Finite Group Databasebeta

← D3×#63446 #13148404

Subgroups — D3×#63446 #13148404

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×#611C211yesmaximal, characteristic, complemented
2C2×D3×#611C211yesmaximal, characteristic, complemented
3C2×D3×D36C211yesmaximal, characteristic, complemented
4C2×C4×D3×D9C211yesmaximal, characteristic, complemented
5#11721730C211yesmaximal, characteristic, complemented
6D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#63446C211yesmaximal, characteristic, complemented
8#11721271C211yesmaximal, characteristic, complemented
9#11721256C211yesmaximal, characteristic, complemented
10D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
11#11721041C211yesmaximal, characteristic, complemented
12#11721039C211yesmaximal, characteristic, complemented
13#11721033C211yesmaximal, characteristic, complemented
14D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
15#11720982C211yesmaximal, characteristic, complemented
16D3×#884—31nomaximal
17C2×#63446—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
24C2×C4×C3⋊D9C2211yescharacteristic, complemented
25C2×C3×#611C2211yescharacteristic, complemented
26C2×C3×#611C2211yescharacteristic, complemented
27C2×C4×D3×C9C2211yescharacteristic
28C2×C4×D3×C9C2211yescharacteristic
29C2×C3×D36C2211yescharacteristic, complemented
30C2×C3×C4×D9C2211yescharacteristic, complemented
31D3×#611—24no—
32D3×#611—24no—
33C2×#6195C2211yescharacteristic, complemented
34C2×#6195C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic, complemented
36C2×#6194C2211yescharacteristic, complemented
37C2×D3×Dic9C2211yescharacteristic
38C2×D3×Dic9C2211yescharacteristic
39C2×#6192C2211yescharacteristic, complemented
40C2×#6192C2211yescharacteristic, complemented
41C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
42C2×Dic3×D9C2211yescharacteristic, complemented
43D3×D36—24no—
44C4×D3×D9—24no—
45C3×C9×C22⋊C4C2211yescharacteristic, complemented
46#88536C2211yescharacteristic, complemented
47#88534C2211yescharacteristic, complemented
48C9×#217C2211yescharacteristic, complemented
49C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
52C3×Dic9⋊C4C2211yescharacteristic, complemented
53#88445C2211yescharacteristic, complemented
54(C2×D9)⋊Dic3C2211yescharacteristic, complemented
55#88442C2211yescharacteristic, complemented
56Dic9⋊Dic3C2211yescharacteristic, complemented
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×D3×D12—31no—
60C2×C4×D32—31no—
61#64093—31no—
62C3×#884—31no—
63C3×D3×C22⋊C4D311yescharacteristic
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—
72C22×#611—31no—
73C22×#611—31no—
74C22×D36—31no—
75C22×C4×D9—31no—
76C2×C9×C22⋊C4—31no—
77C2×(C2×D9)⋊C4—31no—
78C2×Dic9⋊C4—31no—
79#63446—31no—
80#63446—31no—
81#63446—31no—
82#63446—31no—
83#63446—31no—
84#63446—31no—
85#63446—31no—
86#63446—61no—
87#63446D311yescharacteristic, direct product factor
88C23×C3×C9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9—22no—
92C22×D3×C9—22no—
93C22×D3×C9—22no—
94C22×D3×C9C2311yescharacteristic
95C22×D3×C9C2311yescharacteristic
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—
112C3×#611—22no—
113C3×#611—22no—
114C2×C9×Dic3C2311yescharacteristic
115C2×C9×Dic3C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C2×C3×Dic9C2311yescharacteristic
118C4×D3×C9—22no—
119C4×D3×C9—22no—
120C3×D36—22no—
121C3×C4×D9—22no—
122#6195—22no—
123#6195—22no—
124#6194—22no—
125#6194—22no—
126D3×Dic9—22no—
127D3×Dic9D414yescomplemented
128#6192—22no—
129#6192—22no—
130(C3⋊D9)⋊C4—22no—
131Dic3×D9—22no—
132D3×#121—91no—
133C2×#884—91no—
134C23×C3×D3C2×D311yescharacteristic
135C22×D32—31no—
136C22×D32—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4×C3⋊D3—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×D12—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3C2×D311yescharacteristic
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—
161C24×C9—31no—
162C23×D9—31no—
163C23×D9—31no—
164C32×C22⋊C4C2×D311yescharacteristic
165#3752—31no—
166#3750—31no—
167C3×#217C2×D311yescharacteristic
168C3×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4C2×D311yescharacteristic
170C3×(C2×D3)⋊C4C2×D311yescharacteristic
171C3×Dic3⋊C4—31no—
172#3724—31no—
173Dic3⋊Dic3—31no—
174#3722—31no—
175(C2×D3)⋊Dic3—31no—
176C22×C4×C9—31no—
177C22×C4×C9—31no—
178C2×#611—31no—
179C2×#611—31no—
180C2×#611—31no—
181C2×#611—31no—
182C2×#611—31no—
183C2×#611—31no—
184C2×#611—64no—
185C2×#611—64no—
186C2×#611—61no—
187C2×#611—61no—
188C2×#611C2×D311yescharacteristic, complemented
189C2×#611C2×D311yescharacteristic, complemented
190C22×Dic9—31no—
191C22×Dic9—31no—
192C2×D36—31no—
193C2×D36—31no—
194C2×D36—31no—
195C2×D36—64no—
196C2×D36—61no—
197C2×D36C2×D311yescharacteristic, complemented
198C2×C4×D9—31no—
199C2×C4×D9—31no—
200C2×C4×D9—31no—
201C2×C4×D9—64no—
202C2×C4×D9—61no—
203C2×C4×D9C2×D311yescharacteristic, complemented
204C9×C22⋊C4—21no—
205C9×C22⋊C4—31no—
206C9×C22⋊C4—31no—
207C9×C22⋊C4—31no—
208C9×C22⋊C4C2×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×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—44no—
233C2×D3×C9C2×D412yes—
234C2×D3×C9C2×D412yes—
235C2×D3×C9#4112yes—
236C2×C3×D9—21no—
237C2×C3×D9—21no—
238C2×C3×D9—21no—
239C2×C3×D9—21no—
240C2×C3×D9—21no—
241C2×C3×D9C2×D412yescomplemented
242D3×D9—28no—
243D3×D9—44no—
244C3×C4×C9—21no—
245C3×C4×C9—21no—
246C3⋊Dic9—21no—
247C3⋊Dic9C2×D412yescomplemented
248C9×Dic3—21no—
249C9×Dic3—21no—
250C3×Dic9—21no—
251C3×Dic9C2×D412yescomplemented
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—91no—
261C2×C3×C22⋊C4—31no—
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—31no—
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—91no—
280#884—181no—
281D3×C22⋊C4—91no—
282D3×C22⋊C4D911yescharacteristic, complemented
283C23×C32C22×D311yescharacteristic
284C22×C3⋊D3—31no—
285C22×C3⋊D3—31no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—31no—
290C22×C3×D3—31no—
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—62no—
308C3×#67—62no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3C22×D311yescharacteristic
312C2×C3×Dic3C22×D311yescharacteristic
313C3×D12—62no—
314C3×C4×D3—22no—
315C3×C4×D3—22no—
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×C9—62no—
331C23×C9—62no—
332C23×C9—62no—
333C23×C9C22×D311yescharacteristic
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
346C2×C4×C9—21no—
347C2×C4×C9—21no—
348C2×C4×C9—31no—
349C2×C4×C9—31no—
350C2×C4×C9—62no—
351C2×C4×C9—62no—
352C2×C4×C9C22×D311yescharacteristic
353C2×C4×C9C22×D311yescharacteristic
354#611—22no—
355#611—22no—
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—34no—
366C2×Dic9—31no—
367C2×Dic9—61no—
368C2×Dic9—61no—
369C2×Dic9—62no—
370C2×Dic9C22×D311yescharacteristic
371C2×Dic9C22×D311yescharacteristic
372D36—22no—
373D36—62no—
374D36—62no—
375D36—62no—
376D36—122no—
377C4×D9—22no—
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—41no—
390D3×C9#12114yescomplemented
391C3×D9—22no—
392C3×D9—41no—
393C24×C3—31no—
394C23×D3—91no—
395C23×D3—91no—
396C23×D3—91no—
397C23×D3—91no—
398C23×D3C2×D911yescharacteristic
399C2×C3×D4—91no—
400C2×C3×D4—91no—
401C2×C3×D4—91no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—91no—
405C2×#67—31no—
406C2×#67—31no—
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—91no—
418C2×#67—91no—
419C2×#67—181no—
420C2×#67—181no—
421C2×#67—184no—
422C2×#67—184no—
423C22×Dic3—91no—
424C22×Dic3—91no—
425C22×Dic3—91no—
426D3×D4—184no—
427D3×D4—184no—
428D3×D4—184no—
429C2×D12—31no—
430C2×D12—91no—
431C2×D12—91no—
432C2×D12—91no—
433C2×D12—91no—
434C2×D12—91no—
435C2×D12—91no—
436C2×D12—181no—
437C2×D12—184no—
438C2×C4×D3—31no—
439C2×C4×D3—91no—
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—181no—
447C2×C4×D3—184no—
448C2×C4×D3—184no—
449C2×C4×D3C2×D911yescharacteristic
450C2×C4×D3C2×D911yescharacteristic
451C3×C4⋊C4—91no—
452C3×C22⋊C4—21no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—31no—
455C3×C22⋊C4—31no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4C2×D911yescharacteristic, complemented
458C3×C22⋊C4D3211yescharacteristic
459#217—91no—
460#217C2×D911yescharacteristic, complemented
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—181no—
468(C2×D3)⋊C4C2×D911yescharacteristic, complemented
469(C2×D3)⋊C4C2×D911yescharacteristic, complemented
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×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—32no—
492C2×C3×D3—44no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C2×C3×D3—61no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3#23512yes—
499C2×C3×D3D3×D412yes—
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—21no—
509C3×Dic3—32no—
510C3×Dic3—61no—
511C22×C9—21no—
512C22×C9—21no—
513C22×C9—21no—
514C22×C9—21no—
515C22×C9—32no—
516C22×C9—32no—
517C22×C9—32no—
518C22×C9—41no—
519C22×C9—41no—
520C22×C9—41no—
521C22×C9—61no—
522C22×C9—61no—
523C22×C9—61no—
524C22×C9—124no—
525C22×C9C23×D311yescharacteristic
526C2×D9—21no—
527C2×D9—21no—
528C2×D9—21no—
529C2×D9—21no—
530C2×D9—21no—
531C2×D9—32no—
532C2×D9—62no—
533C2×D9—68no—
534C2×D9—61no—
535C2×D9—61no—
536C2×D9—61no—
537C2×D9—61no—
538C2×D9—61no—
539C2×D9—121no—
540C2×D9—121no—
541C2×D9—121no—
542C2×D9—121no—
543C2×D9—121no—
544C2×D9—124no—
545C2×D9D3×D412yescomplemented
546C4×C9—21no—
547C4×C9—21no—
548C4×C9—41no—
549C4×C9—41no—
550C4×C9—61no—
551C4×C9—61no—
552Dic9—21no—
553Dic9—32no—
554Dic9—62no—
555Dic9—61no—
556Dic9—121no—
557Dic9D3×D412yescomplemented
558C22×D4—271no—
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—31no—
572C2×C22⋊C4—271no—
573C3×C9C2×#12111yescharacteristic, complemented, Sylow
574C23×C3—21no—
575C23×C3—31no—
576C23×C3—31no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3—91no—
581C23×C3—91no—
582C23×C3C22×D911yescharacteristic
583C23×C3C2×D3211yescharacteristic
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—31no—
588C22×D3—31no—
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—182no—
610C3×D4—182no—
611C3×D4—182no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—31no—
615C2×C3×C4—31no—
616C2×C3×C4—62no—
617C2×C3×C4—62no—
618C2×C3×C4—91no—
619C2×C3×C4—91no—
620C2×C3×C4—182no—
621C2×C3×C4C22×D911yescharacteristic
622C2×C3×C4C22×D911yescharacteristic
623C2×C3×C4C2×D3211yescharacteristic
624C2×C3×C4C2×D3211yescharacteristic
625#67—62no—
626#67—62no—
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—94no—
644C2×Dic3—91no—
645C2×Dic3—91no—
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—62no—
655D12—182no—
656D12—182no—
657D12—182no—
658D12—182no—
659D12—182no—
660D12—182no—
661D12—362no—
662C4×D3—22no—
663C4×D3—22no—
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×#23511yescharacteristic
675C2×C32C2×D3×D411yescharacteristic
676C2×C32C2×D3×D411yescharacteristic
677C3⋊D3—62no—
678C3⋊D3—121no—
679C3×D3—41no—
680C3×D3—62no—
681C3×D3—121no—
682C3×D3#88414yes—
683C2×C9—21no—
684C2×C9—21no—
685C2×C9—21no—
686C2×C9—34no—
687C2×C9—41no—
688C2×C9—81no—
689C2×C9—121no—
690C2×C9C2×D3×D411yescharacteristic
691C2×C9C2×D3×D411yescharacteristic
692C2×C9D3×#4111yescharacteristic
693D9—22no—
694D9—41no—
695D9—62no—
696D9—122no—
697D9—121no—
698D9—241no—
699C24—31no—
700C24—271no—
701C24—271no—
702C2×D4—91no—
703C2×D4—91no—
704C2×D4—91no—
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—31no—
719C22×C4—91no—
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—31no—
731C22⋊C4—31no—
732C22⋊C4—31no—
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—32no—
747C22×C3—32no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—92no—
755C22×C3—124no—
756C22×C3—181no—
757C22×C3—181no—
758C22×C3—181no—
759C22×C3—181no—
760C22×C3—181no—
761C22×C3C23×D911yescharacteristic
762C22×C3C22×D3211yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—32no—
767C2×D3—44no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—92no—
774C2×D3—92no—
775C2×D3—182no—
776C2×D3—188no—
777C2×D3—181no—
778C2×D3—181no—
779C2×D3—181no—
780C2×D3—181no—
781C2×D3—188no—
782C2×D3—181no—
783C2×D3—181no—
784C2×D3—181no—
785C2×D3—181no—
786C2×D3—181no—
787C2×D3—181no—
788C2×D3—361no—
789C2×D3—361no—
790C2×D3—361no—
791C2×D3—361no—
792C2×D3—361no—
793C2×D3—364no—
794C2×D3—364no—
795C2×D3#369712yes—
796C2×D3D4×D912yes—
797C2×D3D4×D912yes—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—92no—
807C3×C4—181no—
808Dic3—21no—
809Dic3—21no—
810Dic3—32no—
811Dic3—61no—
812Dic3—92no—
813Dic3—92no—
814Dic3—182no—
815Dic3—181no—
816Dic3—181no—
817Dic3—361no—
818C32C2×#88411yescharacteristic
819C9—21no—
820C9D3×#12111yescharacteristic, complemented
821C23—31no—
822C23—31no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—91no—
827C23—91no—
828C23—274no—
829C23—271no—
830C23—271no—
831C23—542no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23—542no—
836C23C2×D3×D911yescharacteristic
837D4—182no—
838D4—182no—
839D4—182no—
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—62no—
853C2×C4—91no—
854C2×C4—91no—
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—34no—
869C2×C3—41no—
870C2×C3—41no—
871C2×C3—81no—
872C2×C3—121no—
873C2×C3—182no—
874C2×C3—361no—
875C2×C3C2×#369711yescharacteristic
876C2×C3C2×D4×D911yescharacteristic
877C2×C3C2×D4×D911yescharacteristic
878C2×C3D3×#23511yescharacteristic
879C2×C3D32×D411yescharacteristic
880C2×C3D32×D411yescharacteristic
881D3—41no—
882D3—62no—
883D3—121no—
884D3—182no—
885D3—182no—
886D3—362no—
887D3—361no—
888D3—361no—
889D3—721no—
890D3#6344614yesdirect product factor
891C22—21no—
892C22—21no—
893C22—21no—
894C22—32no—
895C22—32no—
896C22—32no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—92no—
901C22—124no—
902C22—181no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—181no—
907C22—272no—
908C22—548no—
909C22—541no—
910C22—541no—
911C22—541no—
912C22—541no—
913C22—541no—
914C22—1084no—
915C22C22×D3×D911yescharacteristic
916C4—21no—
917C4—21no—
918C4—61no—
919C4—61no—
920C4—92no—
921C4—181no—
922C4—272no—
923C4—541no—
924C3—21no—
925C3C2×#6344611yescharacteristic, complemented
926C3D3×#88411yescharacteristic
927C2—34no—
928C2—41no—
929C2—121no—
930C2—182no—
931C2—361no—
932C2—542no—
933C2—1081no—
934C2D3×#369711yescharacteristic
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×D3×#611C2semidirect
2. C2×D3×#611C2semidirect
3. C2×D3×D36C2semidirect
4. C2×C4×D3×D9C2semidirect
5. #11721730C2semidirect
6. D3×C9×C22⋊C4C2semidirect
7. C3×#63446C2semidirect
8. #11721271C2semidirect
9. #11721256C2semidirect
10. D3×(C2×D9)⋊C4C2semidirect
11. #11721041C2semidirect
12. #11721039C2semidirect
13. #11721033C2semidirect
14. D3×Dic9⋊C4C2semidirect
15. #11720982C2semidirect
21. C2×#6233C22semidirect
22. C2×#6233C22semidirect
23. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C4×C3⋊D9C22semidirect
25. C2×C3×#611C22semidirect
26. C2×C3×#611C22semidirect
29. C2×C3×D36C22semidirect
30. C2×C3×C4×D9C22semidirect
33. C2×#6195C22semidirect
34. C2×#6195C22semidirect
35. C2×#6194C22semidirect
36. C2×#6194C22semidirect
39. C2×#6192C22semidirect
40. C2×#6192C22semidirect
41. C2×(C3⋊D9)⋊C4C22semidirect
42. C2×Dic3×D9C22semidirect
45. C3×C9×C22⋊C4C22semidirect
46. #88536C22semidirect
47. #88534C22semidirect
48. C9×#217C22semidirect
49. C9×(C2×D3)⋊C4C22semidirect
50. C9×(C2×D3)⋊C4C22semidirect
51. C3×(C2×D9)⋊C4C22semidirect
52. C3×Dic9⋊C4C22semidirect
53. #88445C22semidirect
54. (C2×D9)⋊Dic3C22semidirect
55. #88442C22semidirect
56. Dic9⋊Dic3C22semidirect
87. #63446D3direct (N × H)
103. C2×D3×D9D4semidirect
127. D3×Dic9D4semidirect
188. C2×#611C2×D3semidirect
189. C2×#611C2×D3semidirect
197. C2×D36C2×D3semidirect
203. C2×C4×D9C2×D3semidirect
208. C9×C22⋊C4C2×D3semidirect
213. (C2×D9)⋊C4C2×D3semidirect
218. Dic9⋊C4C2×D3semidirect
228. C2×C3⋊D9C2×D4semidirect
241. C2×C3×D9C2×D4semidirect
247. C3⋊Dic9C2×D4semidirect
251. C3×Dic9C2×D4semidirect
282. D3×C22⋊C4D9semidirect
390. D3×C9#121semidirect
457. C3×C22⋊C4C2×D9semidirect
460. #217C2×D9semidirect
468. (C2×D3)⋊C4C2×D9semidirect
469. (C2×D3)⋊C4C2×D9semidirect
545. C2×D9D3×D4semidirect
557. Dic9D3×D4semidirect
573. C3×C9C2×#121semidirect
737. C22⋊C4D3×D9semidirect
820. C9D3×#121semidirect
890. D3#63446direct (N × H)
925. C3C2×#63446semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×D3×D362
C2×C4×D3×D92
#117217302
D3×C9×C22⋊C42
C3×#634462
#117212712
#117212562
D3×(C2×D9)⋊C42
#117210412
#117210392
#117210332
D3×Dic9⋊C42
#117209822
D3×#8843
C2×#634463