Finite Group Databasebeta

← C2×#13120870 #16029543

Subgroups — C2×#13120870 #16029543

Order 3328.

2222 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120870C2116yesmaximal, direct product factor
2C2×#11718610C211yesmaximal, characteristic, complemented
3C2×#11718645C211yesmaximal, characteristic, complemented
4C2×#11718322C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718614C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718883C211yesmaximal, characteristic
9C2×#11718882C211yesmaximal, characteristic
10C2×#11718606C211yesmaximal, characteristic, complemented
11C2×#11718612C211yesmaximal, characteristic, complemented
12C2×#11718612C211yesmaximal, characteristic, complemented
13C2×#11718605C211yesmaximal, characteristic, complemented
14C2×#11718313C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#394C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C13×#394C2218yes—
43C2×C13×#95C2211yescharacteristic
44#11718883C2218yes—
45#11718882C2218yes—
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718645C2218yescomplemented
56C4⋊C4×Dic13C2218yescomplemented
57#11718614C2218yescomplemented
58#11718614C2218yescomplemented
59#11718612C2218yescomplemented
60#11718612C2218yescomplemented
61#11718610C2218yescomplemented
62#11718609C2218yescomplemented
63#11718606C2218yescomplemented
64#11718605C2218yescomplemented
65#11718322C2218yescomplemented
66#11718313C2218yescomplemented
67C25×C13C2311yescharacteristic
68C25×C13C2311yescharacteristic
69C22×D4×C13—24no—
70C22×D4×C13—42no—
71C22×D4×C13—42no—
72C22×D4×C13C2314yes—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C2×C13×C4⋊C4—24no—
87C2×C13×C4⋊C4C2314yes—
88C2×C13×C22⋊C4—24no—
89C2×C13×C22⋊C4—24no—
90C2×C13×C22⋊C4—42no—
91C2×C13×C22⋊C4—42no—
92C2×C13×C22⋊C4C2314yes—
93C2×C13×C22⋊C4C2314yes—
94C2×C13×C22⋊C4C2314yes—
95C2×C13×C22⋊C4C2314yes—
96C2×C22⋊Dic13—24no—
97C2×C22⋊Dic13—24no—
98C2×C22⋊Dic13—42no—
99C2×C22⋊Dic13—42no—
100C2×C22⋊Dic13—42no—
101C2×C22⋊Dic13—42no—
102C2×C22⋊Dic13—42no—
103C2×C22⋊Dic13—42no—
104C2×C22⋊Dic13C2314yes—
105C2×C22⋊Dic13C2314yes—
106C2×C22⋊Dic13C2314yes—
107C2×C22⋊Dic13C2314yes—
108C2×C22⋊Dic13C2314yes—
109C2×C22⋊Dic13C2314yes—
110C2×C22⋊Dic13C2314yes—
111C2×C22⋊Dic13C2314yes—
112C2×C4⋊Dic13—24no—
113C2×C4⋊Dic13—42no—
114C2×C4⋊Dic13—42no—
115C2×C4⋊Dic13—42no—
116C2×C4⋊Dic13C2314yes—
117C2×C4⋊Dic13C2314yes—
118C2×C4⋊Dic13C2314yes—
119C2×C4⋊Dic13C2314yes—
120C2×#6101—24no—
121C2×#6101—42no—
122C2×#6101—42no—
123C2×#6101—42no—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×#6101C2314yes—
128C2×C4×Dic13—24no—
129C2×C4×Dic13—42no—
130C2×C4×Dic13—42no—
131C2×C4×Dic13C2314yes—
132C2×C4×Dic13C2314yes—
133C2×C4×Dic13C2314yes—
134C13×#95C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2651—131nomaximal, Sylow
145C24×C13—22no—
146C24×C13—22no—
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—22no—
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13C2412yes—
160C24×C13C2412yes—
161C24×C13C2411yescharacteristic
162C2×D4×C13—28no—
163C2×D4×C13—44no—
164C2×D4×C13—44no—
165C2×D4×C13—416no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13#4114yes—
180C22×C4×C13#4114yes—
181C22×C4×C13C2412yes—
182C22×C4×C13C2412yes—
183C22×C4×C13C2412yes—
184C22×C4×C13C2412yes—
185C22×C4×C13C2412yes—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13#4114yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C13×C4⋊C4—28no—
219C13×C22⋊C4—28no—
220C13×C22⋊C4—28no—
221C13×C22⋊C4—44no—
222C13×C22⋊C4—44no—
223C22⋊Dic13—28no—
224C22⋊Dic13—28no—
225C22⋊Dic13—44no—
226C22⋊Dic13—44no—
227C22⋊Dic13—44no—
228C22⋊Dic13—44no—
229C22⋊Dic13—44no—
230C22⋊Dic13—44no—
231C4⋊Dic13—28no—
232C4⋊Dic13—44no—
233C4⋊Dic13—44no—
234C4⋊Dic13—44no—
235#6101—28no—
236#6101—44no—
237#6101—44no—
238#6101—44no—
239C4×Dic13—28no—
240C4×Dic13—44no—
241C4×Dic13—44no—
242#2651—1316no—
243C2×#399—131no—
244C2×#398—131no—
245C2×#398—131no—
246C2×#397—131no—
247C2×#397—131no—
248C2×#396—131no—
249C2×#394—131no—
250C2×#394D1311yescharacteristic
251C2×#390—131no—
252C2×#388—131no—
253C2×#388—131no—
254C2×#388—131no—
255C2×#388—131no—
256C2×#387—131no—
257C2×C4×C4⋊C4—131no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—22no—
267C23×C13—22no—
268C23×C13—22no—
269C23×C13—22no—
270C23×C13—22no—
271C23×C13—22no—
272C23×C13—44no—
273C23×C13—44no—
274C23×C13—44no—
275C23×C13—44no—
276C23×C13—44no—
277C23×C13—44no—
278C23×C13—44no—
279C23×C13—44no—
280C23×C13—44no—
281C23×C13—44no—
282C23×C13—44no—
283C23×C13—44no—
284C23×C13—44no—
285C23×C13—44no—
286C23×C13C2×#4112yes—
287C23×C13C2×#4112yes—
288C23×C13C2×#4112yes—
289C23×C13H(5,𝔽2)12yes—
290C23×C13H(5,𝔽2)12yes—
291C23×C13H(5,𝔽2)12yes—
292C23×C132−1+412yes—
293C23×C13C2511yescharacteristic
294D4×C13—416no—
295C2×C4×C13—28no—
296C2×C4×C13—28no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—44no—
311C2×C4×C13—44no—
312C2×C4×C13—44no—
313C2×C4×C13C2×#4114yes—
314C2×C4×C13C2×#4114yes—
315C2×Dic13—28no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—44no—
340C2×Dic13—44no—
341C2×Dic13—44no—
342C2×Dic13—44no—
343C2×Dic13—44no—
344C2×Dic13—44no—
345C2×Dic13—44no—
346C2×Dic13C2×#4114yes—
347C23×D4C2×D1311yescharacteristic
348C22×C4⋊C4—131no—
349C22×C4⋊C4—131no—
350C22×C4⋊C4—131no—
351C22×C4⋊C4—131no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4C2×D1311yescharacteristic
357C22×C22⋊C4—131no—
358C22×C22⋊C4—131no—
359C22×C22⋊C4—131no—
360C22×C22⋊C4—131no—
361C22×C22⋊C4—131no—
362C22×C22⋊C4—131no—
363C22×C22⋊C4—131no—
364C22×C22⋊C4—131no—
365C22×C22⋊C4C2×D1311yescharacteristic
366C22×C22⋊C4C2×D1311yescharacteristic
367C22×C22⋊C4C2×D1311yescharacteristic
368C22×C22⋊C4C2×D1311yescharacteristic
369C22×C42—131no—
370C22×C42—131no—
371C22×C42—131no—
372#399—138no—
373#398—138no—
374#398—138no—
375#397—138no—
376#397—138no—
377#396—138no—
378#394—138no—
379#394C2×D1318yes—
380#390—138no—
381#388—138no—
382#388—138no—
383#388—138no—
384#388—138no—
385#387—138no—
386C4×C4⋊C4—138no—
387C2×#95—131no—
388C2×#95—131no—
389C2×#95—131no—
390C2×#95—131no—
391C2×#95—131no—
392C2×#95—131no—
393C2×#95—131no—
394C2×#95—131no—
395C2×#95—131no—
396C2×#95C2×D1311yescharacteristic
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—42no—
402C22×C13—42no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—42no—
409C22×C13—42no—
410C22×C13—42no—
411C22×C13—88no—
412C22×C13—88no—
413C22×C13#52914yes—
414C22×C13#53814yes—
415C22×C13#53914yes—
416C22×C13#54014yes—
417C22×C13#54014yes—
418C22×C13#54214yes—
419C22×C13#54214yes—
420C22×C13C22×#4111yescharacteristic
421C22×C13C22×#4111yescharacteristic
422C22×C13C22×#4111yescharacteristic
423C22×C13C2×H(5,𝔽2)11yescharacteristic
424C22×C13C2×H(5,𝔽2)11yescharacteristic
425C22×C13C2×H(5,𝔽2)11yescharacteristic
426C22×C13C2×2−1+411yescharacteristic
427C4×C13—24no—
428C4×C13—24no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13—42no—
432Dic13—24no—
433Dic13—42no—
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440C25C22×D1311yescharacteristic
441C25C22×D1311yescharacteristic
442C22×D4—24no—
443C22×D4—42no—
444C22×D4—42no—
445C22×D4C22×D1314yes—
446C23×C4—131no—
447C23×C4—131no—
448C23×C4—131no—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—131no—
453C23×C4—131no—
454C23×C4C22×D1311yescharacteristic
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C2×C4⋊C4—24no—
460C2×C4⋊C4—134no—
461C2×C4⋊C4—134no—
462C2×C4⋊C4—134no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—134no—
466C2×C4⋊C4—134no—
467C2×C4⋊C4—134no—
468C2×C4⋊C4—264no—
469C2×C4⋊C4—264no—
470C2×C4⋊C4—522no—
471C2×C4⋊C4—522no—
472C2×C4⋊C4—522no—
473C2×C4⋊C4—522no—
474C2×C4⋊C4—522no—
475C2×C4⋊C4—522no—
476C2×C4⋊C4C22×D1314yes—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—134no—
482C2×C22⋊C4—134no—
483C2×C22⋊C4—134no—
484C2×C22⋊C4—134no—
485C2×C22⋊C4—134no—
486C2×C22⋊C4—134no—
487C2×C22⋊C4—134no—
488C2×C22⋊C4—134no—
489C2×C22⋊C4—264no—
490C2×C22⋊C4—264no—
491C2×C22⋊C4—522no—
492C2×C22⋊C4—522no—
493C2×C22⋊C4—522no—
494C2×C22⋊C4—522no—
495C2×C22⋊C4—522no—
496C2×C22⋊C4—522no—
497C2×C22⋊C4C22×D1314yes—
498C2×C22⋊C4C22×D1314yes—
499C2×C22⋊C4C22×D1314yes—
500C2×C22⋊C4C22×D1314yes—
501C2×C42—134no—
502C2×C42—134no—
503C2×C42—134no—
504C2×C42—264no—
505C2×C42—522no—
506C2×C42—522no—
507#95—134no—
508#95—134no—
509#95—134no—
510#95—134no—
511#95—134no—
512#95—134no—
513#95—134no—
514#95—134no—
515#95—134no—
516#95C22×D1314yes—
517C2×C13—82no—
518C2×C13—82no—
519C2×C13#265118yescomplemented
520C2×C13C2×#52911yescharacteristic
521C2×C13C2×#53811yescharacteristic
522C2×C13C2×#53911yescharacteristic
523C2×C13C2×#54011yescharacteristic
524C2×C13C2×#54011yescharacteristic
525C2×C13C2×#54211yescharacteristic
526C2×C13C2×#54211yescharacteristic
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24C23×D1312yes—
542C24C23×D1312yes—
543C24C23×D1311yescharacteristic
544C2×D4—28no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—416no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—134no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—132no—
565C22×C4—132no—
566C22×C4—132no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4#612914yes—
594C22×C4#612914yes—
595C22×C4C23×D1312yes—
596C22×C4C23×D1312yes—
597C22×C4C23×D1312yes—
598C22×C4C23×D1312yes—
599C22×C4C23×D1312yes—
600C4⋊C4—28no—
601C4⋊C4—268no—
602C4⋊C4—268no—
603C4⋊C4—524no—
604C4⋊C4—524no—
605C4⋊C4—524no—
606C4⋊C4—524no—
607C4⋊C4—524no—
608C4⋊C4—524no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—268no—
614C22⋊C4—268no—
615C22⋊C4—524no—
616C22⋊C4—524no—
617C22⋊C4—524no—
618C22⋊C4—524no—
619C22⋊C4—524no—
620C22⋊C4—524no—
621C42—268no—
622C42—524no—
623C42—524no—
624C13C2×#265111yescharacteristic, complemented, Sylow
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23C2×#612912yes—
654C23C2×#612912yes—
655C23#8825112yes—
656C23#8825112yes—
657C23#41×D1312yes—
658C23#8825612yes—
659C23#8825712yes—
660C23C24×D1311yescharacteristic
661D4—416no—
662C2×C4—28no—
663C2×C4—28no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—134no—
681C2×C4—268no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—524no—
706C2×C4—524no—
707C2×C4—524no—
708C2×C4—524no—
709C2×C4—524no—
710C2×C4—524no—
711C2×C4—524no—
712C2×C4C2×#612914yes—
713C2×C4C2×#612914yes—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—88no—
729C22—88no—
730C22#1171929814yes—
731C22#1171930514yes—
732C22#1171930814yes—
733C22#1171932414yes—
734C22#1171936514yes—
735C22#1171936814yes—
736C22#1171938714yes—
737C22C22×#612911yescharacteristic
738C22C22×#612911yescharacteristic
739C22C2×#8825111yescharacteristic
740C22C2×#8825111yescharacteristic
741C22C2×#41×D1311yescharacteristic
742C22C2×#8825611yescharacteristic
743C22C2×#8825711yescharacteristic
744C4—24no—
745C4—24no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—264no—
750C4—522no—
751C4—522no—
752C4—522no—
753C4—522no—
754C4—522no—
755C4—522no—
756C4—522no—
757C2—82no—
758C2—82no—
759C2#1312087018yesdirect product factor
760C2C2×#1171930511yescharacteristic
761C2C2×#1171929811yescharacteristic
762C2C2×#1171936511yescharacteristic
763C2C2×#1171936811yescharacteristic
764C2C2×#1171932411yescharacteristic
765C2C2×#1171930811yescharacteristic
766C2C2×#1171938711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#394C2
socleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#394D13
hypocenterC13C2×#2651
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13120870C2direct (N × H)
2. C2×#11718610C2semidirect
3. C2×#11718645C2semidirect
4. C2×#11718322C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718614C2semidirect
7. C2×#11718609C2semidirect
10. C2×#11718606C2semidirect
11. C2×#11718612C2semidirect
12. C2×#11718612C2semidirect
13. C2×#11718605C2semidirect
14. C2×#11718313C2semidirect
15. C2×C4⋊C4×Dic13C2semidirect
55. #11718645C22semidirect
56. C4⋊C4×Dic13C22semidirect
57. #11718614C22semidirect
58. #11718614C22semidirect
59. #11718612C22semidirect
60. #11718612C22semidirect
61. #11718610C22semidirect
62. #11718609C22semidirect
63. #11718606C22semidirect
64. #11718605C22semidirect
65. #11718322C22semidirect
66. #11718313C22semidirect
519. C2×C13#2651semidirect
624. C13C2×#2651semidirect
759. C2#13120870direct (N × H)

Maximal subgroups

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

subgroupindex
#131208702
C2×#117186102
C2×#117186452
C2×#117183222
C2×#117186142
C2×#117186092
C2×#117188832
C2×#117188822
C2×#117186062
C2×#117186122
C2×#117186052
C2×#117183132
C2×C4⋊C4×Dic132
C2×C13×#3942
C2×#265113