233C22semidirect
24. C22×C3⋊Dic9C22semidirect
25. C2×C9×#67C22semidirect
26. C2×C9×#67C22semidirect
27. C2×C3×#611C22semidirect
28. C2×C3×#611C22semidirect
29. C22×C9×Dic3C22semidirect
31. C2×C3×D36C22semidirect
35. C2×#6194C22semidirect
36. C2×#6194C22semidirect
37. C2×#6192C22semidirect
38. C2×#6192C22semidirect
43. C2×Dic3×D9C22semidirect
44. C2×Dic3×D9C22semidirect
45. #88551C22semidirect
46. #88536C22semidirect
47. #88534C22semidirect
48. C9×#217C22semidirect
49. C9×(C2×D3)⋊C4C22semidirect
50. C9×Dic3⋊C4C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. #88445C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. (C2×D9)⋊Dic3C22semidirect
55. Dic3⋊Dic9C22semidirect
56. #88442C22semidirect
74. C2×D4×D9D3semidirect
97. C22×C3×D9D4semidirect
131. Dic3×D9D4semidirect
179. C2×D4×C9C2×D3semidirect
187. C2×#611C2×D3semidirect
188. C2×#611C2×D3semidirect
196. C2×D36C2×D3semidirect
224. C22×C3×C9C2×D4semidirect
241. C2×C3×D9C2×D4semidirect
247. C3⋊Dic9C2×D4semidirect
250. C9×Dic3C2×D4semidirect
272. #939D9direct (N × H)
342. C22×D9#67semidirect
392. C3×D9#121semidirect
406. C2×C3×D4C2×D9semidirect
426. C2×#67C2×D9semidirect
427. C2×#67C2×D9semidirect
437. C22×Dic3C2×D9semidirect
460. #217C2×D9semidirect
469. (C2×D3)⋊C4C2×D9semidirect
477. Dic3⋊C4C2×D9semidirect
526. C22×C9C2×#67semidirect
545. C2×D9C2×#67semidirect
573. C3×C9C2×#121semidirect
698. D9#939direct (N × H)
716. C2×D4D3×D9semidirect
769. C22×C3D4×D9semidirect
817. Dic3D4×D9semidirect
820. C9C2×#939semidirect
914. C22D9×#67semidirect
925. C3D9×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×D92
C2×D9×#672
C22×Dic3×D92
#117218392
C9×#9392
#117212902
#117212772
#117212712
#117212702
D9×#2172
D9×(C2×D3)⋊C42
#117209832
#117209822
D9×Dic3⋊C42
D3×#9393
D9×#1213