Finite Group Databasebeta

← C113×#13873 #43281893

Subgroups — C113×#13873 #43281893

Order 28928.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C113C211yesmaximal, characteristic
2C2×#388×C113C212yesmaximal, complemented
3C2×#380×C113C211yesmaximal, characteristic, complemented
4C2×#379×C113C211yesmaximal, characteristic
5C2×#379×C113C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
7C113×#1440C212yesmaximal, complemented
8C113×#1439C212yesmaximal, complemented
9C113×#1437C212yesmaximal, complemented
10C113×C22⋊#95C211yesmaximal, characteristic, complemented
11C113×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C113C2211yescharacteristic
13C24×C4×C113C2211yescharacteristic
14C24×C4×C113C2211yescharacteristic
15C22×C4⋊C4×C113C2212yescomplemented
16C22×C22⋊C4×C113—28no—
17C22×C22⋊C4×C113C418yescomplemented
18C22×C22⋊C4×C113C2211yescharacteristic
19C22×C22⋊C4×C113C2211yescharacteristic
20C22×C22⋊C4×C113C2212yes—
21C22×C22⋊C4×C113C2212yes—
22C22×C22⋊C4×C113C2212yes—
23C22×C22⋊C4×C113C2212yes—
24C22×C22⋊C4×C113C2211yescharacteristic
25C22×C22⋊C4×C113C2211yescharacteristic
26C22×C22⋊C4×C113C2211yescharacteristic
27C22×C22⋊C4×C113C2211yescharacteristic
28C22×C22⋊C4×C113C2211yescharacteristic
29C22×C22⋊C4×C113C2211yescharacteristic
30C22×C42×C113C2212yescomplemented
31#388×C113—28no—
32#380×C113—24no—
33#379×C113—24no—
34#379×C113—24no—
35C4×C22⋊C4×C113—24no—
36C2×#95×C113C2212yescomplemented
37C2×#95×C113C2212yescomplemented
38C2×#95×C113C2212yescomplemented
39C2×#95×C113C2212yescomplemented
40C2×#95×C113C2212yescomplemented
41C2×#95×C113C2212yescomplemented
42C25×C113—24no—
43C25×C113—24no—
44C25×C113—22no—
45C25×C113—22no—
46C25×C113—22no—
47C25×C113—22no—
48C25×C113—22no—
49C25×C113—22no—
50C25×C113—42no—
51C25×C113—42no—
52C25×C113C2×C414yes—
53C25×C113C2311yescharacteristic
54C25×C113C2311yescharacteristic
55C25×C113C2311yescharacteristic
56C23×C4×C113—22no—
57C23×C4×C113—22no—
58C23×C4×C113—22no—
59C23×C4×C113—22no—
60C23×C4×C113—24no—
61C23×C4×C113—24no—
62C23×C4×C113—42no—
63C23×C4×C113—42no—
64C23×C4×C113C2×C414yes—
65C23×C4×C113C2×C414yes—
66C23×C4×C113C2312yes—
67C23×C4×C113C2312yes—
68C23×C4×C113C2311yescharacteristic
69C23×C4×C113C2311yescharacteristic
70C23×C4×C113C2312yes—
71C23×C4×C113C2312yes—
72C23×C4×C113C2311yescharacteristic
73C23×C4×C113C2311yescharacteristic
74C2×C4⋊C4×C113—24no—
75C2×C4⋊C4×C113—24no—
76C2×C4⋊C4×C113—42no—
77C2×C22⋊C4×C113—24no—
78C2×C22⋊C4×C113—22no—
79C2×C22⋊C4×C113—22no—
80C2×C22⋊C4×C113—22no—
81C2×C22⋊C4×C113—22no—
82C2×C22⋊C4×C113—24no—
83C2×C22⋊C4×C113—24no—
84C2×C22⋊C4×C113—232no—
85C2×C22⋊C4×C113—22no—
86C2×C22⋊C4×C113—22no—
87C2×C22⋊C4×C113—22no—
88C2×C22⋊C4×C113—24no—
89C2×C22⋊C4×C113—24no—
90C2×C22⋊C4×C113—24no—
91C2×C22⋊C4×C113—24no—
92C2×C22⋊C4×C113—22no—
93C2×C22⋊C4×C113—22no—
94C2×C22⋊C4×C113—22no—
95C2×C22⋊C4×C113—24no—
96C2×C22⋊C4×C113—24no—
97C2×C22⋊C4×C113—24no—
98C2×C22⋊C4×C113—24no—
99C2×C22⋊C4×C113—42no—
100C2×C22⋊C4×C113—42no—
101C2×C22⋊C4×C113—42no—
102C2×C22⋊C4×C113—42no—
103C2×C22⋊C4×C113C2×C414yes—
104C2×C22⋊C4×C113C2×C414yes—
105C2×C22⋊C4×C113C2×C414yes—
106C2×C22⋊C4×C113C2×C414yes—
107C2×C22⋊C4×C113D414yes—
108C2×C22⋊C4×C113D414yes—
109C2×C22⋊C4×C113D418yes—
110C2×C42×C113—24no—
111C2×C42×C113—24no—
112C2×C42×C113—42no—
113#95×C113—24no—
114#95×C113—24no—
115#95×C113—24no—
116#95×C113—24no—
117#95×C113—42no—
118#95×C113—42no—
119C24×C113—22no—
120C24×C113—22no—
121C24×C113—22no—
122C24×C113—22no—
123C24×C113—216no—
124C24×C113—216no—
125C24×C113—28no—
126C24×C113—28no—
127C24×C113—28no—
128C24×C113—22no—
129C24×C113—21no—
130C24×C113—21no—
131C24×C113—21no—
132C24×C113—21no—
133C24×C113—21no—
134C24×C113—21no—
135C24×C113—22no—
136C24×C113—21no—
137C24×C113—21no—
138C24×C113—21no—
139C24×C113—21no—
140C24×C113—21no—
141C24×C113—21no—
142C24×C113—22no—
143C24×C113—22no—
144C24×C113—22no—
145C24×C113—22no—
146C24×C113—28no—
147C24×C113—28no—
148C24×C113—44no—
149C24×C113—44no—
150C24×C113—48no—
151C24×C113—48no—
152C24×C113—48no—
153C24×C113—48no—
154C24×C113—48no—
155C24×C113—48no—
156C24×C113—48no—
157C24×C113—48no—
158C24×C113—48no—
159C24×C113—48no—
160C24×C113—44no—
161C24×C113—44no—
162C24×C113—44no—
163C24×C113—44no—
164C24×C113C22×C412yes—
165C24×C113C22×C412yes—
166C24×C113C22×C412yes—
167C24×C113C2×D414yes—
168C24×C113C2×D412yes—
169C24×C113C2×D412yes—
170C24×C113#4114yes—
171C24×C113#4112yes—
172C24×C113#4112yes—
173C24×C113#4112yes—
174C24×C113#4112yes—
175C24×C113C2411yescharacteristic
176C22×C4×C113—21no—
177C22×C4×C113—21no—
178C22×C4×C113—21no—
179C22×C4×C113—21no—
180C22×C4×C113—22no—
181C22×C4×C113—22no—
182C22×C4×C113—28no—
183C22×C4×C113—28no—
184C22×C4×C113—21no—
185C22×C4×C113—21no—
186C22×C4×C113—22no—
187C22×C4×C113—22no—
188C22×C4×C113—22no—
189C22×C4×C113—22no—
190C22×C4×C113—22no—
191C22×C4×C113—22no—
192C22×C4×C113—22no—
193C22×C4×C113—22no—
194C22×C4×C113—22no—
195C22×C4×C113—22no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—22no—
199C22×C4×C113—22no—
200C22×C4×C113—22no—
201C22×C4×C113—22no—
202C22×C4×C113—22no—
203C22×C4×C113—22no—
204C22×C4×C113—28no—
205C22×C4×C113—28no—
206C22×C4×C113—22no—
207C22×C4×C113—22no—
208C22×C4×C113—22no—
209C22×C4×C113—22no—
210C22×C4×C113—22no—
211C22×C4×C113—22no—
212C22×C4×C113—22no—
213C22×C4×C113—22no—
214C22×C4×C113—22no—
215C22×C4×C113—22no—
216C22×C4×C113—22no—
217C22×C4×C113—22no—
218C22×C4×C113—22no—
219C22×C4×C113—22no—
220C22×C4×C113—44no—
221C22×C4×C113—44no—
222C22×C4×C113—48no—
223C22×C4×C113—48no—
224C22×C4×C113—48no—
225C22×C4×C113—48no—
226C22×C4×C113C22×C412yes—
227C22×C4×C113C22×C412yes—
228C22×C4×C113C22×C412yes—
229C22×C4×C113C22×C412yes—
230C22×C4×C113C2×D414yes—
231C22×C4×C113C2×D414yes—
232C22×C4×C113C2×D414yes—
233C22×C4×C113C2×D414yes—
234C4⋊C4×C113—48no—
235C22⋊C4×C113—28no—
236C22⋊C4×C113—28no—
237C22⋊C4×C113—28no—
238C22⋊C4×C113—28no—
239C22⋊C4×C113—28no—
240C22⋊C4×C113—48no—
241C22⋊C4×C113—48no—
242C22⋊C4×C113—48no—
243C22⋊C4×C113—48no—
244C22⋊C4×C113—44no—
245C22⋊C4×C113—44no—
246C22⋊C4×C113C22⋊C4116yescomplemented
247C42×C113—48no—
248C23×C113—22no—
249C23×C113—22no—
250C23×C113—22no—
251C23×C113—22no—
252C23×C113—24no—
253C23×C113—24no—
254C23×C113—24no—
255C23×C113—24no—
256C23×C113—24no—
257C23×C113—24no—
258C23×C113—24no—
259C23×C113—24no—
260C23×C113—24no—
261C23×C113—24no—
262C23×C113—24no—
263C23×C113—24no—
264C23×C113—232no—
265C23×C113—22no—
266C23×C113—22no—
267C23×C113—22no—
268C23×C113—22no—
269C23×C113—22no—
270C23×C113—22no—
271C23×C113—22no—
272C23×C113—22no—
273C23×C113—22no—
274C23×C113—22no—
275C23×C113—22no—
276C23×C113—22no—
277C23×C113—24no—
278C23×C113—24no—
279C23×C113—24no—
280C23×C113—24no—
281C23×C113—24no—
282C23×C113—24no—
283C23×C113—24no—
284C23×C113—24no—
285C23×C113—24no—
286C23×C113—24no—
287C23×C113—24no—
288C23×C113—24no—
289C23×C113—416no—
290C23×C113—416no—
291C23×C113—416no—
292C23×C113—416no—
293C23×C113—416no—
294C23×C113—432no—
295C23×C113—432no—
296C23×C113—432no—
297C23×C113—432no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113—41no—
302C23×C113—41no—
303C23×C113—41no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—42no—
307C23×C113—42no—
308C23×C113—42no—
309C23×C113—42no—
310C23×C113—42no—
311C23×C113—42no—
312C23×C113—42no—
313C23×C113—42no—
314C23×C113—42no—
315C23×C113—42no—
316C23×C113—42no—
317C23×C113—42no—
318C23×C113—416no—
319C23×C113C2×C22⋊C414yes—
320C23×C113#11714yes—
321C23×C113#11714yes—
322C23×C113C4×D414yes—
323C23×C113C4×D414yes—
324C23×C113#12114yes—
325C23×C113#12314yes—
326C23×C113#12414yes—
327C23×C113#12614yes—
328C23×C113C23×C411yescharacteristic
329C23×C113C22×D412yes—
330C23×C113C22×D411yescharacteristic
331C23×C113C22×D411yescharacteristic
332C23×C113C2×#4111yescharacteristic
333C23×C113C2×#4111yescharacteristic
334C23×C113C2×#4112yes—
335C23×C113C2×#4111yescharacteristic
336C23×C113C2×#4111yescharacteristic
337C23×C113H(5,𝔽2)12yes—
338C23×C113H(5,𝔽2)12yes—
339C2×C4×C113—22no—
340C2×C4×C113—22no—
341C2×C4×C113—22no—
342C2×C4×C113—22no—
343C2×C4×C113—24no—
344C2×C4×C113—24no—
345C2×C4×C113—24no—
346C2×C4×C113—24no—
347C2×C4×C113—22no—
348C2×C4×C113—22no—
349C2×C4×C113—22no—
350C2×C4×C113—22no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—24no—
354C2×C4×C113—24no—
355C2×C4×C113—24no—
356C2×C4×C113—24no—
357C2×C4×C113—24no—
358C2×C4×C113—24no—
359C2×C4×C113—416no—
360C2×C4×C113—416no—
361C2×C4×C113—42no—
362C2×C4×C113—42no—
363C2×C4×C113—42no—
364C2×C4×C113—42no—
365C2×C4×C113—42no—
366C2×C4×C113—42no—
367C2×C4×C113—42no—
368C2×C4×C113—42no—
369C2×C4×C113—42no—
370C2×C4×C113—42no—
371C2×C4×C113—42no—
372C2×C4×C113—42no—
373C2×C4×C113—42no—
374C2×C4×C113—42no—
375C2×C4×C113—42no—
376C2×C4×C113—42no—
377C2×C4×C113—42no—
378C2×C4×C113—42no—
379C2×C4×C113—42no—
380C2×C4×C113—42no—
381C2×C4×C113—42no—
382C2×C4×C113—42no—
383C2×C4×C113—42no—
384C2×C4×C113—42no—
385C2×C4×C113—42no—
386C2×C4×C113—42no—
387C2×C4×C113C2×C22⋊C414yes—
388C2×C4×C113C2×C22⋊C414yes—
389C22×C113—24no—
390C22×C113—24no—
391C22×C113—24no—
392C22×C113—24no—
393C22×C113—24no—
394C22×C113—28no—
395C22×C113—28no—
396C22×C113—28no—
397C22×C113—28no—
398C22×C113—24no—
399C22×C113—24no—
400C22×C113—24no—
401C22×C113—24no—
402C22×C113—24no—
403C22×C113—24no—
404C22×C113—24no—
405C22×C113—464no—
406C22×C113—42no—
407C22×C113—42no—
408C22×C113—42no—
409C22×C113—42no—
410C22×C113—42no—
411C22×C113—42no—
412C22×C113—44no—
413C22×C113—44no—
414C22×C113—44no—
415C22×C113—44no—
416C22×C113—44no—
417C22×C113—44no—
418C22×C113—44no—
419C22×C113—44no—
420C22×C113—42no—
421C22×C113—42no—
422C22×C113#38818yescomplemented
423C22×C113C22×C22⋊C411yescharacteristic
424C22×C113C2×#11711yescharacteristic
425C22×C113C2×#11711yescharacteristic
426C22×C113C2×C4×D411yescharacteristic
427C22×C113C2×C4×D411yescharacteristic
428C22×C113#51811yescharacteristic
429C22×C113#51811yescharacteristic
430C22×C113C2×#12111yescharacteristic
431C22×C113C2×#12311yescharacteristic
432C22×C113#52512yes—
433C22×C113#52512yes—
434C22×C113C2×#12411yescharacteristic
435C22×C113C2×#12611yescharacteristic
436C22×C113#53812yes—
437C22×C113#53812yes—
438C22×C113D4212yes—
439C22×C113D4212yes—
440C22×C113#54612yes—
441C22×C113#54612yes—
442C22×C113#54612yes—
443C22×C113#54612yes—
444C22×C113#55112yes—
445C22×C113#55112yes—
446C4×C113—24no—
447C4×C113—24no—
448C4×C113—42no—
449C4×C113—42no—
450C4×C113—44no—
451C4×C113—44no—
452C4×C113—82no—
453C4×C113—82no—
454#13873C11311yesmaximal, characteristic, direct product factor, Sylow
455C2×C113—28no—
456C2×C113—44no—
457C2×C113—44no—
458C2×C113#228011yescharacteristic
459C2×C113C2×#38811yescharacteristic
460C2×C113#231211yescharacteristic
461C2×C113D4×C22⋊C411yescharacteristic
462C2×C113D4×C22⋊C411yescharacteristic
463C2×C113#234211yescharacteristic
464C2×C113#234211yescharacteristic
465C2×C113#241812yes—
466C2×C113#242412yes—
467C2×C113#247212yes—
468C2×C113#248012yes—
469C23×C22⋊C4C2×C11311yescharacteristic
470C2×#388C2×C11312yescomplemented
471C2×#380C2×C11311yescharacteristic, complemented
472C2×#379C2×C11311yescharacteristic
473C2×#379C2×C11311yescharacteristic
474C2×C4×C22⋊C4C2×C11311yescharacteristic, complemented
475#1440C2×C11312yescomplemented
476#1439C2×C11312yescomplemented
477#1437C2×C11312yescomplemented
478C22⋊#95C2×C11311yescharacteristic, complemented
479C22⋊#95C2×C11311yescharacteristic, complemented
480C113#1387311yescharacteristic, direct product factor, Sylow
481C26C22×C11311yescharacteristic
482C24×C4C22×C11311yescharacteristic
483C24×C4C22×C11311yescharacteristic
484C22×C4⋊C4C22×C11312yescomplemented
485C22×C22⋊C4—28no—
486C22×C22⋊C4C4×C11318yescomplemented
487C22×C22⋊C4C22×C11311yescharacteristic
488C22×C22⋊C4C22×C11311yescharacteristic
489C22×C22⋊C4C22×C11312yes—
490C22×C22⋊C4C22×C11312yes—
491C22×C22⋊C4C22×C11312yes—
492C22×C22⋊C4C22×C11312yes—
493C22×C22⋊C4C22×C11311yescharacteristic
494C22×C22⋊C4C22×C11311yescharacteristic
495C22×C22⋊C4C22×C11311yescharacteristic
496C22×C22⋊C4C22×C11311yescharacteristic
497C22×C22⋊C4C22×C11311yescharacteristic
498C22×C22⋊C4C22×C11311yescharacteristic
499C22×C42C22×C11312yescomplemented
500#388—28no—
501#380—24no—
502#379—24no—
503#379—24no—
504C4×C22⋊C4—24no—
505C2×#95C22×C11312yescomplemented
506C2×#95C22×C11312yescomplemented
507C2×#95C22×C11312yescomplemented
508C2×#95C22×C11312yescomplemented
509C2×#95C22×C11312yescomplemented
510C2×#95C22×C11312yescomplemented
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C11314yes—
522C25C23×C11311yescharacteristic
523C25C23×C11311yescharacteristic
524C25C23×C11311yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C11314yes—
534C23×C4C2×C4×C11314yes—
535C23×C4C23×C11312yes—
536C23×C4C23×C11312yes—
537C23×C4C23×C11311yescharacteristic
538C23×C4C23×C11311yescharacteristic
539C23×C4C23×C11312yes—
540C23×C4C23×C11312yes—
541C23×C4C23×C11311yescharacteristic
542C23×C4C23×C11311yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C11314yes—
573C2×C22⋊C4C2×C4×C11314yes—
574C2×C22⋊C4C2×C4×C11314yes—
575C2×C22⋊C4C2×C4×C11314yes—
576C2×C22⋊C4D4×C11314yes—
577C2×C22⋊C4D4×C11314yes—
578C2×C22⋊C4D4×C11318yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C11312yes—
634C24C22×C4×C11312yes—
635C24C22×C4×C11312yes—
636C24C2×D4×C11314yes—
637C24C2×D4×C11312yes—
638C24C2×D4×C11312yes—
639C24#41×C11314yes—
640C24#41×C11312yes—
641C24#41×C11312yes—
642C24#41×C11312yes—
643C24#41×C11312yes—
644C24C24×C11311yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C11312yes—
696C22×C4C22×C4×C11312yes—
697C22×C4C22×C4×C11312yes—
698C22×C4C22×C4×C11312yes—
699C22×C4C2×D4×C11314yes—
700C22×C4C2×D4×C11314yes—
701C22×C4C2×D4×C11314yes—
702C22×C4C2×D4×C11314yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C113116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C11314yes—
789C23#117×C11314yes—
790C23#117×C11314yes—
791C23C4×D4×C11314yes—
792C23C4×D4×C11314yes—
793C23#121×C11314yes—
794C23#123×C11314yes—
795C23#124×C11314yes—
796C23#126×C11314yes—
797C23C23×C4×C11311yescharacteristic
798C23C22×D4×C11312yes—
799C23C22×D4×C11311yescharacteristic
800C23C22×D4×C11311yescharacteristic
801C23C2×#41×C11311yescharacteristic
802C23C2×#41×C11311yescharacteristic
803C23C2×#41×C11312yes—
804C23C2×#41×C11311yescharacteristic
805C23C2×#41×C11311yescharacteristic
806C23H(5,𝔽2)×C11312yes—
807C23H(5,𝔽2)×C11312yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C11314yes—
857C2×C4C2×C22⋊C4×C11314yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22#388×C11318yescomplemented
892C22C22×C22⋊C4×C11311yescharacteristic
893C22C2×#117×C11311yescharacteristic
894C22C2×#117×C11311yescharacteristic
895C22C2×C4×D4×C11311yescharacteristic
896C22C2×C4×D4×C11311yescharacteristic
897C22#518×C11311yescharacteristic
898C22#518×C11311yescharacteristic
899C22C2×#121×C11311yescharacteristic
900C22C2×#123×C11311yescharacteristic
901C22#525×C11312yes—
902C22#525×C11312yes—
903C22C2×#124×C11311yescharacteristic
904C22C2×#126×C11311yescharacteristic
905C22#538×C11312yes—
906C22#538×C11312yes—
907C22D42×C11312yes—
908C22D42×C11312yes—
909C22#546×C11312yes—
910C22#546×C11312yes—
911C22#546×C11312yes—
912C22#546×C11312yes—
913C22#551×C11312yes—
914C22#551×C11312yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C113×#228011yescharacteristic
927C2C2×#388×C11311yescharacteristic
928C2C113×#231211yescharacteristic
929C2D4×C22⋊C4×C11311yescharacteristic
930C2D4×C22⋊C4×C11311yescharacteristic
931C2C113×#234211yescharacteristic
932C2C113×#234211yescharacteristic
933C2C113×#241812yes—
934C2C113×#242412yes—
935C2C113×#247212yes—
936C2C113×#248012yes—
subgroupG/H
center, socleC24×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
prime radicalC26×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×#380×C113C2semidirect
6. C2×C4×C22⋊C4×C113C2semidirect
7. C113×#1440C2semidirect
8. C113×#1439C2semidirect
9. C113×#1437C2semidirect
10. C113×C22⋊#95C2semidirect
11. C113×C22⋊#95C2semidirect
15. C22×C4⋊C4×C113C22semidirect
17. C22×C22⋊C4×C113C4semidirect
30. C22×C42×C113C22semidirect
36. C2×#95×C113C22semidirect
37. C2×#95×C113C22semidirect
38. C2×#95×C113C22semidirect
39. C2×#95×C113C22semidirect
40. C2×#95×C113C22semidirect
41. C2×#95×C113C22semidirect
246. C22⋊C4×C113C22⋊C4semidirect
422. C22×C113#388semidirect
454. #13873C113direct (N × H)
470. C2×#388C2×C113semidirect
471. C2×#380C2×C113semidirect
474. C2×C4×C22⋊C4C2×C113semidirect
475. #1440C2×C113semidirect
476. #1439C2×C113semidirect
477. #1437C2×C113semidirect
478. C22⋊#95C2×C113semidirect
479. C22⋊#95C2×C113semidirect
480. C113#13873direct (N × H)
484. C22×C4⋊C4C22×C113semidirect
486. C22×C22⋊C4C4×C113semidirect
499. C22×C42C22×C113semidirect
505. C2×#95C22×C113semidirect
506. C2×#95C22×C113semidirect
507. C2×#95C22×C113semidirect
508. C2×#95C22×C113semidirect
509. C2×#95C22×C113semidirect
510. C2×#95C22×C113semidirect
715. C22⋊C4C22⋊C4×C113semidirect
891. C22#388×C113semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1132
C2×#388×C1132
C2×#380×C1132
C2×#379×C1132
C2×C4×C22⋊C4×C1132
C113×#14402
C113×#14392
C113×#14372
C113×C22⋊#952
#13873113