Finite Group Databasebeta

← C2×#13119811 #16034253

Subgroups — C2×#13119811 #16034253

Order 3328.

3310 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic, complemented
2C22×#88139C211yesmaximal, characteristic
3C22×#88139C211yesmaximal, characteristic
4C22×#88141C211yesmaximal, characteristic, complemented
5#13119811C2116yesmaximal, direct product factor
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718655C211yesmaximal, characteristic, complemented
9C2×#11718307C211yesmaximal, characteristic, complemented
10C2×#11718618C211yesmaximal, characteristic
11C2×#11718606C211yesmaximal, characteristic, complemented
12C2×#11718612C211yesmaximal, characteristic, complemented
13C2×#11718651C211yesmaximal, characteristic, complemented
14C2×#11718330C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C23×Dic26C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88142—28no—
47C2×#88142C2218yescomplemented
48C2×#88141—28no—
49C2×#88141C2218yescomplemented
50C2×#88139—28no—
51C2×#88139—28no—
52C2×#88139C2218yes—
53C2×#88139C2218yes—
54C13×#396C2218yescomplemented
55C2×C13×#95C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61#11718655C2218yescomplemented
62#11718655C2218yescomplemented
63#11718651C2218yescomplemented
64C4⋊C4×Dic13C2218yescomplemented
65#11718618C2218yes—
66#11718612C2218yescomplemented
67#11718609C2218yescomplemented
68#11718606C2218yescomplemented
69#11718330C2218yescomplemented
70#11718307C2218yescomplemented
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×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C22×Dic26—24no—
91C22×Dic26—24no—
92C22×Dic26—24no—
93C22×Dic26—24no—
94C22×Dic26—24no—
95C22×Dic26D418yes—
96C22×Dic26C2314yes—
97C22×Dic26C2314yes—
98C2×C13×C4⋊C4—24no—
99C2×C13×C4⋊C4—24no—
100C2×C13×C4⋊C4—24no—
101C2×C13×C4⋊C4C2314yes—
102C2×C13×C4⋊C4C2314yes—
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×C22⋊Dic13—24no—
111C2×C22⋊Dic13—24no—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13C2314yes—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×#6103—24no—
117C2×#6103—24no—
118C2×#6103—24no—
119C2×#6103—24no—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×C4⋊Dic13—24no—
129C2×C4⋊Dic13—24no—
130C2×C4⋊Dic13C2314yes—
131C2×C4⋊Dic13C2314yes—
132C2×#6101—24no—
133C2×#6101—24no—
134C2×#6101—24no—
135C2×#6101—24no—
136C2×#6101C2314yes—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×C4×Dic13—24no—
141C2×C4×Dic13—24no—
142C2×C4×Dic13—24no—
143C2×C4×Dic13—24no—
144C2×C4×Dic13D418yes—
145C2×C4×Dic13C2314yes—
146C2×C4×Dic13C2314yes—
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149C2×C4×Dic13C2314yes—
150#88142—232no—
151#88141—232no—
152#88139—232no—
153#88139—232no—
154C13×#95C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160C2×#2545—131nomaximal, Sylow
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13C2412yes—
169C24×C13C2411yescharacteristic
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
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×C13C2×D414yes—
194C22×C4×C13C2×D414yes—
195C22×C4×C13#4114yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C2×C22⋊D13—28no—
203C2×C22⋊D13—28no—
204C2×C22⋊D13—28no—
205C2×C22⋊D13—416no—
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×Dic13C2×D414yes—
222C22×Dic13C2×D414yes—
223C22×Dic13C2×D414yes—
224C22×Dic13C2×D414yes—
225C22×Dic13#4114yes—
226C22×Dic13#4114yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C2×Dic26—232no—
235C2×Dic26—28no—
236C2×Dic26—28no—
237C2×Dic26—28no—
238C2×Dic26—28no—
239C2×Dic26—28no—
240C2×Dic26—416no—
241C2×Dic26C2×D4116yes—
242C13×C4⋊C4—28no—
243C13×C4⋊C4—28no—
244C13×C4⋊C4—28no—
245C13×C22⋊C4—28no—
246C13×C22⋊C4—28no—
247C13×C22⋊C4—28no—
248C22⋊Dic13—28no—
249C22⋊Dic13—28no—
250C22⋊Dic13—28no—
251#6103—28no—
252#6103—28no—
253#6103—28no—
254#6103—28no—
255#6103—28no—
256#6103—28no—
257C4⋊Dic13—28no—
258C4⋊Dic13—28no—
259#6101—28no—
260#6101—28no—
261#6101—28no—
262#6101—28no—
263C4×Dic13—28no—
264C4×Dic13—28no—
265C4×Dic13—28no—
266C4×Dic13—28no—
267C4×Dic13C2×D4116yes—
268C22×C4⋊Q8—131no—
269C22×#124—131no—
270C22×#124—131no—
271C22×C4×Q8—131no—
272#2545—1316no—
273C2×#396—131no—
274C2×#396—131no—
275C2×#396—131no—
276C2×#396D1311yescharacteristic, complemented
277C2×#391—131no—
278C2×#390—131no—
279C2×#388—131no—
280C2×#388—131no—
281C2×#388—131no—
282C2×#388—131no—
283C2×C4×C4⋊C4—131no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—44no—
292C23×C13—44no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13—44no—
297C23×C13—44no—
298C23×C13C22×D412yes—
299C23×C13C22×D412yes—
300C23×C13C2×#4112yes—
301C23×C13C2×#4112yes—
302C23×C13C2×#4112yes—
303C23×C132−1+412yes—
304C23×C132−1+412yes—
305C23×C13C2511yescharacteristic
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—44no—
314C22×D13—44no—
315C22×D13—44no—
316C22×D13—44no—
317C22×D13—44no—
318C22×D13—44no—
319C22×D13—44no—
320C2×C4×C13—28no—
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—44no—
339C2×C4×C13—44no—
340C2×C4×C13—44no—
341C2×C4×C13C22×D414yes—
342C2×C4×C13C22×D414yes—
343C2×C4×C13C2×#4114yes—
344C22⋊D13—416no—
345C2×Dic13—28no—
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—44no—
364C2×Dic13—44no—
365C2×Dic13—44no—
366C2×Dic13#121116yes—
367C2×Dic13C22×D414yes—
368C2×Dic13C22×D414yes—
369C2×Dic13C22×D414yes—
370C2×Dic13C22×D414yes—
371C2×Dic13C2×#4114yes—
372C2×Dic13C2×#4114yes—
373Dic26—232no—
374Dic26—416no—
375C23×Q8—131no—
376C23×Q8—131no—
377C23×D4—131no—
378C2×C4⋊Q8—138no—
379C2×C4⋊Q8—268no—
380C2×#124—138no—
381C2×#124—138no—
382C2×#124—268no—
383C2×#124—268no—
384C2×C4×Q8—138no—
385C2×C4×Q8—268no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4—131no—
391C22×C4⋊C4—131no—
392C22×C4⋊C4C2×D1311yescharacteristic
393C22×C4⋊C4C2×D1311yescharacteristic
394C22×C4⋊C4C2×D1311yescharacteristic
395C22×C22⋊C4—131no—
396C22×C22⋊C4—131no—
397C22×C22⋊C4—131no—
398C22×C22⋊C4—131no—
399C22×C22⋊C4—131no—
400C22×C22⋊C4—131no—
401C22×C22⋊C4—131no—
402C22×C22⋊C4—131no—
403C22×C22⋊C4—131no—
404C22×C22⋊C4C2×D1311yescharacteristic
405C22×C22⋊C4C2×D1311yescharacteristic
406C22×C22⋊C4C2×D1311yescharacteristic
407C22×C42—131no—
408C22×C42—131no—
409C22×C42—131no—
410C22×C42—131no—
411C22×C42—131no—
412#396—138no—
413#396—138no—
414#396—138no—
415#396C2×D1318yescomplemented
416#391—138no—
417#390—138no—
418#388—138no—
419#388—138no—
420#388—138no—
421#388—138no—
422C4×C4⋊C4—138no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95—131no—
427C2×#95—131no—
428C2×#95C2×D1311yescharacteristic
429C22×C13—42no—
430C22×C13—42no—
431C22×C13—42no—
432C22×C13—42no—
433C22×C13—42no—
434C22×C13—42no—
435C22×C13—42no—
436C22×C13—88no—
437C22×C13C2×#12114yes—
438C22×C13#53214yes—
439C22×C13#53614yes—
440C22×C13#54814yes—
441C22×C13#54814yes—
442C22×C13#55614yes—
443C22×C13#55614yes—
444C22×C13C23×D411yescharacteristic
445C22×C13C23×D411yescharacteristic
446C22×C13C22×#4111yescharacteristic
447C22×C13C22×#4111yescharacteristic
448C22×C13C22×#4111yescharacteristic
449C22×C13C2×2−1+411yescharacteristic
450C22×C13C2×2−1+411yescharacteristic
451C2×D13—42no—
452C2×D13—42no—
453C2×D13—42no—
454C2×D13—42no—
455C2×D13—42no—
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—88no—
459C4×C13—24no—
460C4×C13—24no—
461C4×C13—24no—
462C4×C13—42no—
463C4×C13—42no—
464C4×C13—42no—
465Dic13—24no—
466Dic13—24no—
467Dic13—24no—
468Dic13—42no—
469Dic13—42no—
470Dic13—42no—
471Dic13C2×#12118yes—
472C25—131no—
473C25C22×D1311yescharacteristic
474C22×Q8—138no—
475C22×Q8—134no—
476C22×Q8—134no—
477C22×Q8—264no—
478C22×Q8—264no—
479C22×Q8—264no—
480C22×Q8—264no—
481C22×Q8—264no—
482C22×D4—134no—
483C22×D4—264no—
484C22×D4—264no—
485C22×D4—264no—
486C23×C4—131no—
487C23×C4—131no—
488C23×C4—131no—
489C23×C4—131no—
490C23×C4—131no—
491C23×C4—131no—
492C23×C4—131no—
493C23×C4C22×D1311yescharacteristic
494C23×C4C22×D1311yescharacteristic
495C23×C4C22×D1311yescharacteristic
496C23×C4C22×D1311yescharacteristic
497C23×C4C22×D1311yescharacteristic
498C23×C4C22×D1311yescharacteristic
499C4⋊Q8—2632no—
500#124—2632no—
501#124—2632no—
502C4×Q8—2632no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—134no—
507C2×C4⋊C4—134no—
508C2×C4⋊C4—134no—
509C2×C4⋊C4—134no—
510C2×C4⋊C4—134no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—264no—
513C2×C4⋊C4—264no—
514C2×C4⋊C4—264no—
515C2×C4⋊C4—264no—
516C2×C4⋊C4—264no—
517C2×C4⋊C4—264no—
518C2×C4⋊C4C22×D1314yes—
519C2×C4⋊C4C22×D1314yes—
520C2×C4⋊C4C22×D1314yes—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—134no—
525C2×C22⋊C4—134no—
526C2×C22⋊C4—134no—
527C2×C22⋊C4—134no—
528C2×C22⋊C4—134no—
529C2×C22⋊C4—134no—
530C2×C22⋊C4—134no—
531C2×C22⋊C4—134no—
532C2×C22⋊C4—134no—
533C2×C22⋊C4—264no—
534C2×C22⋊C4—264no—
535C2×C22⋊C4—264no—
536C2×C22⋊C4—264no—
537C2×C22⋊C4—264no—
538C2×C22⋊C4—264no—
539C2×C22⋊C4—264no—
540C2×C22⋊C4—264no—
541C2×C22⋊C4—264no—
542C2×C22⋊C4C22×D1314yes—
543C2×C22⋊C4C22×D1314yes—
544C2×C22⋊C4C22×D1314yes—
545C2×C42—138no—
546C2×C42—134no—
547C2×C42—134no—
548C2×C42—134no—
549C2×C42—134no—
550C2×C42—134no—
551C2×C42—264no—
552C2×C42—264no—
553C2×C42—264no—
554C2×C42—264no—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559#95—134no—
560#95C22×D1314yes—
561C2×C13—82no—
562C2×C13#254518yescomplemented
563C2×C13C22×#12111yescharacteristic
564C2×C13C2×#53211yescharacteristic
565C2×C13C2×#53611yescharacteristic
566C2×C13C2×#54811yescharacteristic
567C2×C13C2×#54811yescharacteristic
568C2×C13C2×#55611yescharacteristic
569C2×C13C2×#55611yescharacteristic
570D13—82no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—132no—
579C24—262no—
580C24—262no—
581C24—262no—
582C24—262no—
583C24—262no—
584C24—262no—
585C24—262no—
586C24C23×D1312yes—
587C24C23×D1311yescharacteristic
588C2×Q8—1316no—
589C2×Q8—268no—
590C2×Q8—2632no—
591C2×Q8—268no—
592C2×Q8—268no—
593C2×Q8—268no—
594C2×Q8—268no—
595C2×Q8—5216no—
596C2×D4—268no—
597C2×D4—268no—
598C2×D4—268no—
599C2×D4—5216no—
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—22no—
615C22×C4—134no—
616C22×C4—134no—
617C22×C4—134no—
618C22×C4—132no—
619C22×C4—134no—
620C22×C4—134no—
621C22×C4—134no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—132no—
625C22×C4—132no—
626C22×C4—132no—
627C22×C4—132no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
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×C4D4×D1314yes—
644C22×C4D4×D1314yes—
645C22×C4#612914yes—
646C22×C4C23×D1312yes—
647C22×C4C23×D1312yes—
648C22×C4C23×D1312yes—
649C22×C4C23×D1312yes—
650C22×C4C23×D1312yes—
651C22×C4C23×D1312yes—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—268no—
656C4⋊C4—268no—
657C4⋊C4—268no—
658C4⋊C4—268no—
659C4⋊C4—268no—
660C4⋊C4—268no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—268no—
665C22⋊C4—268no—
666C22⋊C4—268no—
667C22⋊C4—268no—
668C22⋊C4—268no—
669C22⋊C4—268no—
670C22⋊C4—268no—
671C22⋊C4—268no—
672C22⋊C4—268no—
673C42—1316no—
674C42—268no—
675C42—268no—
676C42—268no—
677C42—268no—
678C13C2×#254511yescharacteristic, complemented, Sylow
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—262no—
694C23—262no—
695C23—262no—
696C23—262no—
697C23—262no—
698C23—262no—
699C23—262no—
700C23—524no—
701C23—524no—
702C23—524no—
703C23—524no—
704C23—524no—
705C23—524no—
706C23—524no—
707C23C2×D4×D1312yes—
708C23C2×D4×D1312yes—
709C23C2×#612912yes—
710C23#8825412yes—
711C23#41×D1312yes—
712C23#41×D1312yes—
713C23#8825712yes—
714C23C24×D1311yescharacteristic
715Q8—2632no—
716Q8—5216no—
717D4—5216no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
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—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—1316no—
740C2×C4—134no—
741C2×C4—134no—
742C2×C4—134no—
743C2×C4—134no—
744C2×C4—134no—
745C2×C4—134no—
746C2×C4—268no—
747C2×C4—268no—
748C2×C4—268no—
749C2×C4—262no—
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—524no—
765C2×C4—524no—
766C2×C4—524no—
767C2×C4C2×D4×D1314yes—
768C2×C4C2×D4×D1314yes—
769C2×C4C2×#612914yes—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—88no—
778C22—522no—
779C22—522no—
780C22—522no—
781C22—522no—
782C22—522no—
783C22—522no—
784C22—522no—
785C22—1048no—
786C22#1171930114yes—
787C22#1171930314yes—
788C22D13×#12114yes—
789C22#1171933314yes—
790C22#1171933814yes—
791C22#1171934614yes—
792C22#1171940714yes—
793C22C22×D4×D1311yescharacteristic
794C22C22×D4×D1311yescharacteristic
795C22C22×#612911yescharacteristic
796C22C2×#8825411yescharacteristic
797C22C2×#41×D1311yescharacteristic
798C22C2×#41×D1311yescharacteristic
799C22C2×#8825711yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—138no—
807C4—264no—
808C4—264no—
809C4—264no—
810C4—522no—
811C4—522no—
812C4—522no—
813C2—82no—
814C2—1042no—
815C2#1311981118yesdirect product factor
816C2C2×D13×#12111yescharacteristic
817C2C2×#1171930111yescharacteristic
818C2C2×#1171933311yescharacteristic
819C2C2×#1171930311yescharacteristic
820C2C2×#1171933811yescharacteristic
821C2C2×#1171940711yescharacteristic
822C2C2×#1171934611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#396C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#396D13
hypocenterC13C2×#2545
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#88142C2semidirect
4. C22×#88141C2semidirect
5. #13119811C2direct (N × H)
6. C2×#11718609C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718655C2semidirect
9. C2×#11718307C2semidirect
11. C2×#11718606C2semidirect
12. C2×#11718612C2semidirect
13. C2×#11718651C2semidirect
14. C2×#11718330C2semidirect
15. C2×C4⋊C4×Dic13C2semidirect
16. C2×C13×#396C2semidirect
47. C2×#88142C22semidirect
49. C2×#88141C22semidirect
54. C13×#396C22semidirect
61. #11718655C22semidirect
62. #11718655C22semidirect
63. #11718651C22semidirect
64. C4⋊C4×Dic13C22semidirect
66. #11718612C22semidirect
67. #11718609C22semidirect
68. #11718606C22semidirect
69. #11718330C22semidirect
70. #11718307C22semidirect
276. C2×#396D13semidirect
415. #396C2×D13semidirect
562. C2×C13#2545semidirect
678. C13C2×#2545semidirect
815. C2#13119811direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881422
C22×#881392
C22×#881412
#131198112
C2×#117186092
C2×#117186552
C2×#117183072
C2×#117186182
C2×#117186062
C2×#117186122
C2×#117186512
C2×#117183302
C2×C4⋊C4×Dic132
C2×C13×#3962
C2×#254513