Finite Group Databasebeta

← C2×#74696 #10962913

Subgroups — C2×#74696 #10962913

Order 768.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#935C211yesmaximal, characteristic, complemented
2C22×#939C211yesmaximal, characteristic
3C22×C4×#67C211yesmaximal, characteristic, complemented
4C22×#886C211yesmaximal, characteristic, complemented
5C2×C3×#386C211yesmaximal, characteristic, complemented
6C22×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×#4959C211yesmaximal, characteristic, complemented
8C2×#4956C211yesmaximal, characteristic, complemented
9C2×#4948C211yesmaximal, characteristic, complemented
10C2×#4951C211yesmaximal, characteristic, complemented
11C2×#4946C211yesmaximal, characteristic, complemented
12#74696C2116yesmaximal, direct product factor
13C2×#4675C211yesmaximal, characteristic, complemented
14C2×#4667C211yesmaximal, characteristic, complemented
15C2×#4657C211yesmaximal, characteristic, complemented
16C2×#4647C211yesmaximal, characteristic, complemented
17C2×#2425—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C24×Dic3C2211yescharacteristic
23C24×Dic3C2211yescharacteristic
24C23×C4×D3C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C2×#939—28no—
33C2×#939C2218yes—
34C2×#935—28no—
35C2×#935C2218yescomplemented
36C2×C4×#67—28no—
37C2×C4×#67C2218yescomplemented
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×(C2×D3)⋊C4C2211yescharacteristic
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×C4⋊Dic3C2211yescharacteristic
43C22×C4⋊Dic3C2211yescharacteristic
44C22×Dic3⋊C4C2211yescharacteristic
45C22×Dic3⋊C4C2211yescharacteristic
46C22×Dic3⋊C4C2211yescharacteristic
47C22×Dic3⋊C4C2211yescharacteristic
48C22×Dic3⋊C4C2211yescharacteristic
49C22×Dic3⋊C4C2211yescharacteristic
50C22×C4×Dic3C2211yescharacteristic
51C2×#886—28no—
52C2×#886C2218yescomplemented
53C3×#386C2218yescomplemented
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58C2×C3⋊#95C2211yescharacteristic
59C2×C3⋊#95C2211yescharacteristic
60C2×C3⋊#95C2211yescharacteristic
61C2×C3⋊#95C2211yescharacteristic
62C2×C3⋊#95C2218yescomplemented
63#4959C2218yescomplemented
64#4956C2218yescomplemented
65#4951C2218yescomplemented
66#4948C2218yescomplemented
67#4946C2218yescomplemented
68#4675C2218yescomplemented
69#4667C2218yescomplemented
70#4657C2218yescomplemented
71#4647C2218yescomplemented
72C22×#123—31no—
73C22×#123—31no—
74C22×#121—31no—
75C22×C4×D4—31no—
76#2425—316no—
77C2×#398—31no—
78C2×#397—31no—
79C2×#396—31no—
80C2×#394—31no—
81C2×#389—31no—
82C2×#388—31no—
83C2×#386—31no—
84C2×#386D311yescharacteristic, complemented
85C2×#385—31no—
86C2×#380—31no—
87C22×#95—31no—
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C24×D3C2311yescharacteristic
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4C2314yes—
95C23×C3×C4—24no—
96C23×C3×C4—24no—
97C23×C3×C4—42no—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2314yes—
103C23×C3×C4C2311yescharacteristic
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—24no—
108C22×#67—42no—
109C22×#67D418yes—
110C22×#67C2314yes—
111C22×#67C2314yes—
112C23×Dic3—24no—
113C23×Dic3—24no—
114C23×Dic3—24no—
115C23×Dic3—24no—
116C23×Dic3—24no—
117C23×Dic3—42no—
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2314yes—
122C23×Dic3C2314yes—
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2311yescharacteristic
127C22×C4×D3—24no—
128C22×C4×D3—24no—
129C22×C4×D3—42no—
130C22×C4×D3C2314yes—
131C2×C3×C22⋊C4—24no—
132C2×C3×C22⋊C4—24no—
133C2×C3×C22⋊C4—42no—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C22⋊C4C2314yes—
136C2×C3×C22⋊C4C2314yes—
137C2×#217—24no—
138C2×#217—24no—
139C2×#217—24no—
140C2×#217D418yescomplemented
141C2×#217C2314yes—
142C2×#217C2314yes—
143C2×#217C2314yes—
144C2×#217C2314yes—
145#939—232no—
146#935—232no—
147C4×#67—232no—
148C2×(C2×D3)⋊C4—24no—
149C2×(C2×D3)⋊C4—24no—
150C2×(C2×D3)⋊C4—24no—
151C2×(C2×D3)⋊C4—24no—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×C4⋊Dic3—24no—
157C2×C4⋊Dic3—24no—
158C2×C4⋊Dic3C2314yes—
159C2×C4⋊Dic3C2314yes—
160C2×Dic3⋊C4—24no—
161C2×Dic3⋊C4—24no—
162C2×Dic3⋊C4—24no—
163C2×Dic3⋊C4—24no—
164C2×Dic3⋊C4—24no—
165C2×Dic3⋊C4—42no—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×Dic3⋊C4C2314yes—
172C2×C4×Dic3—24no—
173C2×C4×Dic3C2314yes—
174#886—232no—
175C3×#95C2314yes—
176C3×#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C23×D4—31no—
184C23×D4—31no—
185C23×D4C2×D311yescharacteristic
186C24×C4—31no—
187C24×C4—31no—
188C24×C4—31no—
189C24×C4C2×D311yescharacteristic
190C2×#123—38no—
191C2×#123—38no—
192C2×#123—68no—
193C2×#123—68no—
194C2×#121—38no—
195C2×#121—68no—
196C2×C4×D4—38no—
197C2×C4×D4—68no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4—31no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4—31no—
203C22×C4⋊C4—31no—
204C22×C4⋊C4—31no—
205C22×C4⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4C2×D311yescharacteristic
215C22×C22⋊C4C2×D311yescharacteristic
216C22×C22⋊C4C2×D311yescharacteristic
217C22×C42—31no—
218#398—38no—
219#397—38no—
220#396—38no—
221#394—38no—
222#389—38no—
223#388—38no—
224#386—38no—
225#386C2×D318yescomplemented
226#385—38no—
227#380—38no—
228C2×#95—31no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—38no—
235C2×#95C2×D311yescharacteristic
236C2×#95C2×D311yescharacteristic
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3C2×D414yes—
249C24×C3C2×D414yes—
250C24×C3#4114yes—
251C24×C3C2412yes—
252C24×C3C2412yes—
253C24×C3C2411yescharacteristic
254C23×D3—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3C2×D414yes—
261C23×D3C2412yes—
262C2×C3×D4—28no—
263C2×C3×D4—28no—
264C2×C3×D4—28no—
265C2×C3×D4—416no—
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—28no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—28no—
282C22×C3×C4—44no—
283C22×C3×C4—416no—
284C22×C3×C4#4114yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C2×#67—232no—
291C2×#67—28no—
292C2×#67—28no—
293C2×#67—28no—
294C2×#67—28no—
295C2×#67—44no—
296C2×#67—416no—
297C2×#67C2×D4116yes—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—28no—
307C22×Dic3—22no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—28no—
313C22×Dic3—28no—
314C22×Dic3—28no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—28no—
320C22×Dic3—44no—
321C22×Dic3—416no—
322C22×Dic3—416no—
323C22×Dic3C2×D414yes—
324C22×Dic3C2×D414yes—
325C22×Dic3C2×D414yes—
326C22×Dic3#4114yes—
327C22×Dic3C2412yes—
328C22×Dic3C2412yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C2×C4×D3—28no—
335C2×C4×D3—28no—
336C2×C4×D3—44no—
337C2×C4×D3—416no—
338C3×C22⋊C4—28no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—44no—
341#217—28no—
342#217—28no—
343#217—28no—
344#217C2×D4116yescomplemented
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—28no—
349C4⋊Dic3—28no—
350C4⋊Dic3—28no—
351Dic3⋊C4—28no—
352Dic3⋊C4—28no—
353Dic3⋊C4—28no—
354Dic3⋊C4—28no—
355Dic3⋊C4—28no—
356Dic3⋊C4—44no—
357C4×Dic3—28no—
358C25—31no—
359C25C22×D311yescharacteristic
360C25C22×D311yescharacteristic
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—38no—
365C22×D4—34no—
366C22×D4—34no—
367C22×D4—64no—
368C22×D4—64no—
369C22×D4—64no—
370C22×D4—64no—
371C22×D4—122no—
372C22×D4C22×D314yes—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—34no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—34no—
384C23×C4—34no—
385C23×C4—42no—
386C23×C4—64no—
387C23×C4—64no—
388C23×C4—64no—
389C23×C4—64no—
390C23×C4—64no—
391C23×C4—64no—
392C23×C4—64no—
393C23×C4—122no—
394C23×C4—122no—
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D314yes—
400C23×C4C22×D311yescharacteristic
401#123—632no—
402#123—632no—
403#121—632no—
404C4×D4—632no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—64no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—64no—
416C2×C4⋊C4—64no—
417C2×C4⋊C4—64no—
418C2×C4⋊C4—64no—
419C2×C4⋊C4—64no—
420C2×C4⋊C4—122no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—38no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
437C2×C22⋊C4—64no—
438C2×C22⋊C4—64no—
439C2×C22⋊C4—64no—
440C2×C22⋊C4C22×D314yes—
441C2×C22⋊C4C22×D314yes—
442C2×C22⋊C4C22×D314yes—
443C2×C42—34no—
444C2×C42—64no—
445#95—34no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95C22×D314yes—
452#95C22×D314yes—
453C23×C3—28no—
454C23×C3—28no—
455C23×C3—28no—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—44no—
471C23×C3—44no—
472C23×C3—44no—
473C23×C3—44no—
474C23×C3—44no—
475C23×C3—44no—
476C23×C3—44no—
477C23×C3#121116yes—
478C23×C3C22×D414yes—
479C23×C3C22×D414yes—
480C23×C3C22×D412yes—
481C23×C3C22×D412yes—
482C23×C3C2×#4114yes—
483C23×C3C2×#4112yes—
484C23×C3C2×#4112yes—
485C23×C3C2×#4112yes—
486C23×C3H(5,𝔽2)12yes—
487C23×C32−1+412yes—
488C23×C3C2511yescharacteristic
489C22×D3—28no—
490C22×D3—28no—
491C22×D3—28no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—44no—
499C22×D3—44no—
500C22×D3—44no—
501C22×D3—44no—
502C22×D3C22×D414yes—
503C3×D4—416no—
504C2×C3×C4—28no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—416no—
520C2×C3×C4—44no—
521C2×C3×C4—44no—
522C2×C3×C4—44no—
523C2×C3×C4—44no—
524C2×C3×C4C2×#4114yes—
525#67—232no—
526#67—416no—
527C2×Dic3—28no—
528C2×Dic3—28no—
529C2×Dic3—28no—
530C2×Dic3—28no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—416no—
549C2×Dic3—416no—
550C2×Dic3—44no—
551C2×Dic3—44no—
552C2×Dic3—44no—
553C2×Dic3C22×D414yes—
554C2×Dic3C22×D414yes—
555C2×Dic3C22×D414yes—
556C2×Dic3C2×#4114yes—
557C4×D3—416no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—34no—
570C24—32no—
571C24—62no—
572C24—62no—
573C24—62no—
574C24—62no—
575C24—62no—
576C24—62no—
577C24#23514yes—
578C24D3×D414yes—
579C24D3×D414yes—
580C24C23×D312yes—
581C24C23×D312yes—
582C24C23×D311yescharacteristic
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—316no—
587C2×D4—416no—
588C2×D4—68no—
589C2×D4—632no—
590C2×D4—68no—
591C2×D4—68no—
592C2×D4—68no—
593C2×D4—124no—
594C2×D4—1216no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—28no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—28no—
611C22×C4—34no—
612C22×C4—34no—
613C22×C4—34no—
614C22×C4—34no—
615C22×C4—32no—
616C22×C4—32no—
617C22×C4—32no—
618C22×C4—32no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—32no—
622C22×C4—44no—
623C22×C4—416no—
624C22×C4—68no—
625C22×C4—68no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—68no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—62no—
642C22×C4—68no—
643C22×C4—68no—
644C22×C4—68no—
645C22×C4—62no—
646C22×C4—62no—
647C22×C4—68no—
648C22×C4—124no—
649C22×C4—1216no—
650C22×C4—124no—
651C22×C4—1216no—
652C22×C4—1216no—
653C22×C4#23714yes—
654C22×C4C23×D312yes—
655C22×C4C23×D312yes—
656C22×C4C23×D312yes—
657C22×C4C23×D312yes—
658C22×C4C23×D312yes—
659C4⋊C4—68no—
660C4⋊C4—68no—
661C4⋊C4—68no—
662C4⋊C4—68no—
663C4⋊C4—68no—
664C4⋊C4—68no—
665C4⋊C4—68no—
666C4⋊C4—124no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—316no—
670C22⋊C4—44no—
671C22⋊C4—68no—
672C22⋊C4—68no—
673C22⋊C4—68no—
674C22⋊C4—68no—
675C22⋊C4—68no—
676C22⋊C4—68no—
677C22⋊C4—68no—
678C42—68no—
679C22×C3—24no—
680C22×C3—232no—
681C22×C3—24no—
682C22×C3—24no—
683C22×C3—24no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—88no—
694C22×C3C2×#12118yes—
695C22×C3C2×#12114yes—
696C22×C3#52914yes—
697C22×C3#53914yes—
698C22×C3#54614yes—
699C22×C3#54614yes—
700C22×C3#54714yes—
701C22×C3#54714yes—
702C22×C3C23×D411yescharacteristic
703C22×C3C23×D411yescharacteristic
704C22×C3C22×#4111yescharacteristic
705C22×C3C22×#4111yescharacteristic
706C22×C3C22×#4111yescharacteristic
707C22×C3C2×H(5,𝔽2)11yescharacteristic
708C22×C3C2×2−1+411yescharacteristic
709C2×D3—24no—
710C2×D3—24no—
711C2×D3—24no—
712C2×D3—42no—
713C2×D3—416no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C3×C4—24no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—42no—
722Dic3—24no—
723Dic3—24no—
724Dic3—24no—
725Dic3—24no—
726Dic3—42no—
727Dic3—42no—
728Dic3—42no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—34no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—62no—
760C23—68no—
761C23—68no—
762C23—68no—
763C23—124no—
764C23—124no—
765C23—124no—
766C23—124no—
767C23#884116yes—
768C23C2×#23514yes—
769C23C2×#23512yes—
770C23C2×D3×D414yes—
771C23C2×D3×D414yes—
772C23C2×D3×D412yes—
773C23C2×D3×D412yes—
774C23C2×#23712yes—
775C23#100412yes—
776C23D3×#4112yes—
777C23#101012yes—
778C23C24×D311yescharacteristic
779D4—416no—
780D4—632no—
781D4—1216no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—28no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—34no—
798C2×C4—34no—
799C2×C4—34no—
800C2×C4—34no—
801C2×C4—416no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—68no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—68no—
816C2×C4—68no—
817C2×C4—68no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—1216no—
828C2×C4—1216no—
829C2×C4—1216no—
830C2×C4—124no—
831C2×C4—124no—
832C2×C4—124no—
833C2×C4C2×#23714yes—
834C2×C3—28no—
835C2×C3—82no—
836C2×C3#242518yescomplemented
837C2×C3C22×#12111yescharacteristic
838C2×C3C2×#52911yescharacteristic
839C2×C3C2×#53911yescharacteristic
840C2×C3C2×#54611yescharacteristic
841C2×C3C2×#54611yescharacteristic
842C2×C3C2×#54711yescharacteristic
843C2×C3C2×#54711yescharacteristic
844D3—44no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—232no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—64no—
860C22—64no—
861C22—64no—
862C22—88no—
863C22—122no—
864C22—1216no—
865C22—122no—
866C22—122no—
867C22—122no—
868C22C2×#88418yes—
869C22C2×#88414yes—
870C22#553814yes—
871C22#556414yes—
872C22#559114yes—
873C22#561014yes—
874C22#561114yes—
875C22#565514yes—
876C22C22×#23511yescharacteristic
877C22C22×D3×D411yescharacteristic
878C22C22×D3×D411yescharacteristic
879C22C22×#23711yescharacteristic
880C22C2×#100411yescharacteristic
881C22C2×D3×#4111yescharacteristic
882C22C2×#101011yescharacteristic
883C4—24no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—64no—
889C4—64no—
890C4—64no—
891C4—64no—
892C4—122no—
893C4—122no—
894C4—122no—
895C3C2×#242511yescharacteristic, complemented, Sylow
896C2—28no—
897C2—82no—
898C2—124no—
899C2#7469618yesdirect product factor
900C2C22×#88411yescharacteristic
901C2C2×#553811yescharacteristic
902C2C2×#556411yescharacteristic
903C2C2×#559111yescharacteristic
904C2C2×#561111yescharacteristic
905C2C2×#561011yescharacteristic
906C2C2×#565511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#386C2
socleC24×C3C24
prime radicalC22×#939C2
hypercenterC2×#386D3
hypocenterC3C2×#2425
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#935C2semidirect
3. C22×C4×#67C2semidirect
4. C22×#886C2semidirect
5. C2×C3×#386C2semidirect
6. C22×C3⋊#95C2semidirect
7. C2×#4959C2semidirect
8. C2×#4956C2semidirect
9. C2×#4948C2semidirect
10. C2×#4951C2semidirect
11. C2×#4946C2semidirect
12. #74696C2direct (N × H)
13. C2×#4675C2semidirect
14. C2×#4667C2semidirect
15. C2×#4657C2semidirect
16. C2×#4647C2semidirect
35. C2×#935C22semidirect
37. C2×C4×#67C22semidirect
52. C2×#886C22semidirect
53. C3×#386C22semidirect
62. C2×C3⋊#95C22semidirect
63. #4959C22semidirect
64. #4956C22semidirect
65. #4951C22semidirect
66. #4948C22semidirect
67. #4946C22semidirect
68. #4675C22semidirect
69. #4667C22semidirect
70. #4657C22semidirect
71. #4647C22semidirect
84. C2×#386D3semidirect
140. C2×#217D4semidirect
225. #386C2×D3semidirect
344. #217C2×D4semidirect
836. C2×C3#2425semidirect
895. C3C2×#2425semidirect
899. C2#74696direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9352
C22×#9392
C22×C4×#672
C22×#8862
C2×C3×#3862
C22×C3⋊#952
C2×#49592
C2×#49562
C2×#49482
C2×#49512
C2×#49462
#746962
C2×#46752
C2×#46672
C2×#46572
C2×#46472
C2×#24253