Finite Group Databasebeta

← #15865241

Subgroups — #15865241

Order 3328.

1226 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718500C211yesmaximal, characteristic, complemented
2C2×#11718387C211yesmaximal, characteristic
3C2×D13×C22⋊C8C211yesmaximal, characteristic
4C2×#11718350C211yesmaximal, characteristic, complemented
5#13117217C211yesmaximal, characteristic
6#13115452C211yesmaximal, characteristic, complemented
7#13115451C211yesmaximal, characteristic, complemented
8#13115448C211yesmaximal, characteristic, complemented
9#13115447C211yesmaximal, characteristic, complemented
10#13115443C211yesmaximal, characteristic, complemented
11#13115442C211yesmaximal, characteristic, complemented
12#13115439C211yesmaximal, characteristic, complemented
13#13114531C211yesmaximal, characteristic, complemented
14#13114531C211yesmaximal, characteristic, complemented
15C13×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×#6094C2211yescharacteristic
18C22×#6094C2211yescharacteristic
19C22×C8×D13C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21C2×#88126C2211yescharacteristic
22C2×#88126C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic, complemented
24C2×C13×C22⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C4×C8×C13C2211yescharacteristic, complemented
27C4×C13×C22⋊C4C2211yescharacteristic
28C4×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88055C2211yescharacteristic, complemented
36C2×#88054C2211yescharacteristic, complemented
37C2×#88054C2211yescharacteristic, complemented
38C2×C8×Dic13C2211yescharacteristic, complemented
39#11718616C411yescharacteristic
40#11718616C411yescharacteristic
41#11718603C411yescharacteristic
42#11718603C411yescharacteristic
43C4×#6103C2211yescharacteristic
44C4×#6103C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic, complemented
46C2×#88043C2211yescharacteristic, complemented
47#11718500—24no—
48#11718387—24no—
49D13×C22⋊C8—24no—
50#11718350—24no—
51#11718328C411yescharacteristic
52#11718328C411yescharacteristic
53#11718325C411yescharacteristic
54#11718325C411yescharacteristic
55C13×#336C2211yescharacteristic, complemented
56C13×#336C2211yescharacteristic, complemented
57#11718142C2211yescharacteristic, complemented
58#11718142C2211yescharacteristic, complemented
59#11718142C2211yescharacteristic, complemented
60#11718142C2211yescharacteristic, complemented
61#11718116C2211yescharacteristic, complemented
62#11718116C2211yescharacteristic, complemented
63C24×D13C2×C411yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13C2×C411yescharacteristic
66C22×C4×D13—22no—
67C22×C4×D13—22no—
68C22×C4×D13—22no—
69C22×C4×D13—22no—
70C22×C4×D13—22no—
71C22×C4×D13—22no—
72C22×C4×D13C2×C411yescharacteristic
73C22×C4×D13C2×C411yescharacteristic
74C22×C4×D13C2311yescharacteristic
75C22×C4×D13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C22×C8×C13C2311yescharacteristic
80C2×C13×C22⋊C4C2×C411yescharacteristic
81C2×C13×C22⋊C4C2×C411yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85C2×C22⋊Dic13C2×C411yescharacteristic
86C2×#6103C2×C411yescharacteristic
87C2×#6103C2×C411yescharacteristic
88C2×#6103C2×C411yescharacteristic
89C2×#6103C2×C411yescharacteristic
90C2×#6103C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×#6103C2×C411yescharacteristic
93C2×#6103C2×C411yescharacteristic
94C2×#6101C2×C411yescharacteristic
95C2×#6101C2×C411yescharacteristic
96C2×#6101C2×C411yescharacteristic
97C2×#6101C2×C411yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C2×#6094—22no—
105C2×#6094—22no—
106C2×#6094—22no—
107C2×#6094—22no—
108C2×#6094—22no—
109C2×#6094D414yes—
110C2×C8×D13—22no—
111C2×C8×D13—22no—
112C2×C8×D13—22no—
113C2×C8×D13—22no—
114C2×C8×D13—22no—
115C2×C8×D13D414yes—
116#88126—22no—
117#88126—22no—
118#88126—22no—
119#88126—22no—
120C13×C4⋊C8—22no—
121C13×C22⋊C8—22no—
122C13×C22⋊C8—22no—
123C4×C8×C13—22no—
124C13×#95C2×C411yescharacteristic
125C13×#95C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130#88071C2×C411yescharacteristic
131#88071C2×C411yescharacteristic
132C22⋊#1055—22no—
133C22⋊#1055—22no—
134#88060—22no—
135#88060—22no—
136#88060—22no—
137#88060—22no—
138#88055—22no—
139#88054—22no—
140#88054—22no—
141C8×Dic13—22no—
142C4⋊#1055—22no—
143#88043—22no—
144#21050—131nomaximal, Sylow
145C24×C13C22×C411yescharacteristic
146C23×D13—22no—
147C23×D13—22no—
148C23×D13—22no—
149C23×D13—22no—
150C23×D13—22no—
151C23×D13—41no—
152C23×D13—41no—
153C23×D13C22×C411yescharacteristic
154C23×D13C22×C411yescharacteristic
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×C13C22×C411yescharacteristic
162C22×C4×C13C22×C411yescharacteristic
163C22×C4×C13C22×C411yescharacteristic
164C22×C4×C13C22×C411yescharacteristic
165C22×C4×C13C22×C411yescharacteristic
166C22×C4×C13C2411yescharacteristic
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13C22×C411yescharacteristic
171C22×Dic13C22×C411yescharacteristic
172C22×Dic13C22×C411yescharacteristic
173C22×Dic13C22×C411yescharacteristic
174C22×Dic13C22×C411yescharacteristic
175C22×Dic13C22×C411yescharacteristic
176C2×C4×D13—22no—
177C2×C4×D13—22no—
178C2×C4×D13—22no—
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—22no—
186C2×C4×D13—22no—
187C2×C4×D13—22no—
188C2×C4×D13—44no—
189C2×C4×D13—44no—
190C2×C4×D13—44no—
191C2×C4×D13—44no—
192C2×C4×D13C2×D412yes—
193C2×C4×D13C2×D412yes—
194C2×C4×D13#4112yes—
195C2×C4×D13#4112yes—
196C2×C4×D13#4112yes—
197C2×C4×D13#4112yes—
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×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13C2×D412yes—
209C2×C8×C13C2×D412yes—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—41no—
212C42×C13—21no—
213C42×C13—21no—
214C42×C13—21no—
215C42×C13—21no—
216C22⋊Dic13—22no—
217C22⋊Dic13—41no—
218#6103—22no—
219#6103—22no—
220#6103—22no—
221#6103—22no—
222#6103—22no—
223#6103—22no—
224#6103—41no—
225#6103—41no—
226#6101—22no—
227#6101—22no—
228#6101—22no—
229#6101—22no—
230C4×Dic13—21no—
231C4×Dic13—21no—
232C4×Dic13—21no—
233C4×Dic13—21no—
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×#1055—21no—
243C2×#1055—21no—
244C2×#1055C2×D412yes—
245C2×#1055C2×D412yes—
246#6094—28no—
247#6094—44no—
248C8×D13—28no—
249C8×D13—44no—
250C2×#424—131no—
251C2×#407—131no—
252C22×C22⋊C8—131no—
253C2×#405—131no—
254#2280—131no—
255#1924—131no—
256#1924—131no—
257#1924—131no—
258#1924—131no—
259#1923—131no—
260#1923—131no—
261#1923—131no—
262#1923D1311yescharacteristic, complemented
263#1729—131no—
264#1729—131no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13#13112yes—
272C23×C13C23×C411yescharacteristic
273C22×D13—21no—
274C22×D13—21no—
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—28no—
278C22×D13—21no—
279C22×D13—21no—
280C22×D13—21no—
281C22×D13—21no—
282C22×D13—21no—
283C22×D13—21no—
284C22×D13—44no—
285C22×D13—44no—
286C22×D13—44no—
287C22×D13—44no—
288C22×D13—44no—
289C22×D13—44no—
290C22×D13#11712yes—
291C22×D13C4×D412yes—
292C22×D13C4×D412yes—
293C22×D13#13112yes—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13C22×D411yescharacteristic
314C2×C4×C13C22×D411yescharacteristic
315C2×C4×C13C2×#4111yescharacteristic
316C2×C4×C13C2×#4111yescharacteristic
317C2×C4×C13C2×#4111yescharacteristic
318C2×C4×C13C2×#4111yescharacteristic
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—21no—
330C2×Dic13—21no—
331C2×Dic13—21no—
332C2×Dic13—21no—
333C2×Dic13—21no—
334C2×Dic13—44no—
335C2×Dic13#11712yes—
336C2×Dic13C4×D412yes—
337C2×Dic13C4×D412yes—
338C4×D13—44no—
339C4×D13—41no—
340C4×D13—41no—
341C4×D13—41no—
342C4×D13—41no—
343C4×D13—44no—
344C4×D13#12114yes—
345C4×D13#12314yes—
346C4×D13#12414yes—
347C4×D13#12614yes—
348C8×C13—22no—
349C8×C13—22no—
350C8×C13—41no—
351C8×C13—41no—
352#1055—22no—
353#1055—22no—
354#1055—41no—
355#1055—41no—
356C24×C4—131no—
357C22×M16—131no—
358C22×M16—131no—
359C23×C8—131no—
360C23×C8—131no—
361C2×#117—131no—
362C2×#117—131no—
363#424—264no—
364C2×C4⋊C8—131no—
365C2×C4⋊C8—131no—
366C2×C4⋊C8—131no—
367C2×C4⋊C8C2×D1311yescharacteristic, complemented
368#407—264no—
369C2×C22⋊C8—131no—
370C2×C22⋊C8—131no—
371C2×C22⋊C8—131no—
372C2×C22⋊C8—131no—
373C2×C22⋊C8—131no—
374C2×C22⋊C8—131no—
375C2×C22⋊C8—264no—
376C2×C22⋊C8C2×D1311yescharacteristic
377C2×C22⋊C8C2×D1311yescharacteristic
378#405—264no—
379C2×#97—131no—
380C2×#97—131no—
381C2×C4×C8—131no—
382C2×C4×C8C2×D1311yescharacteristic, complemented
383#381—131no—
384#381—131no—
385#380—131no—
386#380—131no—
387#380—131no—
388#380—131no—
389#379—131no—
390#379—131no—
391C4×C22⋊C4—131no—
392C4×C22⋊C4—131no—
393C4×C22⋊C4—131no—
394C4×C22⋊C4C2×D1311yescharacteristic
395#336—131no—
396#336—131no—
397#336—131no—
398#336—131no—
399#336—131no—
400#336—131no—
401#336C2×D1311yescharacteristic, complemented
402#336C2×D1311yescharacteristic, complemented
403C22×C13—22no—
404C22×C13—22no—
405C22×C13—22no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13—41no—
410C22×C13C2×#11711yescharacteristic
411C22×C13C2×C4×D411yescharacteristic
412C22×C13C2×C4×D411yescharacteristic
413C22×C13C2×#13111yescharacteristic
414C22×C13C2×#13111yescharacteristic
415C22×C13#56811yescharacteristic
416C22×C13#56811yescharacteristic
417C2×D13—22no—
418C2×D13—22no—
419C2×D13—22no—
420C2×D13—22no—
421C2×D13—22no—
422C2×D13—22no—
423C2×D13—22no—
424C2×D13—22no—
425C2×D13—22no—
426C2×D13—416no—
427C2×D13—41no—
428C2×D13—41no—
429C2×D13—41no—
430C2×D13—41no—
431C2×D13#38814yes—
432C4×C13—41no—
433C4×C13—41no—
434C4×C13—41no—
435C4×C13—41no—
436C4×C13—41no—
437C4×C13C2×#12111yescharacteristic
438C4×C13C2×#12311yescharacteristic
439C4×C13C2×#12411yescharacteristic
440C4×C13C2×#12611yescharacteristic
441Dic13—41no—
442Dic13—41no—
443Dic13—41no—
444Dic13—41no—
445Dic13—41no—
446Dic13#38814yes—
447C25—131no—
448C23×C4—131no—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—131no—
453C23×C4—262no—
454C23×C4—262no—
455C23×C4—262no—
456C23×C4—262no—
457C23×C4—262no—
458C23×C4—262no—
459C23×C4C22×D1311yescharacteristic
460C2×M16—134no—
461C2×M16—262no—
462C2×M16—262no—
463C2×M16—262no—
464C2×M16—262no—
465C2×M16—262no—
466C22×C8—131no—
467C22×C8—131no—
468C22×C8—134no—
469C22×C8—131no—
470C22×C8—131no—
471C22×C8—262no—
472C22×C8—262no—
473C22×C8—262no—
474C22×C8—262no—
475C22×C8—262no—
476C22×C8C22×D1311yescharacteristic
477C22×C8C22×D1311yescharacteristic
478C22×C8C22×D1311yescharacteristic
479C22×C8C22×D1311yescharacteristic
480#117—262no—
481#117—262no—
482#117—262no—
483#117—262no—
484C2×C4⋊C4—131no—
485C2×C4⋊C4—131no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—131no—
488C2×C22⋊C4—131no—
489C2×C22⋊C4—131no—
490C2×C22⋊C4—131no—
491C2×C22⋊C4—131no—
492C2×C22⋊C4—131no—
493C2×C22⋊C4—131no—
494C2×C22⋊C4—131no—
495C2×C22⋊C4—131no—
496C2×C22⋊C4—131no—
497C2×C22⋊C4—131no—
498C2×C22⋊C4C4×D1311yescharacteristic
499C2×C22⋊C4C4×D1311yescharacteristic
500C2×C42—131no—
501C2×C42—131no—
502C2×C42C22×D1311yescharacteristic
503C2×C42C22×D1311yescharacteristic
504C4⋊C8—22no—
505C4⋊C8—262no—
506C4⋊C8—262no—
507C4⋊C8—262no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—262no—
511C22⋊C8—262no—
512C22⋊C8—262no—
513C22⋊C8—262no—
514C22⋊C8—262no—
515C22⋊C8—262no—
516#97—262no—
517#97—262no—
518C4×C8—22no—
519C4×C8—262no—
520#95—131no—
521#95—131no—
522#95—131no—
523#95—131no—
524#95—131no—
525#95—131no—
526#95C4×D1311yescharacteristic
527#95C4×D1311yescharacteristic
528C2×C13—42no—
529C2×C13C2×#38811yescharacteristic
530C2×C13#292411yescharacteristic
531C2×C13#292411yescharacteristic
532C2×C13#292911yescharacteristic
533C2×C13#293011yescharacteristic
534C2×C13#293311yescharacteristic
535C2×C13#293311yescharacteristic
536D13—24no—
537D13—42no—
538C24—131no—
539C24—131no—
540C24—262no—
541C24—262no—
542C24—262no—
543C24—262no—
544C24—262no—
545C24—521no—
546C24—521no—
547C24C2×C4×D1311yescharacteristic
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—131no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—131no—
562C22×C4—131no—
563C22×C4—131no—
564C22×C4—131no—
565C22×C4—131no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—524no—
582C22×C4—524no—
583C22×C4—524no—
584C22×C4—524no—
585C22×C4C2×C4×D1311yescharacteristic
586C22×C4C2×C4×D1311yescharacteristic
587C22×C4C2×C4×D1311yescharacteristic
588C22×C4C2×C4×D1311yescharacteristic
589C22×C4C2×C4×D1311yescharacteristic
590C22×C4C23×D1311yescharacteristic
591M16—268no—
592M16—524no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—132no—
604C2×C8—132no—
605C2×C8—268no—
606C2×C8—261no—
607C2×C8—261no—
608C2×C8—261no—
609C2×C8—261no—
610C2×C8—261no—
611C2×C8—261no—
612C2×C8—261no—
613C2×C8—261no—
614C2×C8—261no—
615C2×C8—261no—
616C2×C8—524no—
617C2×C8D4×D1312yes—
618C2×C8D4×D1312yes—
619C4⋊C4—262no—
620C4⋊C4—262no—
621C4⋊C4—262no—
622C4⋊C4—262no—
623C22⋊C4—22no—
624C22⋊C4—41no—
625C22⋊C4—262no—
626C22⋊C4—262no—
627C22⋊C4—262no—
628C22⋊C4—262no—
629C22⋊C4—262no—
630C22⋊C4—262no—
631C22⋊C4—262no—
632C22⋊C4—521no—
633C22⋊C4—521no—
634C22⋊C4—521no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—261no—
640C42—261no—
641C42—261no—
642C42—261no—
643C13#2105011yescharacteristic, complemented, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—132no—
651C23—132no—
652C23—132no—
653C23—132no—
654C23—268no—
655C23—261no—
656C23—261no—
657C23—261no—
658C23—261no—
659C23—261no—
660C23—261no—
661C23—261no—
662C23—261no—
663C23—261no—
664C23—261no—
665C23—524no—
666C23—524no—
667C23—524no—
668C23—524no—
669C23—524no—
670C23—524no—
671C23#8815512yes—
672C23C22×C4×D1311yescharacteristic
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—132no—
693C2×C4—132no—
694C2×C4—132no—
695C2×C4—134no—
696C2×C4—134no—
697C2×C4—134no—
698C2×C4—134no—
699C2×C4—261no—
700C2×C4—261no—
701C2×C4—261no—
702C2×C4—261no—
703C2×C4—261no—
704C2×C4—261no—
705C2×C4—261no—
706C2×C4—261no—
707C2×C4—261no—
708C2×C4—261no—
709C2×C4—261no—
710C2×C4—261no—
711C2×C4—261no—
712C2×C4—261no—
713C2×C4—261no—
714C2×C4—524no—
715C2×C4—524no—
716C2×C4—524no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—521no—
720C2×C4—521no—
721C2×C4C2×D4×D1311yescharacteristic
722C2×C4C2×D4×D1311yescharacteristic
723C2×C4#41×D1311yescharacteristic
724C2×C4#41×D1311yescharacteristic
725C2×C4#41×D1311yescharacteristic
726C2×C4#41×D1311yescharacteristic
727C8—22no—
728C8—22no—
729C8—41no—
730C8—41no—
731C8—262no—
732C8—262no—
733C8—521no—
734C8—521no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—134no—
743C22—262no—
744C22—262no—
745C22—262no—
746C22—262no—
747C22—262no—
748C22—262no—
749C22—262no—
750C22—262no—
751C22—262no—
752C22—5216no—
753C22—521no—
754C22—521no—
755C22—521no—
756C22—521no—
757C22D13×#11711yescharacteristic
758C22C4×D4×D1311yescharacteristic
759C22C4×D4×D1311yescharacteristic
760C22C2×#8815511yescharacteristic
761C22#1171945011yescharacteristic
762C22D13×#13111yescharacteristic
763C22#1171945511yescharacteristic
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—134no—
770C4—521no—
771C4—521no—
772C4—521no—
773C4—521no—
774C4—521no—
775C4D13×#12111yescharacteristic
776C4D13×#12311yescharacteristic
777C4D13×#12411yescharacteristic
778C4D13×#12611yescharacteristic
779C2—42no—
780C2—264no—
781C2—522no—
782C2D13×#38811yescharacteristic
783C2#1312348911yescharacteristic
784C2#1312349211yescharacteristic
785C2#1312352511yescharacteristic
786C2#1312353411yescharacteristic
787C2#1312355611yescharacteristic
788C2#1312356511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1923C2
prime radicalC24×D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1923D13
hypocenterC13#21050
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#11718500C2semidirect
4. C2×#11718350C2semidirect
6. #13115452C2semidirect
7. #13115451C2semidirect
8. #13115448C2semidirect
9. #13115447C2semidirect
10. #13115443C2semidirect
11. #13115442C2semidirect
12. #13115439C2semidirect
13. #13114531C2semidirect
14. #13114531C2semidirect
15. C13×#1923C2semidirect
23. C2×C13×C4⋊C8C22semidirect
26. C2×C4×C8×C13C22semidirect
35. C2×#88055C22semidirect
36. C2×#88054C22semidirect
37. C2×#88054C22semidirect
38. C2×C8×Dic13C22semidirect
45. C2×C4⋊#1055C22semidirect
46. C2×#88043C22semidirect
55. C13×#336C22semidirect
56. C13×#336C22semidirect
57. #11718142C22semidirect
58. #11718142C22semidirect
59. #11718142C22semidirect
60. #11718142C22semidirect
61. #11718116C22semidirect
62. #11718116C22semidirect
262. #1923D13semidirect
367. C2×C4⋊C8C2×D13semidirect
382. C2×C4×C8C2×D13semidirect
401. #336C2×D13semidirect
402. #336C2×D13semidirect
643. C13#21050semidirect

Maximal subgroups

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

subgroupindex
C2×#117185002
C2×#117183872
C2×D13×C22⋊C82
C2×#117183502
#131172172
#131154522
#131154512
#131154482
#131154472
#131154432
#131154422
#131154392
#131145312
C13×#19232
#2105013