Finite Group Databasebeta

← C2×#13129328 #16770754

Subgroups — C2×#13129328 #16770754

Order 3328.

6338 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129328C2132yesmaximal, direct product factor
2C2×C13⋊#564C214yesmaximal, complemented
3C2×#11719275C211yesmaximal, characteristic, complemented
4C2×#11719272C211yesmaximal, characteristic, complemented
5C2×#11719272C212yesmaximal, complemented
6C2×#11719390C212yesmaximal, complemented
7C2×#11719274C212yesmaximal, complemented
8C2×#11719426C212yesmaximal, complemented
9C2×#11719426C211yesmaximal, characteristic, complemented
10C2×#11719402C212yesmaximal
11C2×#11719436C212yesmaximal
12C2×#11719401C214yesmaximal
13C2×#11719288C212yesmaximal
14C2×#11719288C212yesmaximal
15C2×#11719433C211yesmaximal, characteristic
16C2×#11719283C211yesmaximal, characteristic
17C2×#11719283C211yesmaximal, characteristic
18C2×C13×#557C211yesmaximal, characteristic, complemented
19C13×#557C22116yescomplemented
20C2×C13×C4⋊Q8C2212yes—
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×#125C2214yes—
23C2×C13×#125C2212yes—
24C2×C4×Q8×C13C2212yes—
25C2×C4×Q8×C13C2212yes—
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×#88200C2211yescharacteristic
29C2×#88200C2212yes—
30C2×#88200C2211yescharacteristic
31C2×Q8×Dic13C2212yes—
32C2×Q8×Dic13C2212yes—
33C2×Q8×Dic13C2212yes—
34C2×#88198C2212yes—
35C2×#88198C2212yes—
36C2×#88198C2211yescharacteristic
37C2×#88198C2211yescharacteristic
38#11719436C22132yes—
39#11719433C22116yes—
40#11719426C22116yescomplemented
41#11719426C22132yescomplemented
42#11719402C22132yes—
43#11719401C22164yes—
44C13⋊#564C22164yescomplemented
45#11719390C22132yescomplemented
46#11719288C22132yes—
47#11719288C22132yes—
48#11719283C22116yes—
49#11719283C22116yes—
50#11719275C22116yescomplemented
51#11719274C22132yescomplemented
52#11719272C22116yescomplemented
53#11719272C22132yescomplemented
54C2×#88152C2214yes—
55C2×#88152C2214yes—
56C2×#88152C2214yes—
57C2×#88151C2211yescharacteristic
58C2×#88151C2212yes—
59C2×#88151C2211yescharacteristic
60C2×#88150C2212yes—
61C2×#88150C2212yes—
62C2×#88146C2212yes—
63C2×#88144C2212yes—
64C2×#88144C2212yes—
65C2×#88144C2214yes—
66C2×#88144C2214yes—
67C2×#88144C2214yes—
68C2×#88144C2212yes—
69C2×#88143C2214yes—
70C2×#88143C2214yes—
71C2×#88143C2214yes—
72C2×#88143C2214yes—
73C2×#88143C2214yes—
74C2×#88143C2214yes—
75C2×#88143C2214yes—
76C2×#88143C2212yes—
77C2×#88143C2212yes—
78C2×#88142C2214yes—
79C2×#88142C2211yescharacteristic
80C2×#88142C2211yescharacteristic
81C2×#88141C2214yes—
82C2×#88141C2212yes—
83C2×#88141C2212yes—
84C2×#88141C2212yes—
85C2×#88130C2214yes—
86C2×#88126C2212yes—
87C2×#88126C2212yes—
88C2×C42×D13C2211yescharacteristic
89C2×#88124C2214yes—
90C2×#88124C2214yes—
91C2×#88124C2212yes—
92C2×#88123C2212yes—
93C2×#88123C2211yescharacteristic
94C2×C4×Dic26C2212yes—
95C2×C4×Dic26C2212yes—
96C2×C4×Dic26C2214yes—
97C2×C4×Dic26C2212yes—
98C2×C4×Dic26C2211yescharacteristic
99C2×C4×Dic26C2211yescharacteristic
100C2×C4×Dic26C2212yes—
101C22×Q8×C13C2311yescharacteristic
102C22×Q8×C13C2312yes—
103C22×Q8×C13C2311yescharacteristic
104C22×C4×D13C2311yescharacteristic
105C22×C4×D13C2311yescharacteristic
106C22×C4×D13C2311yescharacteristic
107C22×Dic26C2312yes—
108C22×Dic26C2311yescharacteristic
109C22×Dic26C2312yes—
110C22×Dic26C2311yescharacteristic
111C22×Dic26C2312yes—
112C13×C4⋊Q8C2318yes—
113C13×C4⋊Q8C23116yes—
114C13×#125C23116yes—
115C13×#125C23132yes—
116C4×Q8×C13C2318yes—
117C4×Q8×C13C23116yes—
118C4×Q8×C13C23116yes—
119C4×Q8×C13C2318yes—
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C4⋊C4C2312yes—
122C2×C13×C4⋊C4C2314yes—
123C2×C13×C4⋊C4C2314yes—
124C2×C13×C4⋊C4C2311yescharacteristic
125C2×C13×C4⋊C4C2312yes—
126C2×C13×C4⋊C4C2314yes—
127C2×C13×C4⋊C4C2312yes—
128C2×C13×C4⋊C4C2312yes—
129C2×C42×C13C2311yescharacteristic
130C2×C42×C13C2312yes—
131C2×C42×C13C2312yes—
132C2×C42×C13C2314yes—
133#88200C23116yes—
134#88200C2318yes—
135#88200C2318yes—
136Q8×Dic13C23116yes—
137Q8×Dic13C23116yes—
138Q8×Dic13C23116yes—
139#88198C2318yes—
140#88198C23116yes—
141#88198C2318yes—
142#88198C23116yes—
143C2×#6103C2312yes—
144C2×#6103C2312yes—
145C2×#6103C2312yes—
146C2×#6103C2312yes—
147C2×#6103C2314yes—
148C2×C4⋊Dic13C2311yescharacteristic
149C2×C4⋊Dic13C2314yes—
150C2×C4⋊Dic13C2312yes—
151C2×C4⋊Dic13C2311yescharacteristic
152C2×C4⋊Dic13C2312yes—
153C2×C4⋊Dic13C2312yes—
154C2×C4⋊Dic13C2312yes—
155C2×C4⋊Dic13C2314yes—
156C2×C4⋊Dic13C2314yes—
157C2×C4⋊Dic13C2314yes—
158C2×#6101C2312yes—
159C2×#6101C2312yes—
160C2×#6101C2314yes—
161C2×#6101C2314yes—
162C2×#6101C2314yes—
163C2×#6101C2312yes—
164C2×#6101C2312yes—
165C2×#6101C2312yes—
166C2×#6101C2312yes—
167C2×#6101C2312yes—
168C2×#6101C2312yes—
169C2×#6101C2314yes—
170C2×#6101C2314yes—
171C2×#6101C2314yes—
172C2×#6101C2312yes—
173C2×#6101C2312yes—
174C2×#6101C2314yes—
175C2×C4×Dic13C2311yescharacteristic
176C2×C4×Dic13C2311yescharacteristic
177C2×C4×Dic13C2312yes—
178C2×C4×Dic13C2312yes—
179C2×C4×Dic13C2314yes—
180C2×C4×Dic13C2314yes—
181C2×C4×Dic13C2314yes—
182C2×C4×Dic13C2314yes—
183C2×C4×Dic13C2311yescharacteristic
184#88152C23132yes—
185#88152C23132yes—
186#88152C23132yes—
187#88151C23116yes—
188#88151C2318yes—
189#88151C2318yes—
190#88150C23116yes—
191#88150C23116yes—
192#88146C23116yes—
193#88144C23116yes—
194#88144C23132yes—
195#88144C23116yes—
196#88144C23116yes—
197#88144C23132yes—
198#88144C23132yes—
199#88143C23132yes—
200#88143C23132yes—
201#88143C23132yes—
202#88143C23132yes—
203#88143C23132yes—
204#88143C23132yes—
205#88143C23116yes—
206#88143C23116yes—
207#88143C23132yes—
208#88142C2318yes—
209#88142C23132yes—
210#88142C2318yes—
211#88141C23116yes—
212#88141C23132yes—
213#88141C23116yes—
214#88141C23116yes—
215#88130C23132yes—
216#88126C23116yes—
217#88126C23116yes—
218C42×D13C2318yes—
219#88124C23116yes—
220#88124C23132yes—
221#88124C23132yes—
222#88123C2318yes—
223#88123C23116yes—
224C4×Dic26C2318yes—
225C4×Dic26C23116yes—
226C4×Dic26C23116yes—
227C4×Dic26C2318yes—
228C4×Dic26C23132yes—
229C4×Dic26C23116yes—
230C4×Dic26C23116yes—
231C2×#3556—131nomaximal, Sylow
232C23×D13C2411yescharacteristic
233C2×Q8×C13—24no—
234C2×Q8×C13—28no—
235C2×Q8×C13—24no—
236C2×Q8×C13C2414yes—
237C2×Q8×C13C2414yes—
238C2×Q8×C13C2418yes—
239C22×C4×C13C2414yes—
240C22×C4×C13C2412yes—
241C22×C4×C13C2412yes—
242C22×C4×C13C2411yescharacteristic
243C22×C4×C13C2412yes—
244C22×C4×C13C2412yes—
245C22×C4×C13C2411yescharacteristic
246C22×C4×C13C2411yescharacteristic
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C22×Dic13C2412yes—
251C22×Dic13C2414yes—
252C22×Dic13C2411yescharacteristic
253C22×Dic13C2411yescharacteristic
254C22×Dic13C2411yescharacteristic
255C2×C4×D13—24no—
256C2×C4×D13—24no—
257C2×C4×D13—24no—
258C2×C4×D13C2414yes—
259C2×C4×D13C2414yes—
260C2×C4×D13C2414yes—
261C2×Dic26—28no—
262C2×Dic26—24no—
263C2×Dic26—24no—
264C2×Dic26—28no—
265C2×Dic26—28no—
266C2×Dic26C2418yes—
267C2×Dic26C2414yes—
268C2×Dic26C2414yes—
269C2×Dic26C2418yes—
270C2×Dic26C2418yes—
271C13×C4⋊C4C2414yes—
272C13×C4⋊C4C2418yes—
273C13×C4⋊C4C24116yes—
274C13×C4⋊C4C24116yes—
275C13×C4⋊C4C2414yes—
276C13×C4⋊C4C2418yes—
277C13×C4⋊C4C24116yes—
278C13×C4⋊C4C2418yes—
279C13×C4⋊C4C2418yes—
280C42×C13C2414yes—
281C42×C13C2418yes—
282C42×C13C2418yes—
283C42×C13C24116yes—
284#6103C2418yes—
285#6103C2418yes—
286#6103C2418yes—
287#6103C2418yes—
288#6103C24116yes—
289C4⋊Dic13C2414yes—
290C4⋊Dic13C24116yes—
291C4⋊Dic13C2418yes—
292C4⋊Dic13C2414yes—
293C4⋊Dic13C2418yes—
294C4⋊Dic13C2418yes—
295C4⋊Dic13C2418yes—
296C4⋊Dic13C24116yes—
297C4⋊Dic13C24116yes—
298C4⋊Dic13C24116yes—
299#6101C2418yes—
300#6101C2418yes—
301#6101C24116yes—
302#6101C24116yes—
303#6101C24116yes—
304#6101C2418yes—
305#6101C2418yes—
306#6101C2418yes—
307#6101C2418yes—
308#6101C2418yes—
309#6101C2418yes—
310#6101C24116yes—
311#6101C24116yes—
312#6101C24116yes—
313#6101C2418yes—
314#6101C2418yes—
315#6101C24116yes—
316C4×Dic13C2414yes—
317C4×Dic13C2414yes—
318C4×Dic13C2418yes—
319C4×Dic13C2418yes—
320C4×Dic13C24116yes—
321C4×Dic13C24116yes—
322C4×Dic13C24116yes—
323C4×Dic13C24116yes—
324C4×Dic13C2414yes—
325#3556—1332no—
326C2×#564—134no—
327C2×#557—132no—
328C2×#557—131no—
329C2×#557—132no—
330C2×#557—132no—
331C2×#557—132no—
332C2×#557—131no—
333C2×#557—131no—
334C2×#557D1311yescharacteristic, complemented
335C2×#541—132no—
336C2×#541—134no—
337C2×#541—132no—
338C2×#541—132no—
339C2×#541—132no—
340C2×#533—131no—
341C2×#533—131no—
342C2×#533—131no—
343C23×C13C2511yescharacteristic
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13C2512yes—
348Q8×C13—28no—
349Q8×C13—28no—
350Q8×C13—216no—
351C2×C4×C13—24no—
352C2×C4×C13—24no—
353C2×C4×C13—22no—
354C2×C4×C13—24no—
355C2×C4×C13—28no—
356C2×C4×C13—24no—
357C2×C4×C132−1+414yes—
358C2×C4×C132−1+414yes—
359C2×C4×C13C2518yes—
360C2×C4×C13C2514yes—
361C2×C4×C13C2514yes—
362C2×C4×C13C2512yes—
363C2×C4×C13C2514yes—
364C2×C4×C13C2514yes—
365C2×C4×C13C2512yes—
366C2×C4×C13C2512yes—
367C2×Dic13—24no—
368C2×Dic13—28no—
369C2×Dic13—24no—
370C2×Dic13—24no—
371C2×Dic13—24no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic132−1+414yes—
375C2×Dic13C2514yes—
376C2×Dic13C2514yes—
377C2×Dic13C2514yes—
378C2×Dic13C2514yes—
379C2×Dic13C2518yes—
380C2×Dic13C2512yes—
381C2×Dic13C2512yes—
382C2×Dic13C2512yes—
383C4×D13—28no—
384C4×D13—28no—
385C4×D13—28no—
386Dic26—28no—
387Dic26—216no—
388Dic26—28no—
389Dic26—216no—
390Dic26—216no—
391#564—1364no—
392#557—1332no—
393#557—1316no—
394#557—1332no—
395#557—1332no—
396#557—1316no—
397#557—1332no—
398#557—1316no—
399#557C2×D13116yescomplemented
400#541—1332no—
401#541—1364no—
402#541—1332no—
403#541—1332no—
404#541—1332no—
405#533—1316no—
406#533—1316no—
407#533—1316no—
408C2×C4⋊Q8—131no—
409C2×C4⋊Q8—131no—
410C2×C4⋊Q8—132no—
411C2×C4⋊Q8—132no—
412C2×C4⋊Q8—131no—
413C2×C4⋊Q8—131no—
414C2×C4⋊Q8—134no—
415C2×C4⋊Q8—131no—
416C2×C4⋊Q8—132no—
417C2×C4⋊Q8C2×D1311yescharacteristic
418C2×C4⋊Q8C2×D1312yes—
419C2×#126—134no—
420C2×#126—134no—
421C2×#126—134no—
422C2×#126—134no—
423C2×#125—132no—
424C2×#125—132no—
425C2×#125—134no—
426C2×#125—134no—
427C2×#125—134no—
428C2×#125—134no—
429C2×#125—134no—
430C2×#125—134no—
431C2×#125—134no—
432C2×#125—132no—
433C2×#125—132no—
434C2×#125—132no—
435C2×#125—134no—
436C2×#125—134no—
437C2×#125—134no—
438C2×#125—132no—
439C2×#125—134no—
440C2×#125—134no—
441C2×#125C2×D1312yes—
442C2×#125C2×D1314yes—
443C2×C22⋊Q8—132no—
444C2×C22⋊Q8—131no—
445C2×C22⋊Q8—131no—
446C2×C22⋊Q8—132no—
447C2×C22⋊Q8—132no—
448C2×C22⋊Q8—132no—
449C2×C22⋊Q8—131no—
450C2×C22⋊Q8—131no—
451C2×C4×Q8—132no—
452C2×C4×Q8—132no—
453C2×C4×Q8—132no—
454C2×C4×Q8—132no—
455C2×C4×Q8—134no—
456C2×C4×Q8—132no—
457C2×C4×Q8—132no—
458C2×C4×Q8—131no—
459C2×C4×Q8—131no—
460C2×C4×Q8—132no—
461C2×C4×Q8—132no—
462C2×C4×Q8—134no—
463C2×C4×Q8—132no—
464C2×C4×Q8—132no—
465C2×C4×Q8C2×D1311yescharacteristic
466C2×C4×Q8C2×D1311yescharacteristic
467C2×C4×Q8C2×D1312yes—
468C2×C4×Q8C2×D1312yes—
469C2×#117—132no—
470C2×#117—132no—
471C2×#117—132no—
472C22×C42—131no—
473C22×C13C2×2−1+412yes—
474C22×C13C2×2−1+412yes—
475C22×C13C2×2−1+412yes—
476C22×C13C2611yescharacteristic
477C2×D13—22no—
478C2×D13—22no—
479C2×D13—22no—
480C2×D13—44no—
481C4×C13—24no—
482C4×C13—24no—
483C4×C13—22no—
484C4×C13—28no—
485C4×C13—24no—
486C4×C13—24no—
487C4×C13C2×2−1+414yes—
488C4×C13C2×2−1+414yes—
489Dic13—24no—
490Dic13—24no—
491Dic13—24no—
492Dic13—24no—
493Dic13—28no—
494Dic13—22no—
495Dic13—22no—
496Dic13C2×2−1+414yes—
497C22×Q8—132no—
498C22×Q8—132no—
499C22×Q8—132no—
500C22×Q8—131no—
501C22×Q8—131no—
502C22×Q8C22×D1312yes—
503C22×Q8C22×D1311yescharacteristic
504C22×Q8C22×D1311yescharacteristic
505C23×C4—131no—
506C23×C4—131no—
507C23×C4—131no—
508C4⋊Q8—138no—
509C4⋊Q8—138no—
510C4⋊Q8—1316no—
511C4⋊Q8—1316no—
512C4⋊Q8—138no—
513C4⋊Q8—138no—
514C4⋊Q8—1332no—
515C4⋊Q8—138no—
516C4⋊Q8—1316no—
517C4⋊Q8C22×D1318yes—
518C4⋊Q8C22×D13116yes—
519#126—1332no—
520#126—1332no—
521#126—1332no—
522#126—1332no—
523#125—1316no—
524#125—1316no—
525#125—1316no—
526#125—1332no—
527#125—1316no—
528#125—1316no—
529#125—1332no—
530#125—1332no—
531#125—1332no—
532#125—1332no—
533#125—1332no—
534#125—1332no—
535#125—1332no—
536#125—1332no—
537#125—1332no—
538#125—1316no—
539#125—1332no—
540#125—1332no—
541#125C22×D13116yes—
542#125C22×D13132yes—
543C22⋊Q8—1316no—
544C22⋊Q8—138no—
545C22⋊Q8—138no—
546C22⋊Q8—1316no—
547C22⋊Q8—1316no—
548C22⋊Q8—1316no—
549C22⋊Q8—138no—
550C22⋊Q8—138no—
551C4×Q8—1316no—
552C4×Q8—1316no—
553C4×Q8—1316no—
554C4×Q8—1316no—
555C4×Q8—1332no—
556C4×Q8—1316no—
557C4×Q8—1316no—
558C4×Q8—1316no—
559C4×Q8—1316no—
560C4×Q8—138no—
561C4×Q8—138no—
562C4×Q8—1332no—
563C4×Q8—1316no—
564C4×Q8—1316no—
565C4×Q8C22×D1318yes—
566C4×Q8C22×D1318yes—
567C4×Q8C22×D13116yes—
568C4×Q8C22×D13116yes—
569#117—1316no—
570#117—1316no—
571#117—1316no—
572C2×C4⋊C4—132no—
573C2×C4⋊C4—132no—
574C2×C4⋊C4—132no—
575C2×C4⋊C4—132no—
576C2×C4⋊C4—132no—
577C2×C4⋊C4—132no—
578C2×C4⋊C4—132no—
579C2×C4⋊C4—131no—
580C2×C4⋊C4—132no—
581C2×C4⋊C4—131no—
582C2×C4⋊C4—132no—
583C2×C4⋊C4—132no—
584C2×C4⋊C4—134no—
585C2×C4⋊C4—132no—
586C2×C4⋊C4—132no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—132no—
589C2×C4⋊C4—132no—
590C2×C4⋊C4—134no—
591C2×C4⋊C4—134no—
592C2×C4⋊C4—134no—
593C2×C4⋊C4—134no—
594C2×C4⋊C4—134no—
595C2×C4⋊C4—134no—
596C2×C4⋊C4—134no—
597C2×C4⋊C4—134no—
598C2×C4⋊C4—134no—
599C2×C4⋊C4C22×D1312yes—
600C2×C4⋊C4C22×D1312yes—
601C2×C4⋊C4C22×D1311yescharacteristic
602C2×C4⋊C4C22×D1314yes—
603C2×C4⋊C4C22×D1311yescharacteristic
604C2×C4⋊C4C22×D1312yes—
605C2×C4⋊C4C22×D1312yes—
606C2×C4⋊C4C22×D1314yes—
607C2×C4⋊C4C22×D1314yes—
608C2×C22⋊C4—134no—
609C2×C22⋊C4—132no—
610C2×C22⋊C4—132no—
611C2×C22⋊C4—132no—
612C2×C22⋊C4—132no—
613C2×C42—134no—
614C2×C42—132no—
615C2×C42—132no—
616C2×C42—131no—
617C2×C42—131no—
618C2×C42—134no—
619C2×C42—134no—
620C2×C42—134no—
621C2×C42—131no—
622C2×C42—138no—
623C2×C42C22×D1312yes—
624C2×C42C22×D1312yes—
625C2×C42C22×D1311yescharacteristic
626C2×C42C22×D1314yes—
627C2×C13#355614yescomplemented
628C2×C13C22×2−1+411yescharacteristic
629C2×C13C22×2−1+411yescharacteristic
630C2×C13C22×2−1+411yescharacteristic
631D13—42no—
632C24—131no—
633C2×Q8—24no—
634C2×Q8—28no—
635C2×Q8—24no—
636C2×Q8—138no—
637C2×Q8—138no—
638C2×Q8—138no—
639C2×Q8—134no—
640C2×Q8—134no—
641C2×Q8—268no—
642C2×Q8—268no—
643C2×Q8—268no—
644C2×Q8—264no—
645C2×Q8—264no—
646C2×Q8C23×D1318yes—
647C2×Q8C23×D1314yes—
648C2×Q8C23×D1314yes—
649C22×C4—131no—
650C22×C4—132no—
651C22×C4—134no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—131no—
656C22×C4—131no—
657C22×C4—134no—
658C22×C4—134no—
659C22×C4—134no—
660C22×C4—264no—
661C22×C4—264no—
662C22×C4—264no—
663C22×C4C23×D1314yes—
664C22×C4C23×D1312yes—
665C22×C4C23×D1312yes—
666C22×C4C23×D1311yescharacteristic
667C22×C4C23×D1312yes—
668C22×C4C23×D1312yes—
669C22×C4C23×D1311yescharacteristic
670C22×C4C23×D1311yescharacteristic
671C4⋊C4—138no—
672C4⋊C4—138no—
673C4⋊C4—138no—
674C4⋊C4—138no—
675C4⋊C4—138no—
676C4⋊C4—138no—
677C4⋊C4—138no—
678C4⋊C4—134no—
679C4⋊C4—138no—
680C4⋊C4—134no—
681C4⋊C4—138no—
682C4⋊C4—138no—
683C4⋊C4—1316no—
684C4⋊C4—138no—
685C4⋊C4—138no—
686C4⋊C4—1316no—
687C4⋊C4—138no—
688C4⋊C4—138no—
689C4⋊C4—1316no—
690C4⋊C4—1316no—
691C4⋊C4—1316no—
692C4⋊C4—1316no—
693C4⋊C4—1316no—
694C4⋊C4—1316no—
695C4⋊C4—1316no—
696C4⋊C4—1316no—
697C4⋊C4—1316no—
698C4⋊C4C23×D1318yes—
699C4⋊C4C23×D1318yes—
700C4⋊C4C23×D1314yes—
701C4⋊C4C23×D13116yes—
702C4⋊C4C23×D1314yes—
703C4⋊C4C23×D1318yes—
704C4⋊C4C23×D1318yes—
705C4⋊C4C23×D13116yes—
706C4⋊C4C23×D13116yes—
707C22⋊C4—1316no—
708C22⋊C4—138no—
709C22⋊C4—138no—
710C22⋊C4—138no—
711C22⋊C4—138no—
712C42—134no—
713C42—134no—
714C42—134no—
715C42—1316no—
716C42—138no—
717C42—138no—
718C42—1316no—
719C42—1316no—
720C42—1316no—
721C42C23×D1314yes—
722C42C23×D1318yes—
723C42C23×D1318yes—
724C42C23×D13116yes—
725C13C2×#355611yescharacteristic, complemented, Sylow
726C23—132no—
727C23—262no—
728C23—262no—
729C23—262no—
730C23C24×D1311yescharacteristic
731Q8—28no—
732Q8—216no—
733Q8—28no—
734Q8—2616no—
735Q8—2616no—
736Q8—2616no—
737Q8—268no—
738Q8—268no—
739C2×C4—24no—
740C2×C4—28no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—134no—
746C2×C4—132no—
747C2×C4—134no—
748C2×C4—134no—
749C2×C4—134no—
750C2×C4—134no—
751C2×C4—138no—
752C2×C4—132no—
753C2×C4—132no—
754C2×C4—268no—
755C2×C4—262no—
756C2×C4—264no—
757C2×C4—268no—
758C2×C4—262no—
759C2×C4—264no—
760C2×C4—264no—
761C2×C4—264no—
762C2×C4—268no—
763C2×C4—268no—
764C2×C4#8825414yes—
765C2×C4#8825714yes—
766C2×C4C24×D1318yes—
767C2×C4C24×D1314yes—
768C2×C4C24×D1314yes—
769C2×C4C24×D1312yes—
770C2×C4C24×D1314yes—
771C2×C4C24×D1314yes—
772C2×C4C24×D1312yes—
773C2×C4C24×D1312yes—
774C22—262no—
775C22—262no—
776C22—262no—
777C22—524no—
778C22C2×#8825412yes—
779C22C2×#8825712yes—
780C22D13×2−1+412yes—
781C22C25×D1311yescharacteristic
782C4—22no—
783C4—24no—
784C4—24no—
785C4—28no—
786C4—24no—
787C4—24no—
788C4—134no—
789C4—264no—
790C4—264no—
791C4—262no—
792C4—264no—
793C4—262no—
794C4—264no—
795C4—268no—
796C4C2×#8825414yes—
797C4C2×#8825714yes—
798C2—522no—
799C2#1312932814yesdirect product factor
800C2C2×D13×2−1+411yescharacteristic
801C2C22×#8825711yescharacteristic
802C2C22×#8825411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#557C2
socleC23×C13C25
prime radicalC23×D13C24
hypercenterC2×#557D13
hypocenterC13C2×#3556
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #13129328C2direct (N × H)
2. C2×C13⋊#564C2semidirect
3. C2×#11719275C2semidirect
4. C2×#11719272C2semidirect
5. C2×#11719272C2semidirect
6. C2×#11719390C2semidirect
7. C2×#11719274C2semidirect
8. C2×#11719426C2semidirect
9. C2×#11719426C2semidirect
18. C2×C13×#557C2semidirect
19. C13×#557C22semidirect
40. #11719426C22semidirect
41. #11719426C22semidirect
44. C13⋊#564C22semidirect
45. #11719390C22semidirect
50. #11719275C22semidirect
51. #11719274C22semidirect
52. #11719272C22semidirect
53. #11719272C22semidirect
334. C2×#557D13semidirect
399. #557C2×D13semidirect
627. C2×C13#3556semidirect
725. C13C2×#3556semidirect
799. C2#13129328direct (N × H)

Maximal subgroups

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

subgroupindex
#131293282
C2×C13⋊#5642
C2×#117192752
C2×#117192722
C2×#117193902
C2×#117192742
C2×#117194262
C2×#117194022
C2×#117194362
C2×#117194012
C2×#117192882
C2×#117194332
C2×#117192832
C2×C13×#5572
C2×#355613