Finite Group Databasebeta

← C2×#13125939 #16734308

Subgroups — C2×#13125939 #16734308

Order 3328.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719231C211yesmaximal, characteristic, complemented
2#13125939C2116yesmaximal, direct product factor
3C2×#11718721C211yesmaximal, characteristic, complemented
4C2×#11718720C211yesmaximal, characteristic, complemented
5C2×#11718750C211yesmaximal, characteristic, complemented
6C2×#11718754C211yesmaximal, characteristic, complemented
7C2×#11718689C211yesmaximal, characteristic, complemented
8C2×#11718692C211yesmaximal, characteristic, complemented
9C2×#11718677C211yesmaximal, characteristic, complemented
10C2×#11718680C211yesmaximal, characteristic, complemented
11C2×#11718708C211yesmaximal, characteristic, complemented
12C2×#11718698C211yesmaximal, characteristic
13C2×#11718711C211yesmaximal, characteristic, complemented
14C2×#11718701C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#542C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C13×#542—24no—
20C13×#542C2218yescomplemented
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×#126—21no—
23C2×C13×#124—21no—
24C2×C13×#124C2211yescharacteristic
25C2×C13×#123—21no—
26C2×C13×C22⋊Q8—21no—
27C2×C13×C22⋊Q8C2211yescharacteristic
28C2×C13×#121C2211yescharacteristic
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×D4×C13C2211yescharacteristic
31C2×C13×#117C2211yescharacteristic
32C22×#6107C2211yescharacteristic
33C22×#6107C2211yescharacteristic
34C22×#6107C2211yescharacteristic
35C22×#6106C2211yescharacteristic
36C22×#6105C2211yescharacteristic
37C22×#6105C2211yescharacteristic
38C22×#6105C2211yescharacteristic
39C22×#6104C2211yescharacteristic
40#11719231—24no—
41#11719231C2218yescomplemented
42C2×#88151—21no—
43C2×#88151—21no—
44C2×#88140—21no—
45C2×#88140—21no—
46C2×#88129C2211yescharacteristic
47C2×#88129C2211yescharacteristic
48C2×#88123C2211yescharacteristic
49C2×#88123C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52#11718754C2218yescomplemented
53#11718750C2218yescomplemented
54#11718721C2218yescomplemented
55#11718720C2218yescomplemented
56#11718711C2218yescomplemented
57#11718708C2218yescomplemented
58#11718701C2218yescomplemented
59#11718698C2218yes—
60#11718692C2218yescomplemented
61#11718689C2218yescomplemented
62#11718680C2218yescomplemented
63#11718677C2218yescomplemented
64#11718661C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88050C2211yescharacteristic
68C2×#88050C2211yescharacteristic
69C2×#88050C2211yescharacteristic
70C2×#88050C2211yescharacteristic
71C2×#88049C2211yescharacteristic
72C2×#88049C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13—21no—
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13C2311yescharacteristic
83C22×C22⋊D13—21no—
84C23×Dic13—21no—
85C2×#6127—22no—
86C2×#6127—42no—
87C2×#6127—42no—
88C2×#6127C2314yes—
89C22×D52C2311yescharacteristic
90C22×C4×D13—21no—
91C22×Dic26—21no—
92C22×Dic26—22no—
93C22×Dic26—42no—
94C22×Dic26—42no—
95C22×Dic26C2311yescharacteristic
96C22×Dic26C2311yescharacteristic
97C22×Dic26C2311yescharacteristic
98C22×Dic26C2314yes—
99C13×C4⋊Q8—22no—
100C13×C4⋊Q8C2314yes—
101C13×#126—28no—
102C13×#124—28no—
103C13×#124—22no—
104C13×#124C2314yes—
105C13×#123—28no—
106C13×C22⋊Q8—22no—
107C13×C22⋊Q8—28no—
108C13×C22⋊Q8C2314yes—
109C13×#121—22no—
110C13×#121C2314yes—
111C4×Q8×C13—22no—
112C4×Q8×C13C2314yes—
113C4×D4×C13—22no—
114C4×D4×C13C2314yes—
115C13×#117D414yes—
116C13×#117C2314yes—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4D411yescharacteristic
121C2×C13×C4⋊C4D411yescharacteristic
122C2×C13×C4⋊C4C2311yescharacteristic
123C2×C13×C4⋊C4C2311yescharacteristic
124C2×C13×C22⋊C4—21no—
125C2×C13×C22⋊C4—21no—
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4—21no—
129C2×C13×C22⋊C4D411yescharacteristic
130C2×C13×C22⋊C4D411yescharacteristic
131C2×C42×C13—21no—
132C2×C42×C13C2311yescharacteristic
133C2×C42×C13C2311yescharacteristic
134C2×#6107—42no—
135C2×#6107—42no—
136C2×#6107—42no—
137C2×#6107C2314yes—
138C2×#6107C2314yes—
139C2×#6107C2314yes—
140C2×#6106—42no—
141C2×#6106C2314yes—
142C2×#6105—42no—
143C2×#6105—42no—
144C2×#6105—42no—
145C2×#6105C2314yes—
146C2×#6105C2314yes—
147C2×#6105C2314yes—
148C2×#6104—42no—
149C2×#6104C2314yes—
150C2×#6103—21no—
151C2×#6103—21no—
152C2×#6103—21no—
153C2×#6103—21no—
154C2×C4⋊Dic13—21no—
155C2×C4⋊Dic13—21no—
156C2×C4⋊Dic13—21no—
157C2×C4⋊Dic13—21no—
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2311yescharacteristic
161C22×#1055C2311yescharacteristic
162#88151—28no—
163#88151—28no—
164#88140—28no—
165#88140—28no—
166#88129—22no—
167#88129—22no—
168#88129C2314yes—
169#88129C2314yes—
170#88123—22no—
171#88123—22no—
172#88123C2314yes—
173#88123C2314yes—
174C22⋊#1055C2314yes—
175C22⋊#1055C2314yes—
176#88050C2314yes—
177#88050C2314yes—
178#88050C2314yes—
179#88050C2314yes—
180#88050C2314yes—
181#88050C2314yes—
182#88049C2314yes—
183#88049C2314yes—
184C4⋊#1055C2314yes—
185C4⋊#1055C2314yes—
186#88043C2314yes—
187C4×#1055C2314yes—
188C2×#3225—131nomaximal, Sylow
189C24×C13—21no—
190C24×C13C2×D411yescharacteristic
191C23×D13—21no—
192C2×Q8×C13—21no—
193C2×Q8×C13—24no—
194C2×Q8×C13—22no—
195C2×Q8×C13—22no—
196C2×Q8×C13—82no—
197C2×Q8×C13C2412yes—
198C2×D4×C13—24no—
199C2×D4×C13—21no—
200C2×D4×C13—22no—
201C2×D4×C13—22no—
202C2×D4×C13—82no—
203C2×D4×C13C2412yes—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—24no—
210C22×C4×C13—82no—
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2411yescharacteristic
219C2×C22⋊D13—24no—
220C2×C22⋊D13—44no—
221C22×Dic13—24no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—44no—
226#6127—44no—
227#6127—44no—
228#6127—48no—
229C2×D52—22no—
230C2×D52—22no—
231C2×D52—21no—
232C2×D52C2412yes—
233C2×C4×D13—24no—
234C2×C4×D13—44no—
235C2×Dic26—22no—
236C2×Dic26—22no—
237C2×Dic26—22no—
238C2×Dic26—22no—
239C2×Dic26—22no—
240C2×Dic26—22no—
241C2×Dic26—21no—
242C2×Dic26—21no—
243C2×Dic26—21no—
244C2×Dic26—24no—
245C2×Dic26—44no—
246C2×Dic26—44no—
247C2×Dic26—44no—
248C2×Dic26—48no—
249C2×Dic26C2412yes—
250C2×Dic26C2412yes—
251C2×Dic26C2412yes—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—24no—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—21no—
257C13×C4⋊C4C2×D414yes—
258C13×C4⋊C4C2×D414yes—
259C13×C4⋊C4C2412yes—
260C13×C4⋊C4C2412yes—
261C13×C22⋊C4—24no—
262C13×C22⋊C4—24no—
263C13×C22⋊C4—24no—
264C13×C22⋊C4—24no—
265C13×C22⋊C4—24no—
266C13×C22⋊C4C2×D414yes—
267C13×C22⋊C4C2×D414yes—
268C42×C13—24no—
269C42×C13C2×D412yes—
270C42×C13C2×D412yes—
271C42×C13C2412yes—
272C42×C13C2412yes—
273#6107—44no—
274#6107—44no—
275#6107—44no—
276#6106—44no—
277#6105—44no—
278#6105—44no—
279#6105—44no—
280#6104—44no—
281#6103—24no—
282#6103—24no—
283#6103—24no—
284#6103—24no—
285C4⋊Dic13—24no—
286C4⋊Dic13—24no—
287C4⋊Dic13—24no—
288C4⋊Dic13—24no—
289C2×#1055—22no—
290C2×#1055—22no—
291C2×#1055—22no—
292C2×#1055—22no—
293C2×#1055C2412yes—
294C2×#1055C2412yes—
295C2×#1055C2412yes—
296C2×#1055C2412yes—
297C2×#542D1311yescharacteristic, complemented
298C2×#536—131no—
299#3225—1316no—
300C2×#497—131no—
301C2×#495—131no—
302C2×#489—131no—
303C2×#487—131no—
304C2×#464—131no—
305C2×#462—131no—
306C2×#463—131no—
307C2×#461—131no—
308C2×#452—131no—
309C2×#449—131no—
310C2×#451—131no—
311C2×#448—131no—
312C2×#433—131no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—42no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13C22×D412yes—
321C23×C13C22×D411yescharacteristic
322C22×D13—22no—
323C22×D13—42no—
324C22×D13—42no—
325C22×D13—42no—
326Q8×C13—22no—
327Q8×C13—22no—
328Q8×C13—42no—
329Q8×C13—84no—
330D4×C13—22no—
331D4×C13—22no—
332D4×C13—42no—
333D4×C13—84no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—24no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13—42no—
348C2×C4×C13—84no—
349C2×C4×C13C22×D412yes—
350C2×C4×C13C22×D412yes—
351C2×C4×C13C22×D412yes—
352C2×C4×C13C22×D412yes—
353C2×C4×C13C22×D412yes—
354C2×C4×C13C22×D411yescharacteristic
355C2×C4×C13H(5,𝔽2)12yes—
356C2×C4×C13H(5,𝔽2)12yes—
357C2×C4×C13C2511yescharacteristic
358C22⋊D13—48no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—48no—
363C2×Dic13—42no—
364C2×Dic13—42no—
365C2×Dic13—42no—
366D52—22no—
367D52—22no—
368D52—42no—
369C4×D13—48no—
370Dic26—22no—
371Dic26—22no—
372Dic26—22no—
373Dic26—22no—
374Dic26—22no—
375Dic26—22no—
376Dic26—48no—
377Dic26—42no—
378Dic26—42no—
379Dic26—42no—
380#1055—22no—
381#1055—22no—
382#1055—22no—
383#1055—22no—
384C22×#41—131no—
385C23×Q8—131no—
386C22×Q16—131no—
387C22×Q16—131no—
388C22×Q16—131no—
389C22×SD16—131no—
390C22×SD16—131no—
391C22×SD16—131no—
392C22×SD16—131no—
393C22×D8—131no—
394#542—24no—
395#542C2×D1318yescomplemented
396#536—138no—
397#536—264no—
398C2×C4⋊Q8—131no—
399C2×C4⋊Q8—131no—
400C2×C4⋊Q8C2×D1311yescharacteristic
401C2×#126—21no—
402C2×#124—21no—
403C2×#124—131no—
404C2×#124—131no—
405C2×#124C2×D1311yescharacteristic
406C2×#123—21no—
407C2×#123—261no—
408C2×#123—261no—
409C2×C22⋊Q8—21no—
410C2×C22⋊Q8—261no—
411C2×C22⋊Q8—261no—
412C2×C22⋊Q8C2×D1311yescharacteristic
413C2×#121C2×D1311yescharacteristic
414C2×C4×Q8C2×D1311yescharacteristic
415C2×C4×D4C2×D1311yescharacteristic
416C2×#117C2×D1311yescharacteristic
417#497—138no—
418#495—138no—
419#489—138no—
420#487—138no—
421#464—138no—
422#463—138no—
423#462—138no—
424#461—138no—
425#452—138no—
426#451—138no—
427#449—138no—
428#448—138no—
429#433—138no—
430C2×C4⋊C8—131no—
431C2×C4⋊C8—131no—
432C2×#103—131no—
433C2×#103—131no—
434C2×#103—131no—
435C2×#103—131no—
436C2×#103—131no—
437C2×#103—131no—
438C2×#102—131no—
439C2×#102—131no—
440C2×C22⋊C8—131no—
441C2×C22⋊C8—131no—
442C2×#97—131no—
443C2×C4×C8—131no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—22no—
447C22×C13—44no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—84no—
452C22×C13#53512yes—
453C22×C13#57712yes—
454C22×C13#57812yes—
455C22×C13C23×D411yescharacteristic
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—84no—
460C4×C13—22no—
461C4×C13—22no—
462C4×C13—22no—
463C4×C13—22no—
464C4×C13—22no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13#53512yes—
469C4×C13C2×H(5,𝔽2)11yescharacteristic
470C4×C13C2×H(5,𝔽2)11yescharacteristic
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474C2×#41—134no—
475C2×#41—262no—
476C2×#41—522no—
477C2×#41—522no—
478C22×Q8—21no—
479C22×Q8—131no—
480C22×Q8—131no—
481C22×Q8—131no—
482C22×Q8—134no—
483C22×Q8—261no—
484C22×Q8—262no—
485C22×Q8—522no—
486C22×Q8—522no—
487C22×Q8C22×D1311yescharacteristic
488C22×D4—21no—
489C22×D4—131no—
490C22×D4—261no—
491C22×D4C22×D1311yescharacteristic
492C23×C4—21no—
493C23×C4—261no—
494C23×C4—261no—
495C23×C4C22×D1311yescharacteristic
496C2×Q16—134no—
497C2×Q16—134no—
498C2×Q16—134no—
499C2×Q16—522no—
500C2×Q16—522no—
501C2×Q16—522no—
502C2×SD16—134no—
503C2×SD16—134no—
504C2×SD16—134no—
505C2×SD16—134no—
506C2×SD16—522no—
507C2×SD16—522no—
508C2×SD16—522no—
509C2×SD16—522no—
510C2×D8—134no—
511C2×D8—522no—
512C22×C8—131no—
513C22×C8—131no—
514C22×C8—131no—
515C22×C8—131no—
516C4⋊Q8—22no—
517C4⋊Q8—134no—
518C4⋊Q8—134no—
519C4⋊Q8—262no—
520C4⋊Q8—262no—
521C4⋊Q8C22×D1314yes—
522#126—28no—
523#124—28no—
524#124—22no—
525#124—134no—
526#124—134no—
527#124—262no—
528#124—262no—
529#124C22×D1314yes—
530#123—28no—
531#123—268no—
532#123—268no—
533C22⋊Q8—22no—
534C22⋊Q8—28no—
535C22⋊Q8—268no—
536C22⋊Q8—268no—
537C22⋊Q8C22×D1314yes—
538#121—22no—
539#121C22×D1314yes—
540C4×Q8—22no—
541C4×Q8C22×D1314yes—
542C4×D4—22no—
543C4×D4C22×D1314yes—
544#117C22⋊D1314yes—
545#117C22×D1314yes—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—261no—
550C2×C4⋊C4—261no—
551C2×C4⋊C4—261no—
552C2×C4⋊C4—261no—
553C2×C4⋊C4C22⋊D1311yescharacteristic
554C2×C4⋊C4C22⋊D1311yescharacteristic
555C2×C4⋊C4C22×D1311yescharacteristic
556C2×C4⋊C4C22×D1311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—261no—
563C2×C22⋊C4—261no—
564C2×C22⋊C4—261no—
565C2×C22⋊C4—261no—
566C2×C22⋊C4C22⋊D1311yescharacteristic
567C2×C22⋊C4C22⋊D1311yescharacteristic
568C2×C42—21no—
569C2×C42C22×D1311yescharacteristic
570C2×C42C22×D1311yescharacteristic
571C4⋊C8—134no—
572C4⋊C8—134no—
573#103—134no—
574#103—134no—
575#103—134no—
576#103—134no—
577#103—134no—
578#103—134no—
579#102—134no—
580#102—134no—
581C22⋊C8—134no—
582C22⋊C8—134no—
583#97—134no—
584C4×C8—134no—
585C2×C13—42no—
586C2×C13—82no—
587C2×C13#322514yescomplemented
588C2×C13C2×#53511yescharacteristic
589C2×C13C2×#57711yescharacteristic
590C2×C13C2×#57811yescharacteristic
591D13—82no—
592C24—21no—
593C24—261no—
594C24C2×C22⋊D1311yescharacteristic
595#41—524no—
596#41—524no—
597#41—528no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—82no—
603C2×Q8—132no—
604C2×Q8—132no—
605C2×Q8—132no—
606C2×Q8—264no—
607C2×Q8—261no—
608C2×Q8—261no—
609C2×Q8—261no—
610C2×Q8—262no—
611C2×Q8—262no—
612C2×Q8—262no—
613C2×Q8—262no—
614C2×Q8—262no—
615C2×Q8—262no—
616C2×Q8—524no—
617C2×Q8—524no—
618C2×Q8—524no—
619C2×Q8—528no—
620C2×Q8C23×D1312yes—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—21no—
625C2×D4—82no—
626C2×D4—132no—
627C2×D4—264no—
628C2×D4—262no—
629C2×D4—262no—
630C2×D4—261no—
631C2×D4—524no—
632C2×D4C23×D1312yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—82no—
640C22×C4—264no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—264no—
645C22×C4—524no—
646C22×C4—524no—
647C22×C4C2×C22⋊D1312yes—
648C22×C4C2×C22⋊D1311yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1311yescharacteristic
651C22×C4C2×C22⋊D1311yescharacteristic
652C22×C4C2×C22⋊D1311yescharacteristic
653C22×C4C23×D1312yes—
654C22×C4C23×D1311yescharacteristic
655Q16—524no—
656Q16—524no—
657Q16—524no—
658SD16—524no—
659SD16—524no—
660SD16—524no—
661SD16—524no—
662D8—524no—
663C2×C8—132no—
664C2×C8—132no—
665C2×C8—132no—
666C2×C8—132no—
667C2×C8—262no—
668C2×C8—262no—
669C2×C8—262no—
670C2×C8—262no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—264no—
677C4⋊C4—264no—
678C4⋊C4—264no—
679C4⋊C4—264no—
680C4⋊C4C2×C22⋊D1314yes—
681C4⋊C4C2×C22⋊D1314yes—
682C4⋊C4C23×D1312yes—
683C4⋊C4C23×D1312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—264no—
690C22⋊C4—264no—
691C22⋊C4—264no—
692C22⋊C4—264no—
693C22⋊C4C2×C22⋊D1314yes—
694C22⋊C4C2×C22⋊D1314yes—
695C42—24no—
696C42C2×C22⋊D1312yes—
697C42C2×C22⋊D1312yes—
698C42C23×D1312yes—
699C42C23×D1312yes—
700C13C2×#322511yescharacteristic, complemented, Sylow
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—262no—
709C23—522no—
710C23—522no—
711C23—522no—
712C23C22×C22⋊D1312yes—
713C23C22×C22⋊D1311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—262no—
719Q8—262no—
720Q8—262no—
721Q8—262no—
722Q8—262no—
723Q8—262no—
724Q8—528no—
725Q8—522no—
726Q8—522no—
727Q8—522no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—262no—
733D4—262no—
734D4—528no—
735D4—522no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—528no—
755C2×C4—528no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4—522no—
759C2×C4#8825612yes—
760C2×C4#8825612yes—
761C2×C4C22×C22⋊D1312yes—
762C2×C4C22×C22⋊D1312yes—
763C2×C4C22×C22⋊D1312yes—
764C2×C4C22×C22⋊D1312yes—
765C2×C4C22×C22⋊D1312yes—
766C2×C4C22×C22⋊D1311yescharacteristic
767C2×C4C24×D1311yescharacteristic
768C8—262no—
769C8—262no—
770C8—262no—
771C8—262no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—522no—
781C22—522no—
782C22—522no—
783C22—1044no—
784C22#1171953512yes—
785C22#1171954112yes—
786C22#1171954312yes—
787C22C23×C22⋊D1311yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—522no—
797C4—522no—
798C4—522no—
799C4#1171953512yes—
800C4C2×#8825611yescharacteristic
801C4C2×#8825611yescharacteristic
802C2—42no—
803C2—82no—
804C2—1042no—
805C2#1312593914yesdirect product factor
806C2C2×#1171953511yescharacteristic
807C2C2×#1171954111yescharacteristic
808C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#542C2
socleC23×C13C22×D4
prime radicalC2×#11718698C2
hypercenterC2×#542D13
hypocenterC13C2×#3225
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11719231C2semidirect
2. #13125939C2direct (N × H)
3. C2×#11718721C2semidirect
4. C2×#11718720C2semidirect
5. C2×#11718750C2semidirect
6. C2×#11718754C2semidirect
7. C2×#11718689C2semidirect
8. C2×#11718692C2semidirect
9. C2×#11718677C2semidirect
10. C2×#11718680C2semidirect
11. C2×#11718708C2semidirect
13. C2×#11718711C2semidirect
14. C2×#11718701C2semidirect
15. C2×#11718661C2semidirect
16. C2×C13×#542C2semidirect
20. C13×#542C22semidirect
41. #11719231C22semidirect
52. #11718754C22semidirect
53. #11718750C22semidirect
54. #11718721C22semidirect
55. #11718720C22semidirect
56. #11718711C22semidirect
57. #11718708C22semidirect
58. #11718701C22semidirect
60. #11718692C22semidirect
61. #11718689C22semidirect
62. #11718680C22semidirect
63. #11718677C22semidirect
64. #11718661C22semidirect
297. C2×#542D13semidirect
395. #542C2×D13semidirect
587. C2×C13#3225semidirect
700. C13C2×#3225semidirect
805. C2#13125939direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192312
#131259392
C2×#117187212
C2×#117187202
C2×#117187502
C2×#117187542
C2×#117186892
C2×#117186922
C2×#117186772
C2×#117186802
C2×#117187082
C2×#117186982
C2×#117187112
C2×#117187012
C2×#117186612
C2×C13×#5422
C2×#322513