Finite Group Databasebeta

← #15786316

Subgroups — #15786316

Order 3328.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D52C211yesmaximal, characteristic
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718600C211yesmaximal, characteristic
4C2×#11718589C211yesmaximal, characteristic, complemented
5C2×#11718650C212yesmaximal, complemented
6#13113080C212yesmaximal, complemented
7#13113078C212yesmaximal, complemented
8#13113066C211yesmaximal, characteristic, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113057C212yesmaximal, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C23×C4×D13C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×#6103C2212yes—
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2212yes—
28C2×C4×D52—24no—
29C2×C4×D52—24no—
30C2×C4×D52—24no—
31C4×C13×C4⋊C4—24no—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39#11718650—28no—
40#11718600—24no—
41#11718600C418yescomplemented
42#11718589—24no—
43C24×D13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2312yes—
53C23×Dic13C2312yes—
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52—22no—
58C22×D52C2×C414yes—
59C22×D52D414yes—
60C22×D52Q814yes—
61C22×C4×D13—24no—
62C22×C4×D13—24no—
63C22×C4×D13—24no—
64C22×C4×D13—24no—
65C22×C4×D13—24no—
66C22×C4×D13—42no—
67C22×C4×D13—42no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4D414yescomplemented
74C2×C42×C13—22no—
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13C2×C414yescomplemented
82C2×C42×C13D414yes—
83C2×#6103—24no—
84C2×#6103—24no—
85C2×#6103—24no—
86C2×#6103—24no—
87C2×#6103—24no—
88C2×#6103—24no—
89C2×#6103—24no—
90C2×#6103—24no—
91C2×#6103—24no—
92C2×#6103—42no—
93C2×#6103—42no—
94C2×#6103—42no—
95C2×#6103—42no—
96C2×#6103C2×C418yescomplemented
97C2×#6103C2×C418yescomplemented
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—22no—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13C2×C414yescomplemented
106C2×C4⋊Dic13D414yes—
107C2×#6101—24no—
108C2×#6101—24no—
109C2×#6101—42no—
110C4×D52—232no—
111C13×#95—22no—
112C13×#95—22no—
113#88071—24no—
114#88071—24no—
115#88071—24no—
116#88071—42no—
117#88071—42no—
118#14018—131nomaximal, Sylow
119C24×C13C2411yescharacteristic
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—22no—
128C23×D13—22no—
129C23×D13—22no—
130C23×D13—22no—
131C23×D13—22no—
132C23×D13C22×C414yes—
133C23×D13C2×D414yes—
134C23×D13C2×Q814yes—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
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×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13C22×C412yes—
168C22×C4×C13C22×C412yes—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2×D412yes—
178C22×C4×C13C2×Q812yes—
179C22×C4×C13#4112yes—
180C22×C4×C13#4112yes—
181C22×C4×C13#4112yes—
182C22×C4×C13#4112yes—
183C22×C4×C13#4112yes—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13C22×C414yes—
204C22×Dic13C2×D414yes—
205C2×D52—28no—
206C2×D52—28no—
207C2×D52—28no—
208C2×D52—28no—
209C2×D52—28no—
210C2×D52—28no—
211C2×D52C4⋊C4116yescomplemented
212C2×C4×D13—216no—
213C2×C4×D13—48no—
214C2×C4×D13—48no—
215C2×C4×D13—48no—
216C2×C4×D13—48no—
217C2×C4×D13—48no—
218C2×C4×D13—48no—
219C13×C4⋊C4—28no—
220C13×C4⋊C4—28no—
221C42×C13—28no—
222C42×C13—28no—
223C42×C13—44no—
224#6103—216no—
225#6103—216no—
226#6103—48no—
227#6103—48no—
228#6103—48no—
229C4⋊Dic13—28no—
230C4⋊Dic13—28no—
231C4⋊Dic13—44no—
232#6101—48no—
233C22×C4×D4—131no—
234C2×#390—131no—
235C2×#390—131no—
236C2×#389—131no—
237C2×#385—132no—
238C2×C4×C4⋊C4D1311yescharacteristic, complemented
239#1439—132no—
240#1439—132no—
241C4⋊#95—131no—
242C4⋊#95—131no—
243C22⋊#95—132no—
244C23×C13C23×C411yescharacteristic
245C23×C13C22×D411yescharacteristic
246C23×C13C22×D411yescharacteristic
247C23×C13C22×D411yescharacteristic
248C23×C13C22×D411yescharacteristic
249C23×C13C22×Q811yescharacteristic
250C23×C13C2×#4111yescharacteristic
251C23×C13C2×#4111yescharacteristic
252C23×C13C2×#4111yescharacteristic
253C23×C13C2×#4111yescharacteristic
254C23×C13C2×#4111yescharacteristic
255C23×C13H(5,𝔽2)11yescharacteristic
256C23×C13H(5,𝔽2)11yescharacteristic
257C23×C13H(5,𝔽2)11yescharacteristic
258C23×C132−1+411yescharacteristic
259C22×D13—24no—
260C22×D13—24no—
261C22×D13—24no—
262C22×D13—24no—
263C22×D13—24no—
264C22×D13—24no—
265C22×D13—24no—
266C22×D13—24no—
267C22×D13—24no—
268C22×D13—24no—
269C22×D13—24no—
270C22×D13—24no—
271C22×D13—24no—
272C22×D13—24no—
273C22×D13—24no—
274C22×D13—24no—
275C22×D13—24no—
276C22×D13—24no—
277C22×D13—42no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
281C22×D13—42no—
282C22×D13—42no—
283C22×D13—42no—
284C22×D13—42no—
285C22×D13—42no—
286C22×D13—42no—
287C22×D13—42no—
288C22×D13—42no—
289C22×D13—42no—
290C22×D13—42no—
291C22×D13—42no—
292C22×D13—42no—
293C22×D13C2×C4⋊C418yes—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13C2×C4⋊C414yes—
335C2×C4×C13C4×D414yes—
336C2×C4×C13C4×D414yes—
337C2×C4×C13C4×D414yescomplemented
338C2×C4×C13#12014yes—
339C2×C4×C13#12114yes—
340C2×C4×C13C22⋊Q814yes—
341C2×C4×C13C22⋊Q814yes—
342C2×C4×C13#12314yes—
343C2×Dic13—24no—
344C2×Dic13—24no—
345C2×Dic13—24no—
346C2×Dic13—24no—
347C2×Dic13—24no—
348C2×Dic13—24no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—42no—
363C2×Dic13—42no—
364D52—232no—
365C4×D13—432no—
366C23×D4—131no—
367C24×C4—132no—
368C2×C4×D4—264no—
369C2×C4×D4—264no—
370C2×C4×D4—264no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4—132no—
375C22×C4⋊C4C2×D1311yescharacteristic
376C22×C4⋊C4C2×D1311yescharacteristic
377C22×C22⋊C4—132no—
378C22×C22⋊C4—132no—
379C22×C22⋊C4—132no—
380C22×C22⋊C4—132no—
381C22×C22⋊C4—132no—
382C22×C42C2×D1311yescharacteristic
383C22×C42C2×D1311yescharacteristic
384C22×C42C2×D1311yescharacteristic
385#390—138no—
386#390—264no—
387#389—264no—
388#385—268no—
389C4×C4⋊C4—24no—
390C2×#95—132no—
391C2×#95—132no—
392C2×#95—132no—
393C2×#95—132no—
394C2×#95—132no—
395C2×#95C2×D1311yescharacteristic
396C2×#95C2×D1311yescharacteristic
397C22×C13C22×C4⋊C411yescharacteristic
398C22×C13C2×C4×D411yescharacteristic
399C22×C13C2×C4×D411yescharacteristic
400C22×C13C2×C4×D411yescharacteristic
401C22×C13C4×#4111yescharacteristic
402C22×C13#51811yescharacteristic
403C22×C13#52011yescharacteristic
404C22×C13C2×#12011yescharacteristic
405C22×C13C2×#12111yescharacteristic
406C22×C13C2×C22⋊Q811yescharacteristic
407C22×C13C2×C22⋊Q811yescharacteristic
408C22×C13C2×#12311yescharacteristic
409C22×C13#52511yescharacteristic
410C22×C13#52911yescharacteristic
411C22×C13#53211yescharacteristic
412C22×C13#53511yescharacteristic
413C22×C13#53711yescharacteristic
414C22×C13#54011yescharacteristic
415C22×C13#54211yescharacteristic
416C22×C13D4211yescharacteristic
417C22×C13D4211yescharacteristic
418C22×C13#54611yescharacteristic
419C22×C13#54611yescharacteristic
420C22×C13#54611yescharacteristic
421C22×C13#54711yescharacteristic
422C22×C13#54811yescharacteristic
423C22×C13D4×Q811yescharacteristic
424C22×C13#55011yescharacteristic
425C22×C13#55011yescharacteristic
426C22×C13#55411yescharacteristic
427C22×C13#55411yescharacteristic
428C22×C13#55411yescharacteristic
429C22×C13#55611yescharacteristic
430C22×C13#55911yescharacteristic
431C22×C13#55911yescharacteristic
432C2×D13—28no—
433C2×D13—28no—
434C2×D13—28no—
435C2×D13—44no—
436C2×D13—44no—
437C2×D13—44no—
438C2×D13—44no—
439C2×D13—44no—
440C2×D13—44no—
441C2×D13—44no—
442C2×D13—44no—
443C2×D13—44no—
444C2×D13—44no—
445C2×D13—44no—
446C2×D13—44no—
447C4×C13—24no—
448C4×C13—24no—
449C4×C13—42no—
450C4×C13—42no—
451C4×C13—42no—
452C4×C13—42no—
453C4×C13#38518yescomplemented
454Dic13—44no—
455Dic13—44no—
456Dic13—82no—
457C25—132no—
458C22×D4—134no—
459C22×D4—134no—
460C22×D4—134no—
461C22×D4—262no—
462C22×D4—262no—
463C22×D4—262no—
464C22×D4—262no—
465C23×C4—132no—
466C23×C4—132no—
467C23×C4—132no—
468C23×C4—264no—
469C23×C4—264no—
470C23×C4—264no—
471C23×C4—264no—
472C23×C4—264no—
473C23×C4—522no—
474C23×C4—522no—
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1311yescharacteristic
482C4×D4—2632no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—134no—
489C2×C4⋊C4—134no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4—264no—
496C2×C4⋊C4—262no—
497C2×C4⋊C4—262no—
498C2×C4⋊C4—262no—
499C2×C4⋊C4—522no—
500C2×C4⋊C4D5214yescomplemented
501C2×C22⋊C4—138no—
502C2×C22⋊C4—138no—
503C2×C22⋊C4—264no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—264no—
508C2×C22⋊C4—264no—
509C2×C22⋊C4—264no—
510C2×C22⋊C4—264no—
511C2×C22⋊C4—264no—
512C2×C22⋊C4—522no—
513C2×C22⋊C4—522no—
514C2×C22⋊C4—522no—
515C2×C22⋊C4—522no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42C4×D1314yescomplemented
524C2×C42C22⋊D1314yes—
525#95—22no—
526#95—22no—
527#95—264no—
528#95—264no—
529#95—264no—
530#95—522no—
531#95—522no—
532C2×C13C2×#38511yescharacteristic
533C2×C13C4×#12111yescharacteristic
534C2×C13#232411yescharacteristic
535C2×C13D4×C4⋊C411yescharacteristic
536C2×C13#234911yescharacteristic
537C2×C13#236611yescharacteristic
538C2×C13#236711yescharacteristic
539C2×C13#240711yescharacteristic
540C2×C13#240811yescharacteristic
541C2×C13#244511yescharacteristic
542C2×C13#244711yescharacteristic
543C2×C13#245211yescharacteristic
544C2×C13#245411yescharacteristic
545C2×C13#253811yescharacteristic
546C2×C13#258011yescharacteristic
547D13—48no—
548C24—134no—
549C24—134no—
550C24—134no—
551C24—262no—
552C24—262no—
553C24—262no—
554C24—262no—
555C24—262no—
556C24—262no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24C23×D1311yescharacteristic
564C2×D4—1316no—
565C2×D4—268no—
566C2×D4—268no—
567C2×D4—268no—
568C2×D4—268no—
569C2×D4—268no—
570C2×D4—268no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—134no—
604C22×C4—134no—
605C22×C4—2616no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—528no—
626C22×C4—528no—
627C22×C4—528no—
628C22×C4—528no—
629C22×C4—528no—
630C22×C4—528no—
631C22×C4C2×C4×D1312yes—
632C22×C4C2×C4×D1312yes—
633C22×C4C2×C4×D1312yes—
634C22×C4C2×D5212yes—
635C22×C4C2×D5212yes—
636C22×C4C2×D5212yes—
637C22×C4#612712yes—
638C22×C4#612712yes—
639C22×C4#612712yes—
640C22×C4#612712yes—
641C22×C4D4×D1312yes—
642C22×C4D4×D1312yes—
643C22×C4Q8×D1312yes—
644C22×C4#613112yes—
645C22×C4C2×C22⋊D1312yes—
646C22×C4C2×C22⋊D1312yes—
647C22×C4C2×C22⋊D1312yes—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—268no—
651C4⋊C4—268no—
652C4⋊C4—528no—
653C4⋊C4—524no—
654C22⋊C4—2616no—
655C22⋊C4—2616no—
656C22⋊C4—528no—
657C22⋊C4—528no—
658C22⋊C4—528no—
659C42—28no—
660C42—28no—
661C42—44no—
662C13#1401811yescharacteristic, complemented, Sylow
663C23—138no—
664C23—264no—
665C23—264no—
666C23—264no—
667C23—264no—
668C23—264no—
669C23—264no—
670C23—264no—
671C23—264no—
672C23—264no—
673C23—264no—
674C23—264no—
675C23—264no—
676C23—264no—
677C23—264no—
678C23—264no—
679C23—264no—
680C23—264no—
681C23—264no—
682C23—522no—
683C23—522no—
684C23—522no—
685C23—522no—
686C23—522no—
687C23—522no—
688C23—522no—
689C23—522no—
690C23—522no—
691C23—522no—
692C23—522no—
693C23—522no—
694C23—522no—
695C23—522no—
696C23—522no—
697C23—522no—
698C23C22×C4×D1311yescharacteristic
699C23C22×D5211yescharacteristic
700C23C2×#612711yescharacteristic
701C23C2×#612711yescharacteristic
702C23C2×#612711yescharacteristic
703C23C2×#612711yescharacteristic
704C23C2×D4×D1311yescharacteristic
705C23C2×D4×D1311yescharacteristic
706C23C2×Q8×D1311yescharacteristic
707C23C2×#613111yescharacteristic
708C23#8825611yescharacteristic
709C23#8825611yescharacteristic
710C23#8825611yescharacteristic
711C23#8825711yescharacteristic
712C23C22×C22⋊D1311yescharacteristic
713D4—2632no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—264no—
755C2×C4—264no—
756C2×C4—264no—
757C2×C4—264no—
758C2×C4—264no—
759C2×C4—264no—
760C2×C4—5232no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4—522no—
770C2×C4—522no—
771C2×C4—522no—
772C2×C4—522no—
773C2×C4—522no—
774C2×C4—522no—
775C2×C4—522no—
776C2×C4C4×D5214yescomplemented
777C2×C4C4⋊C4×D1314yes—
778C2×C4#8814714yes—
779C2×C4#8814814yes—
780C2×C4#8815014yes—
781C2×C4C4×C22⋊D1314yes—
782C2×C4#8818414yes—
783C2×C4#8819114yes—
784C2×C4#8820014yes—
785C22—268no—
786C22—268no—
787C22—268no—
788C22—524no—
789C22—524no—
790C22—524no—
791C22—524no—
792C22—524no—
793C22—524no—
794C22—524no—
795C22—524no—
796C22—524no—
797C22—524no—
798C22—524no—
799C22—524no—
800C22C2×C4×D5211yescharacteristic
801C22C4×#612711yescharacteristic
802C22#1171918211yescharacteristic
803C22#1171918411yescharacteristic
804C22C2×C4⋊C4×D1311yescharacteristic
805C22C2×#8814711yescharacteristic
806C22C2×#8814811yescharacteristic
807C22C2×#8815011yescharacteristic
808C22#1171922611yescharacteristic
809C22#1171922811yescharacteristic
810C22#1171923911yescharacteristic
811C22#1171924011yescharacteristic
812C22D4×D5211yescharacteristic
813C22D4×D5211yescharacteristic
814C22#1171925511yescharacteristic
815C22#1171925511yescharacteristic
816C22#1171925511yescharacteristic
817C22#1171925611yescharacteristic
818C22#1171925711yescharacteristic
819C22#1171925811yescharacteristic
820C22Q8×D5211yescharacteristic
821C22#1171928211yescharacteristic
822C22#1171928411yescharacteristic
823C22#1171928411yescharacteristic
824C22#1171928411yescharacteristic
825C22#1171928911yescharacteristic
826C22#1171929011yescharacteristic
827C22#1171929011yescharacteristic
828C22C2×C4×C22⋊D1311yescharacteristic
829C22C2×#8818411yescharacteristic
830C22#1171949611yescharacteristic
831C22C2×#8819111yescharacteristic
832C22C2×#8820011yescharacteristic
833C22#1171953511yescharacteristic
834C22#1171953811yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—524no—
842C4—524no—
843C4—1042no—
844C4#1171865018yescomplemented
845C2—528no—
846C2C2×#1171865011yescharacteristic
847C2C4×#8818411yescharacteristic
848C2#1311752911yescharacteristic
849C2C4⋊C4×D5211yescharacteristic
850C2#1311774711yescharacteristic
851C2#1311790011yescharacteristic
852C2#1311790511yescharacteristic
853C2#1311818111yescharacteristic
854C2#1311819211yescharacteristic
855C2#1311860111yescharacteristic
856C2#1311862311yescharacteristic
857C2#1311868611yescharacteristic
858C2#1311870811yescharacteristic
859C2#1311975411yescharacteristic
860C2#1312019411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#14018
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#11718589C2semidirect
5. C2×#11718650C2semidirect
6. #13113080C2semidirect
7. #13113078C2semidirect
8. #13113066C2semidirect
9. #13113066C2semidirect
10. #13113057C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
41. #11718600C4semidirect
73. C2×C13×C4⋊C4D4semidirect
81. C2×C42×C13C2×C4semidirect
96. C2×#6103C2×C4semidirect
97. C2×#6103C2×C4semidirect
105. C2×C4⋊Dic13C2×C4semidirect
211. C2×D52C4⋊C4semidirect
238. C2×C4×C4⋊C4D13semidirect
337. C2×C4×C13C4×D4semidirect
453. C4×C13#385semidirect
500. C2×C4⋊C4D52semidirect
523. C2×C42C4×D13semidirect
662. C13#14018semidirect
776. C2×C4C4×D52semidirect
844. C4#11718650semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D522
C2×#117186002
C2×#117185892
C2×#117186502
#131130802
#131130782
#131130662
#131130572
C2×C4×C13×C4⋊C42
#1401813