Finite Group Databasebeta

← C2×#13126881 #16739519

Subgroups — C2×#13126881 #16739519

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×D4×Dic26C211yesmaximal, characteristic
2#13126881C2116yesmaximal, direct product factor
3C2×#11718730C211yesmaximal, characteristic, complemented
4C2×#11718657C211yesmaximal, characteristic, complemented
5C2×#11718632C211yesmaximal, characteristic, complemented
6C2×#11718724C211yesmaximal, characteristic, complemented
7C2×#11718713C211yesmaximal, characteristic, complemented
8C2×#11718712C211yesmaximal, characteristic, complemented
9C2×#11718692C211yesmaximal, characteristic, complemented
10C2×#11718711C211yesmaximal, characteristic, complemented
11C2×#11718711C211yesmaximal, characteristic, complemented
12C2×#11718691C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic
14C2×#11718665C211yesmaximal, characteristic, complemented
15C22×#88050C211yesmaximal, characteristic, complemented
16C2×C13×#552C211yesmaximal, characteristic
17C23×Dic26C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C13×#552—24no—
20C13×#552C2218yes—
21C2×C13×#126—21no—
22C2×C13×#125—21no—
23C2×C13×#125C2211yescharacteristic
24C2×C13×#123—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117—21no—
30C2×C13×#117C2211yescharacteristic
31C22×C13×C4⋊C4C2211yescharacteristic
32C22×#6107C2211yescharacteristic
33C22×#6107C2211yescharacteristic
34C22×#6107C2211yescharacteristic
35C2×D4×Dic13—21no—
36C2×#88178C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40D4×Dic26—24no—
41D4×Dic26C2218yes—
42C2×#88142—21no—
43C2×#88132—21no—
44C2×#88132—21no—
45C2×#88123C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718730C2218yescomplemented
51#11718724C2218yescomplemented
52#11718713C2218yescomplemented
53#11718712C2218yescomplemented
54#11718711C2218yescomplemented
55#11718711C2218yescomplemented
56#11718692C2218yescomplemented
57#11718691C2218yescomplemented
58#11718672C2218yes—
59#11718665C2218yescomplemented
60#11718657C2218yescomplemented
61#11718632C2218yescomplemented
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88050C2211yescharacteristic
68C2×#88050C2211yescharacteristic
69C2×#88050C2211yescharacteristic
70C2×#88050C2211yescharacteristic
71C2×#88050C2218yescomplemented
72C2×#88048C2211yescharacteristic
73C2×#88048C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13D411yescharacteristic
79C23×C4×C13—21no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×Dic13—21no—
83C23×Dic13—21no—
84C22×Dic26—24no—
85C22×Dic26—24no—
86C22×Dic26—21no—
87C22×Dic26—21no—
88C22×Dic26—22no—
89C22×Dic26—22no—
90C22×Dic26—42no—
91C22×Dic26—42no—
92C22×Dic26C2311yescharacteristic
93C22×Dic26C2311yescharacteristic
94C22×Dic26C2314yes—
95C22×Dic26C2314yes—
96C22×Dic26C2311yescharacteristic
97C13×#126—28no—
98C13×#125—28no—
99C13×#125—22no—
100C13×#125C2314yes—
101C13×#123—28no—
102C13×C22⋊Q8—22no—
103C13×C22⋊Q8—22no—
104C13×C22⋊Q8C2314yes—
105C13×C22⋊Q8C2314yes—
106C4×Q8×C13—22no—
107C4×Q8×C13C2314yes—
108C4×D4×C13D414yes—
109C4×D4×C13C2314yes—
110C13×#117—22no—
111C13×#117—28no—
112C13×#117C2314yes—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—22no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4D411yescharacteristic
121C2×C13×C4⋊C4C2311yescharacteristic
122C2×C13×C4⋊C4C2311yescharacteristic
123C2×C13×C4⋊C4C2314yes—
124C2×C13×C4⋊C4C2311yescharacteristic
125C2×C13×C22⋊C4—21no—
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4D411yescharacteristic
129C2×C13×C22⋊C4D411yescharacteristic
130C2×C42×C13—21no—
131C2×C42×C13—21no—
132C2×C42×C13C2311yescharacteristic
133C2×C22⋊Dic13—21no—
134C2×C22⋊Dic13—21no—
135C2×#6107—24no—
136C2×#6107—42no—
137C2×#6107—42no—
138C2×#6107C2314yes—
139C2×#6107C2314yes—
140C2×#6107C2314yes—
141D4×Dic13—28no—
142C2×C4⋊Dic13—21no—
143C2×C4⋊Dic13—21no—
144C2×C4⋊Dic13C2311yescharacteristic
145#88178—22no—
146#88178—22no—
147#88178C2314yes—
148#88178C2314yes—
149C2×#6101—21no—
150C2×#6101—21no—
151C2×#6101—21no—
152C2×C4×Dic13—21no—
153C2×#6099—42no—
154C2×#6099C2314yes—
155C22×#1055—42no—
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2314yes—
161#88142—28no—
162#88132—28no—
163#88132—28no—
164#88123—22no—
165#88123C2314yes—
166C4×Dic26—22no—
167C4×Dic26C2314yes—
168#88075C2314yes—
169C22⋊#1055C2314yes—
170C22⋊#1055C2314yes—
171#88050C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88050C2314yes—
175#88050C2314yes—
176#88050C2314yes—
177#88050C2314yes—
178#88050C2314yes—
179#88050C2314yes—
180#88048C2314yes—
181#88048C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184#88043C2314yes—
185C2×#3312—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C24×C13C2×D411yescharacteristic
188C2×Q8×C13—21no—
189C2×Q8×C13—22no—
190C2×Q8×C13—22no—
191C2×Q8×C13C2412yes—
192C2×D4×C13—24no—
193C2×D4×C13C2×D414yes—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—24no—
203C22×C4×C13—44no—
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2411yescharacteristic
213C22×Dic13—21no—
214C22×Dic13—24no—
215C22×Dic13—24no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—44no—
220C22×Dic13—44no—
221C2×Dic26—21no—
222C2×Dic26—22no—
223C2×Dic26—22no—
224C2×Dic26—22no—
225C2×Dic26—22no—
226C2×Dic26—22no—
227C2×Dic26—28no—
228C2×Dic26—28no—
229C2×Dic26—21no—
230C2×Dic26—21no—
231C2×Dic26—24no—
232C2×Dic26—24no—
233C2×Dic26—44no—
234C2×Dic26—44no—
235C2×Dic26—48no—
236C2×Dic26—48no—
237C2×Dic26—44no—
238C2×Dic26—44no—
239C2×Dic26#4114yes—
240C2×Dic26C2412yes—
241C2×Dic26C2412yes—
242C2×Dic26C2412yes—
243C13×C4⋊C4—21no—
244C13×C4⋊C4—21no—
245C13×C4⋊C4—24no—
246C13×C4⋊C4—24no—
247C13×C4⋊C4—24no—
248C13×C4⋊C4—24no—
249C13×C4⋊C4—24no—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—21no—
252C13×C4⋊C4C2×D414yes—
253C13×C4⋊C4C2412yes—
254C13×C4⋊C4C2412yes—
255C13×C4⋊C4C2412yes—
256C13×C22⋊C4—24no—
257C13×C22⋊C4—24no—
258C13×C22⋊C4—24no—
259C13×C22⋊C4C2×D414yes—
260C13×C22⋊C4C2×D414yes—
261C42×C13—24no—
262C42×C13—24no—
263C42×C13C2×D412yes—
264C42×C13C2412yes—
265C22⋊Dic13—24no—
266C22⋊Dic13—24no—
267#6107—28no—
268#6107—44no—
269#6107—44no—
270C4⋊Dic13—21no—
271C4⋊Dic13—24no—
272C4⋊Dic13—24no—
273C4⋊Dic13C2412yes—
274#6101—24no—
275#6101—24no—
276#6101—24no—
277C4×Dic13—24no—
278#6099—44no—
279C2×#1055—22no—
280C2×#1055—22no—
281C2×#1055—22no—
282C2×#1055—22no—
283C2×#1055—44no—
284C2×#1055C2412yes—
285C2×#1055C2412yes—
286C2×#1055C2412yes—
287C2×#1055C2412yes—
288C2×#552D1311yescharacteristic
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×#435—131no—
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
313Q8×C13—22no—
314Q8×C13—22no—
315Q8×C13—42no—
316D4×C13—28no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—24no—
322C2×C4×C13—24no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—42no—
332C2×C4×C13—48no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
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×C13H(5,𝔽2)12yes—
343C2×C4×C13C2511yescharacteristic
344C2×Dic13—24no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—48no—
350C2×Dic13—48no—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354Dic26—24no—
355Dic26—22no—
356Dic26—22no—
357Dic26—22no—
358Dic26—22no—
359Dic26—22no—
360Dic26—48no—
361Dic26—48no—
362Dic26—42no—
363Dic26—42no—
364Dic26C2×#4114yes—
365#1055—22no—
366#1055—22no—
367#1055—22no—
368#1055—22no—
369C23×Q8—131no—
370C23×Q8—131no—
371C22×Q16—131no—
372C22×Q16—131no—
373C22×Q16—131no—
374C22×M16—131no—
375C23×C8—131no—
376#552—24no—
377#552C2×D1318yes—
378D4×Q8—138no—
379D4×Q8—264no—
380C2×C4⋊Q8—131no—
381C2×C4⋊Q8—261no—
382C2×#126—21no—
383C2×#125—21no—
384C2×#125C2×D1311yescharacteristic
385C2×#123—21no—
386C2×C22⋊Q8—131no—
387C2×C22⋊Q8—131no—
388C2×C22⋊Q8—261no—
389C2×C22⋊Q8—261no—
390C2×C22⋊Q8C2×D1311yescharacteristic
391C2×C22⋊Q8C2×D1311yescharacteristic
392C2×C4×Q8—131no—
393C2×C4×Q8C2×D1311yescharacteristic
394C2×C4×D4—261no—
395C2×C4×D4C2×D1311yescharacteristic
396C2×#117—21no—
397C2×#117C2×D1311yescharacteristic
398C22×C4⋊C4C2×D1311yescharacteristic
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#435—138no—
410C2×#107—131no—
411C2×#106—131no—
412C2×#106—131no—
413C2×C4⋊C8—131no—
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—131no—
425C2×#103—138no—
426C2×C22⋊C8—131no—
427C2×C22⋊C8—131no—
428C2×#97—131no—
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—42no—
446C4×C13—42no—
447C4×C13—42no—
448C4×C13—42no—
449C4×C13#54612yes—
450C4×C13C22×#4111yescharacteristic
451C4×C13C2×H(5,𝔽2)11yescharacteristic
452Dic13—24no—
453Dic13—42no—
454Dic13—42no—
455Dic13—42no—
456C22×Q8—131no—
457C22×Q8—131no—
458C22×Q8—131no—
459C22×Q8—134no—
460C22×Q8—134no—
461C22×Q8—264no—
462C22×Q8—264no—
463C22×Q8—261no—
464C22×Q8—261no—
465C22×Q8—262no—
466C22×Q8—262no—
467C22×Q8—522no—
468C22×Q8—522no—
469C22×Q8C22×D1311yescharacteristic
470C22×D4C22⋊D1311yescharacteristic
471C23×C4—21no—
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—134no—
483C2×M16—522no—
484C22×C8—131no—
485C22×C8—131no—
486C22×C8—131no—
487C22×C8—131no—
488C22×C8—134no—
489C22×C8—522no—
490C4⋊Q8—134no—
491C4⋊Q8—268no—
492C4⋊Q8—262no—
493#126—28no—
494#125—28no—
495#125—22no—
496#125C22×D1314yes—
497#123—28no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—134no—
501C22⋊Q8—134no—
502C22⋊Q8—262no—
503C22⋊Q8—262no—
504C22⋊Q8—268no—
505C22⋊Q8—268no—
506C22⋊Q8C22×D1314yes—
507C22⋊Q8C22×D1314yes—
508C4×Q8—22no—
509C4×Q8—134no—
510C4×Q8—262no—
511C4×Q8C22×D1314yes—
512C4×D4—268no—
513C4×D4C22⋊D1314yes—
514C4×D4C22×D1314yes—
515#117—22no—
516#117—28no—
517#117C22×D1314yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—131no—
526C2×C4⋊C4—261no—
527C2×C4⋊C4—261no—
528C2×C4⋊C4—261no—
529C2×C4⋊C4—261no—
530C2×C4⋊C4—261no—
531C2×C4⋊C4C22⋊D1311yescharacteristic
532C2×C4⋊C4C22×D1311yescharacteristic
533C2×C4⋊C4C22×D1311yescharacteristic
534C2×C4⋊C4C22×D1314yes—
535C2×C4⋊C4C22×D1311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—261no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4C22⋊D1311yescharacteristic
542C2×C22⋊C4C22⋊D1311yescharacteristic
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—261no—
546C2×C42C22×D1311yescharacteristic
547#107—134no—
548#106—134no—
549#106—134no—
550C4⋊C8—134no—
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⋊C8—134no—
562C22⋊C8—134no—
563#97—134no—
564C2×C13—24no—
565C2×C13—42no—
566C2×C13#331214yescomplemented
567C2×C13C2×#54611yescharacteristic
568C2×C13C22×#13711yescharacteristic
569C2×C13C2×#57811yescharacteristic
570C24C2×C22⋊D1311yescharacteristic
571C24C2×C22⋊D1311yescharacteristic
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—134no—
576C2×Q8—132no—
577C2×Q8—132no—
578C2×Q8—132no—
579C2×Q8—268no—
580C2×Q8—268no—
581C2×Q8—262no—
582C2×Q8—261no—
583C2×Q8—264no—
584C2×Q8—264no—
585C2×Q8—261no—
586C2×Q8—261no—
587C2×Q8—262no—
588C2×Q8—262no—
589C2×Q8—262no—
590C2×Q8—262no—
591C2×Q8—524no—
592C2×Q8—524no—
593C2×Q8—524no—
594C2×Q8—524no—
595C2×Q8—528no—
596C2×Q8—528no—
597C2×Q8C23×D1312yes—
598C2×D4—24no—
599C2×D4C2×C22⋊D1314yes—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—44no—
610C22×C4—261no—
611C22×C4—264no—
612C22×C4—264no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—524no—
617C22×C4—524no—
618C22×C4C2×C22⋊D1312yes—
619C22×C4C2×C22⋊D1312yes—
620C22×C4C2×C22⋊D1311yescharacteristic
621C22×C4C2×C22⋊D1311yescharacteristic
622C22×C4C2×C22⋊D1311yescharacteristic
623C22×C4C2×C22⋊D1311yescharacteristic
624C22×C4C23×D1312yes—
625C22×C4C23×D1312yes—
626C22×C4C23×D1311yescharacteristic
627Q16—268no—
628Q16—524no—
629Q16—524no—
630M16—524no—
631C2×C8—132no—
632C2×C8—132no—
633C2×C8—132no—
634C2×C8—132no—
635C2×C8—262no—
636C2×C8—262no—
637C2×C8—262no—
638C2×C8—262no—
639C2×C8—524no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—21no—
649C4⋊C4—132no—
650C4⋊C4—261no—
651C4⋊C4—264no—
652C4⋊C4—264no—
653C4⋊C4—264no—
654C4⋊C4—264no—
655C4⋊C4—264no—
656C4⋊C4C2×C22⋊D1314yes—
657C4⋊C4C23×D1312yes—
658C4⋊C4C23×D1312yes—
659C4⋊C4C23×D1312yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—264no—
664C22⋊C4—264no—
665C22⋊C4C2×C22⋊D1314yes—
666C22⋊C4C2×C22⋊D1314yes—
667C42—24no—
668C42—24no—
669C42—264no—
670C42C2×C22⋊D1312yes—
671C42C23×D1312yes—
672C13C2×#331211yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#8820514yes—
679C23C22×C22⋊D1312yes—
680C23C22×C22⋊D1312yes—
681C23C22×C22⋊D1311yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—134no—
686Q8—264no—
687Q8—262no—
688Q8—262no—
689Q8—262no—
690Q8—262no—
691Q8—262no—
692Q8—528no—
693Q8—528no—
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—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—264no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—528no—
722C2×C4—528no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4#41×D1312yes—
727C2×C4#8825612yes—
728C2×C4C22×C22⋊D1312yes—
729C2×C4C22×C22⋊D1312yes—
730C2×C4C22×C22⋊D1312yes—
731C2×C4C22×C22⋊D1312yes—
732C2×C4C22×C22⋊D1311yescharacteristic
733C2×C4C24×D1311yescharacteristic
734C8—262no—
735C8—262no—
736C8—262no—
737C8—262no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22C2×#8820514yes—
746C22C2×#8820512yes—
747C22#1171953412yes—
748C22#1171954312yes—
749C22C23×C22⋊D1311yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—264no—
759C4—522no—
760C4—522no—
761C4—522no—
762C4#1171953412yes—
763C4C2×#41×D1311yescharacteristic
764C4C2×#8825611yescharacteristic
765C2—24no—
766C2—42no—
767C2#1312688114yesdirect product factor
768C2C2×#1171953411yescharacteristic
769C2C22×#8820511yescharacteristic
770C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#552D13
hypocenterC13C2×#3312
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13126881C2direct (N × H)
3. C2×#11718730C2semidirect
4. C2×#11718657C2semidirect
5. C2×#11718632C2semidirect
6. C2×#11718724C2semidirect
7. C2×#11718713C2semidirect
8. C2×#11718712C2semidirect
9. C2×#11718692C2semidirect
10. C2×#11718711C2semidirect
11. C2×#11718711C2semidirect
12. C2×#11718691C2semidirect
14. C2×#11718665C2semidirect
15. C22×#88050C2semidirect
50. #11718730C22semidirect
51. #11718724C22semidirect
52. #11718713C22semidirect
53. #11718712C22semidirect
54. #11718711C22semidirect
55. #11718711C22semidirect
56. #11718692C22semidirect
57. #11718691C22semidirect
59. #11718665C22semidirect
60. #11718657C22semidirect
61. #11718632C22semidirect
71. C2×#88050C22semidirect
566. C2×C13#3312semidirect
672. C13C2×#3312semidirect
767. C2#13126881direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic262
#131268812
C2×#117187302
C2×#117186572
C2×#117186322
C2×#117187242
C2×#117187132
C2×#117187122
C2×#117186922
C2×#117187112
C2×#117186912
C2×#117186722
C2×#117186652
C22×#880502
C2×C13×#5522
C2×#331213