Finite Group Databasebeta

← C2×#13125050 #16731182

Subgroups — C2×#13125050 #16731182

Order 3328.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719223C211yesmaximal, characteristic, complemented
2#13125050C2116yesmaximal, direct product factor
3C2×#11718631C211yesmaximal, characteristic, complemented
4C2×#11718632C211yesmaximal, characteristic, complemented
5C2×#11718683C211yesmaximal, characteristic, complemented
6C2×#11718670C211yesmaximal, characteristic, complemented
7C2×#11718692C211yesmaximal, characteristic, complemented
8C2×#11718680C211yesmaximal, characteristic, complemented
9C2×#11718900C211yesmaximal, characteristic
10C2×#11718900C211yesmaximal, characteristic
11C2×#11718691C211yesmaximal, characteristic, complemented
12C2×#11718679C211yesmaximal, characteristic, complemented
13C2×C4×#6107C211yesmaximal, characteristic, complemented
14C2×C4×#6105C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#520C211yesmaximal, characteristic
17C22×C13×#41C2211yescharacteristic
18C13×#520—24no—
19C13×#520C2218yes—
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×#6107C2211yescharacteristic
32C22×#6105C2211yescharacteristic
33C22×#6105C2211yescharacteristic
34C2×#88178C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36#11719223—24no—
37#11719223C2218yescomplemented
38C2×#88143—21no—
39C2×#88143—21no—
40C2×#88133—21no—
41C2×#88133—21no—
42C2×#88124C2211yescharacteristic
43C2×#88123C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46#11718900C2218yes—
47#11718900C2218yes—
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×C22⋊#1055C2211yescharacteristic
53C2×C22⋊#1055C2211yescharacteristic
54#11718692C2218yescomplemented
55#11718691C2218yescomplemented
56C4×#6107C2218yescomplemented
57#11718683C2218yescomplemented
58#11718680C2218yescomplemented
59#11718679C2218yescomplemented
60C4×#6105C2218yescomplemented
61#11718670C2218yescomplemented
62#11718661C2218yescomplemented
63#11718632C2218yescomplemented
64#11718631C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88050C2211yescharacteristic
68C2×#88050C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
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×Dic26C2311yescharacteristic
90C22×Dic26C2311yescharacteristic
91C4×Q8×C13—22no—
92C4×Q8×C13—22no—
93C4×Q8×C13C2314yes—
94C4×Q8×C13C2314yes—
95C4×D4×C13—28no—
96C4×D4×C13—28no—
97C4×D4×C13—22no—
98C4×D4×C13—22no—
99C4×D4×C13C2314yes—
100C4×D4×C13C2314yes—
101C13×#117—28no—
102C13×#117D414yes—
103C13×#117C2314yes—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—28no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C4⋊C4C2314yes—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4D411yescharacteristic
117C2×C13×C22⋊C4D411yescharacteristic
118C2×C42×C13—21no—
119C2×C42×C13—21no—
120C2×C42×C13C2311yescharacteristic
121C2×C42×C13C2311yescharacteristic
122C2×C22⋊Dic13—21no—
123C2×C22⋊Dic13—21no—
124C2×#6107—24no—
125C2×#6107—24no—
126C2×#6107C2314yes—
127C2×#6107C2314yes—
128C2×#6105—24no—
129C2×#6105—24no—
130C2×#6105C2314yes—
131C2×#6105C2314yes—
132C2×C4⋊Dic13—21no—
133C2×C4⋊Dic13—21no—
134C2×C4⋊Dic13C2311yescharacteristic
135C2×C4⋊Dic13C2311yescharacteristic
136#88178—22no—
137#88178—22no—
138#88178C2314yes—
139#88178C2314yes—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6101—21no—
146C2×C4×Dic13—21no—
147C2×C4×Dic13—21no—
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152#88143—28no—
153#88143—28no—
154#88133—28no—
155#88133—28no—
156#88124—22no—
157#88124C2314yes—
158#88123—22no—
159#88123C2314yes—
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#88050C2314yes—
173#88050C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179C4⋊#1055C2314yes—
180#88043C2314yes—
181C4×#1055C2314yes—
182C2×#3120—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C13×#41—216no—
186C13×#41—28no—
187C13×#41—28no—
188C2×Q8×C13—21no—
189C2×Q8×C13—22no—
190C2×Q8×C13#4114yes—
191C2×Q8×C13C2412yes—
192C2×D4×C13—28no—
193C2×D4×C13—24no—
194C2×D4×C13—21no—
195C2×D4×C13—22no—
196C2×D4×C13#4114yes—
197C2×D4×C13C2412yes—
198C22×C4×C13—28no—
199C22×C4×C13—21no—
200C22×C4×C13—24no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—24no—
206C22×C4×C13—24no—
207C22×C4×C13—24no—
208C22×C4×C13—82no—
209C22×C4×C13—82no—
210C22×C4×C13—82no—
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2411yescharacteristic
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
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—21no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4C2×D414yes—
237C13×C4⋊C4C2×D414yes—
238C13×C4⋊C4C2412yes—
239C13×C4⋊C4C2412yes—
240C13×C22⋊C4—24no—
241C13×C22⋊C4—24no—
242C13×C22⋊C4C2×D414yes—
243C13×C22⋊C4C2×D414yes—
244C42×C13—24no—
245C42×C13—24no—
246C42×C13C2×D412yes—
247C42×C13C2×D412yes—
248C42×C13C2412yes—
249C42×C13C2412yes—
250C22⋊Dic13—24no—
251C22⋊Dic13—24no—
252#6107—28no—
253#6107—28no—
254#6105—28no—
255#6105—28no—
256C4⋊Dic13—21no—
257C4⋊Dic13—21no—
258C4⋊Dic13—24no—
259C4⋊Dic13—24no—
260C4⋊Dic13C2412yes—
261C4⋊Dic13C2412yes—
262#6101—24no—
263#6101—24no—
264#6101—24no—
265#6101—24no—
266#6101—24no—
267#6101—24no—
268C4×Dic13—24no—
269C4×Dic13—24no—
270C2×#1055—22no—
271C2×#1055—22no—
272C2×#1055—22no—
273C2×#1055—22no—
274C2×#1055C2412yes—
275C2×#1055C2412yes—
276C2×#1055C2412yes—
277C2×#1055C2412yes—
278C2×#541—131no—
279C2×#520D1311yescharacteristic
280#3120—1316no—
281C2×#484—131no—
282C2×#483—131no—
283C2×#479—131no—
284C2×#478—131no—
285C2×#462—131no—
286C2×#461—131no—
287C2×#452—131no—
288C2×#452—131no—
289C2×#441—131no—
290C2×#440—131no—
291C2×C4×Q16—131no—
292C2×C4×SD16—131no—
293C2×#433—131no—
294C23×C13—22no—
295C23×C13—24no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—42no—
300C23×C13—42no—
301C23×C13C22×D412yes—
302C23×C13C22×D411yescharacteristic
303Q8×C13—24no—
304Q8×C13—22no—
305Q8×C13C2×#4114yes—
306D4×C13—216no—
307D4×C13—24no—
308D4×C13—22no—
309D4×C13C2×#4114yes—
310C2×C4×C13—216no—
311C2×C4×C13—22no—
312C2×C4×C13—24no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—24no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13—84no—
326C2×C4×C13—84no—
327C2×C4×C13—84no—
328C2×C4×C13C22×D412yes—
329C2×C4×C13C22×D412yes—
330C2×C4×C13C22×D412yes—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×D411yescharacteristic
334C2×C4×C13C2×#4112yes—
335C2×C4×C13C2×#4112yes—
336C2×C4×C13C2511yescharacteristic
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345Dic26—22no—
346Dic26—22no—
347Dic26—22no—
348Dic26—22no—
349Dic26—42no—
350Dic26—42no—
351#1055—22no—
352#1055—22no—
353#1055—22no—
354#1055—22no—
355C22×#41C2×D1311yescharacteristic
356C22×Q16—131no—
357C22×Q16—131no—
358C22×SD16—131no—
359C22×SD16—131no—
360#541—138no—
361#541—264no—
362C2×C4⋊Q8—131no—
363C2×#126—261no—
364C2×#126—261no—
365C2×#125—131no—
366C2×#125—261no—
367C2×#125—261no—
368C2×C22⋊Q8—131no—
369C2×C22⋊Q8—131no—
370#520—24no—
371#520C2×D1318yes—
372C2×C4×Q8—131no—
373C2×C4×Q8—131no—
374C2×C4×Q8C2×D1311yescharacteristic
375C2×C4×Q8C2×D1311yescharacteristic
376C2×C4×D4—21no—
377C2×C4×D4—21no—
378C2×C4×D4C2×D1311yescharacteristic
379C2×C4×D4C2×D1311yescharacteristic
380C2×#117—21no—
381C2×#117C2×D1311yescharacteristic
382C22×C4⋊C4—21no—
383C22×C4⋊C4C2×D1311yescharacteristic
384#484—138no—
385#483—138no—
386#479—138no—
387#478—138no—
388#462—138no—
389#461—138no—
390#452—138no—
391#452—138no—
392#441—138no—
393#440—138no—
394C4×Q16—138no—
395C4×SD16—138no—
396#433—138no—
397C2×#107—131no—
398C2×#107—131no—
399C2×#106—131no—
400C2×#106—131no—
401C2×C4⋊C8—131no—
402C2×C4⋊C8—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—131no—
409C2×#102—131no—
410C2×#102—131no—
411C2×C22⋊C8—131no—
412C2×C22⋊C8—131no—
413C2×#97—131no—
414C2×C4×C8—131no—
415C22×C13—22no—
416C22×C13—24no—
417C22×C13—22no—
418C22×C13—22no—
419C22×C13—44no—
420C22×C13—48no—
421C22×C13—42no—
422C22×C13—42no—
423C22×C13#52512yes—
424C22×C13#57712yes—
425C22×C13#57812yes—
426C22×C13C23×D411yescharacteristic
427C4×C13—22no—
428C4×C13—24no—
429C4×C13—22no—
430C4×C13—22no—
431C4×C13—22no—
432C4×C13—22no—
433C4×C13—42no—
434C4×C13—42no—
435C4×C13#52512yes—
436C4×C13C22×#4111yescharacteristic
437C4×C13C22×#4111yescharacteristic
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441Dic13—42no—
442C2×#41—24no—
443C2×#41—24no—
444C2×#41—22no—
445C2×#41C22×D1314yes—
446C22×Q8—131no—
447C22×Q8—131no—
448C22×Q8C22×D1311yescharacteristic
449C22×D4—21no—
450C22×D4C22×D1311yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—21no—
455C23×C4C22×D1311yescharacteristic
456C2×Q16—134no—
457C2×Q16—134no—
458C2×Q16—264no—
459C2×Q16—264no—
460C2×SD16—134no—
461C2×SD16—134no—
462C2×SD16—264no—
463C2×SD16—264no—
464C22×C8—131no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—131no—
468C4⋊Q8—134no—
469C4⋊Q8—262no—
470#126—268no—
471#126—268no—
472#125—134no—
473#125—268no—
474#125—268no—
475#125—262no—
476C22⋊Q8—134no—
477C22⋊Q8—134no—
478C22⋊Q8—262no—
479C22⋊Q8—262no—
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8—134no—
483C4×Q8—134no—
484C4×Q8—262no—
485C4×Q8—262no—
486C4×Q8C22×D1314yes—
487C4×Q8C22×D1314yes—
488C4×D4—28no—
489C4×D4—28no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4C22×D1314yes—
493C4×D4C22×D1314yes—
494#117—28no—
495#117C22⋊D1314yes—
496#117C22×D1314yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—28no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4C22⋊D1311yescharacteristic
513C2×C4⋊C4C22⋊D1311yescharacteristic
514C2×C4⋊C4C22×D1311yescharacteristic
515C2×C4⋊C4C22×D1311yescharacteristic
516C2×C4⋊C4C22×D1314yes—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4C22⋊D1311yescharacteristic
522C2×C22⋊C4C22⋊D1311yescharacteristic
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—261no—
526C2×C42—261no—
527C2×C42C22×D1311yescharacteristic
528C2×C42C22×D1311yescharacteristic
529#107—134no—
530#107—134no—
531#106—134no—
532#106—134no—
533C4⋊C8—134no—
534C4⋊C8—134no—
535#103—134no—
536#103—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#103—134no—
541#102—134no—
542#102—134no—
543C22⋊C8—134no—
544C22⋊C8—134no—
545#97—134no—
546C4×C8—134no—
547C2×C13—42no—
548C2×C13—44no—
549C2×C13#312014yescomplemented
550C2×C13C2×#52511yescharacteristic
551C2×C13C2×#57711yescharacteristic
552C2×C13C2×#57811yescharacteristic
553C24—21no—
554C24C2×C22⋊D1311yescharacteristic
555#41—216no—
556#41—28no—
557#41—28no—
558C2×Q8—22no—
559C2×Q8—21no—
560C2×Q8—132no—
561C2×Q8—132no—
562C2×Q8—261no—
563C2×Q8—261no—
564C2×Q8—262no—
565C2×Q8—262no—
566C2×Q8—262no—
567C2×Q8—262no—
568C2×Q8#612714yes—
569C2×Q8C23×D1312yes—
570C2×D4—28no—
571C2×D4—24no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4#612714yes—
575C2×D4C23×D1312yes—
576C22×C4—28no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4C2×C22⋊D1312yes—
594C22×C4C2×C22⋊D1311yescharacteristic
595C22×C4C2×C22⋊D1311yescharacteristic
596C22×C4C2×C22⋊D1311yescharacteristic
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C2×C22⋊D1311yescharacteristic
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601Q16—268no—
602Q16—268no—
603SD16—268no—
604SD16—268no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—132no—
608C2×C8—132no—
609C2×C8—262no—
610C2×C8—262no—
611C2×C8—262no—
612C2×C8—262no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—132no—
619C4⋊C4—132no—
620C4⋊C4—261no—
621C4⋊C4—261no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4—264no—
626C4⋊C4—264no—
627C4⋊C4—264no—
628C4⋊C4—264no—
629C4⋊C4—264no—
630C4⋊C4C2×C22⋊D1314yes—
631C4⋊C4C2×C22⋊D1314yes—
632C4⋊C4C23×D1312yes—
633C4⋊C4C23×D1312yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—264no—
637C22⋊C4—264no—
638C22⋊C4C2×C22⋊D1314yes—
639C22⋊C4C2×C22⋊D1314yes—
640C42—24no—
641C42—24no—
642C42—264no—
643C42—264no—
644C42C2×C22⋊D1312yes—
645C42C2×C22⋊D1312yes—
646C42C23×D1312yes—
647C42C23×D1312yes—
648C13C2×#312011yescharacteristic, complemented, Sylow
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23C22×C22⋊D1312yes—
657C23C22×C22⋊D1311yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—262no—
661Q8—262no—
662Q8—262no—
663Q8—262no—
664Q8—522no—
665Q8—522no—
666Q8C2×#612714yes—
667D4—216no—
668D4—24no—
669D4—22no—
670D4C2×#612714yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—522no—
694C2×C4—522no—
695C2×C4—522no—
696C2×C4—522no—
697C2×C4C2×#612712yes—
698C2×C4C2×#612712yes—
699C2×C4C22×C22⋊D1312yes—
700C2×C4C22×C22⋊D1312yes—
701C2×C4C22×C22⋊D1312yes—
702C2×C4C22×C22⋊D1312yes—
703C2×C4C22×C22⋊D1312yes—
704C2×C4C22×C22⋊D1311yescharacteristic
705C2×C4C24×D1311yescharacteristic
706C8—262no—
707C8—262no—
708C8—262no—
709C8—262no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#1171949612yes—
719C22#1171954112yes—
720C22#1171954312yes—
721C22C23×C22⋊D1311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4—522no—
734C4#1171949612yes—
735C4C22×#612711yescharacteristic
736C4C22×#612711yescharacteristic
737C2—42no—
738C2—44no—
739C2#1312505014yesdirect product factor
740C2C2×#1171949611yescharacteristic
741C2C2×#1171954111yescharacteristic
742C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#520C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenterC2×#520D13
hypocenterC13C2×#3120
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×#11719223C2semidirect
2. #13125050C2direct (N × H)
3. C2×#11718631C2semidirect
4. C2×#11718632C2semidirect
5. C2×#11718683C2semidirect
6. C2×#11718670C2semidirect
7. C2×#11718692C2semidirect
8. C2×#11718680C2semidirect
11. C2×#11718691C2semidirect
12. C2×#11718679C2semidirect
13. C2×C4×#6107C2semidirect
14. C2×C4×#6105C2semidirect
15. C2×#11718661C2semidirect
37. #11719223C22semidirect
54. #11718692C22semidirect
55. #11718691C22semidirect
56. C4×#6107C22semidirect
57. #11718683C22semidirect
58. #11718680C22semidirect
59. #11718679C22semidirect
60. C4×#6105C22semidirect
61. #11718670C22semidirect
62. #11718661C22semidirect
63. #11718632C22semidirect
64. #11718631C22semidirect
549. C2×C13#3120semidirect
648. C13C2×#3120semidirect
739. C2#13125050direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192232
#131250502
C2×#117186312
C2×#117186322
C2×#117186832
C2×#117186702
C2×#117186922
C2×#117186802
C2×#117189002
C2×#117186912
C2×#117186792
C2×C4×#61072
C2×C4×#61052
C2×#117186612
C2×C13×#5202
C2×#312013