Finite Group Databasebeta

← #15865232

Subgroups — #15865232

Order 3328.

1330 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718498C211yesmaximal, characteristic, complemented
2C2×#11718387C211yesmaximal, characteristic
3C2×#11718387C211yesmaximal, characteristic
4C2×C4×#6094C211yesmaximal, characteristic, complemented
5C4×C22⋊C4×D13C211yesmaximal, characteristic
6#13115452C211yesmaximal, characteristic, complemented
7#13115450C211yesmaximal, characteristic, complemented
8#13115448C211yesmaximal, characteristic, complemented
9#13115446C211yesmaximal, characteristic, complemented
10#13115444C211yesmaximal, characteristic, complemented
11#13115442C211yesmaximal, characteristic, complemented
12#13115440C211yesmaximal, characteristic, complemented
13#13114528C211yesmaximal, characteristic, complemented
14#13114528C211yesmaximal, characteristic, complemented
15C13×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×#6094C2211yescharacteristic
18C22×#6094C2211yescharacteristic
19C22×#6094C2211yescharacteristic
20C22×#6094C2211yescharacteristic
21C2×C22⋊C4×D13C411yescharacteristic
22C2×C22⋊C4×D13C411yescharacteristic
23C2×C42×D13C2211yescharacteristic
24C2×C42×D13C2211yescharacteristic
25C2×C13×C4⋊C8C2211yescharacteristic, complemented
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C13×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C13C2211yescharacteristic, complemented
29C4×C13×C22⋊C4C2211yescharacteristic
30C4×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88060C2211yescharacteristic
37C2×#88055C2211yescharacteristic, complemented
38C2×#88055C2211yescharacteristic, complemented
39C2×#88054C2211yescharacteristic, complemented
40C2×#88054C2211yescharacteristic, complemented
41C22⋊C4×Dic13C411yescharacteristic
42C22⋊C4×Dic13C411yescharacteristic
43C4×#6103C2211yescharacteristic
44C4×#6103C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic, complemented
46C2×C4×#1055C2211yescharacteristic, complemented
47#11718498—24no—
48#11718387—24no—
49#11718387—24no—
50C4×#6094—24no—
51#11718327C411yescharacteristic
52#11718327C411yescharacteristic
53D13×#95C411yescharacteristic
54D13×#95C411yescharacteristic
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×D13C2×C411yescharacteristic
75C22×C4×D13C2×C411yescharacteristic
76C22×C4×D13C2×C411yescharacteristic
77C22×C4×D13C2×C411yescharacteristic
78C22×C4×D13C2311yescharacteristic
79C22×C4×D13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C22×C8×C13C2311yescharacteristic
82C22×C8×C13C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C2×C13×C22⋊C4C2×C411yescharacteristic
85C2×C13×C22⋊C4C2×C411yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C2×C22⋊Dic13C2×C411yescharacteristic
90C2×#6103C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×#6103C2×C411yescharacteristic
93C2×#6103C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2×C411yescharacteristic
96C2×C4×Dic13C2×C411yescharacteristic
97C2×C4×Dic13C2×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×#6094—22no—
110C2×#6094—22no—
111C2×#6094—22no—
112C2×#6094—22no—
113C2×#6094—22no—
114C2×#6094D414yes—
115C2×#6094D414yes—
116C22⋊C4×D13—24no—
117C22⋊C4×D13—24no—
118C42×D13—22no—
119C42×D13—22no—
120C42×D13—22no—
121C42×D13—22no—
122C13×C4⋊C8—22no—
123C13×C22⋊C8—22no—
124C13×C22⋊C8—22no—
125C4×C8×C13—22no—
126C13×#95C2×C411yescharacteristic
127C13×#95C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130#88071C2×C411yescharacteristic
131#88071C2×C411yescharacteristic
132#88071C2×C411yescharacteristic
133#88071C2×C411yescharacteristic
134C22⋊#1055—22no—
135C22⋊#1055—22no—
136#88060—22no—
137#88060—22no—
138#88060—22no—
139#88060—22no—
140#88055—22no—
141#88055—22no—
142#88054—22no—
143#88054—22no—
144C4⋊#1055—22no—
145C4×#1055—22no—
146#21049—131nomaximal, Sylow
147C24×C13C22×C411yescharacteristic
148C23×D13—22no—
149C23×D13—22no—
150C23×D13—22no—
151C23×D13—22no—
152C23×D13—22no—
153C23×D13—41no—
154C23×D13—41no—
155C23×D13C22×C411yescharacteristic
156C23×D13C22×C411yescharacteristic
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13C22×C411yescharacteristic
164C22×C4×C13C22×C411yescharacteristic
165C22×C4×C13C22×C411yescharacteristic
166C22×C4×C13C22×C411yescharacteristic
167C22×C4×C13C22×C411yescharacteristic
168C22×C4×C13C2411yescharacteristic
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13C22×C411yescharacteristic
173C22×Dic13C22×C411yescharacteristic
174C22×Dic13C22×C411yescharacteristic
175C22×Dic13C22×C411yescharacteristic
176C22×Dic13C22×C411yescharacteristic
177C22×Dic13C22×C411yescharacteristic
178C2×C4×D13—22no—
179C2×C4×D13—22no—
180C2×C4×D13—22no—
181C2×C4×D13—22no—
182C2×C4×D13—22no—
183C2×C4×D13—22no—
184C2×C4×D13—22no—
185C2×C4×D13—22no—
186C2×C4×D13—22no—
187C2×C4×D13—22no—
188C2×C4×D13—21no—
189C2×C4×D13—21no—
190C2×C4×D13—21no—
191C2×C4×D13—21no—
192C2×C4×D13—21no—
193C2×C4×D13—21no—
194C2×C4×D13—22no—
195C2×C4×D13—22no—
196C2×C4×D13—22no—
197C2×C4×D13—22no—
198C2×C4×D13—41no—
199C2×C4×D13—41no—
200C2×C4×D13—41no—
201C2×C4×D13—41no—
202C2×C4×D13—44no—
203C2×C4×D13—44no—
204C2×C4×D13—44no—
205C2×C4×D13—44no—
206C2×C4×D13C2×D412yes—
207C2×C4×D13C2×D412yes—
208C2×C4×D13#4112yes—
209C2×C4×D13#4112yes—
210C2×C4×D13#4112yes—
211C2×C4×D13#4112yes—
212C2×C8×C13—21no—
213C2×C8×C13—21no—
214C2×C8×C13—21no—
215C2×C8×C13—21no—
216C2×C8×C13—21no—
217C2×C8×C13—21no—
218C2×C8×C13—21no—
219C2×C8×C13—21no—
220C2×C8×C13—21no—
221C2×C8×C13—21no—
222C2×C8×C13C2×D412yes—
223C2×C8×C13C2×D412yes—
224C13×C22⋊C4—22no—
225C13×C22⋊C4M1614yescomplemented
226C42×C13—21no—
227C42×C13—21no—
228C42×C13—21no—
229C42×C13—21no—
230C22⋊Dic13—22no—
231C22⋊Dic13—22no—
232#6103—22no—
233#6103—22no—
234#6103—22no—
235#6103M1614yescomplemented
236C4×Dic13—21no—
237C4×Dic13—21no—
238C4×Dic13—21no—
239C4×Dic13—21no—
240C4×Dic13—22no—
241C4×Dic13—22no—
242C4×Dic13—22no—
243C4×Dic13—22no—
244C2×#1055—21no—
245C2×#1055—21no—
246C2×#1055—21no—
247C2×#1055—21no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055—21no—
251C2×#1055—21no—
252C2×#1055—21no—
253C2×#1055—21no—
254C2×#1055C2×D412yes—
255C2×#1055C2×D412yes—
256#6094—28no—
257#6094—28no—
258#6094—44no—
259#6094—44no—
260C2×#423—131no—
261C2×#407—131no—
262C2×#407—131no—
263C2×C4×M16—131no—
264C2×C4×C22⋊C4—131no—
265#1924—131no—
266#1924—131no—
267#1924—131no—
268#1924—131no—
269#1923—131no—
270#1923—131no—
271#1923—131no—
272#1923D1311yescharacteristic, complemented
273#1728—131no—
274#1728—131no—
275C23×C13—21no—
276C23×C13—21no—
277C23×C13—21no—
278C23×C13—21no—
279C23×C13—21no—
280C23×C13—21no—
281C23×C13C2×M1612yes—
282C23×C13C23×C411yescharacteristic
283C22×D13—21no—
284C22×D13—21no—
285C22×D13—21no—
286C22×D13—21no—
287C22×D13—28no—
288C22×D13—21no—
289C22×D13—21no—
290C22×D13—21no—
291C22×D13—21no—
292C22×D13—21no—
293C22×D13—21no—
294C22×D13—44no—
295C22×D13—44no—
296C22×D13—44no—
297C22×D13—44no—
298C22×D13—44no—
299C22×D13—44no—
300C22×D13#11712yes—
301C22×D13C4×D412yes—
302C22×D13C4×D412yes—
303C22×D13C2×M1612yes—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
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—21no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13C2×M1612yes—
321C2×C4×C13C2×M1612yes—
322C2×C4×C13C2×M1612yes—
323C2×C4×C13C22×D411yescharacteristic
324C2×C4×C13C22×D411yescharacteristic
325C2×C4×C13C2×#4111yescharacteristic
326C2×C4×C13C2×#4111yescharacteristic
327C2×C4×C13C2×#4111yescharacteristic
328C2×C4×C13C2×#4111yescharacteristic
329C2×Dic13—21no—
330C2×Dic13—21no—
331C2×Dic13—21no—
332C2×Dic13—21no—
333C2×Dic13—21no—
334C2×Dic13—21no—
335C2×Dic13—21no—
336C2×Dic13—21no—
337C2×Dic13—21no—
338C2×Dic13—21no—
339C2×Dic13—21no—
340C2×Dic13—21no—
341C2×Dic13—21no—
342C2×Dic13—21no—
343C2×Dic13—44no—
344C2×Dic13#11712yes—
345C2×Dic13C4×D412yes—
346C2×Dic13C4×D412yes—
347C2×Dic13C2×M1612yes—
348C4×D13—44no—
349C4×D13—44no—
350C4×D13—44no—
351C4×D13—44no—
352C4×D13—44no—
353C4×D13—41no—
354C4×D13—41no—
355C4×D13—41no—
356C4×D13—41no—
357C4×D13—44no—
358C4×D13#12114yes—
359C4×D13#12314yes—
360C4×D13#12414yes—
361C4×D13#12614yes—
362C8×C13—22no—
363C8×C13—22no—
364C8×C13—41no—
365C8×C13—41no—
366#1055—22no—
367#1055—22no—
368#1055—41no—
369#1055—41no—
370C24×C4—131no—
371C22×M16—131no—
372C22×M16—131no—
373C22×M16—131no—
374C22×M16—131no—
375C22×C22⋊C4—131no—
376C22×C22⋊C4—131no—
377C22×C42—131no—
378C22×C42—131no—
379#423—264no—
380C2×C4⋊C8—131no—
381C2×C4⋊C8—131no—
382C2×C4⋊C8—131no—
383C2×C4⋊C8C2×D1311yescharacteristic, complemented
384#407—264no—
385#407—264no—
386C2×C22⋊C8—131no—
387C2×C22⋊C8—131no—
388C2×C22⋊C8—131no—
389C2×C22⋊C8—131no—
390C2×C22⋊C8—131no—
391C2×C22⋊C8—131no—
392C2×C22⋊C8C2×D1311yescharacteristic
393C2×C22⋊C8C2×D1311yescharacteristic
394C4×M16—264no—
395C2×#97—131no—
396C2×#97—131no—
397C2×C4×C8—131no—
398C2×C4×C8C2×D1311yescharacteristic, complemented
399C4×C22⋊C4—131no—
400C4×C22⋊C4—131no—
401C4×C22⋊C4—131no—
402C4×C22⋊C4—131no—
403C4×C22⋊C4—131no—
404C4×C22⋊C4—131no—
405C4×C22⋊C4—131no—
406C4×C22⋊C4C2×D1311yescharacteristic
407C2×#95—131no—
408C2×#95—131no—
409#336—131no—
410#336—131no—
411#336—131no—
412#336—131no—
413#336—131no—
414#336—131no—
415#336C2×D1311yescharacteristic, complemented
416#336C2×D1311yescharacteristic, complemented
417C22×C13—22no—
418C22×C13—22no—
419C22×C13—22no—
420C22×C13—41no—
421C22×C13—41no—
422C22×C13—41no—
423C22×C13—41no—
424C22×C13C2×#11711yescharacteristic
425C22×C13C2×C4×D411yescharacteristic
426C22×C13C2×C4×D411yescharacteristic
427C22×C13C22×M1611yescharacteristic
428C22×C13C22×M1611yescharacteristic
429C22×C13#56811yescharacteristic
430C22×C13#56811yescharacteristic
431C2×D13—22no—
432C2×D13—22no—
433C2×D13—22no—
434C2×D13—22no—
435C2×D13—22no—
436C2×D13—22no—
437C2×D13—22no—
438C2×D13—22no—
439C2×D13—22no—
440C2×D13—416no—
441C2×D13—41no—
442C2×D13—41no—
443C2×D13—41no—
444C2×D13—41no—
445C2×D13#38814yes—
446C4×C13—22no—
447C4×C13—22no—
448C4×C13—22no—
449C4×C13—41no—
450C4×C13—41no—
451C4×C13C2×#12111yescharacteristic
452C4×C13C2×#12311yescharacteristic
453C4×C13C2×#12411yescharacteristic
454C4×C13C2×#12611yescharacteristic
455Dic13—22no—
456Dic13—41no—
457Dic13—41no—
458Dic13—41no—
459Dic13—41no—
460Dic13#38814yes—
461C25—131no—
462C23×C4—131no—
463C23×C4—131no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—131no—
471C23×C4—262no—
472C23×C4—262no—
473C23×C4—262no—
474C23×C4—262no—
475C23×C4—262no—
476C23×C4—262no—
477C23×C4C22×D1311yescharacteristic
478C2×M16—134no—
479C2×M16—134no—
480C2×M16—262no—
481C2×M16—262no—
482C2×M16—262no—
483C2×M16—262no—
484C2×M16—262no—
485C2×M16—262no—
486C2×M16—262no—
487C2×M16—262no—
488C2×M16—262no—
489C2×M16—262no—
490C22×C8—131no—
491C22×C8—131no—
492C22×C8—131no—
493C22×C8—131no—
494C22×C8C22×D1311yescharacteristic
495C22×C8C22×D1311yescharacteristic
496C22×C8C22×D1311yescharacteristic
497C22×C8C22×D1311yescharacteristic
498C2×C22⋊C4—131no—
499C2×C22⋊C4—131no—
500C2×C22⋊C4—131no—
501C2×C22⋊C4—131no—
502C2×C22⋊C4—131no—
503C2×C22⋊C4—131no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4C4×D1311yescharacteristic
507C2×C22⋊C4C4×D1311yescharacteristic
508C2×C42—131no—
509C2×C42—131no—
510C2×C42—131no—
511C2×C42—131no—
512C2×C42—131no—
513C2×C42—131no—
514C2×C42—262no—
515C2×C42—262no—
516C2×C42—262no—
517C2×C42—262no—
518C2×C42C22×D1311yescharacteristic
519C2×C42C22×D1311yescharacteristic
520C4⋊C8—22no—
521C4⋊C8—262no—
522C4⋊C8—262no—
523C4⋊C8—262no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—262no—
527C22⋊C8—262no—
528C22⋊C8—262no—
529C22⋊C8—262no—
530C22⋊C8—262no—
531C22⋊C8—262no—
532#97—262no—
533#97—262no—
534C4×C8—22no—
535C4×C8—262no—
536#95—131no—
537#95—131no—
538#95—131no—
539#95—131no—
540#95—131no—
541#95—131no—
542#95C4×D1311yescharacteristic
543#95C4×D1311yescharacteristic
544C2×C13—42no—
545C2×C13C2×#38811yescharacteristic
546C2×C13#292011yescharacteristic
547C2×C13#292111yescharacteristic
548C2×C13D4×M1611yescharacteristic
549C2×C13D4×M1611yescharacteristic
550C2×C13D4×M1611yescharacteristic
551C2×C13D4×M1611yescharacteristic
552D13—24no—
553D13—42no—
554C24—131no—
555C24—131no—
556C24—262no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—521no—
562C24—521no—
563C24C2×C4×D1311yescharacteristic
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—131no—
571C22×C4—132no—
572C22×C4—132no—
573C22×C4—132no—
574C22×C4—132no—
575C22×C4—132no—
576C22×C4—132no—
577C22×C4—131no—
578C22×C4—131no—
579C22×C4—131no—
580C22×C4—131no—
581C22×C4—131no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—521no—
606C22×C4—521no—
607C22×C4—521no—
608C22×C4—521no—
609C22×C4—524no—
610C22×C4—524no—
611C22×C4—524no—
612C22×C4—524no—
613C22×C4C2×C4×D1311yescharacteristic
614C22×C4C2×C4×D1311yescharacteristic
615C22×C4C2×C4×D1311yescharacteristic
616C22×C4C2×C4×D1311yescharacteristic
617C22×C4C2×C4×D1311yescharacteristic
618C22×C4C23×D1311yescharacteristic
619M16—268no—
620M16—268no—
621M16—524no—
622M16—524no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—132no—
634C2×C8—132no—
635C2×C8—261no—
636C2×C8—261no—
637C2×C8—261no—
638C2×C8—261no—
639C2×C8—261no—
640C2×C8—261no—
641C2×C8—261no—
642C2×C8—261no—
643C2×C8—261no—
644C2×C8—261no—
645C2×C8D4×D1312yes—
646C2×C8D4×D1312yes—
647C22⋊C4—22no—
648C22⋊C4—134no—
649C22⋊C4—262no—
650C22⋊C4—262no—
651C22⋊C4—262no—
652C22⋊C4—262no—
653C22⋊C4—262no—
654C22⋊C4#609414yescomplemented
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—262no—
660C42—262no—
661C42—262no—
662C42—262no—
663C42—261no—
664C42—261no—
665C42—261no—
666C42—261no—
667C13#2104911yescharacteristic, complemented, Sylow
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—132no—
675C23—132no—
676C23—132no—
677C23—132no—
678C23—268no—
679C23—261no—
680C23—261no—
681C23—261no—
682C23—261no—
683C23—261no—
684C23—261no—
685C23—261no—
686C23—261no—
687C23—261no—
688C23—261no—
689C23—524no—
690C23—524no—
691C23—524no—
692C23—524no—
693C23—524no—
694C23—524no—
695C23C2×#609412yes—
696C23C22×C4×D1311yescharacteristic
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—132no—
714C2×C4—132no—
715C2×C4—132no—
716C2×C4—134no—
717C2×C4—134no—
718C2×C4—134no—
719C2×C4—134no—
720C2×C4—132no—
721C2×C4—261no—
722C2×C4—261no—
723C2×C4—261no—
724C2×C4—261no—
725C2×C4—261no—
726C2×C4—261no—
727C2×C4—261no—
728C2×C4—261no—
729C2×C4—261no—
730C2×C4—261no—
731C2×C4—261no—
732C2×C4—261no—
733C2×C4—261no—
734C2×C4—261no—
735C2×C4—524no—
736C2×C4—524no—
737C2×C4—524no—
738C2×C4—524no—
739C2×C4—524no—
740C2×C4—524no—
741C2×C4—524no—
742C2×C4—521no—
743C2×C4—521no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4C2×#609412yes—
747C2×C4C2×#609412yes—
748C2×C4M16×D1312yes—
749C2×C4C2×D4×D1311yescharacteristic
750C2×C4C2×D4×D1311yescharacteristic
751C2×C4#41×D1311yescharacteristic
752C2×C4#41×D1311yescharacteristic
753C2×C4#41×D1311yescharacteristic
754C2×C4#41×D1311yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C8—262no—
760C8—262no—
761C8—521no—
762C8—521no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—134no—
771C22—262no—
772C22—262no—
773C22—262no—
774C22—262no—
775C22—262no—
776C22—262no—
777C22—262no—
778C22—262no—
779C22—262no—
780C22—5216no—
781C22—521no—
782C22—521no—
783C22—521no—
784C22—521no—
785C22D13×#11711yescharacteristic
786C22C4×D4×D1311yescharacteristic
787C22C4×D4×D1311yescharacteristic
788C22C22×#609411yescharacteristic
789C22C2×M16×D1311yescharacteristic
790C22#1171945511yescharacteristic
791C22#1171945511yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—134no—
798C4—262no—
799C4—521no—
800C4—521no—
801C4—521no—
802C4—521no—
803C4D13×#12111yescharacteristic
804C4D13×#12311yescharacteristic
805C4D13×#12411yescharacteristic
806C4D13×#12611yescharacteristic
807C2—42no—
808C2—264no—
809C2—522no—
810C2D13×#38811yescharacteristic
811C2#1312346411yescharacteristic
812C2#1312347011yescharacteristic
813C2D4×#609411yescharacteristic
814C2D4×#609411yescharacteristic
815C2#1312356911yescharacteristic
816C2#1312357211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1923C2
prime radicalC24×D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1923D13
hypocenterC13#21049
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#11718498C2semidirect
4. C2×C4×#6094C2semidirect
6. #13115452C2semidirect
7. #13115450C2semidirect
8. #13115448C2semidirect
9. #13115446C2semidirect
10. #13115444C2semidirect
11. #13115442C2semidirect
12. #13115440C2semidirect
13. #13114528C2semidirect
14. #13114528C2semidirect
15. C13×#1923C2semidirect
25. C2×C13×C4⋊C8C22semidirect
28. C2×C4×C8×C13C22semidirect
37. C2×#88055C22semidirect
38. C2×#88055C22semidirect
39. C2×#88054C22semidirect
40. C2×#88054C22semidirect
45. C2×C4⋊#1055C22semidirect
46. C2×C4×#1055C22semidirect
55. C13×#336C22semidirect
56. C13×#336C22semidirect
57. #11718142C22semidirect
58. #11718142C22semidirect
59. #11718142C22semidirect
60. #11718142C22semidirect
61. #11718116C22semidirect
62. #11718116C22semidirect
225. C13×C22⋊C4M16semidirect
235. #6103M16semidirect
272. #1923D13semidirect
383. C2×C4⋊C8C2×D13semidirect
398. C2×C4×C8C2×D13semidirect
415. #336C2×D13semidirect
416. #336C2×D13semidirect
654. C22⋊C4#6094semidirect
667. C13#21049semidirect

Maximal subgroups

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

subgroupindex
C2×#117184982
C2×#117183872
C2×C4×#60942
C4×C22⋊C4×D132
#131154522
#131154502
#131154482
#131154462
#131154442
#131154422
#131154402
#131145282
C13×#19232
#2104913