Finite Group Databasebeta

← C2×#13120673 #16029302

Subgroups — C2×#13120673 #16029302

Order 3328.

3218 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88183C211yesmaximal, characteristic, complemented
2#13120673C2116yesmaximal, direct product factor
3C2×#11718645C211yesmaximal, characteristic, complemented
4C2×#11718613C211yesmaximal, characteristic, complemented
5C2×#11718609C211yesmaximal, characteristic, complemented
6C2×#11718655C211yesmaximal, characteristic, complemented
7C2×#11718622C211yesmaximal, characteristic, complemented
8C2×#11718620C211yesmaximal, characteristic, complemented
9C2×#11718883C211yesmaximal, characteristic, complemented
10C2×#11718884C211yesmaximal, characteristic
11C2×#11718601C211yesmaximal, characteristic, complemented
12C2×#11718594C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718871C211yesmaximal, characteristic, complemented
15C2×#11718873C211yesmaximal, characteristic, complemented
16C22×C4×D4×C13C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C22⋊D13C2211yescharacteristic
22C2×C4×D4×C13—28no—
23C2×C4×D4×C13C2218yescomplemented
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C2×#88183—28no—
35C2×#88183C2218yescomplemented
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×C4⋊Dic13C2211yescharacteristic
42C22×C4⋊Dic13C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48#11718884C2218yes—
49#11718883C2218yescomplemented
50#11718874C2218yescomplemented
51#11718873C2218yescomplemented
52#11718871C2218yescomplemented
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61#11718655C2218yescomplemented
62#11718645C2218yescomplemented
63#11718622C2218yescomplemented
64#11718620C2218yescomplemented
65#11718613C2218yescomplemented
66#11718609C2218yescomplemented
67#11718601C2218yescomplemented
68#11718594C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—24no—
75C22×D4×C13C2314yes—
76C23×C4×C13—24no—
77C23×C4×C13—42no—
78C23×C4×C13—42no—
79C23×C4×C13—42no—
80C23×C4×C13—42no—
81C23×C4×C13D418yescomplemented
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2314yes—
88C23×C4×C13C2314yes—
89C22×C22⋊D13—24no—
90C22×C22⋊D13—24no—
91C22×C22⋊D13—42no—
92C22×C22⋊D13—42no—
93C22×C22⋊D13—42no—
94C22×C22⋊D13—42no—
95C22×C22⋊D13C2314yes—
96C22×C22⋊D13C2314yes—
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C4×D4×C13—232no—
105C2×C13×C4⋊C4—24no—
106C2×C13×C4⋊C4C2314yes—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4—24no—
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C42×C13—24no—
112C2×C42×C13C2314yes—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—24no—
115C2×C22⋊Dic13—42no—
116C2×C22⋊Dic13—42no—
117C2×C22⋊Dic13—42no—
118C2×C22⋊Dic13—42no—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125#88183—232no—
126C2×#6103—24no—
127C2×#6103—24no—
128C2×#6103—24no—
129C2×#6103—42no—
130C2×#6103—42no—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×C4⋊Dic13—42no—
137C2×C4⋊Dic13—42no—
138C2×C4⋊Dic13C2314yes—
139C2×C4⋊Dic13C2314yes—
140C2×#6101—24no—
141C2×#6101—24no—
142C2×#6101—24no—
143C2×#6101—42no—
144C2×#6101—42no—
145C2×#6101C2314yes—
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×#6101C2314yes—
149C2×#6101C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2630—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13C2×D414yes—
172C24×C13#4114yes—
173C24×C13C2412yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—22no—
183C23×D13C2412yes—
184C2×D4×C13—232no—
185C2×D4×C13—28no—
186C2×D4×C13—28no—
187C2×D4×C13—28no—
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×C13—28no—
201C22×C4×C13—416no—
202C22×C4×C13—44no—
203C22×C4×C13—44no—
204C22×C4×C13—44no—
205C22×C4×C13—44no—
206C22×C4×C13—416no—
207C22×C4×C13C2×D414yes—
208C22×C4×C13C2×D414yes—
209C22×C4×C13C2×D4116yescomplemented
210C22×C4×C13#4114yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2412yes—
216C2×C22⋊D13—28no—
217C2×C22⋊D13—28no—
218C2×C22⋊D13—44no—
219C2×C22⋊D13—44no—
220C2×C22⋊D13—44no—
221C2×C22⋊D13—44no—
222C2×C22⋊D13—416no—
223C2×C22⋊D13—416no—
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—22no—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C13×C4⋊C4—28no—
253C13×C22⋊C4—28no—
254C13×C22⋊C4—28no—
255C42×C13—28no—
256C22⋊Dic13—28no—
257C22⋊Dic13—28no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260C22⋊Dic13—44no—
261C22⋊Dic13—44no—
262#6103—28no—
263#6103—28no—
264#6103—28no—
265#6103—44no—
266#6103—44no—
267C4⋊Dic13—44no—
268C4⋊Dic13—44no—
269#6101—28no—
270#6101—28no—
271#6101—28no—
272#6101—44no—
273#6101—44no—
274C22×#123—131no—
275C22×C4×D4D1311yescharacteristic, complemented
276#2630—1316no—
277C2×#398—131no—
278C2×#397—131no—
279C2×#396—131no—
280C2×#396—131no—
281C2×#394—131no—
282C2×#394—131no—
283C2×#394—131no—
284C2×#392—131no—
285C2×#388—131no—
286C2×#387—131no—
287C2×#386—131no—
288C2×#385—131no—
289C2×#380—131no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—28no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—44no—
309C23×C13—44no—
310C23×C13—44no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13C22×D414yes—
317C23×C13C22×D412yes—
318C23×C13C2×#4114yes—
319C23×C13C2×#4112yes—
320C23×C13C2×#4112yes—
321C23×C13H(5,𝔽2)12yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C132−1+412yes—
325C23×C13C2511yescharacteristic
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13—44no—
340D4×C13—232no—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
343C2×C4×C13—28no—
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—416no—
357C2×C4×C13—416no—
358C2×C4×C13—44no—
359C2×C4×C13—44no—
360C2×C4×C13C22×D414yes—
361C2×C4×C13C22×D414yes—
362C2×C4×C13C2×#4114yes—
363C22⋊D13—416no—
364C22⋊D13—416no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
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—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13—44no—
389C2×Dic13—44no—
390C2×Dic13—44no—
391C2×Dic13—44no—
392C2×Dic13—44no—
393C23×D4—131no—
394C23×D4—131no—
395C23×D4C2×D1311yescharacteristic
396C24×C4C2×D1311yescharacteristic
397C24×C4C2×D1311yescharacteristic
398C2×#123—138no—
399C2×#123—268no—
400C2×C4×D4—28no—
401C2×C4×D4C2×D1318yescomplemented
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
420C22×C22⋊C4—131no—
421C22×C22⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4C2×D1311yescharacteristic
423C22×C42C2×D1311yescharacteristic
424#398—138no—
425#397—138no—
426#396—138no—
427#396—138no—
428#394—138no—
429#394—138no—
430#394—138no—
431#392—138no—
432#388—138no—
433#387—138no—
434#386—138no—
435#385—138no—
436#380—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—24no—
449C22×C13—24no—
450C22×C13—24no—
451C22×C13—416no—
452C22×C13—416no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13#52514yes—
462C22×C13#53414yes—
463C22×C13#53714yes—
464C22×C13#53814yes—
465C22×C13#53914yes—
466C22×C13#54014yes—
467C22×C13#54214yes—
468C22×C13C23×D411yescharacteristic
469C22×C13C22×#4111yescharacteristic
470C22×C13C22×#4111yescharacteristic
471C22×C13C2×H(5,𝔽2)11yescharacteristic
472C22×C13C2×H(5,𝔽2)11yescharacteristic
473C22×C13C2×H(5,𝔽2)11yescharacteristic
474C22×C13C2×2−1+411yescharacteristic
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—88no—
483C4×C13—24no—
484C4×C13—24no—
485C4×C13—24no—
486C4×C13—42no—
487C4×C13—42no—
488Dic13—42no—
489Dic13—42no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493Dic13—42no—
494Dic13—42no—
495C25—131no—
496C25C22×D1311yescharacteristic
497C25C22×D1311yescharacteristic
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—24no—
501C22×D4—134no—
502C22×D4—134no—
503C22×D4—264no—
504C22×D4—264no—
505C22×D4—522no—
506C22×D4—522no—
507C22×D4—522no—
508C22×D4—522no—
509C22×D4C22×D1314yes—
510C23×C4—24no—
511C23×C4—42no—
512C23×C4—42no—
513C23×C4—42no—
514C23×C4—42no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—131no—
521C23×C4—131no—
522C23×C4C22⋊D1318yescomplemented
523C23×C4C22×D1311yescharacteristic
524C23×C4C22×D1311yescharacteristic
525C23×C4C22×D1311yescharacteristic
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1314yes—
529C23×C4C22×D1314yes—
530#123—2632no—
531C4×D4—232no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—264no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—264no—
543C2×C4⋊C4—522no—
544C2×C4⋊C4—522no—
545C2×C4⋊C4—522no—
546C2×C4⋊C4—522no—
547C2×C4⋊C4C22×D1314yes—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
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—134no—
557C2×C22⋊C4—134no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—264no—
563C2×C22⋊C4—264no—
564C2×C22⋊C4—264no—
565C2×C22⋊C4—264no—
566C2×C22⋊C4—522no—
567C2×C22⋊C4—522no—
568C2×C22⋊C4—522no—
569C2×C22⋊C4—522no—
570C2×C22⋊C4—522no—
571C2×C22⋊C4—522no—
572C2×C22⋊C4C22×D1314yes—
573C2×C22⋊C4C22×D1314yes—
574C2×C42—24no—
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—
584C2×C13—44no—
585C2×C13—44no—
586C2×C13#263018yescomplemented
587C2×C13C2×#52511yescharacteristic
588C2×C13C2×#53411yescharacteristic
589C2×C13C2×#53711yescharacteristic
590C2×C13C2×#53811yescharacteristic
591C2×C13C2×#53911yescharacteristic
592C2×C13C2×#54011yescharacteristic
593C2×C13C2×#54211yescharacteristic
594D13—82no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—132no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24#612714yes—
616C24C2×C22⋊D1314yes—
617C24C23×D1312yes—
618C24C23×D1312yes—
619C24C23×D1311yescharacteristic
620C2×D4—232no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—268no—
625C2×D4—268no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—524no—
629C2×D4—524no—
630C2×D4—5216no—
631C2×D4—5216no—
632C22×C4—22no—
633C22×C4—22no—
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—28no—
645C22×C4—416no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—416no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—132no—
658C22×C4—262no—
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×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4#612714yes—
680C22×C4C2×C22⋊D1314yes—
681C22×C4C2×C22⋊D1314yes—
682C22×C4C2×C22⋊D13116yescomplemented
683C22×C4C23×D1312yes—
684C22×C4C23×D1312yes—
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1312yes—
688C4⋊C4—28no—
689C4⋊C4—268no—
690C4⋊C4—268no—
691C4⋊C4—268no—
692C4⋊C4—524no—
693C4⋊C4—524no—
694C4⋊C4—524no—
695C4⋊C4—524no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—268no—
701C22⋊C4—268no—
702C22⋊C4—268no—
703C22⋊C4—524no—
704C22⋊C4—524no—
705C22⋊C4—524no—
706C22⋊C4—524no—
707C22⋊C4—524no—
708C22⋊C4—524no—
709C42—28no—
710C13C2×#263011yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
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—
751C23C2×#612714yes—
752C23C2×#612712yes—
753C23C2×#612712yes—
754C23#8825112yes—
755C23#8825112yes—
756C23#8825612yes—
757C23#8825712yes—
758C23C22×C22⋊D1314yes—
759C23C22×C22⋊D1312yes—
760C23C24×D1311yescharacteristic
761D4—232no—
762D4—5216no—
763D4—5216no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
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—416no—
780C2×C4—416no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
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—524no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4—524no—
810C2×C4—524no—
811C2×C4C2×#612714yes—
812C2×C4C22×C22⋊D1314yes—
813C2×C4C22×C22⋊D1314yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—416no—
825C22—416no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—522no—
831C22—522no—
832C22—522no—
833C22—522no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—1048no—
838C22#1171926514yes—
839C22#1171926614yes—
840C22#1171926714yes—
841C22#1171926914yes—
842C22#1171949614yes—
843C22#1171950914yes—
844C22#1171953814yes—
845C22C22×#612711yescharacteristic
846C22C22×#612711yescharacteristic
847C22C2×#8825111yescharacteristic
848C22C2×#8825111yescharacteristic
849C22C2×#8825611yescharacteristic
850C22C2×#8825711yescharacteristic
851C22C23×C22⋊D1311yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—522no—
858C4—522no—
859C4—522no—
860C4—522no—
861C4—522no—
862C4—522no—
863C4—522no—
864C2—44no—
865C2—44no—
866C2—1042no—
867C2#1312067318yesdirect product factor
868C2C2×#1171949611yescharacteristic
869C2C2×#1171950911yescharacteristic
870C2C2×#1171953811yescharacteristic
871C2C2×#1171926511yescharacteristic
872C2C2×#1171926911yescharacteristic
873C2C2×#1171926711yescharacteristic
874C2C2×#1171926611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC22×C4×D4D13
hypocenterC13C2×#2630
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88183C2semidirect
2. #13120673C2direct (N × H)
3. C2×#11718645C2semidirect
4. C2×#11718613C2semidirect
5. C2×#11718609C2semidirect
6. C2×#11718655C2semidirect
7. C2×#11718622C2semidirect
8. C2×#11718620C2semidirect
9. C2×#11718883C2semidirect
11. C2×#11718601C2semidirect
12. C2×#11718594C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718871C2semidirect
15. C2×#11718873C2semidirect
16. C22×C4×D4×C13C2semidirect
23. C2×C4×D4×C13C22semidirect
35. C2×#88183C22semidirect
49. #11718883C22semidirect
50. #11718874C22semidirect
51. #11718873C22semidirect
52. #11718871C22semidirect
61. #11718655C22semidirect
62. #11718645C22semidirect
63. #11718622C22semidirect
64. #11718620C22semidirect
65. #11718613C22semidirect
66. #11718609C22semidirect
67. #11718601C22semidirect
68. #11718594C22semidirect
81. C23×C4×C13D4semidirect
209. C22×C4×C13C2×D4semidirect
275. C22×C4×D4D13semidirect
401. C2×C4×D4C2×D13semidirect
522. C23×C4C22⋊D13semidirect
586. C2×C13#2630semidirect
682. C22×C4C2×C22⋊D13semidirect
710. C13C2×#2630semidirect
867. C2#13120673direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881832
#131206732
C2×#117186452
C2×#117186132
C2×#117186092
C2×#117186552
C2×#117186222
C2×#117186202
C2×#117188832
C2×#117188842
C2×#117186012
C2×#117185942
C2×#117188742
C2×#117188712
C2×#117188732
C22×C4×D4×C132
C2×#263013