Finite Group Databasebeta

← C113×#13912 #43281932

Subgroups — C113×#13912 #43281932

Order 28928.

2314 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C113C211yesmaximal, characteristic
2C2×#388×C113C212yesmaximal, complemented
3C2×#381×C113C211yesmaximal, characteristic, complemented
4C2×#380×C113C211yesmaximal, characteristic, complemented
5C113×#1441C212yesmaximal, complemented
6C113×#1438C212yesmaximal
7C113×#1437C212yesmaximal, complemented
8C113×#1434C211yesmaximal, characteristic, complemented
9C113×C22⋊#95C211yesmaximal, characteristic, complemented
10C113×C22⋊#95C211yesmaximal, characteristic, complemented
11C4×#95×C113C211yesmaximal, characteristic, complemented
12C23×D4×C113C2211yescharacteristic
13C24×C4×C113C2211yescharacteristic
14C24×C4×C113C2211yescharacteristic
15C2×C4×D4×C113—28no—
16C2×C4×D4×C113C418yescomplemented
17C22×C4⋊C4×C113C2212yes—
18C22×C4⋊C4×C113C2211yescharacteristic
19C22×C22⋊C4×C113C2212yes—
20C22×C22⋊C4×C113C2212yes—
21C22×C22⋊C4×C113C2212yes—
22C22×C22⋊C4×C113C2212yes—
23C22×C22⋊C4×C113C2211yescharacteristic
24C22×C22⋊C4×C113C2211yescharacteristic
25C22×C42×C113C2212yes—
26C22×C42×C113C2211yescharacteristic
27#388×C113—28no—
28#381×C113—24no—
29#380×C113—24no—
30C2×#95×C113C2211yescharacteristic
31C2×#95×C113C2211yescharacteristic
32C2×#95×C113C2212yes—
33C2×#95×C113C2212yes—
34C2×#95×C113C2212yes—
35C2×#95×C113C2211yescharacteristic
36C2×#95×C113C2212yes—
37C2×#95×C113C2212yes—
38C2×#95×C113C2212yes—
39C2×#95×C113C2211yescharacteristic
40C25×C113C2311yescharacteristic
41C25×C113C2311yescharacteristic
42C22×D4×C113—24no—
43C22×D4×C113—22no—
44C22×D4×C113—22no—
45C22×D4×C113—24no—
46C22×D4×C113C2×C414yes—
47C23×C4×C113—24no—
48C23×C4×C113—24no—
49C23×C4×C113—22no—
50C23×C4×C113—22no—
51C23×C4×C113—22no—
52C23×C4×C113—22no—
53C23×C4×C113—42no—
54C23×C4×C113—42no—
55C23×C4×C113C2×C414yes—
56C23×C4×C113C2×C414yes—
57C23×C4×C113C2312yes—
58C23×C4×C113C2312yes—
59C23×C4×C113C2311yescharacteristic
60C23×C4×C113C2312yes—
61C23×C4×C113C2312yes—
62C23×C4×C113C2311yescharacteristic
63C23×C4×C113C2311yescharacteristic
64C23×C4×C113C2311yescharacteristic
65C23×C4×C113C2311yescharacteristic
66C4×D4×C113—232no—
67C2×C4⋊C4×C113—24no—
68C2×C4⋊C4×C113—24no—
69C2×C4⋊C4×C113—24no—
70C2×C4⋊C4×C113—42no—
71C2×C4⋊C4×C113C2×C414yes—
72C2×C22⋊C4×C113—24no—
73C2×C22⋊C4×C113—24no—
74C2×C22⋊C4×C113—24no—
75C2×C22⋊C4×C113—24no—
76C2×C22⋊C4×C113—24no—
77C2×C22⋊C4×C113—24no—
78C2×C22⋊C4×C113—24no—
79C2×C22⋊C4×C113—24no—
80C2×C22⋊C4×C113—24no—
81C2×C22⋊C4×C113—42no—
82C2×C22⋊C4×C113—42no—
83C2×C22⋊C4×C113—42no—
84C2×C22⋊C4×C113—42no—
85C2×C22⋊C4×C113C2×C414yes—
86C2×C22⋊C4×C113C2×C414yes—
87C2×C22⋊C4×C113D418yes—
88C2×C42×C113—24no—
89C2×C42×C113—24no—
90C2×C42×C113—24no—
91C2×C42×C113—42no—
92C2×C42×C113C2×C414yes—
93#95×C113—22no—
94#95×C113—24no—
95#95×C113—22no—
96#95×C113—24no—
97#95×C113—24no—
98#95×C113—24no—
99#95×C113—22no—
100#95×C113—24no—
101#95×C113—42no—
102#95×C113D414yescomplemented
103C24×C113—21no—
104C24×C113—21no—
105C24×C113—22no—
106C24×C113—22no—
107C24×C113—22no—
108C24×C113—21no—
109C24×C113—21no—
110C24×C113—22no—
111C24×C113—21no—
112C24×C113—21no—
113C24×C113—22no—
114C24×C113—21no—
115C24×C113—21no—
116C24×C113—22no—
117C24×C113—22no—
118C24×C113—21no—
119C24×C113—21no—
120C24×C113C22×C412yes—
121C24×C113C22×C412yes—
122C24×C113C2×D414yes—
123C24×C113#4112yes—
124C24×C113#4112yes—
125C24×C113C2411yescharacteristic
126C2×D4×C113—216no—
127C2×D4×C113—216no—
128C2×D4×C113—28no—
129C2×D4×C113—28no—
130C2×D4×C113—28no—
131C22×C4×C113—22no—
132C22×C4×C113—22no—
133C22×C4×C113—21no—
134C22×C4×C113—22no—
135C22×C4×C113—21no—
136C22×C4×C113—21no—
137C22×C4×C113—21no—
138C22×C4×C113—21no—
139C22×C4×C113—22no—
140C22×C4×C113—22no—
141C22×C4×C113—21no—
142C22×C4×C113—28no—
143C22×C4×C113—21no—
144C22×C4×C113—22no—
145C22×C4×C113—22no—
146C22×C4×C113—22no—
147C22×C4×C113—22no—
148C22×C4×C113—22no—
149C22×C4×C113—22no—
150C22×C4×C113—22no—
151C22×C4×C113—22no—
152C22×C4×C113—22no—
153C22×C4×C113—21no—
154C22×C4×C113—22no—
155C22×C4×C113—22no—
156C22×C4×C113—22no—
157C22×C4×C113—22no—
158C22×C4×C113—22no—
159C22×C4×C113—28no—
160C22×C4×C113—28no—
161C22×C4×C113—28no—
162C22×C4×C113—22no—
163C22×C4×C113—22no—
164C22×C4×C113—22no—
165C22×C4×C113—22no—
166C22×C4×C113—22no—
167C22×C4×C113—22no—
168C22×C4×C113—22no—
169C22×C4×C113—22no—
170C22×C4×C113—22no—
171C22×C4×C113—22no—
172C22×C4×C113—22no—
173C22×C4×C113—22no—
174C22×C4×C113—22no—
175C22×C4×C113—22no—
176C22×C4×C113—44no—
177C22×C4×C113—44no—
178C22×C4×C113—48no—
179C22×C4×C113—48no—
180C22×C4×C113—48no—
181C22×C4×C113—48no—
182C22×C4×C113C22×C412yes—
183C22×C4×C113C22×C412yes—
184C22×C4×C113C22×C412yes—
185C22×C4×C113C22×C412yes—
186C22×C4×C113C22×C412yes—
187C22×C4×C113C2×D414yes—
188C22×C4×C113C2×D414yes—
189C22×C4×C113C2×D414yes—
190C22×C4×C113C2×D412yes—
191C22×C4×C113#4114yes—
192C22×C4×C113#4114yes—
193C22×C4×C113#4112yes—
194C4⋊C4×C113—28no—
195C4⋊C4×C113—48no—
196C22⋊C4×C113—28no—
197C22⋊C4×C113—48no—
198C22⋊C4×C113—48no—
199C22⋊C4×C113—48no—
200C22⋊C4×C113—48no—
201C22⋊C4×C113C22⋊C4116yescomplemented
202C42×C113—28no—
203C42×C113—48no—
204C23×C113—22no—
205C23×C113—22no—
206C23×C113—22no—
207C23×C113—22no—
208C23×C113—22no—
209C23×C113—22no—
210C23×C113—22no—
211C23×C113—22no—
212C23×C113—22no—
213C23×C113—22no—
214C23×C113—22no—
215C23×C113—22no—
216C23×C113—24no—
217C23×C113—24no—
218C23×C113—24no—
219C23×C113—24no—
220C23×C113—24no—
221C23×C113—22no—
222C23×C113—24no—
223C23×C113—24no—
224C23×C113—24no—
225C23×C113—22no—
226C23×C113—24no—
227C23×C113—22no—
228C23×C113—22no—
229C23×C113—24no—
230C23×C113—42no—
231C23×C113—42no—
232C23×C113—42no—
233C23×C113—42no—
234C23×C113—42no—
235C23×C113—42no—
236C23×C113—42no—
237C23×C113—42no—
238C23×C113—42no—
239C23×C113—42no—
240C23×C113—42no—
241C23×C113—41no—
242C23×C113—42no—
243C23×C113—41no—
244C23×C113—42no—
245C23×C113—41no—
246C23×C113—41no—
247C23×C113—42no—
248C23×C113C2×C22⋊C414yes—
249C23×C113#11714yes—
250C23×C113C23×C411yescharacteristic
251C23×C113C22×D412yes—
252C23×C113C22×D411yescharacteristic
253C23×C113C2×#4112yes—
254C23×C113C2×#4111yescharacteristic
255C23×C113C2×#4111yescharacteristic
256C23×C113C2×#4111yescharacteristic
257C23×C113C2×#4112yes—
258C23×C113H(5,𝔽2)12yes—
259C23×C113H(5,𝔽2)11yescharacteristic
260C23×C1132−1+411yescharacteristic
261D4×C113—232no—
262C2×C4×C113—22no—
263C2×C4×C113—22no—
264C2×C4×C113—22no—
265C2×C4×C113—22no—
266C2×C4×C113—22no—
267C2×C4×C113—22no—
268C2×C4×C113—22no—
269C2×C4×C113—22no—
270C2×C4×C113—24no—
271C2×C4×C113—24no—
272C2×C4×C113—24no—
273C2×C4×C113—24no—
274C2×C4×C113—24no—
275C2×C4×C113—24no—
276C2×C4×C113—24no—
277C2×C4×C113—24no—
278C2×C4×C113—22no—
279C2×C4×C113—22no—
280C2×C4×C113—22no—
281C2×C4×C113—24no—
282C2×C4×C113—24no—
283C2×C4×C113—24no—
284C2×C4×C113—24no—
285C2×C4×C113—24no—
286C2×C4×C113—24no—
287C2×C4×C113—416no—
288C2×C4×C113—416no—
289C2×C4×C113—42no—
290C2×C4×C113—42no—
291C2×C4×C113—42no—
292C2×C4×C113—42no—
293C2×C4×C113—42no—
294C2×C4×C113—42no—
295C2×C4×C113—42no—
296C2×C4×C113—42no—
297C2×C4×C113—42no—
298C2×C4×C113—42no—
299C2×C4×C113—42no—
300C2×C4×C113—42no—
301C2×C4×C113—42no—
302C2×C4×C113—42no—
303C2×C4×C113—42no—
304C2×C4×C113—42no—
305C2×C4×C113—42no—
306C2×C4×C113—42no—
307C2×C4×C113—42no—
308C2×C4×C113—42no—
309C2×C4×C113—42no—
310C2×C4×C113—42no—
311C2×C4×C113—42no—
312C2×C4×C113—42no—
313C2×C4×C113C2×C22⋊C414yes—
314C2×C4×C113C2×C22⋊C414yes—
315C2×C4×C113#11714yes—
316C2×C4×C113C4×D414yes—
317C22×C113—24no—
318C22×C113—24no—
319C22×C113—24no—
320C22×C113—24no—
321C22×C113—24no—
322C22×C113—24no—
323C22×C113—42no—
324C22×C113—42no—
325C22×C113—42no—
326C22×C113—42no—
327C22×C113—42no—
328C22×C113—42no—
329C22×C113—44no—
330C22×C113—44no—
331C22×C113—44no—
332C22×C113—44no—
333C22×C113—44no—
334C22×C113—44no—
335C22×C113—44no—
336C22×C113—44no—
337C22×C113—42no—
338C22×C113—42no—
339C22×C113C22×C22⋊C411yescharacteristic
340C22×C113C2×#11711yescharacteristic
341C22×C113C2×#11711yescharacteristic
342C22×C113C2×C4×D411yescharacteristic
343C22×C113C4×#4111yescharacteristic
344C22×C113#51811yescharacteristic
345C22×C113#52011yescharacteristic
346C22×C113#52512yes—
347C22×C113#52512yes—
348C22×C113#52912yes—
349C22×C113#53212yes—
350C22×C113#54012yes—
351C22×C113#54212yes—
352C22×C113D4212yes—
353C22×C113#54612yes—
354C22×C113#54612yes—
355C22×C113#54611yescharacteristic
356C22×C113#54712yes—
357C22×C113#54811yescharacteristic
358C22×C113#55112yes—
359C22×C113#55211yescharacteristic
360C22×C113#55311yescharacteristic
361C22×C113#55312yes—
362C4×C113—24no—
363C4×C113—24no—
364C4×C113—24no—
365C4×C113—24no—
366C4×C113—42no—
367C4×C113—44no—
368C4×C113—44no—
369C4×C113—82no—
370C4×C113—82no—
371#13912C11311yesmaximal, characteristic, direct product factor, Sylow
372C2×C113—44no—
373C2×C113—44no—
374C2×C113#228011yescharacteristic
375C2×C113#229311yescharacteristic
376C2×C113#231911yescharacteristic
377C2×C113D4×C22⋊C411yescharacteristic
378C2×C113#233911yescharacteristic
379C2×C113#235211yescharacteristic
380C2×C113#235311yescharacteristic
381C2×C113#245712yes—
382C2×C113#246112yes—
383C2×C113#246412yes—
384C2×C113#246812yes—
385C22×C4×D4C2×C11311yescharacteristic
386C2×#388C2×C11312yescomplemented
387C2×#381C2×C11311yescharacteristic, complemented
388C2×#380C2×C11311yescharacteristic, complemented
389#1441C2×C11312yescomplemented
390#1438C2×C11312yes—
391#1437C2×C11312yescomplemented
392#1434C2×C11311yescharacteristic, complemented
393C22⋊#95C2×C11311yescharacteristic, complemented
394C22⋊#95C2×C11311yescharacteristic, complemented
395C4×#95C2×C11311yescharacteristic, complemented
396C113#1391211yescharacteristic, direct product factor, Sylow
397C23×D4C22×C11311yescharacteristic
398C24×C4C22×C11311yescharacteristic
399C24×C4C22×C11311yescharacteristic
400C2×C4×D4—28no—
401C2×C4×D4C4×C11318yescomplemented
402C22×C4⋊C4C22×C11312yes—
403C22×C4⋊C4C22×C11311yescharacteristic
404C22×C22⋊C4C22×C11312yes—
405C22×C22⋊C4C22×C11312yes—
406C22×C22⋊C4C22×C11312yes—
407C22×C22⋊C4C22×C11312yes—
408C22×C22⋊C4C22×C11311yescharacteristic
409C22×C22⋊C4C22×C11311yescharacteristic
410C22×C42C22×C11312yes—
411C22×C42C22×C11311yescharacteristic
412#388—28no—
413#381—24no—
414#380—24no—
415C2×#95C22×C11311yescharacteristic
416C2×#95C22×C11312yes—
417C2×#95C22×C11311yescharacteristic
418C2×#95C22×C11311yescharacteristic
419C2×#95C22×C11312yes—
420C2×#95C22×C11312yes—
421C2×#95C22×C11312yes—
422C2×#95C22×C11312yes—
423C2×#95C22×C11312yes—
424C2×#95C22×C11311yescharacteristic
425C25C23×C11311yescharacteristic
426C25C23×C11311yescharacteristic
427C22×D4—24no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—24no—
431C22×D4C2×C4×C11314yes—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4C2×C4×C11314yes—
441C23×C4C2×C4×C11314yes—
442C23×C4C23×C11312yes—
443C23×C4C23×C11312yes—
444C23×C4C23×C11311yescharacteristic
445C23×C4C23×C11312yes—
446C23×C4C23×C11312yes—
447C23×C4C23×C11311yescharacteristic
448C23×C4C23×C11311yescharacteristic
449C23×C4C23×C11311yescharacteristic
450C23×C4C23×C11311yescharacteristic
451C4×D4—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4C2×C4×C11314yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4C2×C4×C11314yes—
471C2×C22⋊C4C2×C4×C11314yes—
472C2×C22⋊C4D4×C11318yes—
473C2×C42—24no—
474C2×C42—24no—
475C2×C42—24no—
476C2×C42—42no—
477C2×C42C2×C4×C11314yes—
478#95—22no—
479#95—24no—
480#95—22no—
481#95—24no—
482#95—24no—
483#95—24no—
484#95—22no—
485#95—24no—
486#95—42no—
487#95D4×C11314yescomplemented
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24C22×C4×C11312yes—
506C24C22×C4×C11312yes—
507C24C2×D4×C11314yes—
508C24#41×C11312yes—
509C24#41×C11312yes—
510C24C24×C11311yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—28no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4C22×C4×C11312yes—
568C22×C4C22×C4×C11312yes—
569C22×C4C22×C4×C11312yes—
570C22×C4C22×C4×C11312yes—
571C22×C4C22×C4×C11312yes—
572C22×C4C2×D4×C11314yes—
573C22×C4C2×D4×C11314yes—
574C22×C4C2×D4×C11314yes—
575C22×C4C2×D4×C11312yes—
576C22×C4#41×C11314yes—
577C22×C4#41×C11314yes—
578C22×C4#41×C11312yes—
579C4⋊C4—28no—
580C4⋊C4—48no—
581C22⋊C4—28no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4C22⋊C4×C113116yescomplemented
587C42—28no—
588C42—48no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23C2×C22⋊C4×C11314yes—
634C23#117×C11314yes—
635C23C23×C4×C11311yescharacteristic
636C23C22×D4×C11312yes—
637C23C22×D4×C11311yescharacteristic
638C23C2×#41×C11312yes—
639C23C2×#41×C11311yescharacteristic
640C23C2×#41×C11311yescharacteristic
641C23C2×#41×C11311yescharacteristic
642C23C2×#41×C11312yes—
643C23H(5,𝔽2)×C11312yes—
644C23H(5,𝔽2)×C11311yescharacteristic
645C232−1+4×C11311yescharacteristic
646D4—232no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—416no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4C2×C22⋊C4×C11314yes—
699C2×C4C2×C22⋊C4×C11314yes—
700C2×C4#117×C11314yes—
701C2×C4C4×D4×C11314yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22C22×C22⋊C4×C11311yescharacteristic
725C22C2×#117×C11311yescharacteristic
726C22C2×#117×C11311yescharacteristic
727C22C2×C4×D4×C11311yescharacteristic
728C22C4×#41×C11311yescharacteristic
729C22#518×C11311yescharacteristic
730C22#520×C11311yescharacteristic
731C22#525×C11312yes—
732C22#525×C11312yes—
733C22#529×C11312yes—
734C22#532×C11312yes—
735C22#540×C11312yes—
736C22#542×C11312yes—
737C22D42×C11312yes—
738C22#546×C11312yes—
739C22#546×C11312yes—
740C22#546×C11311yescharacteristic
741C22#547×C11312yes—
742C22#548×C11311yescharacteristic
743C22#551×C11312yes—
744C22#552×C11311yescharacteristic
745C22#553×C11311yescharacteristic
746C22#553×C11312yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—44no—
753C4—44no—
754C4—82no—
755C4—82no—
756C2—44no—
757C2—44no—
758C2C113×#228011yescharacteristic
759C2C113×#229311yescharacteristic
760C2C113×#231911yescharacteristic
761C2D4×C22⋊C4×C11311yescharacteristic
762C2C113×#233911yescharacteristic
763C2C113×#235211yescharacteristic
764C2C113×#235311yescharacteristic
765C2C113×#245712yes—
766C2C113×#246112yes—
767C2C113×#246412yes—
768C2C113×#246812yes—
subgroupG/H
center, socleC24×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
prime radicalC23×D4×C113C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C113C2semidirect
3. C2×#381×C113C2semidirect
4. C2×#380×C113C2semidirect
5. C113×#1441C2semidirect
7. C113×#1437C2semidirect
8. C113×#1434C2semidirect
9. C113×C22⋊#95C2semidirect
10. C113×C22⋊#95C2semidirect
11. C4×#95×C113C2semidirect
16. C2×C4×D4×C113C4semidirect
102. #95×C113D4semidirect
201. C22⋊C4×C113C22⋊C4semidirect
371. #13912C113direct (N × H)
386. C2×#388C2×C113semidirect
387. C2×#381C2×C113semidirect
388. C2×#380C2×C113semidirect
389. #1441C2×C113semidirect
391. #1437C2×C113semidirect
392. #1434C2×C113semidirect
393. C22⋊#95C2×C113semidirect
394. C22⋊#95C2×C113semidirect
395. C4×#95C2×C113semidirect
396. C113#13912direct (N × H)
401. C2×C4×D4C4×C113semidirect
487. #95D4×C113semidirect
586. C22⋊C4C22⋊C4×C113semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1132
C2×#388×C1132
C2×#381×C1132
C2×#380×C1132
C113×#14412
C113×#14382
C113×#14372
C113×#14342
C113×C22⋊#952
C4×#95×C1132
#13912113