Finite Group Databasebeta

← C2×#13126262 #16735845

Subgroups — C2×#13126262 #16735845

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719223C211yesmaximal, characteristic, complemented
2#13126262C2116yesmaximal, direct product factor
3C2×#11718683C211yesmaximal, characteristic, complemented
4C2×#11718752C211yesmaximal, characteristic, complemented
5C2×#11718755C211yesmaximal, characteristic, complemented
6C2×#11718670C211yesmaximal, characteristic, complemented
7C2×#11718713C211yesmaximal, characteristic, complemented
8C2×#11718703C211yesmaximal, characteristic
9C2×#11718712C211yesmaximal, characteristic, complemented
10C2×#11718702C211yesmaximal, characteristic
11C2×#11718715C211yesmaximal, characteristic, complemented
12C2×#11718715C211yesmaximal, characteristic, complemented
13C2×#11718692C211yesmaximal, characteristic, complemented
14C2×#11718680C211yesmaximal, characteristic, complemented
15C2×#11718660C211yesmaximal, characteristic, complemented
16C2×C13×#542C211yesmaximal, characteristic
17C13×#542—24no—
18C13×#542C2218yes—
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#126—21no—
21C2×C13×#124—21no—
22C2×C13×#124C2211yescharacteristic
23C2×C13×#123—21no—
24C2×C13×C22⋊Q8—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C22×#6107C2211yescharacteristic
32C22×#6105C2211yescharacteristic
33C22×#6105C2211yescharacteristic
34C2×#88178C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719223—24no—
39#11719223C2218yescomplemented
40C2×#88143—21no—
41C2×#88143—21no—
42C2×#88133—21no—
43C2×#88133—21no—
44C2×#88124C2211yescharacteristic
45C2×#88123C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C2×C4×Dic26C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52#11718755C2218yescomplemented
53#11718752C2218yescomplemented
54#11718715C2218yescomplemented
55#11718715C2218yescomplemented
56#11718713C2218yescomplemented
57#11718712C2218yescomplemented
58#11718703C2218yes—
59#11718702C2218yes—
60#11718692C2218yescomplemented
61#11718683C2218yescomplemented
62#11718680C2218yescomplemented
63#11718670C2218yescomplemented
64#11718660C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88050C2211yescharacteristic
68C2×#88050C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
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×Dic26C2311yescharacteristic
84C22×Dic26C2311yescharacteristic
85C13×C4⋊Q8—22no—
86C13×C4⋊Q8C2314yes—
87C13×#126—28no—
88C13×#124—28no—
89C13×#124—22no—
90C13×#124C2314yes—
91C13×#123—28no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—28no—
94C13×C22⋊Q8C2314yes—
95C13×#121—22no—
96C13×#121C2314yes—
97C4×Q8×C13—22no—
98C4×Q8×C13C2314yes—
99C4×D4×C13—22no—
100C4×D4×C13C2314yes—
101C13×#117D414yes—
102C13×#117C2314yes—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4D411yescharacteristic
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
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×C13C2311yescharacteristic
119C2×C42×C13C2311yescharacteristic
120C2×C22⋊Dic13—21no—
121C2×C22⋊Dic13—21no—
122C2×#6107—42no—
123C2×#6107—42no—
124C2×#6107C2314yes—
125C2×#6107C2314yes—
126C2×#6105—42no—
127C2×#6105—42no—
128C2×#6105C2314yes—
129C2×#6105C2314yes—
130C2×C4⋊Dic13—21no—
131C2×C4⋊Dic13—21no—
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×#6101—21no—
144C2×C4×Dic13—21no—
145C2×C4×Dic13—21no—
146C2×#6099—42no—
147C2×#6099C2314yes—
148C22×#1055—42no—
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153C22×#1055C2314yes—
154#88143—28no—
155#88143—28no—
156#88133—28no—
157#88133—28no—
158#88124—22no—
159#88124C2314yes—
160#88123—22no—
161#88123C2314yes—
162C4×Dic26—22no—
163C4×Dic26—22no—
164C4×Dic26C2314yes—
165C4×Dic26C2314yes—
166#88075C2314yes—
167#88075C2314yes—
168#88072C2314yes—
169#88072C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179C4⋊#1055C2314yes—
180C4⋊#1055C2314yes—
181C4⋊#1055C2314yes—
182C2×#3258—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C2×Q8×C13—21no—
186C2×Q8×C13—24no—
187C2×Q8×C13—22no—
188C2×Q8×C13—22no—
189C2×Q8×C13—82no—
190C2×Q8×C13C2412yes—
191C2×D4×C13—24no—
192C2×D4×C13—21no—
193C2×D4×C13—22no—
194C2×D4×C13—22no—
195C2×D4×C13—82no—
196C2×D4×C13C2412yes—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—24no—
203C22×C4×C13—82no—
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2411yescharacteristic
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C2×Dic26—22no—
217C2×Dic26—22no—
218C2×Dic26—22no—
219C2×Dic26—22no—
220C2×Dic26—21no—
221C2×Dic26—21no—
222C2×Dic26C2412yes—
223C2×Dic26C2412yes—
224C13×C4⋊C4—24no—
225C13×C4⋊C4—24no—
226C13×C4⋊C4—24no—
227C13×C4⋊C4—21no—
228C13×C4⋊C4—21no—
229C13×C4⋊C4C2×D414yes—
230C13×C4⋊C4C2×D414yes—
231C13×C4⋊C4C2412yes—
232C13×C4⋊C4C2412yes—
233C13×C22⋊C4—24no—
234C13×C22⋊C4—24no—
235C13×C22⋊C4—24no—
236C13×C22⋊C4—24no—
237C13×C22⋊C4—24no—
238C13×C22⋊C4C2×D414yes—
239C13×C22⋊C4C2×D414yes—
240C42×C13—24no—
241C42×C13C2×D412yes—
242C42×C13C2×D412yes—
243C42×C13C2412yes—
244C42×C13C2412yes—
245C22⋊Dic13—24no—
246C22⋊Dic13—24no—
247#6107—44no—
248#6107—44no—
249#6105—44no—
250#6105—44no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—24no—
254C4⋊Dic13—24no—
255C4⋊Dic13C2412yes—
256C4⋊Dic13C2412yes—
257#6101—24no—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101—24no—
262#6101—24no—
263C4×Dic13—24no—
264C4×Dic13—24no—
265#6099—44no—
266C2×#1055—22no—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055—22no—
270C2×#1055—44no—
271C2×#1055C2412yes—
272C2×#1055C2412yes—
273C2×#1055C2412yes—
274C2×#1055C2412yes—
275C2×#542D1311yescharacteristic
276C2×#541—131no—
277#3258—1316no—
278C2×#479—131no—
279C2×#477—131no—
280C2×#475—131no—
281C2×#478—131no—
282C2×#470—131no—
283C2×#468—131no—
284C2×#467—131no—
285C2×#465—131no—
286C2×#464—131no—
287C2×#464—131no—
288C2×#462—131no—
289C2×#461—131no—
290C2×#424—131no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—42no—
296C23×C13—42no—
297C23×C13—42no—
298C23×C13C22×D412yes—
299C23×C13C22×D411yescharacteristic
300Q8×C13—22no—
301Q8×C13—22no—
302Q8×C13—42no—
303Q8×C13—84no—
304D4×C13—22no—
305D4×C13—22no—
306D4×C13—42no—
307D4×C13—84no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—24no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—42no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13—84no—
323C2×C4×C13C22×D412yes—
324C2×C4×C13C22×D412yes—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D412yes—
328C2×C4×C13C22×D411yescharacteristic
329C2×C4×C13H(5,𝔽2)12yes—
330C2×C4×C132−1+412yes—
331C2×C4×C13C2511yescharacteristic
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340Dic26—22no—
341Dic26—22no—
342Dic26—22no—
343Dic26—22no—
344Dic26—42no—
345Dic26—42no—
346#1055—22no—
347#1055—22no—
348#1055—22no—
349#1055—22no—
350C22×Q16—131no—
351C22×Q16—131no—
352C22×SD16—131no—
353C22×SD16—131no—
354C22×M16—131no—
355C23×C8—131no—
356#542—24no—
357#542C2×D1318yes—
358#541—138no—
359#541—264no—
360C2×C4⋊Q8—131no—
361C2×C4⋊Q8C2×D1311yescharacteristic
362C2×#126—21no—
363C2×#126—261no—
364C2×#126—261no—
365C2×#125—131no—
366C2×#125—261no—
367C2×#125—261no—
368C2×#124—21no—
369C2×#124C2×D1311yescharacteristic
370C2×#123—21no—
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8—131no—
373C2×C22⋊Q8—131no—
374C2×C22⋊Q8C2×D1311yescharacteristic
375C2×#121C2×D1311yescharacteristic
376C2×C4×Q8—131no—
377C2×C4×Q8—131no—
378C2×C4×Q8C2×D1311yescharacteristic
379C2×C4×D4C2×D1311yescharacteristic
380C2×#117C2×D1311yescharacteristic
381#479—138no—
382#478—138no—
383#477—138no—
384#475—138no—
385#470—138no—
386#468—138no—
387#467—138no—
388#465—138no—
389#464—138no—
390#464—138no—
391#462—138no—
392#461—138no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#106—131no—
396C2×#106—131no—
397#424—138no—
398C2×C4⋊C8—131no—
399C2×C4⋊C8—131no—
400C2×C4⋊C8—131no—
401C2×C4⋊C8—131no—
402C2×#103—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#102—131no—
409C2×#102—131no—
410C22×C13—22no—
411C22×C13—22no—
412C22×C13—22no—
413C22×C13—44no—
414C22×C13—42no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13—84no—
418C22×C13#53712yes—
419C22×C13#57712yes—
420C22×C13#57812yes—
421C22×C13C23×D411yescharacteristic
422C4×C13—22no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—22no—
426C4×C13—22no—
427C4×C13—42no—
428C4×C13—42no—
429C4×C13—42no—
430C4×C13#53712yes—
431C4×C13C2×H(5,𝔽2)11yescharacteristic
432C4×C13C2×2−1+411yescharacteristic
433Dic13—42no—
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437C22×Q8—21no—
438C22×Q8—131no—
439C22×Q8—131no—
440C22×Q8C22×D1311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D1311yescharacteristic
443C23×C4—21no—
444C23×C4C22×D1311yescharacteristic
445C2×Q16—134no—
446C2×Q16—134no—
447C2×Q16—522no—
448C2×Q16—522no—
449C2×SD16—134no—
450C2×SD16—134no—
451C2×SD16—522no—
452C2×SD16—522no—
453C2×M16—134no—
454C2×M16—522no—
455C22×C8—131no—
456C22×C8—131no—
457C22×C8—131no—
458C22×C8—131no—
459C22×C8—134no—
460C22×C8—522no—
461C4⋊Q8—22no—
462C4⋊Q8—134no—
463C4⋊Q8—262no—
464C4⋊Q8C22×D1314yes—
465#126—28no—
466#126—268no—
467#126—268no—
468#125—134no—
469#125—268no—
470#125—268no—
471#125—262no—
472#124—28no—
473#124—22no—
474#124C22×D1314yes—
475#123—28no—
476C22⋊Q8—22no—
477C22⋊Q8—28no—
478C22⋊Q8—134no—
479C22⋊Q8—134no—
480C22⋊Q8—262no—
481C22⋊Q8—262no—
482C22⋊Q8C22×D1314yes—
483#121—22no—
484#121C22×D1314yes—
485C4×Q8—22no—
486C4×Q8—134no—
487C4×Q8—134no—
488C4×Q8—262no—
489C4×Q8—262no—
490C4×Q8C22×D1314yes—
491C4×D4—22no—
492C4×D4C22×D1314yes—
493#117C22⋊D1314yes—
494#117C22×D1314yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—131no—
499C2×C4⋊C4—131no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4C22⋊D1311yescharacteristic
509C2×C4⋊C4C22⋊D1311yescharacteristic
510C2×C4⋊C4C22×D1311yescharacteristic
511C2×C4⋊C4C22×D1311yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4C22⋊D1311yescharacteristic
520C2×C22⋊C4C22⋊D1311yescharacteristic
521C2×C42—21no—
522C2×C42—261no—
523C2×C42—261no—
524C2×C42C22×D1311yescharacteristic
525C2×C42C22×D1311yescharacteristic
526#107—134no—
527#107—134no—
528#106—134no—
529#106—134no—
530C4⋊C8—134no—
531C4⋊C8—134no—
532C4⋊C8—134no—
533C4⋊C8—134no—
534#103—134no—
535#103—134no—
536#103—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#102—134no—
541#102—134no—
542C2×C13—42no—
543C2×C13—82no—
544C2×C13#325814yescomplemented
545C2×C13C2×#53711yescharacteristic
546C2×C13C2×#57711yescharacteristic
547C2×C13C2×#57811yescharacteristic
548C24—21no—
549C24C2×C22⋊D1311yescharacteristic
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—82no—
555C2×Q8—132no—
556C2×Q8—132no—
557C2×Q8—261no—
558C2×Q8—261no—
559C2×Q8—262no—
560C2×Q8—262no—
561C2×Q8—262no—
562C2×Q8—262no—
563C2×Q8C23×D1312yes—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—82no—
569C2×D4C23×D1312yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—82no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4C2×C22⋊D1312yes—
582C22×C4C2×C22⋊D1311yescharacteristic
583C22×C4C2×C22⋊D1311yescharacteristic
584C22×C4C2×C22⋊D1311yescharacteristic
585C22×C4C2×C22⋊D1311yescharacteristic
586C22×C4C2×C22⋊D1311yescharacteristic
587C22×C4C23×D1312yes—
588C22×C4C23×D1311yescharacteristic
589Q16—524no—
590Q16—524no—
591SD16—524no—
592SD16—524no—
593M16—524no—
594C2×C8—132no—
595C2×C8—132no—
596C2×C8—132no—
597C2×C8—132no—
598C2×C8—262no—
599C2×C8—262no—
600C2×C8—262no—
601C2×C8—262no—
602C2×C8—524no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—132no—
609C4⋊C4—132no—
610C4⋊C4—261no—
611C4⋊C4—261no—
612C4⋊C4—264no—
613C4⋊C4—264no—
614C4⋊C4—264no—
615C4⋊C4—264no—
616C4⋊C4—264no—
617C4⋊C4—264no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4C2×C22⋊D1314yes—
621C4⋊C4C2×C22⋊D1314yes—
622C4⋊C4C23×D1312yes—
623C4⋊C4C23×D1312yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—264no—
630C22⋊C4—264no—
631C22⋊C4C2×C22⋊D1314yes—
632C22⋊C4C2×C22⋊D1314yes—
633C42—24no—
634C42—264no—
635C42—264no—
636C42C2×C22⋊D1312yes—
637C42C2×C22⋊D1312yes—
638C42C23×D1312yes—
639C42C23×D1312yes—
640C13C2×#325811yescharacteristic, complemented, Sylow
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C22×C22⋊D1312yes—
649C23C22×C22⋊D1311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—84no—
654Q8—262no—
655Q8—262no—
656Q8—262no—
657Q8—262no—
658Q8—522no—
659Q8—522no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
686C2×C4—522no—
687C2×C4#8825612yes—
688C2×C4#8825712yes—
689C2×C4C22×C22⋊D1312yes—
690C2×C4C22×C22⋊D1312yes—
691C2×C4C22×C22⋊D1312yes—
692C2×C4C22×C22⋊D1312yes—
693C2×C4C22×C22⋊D1312yes—
694C2×C4C22×C22⋊D1311yescharacteristic
695C2×C4C24×D1311yescharacteristic
696C8—262no—
697C8—262no—
698C8—262no—
699C8—262no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1171953812yes—
709C22#1171954112yes—
710C22#1171954312yes—
711C22C23×C22⋊D1311yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—522no—
721C4—522no—
722C4—522no—
723C4—522no—
724C4#1171953812yes—
725C4C2×#8825611yescharacteristic
726C4C2×#8825711yescharacteristic
727C2—42no—
728C2—82no—
729C2#1312626214yesdirect product factor
730C2C2×#1171953811yescharacteristic
731C2C2×#1171954111yescharacteristic
732C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#542C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#542D13
hypocenterC13C2×#3258
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×#11719223C2semidirect
2. #13126262C2direct (N × H)
3. C2×#11718683C2semidirect
4. C2×#11718752C2semidirect
5. C2×#11718755C2semidirect
6. C2×#11718670C2semidirect
7. C2×#11718713C2semidirect
9. C2×#11718712C2semidirect
11. C2×#11718715C2semidirect
12. C2×#11718715C2semidirect
13. C2×#11718692C2semidirect
14. C2×#11718680C2semidirect
15. C2×#11718660C2semidirect
39. #11719223C22semidirect
52. #11718755C22semidirect
53. #11718752C22semidirect
54. #11718715C22semidirect
55. #11718715C22semidirect
56. #11718713C22semidirect
57. #11718712C22semidirect
60. #11718692C22semidirect
61. #11718683C22semidirect
62. #11718680C22semidirect
63. #11718670C22semidirect
64. #11718660C22semidirect
544. C2×C13#3258semidirect
640. C13C2×#3258semidirect
729. C2#13126262direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192232
#131262622
C2×#117186832
C2×#117187522
C2×#117187552
C2×#117186702
C2×#117187132
C2×#117187032
C2×#117187122
C2×#117187022
C2×#117187152
C2×#117186922
C2×#117186802
C2×#117186602
C2×C13×#5422
C2×#325813