Finite Group Databasebeta

← C2×#13125098 #16731234

Subgroups — C2×#13125098 #16731234

Order 3328.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719239C211yesmaximal, characteristic, complemented
2#13125098C2116yesmaximal, direct product factor
3C2×#11718631C211yesmaximal, characteristic, complemented
4C2×#11718628C211yesmaximal, characteristic, complemented
5C2×#11718682C211yesmaximal, characteristic, complemented
6C2×#11718668C211yesmaximal, characteristic, complemented
7C2×#11718689C211yesmaximal, characteristic, complemented
8C2×#11718677C211yesmaximal, characteristic, complemented
9C2×#11718900C211yesmaximal, characteristic, complemented
10C2×#11718899C211yesmaximal, characteristic
11C2×#11718679C211yesmaximal, characteristic, complemented
12C2×#11718687C211yesmaximal, characteristic, complemented
13C2×C4×#6107C211yesmaximal, characteristic, complemented
14C2×C4×#6104C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#520C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C13×#520—24no—
19C13×#520C2218yescomplemented
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×D4×C13—21no—
23C2×C4×D4×C13—21no—
24C2×C4×D4×C13C2211yescharacteristic
25C2×C4×D4×C13C2211yescharacteristic
26C2×C13×#117—21no—
27C2×C13×#117C2211yescharacteristic
28C22×C13×C4⋊C4—21no—
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C22×#6106C2211yescharacteristic
32C22×#6105C2211yescharacteristic
33C22×#6104C2211yescharacteristic
34C2×#88184C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36#11719239—24no—
37#11719239C2218yescomplemented
38C2×#88152—21no—
39C2×#88150—21no—
40C2×#88139—21no—
41C2×#88137—21no—
42C2×#88129C2211yescharacteristic
43C2×C4×D52C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46#11718900C2218yescomplemented
47#11718899C2218yes—
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×C22⋊#1055C2211yescharacteristic
53C2×C22⋊#1055C2211yescharacteristic
54C4×#6107C2218yescomplemented
55#11718689C2218yescomplemented
56#11718687C2218yescomplemented
57#11718682C2218yescomplemented
58#11718679C2218yescomplemented
59#11718677C2218yescomplemented
60C4×#6104C2218yescomplemented
61#11718668C2218yescomplemented
62#11718661C2218yescomplemented
63#11718631C2218yescomplemented
64C2×#88050C2211yescharacteristic
65C2×#88050C2211yescharacteristic
66#11718628C2218yescomplemented
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C2×C13×#41—24no—
78C2×C13×#41—24no—
79C2×C13×#41—22no—
80C2×C13×#41C2314yes—
81C22×Q8×C13C2311yescharacteristic
82C22×D4×C13—21no—
83C22×D4×C13C2311yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13—21no—
86C23×C4×C13—21no—
87C23×C4×C13—21no—
88C23×C4×C13C2311yescharacteristic
89C22×C22⋊D13—21no—
90C22×D52C2311yescharacteristic
91C22×C4×D13—21no—
92C22×Dic26—21no—
93C22×Dic26C2311yescharacteristic
94C4×Q8×C13—22no—
95C4×Q8×C13—22no—
96C4×Q8×C13C2314yes—
97C4×Q8×C13C2314yes—
98C4×D4×C13—28no—
99C4×D4×C13—28no—
100C4×D4×C13—22no—
101C4×D4×C13—22no—
102C4×D4×C13C2314yes—
103C4×D4×C13C2314yes—
104C13×#117—28no—
105C13×#117D414yes—
106C13×#117C2314yes—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—28no—
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C13×C4⋊C4C2311yescharacteristic
115C2×C13×C4⋊C4C2311yescharacteristic
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4D411yescharacteristic
120C2×C13×C22⋊C4D411yescharacteristic
121C2×C42×C13—21no—
122C2×C42×C13—21no—
123C2×C42×C13C2311yescharacteristic
124C2×C42×C13C2311yescharacteristic
125C2×C22⋊Dic13—21no—
126C2×#6107—24no—
127C2×#6107C2314yes—
128C2×#6106—24no—
129C2×#6106C2314yes—
130C2×#6105—24no—
131C2×#6105C2314yes—
132C2×#6104—24no—
133C2×#6104C2314yes—
134#88184—22no—
135#88184C2314yes—
136C2×#6103—21no—
137C2×#6103—21no—
138C2×#6103—21no—
139C2×#6103—21no—
140C2×C4⋊Dic13—21no—
141C2×C4⋊Dic13C2311yescharacteristic
142C2×C4⋊Dic13C2311yescharacteristic
143#88178—22no—
144#88178C2314yes—
145C2×#6101—21no—
146C2×#6101—21no—
147C2×C4×Dic13—21no—
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152#88152—28no—
153#88150—28no—
154#88139—28no—
155#88137—28no—
156#88129—22no—
157#88129C2314yes—
158C4×D52—22no—
159C4×D52C2314yes—
160#88123—22no—
161#88123C2314yes—
162C4×Dic26—22no—
163C4×Dic26C2314yes—
164#88075C2314yes—
165#88075C2314yes—
166#88072C2314yes—
167#88072C2314yes—
168C22⋊#1055C2314yes—
169C22⋊#1055C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88049C2314yes—
173#88049C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179C4⋊#1055C2314yes—
180#88043C2314yes—
181C4×#1055C2314yes—
182C2×#3124—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C23×D13—21no—
186C13×#41—216no—
187C13×#41—28no—
188C13×#41—28no—
189C2×Q8×C13—21no—
190C2×Q8×C13—22no—
191C2×Q8×C13#4114yes—
192C2×Q8×C13C2412yes—
193C2×D4×C13—28no—
194C2×D4×C13—24no—
195C2×D4×C13—21no—
196C2×D4×C13—22no—
197C2×D4×C13#4114yes—
198C2×D4×C13C2412yes—
199C22×C4×C13—28no—
200C22×C4×C13—21no—
201C22×C4×C13—24no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—24no—
207C22×C4×C13—24no—
208C22×C4×C13—24no—
209C22×C4×C13—82no—
210C22×C4×C13—82no—
211C22×C4×C13—82no—
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D412yes—
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2412yes—
219C22×C4×C13C2411yescharacteristic
220C2×C22⋊D13—24no—
221C2×C22⋊D13—82no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C2×D52—22no—
226C2×D52—22no—
227C2×D52—21no—
228C2×D52C2412yes—
229C2×C4×D13—24no—
230C2×C4×D13—82no—
231C2×Dic26—22no—
232C2×Dic26—22no—
233C2×Dic26—21no—
234C2×Dic26—24no—
235C2×Dic26—82no—
236C2×Dic26C2412yes—
237C13×C4⋊C4—24no—
238C13×C4⋊C4—24no—
239C13×C4⋊C4—24no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4—21no—
242C13×C4⋊C4C2×D414yes—
243C13×C4⋊C4C2×D414yes—
244C13×C4⋊C4C2412yes—
245C13×C4⋊C4C2412yes—
246C13×C22⋊C4—24no—
247C13×C22⋊C4—24no—
248C13×C22⋊C4C2×D414yes—
249C13×C22⋊C4C2×D414yes—
250C42×C13—24no—
251C42×C13—24no—
252C42×C13C2×D412yes—
253C42×C13C2×D412yes—
254C42×C13C2412yes—
255C42×C13C2412yes—
256C22⋊Dic13—24no—
257#6107—28no—
258#6106—28no—
259#6105—28no—
260#6104—28no—
261#6103—24no—
262#6103—24no—
263#6103—24no—
264#6103—24no—
265C4⋊Dic13—21no—
266C4⋊Dic13—21no—
267C4⋊Dic13—24no—
268C4⋊Dic13C2412yes—
269C4⋊Dic13C2412yes—
270#6101—24no—
271#6101—24no—
272C4×Dic13—24no—
273C2×#1055—22no—
274C2×#1055—22no—
275C2×#1055—22no—
276C2×#1055—22no—
277C2×#1055C2412yes—
278C2×#1055C2412yes—
279C2×#1055C2412yes—
280C2×#1055C2412yes—
281C2×#542—131no—
282C2×#520D1311yescharacteristic, complemented
283#3124—1316no—
284C2×#484—131no—
285C2×#480—131no—
286C2×#477—131no—
287C2×#474—131no—
288C2×#464—131no—
289C2×#463—131no—
290C2×#452—131no—
291C2×#449—131no—
292C2×#440—131no—
293C2×#440—131no—
294C2×C4×Q16—131no—
295C2×C4×D8—131no—
296C2×#433—131no—
297C23×C13—22no—
298C23×C13—24no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—42no—
303C23×C13—42no—
304C23×C13C22×D412yes—
305C23×C13C22×D411yescharacteristic
306C22×D13—22no—
307C22×D13—42no—
308C22×D13—42no—
309C22×D13—42no—
310Q8×C13—24no—
311Q8×C13—22no—
312Q8×C13C2×#4114yes—
313D4×C13—216no—
314D4×C13—24no—
315D4×C13—22no—
316D4×C13C2×#4114yes—
317C2×C4×C13—216no—
318C2×C4×C13—22no—
319C2×C4×C13—24no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—24no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—84no—
333C2×C4×C13—84no—
334C2×C4×C13—84no—
335C2×C4×C13C22×D412yes—
336C2×C4×C13C22×D412yes—
337C2×C4×C13C22×D412yes—
338C2×C4×C13C22×D412yes—
339C2×C4×C13C22×D412yes—
340C2×C4×C13C22×D411yescharacteristic
341C2×C4×C13C2×#4112yes—
342C2×C4×C13C2×#4112yes—
343C2×C4×C13C2511yescharacteristic
344C22⋊D13—84no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351D52—22no—
352D52—22no—
353D52—42no—
354C4×D13—84no—
355Dic26—22no—
356Dic26—22no—
357Dic26—42no—
358Dic26—84no—
359#1055—22no—
360#1055—22no—
361#1055—22no—
362#1055—22no—
363C22×#41C2×D1311yescharacteristic
364C22×Q16—131no—
365C22×SD16—131no—
366C22×SD16—131no—
367C22×D8—131no—
368#542—138no—
369#542—264no—
370C2×C4⋊Q8—131no—
371C2×#126—261no—
372C2×#124—131no—
373C2×#124—261no—
374C2×#123—261no—
375C2×C22⋊Q8—131no—
376C2×C22⋊Q8—261no—
377C2×#121—131no—
378#520—24no—
379#520C2×D1318yescomplemented
380C2×C4×Q8—131no—
381C2×C4×Q8C2×D1311yescharacteristic
382C2×C4×Q8C2×D1311yescharacteristic
383C2×C4×D4—21no—
384C2×C4×D4—21no—
385C2×C4×D4—131no—
386C2×C4×D4C2×D1311yescharacteristic
387C2×C4×D4C2×D1311yescharacteristic
388C2×#117—21no—
389C2×#117C2×D1311yescharacteristic
390C22×C4⋊C4—21no—
391C22×C4⋊C4C2×D1311yescharacteristic
392#484—138no—
393#480—138no—
394#477—138no—
395#474—138no—
396#464—138no—
397#463—138no—
398#452—138no—
399#449—138no—
400#440—138no—
401#440—138no—
402C4×Q16—138no—
403C4×D8—138no—
404#433—138no—
405C2×#107—131no—
406C2×#107—131no—
407C2×#107—131no—
408C2×#107—131no—
409C2×C4⋊C8—131no—
410C2×C4⋊C8—131no—
411C2×#103—131no—
412C2×#103—131no—
413C2×#103—131no—
414C2×#103—131no—
415C2×#102—131no—
416C2×#102—131no—
417C2×#102—131no—
418C2×#102—131no—
419C2×C22⋊C8—131no—
420C2×C22⋊C8—131no—
421C2×#97—131no—
422C2×C4×C8—131no—
423C22×C13—22no—
424C22×C13—24no—
425C22×C13—22no—
426C22×C13—22no—
427C22×C13—44no—
428C22×C13—48no—
429C22×C13—42no—
430C22×C13—42no—
431C22×C13#52512yes—
432C22×C13#57612yes—
433C22×C13#57812yes—
434C22×C13C23×D411yescharacteristic
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—84no—
439C4×C13—22no—
440C4×C13—24no—
441C4×C13—22no—
442C4×C13—22no—
443C4×C13—22no—
444C4×C13—22no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13#52512yes—
448C4×C13C22×#4111yescharacteristic
449C4×C13C22×#4111yescharacteristic
450Dic13—42no—
451Dic13—42no—
452Dic13—42no—
453C2×#41—24no—
454C2×#41—24no—
455C2×#41—22no—
456C2×#41C22×D1314yes—
457C22×Q8—131no—
458C22×Q8—261no—
459C22×Q8C22×D1311yescharacteristic
460C22×D4—21no—
461C22×D4—131no—
462C22×D4—261no—
463C22×D4C22×D1311yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—261no—
469C23×C4C22×D1311yescharacteristic
470C2×Q16—134no—
471C2×Q16—264no—
472C2×SD16—134no—
473C2×SD16—134no—
474C2×SD16—264no—
475C2×SD16—264no—
476C2×D8—134no—
477C2×D8—264no—
478C22×C8—131no—
479C22×C8—131no—
480C22×C8—131no—
481C22×C8—131no—
482C4⋊Q8—134no—
483C4⋊Q8—262no—
484#126—268no—
485#124—134no—
486#124—268no—
487#124—262no—
488#123—268no—
489C22⋊Q8—134no—
490C22⋊Q8—262no—
491C22⋊Q8—268no—
492#121—134no—
493#121—262no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—134no—
497C4×Q8—262no—
498C4×Q8C22×D1314yes—
499C4×Q8C22×D1314yes—
500C4×D4—28no—
501C4×D4—28no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—134no—
505C4×D4—262no—
506C4×D4C22×D1314yes—
507C4×D4C22×D1314yes—
508#117—28no—
509#117C22⋊D1314yes—
510#117C22×D1314yes—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—28no—
516C2×C4⋊C4—131no—
517C2×C4⋊C4—131no—
518C2×C4⋊C4—261no—
519C2×C4⋊C4—261no—
520C2×C4⋊C4—261no—
521C2×C4⋊C4C22⋊D1311yescharacteristic
522C2×C4⋊C4C22⋊D1311yescharacteristic
523C2×C4⋊C4C22×D1311yescharacteristic
524C2×C4⋊C4C22×D1311yescharacteristic
525C2×C4⋊C4C22×D1314yes—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—261no—
529C2×C22⋊C4—261no—
530C2×C22⋊C4—261no—
531C2×C22⋊C4—261no—
532C2×C22⋊C4—261no—
533C2×C22⋊C4C22⋊D1311yescharacteristic
534C2×C22⋊C4C22⋊D1311yescharacteristic
535C2×C42—21no—
536C2×C42—21no—
537C2×C42—261no—
538C2×C42C22×D1311yescharacteristic
539C2×C42C22×D1311yescharacteristic
540#107—134no—
541#107—134no—
542#107—134no—
543#107—134no—
544C4⋊C8—134no—
545C4⋊C8—134no—
546#103—134no—
547#103—134no—
548#103—134no—
549#103—134no—
550#102—134no—
551#102—134no—
552#102—134no—
553#102—134no—
554C22⋊C8—134no—
555C22⋊C8—134no—
556#97—134no—
557C4×C8—134no—
558C2×C13—42no—
559C2×C13—44no—
560C2×C13#312414yescomplemented
561C2×C13C2×#52511yescharacteristic
562C2×C13C2×#57611yescharacteristic
563C2×C13C2×#57811yescharacteristic
564D13—82no—
565C24—21no—
566C24—261no—
567C24C2×C22⋊D1311yescharacteristic
568#41—216no—
569#41—28no—
570#41—28no—
571C2×Q8—22no—
572C2×Q8—21no—
573C2×Q8—132no—
574C2×Q8—261no—
575C2×Q8—264no—
576C2×Q8—262no—
577C2×Q8—262no—
578C2×Q8—1042no—
579C2×Q8#612714yes—
580C2×Q8C23×D1312yes—
581C2×D4—28no—
582C2×D4—24no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—132no—
586C2×D4—264no—
587C2×D4—262no—
588C2×D4—262no—
589C2×D4—261no—
590C2×D4—1042no—
591C2×D4#612714yes—
592C2×D4C23×D1312yes—
593C22×C4—28no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—264no—
610C22×C4—1042no—
611C22×C4C2×C22⋊D1312yes—
612C22×C4C2×C22⋊D1311yescharacteristic
613C22×C4C2×C22⋊D1311yescharacteristic
614C22×C4C2×C22⋊D1311yescharacteristic
615C22×C4C2×C22⋊D1311yescharacteristic
616C22×C4C2×C22⋊D1311yescharacteristic
617C22×C4C23×D1312yes—
618C22×C4C23×D1311yescharacteristic
619Q16—268no—
620SD16—268no—
621SD16—268no—
622D8—268no—
623C2×C8—132no—
624C2×C8—132no—
625C2×C8—132no—
626C2×C8—132no—
627C2×C8—262no—
628C2×C8—262no—
629C2×C8—262no—
630C2×C8—262no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—132no—
637C4⋊C4—132no—
638C4⋊C4—261no—
639C4⋊C4—261no—
640C4⋊C4—264no—
641C4⋊C4—264no—
642C4⋊C4—264no—
643C4⋊C4C2×C22⋊D1314yes—
644C4⋊C4C2×C22⋊D1314yes—
645C4⋊C4C23×D1312yes—
646C4⋊C4C23×D1312yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—264no—
650C22⋊C4—264no—
651C22⋊C4—264no—
652C22⋊C4—264no—
653C22⋊C4—264no—
654C22⋊C4C2×C22⋊D1314yes—
655C22⋊C4C2×C22⋊D1314yes—
656C42—24no—
657C42—24no—
658C42—264no—
659C42C2×C22⋊D1312yes—
660C42C2×C22⋊D1312yes—
661C42C23×D1312yes—
662C42C23×D1312yes—
663C13C2×#312411yescharacteristic, complemented, Sylow
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—262no—
672C23—522no—
673C23—522no—
674C23—522no—
675C23C22×C22⋊D1312yes—
676C23C22×C22⋊D1311yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—262no—
680Q8—262no—
681Q8—522no—
682Q8—1044no—
683Q8C2×#612714yes—
684D4—216no—
685D4—24no—
686D4—22no—
687D4—262no—
688D4—262no—
689D4—522no—
690D4—1044no—
691D4C2×#612714yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4—522no—
716C2×C4—1044no—
717C2×C4C2×#612712yes—
718C2×C4C2×#612712yes—
719C2×C4C22×C22⋊D1312yes—
720C2×C4C22×C22⋊D1312yes—
721C2×C4C22×C22⋊D1312yes—
722C2×C4C22×C22⋊D1312yes—
723C2×C4C22×C22⋊D1312yes—
724C2×C4C22×C22⋊D1311yescharacteristic
725C2×C4C24×D1311yescharacteristic
726C8—262no—
727C8—262no—
728C8—262no—
729C8—262no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—48no—
738C22—522no—
739C22—522no—
740C22—522no—
741C22—1044no—
742C22#1171949612yes—
743C22#1171954012yes—
744C22#1171954312yes—
745C22C23×C22⋊D1311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—522no—
755C4—522no—
756C4—522no—
757C4#1171949612yes—
758C4C22×#612711yescharacteristic
759C4C22×#612711yescharacteristic
760C2—42no—
761C2—44no—
762C2—1042no—
763C2#1312509814yesdirect product factor
764C2C2×#1171949611yescharacteristic
765C2C2×#1171954011yescharacteristic
766C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#520C2
socleC23×C13C22×D4
prime radicalC2×#11718899C2
hypercenterC2×#520D13
hypocenterC13C2×#3124
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#11719239C2semidirect
2. #13125098C2direct (N × H)
3. C2×#11718631C2semidirect
4. C2×#11718628C2semidirect
5. C2×#11718682C2semidirect
6. C2×#11718668C2semidirect
7. C2×#11718689C2semidirect
8. C2×#11718677C2semidirect
9. C2×#11718900C2semidirect
11. C2×#11718679C2semidirect
12. C2×#11718687C2semidirect
13. C2×C4×#6107C2semidirect
14. C2×C4×#6104C2semidirect
15. C2×#11718661C2semidirect
16. C2×C13×#520C2semidirect
19. C13×#520C22semidirect
37. #11719239C22semidirect
46. #11718900C22semidirect
54. C4×#6107C22semidirect
55. #11718689C22semidirect
56. #11718687C22semidirect
57. #11718682C22semidirect
58. #11718679C22semidirect
59. #11718677C22semidirect
60. C4×#6104C22semidirect
61. #11718668C22semidirect
62. #11718661C22semidirect
63. #11718631C22semidirect
66. #11718628C22semidirect
282. C2×#520D13semidirect
379. #520C2×D13semidirect
560. C2×C13#3124semidirect
663. C13C2×#3124semidirect
763. C2#13125098direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192392
#131250982
C2×#117186312
C2×#117186282
C2×#117186822
C2×#117186682
C2×#117186892
C2×#117186772
C2×#117189002
C2×#117188992
C2×#117186792
C2×#117186872
C2×C4×#61072
C2×C4×#61042
C2×#117186612
C2×C13×#5202
C2×#312413