Finite Group Databasebeta

← C2×#13127330 #16741508

Subgroups — C2×#13127330 #16741508

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719268C211yesmaximal, characteristic, complemented
2#13127330C2116yesmaximal, direct product factor
3C2×#11718726C211yesmaximal, characteristic, complemented
4C2×#11718664C211yesmaximal, characteristic, complemented
5C2×#11718696C211yesmaximal, characteristic, complemented
6C2×#11718696C211yesmaximal, characteristic, complemented
7C2×#11718628C211yesmaximal, characteristic, complemented
8C2×#11718727C211yesmaximal, characteristic, complemented
9C2×#11718668C211yesmaximal, characteristic, complemented
10C2×#11718700C211yesmaximal, characteristic, complemented
11C2×#11718699C211yesmaximal, characteristic, complemented
12C2×#11718675C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718625C211yesmaximal, characteristic, complemented
15C2×#11718659C211yesmaximal, characteristic, complemented
16C2×C13×#553C211yesmaximal, characteristic, complemented
17C13×#553—24no—
18C13×#553C2218yescomplemented
19C2×C13×#126—21no—
20C2×C13×#125C2211yescharacteristic
21C2×C13×#123—21no—
22C2×C13×#121—21no—
23C2×C13×#121C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C2×C4×D4×C13—21no—
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C2×#88192—21no—
31C22×#6104C2211yescharacteristic
32C2×#88184C2211yescharacteristic
33C2×#88184C2211yescharacteristic
34C2×#88180C2211yescharacteristic
35C2×#88180C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719268—24no—
39#11719268C2218yescomplemented
40C2×#88146—21no—
41C2×#88139—21no—
42C2×#88139—21no—
43C2×C4×D52C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718727C2218yescomplemented
51#11718726C2218yescomplemented
52#11718700C2218yescomplemented
53#11718699C2218yescomplemented
54#11718696C2218yescomplemented
55#11718696C2218yescomplemented
56#11718675C2218yescomplemented
57#11718672C2218yescomplemented
58#11718668C2218yescomplemented
59#11718664C2218yescomplemented
60#11718659C2218yescomplemented
61#11718628C2218yescomplemented
62C2×#88049C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65#11718625C2218yescomplemented
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13D411yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13—21no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C22×C22⋊D13—21no—
86C22×C22⋊D13—21no—
87C22×D52C2311yescharacteristic
88C22×C4×D13—21no—
89C22×Dic26—21no—
90C13×#126—28no—
91C13×#125—22no—
92C13×#125C2314yes—
93C13×#123—28no—
94C13×#121—28no—
95C13×#121—22no—
96C13×#121—22no—
97C13×#121C2314yes—
98C13×#121C2314yes—
99C4×D4×C13—28no—
100C4×D4×C13—22no—
101C4×D4×C13D414yes—
102C4×D4×C13C2314yes—
103C4×D4×C13C2314yes—
104C13×#117—22no—
105C13×#117C2314yes—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C4⋊C4C2314yes—
114C2×C13×C4⋊C4C2311yescharacteristic
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4D411yescharacteristic
120C2×C13×C22⋊C4D411yescharacteristic
121C2×C42×C13—21no—
122C2×C42×C13C2311yescharacteristic
123C2×C22⋊Dic13—21no—
124C2×C22⋊Dic13—21no—
125#88192—28no—
126C2×#6104—24no—
127C2×#6104C2314yes—
128#88184—22no—
129#88184—22no—
130#88184C2314yes—
131#88184C2314yes—
132C2×#6103—21no—
133C2×#6103—21no—
134C2×#6103—21no—
135#88180—22no—
136#88180—22no—
137#88180C2314yes—
138#88180C2314yes—
139C2×C4⋊Dic13—21no—
140C2×C4⋊Dic13C2311yescharacteristic
141C2×C4⋊Dic13C2311yescharacteristic
142C2×C4⋊Dic13C2311yescharacteristic
143C2×C4×Dic13—21no—
144C2×C4×Dic13—21no—
145C2×#6099—24no—
146C2×#6099C2314yes—
147C22×#1055—24no—
148C22×#1055C2314yes—
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153#88146—28no—
154#88139—28no—
155#88139—28no—
156C4×D52—22no—
157C4×D52C2314yes—
158#88123—22no—
159#88123C2314yes—
160#88072C2314yes—
161#88072C2314yes—
162#88072C2314yes—
163C22⋊#1055C2314yes—
164C22⋊#1055C2314yes—
165#88049C2314yes—
166#88049C2314yes—
167#88049C2314yes—
168#88048C2314yes—
169#88048C2314yes—
170#88048C2314yes—
171#88048C2314yes—
172#88047C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177C4⋊#1055C2314yes—
178#88043C2314yes—
179C2×#3347—131nomaximal, Sylow
180C24×C13—21no—
181C24×C13C2×D411yescharacteristic
182C24×C13C2×D411yescharacteristic
183C23×D13—21no—
184C2×D4×C13—24no—
185C2×D4×C13—24no—
186C2×D4×C13—21no—
187C2×D4×C13—22no—
188C2×D4×C13—22no—
189C2×D4×C13—42no—
190C2×D4×C13—44no—
191C2×D4×C13—82no—
192C2×D4×C13C2×D414yes—
193C2×D4×C13C2412yes—
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—24no—
202C22×C4×C13—24no—
203C22×C4×C13—82no—
204C22×C4×C13—82no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2411yescharacteristic
214C2×C22⋊D13—24no—
215C2×C22⋊D13—24no—
216C2×C22⋊D13—82no—
217C2×C22⋊D13—82no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C2×D52—22no—
222C2×D52—22no—
223C2×D52—21no—
224C2×D52C2412yes—
225C2×C4×D13—24no—
226C2×C4×D13—44no—
227C2×Dic26—24no—
228C2×Dic26—82no—
229C13×C4⋊C4—21no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4C2×D414yes—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C4⋊C4C2412yes—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C13×C22⋊C4—24no—
242C13×C22⋊C4—24no—
243C13×C22⋊C4C2×D414yes—
244C13×C22⋊C4C2×D414yes—
245C42×C13—24no—
246C42×C13C2×D412yes—
247C42×C13C2412yes—
248C22⋊Dic13—24no—
249C22⋊Dic13—24no—
250#6104—28no—
251#6103—24no—
252#6103—24no—
253#6103—24no—
254C4⋊Dic13—21no—
255C4⋊Dic13—21no—
256C4⋊Dic13—24no—
257C4⋊Dic13—21no—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260C4⋊Dic13C2412yes—
261C4×Dic13—24no—
262C4×Dic13—24no—
263#6099—28no—
264C2×#1055—22no—
265C2×#1055—22no—
266C2×#1055—22no—
267C2×#1055—28no—
268C2×#1055#4114yes—
269C2×#1055C2412yes—
270C2×#1055C2412yes—
271C2×#1055C2412yes—
272C2×#1055C2412yes—
273C2×#555—131no—
274C2×#553D1311yescharacteristic, complemented
275#3347—1316no—
276C2×#501—131no—
277C2×#482—131no—
278C2×#482—131no—
279C2×#482—131no—
280C2×#480—131no—
281C2×#478—131no—
282C2×#474—131no—
283C2×#469—131no—
284C2×#466—131no—
285C2×#442—131no—
286C2×#435—131no—
287C2×#428—131no—
288C2×#427—131no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—42no—
297C23×C13—42no—
298C23×C13—42no—
299C23×C13C22×D412yes—
300C23×C13C22×D412yes—
301C23×C13C22×D411yescharacteristic
302C22×D13—22no—
303C22×D13—42no—
304C22×D13—42no—
305C22×D13—42no—
306D4×C13—22no—
307D4×C13—22no—
308D4×C13—44no—
309D4×C13—48no—
310D4×C13—42no—
311D4×C13—84no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—24no—
317C2×C4×C13—24no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13—84no—
329C2×C4×C13—84no—
330C2×C4×C13C22×D412yes—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D411yescharacteristic
335C2×C4×C13C2×#4112yes—
336C2×C4×C132−1+412yes—
337C2×C4×C13C2511yescharacteristic
338C22⋊D13—84no—
339C22⋊D13—84no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346D52—22no—
347D52—22no—
348D52—42no—
349C4×D13—48no—
350Dic26—84no—
351#1055—22no—
352#1055—22no—
353#1055—22no—
354#1055C2×#4114yes—
355C22×D8—131no—
356C22×M16—131no—
357C23×C8—131no—
358#555—138no—
359#555—264no—
360#553—24no—
361#553C2×D1318yescomplemented
362C2×C4⋊Q8—131no—
363C2×#126—21no—
364C2×#125C2×D1311yescharacteristic
365C2×#124—261no—
366C2×#124—261no—
367C2×#123—21no—
368C2×#121—21no—
369C2×#121—131no—
370C2×#121—131no—
371C2×#121—261no—
372C2×#121C2×D1311yescharacteristic
373C2×#121C2×D1311yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4—131no—
376C2×C4×D4C2×D1311yescharacteristic
377C2×C4×D4C2×D1311yescharacteristic
378C2×#117—131no—
379C2×#117—131no—
380C2×#117—261no—
381C2×#117C2×D1311yescharacteristic
382C22×C4⋊C4C2×D1311yescharacteristic
383#501—138no—
384#482—138no—
385#482—138no—
386#482—138no—
387#480—138no—
388#478—138no—
389#474—138no—
390#469—138no—
391#466—138no—
392#442—138no—
393#435—138no—
394#428—138no—
395#427—138no—
396C2×#107—131no—
397C2×#107—131no—
398C2×#107—131no—
399C2×#107—131no—
400C2×#107—131no—
401C2×#106—131no—
402C2×#106—131no—
403C2×#106—131no—
404C2×#106—131no—
405C2×C4⋊C8—131no—
406C2×#102—131no—
407C2×#102—131no—
408C2×#102—131no—
409C2×#102—131no—
410C2×#102—131no—
411C2×#102—131no—
412C2×C22⋊C8—131no—
413C2×C22⋊C8—131no—
414C2×#97—131no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—22no—
418C22×C13—22no—
419C22×C13—22no—
420C22×C13—22no—
421C22×C13—44no—
422C22×C13—44no—
423C22×C13—42no—
424C22×C13—42no—
425C22×C13—42no—
426C22×C13—84no—
427C22×C13#54712yes—
428C22×C13#57512yes—
429C22×C13#57612yes—
430C22×C13C23×D411yescharacteristic
431C2×D13—42no—
432C2×D13—42no—
433C2×D13—42no—
434C2×D13—84no—
435C4×C13—22no—
436C4×C13—22no—
437C4×C13—22no—
438C4×C13—22no—
439C4×C13—42no—
440C4×C13—42no—
441C4×C13—42no—
442C4×C13#54712yes—
443C4×C13C22×#4111yescharacteristic
444C4×C13C2×2−1+411yescharacteristic
445Dic13—42no—
446Dic13—42no—
447Dic13—42no—
448C22×Q8—261no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—131no—
452C22×D4—261no—
453C22×D4—261no—
454C22×D4C22⋊D1311yescharacteristic
455C22×D4C22×D1311yescharacteristic
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—261no—
459C23×C4C22×D1311yescharacteristic
460C23×C4C22×D1311yescharacteristic
461C2×D8—134no—
462C2×D8—264no—
463C2×M16—134no—
464C2×M16—264no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—134no—
468C22×C8—131no—
469C22×C8—131no—
470C22×C8—264no—
471C4⋊Q8—134no—
472C4⋊Q8—262no—
473#126—28no—
474#125—22no—
475#125C22×D1314yes—
476#124—268no—
477#124—268no—
478#123—28no—
479#121—28no—
480#121—22no—
481#121—22no—
482#121—134no—
483#121—134no—
484#121—268no—
485#121—262no—
486#121—262no—
487#121C22×D1314yes—
488#121C22×D1314yes—
489C4×D4—28no—
490C4×D4—22no—
491C4×D4—134no—
492C4×D4—262no—
493C4×D4C22⋊D1314yes—
494C4×D4C22×D1314yes—
495C4×D4C22×D1314yes—
496#117—22no—
497#117—134no—
498#117—134no—
499#117—262no—
500#117—262no—
501#117—268no—
502#117C22×D1314yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—131no—
508C2×C4⋊C4—131no—
509C2×C4⋊C4—131no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4C22⋊D1311yescharacteristic
512C2×C4⋊C4C22×D1311yescharacteristic
513C2×C4⋊C4C22×D1311yescharacteristic
514C2×C4⋊C4C22×D1314yes—
515C2×C4⋊C4C22×D1311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4—261no—
523C2×C22⋊C4—261no—
524C2×C22⋊C4—261no—
525C2×C22⋊C4C22⋊D1311yescharacteristic
526C2×C22⋊C4C22⋊D1311yescharacteristic
527C2×C42—21no—
528C2×C42—261no—
529C2×C42—261no—
530C2×C42C22×D1311yescharacteristic
531#107—134no—
532#107—134no—
533#107—134no—
534#107—134no—
535#107—134no—
536#106—134no—
537#106—134no—
538#106—134no—
539#106—134no—
540C4⋊C8—134no—
541#102—134no—
542#102—134no—
543#102—134no—
544#102—134no—
545#102—134no—
546#102—134no—
547C22⋊C8—134no—
548C22⋊C8—134no—
549#97—134no—
550C2×C13—42no—
551C2×C13—42no—
552C2×C13—82no—
553C2×C13#334714yescomplemented
554C2×C13C2×#54711yescharacteristic
555C2×C13C2×#57511yescharacteristic
556C2×C13C2×#57611yescharacteristic
557D13—82no—
558C24—21no—
559C24—261no—
560C24C2×C22⋊D1311yescharacteristic
561C24C2×C22⋊D1311yescharacteristic
562C2×Q8—264no—
563C2×Q8—1042no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—82no—
572C2×D4—132no—
573C2×D4—264no—
574C2×D4—264no—
575C2×D4—262no—
576C2×D4—262no—
577C2×D4—261no—
578C2×D4—1042no—
579C2×D4—1042no—
580C2×D4C2×C22⋊D1314yes—
581C2×D4C23×D1312yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—264no—
597C22×C4—524no—
598C22×C4C2×C22⋊D1312yes—
599C22×C4C2×C22⋊D1312yes—
600C22×C4C2×C22⋊D1311yescharacteristic
601C22×C4C2×C22⋊D1311yescharacteristic
602C22×C4C2×C22⋊D1311yescharacteristic
603C22×C4C2×C22⋊D1311yescharacteristic
604C22×C4C23×D1312yes—
605C22×C4C23×D1312yes—
606C22×C4C23×D1311yescharacteristic
607D8—268no—
608M16—268no—
609C2×C8—134no—
610C2×C8—132no—
611C2×C8—132no—
612C2×C8—132no—
613C2×C8—132no—
614C2×C8—268no—
615C2×C8—262no—
616C2×C8—262no—
617C2×C8—262no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—132no—
625C4⋊C4—132no—
626C4⋊C4—132no—
627C4⋊C4—261no—
628C4⋊C4—261no—
629C4⋊C4—261no—
630C4⋊C4—264no—
631C4⋊C4C2×C22⋊D1314yes—
632C4⋊C4C23×D1312yes—
633C4⋊C4C23×D1312yes—
634C4⋊C4C23×D1312yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—264no—
640C22⋊C4—264no—
641C22⋊C4—264no—
642C22⋊C4—264no—
643C22⋊C4—264no—
644C22⋊C4C2×C22⋊D1314yes—
645C22⋊C4C2×C22⋊D1314yes—
646C42—24no—
647C42—264no—
648C42—264no—
649C42C2×C22⋊D1312yes—
650C42C23×D1312yes—
651C13C2×#334711yescharacteristic, complemented, Sylow
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—262no—
663C23—522no—
664C23—522no—
665C23—522no—
666C23C22×C22⋊D1312yes—
667C23C22×C22⋊D1312yes—
668C23C22×C22⋊D1311yescharacteristic
669Q8—1044no—
670D4—22no—
671D4—22no—
672D4—44no—
673D4—48no—
674D4—42no—
675D4—84no—
676D4—262no—
677D4—262no—
678D4—522no—
679D4—1044no—
680D4—1044no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—528no—
703C2×C4—522no—
704C2×C4—522no—
705C2×C4—522no—
706C2×C4#41×D1312yes—
707C2×C4#8825712yes—
708C2×C4C22×C22⋊D1312yes—
709C2×C4C22×C22⋊D1312yes—
710C2×C4C22×C22⋊D1312yes—
711C2×C4C22×C22⋊D1312yes—
712C2×C4C22×C22⋊D1311yescharacteristic
713C2×C4C24×D1311yescharacteristic
714C8—134no—
715C8—262no—
716C8—262no—
717C8—262no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—522no—
731C22—522no—
732C22—522no—
733C22—1044no—
734C22#1171952712yes—
735C22#1171952912yes—
736C22#1171954012yes—
737C22C23×C22⋊D1311yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—522no—
746C4—522no—
747C4—522no—
748C4#1171952912yes—
749C4C2×#41×D1311yescharacteristic
750C4C2×#8825711yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—1042no—
755C2#1312733014yesdirect product factor
756C2C2×#1171952911yescharacteristic
757C2C2×#1171952711yescharacteristic
758C2C2×#1171954011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#553C2
socleC23×C13C22×D4
hypercenterC2×#553D13
hypocenterC13C2×#3347
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11719268C2semidirect
2. #13127330C2direct (N × H)
3. C2×#11718726C2semidirect
4. C2×#11718664C2semidirect
5. C2×#11718696C2semidirect
6. C2×#11718696C2semidirect
7. C2×#11718628C2semidirect
8. C2×#11718727C2semidirect
9. C2×#11718668C2semidirect
10. C2×#11718700C2semidirect
11. C2×#11718699C2semidirect
12. C2×#11718675C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718625C2semidirect
15. C2×#11718659C2semidirect
16. C2×C13×#553C2semidirect
18. C13×#553C22semidirect
39. #11719268C22semidirect
50. #11718727C22semidirect
51. #11718726C22semidirect
52. #11718700C22semidirect
53. #11718699C22semidirect
54. #11718696C22semidirect
55. #11718696C22semidirect
56. #11718675C22semidirect
57. #11718672C22semidirect
58. #11718668C22semidirect
59. #11718664C22semidirect
60. #11718659C22semidirect
61. #11718628C22semidirect
65. #11718625C22semidirect
274. C2×#553D13semidirect
361. #553C2×D13semidirect
553. C2×C13#3347semidirect
651. C13C2×#3347semidirect
755. C2#13127330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192682
#131273302
C2×#117187262
C2×#117186642
C2×#117186962
C2×#117186282
C2×#117187272
C2×#117186682
C2×#117187002
C2×#117186992
C2×#117186752
C2×#117186722
C2×#117186252
C2×#117186592
C2×C13×#5532
C2×#334713