Finite Group Databasebeta

← C2×#13131702 #16808645

Subgroups — C2×#13131702 #16808645

Order 3328.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131702C2116yesmaximal, direct product factor
2C2×#11719145C211yesmaximal, characteristic, complemented
3C2×#11719066C211yesmaximal, characteristic, complemented
4C2×#11719065C211yesmaximal, characteristic, complemented
5C2×#11719144C211yesmaximal, characteristic, complemented
6C2×#11719144C211yesmaximal, characteristic, complemented
7C2×#11719064C211yesmaximal, characteristic, complemented
8C2×#11719063C211yesmaximal, characteristic, complemented
9C2×D4×#1057C211yesmaximal, characteristic, complemented
10C2×#11719068C211yesmaximal, characteristic, complemented
11C2×#11719068C211yesmaximal, characteristic, complemented
12C2×#11719147C211yesmaximal, characteristic, complemented
13C2×#11719146C211yesmaximal, characteristic, complemented
14C2×#11719169C211yesmaximal, characteristic, complemented
15C22×C22⋊#1057C211yesmaximal, characteristic, complemented
16C2×#11719291C211yesmaximal, characteristic
17C24×Dic13C2211yescharacteristic
18C22×#6129C2211yescharacteristic
19C22×#6122C2211yescharacteristic
20C22×#6122C2211yescharacteristic
21C22×#6122C2211yescharacteristic, complemented
22C23×#1057C2211yescharacteristic
23C23×#1057C2211yescharacteristic
24C23×#1057C2211yescharacteristic, complemented
25C22×#6118C2211yescharacteristic, complemented
26C22×D13⋊C8C2211yescharacteristic, complemented
27C2×C13×#120C411yescharacteristic
28C2×#88207C411yescharacteristic
29C2×#88193C411yescharacteristic
30C2×#88193C411yescharacteristic
31C2×#88189C411yescharacteristic
32C2×D4×Dic13C2211yescharacteristic
33C2×D4×Dic13C2211yescharacteristic
34#11719291C418yes—
35#11719291C2218yes—
36C2×#88140C411yescharacteristic
37C2×#88135C2211yescharacteristic
38C2×#88135C2211yescharacteristic
39C2×#88132C411yescharacteristic
40C2×#88132C411yescharacteristic
41C2×#88131C2211yescharacteristic
42#11719169C2218yescomplemented
43C2×C22⋊#1057C2211yescharacteristic
44C2×C22⋊#1057C2211yescharacteristic
45C2×C22⋊#1057C2211yescharacteristic
46C2×C22⋊#1057C2211yescharacteristic
47C2×C22⋊#1057C2211yescharacteristic
48C2×C22⋊#1057C2211yescharacteristic
49C2×C22⋊#1057C2211yescharacteristic
50C2×C22⋊#1057C2211yescharacteristic
51C2×C22⋊#1057C2218yescomplemented
52C2×C22⋊#1057C2211yescharacteristic, complemented
53C2×C22⋊#1057C2211yescharacteristic, complemented
54#11719147C2218yescomplemented
55#11719146C2218yescomplemented
56#11719145C2218yescomplemented
57#11719144C2218yescomplemented
58#11719144C2218yescomplemented
59D4×#1057C2218yescomplemented
60C2×#88112C2211yescharacteristic, complemented
61C2×#88112C2211yescharacteristic, complemented
62C2×#88111C2211yescharacteristic, complemented
63C2×#88111C2211yescharacteristic, complemented
64C2×#88110C2211yescharacteristic, complemented
65C2×#88110C2211yescharacteristic, complemented
66C2×C4⋊#1057C2211yescharacteristic, complemented
67C2×C4⋊#1057C2211yescharacteristic, complemented
68C2×C4×#1057C2211yescharacteristic, complemented
69C2×C4×#1057C2211yescharacteristic, complemented
70#11719068C2218yescomplemented
71#11719068C2218yescomplemented
72#11719066C2218yescomplemented
73#11719065C2218yescomplemented
74#11719064C2218yescomplemented
75#11719063C2218yescomplemented
76C25×C13C2×C411yescharacteristic
77C22×D4×C13C2×C411yescharacteristic
78C22×D4×C13C2×C411yescharacteristic
79C22×D4×C13C2×C411yescharacteristic
80C22×C22⋊D13C2×C411yescharacteristic
81C22×C22⋊D13C2×C411yescharacteristic
82C22×C22⋊D13C2×C411yescharacteristic
83C22×C22⋊D13C2×C411yescharacteristic
84C23×Dic13—42no—
85C23×Dic13—42no—
86C23×Dic13C2×C411yescharacteristic
87C23×Dic13C2×C411yescharacteristic
88C23×Dic13C2×C411yescharacteristic
89C23×Dic13C2×C414yes—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2314yes—
95C2×#6129—42no—
96C2×#6129—42no—
97C2×#6129C2×C414yes—
98C2×#6129C2314yes—
99C22×C4×D13C2311yescharacteristic
100C22×Dic26C2×C411yescharacteristic
101C2×#6122—42no—
102C2×#6122—42no—
103C2×#6122—42no—
104C2×#6122C2314yes—
105C2×#6122C2314yes—
106C2×#6122C2314yescomplemented
107C22×#1057—42no—
108C22×#1057—42no—
109C22×#1057—42no—
110C22×#1057C2311yescharacteristic
111C22×#1057C2311yescharacteristic
112C22×#1057C2311yescharacteristic
113C22×#1057C2311yescharacteristic
114C22×#1057C2311yescharacteristic
115C22×#1057C2311yescharacteristic
116C22×#1057C2311yescharacteristic
117C22×#1057C2311yescharacteristic
118C22×#1057C2314yes—
119C22×#1057C2314yes—
120C22×#1057C2314yescomplemented
121C2×#6118—42no—
122C2×#6118C2314yescomplemented
123C2×D13⋊C8—42no—
124C2×D13⋊C8C2314yescomplemented
125C13×#120C2×C418yes—
126C2×C13×C22⋊C4C2×C411yescharacteristic
127C2×C13×C22⋊C4C2×C411yescharacteristic
128C2×C13×C22⋊C4C2×C411yescharacteristic
129#88207C2×C418yes—
130C2×C22⋊Dic13C2×C411yescharacteristic
131C2×C22⋊Dic13C2×C411yescharacteristic
132C2×C22⋊Dic13C2×C411yescharacteristic
133C2×C22⋊Dic13C2×C411yescharacteristic
134C2×C22⋊Dic13C2×C411yescharacteristic
135#88193C2×C418yes—
136#88193C2×C418yes—
137#88189C2×C418yes—
138D4×Dic13C2×C414yes—
139D4×Dic13C2×C414yes—
140D4×Dic13C2314yes—
141D4×Dic13C2314yes—
142C2×#6103C2×C411yescharacteristic
143C2×#6103C2×C411yescharacteristic
144C2×C4⋊Dic13C2×C411yescharacteristic
145C2×C4⋊Dic13C2×C411yescharacteristic
146C2×#6101C2×C411yescharacteristic
147C2×#6101C2×C411yescharacteristic
148C2×#6101C2×C411yescharacteristic
149C2×#6101C2×C411yescharacteristic
150C2×C4×Dic13C2311yescharacteristic
151C2×C4×Dic13C2311yescharacteristic
152#88140C2×C418yes—
153#88135C2×C414yes—
154#88135C2×C414yes—
155#88135C2314yes—
156#88135C2314yes—
157#88132C2×C418yes—
158#88132C2×C418yes—
159#88131C2×C414yes—
160#88131C2314yes—
161C22⋊#1057C2314yes—
162C22⋊#1057C2314yes—
163C22⋊#1057C2314yes—
164C22⋊#1057C2314yes—
165C22⋊#1057C2314yes—
166C22⋊#1057C2314yes—
167C22⋊#1057C2314yes—
168C22⋊#1057C2314yes—
169C22⋊#1057C2314yescomplemented
170C22⋊#1057C2314yescomplemented
171#88112C2314yescomplemented
172#88112C2314yescomplemented
173#88111C2314yescomplemented
174#88111C2314yescomplemented
175#88110C2314yescomplemented
176#88110C2314yescomplemented
177C4⋊#1057C2314yescomplemented
178C4⋊#1057C2314yescomplemented
179C4×#1057C2314yescomplemented
180C4×#1057C2314yescomplemented
181C2×#2976—131nomaximal, Sylow
182C24×C13—24no—
183C24×C13—42no—
184C24×C13—42no—
185C24×C13C22×C411yescharacteristic
186C24×C13C22×C411yescharacteristic
187C24×C13C22×C411yescharacteristic
188C24×C13C22×C411yescharacteristic
189C24×C13C22×C414yes—
190C23×D13C22×C411yescharacteristic
191C2×D4×C13—24no—
192C2×D4×C13—42no—
193C2×D4×C13—42no—
194C2×D4×C13C22×C414yes—
195C2×D4×C13C22×C414yes—
196C2×D4×C13C22×C414yes—
197C22×C4×C13C22×C411yescharacteristic
198C22×C4×C13C22×C411yescharacteristic
199C22×C4×C13C22×C411yescharacteristic
200C2×C22⋊D13—24no—
201C2×C22⋊D13—42no—
202C2×C22⋊D13—42no—
203C2×C22⋊D13—42no—
204C2×C22⋊D13C22×C414yes—
205C2×C22⋊D13C22×C414yes—
206C2×C22⋊D13C22×C414yes—
207C2×C22⋊D13C22×C414yes—
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—48no—
217C22×Dic13—44no—
218C22×Dic13—44no—
219C22×Dic13—42no—
220C22×Dic13—42no—
221C22×Dic13—42no—
222C22×Dic13C22×C412yes—
223C22×Dic13C22×C412yes—
224C22×Dic13C22×C412yes—
225C22×Dic13C22×C411yescharacteristic
226C22×Dic13C22×C411yescharacteristic
227C22×Dic13C22×C411yescharacteristic
228C22×Dic13C22×C411yescharacteristic
229C22×Dic13C22×C411yescharacteristic
230C22×Dic13C22×C411yescharacteristic
231C22×Dic13C22×C412yes—
232C22×Dic13C22×C414yes—
233C22×Dic13C22×C414yes—
234C22×Dic13C22×C414yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2411yescharacteristic
240#6129—48no—
241#6129—44no—
242#6129—44no—
243C2×C4×D13—22no—
244C2×C4×D13—22no—
245C2×C4×D13C22×C412yes—
246C2×C4×D13C2412yes—
247C2×Dic26—42no—
248C2×Dic26C22×C414yes—
249#6122—44no—
250#6122—44no—
251#6122—44no—
252C2×#1057—22no—
253C2×#1057—22no—
254C2×#1057—22no—
255C2×#1057—22no—
256C2×#1057—22no—
257C2×#1057—22no—
258C2×#1057—22no—
259C2×#1057—22no—
260C2×#1057—44no—
261C2×#1057—44no—
262C2×#1057—44no—
263C2×#1057C2412yes—
264C2×#1057C2412yes—
265C2×#1057C2412yes—
266C2×#1057C2412yes—
267C2×#1057C2412yes—
268C2×#1057C2412yes—
269C2×#1057C2412yes—
270C2×#1057C2412yes—
271#6118—44no—
272D13⋊C8—44no—
273C13×C22⋊C4C22×C414yes—
274C13×C22⋊C4C22×C414yes—
275C13×C22⋊C4C22×C414yes—
276C22⋊Dic13C22×C414yes—
277C22⋊Dic13C22×C414yes—
278C22⋊Dic13C22×C414yes—
279C22⋊Dic13C22×C414yes—
280C22⋊Dic13C22×C414yes—
281#6103C22×C414yes—
282#6103C22×C414yes—
283C4⋊Dic13C22×C414yes—
284C4⋊Dic13C22×C414yes—
285#6101C22×C414yes—
286#6101C22×C414yes—
287#6101C22×C414yes—
288#6101C22×C414yes—
289C4×Dic13C22×C412yes—
290C4×Dic13C22×C412yes—
291C4×Dic13C2412yes—
292C4×Dic13C2412yes—
293C2×#525—131no—
294#2976—1316no—
295C2×#436—131no—
296C2×#436—131no—
297C2×#435—131no—
298C2×#435—131no—
299C2×#435—131no—
300C2×#435—131no—
301C2×C8×D4—131no—
302C2×C8×D4—131no—
303C2×#433—131no—
304C2×#433—131no—
305C2×#408—131no—
306C2×#408—131no—
307C2×#407—131no—
308C22×C22⋊C8—131no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—28no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—44no—
322C23×C13—44no—
323C23×C13—416no—
324C23×C13#13114yes—
325C23×C13C23×C412yes—
326C23×C13C23×C412yes—
327C23×C13C23×C412yes—
328C23×C13C23×C412yes—
329C23×C13C23×C411yescharacteristic
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13C23×C412yes—
334D4×C13—28no—
335D4×C13—44no—
336D4×C13—44no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13C23×C412yes—
341C2×C4×C13C23×C412yes—
342C2×C4×C13C23×C412yes—
343C22⋊D13—28no—
344C22⋊D13—44no—
345C22⋊D13—44no—
346C22⋊D13—44no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—24no—
354C2×Dic13—24no—
355C2×Dic13—24no—
356C2×Dic13—24no—
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—44no—
366C2×Dic13—44no—
367C2×Dic13—44no—
368C2×Dic13C23×C412yes—
369C2×Dic13C23×C412yes—
370C2×Dic13C23×C412yes—
371C2×Dic13C23×C412yes—
372C2×Dic13C23×C412yes—
373C2×Dic13C23×C412yes—
374C2×Dic13C23×C411yescharacteristic
375C2×Dic13H(5,𝔽2)12yes—
376C2×Dic13H(5,𝔽2)12yes—
377C2×Dic13C2511yescharacteristic
378C4×D13—24no—
379C4×D13—22no—
380C4×D13—22no—
381Dic26—44no—
382#1057—22no—
383#1057—22no—
384#1057—22no—
385#1057—22no—
386#1057—22no—
387#1057—22no—
388#1057—22no—
389#1057—22no—
390C22×#41—131no—
391C24×C4—131no—
392C22×M16—131no—
393C22×M16—131no—
394C22×M16—131no—
395C22×M16—131no—
396C23×C8—131no—
397C23×C8—131no—
398C23×C8—131no—
399C23×C8—131no—
400#525—138no—
401#525—138no—
402C2×#123—131no—
403C2×#123—131no—
404C2×C22⋊Q8—131no—
405C2×C22⋊Q8—131no—
406C2×#121—131no—
407C2×#121—131no—
408C2×#120—131no—
409C2×#120#26111yescharacteristic
410C2×C4×D4—131no—
411C2×C4×D4—131no—
412C2×C4×D4—131no—
413C2×C4×D4—131no—
414C2×#117—131no—
415#436—138no—
416#436—138no—
417#435—138no—
418#435—138no—
419#435—138no—
420#435—138no—
421C8×D4—138no—
422C8×D4—138no—
423#433—138no—
424#433—138no—
425C2×C4⋊C8—131no—
426C2×C4⋊C8—131no—
427C2×C4⋊C8—131no—
428C2×C4⋊C8—131no—
429#408—138no—
430#408—138no—
431#407—138no—
432C2×C22⋊C8—131no—
433C2×C22⋊C8—131no—
434C2×C22⋊C8—131no—
435C2×C22⋊C8—131no—
436C2×C22⋊C8—131no—
437C2×C22⋊C8—131no—
438C2×C22⋊C8—131no—
439C2×C22⋊C8—131no—
440C2×C22⋊C8—138no—
441C2×C22⋊C8—131no—
442C2×C22⋊C8—131no—
443C2×C22⋊C8—131no—
444C2×C22⋊C8—131no—
445C2×#97—131no—
446C2×#97—131no—
447C2×C4×C8—131no—
448C2×C4×C8—131no—
449C22×C13—22no—
450C22×C13—28no—
451C22×C13—22no—
452C22×C13—22no—
453C22×C13—22no—
454C22×C13—22no—
455C22×C13—22no—
456C22×C13—22no—
457C22×C13—22no—
458C22×C13—22no—
459C22×C13—22no—
460C22×C13—22no—
461C22×C13—416no—
462C22×C13—44no—
463C22×C13—44no—
464C22×C13—44no—
465C22×C13#51812yes—
466C22×C13C2×#13114yes—
467C22×C13C2×#13112yes—
468C22×C13#56812yes—
469C22×C13C24×C411yescharacteristic
470C2×D13—22no—
471C2×D13—22no—
472C2×D13—22no—
473C2×D13—44no—
474C4×C13—22no—
475C4×C13—22no—
476C4×C13—22no—
477Dic13—22no—
478Dic13—22no—
479Dic13—22no—
480Dic13—22no—
481Dic13—22no—
482Dic13—22no—
483Dic13#51812yes—
484Dic13C2×H(5,𝔽2)11yescharacteristic
485Dic13C2×H(5,𝔽2)11yescharacteristic
486C25C2×#26111yescharacteristic
487C2×#41—134no—
488C2×#41—134no—
489C2×#41—522no—
490C2×#41—522no—
491C22×Q8—131no—
492C22×D4—131no—
493C22×D4—131no—
494C22×D4—131no—
495C22×D4—131no—
496C22×D4C2×#26111yescharacteristic
497C22×D4C2×#26111yescharacteristic
498C22×D4C2×#26111yescharacteristic
499C23×C4—131no—
500C23×C4—131no—
501C23×C4—131no—
502C23×C4—131no—
503C23×C4—131no—
504C23×C4—131no—
505C23×C4—131no—
506C23×C4—134no—
507C23×C4—134no—
508C23×C4—131no—
509C23×C4—522no—
510C23×C4—522no—
511C2×M16—134no—
512C2×M16—134no—
513C2×M16—134no—
514C2×M16—134no—
515C2×M16—522no—
516C2×M16—522no—
517C2×M16—522no—
518C2×M16—522no—
519C22×C8—131no—
520C22×C8—131no—
521C22×C8—131no—
522C22×C8—131no—
523C22×C8—131no—
524C22×C8—131no—
525C22×C8—131no—
526C22×C8—131no—
527C22×C8—134no—
528C22×C8—134no—
529C22×C8—134no—
530C22×C8—134no—
531C22×C8—522no—
532C22×C8—522no—
533C22×C8—522no—
534C22×C8—522no—
535#123—138no—
536#123—138no—
537C22⋊Q8—138no—
538C22⋊Q8—138no—
539#121—138no—
540#121—138no—
541#120—138no—
542#120C2×#26118yes—
543C4×D4—134no—
544C4×D4—134no—
545C4×D4—134no—
546C4×D4—134no—
547C4×D4—134no—
548C4×D4—134no—
549C4×D4—134no—
550C4×D4—134no—
551#117—134no—
552#117—134no—
553C2×C4⋊C4—131no—
554C2×C4⋊C4—131no—
555C2×C4⋊C4—131no—
556C2×C4⋊C4—131no—
557C2×C4⋊C4—131no—
558C2×C4⋊C4—131no—
559C2×C22⋊C4—131no—
560C2×C22⋊C4—131no—
561C2×C22⋊C4—131no—
562C2×C22⋊C4—131no—
563C2×C22⋊C4—131no—
564C2×C22⋊C4—131no—
565C2×C22⋊C4—131no—
566C2×C22⋊C4C2×#26111yescharacteristic
567C2×C22⋊C4C2×#26111yescharacteristic
568C2×C22⋊C4C2×#26111yescharacteristic
569C2×C42—131no—
570C2×C42—131no—
571C4⋊C8—134no—
572C4⋊C8—134no—
573C4⋊C8—134no—
574C4⋊C8—134no—
575C22⋊C8—134no—
576C22⋊C8—134no—
577C22⋊C8—134no—
578C22⋊C8—134no—
579C22⋊C8—134no—
580C22⋊C8—134no—
581C22⋊C8—134no—
582C22⋊C8—134no—
583C22⋊C8—134no—
584C22⋊C8—134no—
585C22⋊C8—134no—
586C22⋊C8—134no—
587#97—134no—
588#97—134no—
589C4×C8—134no—
590C4×C8—134no—
591C2×C13—24no—
592C2×C13—42no—
593C2×C13—42no—
594C2×C13—42no—
595C2×C13#297614yescomplemented
596C2×C13C2×#51811yescharacteristic
597C2×C13C22×#13111yescharacteristic
598C2×C13C2×#56811yescharacteristic
599D13—42no—
600C24—24no—
601C24—42no—
602C24—42no—
603C24—131no—
604C24C22×#26111yescharacteristic
605C24C22×#26111yescharacteristic
606C24C22×#26111yescharacteristic
607C24C22×#26111yescharacteristic
608C24C22×#26114yes—
609#41—524no—
610#41—524no—
611#41—528no—
612C2×Q8—134no—
613C2×Q8—522no—
614C2×D4—24no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—134no—
618C2×D4—134no—
619C2×D4—134no—
620C2×D4—134no—
621C2×D4—264no—
622C2×D4—522no—
623C2×D4—522no—
624C2×D4—522no—
625C2×D4C22×#26114yes—
626C2×D4C22×#26114yes—
627C2×D4C22×#26114yes—
628C22×C4—131no—
629C22×C4—132no—
630C22×C4—132no—
631C22×C4—132no—
632C22×C4—132no—
633C22×C4—132no—
634C22×C4—132no—
635C22×C4—132no—
636C22×C4—132no—
637C22×C4—131no—
638C22×C4—131no—
639C22×C4—131no—
640C22×C4—131no—
641C22×C4—131no—
642C22×C4—131no—
643C22×C4—134no—
644C22×C4—134no—
645C22×C4—134no—
646C22×C4—132no—
647C22×C4—132no—
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—524no—
659C22×C4—524no—
660C22×C4—528no—
661C22×C4—522no—
662C22×C4—522no—
663C22×C4—522no—
664C22×C4C22×#26111yescharacteristic
665C22×C4C22×#26111yescharacteristic
666C22×C4C22×#26111yescharacteristic
667M16—524no—
668M16—524no—
669M16—524no—
670M16—524no—
671C2×C8—132no—
672C2×C8—132no—
673C2×C8—132no—
674C2×C8—132no—
675C2×C8—132no—
676C2×C8—132no—
677C2×C8—132no—
678C2×C8—132no—
679C2×C8—262no—
680C2×C8—262no—
681C2×C8—262no—
682C2×C8—262no—
683C2×C8—262no—
684C2×C8—262no—
685C2×C8—262no—
686C2×C8—262no—
687C2×C8—524no—
688C2×C8—524no—
689C2×C8—524no—
690C2×C8—524no—
691C4⋊C4—134no—
692C4⋊C4—134no—
693C4⋊C4—134no—
694C4⋊C4—134no—
695C4⋊C4—134no—
696C4⋊C4—134no—
697C22⋊C4—134no—
698C22⋊C4—134no—
699C22⋊C4—134no—
700C22⋊C4—134no—
701C22⋊C4—134no—
702C22⋊C4—134no—
703C22⋊C4—134no—
704C22⋊C4C22×#26114yes—
705C22⋊C4C22×#26114yes—
706C22⋊C4C22×#26114yes—
707C42—132no—
708C42—132no—
709C42—132no—
710C42—132no—
711C13C2×#297611yescharacteristic, complemented, Sylow
712C23—22no—
713C23—22no—
714C23—22no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—44no—
726C23—416no—
727C23—132no—
728C23—262no—
729C23—262no—
730C23—262no—
731C23#8823814yes—
732C23C23×#26112yes—
733C23C23×#26112yes—
734C23C23×#26112yes—
735C23C23×#26112yes—
736C23C23×#26111yescharacteristic
737Q8—524no—
738D4—28no—
739D4—44no—
740D4—44no—
741D4—268no—
742D4—524no—
743D4—524no—
744D4—524no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—132no—
749C2×C4—132no—
750C2×C4—131no—
751C2×C4—131no—
752C2×C4—132no—
753C2×C4—132no—
754C2×C4—132no—
755C2×C4—132no—
756C2×C4—132no—
757C2×C4—132no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—264no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—262no—
767C2×C4—264no—
768C2×C4—264no—
769C2×C4—264no—
770C2×C4—262no—
771C2×C4—262no—
772C2×C4—264no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—262no—
779C2×C4—524no—
780C2×C4—524no—
781C2×C4—524no—
782C2×C4C23×#26112yes—
783C2×C4C23×#26112yes—
784C2×C4C23×#26112yes—
785C8—262no—
786C8—262no—
787C8—262no—
788C8—262no—
789C8—262no—
790C8—262no—
791C8—262no—
792C8—262no—
793C22—22no—
794C22—22no—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—416no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—262no—
810C22—262no—
811C22—262no—
812C22—524no—
813C22C2×#8823814yes—
814C22C2×#8823812yes—
815C22#1171962112yes—
816C22#1171962312yes—
817C22C24×#26111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—132no—
822C4—131no—
823C4—131no—
824C4—262no—
825C4—262no—
826C4—262no—
827C4—262no—
828C4—262no—
829C4—262no—
830C2—24no—
831C2—42no—
832C2—42no—
833C2—42no—
834C2—522no—
835C2#1313170214yesdirect product factor
836C2C2×#1171962311yescharacteristic
837C2C22×#8823811yescharacteristic
838C2C2×#1171962111yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#120C4
socleC23×C13C23×C4
prime radicalC2×#11719291C2
cosocleC2×Dic13C25
hypercenterC2×#120#261
hypocenterC13C2×#2976
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #13131702C2direct (N × H)
2. C2×#11719145C2semidirect
3. C2×#11719066C2semidirect
4. C2×#11719065C2semidirect
5. C2×#11719144C2semidirect
6. C2×#11719144C2semidirect
7. C2×#11719064C2semidirect
8. C2×#11719063C2semidirect
9. C2×D4×#1057C2semidirect
10. C2×#11719068C2semidirect
11. C2×#11719068C2semidirect
12. C2×#11719147C2semidirect
13. C2×#11719146C2semidirect
14. C2×#11719169C2semidirect
15. C22×C22⋊#1057C2semidirect
21. C22×#6122C22semidirect
24. C23×#1057C22semidirect
25. C22×#6118C22semidirect
26. C22×D13⋊C8C22semidirect
42. #11719169C22semidirect
51. C2×C22⋊#1057C22semidirect
52. C2×C22⋊#1057C22semidirect
53. C2×C22⋊#1057C22semidirect
54. #11719147C22semidirect
55. #11719146C22semidirect
56. #11719145C22semidirect
57. #11719144C22semidirect
58. #11719144C22semidirect
59. D4×#1057C22semidirect
60. C2×#88112C22semidirect
61. C2×#88112C22semidirect
62. C2×#88111C22semidirect
63. C2×#88111C22semidirect
64. C2×#88110C22semidirect
65. C2×#88110C22semidirect
66. C2×C4⋊#1057C22semidirect
67. C2×C4⋊#1057C22semidirect
68. C2×C4×#1057C22semidirect
69. C2×C4×#1057C22semidirect
70. #11719068C22semidirect
71. #11719068C22semidirect
72. #11719066C22semidirect
73. #11719065C22semidirect
74. #11719064C22semidirect
75. #11719063C22semidirect
106. C2×#6122C23semidirect
120. C22×#1057C23semidirect
122. C2×#6118C23semidirect
124. C2×D13⋊C8C23semidirect
169. C22⋊#1057C23semidirect
170. C22⋊#1057C23semidirect
171. #88112C23semidirect
172. #88112C23semidirect
173. #88111C23semidirect
174. #88111C23semidirect
175. #88110C23semidirect
176. #88110C23semidirect
177. C4⋊#1057C23semidirect
178. C4⋊#1057C23semidirect
179. C4×#1057C23semidirect
180. C4×#1057C23semidirect
595. C2×C13#2976semidirect
711. C13C2×#2976semidirect
835. C2#13131702direct (N × H)

Maximal subgroups

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

subgroupindex
#131317022
C2×#117191452
C2×#117190662
C2×#117190652
C2×#117191442
C2×#117190642
C2×#117190632
C2×D4×#10572
C2×#117190682
C2×#117191472
C2×#117191462
C2×#117191692
C22×C22⋊#10572
C2×#117192912
C2×#297613