Finite Group Databasebeta

← C2×#13120176 #16033396

Subgroups — C2×#13120176 #16033396

Order 3328.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120176C2116yesmaximal, direct product factor
2C2×#11718320C211yesmaximal, characteristic, complemented
3C2×#11718613C211yesmaximal, characteristic, complemented
4C2×#11718654C211yesmaximal, characteristic, complemented
5C2×#11718622C211yesmaximal, characteristic
6C2×#11718330C211yesmaximal, characteristic, complemented
7C2×#11718316C211yesmaximal, characteristic, complemented
8C2×#11718639C211yesmaximal, characteristic, complemented
9C2×#11718619C211yesmaximal, characteristic
10C2×#11718617C211yesmaximal, characteristic
11C2×#11718607C211yesmaximal, characteristic, complemented
12C2×#11718598C211yesmaximal, characteristic, complemented
13C2×#11718328C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C13×#388C2218yescomplemented
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718654C2218yescomplemented
54#11718639C2218yescomplemented
55#11718622C2218yes—
56#11718619C2218yes—
57#11718617C2218yes—
58#11718613C2218yescomplemented
59#11718607C2218yescomplemented
60C22⋊C4×Dic13C2218yescomplemented
61C4×#6103C2218yescomplemented
62#11718598C2218yescomplemented
63#11718330C2218yescomplemented
64#11718328C2218yescomplemented
65#11718320C2218yescomplemented
66#11718316C2218yescomplemented
67C25×C13C2311yescharacteristic
68C24×D13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C22×C22⋊D13—24no—
76C22×C22⋊D13—24no—
77C22×C22⋊D13—42no—
78C22×C22⋊D13C2314yes—
79C23×Dic13—24no—
80C23×Dic13—42no—
81C23×Dic13—42no—
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2314yes—
90C22×C4×D13—24no—
91C22×C4×D13—24no—
92C22×C4×D13—42no—
93C22×C4×D13C2314yes—
94C2×C13×C4⋊C4—42no—
95C2×C13×C4⋊C4C2314yes—
96C2×C13×C22⋊C4—24no—
97C2×C13×C22⋊C4—24no—
98C2×C13×C22⋊C4—42no—
99C2×C13×C22⋊C4C2314yes—
100C2×C13×C22⋊C4C2314yes—
101C2×C13×C22⋊C4C2314yes—
102C2×C42×C13—24no—
103C2×C42×C13C2314yes—
104C2×C22⋊Dic13—24no—
105C2×C22⋊Dic13—24no—
106C2×C22⋊Dic13C2314yes—
107C2×C22⋊Dic13C2314yes—
108C2×#6103—24no—
109C2×#6103—24no—
110C2×#6103—24no—
111C2×#6103—42no—
112C2×#6103—42no—
113C2×#6103C2314yes—
114C2×#6103C2314yes—
115C2×#6103C2314yes—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×C4⋊Dic13—42no—
119C2×C4⋊Dic13C2314yes—
120C2×#6101—24no—
121C2×#6101—24no—
122C2×#6101—42no—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×C4×Dic13—42no—
127C2×C4×Dic13—42no—
128C2×C4×Dic13C2314yes—
129C2×C4×Dic13C2314yes—
130C13×#95C2314yes—
131C13×#95C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2578—131nomaximal, Sylow
145C24×C13—22no—
146C24×C13—22no—
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—22no—
151C24×C13#4114yes—
152C24×C13C2412yes—
153C24×C13C2411yescharacteristic
154C23×D13—22no—
155C23×D13—22no—
156C23×D13—22no—
157C23×D13—22no—
158C23×D13—22no—
159C23×D13—22no—
160C23×D13#4114yes—
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#4114yes—
180C22×C4×C13C2412yes—
181C22×C4×C13C2412yes—
182C22×C4×C13C2412yes—
183C22×C4×C13C2412yes—
184C22×C4×C13C2412yes—
185C22×C4×C13C2412yes—
186C2×C22⋊D13—28no—
187C2×C22⋊D13—28no—
188C2×C22⋊D13—44no—
189C2×C22⋊D13—416no—
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—28no—
210C22×Dic13—44no—
211C22×Dic13—44no—
212C22×Dic13—416no—
213C22×Dic13#4114yes—
214C22×Dic13#4114yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C2×C4×D13—28no—
223C2×C4×D13—28no—
224C2×C4×D13—44no—
225C2×C4×D13—416no—
226C13×C4⋊C4—44no—
227C13×C22⋊C4—28no—
228C13×C22⋊C4—28no—
229C13×C22⋊C4—44no—
230C42×C13—28no—
231C22⋊Dic13—28no—
232C22⋊Dic13—28no—
233#6103—28no—
234#6103—28no—
235#6103—28no—
236#6103—44no—
237#6103—44no—
238C4⋊Dic13—44no—
239#6101—28no—
240#6101—28no—
241#6101—44no—
242C4×Dic13—44no—
243C4×Dic13—44no—
244#2578—1316no—
245C2×#400—131no—
246C2×#397—131no—
247C2×#397—131no—
248C2×#394—131no—
249C2×#388—131no—
250C2×#388D1311yescharacteristic, complemented
251C2×#387—131no—
252C2×#387—131no—
253C2×#386—131no—
254C2×#386—131no—
255C2×#385—131no—
256C2×#383—131no—
257C2×#380—131no—
258C2×C4×C22⋊C4—131no—
259C2×C4×C22⋊C4—131no—
260C23×C13—28no—
261C23×C13—28no—
262C23×C13—28no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—22no—
267C23×C13—22no—
268C23×C13—22no—
269C23×C13—44no—
270C23×C13—44no—
271C23×C13—44no—
272C23×C13—44no—
273C23×C13C2×#4114yes—
274C23×C13C2×#4112yes—
275C23×C13C2×#4112yes—
276C23×C13C2×#4112yes—
277C23×C13C2×#4112yes—
278C23×C13C2×#4112yes—
279C23×C13H(5,𝔽2)12yes—
280C23×C13H(5,𝔽2)12yes—
281C23×C13C2511yescharacteristic
282C22×D13—28no—
283C22×D13—28no—
284C22×D13—28no—
285C22×D13—22no—
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—44no—
292C22×D13—44no—
293C22×D13—44no—
294C22×D13—44no—
295C22×D13C2×#4114yes—
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—44no—
315C2×C4×C13—44no—
316C2×C4×C13—44no—
317C2×C4×C13—44no—
318C2×C4×C13—44no—
319C2×C4×C13C2×#4114yes—
320C22⋊D13—416no—
321C2×Dic13—28no—
322C2×Dic13—28no—
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—22no—
341C2×Dic13—22no—
342C2×Dic13—416no—
343C2×Dic13—44no—
344C2×Dic13—44no—
345C2×Dic13—44no—
346C2×Dic13—44no—
347C2×Dic13—44no—
348C2×Dic13C2×#4114yes—
349C2×Dic13C2×#4114yes—
350C4×D13—416no—
351C23×D4—131no—
352C24×C4—131no—
353C24×C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4C2×D1311yescharacteristic
367C22×C22⋊C4C2×D1311yescharacteristic
368C22×C22⋊C4C2×D1311yescharacteristic
369C22×C42—131no—
370C22×C42—131no—
371C22×C42C2×D1311yescharacteristic
372#400—138no—
373#397—138no—
374#397—138no—
375#394—138no—
376#388—138no—
377#388C2×D1318yescomplemented
378#387—138no—
379#387—138no—
380#386—138no—
381#386—138no—
382#385—138no—
383#383—138no—
384#380—138no—
385C4×C22⋊C4—138no—
386C4×C22⋊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×#95—131no—
397C2×#95—131no—
398C2×#95—131no—
399C2×#95C2×D1311yescharacteristic
400C2×#95C2×D1311yescharacteristic
401C22×C13—24no—
402C22×C13—24no—
403C22×C13—24no—
404C22×C13—416no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—42no—
409C22×C13#52914yes—
410C22×C13#52914yes—
411C22×C13#53814yes—
412C22×C13#55114yes—
413C22×C13#55114yes—
414C22×C13#55314yes—
415C22×C13#55314yes—
416C22×C13C22×#4111yescharacteristic
417C22×C13C22×#4111yescharacteristic
418C22×C13C22×#4111yescharacteristic
419C22×C13C22×#4111yescharacteristic
420C22×C13C22×#4111yescharacteristic
421C22×C13C2×H(5,𝔽2)11yescharacteristic
422C22×C13C2×H(5,𝔽2)11yescharacteristic
423C2×D13—24no—
424C2×D13—24no—
425C2×D13—24no—
426C2×D13—416no—
427C2×D13—42no—
428C2×D13—42no—
429C2×D13—42no—
430C2×D13—42no—
431C4×C13—24no—
432C4×C13—42no—
433C4×C13—42no—
434C4×C13—42no—
435C4×C13—42no—
436C4×C13—42no—
437Dic13—24no—
438Dic13—24no—
439Dic13—42no—
440Dic13—42no—
441Dic13—42no—
442Dic13—42no—
443Dic13—42no—
444C25—131no—
445C25C22×D1311yescharacteristic
446C22×D4—134no—
447C22×D4—264no—
448C22×D4—264no—
449C22×D4—522no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—131no—
453C23×C4—131no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—131no—
457C23×C4—134no—
458C23×C4—134no—
459C23×C4—264no—
460C23×C4—264no—
461C23×C4—264no—
462C23×C4—522no—
463C23×C4—522no—
464C23×C4—522no—
465C23×C4C22×D1311yescharacteristic
466C23×C4C22×D1311yescharacteristic
467C23×C4C22×D1311yescharacteristic
468C23×C4C22×D1311yescharacteristic
469C23×C4C22×D1311yescharacteristic
470C23×C4C22×D1311yescharacteristic
471C2×C4⋊C4—42no—
472C2×C4⋊C4—134no—
473C2×C4⋊C4—134no—
474C2×C4⋊C4—134no—
475C2×C4⋊C4—134no—
476C2×C4⋊C4—264no—
477C2×C4⋊C4—264no—
478C2×C4⋊C4—522no—
479C2×C4⋊C4—522no—
480C2×C4⋊C4C22×D1314yes—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—134no—
485C2×C22⋊C4—134no—
486C2×C22⋊C4—134no—
487C2×C22⋊C4—134no—
488C2×C22⋊C4—134no—
489C2×C22⋊C4—134no—
490C2×C22⋊C4—134no—
491C2×C22⋊C4—264no—
492C2×C22⋊C4—264no—
493C2×C22⋊C4—264no—
494C2×C22⋊C4—264no—
495C2×C22⋊C4—264no—
496C2×C22⋊C4—522no—
497C2×C22⋊C4—522no—
498C2×C22⋊C4C22×D1314yes—
499C2×C22⋊C4C22×D1314yes—
500C2×C22⋊C4C22×D1314yes—
501C2×C42—24no—
502C2×C42—134no—
503C2×C42—134no—
504C2×C42—522no—
505C2×C42—522no—
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#95—134no—
516#95—134no—
517#95—134no—
518#95—134no—
519#95C22×D1314yes—
520#95C22×D1314yes—
521C2×C13—44no—
522C2×C13#257818yescomplemented
523C2×C13C2×#52911yescharacteristic
524C2×C13C2×#52911yescharacteristic
525C2×C13C2×#53811yescharacteristic
526C2×C13C2×#55111yescharacteristic
527C2×C13C2×#55111yescharacteristic
528C2×C13C2×#55311yescharacteristic
529C2×C13C2×#55311yescharacteristic
530D13—44no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—134no—
538C24—132no—
539C24—262no—
540C24—262no—
541C24—262no—
542C24—262no—
543C24—262no—
544C24—262no—
545C24#612714yes—
546C24C23×D1312yes—
547C24C23×D1311yescharacteristic
548C2×D4—268no—
549C2×D4—268no—
550C2×D4—524no—
551C2×D4—5216no—
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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—134no—
570C22×C4—134no—
571C22×C4—132no—
572C22×C4—132no—
573C22×C4—132no—
574C22×C4—132no—
575C22×C4—132no—
576C22×C4—132no—
577C22×C4—132no—
578C22×C4—268no—
579C22×C4—268no—
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—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—268no—
600C22×C4—524no—
601C22×C4—5216no—
602C22×C4—524no—
603C22×C4—524no—
604C22×C4—5216no—
605C22×C4#612914yes—
606C22×C4C23×D1312yes—
607C22×C4C23×D1312yes—
608C22×C4C23×D1312yes—
609C22×C4C23×D1312yes—
610C22×C4C23×D1312yes—
611C22×C4C23×D1312yes—
612C4⋊C4—44no—
613C4⋊C4—268no—
614C4⋊C4—268no—
615C4⋊C4—524no—
616C4⋊C4—524no—
617C22⋊C4—28no—
618C22⋊C4—28no—
619C22⋊C4—44no—
620C22⋊C4—268no—
621C22⋊C4—268no—
622C22⋊C4—268no—
623C22⋊C4—268no—
624C22⋊C4—268no—
625C22⋊C4—524no—
626C22⋊C4—524no—
627C42—28no—
628C42—524no—
629C42—524no—
630C13C2×#257811yescharacteristic, complemented, Sylow
631C23—28no—
632C23—28no—
633C23—28no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—134no—
645C23—268no—
646C23—268no—
647C23—262no—
648C23—262no—
649C23—262no—
650C23—262no—
651C23—262no—
652C23—262no—
653C23—268no—
654C23—524no—
655C23—524no—
656C23—524no—
657C23—524no—
658C23C2×#612714yes—
659C23C2×#612712yes—
660C23C2×#612912yes—
661C23#8825112yes—
662C23#41×D1312yes—
663C23#41×D1312yes—
664C23#41×D1312yes—
665C23#8825612yes—
666C23C24×D1311yescharacteristic
667D4—5216no—
668C2×C4—28no—
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—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—134no—
692C2×C4—134no—
693C2×C4—268no—
694C2×C4—268no—
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—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—5216no—
715C2×C4—5216no—
716C2×C4—524no—
717C2×C4—524no—
718C2×C4—524no—
719C2×C4—524no—
720C2×C4—524no—
721C2×C4C2×#612914yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—416no—
729C22—42no—
730C22—264no—
731C22—264no—
732C22—264no—
733C22—522no—
734C22—522no—
735C22—522no—
736C22—5216no—
737C22—522no—
738C22#1171923214yes—
739C22#1171924314yes—
740C22#1171924514yes—
741C22#1171931914yes—
742C22#1171936314yes—
743C22#1171938314yes—
744C22#1171941114yes—
745C22C22×#612711yescharacteristic
746C22C22×#612911yescharacteristic
747C22C2×#8825111yescharacteristic
748C22C2×#41×D1311yescharacteristic
749C22C2×#41×D1311yescharacteristic
750C22C2×#41×D1311yescharacteristic
751C22C2×#8825611yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—264no—
759C4—264no—
760C4—522no—
761C4—522no—
762C4—522no—
763C4—522no—
764C4—522no—
765C2—44no—
766C2—524no—
767C2#1312017618yesdirect product factor
768C2C2×#1171924311yescharacteristic
769C2C2×#1171941111yescharacteristic
770C2C2×#1171938311yescharacteristic
771C2C2×#1171936311yescharacteristic
772C2C2×#1171923211yescharacteristic
773C2C2×#1171931911yescharacteristic
774C2C2×#1171924511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#388D13
hypocenterC13C2×#2578
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #13120176C2direct (N × H)
2. C2×#11718320C2semidirect
3. C2×#11718613C2semidirect
4. C2×#11718654C2semidirect
6. C2×#11718330C2semidirect
7. C2×#11718316C2semidirect
8. C2×#11718639C2semidirect
11. C2×#11718607C2semidirect
12. C2×#11718598C2semidirect
13. C2×#11718328C2semidirect
14. C2×C22⋊C4×Dic13C2semidirect
15. C2×C4×#6103C2semidirect
16. C2×C13×#388C2semidirect
38. C13×#388C22semidirect
53. #11718654C22semidirect
54. #11718639C22semidirect
58. #11718613C22semidirect
59. #11718607C22semidirect
60. C22⋊C4×Dic13C22semidirect
61. C4×#6103C22semidirect
62. #11718598C22semidirect
63. #11718330C22semidirect
64. #11718328C22semidirect
65. #11718320C22semidirect
66. #11718316C22semidirect
250. C2×#388D13semidirect
377. #388C2×D13semidirect
522. C2×C13#2578semidirect
630. C13C2×#2578semidirect
767. C2#13120176direct (N × H)

Maximal subgroups

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

subgroupindex
#131201762
C2×#117183202
C2×#117186132
C2×#117186542
C2×#117186222
C2×#117183302
C2×#117183162
C2×#117186392
C2×#117186192
C2×#117186172
C2×#117186072
C2×#117185982
C2×#117183282
C2×C22⋊C4×Dic132
C2×C4×#61032
C2×C13×#3882
C2×#257813