Finite Group Databasebeta

← C2×#13119163 #16031850

Subgroups — C2×#13119163 #16031850

Order 3328.

3114 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88148C211yesmaximal, characteristic
2C22×#88151C211yesmaximal, characteristic, complemented
3#13119163C2116yesmaximal, direct product factor
4C2×#11718321C211yesmaximal, characteristic, complemented
5C2×#11718335C211yesmaximal, characteristic, complemented
6C2×#11718334C211yesmaximal, characteristic, complemented
7C2×#11718307C211yesmaximal, characteristic, complemented
8C2×#11718331C211yesmaximal, characteristic, complemented
9C2×#11718651C211yesmaximal, characteristic, complemented
10C2×#11718326C211yesmaximal, characteristic
11C2×#11718326C211yesmaximal, characteristic
12C2×#11718638C211yesmaximal, characteristic, complemented
13C2×#11718325C211yesmaximal, characteristic, complemented
14C2×#11718327C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#400C211yesmaximal, characteristic, complemented
17C23×D52C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C2×#88151—28no—
39C2×#88151C2218yescomplemented
40C2×#88148—28no—
41C2×#88148C2218yes—
42C13×#400C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718651C2218yescomplemented
58#11718638C2218yescomplemented
59#11718335C2218yescomplemented
60#11718334C2218yescomplemented
61#11718331C2218yescomplemented
62#11718327C2218yescomplemented
63#11718326C2218yes—
64#11718326C2218yes—
65#11718325C2218yescomplemented
66D13×#95C2218yescomplemented
67#11718321C2218yescomplemented
68#11718307C2218yescomplemented
69C24×D13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C22×D52—24no—
85C22×D52—24no—
86C22×D52—24no—
87C22×D52C2314yes—
88C22×C4×D13—24no—
89C22×C4×D13—24no—
90C22×C4×D13—24no—
91C22×C4×D13—24no—
92C22×C4×D13—24no—
93C22×C4×D13—24no—
94C22×C4×D13—24no—
95C22×C4×D13—42no—
96C22×C4×D13—42no—
97C22×C4×D13C2314yes—
98C22×C4×D13C2314yes—
99C22×C4×D13C2314yes—
100C22×Dic26—24no—
101C22×Dic26—24no—
102C22×Dic26—42no—
103C22×Dic26C2314yes—
104C2×C13×C4⋊C4—24no—
105C2×C13×C4⋊C4—24no—
106C2×C13×C4⋊C4C2314yes—
107C2×C13×C4⋊C4C2314yes—
108C2×#6103—24no—
109C2×#6103—24no—
110C2×#6103—24no—
111C2×#6103—24no—
112C2×#6103—24no—
113C2×#6103—24no—
114C2×#6103—42no—
115C2×#6103—42no—
116C2×#6103D418yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×C4⋊Dic13—24no—
127C2×C4⋊Dic13—24no—
128C2×C4⋊Dic13C2314yes—
129C2×C4⋊Dic13C2314yes—
130C2×#6101—24no—
131C2×#6101C2314yes—
132C2×C4×Dic13—24no—
133C2×C4×Dic13—42no—
134C2×C4×Dic13C2314yes—
135C2×C4×Dic13C2314yes—
136#88151—232no—
137#88148—232no—
138C13×#95C2314yes—
139C13×#95C2314yes—
140C13×#95C2314yes—
141C13×#95C2314yes—
142C13×#95C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2488—131nomaximal, Sylow
153C24×C13C2411yescharacteristic
154C23×D13—22no—
155C23×D13—22no—
156C23×D13—22no—
157C23×D13—22no—
158C23×D13—22no—
159C23×D13—22no—
160C23×D13—22no—
161C23×D13—22no—
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13C2×D414yes—
166C23×D13#4114yes—
167C23×D13#4114yes—
168C23×D13C2412yes—
169C23×D13C2412yes—
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—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×C13C2×D414yes—
190C22×C4×C13#4114yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
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—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13C2×D414yes—
215C22×Dic13#4114yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C2×D52—28no—
223C2×D52—28no—
224C2×D52—28no—
225C2×D52—416no—
226C2×C4×D13—28no—
227C2×C4×D13—28no—
228C2×C4×D13—28no—
229C2×C4×D13—28no—
230C2×C4×D13—28no—
231C2×C4×D13—28no—
232C2×C4×D13—28no—
233C2×C4×D13—44no—
234C2×C4×D13—44no—
235C2×C4×D13—416no—
236C2×C4×D13—416no—
237C2×C4×D13—416no—
238C2×Dic26—28no—
239C2×Dic26—28no—
240C2×Dic26—44no—
241C2×Dic26—416no—
242C13×C4⋊C4—28no—
243C13×C4⋊C4—28no—
244#6103—28no—
245#6103—28no—
246#6103—28no—
247#6103—28no—
248#6103—28no—
249#6103—28no—
250#6103—44no—
251#6103—44no—
252#6103C2×D4116yes—
253C4⋊Dic13—28no—
254C4⋊Dic13—28no—
255#6101—28no—
256C4×Dic13—28no—
257C4×Dic13—44no—
258C22×#123—131no—
259C22×C22⋊Q8—131no—
260#2488—1316no—
261C2×#400—131no—
262C2×#400D1311yescharacteristic, complemented
263C2×#397—131no—
264C2×#393—131no—
265C2×#391—131no—
266C2×#388—131no—
267C2×#388—131no—
268C2×#386—131no—
269C2×#386—131no—
270C2×#382—131no—
271C2×#381—131no—
272C2×C4×C22⋊C4—131no—
273C22×#95—131no—
274C23×C13C22×D412yes—
275C23×C13C2×#4112yes—
276C23×C13C2×#4112yes—
277C23×C13C2×#4112yes—
278C23×C13C2×#4112yes—
279C23×C13H(5,𝔽2)12yes—
280C23×C132−1+412yes—
281C23×C13C2511yescharacteristic
282C22×D13—28no—
283C22×D13—28no—
284C22×D13—28no—
285C22×D13—28no—
286C22×D13—28no—
287C22×D13—28no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—22no—
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—44no—
300C22×D13—44no—
301C22×D13—44no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C22×D13#124116yes—
307C22×D13C22×D414yes—
308C22×D13C2×#4114yes—
309C22×D13C2×#4114yes—
310C2×C4×C13—28no—
311C2×C4×C13—28no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—44no—
332C2×C4×C13—44no—
333C2×C4×C13—44no—
334C2×C4×C13—44no—
335C2×C4×C13—44no—
336C2×C4×C13C22×D414yes—
337C2×C4×C13C2×#4114yes—
338C2×Dic13—28no—
339C2×Dic13—28no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
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—44no—
357C2×Dic13—44no—
358C2×Dic13—44no—
359C2×Dic13—44no—
360C2×Dic13C22×D414yes—
361C2×Dic13C2×#4114yes—
362D52—416no—
363C4×D13—416no—
364C4×D13—416no—
365C4×D13—416no—
366Dic26—416no—
367C23×Q8—131no—
368C23×D4—131no—
369C24×C4—131no—
370C24×C4—131no—
371C24×C4—131no—
372C2×#123—138no—
373C2×#123—268no—
374C2×C22⋊Q8—138no—
375C2×C22⋊Q8—268no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4C2×D1311yescharacteristic
380C22×C4⋊C4C2×D1311yescharacteristic
381C22×C22⋊C4—131no—
382C22×C22⋊C4—131no—
383C22×C22⋊C4—131no—
384C22×C22⋊C4—131no—
385C22×C22⋊C4—131no—
386C22×C22⋊C4—131no—
387C22×C22⋊C4—131no—
388C22×C22⋊C4—131no—
389C22×C22⋊C4—131no—
390C22×C42—131no—
391C22×C42—131no—
392#400—138no—
393#400C2×D1318yescomplemented
394#397—138no—
395#393—138no—
396#391—138no—
397#388—138no—
398#388—138no—
399#386—138no—
400#386—138no—
401#382—138no—
402#381—138no—
403C4×C22⋊C4—138no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95—131no—
413C2×#95—138no—
414C2×#95C2×D1311yescharacteristic
415C2×#95C2×D1311yescharacteristic
416C2×#95C2×D1311yescharacteristic
417C2×#95C2×D1311yescharacteristic
418C2×#95C2×D1311yescharacteristic
419C22×C13C2×#12414yes—
420C22×C13#52914yes—
421C22×C13#53914yes—
422C22×C13#54614yes—
423C22×C13#54714yes—
424C22×C13#55114yes—
425C22×C13#55214yes—
426C22×C13C23×D411yescharacteristic
427C22×C13C22×#4111yescharacteristic
428C22×C13C22×#4111yescharacteristic
429C22×C13C22×#4111yescharacteristic
430C22×C13C22×#4111yescharacteristic
431C22×C13C2×H(5,𝔽2)11yescharacteristic
432C22×C13C2×2−1+411yescharacteristic
433C2×D13—24no—
434C2×D13—24no—
435C2×D13—24no—
436C2×D13—24no—
437C2×D13—24no—
438C2×D13—24no—
439C2×D13—232no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C2×D13—42no—
445C2×D13—42no—
446C2×D13—42no—
447C2×D13—88no—
448C2×D13C2×#12418yes—
449C4×C13—24no—
450C4×C13—24no—
451C4×C13—42no—
452C4×C13—42no—
453C4×C13—42no—
454C4×C13—42no—
455C4×C13—42no—
456Dic13—24no—
457Dic13—24no—
458Dic13—42no—
459Dic13—42no—
460Dic13—42no—
461Dic13—42no—
462C25—131no—
463C25—131no—
464C22×Q8—134no—
465C22×Q8—264no—
466C22×Q8—264no—
467C22×Q8—522no—
468C22×D4—134no—
469C22×D4—264no—
470C22×D4—264no—
471C22×D4—264no—
472C23×C4—131no—
473C23×C4—131no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—131no—
478C23×C4—134no—
479C23×C4—134no—
480C23×C4—134no—
481C23×C4—264no—
482C23×C4—264no—
483C23×C4—264no—
484C23×C4—264no—
485C23×C4—264no—
486C23×C4—264no—
487C23×C4—264no—
488C23×C4—522no—
489C23×C4—522no—
490C23×C4C22×D1311yescharacteristic
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C23×C4C22×D1311yescharacteristic
495C23×C4C22×D1311yescharacteristic
496C23×C4C22×D1311yescharacteristic
497#123—2632no—
498C22⋊Q8—2632no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—134no—
504C2×C4⋊C4—264no—
505C2×C4⋊C4—264no—
506C2×C4⋊C4—264no—
507C2×C4⋊C4C22×D1314yes—
508C2×C4⋊C4C22×D1314yes—
509C2×C22⋊C4—138no—
510C2×C22⋊C4—134no—
511C2×C22⋊C4—134no—
512C2×C22⋊C4—134no—
513C2×C22⋊C4—134no—
514C2×C22⋊C4—134no—
515C2×C22⋊C4—134no—
516C2×C22⋊C4—134no—
517C2×C22⋊C4—134no—
518C2×C22⋊C4—134no—
519C2×C22⋊C4—264no—
520C2×C22⋊C4—264no—
521C2×C22⋊C4—264no—
522C2×C22⋊C4—264no—
523C2×C22⋊C4—264no—
524C2×C22⋊C4—264no—
525C2×C22⋊C4—522no—
526C2×C22⋊C4—522no—
527C2×C42—134no—
528C2×C42—134no—
529C2×C42—264no—
530C2×C42—522no—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—134no—
536#95—134no—
537#95—134no—
538#95—134no—
539#95—134no—
540#95C22×D1314yes—
541#95C22×D1314yes—
542#95C22×D1314yes—
543#95C22×D1314yes—
544#95C22×D1314yes—
545C2×C13#248818yescomplemented
546C2×C13C22×#12411yescharacteristic
547C2×C13C2×#52911yescharacteristic
548C2×C13C2×#53911yescharacteristic
549C2×C13C2×#54611yescharacteristic
550C2×C13C2×#54711yescharacteristic
551C2×C13C2×#55111yescharacteristic
552C2×C13C2×#55211yescharacteristic
553D13—28no—
554D13—82no—
555C24—134no—
556C24—134no—
557C24—134no—
558C24—132no—
559C24—132no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24—262no—
564C24—262no—
565C24—262no—
566C24—262no—
567C24—262no—
568C24—262no—
569C24—262no—
570C24—262no—
571C24C23×D1311yescharacteristic
572C2×Q8—268no—
573C2×Q8—268no—
574C2×Q8—524no—
575C2×Q8—5216no—
576C2×D4—268no—
577C2×D4—268no—
578C2×D4—268no—
579C2×D4—5216no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—134no—
600C22×C4—134no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—132no—
604C22×C4—132no—
605C22×C4—132no—
606C22×C4—132no—
607C22×C4—268no—
608C22×C4—268no—
609C22×C4—268no—
610C22×C4—268no—
611C22×C4—268no—
612C22×C4—268no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—268no—
630C22×C4—524no—
631C22×C4—524no—
632C22×C4—5216no—
633C22×C4—5216no—
634C22×C4—5216no—
635C22×C4D4×D1314yes—
636C22×C4#613114yes—
637C22×C4C23×D1312yes—
638C22×C4C23×D1312yes—
639C22×C4C23×D1312yes—
640C22×C4C23×D1312yes—
641C22×C4C23×D1312yes—
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—268no—
647C4⋊C4—268no—
648C4⋊C4—268no—
649C22⋊C4—1316no—
650C22⋊C4—268no—
651C22⋊C4—268no—
652C22⋊C4—268no—
653C22⋊C4—268no—
654C22⋊C4—268no—
655C22⋊C4—268no—
656C22⋊C4—524no—
657C22⋊C4—524no—
658C42—268no—
659C42—524no—
660C13C2×#248811yescharacteristic, complemented, Sylow
661C23—1316no—
662C23—134no—
663C23—134no—
664C23—134no—
665C23—268no—
666C23—268no—
667C23—262no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—268no—
672C23—268no—
673C23—268no—
674C23—268no—
675C23—262no—
676C23—262no—
677C23—262no—
678C23—262no—
679C23—262no—
680C23—262no—
681C23—262no—
682C23—524no—
683C23—524no—
684C23—524no—
685C23—524no—
686C23—524no—
687C23—524no—
688C23—524no—
689C23C2×D4×D1312yes—
690C23C2×#613112yes—
691C23#41×D1312yes—
692C23#41×D1312yes—
693C23#41×D1312yes—
694C23#8825612yes—
695C23#8825712yes—
696C23C24×D1311yescharacteristic
697Q8—5216no—
698D4—5216no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—134no—
726C2×C4—134no—
727C2×C4—268no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—268no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—5216no—
746C2×C4—5216no—
747C2×C4—5216no—
748C2×C4—524no—
749C2×C4—524no—
750C2×C4—524no—
751C2×C4—524no—
752C2×C4C2×D4×D1314yes—
753C2×C4C2×#613114yes—
754C22—138no—
755C22—264no—
756C22—264no—
757C22—264no—
758C22—264no—
759C22—264no—
760C22—2632no—
761C22—264no—
762C22—522no—
763C22—522no—
764C22—522no—
765C22—522no—
766C22—522no—
767C22—522no—
768C22—522no—
769C22—1048no—
770C22#1171933514yes—
771C22#1171936014yes—
772C22D13×#12414yes—
773C22#1171939614yes—
774C22#1171939914yes—
775C22#1171941014yes—
776C22#1171941214yes—
777C22C22×D4×D1311yescharacteristic
778C22C22×#613111yescharacteristic
779C22C2×#41×D1311yescharacteristic
780C22C2×#41×D1311yescharacteristic
781C22C2×#41×D1311yescharacteristic
782C22C2×#8825611yescharacteristic
783C22C2×#8825711yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—264no—
792C4—264no—
793C4—522no—
794C4—522no—
795C4—522no—
796C4—522no—
797C2—268no—
798C2—1042no—
799C2#1311916318yesdirect product factor
800C2C2×D13×#12411yescharacteristic
801C2C2×#1171939611yescharacteristic
802C2C2×#1171941211yescharacteristic
803C2C2×#1171933511yescharacteristic
804C2C2×#1171936011yescharacteristic
805C2C2×#1171941011yescharacteristic
806C2C2×#1171939911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#400C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#400D13
hypocenterC13C2×#2488
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
2. C22×#88151C2semidirect
3. #13119163C2direct (N × H)
4. C2×#11718321C2semidirect
5. C2×#11718335C2semidirect
6. C2×#11718334C2semidirect
7. C2×#11718307C2semidirect
8. C2×#11718331C2semidirect
9. C2×#11718651C2semidirect
12. C2×#11718638C2semidirect
13. C2×#11718325C2semidirect
14. C2×#11718327C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#400C2semidirect
39. C2×#88151C22semidirect
42. C13×#400C22semidirect
57. #11718651C22semidirect
58. #11718638C22semidirect
59. #11718335C22semidirect
60. #11718334C22semidirect
61. #11718331C22semidirect
62. #11718327C22semidirect
65. #11718325C22semidirect
66. D13×#95C22semidirect
67. #11718321C22semidirect
68. #11718307C22semidirect
262. C2×#400D13semidirect
393. #400C2×D13semidirect
545. C2×C13#2488semidirect
660. C13C2×#2488semidirect
799. C2#13119163direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881482
C22×#881512
#131191632
C2×#117183212
C2×#117183352
C2×#117183342
C2×#117183072
C2×#117183312
C2×#117186512
C2×#117183262
C2×#117186382
C2×#117183252
C2×#117183272
C2×D13×#952
C2×C13×#4002
C2×#248813