Finite Group Databasebeta

← C2×#13119924 #16033022

Subgroups — C2×#13119924 #16033022

Order 3328.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88124C211yesmaximal, characteristic, complemented
2C22×#88150C211yesmaximal, characteristic
3#13119924C2116yesmaximal, direct product factor
4C2×#11718653C211yesmaximal, characteristic
5C2×#11718318C211yesmaximal, characteristic, complemented
6C2×#11718337C211yesmaximal, characteristic
7C2×#11718317C211yesmaximal, characteristic, complemented
8C2×#11718307C211yesmaximal, characteristic, complemented
9C2×#11718634C211yesmaximal, characteristic, complemented
10C2×#11718633C211yesmaximal, characteristic, complemented
11C2×#11718331C211yesmaximal, characteristic
12C2×#11718331C211yesmaximal, characteristic
13C2×#11718329C211yesmaximal, characteristic
14C2×#11718310C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic
16C2×C13×#387C211yesmaximal, characteristic, complemented
17C23×C4×D13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
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×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88150—28no—
43C2×#88150C2218yes—
44C2×#88124—28no—
45C2×#88124C2218yescomplemented
46C13×#387C2218yescomplemented
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718653C2218yes—
58#11718634C2218yescomplemented
59#11718633C2218yescomplemented
60C4×#6103C2218yes—
61#11718337C2218yes—
62#11718331C2218yes—
63#11718331C2218yes—
64#11718329C2218yes—
65#11718318C2218yescomplemented
66#11718317C2218yescomplemented
67#11718310C2218yescomplemented
68#11718307C2218yescomplemented
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×D13—42no—
87C22×C4×D13C2314yes—
88C22×Dic26—24no—
89C22×Dic26—24no—
90C22×Dic26—42no—
91C22×Dic26C2314yes—
92C2×C13×C4⋊C4—24no—
93C2×C13×C4⋊C4—24no—
94C2×C13×C4⋊C4C2314yes—
95C2×C13×C4⋊C4C2314yes—
96C2×C42×C13—24no—
97C2×C42×C13C2314yes—
98C2×#6103—24no—
99C2×#6103—24no—
100C2×#6103—24no—
101C2×#6103—24no—
102C2×#6103—42no—
103C2×#6103Q818yescomplemented
104C2×#6103C2314yes—
105C2×#6103C2314yes—
106C2×#6103C2314yes—
107C2×#6103C2314yes—
108C2×#6103C2314yes—
109C2×#6103C2314yes—
110C2×C4⋊Dic13—24no—
111C2×C4⋊Dic13—24no—
112C2×C4⋊Dic13—24no—
113C2×C4⋊Dic13C2314yes—
114C2×C4⋊Dic13C2314yes—
115C2×C4⋊Dic13C2314yes—
116C2×#6101—24no—
117C2×#6101—24no—
118C2×#6101—24no—
119C2×#6101—24no—
120C2×#6101—24no—
121C2×#6101—24no—
122C2×#6101—42no—
123C2×#6101D418yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×#6101C2314yes—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×C4×Dic13—24no—
133C2×C4×Dic13—42no—
134C2×C4×Dic13—42no—
135C2×C4×Dic13C2314yes—
136C2×C4×Dic13C2314yes—
137C2×C4×Dic13C2314yes—
138#88150—232no—
139#88124—232no—
140C13×#95C2314yes—
141C13×#95C2314yes—
142C13×#95C2314yes—
143C13×#95C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2556—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—28no—
217C2×C4×D13—28no—
218C2×C4×D13—44no—
219C2×C4×D13—416no—
220C2×Dic26—28no—
221C2×Dic26—28no—
222C2×Dic26—44no—
223C2×Dic26—416no—
224C13×C4⋊C4—28no—
225C13×C4⋊C4—28no—
226C42×C13—28no—
227#6103—28no—
228#6103—28no—
229#6103—28no—
230#6103—28no—
231#6103—44no—
232#6103C2×Q8116yescomplemented
233C4⋊Dic13—28no—
234C4⋊Dic13—28no—
235C4⋊Dic13—28no—
236#6101—28no—
237#6101—28no—
238#6101—28no—
239#6101—28no—
240#6101—28no—
241#6101—28no—
242#6101—44no—
243#6101C2×D4116yes—
244C4×Dic13—28no—
245C4×Dic13—44no—
246C4×Dic13—44no—
247C22×#125—131no—
248C22×C22⋊Q8—131no—
249#2556—1316no—
250C2×#399—131no—
251C2×#398—131no—
252C2×#396—131no—
253C2×#395—131no—
254C2×#391—131no—
255C2×#389—131no—
256C2×#389—131no—
257C2×#388—131no—
258C2×#388—131no—
259C2×#387D1311yescharacteristic, complemented
260C2×#385—131no—
261C2×C4×C4⋊C4—131no—
262C2×C4×C22⋊C4—131no—
263C23×C13C22×D412yes—
264C23×C13C22×Q812yes—
265C23×C13C2×#4112yes—
266C23×C13C2×#4112yes—
267C23×C13C2×#4112yes—
268C23×C13H(5,𝔽2)12yes—
269C23×C132−1+412yes—
270C23×C13C2511yescharacteristic
271C22×D13—28no—
272C22×D13—28no—
273C22×D13—28no—
274C22×D13—22no—
275C22×D13—22no—
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—22no—
279C22×D13—22no—
280C22×D13—44no—
281C22×D13—44no—
282C22×D13—44no—
283C22×D13—44no—
284C22×D13C22×Q814yes—
285C2×C4×C13—28no—
286C2×C4×C13—28no—
287C2×C4×C13—28no—
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—22no—
306C2×C4×C13—44no—
307C2×C4×C13—44no—
308C2×C4×C13—44no—
309C2×C4×C13—44no—
310C2×C4×C13C22×D414yes—
311C2×C4×C13C22×Q814yes—
312C2×C4×C13C2×#4114yes—
313C2×Dic13—28no—
314C2×Dic13—28no—
315C2×Dic13—28no—
316C2×Dic13—28no—
317C2×Dic13—28no—
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—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—44no—
335C2×Dic13—44no—
336C2×Dic13C22×D414yes—
337C2×Dic13C22×D414yes—
338C2×Dic13C22×Q814yes—
339C2×Dic13C2×#4114yes—
340C2×Dic13C2×#4114yes—
341C4×D13—416no—
342Dic26—416no—
343C23×Q8—131no—
344C24×C4—131no—
345C2×#125—138no—
346C2×#125—268no—
347C2×C22⋊Q8—138no—
348C2×C22⋊Q8—268no—
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#398—138no—
374#396—138no—
375#395—138no—
376#391—138no—
377#389—138no—
378#389—138no—
379#388—138no—
380#388—138no—
381#387C2×D1318yescomplemented
382#385—138no—
383C4×C4⋊C4—138no—
384C4×C22⋊C4—138no—
385C2×#95—131no—
386C2×#95—131no—
387C2×#95—131no—
388C2×#95—131no—
389C2×#95—131no—
390C2×#95—131no—
391C2×#95C2×D1311yescharacteristic
392C2×#95C2×D1311yescharacteristic
393C2×#95C2×D1311yescharacteristic
394C2×#95C2×D1311yescharacteristic
395C22×C13#53214yes—
396C22×C13#53314yes—
397C22×C13#53914yes—
398C22×C13#54614yes—
399C22×C13D4×Q814yes—
400C22×C13#55214yes—
401C22×C13#55414yes—
402C22×C13C23×D411yescharacteristic
403C22×C13C23×Q811yescharacteristic
404C22×C13C22×#4111yescharacteristic
405C22×C13C22×#4111yescharacteristic
406C22×C13C22×#4111yescharacteristic
407C22×C13C2×H(5,𝔽2)11yescharacteristic
408C22×C13C2×2−1+411yescharacteristic
409C2×D13—24no—
410C2×D13—24no—
411C2×D13—24no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—416no—
417C4×C13—24no—
418C4×C13—24no—
419C4×C13—24no—
420C4×C13—42no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13—42no—
424Dic13—24no—
425Dic13—24no—
426Dic13—24no—
427Dic13—24no—
428Dic13—24no—
429Dic13—42no—
430Dic13—42no—
431C25—131no—
432C22×Q8—134no—
433C22×Q8—264no—
434C22×Q8—264no—
435C22×Q8—522no—
436C23×C4—131no—
437C23×C4—131no—
438C23×C4—131no—
439C23×C4—131no—
440C23×C4—131no—
441C23×C4—131no—
442C23×C4—131no—
443C23×C4—134no—
444C23×C4—264no—
445C23×C4—264no—
446C23×C4—522no—
447C23×C4C22×D1311yescharacteristic
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C23×C4C22×D1311yescharacteristic
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C23×C4C22×D1311yescharacteristic
454#125—2632no—
455C22⋊Q8—2632no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—138no—
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—134no—
468C2×C4⋊C4—134no—
469C2×C4⋊C4—134no—
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—264no—
477C2×C4⋊C4—264no—
478C2×C4⋊C4—264no—
479C2×C4⋊C4—522no—
480C2×C4⋊C4C22×D1314yes—
481C2×C4⋊C4C22×D1314yes—
482C2×C22⋊C4—138no—
483C2×C22⋊C4—134no—
484C2×C22⋊C4—134no—
485C2×C22⋊C4—134no—
486C2×C22⋊C4—134no—
487C2×C22⋊C4—134no—
488C2×C22⋊C4—134no—
489C2×C22⋊C4—264no—
490C2×C22⋊C4—264no—
491C2×C22⋊C4—264no—
492C2×C22⋊C4—264no—
493C2×C22⋊C4—522no—
494C2×C42—24no—
495C2×C42—134no—
496C2×C42—134no—
497C2×C42—134no—
498C2×C42—264no—
499C2×C42—522no—
500C2×C42—522no—
501C2×C42C22×D1314yes—
502#95—134no—
503#95—134no—
504#95—134no—
505#95—134no—
506#95—134no—
507#95—134no—
508#95C22×D1314yes—
509#95C22×D1314yes—
510#95C22×D1314yes—
511#95C22×D1314yes—
512C2×C13#255618yescomplemented
513C2×C13C2×#53211yescharacteristic
514C2×C13C2×#53311yescharacteristic
515C2×C13C2×#53911yescharacteristic
516C2×C13C2×#54611yescharacteristic
517C2×C13C2×D4×Q811yescharacteristic
518C2×C13C2×#55211yescharacteristic
519C2×C13C2×#55411yescharacteristic
520D13—44no—
521C24—134no—
522C24—132no—
523C24—262no—
524C24—262no—
525C24—262no—
526C24—262no—
527C24—262no—
528C24—262no—
529C24C23×D1311yescharacteristic
530C2×Q8—268no—
531C2×Q8—268no—
532C2×Q8—524no—
533C2×Q8—5216no—
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—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—134no—
553C22×C4—134no—
554C22×C4—134no—
555C22×C4—134no—
556C22×C4—134no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—268no—
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—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—268no—
582C22×C4—524no—
583C22×C4—5216no—
584C22×C4#612714yes—
585C22×C4D4×D1314yes—
586C22×C4Q8×D1314yes—
587C22×C4C23×D1312yes—
588C22×C4C23×D1312yes—
589C22×C4C23×D1312yes—
590C22×C4C23×D1312yes—
591C22×C4C23×D1312yes—
592C22×C4C23×D1312yes—
593C22×C4C23×D1312yes—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—1316no—
597C4⋊C4—268no—
598C4⋊C4—268no—
599C4⋊C4—268no—
600C4⋊C4—268no—
601C4⋊C4—268no—
602C4⋊C4—268no—
603C4⋊C4—268no—
604C4⋊C4—268no—
605C4⋊C4—268no—
606C4⋊C4—524no—
607C22⋊C4—1316no—
608C22⋊C4—268no—
609C22⋊C4—268no—
610C22⋊C4—268no—
611C22⋊C4—268no—
612C22⋊C4—524no—
613C42—28no—
614C42—268no—
615C42—524no—
616C42—524no—
617C13C2×#255611yescharacteristic, complemented, Sylow
618C23—134no—
619C23—268no—
620C23—268no—
621C23—262no—
622C23—262no—
623C23—262no—
624C23—262no—
625C23—262no—
626C23—262no—
627C23—268no—
628C23—524no—
629C23—524no—
630C23—524no—
631C23—524no—
632C23C2×#612712yes—
633C23C2×D4×D1312yes—
634C23C2×Q8×D1312yes—
635C23#41×D1312yes—
636C23#41×D1312yes—
637C23#8825612yes—
638C23#8825712yes—
639C23C24×D1311yescharacteristic
640Q8—5216no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
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—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—134no—
667C2×C4—134no—
668C2×C4—134no—
669C2×C4—134no—
670C2×C4—134no—
671C2×C4—268no—
672C2×C4—268no—
673C2×C4—268no—
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—268no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—5216no—
693C2×C4—524no—
694C2×C4—524no—
695C2×C4C2×#612714yes—
696C2×C4C2×D4×D1314yes—
697C2×C4C2×Q8×D1314yes—
698C22—264no—
699C22—264no—
700C22—264no—
701C22—522no—
702C22—522no—
703C22—5216no—
704C22—522no—
705C22—522no—
706C22#1171923614yes—
707C22#1171925314yes—
708C22#1171928414yes—
709C22#1171933714yes—
710C22#1171935914yes—
711C22#1171939314yes—
712C22#1171941214yes—
713C22C22×#612711yescharacteristic
714C22C22×D4×D1311yescharacteristic
715C22C22×Q8×D1311yescharacteristic
716C22C2×#41×D1311yescharacteristic
717C22C2×#41×D1311yescharacteristic
718C22C2×#8825611yescharacteristic
719C22C2×#8825711yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—264no—
728C4—264no—
729C4—264no—
730C4—264no—
731C4—264no—
732C4—522no—
733C4—522no—
734C2—524no—
735C2#1311992418yesdirect product factor
736C2C2×#1171925311yescharacteristic
737C2C2×#1171939311yescharacteristic
738C2C2×#1171941211yescharacteristic
739C2C2×#1171935911yescharacteristic
740C2C2×#1171933711yescharacteristic
741C2C2×#1171923611yescharacteristic
742C2C2×#1171928411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#387C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#387D13
hypocenterC13C2×#2556
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#88124C2semidirect
3. #13119924C2direct (N × H)
5. C2×#11718318C2semidirect
7. C2×#11718317C2semidirect
8. C2×#11718307C2semidirect
9. C2×#11718634C2semidirect
10. C2×#11718633C2semidirect
14. C2×#11718310C2semidirect
16. C2×C13×#387C2semidirect
45. C2×#88124C22semidirect
46. C13×#387C22semidirect
58. #11718634C22semidirect
59. #11718633C22semidirect
65. #11718318C22semidirect
66. #11718317C22semidirect
67. #11718310C22semidirect
68. #11718307C22semidirect
103. C2×#6103Q8semidirect
232. #6103C2×Q8semidirect
259. C2×#387D13semidirect
381. #387C2×D13semidirect
512. C2×C13#2556semidirect
617. C13C2×#2556semidirect
735. C2#13119924direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881242
C22×#881502
#131199242
C2×#117186532
C2×#117183182
C2×#117183372
C2×#117183172
C2×#117183072
C2×#117186342
C2×#117186332
C2×#117183312
C2×#117183292
C2×#117183102
C2×C4×#61032
C2×C13×#3872
C2×#255613