Finite Group Databasebeta

← C2×#13119081 #16030523

Subgroups — C2×#13119081 #16030523

Order 3328.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88133C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic13C211yesmaximal, characteristic
3#13119081C2116yesmaximal, direct product factor
4C2×#11718613C211yesmaximal, characteristic, complemented
5C2×#11718613C211yesmaximal, characteristic, complemented
6C2×#11718614C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718606C211yesmaximal, characteristic, complemented
9C2×#11718612C211yesmaximal, characteristic, complemented
10C2×#11718605C211yesmaximal, characteristic, complemented
11C2×#11718611C211yesmaximal, characteristic, complemented
12C2×#11718607C211yesmaximal, characteristic, complemented
13C2×#11718603C211yesmaximal, characteristic, complemented
14C2×#11718908C211yesmaximal, characteristic
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#379C211yesmaximal, characteristic
17C26×C13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13—28no—
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2218yes—
34C22×C22⋊Dic13C2211yescharacteristic
35C22×C22⋊Dic13C2211yescharacteristic
36C22×C22⋊Dic13C2211yescharacteristic
37C22×C22⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic, complemented
39C22×C4⋊Dic13C2211yescharacteristic, complemented
40C22×#6101C2211yescharacteristic, complemented
41C22×#6101C2211yescharacteristic, complemented
42C22×#6101C2211yescharacteristic, complemented
43C22×#6101C2211yescharacteristic, complemented
44C22×C4×Dic13C2211yescharacteristic, complemented
45C22×C4×Dic13C2211yescharacteristic, complemented
46C2×#88133—28no—
47C2×#88133C2218yescomplemented
48C13×#379C2218yes—
49#11718908C2218yes—
50C2×#88071C2211yescharacteristic, complemented
51C2×#88071C2211yescharacteristic, complemented
52C2×#88071C2211yescharacteristic, complemented
53C2×#88071C2211yescharacteristic, complemented
54C2×#88071C2211yescharacteristic, complemented
55C2×#88071C2211yescharacteristic, complemented
56C2×#88071C2211yescharacteristic, complemented
57C2×#88071C2211yescharacteristic, complemented
58#11718614C2218yescomplemented
59#11718613C2218yescomplemented
60#11718613C2218yescomplemented
61#11718612C2218yescomplemented
62#11718611C2218yescomplemented
63#11718609C2218yescomplemented
64#11718607C2218yescomplemented
65#11718606C2218yescomplemented
66#11718605C2218yescomplemented
67#11718603C2218yescomplemented
68C22⋊C4×Dic13C2218yescomplemented
69C25×C13—24no—
70C25×C13—24no—
71C25×C13—24no—
72C25×C13—24no—
73C25×C13—24no—
74C25×C13—42no—
75C25×C13—42no—
76C25×C13C2311yescharacteristic
77C25×C13C2311yescharacteristic
78C25×C13C2314yes—
79C25×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×Dic13—24no—
85C23×Dic13—24no—
86C23×Dic13—24no—
87C23×Dic13—24no—
88C23×Dic13—42no—
89C23×Dic13—42no—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2314yes—
97C23×Dic13C2314yes—
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4—42no—
105C2×C13×C22⋊C4—42no—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—24no—
115C2×C22⋊Dic13—24no—
116C2×C22⋊Dic13—24no—
117C2×C22⋊Dic13—24no—
118C2×C22⋊Dic13—24no—
119C2×C22⋊Dic13—232no—
120C2×C22⋊Dic13—42no—
121C2×C22⋊Dic13—42no—
122C2×C22⋊Dic13D418yes—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131C2×C22⋊Dic13C2314yes—
132C2×C22⋊Dic13C2314yes—
133C2×C4⋊Dic13—24no—
134C2×C4⋊Dic13—42no—
135C2×C4⋊Dic13C2314yescomplemented
136C2×C4⋊Dic13C2314yescomplemented
137C2×#6101—24no—
138C2×#6101—24no—
139C2×#6101—42no—
140C2×#6101—42no—
141C2×#6101C2314yescomplemented
142C2×#6101C2314yescomplemented
143C2×#6101C2314yescomplemented
144C2×#6101C2314yescomplemented
145C2×C4×Dic13—24no—
146C2×C4×Dic13—42no—
147C2×C4×Dic13C2314yescomplemented
148C2×C4×Dic13C2314yescomplemented
149#88133—232no—
150#88071C2314yescomplemented
151#88071C2314yescomplemented
152#88071C2314yescomplemented
153#88071C2314yescomplemented
154#88071C2314yescomplemented
155#88071C2314yescomplemented
156#88071C2314yescomplemented
157#88071C2314yescomplemented
158C2×#2480—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—232no—
164C24×C13—28no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—28no—
169C24×C13—28no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13—22no—
178C24×C13—22no—
179C24×C13—28no—
180C24×C13—28no—
181C24×C13—44no—
182C24×C13—44no—
183C24×C13—416no—
184C24×C13—416no—
185C24×C13—416no—
186C24×C13—416no—
187C24×C13—416no—
188C24×C13—416no—
189C24×C13C2×D414yes—
190C24×C13#4114yes—
191C24×C13#4114yes—
192C24×C13#4114yes—
193C24×C13#4114yes—
194C24×C13C2412yes—
195C24×C13C2412yes—
196C24×C13C2412yes—
197C24×C13C2411yescharacteristic
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
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×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×Dic13—22no—
215C22×Dic13—22no—
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—28no—
229C22×Dic13—28no—
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—28no—
239C22×Dic13—28no—
240C22×Dic13—44no—
241C22×Dic13—44no—
242C22×Dic13—416no—
243C22×Dic13—416no—
244C22×Dic13C2×D414yes—
245C22×Dic13C2×D414yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C22×Dic13C2412yes—
253C22×Dic13C2412yes—
254C13×C22⋊C4—28no—
255C13×C22⋊C4—28no—
256C13×C22⋊C4—28no—
257C13×C22⋊C4—28no—
258C13×C22⋊C4—44no—
259C13×C22⋊C4—44no—
260C22⋊Dic13—28no—
261C22⋊Dic13—28no—
262C22⋊Dic13—28no—
263C22⋊Dic13—28no—
264C22⋊Dic13—28no—
265C22⋊Dic13—28no—
266C22⋊Dic13—28no—
267C22⋊Dic13—44no—
268C22⋊Dic13—44no—
269C22⋊Dic13C2×D4116yes—
270C4⋊Dic13—28no—
271C4⋊Dic13—44no—
272#6101—28no—
273#6101—28no—
274#6101—44no—
275#6101—44no—
276C4×Dic13—28no—
277C4×Dic13—44no—
278C22×#126—131no—
279C23×C22⋊C4—131no—
280#2480—1316no—
281C2×#397—131no—
282C2×#397—131no—
283C2×#397—131no—
284C2×#396—131no—
285C2×#388—131no—
286C2×#388—131no—
287C2×#388—131no—
288C2×#385—131no—
289C2×#385—131no—
290C2×#380—131no—
291C2×#379—131no—
292C2×#379D1311yescharacteristic
293C2×C4×C22⋊C4—131no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—28no—
298C23×C13—28no—
299C23×C13—28no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—232no—
305C23×C13—28no—
306C23×C13—28no—
307C23×C13—28no—
308C23×C13—28no—
309C23×C13—28no—
310C23×C13—28no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—416no—
324C23×C13—416no—
325C23×C13—416no—
326C23×C13—416no—
327C23×C13—416no—
328C23×C13—4128no—
329C23×C13—44no—
330C23×C13—44no—
331C23×C13—416no—
332C23×C13—44no—
333C23×C13—44no—
334C23×C13—44no—
335C23×C13—44no—
336C23×C13—44no—
337C23×C13—44no—
338C23×C13#126116yescomplemented
339C23×C13C22×D414yes—
340C23×C13C22×D412yes—
341C23×C13C2×#4114yes—
342C23×C13C2×#4114yes—
343C23×C13C2×#4114yes—
344C23×C13C2×#4114yes—
345C23×C13C2×#4112yes—
346C23×C13C2×#4112yes—
347C23×C13C2×#4112yes—
348C23×C13C2×#4112yes—
349C23×C13H(5,𝔽2)12yes—
350C23×C13H(5,𝔽2)12yes—
351C23×C13C2511yescharacteristic
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—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—44no—
365C2×C4×C13—44no—
366C2×C4×C13—44no—
367C2×C4×C13—44no—
368C2×Dic13—28no—
369C2×Dic13—28no—
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—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—416no—
393C2×Dic13—416no—
394C2×Dic13—44no—
395C2×Dic13—44no—
396C2×Dic13—44no—
397C2×Dic13—44no—
398C2×Dic13—44no—
399C2×Dic13—44no—
400C2×Dic13C22×D414yes—
401C2×Dic13C22×D414yes—
402C26C2×D1311yescharacteristic
403C24×C4—131no—
404C24×C4—131no—
405C2×#126—138no—
406C2×#126—268no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C4⋊C4—131no—
411C22×C4⋊C4—131no—
412C22×C4⋊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—138no—
419C22×C22⋊C4—131no—
420C22×C22⋊C4—131no—
421C22×C22⋊C4—131no—
422C22×C22⋊C4—131no—
423C22×C22⋊C4—131no—
424C22×C22⋊C4—268no—
425C22×C22⋊C4C2×D1311yescharacteristic
426C22×C22⋊C4C2×D1311yescharacteristic
427C22×C22⋊C4C2×D1311yescharacteristic
428C22×C22⋊C4C2×D1311yescharacteristic
429C22×C22⋊C4C2×D1311yescharacteristic
430C22×C22⋊C4C2×D1311yescharacteristic
431C22×C42—131no—
432C22×C42—131no—
433#397—138no—
434#397—138no—
435#397—138no—
436#396—138no—
437#388—138no—
438#388—138no—
439#388—138no—
440#385—138no—
441#385—138no—
442#380—138no—
443#379—138no—
444#379C2×D1318yes—
445C4×C22⋊C4—138no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C22×C13—24no—
455C22×C13—24no—
456C22×C13—24no—
457C22×C13—24no—
458C22×C13—24no—
459C22×C13—24no—
460C22×C13—232no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—464no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—416no—
477C22×C13—416no—
478C22×C13#52514yes—
479C22×C13C2×#12614yes—
480C22×C13C2×#12618yescomplemented
481C22×C13#53814yes—
482C22×C13#54614yes—
483C22×C13#54614yes—
484C22×C13#55114yes—
485C22×C13#55114yes—
486C22×C13C23×D411yescharacteristic
487C22×C13C22×#4111yescharacteristic
488C22×C13C22×#4111yescharacteristic
489C22×C13C22×#4111yescharacteristic
490C22×C13C22×#4111yescharacteristic
491C22×C13C2×H(5,𝔽2)11yescharacteristic
492C22×C13C2×H(5,𝔽2)11yescharacteristic
493C4×C13—42no—
494C4×C13—42no—
495C4×C13—42no—
496C4×C13—42no—
497Dic13—24no—
498Dic13—24no—
499Dic13—42no—
500Dic13—42no—
501Dic13—42no—
502Dic13—42no—
503Dic13—42no—
504Dic13—42no—
505C25—24no—
506C25—24no—
507C25—24no—
508C25—24no—
509C25—24no—
510C25—42no—
511C25—42no—
512C25C22×D1311yescharacteristic
513C25C22×D1311yescharacteristic
514C25C22×D1314yes—
515C25C22×D1311yescharacteristic
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—131no—
521C23×C4—131no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—134no—
525C23×C4—134no—
526C23×C4—264no—
527C23×C4—264no—
528C23×C4—264no—
529C23×C4—264no—
530C23×C4—522no—
531C23×C4—522no—
532C23×C4C22×D1311yescharacteristic
533C23×C4C22×D1311yescharacteristic
534C23×C4C22×D1311yescharacteristic
535C23×C4C22×D1311yescharacteristic
536#126—2632no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—134no—
541C2×C4⋊C4—134no—
542C2×C4⋊C4—134no—
543C2×C4⋊C4—264no—
544C2×C4⋊C4—264no—
545C2×C4⋊C4—264no—
546C2×C4⋊C4—522no—
547C2×C4⋊C4—522no—
548C2×C4⋊C4—522no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—138no—
556C2×C22⋊C4—134no—
557C2×C22⋊C4—134no—
558C2×C22⋊C4—134no—
559C2×C22⋊C4—134no—
560C2×C22⋊C4—134no—
561C2×C22⋊C4—134no—
562C2×C22⋊C4—134no—
563C2×C22⋊C4—134no—
564C2×C22⋊C4—134no—
565C2×C22⋊C4—134no—
566C2×C22⋊C4—2632no—
567C2×C22⋊C4—264no—
568C2×C22⋊C4—264no—
569C2×C22⋊C4—264no—
570C2×C22⋊C4—264no—
571C2×C22⋊C4—264no—
572C2×C22⋊C4—264no—
573C2×C22⋊C4—264no—
574C2×C22⋊C4—522no—
575C2×C22⋊C4—522no—
576C2×C22⋊C4C22×D1314yes—
577C2×C22⋊C4C22×D1314yes—
578C2×C22⋊C4C22×D1314yes—
579C2×C22⋊C4C22×D1314yes—
580C2×C22⋊C4C22×D1314yes—
581C2×C22⋊C4C22×D1314yes—
582C2×C42—134no—
583C2×C42—134no—
584C2×C42—264no—
585C2×C42—522no—
586#95—134no—
587#95—134no—
588#95—134no—
589#95—134no—
590#95—134no—
591#95—134no—
592#95—134no—
593#95—134no—
594C2×C13—28no—
595C2×C13—44no—
596C2×C13—44no—
597C2×C13#248018yescomplemented
598C2×C13C2×#52511yescharacteristic
599C2×C13C22×#12611yescharacteristic
600C2×C13C2×#53811yescharacteristic
601C2×C13C2×#54611yescharacteristic
602C2×C13C2×#54611yescharacteristic
603C2×C13C2×#55111yescharacteristic
604C2×C13C2×#55111yescharacteristic
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—232no—
610C24—22no—
611C24—22no—
612C24—28no—
613C24—22no—
614C24—28no—
615C24—28no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—28no—
626C24—28no—
627C24—44no—
628C24—44no—
629C24—416no—
630C24—416no—
631C24—416no—
632C24—416no—
633C24—416no—
634C24—416no—
635C24#612714yes—
636C24D4×D1314yes—
637C24#612914yes—
638C24#612914yes—
639C24#612914yes—
640C24C23×D1312yes—
641C24C23×D1312yes—
642C24C23×D1312yes—
643C24C23×D1311yescharacteristic
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—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—134no—
657C22×C4—134no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—132no—
661C22×C4—132no—
662C22×C4—132no—
663C22×C4—132no—
664C22×C4—132no—
665C22×C4—132no—
666C22×C4—268no—
667C22×C4—268no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—268no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—268no—
685C22×C4—262no—
686C22×C4—262no—
687C22×C4—262no—
688C22×C4—262no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—524no—
693C22×C4—524no—
694C22×C4—5216no—
695C22×C4—5216no—
696C22×C4C23×D1312yes—
697C22×C4C23×D1312yes—
698C22×C4C23×D1312yes—
699C22×C4C23×D1312yes—
700C4⋊C4—268no—
701C4⋊C4—268no—
702C4⋊C4—268no—
703C4⋊C4—524no—
704C4⋊C4—524no—
705C4⋊C4—524no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—1316no—
713C22⋊C4—268no—
714C22⋊C4—268no—
715C22⋊C4—268no—
716C22⋊C4—268no—
717C22⋊C4—268no—
718C22⋊C4—268no—
719C22⋊C4—268no—
720C22⋊C4—524no—
721C22⋊C4—524no—
722C42—268no—
723C42—524no—
724C13C2×#248011yescharacteristic, complemented, Sylow
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—232no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—416no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—4128no—
759C23—416no—
760C23—44no—
761C23—44no—
762C23—416no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23#88133116yescomplemented
770C23C2×#612714yes—
771C23C2×#612712yes—
772C23C2×D4×D1314yes—
773C23C2×D4×D1312yes—
774C23C2×#612914yes—
775C23C2×#612914yes—
776C23C2×#612914yes—
777C23C2×#612912yes—
778C23C2×#612912yes—
779C23C2×#612912yes—
780C23#8825112yes—
781C23#8825112yes—
782C23C24×D1311yescharacteristic
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—134no—
800C2×C4—134no—
801C2×C4—268no—
802C2×C4—268no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—262no—
806C2×C4—262no—
807C2×C4—262no—
808C2×C4—262no—
809C2×C4—262no—
810C2×C4—262no—
811C2×C4—262no—
812C2×C4—262no—
813C2×C4—262no—
814C2×C4—262no—
815C2×C4—262no—
816C2×C4—262no—
817C2×C4—262no—
818C2×C4—262no—
819C2×C4—262no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—5216no—
826C2×C4—5216no—
827C2×C4—524no—
828C2×C4—524no—
829C2×C4—524no—
830C2×C4—524no—
831C2×C4—524no—
832C2×C4—524no—
833C22—24no—
834C22—24no—
835C22—232no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—464no—
847C22—42no—
848C22—42no—
849C22—416no—
850C22—416no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22C2×#8813314yes—
858C22C2×#8813318yescomplemented
859C22#1171919514yes—
860C22#1171920014yes—
861C22#1171929114yes—
862C22#1171929214yes—
863C22#1171929614yes—
864C22#1171929814yes—
865C22C22×#612711yescharacteristic
866C22C22×D4×D1311yescharacteristic
867C22C22×#612911yescharacteristic
868C22C22×#612911yescharacteristic
869C22C22×#612911yescharacteristic
870C22C2×#8825111yescharacteristic
871C22C2×#8825111yescharacteristic
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—264no—
877C4—264no—
878C4—522no—
879C4—522no—
880C4—522no—
881C4—522no—
882C4—522no—
883C4—522no—
884C2—28no—
885C2—44no—
886C2—44no—
887C2#1311908118yesdirect product factor
888C2C2×#1171929111yescharacteristic
889C2C22×#8813311yescharacteristic
890C2C2×#1171929811yescharacteristic
891C2C2×#1171929611yescharacteristic
892C2C2×#1171919511yescharacteristic
893C2C2×#1171920011yescharacteristic
894C2C2×#1171929211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#379C2
socleC24×C13C24
prime radicalC26×C13C22
hypercenterC2×#379D13
hypocenterC13C2×#2480
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#88133C2semidirect
3. #13119081C2direct (N × H)
4. C2×#11718613C2semidirect
5. C2×#11718613C2semidirect
6. C2×#11718614C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718606C2semidirect
9. C2×#11718612C2semidirect
10. C2×#11718605C2semidirect
11. C2×#11718611C2semidirect
12. C2×#11718607C2semidirect
13. C2×#11718603C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
38. C22×C4⋊Dic13C22semidirect
39. C22×C4⋊Dic13C22semidirect
40. C22×#6101C22semidirect
41. C22×#6101C22semidirect
42. C22×#6101C22semidirect
43. C22×#6101C22semidirect
44. C22×C4×Dic13C22semidirect
45. C22×C4×Dic13C22semidirect
47. C2×#88133C22semidirect
50. C2×#88071C22semidirect
51. C2×#88071C22semidirect
52. C2×#88071C22semidirect
53. C2×#88071C22semidirect
54. C2×#88071C22semidirect
55. C2×#88071C22semidirect
56. C2×#88071C22semidirect
57. C2×#88071C22semidirect
58. #11718614C22semidirect
59. #11718613C22semidirect
60. #11718613C22semidirect
61. #11718612C22semidirect
62. #11718611C22semidirect
63. #11718609C22semidirect
64. #11718607C22semidirect
65. #11718606C22semidirect
66. #11718605C22semidirect
67. #11718603C22semidirect
68. C22⋊C4×Dic13C22semidirect
135. C2×C4⋊Dic13C23semidirect
136. C2×C4⋊Dic13C23semidirect
141. C2×#6101C23semidirect
142. C2×#6101C23semidirect
143. C2×#6101C23semidirect
144. C2×#6101C23semidirect
147. C2×C4×Dic13C23semidirect
148. C2×C4×Dic13C23semidirect
150. #88071C23semidirect
151. #88071C23semidirect
152. #88071C23semidirect
153. #88071C23semidirect
154. #88071C23semidirect
155. #88071C23semidirect
156. #88071C23semidirect
157. #88071C23semidirect
338. C23×C13#126semidirect
480. C22×C13C2×#126semidirect
597. C2×C13#2480semidirect
724. C13C2×#2480semidirect
769. C23#88133semidirect
858. C22C2×#88133semidirect
887. C2#13119081direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881332
C23×C22⋊Dic132
#131190812
C2×#117186132
C2×#117186142
C2×#117186092
C2×#117186062
C2×#117186122
C2×#117186052
C2×#117186112
C2×#117186072
C2×#117186032
C2×#117189082
C2×C22⋊C4×Dic132
C2×C13×#3792
C2×#248013