Finite Group Databasebeta

← C2×#13127405 #16741607

Subgroups — C2×#13127405 #16741607

Order 3328.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719246C211yesmaximal, characteristic
2#13127405C2116yesmaximal, direct product factor
3C2×#11718725C211yesmaximal, characteristic, complemented
4C2×#11718631C211yesmaximal, characteristic, complemented
5C2×#11718705C211yesmaximal, characteristic, complemented
6C2×#11718657C211yesmaximal, characteristic, complemented
7C2×#11718706C211yesmaximal, characteristic, complemented
8C2×#11718683C211yesmaximal, characteristic, complemented
9C2×#11718724C211yesmaximal, characteristic, complemented
10C2×#11718713C211yesmaximal, characteristic, complemented
11C2×#11718713C211yesmaximal, characteristic, complemented
12C2×C4×#6107C211yesmaximal, characteristic, complemented
13C2×#11718673C211yesmaximal, characteristic
14C2×#11718656C211yesmaximal, characteristic, complemented
15C2×#11718625C211yesmaximal, characteristic, complemented
16C2×C13×#552C211yesmaximal, characteristic
17C13×#552—24no—
18C13×#552C2218yes—
19C2×C13×#126—21no—
20C2×C13×#125—21no—
21C2×C13×#125C2211yescharacteristic
22C2×C13×#123—21no—
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C13×#117—21no—
28C2×C13×#117C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C2×#88189—21no—
32C2×#88180C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C2×#88178C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C22×#6099C2211yescharacteristic
38#11719246—24no—
39#11719246C2218yes—
40C2×#88143—21no—
41C2×#88133—21no—
42C2×#88131—21no—
43C2×#88124C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×#88075C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718725C2218yescomplemented
51#11718724C2218yescomplemented
52#11718713C2218yescomplemented
53#11718713C2218yescomplemented
54#11718706C2218yescomplemented
55#11718705C2218yescomplemented
56C4×#6107C2218yescomplemented
57#11718683C2218yescomplemented
58#11718673C2218yes—
59#11718657C2218yescomplemented
60#11718656C2218yescomplemented
61#11718631C2218yescomplemented
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65#11718625C2218yescomplemented
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13D411yescharacteristic
79C23×C4×C13—21no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×Dic13—21no—
83C22×Dic26C2311yescharacteristic
84C13×#126—28no—
85C13×#125—28no—
86C13×#125—22no—
87C13×#125C2314yes—
88C13×#123—28no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8C2314yes—
92C13×C22⋊Q8C2314yes—
93C4×Q8×C13—22no—
94C4×Q8×C13C2314yes—
95C4×D4×C13D414yes—
96C4×D4×C13C2314yes—
97C13×#117—22no—
98C13×#117—28no—
99C13×#117C2314yes—
100C2×C13×C4⋊C4—21no—
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4D411yescharacteristic
116C2×C13×C22⋊C4D411yescharacteristic
117C2×C42×C13—21no—
118C2×C42×C13—21no—
119C2×C42×C13C2311yescharacteristic
120C2×C22⋊Dic13—21no—
121C2×C22⋊Dic13—21no—
122C2×C22⋊Dic13—21no—
123C2×#6107—24no—
124C2×#6107C2314yes—
125#88189—28no—
126#88180—22no—
127#88180C2314yes—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—22no—
130C2×C4⋊Dic13C2314yes—
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2311yescharacteristic
134#88178—22no—
135#88178—22no—
136#88178C2314yes—
137#88178C2314yes—
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×C4×Dic13—21no—
144C2×C4×Dic13—21no—
145C2×#6099—24no—
146C2×#6099—24no—
147C2×#6099C2314yes—
148C2×#6099C2314yes—
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153#88143—28no—
154#88133—28no—
155#88131—28no—
156#88124—22no—
157#88124C2314yes—
158C4×Dic26—22no—
159C4×Dic26C2314yes—
160#88075C2314yes—
161#88075C2314yes—
162#88075C2314yes—
163C22⋊#1055C2314yes—
164C22⋊#1055C2314yes—
165#88050C2314yes—
166#88050C2314yes—
167#88050C2314yes—
168#88048C2314yes—
169#88048C2314yes—
170#88048C2314yes—
171#88048C2314yes—
172#88047C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177C4⋊#1055C2314yes—
178C4×#1055C2314yes—
179C2×#3352—131nomaximal, Sylow
180C24×C13C2×D411yescharacteristic
181C24×C13C2×D411yescharacteristic
182C2×Q8×C13—21no—
183C2×Q8×C13—22no—
184C2×Q8×C13—22no—
185C2×Q8×C13C2412yes—
186C2×D4×C13—42no—
187C2×D4×C13C2×D414yes—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—24no—
197C22×C4×C13—44no—
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2411yescharacteristic
207C22×Dic13—24no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—44no—
213C2×Dic26—22no—
214C2×Dic26—22no—
215C2×Dic26—21no—
216C2×Dic26C2412yes—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—24no—
220C13×C4⋊C4—24no—
221C13×C4⋊C4—24no—
222C13×C4⋊C4—24no—
223C13×C4⋊C4—24no—
224C13×C4⋊C4—24no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4C2×D414yes—
227C13×C4⋊C4C2412yes—
228C13×C4⋊C4C2412yes—
229C13×C4⋊C4C2412yes—
230C13×C22⋊C4—24no—
231C13×C22⋊C4—24no—
232C13×C22⋊C4—24no—
233C13×C22⋊C4C2×D414yes—
234C13×C22⋊C4C2×D414yes—
235C42×C13—24no—
236C42×C13—24no—
237C42×C13C2×D412yes—
238C42×C13C2412yes—
239C22⋊Dic13—24no—
240C22⋊Dic13—24no—
241C22⋊Dic13—24no—
242#6107—28no—
243C4⋊Dic13—21no—
244C4⋊Dic13—21no—
245C4⋊Dic13—21no—
246C4⋊Dic13—24no—
247C4⋊Dic13C2412yes—
248C4⋊Dic13C2412yes—
249C4⋊Dic13C2412yes—
250#6101—24no—
251#6101—24no—
252#6101—24no—
253#6101—24no—
254#6101—24no—
255C4×Dic13—24no—
256C4×Dic13—24no—
257#6099—28no—
258#6099—28no—
259C2×#1055—22no—
260C2×#1055—22no—
261C2×#1055—22no—
262C2×#1055#4114yes—
263C2×#1055C2412yes—
264C2×#1055C2412yes—
265C2×#1055C2412yes—
266C2×#1055C2412yes—
267C2×#552—131no—
268C2×#552D1311yescharacteristic
269#3352—1316no—
270C2×#499—131no—
271C2×#484—131no—
272C2×#484—131no—
273C2×#485—131no—
274C2×#485—131no—
275C2×#479—131no—
276C2×#479—131no—
277C2×#470—131no—
278C2×#470—131no—
279C2×C4×Q16—131no—
280C2×#436—131no—
281C2×#428—131no—
282C2×#428—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13C22×D412yes—
290C23×C13C22×D412yes—
291C23×C13C22×D411yescharacteristic
292Q8×C13—22no—
293Q8×C13—22no—
294Q8×C13—42no—
295D4×C13—44no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—24no—
301C2×C4×C13—24no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—48no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13C22×D412yes—
316C2×C4×C13C22×D412yes—
317C2×C4×C13C22×D412yes—
318C2×C4×C13C22×D412yes—
319C2×C4×C13C22×D411yescharacteristic
320C2×C4×C13C2×#4112yes—
321C2×C4×C132−1+412yes—
322C2×C4×C13C2511yescharacteristic
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—48no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332Dic26—22no—
333Dic26—22no—
334Dic26—42no—
335#1055—22no—
336#1055—22no—
337#1055—22no—
338#1055C2×#4114yes—
339C22×Q16—131no—
340C22×M16—131no—
341C22×M16—131no—
342#552—24no—
343#552—138no—
344#552—264no—
345#552C2×D1318yes—
346C2×#126—21no—
347C2×#126—261no—
348C2×#125—21no—
349C2×#125—131no—
350C2×#125—261no—
351C2×#125C2×D1311yescharacteristic
352C2×#123—21no—
353C2×#123—261no—
354C2×C22⋊Q8—131no—
355C2×C22⋊Q8—131no—
356C2×C22⋊Q8C2×D1311yescharacteristic
357C2×C22⋊Q8C2×D1311yescharacteristic
358C2×C4×Q8—131no—
359C2×C4×Q8C2×D1311yescharacteristic
360C2×C4×D4C2×D1311yescharacteristic
361C2×#117—21no—
362C2×#117—131no—
363C2×#117—261no—
364C2×#117C2×D1311yescharacteristic
365C22×C4⋊C4—131no—
366C22×C4⋊C4C2×D1311yescharacteristic
367#499—138no—
368#485—138no—
369#485—138no—
370#484—138no—
371#484—138no—
372#479—138no—
373#479—138no—
374#470—138no—
375#470—138no—
376C4×Q16—138no—
377#436—138no—
378#428—138no—
379#428—138no—
380C2×#107—131no—
381C2×#107—131no—
382C2×#107—131no—
383C2×#107—131no—
384C2×#107—131no—
385C2×#106—131no—
386C2×#106—131no—
387C2×#106—131no—
388C2×#106—131no—
389C2×C4⋊C8—131no—
390C2×#103—131no—
391C2×#103—131no—
392C2×#103—131no—
393C2×#103—131no—
394C2×#103—131no—
395C2×#103—131no—
396C2×C22⋊C8—131no—
397C2×C22⋊C8—131no—
398C2×C4×C8—131no—
399C22×C13—22no—
400C22×C13—22no—
401C22×C13—22no—
402C22×C13—22no—
403C22×C13—22no—
404C22×C13—22no—
405C22×C13—44no—
406C22×C13—44no—
407C22×C13#54712yes—
408C22×C13#57512yes—
409C22×C13#57812yes—
410C22×C13C23×D411yescharacteristic
411C4×C13—22no—
412C4×C13—22no—
413C4×C13—22no—
414C4×C13—22no—
415C4×C13—42no—
416C4×C13—42no—
417C4×C13—42no—
418C4×C13—42no—
419C4×C13#54712yes—
420C4×C13C22×#4111yescharacteristic
421C4×C13C2×2−1+411yescharacteristic
422Dic13—42no—
423Dic13—42no—
424Dic13—42no—
425Dic13—42no—
426C22×Q8—131no—
427C22×Q8C22×D1311yescharacteristic
428C22×D4C22⋊D1311yescharacteristic
429C23×C4—21no—
430C23×C4—261no—
431C23×C4C22×D1311yescharacteristic
432C23×C4C22×D1311yescharacteristic
433C2×Q16—134no—
434C2×Q16—264no—
435C2×M16—134no—
436C2×M16—134no—
437C2×M16—264no—
438C2×M16—264no—
439C22×C8—131no—
440C22×C8—131no—
441C22×C8—131no—
442C22×C8—131no—
443#126—28no—
444#126—268no—
445#125—28no—
446#125—22no—
447#125—134no—
448#125—268no—
449#125—262no—
450#125C22×D1314yes—
451#123—28no—
452#123—268no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—134no—
456C22⋊Q8—134no—
457C22⋊Q8—262no—
458C22⋊Q8—262no—
459C22⋊Q8C22×D1314yes—
460C22⋊Q8C22×D1314yes—
461C4×Q8—22no—
462C4×Q8—134no—
463C4×Q8—262no—
464C4×Q8C22×D1314yes—
465C4×D4C22⋊D1314yes—
466C4×D4C22×D1314yes—
467#117—22no—
468#117—28no—
469#117—134no—
470#117—262no—
471#117—268no—
472#117C22×D1314yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—131no—
481C2×C4⋊C4—131no—
482C2×C4⋊C4—134no—
483C2×C4⋊C4—131no—
484C2×C4⋊C4—261no—
485C2×C4⋊C4—262no—
486C2×C4⋊C4—261no—
487C2×C4⋊C4—261no—
488C2×C4⋊C4—261no—
489C2×C4⋊C4—261no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4C22⋊D1311yescharacteristic
492C2×C4⋊C4C22×D1311yescharacteristic
493C2×C4⋊C4C22×D1311yescharacteristic
494C2×C4⋊C4C22×D1314yes—
495C2×C4⋊C4C22×D1311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—261no—
500C2×C22⋊C4—261no—
501C2×C22⋊C4—261no—
502C2×C22⋊C4C22⋊D1311yescharacteristic
503C2×C22⋊C4C22⋊D1311yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—261no—
507C2×C42—261no—
508C2×C42C22×D1311yescharacteristic
509#107—134no—
510#107—134no—
511#107—134no—
512#107—134no—
513#107—134no—
514#106—134no—
515#106—134no—
516#106—134no—
517#106—134no—
518C4⋊C8—134no—
519#103—134no—
520#103—134no—
521#103—134no—
522#103—134no—
523#103—134no—
524#103—134no—
525C22⋊C8—134no—
526C22⋊C8—134no—
527C4×C8—134no—
528C2×C13—42no—
529C2×C13—42no—
530C2×C13#335214yescomplemented
531C2×C13C2×#54711yescharacteristic
532C2×C13C2×#57511yescharacteristic
533C2×C13C2×#57811yescharacteristic
534C24C2×C22⋊D1311yescharacteristic
535C24C2×C22⋊D1311yescharacteristic
536C2×Q8—21no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—132no—
540C2×Q8—261no—
541C2×Q8—262no—
542C2×Q8—262no—
543C2×Q8C23×D1312yes—
544C2×D4—42no—
545C2×D4C2×C22⋊D1314yes—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—44no—
556C22×C4—264no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—524no—
562C22×C4C2×C22⋊D1312yes—
563C22×C4C2×C22⋊D1312yes—
564C22×C4C2×C22⋊D1311yescharacteristic
565C22×C4C2×C22⋊D1311yescharacteristic
566C22×C4C2×C22⋊D1311yescharacteristic
567C22×C4C2×C22⋊D1311yescharacteristic
568C22×C4C23×D1312yes—
569C22×C4C23×D1312yes—
570C22×C4C23×D1311yescharacteristic
571Q16—268no—
572M16—268no—
573M16—268no—
574C2×C8—134no—
575C2×C8—132no—
576C2×C8—132no—
577C2×C8—132no—
578C2×C8—132no—
579C2×C8—262no—
580C2×C8—262no—
581C2×C8—262no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—21no—
591C4⋊C4—132no—
592C4⋊C4—132no—
593C4⋊C4—132no—
594C4⋊C4—261no—
595C4⋊C4—261no—
596C4⋊C4—264no—
597C4⋊C4—261no—
598C4⋊C4—264no—
599C4⋊C4—264no—
600C4⋊C4—264no—
601C4⋊C4—264no—
602C4⋊C4—264no—
603C4⋊C4C2×C22⋊D1314yes—
604C4⋊C4C23×D1312yes—
605C4⋊C4C23×D1312yes—
606C4⋊C4C23×D1312yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—264no—
611C22⋊C4—264no—
612C22⋊C4—264no—
613C22⋊C4C2×C22⋊D1314yes—
614C22⋊C4C2×C22⋊D1314yes—
615C42—24no—
616C42—24no—
617C42—264no—
618C42—264no—
619C42C2×C22⋊D1312yes—
620C42C23×D1312yes—
621C13C2×#335211yescharacteristic, complemented, Sylow
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×C22⋊D1312yes—
629C23C22×C22⋊D1312yes—
630C23C22×C22⋊D1311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—262no—
635Q8—262no—
636Q8—522no—
637D4—44no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—262no—
658C2×C4—262no—
659C2×C4—262no—
660C2×C4—262no—
661C2×C4—528no—
662C2×C4—522no—
663C2×C4—522no—
664C2×C4—522no—
665C2×C4—522no—
666C2×C4#41×D1312yes—
667C2×C4#8825712yes—
668C2×C4C22×C22⋊D1312yes—
669C2×C4C22×C22⋊D1312yes—
670C2×C4C22×C22⋊D1312yes—
671C2×C4C22×C22⋊D1312yes—
672C2×C4C22×C22⋊D1311yescharacteristic
673C2×C4C24×D1311yescharacteristic
674C8—134no—
675C8—262no—
676C8—262no—
677C8—262no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1171952712yes—
687C22#1171952912yes—
688C22#1171954312yes—
689C22C23×C22⋊D1311yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—522no—
699C4—522no—
700C4—522no—
701C4—522no—
702C4#1171952912yes—
703C4C2×#41×D1311yescharacteristic
704C4C2×#8825711yescharacteristic
705C2—42no—
706C2—42no—
707C2#1312740514yesdirect product factor
708C2C2×#1171952911yescharacteristic
709C2C2×#1171952711yescharacteristic
710C2C2×#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×#3352
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. #13127405C2direct (N × H)
3. C2×#11718725C2semidirect
4. C2×#11718631C2semidirect
5. C2×#11718705C2semidirect
6. C2×#11718657C2semidirect
7. C2×#11718706C2semidirect
8. C2×#11718683C2semidirect
9. C2×#11718724C2semidirect
10. C2×#11718713C2semidirect
11. C2×#11718713C2semidirect
12. C2×C4×#6107C2semidirect
14. C2×#11718656C2semidirect
15. C2×#11718625C2semidirect
50. #11718725C22semidirect
51. #11718724C22semidirect
52. #11718713C22semidirect
53. #11718713C22semidirect
54. #11718706C22semidirect
55. #11718705C22semidirect
56. C4×#6107C22semidirect
57. #11718683C22semidirect
59. #11718657C22semidirect
60. #11718656C22semidirect
61. #11718631C22semidirect
65. #11718625C22semidirect
530. C2×C13#3352semidirect
621. C13C2×#3352semidirect
707. C2#13127405direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192462
#131274052
C2×#117187252
C2×#117186312
C2×#117187052
C2×#117186572
C2×#117187062
C2×#117186832
C2×#117187242
C2×#117187132
C2×C4×#61072
C2×#117186732
C2×#117186562
C2×#117186252
C2×C13×#5522
C2×#335213