Finite Group Databasebeta

← C2×#13118548 #16031408

Subgroups — C2×#13118548 #16031408

Order 3328.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic, complemented
2C22×#88126C211yesmaximal, characteristic
3#13118548C2116yesmaximal, direct product factor
4C2×#11718338C211yesmaximal, characteristic
5C2×#11718653C211yesmaximal, characteristic
6C2×#11718337C211yesmaximal, characteristic
7C2×#11718655C211yesmaximal, characteristic
8C2×#11718589C211yesmaximal, characteristic, complemented
9C2×#11718308C211yesmaximal, characteristic, complemented
10C2×#11718308C211yesmaximal, characteristic, complemented
11C2×#11718308C211yesmaximal, characteristic, complemented
12C2×#11718315C211yesmaximal, characteristic, complemented
13C2×#11718637C211yesmaximal, characteristic, complemented
14C2×#11718328C211yesmaximal, characteristic
15C2×#11718327C211yesmaximal, characteristic
16C2×C13×#387C211yesmaximal, characteristic, complemented
17C23×C4×D13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88143—28no—
45C2×#88143C2218yescomplemented
46C2×#88126—28no—
47C2×#88126C2218yes—
48C13×#387C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718655C2218yes—
58#11718653C2218yes—
59#11718637C2218yescomplemented
60#11718589C2218yescomplemented
61#11718338C2218yes—
62#11718337C2218yes—
63#11718328C2218yes—
64#11718327C2218yes—
65#11718315C2218yescomplemented
66#11718308C2218yescomplemented
67#11718308C2218yescomplemented
68#11718308C2218yescomplemented
69C24×D13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C22×C4×D13—24no—
85C22×C4×D13—24no—
86C22×C4×D13Q818yes—
87C22×C4×D13C2314yes—
88C2×C13×C4⋊C4—24no—
89C2×C13×C4⋊C4—24no—
90C2×C13×C4⋊C4C2314yes—
91C2×C13×C4⋊C4C2314yes—
92C2×C42×C13—24no—
93C2×C42×C13C2314yes—
94C2×#6103—24no—
95C2×#6103—24no—
96C2×#6103—24no—
97C2×#6103—24no—
98C2×#6103—42no—
99C2×#6103—42no—
100C2×#6103C2314yes—
101C2×#6103C2314yes—
102C2×#6103C2314yes—
103C2×#6103C2314yes—
104C2×#6103C2314yes—
105C2×#6103C2314yes—
106C2×C4⋊Dic13—24no—
107C2×C4⋊Dic13—24no—
108C2×C4⋊Dic13—24no—
109C2×C4⋊Dic13—42no—
110C2×C4⋊Dic13C2314yes—
111C2×C4⋊Dic13C2314yes—
112C2×C4⋊Dic13C2314yes—
113C2×C4⋊Dic13C2314yes—
114C2×#6101—24no—
115C2×#6101—24no—
116C2×#6101—24no—
117C2×#6101—24no—
118C2×#6101—24no—
119C2×#6101—24no—
120C2×#6101—42no—
121C2×#6101—42no—
122C2×#6101—42no—
123C2×#6101D418yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×#6101C2314yes—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×C4×Dic13—24no—
135C2×C4×Dic13—24no—
136C2×C4×Dic13—24no—
137C2×C4×Dic13C2314yes—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140#88143—232no—
141#88126—232no—
142C13×#95C2314yes—
143C13×#95C2314yes—
144C13×#95C2314yes—
145C13×#95C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2441—131nomaximal, Sylow
151C24×C13C2411yescharacteristic
152C23×D13—22no—
153C23×D13—22no—
154C23×D13—22no—
155C23×D13—22no—
156C23×D13—22no—
157C23×D13—22no—
158C23×D13C2×Q814yes—
159C23×D13C2412yes—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
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×C13C2×D414yes—
179C22×C4×C13C2×Q814yes—
180C22×C4×C13#4114yes—
181C22×C4×C13C2412yes—
182C22×C4×C13C2412yes—
183C22×C4×C13C2412yes—
184C22×C4×C13C2412yes—
185C22×C4×C13C2412yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2412yes—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
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×Dic13C2×D414yes—
205C22×Dic13C2×D414yes—
206C22×Dic13C2×Q814yes—
207C22×Dic13#4114yes—
208C22×Dic13#4114yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C2×C4×D13—232no—
217C2×C4×D13—28no—
218C2×C4×D13—28no—
219C2×C4×D13C2×Q8116yes—
220C13×C4⋊C4—28no—
221C13×C4⋊C4—28no—
222C42×C13—28no—
223#6103—28no—
224#6103—28no—
225#6103—28no—
226#6103—28no—
227#6103—44no—
228#6103—44no—
229C4⋊Dic13—28no—
230C4⋊Dic13—28no—
231C4⋊Dic13—28no—
232C4⋊Dic13—44no—
233#6101—28no—
234#6101—28no—
235#6101—28no—
236#6101—28no—
237#6101—28no—
238#6101—28no—
239#6101—44no—
240#6101—44no—
241#6101—44no—
242#6101C2×D4116yes—
243C4×Dic13—28no—
244C4×Dic13—28no—
245C4×Dic13—28no—
246C22×#125—131no—
247C22×#117—131no—
248#2441—1316no—
249C2×#399—131no—
250C2×#399—131no—
251C2×#396—131no—
252C2×#396—131no—
253C2×#389—131no—
254C2×#389—131no—
255C2×#389—131no—
256C2×#389—131no—
257C2×#387—131no—
258C2×#387D1311yescharacteristic, complemented
259C2×#384—131no—
260C2×#380—131no—
261C2×C4×C22⋊C4—131no—
262C23×C13C22×D412yes—
263C23×C13C22×Q812yes—
264C23×C13C2×#4112yes—
265C23×C13C2×#4112yes—
266C23×C13C2×#4112yes—
267C23×C13H(5,𝔽2)12yes—
268C23×C132−1+412yes—
269C23×C13C2511yescharacteristic
270C22×D13—28no—
271C22×D13—28no—
272C22×D13—28no—
273C22×D13—22no—
274C22×D13—22no—
275C22×D13—22no—
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—22no—
279C22×D13—44no—
280C22×D13—44no—
281C22×D13—44no—
282C22×D13—44no—
283C22×D13C22×Q814yes—
284C2×C4×C13—28no—
285C2×C4×C13—28no—
286C2×C4×C13—28no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—44no—
306C2×C4×C13—44no—
307C2×C4×C13—44no—
308C2×C4×C13—44no—
309C2×C4×C13C22×D414yes—
310C2×C4×C13C22×Q814yes—
311C2×C4×C13C2×#4114yes—
312C2×Dic13—28no—
313C2×Dic13—28no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—44no—
331C2×Dic13—44no—
332C2×Dic13—44no—
333C2×Dic13—44no—
334C2×Dic13C22⋊Q8116yes—
335C2×Dic13C22×D414yes—
336C2×Dic13C22×D414yes—
337C2×Dic13C22×Q814yes—
338C2×Dic13C2×#4114yes—
339C2×Dic13C2×#4114yes—
340C4×D13—232no—
341C24×C4—131no—
342C2×#125—138no—
343C2×#125—268no—
344C2×#117—138no—
345C2×#117—268no—
346C22×C4⋊C4—131no—
347C22×C4⋊C4—131no—
348C22×C4⋊C4—131no—
349C22×C4⋊C4—131no—
350C22×C4⋊C4—131no—
351C22×C4⋊C4—131no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4C2×D1311yescharacteristic
361C22×C4⋊C4C2×D1311yescharacteristic
362C22×C22⋊C4—131no—
363C22×C22⋊C4—131no—
364C22×C22⋊C4—131no—
365C22×C22⋊C4—131no—
366C22×C22⋊C4—131no—
367C22×C22⋊C4—131no—
368C22×C42—131no—
369C22×C42—131no—
370C22×C42—131no—
371C22×C42C2×D1311yescharacteristic
372#399—138no—
373#399—138no—
374#396—138no—
375#396—138no—
376#389—138no—
377#389—138no—
378#389—138no—
379#389—138no—
380#387—138no—
381#387C2×D1318yescomplemented
382#384—138no—
383#380—138no—
384C4×C22⋊C4—138no—
385C2×#95—131no—
386C2×#95—131no—
387C2×#95—131no—
388C2×#95—131no—
389C2×#95C2×D1311yescharacteristic
390C2×#95C2×D1311yescharacteristic
391C2×#95C2×D1311yescharacteristic
392C2×#95C2×D1311yescharacteristic
393C22×C13C2×C22⋊Q814yes—
394C22×C13#53314yes—
395C22×C13#54414yes—
396C22×C13#54714yes—
397C22×C13#55014yes—
398C22×C13#55214yes—
399C22×C13#55314yes—
400C22×C13C23×D411yescharacteristic
401C22×C13C23×Q811yescharacteristic
402C22×C13C22×#4111yescharacteristic
403C22×C13C22×#4111yescharacteristic
404C22×C13C22×#4111yescharacteristic
405C22×C13C2×H(5,𝔽2)11yescharacteristic
406C22×C13C2×2−1+411yescharacteristic
407C2×D13—24no—
408C2×D13—24no—
409C2×D13—24no—
410C2×D13—42no—
411C2×D13—416no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C4×C13—24no—
416C4×C13—24no—
417C4×C13—24no—
418C4×C13—42no—
419C4×C13—42no—
420C4×C13—42no—
421C4×C13—42no—
422Dic13—24no—
423Dic13—24no—
424Dic13—42no—
425Dic13—42no—
426Dic13—42no—
427Dic13—42no—
428Dic13C2×C22⋊Q818yes—
429C25—131no—
430C23×C4—131no—
431C23×C4—131no—
432C23×C4—131no—
433C23×C4—138no—
434C23×C4—134no—
435C23×C4—131no—
436C23×C4—131no—
437C23×C4—131no—
438C23×C4—131no—
439C23×C4—264no—
440C23×C4—264no—
441C23×C4C22×D1311yescharacteristic
442C23×C4C22×D1311yescharacteristic
443C23×C4C22×D1311yescharacteristic
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C23×C4C22×D1311yescharacteristic
447C23×C4C22×D1311yescharacteristic
448#125—2632no—
449#117—2632no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—138no—
453C2×C4⋊C4—134no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—134no—
456C2×C4⋊C4—134no—
457C2×C4⋊C4—134no—
458C2×C4⋊C4—134no—
459C2×C4⋊C4—134no—
460C2×C4⋊C4—134no—
461C2×C4⋊C4—134no—
462C2×C4⋊C4—134no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—134no—
466C2×C4⋊C4—134no—
467C2×C4⋊C4—264no—
468C2×C4⋊C4—264no—
469C2×C4⋊C4—264no—
470C2×C4⋊C4—264no—
471C2×C4⋊C4—264no—
472C2×C4⋊C4—264no—
473C2×C4⋊C4—264no—
474C2×C4⋊C4—264no—
475C2×C4⋊C4—264no—
476C2×C4⋊C4—522no—
477C2×C4⋊C4—522no—
478C2×C4⋊C4—522no—
479C2×C4⋊C4—522no—
480C2×C4⋊C4C22×D1314yes—
481C2×C4⋊C4C22×D1314yes—
482C2×C22⋊C4—134no—
483C2×C22⋊C4—134no—
484C2×C22⋊C4—134no—
485C2×C22⋊C4—134no—
486C2×C22⋊C4—134no—
487C2×C22⋊C4—134no—
488C2×C22⋊C4—264no—
489C2×C22⋊C4—264no—
490C2×C22⋊C4—264no—
491C2×C22⋊C4—264no—
492C2×C22⋊C4—522no—
493C2×C22⋊C4—522no—
494C2×C42—24no—
495C2×C42—134no—
496C2×C42—134no—
497C2×C42—134no—
498C2×C42—264no—
499C2×C42—264no—
500C2×C42—264no—
501C2×C42C22×D1314yes—
502#95—134no—
503#95—134no—
504#95—134no—
505#95—134no—
506#95C22×D1314yes—
507#95C22×D1314yes—
508#95C22×D1314yes—
509#95C22×D1314yes—
510C2×C13#244118yescomplemented
511C2×C13C22×C22⋊Q811yescharacteristic
512C2×C13C2×#53311yescharacteristic
513C2×C13C2×#54411yescharacteristic
514C2×C13C2×#54711yescharacteristic
515C2×C13C2×#55011yescharacteristic
516C2×C13C2×#55211yescharacteristic
517C2×C13C2×#55311yescharacteristic
518D13—44no—
519C24—134no—
520C24—132no—
521C24—262no—
522C24—262no—
523C24—262no—
524C24—262no—
525C24—262no—
526C24—262no—
527C24C23×D1311yescharacteristic
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—134no—
547C22×C4—134no—
548C22×C4—134no—
549C22×C4—132no—
550C22×C4—134no—
551C22×C4—134no—
552C22×C4—132no—
553C22×C4—132no—
554C22×C4—1316no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—268no—
560C22×C4—2632no—
561C22×C4—268no—
562C22×C4—262no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—262no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4#612714yes—
579C22×C4D4×D1314yes—
580C22×C4Q8×D1314yes—
581C22×C4C23×D1312yes—
582C22×C4C23×D1312yes—
583C22×C4C23×D1312yes—
584C22×C4C23×D1312yes—
585C22×C4C23×D1312yes—
586C22×C4C23×D1312yes—
587C22×C4C23×D1312yes—
588C4⋊C4—28no—
589C4⋊C4—28no—
590C4⋊C4—1316no—
591C4⋊C4—268no—
592C4⋊C4—268no—
593C4⋊C4—268no—
594C4⋊C4—268no—
595C4⋊C4—268no—
596C4⋊C4—268no—
597C4⋊C4—268no—
598C4⋊C4—268no—
599C4⋊C4—268no—
600C4⋊C4—524no—
601C4⋊C4—524no—
602C4⋊C4—524no—
603C4⋊C4—524no—
604C22⋊C4—268no—
605C22⋊C4—268no—
606C22⋊C4—268no—
607C22⋊C4—268no—
608C22⋊C4—524no—
609C22⋊C4—524no—
610C42—28no—
611C42—268no—
612C42—268no—
613C42—268no—
614C13C2×#244111yescharacteristic, complemented, Sylow
615C23—134no—
616C23—268no—
617C23—268no—
618C23—262no—
619C23—262no—
620C23—262no—
621C23—262no—
622C23—262no—
623C23—262no—
624C23—268no—
625C23—524no—
626C23—524no—
627C23—524no—
628C23—524no—
629C23C2×#612712yes—
630C23C2×D4×D1312yes—
631C23C2×Q8×D1312yes—
632C23#41×D1312yes—
633C23#41×D1312yes—
634C23#8825612yes—
635C23#8825712yes—
636C23C24×D1311yescharacteristic
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—28no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—1316no—
663C2×C4—134no—
664C2×C4—134no—
665C2×C4—134no—
666C2×C4—134no—
667C2×C4—134no—
668C2×C4—2632no—
669C2×C4—268no—
670C2×C4—262no—
671C2×C4—262no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—268no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—524no—
688C2×C4—524no—
689C2×C4—524no—
690C2×C4—524no—
691C2×C4C2×#612714yes—
692C2×C4C2×D4×D1314yes—
693C2×C4C2×Q8×D1314yes—
694C22—264no—
695C22—264no—
696C22—264no—
697C22—5216no—
698C22—522no—
699C22—522no—
700C22—522no—
701C22—522no—
702C22#1171923614yes—
703C22#1171925814yes—
704C22#1171928314yes—
705C22D13×C22⋊Q814yes—
706C22#1171936014yes—
707C22#1171939414yes—
708C22#1171941414yes—
709C22C22×#612711yescharacteristic
710C22C22×D4×D1311yescharacteristic
711C22C22×Q8×D1311yescharacteristic
712C22C2×#41×D1311yescharacteristic
713C22C2×#41×D1311yescharacteristic
714C22C2×#8825611yescharacteristic
715C22C2×#8825711yescharacteristic
716C4—24no—
717C4—24no—
718C4—24no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—138no—
724C4—264no—
725C4—264no—
726C4—522no—
727C4—522no—
728C4—522no—
729C4—522no—
730C2—524no—
731C2#1311854818yesdirect product factor
732C2C2×D13×C22⋊Q811yescharacteristic
733C2C2×#1171928311yescharacteristic
734C2C2×#1171939411yescharacteristic
735C2C2×#1171936011yescharacteristic
736C2C2×#1171925811yescharacteristic
737C2C2×#1171923611yescharacteristic
738C2C2×#1171941411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#387C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#387D13
hypocenterC13C2×#2441
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#88143C2semidirect
3. #13118548C2direct (N × H)
8. C2×#11718589C2semidirect
9. C2×#11718308C2semidirect
10. C2×#11718308C2semidirect
11. C2×#11718308C2semidirect
12. C2×#11718315C2semidirect
13. C2×#11718637C2semidirect
16. C2×C13×#387C2semidirect
45. C2×#88143C22semidirect
48. C13×#387C22semidirect
59. #11718637C22semidirect
60. #11718589C22semidirect
65. #11718315C22semidirect
66. #11718308C22semidirect
67. #11718308C22semidirect
68. #11718308C22semidirect
258. C2×#387D13semidirect
381. #387C2×D13semidirect
510. C2×C13#2441semidirect
614. C13C2×#2441semidirect
731. C2#13118548direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
C22×#881262
#131185482
C2×#117183382
C2×#117186532
C2×#117183372
C2×#117186552
C2×#117185892
C2×#117183082
C2×#117183152
C2×#117186372
C2×#117183282
C2×#117183272
C2×C13×#3872
C2×#244113