Finite Group Databasebeta

← C2×#20278311 #27552106

Subgroups — C2×#20278311 #27552106

Order 13568.

3246 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×#13133216C211yesmaximal, characteristic, complemented
2C22×#13133194C211yesmaximal, characteristic
3C22×#13133194C211yesmaximal, characteristic
4C22×C4×Dic106C211yesmaximal, characteristic, complemented
5#20278311C2116yesmaximal, direct product factor
6C2×#16810556C211yesmaximal, characteristic, complemented
7C2×#16810555C211yesmaximal, characteristic, complemented
8C2×#16810546C211yesmaximal, characteristic
9C2×#16810546C211yesmaximal, characteristic
10C2×#16810527C211yesmaximal, characteristic, complemented
11C2×#16810521C211yesmaximal, characteristic, complemented
12C2×#16810520C211yesmaximal, characteristic, complemented
13C2×#16810520C211yesmaximal, characteristic, complemented
14C2×#16810516C211yesmaximal, characteristic
15C2×C22⋊C4×Dic53C211yesmaximal, characteristic
16C2×C53×#388C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C24×Dic53C2211yescharacteristic
20C2×#13133216—28no—
21C2×#13133216C2218yescomplemented
22C2×#13133194—28no—
23C2×#13133194—28no—
24C2×#13133194C2218yes—
25C2×#13133194C2218yes—
26C2×C4×Dic106—28no—
27C2×C4×Dic106C2218yescomplemented
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
30C22×C4⋊Dic53C2211yescharacteristic
31C22×C4⋊Dic53C2211yescharacteristic
32C22×C4⋊Dic53C2211yescharacteristic
33C22×#11719919C2211yescharacteristic
34C22×#11719919C2211yescharacteristic
35C22×#11719919C2211yescharacteristic
36C22×#11719919C2211yescharacteristic
37C22×#11719919C2211yescharacteristic
38C22×#11719919C2211yescharacteristic
39C22×#11719919C2211yescharacteristic
40C22×#11719919C2211yescharacteristic
41C22×C22⋊Dic53C2211yescharacteristic
42C22×C22⋊Dic53C2211yescharacteristic
43C22×C22⋊Dic53C2211yescharacteristic
44C22×C4×Dic53C2211yescharacteristic
45C22×C4×Dic53C2211yescharacteristic
46C22×C4×Dic53C2211yescharacteristic
47#16810556C2218yescomplemented
48#16810555C2218yescomplemented
49#16810546C2218yes—
50#16810546C2218yes—
51#16810527C2218yescomplemented
52#16810521C2218yescomplemented
53#16810520C2218yescomplemented
54#16810520C2218yescomplemented
55#16810516C2218yes—
56C22⋊C4×Dic53C2218yes—
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C2×#13133124C2211yescharacteristic
62C2×#13133124C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C22×C22⋊C4×C53C2211yescharacteristic
67C22×C42×C53C2211yescharacteristic
68C53×#388C2218yes—
69C2×#95×C53C2211yescharacteristic
70C2×#95×C53C2211yescharacteristic
71C22×Dic106—24no—
72C22×Dic106—24no—
73C22×Dic106—24no—
74C22×Dic106—24no—
75C22×Dic106—24no—
76C22×Dic106D418yes—
77C22×Dic106C2314yes—
78C22×Dic106C2314yes—
79C23×Dic53—24no—
80C23×Dic53—24no—
81C23×Dic53—24no—
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2311yescharacteristic
86C23×Dic53C2314yes—
87C23×Dic53C2311yescharacteristic
88C23×Dic53C2311yescharacteristic
89C23×Dic53C2311yescharacteristic
90C23×Dic53C2311yescharacteristic
91#13133216—232no—
92#13133194—232no—
93#13133194—232no—
94C4×Dic106—232no—
95C2×C4⋊Dic53—24no—
96C2×C4⋊Dic53—24no—
97C2×C4⋊Dic53—24no—
98C2×C4⋊Dic53—24no—
99C2×C4⋊Dic53—24no—
100C2×C4⋊Dic53C2314yes—
101C2×C4⋊Dic53C2314yes—
102C2×C4⋊Dic53C2314yes—
103C2×C4⋊Dic53C2314yes—
104C2×C4⋊Dic53C2314yes—
105C2×#11719919—24no—
106C2×#11719919—24no—
107C2×#11719919—24no—
108C2×#11719919—24no—
109C2×#11719919—24no—
110C2×#11719919—24no—
111C2×#11719919—24no—
112C2×#11719919D418yes—
113C2×#11719919C2314yes—
114C2×#11719919C2314yes—
115C2×#11719919C2314yes—
116C2×#11719919C2314yes—
117C2×#11719919C2314yes—
118C2×#11719919C2314yes—
119C2×#11719919C2314yes—
120C2×#11719919C2314yes—
121C2×C22⋊Dic53—24no—
122C2×C22⋊Dic53—24no—
123C2×C22⋊Dic53—24no—
124C2×C22⋊Dic53C2314yes—
125C2×C22⋊Dic53C2314yes—
126C2×C22⋊Dic53C2314yes—
127C2×C4×Dic53—24no—
128C2×C4×Dic53—24no—
129C2×C4×Dic53—24no—
130C2×C4×Dic53C2314yes—
131C2×C4×Dic53C2314yes—
132C2×C4×Dic53C2314yes—
133#13133124C2314yes—
134#13133124C2314yes—
135#13133124C2314yes—
136#13133124C2314yes—
137#13133124C2314yes—
138#13133124C2314yes—
139C25×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C2×C4⋊C4×C53—24no—
147C2×C4⋊C4×C53C2314yes—
148C2×C22⋊C4×C53—24no—
149C2×C22⋊C4×C53—24no—
150C2×C22⋊C4×C53Q818yescomplemented
151C2×C22⋊C4×C53C2314yes—
152C2×C22⋊C4×C53C2314yes—
153C2×C22⋊C4×C53C2314yes—
154C2×C42×C53—24no—
155C2×C42×C53C2314yes—
156#95×C53C2314yes—
157#95×C53C2314yes—
158C24×C53—22no—
159C24×C53—22no—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53—22no—
163C24×C53—22no—
164C24×C53C2×Q814yes—
165C24×C53C2412yes—
166C24×C53C2411yescharacteristic
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×C53C2×D414yes—
182C22×C4×C53C2×D414yes—
183C22×C4×C53C2×Q814yes—
184C22×C4×C53C2×Q814yes—
185C22×C4×C53C2412yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C22×C4×C53C2412yes—
190C22×C4×C53C2412yes—
191C22×Dic53—22no—
192C22×Dic53—22no—
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×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—28no—
210C22×Dic53—28no—
211C22×Dic53—28no—
212C22×Dic53—416no—
213C22×Dic53C2×D414yes—
214C22×Dic53C2×D414yes—
215C22×Dic53C2×D414yes—
216C22×Dic53C2×D414yes—
217C22×Dic53#4114yes—
218C22×Dic53#4114yes—
219C22×Dic53C2412yes—
220C22×Dic53C2412yes—
221C22×Dic53C2412yes—
222C22×Dic53C2412yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C22×Dic53C2412yes—
226C22×Dic53C2412yes—
227C2×Dic106—232no—
228C2×Dic106—28no—
229C2×Dic106—28no—
230C2×Dic106—28no—
231C2×Dic106—28no—
232C2×Dic106—28no—
233C2×Dic106—416no—
234C2×Dic106C2×D4116yes—
235C4⋊C4×C53—28no—
236C22⋊C4×C53—28no—
237C22⋊C4×C53—28no—
238C22⋊C4×C53C2×Q8116yescomplemented
239C42×C53—28no—
240C22⋊Dic53—28no—
241C22⋊Dic53—28no—
242C22⋊Dic53—28no—
243C4⋊Dic53—28no—
244C4⋊Dic53—28no—
245C4⋊Dic53—28no—
246C4⋊Dic53—28no—
247C4⋊Dic53—28no—
248#11719919—28no—
249#11719919—28no—
250#11719919—28no—
251#11719919—28no—
252#11719919—28no—
253#11719919—28no—
254#11719919—28no—
255#11719919C2×D4116yes—
256C4×Dic53—28no—
257C4×Dic53—28no—
258C4×Dic53—28no—
259C23×C53—28no—
260C23×C53—28no—
261C23×C53—28no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—44no—
269C23×C53—44no—
270C23×C53—44no—
271C23×C53—44no—
272C23×C53C22×D412yes—
273C23×C53C22×D412yes—
274C23×C53C22×Q814yes—
275C23×C53C22×Q812yes—
276C23×C53C2×#4112yes—
277C23×C53C2×#4112yes—
278C23×C532−1+412yes—
279C23×C532−1+412yes—
280C23×C53C2511yescharacteristic
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—44no—
300C2×C4×C53—44no—
301C2×C4×C53C22×D414yes—
302C2×C4×C53C22×D414yes—
303C2×C4×C53C22×Q814yes—
304C2×C4×C53C22×Q814yes—
305C2×Dic53—28no—
306C2×Dic53—28no—
307C2×Dic53—28no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
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×Dic53—44no—
329C2×Dic53—44no—
330C2×Dic53—416no—
331C2×Dic53#121116yes—
332C2×Dic53C22×D414yes—
333C2×Dic53C22×D414yes—
334C2×Dic53C22×D414yes—
335C2×Dic53C22×D414yes—
336C2×Dic53C2×#4114yes—
337C2×Dic53C2×#4114yes—
338Dic106—232no—
339Dic106—416no—
340C2×#2429—531nomaximal, Sylow
341C22×C53—24no—
342C22×C53—24no—
343C22×C53—24no—
344C22×C53—42no—
345C22×C53—416no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53C2×#12114yes—
350C22×C53#53314yes—
351C22×C53#54114yes—
352C22×C53#54714yes—
353C22×C53#54814yes—
354C22×C53D4×Q814yes—
355C22×C53D4×Q814yes—
356C22×C53C23×D411yescharacteristic
357C22×C53C23×D411yescharacteristic
358C22×C53C23×Q811yescharacteristic
359C22×C53C22×#4111yescharacteristic
360C22×C53C22×#4111yescharacteristic
361C22×C53C2×2−1+411yescharacteristic
362C22×C53C2×2−1+411yescharacteristic
363C4×C53—24no—
364C4×C53—24no—
365C4×C53—24no—
366C4×C53—24no—
367C4×C53—42no—
368C4×C53—42no—
369Dic53—24no—
370Dic53—24no—
371Dic53—24no—
372Dic53—42no—
373Dic53—42no—
374Dic53—42no—
375Dic53—42no—
376Dic53C2×#12118yes—
377C22×C4⋊Q8—531no—
378C22×C22⋊Q8—531no—
379C22×C22⋊Q8—531no—
380C22×C4×Q8—531no—
381#2429—5316no—
382C2×#398—531no—
383C2×#398—531no—
384C2×#396—531no—
385C2×#396—531no—
386C2×#391—531no—
387C2×#389—531no—
388C2×#389—531no—
389C2×#389—531no—
390C2×#388—531no—
391C2×#388D5311yescharacteristic
392C2×C4×C22⋊C4—531no—
393C2×C53—44no—
394C2×C53#242918yescomplemented
395C2×C53C22×#12111yescharacteristic
396C2×C53C2×#53311yescharacteristic
397C2×C53C2×#54111yescharacteristic
398C2×C53C2×#54711yescharacteristic
399C2×C53C2×#54811yescharacteristic
400C2×C53C2×D4×Q811yescharacteristic
401C2×C53C2×D4×Q811yescharacteristic
402C23×Q8—531no—
403C23×Q8—531no—
404C24×C4—531no—
405C2×C4⋊Q8—538no—
406C2×C4⋊Q8—1068no—
407C2×C22⋊Q8—538no—
408C2×C22⋊Q8—538no—
409C2×C22⋊Q8—1068no—
410C2×C22⋊Q8—1068no—
411C2×C4×Q8—538no—
412C2×C4×Q8—1068no—
413C22×C4⋊C4—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4—531no—
418C22×C4⋊C4—531no—
419C22×C4⋊C4—531no—
420C22×C4⋊C4—531no—
421C22×C4⋊C4—531no—
422C22×C4⋊C4—531no—
423C22×C4⋊C4—531no—
424C22×C4⋊C4—531no—
425C22×C4⋊C4—531no—
426C22×C4⋊C4C2×D5311yescharacteristic
427C22×C22⋊C4—531no—
428C22×C22⋊C4—531no—
429C22×C22⋊C4—531no—
430C22×C22⋊C4C2×D5311yescharacteristic
431C22×C22⋊C4C2×D5311yescharacteristic
432C22×C22⋊C4C2×D5311yescharacteristic
433C22×C42—531no—
434C22×C42—531no—
435C22×C42—531no—
436C22×C42C2×D5311yescharacteristic
437#398—538no—
438#398—538no—
439#396—538no—
440#396—538no—
441#391—538no—
442#389—538no—
443#389—538no—
444#389—538no—
445#388—538no—
446#388C2×D5318yes—
447C4×C22⋊C4—538no—
448C2×#95—531no—
449C2×#95—531no—
450C2×#95—531no—
451C2×#95—531no—
452C2×#95—531no—
453C2×#95—531no—
454C2×#95C2×D5311yescharacteristic
455C2×#95C2×D5311yescharacteristic
456C53C2×#242911yescharacteristic, complemented, Sylow
457C25C22×D5311yescharacteristic
458C22×Q8—538no—
459C22×Q8—534no—
460C22×Q8—534no—
461C22×Q8—1064no—
462C22×Q8—1064no—
463C22×Q8—1064no—
464C22×Q8—1064no—
465C22×Q8—1064no—
466C23×C4—531no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4—534no—
471C23×C4—531no—
472C23×C4—531no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—1064no—
476C23×C4—1064no—
477C23×C4—1064no—
478C23×C4C22×D5311yescharacteristic
479C23×C4C22×D5311yescharacteristic
480C23×C4C22×D5311yescharacteristic
481C23×C4C22×D5311yescharacteristic
482C23×C4C22×D5311yescharacteristic
483C23×C4C22×D5311yescharacteristic
484C4⋊Q8—10632no—
485C22⋊Q8—10632no—
486C22⋊Q8—10632no—
487C4×Q8—10632no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—538no—
490C2×C4⋊C4—534no—
491C2×C4⋊C4—534no—
492C2×C4⋊C4—534no—
493C2×C4⋊C4—534no—
494C2×C4⋊C4—534no—
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—534no—
503C2×C4⋊C4—1064no—
504C2×C4⋊C4—1064no—
505C2×C4⋊C4—1064no—
506C2×C4⋊C4—1064no—
507C2×C4⋊C4—1064no—
508C2×C4⋊C4—1064no—
509C2×C4⋊C4—1064no—
510C2×C4⋊C4—1064no—
511C2×C4⋊C4—1064no—
512C2×C4⋊C4—1064no—
513C2×C4⋊C4—1064no—
514C2×C4⋊C4—1064no—
515C2×C4⋊C4C22×D5314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—534no—
519C2×C22⋊C4—534no—
520C2×C22⋊C4—534no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—1064no—
523C2×C22⋊C4—1064no—
524C2×C22⋊C4Dic10618yescomplemented
525C2×C22⋊C4C22×D5314yes—
526C2×C22⋊C4C22×D5314yes—
527C2×C22⋊C4C22×D5314yes—
528C2×C42—24no—
529C2×C42—534no—
530C2×C42—534no—
531C2×C42—534no—
532C2×C42—1064no—
533C2×C42—1064no—
534C2×C42—1064no—
535C2×C42C22×D5314yes—
536#95—534no—
537#95—534no—
538#95—534no—
539#95—534no—
540#95—534no—
541#95—534no—
542#95C22×D5314yes—
543#95C22×D5314yes—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24C2×Dic10614yes—
551C24C23×D5312yes—
552C24C23×D5311yescharacteristic
553C2×Q8—5316no—
554C2×Q8—1068no—
555C2×Q8—10632no—
556C2×Q8—1068no—
557C2×Q8—1068no—
558C2×Q8—1068no—
559C2×Q8—1068no—
560C2×Q8—21216no—
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—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—534no—
576C22×C4—534no—
577C22×C4—534no—
578C22×C4—532no—
579C22×C4—534no—
580C22×C4—534no—
581C22×C4—534no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—532no—
587C22×C4—532no—
588C22×C4—532no—
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—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—21216no—
611C22×C4C2×Dic10614yes—
612C22×C4C2×Dic10614yes—
613C22×C4D4×D5314yes—
614C22×C4D4×D5314yes—
615C22×C4C23×D5312yes—
616C22×C4C23×D5312yes—
617C22×C4C23×D5312yes—
618C22×C4C23×D5312yes—
619C22×C4C23×D5312yes—
620C22×C4C23×D5312yes—
621C4⋊C4—28no—
622C4⋊C4—5316no—
623C4⋊C4—1068no—
624C4⋊C4—1068no—
625C4⋊C4—1068no—
626C4⋊C4—1068no—
627C4⋊C4—1068no—
628C4⋊C4—1068no—
629C4⋊C4—1068no—
630C4⋊C4—1068no—
631C4⋊C4—1068no—
632C4⋊C4—1068no—
633C4⋊C4—1068no—
634C4⋊C4—1068no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—1068no—
638C22⋊C4—1068no—
639C22⋊C4—1068no—
640C22⋊C4C2×Dic106116yescomplemented
641C42—28no—
642C42—1068no—
643C42—1068no—
644C42—1068no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23C2×D4×D5312yes—
659C23C2×D4×D5312yes—
660C23C22×Dic10614yes—
661C23C22×Dic10612yes—
662C23#41×D5312yes—
663C23#41×D5312yes—
664C23#1313326412yes—
665C23#1313326412yes—
666C23C24×D5311yescharacteristic
667Q8—10632no—
668Q8—21216no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—28no—
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—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—5316no—
690C2×C4—534no—
691C2×C4—534no—
692C2×C4—534no—
693C2×C4—534no—
694C2×C4—534no—
695C2×C4—534no—
696C2×C4—1068no—
697C2×C4—1068no—
698C2×C4—1068no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
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—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—21216no—
718C2×C4—2124no—
719C2×C4—2124no—
720C2×C4—2124no—
721C2×C4—2124no—
722C2×C4C2×D4×D5314yes—
723C2×C4C2×D4×D5314yes—
724C2×C4C22×Dic10614yes—
725C2×C4C22×Dic10614yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22#121×D5314yes—
735C22#1681117614yes—
736C22#1681123014yes—
737C22#1681127114yes—
738C22#1681128114yes—
739C22D4×Dic10614yes—
740C22D4×Dic10614yes—
741C22C22×D4×D5311yescharacteristic
742C22C22×D4×D5311yescharacteristic
743C22C23×Dic10611yescharacteristic
744C22C2×#41×D5311yescharacteristic
745C22C2×#41×D5311yescharacteristic
746C22C2×#1313326411yescharacteristic
747C22C2×#1313326411yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—538no—
755C4—1064no—
756C4—1064no—
757C4—1064no—
758C4—2122no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C2—44no—
763C2#2027831118yesdirect product factor
764C2C2×#121×D5311yescharacteristic
765C2C2×#1681117611yescharacteristic
766C2C2×#1681123011yescharacteristic
767C2C2×#1681127111yescharacteristic
768C2C2×#1681128111yescharacteristic
769C2C2×D4×Dic10611yescharacteristic
770C2C2×D4×Dic10611yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#388C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#388D53
hypocenterC53C2×#2429
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13133216C2semidirect
4. C22×C4×Dic106C2semidirect
5. #20278311C2direct (N × H)
6. C2×#16810556C2semidirect
7. C2×#16810555C2semidirect
10. C2×#16810527C2semidirect
11. C2×#16810521C2semidirect
12. C2×#16810520C2semidirect
13. C2×#16810520C2semidirect
21. C2×#13133216C22semidirect
27. C2×C4×Dic106C22semidirect
47. #16810556C22semidirect
48. #16810555C22semidirect
51. #16810527C22semidirect
52. #16810521C22semidirect
53. #16810520C22semidirect
54. #16810520C22semidirect
150. C2×C22⋊C4×C53Q8semidirect
238. C22⋊C4×C53C2×Q8semidirect
394. C2×C53#2429semidirect
456. C53C2×#2429semidirect
524. C2×C22⋊C4Dic106semidirect
640. C22⋊C4C2×Dic106semidirect
763. C2#20278311direct (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×#131331942
C22×C4×Dic1062
#202783112
C2×#168105562
C2×#168105552
C2×#168105462
C2×#168105272
C2×#168105212
C2×#168105202
C2×#168105162
C2×C22⋊C4×Dic532
C2×C53×#3882
C2×#242953