Finite Group Databasebeta

← C2×C3×#4959 #11808138

Subgroups — C2×C3×#4959 #11808138

Order 1152.

2841 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4959C218yesmaximal, direct product factor
9C2×C3×#394—31nomaximal
10C2×#4959C311yesmaximal, characteristic, direct product factor
11C25×C32C2211yescharacteristic
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67—24no—
16C22×C3×#67—24no—
17C22×C3×#67—24no—
18C22×C3×#67C2214yes—
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C2×C32×C22⋊C4—24no—
23C2×C32×C22⋊C4C2214yescomplemented
24C2×C3×#217—24no—
25C2×C3×#217C2214yescomplemented
26C2×C3×(C2×D3)⋊C4—24no—
27C2×C3×(C2×D3)⋊C4—24no—
28C2×C3×(C2×D3)⋊C4C2214yescomplemented
29C2×C3×(C2×D3)⋊C4C2214yescomplemented
30C2×C3×Dic3⋊C4—24no—
31C2×C3×Dic3⋊C4C2214yescomplemented
32C3×C3⋊#95C2214yescomplemented
33C23×C3×D4—31no—
34C23×#67C2×C311yescharacteristic
35C22×C3×C4⋊C4—31no—
36C22×C3×C22⋊C4—21no—
37C22×C3×C22⋊C4—31no—
38C22×C3×C22⋊C4—31no—
39C22×C3×C22⋊C4—31no—
40C22×C3×C22⋊C4D311yescharacteristic, complemented
41C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
42C22×#217C2×C311yescharacteristic, complemented
43C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
44C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
45C22×Dic3⋊C4C2×C311yescharacteristic, complemented
46C3×#394—38no—
47C2×C3×#95—31no—
48C2×C3⋊#95C2×C311yescharacteristic, complemented
49#4959C2×C318yesdirect product factor
50C24×C32—22no—
51C24×C32—22no—
52C24×C32—22no—
53C24×C32—22no—
54C24×C32—22no—
55C24×C32—22no—
56C24×C32D414yes—
57C24×C32C2312yes—
58C24×C32C2311yescharacteristic
59C23×C3×D3—22no—
60C23×C3×D3—22no—
61C23×C3×D3—22no—
62C23×C3×D3—22no—
63C23×C3×D3—22no—
64C23×C3×D3—22no—
65C23×C3×D3D414yes—
66C23×C3×D3C2312yes—
67C22×C32×C4—22no—
68C22×C32×C4—22no—
69C22×C32×C4—22no—
70C22×C32×C4—22no—
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4C2312yes—
74C22×C32×C4C2312yes—
75C2×C3×#67—232no—
76C2×C3×#67—28no—
77C2×C3×#67—28no—
78C2×C3×#67—28no—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—22no—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3—22no—
85C22×C3×Dic3—22no—
86C22×C3×Dic3D414yes—
87C22×C3×Dic3D414yescomplemented
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C32×C22⋊C4—28no—
92C3×#217—28no—
93C3×(C2×D3)⋊C4—28no—
94C3×(C2×D3)⋊C4—28no—
95C3×Dic3⋊C4—28no—
96C2×#394—31noSylow
97C25×C3—21no—
98C25×C3—31no—
99C25×C3C2×D311yescharacteristic
100C25×C3C22×C311yescharacteristic
101C24×D3C22×C311yescharacteristic
102C22×C3×D4—34no—
103C22×C3×D4—64no—
104C22×C3×D4—64no—
105C22×C3×D4—64no—
106C23×C3×C4—21no—
107C23×C3×C4—21no—
108C23×C3×C4—31no—
109C23×C3×C4—31no—
110C23×C3×C4—31no—
111C23×C3×C4C2×D311yescharacteristic
112C23×C3×C4C2×D311yescharacteristic
113C23×C3×C4C22×C311yescharacteristic
114C23×C3×C4C22×C311yescharacteristic
115C22×#67—24no—
116C22×#67—24no—
117C22×#67—24no—
118C22×#67C22×C314yes—
119C23×Dic3C22×C311yescharacteristic
120C23×Dic3C22×C311yescharacteristic
121C23×Dic3C22×C311yescharacteristic
122C2×C3×C4⋊C4—34no—
123C2×C3×C4⋊C4—64no—
124C2×C3×C22⋊C4—28no—
125C2×C3×C22⋊C4—24no—
126C2×C3×C22⋊C4—24no—
127C2×C3×C22⋊C4—24no—
128C2×C3×C22⋊C4—34no—
129C2×C3×C22⋊C4—34no—
130C2×C3×C22⋊C4—34no—
131C2×C3×C22⋊C4—64no—
132C2×C3×C22⋊C4—64no—
133C2×C3×C22⋊C4—64no—
134C2×C3×C22⋊C4C2×D314yescomplemented
135C2×C3×C22⋊C4C22×C314yescomplemented
136C2×#217—24no—
137C2×#217C22×C314yescomplemented
138C2×(C2×D3)⋊C4—24no—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4C22×C314yescomplemented
141C2×(C2×D3)⋊C4C22×C314yescomplemented
142C2×Dic3⋊C4—24no—
143C2×Dic3⋊C4C22×C314yescomplemented
144C3×#95—34no—
145C3⋊#95C22×C314yescomplemented
146C23×C32—28no—
147C23×C32—22no—
148C23×C32—22no—
149C23×C32—28no—
150C23×C32—28no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—44no—
156C23×C32—44no—
157C23×C32—44no—
158C23×C32—44no—
159C23×C32C2×D412yes—
160C23×C32C2×D412yes—
161C23×C32C2×D412yes—
162C23×C32C2×D414yes—
163C23×C32C2×D412yes—
164C23×C32#4112yes—
165C23×C32#4112yes—
166C23×C32#4112yes—
167C23×C32C2411yescharacteristic
168C22×C3×D3—28no—
169C22×C3×D3—28no—
170C22×C3×D3—28no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—44no—
178C22×C3×D3—44no—
179C22×C3×D3—44no—
180C22×C3×D3—44no—
181C22×C3×D3C2×D414yes—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—44no—
189C2×C32×C4—44no—
190C3×#67—232no—
191C2×C3×Dic3—28no—
192C2×C3×Dic3—28no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—44no—
201C2×C3×Dic3C2×D414yes—
202C2×C3×Dic3C2×D414yescomplemented
203C23×D4—31no—
204C22×C4⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4C3×D311yescharacteristic, complemented
209#394—38no—
210C2×#95—31no—
211C24×C3—24no—
212C24×C3—24no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—24no—
226C24×C3—21no—
227C24×C3—22no—
228C24×C3—34no—
229C24×C3—32no—
230C24×C3—42no—
231C24×C3—42no—
232C24×C3—42no—
233C24×C3—42no—
234C24×C3—62no—
235C24×C3—62no—
236C24×C3—62no—
237C24×C3—62no—
238C24×C3—62no—
239C24×C3—62no—
240C24×C3#6714yes—
241C24×C3C3×D414yes—
242C24×C3C22×D312yes—
243C24×C3C22×D311yescharacteristic
244C24×C3C23×C312yes—
245C24×C3C23×C311yescharacteristic
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—22no—
252C23×D3C3×D414yes—
253C23×D3C23×C312yes—
254C2×C3×D4—68no—
255C2×C3×D4—68no—
256C2×C3×D4—632no—
257C2×C3×D4—68no—
258C22×C3×C4—24no—
259C22×C3×C4—24no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—34no—
275C22×C3×C4—34no—
276C22×C3×C4—32no—
277C22×C3×C4—32no—
278C22×C3×C4—32no—
279C22×C3×C4—42no—
280C22×C3×C4—42no—
281C22×C3×C4—42no—
282C22×C3×C4—42no—
283C22×C3×C4—62no—
284C22×C3×C4—62no—
285C22×C3×C4—62no—
286C22×C3×C4—62no—
287C22×C3×C4—62no—
288C22×C3×C4—62no—
289C22×C3×C4—62no—
290C22×C3×C4C22×D312yes—
291C22×C3×C4C22×D312yes—
292C22×C3×C4C23×C312yes—
293C22×C3×C4C23×C312yes—
294C2×#67—232no—
295C2×#67—28no—
296C2×#67—28no—
297C2×#67—28no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3C3×D414yes—
306C22×Dic3C3×D414yescomplemented
307C22×Dic3C23×C312yes—
308C22×Dic3C23×C312yes—
309C22×Dic3C23×C312yes—
310C3×C4⋊C4—68no—
311C3×C22⋊C4—216no—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—28no—
314C3×C22⋊C4—68no—
315C3×C22⋊C4—68no—
316C3×C22⋊C4—68no—
317#217—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—28no—
320Dic3⋊C4—28no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—24no—
324C22×C32—42no—
325C22×C32—42no—
326C22×C32—42no—
327C22×C32—42no—
328C22×C32—416no—
329C22×C32#12014yes—
330C22×C32#12114yes—
331C22×C32#12114yes—
332C22×C32#12114yes—
333C22×C32#12314yes—
334C22×C32#12314yes—
335C22×C32#12414yes—
336C22×C32C22×D411yescharacteristic
337C22×C32C22×D411yescharacteristic
338C22×C32C22×D411yescharacteristic
339C22×C32C22×D411yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C22×C32C2×#4111yescharacteristic
343C2×C3×D3—24no—
344C2×C3×D3—24no—
345C2×C3×D3—24no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C2×C3×D3—42no—
349C2×C3×D3—42no—
350C2×C3×D3—416no—
351C32×C4—42no—
352C32×C4—42no—
353C3×Dic3—24no—
354C3×Dic3—24no—
355C3×Dic3—42no—
356C25—31no—
357C25C2×C3×D311yescharacteristic
358C22×D4—34no—
359C22×D4—64no—
360C22×D4—64no—
361C22×D4—64no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4C2×C3×D311yescharacteristic
366C23×C4C2×C3×D311yescharacteristic
367C2×C4⋊C4—34no—
368C2×C4⋊C4—64no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—34no—
371C2×C22⋊C4—34no—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—64no—
374C2×C22⋊C4—64no—
375C2×C22⋊C4—64no—
376C2×C22⋊C4C2×C3×D314yescomplemented
377#95—34no—
378C23×C3—216no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—28no—
382C23×C3—28no—
383C23×C3—28no—
384C23×C3—28no—
385C23×C3—28no—
386C23×C3—28no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—24no—
408C23×C3—34no—
409C23×C3—48no—
410C23×C3—48no—
411C23×C3—42no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3—42no—
415C23×C3—48no—
416C23×C3—48no—
417C23×C3—48no—
418C23×C3—48no—
419C23×C3—44no—
420C23×C3—44no—
421C23×C3—44no—
422C23×C3—44no—
423C23×C3—44no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—68no—
428C23×C3—68no—
429C23×C3—68no—
430C23×C3—62no—
431C23×C3—62no—
432C23×C3—62no—
433C23×C3—62no—
434C23×C3—62no—
435C23×C3—62no—
436C23×C3—124no—
437C23×C3—124no—
438C23×C3—124no—
439C23×C3—124no—
440C23×C3#23512yes—
441C23×C3#23512yes—
442C23×C3D3×D412yes—
443C23×C3D3×D412yes—
444C23×C3D3×D412yes—
445C23×C3#23712yes—
446C23×C3C2×#6714yes—
447C23×C3C2×#6712yes—
448C23×C3C2×C3×D412yes—
449C23×C3C2×C3×D412yes—
450C23×C3C2×C3×D412yes—
451C23×C3C2×C3×D414yes—
452C23×C3C2×C3×D412yes—
453C23×C3C3×#4112yes—
454C23×C3C3×#4112yes—
455C23×C3C3×#4112yes—
456C23×C3C23×D311yescharacteristic
457C23×C3C24×C311yescharacteristic
458C22×D3—28no—
459C22×D3—28no—
460C22×D3—28no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—44no—
468C22×D3—44no—
469C22×D3—44no—
470C22×D3—44no—
471C22×D3C2×C3×D414yes—
472C3×D4—632no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—34no—
488C2×C3×C4—34no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—48no—
494C2×C3×C4—48no—
495C2×C3×C4—44no—
496C2×C3×C4—44no—
497C2×C3×C4—44no—
498C2×C3×C4—44no—
499C2×C3×C4—68no—
500C2×C3×C4—68no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—124no—
509#67—232no—
510C2×Dic3—28no—
511C2×Dic3—28no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—44no—
520C2×Dic3C2×C3×D414yes—
521C2×Dic3C2×C3×D414yescomplemented
522C2×C32—44no—
523C2×C32#39418yescomplemented
524C2×C32C2×#12011yescharacteristic
525C2×C32C2×#12111yescharacteristic
526C2×C32C2×#12111yescharacteristic
527C2×C32C2×#12111yescharacteristic
528C2×C32C2×#12311yescharacteristic
529C2×C32C2×#12311yescharacteristic
530C2×C32C2×#12411yescharacteristic
531C3×D3—44no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—32no—
539C24—34no—
540C24—62no—
541C24—62no—
542C24—62no—
543C24—62no—
544C24—62no—
545C24—62no—
546C24C3×#6714yes—
547C24C22×C3×D312yes—
548C24C22×C3×D311yescharacteristic
549C2×D4—68no—
550C2×D4—68no—
551C2×D4—632no—
552C2×D4—68no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—34no—
562C22×C4—34no—
563C22×C4—32no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4C22×C3×D312yes—
572C22×C4C22×C3×D312yes—
573C4⋊C4—68no—
574C22⋊C4—28no—
575C22⋊C4—68no—
576C22⋊C4—68no—
577C22⋊C4—68no—
578C22×C3—28no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—24no—
584C22×C3—24no—
585C22×C3—24no—
586C22×C3—24no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—432no—
606C22×C3—416no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—416no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—64no—
617C22×C3—64no—
618C22×C3—64no—
619C22×C3—1216no—
620C22×C3—122no—
621C22×C3—122no—
622C22×C3—122no—
623C22×C3—122no—
624C22×C3#88314yes—
625C22×C3#88414yes—
626C22×C3#88414yes—
627C22×C3#88514yes—
628C22×C3#92914yes—
629C22×C3#93714yes—
630C22×C3#93914yes—
631C22×C3C3×#12014yes—
632C22×C3C3×#12114yes—
633C22×C3C3×#12114yes—
634C22×C3C3×#12114yes—
635C22×C3C3×#12314yes—
636C22×C3C3×#12314yes—
637C22×C3C3×#12414yes—
638C22×C3C2×#23511yescharacteristic
639C22×C3C2×#23511yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×#23711yescharacteristic
644C22×C3C22×#6711yescharacteristic
645C22×C3C22×C3×D411yescharacteristic
646C22×C3C22×C3×D411yescharacteristic
647C22×C3C22×C3×D411yescharacteristic
648C22×C3C22×C3×D411yescharacteristic
649C22×C3C2×C3×#4111yescharacteristic
650C22×C3C2×C3×#4111yescharacteristic
651C22×C3C2×C3×#4111yescharacteristic
652C2×D3—24no—
653C2×D3—24no—
654C2×D3—24no—
655C2×D3—416no—
656C2×D3—42no—
657C2×D3—42no—
658C2×D3—42no—
659C2×D3—42no—
660C3×C4—44no—
661C3×C4—44no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—64no—
667C3×C4—64no—
668C3×C4—122no—
669Dic3—24no—
670Dic3—24no—
671Dic3—42no—
672C32C2×#39411yescharacteristic, complemented, Sylow
673C23—28no—
674C23—28no—
675C23—28no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—34no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—68no—
688C23—68no—
689C23—68no—
690C23—62no—
691C23—62no—
692C23—62no—
693C23—62no—
694C23—62no—
695C23—62no—
696C23—124no—
697C23—124no—
698C23—124no—
699C23—124no—
700C23C3×#23512yes—
701C23C3×#23512yes—
702C23C3×D3×D412yes—
703C23C3×D3×D412yes—
704C23C3×D3×D412yes—
705C23C3×#23712yes—
706C23C2×C3×#6714yes—
707C23C2×C3×#6712yes—
708C23C23×C3×D311yescharacteristic
709D4—632no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—34no—
717C2×C4—34no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—68no—
721C2×C4—68no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—124no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—28no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—48no—
739C2×C3—44no—
740C2×C3—44no—
741C2×C3—124no—
742C2×C3#495918yesdirect product factor
743C2×C3C3×#39418yescomplemented
744C2×C3C2×#88311yescharacteristic
745C2×C3C2×#88411yescharacteristic
746C2×C3C2×#88411yescharacteristic
747C2×C3C2×#88511yescharacteristic
748C2×C3C2×#92911yescharacteristic
749C2×C3C2×#93711yescharacteristic
750C2×C3C2×#93911yescharacteristic
751C2×C3C2×C3×#12011yescharacteristic
752C2×C3C2×C3×#12111yescharacteristic
753C2×C3C2×C3×#12111yescharacteristic
754C2×C3C2×C3×#12111yescharacteristic
755C2×C3C2×C3×#12311yescharacteristic
756C2×C3C2×C3×#12311yescharacteristic
757C2×C3C2×C3×#12411yescharacteristic
758D3—44no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—416no—
767C22—64no—
768C22—64no—
769C22—64no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22—1216no—
774C22—122no—
775C22C3×#88314yes—
776C22C3×#88414yes—
777C22C3×#88414yes—
778C22C3×#88514yes—
779C22C3×#92914yes—
780C22C3×#93714yes—
781C22C3×#93914yes—
782C22C2×C3×#23511yescharacteristic
783C22C2×C3×#23511yescharacteristic
784C22C2×C3×D3×D411yescharacteristic
785C22C2×C3×D3×D411yescharacteristic
786C22C2×C3×D3×D411yescharacteristic
787C22C2×C3×#23711yescharacteristic
788C22C22×C3×#6711yescharacteristic
789C4—42no—
790C4—42no—
791C4—64no—
792C4—64no—
793C4—122no—
794C3—21no—
795C3C2×#495911yescharacteristic, direct product factor
796C3C2×C3×#39411yescharacteristic, complemented
797C2—44no—
798C2—124no—
799C2C3×#495918yesdirect product factor
800C2C2×C3×#88311yescharacteristic
801C2C2×C3×#88411yescharacteristic
802C2C2×C3×#88411yescharacteristic
803C2C2×C3×#88511yescharacteristic
804C2C2×C3×#92911yescharacteristic
805C2C2×C3×#93711yescharacteristic
806C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
prime radicalC23×C3×#67C2
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C2×C3×#394
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C32×C22⋊C4C2semidirect
3. C22×C3×#217C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C22×C3×(C2×D3)⋊C4C2semidirect
6. C22×C3×Dic3⋊C4C2semidirect
7. C2×C3×C3⋊#95C2semidirect
8. C3×#4959C2direct (N × H)
10. C2×#4959C3direct (N × H)
23. C2×C32×C22⋊C4C22semidirect
25. C2×C3×#217C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
29. C2×C3×(C2×D3)⋊C4C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
32. C3×C3⋊#95C22semidirect
40. C22×C3×C22⋊C4D3semidirect
41. C22×C3×C22⋊C4C2×C3semidirect
42. C22×#217C2×C3semidirect
43. C22×(C2×D3)⋊C4C2×C3semidirect
44. C22×(C2×D3)⋊C4C2×C3semidirect
45. C22×Dic3⋊C4C2×C3semidirect
48. C2×C3⋊#95C2×C3semidirect
49. #4959C2×C3direct (N × H)
87. C22×C3×Dic3D4semidirect
134. C2×C3×C22⋊C4C2×D3semidirect
135. C2×C3×C22⋊C4C22×C3semidirect
137. C2×#217C22×C3semidirect
140. C2×(C2×D3)⋊C4C22×C3semidirect
141. C2×(C2×D3)⋊C4C22×C3semidirect
143. C2×Dic3⋊C4C22×C3semidirect
145. C3⋊#95C22×C3semidirect
202. C2×C3×Dic3C2×D4semidirect
208. C22×C22⋊C4C3×D3semidirect
306. C22×Dic3C3×D4semidirect
376. C2×C22⋊C4C2×C3×D3semidirect
521. C2×Dic3C2×C3×D4semidirect
523. C2×C32#394semidirect
672. C32C2×#394semidirect
742. C2×C3#4959direct (N × H)
743. C2×C3C3×#394semidirect
795. C3C2×#4959direct (N × H)
796. C3C2×C3×#394semidirect
799. C2C3×#4959direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×C32×C22⋊C42
C22×C3×#2172
C22×C3×(C2×D3)⋊C42
C22×C3×Dic3⋊C42
C2×C3×C3⋊#952
C3×#49592
C2×C3×#3943
C2×#49593