Finite Group Databasebeta

← D3×#63501 #13151131

Subgroups — D3×#63501 #13151131

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×D3×D4×C9C211yesmaximal, characteristic, complemented
2C2×D3×#611C211yesmaximal, characteristic, complemented
3C2×D3×#611C211yesmaximal, characteristic, complemented
4C22×D3×Dic9C211yesmaximal, characteristic, complemented
5#11721839C211yesmaximal, characteristic, complemented
6C3×#63501C211yesmaximal, characteristic, complemented
7#11721290C211yesmaximal, characteristic, complemented
8#11721288C211yesmaximal, characteristic, complemented
9#11721282C211yesmaximal, characteristic, complemented
10#11721281C211yesmaximal, characteristic, complemented
11D3×#3676C211yesmaximal, characteristic, complemented
12D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
13#11721017C211yesmaximal, characteristic, complemented
14#11721016C211yesmaximal, characteristic, complemented
15D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
16D3×#939—31nomaximal
17C2×#63501—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C23×D3×C9C2211yescharacteristic
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×C3×Dic9C2211yescharacteristic, complemented
30D3×D4×C9—24no—
31C2×C9×D12C2211yescharacteristic, complemented
32C2×C4×D3×C9C2211yescharacteristic
33D3×#611—24no—
34D3×#611—24no—
35C2×#6195C2211yescharacteristic, complemented
36C2×#6195C2211yescharacteristic, complemented
37C2×#6194C2211yescharacteristic, complemented
38C2×#6194C2211yescharacteristic, complemented
39C2×D3×Dic9—24no—
40C2×D3×Dic9C2211yescharacteristic
41C2×D3×Dic9C2211yescharacteristic
42C2×D3×Dic9C2211yescharacteristic
43C2×D3×Dic9C2211yescharacteristic, complemented
44C2×D3×Dic9C2211yescharacteristic, complemented
45#88551C2211yescharacteristic, complemented
46#88536C2211yescharacteristic, complemented
47#88534C2211yescharacteristic, complemented
48C3×#3676C2211yescharacteristic, complemented
49C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
50C3×Dic9⋊C4C2211yescharacteristic, complemented
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52(C2×D3)⋊Dic9C2211yescharacteristic, complemented
53#88445C2211yescharacteristic, complemented
54(C2×D9)⋊Dic3C2211yescharacteristic, complemented
55#88442C2211yescharacteristic, complemented
56Dic9⋊Dic3C2211yescharacteristic, complemented
57C2×C3×D3×D4D311yescharacteristic
58C2×D3×#67—31no—
59C2×D3×#67—31no—
60C22×D3×Dic3—31no—
61#64148—31no—
62C3×#939—31no—
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—
72C22×D4×C9—31no—
73C22×#611—31no—
74C22×#611—31no—
75C23×Dic9—31no—
76C2×#3676—31no—
77#63501—31no—
78#63501—31no—
79#63501—31no—
80#63501—31no—
81#63501—31no—
82#63501—31no—
83#63501—31no—
84#63501—61no—
85#63501D311yescharacteristic, direct product factor
86C2×(C2×D9)⋊C4—31no—
87C2×Dic9⋊C4—31no—
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9—22no—
92C22×D3×C9—22no—
93C22×D3×C9—22no—
94C22×D3×C9—22no—
95C22×D3×C9—22no—
96C22×D3×C9D414yescomplemented
97C22×D3×C9C2311yescharacteristic
98C22×D3×C9C2311yescharacteristic
99C22×D3×C9C2311yescharacteristic
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×Dic3C2311yescharacteristic
117C2×C3×Dic9—22no—
118C2×C3×Dic9C2311yescharacteristic
119C2×C3×Dic9C2311yescharacteristic
120C2×C3×Dic9C2311yescharacteristic
121C9×D12—22no—
122C4×D3×C9—22no—
123#6195—22no—
124#6195—22no—
125#6194—22no—
126#6194—22no—
127D3×Dic9—22no—
128D3×Dic9—22no—
129D3×Dic9—22no—
130D3×Dic9—22no—
131D3×Dic9D414yescomplemented
132C2×#939—91no—
133D3×#121—91no—
134C23×C3×D3C2×D311yescharacteristic
135C23×C3×D3C2×D311yescharacteristic
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×Dic3—31no—
146C3×D3×D4—24no—
147C2×C3×D12C2×D311yescharacteristic
148C2×C3×C4×D3C2×D311yescharacteristic
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—
161C24×C9—31no—
162C24×C9—31no—
163C23×D9—31no—
164#3757—31no—
165#3752—31no—
166#3750—31no—
167C3×#217—31no—
168C3×(C2×D3)⋊C4—31no—
169C3×Dic3⋊C4—31no—
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×C9—31no—
180C2×D4×C9—64no—
181C2×D4×C9C2×D311yescharacteristic, complemented
182C22×C4×C9—31no—
183C2×#611—31no—
184C2×#611—31no—
185C2×#611—31no—
186C2×#611—31no—
187C2×#611—31no—
188C2×#611—31no—
189C2×#611—64no—
190C2×#611—64no—
191C2×#611—61no—
192C2×#611—61no—
193C2×#611C2×D311yescharacteristic, complemented
194C2×#611C2×D311yescharacteristic, complemented
195C22×Dic9—31no—
196C22×Dic9—31no—
197C22×Dic9—31no—
198C22×Dic9—31no—
199C22×Dic9—31no—
200C22×Dic9—31no—
201C22×Dic9—64no—
202C22×Dic9—61no—
203C22×Dic9C2×D311yescharacteristic, complemented
204#3676—31no—
205#3676—31no—
206#3676—31no—
207#3676—61no—
208#3676C2×D311yescharacteristic, complemented
209(C2×D9)⋊C4—31no—
210(C2×D9)⋊C4—31no—
211(C2×D9)⋊C4—31no—
212(C2×D9)⋊C4—61no—
213(C2×D9)⋊C4C2×D311yescharacteristic, complemented
214Dic9⋊C4—31no—
215Dic9⋊C4—31no—
216Dic9⋊C4—31no—
217Dic9⋊C4—61no—
218Dic9⋊C4C2×D311yescharacteristic, complemented
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—28no—
232C2×D3×C9—21no—
233C2×D3×C9—21no—
234C2×D3×C9—21no—
235C2×D3×C9—44no—
236C2×D3×C9C2×D412yes—
237C2×D3×C9C2×D412yes—
238C2×D3×C9C2×D412yescomplemented
239C2×D3×C9#4112yes—
240C2×C3×D9—21no—
241C2×C3×D9—21no—
242C2×C3×D9—21no—
243D3×D9—44no—
244C3×C4×C9—21no—
245C3⋊Dic9—21no—
246C3⋊Dic9—21no—
247C3⋊Dic9C2×D412yescomplemented
248C9×Dic3—21no—
249C3×Dic9—21no—
250C3×Dic9—21no—
251C3×Dic9C2×D412yescomplemented
252C22×C3×D4—31no—
253C22×#67—91no—
254C22×#67—91no—
255C23×Dic3—91no—
256C2×D3×D4—91no—
257C2×D3×D4—91no—
258C2×D3×D4D911yescharacteristic, complemented
259C22×C4×D3—91no—
260C3×#121—91no—
261C2×#217—91no—
262#939—31no—
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—91no—
272#939—181no—
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—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—31no—
292C22×C3×D3#6714yes—
293C22×C3×D3C22×D311yescharacteristic
294C22×C3×D3C22×D311yescharacteristic
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—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—62no—
315C2×C3×Dic3C22×D311yescharacteristic
316C3×D12—22no—
317C3×C4×D3—22no—
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×C9—34no—
331C23×C9—31no—
332C23×C9—31no—
333C23×C9—62no—
334C23×C9—62no—
335C23×C9—62no—
336C23×C9—62no—
337C23×C9—62no—
338C23×C9C22×D311yescharacteristic
339C23×C9C22×D311yescharacteristic
340C22×D9—31no—
341C22×D9—61no—
342C22×D9—62no—
343C22×D9—62no—
344C22×D9—62no—
345C22×D9C22×D311yescharacteristic
346D4×C9—22no—
347D4×C9—42no—
348D4×C9—62no—
349D4×C9—62no—
350D4×C9—62no—
351C2×C4×C9—21no—
352C2×C4×C9—31no—
353C2×C4×C9—62no—
354C2×C4×C9C22×D311yescharacteristic
355#611—22no—
356#611—22no—
357#611—62no—
358#611—62no—
359#611—62no—
360#611—62no—
361#611—62no—
362#611—62no—
363#611—122no—
364#611—122no—
365C2×Dic9—22no—
366C2×Dic9—31no—
367C2×Dic9—34no—
368C2×Dic9—31no—
369C2×Dic9—31no—
370C2×Dic9—61no—
371C2×Dic9—61no—
372C2×Dic9—61no—
373C2×Dic9—62no—
374C2×Dic9—62no—
375C2×Dic9—62no—
376C2×Dic9—62no—
377C2×Dic9—62no—
378C2×Dic9—122no—
379C2×Dic9C22×D311yescharacteristic
380C2×Dic9C22×D311yescharacteristic
381C2×Dic9C22×D311yescharacteristic
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—22no—
390D3×C9—41no—
391D3×C9#12114yescomplemented
392C3×D9—41no—
393C24×C3—31no—
394C24×C3—31no—
395C23×D3—91no—
396C23×D3—91no—
397C23×D3C2×D911yescharacteristic
398C23×D3C2×D911yescharacteristic
399C2×C3×D4—21no—
400C2×C3×D4—31no—
401C2×C3×D4—31no—
402C2×C3×D4—31no—
403C2×C3×D4—64no—
404C2×C3×D4—91no—
405C2×C3×D4—91no—
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—31no—
429C22×Dic3—91no—
430C22×Dic3—91no—
431C22×Dic3—91no—
432C22×Dic3—91no—
433C22×Dic3—91no—
434C22×Dic3—91no—
435C22×Dic3—91no—
436C22×Dic3—181no—
437C22×Dic3—184no—
438D3×D4—24no—
439D3×D4—184no—
440D3×D4—184no—
441C2×D12—91no—
442C2×D12—91no—
443C2×D12C2×D911yescharacteristic, complemented
444C2×C4×D3—91no—
445C2×C4×D3—91no—
446C2×C4×D3—91no—
447C2×C4×D3—91no—
448C2×C4×D3—91no—
449C2×C4×D3—184no—
450C2×C4×D3C2×D911yescharacteristic
451C3×C4⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454#217—31no—
455#217—91no—
456#217—91no—
457#217—91no—
458#217—91no—
459#217—91no—
460#217—181no—
461(C2×D3)⋊C4—31no—
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—91no—
469(C2×D3)⋊C4—181no—
470C4⋊Dic3—91no—
471Dic3⋊C4—31no—
472Dic3⋊C4—91no—
473Dic3⋊C4—91no—
474Dic3⋊C4—91no—
475Dic3⋊C4—91no—
476Dic3⋊C4—91no—
477Dic3⋊C4—181no—
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—21no—
483C22×C32C2×#6712yes—
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—28no—
491C2×C3×D3—21no—
492C2×C3×D3—21no—
493C2×C3×D3—21no—
494C2×C3×D3—44no—
495C2×C3×D3—61no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3D3×D412yes—
499C2×C3×D3#23712yes—
500C2×C3×D3C2×#6712yes—
501C2×C3×D3C2×#6712yes—
502D32—124no—
503C32×C4—21no—
504C3⋊Dic3—32no—
505C3⋊Dic3—61no—
506C3⋊Dic3—61no—
507C3×Dic3—21no—
508C3×Dic3—32no—
509C3×Dic3—61no—
510C3×Dic3—61no—
511C22×C9—21no—
512C22×C9—21no—
513C22×C9—21no—
514C22×C9—21no—
515C22×C9—21no—
516C22×C9—21no—
517C22×C9—22no—
518C22×C9—32no—
519C22×C9—32no—
520C22×C9—32no—
521C22×C9—32no—
522C22×C9—41no—
523C22×C9—41no—
524C22×C9—41no—
525C22×C9—41no—
526C22×C9—41no—
527C22×C9—68no—
528C22×C9—61no—
529C22×C9—61no—
530C22×C9—61no—
531C22×C9—61no—
532C22×C9—61no—
533C22×C9—124no—
534C22×C9D3×D412yescomplemented
535C22×C9C23×D311yescharacteristic
536C2×D9—21no—
537C2×D9—21no—
538C2×D9—21no—
539C2×D9—61no—
540C2×D9—61no—
541C2×D9—61no—
542C2×D9—121no—
543C2×D9—121no—
544C2×D9—121no—
545C2×D9—124no—
546C4×C9—21no—
547C4×C9—41no—
548C4×C9—61no—
549Dic9—21no—
550Dic9—21no—
551Dic9—32no—
552Dic9—62no—
553Dic9—61no—
554Dic9—61no—
555Dic9—121no—
556Dic9—121no—
557Dic9D3×D412yescomplemented
558C22×D4—31no—
559C22×D4—271no—
560C22×D4—271no—
561C23×C4—271no—
562#121—91no—
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—31no—
578C23×C3—34no—
579C23×C3—31no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—62no—
583C23×C3—62no—
584C23×C3—62no—
585C23×C3—91no—
586C23×C3C22×D911yescharacteristic
587C23×C3C22×D911yescharacteristic
588C23×C3C2×D3211yescharacteristic
589C23×C3C2×D3211yescharacteristic
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—31no—
596C22×D3—91no—
597C22×D3—91no—
598C22×D3—181no—
599C22×D3—182no—
600C22×D3—182no—
601C22×D3—182no—
602C22×D3—182no—
603C22×D3—182no—
604C22×D3—182no—
605C22×D3#61114yescomplemented
606C22×D3C22×D911yescharacteristic
607C22×D3C22×D911yescharacteristic
608C22×D3C22×D911yescharacteristic
609C3×D4—22no—
610C3×D4—22no—
611C3×D4—42no—
612C3×D4—62no—
613C3×D4—62no—
614C3×D4—62no—
615C3×D4—182no—
616C3×D4—182no—
617C2×C3×C4—21no—
618C2×C3×C4—31no—
619C2×C3×C4—62no—
620C2×C3×C4—91no—
621C2×C3×C4—91no—
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—31no—
643C2×Dic3—31no—
644C2×Dic3—31no—
645C2×Dic3—62no—
646C2×Dic3—94no—
647C2×Dic3—91no—
648C2×Dic3—91no—
649C2×Dic3—91no—
650C2×Dic3—91no—
651C2×Dic3—91no—
652C2×Dic3—91no—
653C2×Dic3—181no—
654C2×Dic3—181no—
655C2×Dic3—181no—
656C2×Dic3—182no—
657C2×Dic3—182no—
658C2×Dic3—182no—
659C2×Dic3—182no—
660C2×Dic3—182no—
661C2×Dic3—182no—
662C2×Dic3—362no—
663C2×Dic3C22×D911yescharacteristic
664D12—22no—
665D12—182no—
666D12—182no—
667C4×D3—22no—
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×#23711yescharacteristic
677C2×C32C22×#6711yescharacteristic
678C3⋊D3—121no—
679C3×D3—22no—
680C3×D3—41no—
681C3×D3—121no—
682C3×D3#93914yes—
683C2×C9—22no—
684C2×C9—21no—
685C2×C9—21no—
686C2×C9—21no—
687C2×C9—34no—
688C2×C9—42no—
689C2×C9—41no—
690C2×C9—62no—
691C2×C9—81no—
692C2×C9—121no—
693C2×C9C2×D3×D411yescharacteristic
694C2×C9C2×D3×D411yescharacteristic
695C2×C9D3×#4111yescharacteristic
696D9—41no—
697D9—121no—
698D9—241no—
699C24—31no—
700C24—31no—
701C24—271no—
702C2×D4—31no—
703C2×D4—31no—
704C2×D4—31no—
705C2×D4—64no—
706C2×D4—91no—
707C2×D4—91no—
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—91no—
727C4⋊C4—271no—
728C4⋊C4—271no—
729C4⋊C4—271no—
730C22⋊C4—91no—
731C22⋊C4—91no—
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—32no—
751C22×C3—32no—
752C22×C3—32no—
753C22×C3—32no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—68no—
760C22×C3—61no—
761C22×C3—61no—
762C22×C3—61no—
763C22×C3—61no—
764C22×C3—61no—
765C22×C3—124no—
766C22×C3—181no—
767C22×C3—181no—
768C22×C3—181no—
769C22×C3C2×#61112yescomplemented
770C22×C3C23×D911yescharacteristic
771C22×C3D3×#6712yes—
772C22×C3C22×D3211yescharacteristic
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—28no—
776C2×D3—21no—
777C2×D3—21no—
778C2×D3—21no—
779C2×D3—44no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—181no—
784C2×D3—181no—
785C2×D3—181no—
786C2×D3—181no—
787C2×D3—181no—
788C2×D3—181no—
789C2×D3—361no—
790C2×D3—361no—
791C2×D3—361no—
792C2×D3—364no—
793C2×D3—364no—
794C2×D3D4×D912yes—
795C2×D3#369912yes—
796C2×D3C2×#61112yes—
797C2×D3C2×#61112yescomplemented
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—41no—
801C3×C4—61no—
802C3×C4—92no—
803C3×C4—181no—
804C3×C4—181no—
805Dic3—21no—
806Dic3—32no—
807Dic3—61no—
808Dic3—61no—
809Dic3—92no—
810Dic3—92no—
811Dic3—182no—
812Dic3—181no—
813Dic3—181no—
814Dic3—181no—
815Dic3—181no—
816Dic3—361no—
817Dic3—361no—
818C32C2×#93911yescharacteristic
819C9—21no—
820C9D3×#12111yescharacteristic, complemented
821C23—31no—
822C23—31no—
823C23—34no—
824C23—31no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—91no—
831C23—271no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23C2×D3×D911yescharacteristic
836C23C2×D3×D911yescharacteristic
837D4—22no—
838D4—62no—
839D4—62no—
840D4—62no—
841D4—182no—
842D4—182no—
843D4—542no—
844D4—542no—
845D4—542no—
846D4—542no—
847D4—542no—
848D4—542no—
849C2×C4—31no—
850C2×C4—62no—
851C2×C4—91no—
852C2×C4—91no—
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—34no—
871C2×C3—42no—
872C2×C3—41no—
873C2×C3—41no—
874C2×C3—62no—
875C2×C3—81no—
876C2×C3—121no—
877C2×C3—361no—
878C2×C3C2×D4×D911yescharacteristic
879C2×C3C2×#369911yescharacteristic
880C2×C3C22×#61111yescharacteristic
881C2×C3D32×D411yescharacteristic
882C2×C3D3×#23711yescharacteristic
883C2×C3C2×D3×#6711yescharacteristic
884D3—22no—
885D3—41no—
886D3—121no—
887D3—361no—
888D3—361no—
889D3—721no—
890D3#6350114yesdirect product factor
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—32no—
897C22—32no—
898C22—32no—
899C22—32no—
900C22—68no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—61no—
905C22—61no—
906C22—124no—
907C22—181no—
908C22—181no—
909C22—181no—
910C22—541no—
911C22—541no—
912C22—541no—
913C22—1084no—
914C22D3×#61112yescomplemented
915C22C22×D3×D911yescharacteristic
916C4—21no—
917C4—61no—
918C4—92no—
919C4—181no—
920C4—181no—
921C4—272no—
922C4—541no—
923C4—541no—
924C3—21no—
925C3C2×#6350111yescharacteristic, complemented
926C3D3×#93911yescharacteristic
927C2—22no—
928C2—34no—
929C2—41no—
930C2—62no—
931C2—121no—
932C2—361no—
933C2—1081no—
934C2D3×D4×D911yescharacteristic
935C2D3×#369911yescharacteristic
936C2C2×D3×#61111yescharacteristic
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×D3×D4×C9C2semidirect
2. C2×D3×#611C2semidirect
3. C2×D3×#611C2semidirect
4. C22×D3×Dic9C2semidirect
5. #11721839C2semidirect
6. C3×#63501C2semidirect
7. #11721290C2semidirect
8. #11721288C2semidirect
9. #11721282C2semidirect
10. #11721281C2semidirect
11. D3×#3676C2semidirect
12. D3×(C2×D9)⋊C4C2semidirect
13. #11721017C2semidirect
14. #11721016C2semidirect
15. D3×Dic9⋊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×C3×Dic9C22semidirect
31. C2×C9×D12C22semidirect
35. C2×#6195C22semidirect
36. C2×#6195C22semidirect
37. C2×#6194C22semidirect
38. C2×#6194C22semidirect
43. C2×D3×Dic9C22semidirect
44. C2×D3×Dic9C22semidirect
45. #88551C22semidirect
46. #88536C22semidirect
47. #88534C22semidirect
48. C3×#3676C22semidirect
49. C3×(C2×D9)⋊C4C22semidirect
50. C3×Dic9⋊C4C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. (C2×D3)⋊Dic9C22semidirect
53. #88445C22semidirect
54. (C2×D9)⋊Dic3C22semidirect
55. #88442C22semidirect
56. Dic9⋊Dic3C22semidirect
85. #63501D3direct (N × H)
96. C22×D3×C9D4semidirect
131. D3×Dic9D4semidirect
181. C2×D4×C9C2×D3semidirect
193. C2×#611C2×D3semidirect
194. C2×#611C2×D3semidirect
203. C22×Dic9C2×D3semidirect
208. #3676C2×D3semidirect
213. (C2×D9)⋊C4C2×D3semidirect
218. Dic9⋊C4C2×D3semidirect
224. C22×C3×C9C2×D4semidirect
238. C2×D3×C9C2×D4semidirect
247. C3⋊Dic9C2×D4semidirect
251. C3×Dic9C2×D4semidirect
258. C2×D3×D4D9semidirect
391. D3×C9#121semidirect
406. C2×C3×D4C2×D9semidirect
426. C2×#67C2×D9semidirect
427. C2×#67C2×D9semidirect
443. C2×D12C2×D9semidirect
534. C22×C9D3×D4semidirect
557. Dic9D3×D4semidirect
573. C3×C9C2×#121semidirect
605. C22×D3#611semidirect
716. C2×D4D3×D9semidirect
769. C22×C3C2×#611semidirect
797. C2×D3C2×#611semidirect
820. C9D3×#121semidirect
890. D3#63501direct (N × H)
914. C22D3×#611semidirect
925. C3C2×#63501semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D4×C92
C2×D3×#6112
C22×D3×Dic92
#117218392
C3×#635012
#117212902
#117212882
#117212822
#117212812
D3×#36762
D3×(C2×D9)⋊C42
#117210172
#117210162
D3×Dic9⋊C42
D3×#9393
C2×#635013