Finite Group Databasebeta

← #15879836

Subgroups — #15879836

Order 3328.

1280 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718494C211yesmaximal, characteristic, complemented
2C22×#88060C211yesmaximal, characteristic
3C4×C22⋊C4×D13C211yesmaximal, characteristic
4#13115443C211yesmaximal, characteristic, complemented
5#13115443C211yesmaximal, characteristic, complemented
6#13115441C211yesmaximal, characteristic, complemented
7#13115441C211yesmaximal, characteristic, complemented
8#13115016C211yesmaximal, characteristic, complemented
9#13114903C211yesmaximal, characteristic, complemented
10#13114813C211yesmaximal, characteristic, complemented
11#13114745C211yesmaximal, characteristic
12#13114610C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic13C211yesmaximal, characteristic, complemented
14#13114593C211yesmaximal, characteristic, complemented
15C13×#1850C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19C2×C22⋊C4×D13C411yescharacteristic
20C2×C22⋊C4×D13C411yescharacteristic
21C2×C42×D13C2211yescharacteristic
22C2×C42×D13C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic, complemented
24C2×C13×C4⋊C8C2211yescharacteristic, complemented
25C2×C13×C22⋊C8C2211yescharacteristic
26C4×C13×C22⋊C4C2211yescharacteristic
27C4×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29C2×#88060—24no—
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88060C2211yescharacteristic
37C2×#88060C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic, complemented
39C2×C8×Dic13C2211yescharacteristic, complemented
40C2×C8×Dic13C2211yescharacteristic, complemented
41C2×C8×Dic13C2211yescharacteristic, complemented
42C22⋊C4×Dic13C411yescharacteristic
43C22⋊C4×Dic13C411yescharacteristic
44C4×#6103C2211yescharacteristic
45C4×#6103C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic, complemented
47C2×C4⋊#1055C2211yescharacteristic, complemented
48#11718494—24no—
49#11718327C411yescharacteristic
50#11718327C411yescharacteristic
51D13×#95C411yescharacteristic
52D13×#95C411yescharacteristic
53C13×#336C2211yescharacteristic, complemented
54C13×#336C2211yescharacteristic, complemented
55#11718142C2211yescharacteristic, complemented
56#11718142C2211yescharacteristic, complemented
57#11718142C2211yescharacteristic, complemented
58#11718142C2211yescharacteristic, complemented
59#11718116C2211yescharacteristic, complemented
60#11718116C2211yescharacteristic, complemented
61C24×D13C2×C411yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13C2×C411yescharacteristic
64C22×C4×D13—22no—
65C22×C4×D13—22no—
66C22×C4×D13—22no—
67C22×C4×D13—22no—
68C22×C4×D13—41no—
69C22×C4×D13—41no—
70C22×C4×D13C2×C411yescharacteristic
71C22×C4×D13C2×C411yescharacteristic
72C22×C4×D13C2×C411yescharacteristic
73C22×C4×D13C2×C411yescharacteristic
74C22×C4×D13C2×C411yescharacteristic
75C22×C4×D13C2×C411yescharacteristic
76C22×C4×D13C2311yescharacteristic
77C22×C4×D13C2311yescharacteristic
78C22×C8×C13—22no—
79C22×C8×C13—22no—
80C22×C8×C13—41no—
81C22×C8×C13C2311yescharacteristic
82C22×C8×C13C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C2×C13×C22⋊C4C2×C411yescharacteristic
86C2×C13×C22⋊C4C2×C411yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13C2×C411yescharacteristic
90C2×C22⋊Dic13C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×#6103C2×C411yescharacteristic
93C2×#6103C2×C411yescharacteristic
94C2×#6103C2×C411yescharacteristic
95C2×C4×Dic13C2×C411yescharacteristic
96C2×C4×Dic13C2×C411yescharacteristic
97C2×C4×Dic13C2×C411yescharacteristic
98C2×C4×Dic13C2×C411yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055—22no—
102C22×#1055—22no—
103C22×#1055—41no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22⋊C4×D13—24no—
109C22⋊C4×D13C818yescomplemented
110C42×D13—22no—
111C42×D13—22no—
112C42×D13—41no—
113C42×D13—41no—
114C13×C4⋊C8—22no—
115C13×C4⋊C8—41no—
116C13×C22⋊C8—22no—
117C13×#95C2×C411yescharacteristic
118C13×#95C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88071C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125C22⋊#1055—22no—
126#88060—22no—
127#88060—22no—
128#88060—22no—
129#88060—22no—
130#88060—22no—
131#88060—41no—
132#88060—41no—
133#88060D414yes—
134C8×Dic13—22no—
135C8×Dic13—22no—
136C8×Dic13—41no—
137C8×Dic13—41no—
138C4⋊#1055—22no—
139C4⋊#1055—41no—
140#22552—131nomaximal, Sylow
141C24×C13C22×C411yescharacteristic
142C23×D13—22no—
143C23×D13—22no—
144C23×D13—22no—
145C23×D13—22no—
146C23×D13—41no—
147C23×D13—41no—
148C23×D13C2×C814yes—
149C23×D13C22×C411yescharacteristic
150C23×D13C22×C411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C22×C411yescharacteristic
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C22×C411yescharacteristic
160C22×C4×C13#4112yes—
161C22×C4×C13#4112yes—
162C22×C4×C13C2411yescharacteristic
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—41no—
166C22×Dic13C22×C411yescharacteristic
167C22×Dic13C22×C411yescharacteristic
168C22×Dic13C22×C411yescharacteristic
169C22×Dic13C22×C411yescharacteristic
170C22×Dic13C22×C411yescharacteristic
171C22×Dic13C22×C411yescharacteristic
172C2×C4×D13—22no—
173C2×C4×D13—22no—
174C2×C4×D13—21no—
175C2×C4×D13—21no—
176C2×C4×D13—21no—
177C2×C4×D13—21no—
178C2×C4×D13—22no—
179C2×C4×D13—22no—
180C2×C4×D13—22no—
181C2×C4×D13—22no—
182C2×C4×D13—22no—
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—22no—
190C2×C4×D13—22no—
191C2×C4×D13—22no—
192C2×C4×D13—44no—
193C2×C4×D13—44no—
194C2×C4×D13—44no—
195C2×C4×D13—44no—
196C2×C4×D13—41no—
197C2×C4×D13—41no—
198C2×C4×D13—41no—
199C2×C4×D13—41no—
200C2×C4×D13—41no—
201C2×C4×D13—41no—
202C2×C4×D13C2×C814yescomplemented
203C2×C4×D13C2×C814yescomplemented
204C2×C4×D13C2×D412yes—
205C2×C4×D13#4112yes—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13—21no—
209C2×C8×C13—21no—
210C2×C8×C13—21no—
211C2×C8×C13—21no—
212C2×C8×C13—21no—
213C2×C8×C13—21no—
214C2×C8×C13—21no—
215C2×C8×C13—21no—
216C2×C8×C13—21no—
217C2×C8×C13—44no—
218C2×C8×C13C2×D412yes—
219C13×C22⋊C4—22no—
220C13×C22⋊C4C2×C814yes—
221C42×C13—21no—
222C42×C13—21no—
223C42×C13—21no—
224C42×C13—21no—
225C22⋊Dic13C2×C814yes—
226C22⋊Dic13M1614yes—
227#6103—22no—
228#6103—22no—
229#6103C2×C814yescomplemented
230#6103C2×C814yescomplemented
231C4×Dic13—21no—
232C4×Dic13—21no—
233C4×Dic13—21no—
234C4×Dic13—21no—
235C4×Dic13—22no—
236C4×Dic13—22no—
237C4×Dic13—41no—
238C4×Dic13—41no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245C2×#1055—21no—
246C2×#1055—21no—
247C2×#1055—21no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055—44no—
251C2×#1055C2×D412yes—
252C2×#431—131no—
253C22×C22⋊C8—131no—
254C2×C4×C22⋊C4—131no—
255#1923—131no—
256#1923—131no—
257#1923—131no—
258#1923—131no—
259#1850—131no—
260#1850D1311yescharacteristic, complemented
261#1817—131no—
262#1797—131no—
263#1779—131no—
264C8×C22⋊C4—131no—
265C8×C22⋊C4—131no—
266C4×C22⋊C8—131no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13#11712yes—
272C23×C13C22×C812yes—
273C23×C13C2×M1612yes—
274C23×C13C23×C411yescharacteristic
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—21no—
278C22×D13—21no—
279C22×D13—21no—
280C22×D13—21no—
281C22×D13—21no—
282C22×D13—21no—
283C22×D13—21no—
284C22×D13—21no—
285C22×D13—28no—
286C22×D13—28no—
287C22×D13—44no—
288C22×D13—44no—
289C22×D13—44no—
290C22×D13—44no—
291C22×D13—44no—
292C22×D13C4×D412yes—
293C22×D13C22×C812yes—
294C22×D13C22×C812yes—
295C22×D13#13112yes—
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—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—21no—
311C2×C4×C13—21no—
312C2×C4×C13#11712yes—
313C2×C4×C13C22×C812yes—
314C2×C4×C13C22×C812yes—
315C2×C4×C13C22×D411yescharacteristic
316C2×C4×C13C2×#4111yescharacteristic
317C2×C4×C13C2×#4111yescharacteristic
318C2×C4×C13C2×#4111yescharacteristic
319C2×C4×C13H(5,𝔽2)11yescharacteristic
320C2×C4×C13H(5,𝔽2)11yescharacteristic
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×Dic13C4×D412yes—
336C2×Dic13C22×C812yes—
337C2×Dic13C22×C812yes—
338C2×Dic13C2×M1612yes—
339C2×Dic13C2×M1612yes—
340C4×D13—28no—
341C4×D13—22no—
342C4×D13—22no—
343C4×D13—22no—
344C4×D13—22no—
345C4×D13—44no—
346C4×D13—44no—
347C4×D13—44no—
348C4×D13—44no—
349C4×D13—44no—
350C4×D13—41no—
351C4×D13—41no—
352C4×D13—41no—
353C4×D13—41no—
354C8×C13—22no—
355C8×C13—41no—
356C8×C13—41no—
357C8×C13—41no—
358#1055—22no—
359#1055—41no—
360#1055—41no—
361#1055—41no—
362C24×C4—131no—
363C23×C8—131no—
364C23×C8C2×D1311yescharacteristic
365C22×C22⋊C4—131no—
366C22×C22⋊C4—131no—
367C22×C42—131no—
368C22×C42—131no—
369#431—264no—
370C2×C4⋊C8—131no—
371C2×C4⋊C8—131no—
372C2×C4⋊C8C2×D1311yescharacteristic, complemented
373C2×C4⋊C8C2×D1311yescharacteristic, complemented
374C2×C22⋊C8—131no—
375C2×C22⋊C8—131no—
376C2×C22⋊C8—131no—
377C2×C22⋊C8—131no—
378C2×C22⋊C8—131no—
379C2×C22⋊C8—131no—
380C2×C22⋊C8—131no—
381C2×C22⋊C8—131no—
382C2×C22⋊C8—131no—
383C2×C22⋊C8—264no—
384C2×C22⋊C8C2×D1311yescharacteristic
385C2×C4×C8—131no—
386C2×C4×C8—131no—
387C2×C4×C8—131no—
388C2×C4×C8—131no—
389C4×C22⋊C4—131no—
390C4×C22⋊C4—131no—
391C4×C22⋊C4—131no—
392C4×C22⋊C4—131no—
393C4×C22⋊C4—131no—
394C4×C22⋊C4—131no—
395C4×C22⋊C4—131no—
396C4×C22⋊C4C2×D1311yescharacteristic
397C2×#95—131no—
398C2×#95—131no—
399#336—131no—
400#336—131no—
401#336—131no—
402#336—131no—
403#336—131no—
404#336—131no—
405#336C2×D1311yescharacteristic, complemented
406#336C2×D1311yescharacteristic, complemented
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—22no—
411C22×C13—22no—
412C22×C13—22no—
413C22×C13#43114yescomplemented
414C22×C13C2×#11711yescharacteristic
415C22×C13C2×C4×D411yescharacteristic
416C22×C13#51811yescharacteristic
417C22×C13C23×C811yescharacteristic
418C22×C13C22×M1611yescharacteristic
419C22×C13C2×#13111yescharacteristic
420C22×C13#56811yescharacteristic
421C2×D13—22no—
422C2×D13—22no—
423C2×D13—22no—
424C2×D13—22no—
425C2×D13—22no—
426C2×D13—22no—
427C2×D13—22no—
428C2×D13—22no—
429C2×D13—22no—
430C2×D13—416no—
431C2×D13—41no—
432C2×D13—41no—
433C2×D13—41no—
434C2×D13—41no—
435C2×D13C8×D414yes—
436C4×C13—22no—
437C4×C13—22no—
438C4×C13—22no—
439C4×C13—41no—
440C4×C13—41no—
441C4×C13#54611yescharacteristic
442C4×C13#54611yescharacteristic
443C4×C13#55111yescharacteristic
444C4×C13#55111yescharacteristic
445Dic13—22no—
446Dic13—22no—
447Dic13—22no—
448Dic13—22no—
449Dic13—22no—
450Dic13—41no—
451C25—131no—
452C23×C4—131no—
453C23×C4—131no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—131no—
457C23×C4—131no—
458C23×C4—131no—
459C23×C4—131no—
460C23×C4—131no—
461C23×C4—262no—
462C23×C4—262no—
463C23×C4—262no—
464C23×C4—262no—
465C23×C4—521no—
466C23×C4—521no—
467C23×C4C22×D1311yescharacteristic
468C22×C8—22no—
469C22×C8—22no—
470C22×C8—41no—
471C22×C8—131no—
472C22×C8—131no—
473C22×C8—131no—
474C22×C8—131no—
475C22×C8—262no—
476C22×C8—262no—
477C22×C8—521no—
478C22×C8C22×D1311yescharacteristic
479C22×C8C22×D1311yescharacteristic
480C22×C8C22×D1311yescharacteristic
481C22×C8C22×D1311yescharacteristic
482C2×C22⋊C4—131no—
483C2×C22⋊C4—131no—
484C2×C22⋊C4—131no—
485C2×C22⋊C4—131no—
486C2×C22⋊C4—138no—
487C2×C22⋊C4—131no—
488C2×C22⋊C4—131no—
489C2×C22⋊C4—264no—
490C2×C22⋊C4C4×D1311yescharacteristic
491C2×C22⋊C4C4×D1311yescharacteristic
492C2×C42—131no—
493C2×C42—131no—
494C2×C42—131no—
495C2×C42—131no—
496C2×C42—131no—
497C2×C42—131no—
498C2×C42—262no—
499C2×C42—262no—
500C2×C42—521no—
501C2×C42—521no—
502C2×C42C22×D1311yescharacteristic
503C2×C42C22×D1311yescharacteristic
504C4⋊C8—22no—
505C4⋊C8—41no—
506C4⋊C8—262no—
507C4⋊C8—521no—
508C22⋊C8—22no—
509C22⋊C8—134no—
510C22⋊C8—262no—
511C22⋊C8—262no—
512C22⋊C8—262no—
513C22⋊C8—262no—
514C22⋊C8—262no—
515C22⋊C8—262no—
516C22⋊C8—521no—
517C22⋊C8—521no—
518C4×C8—262no—
519C4×C8—262no—
520C4×C8—521no—
521C4×C8—521no—
522#95—131no—
523#95—131no—
524#95—131no—
525#95—131no—
526#95—131no—
527#95—131no—
528#95C4×D1311yescharacteristic
529#95C4×D1311yescharacteristic
530C2×C13—24no—
531C2×C13#234211yescharacteristic
532C2×C13C2×#43111yescharacteristic
533C2×C13#292411yescharacteristic
534C2×C13C2×C8×D411yescharacteristic
535C2×C13D4×M1611yescharacteristic
536C2×C13#297211yescharacteristic
537C2×C13#297411yescharacteristic
538D13—24no—
539D13—42no—
540C24—131no—
541C24—131no—
542C24—134no—
543C24—262no—
544C24—262no—
545C24—262no—
546C24—262no—
547C24—521no—
548C24—521no—
549C24C2×C4×D1311yescharacteristic
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—131no—
555C22×C4—131no—
556C22×C4—131no—
557C22×C4—131no—
558C22×C4—131no—
559C22×C4—134no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—134no—
563C22×C4—131no—
564C22×C4—262no—
565C22×C4—262no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—521no—
587C22×C4—521no—
588C22×C4—521no—
589C22×C4—521no—
590C22×C4—521no—
591C22×C4—521no—
592C22×C4—524no—
593C22×C4—524no—
594C22×C4—524no—
595C22×C4—524no—
596C22×C4—521no—
597C22×C4C2×C4×D1311yescharacteristic
598C22×C4C2×C4×D1311yescharacteristic
599C22×C4C2×C4×D1311yescharacteristic
600C22×C4C2×C4×D1311yescharacteristic
601C22×C4C2×C4×D1311yescharacteristic
602C22×C4#612912yes—
603C22×C4#613112yes—
604C22×C4C23×D1311yescharacteristic
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8—132no—
618C2×C8—261no—
619C2×C8—261no—
620C2×C8—261no—
621C2×C8—261no—
622C2×C8—261no—
623C2×C8—261no—
624C2×C8—261no—
625C2×C8—261no—
626C2×C8—261no—
627C2×C8—261no—
628C2×C8—261no—
629C2×C8—524no—
630C2×C8D4×D1312yes—
631C22⋊C4—22no—
632C22⋊C4—134no—
633C22⋊C4—134no—
634C22⋊C4—134no—
635C22⋊C4—134no—
636C22⋊C4—262no—
637C22⋊C4—262no—
638C22⋊C4C8×D1314yes—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—262no—
644C42—262no—
645C42—261no—
646C42—261no—
647C42—261no—
648C42—261no—
649C42—521no—
650C42—521no—
651C13#2255211yescharacteristic, complemented, Sylow
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—132no—
657C23—132no—
658C23—132no—
659C23—132no—
660C23—268no—
661C23—261no—
662C23—261no—
663C23—261no—
664C23—261no—
665C23—261no—
666C23—261no—
667C23—261no—
668C23—261no—
669C23—261no—
670C23—261no—
671C23—268no—
672C23—524no—
673C23—524no—
674C23—524no—
675C23—524no—
676C23—524no—
677C23#8814612yes—
678C23C2×C8×D1312yes—
679C23M16×D1312yes—
680C23C22×C4×D1311yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—132no—
698C2×C4—132no—
699C2×C4—132no—
700C2×C4—132no—
701C2×C4—132no—
702C2×C4—268no—
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—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—261no—
718C2×C4—261no—
719C2×C4—261no—
720C2×C4—524no—
721C2×C4—524no—
722C2×C4—524no—
723C2×C4—524no—
724C2×C4—524no—
725C2×C4—524no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—521no—
730C2×C4#8814612yes—
731C2×C4C2×C8×D1312yes—
732C2×C4C2×C8×D1312yes—
733C2×C4C2×D4×D1311yescharacteristic
734C2×C4C2×#612911yescharacteristic
735C2×C4#8825111yescharacteristic
736C2×C4C2×#613111yescharacteristic
737C2×C4#41×D1311yescharacteristic
738C2×C4#8825611yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—262no—
744C8—521no—
745C8—521no—
746C8—521no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—134no—
754C22—262no—
755C22—262no—
756C22—262no—
757C22—262no—
758C22—262no—
759C22—262no—
760C22—262no—
761C22—262no—
762C22—262no—
763C22—5216no—
764C22—521no—
765C22—521no—
766C22—521no—
767C22—521no—
768C22#1171849414yescomplemented
769C22C2×#8814611yescharacteristic
770C22C4×D4×D1311yescharacteristic
771C22#1171925011yescharacteristic
772C22C22×C8×D1311yescharacteristic
773C22C2×M16×D1311yescharacteristic
774C22D13×#13111yescharacteristic
775C22#1171945511yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—262no—
782C4—262no—
783C4—262no—
784C4—262no—
785C4—262no—
786C4—521no—
787C4#1171929611yescharacteristic
788C4#1171933511yescharacteristic
789C4#1171934211yescharacteristic
790C4#1171936311yescharacteristic
791C2—24no—
792C2—264no—
793C2—522no—
794C2#1311768311yescharacteristic
795C2C2×#1171849411yescharacteristic
796C2#1312349311yescharacteristic
797C2C8×D4×D1311yescharacteristic
798C2#1312356911yescharacteristic
799C2#1312385711yescharacteristic
800C2#1312386611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC13×#1850C2
socleC23×C13C23×C4
prime radicalC24×D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1850D13
hypocenterC13#22552
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#11718494C2semidirect
4. #13115443C2semidirect
5. #13115443C2semidirect
6. #13115441C2semidirect
7. #13115441C2semidirect
8. #13115016C2semidirect
9. #13114903C2semidirect
10. #13114813C2semidirect
12. #13114610C2semidirect
13. C8×C22⋊Dic13C2semidirect
14. #13114593C2semidirect
15. C13×#1850C2semidirect
23. C2×C13×C4⋊C8C22semidirect
24. C2×C13×C4⋊C8C22semidirect
38. C2×C8×Dic13C22semidirect
39. C2×C8×Dic13C22semidirect
40. C2×C8×Dic13C22semidirect
41. C2×C8×Dic13C22semidirect
46. C2×C4⋊#1055C22semidirect
47. C2×C4⋊#1055C22semidirect
53. C13×#336C22semidirect
54. C13×#336C22semidirect
55. #11718142C22semidirect
56. #11718142C22semidirect
57. #11718142C22semidirect
58. #11718142C22semidirect
59. #11718116C22semidirect
60. #11718116C22semidirect
109. C22⋊C4×D13C8semidirect
202. C2×C4×D13C2×C8semidirect
203. C2×C4×D13C2×C8semidirect
229. #6103C2×C8semidirect
230. #6103C2×C8semidirect
260. #1850D13semidirect
372. C2×C4⋊C8C2×D13semidirect
373. C2×C4⋊C8C2×D13semidirect
405. #336C2×D13semidirect
406. #336C2×D13semidirect
413. C22×C13#431semidirect
651. C13#22552semidirect
768. C22#11718494semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
C22×#880602
C4×C22⋊C4×D132
#131154432
#131154412
#131150162
#131149032
#131148132
#131147452
#131146102
C8×C22⋊Dic132
#131145932
C13×#18502
#2255213