Finite Group Databasebeta

← C2×#20277717 #27543606

Subgroups — C2×#20277717 #27543606

Order 13568.

3614 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133195C211yesmaximal, characteristic
2C22×#13133182C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D53C211yesmaximal, characteristic
4#20277717C2116yesmaximal, direct product factor
5C2×#16810527C211yesmaximal, characteristic, complemented
6C2×#16810520C211yesmaximal, characteristic, complemented
7C2×#16810518C211yesmaximal, characteristic, complemented
8C2×#16810509C211yesmaximal, characteristic, complemented
9C2×#16810504C211yesmaximal, characteristic, complemented
10C2×#16810494C211yesmaximal, characteristic
11C2×#16810494C211yesmaximal, characteristic
12C2×C4×#11719919C211yesmaximal, characteristic, complemented
13C2×C4×#11719921C211yesmaximal, characteristic
14C2×#16810470C211yesmaximal, characteristic
15C2×#16810470C211yesmaximal, characteristic
16C2×C53×#389C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C2×#13133195C4116yescomplemented
22C2×#13133195C2218yes—
23C2×#13133182—28no—
24C2×#13133182C2218yescomplemented
25C22×C4⋊Dic53C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C2×C4⋊C4×D53—28no—
33C2×C4⋊C4×D53C2218yes—
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40C22×C4×Dic53C2211yescharacteristic
41C22×C4×Dic53C2211yescharacteristic
42C22×C4×Dic53C2211yescharacteristic
43#16810527C2218yescomplemented
44#16810520C2218yescomplemented
45#16810518C2218yescomplemented
46#16810509C2218yescomplemented
47#16810504C2218yescomplemented
48#16810494C2218yes—
49#16810494C2218yes—
50C4×#11719919C2218yescomplemented
51C4×#11719921C2218yes—
52#16810470C2218yes—
53#16810470C2218yes—
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C2×#13133124C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C4⋊C4×C53C2211yescharacteristic
65C22×C4⋊C4×C53C2211yescharacteristic
66C22×C42×C53C2211yescharacteristic
67C53×#389C2218yescomplemented
68C2×#95×C53C2211yescharacteristic
69C2×#95×C53C2211yescharacteristic
70C24×D53C2311yescharacteristic
71C22×Dic106—24no—
72C22×Dic106—24no—
73C22×Dic106C2×C418yescomplemented
74C22×Dic106C2314yes—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C22×C4×D53—24no—
83C22×C4×D53—24no—
84C22×C4×D53—24no—
85C22×C4×D53—24no—
86C22×C4×D53—24no—
87C22×C4×D53—24no—
88C22×C4×D53—42no—
89C22×C4×D53—42no—
90C22×C4×D53C2×C418yes—
91C22×C4×D53C2314yes—
92C22×C4×D53C2314yes—
93C22×C4×D53C2314yes—
94#13133195C2×C4164yescomplemented
95#13133182—232no—
96C2×C4⋊Dic53—24no—
97C2×C4⋊Dic53C2314yes—
98C2×#11719919—24no—
99C2×#11719919—24no—
100C2×#11719919—42no—
101C2×#11719919C2×C418yescomplemented
102C2×#11719919C2×C418yescomplemented
103C2×#11719919D418yes—
104C2×#11719919C2314yes—
105C2×#11719919C2314yes—
106C2×#11719919C2314yes—
107C2×#11719919C2314yes—
108C2×#11719919C2314yes—
109C2×#11719919C2314yes—
110C4⋊C4×D53—232no—
111C2×#11719921—24no—
112C2×#11719921C2×C418yes—
113C2×#11719921C2×C418yes—
114C2×#11719921Q818yescomplemented
115C2×#11719921C2314yes—
116C2×#11719921C2314yes—
117C2×#11719921C2314yes—
118C2×#11719921C2314yes—
119C2×C4×Dic53—24no—
120C2×C4×Dic53—24no—
121C2×C4×Dic53—24no—
122C2×C4×Dic53—24no—
123C2×C4×Dic53—42no—
124C2×C4×Dic53C2314yes—
125C2×C4×Dic53C2314yes—
126C2×C4×Dic53C2314yes—
127C2×C4×Dic53C2314yes—
128C2×C4×Dic53C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131#13133124C2314yes—
132#13133124C2314yes—
133#13133124C2314yes—
134#13133124C2314yes—
135#13133124C2314yes—
136#13133124C2314yes—
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C2×C4⋊C4×C53—24no—
145C2×C4⋊C4×C53—24no—
146C2×C4⋊C4×C53—42no—
147C2×C4⋊C4×C53C2×C418yescomplemented
148C2×C4⋊C4×C53C2314yes—
149C2×C4⋊C4×C53C2314yes—
150C2×C4⋊C4×C53C2314yes—
151C2×C4⋊C4×C53C2314yes—
152C2×C42×C53—42no—
153C2×C42×C53C2314yes—
154#95×C53C2314yes—
155#95×C53C2314yes—
156C24×C53C2411yescharacteristic
157C23×D53—22no—
158C23×D53—22no—
159C23×D53—22no—
160C23×D53—22no—
161C23×D53C22×C414yes—
162C23×D53C2×Q814yes—
163C23×D53#4114yes—
164C23×D53C2412yes—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
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×C53C22×C414yes—
182C22×C4×C53C22×C414yes—
183C22×C4×C53C22×C414yes—
184C22×C4×C53C2×D414yes—
185C22×C4×C53C2×Q814yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C22×C4×C53C2412yes—
190C22×C4×C53C2412yes—
191C22×C4×C53C2412yes—
192C22×C4×C53C2412yes—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
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×Dic53C22×C414yes—
208C22×Dic53C22×C414yes—
209C22×Dic53C22×C414yes—
210C22×Dic53C2×D414yes—
211C22×Dic53C2×D414yes—
212C22×Dic53C2×Q814yes—
213C22×Dic53#4114yes—
214C22×Dic53C2412yes—
215C22×Dic53C2412yes—
216C22×Dic53C2412yes—
217C22×Dic53C2412yes—
218C22×Dic53C2412yes—
219C22×Dic53C2412yes—
220C22×Dic53C2412yes—
221C2×C4×D53—232no—
222C2×C4×D53—28no—
223C2×C4×D53—28no—
224C2×C4×D53—28no—
225C2×C4×D53—28no—
226C2×C4×D53—28no—
227C2×C4×D53—28no—
228C2×C4×D53—44no—
229C2×C4×D53—44no—
230C2×C4×D53—416no—
231C2×C4×D53—416no—
232C2×C4×D53C22×C4116yes—
233C2×Dic106—232no—
234C2×Dic106—28no—
235C2×Dic106—28no—
236C2×Dic106C22×C4116yescomplemented
237C4⋊C4×C53—28no—
238C4⋊C4×C53—28no—
239C4⋊C4×C53—44no—
240C4⋊C4×C53C22×C4116yescomplemented
241C42×C53—44no—
242#11719921—28no—
243#11719921C22×C4116yes—
244#11719921C22×C4116yes—
245#11719921C2×Q8116yescomplemented
246C4⋊Dic53—28no—
247#11719919—28no—
248#11719919—28no—
249#11719919—44no—
250#11719919C22×C4116yescomplemented
251#11719919C22×C4116yescomplemented
252#11719919C2×D4116yes—
253C4×Dic53—28no—
254C4×Dic53—28no—
255C4×Dic53—28no—
256C4×Dic53—28no—
257C4×Dic53—44no—
258C23×C53C23×C412yes—
259C23×C53C22×D412yes—
260C23×C53C22×Q812yes—
261C23×C53C2×#4112yes—
262C23×C53C2×#4112yes—
263C23×C53H(5,𝔽2)12yes—
264C23×C532−1+412yes—
265C23×C53C2511yescharacteristic
266C22×D53—28no—
267C22×D53—28no—
268C22×D53—28no—
269C22×D53—28no—
270C22×D53—28no—
271C22×D53—28no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53C4×Q8116yescomplemented
277C22×D53C23×C414yes—
278C22×D53C22×Q814yes—
279C22×D53C2×#4114yes—
280C2×C4×C53—28no—
281C2×C4×C53—28no—
282C2×C4×C53—28no—
283C2×C4×C53—28no—
284C2×C4×C53—28no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
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—44no—
302C2×C4×C53—44no—
303C2×C4×C53C23×C414yes—
304C2×C4×C53C23×C414yes—
305C2×C4×C53C23×C414yes—
306C2×C4×C53C22×D414yes—
307C2×C4×C53C22×Q814yes—
308C2×Dic53—28no—
309C2×Dic53—28no—
310C2×Dic53—28no—
311C2×Dic53—28no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—44no—
327C2×Dic53—44no—
328C2×Dic53C4×D4116yes—
329C2×Dic53C23×C414yes—
330C2×Dic53C23×C414yes—
331C2×Dic53C23×C414yes—
332C2×Dic53C22×D414yes—
333C2×Dic53C22×D414yes—
334C2×Dic53C22×Q814yes—
335C2×Dic53C2×#4114yes—
336C4×D53—232no—
337C4×D53—416no—
338C4×D53—416no—
339Dic106—232no—
340C2×#2360—531nomaximal, Sylow
341C22×C53C2×C4×D414yes—
342C22×C53C2×C4×Q814yes—
343C22×C53#52014yes—
344C22×C53#54614yes—
345C22×C53D4×Q814yes—
346C22×C53#55214yes—
347C22×C53#55414yes—
348C22×C53C24×C411yescharacteristic
349C22×C53C23×D411yescharacteristic
350C22×C53C23×Q811yescharacteristic
351C22×C53C22×#4111yescharacteristic
352C22×C53C22×#4111yescharacteristic
353C22×C53C2×H(5,𝔽2)11yescharacteristic
354C22×C53C2×2−1+411yescharacteristic
355C2×D53—232no—
356C2×D53—24no—
357C2×D53—24no—
358C2×D53—24no—
359C2×D53—24no—
360C2×D53—24no—
361C2×D53—24no—
362C2×D53C2×C4×Q818yescomplemented
363C4×C53—24no—
364C4×C53—24no—
365C4×C53—24no—
366C4×C53—24no—
367C4×C53—24no—
368C4×C53—42no—
369C4×C53—42no—
370Dic53—24no—
371Dic53—24no—
372Dic53—24no—
373Dic53—24no—
374Dic53—42no—
375Dic53—42no—
376Dic53C2×C4×D418yes—
377C22×C22⋊Q8—531no—
378C22×C4×Q8—531no—
379C23×C4⋊C4—531no—
380#2360—5316no—
381C2×#391—531no—
382C2×#389—531no—
383C2×#389—531no—
384C2×#389D5311yescharacteristic, complemented
385C2×#387—531no—
386C2×#387—531no—
387C2×#385—531no—
388C2×#385—531no—
389C2×C4×C4⋊C4—531no—
390C2×C4×C22⋊C4—531no—
391C2×C4×C22⋊C4—531no—
392C2×C4×C22⋊C4—531no—
393C2×C53#236018yescomplemented
394C2×C53C22×C4×D411yescharacteristic
395C2×C53C22×C4×Q811yescharacteristic
396C2×C53C2×#52011yescharacteristic
397C2×C53C2×#54611yescharacteristic
398C2×C53C2×D4×Q811yescharacteristic
399C2×C53C2×#55211yescharacteristic
400C2×C53C2×#55411yescharacteristic
401D53—28no—
402C23×Q8—531no—
403C24×C4—531no—
404C24×C4—531no—
405C24×C4—531no—
406C2×C22⋊Q8—5316no—
407C2×C22⋊Q8—538no—
408C2×C4×Q8—538no—
409C2×C4×Q8—1068no—
410C22×C4⋊C4—531no—
411C22×C4⋊C4—531no—
412C22×C4⋊C4—531no—
413C22×C4⋊C4—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4—538no—
418C22×C4⋊C4—1068no—
419C22×C4⋊C4C2×D5311yescharacteristic
420C22×C4⋊C4C2×D5311yescharacteristic
421C22×C4⋊C4C2×D5311yescharacteristic
422C22×C4⋊C4C2×D5311yescharacteristic
423C22×C22⋊C4—531no—
424C22×C22⋊C4—531no—
425C22×C22⋊C4—531no—
426C22×C22⋊C4—531no—
427C22×C42—531no—
428C22×C42—531no—
429C22×C42—531no—
430C22×C42—531no—
431C22×C42—531no—
432C22×C42C2×D5311yescharacteristic
433#391—538no—
434#389—538no—
435#389—538no—
436#389C2×D5318yescomplemented
437#387—538no—
438#387—538no—
439#385—538no—
440#385—538no—
441C4×C4⋊C4—538no—
442C4×C22⋊C4—538no—
443C4×C22⋊C4—538no—
444C4×C22⋊C4—538no—
445C2×#95—531no—
446C2×#95—531no—
447C2×#95—531no—
448C2×#95—531no—
449C2×#95—531no—
450C2×#95—531no—
451C2×#95—531no—
452C2×#95—531no—
453C2×#95C2×D5311yescharacteristic
454C2×#95C2×D5311yescharacteristic
455C53C2×#236011yescharacteristic, complemented, Sylow
456C25—531no—
457C22×Q8—538no—
458C22×Q8—534no—
459C22×Q8—1064no—
460C22×Q8—1064no—
461C23×C4—531no—
462C23×C4—531no—
463C23×C4—531no—
464C23×C4—531no—
465C23×C4—531no—
466C23×C4—538no—
467C23×C4—534no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4—534no—
471C23×C4—534no—
472C23×C4—1064no—
473C23×C4—1064no—
474C23×C4—1064no—
475C23×C4—1064no—
476C23×C4—1064no—
477C23×C4—1064no—
478C23×C4—2122no—
479C23×C4—2122no—
480C23×C4C22×D5311yescharacteristic
481C23×C4C22×D5311yescharacteristic
482C23×C4C22×D5311yescharacteristic
483C23×C4C22×D5311yescharacteristic
484C23×C4C22×D5311yescharacteristic
485C23×C4C22×D5311yescharacteristic
486C23×C4C22×D5311yescharacteristic
487C22⋊Q8—5364no—
488C4×Q8—10632no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—538no—
493C2×C4⋊C4—538no—
494C2×C4⋊C4—538no—
495C2×C4⋊C4—534no—
496C2×C4⋊C4—534no—
497C2×C4⋊C4—534no—
498C2×C4⋊C4—534no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—10632no—
503C2×C4⋊C4—1064no—
504C2×C4⋊C4—1064no—
505C2×C4⋊C4—1064no—
506C2×C4⋊C4—2122no—
507C2×C4⋊C4C4×D5318yescomplemented
508C2×C4⋊C4C22×D5314yes—
509C2×C4⋊C4C22×D5314yes—
510C2×C4⋊C4C22×D5314yes—
511C2×C4⋊C4C22×D5314yes—
512C2×C22⋊C4—538no—
513C2×C22⋊C4—538no—
514C2×C22⋊C4—538no—
515C2×C22⋊C4—534no—
516C2×C22⋊C4—534no—
517C2×C22⋊C4—534no—
518C2×C22⋊C4—534no—
519C2×C22⋊C4—1064no—
520C2×C42—42no—
521C2×C42—534no—
522C2×C42—534no—
523C2×C42—534no—
524C2×C42—534no—
525C2×C42—534no—
526C2×C42—1064no—
527C2×C42—1064no—
528C2×C42—1064no—
529C2×C42—1064no—
530C2×C42—2122no—
531C2×C42C22×D5314yes—
532#95—534no—
533#95—534no—
534#95—534no—
535#95—534no—
536#95—534no—
537#95—534no—
538#95—534no—
539#95—534no—
540#95C22×D5314yes—
541#95C22×D5314yes—
542C24—534no—
543C24—534no—
544C24—534no—
545C24—532no—
546C24—1062no—
547C24—1062no—
548C24—1062no—
549C24—1062no—
550C24C23×D5311yescharacteristic
551C2×Q8—5316no—
552C2×Q8—1068no—
553C2×Q8—10632no—
554C2×Q8—1068no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—534no—
572C22×C4—534no—
573C22×C4—534no—
574C22×C4—532no—
575C22×C4—534no—
576C22×C4—534no—
577C22×C4—534no—
578C22×C4—534no—
579C22×C4—532no—
580C22×C4—532no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—5316no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—1068no—
587C22×C4—10632no—
588C22×C4—1068no—
589C22×C4—1068no—
590C22×C4—1068no—
591C22×C4—1068no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1068no—
607C22×C4—2124no—
608C22×C4—2124no—
609C22×C4—21216no—
610C22×C4—21216no—
611C22×C4C2×C4×D5314yes—
612C22×C4C2×C4×D5314yes—
613C22×C4C2×C4×D5314yes—
614C22×C4D4×D5314yes—
615C22×C4Q8×D5314yes—
616C22×C4C23×D5312yes—
617C22×C4C23×D5312yes—
618C22×C4C23×D5312yes—
619C22×C4C23×D5312yes—
620C22×C4C23×D5312yes—
621C22×C4C23×D5312yes—
622C22×C4C23×D5312yes—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—44no—
626C4⋊C4—5316no—
627C4⋊C4—5316no—
628C4⋊C4—5316no—
629C4⋊C4—1068no—
630C4⋊C4—1068no—
631C4⋊C4—1068no—
632C4⋊C4—2124no—
633C4⋊C4C2×C4×D53116yescomplemented
634C22⋊C4—5316no—
635C22⋊C4—5316no—
636C22⋊C4—5316no—
637C22⋊C4—1068no—
638C42—44no—
639C42—1068no—
640C42—1068no—
641C42—1068no—
642C42—1068no—
643C42—2124no—
644C23—5316no—
645C23—534no—
646C23—534no—
647C23—534no—
648C23—1068no—
649C23—1068no—
650C23—1068no—
651C23—1068no—
652C23—1068no—
653C23—1062no—
654C23—1062no—
655C23—1062no—
656C23—1062no—
657C23—1068no—
658C23C22×C4×D5312yes—
659C23C2×D4×D5312yes—
660C23C2×Q8×D5312yes—
661C23#41×D5312yes—
662C23#41×D5312yes—
663C23#1313326212yes—
664C23#1313326512yes—
665C23C24×D5311yescharacteristic
666Q8—10632no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—28no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—5316no—
691C2×C4—534no—
692C2×C4—534no—
693C2×C4—534no—
694C2×C4—534no—
695C2×C4—534no—
696C2×C4—534no—
697C2×C4—534no—
698C2×C4—10632no—
699C2×C4—1068no—
700C2×C4—1068no—
701C2×C4—1068no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1068no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—21216no—
718C2×C4—21216no—
719C2×C4—2124no—
720C2×C4—2124no—
721C2×C4C22×C4×D5314yes—
722C2×C4C22×C4×D5314yes—
723C2×C4C22×C4×D5314yes—
724C2×C4C2×D4×D5314yes—
725C2×C4C2×Q8×D5314yes—
726C22—538no—
727C22—1064no—
728C22—1064no—
729C22—1064no—
730C22—1064no—
731C22—10632no—
732C22—1064no—
733C22—1064no—
734C22C4×D4×D5314yes—
735C22C4×Q8×D5314yes—
736C22#1681110414yes—
737C22#1681126214yes—
738C22#1681128814yes—
739C22#1681130514yes—
740C22#1681132714yes—
741C22C23×C4×D5311yescharacteristic
742C22C22×D4×D5311yescharacteristic
743C22C22×Q8×D5311yescharacteristic
744C22C2×#41×D5311yescharacteristic
745C22C2×#41×D5311yescharacteristic
746C22C2×#1313326211yescharacteristic
747C22C2×#1313326511yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—42no—
755C4—538no—
756C4—1064no—
757C4—1064no—
758C4—1064no—
759C4—1064no—
760C4—2122no—
761C4—2122no—
762C2—1068no—
763C2#2027771718yesdirect product factor
764C2C2×C4×D4×D5311yescharacteristic
765C2C2×C4×Q8×D5311yescharacteristic
766C2C2×#1681110411yescharacteristic
767C2C2×#1681126211yescharacteristic
768C2C2×#1681128811yescharacteristic
769C2C2×#1681130511yescharacteristic
770C2C2×#1681132711yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C53×#389C2
socleC24×C53C24
prime radicalC24×D53C23
cosocleC23×C53C25
hypercenterC2×#389D53
hypocenterC53C2×#2360
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#13133182C2semidirect
4. #20277717C2direct (N × H)
5. C2×#16810527C2semidirect
6. C2×#16810520C2semidirect
7. C2×#16810518C2semidirect
8. C2×#16810509C2semidirect
9. C2×#16810504C2semidirect
12. C2×C4×#11719919C2semidirect
16. C2×C53×#389C2semidirect
21. C2×#13133195C4semidirect
24. C2×#13133182C22semidirect
43. #16810527C22semidirect
44. #16810520C22semidirect
45. #16810518C22semidirect
46. #16810509C22semidirect
47. #16810504C22semidirect
50. C4×#11719919C22semidirect
67. C53×#389C22semidirect
73. C22×Dic106C2×C4semidirect
94. #13133195C2×C4semidirect
101. C2×#11719919C2×C4semidirect
102. C2×#11719919C2×C4semidirect
114. C2×#11719921Q8semidirect
147. C2×C4⋊C4×C53C2×C4semidirect
236. C2×Dic106C22×C4semidirect
240. C4⋊C4×C53C22×C4semidirect
245. #11719921C2×Q8semidirect
250. #11719919C22×C4semidirect
251. #11719919C22×C4semidirect
276. C22×D53C4×Q8semidirect
362. C2×D53C2×C4×Q8semidirect
384. C2×#389D53semidirect
393. C2×C53#2360semidirect
436. #389C2×D53semidirect
455. C53C2×#2360semidirect
507. C2×C4⋊C4C4×D53semidirect
633. C4⋊C4C2×C4×D53semidirect
763. C2#20277717direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331952
C22×#131331822
C22×C4⋊C4×D532
#202777172
C2×#168105272
C2×#168105202
C2×#168105182
C2×#168105092
C2×#168105042
C2×#168104942
C2×C4×#117199192
C2×C4×#117199212
C2×#168104702
C2×C53×#3892
C2×#236053