Finite Group Databasebeta

← #16031698

Subgroups — #16031698

Order 3328.

5570 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6127C211yesmaximal, characteristic, complemented
2C2×#11719182C212yesmaximal, complemented
3C2×#11719496C211yesmaximal, characteristic, complemented
4#13118494C211yesmaximal, characteristic, complemented
5#13118487C211yesmaximal, characteristic, complemented
6#13118480C211yesmaximal, characteristic, complemented
7#13118473C211yesmaximal, characteristic, complemented
8#13118464C212yesmaximal, complemented
9#13118455C212yesmaximal, complemented
10#13118446C214yesmaximal, complemented
11#13118204C214yesmaximal, complemented
12#13118052C214yesmaximal, complemented
13C4×#88136C214yesmaximal, complemented
14#13117326C212yesmaximal, complemented
15C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C23×C22⋊D13C2212yes—
18C22×#6127—28no—
19C22×#6127—216no—
20C22×#6127C2212yes—
21C22×#6127C2212yes—
22C22×#6127C2212yes—
23C22×#6127C2212yes—
24C22×#6127C2211yescharacteristic, complemented
25C23×D52C2211yescharacteristic
26C23×C4×D13C2212yes—
27C23×Dic26C2211yescharacteristic
28C22×C13×C22⋊C4C2212yes—
29C22×C42×C13C2212yescomplemented
30C2×#88207C2212yes—
31#11719496—28no—
32C2×#88184C2211yescharacteristic
33C2×#88184C2211yescharacteristic, complemented
34C2×#88184C2218yescomplemented
35C2×#88183C2212yescomplemented
36C2×C4×C22⋊D13C2212yes—
37C2×C4×C22⋊D13C2212yescomplemented
38C2×#88180C2211yescharacteristic, complemented
39C2×#88178C2211yescharacteristic
40C2×#88178C2211yescharacteristic, complemented
41C2×#88136C2214yes—
42#11719182—216no—
43C2×#88129C2212yescomplemented
44C2×#88129C2212yescomplemented
45C2×#88128C2212yescomplemented
46C2×C4×D52C2218yescomplemented
47C2×#88123C2212yescomplemented
48C4×C13×C22⋊C4C2211yescharacteristic
49C4×C13×C22⋊C4C2211yescharacteristic
50C4×C13×C22⋊C4C2212yes—
51C4×C13×C22⋊C4C2212yescomplemented
52C4×C13×C22⋊C4C2212yescomplemented
53C2×C13×#95C2212yescomplemented
54#11718874C2218yescomplemented
55#11718622C2218yescomplemented
56#11718621C2218yescomplemented
57#11718619C2214yes—
58#11718616C2214yes—
59#11718611C2214yes—
60#11718600C2212yescomplemented
61#11718600C2212yescomplemented
62C4×#6103C2218yescomplemented
63#11718590C2212yescomplemented
64#11718590C2212yescomplemented
65#11718334C2214yescomplemented
66#11718333C2214yescomplemented
67#11718332C2214yescomplemented
68#11718329C2218yescomplemented
69#11718326C2218yescomplemented
70#11718317C2214yescomplemented
71C25×C13C2311yescharacteristic
72C24×D13C2312yes—
73C23×C4×C13—28no—
74C23×C4×C13D418yescomplemented
75C23×C4×C13C2314yes—
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—28no—
83C22×C22⋊D13—216no—
84C22×C22⋊D13C2312yes—
85C22×C22⋊D13C2312yes—
86C22×C22⋊D13C2314yes—
87C22×C22⋊D13C2314yes—
88C22×C22⋊D13C2312yes—
89C23×Dic13C2312yes—
90C2×#6127—2128no—
91C2×#6127—28no—
92C2×#6127—28no—
93C2×#6127—28no—
94C2×#6127—28no—
95C2×#6127—28no—
96C2×#6127—216no—
97C2×#6127—28no—
98C2×#6127—24no—
99C2×#6127—28no—
100C2×#6127—216no—
101C2×#6127—28no—
102C2×#6127D4116yescomplemented
103C22×D52—24no—
104C22×D52—28no—
105C22×D52C2311yescharacteristic
106C22×D52C2312yes—
107C22×D52C2318yes—
108C22×D52C2312yes—
109C22×C4×D13—28no—
110C22×C4×D13—216no—
111C22×C4×D13C2312yes—
112C22×C4×D13C2314yes—
113C22×C4×D13C2314yes—
114C22×Dic26—24no—
115C22×Dic26—28no—
116C22×Dic26C2311yescharacteristic
117C22×Dic26C2312yes—
118C22×Dic26C2312yes—
119C2×C13×C22⋊C4—28no—
120C2×C13×C22⋊C4C2312yes—
121C2×C13×C22⋊C4C2314yes—
122C2×C13×C22⋊C4C2312yes—
123C2×C42×C13—28no—
124C2×C42×C13C2312yes—
125C2×C42×C13C2314yes—
126C2×C42×C13C2312yes—
127#88207—28no—
128C2×C22⋊Dic13C2312yes—
129C2×C22⋊Dic13C2312yes—
130C2×C22⋊Dic13C2312yes—
131#88184—24no—
132#88184—24no—
133#88184—232no—
134#88183—28no—
135C4×C22⋊D13—28no—
136C4×C22⋊D13—28no—
137C2×#6103C2318yes—
138C2×#6103C2318yes—
139C2×#6103C2318yes—
140C2×#6103C2312yes—
141C2×#6103C2312yes—
142C2×#6103C2318yes—
143#88180—24no—
144C2×C4⋊Dic13C2318yes—
145C2×C4⋊Dic13C2311yescharacteristic
146C2×C4⋊Dic13C2311yescharacteristic
147#88178—24no—
148#88178—24no—
149C2×#6101C2312yes—
150C2×#6101C2312yes—
151C2×C4×Dic13C2312yes—
152#88136—216no—
153#88129—28no—
154#88129—28no—
155#88128—28no—
156C4×D52—232no—
157#88123—28no—
158C13×#95C2312yes—
159C13×#95C2314yes—
160C13×#95C2312yes—
161#88071C2318yes—
162#88071C2318yes—
163#34738—131nomaximal, Sylow
164C24×C13—24no—
165C24×C13—24no—
166C24×C13—42no—
167C24×C13C2×D414yes—
168C24×C13C2411yescharacteristic
169C24×C13C2411yescharacteristic
170C24×C13C2411yescharacteristic
171C23×D13—24no—
172C23×D13—28no—
173C23×D13—28no—
174C23×D13—44no—
175C23×D13C2412yes—
176C23×D13C2414yes—
177C22×C4×C13—24no—
178C22×C4×C13—232no—
179C22×C4×C13—24no—
180C22×C4×C13—24no—
181C22×C4×C13—24no—
182C22×C4×C13—24no—
183C22×C4×C13—28no—
184C22×C4×C13—28no—
185C22×C4×C13—44no—
186C22×C4×C13C2×D414yes—
187C22×C4×C13C2×D414yes—
188C22×C4×C13C2×D414yes—
189C22×C4×C13C2×D414yes—
190C22×C4×C13C2×D414yes—
191C22×C4×C13C2×D414yes—
192C22×C4×C13C2×D418yes—
193C22×C4×C13C2414yes—
194C22×C4×C13C2411yescharacteristic
195C22×C4×C13C2411yescharacteristic
196C22×C4×C13C2414yes—
197C22×C4×C13C2411yescharacteristic
198C22×C4×C13C2411yescharacteristic
199C2×C22⋊D13—264no—
200C2×C22⋊D13—28no—
201C2×C22⋊D13—28no—
202C2×C22⋊D13—28no—
203C2×C22⋊D13—28no—
204C2×C22⋊D13—24no—
205C2×C22⋊D13—24no—
206C2×C22⋊D13—24no—
207C2×C22⋊D13—28no—
208C2×C22⋊D13—28no—
209C2×C22⋊D13—28no—
210C2×C22⋊D13—44no—
211C2×C22⋊D13C2×D4116yes—
212C22×Dic13—24no—
213C22×Dic13—28no—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2414yes—
218#6127—264no—
219#6127—264no—
220#6127—264no—
221#6127—264no—
222#6127—416no—
223C2×D52—232no—
224C2×D52—28no—
225C2×D52—24no—
226C2×D52—24no—
227C2×D52—24no—
228C2×D52—216no—
229C2×D52—24no—
230C2×D52—22no—
231C2×D52—216no—
232C2×D52—48no—
233C2×D52C2×D418yes—
234C2×C4×D13—264no—
235C2×C4×D13—28no—
236C2×C4×D13—28no—
237C2×C4×D13—28no—
238C2×C4×D13—28no—
239C2×C4×D13—28no—
240C2×C4×D13—28no—
241C2×C4×D13—24no—
242C2×C4×D13C2×D4116yes—
243C2×Dic26—232no—
244C2×Dic26—24no—
245C2×Dic26—24no—
246C2×Dic26—24no—
247C2×Dic26—28no—
248C2×Dic26—24no—
249C2×Dic26—22no—
250C2×Dic26C2×D418yes—
251C13×C22⋊C4—24no—
252C13×C22⋊C4—28no—
253C13×C22⋊C4#4118yescomplemented
254C42×C13—24no—
255C42×C13—28no—
256C42×C13—24no—
257C22⋊Dic13—24no—
258C22⋊Dic13—24no—
259C22⋊Dic13—24no—
260#6103—216no—
261#6103—24no—
262#6103—24no—
263#6103—216no—
264#6103—216no—
265#6103—48no—
266C4⋊Dic13—22no—
267C4⋊Dic13—22no—
268C4⋊Dic13—216no—
269#6101—24no—
270#6101—24no—
271C4×Dic13—24no—
272C23×#41—131no—
273C2×#532—132no—
274C2×#525—131no—
275#2436—131no—
276#2435—131no—
277#2434—131no—
278#2433—131no—
279#2432—132no—
280#2431—132no—
281#2430—134no—
282#2410—134no—
283#2388—134no—
284C4×#120—134no—
285#2297—132no—
286C2×C4×C22⋊C4D1311yescharacteristic, complemented
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—28no—
292C23×C13—28no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—44no—
297C23×C13—416no—
298C23×C13C22×D412yes—
299C23×C13C22×D412yes—
300C23×C13C22×D414yes—
301C23×C13C22×D412yes—
302C23×C13C2×#4114yes—
303C23×C13C2511yescharacteristic
304C22×D13—216no—
305C22×D13—24no—
306C22×D13—24no—
307C22×D13—28no—
308C22×D13—28no—
309C22×D13—24no—
310C22×D13—22no—
311C22×D13—24no—
312C22×D13—24no—
313C22×D13—432no—
314C22×D13—48no—
315C22×D13—48no—
316C22×D13C22×D418yes—
317C2×C4×C13—28no—
318C2×C4×C13—24no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—24no—
322C2×C4×C13—28no—
323C2×C4×C13—28no—
324C2×C4×C13—28no—
325C2×C4×C13—28no—
326C2×C4×C13—24no—
327C2×C4×C13—24no—
328C2×C4×C13—24no—
329C2×C4×C13—416no—
330C2×C4×C13#120116yescomplemented
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D414yes—
336C2×C4×C13C22×D414yes—
337C2×C4×C13C2×#4118yescomplemented
338C22⋊D13—232no—
339C22⋊D13—232no—
340C22⋊D13—48no—
341C22⋊D13—48no—
342C22⋊D13—48no—
343C2×Dic13—216no—
344C2×Dic13—24no—
345C2×Dic13—24no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—24no—
350C2×Dic13—24no—
351C2×Dic13—24no—
352C2×Dic13C22×D418yes—
353D52—216no—
354D52—216no—
355D52—432no—
356D52—44no—
357C4×D13—232no—
358C4×D13—232no—
359C4×D13—48no—
360Dic26—216no—
361Dic26—216no—
362Dic26—44no—
363C22×#41—132no—
364C22×#41—132no—
365C22×#41—132no—
366C22×#41—132no—
367C22×#41—131no—
368C22×#41—2616no—
369C22×#41—268no—
370C23×Q8—131no—
371C23×D4—132no—
372C23×D4—131no—
373C24×C4—132no—
374C24×C4C2×D1311yescharacteristic
375#532—2616no—
376C2×C4⋊Q8—132no—
377C2×#127—132no—
378C2×#124—132no—
379C2×#124—132no—
380#525—268no—
381C2×#123—132no—
382C2×C22⋊Q8—131no—
383C2×C22⋊Q8—131no—
384C2×#121—131no—
385C2×#121—138no—
386C2×#121—131no—
387C2×#120—132no—
388C2×#120—134no—
389C2×C4×D4—132no—
390C2×C4×D4—132no—
391C2×C4×D4—138no—
392C2×#117—131no—
393C22×C22⋊C4C2×D1312yes—
394C22×C42C2×D1312yescomplemented
395#395—134no—
396#394—138no—
397#394—134no—
398#393—134no—
399#392—138no—
400#392—134no—
401#391—132no—
402#391—132no—
403#390—132no—
404#390—132no—
405#386—138no—
406#386—134no—
407#386—138no—
408#385—134no—
409#385—138no—
410#379—134no—
411C4×C22⋊C4—138no—
412C4×C22⋊C4C2×D1311yescharacteristic
413C4×C22⋊C4C2×D1311yescharacteristic
414C4×C22⋊C4C2×D1312yes—
415C4×C22⋊C4C2×D1312yescomplemented
416C4×C22⋊C4C2×D1312yescomplemented
417C2×#95C2×D1312yescomplemented
418C22×C13—22no—
419C22×C13—22no—
420C22×C13—22no—
421C22×C13—22no—
422C22×C13—28no—
423C22×C13—28no—
424C22×C13—22no—
425C22×C13—22no—
426C22×C13—22no—
427C22×C13—416no—
428C22×C13—44no—
429C22×C13C2×#12014yes—
430C22×C13#53214yescomplemented
431C22×C13C23×D411yescharacteristic
432C22×C13C23×D412yes—
433C22×C13C22×#4112yes—
434C22×C13#58512yes—
435C2×D13—28no—
436C2×D13—216no—
437C2×D13—432no—
438C2×D13—44no—
439C2×D13—44no—
440C2×D13—48no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C2×D13—48no—
445C4×C13—22no—
446C4×C13—22no—
447C4×C13—28no—
448C4×C13—44no—
449C4×C13C2×#12014yes—
450C4×C13C2×#12014yes—
451Dic13—28no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455C25—132no—
456C25C22×D1311yescharacteristic
457C2×#41—1316no—
458C2×#41—2616no—
459C2×#41—2616no—
460C2×#41—268no—
461C2×#41—268no—
462C2×#41—26128no—
463C2×#41—268no—
464C2×#41—268no—
465C2×#41—268no—
466C2×#41—268no—
467C2×#41—264no—
468C2×#41—268no—
469C2×#41—268no—
470C22×Q8—132no—
471C22×Q8—131no—
472C22×Q8—132no—
473C22×Q8—268no—
474C22×Q8—264no—
475C22×D4—134no—
476C22×D4—132no—
477C22×D4—132no—
478C22×D4—134no—
479C22×D4—132no—
480C22×D4—132no—
481C22×D4—131no—
482C22×D4—132no—
483C22×D4—138no—
484C22×D4—268no—
485C22×D4—2616no—
486C22×D4—268no—
487C22×D4—264no—
488C23×C4—28no—
489C23×C4—134no—
490C23×C4—132no—
491C23×C4—134no—
492C23×C4—132no—
493C23×C4—2616no—
494C23×C4—268no—
495C23×C4D5218yescomplemented
496C23×C4C22×D1314yes—
497C23×C4C22×D1311yescharacteristic
498C23×C4C22×D1311yescharacteristic
499C23×C4C22×D1311yescharacteristic
500C23×C4C22×D1311yescharacteristic
501C23×C4C22×D1311yescharacteristic
502C23×C4C22×D1311yescharacteristic
503C4⋊Q8—268no—
504#127—268no—
505#124—268no—
506#124—268no—
507#123—268no—
508C22⋊Q8—264no—
509C22⋊Q8—264no—
510#121—2632no—
511#121—264no—
512#121—264no—
513#120—268no—
514#120—2616no—
515C4×D4—2632no—
516C4×D4—268no—
517C4×D4—268no—
518#117—264no—
519C2×C4⋊C4—131no—
520C2×C4⋊C4—131no—
521C2×C4⋊C4—138no—
522C2×C4⋊C4—132no—
523C2×C4⋊C4—132no—
524C2×C22⋊C4—28no—
525C2×C22⋊C4—132no—
526C2×C22⋊C4—132no—
527C2×C22⋊C4—132no—
528C2×C22⋊C4—132no—
529C2×C22⋊C4—132no—
530C2×C22⋊C4—138no—
531C2×C22⋊C4—138no—
532C2×C22⋊C4—138no—
533C2×C22⋊C4—138no—
534C2×C22⋊C4C22×D1312yes—
535C2×C22⋊C4C22×D1314yes—
536C2×C22⋊C4C22×D1312yes—
537C2×C42—28no—
538C2×C42—132no—
539C2×C42C22×D1312yes—
540C2×C42C22×D1312yes—
541C2×C42C22×D1314yes—
542#95—138no—
543#95—138no—
544#95C22×D1314yes—
545#95C22×D1312yes—
546#95C22×D1312yes—
547C2×C13—24no—
548C2×C13—24no—
549C2×C13—42no—
550C2×C13C22×#12011yescharacteristic
551C2×C13C2×#53211yescharacteristic
552C2×C13#344911yescharacteristic
553C2×C13D4×#4114yes—
554D13—48no—
555D13—82no—
556C24—24no—
557C24—24no—
558C24—42no—
559C24—134no—
560C24—132no—
561C24—268no—
562C24—264no—
563C24—268no—
564C24—524no—
565C24C2×D5214yes—
566C24C23×D1311yescharacteristic
567C24C23×D1311yescharacteristic
568C24C23×D1311yescharacteristic
569#41—2664no—
570#41—2664no—
571#41—2664no—
572#41—2664no—
573#41—5216no—
574C2×Q8—138no—
575C2×Q8—268no—
576C2×Q8—2632no—
577C2×Q8—264no—
578C2×Q8—264no—
579C2×Q8—262no—
580C2×Q8—264no—
581C2×Q8—264no—
582C2×D4—1316no—
583C2×D4—138no—
584C2×D4—268no—
585C2×D4—2632no—
586C2×D4—2616no—
587C2×D4—268no—
588C2×D4—268no—
589C2×D4—2664no—
590C2×D4—268no—
591C2×D4—268no—
592C2×D4—268no—
593C2×D4—264no—
594C2×D4—264no—
595C2×D4—264no—
596C2×D4—268no—
597C2×D4—268no—
598C2×D4—264no—
599C2×D4—264no—
600C2×D4—262no—
601C2×D4—2616no—
602C2×D4—264no—
603C2×D4—264no—
604C2×D4—528no—
605C2×D4—524no—
606C22×C4—24no—
607C22×C4—232no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—44no—
615C22×C4—134no—
616C22×C4—1316no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—268no—
621C22×C4—268no—
622C22×C4—2664no—
623C22×C4—268no—
624C22×C4—264no—
625C22×C4—268no—
626C22×C4—268no—
627C22×C4—268no—
628C22×C4—264no—
629C22×C4—268no—
630C22×C4C2×D5214yes—
631C22×C4C2×D5214yes—
632C22×C4C2×D5214yes—
633C22×C4C2×D5214yes—
634C22×C4C2×D5214yes—
635C22×C4C2×D5214yes—
636C22×C4D4×D1318yes—
637C22×C4C23×D1314yes—
638C22×C4C23×D1311yescharacteristic
639C22×C4C23×D1311yescharacteristic
640C22×C4C23×D1314yes—
641C22×C4C23×D1311yescharacteristic
642C22×C4C23×D1311yescharacteristic
643C4⋊C4—2616no—
644C4⋊C4—262no—
645C4⋊C4—262no—
646C4⋊C4—264no—
647C4⋊C4—264no—
648C22⋊C4—24no—
649C22⋊C4—28no—
650C22⋊C4—2616no—
651C22⋊C4—2616no—
652C22⋊C4—264no—
653C22⋊C4—264no—
654C22⋊C4—264no—
655C22⋊C4—264no—
656C22⋊C4—264no—
657C22⋊C4—2616no—
658C22⋊C4—528no—
659C22⋊C4#612718yescomplemented
660C42—28no—
661C42—24no—
662C42—24no—
663C42—264no—
664C13#3473811yescharacteristic, complemented, Sylow
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—28no—
670C23—28no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—44no—
675C23—416no—
676C23—138no—
677C23—2616no—
678C23—264no—
679C23—268no—
680C23—264no—
681C23—268no—
682C23—262no—
683C23—264no—
684C23—264no—
685C23—264no—
686C23—5232no—
687C23—528no—
688C23—528no—
689C23C22×D5212yes—
690C23C22×D5212yes—
691C23C22×D5212yes—
692C23C2×#612714yes—
693C23C2×D4×D1314yes—
694C23C24×D1311yescharacteristic
695Q8—2616no—
696Q8—2616no—
697Q8—524no—
698D4—2616no—
699D4—2632no—
700D4—2632no—
701D4—2616no—
702D4—5232no—
703D4—528no—
704D4—528no—
705D4—528no—
706D4—524no—
707C2×C4—28no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—416no—
720C2×C4—138no—
721C2×C4—2632no—
722C2×C4—2616no—
723C2×C4—264no—
724C2×C4—264no—
725C2×C4—2632no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—264no—
730C2×C4—264no—
731C2×C4—264no—
732C2×C4—528no—
733C2×C4#88136116yescomplemented
734C2×C4C22×D5212yes—
735C2×C4C22×D5212yes—
736C2×C4C22×D5212yes—
737C2×C4C22×D5212yes—
738C2×C4C2×#612718yescomplemented
739C2×C4C2×D4×D1314yes—
740C2×C4C2×D4×D1314yes—
741C22—22no—
742C22—28no—
743C22—28no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—44no—
752C22—268no—
753C22—2616no—
754C22—5232no—
755C22—528no—
756C22—524no—
757C22—524no—
758C22—522no—
759C22—528no—
760C22—522no—
761C22—522no—
762C22#1171918214yescomplemented
763C22C2×#8813614yes—
764C22C23×D5211yescharacteristic
765C22C22×#612712yes—
766C22C22×D4×D1312yes—
767C22#1171964812yes—
768C4—22no—
769C4—22no—
770C4—28no—
771C4—44no—
772C4—268no—
773C4—522no—
774C4—522no—
775C4—522no—
776C4C2×#8813614yes—
777C4C2×#8813614yes—
778C2—24no—
779C2—24no—
780C2—42no—
781C2—528no—
782C2—1042no—
783C2C22×#8813611yescharacteristic
784C2C2×#1171918211yescharacteristic
785C2#1312816911yescharacteristic
786C2D4×#612714yes—
subgroupG/H
centerC22×C4C23×D13
commutator, socle, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#34738
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#6127C2semidirect
2. C2×#11719182C2semidirect
3. C2×#11719496C2semidirect
4. #13118494C2semidirect
5. #13118487C2semidirect
6. #13118480C2semidirect
7. #13118473C2semidirect
8. #13118464C2semidirect
9. #13118455C2semidirect
10. #13118446C2semidirect
11. #13118204C2semidirect
12. #13118052C2semidirect
13. C4×#88136C2semidirect
14. #13117326C2semidirect
15. C2×C4×C13×C22⋊C4C2semidirect
24. C22×#6127C22semidirect
29. C22×C42×C13C22semidirect
33. C2×#88184C22semidirect
34. C2×#88184C22semidirect
35. C2×#88183C22semidirect
37. C2×C4×C22⋊D13C22semidirect
38. C2×#88180C22semidirect
40. C2×#88178C22semidirect
43. C2×#88129C22semidirect
44. C2×#88129C22semidirect
45. C2×#88128C22semidirect
46. C2×C4×D52C22semidirect
47. C2×#88123C22semidirect
51. C4×C13×C22⋊C4C22semidirect
52. C4×C13×C22⋊C4C22semidirect
53. C2×C13×#95C22semidirect
54. #11718874C22semidirect
55. #11718622C22semidirect
56. #11718621C22semidirect
60. #11718600C22semidirect
61. #11718600C22semidirect
62. C4×#6103C22semidirect
63. #11718590C22semidirect
64. #11718590C22semidirect
65. #11718334C22semidirect
66. #11718333C22semidirect
67. #11718332C22semidirect
68. #11718329C22semidirect
69. #11718326C22semidirect
70. #11718317C22semidirect
74. C23×C4×C13D4semidirect
102. C2×#6127D4semidirect
253. C13×C22⋊C4#41semidirect
286. C2×C4×C22⋊C4D13semidirect
330. C2×C4×C13#120semidirect
337. C2×C4×C13C2×#41semidirect
394. C22×C42C2×D13semidirect
415. C4×C22⋊C4C2×D13semidirect
416. C4×C22⋊C4C2×D13semidirect
417. C2×#95C2×D13semidirect
430. C22×C13#532semidirect
495. C23×C4D52semidirect
659. C22⋊C4#6127semidirect
664. C13#34738semidirect
733. C2×C4#88136semidirect
738. C2×C4C2×#6127semidirect
762. C22#11719182semidirect

Maximal subgroups

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

subgroupindex
C23×#61272
C2×#117191822
C2×#117194962
#131184942
#131184872
#131184802
#131184732
#131184642
#131184552
#131184462
#131182042
#131180522
C4×#881362
#131173262
C2×C4×C13×C22⋊C42
#3473813