Finite Group Databasebeta

← C113×#13967 #43281987

Subgroups — C113×#13967 #43281987

Order 28928.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C113C211yesmaximal, characteristic
2C22×C4×D4×C113C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C113C211yesmaximal, characteristic, complemented
4C2×#386×C113C212yesmaximal, complemented
5C2×#386×C113C211yesmaximal, characteristic, complemented
6C2×#379×C113C211yesmaximal, characteristic, complemented
7C113×#1439C212yesmaximal, complemented
8C113×#1438C212yesmaximal, complemented
9C113×#1437C212yesmaximal, complemented
10C113×C22⋊#95C211yesmaximal, characteristic, complemented
11C113×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C113C2211yescharacteristic
13C23×D4×C113C2212yes—
14C23×D4×C113C2211yescharacteristic
15C24×C4×C113C2211yescharacteristic
16C24×C4×C113C2211yescharacteristic
17C24×C4×C113C2211yescharacteristic, complemented
18C2×#120×C113—24no—
19C2×#120×C113—24no—
20C2×#120×C113C418yescomplemented
21C2×C4×D4×C113—24no—
22C2×C4×D4×C113—24no—
23C2×C4×D4×C113—24no—
24C22×C4⋊C4×C113C2211yescharacteristic, complemented
25C22×C22⋊C4×C113—24no—
26C22×C22⋊C4×C113—28no—
27C22×C22⋊C4×C113C2211yescharacteristic
28C22×C22⋊C4×C113C2212yes—
29C22×C22⋊C4×C113C2212yes—
30C22×C22⋊C4×C113C2212yes—
31C22×C22⋊C4×C113C2211yescharacteristic
32C22×C22⋊C4×C113C2212yes—
33C22×C22⋊C4×C113C2211yescharacteristic
34C22×C22⋊C4×C113C2212yes—
35C22×C22⋊C4×C113C2211yescharacteristic, complemented
36C22×C22⋊C4×C113C2212yescomplemented
37C22×C42×C113C2211yescharacteristic, complemented
38#386×C113—24no—
39#386×C113—28no—
40#379×C113—24no—
41C2×#95×C113C2212yescomplemented
42C2×#95×C113C2212yescomplemented
43C2×#95×C113C2212yescomplemented
44C2×#95×C113C2212yescomplemented
45C2×#95×C113C2212yescomplemented
46C25×C113—24no—
47C25×C113—22no—
48C25×C113—24no—
49C25×C113—22no—
50C25×C113—22no—
51C25×C113—22no—
52C25×C113—22no—
53C25×C113—22no—
54C25×C113—42no—
55C25×C113—42no—
56C25×C113C2×C414yescomplemented
57C25×C113C2311yescharacteristic
58C25×C113C2312yes—
59C25×C113C2311yescharacteristic
60C22×D4×C113—22no—
61C22×D4×C113—22no—
62C22×D4×C113—22no—
63C22×D4×C113—22no—
64C22×D4×C113—24no—
65C22×D4×C113—24no—
66C22×D4×C113—24no—
67C22×D4×C113—24no—
68C22×D4×C113—42no—
69C22×D4×C113—42no—
70C22×D4×C113C2×C414yes—
71C22×D4×C113C2×C418yescomplemented
72C22×D4×C113D414yes—
73C22×D4×C113D414yes—
74C23×C4×C113—22no—
75C23×C4×C113—22no—
76C23×C4×C113—22no—
77C23×C4×C113—22no—
78C23×C4×C113—24no—
79C23×C4×C113—24no—
80C23×C4×C113—22no—
81C23×C4×C113—22no—
82C23×C4×C113—22no—
83C23×C4×C113—22no—
84C23×C4×C113—24no—
85C23×C4×C113—42no—
86C23×C4×C113—42no—
87C23×C4×C113—42no—
88C23×C4×C113D414yescomplemented
89C23×C4×C113C2312yes—
90C23×C4×C113C2312yes—
91C23×C4×C113C2311yescharacteristic
92C23×C4×C113C2311yescharacteristic
93C23×C4×C113C2311yescharacteristic
94C23×C4×C113C2312yes—
95C23×C4×C113C2311yescharacteristic
96C23×C4×C113C2311yescharacteristic
97#120×C113—232no—
98C4×D4×C113—232no—
99C2×C4⋊C4×C113—22no—
100C2×C4⋊C4×C113—22no—
101C2×C4⋊C4×C113—22no—
102C2×C22⋊C4×C113—232no—
103C2×C22⋊C4×C113—24no—
104C2×C22⋊C4×C113—22no—
105C2×C22⋊C4×C113—22no—
106C2×C22⋊C4×C113—22no—
107C2×C22⋊C4×C113—22no—
108C2×C22⋊C4×C113—22no—
109C2×C22⋊C4×C113—24no—
110C2×C22⋊C4×C113—24no—
111C2×C22⋊C4×C113—24no—
112C2×C22⋊C4×C113—24no—
113C2×C22⋊C4×C113—24no—
114C2×C22⋊C4×C113—24no—
115C2×C22⋊C4×C113—22no—
116C2×C22⋊C4×C113—22no—
117C2×C22⋊C4×C113—22no—
118C2×C22⋊C4×C113—24no—
119C2×C22⋊C4×C113—22no—
120C2×C22⋊C4×C113—24no—
121C2×C22⋊C4×C113—24no—
122C2×C22⋊C4×C113—22no—
123C2×C22⋊C4×C113—24no—
124C2×C22⋊C4×C113—24no—
125C2×C22⋊C4×C113—24no—
126C2×C22⋊C4×C113—42no—
127C2×C22⋊C4×C113—42no—
128C2×C22⋊C4×C113—42no—
129C2×C22⋊C4×C113C2×C414yescomplemented
130C2×C22⋊C4×C113C2×C418yescomplemented
131C2×C22⋊C4×C113D418yescomplemented
132C2×C22⋊C4×C113D414yescomplemented
133C2×C42×C113—22no—
134C2×C42×C113—22no—
135C2×C42×C113—22no—
136#95×C113—24no—
137#95×C113—24no—
138#95×C113—24no—
139#95×C113—42no—
140#95×C113—42no—
141C24×C113—22no—
142C24×C113—22no—
143C24×C113—22no—
144C24×C113—22no—
145C24×C113—28no—
146C24×C113—28no—
147C24×C113—216no—
148C24×C113—28no—
149C24×C113—216no—
150C24×C113—22no—
151C24×C113—22no—
152C24×C113—22no—
153C24×C113—21no—
154C24×C113—21no—
155C24×C113—22no—
156C24×C113—22no—
157C24×C113—22no—
158C24×C113—21no—
159C24×C113—21no—
160C24×C113—22no—
161C24×C113—22no—
162C24×C113—22no—
163C24×C113—22no—
164C24×C113—22no—
165C24×C113—22no—
166C24×C113—22no—
167C24×C113—22no—
168C24×C113—22no—
169C24×C113—22no—
170C24×C113—28no—
171C24×C113—28no—
172C24×C113—48no—
173C24×C113—48no—
174C24×C113—48no—
175C24×C113—48no—
176C24×C113—48no—
177C24×C113—48no—
178C24×C113—48no—
179C24×C113—48no—
180C24×C113—48no—
181C24×C113—44no—
182C24×C113—44no—
183C24×C113—48no—
184C24×C113—44no—
185C24×C113—44no—
186C24×C113—44no—
187C24×C113—44no—
188C24×C113C22×C412yes—
189C24×C113C22×C414yes—
190C24×C113C22×C412yes—
191C24×C113C2×D412yes—
192C24×C113C2×D412yes—
193C24×C113C2×D414yes—
194C24×C113C2×D412yes—
195C24×C113C2×D412yes—
196C24×C113C2×D412yes—
197C24×C113C2×D412yes—
198C24×C113#4114yes—
199C24×C113#4112yes—
200C24×C113#4112yes—
201C24×C113C2411yescharacteristic
202C2×D4×C113—28no—
203C2×D4×C113—28no—
204C2×D4×C113—28no—
205C2×D4×C113—28no—
206C2×D4×C113—28no—
207C2×D4×C113—28no—
208C2×D4×C113—216no—
209C2×D4×C113—216no—
210C2×D4×C113—48no—
211C2×D4×C113—48no—
212C2×D4×C113—48no—
213C2×D4×C113—48no—
214C2×D4×C113—48no—
215C2×D4×C113C22⋊C4116yescomplemented
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—22no—
223C22×C4×C113—28no—
224C22×C4×C113—28no—
225C22×C4×C113—28no—
226C22×C4×C113—22no—
227C22×C4×C113—22no—
228C22×C4×C113—22no—
229C22×C4×C113—21no—
230C22×C4×C113—21no—
231C22×C4×C113—22no—
232C22×C4×C113—22no—
233C22×C4×C113—22no—
234C22×C4×C113—22no—
235C22×C4×C113—22no—
236C22×C4×C113—21no—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—21no—
240C22×C4×C113—22no—
241C22×C4×C113—22no—
242C22×C4×C113—22no—
243C22×C4×C113—22no—
244C22×C4×C113—22no—
245C22×C4×C113—22no—
246C22×C4×C113—22no—
247C22×C4×C113—22no—
248C22×C4×C113—22no—
249C22×C4×C113—22no—
250C22×C4×C113—28no—
251C22×C4×C113—22no—
252C22×C4×C113—22no—
253C22×C4×C113—22no—
254C22×C4×C113—22no—
255C22×C4×C113—22no—
256C22×C4×C113—22no—
257C22×C4×C113—22no—
258C22×C4×C113—44no—
259C22×C4×C113—48no—
260C22×C4×C113—48no—
261C22×C4×C113—48no—
262C22×C4×C113—48no—
263C22×C4×C113—48no—
264C22×C4×C113—48no—
265C22×C4×C113—44no—
266C22×C4×C113—44no—
267C22×C4×C113—44no—
268C22×C4×C113—44no—
269C22×C4×C113C22×C414yes—
270C22×C4×C113C22×C412yes—
271C22×C4×C113C2×D414yes—
272C22×C4×C113C2×D412yes—
273C22×C4×C113C2×D412yes—
274C22×C4×C113C2×D412yes—
275C22×C4×C113C2×D412yes—
276C22×C4×C113C2×D412yes—
277C22×C4×C113C2×D414yes—
278C22×C4×C113C2×D412yes—
279C4⋊C4×C113—28no—
280C22⋊C4×C113—216no—
281C22⋊C4×C113—28no—
282C22⋊C4×C113—28no—
283C22⋊C4×C113—28no—
284C22⋊C4×C113—216no—
285C22⋊C4×C113—216no—
286C22⋊C4×C113—48no—
287C22⋊C4×C113—48no—
288C22⋊C4×C113—48no—
289C22⋊C4×C113—44no—
290C42×C113—28no—
291C23×C113—24no—
292C23×C113—24no—
293C23×C113—22no—
294C23×C113—22no—
295C23×C113—24no—
296C23×C113—22no—
297C23×C113—22no—
298C23×C113—24no—
299C23×C113—24no—
300C23×C113—24no—
301C23×C113—24no—
302C23×C113—24no—
303C23×C113—24no—
304C23×C113—24no—
305C23×C113—24no—
306C23×C113—24no—
307C23×C113—232no—
308C23×C113—24no—
309C23×C113—24no—
310C23×C113—22no—
311C23×C113—22no—
312C23×C113—24no—
313C23×C113—24no—
314C23×C113—24no—
315C23×C113—24no—
316C23×C113—24no—
317C23×C113—24no—
318C23×C113—24no—
319C23×C113—22no—
320C23×C113—22no—
321C23×C113—22no—
322C23×C113—22no—
323C23×C113—24no—
324C23×C113—24no—
325C23×C113—24no—
326C23×C113—24no—
327C23×C113—24no—
328C23×C113—24no—
329C23×C113—24no—
330C23×C113—24no—
331C23×C113—24no—
332C23×C113—24no—
333C23×C113—24no—
334C23×C113—24no—
335C23×C113—24no—
336C23×C113—24no—
337C23×C113—24no—
338C23×C113—432no—
339C23×C113—432no—
340C23×C113—416no—
341C23×C113—416no—
342C23×C113—416no—
343C23×C113—416no—
344C23×C113—432no—
345C23×C113—432no—
346C23×C113—416no—
347C23×C113—41no—
348C23×C113—42no—
349C23×C113—42no—
350C23×C113—42no—
351C23×C113—42no—
352C23×C113—41no—
353C23×C113—42no—
354C23×C113—41no—
355C23×C113—42no—
356C23×C113—41no—
357C23×C113—42no—
358C23×C113—42no—
359C23×C113—42no—
360C23×C113—42no—
361C23×C113—42no—
362C23×C113—42no—
363C23×C113—42no—
364C23×C113—42no—
365C23×C113—42no—
366C23×C113—42no—
367C23×C113—42no—
368C23×C113—42no—
369C23×C113—42no—
370C23×C113—42no—
371C23×C113—42no—
372C23×C113—42no—
373C23×C113—416no—
374C23×C113C2×C22⋊C414yes—
375C23×C113C2×C22⋊C414yescomplemented
376C23×C113C4×D414yes—
377C23×C113C4×D414yes—
378C23×C113C4×D418yescomplemented
379C23×C113#12014yes—
380C23×C113#12114yes—
381C23×C113#12114yes—
382C23×C113#12314yes—
383C23×C113C23×C411yescharacteristic
384C23×C113C22×D411yescharacteristic
385C23×C113C22×D411yescharacteristic
386C23×C113C22×D411yescharacteristic
387C23×C113C22×D411yescharacteristic
388C23×C113C22×D412yes—
389C23×C113C2×#4111yescharacteristic
390C23×C113C2×#4111yescharacteristic
391C23×C113C2×#4112yes—
392C23×C113H(5,𝔽2)12yes—
393C23×C113H(5,𝔽2)12yes—
394D4×C113—232no—
395D4×C113—432no—
396C2×C4×C113—22no—
397C2×C4×C113—22no—
398C2×C4×C113—22no—
399C2×C4×C113—22no—
400C2×C4×C113—22no—
401C2×C4×C113—22no—
402C2×C4×C113—22no—
403C2×C4×C113—22no—
404C2×C4×C113—24no—
405C2×C4×C113—24no—
406C2×C4×C113—24no—
407C2×C4×C113—24no—
408C2×C4×C113—24no—
409C2×C4×C113—22no—
410C2×C4×C113—22no—
411C2×C4×C113—24no—
412C2×C4×C113—22no—
413C2×C4×C113—22no—
414C2×C4×C113—22no—
415C2×C4×C113—24no—
416C2×C4×C113—24no—
417C2×C4×C113—24no—
418C2×C4×C113—24no—
419C2×C4×C113—416no—
420C2×C4×C113—416no—
421C2×C4×C113—416no—
422C2×C4×C113—41no—
423C2×C4×C113—42no—
424C2×C4×C113—41no—
425C2×C4×C113—41no—
426C2×C4×C113—41no—
427C2×C4×C113—42no—
428C2×C4×C113—42no—
429C2×C4×C113—42no—
430C2×C4×C113—42no—
431C2×C4×C113—42no—
432C2×C4×C113—42no—
433C2×C4×C113—42no—
434C2×C4×C113—42no—
435C2×C4×C113—42no—
436C2×C4×C113—42no—
437C2×C4×C113—42no—
438C2×C4×C113—42no—
439C2×C4×C113—42no—
440C2×C4×C113—42no—
441C2×C4×C113—42no—
442C2×C4×C113—42no—
443C2×C4×C113—42no—
444C2×C4×C113—42no—
445C2×C4×C113C2×C22⋊C414yescomplemented
446C2×C4×C113#12014yescomplemented
447C22×C113—24no—
448C22×C113—28no—
449C22×C113—28no—
450C22×C113—24no—
451C22×C113—24no—
452C22×C113—24no—
453C22×C113—28no—
454C22×C113—28no—
455C22×C113—24no—
456C22×C113—24no—
457C22×C113—28no—
458C22×C113—28no—
459C22×C113—28no—
460C22×C113—24no—
461C22×C113—28no—
462C22×C113—464no—
463C22×C113—42no—
464C22×C113—44no—
465C22×C113—44no—
466C22×C113—44no—
467C22×C113—44no—
468C22×C113—42no—
469C22×C113—44no—
470C22×C113—42no—
471C22×C113—44no—
472C22×C113—42no—
473C22×C113—44no—
474C22×C113—44no—
475C22×C113—44no—
476C22×C113—44no—
477C22×C113—44no—
478C22×C113—44no—
479C22×C113—44no—
480C22×C113—42no—
481C22×C113—44no—
482C22×C113—44no—
483C22×C113—42no—
484C22×C113#38618yescomplemented
485C22×C113C22×C22⋊C411yescharacteristic
486C22×C113C2×C4×D411yescharacteristic
487C22×C113C2×C4×D412yes—
488C22×C113C2×C4×D411yescharacteristic
489C22×C113#51812yes—
490C22×C113C2×#12011yescharacteristic
491C22×C113C2×#12011yescharacteristic
492C22×C113C2×#12111yescharacteristic
493C22×C113C2×#12111yescharacteristic
494C22×C113C2×#12311yescharacteristic
495C22×C113#52511yescharacteristic
496C22×C113#52512yes—
497C22×C113#53411yescharacteristic
498C22×C113#53511yescharacteristic
499C22×C113#53812yes—
500C22×C113D4212yes—
501C22×C113D4212yes—
502C22×C113D4212yes—
503C22×C113#54612yes—
504C22×C113#54612yes—
505C22×C113#54612yes—
506C22×C113#54612yes—
507C22×C113#55112yes—
508C4×C113—24no—
509C4×C113—24no—
510C4×C113—44no—
511C4×C113—42no—
512C4×C113—42no—
513C4×C113—42no—
514C4×C113—44no—
515C4×C113—82no—
516#13967C11311yesmaximal, characteristic, direct product factor, Sylow
517C2×C113—28no—
518C2×C113—44no—
519C2×C113—48no—
520C2×C113C2×#38611yescharacteristic
521C2×C113C4×#12011yescharacteristic
522C2×C113#232111yescharacteristic
523C2×C113D4×C22⋊C412yes—
524C2×C113#235812yes—
525C2×C113#240311yescharacteristic
526C2×C113#240411yescharacteristic
527C2×C113#240811yescharacteristic
528C2×C113#241812yes—
529C2×C113#242412yes—
530C2×C113#253411yescharacteristic
531C22×#120C2×C11311yescharacteristic
532C22×C4×D4C2×C11311yescharacteristic, complemented
533C23×C22⋊C4C2×C11311yescharacteristic, complemented
534C2×#386C2×C11312yescomplemented
535C2×#386C2×C11311yescharacteristic, complemented
536C2×#379C2×C11311yescharacteristic, complemented
537#1439C2×C11312yescomplemented
538#1438C2×C11312yescomplemented
539#1437C2×C11312yescomplemented
540C22⋊#95C2×C11311yescharacteristic, complemented
541C22⋊#95C2×C11311yescharacteristic, complemented
542C113#1396711yescharacteristic, direct product factor, Sylow
543C26C22×C11311yescharacteristic
544C23×D4C22×C11312yes—
545C23×D4C22×C11311yescharacteristic
546C24×C4C22×C11311yescharacteristic
547C24×C4C22×C11311yescharacteristic
548C24×C4C22×C11311yescharacteristic, complemented
549C2×#120—24no—
550C2×#120—24no—
551C2×#120C4×C11318yescomplemented
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C2×C4×D4—24no—
555C22×C4⋊C4C22×C11311yescharacteristic, complemented
556C22×C22⋊C4—24no—
557C22×C22⋊C4—28no—
558C22×C22⋊C4C22×C11312yes—
559C22×C22⋊C4C22×C11311yescharacteristic
560C22×C22⋊C4C22×C11312yes—
561C22×C22⋊C4C22×C11312yes—
562C22×C22⋊C4C22×C11311yescharacteristic
563C22×C22⋊C4C22×C11312yes—
564C22×C22⋊C4C22×C11312yes—
565C22×C22⋊C4C22×C11311yescharacteristic
566C22×C22⋊C4C22×C11311yescharacteristic, complemented
567C22×C22⋊C4C22×C11312yescomplemented
568C22×C42C22×C11311yescharacteristic, complemented
569#386—24no—
570#386—28no—
571#379—24no—
572C2×#95C22×C11312yescomplemented
573C2×#95C22×C11312yescomplemented
574C2×#95C22×C11312yescomplemented
575C2×#95C22×C11312yescomplemented
576C2×#95C22×C11312yescomplemented
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C11314yescomplemented
588C25C23×C11311yescharacteristic
589C25C23×C11312yes—
590C25C23×C11311yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C11314yes—
602C22×D4C2×C4×C11318yescomplemented
603C22×D4D4×C11314yes—
604C22×D4D4×C11314yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C11314yescomplemented
620C23×C4C23×C11312yes—
621C23×C4C23×C11312yes—
622C23×C4C23×C11311yescharacteristic
623C23×C4C23×C11311yescharacteristic
624C23×C4C23×C11311yescharacteristic
625C23×C4C23×C11312yes—
626C23×C4C23×C11311yescharacteristic
627C23×C4C23×C11311yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C11314yescomplemented
661C2×C22⋊C4C2×C4×C11318yescomplemented
662C2×C22⋊C4D4×C11318yescomplemented
663C2×C22⋊C4D4×C11314yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C11312yes—
720C24C22×C4×C11314yes—
721C24C22×C4×C11312yes—
722C24C2×D4×C11312yes—
723C24C2×D4×C11312yes—
724C24C2×D4×C11314yes—
725C24C2×D4×C11312yes—
726C24C2×D4×C11312yes—
727C24C2×D4×C11312yes—
728C24C2×D4×C11312yes—
729C24#41×C11314yes—
730C24#41×C11312yes—
731C24#41×C11312yes—
732C24C24×C11311yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C113116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C11314yes—
801C22×C4C22×C4×C11312yes—
802C22×C4C2×D4×C11314yes—
803C22×C4C2×D4×C11312yes—
804C22×C4C2×D4×C11312yes—
805C22×C4C2×D4×C11312yes—
806C22×C4C2×D4×C11312yes—
807C22×C4C2×D4×C11312yes—
808C22×C4C2×D4×C11314yes—
809C22×C4C2×D4×C11312yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23—42no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—416no—
905C23C2×C22⋊C4×C11314yes—
906C23C2×C22⋊C4×C11314yescomplemented
907C23C4×D4×C11314yes—
908C23C4×D4×C11314yes—
909C23C4×D4×C11318yescomplemented
910C23#120×C11314yes—
911C23#121×C11314yes—
912C23#121×C11314yes—
913C23#123×C11314yes—
914C23C23×C4×C11311yescharacteristic
915C23C22×D4×C11311yescharacteristic
916C23C22×D4×C11311yescharacteristic
917C23C22×D4×C11311yescharacteristic
918C23C22×D4×C11311yescharacteristic
919C23C22×D4×C11312yes—
920C23C2×#41×C11311yescharacteristic
921C23C2×#41×C11311yescharacteristic
922C23C2×#41×C11312yes—
923C23H(5,𝔽2)×C11312yes—
924C23H(5,𝔽2)×C11312yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C11314yescomplemented
977C2×C4#120×C11314yescomplemented
978C22—24no—
979C22—24no—
980C22—24no—
981C22—28no—
982C22—28no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—28no—
987C22—28no—
988C22—24no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—42no—
996C22—44no—
997C22—42no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—42no—
1004C22—44no—
1005C22—44no—
1006C22—42no—
1007C22—44no—
1008C22—42no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22#386×C11318yescomplemented
1016C22C22×C22⋊C4×C11311yescharacteristic
1017C22C2×C4×D4×C11311yescharacteristic
1018C22C2×C4×D4×C11311yescharacteristic
1019C22C2×C4×D4×C11312yes—
1020C22#518×C11312yes—
1021C22C2×#120×C11311yescharacteristic
1022C22C2×#120×C11311yescharacteristic
1023C22C2×#121×C11311yescharacteristic
1024C22C2×#121×C11311yescharacteristic
1025C22C2×#123×C11311yescharacteristic
1026C22#525×C11311yescharacteristic
1027C22#525×C11312yes—
1028C22#534×C11311yescharacteristic
1029C22#535×C11311yescharacteristic
1030C22#538×C11312yes—
1031C22D42×C11312yes—
1032C22D42×C11312yes—
1033C22D42×C11312yes—
1034C22#546×C11312yes—
1035C22#546×C11312yes—
1036C22#546×C11312yes—
1037C22#546×C11312yes—
1038C22#551×C11312yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×#386×C11311yescharacteristic
1051C2C4×#120×C11311yescharacteristic
1052C2C113×#232111yescharacteristic
1053C2D4×C22⋊C4×C11312yes—
1054C2C113×#235812yes—
1055C2C113×#240311yescharacteristic
1056C2C113×#240411yescharacteristic
1057C2C113×#240811yescharacteristic
1058C2C113×#241812yes—
1059C2C113×#242412yes—
1060C2C113×#253411yescharacteristic
subgroupG/H
center, socleC24×C113C24
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
prime radicalC22×#120×C113C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C113C2semidirect
3. C23×C22⋊C4×C113C2semidirect
4. C2×#386×C113C2semidirect
5. C2×#386×C113C2semidirect
6. C2×#379×C113C2semidirect
7. C113×#1439C2semidirect
8. C113×#1438C2semidirect
9. C113×#1437C2semidirect
10. C113×C22⋊#95C2semidirect
11. C113×C22⋊#95C2semidirect
17. C24×C4×C113C22semidirect
20. C2×#120×C113C4semidirect
24. C22×C4⋊C4×C113C22semidirect
35. C22×C22⋊C4×C113C22semidirect
36. C22×C22⋊C4×C113C22semidirect
37. C22×C42×C113C22semidirect
41. C2×#95×C113C22semidirect
42. C2×#95×C113C22semidirect
43. C2×#95×C113C22semidirect
44. C2×#95×C113C22semidirect
45. C2×#95×C113C22semidirect
56. C25×C113C2×C4semidirect
71. C22×D4×C113C2×C4semidirect
88. C23×C4×C113D4semidirect
129. C2×C22⋊C4×C113C2×C4semidirect
130. C2×C22⋊C4×C113C2×C4semidirect
131. C2×C22⋊C4×C113D4semidirect
132. C2×C22⋊C4×C113D4semidirect
215. C2×D4×C113C22⋊C4semidirect
375. C23×C113C2×C22⋊C4semidirect
378. C23×C113C4×D4semidirect
445. C2×C4×C113C2×C22⋊C4semidirect
446. C2×C4×C113#120semidirect
484. C22×C113#386semidirect
516. #13967C113direct (N × H)
532. C22×C4×D4C2×C113semidirect
533. C23×C22⋊C4C2×C113semidirect
534. C2×#386C2×C113semidirect
535. C2×#386C2×C113semidirect
536. C2×#379C2×C113semidirect
537. #1439C2×C113semidirect
538. #1438C2×C113semidirect
539. #1437C2×C113semidirect
540. C22⋊#95C2×C113semidirect
541. C22⋊#95C2×C113semidirect
542. C113#13967direct (N × H)
548. C24×C4C22×C113semidirect
551. C2×#120C4×C113semidirect
555. C22×C4⋊C4C22×C113semidirect
566. C22×C22⋊C4C22×C113semidirect
567. C22×C22⋊C4C22×C113semidirect
568. C22×C42C22×C113semidirect
572. C2×#95C22×C113semidirect
573. C2×#95C22×C113semidirect
574. C2×#95C22×C113semidirect
575. C2×#95C22×C113semidirect
576. C2×#95C22×C113semidirect
587. C25C2×C4×C113semidirect
602. C22×D4C2×C4×C113semidirect
619. C23×C4D4×C113semidirect
660. C2×C22⋊C4C2×C4×C113semidirect
661. C2×C22⋊C4C2×C4×C113semidirect
662. C2×C22⋊C4D4×C113semidirect
663. C2×C22⋊C4D4×C113semidirect
746. C2×D4C22⋊C4×C113semidirect
906. C23C2×C22⋊C4×C113semidirect
909. C23C4×D4×C113semidirect
976. C2×C4C2×C22⋊C4×C113semidirect
977. C2×C4#120×C113semidirect
1015. C22#386×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1132
C22×C4×D4×C1132
C23×C22⋊C4×C1132
C2×#386×C1132
C2×#379×C1132
C113×#14392
C113×#14382
C113×#14372
C113×C22⋊#952
#13967113