Finite Group Databasebeta

← #15868977

Subgroups — #15868977

Order 3328.

1090 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
1C2×#11718673C211yesmaximal, characteristic, complemented
2C2×#11718390C211yesmaximal, characteristic, complemented
3C2×#11718390C211yesmaximal, characteristic, complemented
4C2×M16×Dic13C211yesmaximal, characteristic, complemented
5C4×#88193C211yesmaximal, characteristic
6#13115628C211yesmaximal, characteristic, complemented
7#13115553C211yesmaximal, characteristic, complemented
8#13115450C211yesmaximal, characteristic, complemented
9#13115446C211yesmaximal, characteristic, complemented
10#13115133C211yesmaximal, characteristic, complemented
11#13114814C211yesmaximal, characteristic, complemented
12#13114697C211yesmaximal, characteristic, complemented
13#13114622C211yesmaximal, characteristic, complemented
14#13114616C211yesmaximal, characteristic, complemented
15C13×#1870C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×#88193C411yescharacteristic
19C2×C4×C22⋊D13C2211yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24C22×#6094C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C13×C22⋊C8C2211yescharacteristic
28#11718881C411yescharacteristic
29C4×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32M16×Dic13—24no—
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×#88054C2211yescharacteristic
40C2×#88054C2211yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43C2×C8×Dic13C2211yescharacteristic
44#11718673—24no—
45#11718651C411yescharacteristic
46#11718633C411yescharacteristic
47#11718619C411yescharacteristic
48#11718618C411yescharacteristic
49#11718606C411yescharacteristic
50#11718603C411yescharacteristic
51C4×#6103C2211yescharacteristic
52C4×#6101C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×C4×#1055C2211yescharacteristic
55#11718390—24no—
56#11718390—24no—
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718142C2211yescharacteristic
62#11718142C2211yescharacteristic
63C22×D4×C13C2×C411yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13C2×C411yescharacteristic
67C22×C22⋊D13C2×C411yescharacteristic
68C23×Dic13C2×C411yescharacteristic
69C23×Dic13C2×C411yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C2×C13×M16—22no—
72C2×C13×M16—22no—
73C2×C13×M16—22no—
74C22×C8×C13C2311yescharacteristic
75C22×C8×C13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C4×D4×C13—22no—
79C4×D4×C13—22no—
80C2×C13×C4⋊C4C2×C411yescharacteristic
81C2×C13×C22⋊C4C2×C411yescharacteristic
82C2×C13×C22⋊C4C2×C411yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85C2×C22⋊Dic13C2×C411yescharacteristic
86C2×C22⋊Dic13C2×C411yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88#88193—24no—
89C4×C22⋊D13—22no—
90C4×C22⋊D13—22no—
91C4×C22⋊D13—22no—
92C4×C22⋊D13—22no—
93C2×#6103C2×C411yescharacteristic
94C2×#6103C2×C411yescharacteristic
95C2×#6103C2×C411yescharacteristic
96C2×#6103C2×C411yescharacteristic
97C2×#6101C2×C411yescharacteristic
98C2×#6101C2×C411yescharacteristic
99C2×#6101C2×C411yescharacteristic
100C2×#6101C2×C411yescharacteristic
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13C2×C411yescharacteristic
104C2×C4×Dic13C2×C411yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×#6099—22no—
109C2×#6099—22no—
110C2×#6099—22no—
111C2×#6099—22no—
112C2×#6099—22no—
113C2×#6099D414yescomplemented
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C22×#1055C2311yescharacteristic
118C2×#6094—22no—
119C2×#6094—22no—
120C2×#6094—22no—
121C13×C22⋊C8—22no—
122C13×C22⋊C8—22no—
123C13×C22⋊C8—22no—
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130C22⋊#1055—22no—
131C22⋊#1055—22no—
132#88060—22no—
133#88060—22no—
134#88060—22no—
135#88055—22no—
136#88055—22no—
137#88054—22no—
138#88054—22no—
139#88054—22no—
140C8×Dic13—22no—
141C8×Dic13—22no—
142C8×Dic13D414yescomplemented
143C4⋊#1055—22no—
144C4×#1055—22no—
145#21488—131nomaximal, Sylow
146C24×C13C22×C411yescharacteristic
147C24×C13C22×C411yescharacteristic
148C23×D13C22×C411yescharacteristic
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—41no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13C22×C411yescharacteristic
163C22×C4×C13C22×C411yescharacteristic
164C22×C4×C13C22×C411yescharacteristic
165C22×C4×C13C22×C411yescharacteristic
166C22×C4×C13C2×D412yes—
167C22×C4×C13#4112yes—
168C22×C4×C13C2411yescharacteristic
169C2×C22⋊D13—22no—
170C2×C22⋊D13—22no—
171C2×C22⋊D13—22no—
172C2×C22⋊D13—22no—
173C2×C22⋊D13—22no—
174C2×C22⋊D13—41no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—41no—
180C22×Dic13—41no—
181C22×Dic13C22×C411yescharacteristic
182C22×Dic13C22×C411yescharacteristic
183C22×Dic13C22×C411yescharacteristic
184C22×Dic13C22×C411yescharacteristic
185C22×Dic13C22×C411yescharacteristic
186C22×Dic13C22×C411yescharacteristic
187C22×Dic13C22×C411yescharacteristic
188C2×C4×D13—21no—
189C2×C4×D13—21no—
190C2×C4×D13—21no—
191C2×C4×D13—21no—
192C2×C4×D13—21no—
193C2×C4×D13—21no—
194C13×M16—28no—
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×C13—21no—
205C2×C8×C13C2×D412yes—
206C2×C8×C13#4112yes—
207C13×C4⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C42×C13—21no—
211C42×C13—21no—
212C22⋊Dic13—22no—
213C22⋊Dic13—22no—
214C22⋊Dic13—22no—
215C22⋊Dic13—41no—
216#6103—22no—
217#6103—22no—
218#6103—22no—
219#6103—41no—
220#6101—22no—
221#6101—22no—
222#6101—22no—
223#6101M1614yescomplemented
224C4×Dic13—21no—
225C4×Dic13—21no—
226C4×Dic13—21no—
227C4×Dic13—21no—
228C4×Dic13—22no—
229C4×Dic13—22no—
230C4×Dic13C2×D412yes—
231C4×Dic13#4112yes—
232#6099—28no—
233#6099—44no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055C2×D412yes—
243C2×#1055C2×D412yes—
244C2×#1055C2×D412yes—
245C2×#1055#4112yes—
246#6094—44no—
247C2×#436—131no—
248C2×#436—131no—
249C2×#436—131no—
250C2×C4×M16—131no—
251C4×#121—131no—
252#1954—131no—
253#1939—131no—
254#1924—131no—
255#1924—131no—
256#1870—131no—
257#1870D1311yescharacteristic, complemented
258#1797—131no—
259C8×C4⋊C4—131no—
260#1753—131no—
261#1753—131no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13—21no—
274C23×C13—21no—
275C23×C13C4×D412yes—
276C23×C13C23×C411yescharacteristic
277C22×D13—21no—
278C22×D13—21no—
279C22×D13—21no—
280C22×D13—21no—
281C22×D13—21no—
282C22×D13—21no—
283C22×D13—21no—
284D4×C13—44no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13C4×D412yes—
304C2×C4×C13C2×M1612yes—
305C2×C4×C13C22×D411yescharacteristic
306C2×C4×C13C22×D411yescharacteristic
307C2×C4×C13C2×#4111yescharacteristic
308C2×C4×C13C2×#4111yescharacteristic
309C2×C4×C13C2×#4111yescharacteristic
310C2×C4×C13C2×#4111yescharacteristic
311C22⋊D13—44no—
312C22⋊D13—44no—
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—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13—21no—
327C2×Dic13—21no—
328C2×Dic13—21no—
329C2×Dic13—44no—
330C2×Dic13—44no—
331C2×Dic13C4×D412yes—
332C2×Dic13C4×D412yes—
333C2×Dic13C2×M1612yes—
334C2×Dic13C2×M1612yes—
335C2×Dic13#13112yes—
336C4×D13—41no—
337C4×D13—41no—
338C4×D13—41no—
339C4×D13—41no—
340C8×C13—22no—
341C8×C13—22no—
342C8×C13—41no—
343C8×C13—41no—
344#1055—22no—
345#1055—41no—
346#1055—41no—
347#1055#12114yescomplemented
348C22×M16—131no—
349C22×M16—131no—
350C22×M16—131no—
351C22×M16C2×D1311yescharacteristic
352C2×#121—131no—
353C2×C4×D4—131no—
354C2×C4×D4—131no—
355C2×C4×D4C2×D1311yescharacteristic
356C22×C42—131no—
357#436—264no—
358#436—264no—
359#436—264no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8—131no—
362C2×C4⋊C8—131no—
363C2×C4⋊C8—131no—
364C2×C22⋊C8—131no—
365C2×C22⋊C8—131no—
366C2×C22⋊C8—131no—
367C2×C22⋊C8—131no—
368C2×C22⋊C8—131no—
369C2×C22⋊C8C2×D1311yescharacteristic
370C2×C22⋊C8C2×D1311yescharacteristic
371C2×C22⋊C8C2×D1311yescharacteristic
372C4×M16—264no—
373C2×#97—131no—
374C2×#97—131no—
375C2×C4×C8—131no—
376C2×C4×C8—131no—
377C2×C4×C8—131no—
378C2×C4×C8—131no—
379#390—131no—
380#389—131no—
381#388—131no—
382#388—131no—
383#386—131no—
384#386—131no—
385#380—131no—
386C4×C4⋊C4—131no—
387C4×C22⋊C4—131no—
388C4×C22⋊C4—131no—
389#336—131no—
390#336—131no—
391#336—131no—
392#336—131no—
393#336C2×D1311yescharacteristic
394#336C2×D1311yescharacteristic
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13C2×C4×D411yescharacteristic
410C22×C13C2×C4×D411yescharacteristic
411C22×C13C4×#4111yescharacteristic
412C22×C13C22×M1611yescharacteristic
413C22×C13C2×#13111yescharacteristic
414C22×C13#56811yescharacteristic
415C22×C13#56811yescharacteristic
416C2×D13—41no—
417C2×D13—41no—
418C2×D13—41no—
419C2×D13—41no—
420C2×D13—41no—
421C2×D13—41no—
422C2×D13—41no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—41no—
426C4×C13—41no—
427C4×C13C2×#12111yescharacteristic
428C4×C13#52511yescharacteristic
429C4×C13#52911yescharacteristic
430C4×C13#53211yescharacteristic
431Dic13—22no—
432Dic13—22no—
433Dic13—41no—
434Dic13—41no—
435Dic13—41no—
436Dic13—41no—
437Dic13#43614yescomplemented
438C22×D4—131no—
439C22×D4—131no—
440C22×D4C4×D1311yescharacteristic
441C23×C4—131no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—134no—
450C2×M16—262no—
451C2×M16—262no—
452C2×M16—262no—
453C2×M16—262no—
454C2×M16—262no—
455C2×M16—262no—
456C2×M16—262no—
457C2×M16—262no—
458C22×C8—131no—
459C22×C8—131no—
460C22×C8—131no—
461C22×C8—131no—
462C22×C8C22×D1311yescharacteristic
463C22×C8C22×D1311yescharacteristic
464C22×C8C22×D1311yescharacteristic
465C22×C8C22×D1311yescharacteristic
466#121—264no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—262no—
470C4×D4—262no—
471C4×D4—262no—
472C4×D4—262no—
473C2×C4⋊C4—131no—
474C2×C4⋊C4—131no—
475C2×C4⋊C4—131no—
476C2×C4⋊C4—131no—
477C2×C4⋊C4C4×D1311yescharacteristic
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—131no—
481C2×C22⋊C4—131no—
482C2×C22⋊C4—131no—
483C2×C22⋊C4—131no—
484C2×C22⋊C4—131no—
485C2×C22⋊C4—131no—
486C2×C22⋊C4C4×D1311yescharacteristic
487C2×C22⋊C4C4×D1311yescharacteristic
488C2×C42—131no—
489C2×C42—131no—
490C2×C42—131no—
491C2×C42—131no—
492C2×C42—131no—
493C2×C42—262no—
494C2×C42—262no—
495C2×C42C22×D1311yescharacteristic
496C4⋊C8—262no—
497C4⋊C8—262no—
498C4⋊C8—262no—
499C4⋊C8—262no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—262no—
504C22⋊C8—262no—
505C22⋊C8—262no—
506C22⋊C8—262no—
507C22⋊C8—262no—
508#97—262no—
509#97—262no—
510C4×C8—134no—
511C4×C8—262no—
512C4×C8—262no—
513C4×C8—262no—
514#95—131no—
515#95—131no—
516#95—131no—
517#95—131no—
518#95—131no—
519#95—131no—
520C2×C13—42no—
521C2×C13—81no—
522C2×C13C4×#12111yescharacteristic
523C2×C13C2×#43611yescharacteristic
524C2×C13#293011yescharacteristic
525C2×C13D4×M1611yescharacteristic
526C2×C13#293511yescharacteristic
527C2×C13#296911yescharacteristic
528C2×C13#297111yescharacteristic
529D13—81no—
530C24—131no—
531C24C2×C4×D1311yescharacteristic
532C24C2×C4×D1311yescharacteristic
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—41no—
536C2×D4—262no—
537C2×D4—262no—
538C2×D4—262no—
539C2×D4—262no—
540C2×D4—262no—
541C2×D4—521no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—131no—
553C22×C4—131no—
554C22×C4—131no—
555C22×C4—131no—
556C22×C4—131no—
557C22×C4—131no—
558C22×C4—131no—
559C22×C4—262no—
560C22×C4—262no—
561C22×C4—262no—
562C22×C4—262no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—521no—
570C22×C4—521no—
571C22×C4C2×C4×D1311yescharacteristic
572C22×C4C2×C4×D1311yescharacteristic
573C22×C4C2×C4×D1311yescharacteristic
574C22×C4C2×C4×D1311yescharacteristic
575C22×C4D4×D1312yes—
576C22×C4#612912yes—
577C22×C4C23×D1311yescharacteristic
578M16—28no—
579M16—268no—
580M16—524no—
581M16—524no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—132no—
593C2×C8—132no—
594C2×C8—132no—
595C2×C8—132no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8—261no—
599C2×C8—261no—
600C2×C8—261no—
601C2×C8—261no—
602C2×C8—261no—
603C2×C8—261no—
604C2×C8D4×D1312yes—
605C2×C8#612912yes—
606C4⋊C4—22no—
607C4⋊C4—134no—
608C4⋊C4—262no—
609C4⋊C4—262no—
610C4⋊C4—262no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—262no—
614C22⋊C4—262no—
615C22⋊C4—262no—
616C22⋊C4—262no—
617C22⋊C4—262no—
618C22⋊C4—262no—
619C22⋊C4—521no—
620C22⋊C4—521no—
621C42—21no—
622C42—21no—
623C42—132no—
624C42—132no—
625C42—262no—
626C42—262no—
627C42—261no—
628C42—261no—
629C42—261no—
630C42—261no—
631C13#2148811yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—261no—
646C23—261no—
647C23—261no—
648C23—261no—
649C23—261no—
650C23—261no—
651C23—261no—
652C23#8813512yes—
653C23C22×C4×D1311yescharacteristic
654D4—44no—
655D4—524no—
656D4—524no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—132no—
676C2×C4—132no—
677C2×C4—132no—
678C2×C4—132no—
679C2×C4—132no—
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—261no—
690C2×C4—261no—
691C2×C4—261no—
692C2×C4—261no—
693C2×C4—261no—
694C2×C4—261no—
695C2×C4—261no—
696C2×C4—524no—
697C2×C4—524no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4—521no—
701C2×C4—521no—
702C2×C4#8813512yes—
703C2×C4M16×D1312yes—
704C2×C4C2×D4×D1311yescharacteristic
705C2×C4C2×D4×D1311yescharacteristic
706C2×C4C2×#612911yescharacteristic
707C2×C4C2×#612911yescharacteristic
708C2×C4#41×D1311yescharacteristic
709C2×C4#41×D1311yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—134no—
715C8—262no—
716C8—521no—
717C8—521no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—521no—
733C22—521no—
734C22—521no—
735C22—521no—
736C22—521no—
737C22—521no—
738C22—521no—
739C22C2×#8813511yescharacteristic
740C22C4×#612911yescharacteristic
741C22C4×D4×D1311yescharacteristic
742C22C2×M16×D1311yescharacteristic
743C22#1171945011yescharacteristic
744C22D13×#13111yescharacteristic
745C22#1171945511yescharacteristic
746C4—22no—
747C4—22no—
748C4—41no—
749C4—41no—
750C4—134no—
751C4—262no—
752C4—262no—
753C4—521no—
754C4—521no—
755C4—521no—
756C4—521no—
757C4#1171929111yescharacteristic
758C4#1171930111yescharacteristic
759C4D13×#12111yescharacteristic
760C4#1171935411yescharacteristic
761C2—42no—
762C2—81no—
763C2—1041no—
764C2#1311734611yescharacteristic
765C2D13×#43611yescharacteristic
766C2#1312353411yescharacteristic
767C2#1312356811yescharacteristic
768C2#1312357611yescharacteristic
769C2#1312383311yescharacteristic
770C2#1312385211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1870C2
prime radicalC2×#88193C4
cosocleC22×C4×C13C24
hypercenter#1870D13
hypocenterC13#21488
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#11718673C2semidirect
2. C2×#11718390C2semidirect
3. C2×#11718390C2semidirect
4. C2×M16×Dic13C2semidirect
6. #13115628C2semidirect
7. #13115553C2semidirect
8. #13115450C2semidirect
9. #13115446C2semidirect
10. #13115133C2semidirect
11. #13114814C2semidirect
12. #13114697C2semidirect
13. #13114622C2semidirect
14. #13114616C2semidirect
15. C13×#1870C2semidirect
113. C2×#6099D4semidirect
142. C8×Dic13D4semidirect
223. #6101M16semidirect
257. #1870D13semidirect
347. #1055#121semidirect
437. Dic13#436semidirect
631. C13#21488semidirect

Maximal subgroups

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

subgroupindex
C2×#117186732
C2×#117183902
C2×M16×Dic132
C4×#881932
#131156282
#131155532
#131154502
#131154462
#131151332
#131148142
#131146972
#131146222
#131146162
C13×#18702
#2148813