Finite Group Databasebeta

← C2×#13119929 #16033032

Subgroups — C2×#13119929 #16033032

Order 3328.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88139C211yesmaximal, characteristic, complemented
2C22×#88137C211yesmaximal, characteristic, complemented
3#13119929C2116yesmaximal, direct product factor
4C2×#11718335C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718334C211yesmaximal, characteristic, complemented
7C2×#11718621C211yesmaximal, characteristic
8C2×#11718590C211yesmaximal, characteristic, complemented
9C2×#11718600C211yesmaximal, characteristic, complemented
10C2×#11718601C211yesmaximal, characteristic, complemented
11C2×#11718314C211yesmaximal, characteristic, complemented
12C2×#11718874C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718326C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×D52C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88139—28no—
43C2×#88139C2218yescomplemented
44C2×#88137—28no—
45C2×#88137C2218yescomplemented
46C4×C13×C22⋊C4C2218yescomplemented
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49#11718874C2218yescomplemented
50#11718874C2218yescomplemented
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718621C2218yes—
60#11718614C2218yescomplemented
61#11718601C2218yescomplemented
62#11718600C2218yescomplemented
63C4×#6103C2218yescomplemented
64#11718590C2218yescomplemented
65#11718335C2218yescomplemented
66#11718334C2218yescomplemented
67#11718326C2218yescomplemented
68#11718314C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13—24no—
73C23×C4×C13—42no—
74C23×C4×C13—42no—
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2314yes—
82C22×C22⋊D13—24no—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13—24no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13—42no—
88C22×C22⋊D13C2314yes—
89C22×C22⋊D13C2314yes—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C22×D52—24no—
97C22×D52—24no—
98C22×D52—42no—
99C22×D52C2314yes—
100C22×C4×D13—24no—
101C22×C4×D13—24no—
102C22×C4×D13—42no—
103C22×C4×D13C2314yes—
104C22×Dic26—24no—
105C22×Dic26—24no—
106C22×Dic26—42no—
107C22×Dic26C2314yes—
108C2×C13×C22⋊C4—24no—
109C2×C13×C22⋊C4D418yescomplemented
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C42×C13—42no—
113C2×C42×C13—42no—
114C2×C42×C13C2314yes—
115C2×C42×C13C2314yes—
116C2×C22⋊Dic13—24no—
117C2×C22⋊Dic13—24no—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×#6103—24no—
121C2×#6103—24no—
122C2×#6103—24no—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103—42no—
127C2×#6103—42no—
128C2×#6103—42no—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×C4⋊Dic13—24no—
139C2×C4⋊Dic13—24no—
140C2×C4⋊Dic13C2314yes—
141C2×C4⋊Dic13C2314yes—
142C2×#6101—24no—
143C2×#6101C2314yes—
144C2×C4×Dic13—24no—
145C2×C4×Dic13C2314yes—
146#88139—232no—
147#88137—232no—
148C13×#95C2314yes—
149C13×#95C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2557—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13C2×D414yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13#4114yes—
182C23×D13C2412yes—
183C23×D13C2412yes—
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×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—28no—
199C22×C4×C13—44no—
200C22×C4×C13—44no—
201C22×C4×C13—416no—
202C22×C4×C13C2×D414yes—
203C22×C4×C13C2×D414yes—
204C22×C4×C13#4114yes—
205C22×C4×C13#4114yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C2×C22⋊D13—28no—
213C2×C22⋊D13—28no—
214C2×C22⋊D13—28no—
215C2×C22⋊D13—28no—
216C2×C22⋊D13—44no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—416no—
219C2×C22⋊D13—416no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13#4114yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C2×D52—28no—
245C2×D52—28no—
246C2×D52—44no—
247C2×D52—416no—
248C2×C4×D13—28no—
249C2×C4×D13—28no—
250C2×C4×D13—44no—
251C2×C4×D13—416no—
252C2×Dic26—28no—
253C2×Dic26—28no—
254C2×Dic26—44no—
255C2×Dic26—416no—
256C13×C22⋊C4—28no—
257C13×C22⋊C4C2×D4116yescomplemented
258C42×C13—44no—
259C42×C13—44no—
260C22⋊Dic13—28no—
261C22⋊Dic13—28no—
262#6103—28no—
263#6103—28no—
264#6103—28no—
265#6103—28no—
266#6103—28no—
267#6103—28no—
268#6103—44no—
269#6103—44no—
270#6103—44no—
271C4⋊Dic13—28no—
272C4⋊Dic13—28no—
273#6101—28no—
274C4×Dic13—28no—
275C22×#124—131no—
276C22×#123—131no—
277#2557—1316no—
278C2×#397—131no—
279C2×#397—131no—
280C2×#393—131no—
281C2×#392—131no—
282C2×#391—131no—
283C2×#390—131no—
284C2×#388—131no—
285C2×#387—131no—
286C2×#386—131no—
287C2×#386—131no—
288C2×#386—131no—
289C2×C4×C22⋊C4—131no—
290C2×C4×C22⋊C4D1311yescharacteristic, complemented
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—28no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13—44no—
303C23×C13—44no—
304C23×C13C22×D414yes—
305C23×C13C22×D412yes—
306C23×C13C2×#4112yes—
307C23×C13C2×#4112yes—
308C23×C13C2×#4112yes—
309C23×C13C2×#4112yes—
310C23×C13H(5,𝔽2)12yes—
311C23×C13H(5,𝔽2)12yes—
312C23×C13C2511yescharacteristic
313C22×D13—28no—
314C22×D13—28no—
315C22×D13—28no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—44no—
330C22×D13—44no—
331C22×D13—44no—
332C22×D13—44no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13—44no—
340C22×D13C2×#4114yes—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
343C2×C4×C13—28no—
344C2×C4×C13—28no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—416no—
360C2×C4×C13—44no—
361C2×C4×C13—44no—
362C2×C4×C13C22×D414yes—
363C2×C4×C13C22×D414yes—
364C2×C4×C13C2×#4114yes—
365C2×C4×C13C2×#4114yes—
366C22⋊D13—416no—
367C22⋊D13—416no—
368C2×Dic13—28no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13—44no—
389C2×Dic13—44no—
390C2×Dic13—44no—
391C2×Dic13C2×#4114yes—
392D52—416no—
393C4×D13—416no—
394Dic26—416no—
395C23×Q8—131no—
396C23×D4—131no—
397C23×D4—131no—
398C23×D4—131no—
399C24×C4—131no—
400C24×C4C2×D1311yescharacteristic
401C2×#124—138no—
402C2×#124—268no—
403C2×#123—138no—
404C2×#123—268no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4—131no—
408C22×C22⋊C4—131no—
409C22×C22⋊C4—131no—
410C22×C22⋊C4—131no—
411C22×C22⋊C4—131no—
412C22×C22⋊C4—131no—
413C22×C22⋊C4—131no—
414C22×C22⋊C4—131no—
415C22×C22⋊C4—131no—
416C22×C22⋊C4—131no—
417C22×C22⋊C4—131no—
418C22×C22⋊C4—131no—
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42C2×D1311yescharacteristic
423C22×C42C2×D1311yescharacteristic
424#397—138no—
425#397—138no—
426#393—138no—
427#392—138no—
428#391—138no—
429#390—138no—
430#388—138no—
431#387—138no—
432#386—138no—
433#386—138no—
434#386—138no—
435C4×C22⋊C4—138no—
436C4×C22⋊C4C2×D1318yescomplemented
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95C2×D1311yescharacteristic
446C2×#95C2×D1311yescharacteristic
447C22×C13—24no—
448C22×C13—24no—
449C22×C13—24no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13—42no—
453C22×C13—42no—
454C22×C13—416no—
455C22×C13#52914yes—
456C22×C13#53214yes—
457C22×C13#53814yes—
458C22×C13#54614yes—
459C22×C13#54614yes—
460C22×C13#55114yes—
461C22×C13#55914yes—
462C22×C13C23×D411yescharacteristic
463C22×C13C22×#4111yescharacteristic
464C22×C13C22×#4111yescharacteristic
465C22×C13C22×#4111yescharacteristic
466C22×C13C22×#4111yescharacteristic
467C22×C13C2×H(5,𝔽2)11yescharacteristic
468C22×C13C2×H(5,𝔽2)11yescharacteristic
469C2×D13—24no—
470C2×D13—24no—
471C2×D13—24no—
472C2×D13—42no—
473C2×D13—42no—
474C2×D13—42no—
475C2×D13—42no—
476C2×D13—416no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—42no—
483C2×D13—42no—
484C2×D13—88no—
485C4×C13—24no—
486C4×C13—24no—
487C4×C13—24no—
488C4×C13—24no—
489C4×C13—42no—
490C4×C13—42no—
491Dic13—24no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495Dic13—42no—
496Dic13—42no—
497C25—131no—
498C25—131no—
499C25C22×D1311yescharacteristic
500C22×Q8—134no—
501C22×Q8—264no—
502C22×Q8—264no—
503C22×Q8—522no—
504C22×D4—134no—
505C22×D4—134no—
506C22×D4—134no—
507C22×D4—264no—
508C22×D4—264no—
509C22×D4—264no—
510C22×D4—264no—
511C22×D4—264no—
512C22×D4—264no—
513C22×D4—522no—
514C22×D4—522no—
515C22×D4—522no—
516C23×C4—24no—
517C23×C4—42no—
518C23×C4—42no—
519C23×C4—131no—
520C23×C4—131no—
521C23×C4—131no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—131no—
525C23×C4—134no—
526C23×C4—264no—
527C23×C4—264no—
528C23×C4—522no—
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C23×C4C22×D1311yescharacteristic
533C23×C4C22×D1311yescharacteristic
534C23×C4C22×D1311yescharacteristic
535C23×C4C22×D1314yes—
536#124—2632no—
537#123—2632no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—134no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—264no—
543C2×C4⋊C4—264no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—134no—
546C2×C22⋊C4—134no—
547C2×C22⋊C4—134no—
548C2×C22⋊C4—134no—
549C2×C22⋊C4—134no—
550C2×C22⋊C4—134no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—264no—
557C2×C22⋊C4—264no—
558C2×C22⋊C4—264no—
559C2×C22⋊C4—264no—
560C2×C22⋊C4—264no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4D5218yescomplemented
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42—134no—
573C2×C42—264no—
574C2×C42C22×D1314yes—
575C2×C42C22×D1314yes—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95—134no—
584#95C22×D1314yes—
585#95C22×D1314yes—
586C2×C13—44no—
587C2×C13#255718yescomplemented
588C2×C13C2×#52911yescharacteristic
589C2×C13C2×#53211yescharacteristic
590C2×C13C2×#53811yescharacteristic
591C2×C13C2×#54611yescharacteristic
592C2×C13C2×#54611yescharacteristic
593C2×C13C2×#55111yescharacteristic
594C2×C13C2×#55911yescharacteristic
595D13—44no—
596D13—82no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—134no—
604C24—132no—
605C24—132no—
606C24—262no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24—262no—
616C24—262no—
617C24—262no—
618C24—262no—
619C24C2×D5214yes—
620C24C23×D1312yes—
621C24C23×D1311yescharacteristic
622C2×Q8—268no—
623C2×Q8—268no—
624C2×Q8—524no—
625C2×Q8—5216no—
626C2×D4—268no—
627C2×D4—268no—
628C2×D4—268no—
629C2×D4—268no—
630C2×D4—268no—
631C2×D4—268no—
632C2×D4—524no—
633C2×D4—5216no—
634C2×D4—524no—
635C2×D4—524no—
636C2×D4—5216no—
637C2×D4—5216no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—28no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—416no—
656C22×C4—134no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—132no—
661C22×C4—132no—
662C22×C4—132no—
663C22×C4—268no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4—268no—
682C22×C4—524no—
683C22×C4—5216no—
684C22×C4C2×D5214yes—
685C22×C4C2×D5214yes—
686C22×C4#612714yes—
687C22×C4#612714yes—
688C22×C4C23×D1312yes—
689C22×C4C23×D1312yes—
690C22×C4C23×D1312yes—
691C22×C4C23×D1312yes—
692C22×C4C23×D1312yes—
693C22×C4C23×D1312yes—
694C4⋊C4—268no—
695C4⋊C4—268no—
696C4⋊C4—268no—
697C22⋊C4—28no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—268no—
703C22⋊C4—268no—
704C22⋊C4—268no—
705C22⋊C4—268no—
706C22⋊C4—524no—
707C22⋊C4—524no—
708C22⋊C4—524no—
709C22⋊C4C2×D52116yescomplemented
710C42—44no—
711C42—44no—
712C42—268no—
713C13C2×#255711yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—134no—
728C23—268no—
729C23—268no—
730C23—268no—
731C23—262no—
732C23—262no—
733C23—262no—
734C23—262no—
735C23—262no—
736C23—262no—
737C23—262no—
738C23—262no—
739C23—262no—
740C23—262no—
741C23—262no—
742C23—262no—
743C23—262no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23—524no—
751C23—524no—
752C23—524no—
753C23—524no—
754C23—524no—
755C23C22×D5214yes—
756C23C22×D5212yes—
757C23C2×#612712yes—
758C23C2×#612712yes—
759C23#8825112yes—
760C23#8825112yes—
761C23#41×D1312yes—
762C23#41×D1312yes—
763C23C24×D1311yescharacteristic
764Q8—5216no—
765D4—5216no—
766D4—5216no—
767D4—5216no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—416no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—134no—
790C2×C4—268no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—262no—
806C2×C4—262no—
807C2×C4—262no—
808C2×C4—5216no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4—524no—
812C2×C4—524no—
813C2×C4—524no—
814C2×C4C22×D5214yes—
815C2×C4C22×D5214yes—
816C2×C4C2×#612714yes—
817C2×C4C2×#612714yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—416no—
824C22—42no—
825C22—42no—
826C22—264no—
827C22—264no—
828C22—264no—
829C22—522no—
830C22—522no—
831C22—5216no—
832C22—522no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—522no—
838C22—522no—
839C22—522no—
840C22—522no—
841C22—1048no—
842C22#1171918214yes—
843C22#1171919914yes—
844C22#1171923314yes—
845C22#1171925914yes—
846C22#1171925914yes—
847C22#1171926114yes—
848C22#1171926414yes—
849C22C23×D5211yescharacteristic
850C22C22×#612711yescharacteristic
851C22C22×#612711yescharacteristic
852C22C2×#8825111yescharacteristic
853C22C2×#8825111yescharacteristic
854C22C2×#41×D1311yescharacteristic
855C22C2×#41×D1311yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—42no—
861C4—42no—
862C4—264no—
863C4—522no—
864C4—522no—
865C4—522no—
866C4—522no—
867C4—522no—
868C2—44no—
869C2—524no—
870C2—1042no—
871C2#1311992918yesdirect product factor
872C2C2×#1171923311yescharacteristic
873C2C2×#1171918211yescharacteristic
874C2C2×#1171919911yescharacteristic
875C2C2×#1171925911yescharacteristic
876C2C2×#1171925911yescharacteristic
877C2C2×#1171926111yescharacteristic
878C2C2×#1171926411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×#2557
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#88139C2semidirect
2. C22×#88137C2semidirect
3. #13119929C2direct (N × H)
4. C2×#11718335C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718334C2semidirect
8. C2×#11718590C2semidirect
9. C2×#11718600C2semidirect
10. C2×#11718601C2semidirect
11. C2×#11718314C2semidirect
12. C2×#11718874C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718326C2semidirect
15. C2×C4×#6103C2semidirect
16. C2×C4×C13×C22⋊C4C2semidirect
43. C2×#88139C22semidirect
45. C2×#88137C22semidirect
46. C4×C13×C22⋊C4C22semidirect
49. #11718874C22semidirect
50. #11718874C22semidirect
60. #11718614C22semidirect
61. #11718601C22semidirect
62. #11718600C22semidirect
63. C4×#6103C22semidirect
64. #11718590C22semidirect
65. #11718335C22semidirect
66. #11718334C22semidirect
67. #11718326C22semidirect
68. #11718314C22semidirect
109. C2×C13×C22⋊C4D4semidirect
257. C13×C22⋊C4C2×D4semidirect
290. C2×C4×C22⋊C4D13semidirect
436. C4×C22⋊C4C2×D13semidirect
567. C2×C22⋊C4D52semidirect
587. C2×C13#2557semidirect
709. C22⋊C4C2×D52semidirect
713. C13C2×#2557semidirect
871. C2#13119929direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881392
C22×#881372
#131199292
C2×#117183352
C2×#117186142
C2×#117183342
C2×#117186212
C2×#117185902
C2×#117186002
C2×#117186012
C2×#117183142
C2×#117188742
C2×#117183262
C2×C4×#61032
C2×C4×C13×C22⋊C42
C2×#255713