Finite Group Databasebeta

← C2×C3×D3×#99 #11857484

Subgroups — C2×C3×D3×#99 #11857484

Order 1152.

2329 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic
2C2×C3×D3×C22⋊C4C212yesmaximal, complemented
3C2×C32×#99C211yesmaximal, characteristic, complemented
4C2×C3×#834C211yesmaximal, characteristic, complemented
5C2×C3×#806C212yesmaximal, complemented
6C3×D3×#99C218yesmaximal, direct product factor
7C22×C3×#99—31nomaximal
8C2×D3×#99C311yesmaximal, characteristic, direct product factor
9C24×C3×D3C411yescharacteristic, complemented
10C24×C3×D3C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67C411yescharacteristic, complemented
13C22×C3×#67C2211yescharacteristic
14C2×C3×D3×D4—22no—
15C2×C3×D3×D4—24no—
16C2×C3×D3×D4—22no—
17C2×C3×D3×D4C414yescomplemented
18C2×C3×D3×D4C2214yes—
19C22×C3×D12C411yescharacteristic, complemented
20C22×C3×C4×D3—22no—
21C22×C3×C4×D3C411yescharacteristic, complemented
22C2×C32×C22⋊C4C2212yescomplemented
23C2×C3×#217C2212yescomplemented
24C2×C3×(C2×D3)⋊C4—22no—
25C3×D3×C22⋊C4—24no—
26C3×D3×C22⋊C4C2218yescomplemented
27C32×#99C2214yescomplemented
28C3×#834C2214yescomplemented
29C3×#806C2218yescomplemented
30C23×C3×D4—31no—
31C22×D3×D4C2×C311yescharacteristic
32C22×C3×C22⋊C4—32no—
33C2×D3×C22⋊C4C2×C312yescomplemented
34C2×C3×#99—21no—
35C2×C3×#99—31no—
36C2×C3×#99—32no—
37C2×C3×#99—38no—
38C2×C3×#99D311yescharacteristic, direct product factor
39C2×C3×#99C2×C311yescharacteristic, complemented
40C2×#834C2×C311yescharacteristic, complemented
41C2×#806C2×C312yescomplemented
42D3×#99C2×C318yesdirect product factor
43C24×C32C2×C411yescharacteristic, complemented
44C24×C32C2311yescharacteristic
45C23×C3×D3—22no—
46C23×C3×D3—21no—
47C23×C3×D3—21no—
48C23×C3×D3—44no—
49C23×C3×D3—44no—
50C23×C3×D3C2×C411yescharacteristic
51C23×C3×D3C2×C411yescharacteristic
52C23×C3×D3C2×C412yes—
53C23×C3×D3C2×C414yescomplemented
54C23×C3×D3C2×C411yescharacteristic, complemented
55C23×C3×D3D412yes—
56C23×C3×D3D414yes—
57C23×C3×D3D412yes—
58C23×C3×D3C2312yes—
59C2×C32×D4—22no—
60C2×C32×D4—22no—
61C2×C32×D4C2×C412yescomplemented
62C2×C32×D4C2312yes—
63C22×C32×C4—22no—
64C22×C32×C4C2×C411yescharacteristic, complemented
65C2×C3×#67—22no—
66C2×C3×#67—22no—
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×#67C2×C414yescomplemented
70C2×C3×#67C2×C412yescomplemented
71C2×C3×#67C2312yes—
72C22×C3×Dic3—22no—
73C22×C3×Dic3C2×C411yescharacteristic, complemented
74C3×D3×D4—28no—
75C3×D3×D4—28no—
76C3×D3×D4—28no—
77C3×D3×D4—28no—
78C2×C3×D12—22no—
79C2×C3×D12—22no—
80C2×C3×D12C2×C414yescomplemented
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—28no—
85C2×C3×C4×D3—48no—
86C2×C3×C4×D3C2×C414yescomplemented
87C32×C22⋊C4—22no—
88C32×C22⋊C4C2314yescomplemented
89C3×#217—22no—
90C3×#217C2314yescomplemented
91C3×(C2×D3)⋊C4—28no—
92C22×#99—31noSylow
93C25×C3—31no—
94C25×C3—31no—
95C24×D3C3×C411yescharacteristic, complemented
96C24×D3C22×C311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4—31no—
99C22×C3×D4—31no—
100C22×C3×D4—34no—
101C22×C3×D4—34no—
102C22×C3×D4—31no—
103C22×C3×D4—62no—
104C22×C3×D4—64no—
105C22×C3×D4—62no—
106C22×C3×D4C2×D311yescharacteristic
107C22×C3×D4C22×C311yescharacteristic
108C23×C3×C4—31no—
109C23×C3×C4—62no—
110C22×#67C3×C411yescharacteristic, complemented
111C22×#67C22×C311yescharacteristic
112C2×D3×D4—22no—
113C2×D3×D4—24no—
114C2×D3×D4—22no—
115C2×D3×D4C3×C414yescomplemented
116C2×D3×D4C22×C314yes—
117C22×D12C3×C411yescharacteristic, complemented
118C22×C4×D3—22no—
119C22×C4×D3C3×C411yescharacteristic, complemented
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—38no—
123C2×C3×C22⋊C4—64no—
124C2×C3×C22⋊C4—62no—
125C2×C3×C22⋊C4C2×D312yescomplemented
126C2×C3×C22⋊C4C22×C312yescomplemented
127C2×#217C22×C312yescomplemented
128C2×(C2×D3)⋊C4—22no—
129D3×C22⋊C4—24no—
130D3×C22⋊C4C22×C318yescomplemented
131C3×#99—24no—
132C3×#99—34no—
133C3×#99—38no—
134C3×#99C2×D314yesdirect product factor
135C3×#99C22×C314yescomplemented
136#834C22×C314yescomplemented
137#806C22×C318yescomplemented
138C23×C32—21no—
139C23×C32—21no—
140C23×C32—42no—
141C23×C32—42no—
142C23×C32C22×C411yescharacteristic
143C23×C32C22×C411yescharacteristic
144C23×C32C22×C412yescomplemented
145C23×C32C2×D412yes—
146C23×C32C2×D412yes—
147C23×C32C2411yescharacteristic
148C22×C3×D3—24no—
149C22×C3×D3—28no—
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3—24no—
153C22×C3×D3—24no—
154C22×C3×D3—44no—
155C22×C3×D3—48no—
156C22×C3×D3—44no—
157C22×C3×D3—42no—
158C22×C3×D3—44no—
159C22×C3×D3—44no—
160C22×C3×D3—48no—
161C22×C3×D3—48no—
162C22×C3×D3—44no—
163C22×C3×D3—42no—
164C22×C3×D3C22⋊C412yes—
165C22×C3×D3C22⋊C411yescharacteristic
166C22×C3×D3C22⋊C412yes—
167C22×C3×D3C22⋊C414yes—
168C22×C3×D3C22⋊C412yes—
169C22×C3×D3C22⋊C414yes—
170C22×C3×D3C22⋊C411yescharacteristic
171C22×C3×D3C22×C412yes—
172C22×C3×D3C22×C412yes—
173C22×C3×D3C22×C412yescomplemented
174C22×C3×D3C2×D414yes—
175C22×C3×D3C2×D414yes—
176C32×D4—24no—
177C32×D4—24no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—24no—
181C2×C32×C4—44no—
182C2×C32×C4C22×C412yescomplemented
183C3×#67—24no—
184C3×#67—24no—
185C3×#67—28no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—44no—
190C2×C3×Dic3C22×C412yescomplemented
191C3×D12—28no—
192C3×C4×D3—24no—
193C3×C4×D3—24no—
194C3×C4×D3—416no—
195C23×D4—31no—
196C22×C22⋊C4—32no—
197C2×#99—31no—
198C2×#99—32no—
199C2×#99—38no—
200C2×#99C3×D311yescharacteristic, direct product factor
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—31no—
204C24×C3—32no—
205C24×C3—32no—
206C24×C3—31no—
207C24×C3—34no—
208C24×C3—32no—
209C24×C3—32no—
210C24×C3—31no—
211C24×C3—34no—
212C24×C3—62no—
213C24×C3—61no—
214C24×C3—61no—
215C24×C3—124no—
216C24×C3—124no—
217C24×C3C4×D311yescharacteristic, complemented
218C24×C3C2×C3×C411yescharacteristic, complemented
219C24×C3C22×D311yescharacteristic
220C24×C3C23×C311yescharacteristic
221C23×D3—22no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—44no—
225C23×D3—44no—
226C23×D3C2×C3×C411yescharacteristic
227C23×D3C2×C3×C411yescharacteristic
228C23×D3C2×C3×C412yes—
229C23×D3C2×C3×C414yescomplemented
230C23×D3C2×C3×C411yescharacteristic, complemented
231C23×D3C3×D412yes—
232C23×D3C3×D414yes—
233C23×D3C3×D412yes—
234C23×D3C23×C312yes—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—22no—
239C2×C3×D4—22no—
240C2×C3×D4—22no—
241C2×C3×D4—32no—
242C2×C3×D4—34no—
243C2×C3×D4—32no—
244C2×C3×D4—34no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—62no—
248C2×C3×D4—62no—
249C2×C3×D4—68no—
250C2×C3×D4—68no—
251C2×C3×D4—68no—
252C2×C3×D4—68no—
253C2×C3×D4—62no—
254C2×C3×D4—62no—
255C2×C3×D4—62no—
256C2×C3×D4—62no—
257C2×C3×D4C4×D312yescomplemented
258C2×C3×D4C2×C3×C412yescomplemented
259C2×C3×D4C22×D312yes—
260C2×C3×D4C23×C312yes—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—21no—
264C22×C3×C4—31no—
265C22×C3×C4—34no—
266C22×C3×C4—42no—
267C22×C3×C4—62no—
268C22×C3×C4—61no—
269C22×C3×C4—61no—
270C22×C3×C4—68no—
271C22×C3×C4—62no—
272C22×C3×C4—128no—
273C22×C3×C4C4×D311yescharacteristic, complemented
274C22×C3×C4C2×C3×C411yescharacteristic, complemented
275C2×#67—22no—
276C2×#67—22no—
277C2×#67—22no—
278C2×#67—22no—
279C2×#67C2×C3×C414yescomplemented
280C2×#67C2×C3×C412yescomplemented
281C2×#67C23×C312yes—
282C22×Dic3—22no—
283C22×Dic3C2×C3×C411yescharacteristic, complemented
284D3×D4—28no—
285D3×D4—28no—
286D3×D4—28no—
287D3×D4—28no—
288C2×D12—22no—
289C2×D12—22no—
290C2×D12C2×C3×C414yescomplemented
291C2×C4×D3—21no—
292C2×C4×D3—22no—
293C2×C4×D3—21no—
294C2×C4×D3—28no—
295C2×C4×D3—48no—
296C2×C4×D3C2×C3×C414yescomplemented
297C3×C22⋊C4—22no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—34no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—68no—
303C3×C22⋊C4—62no—
304C3×C22⋊C4C22×D314yescomplemented
305C3×C22⋊C4C23×C314yescomplemented
306#217—22no—
307#217C23×C314yescomplemented
308(C2×D3)⋊C4—28no—
309C22×C32—24no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32—41no—
313C22×C32—42no—
314C22×C32—41no—
315C22×C32—42no—
316C22×C32—42no—
317C22×C32—42no—
318C22×C32C2×C22⋊C411yescharacteristic
319C22×C32C2×C22⋊C412yes—
320C22×C32C2×C22⋊C411yescharacteristic
321C22×C32C23×C411yescharacteristic
322C22×C32C22×D412yes—
323C2×C3×D3—22no—
324C2×C3×D3—24no—
325C2×C3×D3—28no—
326C2×C3×D3—24no—
327C2×C3×D3—24no—
328C2×C3×D3—28no—
329C2×C3×D3—22no—
330C2×C3×D3—44no—
331C2×C3×D3—42no—
332C2×C3×D3—42no—
333C2×C3×D3—44no—
334C2×C3×D3—48no—
335C2×C3×D3—42no—
336C2×C3×D3—42no—
337C2×C3×D3—48no—
338C2×C3×D3—42no—
339C2×C3×D3#9914yesdirect product factor
340C2×C3×D3C2×C22⋊C412yes—
341C2×C3×D3C2×C22⋊C414yes—
342C2×C3×D3C2×C22⋊C412yes—
343C32×C4—22no—
344C32×C4—44no—
345C3×Dic3—22no—
346C3×Dic3—44no—
347C25—31no—
348C25—31no—
349C22×D4—31no—
350C22×D4—31no—
351C22×D4—34no—
352C22×D4—34no—
353C22×D4—31no—
354C22×D4—62no—
355C22×D4—62no—
356C22×D4—64no—
357C22×D4C2×C3×D311yescharacteristic
358C23×C4—31no—
359C23×C4—62no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4—38no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4—62no—
364C2×C22⋊C4C2×C3×D312yescomplemented
365#99—34no—
366#99—38no—
367#99C2×C3×D314yesdirect product factor
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—31no—
379C23×C3—32no—
380C23×C3—34no—
381C23×C3—31no—
382C23×C3—32no—
383C23×C3—32no—
384C23×C3—34no—
385C23×C3—34no—
386C23×C3—32no—
387C23×C3—32no—
388C23×C3—34no—
389C23×C3—32no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—68no—
397C23×C3—64no—
398C23×C3—64no—
399C23×C3—64no—
400C23×C3—61no—
401C23×C3—61no—
402C23×C3—82no—
403C23×C3—82no—
404C23×C3—124no—
405C23×C3—122no—
406C23×C3—122no—
407C23×C3—124no—
408C23×C3—124no—
409C23×C3—128no—
410C23×C3—124no—
411C23×C3—128no—
412C23×C3—128no—
413C23×C3—124no—
414C23×C3C2×C4×D311yescharacteristic
415C23×C3C2×C4×D311yescharacteristic
416C23×C3C2×C4×D312yescomplemented
417C23×C3D3×D412yes—
418C23×C3D3×D412yes—
419C23×C3C22×C3×C411yescharacteristic
420C23×C3C22×C3×C411yescharacteristic
421C23×C3C22×C3×C412yescomplemented
422C23×C3C2×C3×D412yes—
423C23×C3C2×C3×D412yes—
424C23×C3C23×D311yescharacteristic
425C23×C3C24×C311yescharacteristic
426C22×D3—28no—
427C22×D3—24no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—44no—
433C22×D3—48no—
434C22×D3—44no—
435C22×D3—42no—
436C22×D3—44no—
437C22×D3—44no—
438C22×D3—48no—
439C22×D3—48no—
440C22×D3—44no—
441C22×D3—42no—
442C22×D3C3×C22⋊C411yescharacteristic
443C22×D3C3×C22⋊C412yes—
444C22×D3C3×C22⋊C412yes—
445C22×D3C3×C22⋊C414yes—
446C22×D3C3×C22⋊C412yes—
447C22×D3C3×C22⋊C414yes—
448C22×D3C3×C22⋊C411yescharacteristic
449C22×D3C22×C3×C412yes—
450C22×D3C22×C3×C412yes—
451C22×D3C22×C3×C412yescomplemented
452C22×D3C2×C3×D414yes—
453C22×D3C2×C3×D414yes—
454C3×D4—24no—
455C3×D4—24no—
456C3×D4—24no—
457C3×D4—24no—
458C3×D4—44no—
459C3×D4—44no—
460C3×D4—68no—
461C3×D4—68no—
462C3×D4—64no—
463C3×D4—64no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—22no—
471C2×C3×C4—32no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—44no—
475C2×C3×C4—44no—
476C2×C3×C4—44no—
477C2×C3×C4—64no—
478C2×C3×C4—64no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—64no—
482C2×C3×C4—84no—
483C2×C3×C4—1216no—
484C2×C3×C4—124no—
485C2×C3×C4C2×C4×D312yescomplemented
486C2×C3×C4C22×C3×C412yescomplemented
487#67—24no—
488#67—24no—
489#67—28no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—24no—
493C2×Dic3—44no—
494C2×Dic3C22×C3×C412yescomplemented
495D12—28no—
496C4×D3—24no—
497C4×D3—24no—
498C4×D3—416no—
499C2×C32—22no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—22no—
503C2×C32—42no—
504C2×C32C2×#9912yescomplemented
505C2×C32C22×C22⋊C411yescharacteristic
506C3×D3—22no—
507C3×D3—24no—
508C3×D3—42no—
509C3×D3C2×#9914yesdirect product factor
510C24—31no—
511C24—32no—
512C24—32no—
513C24—32no—
514C24—31no—
515C24—34no—
516C24—32no—
517C24—31no—
518C24—34no—
519C24—61no—
520C24—62no—
521C24—61no—
522C24—124no—
523C24—124no—
524C24C3×C4×D311yescharacteristic, complemented
525C24C22×C3×D311yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—32no—
529C2×D4—32no—
530C2×D4—34no—
531C2×D4—34no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—68no—
535C2×D4—68no—
536C2×D4—68no—
537C2×D4—68no—
538C2×D4—62no—
539C2×D4—62no—
540C2×D4—62no—
541C2×D4—62no—
542C2×D4C3×C4×D312yescomplemented
543C2×D4C22×C3×D312yes—
544C22×C4—22no—
545C22×C4—31no—
546C22×C4—34no—
547C22×C4—61no—
548C22×C4—62no—
549C22×C4—61no—
550C22×C4—68no—
551C22×C4—62no—
552C22×C4—128no—
553C22×C4C3×C4×D311yescharacteristic, complemented
554C22⋊C4—22no—
555C22⋊C4—34no—
556C22⋊C4—68no—
557C22⋊C4—62no—
558C22⋊C4C22×C3×D314yescomplemented
559C22×C3—24no—
560C22×C3—22no—
561C22×C3—24no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—22no—
568C22×C3—21no—
569C22×C3—22no—
570C22×C3—32no—
571C22×C3—34no—
572C22×C3—32no—
573C22×C3—34no—
574C22×C3—44no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—41no—
578C22×C3—42no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—42no—
582C22×C3—41no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—68no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—68no—
593C22×C3—62no—
594C22×C3—64no—
595C22×C3—62no—
596C22×C3—82no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—82no—
600C22×C3—82no—
601C22×C3—82no—
602C22×C3—124no—
603C22×C3—122no—
604C22×C3—122no—
605C22×C3—124no—
606C22×C3—122no—
607C22×C3—122no—
608C22×C3—128no—
609C22×C3—128no—
610C22×C3—122no—
611C22×C3D3×C22⋊C411yescharacteristic
612C22×C3D3×C22⋊C412yes—
613C22×C3D3×C22⋊C411yescharacteristic
614C22×C3C2×C3×C22⋊C411yescharacteristic
615C22×C3C2×C3×C22⋊C412yes—
616C22×C3C2×C3×C22⋊C411yescharacteristic
617C22×C3C22×C4×D311yescharacteristic
618C22×C3C2×D3×D412yes—
619C22×C3C23×C3×C411yescharacteristic
620C22×C3C22×C3×D412yes—
621C2×D3—22no—
622C2×D3—24no—
623C2×D3—28no—
624C2×D3—24no—
625C2×D3—24no—
626C2×D3—28no—
627C2×D3—22no—
628C2×D3—44no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—44no—
632C2×D3—48no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—48no—
636C2×D3—42no—
637C2×D3C3×#9914yesdirect product factor
638C2×D3C2×C3×C22⋊C412yes—
639C2×D3C2×C3×C22⋊C414yes—
640C2×D3C2×C3×C22⋊C412yes—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—42no—
644C3×C4—44no—
645C3×C4—44no—
646C3×C4—62no—
647C3×C4—84no—
648C3×C4—124no—
649Dic3—22no—
650Dic3—44no—
651C32C22×#9911yescharacteristic, complemented, Sylow
652C23—21no—
653C23—21no—
654C23—31no—
655C23—32no—
656C23—31no—
657C23—34no—
658C23—32no—
659C23—32no—
660C23—34no—
661C23—34no—
662C23—32no—
663C23—32no—
664C23—34no—
665C23—32no—
666C23—42no—
667C23—42no—
668C23—68no—
669C23—64no—
670C23—64no—
671C23—64no—
672C23—61no—
673C23—61no—
674C23—124no—
675C23—122no—
676C23—122no—
677C23—124no—
678C23—124no—
679C23—124no—
680C23—128no—
681C23—128no—
682C23—128no—
683C23—124no—
684C23C2×C3×C4×D311yescharacteristic
685C23C2×C3×C4×D311yescharacteristic
686C23C2×C3×C4×D312yescomplemented
687C23C3×D3×D412yes—
688C23C3×D3×D412yes—
689C23C23×C3×D311yescharacteristic
690D4—24no—
691D4—24no—
692D4—68no—
693D4—68no—
694D4—64no—
695D4—64no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—24no—
699C2×C4—32no—
700C2×C4—44no—
701C2×C4—64no—
702C2×C4—64no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—64no—
706C2×C4—1216no—
707C2×C4—124no—
708C2×C4C2×C3×C4×D312yescomplemented
709C2×C3—22no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—22no—
713C2×C3—22no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—22no—
717C2×C3—22no—
718C2×C3—21no—
719C2×C3—34no—
720C2×C3—42no—
721C2×C3—41no—
722C2×C3—41no—
723C2×C3—42no—
724C2×C3—42no—
725C2×C3—42no—
726C2×C3—62no—
727C2×C3—64no—
728C2×C3—82no—
729C2×C3—122no—
730C2×C3D3×#9912yesdirect product factor
731C2×C3C2×C3×#9912yescomplemented
732C2×C3C2×D3×C22⋊C411yescharacteristic
733C2×C3C22×C3×C22⋊C411yescharacteristic
734D3—22no—
735D3—24no—
736D3—42no—
737D3C2×C3×#9914yesdirect product factor
738C22—24no—
739C22—22no—
740C22—22no—
741C22—34no—
742C22—32no—
743C22—32no—
744C22—34no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—68no—
752C22—64no—
753C22—64no—
754C22—68no—
755C22—62no—
756C22—64no—
757C22—62no—
758C22—124no—
759C22—122no—
760C22—122no—
761C22—124no—
762C22—122no—
763C22—122no—
764C22—128no—
765C22—128no—
766C22—122no—
767C22C3×D3×C22⋊C411yescharacteristic
768C22C3×D3×C22⋊C412yes—
769C22C3×D3×C22⋊C411yescharacteristic
770C22C22×C3×C4×D311yescharacteristic
771C22C2×C3×D3×D412yes—
772C4—22no—
773C4—44no—
774C4—62no—
775C4—124no—
776C3—21no—
777C3C2×D3×#9911yescharacteristic, direct product factor
778C3C22×C3×#9911yescharacteristic, complemented
779C2—22no—
780C2—21no—
781C2—21no—
782C2—22no—
783C2—34no—
784C2—42no—
785C2—62no—
786C2—64no—
787C2—122no—
788C2C3×D3×#9912yesdirect product factor
789C2C2×C3×D3×C22⋊C411yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#99C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3×D4C2
cosocleC23×C3C24×C3
hypercenterC2×C3×#99D3
hypocenterC3C22×C3×#99
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C22⋊C4C2semidirect
3. C2×C32×#99C2semidirect
4. C2×C3×#834C2semidirect
5. C2×C3×#806C2semidirect
6. C3×D3×#99C2direct (N × H)
8. C2×D3×#99C3direct (N × H)
9. C24×C3×D3C4semidirect
12. C22×C3×#67C4semidirect
17. C2×C3×D3×D4C4semidirect
19. C22×C3×D12C4semidirect
21. C22×C3×C4×D3C4semidirect
22. C2×C32×C22⋊C4C22semidirect
23. C2×C3×#217C22semidirect
26. C3×D3×C22⋊C4C22semidirect
27. C32×#99C22semidirect
28. C3×#834C22semidirect
29. C3×#806C22semidirect
33. C2×D3×C22⋊C4C2×C3semidirect
38. C2×C3×#99D3direct (N × H)
39. C2×C3×#99C2×C3semidirect
40. C2×#834C2×C3semidirect
41. C2×#806C2×C3semidirect
42. D3×#99C2×C3direct (N × H)
43. C24×C32C2×C4semidirect
53. C23×C3×D3C2×C4semidirect
54. C23×C3×D3C2×C4semidirect
61. C2×C32×D4C2×C4semidirect
64. C22×C32×C4C2×C4semidirect
69. C2×C3×#67C2×C4semidirect
70. C2×C3×#67C2×C4semidirect
73. C22×C3×Dic3C2×C4semidirect
80. C2×C3×D12C2×C4semidirect
86. C2×C3×C4×D3C2×C4semidirect
88. C32×C22⋊C4C23semidirect
90. C3×#217C23semidirect
95. C24×D3C3×C4semidirect
110. C22×#67C3×C4semidirect
115. C2×D3×D4C3×C4semidirect
117. C22×D12C3×C4semidirect
119. C22×C4×D3C3×C4semidirect
125. C2×C3×C22⋊C4C2×D3semidirect
126. C2×C3×C22⋊C4C22×C3semidirect
127. C2×#217C22×C3semidirect
130. D3×C22⋊C4C22×C3semidirect
134. C3×#99C2×D3direct (N × H)
135. C3×#99C22×C3semidirect
136. #834C22×C3semidirect
137. #806C22×C3semidirect
144. C23×C32C22×C4semidirect
173. C22×C3×D3C22×C4semidirect
182. C2×C32×C4C22×C4semidirect
190. C2×C3×Dic3C22×C4semidirect
200. C2×#99C3×D3direct (N × H)
217. C24×C3C4×D3semidirect
218. C24×C3C2×C3×C4semidirect
229. C23×D3C2×C3×C4semidirect
230. C23×D3C2×C3×C4semidirect
257. C2×C3×D4C4×D3semidirect
258. C2×C3×D4C2×C3×C4semidirect
273. C22×C3×C4C4×D3semidirect
274. C22×C3×C4C2×C3×C4semidirect
279. C2×#67C2×C3×C4semidirect
280. C2×#67C2×C3×C4semidirect
283. C22×Dic3C2×C3×C4semidirect
290. C2×D12C2×C3×C4semidirect
296. C2×C4×D3C2×C3×C4semidirect
304. C3×C22⋊C4C22×D3semidirect
305. C3×C22⋊C4C23×C3semidirect
307. #217C23×C3semidirect
339. C2×C3×D3#99direct (N × H)
364. C2×C22⋊C4C2×C3×D3semidirect
367. #99C2×C3×D3direct (N × H)
416. C23×C3C2×C4×D3semidirect
421. C23×C3C22×C3×C4semidirect
451. C22×D3C22×C3×C4semidirect
485. C2×C3×C4C2×C4×D3semidirect
486. C2×C3×C4C22×C3×C4semidirect
494. C2×Dic3C22×C3×C4semidirect
504. C2×C32C2×#99semidirect
509. C3×D3C2×#99direct (N × H)
524. C24C3×C4×D3semidirect
542. C2×D4C3×C4×D3semidirect
553. C22×C4C3×C4×D3semidirect
558. C22⋊C4C22×C3×D3semidirect
637. C2×D3C3×#99direct (N × H)
651. C32C22×#99semidirect
686. C23C2×C3×C4×D3semidirect
708. C2×C4C2×C3×C4×D3semidirect
730. C2×C3D3×#99direct (N × H)
731. C2×C3C2×C3×#99semidirect
737. D3C2×C3×#99direct (N × H)
777. C3C2×D3×#99direct (N × H)
778. C3C22×C3×#99semidirect
788. C2C3×D3×#99direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×C3×D3×C22⋊C42
C2×C32×#992
C2×C3×#8342
C2×C3×#8062
C3×D3×#992
C22×C3×#993
C2×D3×#993