Finite Group Databasebeta

← C2×#13122968 #16069238

Subgroups — C2×#13122968 #16069238

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#13122968C2116yesmaximal, direct product factor
2C2×#11718610C211yesmaximal, characteristic, complemented
3C2×#11718318C211yesmaximal, characteristic, complemented
4C2×#11718613C211yesmaximal, characteristic, complemented
5C2×#11718613C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718883C211yesmaximal, characteristic, complemented
9C2×#11718883C211yesmaximal, characteristic, complemented
10C2×#11718883C211yesmaximal, characteristic, complemented
11C2×#11718883C211yesmaximal, characteristic, complemented
12C2×#11718883C211yesmaximal, characteristic, complemented
13C2×#11718882C211yesmaximal, characteristic, complemented
14C2×#11718612C211yesmaximal, characteristic, complemented
15C2×#11718313C211yesmaximal, characteristic, complemented
16C2×C13×#392C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C23×D4×C13C2211yescharacteristic
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×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C13×#392C2218yes—
45C2×C13×#95C2211yescharacteristic
46#11718883C2218yescomplemented
47#11718883C2218yescomplemented
48#11718883C2218yescomplemented
49#11718883C2218yescomplemented
50#11718883C2218yescomplemented
51#11718882C2218yescomplemented
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718613C2218yescomplemented
60#11718613C2218yescomplemented
61#11718612C2218yescomplemented
62#11718610C2218yescomplemented
63#11718609C2218yescomplemented
64#11718609C2218yescomplemented
65#11718318C2218yescomplemented
66#11718313C2218yescomplemented
67C25×C13C2311yescharacteristic
68C25×C13C2311yescharacteristic
69C25×C13C2311yescharacteristic
70C22×D4×C13—24no—
71C22×D4×C13—42no—
72C22×D4×C13—42no—
73C22×D4×C13—42no—
74C22×D4×C13—42no—
75C22×D4×C13—42no—
76C22×D4×C13—42no—
77C22×D4×C13—42no—
78C22×D4×C13—42no—
79C22×D4×C13C2314yes—
80C22×D4×C13C2314yes—
81C22×D4×C13C2314yes—
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C2×C13×C22⋊C4—24no—
95C2×C13×C22⋊C4—42no—
96C2×C13×C22⋊C4—42no—
97C2×C13×C22⋊C4C2314yes—
98C2×C13×C22⋊C4C2314yes—
99C2×C13×C22⋊C4C2314yes—
100C2×C22⋊Dic13—42no—
101C2×C22⋊Dic13—42no—
102C2×C22⋊Dic13—42no—
103C2×C22⋊Dic13—42no—
104C2×C22⋊Dic13—42no—
105C2×C22⋊Dic13—42no—
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×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123C2×C22⋊Dic13C2314yes—
124C2×C4⋊Dic13—42no—
125C2×C4⋊Dic13—42no—
126C2×C4⋊Dic13C2314yes—
127C2×C4⋊Dic13C2314yes—
128C2×#6101—24no—
129C2×#6101—42no—
130C2×#6101—42no—
131C2×#6101—42no—
132C2×#6101—42no—
133C2×#6101—42no—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×#6101C2314yes—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×C4×Dic13—42no—
141C2×C4×Dic13C2314yes—
142C13×#95C2314yes—
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×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13C2412yes—
173C24×C13C2412yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C2×D4×C13—28no—
177C2×D4×C13—44no—
178C2×D4×C13—44no—
179C2×D4×C13—44no—
180C2×D4×C13—44no—
181C2×D4×C13—44no—
182C2×D4×C13—44no—
183C2×D4×C13—44no—
184C2×D4×C13—44no—
185C2×D4×C13—416no—
186C2×D4×C13—416no—
187C2×D4×C13—416no—
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—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13#4114yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
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×Dic13C2412yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C13×C22⋊C4—28no—
237C13×C22⋊C4—44no—
238C13×C22⋊C4—44no—
239C22⋊Dic13—44no—
240C22⋊Dic13—44no—
241C22⋊Dic13—44no—
242C22⋊Dic13—44no—
243C22⋊Dic13—44no—
244C22⋊Dic13—44no—
245C22⋊Dic13—44no—
246C22⋊Dic13—44no—
247C22⋊Dic13—44no—
248C22⋊Dic13—44no—
249C22⋊Dic13—44no—
250C22⋊Dic13—44no—
251C4⋊Dic13—44no—
252C4⋊Dic13—44no—
253#6101—28no—
254#6101—44no—
255#6101—44no—
256#6101—44no—
257#6101—44no—
258#6101—44no—
259C4×Dic13—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×#392D1311yescharacteristic
273C2×#390—131no—
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—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—44no—
298C23×C13—44no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13—44no—
303C23×C13—44no—
304C23×C13—44no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C13—44no—
308C23×C13—44no—
309C23×C13—44no—
310C23×C13—44no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13—44no—
317C23×C13—44no—
318C23×C13C2×#4112yes—
319C23×C13H(5,𝔽2)12yes—
320C23×C13H(5,𝔽2)12yes—
321C23×C13H(5,𝔽2)12yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C132−1+412yes—
325C23×C13C2511yescharacteristic
326D4×C13—416no—
327D4×C13—416no—
328D4×C13—416no—
329C2×C4×C13—28no—
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—44no—
342C2×C4×C13—44no—
343C2×C4×C13—44no—
344C2×C4×C13C2×#4114yes—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
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—44no—
370C2×Dic13—44no—
371C2×Dic13—44no—
372C2×Dic13—44no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13—44no—
376C2×Dic13—44no—
377C23×D4C2×D1311yescharacteristic
378C23×D4C2×D1311yescharacteristic
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⋊C4—131no—
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⋊C4—131no—
400C22×C22⋊C4C2×D1311yescharacteristic
401C22×C22⋊C4C2×D1311yescharacteristic
402C22×C22⋊C4C2×D1311yescharacteristic
403C22×C42—131no—
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#392C2×D1318yes—
416#390—138no—
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×#95C2×D1311yescharacteristic
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—42no—
442C22×C13—42no—
443C22×C13—42no—
444C22×C13—42no—
445C22×C13—42no—
446C22×C13—42no—
447C22×C13—42no—
448C22×C13—88no—
449C22×C13—88no—
450C22×C13—88no—
451C22×C13#53814yes—
452C22×C13#54014yes—
453C22×C13#54214yes—
454C22×C13#56014yes—
455C22×C13#56014yes—
456C22×C13#56214yes—
457C22×C13#56214yes—
458C22×C13C22×#4111yescharacteristic
459C22×C13C2×H(5,𝔽2)11yescharacteristic
460C22×C13C2×H(5,𝔽2)11yescharacteristic
461C22×C13C2×H(5,𝔽2)11yescharacteristic
462C22×C13C2×H(5,𝔽2)11yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×2−1+411yescharacteristic
465C4×C13—24no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13—42no—
469Dic13—42no—
470Dic13—42no—
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474Dic13—42no—
475Dic13—42no—
476Dic13—42no—
477C25C22×D1311yescharacteristic
478C25C22×D1311yescharacteristic
479C25C22×D1311yescharacteristic
480C22×D4—24no—
481C22×D4—42no—
482C22×D4—42no—
483C22×D4—42no—
484C22×D4—42no—
485C22×D4—42no—
486C22×D4—42no—
487C22×D4—42no—
488C22×D4—42no—
489C22×D4C22×D1314yes—
490C22×D4C22×D1314yes—
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×C4—131no—
500C23×C4C22×D1311yescharacteristic
501C23×C4C22×D1311yescharacteristic
502C23×C4C22×D1311yescharacteristic
503C23×C4C22×D1311yescharacteristic
504C2×C4⋊C4—134no—
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⋊C4—522no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—134no—
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—522no—
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⋊C4—522no—
547C2×C22⋊C4C22×D1314yes—
548C2×C22⋊C4C22×D1314yes—
549C2×C22⋊C4C22×D1314yes—
550C2×C42—134no—
551C2×C42—522no—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559#95C22×D1314yes—
560C2×C13—82no—
561C2×C13—82no—
562C2×C13—82no—
563C2×C13#282918yescomplemented
564C2×C13C2×#53811yescharacteristic
565C2×C13C2×#54011yescharacteristic
566C2×C13C2×#54211yescharacteristic
567C2×C13C2×#56011yescharacteristic
568C2×C13C2×#56011yescharacteristic
569C2×C13C2×#56211yescharacteristic
570C2×C13C2×#56211yescharacteristic
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—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24C23×D1312yes—
593C24C23×D1312yes—
594C24C23×D1312yes—
595C24C23×D1311yescharacteristic
596C2×D4—28no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—416no—
606C2×D4—416no—
607C2×D4—416no—
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—132no—
620C22×C4—132no—
621C22×C4—132no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—132no—
625C22×C4—132no—
626C22×C4—132no—
627C22×C4—262no—
628C22×C4—262no—
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—262no—
651C22×C4#612914yes—
652C22×C4C23×D1312yes—
653C22×C4C23×D1312yes—
654C22×C4C23×D1312yes—
655C22×C4C23×D1312yes—
656C4⋊C4—268no—
657C4⋊C4—524no—
658C4⋊C4—524no—
659C4⋊C4—524no—
660C4⋊C4—524no—
661C4⋊C4—524no—
662C4⋊C4—524no—
663C4⋊C4—524no—
664C22⋊C4—28no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—524no—
668C22⋊C4—524no—
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—524no—
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—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23C2×#612912yes—
724C23#8825112yes—
725C23#8825112yes—
726C23#8825112yes—
727C23#8825112yes—
728C23#8825112yes—
729C23#8825712yes—
730C23C24×D1311yescharacteristic
731D4—416no—
732D4—416no—
733D4—416no—
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—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
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—524no—
774C2×C4—524no—
775C2×C4—524no—
776C2×C4—524no—
777C2×C4—524no—
778C2×C4—524no—
779C2×C4—524no—
780C2×C4—524no—
781C2×C4C2×#612914yes—
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—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—88no—
804C22—88no—
805C22—88no—
806C22#1171929814yes—
807C22#1171930014yes—
808C22#1171930014yes—
809C22#1171930814yes—
810C22#1171932614yes—
811C22#1171932614yes—
812C22#1171942414yes—
813C22C22×#612911yescharacteristic
814C22C2×#8825111yescharacteristic
815C22C2×#8825111yescharacteristic
816C22C2×#8825111yescharacteristic
817C22C2×#8825111yescharacteristic
818C22C2×#8825111yescharacteristic
819C22C2×#8825711yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—522no—
825C4—522no—
826C4—522no—
827C4—522no—
828C4—522no—
829C4—522no—
830C4—522no—
831C4—522no—
832C2—82no—
833C2—82no—
834C2—82no—
835C2#1312296818yesdirect product factor
836C2C2×#1171929811yescharacteristic
837C2C2×#1171942411yescharacteristic
838C2C2×#1171930811yescharacteristic
839C2C2×#1171930011yescharacteristic
840C2C2×#1171930011yescharacteristic
841C2C2×#1171932611yescharacteristic
842C2C2×#1171932611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
Fitting, prime radicalC2×C13×#392C2
socleC24×C13C24
hypercenterC2×#392D13
hypocenterC13C2×#2829
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #13122968C2direct (N × H)
2. C2×#11718610C2semidirect
3. C2×#11718318C2semidirect
4. C2×#11718613C2semidirect
5. C2×#11718613C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718883C2semidirect
9. C2×#11718883C2semidirect
10. C2×#11718883C2semidirect
11. C2×#11718883C2semidirect
12. C2×#11718883C2semidirect
13. C2×#11718882C2semidirect
14. C2×#11718612C2semidirect
15. C2×#11718313C2semidirect
46. #11718883C22semidirect
47. #11718883C22semidirect
48. #11718883C22semidirect
49. #11718883C22semidirect
50. #11718883C22semidirect
51. #11718882C22semidirect
59. #11718613C22semidirect
60. #11718613C22semidirect
61. #11718612C22semidirect
62. #11718610C22semidirect
63. #11718609C22semidirect
64. #11718609C22semidirect
65. #11718318C22semidirect
66. #11718313C22semidirect
563. C2×C13#2829semidirect
680. C13C2×#2829semidirect
835. C2#13122968direct (N × H)

Maximal subgroups

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

subgroupindex
#131229682
C2×#117186102
C2×#117183182
C2×#117186132
C2×#117186092
C2×#117188832
C2×#117188822
C2×#117186122
C2×#117183132
C2×C13×#3922
C2×#282913