Finite Group Databasebeta

← D3×#63460 #13149332

Subgroups — D3×#63460 #13149332

Order 1728.

798 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721754C211yesmaximal, characteristic, complemented
2D3×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#63460C211yesmaximal, characteristic, complemented
4D3×(C2×D9)⋊C4C211yesmaximal, characteristic
5D3×(C2×D9)⋊C4C211yesmaximal, characteristic
6D3×(C2×D9)⋊C4C211yesmaximal, characteristic
7D3×C4⋊Dic9C211yesmaximal, characteristic, complemented
8D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
9C4×D3×Dic9C211yesmaximal, characteristic, complemented
10#11720950C211yesmaximal, characteristic, complemented
11#11720949C211yesmaximal, characteristic, complemented
12#11720946C211yesmaximal, characteristic, complemented
13#11720934C211yesmaximal, characteristic, complemented
14#11720921C211yesmaximal, characteristic, complemented
15#11720920C211yesmaximal, characteristic, complemented
16D3×#898—31nomaximal
17C2×#63460—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×D3×C9C2211yescharacteristic
20C2×C4×D3×C9C2211yescharacteristic
21C2×C4×D3×C9C2211yescharacteristic
22C2×D3×Dic9C2211yescharacteristic
23C2×D3×Dic9C2211yescharacteristic
24C2×D3×Dic9C2211yescharacteristic
25C3×C9×C4⋊C4C2211yescharacteristic, complemented
26#88536C2211yescharacteristic
27#88536C2211yescharacteristic
28#88536C2211yescharacteristic
29C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
30#88534C2211yescharacteristic, complemented
31C4×C3⋊Dic9C2211yescharacteristic, complemented
32C3×(C2×D9)⋊C4C2211yescharacteristic
33C3×(C2×D9)⋊C4C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C9×C4⋊Dic3C2211yescharacteristic, complemented
36C9×Dic3⋊C4C2211yescharacteristic, complemented
37C9×Dic3⋊C4C2211yescharacteristic, complemented
38C3×C4⋊Dic9C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic9C2211yescharacteristic, complemented
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic, complemented
48Dic3⋊Dic9C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64107—31no—
54C3×#898—31no—
55C3×D3×C4⋊C4D311yescharacteristic
56D3×(C2×D3)⋊C4—31no—
57D3×(C2×D3)⋊C4—31no—
58D3×(C2×D3)⋊C4—31no—
59D3×C4⋊Dic3—31no—
60D3×Dic3⋊C4—31no—
61C4×D3×Dic3—31no—
62#63868—31no—
63#63862—31no—
64#63861—31no—
65#63858—31no—
66#63848—31no—
67#63848—31no—
68C2×C9×C4⋊C4—31no—
69C2×(C2×D9)⋊C4—31no—
70C2×(C2×D9)⋊C4—31no—
71C2×(C2×D9)⋊C4—31no—
72C2×C4⋊Dic9—31no—
73C2×Dic9⋊C4—31no—
74C2×C4×Dic9—31no—
75#63460—31no—
76#63460—31no—
77#63460—31no—
78#63460—31no—
79#63460—31no—
80#63460—31no—
81#63460—31no—
82#63460—61no—
83#63460D311yescharacteristic, direct product factor
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C2×D3×D9—22no—
88C2×D3×D9—22no—
89C2×D3×D9—22no—
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C4×D3×C9—22no—
103C4×D3×C9—22no—
104C4×D3×C9—22no—
105D3×Dic9—22no—
106D3×Dic9—22no—
107D3×Dic9—22no—
108D3×#126—91no—
109C2×#898—91no—
110C22×D32—31no—
111C2×C3×C4×D3C2×D311yescharacteristic
112C2×C3×C4×D3C2×D311yescharacteristic
113C2×C3×C4×D3C2×D311yescharacteristic
114C2×D3×Dic3—31no—
115C2×D3×Dic3—31no—
116C2×D3×Dic3—31no—
117C23×D9—31no—
118C32×C4⋊C4C2×D311yescharacteristic
119#3752—31no—
120#3752—31no—
121#3752—31no—
122C4⋊(C3⋊Dic3)—31no—
123#3750—31no—
124C4×C3⋊Dic3—31no—
125C3×(C2×D3)⋊C4—31no—
126C3×(C2×D3)⋊C4—31no—
127C3×(C2×D3)⋊C4—31no—
128C3×C4⋊Dic3—31no—
129C3×C4⋊Dic3C2×D311yescharacteristic
130C3×Dic3⋊C4—31no—
131C3×Dic3⋊C4C2×D311yescharacteristic
132C3×Dic3⋊C4C2×D311yescharacteristic
133C3×C4×Dic3—31no—
134#3724—31no—
135Dic3⋊Dic3—31no—
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—31no—
138#3722—31no—
139#3722—31no—
140#3722—31no—
141(C2×D3)⋊Dic3—31no—
142(C2×D3)⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144Dic32—31no—
145Dic32—31no—
146C22×C4×C9—31no—
147C22×C4×C9—31no—
148C22×C4×C9—31no—
149C22×Dic9—31no—
150C22×Dic9—31no—
151C22×Dic9—31no—
152C9×C4⋊C4—21no—
153C9×C4⋊C4—31no—
154C9×C4⋊C4—31no—
155C9×C4⋊C4—31no—
156C9×C4⋊C4C2×D311yescharacteristic, complemented
157(C2×D9)⋊C4—31no—
158(C2×D9)⋊C4—31no—
159(C2×D9)⋊C4—31no—
160(C2×D9)⋊C4—31no—
161(C2×D9)⋊C4—31no—
162(C2×D9)⋊C4—31no—
163(C2×D9)⋊C4—31no—
164(C2×D9)⋊C4—31no—
165(C2×D9)⋊C4—31no—
166(C2×D9)⋊C4—61no—
167(C2×D9)⋊C4—61no—
168(C2×D9)⋊C4—61no—
169(C2×D9)⋊C4C2×D311yescharacteristic
170(C2×D9)⋊C4C2×D311yescharacteristic
171(C2×D9)⋊C4C2×D311yescharacteristic
172C4⋊Dic9—31no—
173C4⋊Dic9—31no—
174C4⋊Dic9—31no—
175C4⋊Dic9—61no—
176C4⋊Dic9C2×D311yescharacteristic, complemented
177Dic9⋊C4—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—61no—
181Dic9⋊C4C2×D311yescharacteristic, complemented
182C4×Dic9—31no—
183C4×Dic9—31no—
184C4×Dic9—31no—
185C4×Dic9—61no—
186C4×Dic9C2×D311yescharacteristic, complemented
187C22×C3×C9C2411yescharacteristic
188C2×C3⋊D9—21no—
189C2×C3⋊D9—21no—
190C2×C3⋊D9—21no—
191C2×D3×C9#4112yes—
192C2×D3×C9#4112yes—
193C2×D3×C9#4112yes—
194C2×C3×D9—21no—
195C2×C3×D9—21no—
196C2×C3×D9—21no—
197D3×D9—44no—
198C3×C4×C9—21no—
199C3×C4×C9—21no—
200C3×C4×C9—21no—
201C3⋊Dic9—21no—
202C3⋊Dic9—21no—
203C3⋊Dic9—21no—
204C9×Dic3—21no—
205C9×Dic3—21no—
206C9×Dic3—21no—
207C3×Dic9—21no—
208C3×Dic9—21no—
209C3×Dic9—21no—
210C3×#126—91no—
211C2×C3×C4⋊C4—31no—
212C2×(C2×D3)⋊C4—91no—
213C2×(C2×D3)⋊C4—91no—
214C2×(C2×D3)⋊C4—91no—
215C2×C4⋊Dic3—91no—
216C2×Dic3⋊C4—91no—
217C2×C4×Dic3—91no—
218#898—31no—
219#898—91no—
220#898—91no—
221#898—91no—
222#898—91no—
223#898—91no—
224#898—91no—
225#898—91no—
226#898—91no—
227#898—91no—
228#898—91no—
229#898—181no—
230D3×C4⋊C4—91no—
231D3×C4⋊C4—91no—
232D3×C4⋊C4D911yescharacteristic, complemented
233D3×C22⋊C4—91no—
234D3×C22⋊C4—91no—
235D3×C22⋊C4—91no—
236#879—91no—
237#879—91no—
238#879—91no—
239#876—91no—
240C42×D3—91no—
241C22×C3⋊D3—31no—
242C22×C3×D3—31no—
243C22×C3×D3C22×D311yescharacteristic
244C2×D32—62no—
245C2×D32—62no—
246C2×D32—62no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—31no—
252C2×C3⋊Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3—31no—
256C2×C3×Dic3C22×D311yescharacteristic
257C2×C3×Dic3C22×D311yescharacteristic
258C2×C3×Dic3C22×D311yescharacteristic
259C3×C4×D3—22no—
260C3×C4×D3—22no—
261C3×C4×D3—22no—
262D3×Dic3—62no—
263D3×Dic3—62no—
264D3×Dic3—62no—
265C23×C9—31no—
266C22×D9—31no—
267C22×D9—61no—
268C22×D9—62no—
269C22×D9—62no—
270C22×D9—62no—
271C22×D9C22×D311yescharacteristic
272C2×C4×C9—21no—
273C2×C4×C9—21no—
274C2×C4×C9—21no—
275C2×C4×C9—31no—
276C2×C4×C9—31no—
277C2×C4×C9—31no—
278C2×C4×C9—62no—
279C2×C4×C9—62no—
280C2×C4×C9—62no—
281C2×C4×C9C22×D311yescharacteristic
282C2×C4×C9C22×D311yescharacteristic
283C2×C4×C9C22×D311yescharacteristic
284C2×Dic9—31no—
285C2×Dic9—31no—
286C2×Dic9—31no—
287C2×Dic9—61no—
288C2×Dic9—61no—
289C2×Dic9—61no—
290C2×Dic9—62no—
291C2×Dic9—62no—
292C2×Dic9—62no—
293C2×Dic9C22×D311yescharacteristic
294C2×Dic9C22×D311yescharacteristic
295C2×Dic9C22×D311yescharacteristic
296C2×#126—271noSylow
297C2×C3×C9C2×#4111yescharacteristic
298C2×C3×C9C2×#4111yescharacteristic
299C2×C3×C9C2×#4111yescharacteristic
300C3⋊D9—41no—
301D3×C9#12614yescomplemented
302C3×D9—41no—
303C23×D3—91no—
304C23×D3—91no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×Dic3—91no—
309C22×Dic3—91no—
310C22×Dic3—91no—
311C2×C4×D3—91no—
312C2×C4×D3—91no—
313C2×C4×D3—91no—
314C2×C4×D3C2×D911yescharacteristic
315C2×C4×D3C2×D911yescharacteristic
316C2×C4×D3C2×D911yescharacteristic
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—91no—
322C3×C4⋊C4—91no—
323C3×C4⋊C4C2×D911yescharacteristic, complemented
324C3×C4⋊C4D3211yescharacteristic
325C3×C22⋊C4—91no—
326C3×C22⋊C4—91no—
327C3×C22⋊C4—91no—
328C3×C42—91no—
329#217—91no—
330#217—91no—
331#217—91no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—31no—
334(C2×D3)⋊C4—31no—
335(C2×D3)⋊C4—91no—
336(C2×D3)⋊C4—91no—
337(C2×D3)⋊C4—91no—
338(C2×D3)⋊C4—91no—
339(C2×D3)⋊C4—91no—
340(C2×D3)⋊C4—91no—
341(C2×D3)⋊C4—91no—
342(C2×D3)⋊C4—91no—
343(C2×D3)⋊C4—91no—
344(C2×D3)⋊C4—91no—
345(C2×D3)⋊C4—91no—
346(C2×D3)⋊C4—91no—
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—181no—
351(C2×D3)⋊C4—181no—
352(C2×D3)⋊C4—181no—
353C4⋊Dic3—31no—
354C4⋊Dic3—91no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—181no—
360C4⋊Dic3C2×D911yescharacteristic, complemented
361Dic3⋊C4—31no—
362Dic3⋊C4—91no—
363Dic3⋊C4—91no—
364Dic3⋊C4—91no—
365Dic3⋊C4—91no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—181no—
370Dic3⋊C4C2×D911yescharacteristic, complemented
371Dic3⋊C4C2×D911yescharacteristic, complemented
372C4×Dic3—31no—
373C4×Dic3—91no—
374C4×Dic3—91no—
375C4×Dic3—91no—
376C4×Dic3—91no—
377C4×Dic3—91no—
378C4×Dic3—91no—
379C4×Dic3—181no—
380C22×C32C23×D311yescharacteristic
381C2×C3⋊D3—61no—
382C2×C3⋊D3—61no—
383C2×C3⋊D3—61no—
384C2×C3×D3—61no—
385C2×C3×D3—61no—
386C2×C3×D3—61no—
387C2×C3×D3#23512yes—
388C2×C3×D3#23712yes—
389C2×C3×D3#23912yes—
390D32—124no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C3⋊Dic3—61no—
395C3⋊Dic3—61no—
396C3⋊Dic3—61no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—61no—
401C3×Dic3—61no—
402C3×Dic3—61no—
403C22×C9—21no—
404C22×C9—32no—
405C22×C9—32no—
406C22×C9—32no—
407C22×C9C23×D311yescharacteristic
408C2×D9—21no—
409C2×D9—21no—
410C2×D9—21no—
411C2×D9—61no—
412C2×D9—61no—
413C2×D9—61no—
414C2×D9—121no—
415C2×D9—121no—
416C2×D9—121no—
417C2×D9—124no—
418C4×C9—21no—
419C4×C9—21no—
420C4×C9—21no—
421C4×C9—41no—
422C4×C9—41no—
423C4×C9—41no—
424C4×C9—61no—
425C4×C9—61no—
426C4×C9—61no—
427Dic9—21no—
428Dic9—21no—
429Dic9—21no—
430Dic9—61no—
431Dic9—61no—
432Dic9—61no—
433Dic9—121no—
434Dic9—121no—
435Dic9—121no—
436#126—91no—
437#126—271no—
438#126—271no—
439#126—271no—
440#126—271no—
441#126—271no—
442#126—271no—
443#126—271no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—271no—
446C2×C4⋊C4—271no—
447C2×C22⋊C4—271no—
448C2×C22⋊C4—271no—
449C2×C22⋊C4—271no—
450C2×C42—271no—
451C3×C9C2×#12611yescharacteristic, complemented, Sylow
452C23×C3—31no—
453C23×C3—91no—
454C22×D3—31no—
455C22×D3—91no—
456C22×D3—91no—
457C22×D3—181no—
458C22×D3—182no—
459C22×D3—182no—
460C22×D3—182no—
461C22×D3—182no—
462C22×D3—182no—
463C22×D3—182no—
464C22×D3C22×D911yescharacteristic
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—91no—
475C2×C3×C4—91no—
476C2×C3×C4—91no—
477C2×C3×C4C22×D911yescharacteristic
478C2×C3×C4C22×D911yescharacteristic
479C2×C3×C4C22×D911yescharacteristic
480C2×C3×C4C2×D3211yescharacteristic
481C2×C3×C4C2×D3211yescharacteristic
482C2×C3×C4C2×D3211yescharacteristic
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—91no—
487C2×Dic3—91no—
488C2×Dic3—91no—
489C2×Dic3—91no—
490C2×Dic3—91no—
491C2×Dic3—91no—
492C2×Dic3—181no—
493C2×Dic3—181no—
494C2×Dic3—181no—
495C2×Dic3—182no—
496C2×Dic3—182no—
497C2×Dic3—182no—
498C2×Dic3C22×D911yescharacteristic
499C2×Dic3C22×D911yescharacteristic
500C2×Dic3C22×D911yescharacteristic
501C4×D3—22no—
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—182no—
505C4×D3—182no—
506C4×D3—182no—
507C2×C32C2×#23511yescharacteristic
508C2×C32C2×#23711yescharacteristic
509C2×C32C2×#23911yescharacteristic
510C3⋊D3—121no—
511C3×D3—121no—
512C3×D3#89814yes—
513C2×C9—21no—
514C2×C9—21no—
515C2×C9—21no—
516C2×C9—34no—
517C2×C9D3×#4111yescharacteristic
518C2×C9D3×#4111yescharacteristic
519C2×C9D3×#4111yescharacteristic
520D9—41no—
521D9—121no—
522D9—241no—
523C24—271no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—271no—
528C22×C4—271no—
529C22×C4—271no—
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—91no—
534C4⋊C4—91no—
535C4⋊C4—271no—
536C4⋊C4—271no—
537C4⋊C4—271no—
538C4⋊C4—271no—
539C4⋊C4—271no—
540C4⋊C4—271no—
541C4⋊C4D3×D911yescharacteristic, complemented
542C22⋊C4—91no—
543C22⋊C4—91no—
544C22⋊C4—91no—
545C22⋊C4—271no—
546C22⋊C4—271no—
547C22⋊C4—271no—
548C22⋊C4—271no—
549C22⋊C4—271no—
550C22⋊C4—271no—
551C22⋊C4—271no—
552C22⋊C4—271no—
553C22⋊C4—271no—
554C42—91no—
555C42—271no—
556C42—271no—
557C42—271no—
558C22×C3—21no—
559C22×C3—32no—
560C22×C3—32no—
561C22×C3—32no—
562C22×C3—181no—
563C22×C3—181no—
564C22×C3—181no—
565C22×C3C23×D911yescharacteristic
566C22×C3C22×D3211yescharacteristic
567C2×D3—61no—
568C2×D3—61no—
569C2×D3—61no—
570C2×D3—181no—
571C2×D3—181no—
572C2×D3—181no—
573C2×D3—181no—
574C2×D3—181no—
575C2×D3—181no—
576C2×D3—361no—
577C2×D3—361no—
578C2×D3—361no—
579C2×D3—364no—
580C2×D3—364no—
581C2×D3#369712yes—
582C2×D3#369912yes—
583C2×D3#370112yes—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—61no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—181no—
597C3×C4—181no—
598C3×C4—181no—
599Dic3—21no—
600Dic3—21no—
601Dic3—21no—
602Dic3—61no—
603Dic3—61no—
604Dic3—61no—
605Dic3—181no—
606Dic3—181no—
607Dic3—181no—
608Dic3—181no—
609Dic3—181no—
610Dic3—181no—
611Dic3—361no—
612Dic3—361no—
613Dic3—361no—
614C32C2×#89811yescharacteristic
615C9—21no—
616C9D3×#12611yescharacteristic, complemented
617C23—31no—
618C23—91no—
619C23—271no—
620C23—542no—
621C23—542no—
622C23—542no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—91no—
630C2×C4—91no—
631C2×C4—91no—
632C2×C4—271no—
633C2×C4—271no—
634C2×C4—271no—
635C2×C4—542no—
636C2×C4—542no—
637C2×C4—542no—
638C2×C4C2×D3×D911yescharacteristic
639C2×C4C2×D3×D911yescharacteristic
640C2×C4C2×D3×D911yescharacteristic
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—34no—
645C2×C3—361no—
646C2×C3C2×#369711yescharacteristic
647C2×C3C2×#369911yescharacteristic
648C2×C3C2×#370111yescharacteristic
649C2×C3D3×#23511yescharacteristic
650C2×C3D3×#23711yescharacteristic
651C2×C3D3×#23911yescharacteristic
652D3—121no—
653D3—361no—
654D3—361no—
655D3—721no—
656D3#6346014yesdirect product factor
657C22—32no—
658C22—32no—
659C22—32no—
660C22—181no—
661C22—181no—
662C22—181no—
663C22—541no—
664C22—541no—
665C22—541no—
666C22—1084no—
667C22C22×D3×D911yescharacteristic
668C4—21no—
669C4—21no—
670C4—21no—
671C4—61no—
672C4—61no—
673C4—61no—
674C4—181no—
675C4—181no—
676C4—181no—
677C4—541no—
678C4—541no—
679C4—541no—
680C3—21no—
681C3C2×#6346011yescharacteristic, complemented
682C3D3×#89811yescharacteristic
683C2—34no—
684C2—361no—
685C2—1081no—
686C2D3×#369711yescharacteristic
687C2D3×#369911yescharacteristic
688C2D3×#370111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC22×D3×D9C22
hypercenterC4⋊C4D3×D9
hypocenterC3×C9C2×#126
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721754C2semidirect
2. D3×C9×C4⋊C4C2semidirect
3. C3×#63460C2semidirect
7. D3×C4⋊Dic9C2semidirect
8. D3×Dic9⋊C4C2semidirect
9. C4×D3×Dic9C2semidirect
10. #11720950C2semidirect
11. #11720949C2semidirect
12. #11720946C2semidirect
13. #11720934C2semidirect
14. #11720921C2semidirect
15. #11720920C2semidirect
25. C3×C9×C4⋊C4C22semidirect
29. C4⋊(C3⋊Dic9)C22semidirect
30. #88534C22semidirect
31. C4×C3⋊Dic9C22semidirect
35. C9×C4⋊Dic3C22semidirect
36. C9×Dic3⋊C4C22semidirect
37. C9×Dic3⋊C4C22semidirect
38. C3×C4⋊Dic9C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. C3×C4×Dic9C22semidirect
47. Dic3⋊Dic9C22semidirect
48. Dic3⋊Dic9C22semidirect
49. #88442C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
83. #63460D3direct (N × H)
156. C9×C4⋊C4C2×D3semidirect
176. C4⋊Dic9C2×D3semidirect
181. Dic9⋊C4C2×D3semidirect
186. C4×Dic9C2×D3semidirect
232. D3×C4⋊C4D9semidirect
301. D3×C9#126semidirect
323. C3×C4⋊C4C2×D9semidirect
360. C4⋊Dic3C2×D9semidirect
370. Dic3⋊C4C2×D9semidirect
371. Dic3⋊C4C2×D9semidirect
451. C3×C9C2×#126semidirect
541. C4⋊C4D3×D9semidirect
616. C9D3×#126semidirect
656. D3#63460direct (N × H)
681. C3C2×#63460semidirect

Maximal subgroups

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

subgroupindex
#117217542
D3×C9×C4⋊C42
C3×#634602
D3×(C2×D9)⋊C42
D3×C4⋊Dic92
D3×Dic9⋊C42
C4×D3×Dic92
#117209502
#117209492
#117209462
#117209342
#117209212
#117209202
D3×#8983
C2×#634603