Finite Group Databasebeta

← C2×#13122964 #16069244

Subgroups — C2×#13122964 #16069244

Order 3328.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13122964C2116yesmaximal, direct product factor
2C2×#11718610C211yesmaximal, characteristic, complemented
3C2×#11718645C211yesmaximal, characteristic, complemented
4C2×#11718613C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718622C211yesmaximal, characteristic, complemented
9C2×#11718620C211yesmaximal, characteristic, complemented
10C2×#11718620C211yesmaximal, characteristic, complemented
11C2×#11718620C211yesmaximal, characteristic, complemented
12C2×#11718883C211yesmaximal, characteristic, complemented
13C2×#11718884C211yesmaximal, characteristic
14C2×#11718601C211yesmaximal, characteristic, complemented
15C2×#11718594C211yesmaximal, characteristic, complemented
16C2×C13×#390C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C13×#390C2218yescomplemented
45#11718884C2218yes—
46#11718883C2218yescomplemented
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718655C2218yescomplemented
56#11718645C2218yescomplemented
57#11718622C2218yescomplemented
58#11718620C2218yescomplemented
59#11718620C2218yescomplemented
60#11718620C2218yescomplemented
61#11718614C2218yescomplemented
62#11718613C2218yescomplemented
63#11718610C2218yescomplemented
64#11718609C2218yescomplemented
65#11718601C2218yescomplemented
66#11718594C2218yescomplemented
67C25×C13C2311yescharacteristic
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C22×D4×C13—24no—
71C22×D4×C13—42no—
72C22×D4×C13—42no—
73C22×D4×C13C2314yes—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—42no—
80C22×C22⋊D13—42no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13—42no—
83C22×C22⋊D13—42no—
84C22×C22⋊D13—42no—
85C22×C22⋊D13C2314yes—
86C22×C22⋊D13C2314yes—
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C2×C13×C4⋊C4—42no—
95C2×C13×C4⋊C4C2314yes—
96C2×C13×C22⋊C4—42no—
97C2×C13×C22⋊C4—42no—
98C2×C13×C22⋊C4—42no—
99C2×C13×C22⋊C4—42no—
100C2×C13×C22⋊C4C2314yes—
101C2×C13×C22⋊C4C2314yes—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2314yes—
104C2×C42×C13—42no—
105C2×C42×C13C2314yes—
106C2×C22⋊Dic13—42no—
107C2×C22⋊Dic13—42no—
108C2×C22⋊Dic13—42no—
109C2×C22⋊Dic13—42no—
110C2×C22⋊Dic13—42no—
111C2×C22⋊Dic13—42no—
112C2×C22⋊Dic13C2314yes—
113C2×C22⋊Dic13C2314yes—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×#6103—24no—
119C2×#6103—42no—
120C2×#6103—42no—
121C2×#6103—42no—
122C2×#6103—42no—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×C4⋊Dic13—42no—
129C2×C4⋊Dic13—42no—
130C2×C4⋊Dic13C2314yes—
131C2×C4⋊Dic13C2314yes—
132C2×#6101—24no—
133C2×#6101—42no—
134C2×#6101—42no—
135C2×#6101—42no—
136C2×#6101—42no—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2829—131nomaximal, Sylow
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×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13C2412yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13C2412yes—
176C2×D4×C13—28no—
177C2×D4×C13—44no—
178C2×D4×C13—44no—
179C2×D4×C13—416no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13#4114yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C2×C22⋊D13—44no—
201C2×C22⋊D13—44no—
202C2×C22⋊D13—44no—
203C2×C22⋊D13—44no—
204C2×C22⋊D13—44no—
205C2×C22⋊D13—44no—
206C2×C22⋊D13—416no—
207C2×C22⋊D13—416no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C13×C4⋊C4—44no—
237C13×C22⋊C4—44no—
238C13×C22⋊C4—44no—
239C13×C22⋊C4—44no—
240C13×C22⋊C4—44no—
241C42×C13—44no—
242C22⋊Dic13—44no—
243C22⋊Dic13—44no—
244C22⋊Dic13—44no—
245C22⋊Dic13—44no—
246C22⋊Dic13—44no—
247C22⋊Dic13—44no—
248#6103—28no—
249#6103—44no—
250#6103—44no—
251#6103—44no—
252#6103—44no—
253C4⋊Dic13—44no—
254C4⋊Dic13—44no—
255#6101—28no—
256#6101—44no—
257#6101—44no—
258#6101—44no—
259#6101—44no—
260#2829—1316no—
261C2×#399—131no—
262C2×#398—131no—
263C2×#397—131no—
264C2×#397—131no—
265C2×#396—131no—
266C2×#396—131no—
267C2×#394—131no—
268C2×#394—131no—
269C2×#394—131no—
270C2×#394—131no—
271C2×#394—131no—
272C2×#392—131no—
273C2×#390D1311yescharacteristic, complemented
274C2×#388—131no—
275C2×#387—131no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—44no—
291C23×C13—44no—
292C23×C13—44no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13—44no—
297C23×C13—44no—
298C23×C13—44no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13—44no—
303C23×C13—44no—
304C23×C13C2×#4112yes—
305C23×C13H(5,𝔽2)12yes—
306C23×C13H(5,𝔽2)12yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C132−1+412yes—
311C23×C13C2511yescharacteristic
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—44no—
320C22×D13—44no—
321C22×D13—44no—
322C22×D13—44no—
323C22×D13—44no—
324C22×D13—44no—
325C22×D13—44no—
326D4×C13—416no—
327C2×C4×C13—28no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—44no—
343C2×C4×C13—44no—
344C2×C4×C13—44no—
345C2×C4×C13—44no—
346C2×C4×C13C2×#4114yes—
347C22⋊D13—416no—
348C22⋊D13—416no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—44no—
371C2×Dic13—44no—
372C2×Dic13—44no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13—44no—
376C2×Dic13—44no—
377C23×D4—131no—
378C23×D4—131no—
379C23×D4C2×D1311yescharacteristic
380C22×C4⋊C4—131no—
381C22×C4⋊C4—131no—
382C22×C4⋊C4—131no—
383C22×C4⋊C4—131no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4—131no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4C2×D1311yescharacteristic
388C22×C22⋊C4—131no—
389C22×C22⋊C4—131no—
390C22×C22⋊C4—131no—
391C22×C22⋊C4—131no—
392C22×C22⋊C4—131no—
393C22×C22⋊C4—131no—
394C22×C22⋊C4—131no—
395C22×C22⋊C4—131no—
396C22×C22⋊C4—131no—
397C22×C22⋊C4—131no—
398C22×C22⋊C4—131no—
399C22×C22⋊C4C2×D1311yescharacteristic
400C22×C22⋊C4C2×D1311yescharacteristic
401C22×C22⋊C4C2×D1311yescharacteristic
402C22×C22⋊C4C2×D1311yescharacteristic
403C22×C42C2×D1311yescharacteristic
404#399—138no—
405#398—138no—
406#397—138no—
407#397—138no—
408#396—138no—
409#396—138no—
410#394—138no—
411#394—138no—
412#394—138no—
413#394—138no—
414#394—138no—
415#392—138no—
416#390C2×D1318yescomplemented
417#388—138no—
418#387—138no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95—131no—
427C22×C13—42no—
428C22×C13—42no—
429C22×C13—42no—
430C22×C13—42no—
431C22×C13—42no—
432C22×C13—42no—
433C22×C13—42no—
434C22×C13—42no—
435C22×C13—42no—
436C22×C13—42no—
437C22×C13—42no—
438C22×C13—42no—
439C22×C13—42no—
440C22×C13—42no—
441C22×C13—88no—
442C22×C13—88no—
443C22×C13#53814yes—
444C22×C13#54014yes—
445C22×C13#54214yes—
446C22×C13#56014yes—
447C22×C13#56014yes—
448C22×C13#56214yes—
449C22×C13#56214yes—
450C22×C13C22×#4111yescharacteristic
451C22×C13C2×H(5,𝔽2)11yescharacteristic
452C22×C13C2×H(5,𝔽2)11yescharacteristic
453C22×C13C2×H(5,𝔽2)11yescharacteristic
454C22×C13C2×H(5,𝔽2)11yescharacteristic
455C22×C13C2×H(5,𝔽2)11yescharacteristic
456C22×C13C2×2−1+411yescharacteristic
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—42no—
462C2×D13—42no—
463C2×D13—42no—
464C2×D13—88no—
465C4×C13—24no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13—42no—
469C4×C13—42no—
470Dic13—42no—
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474Dic13—42no—
475Dic13—42no—
476Dic13—42no—
477C25—131no—
478C25C22×D1311yescharacteristic
479C25C22×D1311yescharacteristic
480C22×D4—24no—
481C22×D4—42no—
482C22×D4—42no—
483C22×D4—134no—
484C22×D4—134no—
485C22×D4—522no—
486C22×D4—522no—
487C22×D4—522no—
488C22×D4—522no—
489C22×D4—522no—
490C22×D4—522no—
491C22×D4C22×D1314yes—
492C23×C4—131no—
493C23×C4—131no—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—131no—
497C23×C4—131no—
498C23×C4—131no—
499C23×C4C22×D1311yescharacteristic
500C23×C4C22×D1311yescharacteristic
501C23×C4C22×D1311yescharacteristic
502C23×C4C22×D1311yescharacteristic
503C23×C4C22×D1311yescharacteristic
504C2×C4⋊C4—42no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—134no—
507C2×C4⋊C4—134no—
508C2×C4⋊C4—134no—
509C2×C4⋊C4—134no—
510C2×C4⋊C4—134no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—264no—
513C2×C4⋊C4—522no—
514C2×C4⋊C4—522no—
515C2×C4⋊C4—522no—
516C2×C4⋊C4—522no—
517C2×C4⋊C4—522no—
518C2×C4⋊C4—522no—
519C2×C4⋊C4C22×D1314yes—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—134no—
525C2×C22⋊C4—134no—
526C2×C22⋊C4—134no—
527C2×C22⋊C4—134no—
528C2×C22⋊C4—134no—
529C2×C22⋊C4—134no—
530C2×C22⋊C4—134no—
531C2×C22⋊C4—134no—
532C2×C22⋊C4—134no—
533C2×C22⋊C4—134no—
534C2×C22⋊C4—134no—
535C2×C22⋊C4—264no—
536C2×C22⋊C4—522no—
537C2×C22⋊C4—522no—
538C2×C22⋊C4—522no—
539C2×C22⋊C4—522no—
540C2×C22⋊C4—522no—
541C2×C22⋊C4—522no—
542C2×C22⋊C4—522no—
543C2×C22⋊C4—522no—
544C2×C22⋊C4—522no—
545C2×C22⋊C4—522no—
546C2×C22⋊C4C22×D1314yes—
547C2×C22⋊C4C22×D1314yes—
548C2×C22⋊C4C22×D1314yes—
549C2×C22⋊C4C22×D1314yes—
550C2×C42—42no—
551C2×C42C22×D1314yes—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559#95—134no—
560C2×C13—82no—
561C2×C13—82no—
562C2×C13#282918yescomplemented
563C2×C13C2×#53811yescharacteristic
564C2×C13C2×#54011yescharacteristic
565C2×C13C2×#54211yescharacteristic
566C2×C13C2×#56011yescharacteristic
567C2×C13C2×#56011yescharacteristic
568C2×C13C2×#56211yescharacteristic
569C2×C13C2×#56211yescharacteristic
570D13—82no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—132no—
586C24—262no—
587C24—262no—
588C24—262no—
589C24—262no—
590C24—262no—
591C24—262no—
592C24—262no—
593C24C23×D1312yes—
594C24C23×D1312yes—
595C24C23×D1311yescharacteristic
596C2×D4—28no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—416no—
600C2×D4—524no—
601C2×D4—524no—
602C2×D4—524no—
603C2×D4—524no—
604C2×D4—524no—
605C2×D4—524no—
606C2×D4—5216no—
607C2×D4—5216no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—132no—
625C22×C4—132no—
626C22×C4—132no—
627C22×C4—132no—
628C22×C4—132no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—262no—
646C22×C4—262no—
647C22×C4—262no—
648C22×C4—262no—
649C22×C4—262no—
650C22×C4#612714yes—
651C22×C4C23×D1312yes—
652C22×C4C23×D1312yes—
653C22×C4C23×D1312yes—
654C22×C4C23×D1312yes—
655C22×C4C23×D1312yes—
656C4⋊C4—44no—
657C4⋊C4—268no—
658C4⋊C4—524no—
659C4⋊C4—524no—
660C4⋊C4—524no—
661C4⋊C4—524no—
662C4⋊C4—524no—
663C4⋊C4—524no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—268no—
669C22⋊C4—524no—
670C22⋊C4—524no—
671C22⋊C4—524no—
672C22⋊C4—524no—
673C22⋊C4—524no—
674C22⋊C4—524no—
675C22⋊C4—524no—
676C22⋊C4—524no—
677C22⋊C4—524no—
678C22⋊C4—524no—
679C42—44no—
680C13C2×#282911yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—262no—
710C23—262no—
711C23—262no—
712C23—262no—
713C23—262no—
714C23—262no—
715C23—262no—
716C23—524no—
717C23—524no—
718C23—524no—
719C23—524no—
720C23—524no—
721C23—524no—
722C23—524no—
723C23C2×#612712yes—
724C23#8825112yes—
725C23#8825112yes—
726C23#8825112yes—
727C23#8825112yes—
728C23#8825612yes—
729C23#8825712yes—
730C23C24×D1311yescharacteristic
731D4—416no—
732D4—5216no—
733D4—5216no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—262no—
767C2×C4—262no—
768C2×C4—262no—
769C2×C4—262no—
770C2×C4—262no—
771C2×C4—262no—
772C2×C4—262no—
773C2×C4—262no—
774C2×C4—524no—
775C2×C4—524no—
776C2×C4—524no—
777C2×C4—524no—
778C2×C4—524no—
779C2×C4—524no—
780C2×C4—524no—
781C2×C4C2×#612714yes—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—88no—
797C22—88no—
798C22—522no—
799C22—522no—
800C22—522no—
801C22—522no—
802C22—522no—
803C22—522no—
804C22—522no—
805C22—1048no—
806C22#1171919914yes—
807C22#1171926614yes—
808C22#1171926714yes—
809C22#1171932514yes—
810C22#1171932614yes—
811C22#1171938914yes—
812C22#1171942514yes—
813C22C22×#612711yescharacteristic
814C22C2×#8825111yescharacteristic
815C22C2×#8825111yescharacteristic
816C22C2×#8825111yescharacteristic
817C22C2×#8825111yescharacteristic
818C22C2×#8825611yescharacteristic
819C22C2×#8825711yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—522no—
826C4—522no—
827C4—522no—
828C4—522no—
829C4—522no—
830C4—522no—
831C4—522no—
832C2—82no—
833C2—82no—
834C2—1042no—
835C2#1312296418yesdirect product factor
836C2C2×#1171919911yescharacteristic
837C2C2×#1171926711yescharacteristic
838C2C2×#1171926611yescharacteristic
839C2C2×#1171942511yescharacteristic
840C2C2×#1171932511yescharacteristic
841C2C2×#1171938911yescharacteristic
842C2C2×#1171932611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#390C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC2×#390D13
hypocenterC13C2×#2829
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. #13122964C2direct (N × H)
2. C2×#11718610C2semidirect
3. C2×#11718645C2semidirect
4. C2×#11718613C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718622C2semidirect
9. C2×#11718620C2semidirect
10. C2×#11718620C2semidirect
11. C2×#11718620C2semidirect
12. C2×#11718883C2semidirect
14. C2×#11718601C2semidirect
15. C2×#11718594C2semidirect
16. C2×C13×#390C2semidirect
44. C13×#390C22semidirect
46. #11718883C22semidirect
55. #11718655C22semidirect
56. #11718645C22semidirect
57. #11718622C22semidirect
58. #11718620C22semidirect
59. #11718620C22semidirect
60. #11718620C22semidirect
61. #11718614C22semidirect
62. #11718613C22semidirect
63. #11718610C22semidirect
64. #11718609C22semidirect
65. #11718601C22semidirect
66. #11718594C22semidirect
273. C2×#390D13semidirect
416. #390C2×D13semidirect
562. C2×C13#2829semidirect
680. C13C2×#2829semidirect
835. C2#13122964direct (N × H)

Maximal subgroups

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

subgroupindex
#131229642
C2×#117186102
C2×#117186452
C2×#117186132
C2×#117186142
C2×#117186092
C2×#117186552
C2×#117186222
C2×#117186202
C2×#117188832
C2×#117188842
C2×#117186012
C2×#117185942
C2×C13×#3902
C2×#282913