Finite Group Databasebeta

← C2×D13×#387 #16021234

Subgroups — C2×D13×#387 #16021234

Order 3328.

4286 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, characteristic
2C22×C4⋊C4×D13C211yesmaximal, characteristic
3C22×C42×D13C211yesmaximal, characteristic
4C2×#11718316C211yesmaximal, characteristic, complemented
5C2×#11718642C211yesmaximal, characteristic, complemented
6C2×#11718314C211yesmaximal, characteristic, complemented
7C2×#11718594C211yesmaximal, characteristic, complemented
8C2×#11718315C211yesmaximal, characteristic, complemented
9C2×#11718313C211yesmaximal, characteristic, complemented
10C2×#11718639C211yesmaximal, characteristic, complemented
11D13×#387C2116yesmaximal, direct product factor
12C2×D13×#95C211yesmaximal, characteristic
13C2×D13×#95C211yesmaximal, characteristic
14C2×D13×#95C211yesmaximal, characteristic
15C2×D13×#95C211yesmaximal, characteristic
16C2×C13×#387C211yesmaximal, characteristic, complemented
17C23×C4×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C2×C4⋊C4×D13—28no—
37C2×C4⋊C4×D13C4116yescomplemented
38C2×C4⋊C4×D13C2218yes—
39C2×C4⋊C4×D13C2218yes—
40C2×C42×D13—28no—
41C2×C42×D13C2218yes—
42C13×#387C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718642C2218yescomplemented
60#11718639C2218yescomplemented
61#11718594C2218yescomplemented
62D13×#95C2218yes—
63D13×#95C2218yes—
64D13×#95C2218yes—
65D13×#95C2218yes—
66#11718316C2218yescomplemented
67#11718315C2218yescomplemented
68#11718314C2218yescomplemented
69#11718313C2218yescomplemented
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C22×C4×D13—24no—
86C22×C4×D13—24no—
87C22×C4×D13—24no—
88C22×C4×D13—24no—
89C22×C4×D13—24no—
90C22×C4×D13—24no—
91C22×C4×D13—24no—
92C22×C4×D13—24no—
93C22×C4×D13—24no—
94C22×C4×D13—24no—
95C22×C4×D13—24no—
96C22×C4×D13—24no—
97C22×C4×D13—24no—
98C22×C4×D13—24no—
99C22×C4×D13—24no—
100C22×C4×D13—24no—
101C22×C4×D13C2×C418yes—
102C22×C4×D13C2×C418yes—
103C22×C4×D13C2×C418yes—
104C22×C4×D13D418yes—
105C22×C4×D13Q818yes—
106C22×C4×D13C2314yes—
107C22×C4×D13C2314yes—
108C22×C4×D13C2314yes—
109C22×C4×D13C2314yes—
110C22×C4×D13C2314yes—
111C22×C4×D13C2314yes—
112C22×C4×D13C2314yes—
113C2×C13×C4⋊C4—24no—
114C2×C13×C4⋊C4C2×C418yescomplemented
115C2×C13×C4⋊C4C2314yes—
116C2×C13×C4⋊C4C2314yes—
117C2×C42×C13—24no—
118C2×C42×C13C2314yes—
119C2×C4⋊Dic13—24no—
120C2×C4⋊Dic13C2×C418yescomplemented
121C2×C4⋊Dic13C2314yes—
122C2×C4⋊Dic13C2314yes—
123C2×#6101—24no—
124C2×#6101—24no—
125C2×#6101C2×C418yescomplemented
126C2×#6101C2×C418yescomplemented
127C2×#6101C2314yes—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×C4×Dic13—24no—
132C2×C4×Dic13—24no—
133C2×C4×Dic13—24no—
134C2×C4×Dic13C2314yes—
135C2×C4×Dic13C2314yes—
136C2×C4×Dic13C2314yes—
137C4⋊C4×D13—232no—
138C4⋊C4×D13C2×C4164yescomplemented
139C42×D13—232no—
140C13×#95C2314yes—
141C13×#95C2314yes—
142C13×#95C2314yes—
143C13×#95C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156C22×#387—131nomaximal, Sylow
157C24×C13C2411yescharacteristic
158C23×D13C22×C414yes—
159C23×D13C2×D414yes—
160C23×D13C2×Q814yes—
161C23×D13#4114yes—
162C23×D13#4114yes—
163C23×D13#4114yes—
164C23×D13#4114yes—
165C23×D13C2412yes—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
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×C13C22×C414yes—
183C22×C4×C13C22×C414yes—
184C22×C4×C13C22×C414yes—
185C22×C4×C13C2×D414yes—
186C22×C4×C13C2×Q814yes—
187C22×C4×C13C2412yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
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×Dic13C22×C414yes—
211C22×Dic13C22×C414yes—
212C22×Dic13C22×C414yes—
213C22×Dic13C2×D414yes—
214C22×Dic13C2×Q814yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C2×C4×D13—232no—
223C2×C4×D13—232no—
224C2×C4×D13—232no—
225C2×C4×D13—232no—
226C2×C4×D13—232no—
227C2×C4×D13—28no—
228C2×C4×D13—28no—
229C2×C4×D13—28no—
230C2×C4×D13—28no—
231C2×C4×D13—28no—
232C2×C4×D13—28no—
233C2×C4×D13—28no—
234C2×C4×D13—28no—
235C2×C4×D13—28no—
236C2×C4×D13—28no—
237C2×C4×D13—28no—
238C2×C4×D13—28no—
239C2×C4×D13—28no—
240C2×C4×D13—28no—
241C2×C4×D13—28no—
242C2×C4×D13—28no—
243C2×C4×D13—416no—
244C2×C4×D13—416no—
245C2×C4×D13C22×C4116yes—
246C2×C4×D13C22×C4116yes—
247C2×C4×D13C22×C4116yes—
248C2×C4×D13C2×D4116yes—
249C2×C4×D13C2×Q8116yes—
250C13×C4⋊C4—28no—
251C13×C4⋊C4C22×C4116yescomplemented
252C42×C13—28no—
253C4⋊Dic13—28no—
254C4⋊Dic13C22×C4116yescomplemented
255#6101—28no—
256#6101—28no—
257#6101C22×C4116yescomplemented
258#6101C22×C4116yescomplemented
259C4×Dic13—28no—
260C4×Dic13—28no—
261C4×Dic13—28no—
262C23×C4⋊C4—131no—
263C23×C4⋊C4—131no—
264C23×C42—131no—
265C2×#387—131no—
266C2×#387—1316no—
267C2×#387—131no—
268C2×#387—131no—
269C2×#387—131no—
270C2×#387—131no—
271C2×#387—131no—
272C2×#387—131no—
273C2×#387D1311yescharacteristic, direct product factor
274C22×#95—131no—
275C22×#95—131no—
276C22×#95—131no—
277C22×#95—131no—
278C23×C13C23×C412yes—
279C23×C13C22×D412yes—
280C23×C13C22×Q812yes—
281C23×C13C2×#4112yes—
282C23×C13C2×#4112yes—
283C23×C13C2×#4112yes—
284C23×C13C2×#4112yes—
285C23×C13C2511yescharacteristic
286C22×D13#117116yes—
287C22×D13C4×D4116yes—
288C22×D13C4×Q8116yes—
289C22×D13C22⋊Q8116yes—
290C22×D13#123116yes—
291C22×D13#125116yes—
292C22×D13#126116yes—
293C22×D13C23×C414yes—
294C22×D13C22×D414yes—
295C22×D13C22×Q814yes—
296C22×D13C2×#4114yes—
297C22×D13C2×#4114yes—
298C22×D13C2×#4114yes—
299C22×D13C2×#4114yes—
300C2×C4×C13—28no—
301C2×C4×C13—28no—
302C2×C4×C13—28no—
303C2×C4×C13—28no—
304C2×C4×C13—28no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
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—44no—
322C2×C4×C13—44no—
323C2×C4×C13C23×C414yes—
324C2×C4×C13C23×C414yes—
325C2×C4×C13C23×C414yes—
326C2×C4×C13C22×D414yes—
327C2×C4×C13C22×Q814yes—
328C2×Dic13—28no—
329C2×Dic13—28no—
330C2×Dic13—28no—
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×Dic13C23×C414yes—
352C2×Dic13C23×C414yes—
353C2×Dic13C23×C414yes—
354C2×Dic13C22×D414yes—
355C2×Dic13C22×Q814yes—
356C4×D13—232no—
357C4×D13—232no—
358C4×D13—232no—
359C4×D13—232no—
360C4×D13—232no—
361C4×D13—416no—
362C4×D13—416no—
363C24×C4—131no—
364C24×C4—131no—
365C24×C4—131no—
366C24×C4—131no—
367C24×C4—131no—
368C24×C4—131no—
369C24×C4—131no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—1316no—
374C22×C4⋊C4—138no—
375C22×C4⋊C4—131no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—138no—
379C22×C4⋊C4—268no—
380C22×C4⋊C4C2×D1311yescharacteristic
381C22×C4⋊C4C2×D1311yescharacteristic
382C22×C42—131no—
383C22×C42—131no—
384C22×C42—131no—
385C22×C42—138no—
386C22×C42—268no—
387C22×C42C2×D1311yescharacteristic
388#387—138no—
389#387—138no—
390#387—138no—
391#387—138no—
392#387—138no—
393#387—138no—
394#387—138no—
395#387C2×D1318yesdirect product factor
396C2×#95—131no—
397C2×#95—131no—
398C2×#95—131no—
399C2×#95—131no—
400C2×#95—131no—
401C2×#95—131no—
402C2×#95—131no—
403C2×#95—131no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—138no—
409C2×#95—138no—
410C2×#95—138no—
411C2×#95—138no—
412C2×#95C2×D1311yescharacteristic
413C2×#95C2×D1311yescharacteristic
414C2×#95C2×D1311yescharacteristic
415C2×#95C2×D1311yescharacteristic
416C22×C13C2×#11714yes—
417C22×C13C2×C4×D414yes—
418C22×C13C2×C4×Q814yes—
419C22×C13C2×C22⋊Q814yes—
420C22×C13C2×#12314yes—
421C22×C13C2×#12514yes—
422C22×C13C2×#12614yes—
423C22×C13C24×C411yescharacteristic
424C22×C13C23×D411yescharacteristic
425C22×C13C23×Q811yescharacteristic
426C22×C13C22×#4111yescharacteristic
427C22×C13C22×#4111yescharacteristic
428C22×C13C22×#4111yescharacteristic
429C22×C13C22×#4111yescharacteristic
430C2×D13#387164yesdirect product factor
431C2×D13C2×#11718yes—
432C2×D13C2×C4×D418yes—
433C2×D13C2×C4×Q818yes—
434C2×D13C2×C22⋊Q818yes—
435C2×D13C2×#12318yes—
436C2×D13C2×#12518yes—
437C2×D13C2×#12618yes—
438C4×C13—24no—
439C4×C13—24no—
440C4×C13—24no—
441C4×C13—24no—
442C4×C13—24no—
443C4×C13—42no—
444C4×C13—42no—
445Dic13—24no—
446Dic13—24no—
447Dic13—24no—
448Dic13—24no—
449Dic13—24no—
450Dic13—42no—
451Dic13—42no—
452C25—131no—
453C23×C4—131no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—131no—
457C23×C4—131no—
458C23×C4—138no—
459C23×C4—138no—
460C23×C4—138no—
461C23×C4—138no—
462C23×C4—138no—
463C23×C4—134no—
464C23×C4—134no—
465C23×C4—134no—
466C23×C4—134no—
467C23×C4—134no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—134no—
471C23×C4—134no—
472C23×C4—264no—
473C23×C4—264no—
474C23×C4—264no—
475C23×C4—264no—
476C23×C4—264no—
477C23×C4—264no—
478C23×C4—264no—
479C23×C4—264no—
480C23×C4—264no—
481C23×C4—264no—
482C23×C4—264no—
483C23×C4—264no—
484C23×C4—264no—
485C23×C4—264no—
486C23×C4—264no—
487C23×C4—264no—
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1311yescharacteristic
490C23×C4C22×D1311yescharacteristic
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C23×C4C22×D1311yescharacteristic
495C2×C4⋊C4—24no—
496C2×C4⋊C4—138no—
497C2×C4⋊C4—138no—
498C2×C4⋊C4—138no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—1364no—
503C2×C4⋊C4—134no—
504C2×C4⋊C4—134no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—2632no—
507C2×C4⋊C4—264no—
508C2×C4⋊C4—264no—
509C2×C4⋊C4—264no—
510C2×C4⋊C4C4×D1318yescomplemented
511C2×C4⋊C4C22×D1314yes—
512C2×C4⋊C4C22×D1314yes—
513C2×C42—24no—
514C2×C42—134no—
515C2×C42—134no—
516C2×C42—134no—
517C2×C42—2632no—
518C2×C42—264no—
519C2×C42—264no—
520C2×C42—264no—
521C2×C42C22×D1314yes—
522#95—134no—
523#95—134no—
524#95—134no—
525#95—134no—
526#95—134no—
527#95—134no—
528#95—134no—
529#95—134no—
530#95—134no—
531#95—134no—
532#95—134no—
533#95—134no—
534#95C22×D1314yes—
535#95C22×D1314yes—
536#95C22×D1314yes—
537#95C22×D1314yes—
538C2×C13C2×#38718yescomplemented
539C2×C13C22×#11711yescharacteristic
540C2×C13C22×C4×D411yescharacteristic
541C2×C13C22×C4×Q811yescharacteristic
542C2×C13C22×C22⋊Q811yescharacteristic
543C2×C13C22×#12311yescharacteristic
544C2×C13C22×#12511yescharacteristic
545C2×C13C22×#12611yescharacteristic
546D13C2×#387116yesdirect product factor
547C24—134no—
548C24—134no—
549C24—134no—
550C24—134no—
551C24—134no—
552C24—134no—
553C24—134no—
554C24—132no—
555C24C23×D1311yescharacteristic
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—134no—
573C22×C4—134no—
574C22×C4—134no—
575C22×C4—134no—
576C22×C4—134no—
577C22×C4—132no—
578C22×C4—132no—
579C22×C4—132no—
580C22×C4—132no—
581C22×C4—132no—
582C22×C4—1316no—
583C22×C4—1316no—
584C22×C4—1316no—
585C22×C4—1316no—
586C22×C4—1316no—
587C22×C4—132no—
588C22×C4—132no—
589C22×C4—268no—
590C22×C4—268no—
591C22×C4—268no—
592C22×C4—2632no—
593C22×C4—2632no—
594C22×C4—2632no—
595C22×C4—2632no—
596C22×C4—2632no—
597C22×C4—268no—
598C22×C4—268no—
599C22×C4—268no—
600C22×C4—268no—
601C22×C4—268no—
602C22×C4—268no—
603C22×C4—268no—
604C22×C4—268no—
605C22×C4—268no—
606C22×C4—268no—
607C22×C4—268no—
608C22×C4—268no—
609C22×C4—268no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—5216no—
627C22×C4—5216no—
628C22×C4C2×C4×D1314yes—
629C22×C4C2×C4×D1314yes—
630C22×C4C2×C4×D1314yes—
631C22×C4D4×D1314yes—
632C22×C4Q8×D1314yes—
633C22×C4C23×D1312yes—
634C22×C4C23×D1312yes—
635C22×C4C23×D1312yes—
636C22×C4C23×D1312yes—
637C22×C4C23×D1312yes—
638C22×C4C23×D1312yes—
639C22×C4C23×D1312yes—
640C4⋊C4—28no—
641C4⋊C4—1316no—
642C4⋊C4—1316no—
643C4⋊C4—1316no—
644C4⋊C4—268no—
645C4⋊C4—268no—
646C4⋊C4—268no—
647C4⋊C4C2×C4×D13116yescomplemented
648C42—28no—
649C42—268no—
650C42—268no—
651C42—268no—
652C13C22×#38711yescharacteristic, complemented, Sylow
653C23—1316no—
654C23—1316no—
655C23—1316no—
656C23—1316no—
657C23—1316no—
658C23—134no—
659C23—134no—
660C23—134no—
661C23—134no—
662C23—134no—
663C23—134no—
664C23—134no—
665C23—1316no—
666C23—1316no—
667C23C22×C4×D1312yes—
668C23C2×D4×D1312yes—
669C23C2×Q8×D1312yes—
670C23#41×D1312yes—
671C23#41×D1312yes—
672C23#41×D1312yes—
673C23#41×D1312yes—
674C23C24×D1311yescharacteristic
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
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—44no—
697C2×C4—44no—
698C2×C4—134no—
699C2×C4—134no—
700C2×C4—134no—
701C2×C4—134no—
702C2×C4—134no—
703C2×C4—2632no—
704C2×C4—2632no—
705C2×C4—2632no—
706C2×C4—2632no—
707C2×C4—2632no—
708C2×C4—268no—
709C2×C4—268no—
710C2×C4—268no—
711C2×C4—268no—
712C2×C4—268no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
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—5216no—
730C2×C4—5216no—
731C2×C4—524no—
732C2×C4—524no—
733C2×C4C22×C4×D1314yes—
734C2×C4C22×C4×D1314yes—
735C2×C4C22×C4×D1314yes—
736C2×C4C2×D4×D1314yes—
737C2×C4C2×Q8×D1314yes—
738C22—138no—
739C22—138no—
740C22—1364no—
741C22—138no—
742C22—138no—
743C22—138no—
744C22—138no—
745C22—138no—
746C22D13×#11714yes—
747C22C4×D4×D1314yes—
748C22C4×Q8×D1314yes—
749C22D13×C22⋊Q814yes—
750C22D13×#12314yes—
751C22D13×#12514yes—
752C22D13×#12614yes—
753C22C23×C4×D1311yescharacteristic
754C22C22×D4×D1311yescharacteristic
755C22C22×Q8×D1311yescharacteristic
756C22C2×#41×D1311yescharacteristic
757C22C2×#41×D1311yescharacteristic
758C22C2×#41×D1311yescharacteristic
759C22C2×#41×D1311yescharacteristic
760C4—24no—
761C4—24no—
762C4—24no—
763C4—24no—
764C4—24no—
765C4—42no—
766C4—42no—
767C4—264no—
768C4—264no—
769C4—264no—
770C4—264no—
771C4—264no—
772C4—522no—
773C4—522no—
774C2—1316no—
775C2D13×#38718yesdirect product factor
776C2C2×D13×#11711yescharacteristic
777C2C2×C4×D4×D1311yescharacteristic
778C2C2×C4×Q8×D1311yescharacteristic
779C2C2×D13×C22⋊Q811yescharacteristic
780C2C2×D13×#12311yescharacteristic
781C2C2×D13×#12511yescharacteristic
782C2C2×D13×#12611yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#387C2
socleC24×C13C24
prime radicalC24×D13C23
cosocleC23×C13C25
hypercenterC2×#387D13
hypocenterC13C22×#387
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
4. C2×#11718316C2semidirect
5. C2×#11718642C2semidirect
6. C2×#11718314C2semidirect
7. C2×#11718594C2semidirect
8. C2×#11718315C2semidirect
9. C2×#11718313C2semidirect
10. C2×#11718639C2semidirect
11. D13×#387C2direct (N × H)
16. C2×C13×#387C2semidirect
37. C2×C4⋊C4×D13C4semidirect
42. C13×#387C22semidirect
59. #11718642C22semidirect
60. #11718639C22semidirect
61. #11718594C22semidirect
66. #11718316C22semidirect
67. #11718315C22semidirect
68. #11718314C22semidirect
69. #11718313C22semidirect
114. C2×C13×C4⋊C4C2×C4semidirect
120. C2×C4⋊Dic13C2×C4semidirect
125. C2×#6101C2×C4semidirect
126. C2×#6101C2×C4semidirect
138. C4⋊C4×D13C2×C4semidirect
251. C13×C4⋊C4C22×C4semidirect
254. C4⋊Dic13C22×C4semidirect
257. #6101C22×C4semidirect
258. #6101C22×C4semidirect
273. C2×#387D13direct (N × H)
395. #387C2×D13direct (N × H)
430. C2×D13#387direct (N × H)
510. C2×C4⋊C4C4×D13semidirect
538. C2×C13C2×#387semidirect
546. D13C2×#387direct (N × H)
647. C4⋊C4C2×C4×D13semidirect
652. C13C22×#387semidirect
775. C2D13×#387direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C22×C42×D132
C2×#117183162
C2×#117186422
C2×#117183142
C2×#117185942
C2×#117183152
C2×#117183132
C2×#117186392
D13×#3872
C2×D13×#952
C2×C13×#3872
C22×#38713