Finite Group Databasebeta

← C2×#13126256 #16735839

Subgroups — C2×#13126256 #16735839

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×#11719239C211yesmaximal, characteristic
2#13126256C2116yesmaximal, direct product factor
3C2×#11718724C211yesmaximal, characteristic, complemented
4C2×#11718682C211yesmaximal, characteristic, complemented
5C2×#11718681C211yesmaximal, characteristic, complemented
6C2×#11718727C211yesmaximal, characteristic, complemented
7C2×#11718713C211yesmaximal, characteristic, complemented
8C2×#11718710C211yesmaximal, characteristic
9C2×#11718712C211yesmaximal, characteristic, complemented
10C2×#11718709C211yesmaximal, characteristic
11C2×#11718689C211yesmaximal, characteristic, complemented
12C2×#11718689C211yesmaximal, characteristic, complemented
13C2×#11718751C211yesmaximal, characteristic, complemented
14C2×#11718744C211yesmaximal, characteristic, complemented
15C2×#11718660C211yesmaximal, characteristic, complemented
16C2×C13×#541C211yesmaximal, characteristic, complemented
17C13×#541—24no—
18C13×#541C2218yescomplemented
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#126—21no—
21C2×C13×#126—21no—
22C2×C13×#125—21no—
23C2×C13×#125—21no—
24C2×C13×#125C2211yescharacteristic
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C22×#6107C2211yescharacteristic
32C22×#6106C2211yescharacteristic
33C22×#6106C2211yescharacteristic
34C2×#88184C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719239—24no—
39#11719239C2218yes—
40C2×#88152—21no—
41C2×#88150—21no—
42C2×#88139—21no—
43C2×#88137—21no—
44C2×#88129C2211yescharacteristic
45C2×C4×D52C2211yescharacteristic
46C2×#88123C2211yescharacteristic
47C2×C4×Dic26C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88075C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52#11718751C2218yescomplemented
53#11718744C2218yescomplemented
54#11718727C2218yescomplemented
55#11718724C2218yescomplemented
56#11718713C2218yescomplemented
57#11718712C2218yescomplemented
58#11718710C2218yes—
59#11718709C2218yes—
60#11718689C2218yescomplemented
61#11718689C2218yescomplemented
62#11718682C2218yescomplemented
63#11718681C2218yescomplemented
64#11718660C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×C4⋊#1055C2211yescharacteristic
77C22×Q8×C13C2311yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C22×D52C2311yescharacteristic
82C22×C4×D13—21no—
83C22×Dic26—21no—
84C22×Dic26C2311yescharacteristic
85C13×C4⋊Q8—22no—
86C13×C4⋊Q8C2314yes—
87C13×#126—28no—
88C13×#126—28no—
89C13×#125—28no—
90C13×#125—28no—
91C13×#125—22no—
92C13×#125C2314yes—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8C2314yes—
96C13×C22⋊Q8C2314yes—
97C4×Q8×C13—22no—
98C4×Q8×C13—22no—
99C4×Q8×C13C2314yes—
100C4×Q8×C13C2314yes—
101C13×#117D414yes—
102C13×#117C2314yes—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4C2311yescharacteristic
114C2×C13×C4⋊C4C2311yescharacteristic
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4D411yescharacteristic
118C2×C13×C22⋊C4D411yescharacteristic
119C2×C42×C13—21no—
120C2×C42×C13—21no—
121C2×C42×C13C2311yescharacteristic
122C2×C42×C13C2311yescharacteristic
123C2×C22⋊Dic13—21no—
124C2×#6107—42no—
125C2×#6107—42no—
126C2×#6107C2314yes—
127C2×#6107C2314yes—
128C2×#6106—42no—
129C2×#6106—42no—
130C2×#6106C2314yes—
131C2×#6106C2314yes—
132#88184—22no—
133#88184C2314yes—
134C2×#6103—21no—
135C2×#6103—21no—
136C2×#6103—21no—
137C2×#6103—21no—
138C2×C4⋊Dic13—21no—
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141#88178—22no—
142#88178C2314yes—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×C4×Dic13—21no—
146C2×#6099—42no—
147C2×#6099C2314yes—
148C22×#1055—42no—
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153C22×#1055C2314yes—
154#88152—28no—
155#88150—28no—
156#88139—28no—
157#88137—28no—
158#88129—22no—
159#88129C2314yes—
160C4×D52—22no—
161C4×D52C2314yes—
162#88123—22no—
163#88123C2314yes—
164C4×Dic26—22no—
165C4×Dic26C2314yes—
166#88075C2314yes—
167#88075C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88049C2314yes—
173#88049C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179C4⋊#1055C2314yes—
180C4⋊#1055C2314yes—
181C4⋊#1055C2314yes—
182C2×#3258—131nomaximal, Sylow
183C24×C13C2×D411yescharacteristic
184C23×D13—21no—
185C2×Q8×C13—21no—
186C2×Q8×C13—21no—
187C2×Q8×C13—22no—
188C2×Q8×C13—22no—
189C2×Q8×C13—22no—
190C2×Q8×C13—22no—
191C2×Q8×C13C2412yes—
192C2×Q8×C13C2412yes—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D412yes—
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2412yes—
206C22×C4×C13C2411yescharacteristic
207C2×C22⋊D13—24no—
208C2×C22⋊D13—82no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C2×D52—22no—
213C2×D52—22no—
214C2×D52—21no—
215C2×D52C2412yes—
216C2×C4×D13—24no—
217C2×C4×D13—82no—
218C2×Dic26—22no—
219C2×Dic26—22no—
220C2×Dic26—21no—
221C2×Dic26—24no—
222C2×Dic26—82no—
223C2×Dic26C2412yes—
224C13×C4⋊C4—24no—
225C13×C4⋊C4—24no—
226C13×C4⋊C4—24no—
227C13×C4⋊C4—24no—
228C13×C4⋊C4—24no—
229C13×C4⋊C4—24no—
230C13×C4⋊C4—24no—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—21no—
233C13×C4⋊C4—21no—
234C13×C4⋊C4C2×D414yes—
235C13×C4⋊C4C2×D414yes—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C22⋊C4—24no—
239C13×C22⋊C4—24no—
240C13×C22⋊C4C2×D414yes—
241C13×C22⋊C4C2×D414yes—
242C42×C13—24no—
243C42×C13—24no—
244C42×C13C2×D412yes—
245C42×C13C2×D412yes—
246C42×C13C2412yes—
247C42×C13C2412yes—
248C22⋊Dic13—24no—
249#6107—44no—
250#6107—44no—
251#6106—44no—
252#6106—44no—
253#6103—24no—
254#6103—24no—
255#6103—24no—
256#6103—24no—
257C4⋊Dic13—21no—
258C4⋊Dic13—21no—
259C4⋊Dic13—24no—
260C4⋊Dic13C2412yes—
261C4⋊Dic13C2412yes—
262#6101—24no—
263#6101—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×#542—131no—
276C2×#541D1311yescharacteristic, complemented
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×C13C22×D412yes—
295C23×C13C22×D411yescharacteristic
296C22×D13—22no—
297C22×D13—42no—
298C22×D13—42no—
299C22×D13—42no—
300Q8×C13—22no—
301Q8×C13—22no—
302Q8×C13—22no—
303Q8×C13—22no—
304Q8×C13—42no—
305Q8×C13—42no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—24no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13C22×D412yes—
323C2×C4×C13C22×D412yes—
324C2×C4×C13C22×D412yes—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D411yescharacteristic
328C2×C4×C13H(5,𝔽2)12yes—
329C2×C4×C132−1+412yes—
330C2×C4×C13C2511yescharacteristic
331C22⋊D13—84no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338D52—22no—
339D52—22no—
340D52—42no—
341C4×D13—84no—
342Dic26—22no—
343Dic26—22no—
344Dic26—42no—
345Dic26—84no—
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—138no—
357#542—264no—
358#541—24no—
359#541C2×D1318yescomplemented
360C2×C4⋊Q8—131no—
361C2×C4⋊Q8C2×D1311yescharacteristic
362C2×#126—21no—
363C2×#126—21no—
364C2×#126—261no—
365C2×#125—21no—
366C2×#125—21no—
367C2×#125C2×D1311yescharacteristic
368C2×#124—131no—
369C2×#124—261no—
370C2×#123—261no—
371C2×C22⋊Q8—131no—
372C2×C22⋊Q8—261no—
373C2×C22⋊Q8C2×D1311yescharacteristic
374C2×C22⋊Q8C2×D1311yescharacteristic
375C2×#121—131no—
376C2×C4×Q8—131no—
377C2×C4×Q8C2×D1311yescharacteristic
378C2×C4×Q8C2×D1311yescharacteristic
379C2×C4×D4—131no—
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#53712yes—
415C22×C13#57712yes—
416C22×C13#57812yes—
417C22×C13C23×D411yescharacteristic
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—84no—
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—42no—
431C4×C13#53712yes—
432C4×C13C2×H(5,𝔽2)11yescharacteristic
433C4×C13C2×2−1+411yescharacteristic
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437C22×Q8—131no—
438C22×Q8—261no—
439C22×Q8C22×D1311yescharacteristic
440C22×Q8C22×D1311yescharacteristic
441C22×D4—131no—
442C22×D4—261no—
443C23×C4—261no—
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—28no—
467#126—268no—
468#125—28no—
469#125—28no—
470#125—22no—
471#125C22×D1314yes—
472#124—134no—
473#124—268no—
474#124—262no—
475#123—268no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—134no—
479C22⋊Q8—262no—
480C22⋊Q8—268no—
481C22⋊Q8C22×D1314yes—
482C22⋊Q8C22×D1314yes—
483#121—134no—
484#121—262no—
485C4×Q8—22no—
486C4×Q8—22no—
487C4×Q8—134no—
488C4×Q8—262no—
489C4×Q8C22×D1314yes—
490C4×Q8C22×D1314yes—
491C4×D4—134no—
492C4×D4—262no—
493#117C22⋊D1314yes—
494#117C22×D1314yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—131no—
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—261no—
515C2×C22⋊C4—261no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4C22⋊D1311yescharacteristic
520C2×C22⋊C4C22⋊D1311yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
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#325814yescomplemented
544C2×C13C2×#53711yescharacteristic
545C2×C13C2×#57711yescharacteristic
546C2×C13C2×#57811yescharacteristic
547D13—82no—
548C24—261no—
549C24C2×C22⋊D1311yescharacteristic
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—132no—
557C2×Q8—261no—
558C2×Q8—264no—
559C2×Q8—262no—
560C2×Q8—262no—
561C2×Q8—1042no—
562C2×Q8C23×D1312yes—
563C2×Q8C23×D1312yes—
564C2×D4—132no—
565C2×D4—264no—
566C2×D4—262no—
567C2×D4—262no—
568C2×D4—261no—
569C2×D4—1042no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—264no—
580C22×C4—1042no—
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—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—132no—
614C4⋊C4—132no—
615C4⋊C4—261no—
616C4⋊C4—261no—
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—264no—
627C22⋊C4—264no—
628C22⋊C4—264no—
629C22⋊C4—264no—
630C22⋊C4—264no—
631C22⋊C4C2×C22⋊D1314yes—
632C22⋊C4C2×C22⋊D1314yes—
633C42—24no—
634C42—24no—
635C42—264no—
636C42C2×C22⋊D1312yes—
637C42C2×C22⋊D1312yes—
638C42C23×D1312yes—
639C42C23×D1312yes—
640C13C2×#325811yescharacteristic, complemented, Sylow
641C23—22no—
642C23—22no—
643C23—22no—
644C23—262no—
645C23—522no—
646C23—522no—
647C23—522no—
648C23C22×C22⋊D1312yes—
649C23C22×C22⋊D1311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—262no—
657Q8—262no—
658Q8—522no—
659Q8—1044no—
660D4—262no—
661D4—262no—
662D4—522no—
663D4—1044no—
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—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
686C2×C4—1044no—
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—522no—
705C22—522no—
706C22—522no—
707C22—1044no—
708C22#1171953812yes—
709C22#1171954212yes—
710C22#1171954312yes—
711C22C23×C22⋊D1311yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—522no—
722C4—522no—
723C4—522no—
724C4#1171953812yes—
725C4C2×#8825611yescharacteristic
726C4C2×#8825711yescharacteristic
727C2—42no—
728C2—1042no—
729C2#1312625614yesdirect product factor
730C2C2×#1171953811yescharacteristic
731C2C2×#1171954211yescharacteristic
732C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#541C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#541D13
hypocenterC13C2×#3258
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #13126256C2direct (N × H)
3. C2×#11718724C2semidirect
4. C2×#11718682C2semidirect
5. C2×#11718681C2semidirect
6. C2×#11718727C2semidirect
7. C2×#11718713C2semidirect
9. C2×#11718712C2semidirect
11. C2×#11718689C2semidirect
12. C2×#11718689C2semidirect
13. C2×#11718751C2semidirect
14. C2×#11718744C2semidirect
15. C2×#11718660C2semidirect
16. C2×C13×#541C2semidirect
18. C13×#541C22semidirect
52. #11718751C22semidirect
53. #11718744C22semidirect
54. #11718727C22semidirect
55. #11718724C22semidirect
56. #11718713C22semidirect
57. #11718712C22semidirect
60. #11718689C22semidirect
61. #11718689C22semidirect
62. #11718682C22semidirect
63. #11718681C22semidirect
64. #11718660C22semidirect
276. C2×#541D13semidirect
359. #541C2×D13semidirect
543. C2×C13#3258semidirect
640. C13C2×#3258semidirect
729. C2#13126256direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192392
#131262562
C2×#117187242
C2×#117186822
C2×#117186812
C2×#117187272
C2×#117187132
C2×#117187102
C2×#117187122
C2×#117187092
C2×#117186892
C2×#117187512
C2×#117187442
C2×#117186602
C2×C13×#5412
C2×#325813