Finite Group Databasebeta

← C2×#13119089 #16030531

Subgroups — C2×#13119089 #16030531

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×#88152C211yesmaximal, characteristic, complemented
2C23×#6103C211yesmaximal, characteristic
3#13119089C2116yesmaximal, direct product factor
4C2×#11718336C211yesmaximal, characteristic, complemented
5C2×#11718335C211yesmaximal, characteristic, complemented
6C2×#11718654C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718331C211yesmaximal, characteristic, complemented
9C2×#11718651C211yesmaximal, characteristic, complemented
10C2×#11718330C211yesmaximal, characteristic, complemented
11C2×#11718607C211yesmaximal, characteristic, complemented
12C2×#11718873C211yesmaximal, characteristic, complemented
13C2×#11718616C211yesmaximal, characteristic
14C2×#11718616C211yesmaximal, characteristic
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#385C211yesmaximal, characteristic, complemented
17C25×D13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic, complemented
21C22×C13×C4⋊C4C2211yescharacteristic, complemented
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×#6103—28no—
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2218yes—
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×C4×Dic13C2211yescharacteristic, complemented
45C22×C4×Dic13C2211yescharacteristic, complemented
46C2×#88152—28no—
47C2×#88152C2218yescomplemented
48C13×#385C2218yescomplemented
49C2×C13×#95C2211yescharacteristic, complemented
50C2×C13×#95C2211yescharacteristic, complemented
51#11718873C2218yescomplemented
52C2×#88071C2211yescharacteristic, complemented
53C2×#88071C2211yescharacteristic, complemented
54C2×#88071C2211yescharacteristic, complemented
55C2×#88071C2211yescharacteristic, complemented
56C2×#88071C2211yescharacteristic, complemented
57C2×#88071C2211yescharacteristic, complemented
58#11718655C2218yescomplemented
59#11718654C2218yescomplemented
60#11718651C2218yescomplemented
61#11718616C2218yes—
62#11718616C2218yes—
63#11718607C2218yescomplemented
64C22⋊C4×Dic13C2218yescomplemented
65#11718336C2218yescomplemented
66#11718335C2218yescomplemented
67#11718331C2218yescomplemented
68#11718330C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13—24no—
71C24×D13—24no—
72C24×D13—24no—
73C24×D13—24no—
74C24×D13—24no—
75C24×D13—42no—
76C24×D13—42no—
77C24×D13C2311yescharacteristic
78C24×D13C2311yescharacteristic
79C24×D13C2314yes—
80C23×C4×C13—24no—
81C23×C4×C13—24no—
82C23×C4×C13—42no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2314yes—
89C23×C4×C13C2311yescharacteristic
90C23×Dic13—24no—
91C23×Dic13—24no—
92C23×Dic13—42no—
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2314yes—
99C23×Dic13C2311yescharacteristic
100C2×C13×C4⋊C4—24no—
101C2×C13×C4⋊C4—42no—
102C2×C13×C4⋊C4C2314yescomplemented
103C2×C13×C4⋊C4C2314yescomplemented
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C22⋊Dic13—24no—
109C2×C22⋊Dic13—24no—
110C2×C22⋊Dic13C2314yes—
111C2×C22⋊Dic13C2314yes—
112C2×#6103—24no—
113C2×#6103—24no—
114C2×#6103—24no—
115C2×#6103—24no—
116C2×#6103—24no—
117C2×#6103—24no—
118C2×#6103—24no—
119C2×#6103—232no—
120C2×#6103—42no—
121C2×#6103—42no—
122C2×#6103—42no—
123C2×#6103—42no—
124C2×#6103D418yes—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×#6103C2314yes—
135C2×#6103C2314yes—
136C2×#6103C2314yes—
137C2×C4⋊Dic13—24no—
138C2×C4⋊Dic13—42no—
139C2×C4⋊Dic13C2314yescomplemented
140C2×C4⋊Dic13C2314yescomplemented
141C2×#6101—24no—
142C2×#6101—42no—
143C2×#6101C2314yescomplemented
144C2×#6101C2314yescomplemented
145C2×C4×Dic13—24no—
146C2×C4×Dic13—42no—
147C2×C4×Dic13C2314yescomplemented
148C2×C4×Dic13C2314yescomplemented
149#88152—232no—
150C13×#95C2314yescomplemented
151C13×#95C2314yescomplemented
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#4114yes—
164C24×C13#4114yes—
165C24×C13#4114yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—232no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—28no—
175C23×D13—22no—
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—28no—
183C23×D13—28no—
184C23×D13—28no—
185C23×D13—28no—
186C23×D13—44no—
187C23×D13—44no—
188C23×D13—416no—
189C23×D13—416no—
190C23×D13—416no—
191C23×D13—416no—
192C23×D13—416no—
193C23×D13—416no—
194C23×D13C2×D414yes—
195C23×D13#4114yes—
196C23×D13C2412yes—
197C23×D13C2412yes—
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—28no—
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—28no—
217C22×C4×C13—44no—
218C22×C4×C13—416no—
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—28no—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—28no—
245C22×Dic13—44no—
246C22×Dic13—416no—
247C22×Dic13C2×D414yes—
248C22×Dic13C2412yes—
249C22×Dic13C2412yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C22×Dic13C2412yes—
253C22×Dic13C2412yes—
254C13×C4⋊C4—28no—
255C13×C4⋊C4—44no—
256C13×C22⋊C4—28no—
257C13×C22⋊C4—28no—
258C22⋊Dic13—28no—
259C22⋊Dic13—28no—
260#6103—28no—
261#6103—28no—
262#6103—28no—
263#6103—28no—
264#6103—28no—
265#6103—28no—
266#6103—28no—
267#6103—44no—
268#6103—44no—
269#6103—44no—
270#6103—44no—
271#6103C2×D4116yes—
272C4⋊Dic13—28no—
273C4⋊Dic13—44no—
274#6101—28no—
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×#385D1311yescharacteristic, complemented
290C2×#380—131no—
291C2×#379—131no—
292C2×#379—131no—
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#126116yescomplemented
305C23×C13C22×D412yes—
306C23×C13C2×#4114yes—
307C23×C13C2×#4114yes—
308C23×C13C2×#4114yes—
309C23×C13C2×#4112yes—
310C23×C13C2×#4112yes—
311C23×C13C2×#4112yes—
312C23×C13C2×#4112yes—
313C23×C13H(5,𝔽2)12yes—
314C23×C13H(5,𝔽2)12yes—
315C23×C13C2511yescharacteristic
316C22×D13—232no—
317C22×D13—28no—
318C22×D13—28no—
319C22×D13—28no—
320C22×D13—28no—
321C22×D13—28no—
322C22×D13—28no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—416no—
336C22×D13—416no—
337C22×D13—416no—
338C22×D13—416no—
339C22×D13—416no—
340C22×D13—4128no—
341C22×D13—44no—
342C22×D13—44no—
343C22×D13—416no—
344C22×D13—44no—
345C22×D13—44no—
346C22×D13—44no—
347C22×D13—44no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13C22×D414yes—
351C22×D13C2×#4114yes—
352C2×C4×C13—28no—
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—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—416no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13—44no—
374C2×C4×C13—44no—
375C2×C4×C13—44no—
376C2×C4×C13C22×D414yes—
377C2×Dic13—28no—
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—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—416no—
396C2×Dic13—44no—
397C2×Dic13—44no—
398C2×Dic13—44no—
399C2×Dic13—44no—
400C2×Dic13—44no—
401C2×Dic13C22×D414yes—
402C26—131no—
403C24×C4—131no—
404C24×C4C2×D1311yescharacteristic
405C2×#126—138no—
406C2×#126—268no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4—131no—
410C22×C4⋊C4—131no—
411C22×C4⋊C4C2×D1311yescharacteristic, complemented
412C22×C4⋊C4C2×D1311yescharacteristic, complemented
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⋊C4—131no—
422C22×C22⋊C4—138no—
423C22×C22⋊C4—131no—
424C22×C22⋊C4—131no—
425C22×C22⋊C4—131no—
426C22×C22⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4—268no—
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#385C2×D1318yescomplemented
442#380—138no—
443#379—138no—
444#379—138no—
445C4×C22⋊C4—138no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95C2×D1311yescharacteristic, complemented
453C2×#95C2×D1311yescharacteristic, complemented
454C22×C13—24no—
455C22×C13—24no—
456C22×C13—24no—
457C22×C13—24no—
458C22×C13—24no—
459C22×C13—24no—
460C22×C13—232no—
461C22×C13#52514yes—
462C22×C13C2×#12614yes—
463C22×C13C2×#12618yescomplemented
464C22×C13#53814yes—
465C22×C13#54614yes—
466C22×C13#54614yes—
467C22×C13#55114yes—
468C22×C13#55114yes—
469C22×C13C23×D411yescharacteristic
470C22×C13C22×#4111yescharacteristic
471C22×C13C22×#4111yescharacteristic
472C22×C13C22×#4111yescharacteristic
473C22×C13C22×#4111yescharacteristic
474C22×C13C2×H(5,𝔽2)11yescharacteristic
475C22×C13C2×H(5,𝔽2)11yescharacteristic
476C2×D13—24no—
477C2×D13—24no—
478C2×D13—24no—
479C2×D13—24no—
480C2×D13—24no—
481C2×D13—24no—
482C2×D13—464no—
483C2×D13—42no—
484C2×D13—42no—
485C2×D13—42no—
486C2×D13—42no—
487C2×D13—42no—
488C2×D13—42no—
489C2×D13—42no—
490C2×D13—42no—
491C2×D13—416no—
492C2×D13—416no—
493C4×C13—24no—
494C4×C13—42no—
495C4×C13—42no—
496C4×C13—42no—
497C4×C13—42no—
498C4×C13—42no—
499Dic13—24no—
500Dic13—42no—
501Dic13—42no—
502Dic13—42no—
503Dic13—42no—
504Dic13—42no—
505C25—131no—
506C25—131no—
507C25—134no—
508C25—264no—
509C25—264no—
510C25—264no—
511C25—264no—
512C25—264no—
513C25—522no—
514C25—522no—
515C25C22×D1311yescharacteristic
516C23×C4—24no—
517C23×C4—24no—
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×D1314yes—
535C23×C4C22×D1311yescharacteristic
536#126—2632no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—42no—
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—522no—
546C2×C4⋊C4—522no—
547C2×C4⋊C4C22×D1314yescomplemented
548C2×C4⋊C4C22×D1314yescomplemented
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—138no—
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—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—264no—
575C2×C22⋊C4—264no—
576C2×C22⋊C4—522no—
577C2×C22⋊C4—522no—
578C2×C22⋊C4—522no—
579C2×C22⋊C4—522no—
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#95C22×D1314yescomplemented
593#95C22×D1314yescomplemented
594C2×C13—28no—
595C2×C13#248018yescomplemented
596C2×C13C2×#52511yescharacteristic
597C2×C13C22×#12611yescharacteristic
598C2×C13C2×#53811yescharacteristic
599C2×C13C2×#54611yescharacteristic
600C2×C13C2×#54611yescharacteristic
601C2×C13C2×#55111yescharacteristic
602C2×C13C2×#55111yescharacteristic
603D13—44no—
604D13—44no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—134no—
610C24—134no—
611C24—132no—
612C24—132no—
613C24—268no—
614C24—268no—
615C24—2632no—
616C24—262no—
617C24—262no—
618C24—262no—
619C24—262no—
620C24—262no—
621C24—262no—
622C24—262no—
623C24—268no—
624C24—262no—
625C24—262no—
626C24—262no—
627C24—262no—
628C24—262no—
629C24—268no—
630C24—268no—
631C24—524no—
632C24—524no—
633C24—5216no—
634C24—5216no—
635C24—5216no—
636C24—5216no—
637C24—5216no—
638C24—5216no—
639C24#612714yes—
640C24#612914yes—
641C24#613114yes—
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—28no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—28no—
663C22×C4—44no—
664C22×C4—416no—
665C22×C4—134no—
666C22×C4—132no—
667C22×C4—132no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—132no—
672C22×C4—268no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—268no—
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—262no—
685C22×C4—262no—
686C22×C4—262no—
687C22×C4—262no—
688C22×C4—262no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—524no—
692C22×C4—5216no—
693C22×C4D4×D1314yes—
694C22×C4C23×D1312yes—
695C22×C4C23×D1312yes—
696C22×C4C23×D1312yes—
697C22×C4C23×D1312yes—
698C22×C4C23×D1312yes—
699C22×C4C23×D1312yes—
700C4⋊C4—28no—
701C4⋊C4—44no—
702C4⋊C4—268no—
703C4⋊C4—268no—
704C4⋊C4—524no—
705C4⋊C4—524no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—1316no—
709C22⋊C4—268no—
710C22⋊C4—268no—
711C22⋊C4—268no—
712C22⋊C4—268no—
713C22⋊C4—268no—
714C22⋊C4—268no—
715C22⋊C4—268no—
716C22⋊C4—268no—
717C22⋊C4—268no—
718C22⋊C4—524no—
719C22⋊C4—524no—
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—134no—
736C23—134no—
737C23—2632no—
738C23—268no—
739C23—268no—
740C23—268no—
741C23—268no—
742C23—268no—
743C23—268no—
744C23—262no—
745C23—262no—
746C23—262no—
747C23—262no—
748C23—262no—
749C23—262no—
750C23—262no—
751C23—262no—
752C23—262no—
753C23—262no—
754C23—262no—
755C23—262no—
756C23—5216no—
757C23—5216no—
758C23—5216no—
759C23—5216no—
760C23—52128no—
761C23—5216no—
762C23—524no—
763C23—524no—
764C23—5216no—
765C23—524no—
766C23—524no—
767C23—524no—
768C23—524no—
769C23—524no—
770C23—524no—
771C23#88152116yescomplemented
772C23C2×#612714yes—
773C23C2×#612712yes—
774C23C2×D4×D1312yes—
775C23C2×#612914yes—
776C23C2×#612912yes—
777C23#8825112yes—
778C23C2×#613114yes—
779C23C2×#613112yes—
780C23#41×D1312yes—
781C23#8825612yes—
782C23C24×D1311yescharacteristic
783C2×C4—28no—
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—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—416no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—134no—
808C2×C4—268no—
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—262no—
826C2×C4—5216no—
827C2×C4—524no—
828C2×C4—524no—
829C2×C4—524no—
830C2×C4—524no—
831C2×C4—524no—
832C2×C4C2×D4×D1314yes—
833C22—24no—
834C22—24no—
835C22—232no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—264no—
841C22—264no—
842C22—264no—
843C22—264no—
844C22—264no—
845C22—264no—
846C22—5264no—
847C22—522no—
848C22—522no—
849C22—5216no—
850C22—5216no—
851C22—522no—
852C22—522no—
853C22—522no—
854C22—522no—
855C22—522no—
856C22—522no—
857C22C2×#8815214yes—
858C22C2×#8815218yescomplemented
859C22#1171925514yes—
860C22#1171926114yes—
861C22#1171929614yes—
862C22#1171933214yes—
863C22#1171934914yes—
864C22#1171936314yes—
865C22C22×#612711yescharacteristic
866C22C22×D4×D1311yescharacteristic
867C22C22×#612911yescharacteristic
868C22C2×#8825111yescharacteristic
869C22C22×#613111yescharacteristic
870C22C2×#41×D1311yescharacteristic
871C22C2×#8825611yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—264no—
879C4—522no—
880C4—522no—
881C4—522no—
882C4—522no—
883C4—522no—
884C2—28no—
885C2—524no—
886C2—524no—
887C2#1311908918yesdirect product factor
888C2C2×#1171933211yescharacteristic
889C2C22×#8815211yescharacteristic
890C2C2×#1171934911yescharacteristic
891C2C2×#1171929611yescharacteristic
892C2C2×#1171925511yescharacteristic
893C2C2×#1171936311yescharacteristic
894C2C2×#1171926111yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#385D13
hypocenterC13C2×#2480
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#88152C2semidirect
3. #13119089C2direct (N × H)
4. C2×#11718336C2semidirect
5. C2×#11718335C2semidirect
6. C2×#11718654C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718331C2semidirect
9. C2×#11718651C2semidirect
10. C2×#11718330C2semidirect
11. C2×#11718607C2semidirect
12. C2×#11718873C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
16. C2×C13×#385C2semidirect
20. C22×C13×C4⋊C4C22semidirect
21. C22×C13×C4⋊C4C22semidirect
40. C22×C4⋊Dic13C22semidirect
41. C22×C4⋊Dic13C22semidirect
42. C22×#6101C22semidirect
43. C22×#6101C22semidirect
44. C22×C4×Dic13C22semidirect
45. C22×C4×Dic13C22semidirect
47. C2×#88152C22semidirect
48. C13×#385C22semidirect
49. C2×C13×#95C22semidirect
50. C2×C13×#95C22semidirect
51. #11718873C22semidirect
52. C2×#88071C22semidirect
53. C2×#88071C22semidirect
54. C2×#88071C22semidirect
55. C2×#88071C22semidirect
56. C2×#88071C22semidirect
57. C2×#88071C22semidirect
58. #11718655C22semidirect
59. #11718654C22semidirect
60. #11718651C22semidirect
63. #11718607C22semidirect
64. C22⋊C4×Dic13C22semidirect
65. #11718336C22semidirect
66. #11718335C22semidirect
67. #11718331C22semidirect
68. #11718330C22semidirect
102. C2×C13×C4⋊C4C23semidirect
103. C2×C13×C4⋊C4C23semidirect
139. C2×C4⋊Dic13C23semidirect
140. C2×C4⋊Dic13C23semidirect
143. C2×#6101C23semidirect
144. C2×#6101C23semidirect
147. C2×C4×Dic13C23semidirect
148. C2×C4×Dic13C23semidirect
150. C13×#95C23semidirect
151. C13×#95C23semidirect
152. #88071C23semidirect
153. #88071C23semidirect
154. #88071C23semidirect
155. #88071C23semidirect
156. #88071C23semidirect
157. #88071C23semidirect
289. C2×#385D13semidirect
304. C23×C13#126semidirect
411. C22×C4⋊C4C2×D13semidirect
412. C22×C4⋊C4C2×D13semidirect
441. #385C2×D13semidirect
452. C2×#95C2×D13semidirect
453. C2×#95C2×D13semidirect
463. C22×C13C2×#126semidirect
547. C2×C4⋊C4C22×D13semidirect
548. C2×C4⋊C4C22×D13semidirect
592. #95C22×D13semidirect
593. #95C22×D13semidirect
595. C2×C13#2480semidirect
724. C13C2×#2480semidirect
771. C23#88152semidirect
858. C22C2×#88152semidirect
887. C2#13119089direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881522
C23×#61032
#131190892
C2×#117183362
C2×#117183352
C2×#117186542
C2×#117186552
C2×#117183312
C2×#117186512
C2×#117183302
C2×#117186072
C2×#117188732
C2×#117186162
C2×C22⋊C4×Dic132
C2×C13×#3852
C2×#248013