Finite Group Databasebeta

← C2×#13120646 #16029263

Subgroups — C2×#13120646 #16029263

Order 3328.

4142 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88150C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D13C211yesmaximal, characteristic
3#13120646C2116yesmaximal, direct product factor
4C2×#11718610C211yesmaximal, characteristic, complemented
5C2×#11718653C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718655C211yesmaximal, characteristic, complemented
9C2×#11718334C211yesmaximal, characteristic, complemented
10C2×#11718608C211yesmaximal, characteristic, complemented
11C2×#11718329C211yesmaximal, characteristic, complemented
12C2×#11718650C211yesmaximal, characteristic, complemented
13C2×#11718648C211yesmaximal, characteristic, complemented
14C2×#11718616C211yesmaximal, characteristic
15C2×#11718616C211yesmaximal, characteristic
16C2×C13×#396C211yesmaximal, characteristic, complemented
17C25×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×Dic26C2211yescharacteristic, complemented
21C22×C13×C4⋊C4C2211yescharacteristic, complemented
22C22×C13×C4⋊C4C2211yescharacteristic, complemented
23C22×C13×C4⋊C4C2211yescharacteristic, complemented
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×C4⋊Dic13C2211yescharacteristic, complemented
41C22×C4⋊Dic13C2211yescharacteristic, complemented
42C22×#6101C2211yescharacteristic, complemented
43C22×#6101C2211yescharacteristic, complemented
44C22×#6101C2211yescharacteristic, complemented
45C22×#6101C2211yescharacteristic, complemented
46C2×#88150—28no—
47C2×#88150C2218yescomplemented
48C2×C22⋊C4×D13—28no—
49C2×C22⋊C4×D13C2218yes—
50C13×#396C2218yescomplemented
51C2×C13×#95C2211yescharacteristic, complemented
52C2×#88071C2211yescharacteristic, complemented
53C2×#88071C2211yescharacteristic, complemented
54C2×#88071C2211yescharacteristic, complemented
55C2×#88071C2211yescharacteristic, complemented
56C2×#88071C2211yescharacteristic, complemented
57#11718655C2218yescomplemented
58#11718655C2218yescomplemented
59#11718653C2218yescomplemented
60#11718650C2218yescomplemented
61#11718648C2218yescomplemented
62#11718616C2218yes—
63#11718616C2218yes—
64#11718610C2218yescomplemented
65#11718609C2218yescomplemented
66#11718608C2218yescomplemented
67#11718334C2218yescomplemented
68#11718329C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13—24no—
71C24×D13—24no—
72C24×D13—42no—
73C24×D13—42no—
74C24×D13—42no—
75C24×D13—42no—
76C24×D13Q818yescomplemented
77C24×D13C2311yescharacteristic
78C24×D13C2311yescharacteristic
79C24×D13C2314yes—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C22×C4×D13—24no—
93C22×C4×D13—42no—
94C22×C4×D13—42no—
95C22×C4×D13—42no—
96C22×C4×D13—42no—
97C22×C4×D13D418yes—
98C22×C4×D13C2314yes—
99C22×C4×D13C2314yes—
100C22×Dic26—24no—
101C22×Dic26—42no—
102C22×Dic26—42no—
103C22×Dic26C2314yescomplemented
104C2×C13×C4⋊C4—24no—
105C2×C13×C4⋊C4—42no—
106C2×C13×C4⋊C4—42no—
107C2×C13×C4⋊C4C2314yescomplemented
108C2×C13×C4⋊C4C2314yescomplemented
109C2×C13×C4⋊C4C2314yescomplemented
110C2×C13×C22⋊C4—24no—
111C2×C13×C22⋊C4—42no—
112C2×C13×C22⋊C4—42no—
113C2×C13×C22⋊C4C2314yes—
114C2×C13×C22⋊C4C2314yes—
115C2×C13×C22⋊C4C2314yes—
116C2×C22⋊Dic13—24no—
117C2×C22⋊Dic13—42no—
118C2×C22⋊Dic13—42no—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C2×#6103—24no—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103—24no—
127C2×#6103—24no—
128C2×#6103—42no—
129C2×#6103—42no—
130C2×#6103—42no—
131C2×#6103—42no—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×C4⋊Dic13—42no—
143C2×C4⋊Dic13—42no—
144C2×C4⋊Dic13C2314yescomplemented
145C2×C4⋊Dic13C2314yescomplemented
146C2×#6101—24no—
147C2×#6101—24no—
148C2×#6101—42no—
149C2×#6101—42no—
150C2×#6101C2314yescomplemented
151C2×#6101C2314yescomplemented
152C2×#6101C2314yescomplemented
153C2×#6101C2314yescomplemented
154#88150—232no—
155C22⋊C4×D13—232no—
156C13×#95C2314yescomplemented
157#88071C2314yescomplemented
158#88071C2314yescomplemented
159#88071C2314yescomplemented
160#88071C2314yescomplemented
161#88071C2314yescomplemented
162C2×#2626—131nomaximal, Sylow
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13C2×Q814yes—
170C24×C13C2412yes—
171C24×C13C2411yescharacteristic
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×D13—232no—
183C23×D13—28no—
184C23×D13—28no—
185C23×D13—416no—
186C23×D13—416no—
187C23×D13—44no—
188C23×D13—44no—
189C23×D13—44no—
190C23×D13—44no—
191C23×D13—416no—
192C23×D13—416no—
193C23×D13—416no—
194C23×D13—416no—
195C23×D13C2×D414yes—
196C23×D13C2×Q814yes—
197C23×D13C2×Q814yes—
198C23×D13C2×Q8116yescomplemented
199C23×D13#4114yes—
200C23×D13C2412yes—
201C23×D13C2412yes—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—22no—
209C22×C4×C13—22no—
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—22no—
214C22×C4×C13—22no—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13C2×D414yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2412yes—
224C22×C4×C13C2412yes—
225C22×C4×C13C2412yes—
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×Dic13C2×D414yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C2×C4×D13—28no—
251C2×C4×D13—416no—
252C2×C4×D13—44no—
253C2×C4×D13—44no—
254C2×C4×D13—44no—
255C2×C4×D13—44no—
256C2×C4×D13—416no—
257C2×C4×D13C2×D4116yes—
258C2×Dic26—28no—
259C2×Dic26—44no—
260C2×Dic26—44no—
261C2×Dic26—416no—
262C13×C4⋊C4—28no—
263C13×C4⋊C4—44no—
264C13×C4⋊C4—44no—
265C13×C22⋊C4—28no—
266C13×C22⋊C4—44no—
267C13×C22⋊C4—44no—
268C22⋊Dic13—28no—
269C22⋊Dic13—44no—
270C22⋊Dic13—44no—
271#6103—28no—
272#6103—28no—
273#6103—28no—
274#6103—28no—
275#6103—28no—
276#6103—28no—
277#6103—44no—
278#6103—44no—
279#6103—44no—
280#6103—44no—
281C4⋊Dic13—44no—
282C4⋊Dic13—44no—
283#6101—28no—
284#6101—28no—
285#6101—44no—
286#6101—44no—
287C22×C22⋊Q8—131no—
288C23×C22⋊C4—131no—
289#2626—1316no—
290C2×#399—131no—
291C2×#399—131no—
292C2×#396—131no—
293C2×#396—131no—
294C2×#396—131no—
295C2×#396D1311yescharacteristic, complemented
296C2×#393—131no—
297C2×#393—131no—
298C2×#385—131no—
299C2×#385—131no—
300C2×#380—131no—
301C2×#379—131no—
302C2×#379—131no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13C22×D412yes—
317C23×C13C22×Q814yes—
318C23×C13C22×Q812yes—
319C23×C13C2×#4112yes—
320C23×C13H(5,𝔽2)12yes—
321C23×C13H(5,𝔽2)12yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C13C2511yescharacteristic
325C22×D13—28no—
326C22×D13—28no—
327C22×D13—28no—
328C22×D13—28no—
329C22×D13—28no—
330C22×D13—28no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—28no—
336C22×D13—28no—
337C22×D13—28no—
338C22×D13—22no—
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—232no—
345C22×D13—416no—
346C22×D13—416no—
347C22×D13—4128no—
348C22×D13—416no—
349C22×D13—416no—
350C22×D13—416no—
351C22×D13—416no—
352C22×D13—44no—
353C22×D13—44no—
354C22×D13—44no—
355C22×D13—44no—
356C22×D13C22⋊Q8116yes—
357C22×D13C22×D414yes—
358C22×D13C22×Q814yes—
359C22×D13C22×Q814yes—
360C22×D13C2×#4114yes—
361C2×C4×C13—28no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—44no—
380C2×C4×C13—44no—
381C2×C4×C13—44no—
382C2×C4×C13—44no—
383C2×C4×C13—44no—
384C2×C4×C13C22×D414yes—
385C2×Dic13—28no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—44no—
404C2×Dic13—44no—
405C2×Dic13—44no—
406C2×Dic13—44no—
407C2×Dic13—44no—
408C2×Dic13C22×D414yes—
409C4×D13—416no—
410C4×D13—416no—
411Dic26—416no—
412C26—131no—
413C23×Q8—131no—
414C24×C4—131no—
415C24×C4—131no—
416C2×C22⋊Q8—138no—
417C2×C22⋊Q8—268no—
418C22×C4⋊C4—131no—
419C22×C4⋊C4—131no—
420C22×C4⋊C4—131no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4—131no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4C2×D1311yescharacteristic, complemented
425C22×C4⋊C4C2×D1311yescharacteristic, complemented
426C22×C4⋊C4C2×D1311yescharacteristic, complemented
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4—138no—
441C22×C22⋊C4—268no—
442C22×C22⋊C4C2×D1311yescharacteristic
443C22×C22⋊C4C2×D1311yescharacteristic
444C22×C22⋊C4C2×D1311yescharacteristic
445#399—138no—
446#399—138no—
447#396—138no—
448#396—138no—
449#396—138no—
450#396C2×D1318yescomplemented
451#393—138no—
452#393—138no—
453#385—138no—
454#385—138no—
455#380—138no—
456#379—138no—
457#379—138no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95C2×D1311yescharacteristic, complemented
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—416no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13C2×C22⋊Q814yes—
473C22×C13#53414yes—
474C22×C13#53514yes—
475C22×C13#53814yes—
476C22×C13#53814yes—
477C22×C13#54314yes—
478C22×C13#54314yes—
479C22×C13C23×D411yescharacteristic
480C22×C13C23×Q811yescharacteristic
481C22×C13C22×#4111yescharacteristic
482C22×C13C2×H(5,𝔽2)11yescharacteristic
483C22×C13C2×H(5,𝔽2)11yescharacteristic
484C22×C13C2×H(5,𝔽2)11yescharacteristic
485C22×C13C2×H(5,𝔽2)11yescharacteristic
486C2×D13—232no—
487C2×D13—24no—
488C2×D13—24no—
489C2×D13—24no—
490C2×D13—24no—
491C2×D13—24no—
492C2×D13—24no—
493C2×D13—24no—
494C2×D13—24no—
495C2×D13—24no—
496C2×D13—464no—
497C2×D13—416no—
498C2×D13—42no—
499C2×D13—42no—
500C2×D13—42no—
501C2×D13—42no—
502C2×D13C2×C22⋊Q818yes—
503C4×C13—24no—
504C4×C13—42no—
505C4×C13—42no—
506C4×C13—42no—
507C4×C13—42no—
508C4×C13—42no—
509Dic13—24no—
510Dic13—42no—
511Dic13—42no—
512Dic13—42no—
513Dic13—42no—
514Dic13—42no—
515C25—131no—
516C25—131no—
517C25—138no—
518C25—134no—
519C25—264no—
520C25—264no—
521C25—522no—
522C25—522no—
523C25—522no—
524C25—522no—
525C25C22×D1311yescharacteristic
526C22×Q8—134no—
527C22×Q8—264no—
528C22×Q8—522no—
529C22×Q8—522no—
530C23×C4—131no—
531C23×C4—138no—
532C23×C4—134no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—134no—
539C23×C4—264no—
540C23×C4—522no—
541C23×C4—522no—
542C23×C4—522no—
543C23×C4—522no—
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1311yescharacteristic
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C22⋊Q8—2632no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—42no—
553C2×C4⋊C4—42no—
554C2×C4⋊C4—134no—
555C2×C4⋊C4—134no—
556C2×C4⋊C4—134no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—134no—
559C2×C4⋊C4—134no—
560C2×C4⋊C4—264no—
561C2×C4⋊C4—264no—
562C2×C4⋊C4—522no—
563C2×C4⋊C4—522no—
564C2×C4⋊C4—522no—
565C2×C4⋊C4—522no—
566C2×C4⋊C4C22×D1314yescomplemented
567C2×C4⋊C4C22×D1314yescomplemented
568C2×C4⋊C4C22×D1314yescomplemented
569C2×C22⋊C4—24no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—134no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—134no—
583C2×C22⋊C4—134no—
584C2×C22⋊C4—134no—
585C2×C22⋊C4—2632no—
586C2×C22⋊C4—264no—
587C2×C22⋊C4—264no—
588C2×C22⋊C4—264no—
589C2×C22⋊C4—264no—
590C2×C22⋊C4—264no—
591C2×C22⋊C4—264no—
592C2×C22⋊C4—264no—
593C2×C22⋊C4—522no—
594C2×C22⋊C4—522no—
595C2×C22⋊C4—522no—
596C2×C22⋊C4—522no—
597C2×C22⋊C4—522no—
598C2×C22⋊C4—522no—
599C2×C22⋊C4C22×D1314yes—
600C2×C22⋊C4C22×D1314yes—
601C2×C22⋊C4C22×D1314yes—
602#95—134no—
603#95—134no—
604#95—134no—
605#95—134no—
606#95—134no—
607#95C22×D1314yescomplemented
608C2×C13—44no—
609C2×C13#262618yescomplemented
610C2×C13C22×C22⋊Q811yescharacteristic
611C2×C13C2×#53411yescharacteristic
612C2×C13C2×#53511yescharacteristic
613C2×C13C2×#53811yescharacteristic
614C2×C13C2×#53811yescharacteristic
615C2×C13C2×#54311yescharacteristic
616C2×C13C2×#54311yescharacteristic
617D13—28no—
618D13—44no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—134no—
626C24—134no—
627C24—134no—
628C24—132no—
629C24—134no—
630C24—132no—
631C24—1316no—
632C24—268no—
633C24—2632no—
634C24—268no—
635C24—262no—
636C24—262no—
637C24—262no—
638C24—262no—
639C24—262no—
640C24—262no—
641C24—262no—
642C24—262no—
643C24—262no—
644C24—262no—
645C24—5216no—
646C24—5216no—
647C24—524no—
648C24—524no—
649C24—524no—
650C24—524no—
651C24—5216no—
652C24—5216no—
653C24—5216no—
654C24—5216no—
655C24Q8×D1314yes—
656C24C23×D1312yes—
657C24C23×D1311yescharacteristic
658C2×Q8—268no—
659C2×Q8—524no—
660C2×Q8—524no—
661C2×Q8—5216no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—134no—
680C22×C4—132no—
681C22×C4—1316no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—268no—
688C22×C4—262no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—262no—
693C22×C4—262no—
694C22×C4—262no—
695C22×C4—262no—
696C22×C4—262no—
697C22×C4—262no—
698C22×C4—262no—
699C22×C4—262no—
700C22×C4—262no—
701C22×C4—262no—
702C22×C4—262no—
703C22×C4—262no—
704C22×C4—262no—
705C22×C4—5216no—
706C22×C4—524no—
707C22×C4—524no—
708C22×C4—524no—
709C22×C4—524no—
710C22×C4—5216no—
711C22×C4D4×D1314yes—
712C22×C4C23×D1312yes—
713C22×C4C23×D1312yes—
714C22×C4C23×D1312yes—
715C22×C4C23×D1312yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C4⋊C4—28no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—268no—
722C4⋊C4—268no—
723C4⋊C4—524no—
724C4⋊C4—524no—
725C4⋊C4—524no—
726C4⋊C4—524no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—268no—
734C22⋊C4—268no—
735C22⋊C4—268no—
736C22⋊C4—268no—
737C22⋊C4—524no—
738C22⋊C4—524no—
739C22⋊C4—524no—
740C22⋊C4—524no—
741C22⋊C4—524no—
742C22⋊C4—524no—
743C13C2×#262611yescharacteristic, complemented, Sylow
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—1316no—
758C23—134no—
759C23—134no—
760C23—134no—
761C23—134no—
762C23—2632no—
763C23—268no—
764C23—268no—
765C23—268no—
766C23—268no—
767C23—268no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—268no—
773C23—268no—
774C23—268no—
775C23—268no—
776C23—262no—
777C23—262no—
778C23—262no—
779C23—262no—
780C23—262no—
781C23—262no—
782C23—5216no—
783C23—5216no—
784C23—52128no—
785C23—5216no—
786C23—5216no—
787C23—5216no—
788C23—5216no—
789C23—524no—
790C23—524no—
791C23—524no—
792C23—524no—
793C23C2×D4×D1312yes—
794C23#8825112yes—
795C23#8825112yes—
796C23C2×Q8×D1314yes—
797C23C2×Q8×D1312yes—
798C23#41×D1312yes—
799C23#8825612yes—
800C23#8825612yes—
801C23C24×D1311yescharacteristic
802Q8—5216no—
803C2×C4—28no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—134no—
827C2×C4—268no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—262no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—5216no—
846C2×C4—5216no—
847C2×C4—524no—
848C2×C4—524no—
849C2×C4—524no—
850C2×C4—524no—
851C2×C4—524no—
852C2×C4C2×D4×D1314yes—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—416no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—138no—
862C22—264no—
863C22—264no—
864C22—2632no—
865C22—264no—
866C22—264no—
867C22—264no—
868C22—264no—
869C22—264no—
870C22—264no—
871C22—264no—
872C22—5264no—
873C22—5216no—
874C22—522no—
875C22—522no—
876C22—522no—
877C22—522no—
878C22#1171931014yes—
879C22#1171931214yes—
880C22#1171931814yes—
881C22D13×C22⋊Q814yes—
882C22#1171933914yes—
883C22#1171933914yes—
884C22#1171940914yes—
885C22C22×D4×D1311yescharacteristic
886C22C2×#8825111yescharacteristic
887C22C2×#8825111yescharacteristic
888C22C22×Q8×D1311yescharacteristic
889C22C2×#41×D1311yescharacteristic
890C22C2×#8825611yescharacteristic
891C22C2×#8825611yescharacteristic
892C4—24no—
893C4—42no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—264no—
899C4—522no—
900C4—522no—
901C4—522no—
902C4—522no—
903C4—522no—
904C2—44no—
905C2—268no—
906C2—524no—
907C2#1312064618yesdirect product factor
908C2C2×D13×C22⋊Q811yescharacteristic
909C2C2×#1171931011yescharacteristic
910C2C2×#1171931211yescharacteristic
911C2C2×#1171931811yescharacteristic
912C2C2×#1171940911yescharacteristic
913C2C2×#1171933911yescharacteristic
914C2C2×#1171933911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#396C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#396D13
hypocenterC13C2×#2626
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#88150C2semidirect
3. #13120646C2direct (N × H)
4. C2×#11718610C2semidirect
5. C2×#11718653C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718655C2semidirect
9. C2×#11718334C2semidirect
10. C2×#11718608C2semidirect
11. C2×#11718329C2semidirect
12. C2×#11718650C2semidirect
13. C2×#11718648C2semidirect
16. C2×C13×#396C2semidirect
20. C23×Dic26C22semidirect
21. C22×C13×C4⋊C4C22semidirect
22. C22×C13×C4⋊C4C22semidirect
23. C22×C13×C4⋊C4C22semidirect
40. C22×C4⋊Dic13C22semidirect
41. C22×C4⋊Dic13C22semidirect
42. C22×#6101C22semidirect
43. C22×#6101C22semidirect
44. C22×#6101C22semidirect
45. C22×#6101C22semidirect
47. C2×#88150C22semidirect
50. C13×#396C22semidirect
51. C2×C13×#95C22semidirect
52. C2×#88071C22semidirect
53. C2×#88071C22semidirect
54. C2×#88071C22semidirect
55. C2×#88071C22semidirect
56. C2×#88071C22semidirect
57. #11718655C22semidirect
58. #11718655C22semidirect
59. #11718653C22semidirect
60. #11718650C22semidirect
61. #11718648C22semidirect
64. #11718610C22semidirect
65. #11718609C22semidirect
66. #11718608C22semidirect
67. #11718334C22semidirect
68. #11718329C22semidirect
76. C24×D13Q8semidirect
103. C22×Dic26C23semidirect
107. C2×C13×C4⋊C4C23semidirect
108. C2×C13×C4⋊C4C23semidirect
109. C2×C13×C4⋊C4C23semidirect
144. C2×C4⋊Dic13C23semidirect
145. C2×C4⋊Dic13C23semidirect
150. C2×#6101C23semidirect
151. C2×#6101C23semidirect
152. C2×#6101C23semidirect
153. C2×#6101C23semidirect
156. C13×#95C23semidirect
157. #88071C23semidirect
158. #88071C23semidirect
159. #88071C23semidirect
160. #88071C23semidirect
161. #88071C23semidirect
198. C23×D13C2×Q8semidirect
295. C2×#396D13semidirect
424. C22×C4⋊C4C2×D13semidirect
425. C22×C4⋊C4C2×D13semidirect
426. C22×C4⋊C4C2×D13semidirect
450. #396C2×D13semidirect
463. C2×#95C2×D13semidirect
566. C2×C4⋊C4C22×D13semidirect
567. C2×C4⋊C4C22×D13semidirect
568. C2×C4⋊C4C22×D13semidirect
607. #95C22×D13semidirect
609. C2×C13#2626semidirect
743. C13C2×#2626semidirect
907. C2#13120646direct (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×C22⋊C4×D132
#131206462
C2×#117186102
C2×#117186532
C2×#117186092
C2×#117186552
C2×#117183342
C2×#117186082
C2×#117183292
C2×#117186502
C2×#117186482
C2×#117186162
C2×C13×#3962
C2×#262613