Finite Group Databasebeta

← C2×#13125107 #16731244

Subgroups — C2×#13125107 #16731244

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×#11719228C211yesmaximal, characteristic, complemented
2#13125107C2116yesmaximal, direct product factor
3C2×#11718695C211yesmaximal, characteristic, complemented
4C2×#11718704C211yesmaximal, characteristic, complemented
5C2×#11718755C211yesmaximal, characteristic, complemented
6C2×#11718745C211yesmaximal, characteristic, complemented
7C2×#11718715C211yesmaximal, characteristic, complemented
8C2×#11718718C211yesmaximal, characteristic, complemented
9C2×#11718708C211yesmaximal, characteristic, complemented
10C2×#11718698C211yesmaximal, characteristic
11C2×#11718675C211yesmaximal, characteristic, complemented
12C2×#11718691C211yesmaximal, characteristic, complemented
13C2×C4×#6106C211yesmaximal, characteristic, complemented
14C2×C4×#6105C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#542C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C13×#542—24no—
19C13×#542C2218yescomplemented
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×#126—21no—
22C2×C13×#124—21no—
23C2×C13×#124C2211yescharacteristic
24C2×C13×#123—21no—
25C2×C13×C22⋊Q8—21no—
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C13×#121C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C2×C13×#117C2211yescharacteristic
31C22×#6107C2211yescharacteristic
32C22×#6106C2211yescharacteristic
33C22×#6105C2211yescharacteristic
34C22×#6104C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36#11719228—24no—
37#11719228C2218yescomplemented
38C2×#88146—21no—
39C2×C4⋊C4×D13—21no—
40C2×#88135—21no—
41C2×#88135—21no—
42C2×C4×D52C2211yescharacteristic
43C2×C4×D52C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×#88072C2211yescharacteristic
49C2×#88072C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52#11718755C2218yescomplemented
53#11718745C2218yescomplemented
54#11718718C2218yescomplemented
55#11718715C2218yescomplemented
56#11718708C2218yescomplemented
57#11718704C2218yescomplemented
58#11718698C2218yes—
59#11718695C2218yescomplemented
60#11718691C2218yescomplemented
61C4×#6106C2218yescomplemented
62C4×#6105C2218yescomplemented
63#11718675C2218yescomplemented
64#11718661C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88048C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13—21no—
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13C2311yescharacteristic
83C22×C22⋊D13—21no—
84C23×Dic13—21no—
85C2×#6127—22no—
86C2×#6127—24no—
87C2×#6127—24no—
88C2×#6127C2314yes—
89C22×D52C2311yescharacteristic
90C22×C4×D13—21no—
91C22×C4×D13—21no—
92C22×C4×D13—21no—
93C22×Dic26C2311yescharacteristic
94C13×C4⋊Q8—22no—
95C13×C4⋊Q8C2314yes—
96C13×#126—28no—
97C13×#124—28no—
98C13×#124—22no—
99C13×#124C2314yes—
100C13×#123—28no—
101C13×C22⋊Q8—22no—
102C13×C22⋊Q8—28no—
103C13×C22⋊Q8C2314yes—
104C13×#121—22no—
105C13×#121C2314yes—
106C4×Q8×C13—22no—
107C4×Q8×C13C2314yes—
108C4×D4×C13—22no—
109C4×D4×C13C2314yes—
110C13×#117D414yes—
111C13×#117C2314yes—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4D411yescharacteristic
116C2×C13×C4⋊C4D411yescharacteristic
117C2×C13×C4⋊C4C2311yescharacteristic
118C2×C13×C4⋊C4C2311yescharacteristic
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4—21no—
124C2×C13×C22⋊C4D411yescharacteristic
125C2×C13×C22⋊C4D411yescharacteristic
126C2×C42×C13—21no—
127C2×C42×C13C2311yescharacteristic
128C2×C42×C13C2311yescharacteristic
129C2×#6107—24no—
130C2×#6107C2314yes—
131C2×#6106—24no—
132C2×#6106C2314yes—
133C2×#6105—24no—
134C2×#6105C2314yes—
135C2×#6104—24no—
136C2×#6104C2314yes—
137C2×#6103—21no—
138C2×#6103—21no—
139C2×C4⋊Dic13—21no—
140C2×C4⋊Dic13—22no—
141C2×C4⋊Dic13C2311yescharacteristic
142C2×C4⋊Dic13C2311yescharacteristic
143C2×C4⋊Dic13C2314yes—
144C2×#6101—21no—
145C2×#6101—21no—
146C2×C4×Dic13—21no—
147C2×C4×Dic13—21no—
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152#88146—28no—
153C4⋊C4×D13—28no—
154#88135—28no—
155#88135—28no—
156C4×D52—22no—
157C4×D52—22no—
158C4×D52C2314yes—
159C4×D52C2314yes—
160C4×Dic26—22no—
161C4×Dic26—22no—
162C4×Dic26C2314yes—
163C4×Dic26C2314yes—
164#88075C2314yes—
165#88075C2314yes—
166#88072C2314yes—
167#88072C2314yes—
168C22⋊#1055C2314yes—
169C22⋊#1055C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88049C2314yes—
173#88049C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178C4⋊#1055C2314yes—
179C4⋊#1055C2314yes—
180#88043C2314yes—
181C4×#1055C2314yes—
182C2×#3125—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C23×D13—21no—
186C2×Q8×C13—21no—
187C2×Q8×C13—24no—
188C2×Q8×C13—22no—
189C2×Q8×C13—22no—
190C2×Q8×C13—82no—
191C2×Q8×C13C2412yes—
192C2×D4×C13—24no—
193C2×D4×C13—21no—
194C2×D4×C13—22no—
195C2×D4×C13—22no—
196C2×D4×C13—82no—
197C2×D4×C13C2412yes—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—24no—
204C22×C4×C13—82no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2411yescharacteristic
213C2×C22⋊D13—28no—
214C2×C22⋊D13—24no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—24no—
219C22×Dic13—82no—
220#6127—216no—
221#6127—28no—
222#6127—28no—
223C2×D52—21no—
224C2×D52—22no—
225C2×D52#4114yes—
226C2×D52C2412yes—
227C2×C4×D13—28no—
228C2×C4×D13—24no—
229C2×C4×D13—24no—
230C2×C4×D13—24no—
231C2×C4×D13—82no—
232C2×C4×D13—82no—
233C2×Dic26—21no—
234C2×Dic26—22no—
235C2×Dic26#4114yes—
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⋊C4—24no—
249C13×C22⋊C4—24no—
250C13×C22⋊C4—24no—
251C13×C22⋊C4C2×D414yes—
252C13×C22⋊C4C2×D414yes—
253C42×C13—24no—
254C42×C13C2×D412yes—
255C42×C13C2×D412yes—
256C42×C13C2412yes—
257C42×C13C2412yes—
258#6107—28no—
259#6106—28no—
260#6105—28no—
261#6104—28no—
262#6103—24no—
263#6103—24no—
264C4⋊Dic13—21no—
265C4⋊Dic13—21no—
266C4⋊Dic13—24no—
267C4⋊Dic13C2412yes—
268C4⋊Dic13C2412yes—
269#6101—24no—
270#6101—24no—
271C4×Dic13—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×#542D1311yescharacteristic, complemented
282C2×#520—131no—
283#3125—1316no—
284C2×#481—131no—
285C2×#483—131no—
286C2×#475—131no—
287C2×#476—131no—
288C2×#464—131no—
289C2×#463—131no—
290C2×#452—131no—
291C2×#449—131no—
292C2×#442—131no—
293C2×#441—131no—
294C2×C4×SD16—131no—
295C2×C4×SD16—131no—
296C2×#433—131no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—42no—
302C23×C13—42no—
303C23×C13—42no—
304C23×C13C22×D412yes—
305C23×C13C22×D411yescharacteristic
306C22×D13—24no—
307C22×D13—22no—
308C22×D13—42no—
309C22×D13—42no—
310Q8×C13—22no—
311Q8×C13—22no—
312Q8×C13—42no—
313Q8×C13—84no—
314D4×C13—22no—
315D4×C13—22no—
316D4×C13—42no—
317D4×C13—84no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—24no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—84no—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D412yes—
336C2×C4×C13C22×D412yes—
337C2×C4×C13C22×D412yes—
338C2×C4×C13C22×D411yescharacteristic
339C2×C4×C13C2×#4112yes—
340C2×C4×C13C2×#4112yes—
341C2×C4×C13C2511yescharacteristic
342C22⋊D13—216no—
343C2×Dic13—24no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—84no—
350D52—24no—
351D52—22no—
352D52C2×#4114yes—
353C4×D13—216no—
354C4×D13—84no—
355C4×D13—84no—
356Dic26—24no—
357Dic26—22no—
358Dic26C2×#4114yes—
359#1055—22no—
360#1055—22no—
361#1055—22no—
362#1055—22no—
363C22×#41—131no—
364C22×Q16—131no—
365C22×SD16—131no—
366C22×SD16—131no—
367C22×D8—131no—
368#542—24no—
369#542C2×D1318yescomplemented
370C2×C4⋊Q8C2×D1311yescharacteristic
371C2×#126—21no—
372C2×#124—21no—
373C2×#124C2×D1311yescharacteristic
374C2×#123—21no—
375C2×C22⋊Q8—21no—
376C2×C22⋊Q8C2×D1311yescharacteristic
377C2×#121C2×D1311yescharacteristic
378#520—138no—
379#520—264no—
380C2×C4×Q8—131no—
381C2×C4×Q8—131no—
382C2×C4×Q8C2×D1311yescharacteristic
383C2×C4×D4—131no—
384C2×C4×D4—131no—
385C2×C4×D4—261no—
386C2×C4×D4—261no—
387C2×C4×D4C2×D1311yescharacteristic
388C2×#117—261no—
389C2×#117C2×D1311yescharacteristic
390C22×C4⋊C4—131no—
391C22×C4⋊C4—261no—
392#483—138no—
393#481—138no—
394#476—138no—
395#475—138no—
396#464—138no—
397#463—138no—
398#452—138no—
399#449—138no—
400#442—138no—
401#441—138no—
402C4×SD16—138no—
403C4×SD16—138no—
404#433—138no—
405C2×#106—131no—
406C2×#106—131no—
407C2×#106—131no—
408C2×#106—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—22no—
425C22×C13—22no—
426C22×C13—44no—
427C22×C13—42no—
428C22×C13—42no—
429C22×C13—42no—
430C22×C13—84no—
431C22×C13#52512yes—
432C22×C13#57712yes—
433C22×C13#57712yes—
434C22×C13C23×D411yescharacteristic
435C2×D13—24no—
436C2×D13—48no—
437C2×D13—42no—
438C2×D13—42no—
439C4×C13—22no—
440C4×C13—22no—
441C4×C13—22no—
442C4×C13—22no—
443C4×C13—22no—
444C4×C13—42no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13#52512yes—
448C4×C13C22×#4111yescharacteristic
449C4×C13C22×#4111yescharacteristic
450Dic13—24no—
451Dic13—42no—
452Dic13—42no—
453C2×#41—134no—
454C2×#41—264no—
455C2×#41—264no—
456C2×#41—262no—
457C22×Q8—21no—
458C22×Q8—131no—
459C22×Q8C22×D1311yescharacteristic
460C22×D4—21no—
461C22×D4—131no—
462C22×D4—261no—
463C22×D4C22×D1311yescharacteristic
464C23×C4—21no—
465C23×C4—261no—
466C23×C4—261no—
467C23×C4—261no—
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—22no—
483C4⋊Q8C22×D1314yes—
484#126—28no—
485#124—28no—
486#124—22no—
487#124C22×D1314yes—
488#123—28no—
489C22⋊Q8—22no—
490C22⋊Q8—28no—
491C22⋊Q8C22×D1314yes—
492#121—22no—
493#121C22×D1314yes—
494C4×Q8—22no—
495C4×Q8—134no—
496C4×Q8—134no—
497C4×Q8—262no—
498C4×Q8—262no—
499C4×Q8C22×D1314yes—
500C4×D4—22no—
501C4×D4—134no—
502C4×D4—134no—
503C4×D4—268no—
504C4×D4—268no—
505C4×D4—262no—
506C4×D4—262no—
507C4×D4C22×D1314yes—
508#117—268no—
509#117C22⋊D1314yes—
510#117C22×D1314yes—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—131no—
515C2×C4⋊C4—131no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—261no—
518C2×C4⋊C4—262no—
519C2×C4⋊C4—261no—
520C2×C4⋊C4—261no—
521C2×C4⋊C4—268no—
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⋊C4C22⋊D1311yescharacteristic
534C2×C22⋊C4C22⋊D1311yescharacteristic
535C2×C42—21no—
536C2×C42—261no—
537C2×C42—261no—
538C2×C42C22×D1311yescharacteristic
539C2×C42C22×D1311yescharacteristic
540#106—134no—
541#106—134no—
542#106—134no—
543#106—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—82no—
560C2×C13#312514yescomplemented
561C2×C13C2×#52511yescharacteristic
562C2×C13C2×#57711yescharacteristic
563C2×C13C2×#57711yescharacteristic
564D13—44no—
565C24—21no—
566C24—261no—
567C24C2×C22⋊D1311yescharacteristic
568#41—268no—
569#41—268no—
570#41—2616no—
571C2×Q8—21no—
572C2×Q8—24no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—82no—
576C2×Q8—134no—
577C2×Q8—132no—
578C2×Q8—262no—
579C2×Q8—261no—
580C2×Q8C23×D1312yes—
581C2×D4—24no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—82no—
586C2×D4—134no—
587C2×D4—132no—
588C2×D4—268no—
589C2×D4—264no—
590C2×D4—262no—
591C2×D4—261no—
592C2×D4C23×D1312yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—82no—
600C22×C4—268no—
601C22×C4—261no—
602C22×C4—264no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—264no—
606C22×C4—264no—
607C22×C4—264no—
608C22×C4—1042no—
609C22×C4—1042no—
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—264no—
639C4⋊C4—261no—
640C4⋊C4—261no—
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—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—264no—
653C22⋊C4—264no—
654C22⋊C4C2×C22⋊D1314yes—
655C22⋊C4C2×C22⋊D1314yes—
656C42—24no—
657C42—264no—
658C42—264no—
659C42C2×C22⋊D1312yes—
660C42C2×C22⋊D1312yes—
661C42C23×D1312yes—
662C42C23×D1312yes—
663C13C2×#312511yescharacteristic, complemented, Sylow
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—264no—
672C23—262no—
673C23—522no—
674C23—522no—
675C23C22×C22⋊D1312yes—
676C23C22×C22⋊D1311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—84no—
681Q8—134no—
682Q8—264no—
683Q8—262no—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—134no—
689D4—2616no—
690D4—264no—
691D4—262no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—84no—
707C2×C4—2616no—
708C2×C4—264no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—522no—
713C2×C4—522no—
714C2×C4—1044no—
715C2×C4—1044no—
716C2×C4—1044no—
717C2×C4#41×D1312yes—
718C2×C4#41×D1312yes—
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—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—264no—
739C22—522no—
740C22—522no—
741C22—528no—
742C22#1171953312yes—
743C22#1171954112yes—
744C22#1171954212yes—
745C22C23×C22⋊D1311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—264no—
755C4—522no—
756C4—522no—
757C4#1171953312yes—
758C4C2×#41×D1311yescharacteristic
759C4C2×#41×D1311yescharacteristic
760C2—42no—
761C2—82no—
762C2—524no—
763C2#1312510714yesdirect product factor
764C2C2×#1171953311yescharacteristic
765C2C2×#1171954211yescharacteristic
766C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#542C2
socleC23×C13C22×D4
prime radicalC2×#11718698C2
hypercenterC2×#542D13
hypocenterC13C2×#3125
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11719228C2semidirect
2. #13125107C2direct (N × H)
3. C2×#11718695C2semidirect
4. C2×#11718704C2semidirect
5. C2×#11718755C2semidirect
6. C2×#11718745C2semidirect
7. C2×#11718715C2semidirect
8. C2×#11718718C2semidirect
9. C2×#11718708C2semidirect
11. C2×#11718675C2semidirect
12. C2×#11718691C2semidirect
13. C2×C4×#6106C2semidirect
14. C2×C4×#6105C2semidirect
15. C2×#11718661C2semidirect
16. C2×C13×#542C2semidirect
19. C13×#542C22semidirect
37. #11719228C22semidirect
52. #11718755C22semidirect
53. #11718745C22semidirect
54. #11718718C22semidirect
55. #11718715C22semidirect
56. #11718708C22semidirect
57. #11718704C22semidirect
59. #11718695C22semidirect
60. #11718691C22semidirect
61. C4×#6106C22semidirect
62. C4×#6105C22semidirect
63. #11718675C22semidirect
64. #11718661C22semidirect
281. C2×#542D13semidirect
369. #542C2×D13semidirect
560. C2×C13#3125semidirect
663. C13C2×#3125semidirect
763. C2#13125107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192282
#131251072
C2×#117186952
C2×#117187042
C2×#117187552
C2×#117187452
C2×#117187152
C2×#117187182
C2×#117187082
C2×#117186982
C2×#117186752
C2×#117186912
C2×C4×#61062
C2×C4×#61052
C2×#117186612
C2×C13×#5422
C2×#312513