Finite Group Databasebeta

← C2×#13119419 #16032056

Subgroups — C2×#13119419 #16032056

Order 3328.

2726 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88130C211yesmaximal, characteristic, complemented
2C22×#88133C211yesmaximal, characteristic, complemented
3#13119419C2116yesmaximal, direct product factor
4C2×#11718336C211yesmaximal, characteristic, complemented
5C2×#11718613C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718618C211yesmaximal, characteristic
9C2×#11718618C211yesmaximal, characteristic
10C2×#11718618C211yesmaximal, characteristic
11C2×#11718308C211yesmaximal, characteristic, complemented
12C2×#11718331C211yesmaximal, characteristic, complemented
13C2×#11718637C211yesmaximal, characteristic, complemented
14C2×C4×#6101C211yesmaximal, characteristic, complemented
15C2×#11718310C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88133—28no—
47C2×#88133C2218yescomplemented
48C2×#88130—28no—
49C2×#88130C2218yescomplemented
50C13×#388C2218yescomplemented
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718655C2218yescomplemented
58#11718637C2218yescomplemented
59#11718618C2218yes—
60#11718618C2218yes—
61#11718618C2218yes—
62#11718613C2218yescomplemented
63#11718609C2218yescomplemented
64C4×#6101C2218yescomplemented
65#11718336C2218yescomplemented
66#11718331C2218yescomplemented
67#11718310C2218yescomplemented
68#11718308C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C22×C22⋊D13—24no—
78C22×C22⋊D13—24no—
79C22×C22⋊D13—24no—
80C22×C22⋊D13C2314yes—
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C2×C13×C4⋊C4—42no—
89C2×C13×C4⋊C4C2314yes—
90C2×C13×C22⋊C4—24no—
91C2×C13×C22⋊C4—24no—
92C2×C13×C22⋊C4—42no—
93C2×C13×C22⋊C4C2314yes—
94C2×C13×C22⋊C4C2314yes—
95C2×C13×C22⋊C4C2314yes—
96C2×C42×C13—24no—
97C2×C42×C13C2314yes—
98C2×C22⋊Dic13—24no—
99C2×C22⋊Dic13—24no—
100C2×C22⋊Dic13—42no—
101C2×C22⋊Dic13C2314yes—
102C2×C22⋊Dic13C2314yes—
103C2×C22⋊Dic13C2314yes—
104C2×#6103—24no—
105C2×#6103—24no—
106C2×#6103—24no—
107C2×#6103—24no—
108C2×#6103—42no—
109C2×#6103—42no—
110C2×#6103C2314yes—
111C2×#6103C2314yes—
112C2×#6103C2314yes—
113C2×#6103C2314yes—
114C2×#6103C2314yes—
115C2×#6103C2314yes—
116C2×C4⋊Dic13—24no—
117C2×C4⋊Dic13—42no—
118C2×C4⋊Dic13C2314yes—
119C2×C4⋊Dic13C2314yes—
120C2×#6101—24no—
121C2×#6101—24no—
122C2×#6101—24no—
123C2×#6101—24no—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101D418yescomplemented
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×C4×Dic13—24no—
137C2×C4×Dic13—24no—
138C2×C4×Dic13—24no—
139C2×C4×Dic13—24no—
140C2×C4×Dic13C2314yes—
141C2×C4×Dic13C2314yes—
142C2×C4×Dic13C2314yes—
143C2×C4×Dic13C2314yes—
144#88133—232no—
145#88130—232no—
146C13×#95C2314yes—
147C13×#95C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2512—131nomaximal, Sylow
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13C2412yes—
161C24×C13C2411yescharacteristic
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13—22no—
167C23×D13—22no—
168C23×D13—22no—
169C23×D13C2412yes—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13C2×D414yes—
187C22×C4×C13#4114yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C2×C22⋊D13—28no—
195C2×C22⋊D13—28no—
196C2×C22⋊D13—28no—
197C2×C22⋊D13—416no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13C2×D414yes—
215C22×Dic13C2×D414yes—
216C22×Dic13#4114yes—
217C22×Dic13#4114yes—
218C22×Dic13#4114yes—
219C22×Dic13C2412yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C22×Dic13C2412yes—
223C22×Dic13C2412yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C13×C4⋊C4—44no—
227C13×C22⋊C4—28no—
228C13×C22⋊C4—28no—
229C13×C22⋊C4—44no—
230C42×C13—28no—
231C22⋊Dic13—28no—
232C22⋊Dic13—28no—
233C22⋊Dic13—44no—
234#6103—28no—
235#6103—28no—
236#6103—28no—
237#6103—28no—
238#6103—44no—
239#6103—44no—
240C4⋊Dic13—28no—
241C4⋊Dic13—44no—
242#6101—28no—
243#6101—28no—
244#6101—28no—
245#6101—28no—
246#6101—28no—
247#6101—28no—
248#6101—28no—
249#6101C2×D4116yescomplemented
250C4×Dic13—28no—
251C4×Dic13—28no—
252C4×Dic13—28no—
253C4×Dic13—28no—
254C22×#126—131no—
255C22×#126—131no—
256#2512—1316no—
257C2×#397—131no—
258C2×#397—131no—
259C2×#396—131no—
260C2×#396—131no—
261C2×#390—131no—
262C2×#390—131no—
263C2×#390—131no—
264C2×#389—131no—
265C2×#388—131no—
266C2×#388D1311yescharacteristic, complemented
267C2×#384—131no—
268C2×C4×C4⋊C4—131no—
269C2×C4×C4⋊C4—131no—
270C23×C13—22no—
271C23×C13—22no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—44no—
278C23×C13—44no—
279C23×C13—44no—
280C23×C13—44no—
281C23×C13—44no—
282C23×C13—44no—
283C23×C13—44no—
284C23×C13C22×D412yes—
285C23×C13C2×#4112yes—
286C23×C13C2×#4112yes—
287C23×C13C2×#4112yes—
288C23×C13C2×#4112yes—
289C23×C13H(5,𝔽2)12yes—
290C23×C132−1+412yes—
291C23×C13C2511yescharacteristic
292C22×D13—22no—
293C22×D13—22no—
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—44no—
300C22×D13—44no—
301C22×D13—44no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C2×C4×C13—28no—
307C2×C4×C13—28no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
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—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—44no—
325C2×C4×C13—44no—
326C2×C4×C13—44no—
327C2×C4×C13—44no—
328C2×C4×C13C22×D414yes—
329C2×C4×C13C2×#4114yes—
330C22⋊D13—416no—
331C2×Dic13—28no—
332C2×Dic13—28no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—44no—
350C2×Dic13—44no—
351C2×Dic13—44no—
352C2×Dic13—44no—
353C2×Dic13#126116yescomplemented
354C2×Dic13C22×D414yes—
355C2×Dic13C22×D414yes—
356C2×Dic13C2×#4114yes—
357C2×Dic13C2×#4114yes—
358C2×Dic13C2×#4114yes—
359C23×D4—131no—
360C2×#126—138no—
361C2×#126—138no—
362C2×#126—268no—
363C2×#126—268no—
364C22×C4⋊C4—131no—
365C22×C4⋊C4—131no—
366C22×C4⋊C4—131no—
367C22×C4⋊C4—131no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—131no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4C2×D1311yescharacteristic
375C22×C22⋊C4—131no—
376C22×C22⋊C4—131no—
377C22×C22⋊C4—131no—
378C22×C22⋊C4—131no—
379C22×C22⋊C4—131no—
380C22×C22⋊C4—131no—
381C22×C22⋊C4—131no—
382C22×C22⋊C4—131no—
383C22×C22⋊C4—131no—
384C22×C22⋊C4C2×D1311yescharacteristic
385C22×C22⋊C4C2×D1311yescharacteristic
386C22×C22⋊C4C2×D1311yescharacteristic
387C22×C42—131no—
388C22×C42—131no—
389C22×C42—131no—
390C22×C42—131no—
391C22×C42C2×D1311yescharacteristic
392#397—138no—
393#397—138no—
394#396—138no—
395#396—138no—
396#390—138no—
397#390—138no—
398#390—138no—
399#389—138no—
400#388—138no—
401#388C2×D1318yescomplemented
402#384—138no—
403C4×C4⋊C4—138no—
404C4×C4⋊C4—138no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95C2×D1311yescharacteristic
410C2×#95C2×D1311yescharacteristic
411C22×C13—42no—
412C22×C13—42no—
413C22×C13—42no—
414C22×C13—42no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—88no—
419C22×C13C2×#12614yes—
420C22×C13#53214yes—
421C22×C13#54214yes—
422C22×C13#54714yes—
423C22×C13#55014yes—
424C22×C13#55314yes—
425C22×C13#55614yes—
426C22×C13C23×D411yescharacteristic
427C22×C13C22×#4111yescharacteristic
428C22×C13C22×#4111yescharacteristic
429C22×C13C22×#4111yescharacteristic
430C22×C13C22×#4111yescharacteristic
431C22×C13C2×H(5,𝔽2)11yescharacteristic
432C22×C13C2×2−1+411yescharacteristic
433C2×D13—42no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—88no—
441C4×C13—24no—
442C4×C13—24no—
443C4×C13—42no—
444C4×C13—42no—
445C4×C13—42no—
446C4×C13—42no—
447Dic13—24no—
448Dic13—24no—
449Dic13—42no—
450Dic13—42no—
451Dic13—42no—
452Dic13—42no—
453Dic13C2×#12618yescomplemented
454C25—131no—
455C25C22×D1311yescharacteristic
456C22×D4—134no—
457C22×D4—264no—
458C22×D4—264no—
459C22×D4—264no—
460C23×C4—131no—
461C23×C4—131no—
462C23×C4—131no—
463C23×C4—131no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4C22×D1311yescharacteristic
468C23×C4C22×D1311yescharacteristic
469C23×C4C22×D1311yescharacteristic
470C23×C4C22×D1311yescharacteristic
471C23×C4C22×D1311yescharacteristic
472C23×C4C22×D1311yescharacteristic
473#126—2632no—
474#126—2632no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—138no—
477C2×C4⋊C4—134no—
478C2×C4⋊C4—134no—
479C2×C4⋊C4—134no—
480C2×C4⋊C4—134no—
481C2×C4⋊C4—134no—
482C2×C4⋊C4—134no—
483C2×C4⋊C4—134no—
484C2×C4⋊C4—134no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—264no—
489C2×C4⋊C4—264no—
490C2×C4⋊C4—264no—
491C2×C4⋊C4—264no—
492C2×C4⋊C4—264no—
493C2×C4⋊C4—264no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4—522no—
496C2×C4⋊C4C22×D1314yes—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—134no—
501C2×C22⋊C4—134no—
502C2×C22⋊C4—134no—
503C2×C22⋊C4—134no—
504C2×C22⋊C4—134no—
505C2×C22⋊C4—134no—
506C2×C22⋊C4—134no—
507C2×C22⋊C4—134no—
508C2×C22⋊C4—134no—
509C2×C22⋊C4—264no—
510C2×C22⋊C4—264no—
511C2×C22⋊C4—264no—
512C2×C22⋊C4—264no—
513C2×C22⋊C4—264no—
514C2×C22⋊C4—264no—
515C2×C22⋊C4—522no—
516C2×C22⋊C4—522no—
517C2×C22⋊C4—522no—
518C2×C22⋊C4C22×D1314yes—
519C2×C22⋊C4C22×D1314yes—
520C2×C22⋊C4C22×D1314yes—
521C2×C42—24no—
522C2×C42—134no—
523C2×C42—134no—
524C2×C42—134no—
525C2×C42—134no—
526C2×C42—264no—
527C2×C42—264no—
528C2×C42—264no—
529C2×C42—264no—
530C2×C42C22×D1314yes—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95C22×D1314yes—
536#95C22×D1314yes—
537C2×C13—82no—
538C2×C13#251218yescomplemented
539C2×C13C22×#12611yescharacteristic
540C2×C13C2×#53211yescharacteristic
541C2×C13C2×#54211yescharacteristic
542C2×C13C2×#54711yescharacteristic
543C2×C13C2×#55011yescharacteristic
544C2×C13C2×#55311yescharacteristic
545C2×C13C2×#55611yescharacteristic
546D13—82no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—132no—
555C24—262no—
556C24—262no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24C23×D1312yes—
563C24C23×D1311yescharacteristic
564C2×D4—268no—
565C2×D4—268no—
566C2×D4—268no—
567C2×D4—5216no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—134no—
585C22×C4—134no—
586C22×C4—134no—
587C22×C4—132no—
588C22×C4—134no—
589C22×C4—134no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4#612714yes—
613C22×C4D4×D1314yes—
614C22×C4C23×D1312yes—
615C22×C4C23×D1312yes—
616C22×C4C23×D1312yes—
617C22×C4C23×D1312yes—
618C22×C4C23×D1312yes—
619C22×C4C23×D1312yes—
620C4⋊C4—44no—
621C4⋊C4—1316no—
622C4⋊C4—268no—
623C4⋊C4—268no—
624C4⋊C4—268no—
625C4⋊C4—268no—
626C4⋊C4—268no—
627C4⋊C4—268no—
628C4⋊C4—268no—
629C4⋊C4—268no—
630C4⋊C4—524no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—44no—
634C22⋊C4—268no—
635C22⋊C4—268no—
636C22⋊C4—268no—
637C22⋊C4—268no—
638C22⋊C4—268no—
639C22⋊C4—268no—
640C22⋊C4—524no—
641C22⋊C4—524no—
642C22⋊C4—524no—
643C42—28no—
644C42—268no—
645C42—268no—
646C42—268no—
647C42—268no—
648C13C2×#251211yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—262no—
664C23—262no—
665C23—262no—
666C23—262no—
667C23—262no—
668C23—262no—
669C23—262no—
670C23—524no—
671C23—524no—
672C23—524no—
673C23—524no—
674C23—524no—
675C23—524no—
676C23—524no—
677C23C2×#612712yes—
678C23C2×D4×D1312yes—
679C23#8825112yes—
680C23#41×D1312yes—
681C23#41×D1312yes—
682C23#41×D1312yes—
683C23#8825712yes—
684C23C24×D1311yescharacteristic
685D4—5216no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—134no—
709C2×C4—134no—
710C2×C4—134no—
711C2×C4—1316no—
712C2×C4—134no—
713C2×C4—134no—
714C2×C4—268no—
715C2×C4—268no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—524no—
733C2×C4—524no—
734C2×C4—524no—
735C2×C4—524no—
736C2×C4C2×#612714yes—
737C2×C4C2×D4×D1314yes—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—522no—
747C22—522no—
748C22—522no—
749C22—522no—
750C22—522no—
751C22—522no—
752C22—522no—
753C22—1048no—
754C22#1171923814yes—
755C22#1171924514yes—
756C22#1171925314yes—
757C22#1171930414yes—
758C22#1171936014yes—
759C22#1171937414yes—
760C22D13×#12614yes—
761C22C22×#612711yescharacteristic
762C22C22×D4×D1311yescharacteristic
763C22C2×#8825111yescharacteristic
764C22C2×#41×D1311yescharacteristic
765C22C2×#41×D1311yescharacteristic
766C22C2×#41×D1311yescharacteristic
767C22C2×#8825711yescharacteristic
768C4—24no—
769C4—24no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—138no—
775C4—264no—
776C4—264no—
777C4—522no—
778C4—522no—
779C4—522no—
780C4—522no—
781C2—82no—
782C2—1042no—
783C2#1311941918yesdirect product factor
784C2C2×D13×#12611yescharacteristic
785C2C2×#1171925311yescharacteristic
786C2C2×#1171937411yescharacteristic
787C2C2×#1171936011yescharacteristic
788C2C2×#1171930411yescharacteristic
789C2C2×#1171924511yescharacteristic
790C2C2×#1171923811yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#388D13
hypocenterC13C2×#2512
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#88130C2semidirect
2. C22×#88133C2semidirect
3. #13119419C2direct (N × H)
4. C2×#11718336C2semidirect
5. C2×#11718613C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718655C2semidirect
11. C2×#11718308C2semidirect
12. C2×#11718331C2semidirect
13. C2×#11718637C2semidirect
14. C2×C4×#6101C2semidirect
15. C2×#11718310C2semidirect
16. C2×C13×#388C2semidirect
47. C2×#88133C22semidirect
49. C2×#88130C22semidirect
50. C13×#388C22semidirect
57. #11718655C22semidirect
58. #11718637C22semidirect
62. #11718613C22semidirect
63. #11718609C22semidirect
64. C4×#6101C22semidirect
65. #11718336C22semidirect
66. #11718331C22semidirect
67. #11718310C22semidirect
68. #11718308C22semidirect
127. C2×#6101D4semidirect
249. #6101C2×D4semidirect
266. C2×#388D13semidirect
353. C2×Dic13#126semidirect
401. #388C2×D13semidirect
453. Dic13C2×#126semidirect
538. C2×C13#2512semidirect
648. C13C2×#2512semidirect
783. C2#13119419direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881302
C22×#881332
#131194192
C2×#117183362
C2×#117186132
C2×#117186092
C2×#117186552
C2×#117186182
C2×#117183082
C2×#117183312
C2×#117186372
C2×C4×#61012
C2×#117183102
C2×C13×#3882
C2×#251213