Finite Group Databasebeta

← C2×#13118311 #16030624

Subgroups — C2×#13118311 #16030624

Order 3328.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88189C211yesmaximal, characteristic
2C22×D4×Dic13C211yesmaximal, characteristic
3#13118311C2116yesmaximal, direct product factor
4C2×#11718320C211yesmaximal, characteristic, complemented
5C2×#11718322C211yesmaximal, characteristic, complemented
6C2×#11718614C211yesmaximal, characteristic, complemented
7C2×#11718614C211yesmaximal, characteristic, complemented
8C2×#11718314C211yesmaximal, characteristic, complemented
9C2×#11718314C211yesmaximal, characteristic, complemented
10C2×#11718611C211yesmaximal, characteristic, complemented
11C2×#11718611C211yesmaximal, characteristic, complemented
12C2×#11718604C211yesmaximal, characteristic, complemented
13C2×#11718604C211yesmaximal, characteristic, complemented
14C2×#11718873C211yesmaximal, characteristic, complemented
15C22×#88071C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C2×#88189—28no—
31C2×#88189C2218yes—
32C2×D4×Dic13—28no—
33C2×D4×Dic13C2218yes—
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C13×#386C2218yes—
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45#11718873C2218yescomplemented
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2218yescomplemented
59#11718614C2218yescomplemented
60#11718614C2218yescomplemented
61#11718611C2218yescomplemented
62#11718611C2218yescomplemented
63#11718604C2218yescomplemented
64#11718604C2218yescomplemented
65#11718322C2218yescomplemented
66#11718320C2218yescomplemented
67#11718314C2218yescomplemented
68#11718314C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C22×D4×C13—24no—
72C22×D4×C13—24no—
73C22×D4×C13D418yes—
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×C13C2314yes—
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×Dic13—24no—
85C23×Dic13—24no—
86C23×Dic13—24no—
87C23×Dic13—24no—
88C23×Dic13—24no—
89C23×Dic13—24no—
90C23×Dic13—24no—
91C23×Dic13—42no—
92C23×Dic13—42no—
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2314yes—
101C23×Dic13C2314yes—
102C23×Dic13C2314yes—
103C23×Dic13C2311yescharacteristic
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4—42no—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C22⋊Dic13—24no—
111C2×C22⋊Dic13—24no—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—24no—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120#88189—232no—
121D4×Dic13—232no—
122C2×C4⋊Dic13—24no—
123C2×C4⋊Dic13—24no—
124C2×C4⋊Dic13—24no—
125C2×C4⋊Dic13—42no—
126C2×C4⋊Dic13—42no—
127C2×C4⋊Dic13C2314yes—
128C2×C4⋊Dic13C2314yes—
129C2×C4⋊Dic13C2314yes—
130C2×C4⋊Dic13C2314yes—
131C2×C4⋊Dic13C2314yes—
132C2×#6101—24no—
133C2×#6101—24no—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×C4×Dic13—24no—
137C2×C4×Dic13C2314yes—
138C13×#95C2314yes—
139C13×#95C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2419—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×C13C2×D414yes—
164C24×C13C2×D414yes—
165C24×C13#4114yes—
166C24×C13#4114yes—
167C24×C13C2412yes—
168C24×C13C2412yes—
169C24×C13C2411yescharacteristic
170C2×D4×C13—232no—
171C2×D4×C13—28no—
172C2×D4×C13—28no—
173C2×D4×C13C2×D4116yes—
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—28no—
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×C13#4114yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
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—28no—
208C22×Dic13—28no—
209C22×Dic13—28no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—28no—
214C22×Dic13—28no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—28no—
227C22×Dic13—28no—
228C22×Dic13—44no—
229C22×Dic13—44no—
230C22×Dic13—416no—
231C22×Dic13—416no—
232C22×Dic13—416no—
233C22×Dic13#4114yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C13×C22⋊C4—28no—
243C13×C22⋊C4—28no—
244C13×C22⋊C4—44no—
245C22⋊Dic13—28no—
246C22⋊Dic13—28no—
247C22⋊Dic13—28no—
248C22⋊Dic13—28no—
249C22⋊Dic13—28no—
250C4⋊Dic13—28no—
251C4⋊Dic13—28no—
252C4⋊Dic13—28no—
253C4⋊Dic13—44no—
254C4⋊Dic13—44no—
255#6101—28no—
256#6101—28no—
257C4×Dic13—28no—
258C22×#123—131no—
259C22×C4×D4—131no—
260#2419—1316no—
261C2×#400—131no—
262C2×#398—131no—
263C2×#397—131no—
264C2×#397—131no—
265C2×#387—131no—
266C2×#387—131no—
267C2×#386D1311yescharacteristic
268C2×#385—131no—
269C2×#385—131no—
270C2×#381—131no—
271C2×#381—131no—
272C2×#380—131no—
273C22×#95—131no—
274C23×C13—28no—
275C23×C13—28no—
276C23×C13—28no—
277C23×C13—28no—
278C23×C13—28no—
279C23×C13—28no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—28no—
285C23×C13—28no—
286C23×C13—28no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13—44no—
297C23×C13#123116yes—
298C23×C13C22×D414yes—
299C23×C13C22×D414yes—
300C23×C13C22×D412yes—
301C23×C13C2×#4114yes—
302C23×C13C2×#4114yes—
303C23×C13C2×#4112yes—
304C23×C13C2×#4112yes—
305C23×C13C2×#4112yes—
306C23×C13C2×#4112yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C132−1+412yes—
309C23×C13C2511yescharacteristic
310D4×C13—232no—
311C2×C4×C13—28no—
312C2×C4×C13—28no—
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—416no—
327C2×C4×C13—44no—
328C2×C4×C13—44no—
329C2×C4×C13—44no—
330C2×C4×C13C22×D414yes—
331C2×C4×C13C2×#4114yes—
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—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—416no—
357C2×Dic13—416no—
358C2×Dic13—416no—
359C2×Dic13—44no—
360C2×Dic13—44no—
361C2×Dic13—44no—
362C2×Dic13—44no—
363C2×Dic13—44no—
364C2×Dic13—44no—
365C2×Dic13—44no—
366C2×Dic13C2×#4114yes—
367C23×D4C2×D1311yescharacteristic
368C24×C4—131no—
369C24×C4—131no—
370C24×C4—131no—
371C24×C4C2×D1311yescharacteristic
372C2×#123—138no—
373C2×#123—268no—
374C2×C4×D4—138no—
375C2×C4×D4—268no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4—131no—
381C22×C4⋊C4—131no—
382C22×C4⋊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×C22⋊C4C2×D1311yescharacteristic
391C22×C42—131no—
392#400—138no—
393#398—138no—
394#397—138no—
395#397—138no—
396#387—138no—
397#387—138no—
398#386C2×D1318yes—
399#385—138no—
400#385—138no—
401#381—138no—
402#381—138no—
403#380—138no—
404C2×#95—131no—
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—138no—
414C2×#95—131no—
415C2×#95—131no—
416C2×#95—131no—
417C2×#95C2×D1311yescharacteristic
418C2×#95C2×D1311yescharacteristic
419C22×C13—24no—
420C22×C13—232no—
421C22×C13—24no—
422C22×C13—24no—
423C22×C13—24no—
424C22×C13—24no—
425C22×C13—24no—
426C22×C13—24no—
427C22×C13—24no—
428C22×C13—24no—
429C22×C13—42no—
430C22×C13—416no—
431C22×C13—42no—
432C22×C13—42no—
433C22×C13—42no—
434C22×C13C2×#12318yes—
435C22×C13C2×#12314yes—
436C22×C13#52914yes—
437C22×C13#53914yes—
438C22×C13#54614yes—
439C22×C13#54714yes—
440C22×C13#55114yes—
441C22×C13#55214yes—
442C22×C13C23×D411yescharacteristic
443C22×C13C22×#4111yescharacteristic
444C22×C13C22×#4111yescharacteristic
445C22×C13C22×#4111yescharacteristic
446C22×C13C22×#4111yescharacteristic
447C22×C13C2×H(5,𝔽2)11yescharacteristic
448C22×C13C2×2−1+411yescharacteristic
449C4×C13—24no—
450C4×C13—24no—
451C4×C13—42no—
452C4×C13—42no—
453C4×C13—42no—
454Dic13—24no—
455Dic13—42no—
456Dic13—42no—
457Dic13—42no—
458Dic13—42no—
459Dic13—42no—
460Dic13—42no—
461Dic13—42no—
462C25C22×D1311yescharacteristic
463C25C22×D1311yescharacteristic
464C22×D4—24no—
465C22×D4—24no—
466C22×D4D5218yes—
467C22×D4C22×D1314yes—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—42no—
471C23×C4—131no—
472C23×C4—134no—
473C23×C4—131no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—134no—
481C23×C4—134no—
482C23×C4—264no—
483C23×C4—264no—
484C23×C4—264no—
485C23×C4—264no—
486C23×C4—264no—
487C23×C4—264no—
488C23×C4—264no—
489C23×C4—522no—
490C23×C4—522no—
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C23×C4C22×D1314yes—
495C23×C4C22×D1311yescharacteristic
496C23×C4C22×D1311yescharacteristic
497#123—2632no—
498C4×D4—2632no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—134no—
504C2×C4⋊C4—134no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—264no—
507C2×C4⋊C4—264no—
508C2×C4⋊C4—264no—
509C2×C4⋊C4—264no—
510C2×C4⋊C4—264no—
511C2×C4⋊C4—522no—
512C2×C4⋊C4—522no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—134no—
517C2×C22⋊C4—134no—
518C2×C22⋊C4—134no—
519C2×C22⋊C4—134no—
520C2×C22⋊C4—134no—
521C2×C22⋊C4—264no—
522C2×C22⋊C4—264no—
523C2×C22⋊C4—264no—
524C2×C22⋊C4—264no—
525C2×C22⋊C4—264no—
526C2×C22⋊C4C22×D1314yes—
527C2×C22⋊C4C22×D1314yes—
528C2×C22⋊C4C22×D1314yes—
529C2×C42—134no—
530C2×C42—264no—
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#95—134no—
542#95—134no—
543#95C22×D1314yes—
544#95C22×D1314yes—
545C2×C13—28no—
546C2×C13—44no—
547C2×C13#241918yescomplemented
548C2×C13C22×#12311yescharacteristic
549C2×C13C2×#52911yescharacteristic
550C2×C13C2×#53911yescharacteristic
551C2×C13C2×#54611yescharacteristic
552C2×C13C2×#54711yescharacteristic
553C2×C13C2×#55111yescharacteristic
554C2×C13C2×#55211yescharacteristic
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24C2×D5214yes—
566C24C2×D5214yes—
567C24#612914yes—
568C24#612914yes—
569C24C23×D1312yes—
570C24C23×D1312yes—
571C24C23×D1311yescharacteristic
572C2×D4—232no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4C2×D52116yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—44no—
592C22×C4—416no—
593C22×C4—134no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—268no—
603C22×C4—268no—
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—262no—
613C22×C4—268no—
614C22×C4—268no—
615C22×C4—268no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—268no—
619C22×C4—268no—
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—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—524no—
633C22×C4—524no—
634C22×C4—5216no—
635C22×C4—5216no—
636C22×C4—5216no—
637C22×C4C2×D5214yes—
638C22×C4#612914yes—
639C22×C4C23×D1312yes—
640C22×C4C23×D1312yes—
641C22×C4C23×D1312yes—
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C4⋊C4—268no—
645C4⋊C4—268no—
646C4⋊C4—268no—
647C4⋊C4—268no—
648C4⋊C4—268no—
649C4⋊C4—524no—
650C4⋊C4—524no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—44no—
654C22⋊C4—268no—
655C22⋊C4—268no—
656C22⋊C4—268no—
657C22⋊C4—268no—
658C22⋊C4—268no—
659C42—268no—
660C13C2×#241911yescharacteristic, complemented, Sylow
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23#88140116yes—
685C23C22×D5214yes—
686C23C22×D5214yes—
687C23C22×D5212yes—
688C23C2×#612914yes—
689C23C2×#612914yes—
690C23C2×#612912yes—
691C23C2×#612912yes—
692C23C2×#612912yes—
693C23#8825112yes—
694C23#41×D1312yes—
695C23#8825712yes—
696C23C24×D1311yescharacteristic
697D4—232no—
698C2×C4—28no—
699C2×C4—28no—
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—134no—
718C2×C4—268no—
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—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—5216no—
743C2×C4—5216no—
744C2×C4—5216no—
745C2×C4—524no—
746C2×C4—524no—
747C2×C4—524no—
748C2×C4—524no—
749C2×C4—524no—
750C2×C4—524no—
751C2×C4—524no—
752C2×C4C22×D5214yes—
753C2×C4C2×#612914yes—
754C22—24no—
755C22—232no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—416no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22C2×#8814018yes—
770C22C2×#8814014yes—
771C22#1171925914yes—
772C22#1171926014yes—
773C22#1171929214yes—
774C22#1171930514yes—
775C22#1171930714yes—
776C22#1171935514yes—
777C22C23×D5211yescharacteristic
778C22C22×#612911yescharacteristic
779C22C22×#612911yescharacteristic
780C22C22×#612911yescharacteristic
781C22C2×#8825111yescharacteristic
782C22C2×#41×D1311yescharacteristic
783C22C2×#8825711yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—264no—
790C4—522no—
791C4—522no—
792C4—522no—
793C4—522no—
794C4—522no—
795C4—522no—
796C4—522no—
797C2—28no—
798C2—44no—
799C2#1311831118yesdirect product factor
800C2C22×#8814011yescharacteristic
801C2C2×#1171930511yescharacteristic
802C2C2×#1171930711yescharacteristic
803C2C2×#1171925911yescharacteristic
804C2C2×#1171926011yescharacteristic
805C2C2×#1171929211yescharacteristic
806C2C2×#1171935511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#386D13
hypocenterC13C2×#2419
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. #13118311C2direct (N × H)
4. C2×#11718320C2semidirect
5. C2×#11718322C2semidirect
6. C2×#11718614C2semidirect
7. C2×#11718614C2semidirect
8. C2×#11718314C2semidirect
9. C2×#11718314C2semidirect
10. C2×#11718611C2semidirect
11. C2×#11718611C2semidirect
12. C2×#11718604C2semidirect
13. C2×#11718604C2semidirect
14. C2×#11718873C2semidirect
15. C22×#88071C2semidirect
45. #11718873C22semidirect
58. C2×#88071C22semidirect
59. #11718614C22semidirect
60. #11718614C22semidirect
61. #11718611C22semidirect
62. #11718611C22semidirect
63. #11718604C22semidirect
64. #11718604C22semidirect
65. #11718322C22semidirect
66. #11718320C22semidirect
67. #11718314C22semidirect
68. #11718314C22semidirect
547. C2×C13#2419semidirect
660. C13C2×#2419semidirect
799. C2#13118311direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881892
C22×D4×Dic132
#131183112
C2×#117183202
C2×#117183222
C2×#117186142
C2×#117183142
C2×#117186112
C2×#117186042
C2×#117188732
C22×#880712
C2×C13×#3862
C2×#241913