Finite Group Databasebeta

← #15879958

Subgroups — #15879958

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718388C211yesmaximal, characteristic
2#13117324C211yesmaximal, characteristic
3#13115449C211yesmaximal, characteristic, complemented
4#13115448C211yesmaximal, characteristic, complemented
5#13115448C211yesmaximal, characteristic, complemented
6#13115442C211yesmaximal, characteristic, complemented
7#13115017C211yesmaximal, characteristic, complemented
8#13115012C211yesmaximal, characteristic, complemented
9#13114907C211yesmaximal, characteristic, complemented
10#13114814C211yesmaximal, characteristic, complemented
11#13114747C211yesmaximal, characteristic
12#13114619C211yesmaximal, characteristic, complemented
13#13114613C211yesmaximal, characteristic, complemented
14#13114600C211yesmaximal, characteristic, complemented
15C2×C13×#433C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C22×#6094C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21C13×#433—24no—
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C13×#97C2211yescharacteristic
27C2×C4×C8×C13C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×#88054C2211yescharacteristic
40#11718649C411yescharacteristic
41#11718649C411yescharacteristic
42#11718635C411yescharacteristic
43#11718635C411yescharacteristic
44#11718619C411yescharacteristic
45#11718619C411yescharacteristic
46#11718619C411yescharacteristic
47#11718619C411yescharacteristic
48C4×#6103C2211yescharacteristic
49C4×#6103C2211yescharacteristic
50C4×#6103C2211yescharacteristic
51C4×#6103C2211yescharacteristic
52#11718388—24no—
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13C2×C411yescharacteristic
63C22×C22⋊D13C2×C411yescharacteristic
64C23×Dic13C2×C411yescharacteristic
65C23×Dic13C2×C411yescharacteristic
66C2×#6127—22no—
67C2×#6127—22no—
68C2×#6127—22no—
69C2×#6127—22no—
70C2×#6127—41no—
71C2×#6127—41no—
72C22×D52C2×C411yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2311yescharacteristic
75C22×Dic26C2×C411yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C22×C8×C13C2311yescharacteristic
80C13×#117—22no—
81C13×#117—22no—
82C2×C13×C4⋊C4C2×C411yescharacteristic
83C2×C13×C4⋊C4C2×C411yescharacteristic
84C2×C13×C22⋊C4C2×C411yescharacteristic
85C2×C13×C22⋊C4C2×C411yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×#6103C2×C411yescharacteristic
89C2×#6103C2×C411yescharacteristic
90C2×#6103C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×#6103C2×C411yescharacteristic
93C2×#6103C2×C411yescharacteristic
94C2×#6103C2×C411yescharacteristic
95C2×#6103C2×C411yescharacteristic
96C2×C4×Dic13—41no—
97C2×C4×Dic13—41no—
98C2×C4×Dic13C2×C411yescharacteristic
99C2×C4×Dic13C2×C411yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C2×#6094—22no—
107C2×#6094—22no—
108C2×#6094—41no—
109C2×C8×D13—22no—
110C2×C8×D13—22no—
111C2×C8×D13—41no—
112C13×C4⋊C8—22no—
113C13×C4⋊C8—22no—
114C13×C22⋊C8—22no—
115C13×C22⋊C8D414yes—
116C13×#97—22no—
117C4×C8×C13—22no—
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88071C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126C22⋊#1055—22no—
127C22⋊#1055—22no—
128#88060—22no—
129#88060—22no—
130#88060—22no—
131#88060—22no—
132#88060—41no—
133#88060—41no—
134#88055—41no—
135#88055—41no—
136#88054—41no—
137#88054—41no—
138#22561—131nomaximal, Sylow
139C24×C13C22×C411yescharacteristic
140C23×D13C22×C411yescharacteristic
141C23×D13C22×C411yescharacteristic
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4112yes—
153C22×C4×C13C2411yescharacteristic
154C2×C22⋊D13—22no—
155C2×C22⋊D13—22no—
156C2×C22⋊D13—22no—
157C2×C22⋊D13—22no—
158C2×C22⋊D13—41no—
159C2×C22⋊D13—41no—
160C22×Dic13—22no—
161C22×Dic13—41no—
162C22×Dic13—41no—
163C22×Dic13—41no—
164C22×Dic13—41no—
165C22×Dic13—41no—
166C22×Dic13C22×C411yescharacteristic
167C22×Dic13C22×C411yescharacteristic
168C22×Dic13C22×C411yescharacteristic
169C22×Dic13C22×C411yescharacteristic
170C22×Dic13C22×C411yescharacteristic
171C22×Dic13C22×C411yescharacteristic
172#6127—44no—
173#6127—44no—
174#6127—44no—
175#6127—44no—
176C2×D52—22no—
177C2×D52—22no—
178C2×D52—41no—
179C2×C4×D13—21no—
180C2×C4×D13—21no—
181C2×C4×D13—21no—
182C2×C4×D13—21no—
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C2×C4×D13—21no—
188C2×C4×D13—21no—
189C2×C4×D13#4112yes—
190C2×C4×D13#4112yes—
191C2×Dic26—22no—
192C2×Dic26—22no—
193C2×Dic26—41no—
194C2×C8×C13—21no—
195C2×C8×C13—21no—
196C2×C8×C13—21no—
197C2×C8×C13—21no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13—21no—
203C2×C8×C13—21no—
204C2×C8×C13C2×D412yes—
205C2×C8×C13C2×D412yes—
206C13×C4⋊C4—22no—
207C13×C4⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C42×C13—21no—
211C42×C13—21no—
212C42×C13—21no—
213C42×C13—21no—
214#6103—22no—
215#6103—22no—
216#6103—41no—
217#6103—41no—
218#6103—41no—
219#6103—41no—
220#6103—41no—
221#6103—41no—
222C4×Dic13—21no—
223C4×Dic13—21no—
224C4×Dic13—21no—
225C4×Dic13—21no—
226C4×Dic13—41no—
227C4×Dic13—41no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240#6094—44no—
241C8×D13—44no—
242C2×#433D1311yescharacteristic, complemented
243C2×#408—131no—
244#2297—131no—
245#1924—131no—
246#1924—131no—
247#1924—131no—
248#1923—131no—
249#1851—131no—
250#1850—131no—
251#1818—131no—
252#1797—131no—
253#1780—131no—
254#1753—131no—
255#1752—131no—
256#1749—131no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13C4×D412yes—
264C23×C13C23×C411yescharacteristic
265C22×D13—21no—
266C22×D13—21no—
267C22×D13—21no—
268C22×D13—21no—
269C22×D13—21no—
270C22×D13—21no—
271C22×D13—21no—
272C22×D13—21no—
273C22×D13—21no—
274C22×D13—21no—
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—21no—
278C22×D13#11712yes—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13C4×D412yes—
298C2×C4×C13C22×D411yescharacteristic
299C2×C4×C13C2×#4111yescharacteristic
300C2×C4×C13C2×#4111yescharacteristic
301C2×C4×C13C2×#4111yescharacteristic
302C2×C4×C13H(5,𝔽2)11yescharacteristic
303C2×C4×C13H(5,𝔽2)11yescharacteristic
304C22⋊D13—44no—
305C22⋊D13—44no—
306C2×Dic13—21no—
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—21no—
312C2×Dic13—21no—
313C2×Dic13—21no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—44no—
323C2×Dic13—44no—
324C2×Dic13#11712yes—
325C2×Dic13#13112yes—
326D52—44no—
327C4×D13—22no—
328C4×D13—22no—
329C4×D13—22no—
330C4×D13—22no—
331C4×D13—41no—
332C4×D13—41no—
333C4×D13—41no—
334C4×D13—41no—
335Dic26—44no—
336C8×C13—22no—
337C8×C13—22no—
338C8×C13—41no—
339C8×C13—41no—
340#1055—41no—
341#1055—41no—
342#1055—41no—
343#1055—41no—
344C22×#41—131no—
345C22×M16—131no—
346C23×C8—131no—
347C2×#117C2×D1311yescharacteristic
348C22×C42—131no—
349#433—24no—
350C2×C4⋊C8—131no—
351C2×C4⋊C8—131no—
352C2×C4⋊C8C2×D1311yescharacteristic
353C2×C4⋊C8C2×D1311yescharacteristic
354#408—264no—
355C2×C22⋊C8—131no—
356C2×C22⋊C8—131no—
357C2×C22⋊C8—131no—
358C2×C22⋊C8—131no—
359C2×C22⋊C8—131no—
360C2×C22⋊C8—131no—
361C2×C22⋊C8—131no—
362C2×C22⋊C8—131no—
363C2×C22⋊C8C2×D1311yescharacteristic
364C2×C22⋊C8C2×D1311yescharacteristic
365C2×#97—131no—
366C2×#97—131no—
367C2×#97C2×D1311yescharacteristic
368C2×C4×C8C2×D1311yescharacteristic
369#391—131no—
370#391—131no—
371#390—131no—
372#390—131no—
373#386—131no—
374#386—131no—
375#386—131no—
376#386—131no—
377C4×C22⋊C4—131no—
378C4×C22⋊C4—131no—
379C4×C22⋊C4—131no—
380C4×C22⋊C4—131no—
381#336—131no—
382#336—131no—
383#336—131no—
384#336—131no—
385#336—131no—
386#336—131no—
387#336—131no—
388#336—131no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13C2×#11711yescharacteristic
397C22×C13C2×C4×D411yescharacteristic
398C22×C13#51811yescharacteristic
399C22×C13C2×#13111yescharacteristic
400C22×C13#56811yescharacteristic
401C22×C13#56811yescharacteristic
402C22×C13#56811yescharacteristic
403C2×D13—22no—
404C2×D13—22no—
405C2×D13—22no—
406C2×D13—41no—
407C2×D13—41no—
408C2×D13—41no—
409C2×D13—41no—
410C2×D13—41no—
411C2×D13—41no—
412C2×D13—41no—
413C2×D13—41no—
414C2×D13—41no—
415C2×D13—41no—
416C2×D13—41no—
417C4×C13—22no—
418C4×C13—41no—
419C4×C13—41no—
420C4×C13—41no—
421C4×C13—41no—
422C4×C13#54611yescharacteristic
423C4×C13#54611yescharacteristic
424C4×C13#55111yescharacteristic
425C4×C13#55111yescharacteristic
426Dic13—22no—
427Dic13—22no—
428Dic13—41no—
429Dic13—41no—
430Dic13—41no—
431Dic13—41no—
432C2×#41—262no—
433C2×#41—262no—
434C2×#41—262no—
435C2×#41—262no—
436C2×#41—521no—
437C2×#41—521no—
438C22×Q8—131no—
439C22×D4—131no—
440C22×D4—131no—
441C22×D4—131no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4C22×D1311yescharacteristic
447C2×M16—262no—
448C2×M16—262no—
449C2×M16—521no—
450C22×C8—131no—
451C22×C8—131no—
452C22×C8—131no—
453C22×C8—131no—
454C22×C8—262no—
455C22×C8—262no—
456C22×C8—521no—
457C22×C8C22×D1311yescharacteristic
458C22×C8C22×D1311yescharacteristic
459C22×C8C22×D1311yescharacteristic
460C22×C8C22×D1311yescharacteristic
461#117—22no—
462#117—22no—
463C2×C4⋊C4C4×D1311yescharacteristic
464C2×C4⋊C4C4×D1311yescharacteristic
465C2×C22⋊C4—131no—
466C2×C22⋊C4—131no—
467C2×C22⋊C4—131no—
468C2×C22⋊C4—131no—
469C2×C22⋊C4—131no—
470C2×C22⋊C4—131no—
471C2×C22⋊C4—131no—
472C2×C22⋊C4—131no—
473C2×C22⋊C4C4×D1311yescharacteristic
474C2×C22⋊C4C4×D1311yescharacteristic
475C2×C42—131no—
476C2×C42—131no—
477C2×C42—131no—
478C2×C42—131no—
479C2×C42—521no—
480C2×C42—521no—
481C2×C42C22×D1311yescharacteristic
482C2×C42C22×D1311yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8—521no—
486C4⋊C8—521no—
487C22⋊C8—22no—
488C22⋊C8—262no—
489C22⋊C8—262no—
490C22⋊C8—262no—
491C22⋊C8—262no—
492C22⋊C8—262no—
493C22⋊C8—262no—
494C22⋊C8—521no—
495C22⋊C8—521no—
496C22⋊C8C22⋊D1314yes—
497#97—22no—
498#97—521no—
499#97—521no—
500C4×C8—22no—
501#95—131no—
502#95—131no—
503#95—131no—
504#95—131no—
505#95—131no—
506#95—131no—
507#95—131no—
508#95—131no—
509C2×C13—42no—
510C2×C13#234211yescharacteristic
511C2×C13#292311yescharacteristic
512C2×C13#292511yescharacteristic
513C2×C13#293211yescharacteristic
514C2×C13#293511yescharacteristic
515C2×C13#297611yescharacteristic
516C2×C13#297811yescharacteristic
517D13—42no—
518D13—81no—
519C24—131no—
520C24—131no—
521C24C2×C4×D1311yescharacteristic
522#41—524no—
523#41—524no—
524#41—524no—
525#41—524no—
526C2×Q8—262no—
527C2×Q8—262no—
528C2×Q8—521no—
529C2×D4—262no—
530C2×D4—262no—
531C2×D4—262no—
532C2×D4—262no—
533C2×D4—262no—
534C2×D4—262no—
535C2×D4—521no—
536C2×D4—521no—
537C2×D4—521no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—131no—
543C22×C4—131no—
544C22×C4—132no—
545C22×C4—132no—
546C22×C4—131no—
547C22×C4—131no—
548C22×C4—131no—
549C22×C4—131no—
550C22×C4—262no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—521no—
562C22×C4—521no—
563C22×C4—521no—
564C22×C4—521no—
565C22×C4—521no—
566C22×C4C2×C4×D1311yescharacteristic
567C22×C4C2×C4×D1311yescharacteristic
568C22×C4C2×C4×D1311yescharacteristic
569C22×C4C2×C4×D1311yescharacteristic
570C22×C4C2×C4×D1311yescharacteristic
571C22×C4#612712yes—
572C22×C4C2×C22⋊D1312yes—
573C22×C4C23×D1311yescharacteristic
574M16—524no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—261no—
595C2×C8—261no—
596C2×C8—261no—
597C2×C8—524no—
598C2×C8C2×C22⋊D1312yes—
599C2×C8C2×C22⋊D1312yes—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—262no—
605C22⋊C4—262no—
606C22⋊C4—521no—
607C22⋊C4—521no—
608C22⋊C4—521no—
609C22⋊C4—521no—
610C22⋊C4—521no—
611C22⋊C4—521no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—261no—
617C42—261no—
618C42—261no—
619C42—261no—
620C42—521no—
621C42—521no—
622C13#2256111yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—132no—
630C23—261no—
631C23—261no—
632C23—261no—
633C23—261no—
634C23—261no—
635C23—261no—
636C23—261no—
637C23—261no—
638C23—261no—
639C23—261no—
640C23—261no—
641C23—261no—
642C23—261no—
643C23C4×C22⋊D1312yes—
644C23C22×C4×D1311yescharacteristic
645Q8—524no—
646D4—524no—
647D4—524no—
648D4—524no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—132no—
668C2×C4—132no—
669C2×C4—261no—
670C2×C4—261no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—261no—
685C2×C4—261no—
686C2×C4—261no—
687C2×C4—261no—
688C2×C4—261no—
689C2×C4—524no—
690C2×C4—524no—
691C2×C4—521no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—521no—
695C2×C4C4×C22⋊D1312yes—
696C2×C4C2×#612711yescharacteristic
697C2×C4#41×D1311yescharacteristic
698C2×C4#41×D1311yescharacteristic
699C2×C4#8825611yescharacteristic
700C2×C4#8825611yescharacteristic
701C2×C4C22×C22⋊D1311yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—521no—
707C8—521no—
708C8—521no—
709C8—521no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—262no—
718C22—262no—
719C22—262no—
720C22—521no—
721C22—521no—
722C22—521no—
723C22—521no—
724C22—521no—
725C22—521no—
726C22—521no—
727C22—521no—
728C22—521no—
729C22—521no—
730C22—521no—
731C22D13×#11711yescharacteristic
732C22#1171922611yescharacteristic
733C22D13×#13111yescharacteristic
734C22#1171945511yescharacteristic
735C22#1171945511yescharacteristic
736C22#1171945511yescharacteristic
737C22C2×C4×C22⋊D1311yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—262no—
744C4—262no—
745C4—521no—
746C4—521no—
747C4—521no—
748C4—521no—
749C4#1171923211yescharacteristic
750C4#1171923211yescharacteristic
751C4#1171953411yescharacteristic
752C4#1171953411yescharacteristic
753C2—42no—
754C2—522no—
755C2—1041no—
756C2#1311768611yescharacteristic
757C2#1312348411yescharacteristic
758C2#1312349911yescharacteristic
759C2#1312355211yescharacteristic
760C2#1312357811yescharacteristic
761C2#1312388211yescharacteristic
762C2#1312389711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#433C2
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#433D13
hypocenterC13#22561
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #13115449C2semidirect
4. #13115448C2semidirect
5. #13115448C2semidirect
6. #13115442C2semidirect
7. #13115017C2semidirect
8. #13115012C2semidirect
9. #13114907C2semidirect
10. #13114814C2semidirect
12. #13114619C2semidirect
13. #13114613C2semidirect
14. #13114600C2semidirect
15. C2×C13×#433C2semidirect
242. C2×#433D13semidirect
622. C13#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#117183882
#131173242
#131154492
#131154482
#131154422
#131150172
#131150122
#131149072
#131148142
#131147472
#131146192
#131146132
#131146002
C2×C13×#4332
#2256113