Finite Group Databasebeta

← C2×#13131658 #16808474

Subgroups — C2×#13131658 #16808474

Order 3328.

1970 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131658C2116yesmaximal, direct product factor
2C2×#11719078C211yesmaximal, characteristic, complemented
3C2×#11719080C211yesmaximal, characteristic, complemented
4C2×#11719145C211yesmaximal, characteristic, complemented
5C2×#11719066C211yesmaximal, characteristic, complemented
6C2×#11719065C211yesmaximal, characteristic, complemented
7C2×#11719065C211yesmaximal, characteristic, complemented
8C2×#11719144C211yesmaximal, characteristic, complemented
9C2×#11719064C211yesmaximal, characteristic, complemented
10C2×#11719077C211yesmaximal, characteristic, complemented
11C2×#11719068C211yesmaximal, characteristic, complemented
12C2×#11719130C211yesmaximal, characteristic, complemented
13C2×#11719072C211yesmaximal, characteristic, complemented
14C2×#11719062C211yesmaximal, characteristic, complemented
15C2×C4×#6122C211yesmaximal, characteristic, complemented
16C2×#11719354C211yesmaximal, characteristic
17C22×#6122C2211yescharacteristic
18C22×#6122C2211yescharacteristic
19C22×#6122C2211yescharacteristic
20C23×#1057C2211yescharacteristic
21C22×#6118C2211yescharacteristic
22C22×D13⋊C8C2211yescharacteristic
23C2×C13×#123C411yescharacteristic
24C2×#88193C411yescharacteristic
25C2×D4×Dic13C2211yescharacteristic
26C2×#88183C411yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28#11719354C418yes—
29#11719354C2218yes—
30C2×#88152C411yescharacteristic
31C2×#88146C2211yescharacteristic
32C2×#88143C411yescharacteristic
33C2×#88141C2211yescharacteristic
34C2×#88139C411yescharacteristic
35C2×#88135C2211yescharacteristic
36C2×#88135C2211yescharacteristic
37C2×#88133C411yescharacteristic
38C2×#88132C411yescharacteristic
39C2×#88131C2211yescharacteristic
40C2×C22⋊#1057C2211yescharacteristic
41C2×C22⋊#1057C2211yescharacteristic
42C2×C22⋊#1057C2211yescharacteristic
43C2×C22⋊#1057C2211yescharacteristic
44#11719145C2218yescomplemented
45#11719144C2218yescomplemented
46#11719130C2218yescomplemented
47C2×#88112C2211yescharacteristic
48C2×#88112C2211yescharacteristic
49C2×#88111C2211yescharacteristic
50C2×#88111C2211yescharacteristic
51C4×#6122C2218yescomplemented
52C2×#88110C2211yescharacteristic
53C2×#88110C2211yescharacteristic
54C2×#88110C2211yescharacteristic
55C2×#88110C2211yescharacteristic
56C2×#88110C2211yescharacteristic
57C2×#88110C2211yescharacteristic
58C2×C4⋊#1057C2211yescharacteristic
59C2×C4⋊#1057C2211yescharacteristic
60C2×C4⋊#1057C2211yescharacteristic
61C2×C4⋊#1057C2211yescharacteristic
62C2×C4×#1057C2211yescharacteristic
63C2×C4×#1057C2211yescharacteristic
64C2×C4×#1057C2211yescharacteristic
65C2×C4×#1057C2211yescharacteristic
66#11719080C2218yescomplemented
67#11719078C2218yescomplemented
68#11719077C2218yescomplemented
69#11719072C2218yescomplemented
70#11719068C2218yescomplemented
71#11719066C2218yescomplemented
72#11719065C2218yescomplemented
73#11719065C2218yescomplemented
74#11719064C2218yescomplemented
75#11719062C2218yescomplemented
76C22×D4×C13C2×C411yescharacteristic
77C23×C4×C13C2×C411yescharacteristic
78C22×C22⋊D13C2×C411yescharacteristic
79C22×C22⋊D13C2×C411yescharacteristic
80C23×Dic13C2×C411yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C22×C4×D13C2311yescharacteristic
84C22×Dic26C2×C411yescharacteristic
85C2×#6122—24no—
86C2×#6122—24no—
87C2×#6122—24no—
88C2×#6122C2314yes—
89C2×#6122C2314yes—
90C2×#6122C2314yes—
91C22×#1057—24no—
92C22×#1057C2311yescharacteristic
93C22×#1057C2311yescharacteristic
94C22×#1057C2311yescharacteristic
95C22×#1057C2311yescharacteristic
96C22×#1057C2311yescharacteristic
97C22×#1057C2311yescharacteristic
98C22×#1057C2314yes—
99C22×#1057C2311yescharacteristic
100C22×#1057C2311yescharacteristic
101C2×#6118—24no—
102C2×#6118C2314yes—
103C2×D13⋊C8—24no—
104C2×D13⋊C8C2314yes—
105C13×#123C2×C418yes—
106C2×C13×C4⋊C4C2×C411yescharacteristic
107C2×C13×C4⋊C4C2×C411yescharacteristic
108C2×C13×C22⋊C4C2×C411yescharacteristic
109C2×C13×C22⋊C4C2×C411yescharacteristic
110C2×C13×C22⋊C4C2×C411yescharacteristic
111C2×C22⋊Dic13C2×C411yescharacteristic
112C2×C22⋊Dic13C2×C411yescharacteristic
113C2×C22⋊Dic13C2×C411yescharacteristic
114#88193C2×C418yes—
115D4×Dic13C2×C414yes—
116D4×Dic13C2314yes—
117#88183C2×C418yes—
118C2×#6103C2×C411yescharacteristic
119C2×#6103C2×C411yescharacteristic
120C2×#6103C2×C411yescharacteristic
121C2×#6103C2×C411yescharacteristic
122C2×C4⋊Dic13C2×C411yescharacteristic
123C2×C4⋊Dic13C2×C411yescharacteristic
124C2×#6101C2×C411yescharacteristic
125C2×#6101C2×C411yescharacteristic
126C2×#6101C2×C411yescharacteristic
127C2×#6101C2×C411yescharacteristic
128C2×#6101C2×C411yescharacteristic
129C2×#6101C2×C411yescharacteristic
130C2×C4×Dic13C2×C411yescharacteristic
131C2×C4×Dic13C2×C411yescharacteristic
132C2×C4×Dic13C2×C414yes—
133C2×C4×Dic13C2311yescharacteristic
134C2×C4×Dic13C2311yescharacteristic
135C2×C4×Dic13C2311yescharacteristic
136C2×C4×Dic13C2311yescharacteristic
137C2×C4×Dic13C2314yes—
138#88152C2×C418yes—
139#88146C2×C414yes—
140#88146C2314yes—
141#88143C2×C418yes—
142#88141C2×C414yes—
143#88141C2314yes—
144#88139C2×C418yes—
145#88135C2×C414yes—
146#88135C2×C414yes—
147#88135C2314yes—
148#88135C2314yes—
149#88133C2×C418yes—
150#88132C2×C418yes—
151#88131C2×C414yes—
152#88131C2314yes—
153C22⋊#1057C2314yes—
154C22⋊#1057C2314yes—
155C22⋊#1057C2314yes—
156C22⋊#1057C2314yes—
157#88112C2314yes—
158#88112C2314yes—
159#88111C2314yes—
160#88111C2314yes—
161#88110C2314yes—
162#88110C2314yes—
163#88110C2314yes—
164#88110C2314yes—
165#88110C2314yes—
166#88110C2314yes—
167C4⋊#1057C2314yes—
168C4⋊#1057C2314yes—
169C4⋊#1057C2314yes—
170C4⋊#1057C2314yes—
171C4×#1057C2314yes—
172C4×#1057C2314yes—
173C4×#1057C2314yes—
174C4×#1057C2314yes—
175C2×#2967—131nomaximal, Sylow
176C24×C13C22×C411yescharacteristic
177C24×C13C22×C411yescharacteristic
178C23×D13C22×C411yescharacteristic
179C2×D4×C13—42no—
180C2×D4×C13C22×C414yes—
181C22×C4×C13—42no—
182C22×C4×C13C22×C411yescharacteristic
183C22×C4×C13C22×C411yescharacteristic
184C22×C4×C13C22×C411yescharacteristic
185C22×C4×C13C22×C411yescharacteristic
186C22×C4×C13C22×C411yescharacteristic
187C22×C4×C13C22×C414yes—
188C2×C22⋊D13—42no—
189C2×C22⋊D13—42no—
190C2×C22⋊D13C22×C414yes—
191C2×C22⋊D13C22×C414yes—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—42no—
197C22×Dic13C22×C412yes—
198C22×Dic13C22×C412yes—
199C22×Dic13C22×C411yescharacteristic
200C22×Dic13C22×C411yescharacteristic
201C22×Dic13C22×C411yescharacteristic
202C22×Dic13C22×C411yescharacteristic
203C22×Dic13C22×C411yescharacteristic
204C22×Dic13C22×C411yescharacteristic
205C22×Dic13C22×C414yes—
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2411yescharacteristic
209C2×C4×D13—22no—
210C2×C4×D13—22no—
211C2×C4×D13C22×C412yes—
212C2×C4×D13C2412yes—
213C2×Dic26—42no—
214C2×Dic26C22×C414yes—
215#6122—28no—
216#6122—28no—
217#6122—28no—
218C2×#1057—22no—
219C2×#1057—22no—
220C2×#1057—22no—
221C2×#1057—22no—
222C2×#1057—22no—
223C2×#1057—22no—
224C2×#1057—28no—
225C2×#1057#4114yes—
226C2×#1057#4114yes—
227C2×#1057C2412yes—
228C2×#1057C2412yes—
229C2×#1057C2412yes—
230C2×#1057C2412yes—
231C2×#1057C2412yes—
232C2×#1057C2412yes—
233C2×#1057C2412yes—
234C2×#1057C2412yes—
235#6118—28no—
236D13⋊C8—28no—
237C13×C4⋊C4C22×C414yes—
238C13×C4⋊C4C22×C414yes—
239C13×C22⋊C4C22×C414yes—
240C13×C22⋊C4C22×C414yes—
241C13×C22⋊C4C22×C414yes—
242C22⋊Dic13C22×C414yes—
243C22⋊Dic13C22×C414yes—
244C22⋊Dic13C22×C414yes—
245#6103C22×C414yes—
246#6103C22×C414yes—
247#6103C22×C414yes—
248#6103C22×C414yes—
249C4⋊Dic13C22×C414yes—
250C4⋊Dic13C22×C414yes—
251#6101C22×C414yes—
252#6101C22×C414yes—
253#6101C22×C414yes—
254#6101C22×C414yes—
255#6101C22×C414yes—
256#6101C22×C414yes—
257C4×Dic13C22×C412yes—
258C4×Dic13C22×C412yes—
259C4×Dic13C22×C414yes—
260C4×Dic13C22×C412yes—
261C4×Dic13C22×C414yes—
262C4×Dic13C22×C412yes—
263C4×Dic13C2412yes—
264C4×Dic13C2412yes—
265C4×Dic13C2412yes—
266C4×Dic13C2412yes—
267C2×#529—131no—
268#2967—1316no—
269C2×#446—131no—
270C2×#446—131no—
271C2×#436—131no—
272C2×#436—131no—
273C2×#435—131no—
274C2×#435—131no—
275C2×#435—131no—
276C2×#435—131no—
277C2×#433—131no—
278C2×#433—131no—
279C2×#432—131no—
280C2×#405—131no—
281C2×#405—131no—
282C2×C4×M16—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13C23×C412yes—
290C23×C13C23×C412yes—
291C23×C13C23×C411yescharacteristic
292C22×D13—22no—
293C22×D13—22no—
294C22×D13—22no—
295C22×D13C23×C412yes—
296D4×C13—44no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—44no—
303C2×C4×C13C23×C412yes—
304C2×C4×C13C23×C412yes—
305C2×C4×C13C23×C412yes—
306C2×C4×C13C23×C412yes—
307C2×C4×C13C23×C412yes—
308C22⋊D13—44no—
309C22⋊D13—44no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—24no—
317C2×Dic13—24no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—44no—
323C2×Dic13C23×C412yes—
324C2×Dic13C23×C412yes—
325C2×Dic13C23×C412yes—
326C2×Dic13C23×C412yes—
327C2×Dic13C23×C412yes—
328C2×Dic13C23×C412yes—
329C2×Dic13C23×C411yescharacteristic
330C2×Dic13C2×#4112yes—
331C2×Dic13C2×#4112yes—
332C2×Dic13C2511yescharacteristic
333C4×D13—24no—
334C4×D13—22no—
335C4×D13—22no—
336Dic26—44no—
337#1057—22no—
338#1057—22no—
339#1057—22no—
340#1057—22no—
341#1057—22no—
342#1057—22no—
343#1057C2×#4114yes—
344#1057C2×#4114yes—
345C22×M16—131no—
346C22×M16—131no—
347C22×M16—131no—
348C22×M16—131no—
349C23×C8—131no—
350C23×C8—131no—
351#529—138no—
352#529—138no—
353C2×#126—131no—
354C2×#126—131no—
355C2×#125—131no—
356C2×#124—131no—
357C2×#123—131no—
358C2×#123#26111yescharacteristic
359C2×C22⋊Q8—131no—
360C2×#121—131no—
361C2×C4×Q8—131no—
362C2×C4×D4—131no—
363C2×C4×D4—131no—
364C2×C4×D4—131no—
365C2×#117—131no—
366C2×#117—131no—
367C22×C42—131no—
368#446—138no—
369#446—138no—
370#436—138no—
371#436—138no—
372#435—138no—
373#435—138no—
374#435—138no—
375#435—138no—
376#433—138no—
377#433—138no—
378#432—138no—
379C2×C4⋊C8—131no—
380C2×C4⋊C8—131no—
381C2×C4⋊C8—131no—
382C2×C4⋊C8—131no—
383C2×C4⋊C8—131no—
384C2×C4⋊C8—131no—
385C2×C22⋊C8—131no—
386C2×C22⋊C8—131no—
387C2×C22⋊C8—131no—
388C2×C22⋊C8—131no—
389C2×C22⋊C8—131no—
390C2×C22⋊C8—131no—
391#405—138no—
392#405—138no—
393C4×M16—138no—
394C2×#97—131no—
395C2×#97—131no—
396C2×#97—131no—
397C2×#97—131no—
398C2×#97—131no—
399C2×#97—131no—
400C2×C4×C8—131no—
401C2×C4×C8—131no—
402C2×C4×C8—131no—
403C2×C4×C8—131no—
404C22×C13—22no—
405C22×C13—22no—
406C22×C13—22no—
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—44no—
411C22×C13—44no—
412C22×C13C4×#4112yes—
413C22×C13#56812yes—
414C22×C13#56812yes—
415C22×C13C24×C411yescharacteristic
416C2×D13—22no—
417C2×D13—22no—
418C2×D13—22no—
419C2×D13—44no—
420C4×C13—22no—
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—22no—
424C4×C13—22no—
425Dic13—22no—
426Dic13—22no—
427Dic13—22no—
428Dic13—22no—
429Dic13—22no—
430Dic13—22no—
431Dic13C4×#4112yes—
432Dic13C22×#4111yescharacteristic
433Dic13C22×#4111yescharacteristic
434C22×Q8—131no—
435C22×D4—131no—
436C22×D4—131no—
437C22×D4C2×#26111yescharacteristic
438C23×C4—131no—
439C23×C4—131no—
440C23×C4—131no—
441C23×C4—131no—
442C23×C4C2×#26111yescharacteristic
443C2×M16—134no—
444C2×M16—134no—
445C2×M16—134no—
446C2×M16—134no—
447C2×M16—264no—
448C2×M16—264no—
449C2×M16—264no—
450C2×M16—264no—
451C22×C8—131no—
452C22×C8—131no—
453C22×C8—131no—
454C22×C8—131no—
455C22×C8—134no—
456C22×C8—134no—
457C22×C8—131no—
458C22×C8—131no—
459C22×C8—131no—
460C22×C8—131no—
461C22×C8—264no—
462C22×C8—264no—
463#126—138no—
464#126—138no—
465#125—138no—
466#124—138no—
467#123—138no—
468#123C2×#26118yes—
469C22⋊Q8—138no—
470#121—138no—
471C4×Q8—134no—
472C4×Q8—134no—
473C4×D4—134no—
474C4×D4—134no—
475C4×D4—134no—
476C4×D4—134no—
477C4×D4—134no—
478C4×D4—134no—
479#117—134no—
480#117—134no—
481#117—134no—
482#117—134no—
483C2×C4⋊C4—131no—
484C2×C4⋊C4—131no—
485C2×C4⋊C4—131no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—131no—
491C2×C4⋊C4C2×#26111yescharacteristic
492C2×C4⋊C4C2×#26111yescharacteristic
493C2×C22⋊C4—131no—
494C2×C22⋊C4—131no—
495C2×C22⋊C4—131no—
496C2×C22⋊C4—131no—
497C2×C22⋊C4—131no—
498C2×C22⋊C4—131no—
499C2×C22⋊C4—131no—
500C2×C22⋊C4C2×#26111yescharacteristic
501C2×C22⋊C4C2×#26111yescharacteristic
502C2×C22⋊C4C2×#26111yescharacteristic
503C2×C42—131no—
504C2×C42—131no—
505C2×C42—131no—
506C2×C42—131no—
507C2×C42—131no—
508C2×C42—131no—
509C2×C42—134no—
510C2×C42—134no—
511C4⋊C8—134no—
512C4⋊C8—134no—
513C4⋊C8—134no—
514C4⋊C8—134no—
515C4⋊C8—134no—
516C4⋊C8—134no—
517C22⋊C8—134no—
518C22⋊C8—134no—
519C22⋊C8—134no—
520C22⋊C8—134no—
521C22⋊C8—134no—
522C22⋊C8—134no—
523#97—134no—
524#97—134no—
525#97—134no—
526#97—134no—
527#97—134no—
528#97—134no—
529C4×C8—134no—
530C4×C8—134no—
531C4×C8—134no—
532C4×C8—134no—
533C2×C13—42no—
534C2×C13—42no—
535C2×C13#296714yescomplemented
536C2×C13C2×C4×#4111yescharacteristic
537C2×C13C2×#56811yescharacteristic
538C2×C13C2×#56811yescharacteristic
539D13—42no—
540C24—131no—
541C24C22×#26111yescharacteristic
542C24C22×#26111yescharacteristic
543C2×Q8—134no—
544C2×Q8—522no—
545C2×D4—42no—
546C2×D4—134no—
547C2×D4—134no—
548C2×D4—522no—
549C2×D4—522no—
550C2×D4C22×#26114yes—
551C22×C4—42no—
552C22×C4—131no—
553C22×C4—132no—
554C22×C4—132no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—131no—
558C22×C4—131no—
559C22×C4—131no—
560C22×C4—131no—
561C22×C4—131no—
562C22×C4—131no—
563C22×C4—134no—
564C22×C4—132no—
565C22×C4—132no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—522no—
573C22×C4C22×#26111yescharacteristic
574C22×C4C22×#26111yescharacteristic
575C22×C4C22×#26111yescharacteristic
576C22×C4C22×#26111yescharacteristic
577C22×C4C22×#26111yescharacteristic
578C22×C4C22×#26114yes—
579M16—268no—
580M16—268no—
581M16—268no—
582M16—268no—
583C2×C8—132no—
584C2×C8—132no—
585C2×C8—134no—
586C2×C8—134no—
587C2×C8—132no—
588C2×C8—132no—
589C2×C8—132no—
590C2×C8—132no—
591C2×C8—132no—
592C2×C8—132no—
593C2×C8—268no—
594C2×C8—268no—
595C2×C8—262no—
596C2×C8—262no—
597C2×C8—262no—
598C2×C8—262no—
599C2×C8—262no—
600C2×C8—262no—
601C4⋊C4—134no—
602C4⋊C4—134no—
603C4⋊C4—134no—
604C4⋊C4—134no—
605C4⋊C4—134no—
606C4⋊C4—134no—
607C4⋊C4—134no—
608C4⋊C4—134no—
609C4⋊C4C22×#26114yes—
610C4⋊C4C22×#26114yes—
611C22⋊C4—134no—
612C22⋊C4—134no—
613C22⋊C4—134no—
614C22⋊C4—134no—
615C22⋊C4—134no—
616C22⋊C4—134no—
617C22⋊C4—134no—
618C22⋊C4C22×#26114yes—
619C22⋊C4C22×#26114yes—
620C22⋊C4C22×#26114yes—
621C42—132no—
622C42—132no—
623C42—132no—
624C42—132no—
625C42—132no—
626C42—132no—
627C42—134no—
628C42—134no—
629C42—132no—
630C42—132no—
631C13C2×#296711yescharacteristic, complemented, Sylow
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—132no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23C23×#26112yes—
643C23C23×#26112yes—
644C23C23×#26111yescharacteristic
645Q8—524no—
646D4—44no—
647D4—524no—
648D4—524no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—44no—
655C2×C4—132no—
656C2×C4—132no—
657C2×C4—131no—
658C2×C4—131no—
659C2×C4—132no—
660C2×C4—132no—
661C2×C4—132no—
662C2×C4—132no—
663C2×C4—132no—
664C2×C4—132no—
665C2×C4—262no—
666C2×C4—262no—
667C2×C4—264no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—262no—
671C2×C4—262no—
672C2×C4—264no—
673C2×C4—264no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—524no—
681C2×C4C23×#26112yes—
682C2×C4C23×#26112yes—
683C2×C4C23×#26112yes—
684C2×C4C23×#26112yes—
685C2×C4C23×#26112yes—
686C8—134no—
687C8—134no—
688C8—262no—
689C8—262no—
690C8—262no—
691C8—262no—
692C8—262no—
693C8—262no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—44no—
702C22—262no—
703C22—262no—
704C22—262no—
705C22—524no—
706C22#1171962112yes—
707C22#1171962912yes—
708C22#41×#26112yes—
709C22C24×#26111yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—132no—
716C4—131no—
717C4—131no—
718C4—262no—
719C4—262no—
720C4—262no—
721C4—262no—
722C4—262no—
723C4—262no—
724C2—42no—
725C2—42no—
726C2—522no—
727C2#1313165814yesdirect product factor
728C2C2×#41×#26111yescharacteristic
729C2C2×#1171962111yescharacteristic
730C2C2×#1171962911yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#123C4
socleC23×C13C23×C4
prime radicalC2×#88193C4
cosocleC2×Dic13C25
hypercenterC2×#123#261
hypocenterC13C2×#2967
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #13131658C2direct (N × H)
2. C2×#11719078C2semidirect
3. C2×#11719080C2semidirect
4. C2×#11719145C2semidirect
5. C2×#11719066C2semidirect
6. C2×#11719065C2semidirect
7. C2×#11719065C2semidirect
8. C2×#11719144C2semidirect
9. C2×#11719064C2semidirect
10. C2×#11719077C2semidirect
11. C2×#11719068C2semidirect
12. C2×#11719130C2semidirect
13. C2×#11719072C2semidirect
14. C2×#11719062C2semidirect
15. C2×C4×#6122C2semidirect
44. #11719145C22semidirect
45. #11719144C22semidirect
46. #11719130C22semidirect
51. C4×#6122C22semidirect
66. #11719080C22semidirect
67. #11719078C22semidirect
68. #11719077C22semidirect
69. #11719072C22semidirect
70. #11719068C22semidirect
71. #11719066C22semidirect
72. #11719065C22semidirect
73. #11719065C22semidirect
74. #11719064C22semidirect
75. #11719062C22semidirect
535. C2×C13#2967semidirect
631. C13C2×#2967semidirect
727. C2#13131658direct (N × H)

Maximal subgroups

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

subgroupindex
#131316582
C2×#117190782
C2×#117190802
C2×#117191452
C2×#117190662
C2×#117190652
C2×#117191442
C2×#117190642
C2×#117190772
C2×#117190682
C2×#117191302
C2×#117190722
C2×#117190622
C2×C4×#61222
C2×#117193542
C2×#296713