Finite Group Databasebeta

← C2×#13119099 #16030549

Subgroups — C2×#13119099 #16030549

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×#88133C211yesmaximal, characteristic, complemented
2C23×#6101C211yesmaximal, characteristic, complemented
3#13119099C2116yesmaximal, direct product factor
4C2×#11718321C211yesmaximal, characteristic, complemented
5C2×#11718319C211yesmaximal, characteristic, complemented
6C2×#11718613C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718606C211yesmaximal, characteristic, complemented
9C2×#11718314C211yesmaximal, characteristic, complemented
10C2×#11718313C211yesmaximal, characteristic, complemented
11C2×#11718881C211yesmaximal, characteristic
12C2×#11718881C211yesmaximal, characteristic
13C2×#11718611C211yesmaximal, characteristic, complemented
14C2×#11718603C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×#6101—28no—
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2218yescomplemented
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88133—28no—
43C2×#88133C2218yescomplemented
44C13×#386C2218yes—
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47#11718881C2218yes—
48#11718881C2218yes—
49C4×C22⋊Dic13C2218yescomplemented
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60#11718613C2218yescomplemented
61#11718611C2218yescomplemented
62#11718609C2218yescomplemented
63#11718606C2218yescomplemented
64#11718603C2218yescomplemented
65#11718321C2218yescomplemented
66#11718319C2218yescomplemented
67#11718314C2218yescomplemented
68#11718313C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C22×D4×C13—24no—
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13C2314yes—
75C23×C4×C13—24no—
76C23×C4×C13—24no—
77C23×C4×C13—42no—
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C23×C4×C13C2311yescharacteristic
84C23×Dic13—24no—
85C23×Dic13—24no—
86C23×Dic13—24no—
87C23×Dic13—24no—
88C23×Dic13—24no—
89C23×Dic13—42no—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2314yes—
96C23×Dic13C2314yes—
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4—42no—
103C2×C13×C22⋊C4C2314yes—
104C2×C13×C22⋊C4C2314yes—
105C2×C13×C22⋊C4C2314yes—
106C2×C22⋊Dic13—24no—
107C2×C22⋊Dic13—24no—
108C2×C22⋊Dic13—24no—
109C2×C22⋊Dic13—24no—
110C2×C22⋊Dic13—24no—
111C2×C22⋊Dic13—42no—
112C2×C22⋊Dic13C2314yes—
113C2×C22⋊Dic13C2314yes—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C4⋊Dic13—24no—
119C2×C4⋊Dic13—24no—
120C2×C4⋊Dic13C2314yes—
121C2×C4⋊Dic13C2314yes—
122C2×#6101—24no—
123C2×#6101—24no—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—232no—
127C2×#6101—42no—
128C2×#6101D418yescomplemented
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×C4×Dic13—24no—
136C2×C4×Dic13—42no—
137C2×C4×Dic13C2314yes—
138C2×C4×Dic13C2314yes—
139#88133—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—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13#4114yes—
165C24×C13#4114yes—
166C24×C13#4114yes—
167C24×C13C2412yes—
168C24×C13C2412yes—
169C24×C13C2411yescharacteristic
170C2×D4×C13—28no—
171C2×D4×C13—28no—
172C2×D4×C13—28no—
173C2×D4×C13—416no—
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—22no—
189C22×C4×C13—28no—
190C22×C4×C13—44no—
191C22×C4×C13—416no—
192C22×C4×C13C2×D414yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×Dic13—232no—
199C22×Dic13—22no—
200C22×Dic13—28no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—28no—
207C22×Dic13—28no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
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—28no—
225C22×Dic13—44no—
226C22×Dic13—416no—
227C22×Dic13C2×D414yes—
228C22×Dic13C2×D414yes—
229C22×Dic13#4114yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C13×C22⋊C4—28no—
239C13×C22⋊C4—28no—
240C13×C22⋊C4—44no—
241C22⋊Dic13—28no—
242C22⋊Dic13—28no—
243C22⋊Dic13—28no—
244C22⋊Dic13—28no—
245C22⋊Dic13—28no—
246C22⋊Dic13—44no—
247C4⋊Dic13—28no—
248C4⋊Dic13—28no—
249#6101—28no—
250#6101—28no—
251#6101—28no—
252#6101—28no—
253#6101—44no—
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×#386D1311yescharacteristic
270C2×#385—131no—
271C2×#380—131no—
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—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—44no—
291C23×C13—44no—
292C23×C13—44no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13—44no—
297C23×C13#126116yescomplemented
298C23×C13C22×D412yes—
299C23×C13C2×#4114yes—
300C23×C13C2×#4114yes—
301C23×C13C2×#4114yes—
302C23×C13C2×#4112yes—
303C23×C13C2×#4112yes—
304C23×C13C2×#4112yes—
305C23×C13C2×#4112yes—
306C23×C13H(5,𝔽2)12yes—
307C23×C132−1+412yes—
308C23×C13C2511yescharacteristic
309D4×C13—416no—
310C2×C4×C13—28no—
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—416no—
326C2×C4×C13—44no—
327C2×C4×C13—44no—
328C2×C4×C13—44no—
329C2×C4×C13—44no—
330C2×C4×C13C22×D414yes—
331C2×Dic13—232no—
332C2×Dic13—28no—
333C2×Dic13—28no—
334C2×Dic13—28no—
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—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—416no—
357C2×Dic13—44no—
358C2×Dic13—44no—
359C2×Dic13—44no—
360C2×Dic13—44no—
361C2×Dic13—44no—
362C2×Dic13C22×D414yes—
363C2×Dic13C22×D414yes—
364C2×Dic13C2×#4114yes—
365C23×D4C2×D1311yescharacteristic
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—131no—
376C22×C4⋊C4—138no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4—268no—
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⋊C4C2×D1311yescharacteristic
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#386C2×D1318yes—
402#385—138no—
403#380—138no—
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—42no—
425C22×C13—42no—
426C22×C13—42no—
427C22×C13—42no—
428C22×C13—42no—
429C22×C13—42no—
430C22×C13—42no—
431C22×C13—88no—
432C22×C13#52514yes—
433C22×C13C2×#12614yes—
434C22×C13C2×#12618yescomplemented
435C22×C13#53914yes—
436C22×C13#54614yes—
437C22×C13#54814yes—
438C22×C13#55214yes—
439C22×C13#55314yes—
440C22×C13C23×D411yescharacteristic
441C22×C13C22×#4111yescharacteristic
442C22×C13C22×#4111yescharacteristic
443C22×C13C22×#4111yescharacteristic
444C22×C13C22×#4111yescharacteristic
445C22×C13C2×H(5,𝔽2)11yescharacteristic
446C22×C13C2×2−1+411yescharacteristic
447C4×C13—24no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13—42no—
451C4×C13—42no—
452Dic13—24no—
453Dic13—24no—
454Dic13—24no—
455Dic13—42no—
456Dic13—42no—
457Dic13—42no—
458Dic13—42no—
459Dic13—42no—
460C25C22×D1311yescharacteristic
461C25C22×D1311yescharacteristic
462C22×D4—24no—
463C22×D4—24no—
464C22×D4—24no—
465C22×D4C22×D1314yes—
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—131no—
478C23×C4—134no—
479C23×C4—264no—
480C23×C4—264no—
481C23×C4—264no—
482C23×C4—264no—
483C23×C4—264no—
484C23×C4—522no—
485C23×C4C22×D1311yescharacteristic
486C23×C4C22×D1311yescharacteristic
487C23×C4C22×D1311yescharacteristic
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1314yes—
490C23×C4C22×D1311yescharacteristic
491#126—2632no—
492C2×C4⋊C4—138no—
493C2×C4⋊C4—134no—
494C2×C4⋊C4—134no—
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⋊C4—264no—
508C2×C4⋊C4—522no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
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⋊C4C22×D1314yes—
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—82no—
545C2×C13#248118yescomplemented
546C2×C13C2×#52511yescharacteristic
547C2×C13C22×#12611yescharacteristic
548C2×C13C2×#53911yescharacteristic
549C2×C13C2×#54611yescharacteristic
550C2×C13C2×#54811yescharacteristic
551C2×C13C2×#55211yescharacteristic
552C2×C13C2×#55311yescharacteristic
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24#612714yes—
565C24#612914yes—
566C24#612914yes—
567C24C23×D1312yes—
568C24C23×D1312yes—
569C24C23×D1311yescharacteristic
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—416no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—44no—
591C22×C4—416no—
592C22×C4—134no—
593C22×C4—134no—
594C22×C4—134no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—268no—
604C22×C4—268no—
605C22×C4—268no—
606C22×C4—2632no—
607C22×C4—268no—
608C22×C4—262no—
609C22×C4—262no—
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—268no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—524no—
631C22×C4—5216no—
632C22×C4D4×D1314yes—
633C22×C4C23×D1312yes—
634C22×C4C23×D1312yes—
635C22×C4C23×D1312yes—
636C22×C4C23×D1312yes—
637C22×C4C23×D1312yes—
638C4⋊C4—1316no—
639C4⋊C4—268no—
640C4⋊C4—268no—
641C4⋊C4—268no—
642C4⋊C4—268no—
643C4⋊C4—268no—
644C4⋊C4—268no—
645C4⋊C4—524no—
646C22⋊C4—28no—
647C22⋊C4—28no—
648C22⋊C4—44no—
649C22⋊C4—268no—
650C22⋊C4—268no—
651C22⋊C4—268no—
652C22⋊C4—268no—
653C22⋊C4—268no—
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—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23#88133116yescomplemented
683C23C2×#612714yes—
684C23C2×#612712yes—
685C23C2×D4×D1312yes—
686C23C2×#612914yes—
687C23C2×#612914yes—
688C23C2×#612912yes—
689C23C2×#612912yes—
690C23#8825112yes—
691C23#41×D1312yes—
692C23#8825712yes—
693C23C24×D1311yescharacteristic
694D4—416no—
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—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—134no—
716C2×C4—134no—
717C2×C4—134no—
718C2×C4—2632no—
719C2×C4—268no—
720C2×C4—268no—
721C2×C4—268no—
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—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—5216no—
744C2×C4—524no—
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—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—88no—
765C22C2×#8813314yes—
766C22C2×#8813318yescomplemented
767C22#1171925214yes—
768C22#1171926914yes—
769C22#1171929614yes—
770C22#1171930314yes—
771C22#1171930614yes—
772C22#1171935514yes—
773C22C22×#612711yescharacteristic
774C22C22×D4×D1311yescharacteristic
775C22C22×#612911yescharacteristic
776C22C22×#612911yescharacteristic
777C22C2×#8825111yescharacteristic
778C22C2×#41×D1311yescharacteristic
779C22C2×#8825711yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—264no—
786C4—264no—
787C4—264no—
788C4—522no—
789C4—522no—
790C4—522no—
791C4—522no—
792C4—522no—
793C2—28no—
794C2—82no—
795C2#1311909918yesdirect product factor
796C2C2×#1171925211yescharacteristic
797C2C22×#8813311yescharacteristic
798C2C2×#1171926911yescharacteristic
799C2C2×#1171929611yescharacteristic
800C2C2×#1171930311yescharacteristic
801C2C2×#1171935511yescharacteristic
802C2C2×#1171930611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#386D13
hypocenterC13C2×#2481
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#88133C2semidirect
2. C23×#6101C2semidirect
3. #13119099C2direct (N × H)
4. C2×#11718321C2semidirect
5. C2×#11718319C2semidirect
6. C2×#11718613C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718606C2semidirect
9. C2×#11718314C2semidirect
10. C2×#11718313C2semidirect
13. C2×#11718611C2semidirect
14. C2×#11718603C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
39. C22×#6101C22semidirect
43. C2×#88133C22semidirect
49. C4×C22⋊Dic13C22semidirect
60. #11718613C22semidirect
61. #11718611C22semidirect
62. #11718609C22semidirect
63. #11718606C22semidirect
64. #11718603C22semidirect
65. #11718321C22semidirect
66. #11718319C22semidirect
67. #11718314C22semidirect
68. #11718313C22semidirect
128. C2×#6101D4semidirect
254. #6101C2×D4semidirect
297. C23×C13#126semidirect
434. C22×C13C2×#126semidirect
545. C2×C13#2481semidirect
657. C13C2×#2481semidirect
682. C23#88133semidirect
766. C22C2×#88133semidirect
795. C2#13119099direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881332
C23×#61012
#131190992
C2×#117183212
C2×#117183192
C2×#117186132
C2×#117186092
C2×#117186062
C2×#117183142
C2×#117183132
C2×#117188812
C2×#117186112
C2×#117186032
C2×C4×C22⋊Dic132
C2×C13×#3862
C2×#248113