Finite Group Databasebeta

← C2×#13127276 #16741450

Subgroups — C2×#13127276 #16741450

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719260C211yesmaximal, characteristic
2#13127276C2116yesmaximal, direct product factor
3C2×#11718726C211yesmaximal, characteristic, complemented
4C2×#11718705C211yesmaximal, characteristic, complemented
5C2×#11718664C211yesmaximal, characteristic, complemented
6C2×#11718704C211yesmaximal, characteristic, complemented
7C2×#11718628C211yesmaximal, characteristic, complemented
8C2×#11718682C211yesmaximal, characteristic, complemented
9C2×#11718727C211yesmaximal, characteristic, complemented
10C2×#11718710C211yesmaximal, characteristic, complemented
11C2×#11718709C211yesmaximal, characteristic, complemented
12C2×#11718687C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718656C211yesmaximal, characteristic, complemented
15C22×#88047C211yesmaximal, characteristic, complemented
16C2×C13×#552C211yesmaximal, characteristic, complemented
17C22×#6129—21no—
18C13×#552—24no—
19C13×#552C2218yescomplemented
20C2×C13×#126—21no—
21C2×C13×#125—21no—
22C2×C13×#125C2211yescharacteristic
23C2×C13×#123—21no—
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117—21no—
29C2×C13×#117C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31C22×#6106C2211yescharacteristic
32C2×#88184C2211yescharacteristic
33C2×#88184C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719260—24no—
39#11719260C2218yes—
40C2×#88151—21no—
41C2×#88140—21no—
42C2×#88140—21no—
43C2×C4×D52C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×#88075C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718727C2218yescomplemented
51#11718726C2218yescomplemented
52#11718710C2218yescomplemented
53#11718709C2218yescomplemented
54#11718705C2218yescomplemented
55#11718704C2218yescomplemented
56#11718687C2218yescomplemented
57#11718682C2218yescomplemented
58#11718672C2218yescomplemented
59#11718664C2218yescomplemented
60#11718656C2218yescomplemented
61#11718628C2218yescomplemented
62C2×#88049C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88047C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2218yescomplemented
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13D411yescharacteristic
79C23×C4×C13—21no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—21no—
83C22×C22⋊D13—21no—
84C23×Dic13—21no—
85C23×Dic13—21no—
86C2×#6129—28no—
87C2×#6129—48no—
88C22×D52C2311yescharacteristic
89C22×C4×D13—21no—
90C22×Dic26—21no—
91C13×#126—28no—
92C13×#125—28no—
93C13×#125—22no—
94C13×#125C2314yes—
95C13×#123—28no—
96C13×C22⋊Q8—22no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8C2314yes—
99C13×C22⋊Q8C2314yes—
100C4×Q8×C13—22no—
101C4×Q8×C13C2314yes—
102C4×D4×C13D414yes—
103C4×D4×C13C2314yes—
104C13×#117—22no—
105C13×#117—28no—
106C13×#117C2314yes—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4D411yescharacteristic
115C2×C13×C4⋊C4C2311yescharacteristic
116C2×C13×C4⋊C4C2311yescharacteristic
117C2×C13×C4⋊C4C2314yes—
118C2×C13×C4⋊C4C2311yescharacteristic
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4D411yescharacteristic
123C2×C13×C22⋊C4D411yescharacteristic
124C2×C42×C13—21no—
125C2×C42×C13—21no—
126C2×C42×C13C2311yescharacteristic
127C2×#6106—24no—
128C2×#6106C2314yes—
129#88184—22no—
130#88184—22no—
131#88184C2314yes—
132#88184C2314yes—
133C2×#6103—21no—
134C2×#6103—21no—
135C2×#6103—21no—
136C2×C4⋊Dic13—21no—
137C2×C4⋊Dic13—21no—
138C2×C4⋊Dic13—21no—
139C2×C4⋊Dic13—22no—
140C2×C4⋊Dic13—22no—
141C2×C4⋊Dic13C2314yes—
142C2×C4⋊Dic13C2311yescharacteristic
143C2×C4⋊Dic13C2311yescharacteristic
144C2×C4⋊Dic13C2311yescharacteristic
145C2×C4⋊Dic13C2314yes—
146C2×#6099—24no—
147C2×#6099C2314yes—
148C22×#1055—24no—
149C22×#1055C2314yes—
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153C22×#1055C2311yescharacteristic
154#88151—28no—
155#88140—28no—
156#88140—28no—
157C4×D52—22no—
158C4×D52C2314yes—
159#88123—22no—
160#88123C2314yes—
161#88075C2314yes—
162#88075C2314yes—
163#88075C2314yes—
164C22⋊#1055C2314yes—
165C22⋊#1055C2314yes—
166#88049C2314yes—
167#88049C2314yes—
168#88049C2314yes—
169#88048C2314yes—
170#88048C2314yes—
171#88048C2314yes—
172#88047C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179#88043C2314yes—
180C2×#3343—131nomaximal, Sylow
181C24×C13C2×D411yescharacteristic
182C24×C13C2×D411yescharacteristic
183C23×D13—21no—
184C2×Q8×C13—21no—
185C2×Q8×C13—22no—
186C2×Q8×C13—22no—
187C2×Q8×C13C2412yes—
188C2×D4×C13—24no—
189C2×D4×C13C2×D414yes—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—24no—
199C22×C4×C13—44no—
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2411yescharacteristic
209C2×C22⋊D13—24no—
210C2×C22⋊D13—24no—
211C2×C22⋊D13—44no—
212C2×C22⋊D13—44no—
213C22×Dic13—24no—
214C22×Dic13—24no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—44no—
219C22×Dic13—44no—
220#6129—432no—
221C2×D52—22no—
222C2×D52—22no—
223C2×D52—21no—
224C2×D52C2412yes—
225C2×C4×D13—24no—
226C2×C4×D13—44no—
227C2×Dic26—24no—
228C2×Dic26—44no—
229C13×C4⋊C4—21no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—24no—
235C13×C4⋊C4—24no—
236C13×C4⋊C4—24no—
237C13×C4⋊C4—21no—
238C13×C4⋊C4C2×D414yes—
239C13×C4⋊C4C2412yes—
240C13×C4⋊C4C2412yes—
241C13×C4⋊C4C2412yes—
242C13×C22⋊C4—24no—
243C13×C22⋊C4—24no—
244C13×C22⋊C4—24no—
245C13×C22⋊C4C2×D414yes—
246C13×C22⋊C4C2×D414yes—
247C42×C13—24no—
248C42×C13—24no—
249C42×C13C2×D412yes—
250C42×C13C2412yes—
251#6106—28no—
252#6103—24no—
253#6103—24no—
254#6103—24no—
255C4⋊Dic13—21no—
256C4⋊Dic13—21no—
257C4⋊Dic13—24no—
258C4⋊Dic13—21no—
259C4⋊Dic13—24no—
260C4⋊Dic13—24no—
261C4⋊Dic13C2412yes—
262C4⋊Dic13C2412yes—
263C4⋊Dic13C2412yes—
264#6099—28no—
265C2×#1055—22no—
266C2×#1055—22no—
267C2×#1055—22no—
268C2×#1055—28no—
269C2×#1055#4114yescomplemented
270C2×#1055C2412yes—
271C2×#1055C2412yes—
272C2×#1055C2412yes—
273C2×#1055C2412yes—
274C2×#552D1311yescharacteristic, complemented
275C2×#547—131no—
276#3343—1316no—
277C2×#501—131no—
278C2×#484—131no—
279C2×#482—131no—
280C2×#483—131no—
281C2×#480—131no—
282C2×#477—131no—
283C2×#478—131no—
284C2×#468—131no—
285C2×#465—131no—
286C2×#440—131no—
287C2×#435—131no—
288C2×#428—131no—
289C22×#107—131no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13AGL(1,ℤ/8)14yes—
296C23×C13C22×D412yes—
297C23×C13C22×D412yes—
298C23×C13C22×D411yescharacteristic
299C22×D13—22no—
300C22×D13—42no—
301C22×D13—42no—
302C22×D13—42no—
303Q8×C13—22no—
304Q8×C13—22no—
305Q8×C13—42no—
306D4×C13—28no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—24no—
312C2×C4×C13—24no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—42no—
322C2×C4×C13—48no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13—42no—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D412yes—
328C2×C4×C13C22×D412yes—
329C2×C4×C13C22×D412yes—
330C2×C4×C13C22×D411yescharacteristic
331C2×C4×C13C2×#4112yes—
332C2×C4×C132−1+412yes—
333C2×C4×C13C2511yescharacteristic
334C22⋊D13—48no—
335C22⋊D13—48no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—48no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—48no—
344D52—22no—
345D52—22no—
346D52—42no—
347C4×D13—48no—
348Dic26—48no—
349#1055—22no—
350#1055—22no—
351#1055—22no—
352#1055C2×#4114yescomplemented
353C22×#41—261no—
354C22×SD16—131no—
355C22×M16—131no—
356C23×C8—131no—
357#552—24no—
358#552C2×D1318yescomplemented
359#547—138no—
360#547—264no—
361C2×C4⋊Q8—131no—
362C2×#126—21no—
363C2×#125—21no—
364C2×#125C2×D1311yescharacteristic
365C2×#123—21no—
366C2×#123—261no—
367C2×#123—261no—
368C2×C22⋊Q8—261no—
369C2×C22⋊Q8C2×D1311yescharacteristic
370C2×C22⋊Q8C2×D1311yescharacteristic
371C2×#121—131no—
372C2×#121—131no—
373C2×C4×Q8C2×D1311yescharacteristic
374C2×C4×D4—131no—
375C2×C4×D4C2×D1311yescharacteristic
376C2×#117—21no—
377C2×#117C2×D1311yescharacteristic
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4C2×D1311yescharacteristic
381#501—138no—
382#484—138no—
383#483—138no—
384#482—138no—
385#480—138no—
386#478—138no—
387#477—138no—
388#468—138no—
389#465—138no—
390#440—138no—
391#435—138no—
392#428—138no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#107—131no—
396C2×#107—131no—
397C2×#107—138no—
398C2×#107—131no—
399C2×#107—131no—
400C2×#106—131no—
401C2×#106—131no—
402C2×#106—131no—
403C2×C4⋊C8—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#102—131no—
408C2×#102—131no—
409C2×#102—131no—
410C2×C22⋊C8—131no—
411C2×C22⋊C8—131no—
412C2×#97—131no—
413C22×C13—28no—
414C22×C13—22no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—22no—
418C22×C13—22no—
419C22×C13—44no—
420C22×C13#54712yes—
421C22×C13C2×AGL(1,ℤ/8)14yes—
422C22×C13C2×AGL(1,ℤ/8)12yes—
423C22×C13#57812yes—
424C22×C13C23×D411yescharacteristic
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C2×D13—84no—
429C4×C13—22no—
430C4×C13—22no—
431C4×C13—22no—
432C4×C13—22no—
433C4×C13—42no—
434C4×C13—42no—
435C4×C13—42no—
436C4×C13—42no—
437C4×C13#54712yes—
438C4×C13C22×#4111yescharacteristic
439C4×C13C2×2−1+411yescharacteristic
440Dic13—42no—
441Dic13—42no—
442Dic13—42no—
443C2×#41—268no—
444C2×#41—528no—
445C22×Q8—261no—
446C22×Q8C22×D1311yescharacteristic
447C22×D4—131no—
448C22×D4—261no—
449C22×D4—261no—
450C22×D4C22⋊D1311yescharacteristic
451C23×C4—21no—
452C23×C4—261no—
453C23×C4—261no—
454C23×C4—261no—
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1311yescharacteristic
457C2×SD16—134no—
458C2×SD16—264no—
459C2×M16—134no—
460C2×M16—264no—
461C22×C8—131no—
462C22×C8—131no—
463C22×C8—134no—
464C22×C8—131no—
465C22×C8—131no—
466C22×C8—264no—
467C4⋊Q8—134no—
468C4⋊Q8—262no—
469#126—28no—
470#125—28no—
471#125—22no—
472#125C22×D1314yes—
473#123—28no—
474#123—268no—
475#123—268no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—268no—
479C22⋊Q8C22×D1314yes—
480C22⋊Q8C22×D1314yes—
481#121—134no—
482#121—134no—
483#121—262no—
484#121—262no—
485C4×Q8—22no—
486C4×Q8C22×D1314yes—
487C4×D4—134no—
488C4×D4—262no—
489C4×D4C22⋊D1314yes—
490C4×D4C22×D1314yes—
491#117—22no—
492#117—28no—
493#117C22×D1314yes—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—134no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—262no—
509C2×C4⋊C4—262no—
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—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4C22⋊D1311yescharacteristic
523C2×C22⋊C4C22⋊D1311yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42C22×D1311yescharacteristic
527#107—134no—
528#107—134no—
529#107—134no—
530#107—134no—
531#107—134no—
532#107—134no—
533#106—134no—
534#106—134no—
535#106—134no—
536C4⋊C8—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#102—134no—
541#102—134no—
542#102—134no—
543C22⋊C8—134no—
544C22⋊C8—134no—
545#97—134no—
546C2×C13—24no—
547C2×C13—42no—
548C2×C13#334314yescomplemented
549C2×C13C2×#54711yescharacteristic
550C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
551C2×C13C2×#57811yescharacteristic
552D13—82no—
553C24—261no—
554C24C2×C22⋊D1311yescharacteristic
555C24C2×C22⋊D1311yescharacteristic
556#41—5232no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—264no—
561C2×Q8—524no—
562C2×Q8C23×D1312yes—
563C2×D4—24no—
564C2×D4—132no—
565C2×D4—264no—
566C2×D4—264no—
567C2×D4—262no—
568C2×D4—262no—
569C2×D4—261no—
570C2×D4—524no—
571C2×D4—524no—
572C2×D4C2×C22⋊D1314yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—44no—
583C22×C4—264no—
584C22×C4—264no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—264no—
589C22×C4—524no—
590C22×C4—524no—
591C22×C4—524no—
592C22×C4C2×C22⋊D1312yes—
593C22×C4C2×C22⋊D1312yes—
594C22×C4C2×C22⋊D1311yescharacteristic
595C22×C4C2×C22⋊D1311yescharacteristic
596C22×C4C2×C22⋊D1311yescharacteristic
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C23×D1312yes—
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601SD16—268no—
602M16—268no—
603C2×C8—134no—
604C2×C8—132no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—132no—
608C2×C8—268no—
609C2×C8—262no—
610C2×C8—262no—
611C2×C8—262no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—132no—
622C4⋊C4—132no—
623C4⋊C4—132no—
624C4⋊C4—261no—
625C4⋊C4—261no—
626C4⋊C4—261no—
627C4⋊C4—264no—
628C4⋊C4—264no—
629C4⋊C4—264no—
630C4⋊C4C2×C22⋊D1314yes—
631C4⋊C4C23×D1312yes—
632C4⋊C4C23×D1312yes—
633C4⋊C4C23×D1312yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—264no—
638C22⋊C4—264no—
639C22⋊C4—264no—
640C22⋊C4C2×C22⋊D1314yes—
641C22⋊C4C2×C22⋊D1314yes—
642C42—24no—
643C42—24no—
644C42C2×C22⋊D1312yes—
645C42C23×D1312yes—
646C13C2×#334311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—262no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23#8820314yes—
657C23C22×C22⋊D1312yes—
658C23C22×C22⋊D1312yes—
659C23C22×C22⋊D1311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—528no—
664D4—28no—
665D4—262no—
666D4—262no—
667D4—528no—
668D4—528no—
669D4—522no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—528no—
693C2×C4—528no—
694C2×C4—522no—
695C2×C4—522no—
696C2×C4—522no—
697C2×C4—528no—
698C2×C4#41×D1312yes—
699C2×C4#8825712yes—
700C2×C4C22×C22⋊D1312yes—
701C2×C4C22×C22⋊D1312yes—
702C2×C4C22×C22⋊D1312yes—
703C2×C4C22×C22⋊D1312yes—
704C2×C4C22×C22⋊D1311yescharacteristic
705C2×C4C24×D1311yescharacteristic
706C8—134no—
707C8—262no—
708C8—262no—
709C8—262no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—522no—
718C22—522no—
719C22—522no—
720C22—1044no—
721C22C2×#8820314yes—
722C22C2×#8820312yes—
723C22#1171952912yes—
724C22#1171954312yes—
725C22C23×C22⋊D1311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—522no—
735C4—522no—
736C4—522no—
737C4#1171952912yes—
738C4C2×#41×D1311yescharacteristic
739C4C2×#8825711yescharacteristic
740C2—24no—
741C2—42no—
742C2—1042no—
743C2#1312727614yesdirect product factor
744C2C2×#1171952911yescharacteristic
745C2C22×#8820311yescharacteristic
746C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC2×#11719260C2
hypercenterC2×#552D13
hypocenterC13C2×#3343
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. #13127276C2direct (N × H)
3. C2×#11718726C2semidirect
4. C2×#11718705C2semidirect
5. C2×#11718664C2semidirect
6. C2×#11718704C2semidirect
7. C2×#11718628C2semidirect
8. C2×#11718682C2semidirect
9. C2×#11718727C2semidirect
10. C2×#11718710C2semidirect
11. C2×#11718709C2semidirect
12. C2×#11718687C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718656C2semidirect
15. C22×#88047C2semidirect
16. C2×C13×#552C2semidirect
19. C13×#552C22semidirect
50. #11718727C22semidirect
51. #11718726C22semidirect
52. #11718710C22semidirect
53. #11718709C22semidirect
54. #11718705C22semidirect
55. #11718704C22semidirect
56. #11718687C22semidirect
57. #11718682C22semidirect
58. #11718672C22semidirect
59. #11718664C22semidirect
60. #11718656C22semidirect
61. #11718628C22semidirect
74. C2×#88047C22semidirect
269. C2×#1055#41semidirect
274. C2×#552D13semidirect
352. #1055C2×#41semidirect
358. #552C2×D13semidirect
548. C2×C13#3343semidirect
646. C13C2×#3343semidirect
743. C2#13127276direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192602
#131272762
C2×#117187262
C2×#117187052
C2×#117186642
C2×#117187042
C2×#117186282
C2×#117186822
C2×#117187272
C2×#117187102
C2×#117187092
C2×#117186872
C2×#117186722
C2×#117186562
C22×#880472
C2×C13×#5522
C2×#334313