Finite Group Databasebeta

← C2×#20278416 #27551921

Subgroups — C2×#20278416 #27551921

Order 13568.

3550 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133216C211yesmaximal, characteristic, complemented
2C22×#13133196C211yesmaximal, characteristic
3C22×#13133194C211yesmaximal, characteristic
4C23×#11719919C211yesmaximal, characteristic
5#20278416C2116yesmaximal, direct product factor
6C2×#16810557C211yesmaximal, characteristic, complemented
7C2×#16810556C211yesmaximal, characteristic, complemented
8C2×#16810544C211yesmaximal, characteristic, complemented
9C2×#16810543C211yesmaximal, characteristic, complemented
10C2×#16810520C211yesmaximal, characteristic, complemented
11C2×#16810520C211yesmaximal, characteristic, complemented
12C2×#16810498C211yesmaximal, characteristic
13C2×#16810492C211yesmaximal, characteristic, complemented
14C2×#16810481C211yesmaximal, characteristic
15C2×C22⋊C4×Dic53C211yesmaximal, characteristic
16C2×C53×#385C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C24×Dic53C2211yescharacteristic
20C24×Dic53C2211yescharacteristic
21C2×#13133216—28no—
22C2×#13133216C2218yescomplemented
23C2×#13133196—28no—
24C2×#13133196C2218yes—
25C2×#13133194—28no—
26C2×#13133194C2218yes—
27C22×C4⋊Dic53C2211yescharacteristic
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
30C22×C4⋊Dic53C2211yescharacteristic
31C22×#11719919—28no—
32C22×#11719919C2211yescharacteristic
33C22×#11719919C2211yescharacteristic
34C22×#11719919C2211yescharacteristic
35C22×#11719919C2211yescharacteristic
36C22×#11719919C2211yescharacteristic
37C22×#11719919C2218yes—
38C22×#11719919C2211yescharacteristic
39C22×#11719919C2211yescharacteristic
40C22×#11719919C2211yescharacteristic
41C22×#11719919C2211yescharacteristic
42C22×#11719919C2211yescharacteristic
43C22×C22⋊Dic53C2211yescharacteristic
44C22×C22⋊Dic53C2211yescharacteristic
45C22×C4×Dic53C2211yescharacteristic
46C22×C4×Dic53C2211yescharacteristic
47#16810557C2218yescomplemented
48#16810556C2218yescomplemented
49#16810544C2218yescomplemented
50#16810543C2218yescomplemented
51#16810520C2218yescomplemented
52#16810520C2218yescomplemented
53#16810498C2218yes—
54#16810492C2218yescomplemented
55#16810481C2218yes—
56C22⋊C4×Dic53C2218yes—
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C2×#13133124C2211yescharacteristic
62C2×#13133124C2211yescharacteristic
63C24×C4×C53C2211yescharacteristic
64C22×C4⋊C4×C53C2211yescharacteristic
65C22×C4⋊C4×C53C2211yescharacteristic
66C22×C22⋊C4×C53C2211yescharacteristic
67C22×C22⋊C4×C53C2211yescharacteristic
68C53×#385C2218yes—
69C2×#95×C53C2211yescharacteristic
70C2×#95×C53C2211yescharacteristic
71C22×Dic106—24no—
72C22×Dic106—24no—
73C22×Dic106—24no—
74C22×Dic106—24no—
75C22×Dic106—42no—
76C22×Dic106—42no—
77C22×Dic106C2314yes—
78C22×Dic106C2314yes—
79C23×Dic53—24no—
80C23×Dic53—24no—
81C23×Dic53—24no—
82C23×Dic53—24no—
83C23×Dic53—42no—
84C23×Dic53Q818yescomplemented
85C23×Dic53C2311yescharacteristic
86C23×Dic53C2311yescharacteristic
87C23×Dic53C2311yescharacteristic
88C23×Dic53C2314yes—
89C23×Dic53C2311yescharacteristic
90C23×Dic53C2311yescharacteristic
91C23×Dic53C2311yescharacteristic
92C23×Dic53C2311yescharacteristic
93C23×Dic53C2314yes—
94C23×Dic53C2311yescharacteristic
95#13133216—232no—
96#13133196—232no—
97#13133194—232no—
98C2×C4⋊Dic53—24no—
99C2×C4⋊Dic53—24no—
100C2×C4⋊Dic53—24no—
101C2×C4⋊Dic53—42no—
102C2×C4⋊Dic53C2314yes—
103C2×C4⋊Dic53C2314yes—
104C2×C4⋊Dic53C2314yes—
105C2×C4⋊Dic53C2314yes—
106C2×#11719919—232no—
107C2×#11719919—24no—
108C2×#11719919—24no—
109C2×#11719919—24no—
110C2×#11719919—24no—
111C2×#11719919—24no—
112C2×#11719919—24no—
113C2×#11719919—24no—
114C2×#11719919—24no—
115C2×#11719919—24no—
116C2×#11719919D418yes—
117C2×#11719919C2314yes—
118C2×#11719919C2314yes—
119C2×#11719919C2314yes—
120C2×#11719919C2314yes—
121C2×#11719919C2314yes—
122C2×#11719919C2314yes—
123C2×#11719919C2314yes—
124C2×#11719919C2314yes—
125C2×#11719919C2314yes—
126C2×#11719919C2314yes—
127C2×C22⋊Dic53—24no—
128C2×C22⋊Dic53D418yes—
129C2×C22⋊Dic53C2314yes—
130C2×C22⋊Dic53C2314yes—
131C2×C4×Dic53—24no—
132C2×C4×Dic53—24no—
133C2×C4×Dic53C2314yes—
134C2×C4×Dic53C2314yes—
135#13133124C2314yes—
136#13133124C2314yes—
137#13133124C2314yes—
138#13133124C2314yes—
139#13133124C2314yes—
140#13133124C2314yes—
141C25×C53C2311yescharacteristic
142C23×C4×C53—24no—
143C23×C4×C53—24no—
144C23×C4×C53—42no—
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2311yescharacteristic
148C23×C4×C53C2314yes—
149C23×C4×C53C2311yescharacteristic
150C23×C4×C53C2311yescharacteristic
151C23×C4×C53C2311yescharacteristic
152C2×C4⋊C4×C53—24no—
153C2×C4⋊C4×C53—42no—
154C2×C4⋊C4×C53C2314yes—
155C2×C4⋊C4×C53C2314yes—
156C2×C22⋊C4×C53—24no—
157C2×C22⋊C4×C53Q818yescomplemented
158C2×C22⋊C4×C53C2314yes—
159C2×C22⋊C4×C53C2314yes—
160#95×C53C2314yes—
161#95×C53C2314yes—
162C24×C53—22no—
163C24×C53—22no—
164C24×C53—22no—
165C24×C53—22no—
166C24×C53C2×D414yes—
167C24×C53C2×Q814yes—
168C24×C53C2×Q814yes—
169C24×C53C2412yes—
170C24×C53C2411yescharacteristic
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—28no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—28no—
188C22×C4×C53—44no—
189C22×C4×C53—416no—
190C22×C4×C53C2×D414yes—
191C22×C4×C53C2×Q814yes—
192C22×C4×C53C2×Q814yes—
193C22×C4×C53C2412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2412yes—
198C22×C4×C53C2412yes—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—232no—
208C22×Dic53—28no—
209C22×Dic53—28no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—22no—
215C22×Dic53—28no—
216C22×Dic53—22no—
217C22×Dic53—22no—
218C22×Dic53—22no—
219C22×Dic53—22no—
220C22×Dic53—28no—
221C22×Dic53—44no—
222C22×Dic53—416no—
223C22×Dic53C2×D414yes—
224C22×Dic53C2×D414yes—
225C22×Dic53C2×D414yes—
226C22×Dic53C2×D414yes—
227C22×Dic53C2×Q814yes—
228C22×Dic53C2×Q814yes—
229C22×Dic53C2×Q8116yescomplemented
230C22×Dic53#4114yes—
231C22×Dic53C2412yes—
232C22×Dic53C2412yes—
233C22×Dic53C2412yes—
234C22×Dic53C2412yes—
235C22×Dic53C2412yes—
236C22×Dic53C2412yes—
237C22×Dic53C2412yes—
238C22×Dic53C2412yes—
239C2×Dic106—28no—
240C2×Dic106—28no—
241C2×Dic106—28no—
242C2×Dic106—28no—
243C2×Dic106—44no—
244C2×Dic106—44no—
245C2×Dic106—416no—
246C2×Dic106—416no—
247C4⋊C4×C53—28no—
248C4⋊C4×C53—44no—
249C22⋊C4×C53—28no—
250C22⋊C4×C53C2×Q8116yescomplemented
251C22⋊Dic53—28no—
252C22⋊Dic53C2×D4116yes—
253C4⋊Dic53—28no—
254C4⋊Dic53—28no—
255C4⋊Dic53—28no—
256C4⋊Dic53—44no—
257#11719919—28no—
258#11719919—28no—
259#11719919—28no—
260#11719919—28no—
261#11719919—28no—
262#11719919—28no—
263#11719919—28no—
264#11719919—28no—
265#11719919—28no—
266#11719919C2×D4116yes—
267C4×Dic53—28no—
268C4×Dic53—28no—
269C23×C53—28no—
270C23×C53—28no—
271C23×C53—28no—
272C23×C53—28no—
273C23×C53—28no—
274C23×C53—28no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53C4⋊Q8116yescomplemented
280C23×C53C22×D414yes—
281C23×C53C22×D412yes—
282C23×C53C22×D412yes—
283C23×C53C22×Q814yes—
284C23×C53C22×Q812yes—
285C23×C53C22×Q814yes—
286C23×C53C22×Q812yes—
287C23×C53C2×#4112yes—
288C23×C53H(5,𝔽2)12yes—
289C23×C532−1+412yes—
290C23×C53C2511yescharacteristic
291C2×C4×C53—28no—
292C2×C4×C53—28no—
293C2×C4×C53—28no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—416no—
310C2×C4×C53—44no—
311C2×C4×C53—44no—
312C2×C4×C53—44no—
313C2×C4×C53C22×D414yes—
314C2×C4×C53C22×Q814yes—
315C2×C4×C53C22×Q814yes—
316C2×Dic53—28no—
317C2×Dic53—28no—
318C2×Dic53—28no—
319C2×Dic53—28no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—232no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—416no—
339C2×Dic53—44no—
340C2×Dic53—44no—
341C2×Dic53—44no—
342C2×Dic53C22⋊Q8116yescomplemented
343C2×Dic53C22×D414yes—
344C2×Dic53C22×D414yes—
345C2×Dic53C22×D414yes—
346C2×Dic53C22×D414yes—
347C2×Dic53C22×Q814yes—
348C2×Dic53C22×Q814yes—
349C2×Dic53C2×#4114yes—
350Dic106—416no—
351Dic106—416no—
352C2×#2440—531nomaximal, Sylow
353C22×C53—24no—
354C22×C53—24no—
355C22×C53—24no—
356C22×C53—232no—
357C22×C53—24no—
358C22×C53—24no—
359C22×C53—24no—
360C22×C53C2×C22⋊Q814yes—
361C22×C53C2×C4⋊Q814yes—
362C22×C53C2×C4⋊Q818yescomplemented
363C22×C53#54414yes—
364C22×C53D4214yes—
365C22×C53#54714yes—
366C22×C53D4×Q814yes—
367C22×C53#55414yes—
368C22×C53C23×D411yescharacteristic
369C22×C53C23×D411yescharacteristic
370C22×C53C23×Q811yescharacteristic
371C22×C53C23×Q811yescharacteristic
372C22×C53C22×#4111yescharacteristic
373C22×C53C2×H(5,𝔽2)11yescharacteristic
374C22×C53C2×2−1+411yescharacteristic
375C4×C53—24no—
376C4×C53—24no—
377C4×C53—24no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—42no—
381Dic53—24no—
382Dic53—24no—
383Dic53—24no—
384Dic53—24no—
385Dic53—42no—
386Dic53—42no—
387Dic53—42no—
388Dic53C2×C22⋊Q818yescomplemented
389C22×C4⋊Q8—531no—
390C22×C22⋊Q8—531no—
391C22×C22⋊Q8—531no—
392C23×C4⋊C4—531no—
393#2440—5316no—
394C2×#398—531no—
395C2×#398—531no—
396C2×#395—531no—
397C2×#395—531no—
398C2×#389—531no—
399C2×#389—531no—
400C2×#385—531no—
401C2×#385D5311yescharacteristic
402C2×#384—531no—
403C2×#380—531no—
404C2×C4×C22⋊C4—531no—
405C2×C53—28no—
406C2×C53#244018yescomplemented
407C2×C53C22×C22⋊Q811yescharacteristic
408C2×C53C22×C4⋊Q811yescharacteristic
409C2×C53C2×#54411yescharacteristic
410C2×C53C2×D4211yescharacteristic
411C2×C53C2×#54711yescharacteristic
412C2×C53C2×D4×Q811yescharacteristic
413C2×C53C2×#55411yescharacteristic
414C23×Q8—531no—
415C23×Q8—531no—
416C24×C4—531no—
417C24×C4—531no—
418C24×C4C2×D5311yescharacteristic
419C2×C4⋊Q8—538no—
420C2×C4⋊Q8—1068no—
421C2×C22⋊Q8—538no—
422C2×C22⋊Q8—538no—
423C2×C22⋊Q8—1068no—
424C2×C22⋊Q8—1068no—
425C22×C4⋊C4—531no—
426C22×C4⋊C4—531no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4—531no—
430C22×C4⋊C4—531no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4—538no—
433C22×C4⋊C4—531no—
434C22×C4⋊C4—531no—
435C22×C4⋊C4—531no—
436C22×C4⋊C4—531no—
437C22×C4⋊C4—531no—
438C22×C4⋊C4—531no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—1068no—
441C22×C4⋊C4C2×D5311yescharacteristic
442C22×C4⋊C4C2×D5311yescharacteristic
443C22×C22⋊C4—531no—
444C22×C22⋊C4—531no—
445C22×C22⋊C4C2×D5311yescharacteristic
446C22×C22⋊C4C2×D5311yescharacteristic
447C22×C42—531no—
448C22×C42—531no—
449#398—538no—
450#398—538no—
451#395—538no—
452#395—538no—
453#389—538no—
454#389—538no—
455#385—538no—
456#385C2×D5318yes—
457#384—538no—
458#380—538no—
459C4×C22⋊C4—538no—
460C2×#95—531no—
461C2×#95—531no—
462C2×#95—531no—
463C2×#95—531no—
464C2×#95—531no—
465C2×#95—531no—
466C2×#95C2×D5311yescharacteristic
467C2×#95C2×D5311yescharacteristic
468C53C2×#244011yescharacteristic, complemented, Sylow
469C25C22×D5311yescharacteristic
470C22×Q8—534no—
471C22×Q8—534no—
472C22×Q8—1064no—
473C22×Q8—1064no—
474C22×Q8—1064no—
475C22×Q8—1064no—
476C22×Q8—2122no—
477C22×Q8—2122no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—531no—
482C23×C4—538no—
483C23×C4—534no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—531no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—531no—
491C23×C4—534no—
492C23×C4—1064no—
493C23×C4—1064no—
494C23×C4—1064no—
495C23×C4—1064no—
496C23×C4—2122no—
497C23×C4C22×D5311yescharacteristic
498C23×C4C22×D5311yescharacteristic
499C23×C4C22×D5311yescharacteristic
500C23×C4C22×D5314yes—
501C23×C4C22×D5311yescharacteristic
502C23×C4C22×D5311yescharacteristic
503C23×C4C22×D5311yescharacteristic
504C4⋊Q8—10632no—
505C22⋊Q8—10632no—
506C22⋊Q8—10632no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—538no—
510C2×C4⋊C4—534no—
511C2×C4⋊C4—534no—
512C2×C4⋊C4—534no—
513C2×C4⋊C4—534no—
514C2×C4⋊C4—534no—
515C2×C4⋊C4—534no—
516C2×C4⋊C4—534no—
517C2×C4⋊C4—534no—
518C2×C4⋊C4—534no—
519C2×C4⋊C4—534no—
520C2×C4⋊C4—534no—
521C2×C4⋊C4—534no—
522C2×C4⋊C4—534no—
523C2×C4⋊C4—534no—
524C2×C4⋊C4—10632no—
525C2×C4⋊C4—1064no—
526C2×C4⋊C4—1064no—
527C2×C4⋊C4—1064no—
528C2×C4⋊C4—1064no—
529C2×C4⋊C4—1064no—
530C2×C4⋊C4—1064no—
531C2×C4⋊C4—1064no—
532C2×C4⋊C4—1064no—
533C2×C4⋊C4—1064no—
534C2×C4⋊C4—1064no—
535C2×C4⋊C4—1064no—
536C2×C4⋊C4—1064no—
537C2×C4⋊C4—2122no—
538C2×C4⋊C4C22×D5314yes—
539C2×C4⋊C4C22×D5314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—538no—
542C2×C22⋊C4—534no—
543C2×C22⋊C4—534no—
544C2×C22⋊C4—1064no—
545C2×C22⋊C4Dic10618yescomplemented
546C2×C22⋊C4C22×D5314yes—
547C2×C22⋊C4C22×D5314yes—
548C2×C42—534no—
549C2×C42—534no—
550C2×C42—1064no—
551C2×C42—1064no—
552#95—534no—
553#95—534no—
554#95—534no—
555#95—534no—
556#95—534no—
557#95—534no—
558#95C22×D5314yes—
559#95C22×D5314yes—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24C2×Dic10614yes—
565C24D4×D5314yes—
566C24Q8×D5314yes—
567C24C23×D5312yes—
568C24C23×D5311yescharacteristic
569C2×Q8—1068no—
570C2×Q8—1068no—
571C2×Q8—1068no—
572C2×Q8—1068no—
573C2×Q8—2124no—
574C2×Q8—2124no—
575C2×Q8—21216no—
576C2×Q8—21216no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—416no—
596C22×C4—534no—
597C22×C4—534no—
598C22×C4—534no—
599C22×C4—532no—
600C22×C4—534no—
601C22×C4—534no—
602C22×C4—534no—
603C22×C4—534no—
604C22×C4—5316no—
605C22×C4—532no—
606C22×C4—532no—
607C22×C4—532no—
608C22×C4—532no—
609C22×C4—532no—
610C22×C4—532no—
611C22×C4—532no—
612C22×C4—1068no—
613C22×C4—10632no—
614C22×C4—1068no—
615C22×C4—1068no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1068no—
630C22×C4—1062no—
631C22×C4—1062no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—2124no—
635C22×C4—21216no—
636C22×C4C2×Dic10614yes—
637C22×C4C2×Dic10614yes—
638C22×C4D4×D5314yes—
639C22×C4C23×D5312yes—
640C22×C4C23×D5312yes—
641C22×C4C23×D5312yes—
642C22×C4C23×D5312yes—
643C22×C4C23×D5312yes—
644C22×C4C23×D5312yes—
645C4⋊C4—28no—
646C4⋊C4—44no—
647C4⋊C4—5316no—
648C4⋊C4—1068no—
649C4⋊C4—1068no—
650C4⋊C4—1068no—
651C4⋊C4—1068no—
652C4⋊C4—1068no—
653C4⋊C4—1068no—
654C4⋊C4—1068no—
655C4⋊C4—1068no—
656C4⋊C4—1068no—
657C4⋊C4—1068no—
658C4⋊C4—1068no—
659C4⋊C4—1068no—
660C4⋊C4—2124no—
661C22⋊C4—28no—
662C22⋊C4—5316no—
663C22⋊C4—1068no—
664C22⋊C4C2×Dic106116yescomplemented
665C42—1068no—
666C42—1068no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—28no—
676C23—28no—
677C23#13133216116yescomplemented
678C23C2×D4×D5314yes—
679C23C2×D4×D5312yes—
680C23C2×D4×D5312yes—
681C23C2×Q8×D5314yes—
682C23C2×Q8×D5312yes—
683C23C22×Dic10614yes—
684C23C22×Dic10612yes—
685C23#41×D5312yes—
686C23#1313326212yes—
687C23#1313326412yes—
688C23C24×D5311yescharacteristic
689Q8—21216no—
690Q8—21216no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—5316no—
714C2×C4—534no—
715C2×C4—534no—
716C2×C4—534no—
717C2×C4—534no—
718C2×C4—534no—
719C2×C4—534no—
720C2×C4—534no—
721C2×C4—10632no—
722C2×C4—1068no—
723C2×C4—1068no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1068no—
733C2×C4—1068no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—21216no—
744C2×C4—2124no—
745C2×C4—2124no—
746C2×C4—2124no—
747C2×C4C2×D4×D5314yes—
748C2×C4C22×Dic10614yes—
749C2×C4C22×Dic10614yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22C22⋊Q8×D5314yes—
758C22C2×#1313321614yes—
759C22C2×#1313321618yescomplemented
760C22#1681125214yes—
761C22#1681125514yes—
762C22#1681127114yes—
763C22D4×Dic10614yes—
764C22#1681133214yes—
765C22C22×D4×D5311yescharacteristic
766C22C22×D4×D5311yescharacteristic
767C22C22×Q8×D5311yescharacteristic
768C22C23×Dic10611yescharacteristic
769C22C2×#41×D5311yescharacteristic
770C22C2×#1313326211yescharacteristic
771C22C2×#1313326411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—538no—
779C4—1064no—
780C4—1064no—
781C4—1064no—
782C4—1064no—
783C4—2122no—
784C4—2122no—
785C4—2122no—
786C2—28no—
787C2#2027841618yesdirect product factor
788C2C2×C22⋊Q8×D5311yescharacteristic
789C2C22×#1313321611yescharacteristic
790C2C2×#1681125211yescharacteristic
791C2C2×#1681125511yescharacteristic
792C2C2×#1681127111yescharacteristic
793C2C2×D4×Dic10611yescharacteristic
794C2C2×#1681133211yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53C2×#2440
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13133216C2semidirect
5. #20278416C2direct (N × H)
6. C2×#16810557C2semidirect
7. C2×#16810556C2semidirect
8. C2×#16810544C2semidirect
9. C2×#16810543C2semidirect
10. C2×#16810520C2semidirect
11. C2×#16810520C2semidirect
13. C2×#16810492C2semidirect
22. C2×#13133216C22semidirect
47. #16810557C22semidirect
48. #16810556C22semidirect
49. #16810544C22semidirect
50. #16810543C22semidirect
51. #16810520C22semidirect
52. #16810520C22semidirect
54. #16810492C22semidirect
84. C23×Dic53Q8semidirect
157. C2×C22⋊C4×C53Q8semidirect
229. C22×Dic53C2×Q8semidirect
250. C22⋊C4×C53C2×Q8semidirect
279. C23×C53C4⋊Q8semidirect
342. C2×Dic53C22⋊Q8semidirect
362. C22×C53C2×C4⋊Q8semidirect
388. Dic53C2×C22⋊Q8semidirect
406. C2×C53#2440semidirect
468. C53C2×#2440semidirect
545. C2×C22⋊C4Dic106semidirect
664. C22⋊C4C2×Dic106semidirect
677. C23#13133216semidirect
759. C22C2×#13133216semidirect
787. C2#20278416direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332162
C22×#131331962
C22×#131331942
C23×#117199192
#202784162
C2×#168105572
C2×#168105562
C2×#168105442
C2×#168105432
C2×#168105202
C2×#168104982
C2×#168104922
C2×#168104812
C2×C22⋊C4×Dic532
C2×C53×#3852
C2×#244053