Finite Group Databasebeta

← C2×#13122913 #16069097

Subgroups — C2×#13122913 #16069097

Order 3328.

2606 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13122913C2116yesmaximal, direct product factor
2C2×#11718321C211yesmaximal, characteristic, complemented
3C2×#11718319C211yesmaximal, characteristic, complemented
4C2×#11718336C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718622C211yesmaximal, characteristic, complemented
7C2×#11718620C211yesmaximal, characteristic, complemented
8C2×#11718620C211yesmaximal, characteristic, complemented
9C2×#11718883C211yesmaximal, characteristic, complemented
10C2×#11718334C211yesmaximal, characteristic, complemented
11C2×#11718608C211yesmaximal, characteristic, complemented
12C2×#11718608C211yesmaximal, characteristic, complemented
13C2×#11718884C211yesmaximal, characteristic
14C2×#11718874C211yesmaximal, characteristic, complemented
15C2×#11718871C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C13×#386C2218yescomplemented
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43#11718884C2218yes—
44#11718883C2218yescomplemented
45#11718874C2218yescomplemented
46#11718871C2218yescomplemented
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718622C2218yescomplemented
58#11718620C2218yescomplemented
59#11718620C2218yescomplemented
60#11718614C2218yescomplemented
61#11718608C2218yescomplemented
62#11718608C2218yescomplemented
63#11718336C2218yescomplemented
64#11718334C2218yescomplemented
65#11718321C2218yescomplemented
66#11718319C2218yescomplemented
67C25×C13C2311yescharacteristic
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C22×D4×C13—24no—
71C22×D4×C13—42no—
72C22×D4×C13—42no—
73C22×D4×C13C2314yes—
74C23×C4×C13—42no—
75C23×C4×C13—42no—
76C23×C4×C13—42no—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—42no—
85C22×C22⋊D13—42no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13—42no—
88C22×C22⋊D13—42no—
89C22×C22⋊D13C2314yes—
90C22×C22⋊D13C2314yes—
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C22×Dic26—42no—
99C22×Dic26—42no—
100C22×Dic26—42no—
101C22×Dic26C2314yes—
102C2×C13×C22⋊C4—42no—
103C2×C13×C22⋊C4—42no—
104C2×C13×C22⋊C4—42no—
105C2×C13×C22⋊C4C2314yes—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C22⋊Dic13—24no—
109C2×C22⋊Dic13—42no—
110C2×C22⋊Dic13—42no—
111C2×C22⋊Dic13—42no—
112C2×C22⋊Dic13—42no—
113C2×C22⋊Dic13—42no—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×#6103—42no—
121C2×#6103—42no—
122C2×#6103—42no—
123C2×#6103—42no—
124C2×#6103—42no—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×C4⋊Dic13—42no—
131C2×C4⋊Dic13C2314yes—
132C2×#6101—42no—
133C2×#6101—42no—
134C2×#6101—42no—
135C2×#6101C2314yes—
136C2×#6101C2314yes—
137C2×#6101C2314yes—
138C13×#95C2314yes—
139C13×#95C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2824—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#4114yes—
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—22no—
195C22×C4×C13—44no—
196C22×C4×C13—44no—
197C22×C4×C13—44no—
198C22×C4×C13—416no—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C2×C22⋊D13—28no—
205C2×C22⋊D13—44no—
206C2×C22⋊D13—44no—
207C2×C22⋊D13—44no—
208C2×C22⋊D13—44no—
209C2×C22⋊D13—44no—
210C2×C22⋊D13—416no—
211C2×C22⋊D13—416no—
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×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C2×Dic26—44no—
241C2×Dic26—44no—
242C2×Dic26—44no—
243C2×Dic26—416no—
244C13×C22⋊C4—44no—
245C13×C22⋊C4—44no—
246C13×C22⋊C4—44no—
247C22⋊Dic13—28no—
248C22⋊Dic13—44no—
249C22⋊Dic13—44no—
250C22⋊Dic13—44no—
251C22⋊Dic13—44no—
252C22⋊Dic13—44no—
253#6103—44no—
254#6103—44no—
255#6103—44no—
256#6103—44no—
257#6103—44no—
258C4⋊Dic13—44no—
259#6101—44no—
260#6101—44no—
261#6101—44no—
262#2824—1316no—
263C2×#400—131no—
264C2×#400—131no—
265C2×#397—131no—
266C2×#397—131no—
267C2×#394—131no—
268C2×#394—131no—
269C2×#394—131no—
270C2×#394—131no—
271C2×#393—131no—
272C2×#393—131no—
273C2×#393—131no—
274C2×#392—131no—
275C2×#386—131no—
276C2×#386D1311yescharacteristic, complemented
277C2×#385—131no—
278C23×C13—28no—
279C23×C13—28no—
280C23×C13—28no—
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—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×C13—44no—
305C23×C13C2×#4114yes—
306C23×C13C2×#4112yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C13H(5,𝔽2)12yes—
311C23×C13H(5,𝔽2)12yes—
312C23×C132−1+412yes—
313C23×C13C2511yescharacteristic
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—44no—
322C22×D13—44no—
323C22×D13—44no—
324C22×D13—44no—
325C22×D13—44no—
326C22×D13—44no—
327C22×D13—44no—
328D4×C13—416no—
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—22no—
343C2×C4×C13—22no—
344C2×C4×C13—416no—
345C2×C4×C13—44no—
346C2×C4×C13—44no—
347C2×C4×C13—44no—
348C2×C4×C13—44no—
349C2×C4×C13—44no—
350C22⋊D13—416no—
351C22⋊D13—416no—
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—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13—44no—
376C2×Dic13—44no—
377C2×Dic13—44no—
378C2×Dic13—44no—
379C2×Dic13—44no—
380Dic26—416no—
381C23×Q8—131no—
382C23×D4—131no—
383C23×D4—131no—
384C23×D4C2×D1311yescharacteristic
385C24×C4C2×D1311yescharacteristic
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊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⋊C4—131no—
401C22×C22⋊C4C2×D1311yescharacteristic
402C22×C22⋊C4C2×D1311yescharacteristic
403C22×C22⋊C4C2×D1311yescharacteristic
404#400—138no—
405#400—138no—
406#397—138no—
407#397—138no—
408#394—138no—
409#394—138no—
410#394—138no—
411#394—138no—
412#393—138no—
413#393—138no—
414#393—138no—
415#392—138no—
416#386—138no—
417#386C2×D1318yescomplemented
418#385—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—
427C2×#95—131no—
428C2×#95—131no—
429C2×#95C2×D1311yescharacteristic
430C2×#95C2×D1311yescharacteristic
431C22×C13—24no—
432C22×C13—24no—
433C22×C13—24no—
434C22×C13—416no—
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—88no—
447C22×C13#53814yes—
448C22×C13#53814yes—
449C22×C13#53914yes—
450C22×C13#56014yes—
451C22×C13H(3,𝔽4)14yes—
452C22×C13#56214yes—
453C22×C13#56214yes—
454C22×C13C22×#4111yescharacteristic
455C22×C13C2×H(5,𝔽2)11yescharacteristic
456C22×C13C2×H(5,𝔽2)11yescharacteristic
457C22×C13C2×H(5,𝔽2)11yescharacteristic
458C22×C13C2×H(5,𝔽2)11yescharacteristic
459C22×C13C2×H(5,𝔽2)11yescharacteristic
460C22×C13C2×2−1+411yescharacteristic
461C2×D13—42no—
462C2×D13—42no—
463C2×D13—42no—
464C2×D13—42no—
465C2×D13—42no—
466C2×D13—42no—
467C2×D13—42no—
468C2×D13—88no—
469C4×C13—42no—
470C4×C13—42no—
471C4×C13—42no—
472C4×C13—42no—
473C4×C13—42no—
474Dic13—42no—
475Dic13—42no—
476Dic13—42no—
477Dic13—42no—
478Dic13—42no—
479Dic13—42no—
480Dic13—42no—
481C25—131no—
482C25C22×D1311yescharacteristic
483C25C22×D1311yescharacteristic
484C22×Q8—134no—
485C22×Q8—522no—
486C22×Q8—522no—
487C22×Q8—522no—
488C22×D4—24no—
489C22×D4—42no—
490C22×D4—42no—
491C22×D4—134no—
492C22×D4—134no—
493C22×D4—264no—
494C22×D4—522no—
495C22×D4—522no—
496C22×D4—522no—
497C22×D4—522no—
498C22×D4—522no—
499C22×D4C22×D1314yes—
500C23×C4—42no—
501C23×C4—42no—
502C23×C4—42no—
503C23×C4—131no—
504C23×C4—131no—
505C23×C4—131no—
506C23×C4—131no—
507C23×C4—131no—
508C23×C4—131no—
509C23×C4—131no—
510C23×C4C22×D1311yescharacteristic
511C23×C4C22×D1311yescharacteristic
512C23×C4C22×D1311yescharacteristic
513C23×C4C22×D1311yescharacteristic
514C23×C4C22×D1311yescharacteristic
515C23×C4C22×D1314yes—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—134no—
519C2×C4⋊C4—134no—
520C2×C4⋊C4—522no—
521C2×C4⋊C4—522no—
522C2×C4⋊C4—522no—
523C2×C4⋊C4—522no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
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—134no—
536C2×C22⋊C4—134no—
537C2×C22⋊C4—134no—
538C2×C22⋊C4—264no—
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⋊C4—522no—
548C2×C22⋊C4—522no—
549C2×C22⋊C4C22×D1314yes—
550C2×C22⋊C4C22×D1314yes—
551C2×C22⋊C4C22×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—
560#95—134no—
561#95—134no—
562#95C22×D1314yes—
563#95C22×D1314yes—
564C2×C13—44no—
565C2×C13—82no—
566C2×C13#282418yescomplemented
567C2×C13C2×#53811yescharacteristic
568C2×C13C2×#53811yescharacteristic
569C2×C13C2×#53911yescharacteristic
570C2×C13C2×#56011yescharacteristic
571C2×C13C2×H(3,𝔽4)11yescharacteristic
572C2×C13C2×#56211yescharacteristic
573C2×C13C2×#56211yescharacteristic
574D13—82no—
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—132no—
589C24—262no—
590C24—262no—
591C24—262no—
592C24—262no—
593C24—262no—
594C24—262no—
595C24—262no—
596C24#612714yes—
597C24C23×D1312yes—
598C24C23×D1312yes—
599C24C23×D1311yescharacteristic
600C2×Q8—524no—
601C2×Q8—524no—
602C2×Q8—524no—
603C2×Q8—5216no—
604C2×D4—28no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4—416no—
608C2×D4—268no—
609C2×D4—524no—
610C2×D4—524no—
611C2×D4—524no—
612C2×D4—524no—
613C2×D4—524no—
614C2×D4—5216no—
615C2×D4—5216no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—416no—
635C22×C4—132no—
636C22×C4—132no—
637C22×C4—132no—
638C22×C4—132no—
639C22×C4—132no—
640C22×C4—132no—
641C22×C4—132no—
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—262no—
652C22×C4—262no—
653C22×C4—262no—
654C22×C4—262no—
655C22×C4—262no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4C23×D1312yes—
664C22×C4C23×D1312yes—
665C22×C4C23×D1312yes—
666C22×C4C23×D1312yes—
667C22×C4C23×D1312yes—
668C4⋊C4—524no—
669C4⋊C4—524no—
670C4⋊C4—524no—
671C4⋊C4—524no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—268no—
676C22⋊C4—524no—
677C22⋊C4—524no—
678C22⋊C4—524no—
679C22⋊C4—524no—
680C22⋊C4—524no—
681C22⋊C4—524no—
682C22⋊C4—524no—
683C22⋊C4—524no—
684C22⋊C4—524no—
685C22⋊C4—524no—
686C13C2×#282411yescharacteristic, complemented, Sylow
687C23—28no—
688C23—28no—
689C23—28no—
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—22no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—262no—
715C23—262no—
716C23—262no—
717C23—262no—
718C23—262no—
719C23—262no—
720C23—262no—
721C23—524no—
722C23—524no—
723C23—524no—
724C23—524no—
725C23—524no—
726C23—524no—
727C23—524no—
728C23C2×#612714yes—
729C23C2×#612712yes—
730C23#8825112yes—
731C23#8825112yes—
732C23#8825112yes—
733C23#8825112yes—
734C23#8825612yes—
735C23#8825712yes—
736C23C24×D1311yescharacteristic
737Q8—5216no—
738D4—416no—
739D4—5216no—
740D4—5216no—
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—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—416no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
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—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—262no—
783C2×C4—524no—
784C2×C4—524no—
785C2×C4—524no—
786C2×C4—524no—
787C2×C4—524no—
788C2×C4—524no—
789C2×C4—524no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—416no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—88no—
806C22—522no—
807C22—522no—
808C22—522no—
809C22—522no—
810C22—522no—
811C22—522no—
812C22—522no—
813C22—1048no—
814C22#1171919914yes—
815C22#1171926514yes—
816C22#1171926914yes—
817C22#1171929914yes—
818C22#1171932514yes—
819C22#1171932614yes—
820C22#1171937214yes—
821C22C22×#612711yescharacteristic
822C22C2×#8825111yescharacteristic
823C22C2×#8825111yescharacteristic
824C22C2×#8825111yescharacteristic
825C22C2×#8825111yescharacteristic
826C22C2×#8825611yescharacteristic
827C22C2×#8825711yescharacteristic
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—522no—
834C4—522no—
835C4—522no—
836C4—522no—
837C4—522no—
838C4—522no—
839C4—522no—
840C2—44no—
841C2—82no—
842C2—1042no—
843C2#1312291318yesdirect product factor
844C2C2×#1171926511yescharacteristic
845C2C2×#1171919911yescharacteristic
846C2C2×#1171926911yescharacteristic
847C2C2×#1171932511yescharacteristic
848C2C2×#1171929911yescharacteristic
849C2C2×#1171932611yescharacteristic
850C2C2×#1171937211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC2×#386D13
hypocenterC13C2×#2824
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #13122913C2direct (N × H)
2. C2×#11718321C2semidirect
3. C2×#11718319C2semidirect
4. C2×#11718336C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718622C2semidirect
7. C2×#11718620C2semidirect
8. C2×#11718620C2semidirect
9. C2×#11718883C2semidirect
10. C2×#11718334C2semidirect
11. C2×#11718608C2semidirect
12. C2×#11718608C2semidirect
14. C2×#11718874C2semidirect
15. C2×#11718871C2semidirect
16. C2×C13×#386C2semidirect
40. C13×#386C22semidirect
44. #11718883C22semidirect
45. #11718874C22semidirect
46. #11718871C22semidirect
57. #11718622C22semidirect
58. #11718620C22semidirect
59. #11718620C22semidirect
60. #11718614C22semidirect
61. #11718608C22semidirect
62. #11718608C22semidirect
63. #11718336C22semidirect
64. #11718334C22semidirect
65. #11718321C22semidirect
66. #11718319C22semidirect
276. C2×#386D13semidirect
417. #386C2×D13semidirect
566. C2×C13#2824semidirect
686. C13C2×#2824semidirect
843. C2#13122913direct (N × H)

Maximal subgroups

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

subgroupindex
#131229132
C2×#117183212
C2×#117183192
C2×#117183362
C2×#117186142
C2×#117186222
C2×#117186202
C2×#117188832
C2×#117183342
C2×#117186082
C2×#117188842
C2×#117188742
C2×#117188712
C2×C13×#3862
C2×#282413