Finite Group Databasebeta

← C2×#13126889 #16739527

Subgroups — C2×#13126889 #16739527

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719246C211yesmaximal, characteristic
2C2×D4×Dic26C211yesmaximal, characteristic
3#13126889C2116yesmaximal, direct product factor
4C2×#11718364C211yesmaximal, characteristic, complemented
5C2×#11718384C211yesmaximal, characteristic, complemented
6C2×#11718382C211yesmaximal, characteristic, complemented
7C2×#11718490C211yesmaximal, characteristic, complemented
8C2×#11718798C211yesmaximal, characteristic, complemented
9C2×#11718777C211yesmaximal, characteristic, complemented
10C2×#11718510C211yesmaximal, characteristic, complemented
11C2×#11718400C211yesmaximal, characteristic, complemented
12C2×#11718400C211yesmaximal, characteristic, complemented
13C2×#11718377C211yesmaximal, characteristic, complemented
14C2×#11718781C211yesmaximal, characteristic, complemented
15C22×#88056C211yesmaximal, characteristic, complemented
16C2×C13×#435C211yesmaximal, characteristic
17C23×Dic26C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×M16C2211yescharacteristic
20C23×C8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×#88189—21no—
23C2×D4×Dic13—21no—
24C2×#88180C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C2×#88178C2211yescharacteristic
27C2×#88178C2211yescharacteristic
28C2×#88178C2211yescharacteristic
29C2×#88178C2211yescharacteristic
30C22×Dic52C2211yescharacteristic
31C22×Dic52C2211yescharacteristic
32C22×Dic52C2211yescharacteristic
33#11719246—24no—
34#11719246C2218yes—
35D4×Dic26—24no—
36D4×Dic26C2218yes—
37C2×#88143—21no—
38C2×#88142—21no—
39C2×#88133—21no—
40C2×#88132—21no—
41C2×#88132—21no—
42C2×#88131—21no—
43C2×#88124C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C13×#435C2218yes—
48C2×C13×C4⋊C8C2211yescharacteristic
49C2×C13×C22⋊C8C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×C13×#97C2211yescharacteristic
52#11718798C2218yescomplemented
53#11718781C2218yescomplemented
54#11718777C2218yescomplemented
55C2×#88058C2211yescharacteristic
56C2×#88057C2211yescharacteristic
57C2×#88057C2211yescharacteristic
58C2×#88056C2211yescharacteristic
59C2×#88056C2211yescharacteristic
60C2×#88056C2211yescharacteristic
61C2×#88056C2211yescharacteristic
62C2×#88056C2211yescharacteristic
63C2×#88056C2211yescharacteristic
64C2×#88056C2211yescharacteristic
65C2×#88056C2211yescharacteristic
66C2×#88056C2211yescharacteristic
67C2×#88056C2211yescharacteristic
68C2×#88056C2218yescomplemented
69#11718510C2218yescomplemented
70#11718490C2218yescomplemented
71#11718400C2218yescomplemented
72#11718400C2218yescomplemented
73#11718384C2218yescomplemented
74#11718382C2218yescomplemented
75#11718377C2218yescomplemented
76#11718364C2218yescomplemented
77C22×D4×C13D411yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×Dic13—21no—
81C23×Dic13—21no—
82C23×Dic13—21no—
83C22×Dic26—24no—
84C22×Dic26—24no—
85C22×Dic26—21no—
86C22×Dic26—21no—
87C22×Dic26—22no—
88C22×Dic26—22no—
89C22×Dic26—42no—
90C22×Dic26—42no—
91C22×Dic26C2311yescharacteristic
92C22×Dic26C2311yescharacteristic
93C22×Dic26C2311yescharacteristic
94C22×Dic26C2314yes—
95C22×Dic26C2314yes—
96C22×Dic26C2311yescharacteristic
97C2×C13×M16—42no—
98C2×C13×M16C2314yes—
99C22×C8×C13—42no—
100C22×C8×C13C2311yescharacteristic
101C22×C8×C13C2311yescharacteristic
102C22×C8×C13C2311yescharacteristic
103C22×C8×C13C2311yescharacteristic
104C22×C8×C13C2314yes—
105C4×D4×C13D414yes—
106C4×D4×C13C2314yes—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C22⋊C4D411yescharacteristic
109C2×C13×C22⋊C4D411yescharacteristic
110C2×C42×C13C2311yescharacteristic
111C2×C22⋊Dic13—21no—
112C2×C22⋊Dic13—21no—
113C2×C22⋊Dic13—21no—
114C2×C22⋊Dic13—21no—
115C2×C22⋊Dic13—21no—
116#88189—28no—
117D4×Dic13—28no—
118#88180—22no—
119#88180C2314yes—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—21no—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13—22no—
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×C4⋊Dic13C2314yes—
129#88178—22no—
130#88178—22no—
131#88178—22no—
132#88178—22no—
133#88178C2314yes—
134#88178C2314yes—
135#88178C2314yes—
136#88178C2314yes—
137C2×#6101—21no—
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×C4×Dic13—21no—
146C2×C4×Dic13—21no—
147C2×C4×Dic13—21no—
148C2×Dic52—24no—
149C2×Dic52—42no—
150C2×Dic52—42no—
151C2×Dic52C2314yes—
152C2×Dic52C2314yes—
153C2×Dic52C2314yes—
154#88143—28no—
155#88142—28no—
156#88133—28no—
157#88132—28no—
158#88132—28no—
159#88131—28no—
160#88124—22no—
161#88124C2314yes—
162#88123—22no—
163#88123C2314yes—
164C4×Dic26—22no—
165C4×Dic26—22no—
166C4×Dic26C2314yes—
167C4×Dic26C2314yes—
168C13×C4⋊C8C2314yes—
169C13×C22⋊C8C2314yes—
170C13×C22⋊C8C2314yes—
171C13×#97C2314yes—
172#88058C2314yes—
173#88057C2314yes—
174#88057C2314yes—
175#88056C2314yes—
176#88056C2314yes—
177#88056C2314yes—
178#88056C2314yes—
179#88056C2314yes—
180#88056C2314yes—
181#88056C2314yes—
182#88056C2314yes—
183#88056C2314yes—
184#88056C2314yes—
185C2×#3312—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C24×C13C2×D411yescharacteristic
188C2×D4×C13—24no—
189C2×D4×C13C2×D414yes—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13C2×D411yescharacteristic
195C22×C4×C13C2×D411yescharacteristic
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D412yes—
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2411yescharacteristic
203C22×Dic13—21no—
204C22×Dic13—24no—
205C22×Dic13—24no—
206C22×Dic13—24no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—44no—
215C22×Dic13—44no—
216C22×Dic13—44no—
217C2×Dic26—21no—
218C2×Dic26—22no—
219C2×Dic26—22no—
220C2×Dic26—22no—
221C2×Dic26—22no—
222C2×Dic26—22no—
223C2×Dic26—22no—
224C2×Dic26—22no—
225C2×Dic26—28no—
226C2×Dic26—28no—
227C2×Dic26—21no—
228C2×Dic26—21no—
229C2×Dic26—21no—
230C2×Dic26—24no—
231C2×Dic26—24no—
232C2×Dic26—44no—
233C2×Dic26—44no—
234C2×Dic26—48no—
235C2×Dic26—48no—
236C2×Dic26—44no—
237C2×Dic26—44no—
238C2×Dic26#4114yes—
239C2×Dic26C2412yes—
240C2×Dic26C2412yes—
241C2×Dic26C2412yes—
242C2×Dic26C2412yes—
243C13×M16—44no—
244C2×C8×C13—22no—
245C2×C8×C13—22no—
246C2×C8×C13—22no—
247C2×C8×C13—22no—
248C2×C8×C13—44no—
249C2×C8×C13C2412yes—
250C2×C8×C13C2412yes—
251C2×C8×C13C2412yes—
252C2×C8×C13C2412yes—
253C13×C4⋊C4C2×D414yes—
254C13×C22⋊C4C2×D414yes—
255C13×C22⋊C4C2×D414yes—
256C42×C13C2×D412yes—
257C42×C13C2412yes—
258C22⋊Dic13—24no—
259C22⋊Dic13—24no—
260C22⋊Dic13—24no—
261C22⋊Dic13—24no—
262C22⋊Dic13—24no—
263C4⋊Dic13—21no—
264C4⋊Dic13—21no—
265C4⋊Dic13—24no—
266C4⋊Dic13—24no—
267C4⋊Dic13—21no—
268C4⋊Dic13—21no—
269C4⋊Dic13—24no—
270C4⋊Dic13C2412yes—
271C4⋊Dic13C2412yes—
272C4⋊Dic13C2412yes—
273C4⋊Dic13C2412yes—
274#6101—24no—
275#6101—24no—
276#6101—24no—
277#6101—24no—
278#6101—24no—
279#6101—24no—
280#6101—24no—
281#6101—24no—
282C4×Dic13—24no—
283C4×Dic13—24no—
284C4×Dic13—24no—
285Dic52—28no—
286Dic52—44no—
287Dic52—44no—
288C2×#552—131no—
289C2×D4×Q8—131no—
290#3312—1316no—
291C2×#491—131no—
292C2×#485—131no—
293C2×#483—131no—
294C2×#479—131no—
295C2×#470—131no—
296C2×#467—131no—
297C2×#462—131no—
298C2×#451—131no—
299C2×#451—131no—
300C2×#441—131no—
301C2×#435D1311yescharacteristic
302C2×#419—131no—
303C22×#103—131no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13#13714yes—
310C23×C13C22×D412yes—
311C23×C13C22×D412yes—
312C23×C13C22×D411yescharacteristic
313D4×C13—28no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—24no—
319C2×C4×C13—24no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13C22×D412yes—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D412yes—
328C2×C4×C13C22×D411yescharacteristic
329C2×C4×C13C2×#4112yes—
330C2×C4×C13H(5,𝔽2)12yes—
331C2×C4×C13C2511yescharacteristic
332C2×Dic13—24no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—48no—
342C2×Dic13—48no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—48no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351Dic26—24no—
352Dic26—22no—
353Dic26—22no—
354Dic26—22no—
355Dic26—22no—
356Dic26—22no—
357Dic26—22no—
358Dic26—22no—
359Dic26—48no—
360Dic26—48no—
361Dic26—42no—
362Dic26—42no—
363Dic26—42no—
364Dic26C2×#4114yes—
365C8×C13—22no—
366C8×C13—22no—
367C8×C13—22no—
368C8×C13—22no—
369C23×Q8—131no—
370C23×Q8—131no—
371C22×Q16—131no—
372C22×Q16—131no—
373C22×Q16—131no—
374C22×M16C2×D1311yescharacteristic
375C23×C8C2×D1311yescharacteristic
376#552—138no—
377#552—264no—
378D4×Q8—138no—
379D4×Q8—264no—
380C2×C4⋊Q8—131no—
381C2×C4⋊Q8—261no—
382C2×#126—261no—
383C2×#125—131no—
384C2×#125—261no—
385C2×#123—261no—
386C2×C22⋊Q8—131no—
387C2×C22⋊Q8—131no—
388C2×C22⋊Q8—131no—
389C2×C22⋊Q8—131no—
390C2×C22⋊Q8—261no—
391C2×C22⋊Q8—261no—
392C2×C4×Q8—131no—
393C2×C4×Q8—131no—
394C2×C4×D4—261no—
395C2×C4×D4C2×D1311yescharacteristic
396C2×#117—131no—
397C2×#117—261no—
398C22×C4⋊C4—131no—
399#491—138no—
400#485—138no—
401#483—138no—
402#479—138no—
403#470—138no—
404#467—138no—
405#462—138no—
406#451—138no—
407#451—138no—
408#441—138no—
409#435C2×D1318yes—
410C2×#107—131no—
411C2×#106—131no—
412C2×#106—131no—
413C2×C4⋊C8C2×D1311yescharacteristic
414#419—138no—
415C2×#103—131no—
416C2×#103—131no—
417C2×#103—131no—
418C2×#103—131no—
419C2×#103—131no—
420C2×#103—131no—
421C2×#103—131no—
422C2×#103—131no—
423C2×#103—131no—
424C2×#103—138no—
425C2×#103—131no—
426C2×C22⋊C8C2×D1311yescharacteristic
427C2×C22⋊C8C2×D1311yescharacteristic
428C2×#97C2×D1311yescharacteristic
429C22×C13—22no—
430C22×C13—28no—
431C22×C13—22no—
432C22×C13—22no—
433C22×C13—22no—
434C22×C13—22no—
435C22×C13—44no—
436C22×C13#54612yes—
437C22×C13C2×#13714yes—
438C22×C13C2×#13712yes—
439C22×C13#57812yes—
440C22×C13C23×D411yescharacteristic
441C4×C13—22no—
442C4×C13—22no—
443C4×C13—22no—
444C4×C13—22no—
445C4×C13#54612yes—
446C4×C13C22×#4111yescharacteristic
447C4×C13C2×H(5,𝔽2)11yescharacteristic
448Dic13—24no—
449Dic13—42no—
450Dic13—42no—
451Dic13—42no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455Dic13—42no—
456C22×Q8—131no—
457C22×Q8—131no—
458C22×Q8—131no—
459C22×Q8—131no—
460C22×Q8—134no—
461C22×Q8—134no—
462C22×Q8—264no—
463C22×Q8—264no—
464C22×Q8—261no—
465C22×Q8—261no—
466C22×Q8—262no—
467C22×Q8—262no—
468C22×Q8—522no—
469C22×Q8—522no—
470C22×D4D5211yescharacteristic
471C23×C4—261no—
472C23×C4—261no—
473C23×C4—261no—
474C23×C4C22×D1311yescharacteristic
475C23×C4C22×D1311yescharacteristic
476C2×Q16—134no—
477C2×Q16—134no—
478C2×Q16—134no—
479C2×Q16—264no—
480C2×Q16—522no—
481C2×Q16—522no—
482C2×M16—42no—
483C2×M16C22×D1314yes—
484C22×C8—42no—
485C22×C8C22×D1311yescharacteristic
486C22×C8C22×D1311yescharacteristic
487C22×C8C22×D1311yescharacteristic
488C22×C8C22×D1311yescharacteristic
489C22×C8C22×D1314yes—
490C4⋊Q8—134no—
491C4⋊Q8—268no—
492C4⋊Q8—262no—
493#126—268no—
494#125—134no—
495#125—268no—
496#125—262no—
497#123—268no—
498C22⋊Q8—134no—
499C22⋊Q8—134no—
500C22⋊Q8—134no—
501C22⋊Q8—134no—
502C22⋊Q8—262no—
503C22⋊Q8—262no—
504C22⋊Q8—262no—
505C22⋊Q8—262no—
506C22⋊Q8—268no—
507C22⋊Q8—268no—
508C4×Q8—134no—
509C4×Q8—134no—
510C4×Q8—262no—
511C4×Q8—262no—
512C4×D4—268no—
513C4×D4D5214yes—
514C4×D4C22×D1314yes—
515#117—134no—
516#117—262no—
517#117—268no—
518C2×C4⋊C4—131no—
519C2×C4⋊C4—131no—
520C2×C4⋊C4—134no—
521C2×C4⋊C4—131no—
522C2×C4⋊C4—131no—
523C2×C4⋊C4—261no—
524C2×C4⋊C4—262no—
525C2×C4⋊C4—261no—
526C2×C4⋊C4—261no—
527C2×C4⋊C4—261no—
528C2×C4⋊C4—261no—
529C2×C4⋊C4—261no—
530C2×C4⋊C4—261no—
531C2×C4⋊C4—261no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—261no—
534C2×C4⋊C4—261no—
535C2×C4⋊C4D5211yescharacteristic
536C2×C22⋊C4—261no—
537C2×C22⋊C4—261no—
538C2×C22⋊C4—261no—
539C2×C22⋊C4—261no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4D5211yescharacteristic
542C2×C22⋊C4D5211yescharacteristic
543C2×C42—261no—
544C2×C42—261no—
545C2×C42—261no—
546C2×C42C22×D1311yescharacteristic
547#107—134no—
548#106—134no—
549#106—134no—
550C4⋊C8C22×D1314yes—
551#103—134no—
552#103—134no—
553#103—134no—
554#103—134no—
555#103—134no—
556#103—134no—
557#103—134no—
558#103—134no—
559#103—134no—
560#103—134no—
561C22⋊C8C22×D1314yes—
562C22⋊C8C22×D1314yes—
563#97C22×D1314yes—
564C2×C13—24no—
565C2×C13—42no—
566C2×C13#331214yescomplemented
567C2×C13C2×#54611yescharacteristic
568C2×C13C22×#13711yescharacteristic
569C2×C13C2×#57811yescharacteristic
570C24C2×D5211yescharacteristic
571C24C2×D5211yescharacteristic
572C2×Q8—134no—
573C2×Q8—132no—
574C2×Q8—132no—
575C2×Q8—132no—
576C2×Q8—132no—
577C2×Q8—268no—
578C2×Q8—268no—
579C2×Q8—261no—
580C2×Q8—261no—
581C2×Q8—264no—
582C2×Q8—264no—
583C2×Q8—261no—
584C2×Q8—261no—
585C2×Q8—262no—
586C2×Q8—262no—
587C2×Q8—262no—
588C2×Q8—262no—
589C2×Q8—262no—
590C2×Q8—262no—
591C2×Q8—262no—
592C2×Q8—524no—
593C2×Q8—524no—
594C2×Q8—524no—
595C2×Q8—524no—
596C2×Q8—528no—
597C2×Q8—528no—
598C2×D4—24no—
599C2×D4C2×D5214yes—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—261no—
605C22×C4—264no—
606C22×C4—264no—
607C22×C4—264no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—524no—
616C22×C4—524no—
617C22×C4—524no—
618C22×C4C2×D5212yes—
619C22×C4C2×D5212yes—
620C22×C4C2×D5211yescharacteristic
621C22×C4C2×D5211yescharacteristic
622C22×C4C2×D5211yescharacteristic
623C22×C4C2×D5211yescharacteristic
624C22×C4C23×D1312yes—
625C22×C4C23×D1312yes—
626C22×C4C23×D1311yescharacteristic
627Q16—268no—
628Q16—524no—
629Q16—524no—
630M16—44no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—44no—
636C2×C8C23×D1312yes—
637C2×C8C23×D1312yes—
638C2×C8C23×D1312yes—
639C2×C8C23×D1312yes—
640C4⋊C4—132no—
641C4⋊C4—132no—
642C4⋊C4—132no—
643C4⋊C4—132no—
644C4⋊C4—261no—
645C4⋊C4—261no—
646C4⋊C4—264no—
647C4⋊C4—261no—
648C4⋊C4—261no—
649C4⋊C4—264no—
650C4⋊C4—264no—
651C4⋊C4—264no—
652C4⋊C4—264no—
653C4⋊C4—264no—
654C4⋊C4—264no—
655C4⋊C4—264no—
656C4⋊C4—264no—
657C4⋊C4—264no—
658C4⋊C4—264no—
659C4⋊C4C2×D5214yes—
660C22⋊C4—264no—
661C22⋊C4—264no—
662C22⋊C4—264no—
663C22⋊C4—264no—
664C22⋊C4—264no—
665C22⋊C4C2×D5214yes—
666C22⋊C4C2×D5214yes—
667C42—264no—
668C42—264no—
669C42—264no—
670C42C2×D5212yes—
671C42C23×D1312yes—
672C13C2×#331211yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#8816314yes—
679C23C22×D5212yes—
680C23C22×D5212yes—
681C23C22×D5211yescharacteristic
682Q8—134no—
683Q8—264no—
684Q8—262no—
685Q8—262no—
686Q8—262no—
687Q8—262no—
688Q8—262no—
689Q8—262no—
690Q8—262no—
691Q8—528no—
692Q8—528no—
693Q8—522no—
694Q8—522no—
695Q8—522no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—264no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—528no—
717C2×C4—528no—
718C2×C4—528no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4C22×D5212yes—
727C2×C4C22×D5212yes—
728C2×C4C22×D5212yes—
729C2×C4C22×D5212yes—
730C2×C4C22×D5211yescharacteristic
731C2×C4#8825112yes—
732C2×C4#41×D1312yes—
733C2×C4C24×D1311yescharacteristic
734C8—22no—
735C8—22no—
736C8—22no—
737C8—22no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1171925912yes—
746C22C2×#8816314yes—
747C22C2×#8816312yes—
748C22#1171945812yes—
749C22C23×D5211yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—264no—
755C4—522no—
756C4—522no—
757C4—522no—
758C4—522no—
759C4—522no—
760C4—522no—
761C4—522no—
762C4#1171925912yes—
763C4C2×#8825111yescharacteristic
764C4C2×#41×D1311yescharacteristic
765C2—24no—
766C2—42no—
767C2#1312688914yesdirect product factor
768C2C2×#1171925911yescharacteristic
769C2C22×#8816311yescharacteristic
770C2C2×#1171945811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#435C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#435D13
hypocenterC13C2×#3312
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #13126889C2direct (N × H)
4. C2×#11718364C2semidirect
5. C2×#11718384C2semidirect
6. C2×#11718382C2semidirect
7. C2×#11718490C2semidirect
8. C2×#11718798C2semidirect
9. C2×#11718777C2semidirect
10. C2×#11718510C2semidirect
11. C2×#11718400C2semidirect
12. C2×#11718400C2semidirect
13. C2×#11718377C2semidirect
14. C2×#11718781C2semidirect
15. C22×#88056C2semidirect
52. #11718798C22semidirect
53. #11718781C22semidirect
54. #11718777C22semidirect
68. C2×#88056C22semidirect
69. #11718510C22semidirect
70. #11718490C22semidirect
71. #11718400C22semidirect
72. #11718400C22semidirect
73. #11718384C22semidirect
74. #11718382C22semidirect
75. #11718377C22semidirect
76. #11718364C22semidirect
566. C2×C13#3312semidirect
672. C13C2×#3312semidirect
767. C2#13126889direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192462
C2×D4×Dic262
#131268892
C2×#117183642
C2×#117183842
C2×#117183822
C2×#117184902
C2×#117187982
C2×#117187772
C2×#117185102
C2×#117184002
C2×#117183772
C2×#117187812
C22×#880562
C2×C13×#4352
C2×#331213