Finite Group Databasebeta

← C2×#13120863 #16029550

Subgroups — C2×#13120863 #16029550

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#13120863C2116yesmaximal, direct product factor
2C2×#11718653C211yesmaximal, characteristic, complemented
3C2×#11718318C211yesmaximal, characteristic, complemented
4C2×#11718645C211yesmaximal, characteristic, complemented
5C2×#11718336C211yesmaximal, characteristic, complemented
6C2×#11718654C211yesmaximal, characteristic, complemented
7C2×#11718337C211yesmaximal, characteristic, complemented
8C2×#11718333C211yesmaximal, characteristic
9C2×#11718652C211yesmaximal, characteristic
10C2×#11718600C211yesmaximal, characteristic
11C2×#11718601C211yesmaximal, characteristic, complemented
12C2×#11718601C211yesmaximal, characteristic, complemented
13C2×#11718601C211yesmaximal, characteristic, complemented
14C2×#11718601C211yesmaximal, characteristic, complemented
15C2×#11718594C211yesmaximal, characteristic, complemented
16C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
17C23×D52C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C4×C13×C4⋊C4C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718654C2218yescomplemented
54#11718653C2218yescomplemented
55#11718652C2218yes—
56#11718645C2218yescomplemented
57#11718601C2218yescomplemented
58#11718601C2218yescomplemented
59#11718601C2218yescomplemented
60#11718601C2218yescomplemented
61#11718600C2218yes—
62#11718594C2218yescomplemented
63#11718337C2218yescomplemented
64#11718336C2218yescomplemented
65#11718333C2218yes—
66#11718318C2218yescomplemented
67C24×D13C2311yescharacteristic
68C24×D13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C22×D52—24no—
83C22×D52—42no—
84C22×D52—42no—
85C22×D52C2314yes—
86C2×C13×C4⋊C4—24no—
87C2×C13×C4⋊C4—24no—
88C2×C13×C4⋊C4C2314yes—
89C2×C13×C4⋊C4C2314yes—
90C2×C42×C13—24no—
91C2×C42×C13—42no—
92C2×C42×C13—42no—
93C2×C42×C13C2314yes—
94C2×C42×C13C2314yes—
95C2×C42×C13C2314yes—
96C2×#6103—24no—
97C2×#6103—24no—
98C2×#6103—24no—
99C2×#6103—24no—
100C2×#6103—42no—
101C2×#6103—42no—
102C2×#6103—42no—
103C2×#6103—42no—
104C2×#6103—42no—
105C2×#6103—42no—
106C2×#6103—42no—
107C2×#6103—42no—
108C2×#6103C2314yes—
109C2×#6103C2314yes—
110C2×#6103C2314yes—
111C2×#6103C2314yes—
112C2×#6103C2314yes—
113C2×#6103C2314yes—
114C2×#6103C2314yes—
115C2×#6103C2314yes—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×C4⋊Dic13—42no—
121C2×C4⋊Dic13C2314yes—
122C2×#6101—24no—
123C2×#6101—42no—
124C2×#6101—42no—
125C2×#6101—42no—
126C2×#6101—42no—
127C2×#6101—42no—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C13×#95C2314yes—
135C13×#95C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2651—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C23×D13—22no—
147C23×D13—22no—
148C23×D13—22no—
149C23×D13—22no—
150C23×D13—22no—
151C23×D13—22no—
152C23×D13—22no—
153C23×D13—22no—
154C23×D13—22no—
155C23×D13—22no—
156C23×D13—22no—
157C23×D13—22no—
158C23×D13—22no—
159C23×D13—22no—
160C23×D13C2412yes—
161C23×D13C2412yes—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
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—22no—
180C22×C4×C13#4114yes—
181C22×C4×C13#4114yes—
182C22×C4×C13#4114yes—
183C22×C4×C13C2412yes—
184C22×C4×C13C2412yes—
185C22×C4×C13C2412yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2412yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
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×Dic13C2412yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C2×D52—28no—
215C2×D52—44no—
216C2×D52—44no—
217C2×D52—416no—
218C13×C4⋊C4—28no—
219C13×C4⋊C4—28no—
220C42×C13—28no—
221C42×C13—44no—
222C42×C13—44no—
223#6103—28no—
224#6103—28no—
225#6103—28no—
226#6103—28no—
227#6103—44no—
228#6103—44no—
229#6103—44no—
230#6103—44no—
231#6103—44no—
232#6103—44no—
233#6103—44no—
234#6103—44no—
235C4⋊Dic13—44no—
236#6101—28no—
237#6101—44no—
238#6101—44no—
239#6101—44no—
240#6101—44no—
241#6101—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×#394—131no—
251C2×#390—131no—
252C2×#388—131no—
253C2×#388—131no—
254C2×#388—131no—
255C2×#388—131no—
256C2×#387—131no—
257C2×C4×C4⋊C4D1311yescharacteristic, complemented
258C23×C13C2×#4112yes—
259C23×C13C2×#4112yes—
260C23×C13C2×#4112yes—
261C23×C13H(5,𝔽2)12yes—
262C23×C13H(5,𝔽2)12yes—
263C23×C13H(5,𝔽2)12yes—
264C23×C132−1+412yes—
265C23×C13C2511yescharacteristic
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—22no—
271C22×D13—22no—
272C22×D13—22no—
273C22×D13—22no—
274C22×D13—22no—
275C22×D13—22no—
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—22no—
279C22×D13—22no—
280C22×D13—44no—
281C22×D13—44no—
282C22×D13—44no—
283C22×D13—44no—
284C22×D13—44no—
285C22×D13—44no—
286C22×D13—44no—
287C22×D13—44no—
288C22×D13—44no—
289C22×D13—44no—
290C22×D13—44no—
291C22×D13—44no—
292C22×D13—44no—
293C22×D13—44no—
294C2×C4×C13—28no—
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—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—44no—
316C2×C4×C13—44no—
317C2×C4×C13—44no—
318C2×C4×C13—44no—
319C2×C4×C13C2×#4114yes—
320C2×C4×C13C2×#4114yes—
321C2×C4×C13C2×#4114yes—
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—22no—
340C2×Dic13—44no—
341C2×Dic13—44no—
342C2×Dic13—44no—
343C2×Dic13—44no—
344C2×Dic13—44no—
345C2×Dic13—44no—
346D52—416no—
347C23×D4—131no—
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⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
366C22×C22⋊C4—131no—
367C22×C22⋊C4—131no—
368C22×C22⋊C4—131no—
369C22×C42C2×D1311yescharacteristic
370C22×C42C2×D1311yescharacteristic
371C22×C42C2×D1311yescharacteristic
372#399—138no—
373#398—138no—
374#398—138no—
375#397—138no—
376#397—138no—
377#396—138no—
378#394—138no—
379#394—138no—
380#390—138no—
381#388—138no—
382#388—138no—
383#388—138no—
384#388—138no—
385#387—138no—
386C4×C4⋊C4C2×D1318yescomplemented
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×#95C2×D1311yescharacteristic
396C2×#95C2×D1311yescharacteristic
397C22×C13#52914yes—
398C22×C13#53814yes—
399C22×C13#53914yes—
400C22×C13#54014yes—
401C22×C13#54014yes—
402C22×C13#54214yes—
403C22×C13#54214yes—
404C22×C13C22×#4111yescharacteristic
405C22×C13C22×#4111yescharacteristic
406C22×C13C22×#4111yescharacteristic
407C22×C13C2×H(5,𝔽2)11yescharacteristic
408C22×C13C2×H(5,𝔽2)11yescharacteristic
409C22×C13C2×H(5,𝔽2)11yescharacteristic
410C22×C13C2×2−1+411yescharacteristic
411C2×D13—42no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—88no—
426C2×D13—88no—
427C4×C13—24no—
428C4×C13—24no—
429C4×C13—24no—
430C4×C13—42no—
431C4×C13—42no—
432C4×C13—42no—
433C4×C13—42no—
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440C25—131no—
441C25—131no—
442C22×D4—134no—
443C22×D4—264no—
444C22×D4—522no—
445C22×D4—522no—
446C23×C4—131no—
447C23×C4—131no—
448C23×C4—131no—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4C22×D1311yescharacteristic
453C23×C4C22×D1311yescharacteristic
454C23×C4C22×D1311yescharacteristic
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
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—522no—
470C2×C4⋊C4—522no—
471C2×C4⋊C4—522no—
472C2×C4⋊C4—522no—
473C2×C4⋊C4—522no—
474C2×C4⋊C4—522no—
475C2×C4⋊C4C22×D1314yes—
476C2×C4⋊C4C22×D1314yes—
477C2×C22⋊C4—134no—
478C2×C22⋊C4—134no—
479C2×C22⋊C4—134no—
480C2×C22⋊C4—134no—
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—264no—
492C2×C22⋊C4—264no—
493C2×C22⋊C4—522no—
494C2×C22⋊C4—522no—
495C2×C22⋊C4—522no—
496C2×C22⋊C4—522no—
497C2×C22⋊C4—522no—
498C2×C22⋊C4—522no—
499C2×C22⋊C4—522no—
500C2×C22⋊C4—522no—
501C2×C42—24no—
502C2×C42—42no—
503C2×C42—42no—
504C2×C42C22×D1314yes—
505C2×C42C22×D1314yes—
506C2×C42C22×D1314yes—
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#95C22×D1314yes—
516#95C22×D1314yes—
517C2×C13#265118yescomplemented
518C2×C13C2×#52911yescharacteristic
519C2×C13C2×#53811yescharacteristic
520C2×C13C2×#53911yescharacteristic
521C2×C13C2×#54011yescharacteristic
522C2×C13C2×#54011yescharacteristic
523C2×C13C2×#54211yescharacteristic
524C2×C13C2×#54211yescharacteristic
525D13—82no—
526D13—82no—
527C24—132no—
528C24—132no—
529C24—262no—
530C24—262no—
531C24—262no—
532C24—262no—
533C24—262no—
534C24—262no—
535C24—262no—
536C24—262no—
537C24—262no—
538C24—262no—
539C24—262no—
540C24—262no—
541C24—262no—
542C24—262no—
543C24C23×D1311yescharacteristic
544C2×D4—268no—
545C2×D4—524no—
546C2×D4—524no—
547C2×D4—5216no—
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—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—132no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—132no—
571C22×C4—132no—
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#612714yes—
591C22×C4#612714yes—
592C22×C4#612714yes—
593C22×C4C23×D1312yes—
594C22×C4C23×D1312yes—
595C22×C4C23×D1312yes—
596C22×C4C23×D1312yes—
597C22×C4C23×D1312yes—
598C22×C4C23×D1312yes—
599C22×C4C23×D1312yes—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—268no—
603C4⋊C4—524no—
604C4⋊C4—524no—
605C4⋊C4—524no—
606C4⋊C4—524no—
607C4⋊C4—524no—
608C4⋊C4—524no—
609C22⋊C4—268no—
610C22⋊C4—268no—
611C22⋊C4—268no—
612C22⋊C4—268no—
613C22⋊C4—524no—
614C22⋊C4—524no—
615C22⋊C4—524no—
616C22⋊C4—524no—
617C22⋊C4—524no—
618C22⋊C4—524no—
619C22⋊C4—524no—
620C22⋊C4—524no—
621C42—28no—
622C42—44no—
623C42—44no—
624C13C2×#265111yescharacteristic, complemented, Sylow
625C23—262no—
626C23—262no—
627C23—262no—
628C23—262no—
629C23—262no—
630C23—262no—
631C23—262no—
632C23—262no—
633C23—262no—
634C23—262no—
635C23—262no—
636C23—262no—
637C23—262no—
638C23—262no—
639C23—524no—
640C23—524no—
641C23—524no—
642C23—524no—
643C23—524no—
644C23—524no—
645C23—524no—
646C23—524no—
647C23—524no—
648C23—524no—
649C23—524no—
650C23—524no—
651C23—524no—
652C23—524no—
653C23C2×#612712yes—
654C23C2×#612712yes—
655C23C2×#612712yes—
656C23#8825112yes—
657C23#8825412yes—
658C23#8825612yes—
659C23#8825612yes—
660C23C24×D1311yescharacteristic
661D4—5216no—
662C2×C4—28no—
663C2×C4—28no—
664C2×C4—28no—
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—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
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×C4C2×#612714yes—
712C2×C4C2×#612714yes—
713C2×C4C2×#612714yes—
714C22—522no—
715C22—522no—
716C22—522no—
717C22—522no—
718C22—522no—
719C22—522no—
720C22—522no—
721C22—522no—
722C22—522no—
723C22—522no—
724C22—522no—
725C22—522no—
726C22—522no—
727C22—522no—
728C22—1048no—
729C22—1048no—
730C22#1171918414yes—
731C22#1171922014yes—
732C22#1171924014yes—
733C22#1171926514yes—
734C22#1171926714yes—
735C22#1171928714yes—
736C22#1171928714yes—
737C22C22×#612711yescharacteristic
738C22C22×#612711yescharacteristic
739C22C22×#612711yescharacteristic
740C22C2×#8825111yescharacteristic
741C22C2×#8825411yescharacteristic
742C22C2×#8825611yescharacteristic
743C22C2×#8825611yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—522no—
752C4—522no—
753C4—522no—
754C4—522no—
755C4—522no—
756C4—522no—
757C2—1042no—
758C2—1042no—
759C2#1312086318yesdirect product factor
760C2C2×#1171918411yescharacteristic
761C2C2×#1171926511yescharacteristic
762C2C2×#1171922011yescharacteristic
763C2C2×#1171926711yescharacteristic
764C2C2×#1171924011yescharacteristic
765C2C2×#1171928711yescharacteristic
766C2C2×#1171928711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C4×C13×C4⋊C4C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C2×#2651
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13120863C2direct (N × H)
2. C2×#11718653C2semidirect
3. C2×#11718318C2semidirect
4. C2×#11718645C2semidirect
5. C2×#11718336C2semidirect
6. C2×#11718654C2semidirect
7. C2×#11718337C2semidirect
11. C2×#11718601C2semidirect
12. C2×#11718601C2semidirect
13. C2×#11718601C2semidirect
14. C2×#11718601C2semidirect
15. C2×#11718594C2semidirect
16. C2×C4×C13×C4⋊C4C2semidirect
42. C4×C13×C4⋊C4C22semidirect
53. #11718654C22semidirect
54. #11718653C22semidirect
56. #11718645C22semidirect
57. #11718601C22semidirect
58. #11718601C22semidirect
59. #11718601C22semidirect
60. #11718601C22semidirect
62. #11718594C22semidirect
63. #11718337C22semidirect
64. #11718336C22semidirect
66. #11718318C22semidirect
257. C2×C4×C4⋊C4D13semidirect
386. C4×C4⋊C4C2×D13semidirect
517. C2×C13#2651semidirect
624. C13C2×#2651semidirect
759. C2#13120863direct (N × H)

Maximal subgroups

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

subgroupindex
#131208632
C2×#117186532
C2×#117183182
C2×#117186452
C2×#117183362
C2×#117186542
C2×#117183372
C2×#117183332
C2×#117186522
C2×#117186002
C2×#117186012
C2×#117185942
C2×C4×C13×C4⋊C42
C2×#265113