Finite Group Databasebeta

← C2×#13119744 #16034183

Subgroups — C2×#13119744 #16034183

Order 3328.

3526 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88150C211yesmaximal, characteristic, complemented
2C22×#88132C211yesmaximal, characteristic, complemented
3C22×C4×Dic26C211yesmaximal, characteristic, complemented
4C22×#88135C211yesmaximal, characteristic
5#13119744C2116yesmaximal, direct product factor
6C2×#11718318C211yesmaximal, characteristic, complemented
7C2×#11718645C211yesmaximal, characteristic, complemented
8C2×#11718622C211yesmaximal, characteristic
9C2×#11718620C211yesmaximal, characteristic
10C2×#11718331C211yesmaximal, characteristic, complemented
11C2×#11718601C211yesmaximal, characteristic, complemented
12C2×#11718605C211yesmaximal, characteristic, complemented
13C2×#11718311C211yesmaximal, characteristic, complemented
14C2×#11718328C211yesmaximal, characteristic, complemented
15C2×#11718603C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×Dic26C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88150—28no—
45C2×#88150C2218yescomplemented
46C2×#88135—28no—
47C2×#88135C2218yes—
48C2×#88132—28no—
49C2×#88132C2218yescomplemented
50C2×C4×Dic26—28no—
51C2×C4×Dic26C2218yescomplemented
52C13×#388C2218yescomplemented
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61#11718645C2218yescomplemented
62#11718622C2218yes—
63#11718620C2218yes—
64#11718605C2218yescomplemented
65#11718603C2218yescomplemented
66#11718601C2218yescomplemented
67#11718331C2218yescomplemented
68#11718328C2218yescomplemented
69#11718318C2218yescomplemented
70#11718311C2218yescomplemented
71C25×C13C2311yescharacteristic
72C24×D13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—24no—
80C22×C22⋊D13—24no—
81C22×C22⋊D13—24no—
82C22×C22⋊D13C2314yes—
83C23×Dic13—24no—
84C23×Dic13—24no—
85C23×Dic13—24no—
86C23×Dic13C2314yes—
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C22×C4×D13—24no—
95C22×C4×D13—24no—
96C22×C4×D13—24no—
97C22×C4×D13C2314yes—
98C22×Dic26—24no—
99C22×Dic26—24no—
100C22×Dic26D418yescomplemented
101C22×Dic26C2314yes—
102C2×C13×C4⋊C4—24no—
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C42×C13—24no—
111C2×C42×C13C2314yes—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×#6103—24no—
117C2×#6103—24no—
118C2×#6103—24no—
119C2×#6103—24no—
120C2×#6103—24no—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×C4⋊Dic13—24no—
127C2×C4⋊Dic13—24no—
128C2×C4⋊Dic13C2314yes—
129C2×C4⋊Dic13C2314yes—
130C2×#6101—24no—
131C2×#6101—24no—
132C2×#6101—24no—
133C2×#6101—24no—
134C2×#6101—24no—
135C2×#6101—24no—
136C2×#6101—24no—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×C4×Dic13—24no—
145C2×C4×Dic13D418yes—
146C2×C4×Dic13C2314yes—
147C2×C4×Dic13C2314yes—
148#88150—232no—
149#88135—232no—
150#88132—232no—
151C4×Dic26—232no—
152C13×#95C2314yes—
153C13×#95C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160C2×#2536—131nomaximal, Sylow
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13#4114yes—
168C24×C13C2412yes—
169C24×C13C2411yescharacteristic
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13—22no—
176C23×D13#4114yes—
177C23×D13C2412yes—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
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—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13C2×D414yes—
195C22×C4×C13C2×D414yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C2×C22⋊D13—232no—
203C2×C22⋊D13—28no—
204C2×C22⋊D13—28no—
205C2×C22⋊D13—28no—
206C22×Dic13—22no—
207C22×Dic13—22no—
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—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—28no—
223C22×Dic13—28no—
224C22×Dic13—28no—
225C22×Dic13—416no—
226C22×Dic13C2×D414yes—
227C22×Dic13C2×D414yes—
228C22×Dic13C2×D414yes—
229C22×Dic13C2×D414yes—
230C22×Dic13#4114yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C2×C4×D13—28no—
239C2×C4×D13—28no—
240C2×C4×D13—28no—
241C2×C4×D13—416no—
242C2×Dic26—232no—
243C2×Dic26—28no—
244C2×Dic26—28no—
245C2×Dic26C2×D4116yescomplemented
246C13×C4⋊C4—28no—
247C13×C22⋊C4—28no—
248C13×C22⋊C4—28no—
249C13×C22⋊C4—28no—
250C42×C13—28no—
251C22⋊Dic13—28no—
252C22⋊Dic13—28no—
253#6103—28no—
254#6103—28no—
255#6103—28no—
256#6103—28no—
257#6103—28no—
258C4⋊Dic13—28no—
259C4⋊Dic13—28no—
260#6101—28no—
261#6101—28no—
262#6101—28no—
263#6101—28no—
264#6101—28no—
265#6101—28no—
266#6101—28no—
267C4×Dic13—28no—
268C4×Dic13C2×D4116yes—
269C22×C22⋊Q8—131no—
270C22×C22⋊Q8—131no—
271C22×C4×Q8—131no—
272C22×C4×D4—131no—
273#2536—1316no—
274C2×#398—131no—
275C2×#398—131no—
276C2×#394—131no—
277C2×#394—131no—
278C2×#388—131no—
279C2×#388—131no—
280C2×#388—131no—
281C2×#388D1311yescharacteristic, complemented
282C2×#382—131no—
283C2×#380—131no—
284C2×#380—131no—
285C23×C13—28no—
286C23×C13—28no—
287C23×C13—28no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13—44no—
297C23×C13—44no—
298C23×C13C22×D412yes—
299C23×C13C22×D412yes—
300C23×C13C2×#4114yes—
301C23×C13C2×#4112yes—
302C23×C13C2×#4112yes—
303C23×C13C2×#4112yes—
304C23×C132−1+412yes—
305C23×C132−1+412yes—
306C23×C13C2511yescharacteristic
307C22×D13—28no—
308C22×D13—28no—
309C22×D13—28no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—44no—
317C22×D13—44no—
318C22×D13—44no—
319C22×D13—44no—
320C22×D13C2×#4114yes—
321C2×C4×C13—28no—
322C2×C4×C13—28no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—44no—
340C2×C4×C13—44no—
341C2×C4×C13—44no—
342C2×C4×C13—44no—
343C2×C4×C13C22×D414yes—
344C2×C4×C13C22×D414yes—
345C22⋊D13—232no—
346C2×Dic13—28no—
347C2×Dic13—28no—
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—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—44no—
365C2×Dic13—44no—
366C2×Dic13—44no—
367C2×Dic13—44no—
368C2×Dic13—416no—
369C2×Dic13#121116yes—
370C2×Dic13C22×D414yes—
371C2×Dic13C22×D414yes—
372C2×Dic13C22×D414yes—
373C2×Dic13C22×D414yes—
374C2×Dic13C2×#4114yes—
375C4×D13—416no—
376Dic26—232no—
377C23×Q8—131no—
378C23×D4—131no—
379C24×C4—131no—
380C24×C4—131no—
381C2×C22⋊Q8—138no—
382C2×C22⋊Q8—138no—
383C2×C22⋊Q8—268no—
384C2×C22⋊Q8—268no—
385C2×C4×Q8—138no—
386C2×C4×Q8—268no—
387C2×C4×D4—138no—
388C2×C4×D4—268no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4—131no—
391C22×C4⋊C4—131no—
392C22×C4⋊C4—131no—
393C22×C4⋊C4—131no—
394C22×C4⋊C4—131no—
395C22×C4⋊C4—131no—
396C22×C4⋊C4—131no—
397C22×C4⋊C4—131no—
398C22×C4⋊C4C2×D1311yescharacteristic
399C22×C22⋊C4—131no—
400C22×C22⋊C4—131no—
401C22×C22⋊C4—131no—
402C22×C22⋊C4—131no—
403C22×C22⋊C4—131no—
404C22×C22⋊C4—131no—
405C22×C22⋊C4—131no—
406C22×C22⋊C4C2×D1311yescharacteristic
407C22×C22⋊C4C2×D1311yescharacteristic
408C22×C22⋊C4C2×D1311yescharacteristic
409C22×C42—131no—
410C22×C42—131no—
411C22×C42C2×D1311yescharacteristic
412#398—138no—
413#398—138no—
414#394—138no—
415#394—138no—
416#388—138no—
417#388—138no—
418#388—138no—
419#388C2×D1318yescomplemented
420#382—138no—
421#380—138no—
422#380—138no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95—131no—
427C2×#95—131no—
428C2×#95—131no—
429C2×#95C2×D1311yescharacteristic
430C2×#95C2×D1311yescharacteristic
431C22×C13—24no—
432C22×C13—24no—
433C22×C13—24no—
434C22×C13—42no—
435C22×C13—42no—
436C22×C13—42no—
437C22×C13—42no—
438C22×C13—416no—
439C22×C13C2×#12114yes—
440C22×C13#52514yes—
441C22×C13#53614yes—
442C22×C13#54814yes—
443C22×C13#54814yes—
444C22×C13#55214yes—
445C22×C13#55214yes—
446C22×C13C23×D411yescharacteristic
447C22×C13C23×D411yescharacteristic
448C22×C13C22×#4111yescharacteristic
449C22×C13C22×#4111yescharacteristic
450C22×C13C22×#4111yescharacteristic
451C22×C13C2×2−1+411yescharacteristic
452C22×C13C2×2−1+411yescharacteristic
453C2×D13—24no—
454C2×D13—24no—
455C2×D13—24no—
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—416no—
461C4×C13—24no—
462C4×C13—24no—
463C4×C13—42no—
464C4×C13—42no—
465C4×C13—42no—
466C4×C13—42no—
467Dic13—24no—
468Dic13—24no—
469Dic13—42no—
470Dic13—42no—
471Dic13—42no—
472Dic13—42no—
473Dic13C2×#12118yes—
474C25—131no—
475C25C22×D1311yescharacteristic
476C22×Q8—138no—
477C22×Q8—134no—
478C22×Q8—264no—
479C22×Q8—264no—
480C22×D4—134no—
481C22×D4—264no—
482C22×D4—264no—
483C22×D4—264no—
484C23×C4—131no—
485C23×C4—131no—
486C23×C4—131no—
487C23×C4—134no—
488C23×C4—131no—
489C23×C4—131no—
490C23×C4—131no—
491C23×C4—131no—
492C23×C4—134no—
493C23×C4—264no—
494C23×C4—264no—
495C23×C4—264no—
496C23×C4—264no—
497C23×C4—264no—
498C23×C4—264no—
499C23×C4C22×D1311yescharacteristic
500C23×C4C22×D1311yescharacteristic
501C23×C4C22×D1311yescharacteristic
502C23×C4C22×D1311yescharacteristic
503C23×C4C22×D1311yescharacteristic
504C23×C4C22×D1311yescharacteristic
505C22⋊Q8—2632no—
506C22⋊Q8—2632no—
507C4×Q8—2632no—
508C4×D4—2632no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—134no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—134no—
513C2×C4⋊C4—134no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—134no—
519C2×C4⋊C4—264no—
520C2×C4⋊C4—264no—
521C2×C4⋊C4—264no—
522C2×C4⋊C4—264no—
523C2×C4⋊C4—264no—
524C2×C4⋊C4—264no—
525C2×C4⋊C4—264no—
526C2×C4⋊C4—264no—
527C2×C4⋊C4—264no—
528C2×C4⋊C4C22×D1314yes—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—134no—
533C2×C22⋊C4—134no—
534C2×C22⋊C4—134no—
535C2×C22⋊C4—134no—
536C2×C22⋊C4—134no—
537C2×C22⋊C4—134no—
538C2×C22⋊C4—134no—
539C2×C22⋊C4—264no—
540C2×C22⋊C4—264no—
541C2×C22⋊C4—264no—
542C2×C22⋊C4—264no—
543C2×C22⋊C4—264no—
544C2×C22⋊C4—264no—
545C2×C22⋊C4—264no—
546C2×C22⋊C4C22×D1314yes—
547C2×C22⋊C4C22×D1314yes—
548C2×C22⋊C4C22×D1314yes—
549C2×C42—24no—
550C2×C42—138no—
551C2×C42—134no—
552C2×C42—134no—
553C2×C42—264no—
554C2×C42C22×D1314yes—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559#95—134no—
560#95—134no—
561#95C22×D1314yes—
562#95C22×D1314yes—
563C2×C13—44no—
564C2×C13#253618yescomplemented
565C2×C13C22×#12111yescharacteristic
566C2×C13C2×#52511yescharacteristic
567C2×C13C2×#53611yescharacteristic
568C2×C13C2×#54811yescharacteristic
569C2×C13C2×#54811yescharacteristic
570C2×C13C2×#55211yescharacteristic
571C2×C13C2×#55211yescharacteristic
572D13—44no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—134no—
580C24—132no—
581C24—262no—
582C24—262no—
583C24—262no—
584C24—262no—
585C24—262no—
586C24—262no—
587C24#612714yes—
588C24C23×D1312yes—
589C24C23×D1311yescharacteristic
590C2×Q8—1316no—
591C2×Q8—268no—
592C2×Q8—2632no—
593C2×Q8—268no—
594C2×D4—268no—
595C2×D4—268no—
596C2×D4—2632no—
597C2×D4—268no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—134no—
615C22×C4—134no—
616C22×C4—134no—
617C22×C4—132no—
618C22×C4—134no—
619C22×C4—134no—
620C22×C4—132no—
621C22×C4—132no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—132no—
625C22×C4—132no—
626C22×C4—268no—
627C22×C4—268no—
628C22×C4—268no—
629C22×C4—268no—
630C22×C4—268no—
631C22×C4—268no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—262no—
646C22×C4—262no—
647C22×C4—262no—
648C22×C4—5216no—
649C22×C4—5216no—
650C22×C4D4×D1314yes—
651C22×C4D4×D1314yes—
652C22×C4C23×D1312yes—
653C22×C4C23×D1312yes—
654C22×C4C23×D1312yes—
655C22×C4C23×D1312yes—
656C22×C4C23×D1312yes—
657C22×C4C23×D1312yes—
658C4⋊C4—28no—
659C4⋊C4—268no—
660C4⋊C4—268no—
661C4⋊C4—268no—
662C4⋊C4—268no—
663C4⋊C4—268no—
664C4⋊C4—268no—
665C4⋊C4—268no—
666C4⋊C4—268no—
667C4⋊C4—268no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—268no—
672C22⋊C4—268no—
673C22⋊C4—268no—
674C22⋊C4—268no—
675C22⋊C4—268no—
676C22⋊C4—268no—
677C22⋊C4—268no—
678C42—28no—
679C42—1316no—
680C42—268no—
681C13C2×#253611yescharacteristic, complemented, Sylow
682C23—28no—
683C23—28no—
684C23—28no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—134no—
696C23—268no—
697C23—268no—
698C23—262no—
699C23—262no—
700C23—262no—
701C23—262no—
702C23—262no—
703C23—262no—
704C23—268no—
705C23—524no—
706C23—524no—
707C23—524no—
708C23—524no—
709C23C2×#612714yes—
710C23C2×#612712yes—
711C23C2×D4×D1312yes—
712C23C2×D4×D1312yes—
713C23#41×D1312yes—
714C23#41×D1312yes—
715C23#8825712yes—
716C23#8825712yes—
717C23C24×D1311yescharacteristic
718Q8—2632no—
719D4—2632no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—1316no—
743C2×C4—134no—
744C2×C4—134no—
745C2×C4—134no—
746C2×C4—134no—
747C2×C4—134no—
748C2×C4—268no—
749C2×C4—268no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—5216no—
767C2×C4—5216no—
768C2×C4—524no—
769C2×C4—524no—
770C2×C4—524no—
771C2×C4—524no—
772C2×C4C2×D4×D1314yes—
773C2×C4C2×D4×D1314yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—264no—
783C22—264no—
784C22—264no—
785C22—5216no—
786C22—522no—
787C22—522no—
788C22—522no—
789C22—522no—
790C22#1171923614yes—
791C22#1171925214yes—
792C22#1171925714yes—
793C22D13×#12114yes—
794C22#1171935314yes—
795C22#1171938214yes—
796C22#1171941314yes—
797C22C22×#612711yescharacteristic
798C22C22×D4×D1311yescharacteristic
799C22C22×D4×D1311yescharacteristic
800C22C2×#41×D1311yescharacteristic
801C22C2×#41×D1311yescharacteristic
802C22C2×#8825711yescharacteristic
803C22C2×#8825711yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—138no—
811C4—264no—
812C4—264no—
813C4—522no—
814C4—522no—
815C4—522no—
816C4—522no—
817C2—44no—
818C2—524no—
819C2#1311974418yesdirect product factor
820C2C2×D13×#12111yescharacteristic
821C2C2×#1171925211yescharacteristic
822C2C2×#1171935311yescharacteristic
823C2C2×#1171938211yescharacteristic
824C2C2×#1171925711yescharacteristic
825C2C2×#1171923611yescharacteristic
826C2C2×#1171941311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#388D13
hypocenterC13C2×#2536
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#88150C2semidirect
2. C22×#88132C2semidirect
3. C22×C4×Dic26C2semidirect
5. #13119744C2direct (N × H)
6. C2×#11718318C2semidirect
7. C2×#11718645C2semidirect
10. C2×#11718331C2semidirect
11. C2×#11718601C2semidirect
12. C2×#11718605C2semidirect
13. C2×#11718311C2semidirect
14. C2×#11718328C2semidirect
15. C2×#11718603C2semidirect
16. C2×C13×#388C2semidirect
45. C2×#88150C22semidirect
49. C2×#88132C22semidirect
51. C2×C4×Dic26C22semidirect
52. C13×#388C22semidirect
61. #11718645C22semidirect
64. #11718605C22semidirect
65. #11718603C22semidirect
66. #11718601C22semidirect
67. #11718331C22semidirect
68. #11718328C22semidirect
69. #11718318C22semidirect
70. #11718311C22semidirect
100. C22×Dic26D4semidirect
245. C2×Dic26C2×D4semidirect
281. C2×#388D13semidirect
419. #388C2×D13semidirect
564. C2×C13#2536semidirect
681. C13C2×#2536semidirect
819. C2#13119744direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881502
C22×#881322
C22×C4×Dic262
C22×#881352
#131197442
C2×#117183182
C2×#117186452
C2×#117186222
C2×#117186202
C2×#117183312
C2×#117186012
C2×#117186052
C2×#117183112
C2×#117183282
C2×#117186032
C2×C13×#3882
C2×#253613