Finite Group Databasebeta

← C2×#13119104 #16030539

Subgroups — C2×#13119104 #16030539

Order 3328.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88152C211yesmaximal, characteristic, complemented
2C23×#6101C211yesmaximal, characteristic, complemented
3#13119104C2116yesmaximal, direct product factor
4C2×#11718321C211yesmaximal, characteristic, complemented
5C2×#11718643C211yesmaximal, characteristic, complemented
6C2×#11718336C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718330C211yesmaximal, characteristic, complemented
9C2×#11718315C211yesmaximal, characteristic, complemented
10C2×#11718639C211yesmaximal, characteristic, complemented
11C2×#11718874C211yesmaximal, characteristic
12C2×#11718619C211yesmaximal, characteristic
13C2×#11718619C211yesmaximal, characteristic
14C2×#11718611C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#380C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×#6101—28no—
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2218yescomplemented
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88152—28no—
43C2×#88152C2218yescomplemented
44C13×#380C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47#11718874C2218yes—
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718655C2218yescomplemented
59#11718643C2218yescomplemented
60#11718639C2218yescomplemented
61#11718619C2218yes—
62#11718619C2218yes—
63#11718611C2218yescomplemented
64C22⋊C4×Dic13C2218yescomplemented
65#11718336C2218yescomplemented
66#11718330C2218yescomplemented
67#11718321C2218yescomplemented
68#11718315C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13—24no—
72C23×C4×C13—24no—
73C23×C4×C13—42no—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2314yes—
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—24no—
82C22×C22⋊D13—24no—
83C22×C22⋊D13—24no—
84C22×C22⋊D13C2314yes—
85C23×Dic13—24no—
86C23×Dic13—24no—
87C23×Dic13—24no—
88C23×Dic13—24no—
89C23×Dic13—24no—
90C23×Dic13—42no—
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2314yes—
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2314yes—
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C2×C13×C4⋊C4—24no—
101C2×C13×C4⋊C4—42no—
102C2×C13×C4⋊C4C2314yes—
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C22⋊Dic13—24no—
109C2×C22⋊Dic13C2314yes—
110C2×#6103—24no—
111C2×#6103—24no—
112C2×#6103—24no—
113C2×#6103—24no—
114C2×#6103—42no—
115C2×#6103—42no—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×C4⋊Dic13—24no—
123C2×C4⋊Dic13—24no—
124C2×C4⋊Dic13C2314yes—
125C2×C4⋊Dic13C2314yes—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101—24no—
129C2×#6101—232no—
130C2×#6101D418yescomplemented
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×C4×Dic13—24no—
136C2×C4×Dic13—42no—
137C2×C4×Dic13C2314yes—
138C2×C4×Dic13C2314yes—
139#88152—232no—
140C13×#95C2314yes—
141C13×#95C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2481—131nomaximal, Sylow
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13#4114yes—
158C24×C13#4114yes—
159C24×C13#4114yes—
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—28no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—28no—
189C22×C4×C13—44no—
190C22×C4×C13—416no—
191C22×C4×C13C2×D414yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C2×C22⋊D13—28no—
199C2×C22⋊D13—28no—
200C2×C22⋊D13—28no—
201C2×C22⋊D13—416no—
202C22×Dic13—232no—
203C22×Dic13—22no—
204C22×Dic13—28no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—28no—
211C22×Dic13—28no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—28no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—28no—
226C22×Dic13—44no—
227C22×Dic13—416no—
228C22×Dic13C2×D414yes—
229C22×Dic13C2×D414yes—
230C22×Dic13#4114yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C13×C4⋊C4—28no—
239C13×C4⋊C4—44no—
240C13×C22⋊C4—28no—
241C13×C22⋊C4—28no—
242C22⋊Dic13—28no—
243#6103—28no—
244#6103—28no—
245#6103—28no—
246#6103—28no—
247#6103—44no—
248#6103—44no—
249C4⋊Dic13—28no—
250C4⋊Dic13—28no—
251#6101—28no—
252#6101—28no—
253#6101—28no—
254#6101C2×D4116yescomplemented
255C4×Dic13—28no—
256C4×Dic13—44no—
257C22×#126—131no—
258C23×C4⋊C4—131no—
259#2481—1316no—
260C2×#400—131no—
261C2×#400—131no—
262C2×#397—131no—
263C2×#396—131no—
264C2×#388—131no—
265C2×#387—131no—
266C2×#387—131no—
267C2×#386—131no—
268C2×#386—131no—
269C2×#386—131no—
270C2×#385—131no—
271C2×#380D1311yescharacteristic, complemented
272C2×C4×C22⋊C4—131no—
273C23×C13—28no—
274C23×C13—28no—
275C23×C13—28no—
276C23×C13—28no—
277C23×C13—28no—
278C23×C13—28no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13#126116yescomplemented
284C23×C13C22×D412yes—
285C23×C13C2×#4114yes—
286C23×C13C2×#4114yes—
287C23×C13C2×#4114yes—
288C23×C13C2×#4112yes—
289C23×C13C2×#4112yes—
290C23×C13C2×#4112yes—
291C23×C13C2×#4112yes—
292C23×C13H(5,𝔽2)12yes—
293C23×C132−1+412yes—
294C23×C13C2511yescharacteristic
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C22×D13—44no—
307C22×D13—44no—
308C22×D13—44no—
309C2×C4×C13—28no—
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—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—416no—
328C2×C4×C13—44no—
329C2×C4×C13—44no—
330C2×C4×C13—44no—
331C2×C4×C13—44no—
332C2×C4×C13—44no—
333C2×C4×C13C22×D414yes—
334C22⋊D13—416no—
335C2×Dic13—232no—
336C2×Dic13—28no—
337C2×Dic13—28no—
338C2×Dic13—28no—
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—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—416no—
358C2×Dic13—44no—
359C2×Dic13—44no—
360C2×Dic13—44no—
361C2×Dic13—44no—
362C2×Dic13C22×D414yes—
363C2×Dic13C22×D414yes—
364C2×Dic13C2×#4114yes—
365C23×D4—131no—
366C24×C4—131no—
367C24×C4—131no—
368C24×C4C2×D1311yescharacteristic
369C2×#126—138no—
370C2×#126—268no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4—131no—
375C22×C4⋊C4—138no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—268no—
379C22×C4⋊C4C2×D1311yescharacteristic
380C22×C4⋊C4C2×D1311yescharacteristic
381C22×C22⋊C4—131no—
382C22×C22⋊C4—131no—
383C22×C22⋊C4—131no—
384C22×C22⋊C4—131no—
385C22×C22⋊C4—131no—
386C22×C22⋊C4—131no—
387C22×C22⋊C4—131no—
388C22×C22⋊C4C2×D1311yescharacteristic
389C22×C22⋊C4C2×D1311yescharacteristic
390C22×C42—131no—
391C22×C42—131no—
392#400—138no—
393#400—138no—
394#397—138no—
395#396—138no—
396#388—138no—
397#387—138no—
398#387—138no—
399#386—138no—
400#386—138no—
401#386—138no—
402#385—138no—
403#380C2×D1318yescomplemented
404C4×C22⋊C4—138no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95—131no—
413C2×#95—131no—
414C2×#95—131no—
415C2×#95C2×D1311yescharacteristic
416C2×#95C2×D1311yescharacteristic
417C22×C13—24no—
418C22×C13—24no—
419C22×C13—24no—
420C22×C13—24no—
421C22×C13—24no—
422C22×C13—24no—
423C22×C13—232no—
424C22×C13#52514yes—
425C22×C13C2×#12614yes—
426C22×C13C2×#12618yescomplemented
427C22×C13#53914yes—
428C22×C13#54614yes—
429C22×C13#54814yes—
430C22×C13#55214yes—
431C22×C13#55314yes—
432C22×C13C23×D411yescharacteristic
433C22×C13C22×#4111yescharacteristic
434C22×C13C22×#4111yescharacteristic
435C22×C13C22×#4111yescharacteristic
436C22×C13C22×#4111yescharacteristic
437C22×C13C2×H(5,𝔽2)11yescharacteristic
438C22×C13C2×2−1+411yescharacteristic
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C2×D13—42no—
445C2×D13—42no—
446C2×D13—88no—
447C4×C13—24no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13—42no—
451C4×C13—42no—
452C4×C13—42no—
453Dic13—24no—
454Dic13—24no—
455Dic13—24no—
456Dic13—42no—
457Dic13—42no—
458Dic13—42no—
459Dic13—42no—
460C25—131no—
461C25C22×D1311yescharacteristic
462C22×D4—134no—
463C22×D4—264no—
464C22×D4—264no—
465C22×D4—264no—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—42no—
469C23×C4—131no—
470C23×C4—131no—
471C23×C4—131no—
472C23×C4—134no—
473C23×C4—131no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—134no—
478C23×C4—264no—
479C23×C4—264no—
480C23×C4—264no—
481C23×C4—264no—
482C23×C4—264no—
483C23×C4—522no—
484C23×C4C22×D1311yescharacteristic
485C23×C4C22×D1311yescharacteristic
486C23×C4C22×D1311yescharacteristic
487C23×C4C22×D1311yescharacteristic
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1314yes—
490C23×C4C22×D1311yescharacteristic
491#126—2632no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—138no—
495C2×C4⋊C4—134no—
496C2×C4⋊C4—134no—
497C2×C4⋊C4—134no—
498C2×C4⋊C4—134no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—2632no—
502C2×C4⋊C4—264no—
503C2×C4⋊C4—264no—
504C2×C4⋊C4—264no—
505C2×C4⋊C4—264no—
506C2×C4⋊C4—264no—
507C2×C4⋊C4C22×D1314yes—
508C2×C4⋊C4C22×D1314yes—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—134no—
512C2×C22⋊C4—134no—
513C2×C22⋊C4—134no—
514C2×C22⋊C4—134no—
515C2×C22⋊C4—134no—
516C2×C22⋊C4—134no—
517C2×C22⋊C4—134no—
518C2×C22⋊C4—264no—
519C2×C22⋊C4—264no—
520C2×C22⋊C4—264no—
521C2×C22⋊C4—264no—
522C2×C22⋊C4—264no—
523C2×C22⋊C4—522no—
524C2×C22⋊C4—522no—
525C2×C22⋊C4C22×D1314yes—
526C2×C22⋊C4C22×D1314yes—
527C2×C42—134no—
528C2×C42—134no—
529C2×C42—264no—
530C2×C42—522no—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—134no—
536#95—134no—
537#95—134no—
538#95—134no—
539#95—134no—
540#95—134no—
541#95C22×D1314yes—
542#95C22×D1314yes—
543C2×C13—28no—
544C2×C13#248118yescomplemented
545C2×C13C2×#52511yescharacteristic
546C2×C13C22×#12611yescharacteristic
547C2×C13C2×#53911yescharacteristic
548C2×C13C2×#54611yescharacteristic
549C2×C13C2×#54811yescharacteristic
550C2×C13C2×#55211yescharacteristic
551C2×C13C2×#55311yescharacteristic
552D13—82no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—132no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24—262no—
564C24—262no—
565C24#612714yes—
566C24#612914yes—
567C24#613114yes—
568C24C23×D1312yes—
569C24C23×D1311yescharacteristic
570C2×D4—268no—
571C2×D4—268no—
572C2×D4—268no—
573C2×D4—5216no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—44no—
594C22×C4—416no—
595C22×C4—134no—
596C22×C4—134no—
597C22×C4—134no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—132no—
604C22×C4—132no—
605C22×C4—268no—
606C22×C4—268no—
607C22×C4—268no—
608C22×C4—2632no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—268no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—268no—
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—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—524no—
630C22×C4—5216no—
631C22×C4D4×D1314yes—
632C22×C4C23×D1312yes—
633C22×C4C23×D1312yes—
634C22×C4C23×D1312yes—
635C22×C4C23×D1312yes—
636C22×C4C23×D1312yes—
637C22×C4C23×D1312yes—
638C4⋊C4—28no—
639C4⋊C4—44no—
640C4⋊C4—1316no—
641C4⋊C4—268no—
642C4⋊C4—268no—
643C4⋊C4—268no—
644C4⋊C4—268no—
645C4⋊C4—268no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—268no—
649C22⋊C4—268no—
650C22⋊C4—268no—
651C22⋊C4—268no—
652C22⋊C4—268no—
653C22⋊C4—524no—
654C22⋊C4—524no—
655C42—268no—
656C42—524no—
657C13C2×#248111yescharacteristic, complemented, Sylow
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—262no—
672C23—262no—
673C23—262no—
674C23—262no—
675C23—524no—
676C23—524no—
677C23—524no—
678C23—524no—
679C23—524no—
680C23—524no—
681C23—524no—
682C23#88152116yescomplemented
683C23C2×#612714yes—
684C23C2×#612712yes—
685C23C2×D4×D1312yes—
686C23C2×#612914yes—
687C23C2×#612912yes—
688C23#8825112yes—
689C23C2×#613114yes—
690C23C2×#613112yes—
691C23#41×D1312yes—
692C23#8825712yes—
693C23C24×D1311yescharacteristic
694D4—5216no—
695C2×C4—28no—
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—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—416no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—134no—
720C2×C4—134no—
721C2×C4—134no—
722C2×C4—2632no—
723C2×C4—268no—
724C2×C4—268no—
725C2×C4—268no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—5216no—
745C2×C4—524no—
746C2×C4—524no—
747C2×C4—524no—
748C2×C4—524no—
749C2×C4C2×D4×D1314yes—
750C22—24no—
751C22—24no—
752C22—232no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—522no—
762C22—522no—
763C22—522no—
764C22—1048no—
765C22#1171919514yes—
766C22C2×#8815214yes—
767C22C2×#8815218yescomplemented
768C22#1171923614yes—
769C22#1171930314yes—
770C22#1171930614yes—
771C22#1171933214yes—
772C22#1171935014yes—
773C22C22×#612711yescharacteristic
774C22C22×D4×D1311yescharacteristic
775C22C22×#612911yescharacteristic
776C22C2×#8825111yescharacteristic
777C22C22×#613111yescharacteristic
778C22C2×#41×D1311yescharacteristic
779C22C2×#8825711yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—264no—
787C4—264no—
788C4—264no—
789C4—522no—
790C4—522no—
791C4—522no—
792C4—522no—
793C2—28no—
794C2—1042no—
795C2#1311910418yesdirect product factor
796C2C2×#1171933211yescharacteristic
797C2C22×#8815211yescharacteristic
798C2C2×#1171935011yescharacteristic
799C2C2×#1171919511yescharacteristic
800C2C2×#1171930311yescharacteristic
801C2C2×#1171923611yescharacteristic
802C2C2×#1171930611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#380D13
hypocenterC13C2×#2481
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#88152C2semidirect
2. C23×#6101C2semidirect
3. #13119104C2direct (N × H)
4. C2×#11718321C2semidirect
5. C2×#11718643C2semidirect
6. C2×#11718336C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718330C2semidirect
9. C2×#11718315C2semidirect
10. C2×#11718639C2semidirect
14. C2×#11718611C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
16. C2×C13×#380C2semidirect
39. C22×#6101C22semidirect
43. C2×#88152C22semidirect
44. C13×#380C22semidirect
58. #11718655C22semidirect
59. #11718643C22semidirect
60. #11718639C22semidirect
63. #11718611C22semidirect
64. C22⋊C4×Dic13C22semidirect
65. #11718336C22semidirect
66. #11718330C22semidirect
67. #11718321C22semidirect
68. #11718315C22semidirect
130. C2×#6101D4semidirect
254. #6101C2×D4semidirect
271. C2×#380D13semidirect
283. C23×C13#126semidirect
403. #380C2×D13semidirect
426. C22×C13C2×#126semidirect
544. C2×C13#2481semidirect
657. C13C2×#2481semidirect
682. C23#88152semidirect
767. C22C2×#88152semidirect
795. C2#13119104direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881522
C23×#61012
#131191042
C2×#117183212
C2×#117186432
C2×#117183362
C2×#117186552
C2×#117183302
C2×#117183152
C2×#117186392
C2×#117188742
C2×#117186192
C2×#117186112
C2×C22⋊C4×Dic132
C2×C13×#3802
C2×#248113