Finite Group Databasebeta

← C2×D3×#3802 #13181257

Subgroups — C2×D3×#3802 #13181257

Order 1728.

6210 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D33C212yesmaximal, complemented
2C2×C4⋊#1113C211yesmaximal, characteristic, complemented
3C2×#89026C212yesmaximal, complemented
4C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
5C2×C3×#3802C211yesmaximal, characteristic, complemented
6C2×C3×D3×D12C212yesmaximal, complemented
7C2×#88954C212yesmaximal, complemented
8C2×#88953C212yesmaximal, complemented
9C2×D3×#625C212yesmaximal, complemented
10D3×#3802C2116yesmaximal, direct product factor
11C2×D32×D4—32nomaximal
12C22×#3802—31nomaximal
13C22×#1113C2212yescomplemented
14C22×D3×C3⋊D3C2211yescharacteristic
15C22×D3×C3⋊D3C2214yescomplemented
16C22×C3×D32C2214yescomplemented
17C22×C3×D32C2212yescomplemented
18C2×D33—216no—
19C2×D33C22116yescomplemented
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C32×D12C2212yescomplemented
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×#6295C2212yescomplemented
26C4⋊#1113C2218yescomplemented
27C2×#6290C2214yescomplemented
28C2×#6289C2211yescharacteristic, complemented
29C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
30C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
31#89026C22116yescomplemented
32C4×D3×C3⋊D3C2218yescomplemented
33C2×C3×#626C2214yescomplemented
34C2×C3×#625C2212yescomplemented
35C3×#3802C2218yescomplemented
36C3×D3×D12C22116yescomplemented
37#88954C22116yescomplemented
38#88953C22116yescomplemented
39D3×#625C22116yescomplemented
40C23×D32—32no—
41C23×D32—34no—
42C2×D4×C3⋊D3—32no—
43C22×C4×C3⋊D3—31no—
44C2×C3×D3×D4—32no—
45C2×C3×D3×D4—32no—
46C22×C3×D12—32no—
47C2×#3811—34no—
48C2×D3×#67—34no—
49C2×D3×#67—34no—
50C22×#625—32no—
51D32×D4—332no—
52C2×#3802—31no—
53C2×#3802—32no—
54C2×#3802—32no—
55C2×#3802—32no—
56C2×#3802—316no—
57C2×#3802—32no—
58C2×#3802—62no—
59C2×#3802D311yescharacteristic, direct product factor
60C2×D3×D12—32no—
61C2×D3×D12D312yescomplemented
62C2×C4×D32—32no—
63C2×C4×D32—61no—
64C22×C3⋊(C3⋊D3)C2311yescharacteristic
65C22×C3×C3⋊D3C2311yescharacteristic
66C22×C3×C3⋊D3C2314yescomplemented
67C22×C32×D3C2311yescharacteristic
68C22×C32×D3C2314yescomplemented
69C2×#1113—28no—
70C2×#1113C2318yescomplemented
71C2×D3×C3⋊D3—216no—
72C2×D3×C3⋊D3D418yescomplemented
73C2×D3×C3⋊D3C2314yes—
74C2×D3×C3⋊D3C23116yescomplemented
75C2×C3×D32—28no—
76C2×C3×D32—216no—
77C2×C3×D32C23116yescomplemented
78C2×C3×D32C2318yescomplemented
79D33—264no—
80C2×C33×C4C2311yescharacteristic, complemented
81C2×C3⋊(C3⋊Dic3)C2311yescharacteristic, complemented
82C4×C3⋊(C3⋊D3)C2314yescomplemented
83C2×C3×C3⋊Dic3C2311yescharacteristic, complemented
84C3×C4⋊(C3⋊D3)C2318yescomplemented
85C3×C4×C3⋊D3C2314yescomplemented
86C2×C32×Dic3C2311yescharacteristic, complemented
87C32×D12C2318yescomplemented
88C32×C4×D3C2314yescomplemented
89#6295C2318yescomplemented
90#6290C23116yescomplemented
91#6289C2314yescomplemented
92Dic3×C3⋊D3C2314yescomplemented
93D3×C3⋊Dic3C2314yescomplemented
94C3×#626C23116yescomplemented
95C3×#625C2318yescomplemented
96C22×D3×D4—92no—
97C22×D3×D4—91no—
98C23×C3⋊D3—31no—
99C23×C3⋊D3—34no—
100C23×C3×D3—34no—
101C23×C3×D3—34no—
102C23×C3×D3—34no—
103C22×D32—32no—
104C22×D32—32no—
105C22×D32—34no—
106C22×D32—34no—
107C22×D32—34no—
108C22×D32—316no—
109C22×D32—332no—
110C22×D32—632no—
111C22×D32—616no—
112C22×D32—61no—
113C22×D32—64no—
114C22×D32C2×D314yescomplemented
115C22×D32C2×D312yescomplemented
116C2×C32×D4—32no—
117C22×C32×C4—31no—
118C2×#638—34no—
119C22×C3⋊Dic3—31no—
120D4×C3⋊D3—316no—
121C2×C4⋊(C3⋊D3)C2×D312yescomplemented
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—32no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—38no—
127C2×C4×C3⋊D3—61no—
128C2×C4×C3⋊D3—62no—
129C2×C4×C3⋊D3—121no—
130C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
131C2×C3×#67—34no—
132C2×C3×#67—34no—
133C3×D3×D4—316no—
134C3×D3×D4—316no—
135C2×C3×D12—22no—
136C2×C3×D12—34no—
137C2×C3×D12—32no—
138C2×C3×D12—32no—
139C2×C3×D12—316no—
140C2×C3×D12—62no—
141C2×C3×D12C2×D312yescomplemented
142C2×C3×D12C2×D312yescomplemented
143C2×C3×C4×D3—21no—
144C2×C3×C4×D3—32no—
145C2×C3×C4×D3—61no—
146C2×C3×C4×D3C2×D312yescomplemented
147#3811—332no—
148D3×#67—332no—
149D3×#67—332no—
150C2×#626—34no—
151C2×#626C2×D314yescomplemented
152C2×#625—34no—
153C2×#625—34no—
154C2×#625—32no—
155C2×#625—316no—
156C2×#625—64no—
157C2×#625C2×D312yescomplemented
158C2×#624—32no—
159C2×#624—61no—
160C2×D3×Dic3—32no—
161C2×D3×Dic3—32no—
162C2×D3×Dic3—61no—
163C2×D3×Dic3—61no—
164#3802—316no—
165#3802—38no—
166#3802—316no—
167#3802—316no—
168#3802—316no—
169#3802—616no—
170#3802C2×D318yesdirect product factor
171D3×D12—316no—
172D3×D12C2×D3116yescomplemented
173C4×D32—316no—
174C4×D32—68no—
175C22×C33C2411yescharacteristic
176C2×C3⋊(C3⋊D3)C2×D414yescomplemented
177C2×C3⋊(C3⋊D3)C2412yes—
178C2×C3×C3⋊D3—28no—
179C2×C3×C3⋊D3C2×D414yescomplemented
180C2×C3×C3⋊D3C2412yes—
181C2×C3×C3⋊D3C2418yescomplemented
182C2×C32×D3—28no—
183C2×C32×D3C2×D414yescomplemented
184C2×C32×D3C2412yes—
185C2×C32×D3C2418yescomplemented
186#1113—216no—
187D3×C3⋊D3—232no—
188D3×C3⋊D3C2×D4116yescomplemented
189C3×D32—216no—
190C3×D32—232no—
191C33×C4C2412yescomplemented
192C3⋊(C3⋊Dic3)C2412yescomplemented
193C3×C3⋊Dic3C2412yescomplemented
194C32×Dic3C2412yescomplemented
195C24×D3—92no—
196C24×D3—94no—
197C22×C3×D4—92no—
198C22×C3×D4—91no—
199C22×#67—92no—
200C22×#67—94no—
201C2×D3×D4—32no—
202C2×D3×D4—32no—
203C2×D3×D4—92no—
204C2×D3×D4—932no—
205C2×D3×D4—94no—
206C2×D3×D4—92no—
207C2×D3×D4—92no—
208C2×D3×D4—94no—
209C2×D3×D4—916no—
210C2×D3×D4—92no—
211C2×D3×D4—92no—
212C2×D3×D4—92no—
213C2×D3×D4—182no—
214C22×D12—32no—
215C22×D12—91no—
216C22×C4×D3—92no—
217C22×C4×D3—91no—
218C22×C4×D3—181no—
219C23×C32—31no—
220C23×C32—34no—
221C22×C3⋊D3—31no—
222C22×C3⋊D3—32no—
223C22×C3⋊D3—38no—
224C22×C3⋊D3—34no—
225C22×C3⋊D3—316no—
226C22×C3⋊D3—62no—
227C22×C3⋊D3—61no—
228C22×C3⋊D3—616no—
229C22×C3⋊D3—121no—
230C22×C3⋊D3C22×D311yescharacteristic
231C22×C3⋊D3C22×D314yescomplemented
232C22×C3×D3—21no—
233C22×C3×D3—24no—
234C22×C3×D3—32no—
235C22×C3×D3—34no—
236C22×C3×D3—34no—
237C22×C3×D3—316no—
238C22×C3×D3—316no—
239C22×C3×D3—316no—
240C22×C3×D3—61no—
241C22×C3×D3—64no—
242C22×C3×D3—616no—
243C22×C3×D3—616no—
244C22×C3×D3—616no—
245C22×C3×D3C22×D312yes—
246C22×C3×D3C22×D314yescomplemented
247C22×C3×D3C22×D314yescomplemented
248C2×D32—28no—
249C2×D32—216no—
250C2×D32—316no—
251C2×D32—38no—
252C2×D32—38no—
253C2×D32—316no—
254C2×D32—316no—
255C2×D32—316no—
256C2×D32—68no—
257C2×D32—64no—
258C2×D32—616no—
259C2×D32—6128no—
260C2×D32—664no—
261C2×D32—616no—
262C2×D32—616no—
263C2×D32—616no—
264C2×D32—68no—
265C2×D32—1216no—
266C2×D32C22×D3116yescomplemented
267C2×D32C22×D318yescomplemented
268C32×D4—38no—
269C2×C32×C4—21no—
270C2×C32×C4—22no—
271C2×C32×C4—31no—
272C2×C32×C4—34no—
273C2×C32×C4—41no—
274C2×C32×C4C22×D312yescomplemented
275C2×C32×C4C22×D311yescharacteristic, complemented
276#638—316no—
277C2×C3⋊Dic3—32no—
278C2×C3⋊Dic3—31no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—61no—
281C2×C3⋊Dic3—62no—
282C2×C3⋊Dic3—121no—
283C2×C3⋊Dic3C22×D311yescharacteristic, complemented
284C4⋊(C3⋊D3)C22×D318yescomplemented
285C4×C3⋊D3—34no—
286C4×C3⋊D3—38no—
287C4×C3⋊D3—34no—
288C4×C3⋊D3—34no—
289C4×C3⋊D3—64no—
290C4×C3⋊D3—68no—
291C4×C3⋊D3—124no—
292C4×C3⋊D3C22×D314yescomplemented
293C3×#67—316no—
294C3×#67—316no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—32no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3C22×D312yescomplemented
299C3×D12—28no—
300C3×D12—316no—
301C3×D12—38no—
302C3×D12—38no—
303C3×D12—68no—
304C3×D12C22×D318yescomplemented
305C3×D12C22×D318yescomplemented
306C3×C4×D3—24no—
307C3×C4×D3—38no—
308C3×C4×D3—64no—
309C3×C4×D3C22×D318yescomplemented
310#626—316no—
311#626C22×D3116yescomplemented
312#625—316no—
313#625—316no—
314#625—38no—
315#625—616no—
316#625C22×D318yescomplemented
317#624—38no—
318#624—64no—
319D3×Dic3—38no—
320D3×Dic3—38no—
321D3×Dic3—64no—
322D3×Dic3—64no—
323C23×D4—271noSylow
324C2×C33C22×D412yescomplemented
325C2×C33C2511yescharacteristic
326C3⋊(C3⋊D3)C22×D414yescomplemented
327C3×C3⋊D3—28no—
328C3×C3⋊D3C22×D414yescomplemented
329C32×D3—28no—
330C32×D3C22×D414yescomplemented
331C24×C3—94no—
332C24×C3—92no—
333C23×D3—34no—
334C23×D3—34no—
335C23×D3—34no—
336C23×D3—92no—
337C23×D3—94no—
338C23×D3—916no—
339C23×D3—932no—
340C23×D3—92no—
341C23×D3—94no—
342C23×D3—94no—
343C23×D3—91no—
344C23×D3—94no—
345C23×D3—181no—
346C23×D3—184no—
347C23×D3—1832no—
348C23×D3—1816no—
349C2×C3×D4—32no—
350C2×C3×D4—32no—
351C2×C3×D4—62no—
352C2×C3×D4—916no—
353C2×C3×D4—94no—
354C2×C3×D4—98no—
355C2×C3×D4—92no—
356C2×C3×D4—92no—
357C22×C3×C4—32no—
358C22×C3×C4—61no—
359C22×C3×C4—91no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—94no—
363C2×#67—916no—
364C2×#67—932no—
365C2×#67—94no—
366C2×#67—94no—
367C2×#67—94no—
368C2×#67—184no—
369C22×Dic3—92no—
370C22×Dic3—91no—
371C22×Dic3—181no—
372D3×D4—316no—
373D3×D4—316no—
374D3×D4—916no—
375D3×D4—932no—
376D3×D4—916no—
377D3×D4—916no—
378D3×D4—932no—
379D3×D4—916no—
380D3×D4—916no—
381D3×D4—916no—
382D3×D4—1816no—
383C2×D12—34no—
384C2×D12—32no—
385C2×D12—32no—
386C2×D12—316no—
387C2×D12—62no—
388C2×D12—98no—
389C2×D12—92no—
390C2×D12D3212yescomplemented
391C2×C4×D3—32no—
392C2×C4×D3—61no—
393C2×C4×D3—916no—
394C2×C4×D3—92no—
395C2×C4×D3—92no—
396C2×C4×D3—91no—
397C2×C4×D3—92no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—98no—
401C2×C4×D3—188no—
402C2×C4×D3—181no—
403C2×C4×D3—181no—
404C2×C4×D3—182no—
405C2×C4×D3—181no—
406C2×C4×D3—361no—
407C2×C4×D3D3211yescharacteristic, complemented
408C22×C32—21no—
409C22×C32—22no—
410C22×C32—34no—
411C22×C32—32no—
412C22×C32—38no—
413C22×C32—41no—
414C22×C32—68no—
415C22×C32C23×D312yes—
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—28no—
418C2×C3⋊D3—38no—
419C2×C3⋊D3—34no—
420C2×C3⋊D3—34no—
421C2×C3⋊D3—32no—
422C2×C3⋊D3—316no—
423C2×C3⋊D3—64no—
424C2×C3⋊D3—68no—
425C2×C3⋊D3—62no—
426C2×C3⋊D3—64no—
427C2×C3⋊D3—632no—
428C2×C3⋊D3—124no—
429C2×C3⋊D3—122no—
430C2×C3⋊D3D3×D414yescomplemented
431C2×C3⋊D3C23×D312yes—
432C2×C3⋊D3C23×D318yescomplemented
433C2×C3×D3—28no—
434C2×C3×D3—28no—
435C2×C3×D3—22no—
436C2×C3×D3—28no—
437C2×C3×D3—24no—
438C2×C3×D3—38no—
439C2×C3×D3—34no—
440C2×C3×D3—38no—
441C2×C3×D3—38no—
442C2×C3×D3—48no—
443C2×C3×D3—64no—
444C2×C3×D3—62no—
445C2×C3×D3—68no—
446C2×C3×D3—632no—
447C2×C3×D3—632no—
448C2×C3×D3—68no—
449C2×C3×D3—68no—
450C2×C3×D3—632no—
451C2×C3×D3—128no—
452C2×C3×D3D3×D418yescomplemented
453C2×C3×D3C23×D314yes—
454C2×C3×D3C23×D318yescomplemented
455C2×C3×D3C23×D318yescomplemented
456D32—216no—
457D32—232no—
458D32—332no—
459D32—616no—
460D32—632no—
461D32—632no—
462D32—632no—
463D32—616no—
464D32—1232no—
465C32×C4—22no—
466C32×C4—24no—
467C32×C4—32no—
468C32×C4—42no—
469C32×C4C23×D314yescomplemented
470C32×C4C23×D312yescomplemented
471C3⋊Dic3—34no—
472C3⋊Dic3—32no—
473C3⋊Dic3—62no—
474C3⋊Dic3—64no—
475C3⋊Dic3—122no—
476C3⋊Dic3C23×D312yescomplemented
477C3×Dic3—22no—
478C3×Dic3—34no—
479C3×Dic3—62no—
480C3×Dic3C23×D314yescomplemented
481C25—272no—
482C22×D4—92no—
483C22×D4—91no—
484C22×D4—271no—
485C22×D4—272no—
486C22×D4—2716no—
487C22×D4—272no—
488C22×D4—272no—
489C22×D4—272no—
490C23×C4—271no—
491C33C23×D411yescharacteristic, complemented, Sylow
492C23×C3—32no—
493C23×C3—34no—
494C23×C3—34no—
495C23×C3—61no—
496C23×C3—64no—
497C23×C3—916no—
498C23×C3—98no—
499C23×C3—91no—
500C23×C3—94no—
501C23×C3—1816no—
502C23×C3—188no—
503C22×D3—32no—
504C22×D3—34no—
505C22×D3—34no—
506C22×D3—316no—
507C22×D3—316no—
508C22×D3—316no—
509C22×D3—61no—
510C22×D3—64no—
511C22×D3—616no—
512C22×D3—616no—
513C22×D3—616no—
514C22×D3—98no—
515C22×D3—916no—
516C22×D3—98no—
517C22×D3—916no—
518C22×D3—916no—
519C22×D3—916no—
520C22×D3—91no—
521C22×D3—92no—
522C22×D3—94no—
523C22×D3—98no—
524C22×D3—916no—
525C22×D3—184no—
526C22×D3—188no—
527C22×D3—1816no—
528C22×D3—181no—
529C22×D3—182no—
530C22×D3—1816no—
531C22×D3—1816no—
532C22×D3—18128no—
533C22×D3—1864no—
534C22×D3—188no—
535C22×D3—1816no—
536C22×D3—1816no—
537C22×D3—361no—
538C22×D3—3616no—
539C22×D3C2×D3211yescharacteristic
540C22×D3C2×D3214yescomplemented
541C3×D4—38no—
542C3×D4—38no—
543C3×D4—68no—
544C3×D4—916no—
545C3×D4—98no—
546C3×D4—98no—
547C2×C3×C4—21no—
548C2×C3×C4—22no—
549C2×C3×C4—32no—
550C2×C3×C4—38no—
551C2×C3×C4—41no—
552C2×C3×C4—64no—
553C2×C3×C4—61no—
554C2×C3×C4—91no—
555C2×C3×C4—94no—
556C2×C3×C4C2×D3212yescomplemented
557C2×C3×C4C2×D3211yescharacteristic, complemented
558#67—316no—
559#67—316no—
560#67—916no—
561#67—916no—
562#67—916no—
563#67—916no—
564#67—1816no—
565C2×Dic3—32no—
566C2×Dic3—61no—
567C2×Dic3—98no—
568C2×Dic3—91no—
569C2×Dic3—92no—
570C2×Dic3—94no—
571C2×Dic3—184no—
572C2×Dic3—181no—
573C2×Dic3—182no—
574C2×Dic3—361no—
575C2×Dic3C2×D3211yescharacteristic, complemented
576D12—316no—
577D12—38no—
578D12—38no—
579D12—68no—
580D12—98no—
581D12C2×D3218yescomplemented
582C4×D3—38no—
583C4×D3—64no—
584C4×D3—98no—
585C4×D3—98no—
586C4×D3—94no—
587C4×D3—98no—
588C4×D3—94no—
589C4×D3—94no—
590C4×D3—184no—
591C4×D3—184no—
592C4×D3—188no—
593C4×D3—184no—
594C4×D3—364no—
595C4×D3C2×D3214yescomplemented
596C2×C32—22no—
597C2×C32—24no—
598C2×C32—21no—
599C2×C32—22no—
600C2×C32—34no—
601C2×C32—42no—
602C2×C32—41no—
603C2×C32—68no—
604C2×C32C2×D3×D414yescomplemented
605C2×C32C2×D3×D412yescomplemented
606C2×C32C24×D312yes—
607C2×C32C24×D311yescharacteristic
608C3⋊D3—28no—
609C3⋊D3—38no—
610C3⋊D3—34no—
611C3⋊D3—64no—
612C3⋊D3—68no—
613C3⋊D3—124no—
614C3⋊D3C2×D3×D414yescomplemented
615C3×D3—28no—
616C3×D3—28no—
617C3×D3—24no—
618C3×D3—38no—
619C3×D3—48no—
620C3×D3—64no—
621C3×D3—68no—
622C3×D3—68no—
623C3×D3—128no—
624C3×D3C2×D3×D418yescomplemented
625C24—94no—
626C24—92no—
627C24—271no—
628C24—274no—
629C24—2716no—
630C24—272no—
631C24—5416no—
632C2×D4—32no—
633C2×D4—916no—
634C2×D4—94no—
635C2×D4—98no—
636C2×D4—92no—
637C2×D4—92no—
638C2×D4—278no—
639C2×D4—272no—
640C2×D4—2716no—
641C2×D4—2716no—
642C2×D4—2716no—
643C2×D4—2716no—
644C2×D4—274no—
645C22×C4—31no—
646C22×C4—91no—
647C22×C4—271no—
648C22×C4—278no—
649C22×C4—271no—
650C22×C4—271no—
651C22×C4—271no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—38no—
655C22×C3—34no—
656C22×C3—38no—
657C22×C3—38no—
658C22×C3—41no—
659C22×C3—62no—
660C22×C3—64no—
661C22×C3—68no—
662C22×C3—68no—
663C22×C3—68no—
664C22×C3—94no—
665C22×C3—92no—
666C22×C3—98no—
667C22×C3—128no—
668C22×C3—1832no—
669C22×C3—1816no—
670C22×C3—188no—
671C22×C3C22×D3211yescharacteristic
672C22×C3C22×D3212yes—
673C2×D3—28no—
674C2×D3—38no—
675C2×D3—34no—
676C2×D3—38no—
677C2×D3—38no—
678C2×D3—62no—
679C2×D3—64no—
680C2×D3—68no—
681C2×D3—632no—
682C2×D3—632no—
683C2×D3—68no—
684C2×D3—68no—
685C2×D3—632no—
686C2×D3—932no—
687C2×D3—94no—
688C2×D3—98no—
689C2×D3—92no—
690C2×D3—94no—
691C2×D3—916no—
692C2×D3—128no—
693C2×D3—1816no—
694C2×D3—182no—
695C2×D3—184no—
696C2×D3—184no—
697C2×D3—188no—
698C2×D3—1832no—
699C2×D3—1832no—
700C2×D3—1816no—
701C2×D3—1832no—
702C2×D3—1832no—
703C2×D3—362no—
704C2×D3—364no—
705C2×D3—3632no—
706C2×D3#380214yesdirect product factor
707C2×D3C22×D3212yes—
708C2×D3C22×D3218yescomplemented
709C3×C4—22no—
710C3×C4—24no—
711C3×C4—34no—
712C3×C4—42no—
713C3×C4—62no—
714C3×C4—92no—
715C3×C4C22×D3214yescomplemented
716C3×C4C22×D3212yescomplemented
717Dic3—34no—
718Dic3—62no—
719Dic3—92no—
720Dic3—94no—
721Dic3—182no—
722Dic3—184no—
723Dic3—362no—
724Dic3C22×D3212yescomplemented
725C32—21no—
726C32—22no—
727C32—41no—
728C32C22×D3×D412yescomplemented
729C32C22×D3×D411yescharacteristic, complemented
730C23—31no—
731C23—34no—
732C23—916no—
733C23—98no—
734C23—91no—
735C23—94no—
736C23—1816no—
737C23—188no—
738C23—274no—
739C23—278no—
740C23—2716no—
741C23—278no—
742C23—271no—
743C23—5416no—
744C23—548no—
745C23—5464no—
746D4—38no—
747D4—916no—
748D4—98no—
749D4—98no—
750D4—278no—
751D4—2716no—
752C2×C4—31no—
753C2×C4—34no—
754C2×C4—91no—
755C2×C4—94no—
756C2×C4—274no—
757C2×C4—274no—
758C2×C4—274no—
759C2×C4—271no—
760C2×C4—274no—
761C2×C4D3311yescharacteristic, complemented
762C2×C3—22no—
763C2×C3—24no—
764C2×C3—21no—
765C2×C3—22no—
766C2×C3—38no—
767C2×C3—42no—
768C2×C3—41no—
769C2×C3—64no—
770C2×C3—68no—
771C2×C3—68no—
772C2×C3—94no—
773C2×C3—128no—
774C2×C3—188no—
775C2×C3C2×#380212yescomplemented
776C2×C3D32×D414yescomplemented
777C2×C3C23×D3211yescharacteristic
778C2×C3C23×D3212yes—
779D3—28no—
780D3—38no—
781D3—64no—
782D3—68no—
783D3—68no—
784D3—94no—
785D3—98no—
786D3—128no—
787D3—184no—
788D3—188no—
789D3—364no—
790D3C2×#380214yesdirect product factor
791C22—34no—
792C22—32no—
793C22—38no—
794C22—68no—
795C22—94no—
796C22—92no—
797C22—98no—
798C22—1832no—
799C22—1816no—
800C22—188no—
801C22—2716no—
802C22—274no—
803C22—272no—
804C22—5432no—
805C22—5416no—
806C22C2×D3311yescharacteristic
807C4—32no—
808C4—92no—
809C4—272no—
810C4C2×D3312yescomplemented
811C3—21no—
812C3—22no—
813C3—41no—
814C3C22×#380211yescharacteristic, complemented
815C3C2×D32×D412yescomplemented
816C2—34no—
817C2—68no—
818C2—94no—
819C2—188no—
820C2—274no—
821C2D3×#380212yesdirect product factor
822C2C22×D3311yescharacteristic
subgroupG/H
centerC22C2×D33
commutator, cosocleC2×C33C25
FrattiniC2C22×D33
FittingC2×C33×C4C23
socleC22×C33C24
hypercenterC2×C4D33
hypocenterC33C23×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D33C2semidirect
2. C2×C4⋊#1113C2semidirect
3. C2×#89026C2semidirect
4. C2×C4×D3×C3⋊D3C2semidirect
5. C2×C3×#3802C2semidirect
6. C2×C3×D3×D12C2semidirect
7. C2×#88954C2semidirect
8. C2×#88953C2semidirect
9. C2×D3×#625C2semidirect
10. D3×#3802C2direct (N × H)
13. C22×#1113C22semidirect
15. C22×D3×C3⋊D3C22semidirect
16. C22×C3×D32C22semidirect
17. C22×C3×D32C22semidirect
19. C2×D33C22semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
21. C2×C3×C4⋊(C3⋊D3)C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
23. C2×C32×D12C22semidirect
24. C2×C32×C4×D3C22semidirect
25. C2×#6295C22semidirect
26. C4⋊#1113C22semidirect
27. C2×#6290C22semidirect
28. C2×#6289C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
30. C2×D3×C3⋊Dic3C22semidirect
31. #89026C22semidirect
32. C4×D3×C3⋊D3C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#625C22semidirect
35. C3×#3802C22semidirect
36. C3×D3×D12C22semidirect
37. #88954C22semidirect
38. #88953C22semidirect
39. D3×#625C22semidirect
59. C2×#3802D3direct (N × H)
61. C2×D3×D12D3semidirect
66. C22×C3×C3⋊D3C23semidirect
68. C22×C32×D3C23semidirect
70. C2×#1113C23semidirect
72. C2×D3×C3⋊D3D4semidirect
74. C2×D3×C3⋊D3C23semidirect
77. C2×C3×D32C23semidirect
78. C2×C3×D32C23semidirect
80. C2×C33×C4C23semidirect
81. C2×C3⋊(C3⋊Dic3)C23semidirect
82. C4×C3⋊(C3⋊D3)C23semidirect
83. C2×C3×C3⋊Dic3C23semidirect
84. C3×C4⋊(C3⋊D3)C23semidirect
85. C3×C4×C3⋊D3C23semidirect
86. C2×C32×Dic3C23semidirect
87. C32×D12C23semidirect
88. C32×C4×D3C23semidirect
89. #6295C23semidirect
90. #6290C23semidirect
91. #6289C23semidirect
92. Dic3×C3⋊D3C23semidirect
93. D3×C3⋊Dic3C23semidirect
94. C3×#626C23semidirect
95. C3×#625C23semidirect
114. C22×D32C2×D3semidirect
115. C22×D32C2×D3semidirect
121. C2×C4⋊(C3⋊D3)C2×D3semidirect
130. C2×C4×C3⋊D3C2×D3semidirect
141. C2×C3×D12C2×D3semidirect
142. C2×C3×D12C2×D3semidirect
146. C2×C3×C4×D3C2×D3semidirect
151. C2×#626C2×D3semidirect
157. C2×#625C2×D3semidirect
170. #3802C2×D3direct (N × H)
172. D3×D12C2×D3semidirect
176. C2×C3⋊(C3⋊D3)C2×D4semidirect
179. C2×C3×C3⋊D3C2×D4semidirect
181. C2×C3×C3⋊D3C24semidirect
183. C2×C32×D3C2×D4semidirect
185. C2×C32×D3C24semidirect
188. D3×C3⋊D3C2×D4semidirect
191. C33×C4C24semidirect
192. C3⋊(C3⋊Dic3)C24semidirect
193. C3×C3⋊Dic3C24semidirect
194. C32×Dic3C24semidirect
231. C22×C3⋊D3C22×D3semidirect
246. C22×C3×D3C22×D3semidirect
247. C22×C3×D3C22×D3semidirect
266. C2×D32C22×D3semidirect
267. C2×D32C22×D3semidirect
274. C2×C32×C4C22×D3semidirect
275. C2×C32×C4C22×D3semidirect
283. C2×C3⋊Dic3C22×D3semidirect
284. C4⋊(C3⋊D3)C22×D3semidirect
292. C4×C3⋊D3C22×D3semidirect
298. C2×C3×Dic3C22×D3semidirect
304. C3×D12C22×D3semidirect
305. C3×D12C22×D3semidirect
309. C3×C4×D3C22×D3semidirect
311. #626C22×D3semidirect
316. #625C22×D3semidirect
324. C2×C33C22×D4semidirect
326. C3⋊(C3⋊D3)C22×D4semidirect
328. C3×C3⋊D3C22×D4semidirect
330. C32×D3C22×D4semidirect
390. C2×D12D32semidirect
407. C2×C4×D3D32semidirect
430. C2×C3⋊D3D3×D4semidirect
432. C2×C3⋊D3C23×D3semidirect
452. C2×C3×D3D3×D4semidirect
454. C2×C3×D3C23×D3semidirect
455. C2×C3×D3C23×D3semidirect
469. C32×C4C23×D3semidirect
470. C32×C4C23×D3semidirect
476. C3⋊Dic3C23×D3semidirect
480. C3×Dic3C23×D3semidirect
491. C33C23×D4semidirect
540. C22×D3C2×D32semidirect
556. C2×C3×C4C2×D32semidirect
557. C2×C3×C4C2×D32semidirect
575. C2×Dic3C2×D32semidirect
581. D12C2×D32semidirect
595. C4×D3C2×D32semidirect
604. C2×C32C2×D3×D4semidirect
605. C2×C32C2×D3×D4semidirect
614. C3⋊D3C2×D3×D4semidirect
624. C3×D3C2×D3×D4semidirect
706. C2×D3#3802direct (N × H)
708. C2×D3C22×D32semidirect
715. C3×C4C22×D32semidirect
716. C3×C4C22×D32semidirect
724. Dic3C22×D32semidirect
728. C32C22×D3×D4semidirect
729. C32C22×D3×D4semidirect
761. C2×C4D33semidirect
775. C2×C3C2×#3802semidirect
776. C2×C3D32×D4semidirect
790. D3C2×#3802direct (N × H)
810. C4C2×D33semidirect
814. C3C22×#3802semidirect
815. C3C2×D32×D4semidirect
821. C2D3×#3802direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D332
C2×C4⋊#11132
C2×#890262
C2×C4×D3×C3⋊D32
C2×C3×#38022
C2×C3×D3×D122
C2×#889542
C2×#889532
C2×D3×#6252
D3×#38022
C2×D32×D43
C22×#38023