Finite Group Databasebeta

← C2×#13127911 #16743935

Subgroups — C2×#13127911 #16743935

Order 3328.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719289C211yesmaximal, characteristic, complemented
2#13127911C2116yesmaximal, direct product factor
3C2×#11718721C211yesmaximal, characteristic, complemented
4C2×#11718747C211yesmaximal, characteristic, complemented
5C2×#11718720C211yesmaximal, characteristic
6C2×#11718689C211yesmaximal, characteristic, complemented
7C2×#11718715C211yesmaximal, characteristic, complemented
8C2×#11718692C211yesmaximal, characteristic, complemented
9C2×#11718751C211yesmaximal, characteristic, complemented
10C2×#11718677C211yesmaximal, characteristic
11C2×#11718718C211yesmaximal, characteristic
12C2×#11718685C211yesmaximal, characteristic, complemented
13C2×#11718679C211yesmaximal, characteristic, complemented
14C2×#11718687C211yesmaximal, characteristic, complemented
15C2×C4×#6107C211yesmaximal, characteristic, complemented
16C2×C13×#556C211yesmaximal, characteristic, complemented
17C13×#556—24no—
18C13×#556C2218yescomplemented
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#126—21no—
21C2×C13×#126—21no—
22C2×C13×#124C2211yescharacteristic
23C2×C13×#124C2211yescharacteristic
24C2×C13×C22⋊Q8—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117—21no—
30C2×#88200—21no—
31C22×#6107C2211yescharacteristic
32C22×#6107C2211yescharacteristic
33C22×#6107C2211yescharacteristic
34C22×#6107C2211yescharacteristic
35C22×#6106C2211yescharacteristic
36C22×#6106C2211yescharacteristic
37C22×#6105C2211yescharacteristic
38C22×#6105C2211yescharacteristic
39C22×#6104C2211yescharacteristic
40#11719289—24no—
41#11719289C2218yescomplemented
42C2×#88152—21no—
43C2×#88152—21no—
44C2×#88146—21no—
45C2×#88129C2211yescharacteristic
46C2×#88129C2211yescharacteristic
47C2×C4×D52C2211yescharacteristic
48C2×#88123C2211yescharacteristic
49C2×C4×Dic26C2211yescharacteristic
50C2×C4×Dic26C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54#11718751C2218yescomplemented
55#11718747C2218yescomplemented
56#11718721C2218yescomplemented
57#11718720C2218yes—
58#11718718C2218yes—
59#11718715C2218yescomplemented
60#11718692C2218yescomplemented
61C4×#6107C2218yescomplemented
62#11718689C2218yescomplemented
63#11718687C2218yescomplemented
64#11718685C2218yescomplemented
65#11718679C2218yescomplemented
66#11718677C2218yes—
67C2×#88050C2211yescharacteristic
68C2×#88050C2211yescharacteristic
69C2×#88049C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×C4⋊#1055C2211yescharacteristic
72C2×C4⋊#1055C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×#88043C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13D411yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C22×Q8×C13C2311yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C22×D52C2311yescharacteristic
83C22×C4×D13—21no—
84C22×Dic26C2311yescharacteristic
85C22×Dic26C2311yescharacteristic
86C13×C4⋊Q8—22no—
87C13×C4⋊Q8C2314yes—
88C13×#126—28no—
89C13×#126—28no—
90C13×#124—22no—
91C13×#124—22no—
92C13×#124C2314yes—
93C13×#124C2314yes—
94C13×C22⋊Q8—28no—
95C4×Q8×C13—22no—
96C4×Q8×C13—22no—
97C4×Q8×C13D414yes—
98C4×Q8×C13C2314yes—
99C4×Q8×C13C2314yes—
100C4×Q8×C13C2314yes—
101C4×D4×C13—22no—
102C4×D4×C13C2314yes—
103C13×#117—28no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4D411yescharacteristic
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C42×C13—21no—
118C2×C42×C13—21no—
119C2×C42×C13C2311yescharacteristic
120C2×C42×C13C2311yescharacteristic
121C2×C42×C13C2311yescharacteristic
122#88200—28no—
123C2×#6107—24no—
124C2×#6107—42no—
125C2×#6107—42no—
126C2×#6107—42no—
127C2×#6107C2314yes—
128C2×#6107C2314yes—
129C2×#6107C2314yes—
130C2×#6107C2314yes—
131C2×#6106—24no—
132C2×#6106—42no—
133C2×#6106C2314yes—
134C2×#6106C2314yes—
135C2×#6105—24no—
136C2×#6105—42no—
137C2×#6105C2314yes—
138C2×#6105C2314yes—
139C2×#6104—42no—
140C2×#6104C2314yes—
141C2×#6103—21no—
142C2×#6103—21no—
143C2×#6103—21no—
144C2×#6103—21no—
145C2×#6103—21no—
146C2×C4⋊Dic13—21no—
147C2×C4⋊Dic13—21no—
148C2×C4⋊Dic13C2311yescharacteristic
149C2×#6101—21no—
150C2×#6101—21no—
151C2×C4×Dic13—21no—
152C2×C4×Dic13—21no—
153C22×#1055C2311yescharacteristic
154C22×#1055C2311yescharacteristic
155C22×#1055C2311yescharacteristic
156C22×#1055C2311yescharacteristic
157#88152—28no—
158#88152—28no—
159#88146—28no—
160#88129—22no—
161#88129—22no—
162#88129C2314yes—
163#88129C2314yes—
164C4×D52—22no—
165C4×D52C2314yes—
166#88123—22no—
167#88123C2314yes—
168C4×Dic26—22no—
169C4×Dic26—22no—
170C4×Dic26C2314yes—
171C4×Dic26C2314yes—
172#88075C2314yes—
173#88075C2314yes—
174#88072C2314yes—
175#88050C2314yes—
176#88050C2314yes—
177#88049C2314yes—
178#88047C2314yes—
179C4⋊#1055C2314yes—
180C4⋊#1055C2314yes—
181C4⋊#1055C2314yes—
182#88043C2314yes—
183#88043C2314yes—
184C4×#1055C2314yes—
185C2×#3402—131nomaximal, Sylow
186C24×C13—21no—
187C23×D13—21no—
188C2×Q8×C13—21no—
189C2×Q8×C13—21no—
190C2×Q8×C13—22no—
191C2×Q8×C13—22no—
192C2×Q8×C13—22no—
193C2×Q8×C13—22no—
194C2×Q8×C13—42no—
195C2×Q8×C13C2×D414yes—
196C2×Q8×C13C2412yes—
197C2×Q8×C13C2412yes—
198C2×D4×C13—21no—
199C2×D4×C13—22no—
200C2×D4×C13—22no—
201C2×D4×C13C2412yes—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—24no—
206C22×C4×C13—44no—
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2411yescharacteristic
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C2×D52—22no—
218C2×D52—22no—
219C2×D52—21no—
220C2×D52C2412yes—
221C2×C4×D13—24no—
222C2×C4×D13—44no—
223C2×Dic26—22no—
224C2×Dic26—22no—
225C2×Dic26—22no—
226C2×Dic26—22no—
227C2×Dic26—21no—
228C2×Dic26—21no—
229C2×Dic26C2412yes—
230C2×Dic26C2412yes—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—24no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4C2×D414yes—
237C13×C4⋊C4C2×D414yes—
238C13×C4⋊C4C2×D414yes—
239C13×C4⋊C4C2412yes—
240C13×C22⋊C4—24no—
241C13×C22⋊C4—24no—
242C13×C22⋊C4—24no—
243C13×C22⋊C4—24no—
244C13×C22⋊C4—24no—
245C42×C13—24no—
246C42×C13—24no—
247C42×C13C2×D412yes—
248C42×C13C2×D412yes—
249C42×C13C2×D412yes—
250C42×C13C2412yes—
251C42×C13C2412yes—
252C42×C13C2412yes—
253#6107—28no—
254#6107—44no—
255#6107—44no—
256#6107—44no—
257#6106—28no—
258#6106—44no—
259#6105—28no—
260#6105—44no—
261#6104—44no—
262#6103—24no—
263#6103—24no—
264#6103—24no—
265#6103—24no—
266#6103—24no—
267C4⋊Dic13—21no—
268C4⋊Dic13—24no—
269C4⋊Dic13—24no—
270C4⋊Dic13C2412yes—
271#6101—24no—
272#6101—24no—
273C4×Dic13—24no—
274C4×Dic13—24no—
275C2×#1055—22no—
276C2×#1055—22no—
277C2×#1055—22no—
278C2×#1055#4114yes—
279C2×#1055C2412yes—
280C2×#1055C2412yes—
281C2×#1055C2412yes—
282C2×#1055C2412yes—
283C2×#556—131no—
284C2×#556D1311yescharacteristic, complemented
285#3402—1316no—
286C2×#497—131no—
287C2×#497—131no—
288C2×#495—131no—
289C2×#464—131no—
290C2×#464—131no—
291C2×#462—131no—
292C2×#462—131no—
293C2×#463—131no—
294C2×#463—131no—
295C2×#446—131no—
296C2×#440—131no—
297C2×#440—131no—
298C2×C4×Q16—131no—
299C23×C13—22no—
300C23×C13—42no—
301C23×C13—42no—
302C23×C13—42no—
303C23×C13C22×D411yescharacteristic
304C22×D13—22no—
305C22×D13—42no—
306C22×D13—42no—
307C22×D13—42no—
308Q8×C13—22no—
309Q8×C13—22no—
310Q8×C13—22no—
311Q8×C13—22no—
312Q8×C13—44no—
313Q8×C13—42no—
314Q8×C13—42no—
315D4×C13—22no—
316D4×C13—22no—
317D4×C13—42no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—48no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D412yes—
336C2×C4×C13C22×D412yes—
337C2×C4×C13C22×D411yescharacteristic
338C2×C4×C13C2×#4112yes—
339C2×C4×C13H(5,𝔽2)12yes—
340C2×C4×C13C2511yescharacteristic
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347D52—22no—
348D52—22no—
349D52—42no—
350C4×D13—48no—
351Dic26—22no—
352Dic26—22no—
353Dic26—22no—
354Dic26—22no—
355Dic26—42no—
356Dic26—42no—
357#1055—22no—
358#1055—22no—
359#1055—22no—
360#1055C2×#4114yes—
361C22×Q16—131no—
362C22×Q16—131no—
363C22×Q16—131no—
364C22×Q16—131no—
365C22×SD16—131no—
366C22×SD16—131no—
367C22×SD16—131no—
368C22×SD16—131no—
369C22×D8—131no—
370#556—24no—
371#556—138no—
372#556—264no—
373#556C2×D1318yescomplemented
374C2×C4⋊Q8—131no—
375C2×C4⋊Q8C2×D1311yescharacteristic
376C2×#126—21no—
377C2×#126—21no—
378C2×#126—261no—
379C2×#126—261no—
380C2×#124—131no—
381C2×#124—131no—
382C2×#124C2×D1311yescharacteristic
383C2×#124C2×D1311yescharacteristic
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—261no—
386C2×C4×Q8—131no—
387C2×C4×Q8—131no—
388C2×C4×Q8C2×D1311yescharacteristic
389C2×C4×Q8C2×D1311yescharacteristic
390C2×C4×Q8C2×D1311yescharacteristic
391C2×C4×D4—131no—
392C2×C4×D4C2×D1311yescharacteristic
393C2×#117—21no—
394C2×#117—261no—
395#497—138no—
396#497—138no—
397#495—138no—
398#464—138no—
399#464—138no—
400#463—138no—
401#463—138no—
402#462—138no—
403#462—138no—
404#446—138no—
405#440—138no—
406#440—138no—
407C4×Q16—138no—
408C2×#107—131no—
409C2×C4⋊C8—131no—
410C2×C4⋊C8—131no—
411C2×C4⋊C8—131no—
412C2×#103—131no—
413C2×#103—131no—
414C2×#103—131no—
415C2×#103—131no—
416C2×#102—131no—
417C2×#102—131no—
418C2×#97—131no—
419C2×#97—131no—
420C2×C4×C8—131no—
421C22×C13—42no—
422C22×C13—42no—
423C22×C13—42no—
424C22×C13—84no—
425C22×C13#55012yes—
426C22×C13#57512yes—
427C22×C13#57812yes—
428C22×C13C23×D411yescharacteristic
429C2×D13—42no—
430C2×D13—42no—
431C2×D13—42no—
432C2×D13—84no—
433C4×C13—22no—
434C4×C13—22no—
435C4×C13—22no—
436C4×C13—22no—
437C4×C13—22no—
438C4×C13—22no—
439C4×C13—42no—
440C4×C13—42no—
441C4×C13—42no—
442C4×C13#55012yes—
443C4×C13C22×#4111yescharacteristic
444C4×C13C2×H(5,𝔽2)11yescharacteristic
445Dic13—42no—
446Dic13—42no—
447Dic13—42no—
448C22×Q8—131no—
449C22×Q8—131no—
450C22×Q8C22⋊D1311yescharacteristic
451C22×Q8C22×D1311yescharacteristic
452C22×Q8C22×D1311yescharacteristic
453C22×D4—131no—
454C22×D4C22×D1311yescharacteristic
455C23×C4—21no—
456C23×C4—261no—
457C2×Q16—134no—
458C2×Q16—134no—
459C2×Q16—134no—
460C2×Q16—134no—
461C2×Q16—264no—
462C2×Q16—522no—
463C2×Q16—522no—
464C2×Q16—522no—
465C2×SD16—134no—
466C2×SD16—134no—
467C2×SD16—134no—
468C2×SD16—134no—
469C2×SD16—264no—
470C2×SD16—264no—
471C2×SD16—522no—
472C2×SD16—522no—
473C2×D8—134no—
474C2×D8—522no—
475C22×C8—131no—
476C22×C8—131no—
477C22×C8—131no—
478C22×C8—131no—
479C4⋊Q8—22no—
480C4⋊Q8—134no—
481C4⋊Q8—262no—
482C4⋊Q8C22×D1314yes—
483#126—28no—
484#126—28no—
485#126—268no—
486#126—268no—
487#124—22no—
488#124—22no—
489#124—134no—
490#124—134no—
491#124—262no—
492#124—262no—
493#124C22×D1314yes—
494#124C22×D1314yes—
495C22⋊Q8—28no—
496C22⋊Q8—268no—
497C4×Q8—22no—
498C4×Q8—22no—
499C4×Q8—134no—
500C4×Q8—134no—
501C4×Q8—262no—
502C4×Q8—262no—
503C4×Q8C22⋊D1314yes—
504C4×Q8C22×D1314yes—
505C4×Q8C22×D1314yes—
506C4×Q8C22×D1314yes—
507C4×D4—22no—
508C4×D4—134no—
509C4×D4—262no—
510C4×D4C22×D1314yes—
511#117—28no—
512#117—268no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—131no—
518C2×C4⋊C4—261no—
519C2×C4⋊C4—261no—
520C2×C4⋊C4—261no—
521C2×C4⋊C4—261no—
522C2×C4⋊C4C22⋊D1311yescharacteristic
523C2×C4⋊C4C22⋊D1311yescharacteristic
524C2×C4⋊C4C22⋊D1311yescharacteristic
525C2×C4⋊C4C22×D1311yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—261no—
532C2×C22⋊C4—261no—
533C2×C22⋊C4—261no—
534C2×C22⋊C4—261no—
535C2×C22⋊C4—261no—
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—261no—
539C2×C42—261no—
540C2×C42C22×D1311yescharacteristic
541C2×C42C22×D1311yescharacteristic
542C2×C42C22×D1311yescharacteristic
543#107—134no—
544C4⋊C8—134no—
545C4⋊C8—134no—
546C4⋊C8—134no—
547#103—134no—
548#103—134no—
549#103—134no—
550#103—134no—
551#102—134no—
552#102—134no—
553#97—134no—
554#97—134no—
555C4×C8—134no—
556C2×C13—82no—
557C2×C13#340214yescomplemented
558C2×C13C2×#55011yescharacteristic
559C2×C13C2×#57511yescharacteristic
560C2×C13C2×#57811yescharacteristic
561D13—82no—
562C24—21no—
563C24—261no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—42no—
571C2×Q8—132no—
572C2×Q8—132no—
573C2×Q8—261no—
574C2×Q8—261no—
575C2×Q8—262no—
576C2×Q8—262no—
577C2×Q8—262no—
578C2×Q8—262no—
579C2×Q8C2×C22⋊D1314yes—
580C2×Q8C23×D1312yes—
581C2×Q8C23×D1312yes—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—132no—
586C2×D4—262no—
587C2×D4—262no—
588C2×D4—261no—
589C2×D4C23×D1312yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—44no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—264no—
599C22×C4—524no—
600C22×C4C2×C22⋊D1311yescharacteristic
601C22×C4C2×C22⋊D1311yescharacteristic
602C22×C4C2×C22⋊D1311yescharacteristic
603C22×C4C2×C22⋊D1311yescharacteristic
604C22×C4C2×C22⋊D1311yescharacteristic
605C22×C4C2×C22⋊D1311yescharacteristic
606C22×C4C23×D1311yescharacteristic
607Q16—268no—
608Q16—524no—
609Q16—524no—
610Q16—524no—
611SD16—268no—
612SD16—268no—
613SD16—524no—
614SD16—524no—
615D8—524no—
616C2×C8—134no—
617C2×C8—132no—
618C2×C8—132no—
619C2×C8—132no—
620C2×C8—132no—
621C2×C8—262no—
622C2×C8—262no—
623C2×C8—262no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—132no—
630C4⋊C4—261no—
631C4⋊C4—264no—
632C4⋊C4—264no—
633C4⋊C4—264no—
634C4⋊C4—264no—
635C4⋊C4C2×C22⋊D1314yes—
636C4⋊C4C2×C22⋊D1314yes—
637C4⋊C4C2×C22⋊D1314yes—
638C4⋊C4C23×D1312yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—264no—
645C22⋊C4—264no—
646C22⋊C4—264no—
647C22⋊C4—264no—
648C22⋊C4—264no—
649C42—24no—
650C42—24no—
651C42—264no—
652C42—264no—
653C42C2×C22⋊D1312yes—
654C42C2×C22⋊D1312yes—
655C42C2×C22⋊D1312yes—
656C42C23×D1312yes—
657C42C23×D1312yes—
658C42C23×D1312yes—
659C13C2×#340211yescharacteristic, complemented, Sylow
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—262no—
665C23—522no—
666C23—522no—
667C23—522no—
668C23C22×C22⋊D1311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—262no—
677Q8—262no—
678Q8—262no—
679Q8—262no—
680Q8—522no—
681Q8—522no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—262no—
686D4—262no—
687D4—522no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—528no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—522no—
708C2×C4#41×D1312yes—
709C2×C4#8825612yes—
710C2×C4C22×C22⋊D1312yes—
711C2×C4C22×C22⋊D1312yes—
712C2×C4C22×C22⋊D1312yes—
713C2×C4C22×C22⋊D1312yes—
714C2×C4C22×C22⋊D1312yes—
715C2×C4C22×C22⋊D1312yes—
716C2×C4C22×C22⋊D1311yescharacteristic
717C2×C4C24×D1311yescharacteristic
718C8—134no—
719C8—262no—
720C8—262no—
721C8—262no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—522no—
727C22—522no—
728C22—522no—
729C22—1044no—
730C22#1171952712yes—
731C22#1171953912yes—
732C22#1171954312yes—
733C22C23×C22⋊D1311yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—522no—
744C4—522no—
745C4—522no—
746C4#1171953912yes—
747C4C2×#41×D1311yescharacteristic
748C4C2×#8825611yescharacteristic
749C2—82no—
750C2—1042no—
751C2#1312791114yesdirect product factor
752C2C2×#1171953911yescharacteristic
753C2C2×#1171952711yescharacteristic
754C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#556C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
hypercenterC2×#556D13
hypocenterC13C2×#3402
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#11719289C2semidirect
2. #13127911C2direct (N × H)
3. C2×#11718721C2semidirect
4. C2×#11718747C2semidirect
6. C2×#11718689C2semidirect
7. C2×#11718715C2semidirect
8. C2×#11718692C2semidirect
9. C2×#11718751C2semidirect
12. C2×#11718685C2semidirect
13. C2×#11718679C2semidirect
14. C2×#11718687C2semidirect
15. C2×C4×#6107C2semidirect
16. C2×C13×#556C2semidirect
18. C13×#556C22semidirect
41. #11719289C22semidirect
54. #11718751C22semidirect
55. #11718747C22semidirect
56. #11718721C22semidirect
59. #11718715C22semidirect
60. #11718692C22semidirect
61. C4×#6107C22semidirect
62. #11718689C22semidirect
63. #11718687C22semidirect
64. #11718685C22semidirect
65. #11718679C22semidirect
284. C2×#556D13semidirect
373. #556C2×D13semidirect
557. C2×C13#3402semidirect
659. C13C2×#3402semidirect
751. C2#13127911direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192892
#131279112
C2×#117187212
C2×#117187472
C2×#117187202
C2×#117186892
C2×#117187152
C2×#117186922
C2×#117187512
C2×#117186772
C2×#117187182
C2×#117186852
C2×#117186792
C2×#117186872
C2×C4×#61072
C2×C13×#5562
C2×#340213