Finite Group Databasebeta

← C2×#13131704 #16808648

Subgroups — C2×#13131704 #16808648

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#13131704C2116yesmaximal, direct product factor
2C2×#11719076C211yesmaximal, characteristic, complemented
3C2×#11719066C211yesmaximal, characteristic, complemented
4C2×#11719065C211yesmaximal, characteristic, complemented
5C2×#11719075C211yesmaximal, characteristic, complemented
6C2×#11719075C211yesmaximal, characteristic, complemented
7C2×#11719064C211yesmaximal, characteristic, complemented
8C2×#11719073C211yesmaximal, characteristic, complemented
9C2×#11719063C211yesmaximal, characteristic, complemented
10C2×#11719068C211yesmaximal, characteristic, complemented
11C2×#11719068C211yesmaximal, characteristic, complemented
12C2×#11719147C211yesmaximal, characteristic, complemented
13C2×#11719146C211yesmaximal, characteristic, complemented
14C2×#11719127C211yesmaximal, characteristic, complemented
15C2×D13⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
16C2×#11719361C211yesmaximal, characteristic
17C22×#6129C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C22×#6122C2211yescharacteristic, complemented
20C23×#1057C2211yescharacteristic, complemented
21C22×#6118C2211yescharacteristic
22C22×#6118C2211yescharacteristic
23C22×#6118C2211yescharacteristic, complemented
24C22×D13⋊C8C2211yescharacteristic
25C22×D13⋊C8C2211yescharacteristic
26C22×D13⋊C8C2211yescharacteristic, complemented
27C2×C13×#123C411yescharacteristic
28C2×#88191C411yescharacteristic
29C2×#88183C411yescharacteristic
30#11719361C418yes—
31#11719361C2218yes—
32C2×#88150C411yescharacteristic
33C2×#88150C411yescharacteristic
34C2×#88147C2211yescharacteristic
35C2×#88147C2211yescharacteristic
36C2×#88138C411yescharacteristic
37C2×#88138C411yescharacteristic
38C2×#88136C411yescharacteristic
39C2×#88135C2211yescharacteristic
40C2×#88135C2211yescharacteristic
41C2×#88131C2211yescharacteristic
42C2×C22⋊#1057C2211yescharacteristic
43C2×C22⋊#1057C2211yescharacteristic
44C2×C22⋊#1057C2211yescharacteristic
45C2×C22⋊#1057C2211yescharacteristic
46C2×C22⋊#1057C2211yescharacteristic, complemented
47C2×C22⋊#1057C2211yescharacteristic, complemented
48#11719147C2218yescomplemented
49#11719146C2218yescomplemented
50#11719127C2218yescomplemented
51D13⋊(C22⋊C8)C2218yescomplemented
52C2×#88112C2211yescharacteristic, complemented
53C2×#88112C2211yescharacteristic, complemented
54C2×#88111C2211yescharacteristic
55C2×#88111C2211yescharacteristic
56C2×#88111C2211yescharacteristic
57C2×#88111C2211yescharacteristic
58C2×#88111C2211yescharacteristic, complemented
59C2×#88111C2211yescharacteristic, complemented
60C2×#88110C2211yescharacteristic, complemented
61C2×#88110C2211yescharacteristic, complemented
62C2×C4⋊#1057C2211yescharacteristic, complemented
63C2×C4⋊#1057C2211yescharacteristic, complemented
64C2×C4×#1057C2211yescharacteristic, complemented
65C2×C4×#1057C2211yescharacteristic, complemented
66#11719076C2218yescomplemented
67#11719075C2218yescomplemented
68#11719075C2218yescomplemented
69#11719073C2218yescomplemented
70#11719068C2218yescomplemented
71#11719068C2218yescomplemented
72#11719066C2218yescomplemented
73#11719065C2218yescomplemented
74#11719064C2218yescomplemented
75#11719063C2218yescomplemented
76C24×D13C2×C411yescharacteristic
77C22×D4×C13C2×C411yescharacteristic
78C23×C4×C13C2×C411yescharacteristic
79C22×C22⋊D13C2×C411yescharacteristic
80C22×C22⋊D13C2×C411yescharacteristic
81C22×C22⋊D13C2×C411yescharacteristic
82C22×C22⋊D13C2×C411yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C2×#6129—42no—
86C2×#6129—42no—
87C2×#6129C2×C414yes—
88C2×#6129C2314yes—
89C22×D52C2×C411yescharacteristic
90C22×D52C2×C411yescharacteristic
91C22×C4×D13—42no—
92C22×C4×D13—42no—
93C22×C4×D13C2×C411yescharacteristic
94C22×C4×D13C2×C411yescharacteristic
95C22×C4×D13C2×C414yes—
96C22×C4×D13C2311yescharacteristic
97C22×C4×D13C2311yescharacteristic
98C22×C4×D13C2311yescharacteristic
99C22×C4×D13C2314yes—
100C22×Dic26C2×C411yescharacteristic
101C2×#6122—42no—
102C2×#6122C2314yescomplemented
103C22×#1057—42no—
104C22×#1057C2311yescharacteristic
105C22×#1057C2311yescharacteristic
106C22×#1057C2311yescharacteristic
107C22×#1057C2311yescharacteristic
108C22×#1057C2311yescharacteristic
109C22×#1057C2311yescharacteristic
110C22×#1057C2311yescharacteristic
111C22×#1057C2311yescharacteristic
112C22×#1057C2314yescomplemented
113C2×#6118—42no—
114C2×#6118—42no—
115C2×#6118—42no—
116C2×#6118C2314yes—
117C2×#6118C2314yes—
118C2×#6118C2314yescomplemented
119C2×D13⋊C8—42no—
120C2×D13⋊C8—42no—
121C2×D13⋊C8—42no—
122C2×D13⋊C8C2314yes—
123C2×D13⋊C8C2314yes—
124C2×D13⋊C8C2314yescomplemented
125C13×#123C2×C418yes—
126C2×C13×C4⋊C4C2×C411yescharacteristic
127C2×C13×C4⋊C4C2×C411yescharacteristic
128C2×C13×C22⋊C4C2×C411yescharacteristic
129C2×C13×C22⋊C4C2×C411yescharacteristic
130C2×C13×C22⋊C4C2×C411yescharacteristic
131C2×C22⋊Dic13C2×C411yescharacteristic
132#88191C2×C418yes—
133#88183C2×C418yes—
134C2×#6103C2×C411yescharacteristic
135C2×#6103C2×C411yescharacteristic
136C2×#6103C2×C411yescharacteristic
137C2×#6103C2×C411yescharacteristic
138C2×#6103C2×C411yescharacteristic
139C2×#6103C2×C411yescharacteristic
140C2×#6101C2×C411yescharacteristic
141C2×#6101C2×C411yescharacteristic
142C2×#6101C2×C411yescharacteristic
143C2×#6101C2×C411yescharacteristic
144C2×C4×Dic13C2311yescharacteristic
145C2×C4×Dic13C2311yescharacteristic
146#88150C2×C418yes—
147#88150C2×C418yes—
148#88147C2×C414yes—
149#88147C2×C414yes—
150#88147C2314yes—
151#88147C2314yes—
152#88138C2×C418yes—
153#88138C2×C418yes—
154#88136C2×C418yes—
155#88135C2×C414yes—
156#88135C2×C414yes—
157#88135C2314yes—
158#88135C2314yes—
159#88131C2×C414yes—
160#88131C2314yes—
161C22⋊#1057C2314yes—
162C22⋊#1057C2314yes—
163C22⋊#1057C2314yes—
164C22⋊#1057C2314yes—
165C22⋊#1057C2314yescomplemented
166C22⋊#1057C2314yescomplemented
167#88112C2314yescomplemented
168#88112C2314yescomplemented
169#88111C2314yes—
170#88111C2314yes—
171#88111C2314yes—
172#88111C2314yes—
173#88111C2314yescomplemented
174#88111C2314yescomplemented
175#88110C2314yescomplemented
176#88110C2314yescomplemented
177C4⋊#1057C2314yescomplemented
178C4⋊#1057C2314yescomplemented
179C4×#1057C2314yescomplemented
180C4×#1057C2314yescomplemented
181C2×#2976—131nomaximal, Sylow
182C24×C13C22×C411yescharacteristic
183C24×C13C22×C411yescharacteristic
184C23×D13—24no—
185C23×D13—42no—
186C23×D13—42no—
187C23×D13C22×C411yescharacteristic
188C23×D13C22×C411yescharacteristic
189C23×D13C22×C411yescharacteristic
190C23×D13C22×C414yes—
191C2×D4×C13—42no—
192C2×D4×C13C22×C414yes—
193C22×C4×C13—42no—
194C22×C4×C13C22×C411yescharacteristic
195C22×C4×C13C22×C411yescharacteristic
196C22×C4×C13C22×C411yescharacteristic
197C22×C4×C13C22×C411yescharacteristic
198C22×C4×C13C22×C411yescharacteristic
199C22×C4×C13C22×C414yes—
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×Dic13C22×C412yes—
213C22×Dic13C22×C412yes—
214C22×Dic13C22×C411yescharacteristic
215C22×Dic13C22×C411yescharacteristic
216C22×Dic13C22×C411yescharacteristic
217C22×Dic13C22×C411yescharacteristic
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C22×Dic13C2411yescharacteristic
221#6129—48no—
222#6129—44no—
223#6129—44no—
224C2×D52—24no—
225C2×D52—42no—
226C2×D52C22×C414yes—
227C2×D52C22×C414yes—
228C2×C4×D13—22no—
229C2×C4×D13—22no—
230C2×C4×D13—22no—
231C2×C4×D13—22no—
232C2×C4×D13—22no—
233C2×C4×D13—22no—
234C2×C4×D13—48no—
235C2×C4×D13—44no—
236C2×C4×D13—44no—
237C2×C4×D13—42no—
238C2×C4×D13—42no—
239C2×C4×D13C22×C412yes—
240C2×C4×D13C22×C412yes—
241C2×C4×D13C22×C412yes—
242C2×C4×D13C22×C414yes—
243C2×C4×D13C22×C414yes—
244C2×C4×D13C2412yes—
245C2×C4×D13C2412yes—
246C2×C4×D13C2412yes—
247C2×Dic26—42no—
248C2×Dic26C22×C414yes—
249#6122—44no—
250C2×#1057—22no—
251C2×#1057—22no—
252C2×#1057—22no—
253C2×#1057—22no—
254C2×#1057—22no—
255C2×#1057—22no—
256C2×#1057—22no—
257C2×#1057—22no—
258C2×#1057—44no—
259C2×#1057C2412yes—
260C2×#1057C2412yes—
261C2×#1057C2412yes—
262C2×#1057C2412yes—
263C2×#1057C2412yes—
264C2×#1057C2412yes—
265C2×#1057C2412yes—
266C2×#1057C2412yes—
267#6118—44no—
268#6118—44no—
269#6118—44no—
270D13⋊C8—44no—
271D13⋊C8—44no—
272D13⋊C8—44no—
273C13×C4⋊C4C22×C414yes—
274C13×C4⋊C4C22×C414yes—
275C13×C22⋊C4C22×C414yes—
276C13×C22⋊C4C22×C414yes—
277C13×C22⋊C4C22×C414yes—
278C22⋊Dic13C22×C414yes—
279#6103C22×C414yes—
280#6103C22×C414yes—
281#6103C22×C414yes—
282#6103C22×C414yes—
283#6103C22×C414yes—
284#6103C22×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×C13C23×C412yes—
316C23×C13C23×C412yes—
317C23×C13C23×C411yescharacteristic
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—28no—
327C22×D13—44no—
328C22×D13—44no—
329C22×D13—416no—
330C22×D13#13114yes—
331C22×D13C23×C412yes—
332C22×D13C23×C412yes—
333C22×D13C23×C412yes—
334D4×C13—44no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—44no—
341C2×C4×C13C23×C412yes—
342C2×C4×C13C23×C412yes—
343C2×C4×C13C23×C412yes—
344C2×C4×C13C23×C412yes—
345C2×C4×C13C23×C412yes—
346C22⋊D13—28no—
347C22⋊D13—44no—
348C22⋊D13—44no—
349C22⋊D13—44no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—24no—
355C2×Dic13—24no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13C23×C412yes—
361C2×Dic13C23×C412yes—
362C2×Dic13C23×C412yes—
363C2×Dic13C23×C412yes—
364C2×Dic13C23×C411yescharacteristic
365C2×Dic13H(5,𝔽2)12yes—
366C2×Dic13H(5,𝔽2)12yes—
367C2×Dic13C2511yescharacteristic
368D52—28no—
369D52—44no—
370C4×D13—24no—
371C4×D13—24no—
372C4×D13—24no—
373C4×D13—22no—
374C4×D13—22no—
375C4×D13—22no—
376C4×D13—22no—
377C4×D13—22no—
378C4×D13—22no—
379C4×D13—44no—
380C4×D13—44no—
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#26111yescharacteristic
404C2×C22⋊Q8—131no—
405C2×C22⋊Q8—131no—
406C2×#121—131no—
407C2×#121—131no—
408C2×#120—131no—
409C2×#120—131no—
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—22no—
451C22×C13—22no—
452C22×C13—22no—
453C22×C13—22no—
454C22×C13—22no—
455C22×C13—44no—
456C22×C13—44no—
457C22×C13#51812yes—
458C22×C13C2×#13112yes—
459C22×C13#56812yes—
460C22×C13C24×C411yescharacteristic
461C2×D13—22no—
462C2×D13—28no—
463C2×D13—22no—
464C2×D13—22no—
465C2×D13—22no—
466C2×D13—22no—
467C2×D13—22no—
468C2×D13—22no—
469C2×D13—22no—
470C2×D13—416no—
471C2×D13—44no—
472C2×D13—44no—
473C2×D13C2×#13114yes—
474C4×C13—22no—
475C4×C13—22no—
476C4×C13—22no—
477C4×C13—22no—
478C4×C13—22no—
479Dic13—22no—
480Dic13—22no—
481Dic13—22no—
482Dic13—22no—
483Dic13#51812yes—
484Dic13C2×H(5,𝔽2)11yescharacteristic
485Dic13C2×H(5,𝔽2)11yescharacteristic
486C25—131no—
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×D4—131no—
497C22×D4—131no—
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—522no—
509C23×C4—522no—
510C23×C4C2×#26111yescharacteristic
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#123C2×#26118yes—
537C22⋊Q8—138no—
538C22⋊Q8—138no—
539#121—138no—
540#121—138no—
541#120—138no—
542#120—138no—
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⋊C4C2×#26111yescharacteristic
558C2×C4⋊C4C2×#26111yescharacteristic
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—42no—
592C2×C13—42no—
593C2×C13#297614yescomplemented
594C2×C13C2×#51811yescharacteristic
595C2×C13C22×#13111yescharacteristic
596C2×C13C2×#56811yescharacteristic
597D13—24no—
598D13—42no—
599D13—42no—
600C24—131no—
601C24—131no—
602C24—131no—
603C24—134no—
604C24—264no—
605C24—522no—
606C24—522no—
607C24C22×#26111yescharacteristic
608C24C22×#26111yescharacteristic
609#41—524no—
610#41—524no—
611#41—528no—
612C2×Q8—134no—
613C2×Q8—522no—
614C2×D4—42no—
615C2×D4—134no—
616C2×D4—134no—
617C2×D4—134no—
618C2×D4—134no—
619C2×D4—134no—
620C2×D4—134no—
621C2×D4—264no—
622C2×D4—264no—
623C2×D4—522no—
624C2×D4—522no—
625C2×D4—522no—
626C2×D4—522no—
627C2×D4C22×#26114yes—
628C22×C4—42no—
629C22×C4—131no—
630C22×C4—132no—
631C22×C4—132no—
632C22×C4—132no—
633C22×C4—132no—
634C22×C4—131no—
635C22×C4—131no—
636C22×C4—131no—
637C22×C4—131no—
638C22×C4—132no—
639C22×C4—132no—
640C22×C4—132no—
641C22×C4—132no—
642C22×C4—132no—
643C22×C4—132no—
644C22×C4—134no—
645C22×C4—134no—
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—522no—
657C22×C4—522no—
658C22×C4—524no—
659C22×C4—524no—
660C22×C4—528no—
661C22×C4C22×#26111yescharacteristic
662C22×C4C22×#26111yescharacteristic
663C22×C4C22×#26111yescharacteristic
664C22×C4C22×#26111yescharacteristic
665C22×C4C22×#26111yescharacteristic
666C22×C4C22×#26114yes—
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⋊C4C22×#26114yes—
696C4⋊C4C22×#26114yes—
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—22no—
716C23—22no—
717C23—22no—
718C23—134no—
719C23—132no—
720C23—132no—
721C23—132no—
722C23—268no—
723C23—262no—
724C23—262no—
725C23—262no—
726C23—262no—
727C23—262no—
728C23—262no—
729C23—262no—
730C23—262no—
731C23—524no—
732C23—524no—
733C23—5216no—
734C23C23×#26112yes—
735C23C23×#26112yes—
736C23C23×#26111yescharacteristic
737Q8—524no—
738D4—44no—
739D4—268no—
740D4—268no—
741D4—524no—
742D4—524no—
743D4—524no—
744D4—524no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—44no—
751C2×C4—132no—
752C2×C4—132no—
753C2×C4—131no—
754C2×C4—131no—
755C2×C4—132no—
756C2×C4—132no—
757C2×C4—132no—
758C2×C4—132no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—264no—
766C2×C4—264no—
767C2×C4—264no—
768C2×C4—262no—
769C2×C4—262no—
770C2×C4—264no—
771C2×C4—262no—
772C2×C4—262no—
773C2×C4—264no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—524no—
779C2×C4—524no—
780C2×C4C23×#26112yes—
781C2×C4C23×#26112yes—
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—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—134no—
802C22—262no—
803C22—262no—
804C22—268no—
805C22—262no—
806C22—262no—
807C22—262no—
808C22—262no—
809C22—262no—
810C22—262no—
811C22—5216no—
812C22—524no—
813C22—524no—
814C22#1171962312yes—
815C22D13⋊#13112yes—
816C22#1171962912yes—
817C22C24×#26111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—132no—
824C4—131no—
825C4—131no—
826C4—262no—
827C4—262no—
828C4—262no—
829C4—262no—
830C2—42no—
831C2—42no—
832C2—264no—
833C2—522no—
834C2—522no—
835C2#1313170414yesdirect product factor
836C2C2×#1171962311yescharacteristic
837C2C2×D13⋊#13111yescharacteristic
838C2C2×#1171962911yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#123C4
socleC23×C13C23×C4
prime radicalC2×#11719361C2
cosocleC2×Dic13C25
hypercenterC2×#123#261
hypocenterC13C2×#2976
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #13131704C2direct (N × H)
2. C2×#11719076C2semidirect
3. C2×#11719066C2semidirect
4. C2×#11719065C2semidirect
5. C2×#11719075C2semidirect
6. C2×#11719075C2semidirect
7. C2×#11719064C2semidirect
8. C2×#11719073C2semidirect
9. C2×#11719063C2semidirect
10. C2×#11719068C2semidirect
11. C2×#11719068C2semidirect
12. C2×#11719147C2semidirect
13. C2×#11719146C2semidirect
14. C2×#11719127C2semidirect
15. C2×D13⋊(C22⋊C8)C2semidirect
19. C22×#6122C22semidirect
20. C23×#1057C22semidirect
23. C22×#6118C22semidirect
26. C22×D13⋊C8C22semidirect
46. C2×C22⋊#1057C22semidirect
47. C2×C22⋊#1057C22semidirect
48. #11719147C22semidirect
49. #11719146C22semidirect
50. #11719127C22semidirect
51. D13⋊(C22⋊C8)C22semidirect
52. C2×#88112C22semidirect
53. C2×#88112C22semidirect
58. C2×#88111C22semidirect
59. C2×#88111C22semidirect
60. C2×#88110C22semidirect
61. C2×#88110C22semidirect
62. C2×C4⋊#1057C22semidirect
63. C2×C4⋊#1057C22semidirect
64. C2×C4×#1057C22semidirect
65. C2×C4×#1057C22semidirect
66. #11719076C22semidirect
67. #11719075C22semidirect
68. #11719075C22semidirect
69. #11719073C22semidirect
70. #11719068C22semidirect
71. #11719068C22semidirect
72. #11719066C22semidirect
73. #11719065C22semidirect
74. #11719064C22semidirect
75. #11719063C22semidirect
102. C2×#6122C23semidirect
112. C22×#1057C23semidirect
118. C2×#6118C23semidirect
124. C2×D13⋊C8C23semidirect
165. C22⋊#1057C23semidirect
166. C22⋊#1057C23semidirect
167. #88112C23semidirect
168. #88112C23semidirect
173. #88111C23semidirect
174. #88111C23semidirect
175. #88110C23semidirect
176. #88110C23semidirect
177. C4⋊#1057C23semidirect
178. C4⋊#1057C23semidirect
179. C4×#1057C23semidirect
180. C4×#1057C23semidirect
593. C2×C13#2976semidirect
711. C13C2×#2976semidirect
835. C2#13131704direct (N × H)

Maximal subgroups

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

subgroupindex
#131317042
C2×#117190762
C2×#117190662
C2×#117190652
C2×#117190752
C2×#117190642
C2×#117190732
C2×#117190632
C2×#117190682
C2×#117191472
C2×#117191462
C2×#117191272
C2×D13⋊(C22⋊C8)2
C2×#117193612
C2×#297613