Finite Group Databasebeta

← C2×#13120974 #16029653

Subgroups — C2×#13120974 #16029653

Order 3328.

3002 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88152C211yesmaximal, characteristic, complemented
2C22×#88139C211yesmaximal, characteristic, complemented
3#13120974C2116yesmaximal, direct product factor
4C2×#11718655C211yesmaximal, characteristic, complemented
5C2×#11718640C211yesmaximal, characteristic, complemented
6C2×#11718652C211yesmaximal, characteristic, complemented
7C2×#11718622C211yesmaximal, characteristic, complemented
8C2×#11718620C211yesmaximal, characteristic, complemented
9C2×#11718334C211yesmaximal, characteristic, complemented
10C2×#11718621C211yesmaximal, characteristic
11C2×#11718649C211yesmaximal, characteristic, complemented
12C2×#11718618C211yesmaximal, characteristic, complemented
13C2×#11718612C211yesmaximal, characteristic, complemented
14C2×#11718331C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×D52C2211yescharacteristic
20C23×Dic26C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
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×#6103C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×C4⋊Dic13C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88152—28no—
47C2×#88152C2218yescomplemented
48C2×#88139—28no—
49C2×#88139C2218yescomplemented
50C13×#396C2218yescomplemented
51C2×C13×#95C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718655C2218yescomplemented
58#11718652C2218yescomplemented
59#11718649C2218yescomplemented
60#11718640C2218yescomplemented
61C4⋊C4×Dic13C2218yescomplemented
62#11718622C2218yescomplemented
63#11718621C2218yes—
64#11718620C2218yescomplemented
65#11718618C2218yescomplemented
66#11718612C2218yescomplemented
67#11718334C2218yescomplemented
68#11718331C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C22×C22⋊D13—24no—
79C22×C22⋊D13—24no—
80C22×C22⋊D13—42no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13—42no—
83C22×C22⋊D13—42no—
84C22×C22⋊D13C2314yes—
85C22×C22⋊D13C2314yes—
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C22×D52—24no—
93C22×D52—42no—
94C22×D52—42no—
95C22×D52C2314yes—
96C22×Dic26—24no—
97C22×Dic26—42no—
98C22×Dic26—42no—
99C22×Dic26C2314yes—
100C2×C13×C4⋊C4—24no—
101C2×C13×C4⋊C4—24no—
102C2×C13×C4⋊C4—42no—
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C4⋊C4C2314yes—
105C2×C13×C4⋊C4C2314yes—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4—42no—
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—42no—
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×#6103—42no—
123C2×#6103—42no—
124C2×#6103—42no—
125C2×#6103—42no—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×C4⋊Dic13—24no—
137C2×C4⋊Dic13—24no—
138C2×C4⋊Dic13C2314yes—
139C2×C4⋊Dic13C2314yes—
140C2×#6101—24no—
141C2×#6101—42no—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×C4×Dic13—42no—
145C2×C4×Dic13—42no—
146C2×C4×Dic13D418yescomplemented
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149C2×C4×Dic13C2314yes—
150#88152—232no—
151#88139—232no—
152C13×#95C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2662—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
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—22no—
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—22no—
199C22×C4×C13—22no—
200C22×C4×C13C2×D414yes—
201C22×C4×C13#4114yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C2×C22⋊D13—28no—
209C2×C22⋊D13—28no—
210C2×C22⋊D13—44no—
211C2×C22⋊D13—44no—
212C2×C22⋊D13—44no—
213C2×C22⋊D13—44no—
214C2×C22⋊D13—416no—
215C2×C22⋊D13—416no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
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×Dic13C2×D414yes—
232C22×Dic13C2×D414yes—
233C22×Dic13#4114yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C2×D52—28no—
241C2×D52—44no—
242C2×D52—44no—
243C2×D52—416no—
244C2×Dic26—28no—
245C2×Dic26—44no—
246C2×Dic26—44no—
247C2×Dic26—416no—
248C13×C4⋊C4—28no—
249C13×C4⋊C4—28no—
250C13×C4⋊C4—44no—
251C13×C22⋊C4—28no—
252C13×C22⋊C4—28no—
253C13×C22⋊C4—44no—
254C22⋊Dic13—28no—
255C22⋊Dic13—44no—
256#6103—28no—
257#6103—28no—
258#6103—28no—
259#6103—28no—
260#6103—28no—
261#6103—28no—
262#6103—44no—
263#6103—44no—
264#6103—44no—
265#6103—44no—
266C4⋊Dic13—28no—
267C4⋊Dic13—28no—
268#6101—28no—
269#6101—44no—
270C4×Dic13—44no—
271C4×Dic13—44no—
272C4×Dic13C2×D4116yescomplemented
273C22×#126—131no—
274C22×#124—131no—
275#2662—1316no—
276C2×#396—131no—
277C2×#396D1311yescharacteristic, complemented
278C2×#395—131no—
279C2×#394—131no—
280C2×#394—131no—
281C2×#394—131no—
282C2×#393—131no—
283C2×#392—131no—
284C2×#390—131no—
285C2×#390—131no—
286C2×#388—131no—
287C2×#388—131no—
288C2×C4×C4⋊C4—131no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—44no—
297C23×C13—44no—
298C23×C13—44no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13—44no—
303C23×C13C22×D412yes—
304C23×C13C2×#4112yes—
305C23×C13C2×#4112yes—
306C23×C13H(5,𝔽2)12yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C132−1+412yes—
310C23×C13C2511yescharacteristic
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
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—44no—
326C22×D13—44no—
327C22×D13—44no—
328C22×D13—44no—
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—
339C2×C4×C13—28no—
340C2×C4×C13—28no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
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—44no—
358C2×C4×C13—44no—
359C2×C4×C13—44no—
360C2×C4×C13—44no—
361C2×C4×C13C22×D414yes—
362C2×C4×C13C2×#4114yes—
363C22⋊D13—416no—
364C22⋊D13—416no—
365C2×Dic13—28no—
366C2×Dic13—28no—
367C2×Dic13—28no—
368C2×Dic13—22no—
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—44no—
384C2×Dic13—44no—
385C2×Dic13—44no—
386C2×Dic13C22×D414yes—
387C2×Dic13C22×D414yes—
388C2×Dic13C2×#4114yes—
389D52—416no—
390Dic26—416no—
391C23×Q8—131no—
392C23×D4—131no—
393C23×D4—131no—
394C23×D4—131no—
395C2×#126—138no—
396C2×#126—268no—
397C2×#124—138no—
398C2×#124—268no—
399C22×C4⋊C4—131no—
400C22×C4⋊C4—131no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4C2×D1311yescharacteristic
404C22×C4⋊C4C2×D1311yescharacteristic
405C22×C4⋊C4C2×D1311yescharacteristic
406C22×C22⋊C4—131no—
407C22×C22⋊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⋊C4C2×D1311yescharacteristic
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42—131no—
423C22×C42—131no—
424#396—138no—
425#396C2×D1318yescomplemented
426#395—138no—
427#394—138no—
428#394—138no—
429#394—138no—
430#393—138no—
431#392—138no—
432#390—138no—
433#390—138no—
434#388—138no—
435#388—138no—
436C4×C4⋊C4—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95C2×D1311yescharacteristic
443C22×C13—42no—
444C22×C13—42no—
445C22×C13—42no—
446C22×C13—42no—
447C22×C13—42no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—88no—
451C22×C13#53214yes—
452C22×C13#53514yes—
453C22×C13#53714yes—
454C22×C13#53814yes—
455C22×C13#53814yes—
456C22×C13#54214yes—
457C22×C13#54214yes—
458C22×C13C23×D411yescharacteristic
459C22×C13C22×#4111yescharacteristic
460C22×C13C22×#4111yescharacteristic
461C22×C13C2×H(5,𝔽2)11yescharacteristic
462C22×C13C2×H(5,𝔽2)11yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×2−1+411yescharacteristic
465C2×D13—42no—
466C2×D13—42no—
467C2×D13—42no—
468C2×D13—42no—
469C2×D13—42no—
470C2×D13—42no—
471C2×D13—42no—
472C2×D13—42no—
473C2×D13—42no—
474C2×D13—42no—
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—88no—
480C2×D13—88no—
481C4×C13—24no—
482C4×C13—24no—
483C4×C13—42no—
484C4×C13—42no—
485C4×C13—42no—
486C4×C13—42no—
487Dic13—24no—
488Dic13—24no—
489Dic13—24no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493C25—131no—
494C25—131no—
495C25C22×D1311yescharacteristic
496C22×Q8—134no—
497C22×Q8—264no—
498C22×Q8—522no—
499C22×Q8—522no—
500C22×D4—134no—
501C22×D4—134no—
502C22×D4—134no—
503C22×D4—264no—
504C22×D4—264no—
505C22×D4—264no—
506C22×D4—522no—
507C22×D4—522no—
508C22×D4—522no—
509C22×D4—522no—
510C22×D4—522no—
511C22×D4—522no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4C22×D1311yescharacteristic
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1311yescharacteristic
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524#126—2632no—
525#124—2632no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—42no—
529C2×C4⋊C4—134no—
530C2×C4⋊C4—134no—
531C2×C4⋊C4—134no—
532C2×C4⋊C4—134no—
533C2×C4⋊C4—264no—
534C2×C4⋊C4—264no—
535C2×C4⋊C4—264no—
536C2×C4⋊C4—522no—
537C2×C4⋊C4C22×D1314yes—
538C2×C4⋊C4C22×D1314yes—
539C2×C4⋊C4C22×D1314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—134no—
544C2×C22⋊C4—134no—
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—264no—
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—522no—
563C2×C22⋊C4—522no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4—522no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4C22×D1314yes—
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—138no—
571C2×C42—134no—
572C2×C42—134no—
573C2×C42—134no—
574C2×C42—522no—
575C2×C42—522no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95C22×D1314yes—
582C2×C13—82no—
583C2×C13#266218yescomplemented
584C2×C13C2×#53211yescharacteristic
585C2×C13C2×#53511yescharacteristic
586C2×C13C2×#53711yescharacteristic
587C2×C13C2×#53811yescharacteristic
588C2×C13C2×#53811yescharacteristic
589C2×C13C2×#54211yescharacteristic
590C2×C13C2×#54211yescharacteristic
591D13—82no—
592D13—82no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—132no—
601C24—132no—
602C24—262no—
603C24—262no—
604C24—262no—
605C24—262no—
606C24—262no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24—262no—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×Q8—268no—
619C2×Q8—524no—
620C2×Q8—524no—
621C2×Q8—5216no—
622C2×D4—268no—
623C2×D4—268no—
624C2×D4—268no—
625C2×D4—524no—
626C2×D4—524no—
627C2×D4—5216no—
628C2×D4—524no—
629C2×D4—524no—
630C2×D4—524no—
631C2×D4—524no—
632C2×D4—5216no—
633C2×D4—5216no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
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—134no—
651C22×C4—134no—
652C22×C4—134no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
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×C4D4×D1314yes—
675C22×C4#612914yes—
676C22×C4C23×D1312yes—
677C22×C4C23×D1312yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—44no—
685C4⋊C4—268no—
686C4⋊C4—268no—
687C4⋊C4—268no—
688C4⋊C4—524no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—44no—
692C22⋊C4—268no—
693C22⋊C4—268no—
694C22⋊C4—268no—
695C22⋊C4—268no—
696C22⋊C4—268no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—524no—
700C22⋊C4—524no—
701C22⋊C4—524no—
702C22⋊C4—524no—
703C22⋊C4—524no—
704C42—1316no—
705C42—524no—
706C42—524no—
707C13C2×#266211yescharacteristic, complemented, Sylow
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—262no—
723C23—262no—
724C23—262no—
725C23—262no—
726C23—262no—
727C23—262no—
728C23—262no—
729C23—262no—
730C23—262no—
731C23—262no—
732C23—262no—
733C23—262no—
734C23—262no—
735C23—262no—
736C23—524no—
737C23—524no—
738C23—524no—
739C23—524no—
740C23—524no—
741C23—524no—
742C23—524no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23C2×D4×D1312yes—
751C23C2×#612912yes—
752C23#8825112yes—
753C23#8825412yes—
754C23#41×D1312yes—
755C23#8825612yes—
756C23#8825612yes—
757C23C24×D1311yescharacteristic
758Q8—5216no—
759D4—5216no—
760D4—5216no—
761D4—5216no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
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—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—134no—
785C2×C4—134no—
786C2×C4—134no—
787C2×C4—268no—
788C2×C4—268no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—268no—
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—524no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4C2×D4×D1314yes—
809C2×C4C2×#612914yes—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—88no—
818C22—522no—
819C22—522no—
820C22—522no—
821C22—522no—
822C22—522no—
823C22—522no—
824C22—522no—
825C22—522no—
826C22—522no—
827C22—522no—
828C22—522no—
829C22—522no—
830C22—522no—
831C22—522no—
832C22—1048no—
833C22—1048no—
834C22#1171930114yes—
835C22#1171931214yes—
836C22#1171932214yes—
837C22#1171933414yes—
838C22#1171934514yes—
839C22#1171934814yes—
840C22#1171940914yes—
841C22C22×D4×D1311yescharacteristic
842C22C22×#612911yescharacteristic
843C22C2×#8825111yescharacteristic
844C22C2×#8825411yescharacteristic
845C22C2×#41×D1311yescharacteristic
846C22C2×#8825611yescharacteristic
847C22C2×#8825611yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—264no—
855C4—264no—
856C4—264no—
857C4—522no—
858C4—522no—
859C4—522no—
860C2—82no—
861C2—1042no—
862C2—1042no—
863C2#1312097418yesdirect product factor
864C2C2×#1171930111yescharacteristic
865C2C2×#1171931211yescharacteristic
866C2C2×#1171933411yescharacteristic
867C2C2×#1171932211yescharacteristic
868C2C2×#1171940911yescharacteristic
869C2C2×#1171934511yescharacteristic
870C2C2×#1171934811yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#396C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC2×#396D13
hypocenterC13C2×#2662
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#88152C2semidirect
2. C22×#88139C2semidirect
3. #13120974C2direct (N × H)
4. C2×#11718655C2semidirect
5. C2×#11718640C2semidirect
6. C2×#11718652C2semidirect
7. C2×#11718622C2semidirect
8. C2×#11718620C2semidirect
9. C2×#11718334C2semidirect
11. C2×#11718649C2semidirect
12. C2×#11718618C2semidirect
13. C2×#11718612C2semidirect
14. C2×#11718331C2semidirect
15. C2×C4⋊C4×Dic13C2semidirect
16. C2×C13×#396C2semidirect
47. C2×#88152C22semidirect
49. C2×#88139C22semidirect
50. C13×#396C22semidirect
57. #11718655C22semidirect
58. #11718652C22semidirect
59. #11718649C22semidirect
60. #11718640C22semidirect
61. C4⋊C4×Dic13C22semidirect
62. #11718622C22semidirect
64. #11718620C22semidirect
65. #11718618C22semidirect
66. #11718612C22semidirect
67. #11718334C22semidirect
68. #11718331C22semidirect
146. C2×C4×Dic13D4semidirect
272. C4×Dic13C2×D4semidirect
277. C2×#396D13semidirect
425. #396C2×D13semidirect
583. C2×C13#2662semidirect
707. C13C2×#2662semidirect
863. C2#13120974direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881522
C22×#881392
#131209742
C2×#117186552
C2×#117186402
C2×#117186522
C2×#117186222
C2×#117186202
C2×#117183342
C2×#117186212
C2×#117186492
C2×#117186182
C2×#117186122
C2×#117183312
C2×C4⋊C4×Dic132
C2×C13×#3962
C2×#266213