Finite Group Databasebeta

← C113×#16260 #43284280

Subgroups — C113×#16260 #43284280

Order 28928.

2790 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C113C211yesmaximal, characteristic, complemented
2C2×#394×C113C212yesmaximal, complemented
3C2×#392×C113C211yesmaximal, characteristic, complemented
4C2×#392×C113C212yesmaximal, complemented
5C2×#386×C113C211yesmaximal, characteristic, complemented
6C2×#380×C113C211yesmaximal, characteristic, complemented
7C113×#1442C211yesmaximal, characteristic, complemented
8C113×#1439C211yesmaximal, characteristic, complemented
9C113×#1439C212yesmaximal, complemented
10C113×#1438C212yesmaximal, complemented
11C113×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C113C2212yes—
13C23×D4×C113C2211yescharacteristic
14C23×D4×C113C2212yes—
15C23×D4×C113C2211yescharacteristic
16C24×C4×C113C2211yescharacteristic
17C2×#121×C113—24no—
18C2×#121×C113—28no—
19C22×C4⋊C4×C113C2211yescharacteristic
20C22×C4⋊C4×C113C2212yes—
21C22×C22⋊C4×C113C2211yescharacteristic
22C22×C22⋊C4×C113C2211yescharacteristic
23C22×C22⋊C4×C113C2212yes—
24C22×C22⋊C4×C113C2212yes—
25C22×C22⋊C4×C113C2212yes—
26C22×C22⋊C4×C113C2211yescharacteristic
27C22×C22⋊C4×C113C2212yes—
28C22×C22⋊C4×C113C2212yes—
29C22×C22⋊C4×C113C2212yes—
30#394×C113—28no—
31#392×C113—28no—
32#392×C113—24no—
33#386×C113—24no—
34#380×C113—24no—
35C2×#95×C113C2211yescharacteristic
36C2×#95×C113C2211yescharacteristic
37C2×#95×C113C2211yescharacteristic
38C2×#95×C113C2212yes—
39C2×#95×C113C2212yes—
40C2×#95×C113C2212yes—
41C2×#95×C113C2211yescharacteristic
42C25×C113C2311yescharacteristic
43C25×C113C2312yes—
44C25×C113C2311yescharacteristic
45C22×D4×C113—24no—
46C22×D4×C113—24no—
47C22×D4×C113—24no—
48C22×D4×C113—22no—
49C22×D4×C113—22no—
50C22×D4×C113—24no—
51C22×D4×C113—24no—
52C22×D4×C113—24no—
53C22×D4×C113—24no—
54C22×D4×C113—24no—
55C22×D4×C113—22no—
56C22×D4×C113—24no—
57C22×D4×C113—22no—
58C22×D4×C113—22no—
59C22×D4×C113—42no—
60C22×D4×C113—42no—
61C22×D4×C113—42no—
62C22×D4×C113—42no—
63C22×D4×C113—42no—
64C22×D4×C113—42no—
65C22×D4×C113—42no—
66C22×D4×C113—42no—
67C22×D4×C113—42no—
68C22×D4×C113D414yescomplemented
69C23×C4×C113—24no—
70C23×C4×C113—22no—
71C23×C4×C113—22no—
72C23×C4×C113—42no—
73C23×C4×C113D414yescomplemented
74C23×C4×C113C2312yes—
75C23×C4×C113C2311yescharacteristic
76C23×C4×C113C2311yescharacteristic
77C23×C4×C113C2312yes—
78C23×C4×C113C2312yes—
79C23×C4×C113C2311yescharacteristic
80C23×C4×C113C2311yescharacteristic
81C23×C4×C113C2311yescharacteristic
82#121×C113—232no—
83C2×C4⋊C4×C113—24no—
84C2×C4⋊C4×C113—22no—
85C2×C4⋊C4×C113—24no—
86C2×C4⋊C4×C113—24no—
87C2×C4⋊C4×C113—42no—
88C2×C22⋊C4×C113—24no—
89C2×C22⋊C4×C113—24no—
90C2×C22⋊C4×C113—22no—
91C2×C22⋊C4×C113—24no—
92C2×C22⋊C4×C113—24no—
93C2×C22⋊C4×C113—24no—
94C2×C22⋊C4×C113—24no—
95C2×C22⋊C4×C113—22no—
96C2×C22⋊C4×C113—22no—
97C2×C22⋊C4×C113—24no—
98C2×C22⋊C4×C113—24no—
99C2×C22⋊C4×C113—22no—
100C2×C22⋊C4×C113—24no—
101C2×C22⋊C4×C113—24no—
102C2×C22⋊C4×C113—22no—
103C2×C22⋊C4×C113—42no—
104C2×C22⋊C4×C113—42no—
105C2×C22⋊C4×C113—42no—
106C2×C22⋊C4×C113—42no—
107C2×C22⋊C4×C113—42no—
108C2×C22⋊C4×C113—42no—
109C2×C22⋊C4×C113—42no—
110C2×C22⋊C4×C113—42no—
111C2×C22⋊C4×C113—42no—
112C2×C22⋊C4×C113D418yescomplemented
113#95×C113—22no—
114#95×C113—22no—
115#95×C113—22no—
116#95×C113—24no—
117#95×C113—24no—
118#95×C113—42no—
119#95×C113D414yescomplemented
120C24×C113—21no—
121C24×C113—22no—
122C24×C113—21no—
123C24×C113—21no—
124C24×C113—22no—
125C24×C113—22no—
126C24×C113—22no—
127C24×C113—21no—
128C24×C113—21no—
129C24×C113—22no—
130C24×C113—22no—
131C24×C113—22no—
132C24×C113—21no—
133C24×C113—22no—
134C24×C113—22no—
135C24×C113—21no—
136C24×C113—21no—
137C24×C113—22no—
138C24×C113—22no—
139C24×C113—22no—
140C24×C113—22no—
141C24×C113—22no—
142C24×C113—22no—
143C24×C113—22no—
144C24×C113—22no—
145C24×C113—22no—
146C24×C113—22no—
147C24×C113—22no—
148C24×C113—21no—
149C24×C113—22no—
150C24×C113—22no—
151C24×C113—21no—
152C24×C113C2×D412yes—
153C24×C113C2×D414yes—
154C24×C113C2×D412yes—
155C24×C113C2×D412yes—
156C24×C113#4112yes—
157C24×C113C2411yescharacteristic
158C2×D4×C113—28no—
159C2×D4×C113—216no—
160C2×D4×C113—28no—
161C2×D4×C113—48no—
162C2×D4×C113—48no—
163C2×D4×C113—48no—
164C2×D4×C113—48no—
165C2×D4×C113—48no—
166C2×D4×C113—48no—
167C2×D4×C113—48no—
168C2×D4×C113—44no—
169C2×D4×C113—48no—
170C2×D4×C113—48no—
171C2×D4×C113—48no—
172C2×D4×C113—48no—
173C2×D4×C113—44no—
174C2×D4×C113—48no—
175C2×D4×C113—44no—
176C2×D4×C113—48no—
177C2×D4×C113—48no—
178C2×D4×C113—48no—
179C2×D4×C113—48no—
180C2×D4×C113—48no—
181C2×D4×C113—44no—
182C22×C4×C113—21no—
183C22×C4×C113—22no—
184C22×C4×C113—21no—
185C22×C4×C113—22no—
186C22×C4×C113—22no—
187C22×C4×C113—21no—
188C22×C4×C113—22no—
189C22×C4×C113—22no—
190C22×C4×C113—22no—
191C22×C4×C113—22no—
192C22×C4×C113—22no—
193C22×C4×C113—21no—
194C22×C4×C113—22no—
195C22×C4×C113—22no—
196C22×C4×C113—22no—
197C22×C4×C113—22no—
198C22×C4×C113—22no—
199C22×C4×C113—22no—
200C22×C4×C113—22no—
201C22×C4×C113—22no—
202C22×C4×C113—22no—
203C22×C4×C113—28no—
204C22×C4×C113—28no—
205C22×C4×C113—21no—
206C22×C4×C113—22no—
207C22×C4×C113—21no—
208C22×C4×C113—22no—
209C22×C4×C113—21no—
210C22×C4×C113—22no—
211C22×C4×C113—22no—
212C22×C4×C113—21no—
213C22×C4×C113—22no—
214C22×C4×C113—22no—
215C22×C4×C113—22no—
216C22×C4×C113—22no—
217C22×C4×C113—21no—
218C22×C4×C113—22no—
219C22×C4×C113—22no—
220C22×C4×C113—22no—
221C22×C4×C113—21no—
222C22×C4×C113—44no—
223C22×C4×C113—48no—
224C22×C4×C113—48no—
225C22×C4×C113C2×D412yes—
226C22×C4×C113C2×D414yes—
227C22×C4×C113C2×D414yes—
228C22×C4×C113C2×D412yes—
229C22×C4×C113C2×D414yes—
230C22×C4×C113C2×D412yes—
231C22×C4×C113C2×D412yes—
232C22×C4×C113#4112yes—
233C4⋊C4×C113—28no—
234C4⋊C4×C113—48no—
235C22⋊C4×C113—216no—
236C22⋊C4×C113—48no—
237C22⋊C4×C113—48no—
238C22⋊C4×C113—48no—
239C22⋊C4×C113—48no—
240C22⋊C4×C113—44no—
241C22⋊C4×C113—48no—
242C22⋊C4×C113—44no—
243C22⋊C4×C113—44no—
244C23×C113—22no—
245C23×C113—22no—
246C23×C113—22no—
247C23×C113—24no—
248C23×C113—22no—
249C23×C113—22no—
250C23×C113—22no—
251C23×C113—24no—
252C23×C113—22no—
253C23×C113—24no—
254C23×C113—24no—
255C23×C113—22no—
256C23×C113—22no—
257C23×C113—22no—
258C23×C113—24no—
259C23×C113—22no—
260C23×C113—24no—
261C23×C113—24no—
262C23×C113—24no—
263C23×C113—24no—
264C23×C113—24no—
265C23×C113—24no—
266C23×C113—22no—
267C23×C113—24no—
268C23×C113—24no—
269C23×C113—22no—
270C23×C113—42no—
271C23×C113—42no—
272C23×C113—42no—
273C23×C113—42no—
274C23×C113—42no—
275C23×C113—42no—
276C23×C113—42no—
277C23×C113—42no—
278C23×C113—41no—
279C23×C113—41no—
280C23×C113—42no—
281C23×C113—42no—
282C23×C113—42no—
283C23×C113—41no—
284C23×C113—42no—
285C23×C113—42no—
286C23×C113—42no—
287C23×C113—41no—
288C23×C113—42no—
289C23×C113—42no—
290C23×C113—42no—
291C23×C113—42no—
292C23×C113—42no—
293C23×C113—42no—
294C23×C113—41no—
295C23×C113—42no—
296C23×C113—42no—
297C23×C113—42no—
298C23×C113—41no—
299C23×C113—42no—
300C23×C113—42no—
301C23×C113—42no—
302C23×C113—42no—
303C23×C113—42no—
304C23×C113—42no—
305C23×C113—42no—
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—41no—
315C23×C113—42no—
316C23×C113—41no—
317C23×C113—42no—
318C23×C113—42no—
319C23×C113—42no—
320C23×C113—42no—
321C23×C113—42no—
322C23×C113—42no—
323C23×C113—42no—
324C23×C113#12114yes—
325C23×C113C22×D411yescharacteristic
326C23×C113C22×D412yes—
327C23×C113C22×D411yescharacteristic
328C23×C113C22×D411yescharacteristic
329C23×C113C2×#4111yescharacteristic
330C23×C113C2×#4111yescharacteristic
331C23×C113H(5,𝔽2)12yes—
332C23×C113H(5,𝔽2)12yes—
333C23×C113H(5,𝔽2)11yescharacteristic
334C23×C113H(5,𝔽2)12yes—
335C23×C1132−1+411yescharacteristic
336D4×C113—416no—
337D4×C113—416no—
338D4×C113—432no—
339D4×C113—432no—
340C2×C4×C113—22no—
341C2×C4×C113—22no—
342C2×C4×C113—22no—
343C2×C4×C113—22no—
344C2×C4×C113—24no—
345C2×C4×C113—24no—
346C2×C4×C113—24no—
347C2×C4×C113—24no—
348C2×C4×C113—24no—
349C2×C4×C113—22no—
350C2×C4×C113—24no—
351C2×C4×C113—24no—
352C2×C4×C113—24no—
353C2×C4×C113—24no—
354C2×C4×C113—24no—
355C2×C4×C113—24no—
356C2×C4×C113—416no—
357C2×C4×C113—42no—
358C2×C4×C113—41no—
359C2×C4×C113—42no—
360C2×C4×C113—41no—
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—41no—
369C2×C4×C113—41no—
370C2×C4×C113—42no—
371C2×C4×C113—41no—
372C2×C4×C113—42no—
373C2×C4×C113—41no—
374C2×C4×C113—42no—
375C2×C4×C113—42no—
376C2×C4×C113—41no—
377C2×C4×C113—42no—
378C2×C4×C113—42no—
379C2×C4×C113—41no—
380C2×C4×C113—42no—
381C2×C4×C113—42no—
382C2×C4×C113—42no—
383C2×C4×C113—42no—
384C2×C4×C113—42no—
385C2×C4×C113#12014yes—
386C2×C4×C113#12114yes—
387C22×C113—24no—
388C22×C113—24no—
389C22×C113—24no—
390C22×C113—42no—
391C22×C113—42no—
392C22×C113—42no—
393C22×C113—44no—
394C22×C113—44no—
395C22×C113—44no—
396C22×C113—44no—
397C22×C113—42no—
398C22×C113—44no—
399C22×C113—42no—
400C22×C113—44no—
401C22×C113—42no—
402C22×C113—44no—
403C22×C113—44no—
404C22×C113—44no—
405C22×C113—44no—
406C22×C113—44no—
407C22×C113—42no—
408C22×C113—44no—
409C22×C113—44no—
410C22×C113—81no—
411C22×C113—82no—
412C22×C113—81no—
413C22×C113—82no—
414C22×C113—81no—
415C22×C113—82no—
416C22×C113—82no—
417C22×C113—82no—
418C22×C113—82no—
419C22×C113—82no—
420C22×C113—82no—
421C22×C113—82no—
422C22×C113—82no—
423C22×C113—81no—
424C22×C113C2×#12011yescharacteristic
425C22×C113C2×#12111yescharacteristic
426C22×C113C2×#12111yescharacteristic
427C22×C113#53411yescharacteristic
428C22×C113#53412yes—
429C22×C113#53511yescharacteristic
430C22×C113#53512yes—
431C22×C113#53511yescharacteristic
432C22×C113#53512yes—
433C22×C113#53712yes—
434C22×C113#53711yescharacteristic
435C22×C113#53812yes—
436C22×C113#54012yes—
437C22×C113D4212yes—
438C22×C113D4212yes—
439C22×C113D4211yescharacteristic
440C22×C113#54612yes—
441C22×C113#54612yes—
442C22×C113#54711yescharacteristic
443C22×C113#54811yescharacteristic
444C22×C113#55311yescharacteristic
445C22×C113#56012yes—
446C22×C113#56212yes—
447C4×C113—24no—
448C4×C113—24no—
449C4×C113—42no—
450C4×C113—44no—
451C4×C113—44no—
452C4×C113—81no—
453C4×C113—81no—
454C4×C113—82no—
455#16260C11311yesmaximal, characteristic, direct product factor, Sylow
456C2×C113—44no—
457C2×C113—84no—
458C2×C113—82no—
459C2×C113#240811yescharacteristic
460C2×C113#241011yescharacteristic
461C2×C113#241611yescharacteristic
462C2×C113#261511yescharacteristic
463C2×C113#261711yescharacteristic
464C2×C113#261911yescharacteristic
465C2×C113#266912yes—
466C2×C113#267112yes—
467C2×C113#267612yes—
468C2×C113#270312yes—
469C2×C113#281311yescharacteristic
470C22×#121C2×C11311yescharacteristic, complemented
471C2×#394C2×C11312yescomplemented
472C2×#392C2×C11311yescharacteristic, complemented
473C2×#392C2×C11312yescomplemented
474C2×#386C2×C11311yescharacteristic, complemented
475C2×#380C2×C11311yescharacteristic, complemented
476#1442C2×C11311yescharacteristic, complemented
477#1439C2×C11311yescharacteristic, complemented
478#1439C2×C11312yescomplemented
479#1438C2×C11312yescomplemented
480#1438C2×C11311yescharacteristic, complemented
481C113#1626011yescharacteristic, direct product factor, Sylow
482C23×D4C22×C11312yes—
483C23×D4C22×C11311yescharacteristic
484C23×D4C22×C11312yes—
485C23×D4C22×C11311yescharacteristic
486C24×C4C22×C11311yescharacteristic
487C2×#121—24no—
488C2×#121—28no—
489C22×C4⋊C4C22×C11311yescharacteristic
490C22×C4⋊C4C22×C11312yes—
491C22×C22⋊C4C22×C11311yescharacteristic
492C22×C22⋊C4C22×C11311yescharacteristic
493C22×C22⋊C4C22×C11312yes—
494C22×C22⋊C4C22×C11312yes—
495C22×C22⋊C4C22×C11312yes—
496C22×C22⋊C4C22×C11312yes—
497C22×C22⋊C4C22×C11312yes—
498C22×C22⋊C4C22×C11312yes—
499C22×C22⋊C4C22×C11311yescharacteristic
500#394—28no—
501#392—28no—
502#392—24no—
503#386—24no—
504#380—24no—
505C2×#95C22×C11312yes—
506C2×#95C22×C11312yes—
507C2×#95C22×C11311yescharacteristic
508C2×#95C22×C11311yescharacteristic
509C2×#95C22×C11311yescharacteristic
510C2×#95C22×C11312yes—
511C2×#95C22×C11311yescharacteristic
512C25C23×C11311yescharacteristic
513C25C23×C11312yes—
514C25C23×C11311yescharacteristic
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—24no—
525C22×D4—22no—
526C22×D4—24no—
527C22×D4—22no—
528C22×D4—22no—
529C22×D4—42no—
530C22×D4—42no—
531C22×D4—42no—
532C22×D4—42no—
533C22×D4—42no—
534C22×D4—42no—
535C22×D4—42no—
536C22×D4—42no—
537C22×D4—42no—
538C22×D4D4×C11314yescomplemented
539C23×C4—24no—
540C23×C4—22no—
541C23×C4—22no—
542C23×C4—42no—
543C23×C4D4×C11314yescomplemented
544C23×C4C23×C11312yes—
545C23×C4C23×C11311yescharacteristic
546C23×C4C23×C11311yescharacteristic
547C23×C4C23×C11312yes—
548C23×C4C23×C11312yes—
549C23×C4C23×C11311yescharacteristic
550C23×C4C23×C11311yescharacteristic
551C23×C4C23×C11311yescharacteristic
552#121—232no—
553C2×C4⋊C4—24no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—42no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4D4×C11318yescomplemented
583#95—22no—
584#95—22no—
585#95—22no—
586#95—24no—
587#95—24no—
588#95—42no—
589#95D4×C11314yescomplemented
590C24—21no—
591C24—22no—
592C24—21no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—21no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—21no—
603C24—22no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—21no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24C2×D4×C11312yes—
623C24C2×D4×C11314yes—
624C24C2×D4×C11312yes—
625C24C2×D4×C11312yes—
626C24#41×C11312yes—
627C24C24×C11311yescharacteristic
628C2×D4—28no—
629C2×D4—216no—
630C2×D4—28no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—48no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—44no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—44no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—48no—
647C2×D4—48no—
648C2×D4—48no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—44no—
652C22×C4—21no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
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—21no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—44no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C2×D4×C11312yes—
696C22×C4C2×D4×C11314yes—
697C22×C4C2×D4×C11314yes—
698C22×C4C2×D4×C11312yes—
699C22×C4C2×D4×C11314yes—
700C22×C4C2×D4×C11312yes—
701C22×C4C2×D4×C11312yes—
702C22×C4#41×C11312yes—
703C4⋊C4—28no—
704C4⋊C4—48no—
705C22⋊C4—216no—
706C22⋊C4—48no—
707C22⋊C4—48no—
708C22⋊C4—48no—
709C22⋊C4—48no—
710C22⋊C4—44no—
711C22⋊C4—48no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—22no—
723C23—24no—
724C23—24no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—41no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—41no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—41no—
785C23—42no—
786C23—41no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23#121×C11314yes—
795C23C22×D4×C11311yescharacteristic
796C23C22×D4×C11312yes—
797C23C22×D4×C11311yescharacteristic
798C23C22×D4×C11311yescharacteristic
799C23C2×#41×C11311yescharacteristic
800C23C2×#41×C11311yescharacteristic
801C23H(5,𝔽2)×C11312yes—
802C23H(5,𝔽2)×C11312yes—
803C23H(5,𝔽2)×C11311yescharacteristic
804C23H(5,𝔽2)×C11312yes—
805C232−1+4×C11311yescharacteristic
806D4—416no—
807D4—416no—
808D4—432no—
809D4—432no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—416no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4#120×C11314yes—
856C2×C4#121×C11314yes—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—42no—
870C22—44no—
871C22—42no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—44no—
879C22—44no—
880C22—82no—
881C22—81no—
882C22—81no—
883C22—82no—
884C22—81no—
885C22—82no—
886C22—81no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22C2×#120×C11311yescharacteristic
895C22C2×#121×C11311yescharacteristic
896C22C2×#121×C11311yescharacteristic
897C22#534×C11311yescharacteristic
898C22#534×C11312yes—
899C22#535×C11311yescharacteristic
900C22#535×C11311yescharacteristic
901C22#535×C11312yes—
902C22#535×C11312yes—
903C22#537×C11311yescharacteristic
904C22#537×C11312yes—
905C22#538×C11312yes—
906C22#540×C11312yes—
907C22D42×C11312yes—
908C22D42×C11312yes—
909C22D42×C11311yescharacteristic
910C22#546×C11312yes—
911C22#546×C11312yes—
912C22#547×C11311yescharacteristic
913C22#548×C11311yescharacteristic
914C22#553×C11311yescharacteristic
915C22#560×C11312yes—
916C22#562×C11312yes—
917C4—24no—
918C4—24no—
919C4—42no—
920C4—44no—
921C4—44no—
922C4—81no—
923C4—81no—
924C4—82no—
925C2—44no—
926C2—84no—
927C2—82no—
928C2C113×#240811yescharacteristic
929C2C113×#241011yescharacteristic
930C2C113×#241611yescharacteristic
931C2C113×#261511yescharacteristic
932C2C113×#261711yescharacteristic
933C2C113×#261911yescharacteristic
934C2C113×#266912yes—
935C2C113×#267112yes—
936C2C113×#267612yes—
937C2C113×#270312yes—
938C2C113×#281311yescharacteristic
subgroupG/H
center, socleC24×C113C24
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C113C2semidirect
2. C2×#394×C113C2semidirect
3. C2×#392×C113C2semidirect
4. C2×#392×C113C2semidirect
5. C2×#386×C113C2semidirect
6. C2×#380×C113C2semidirect
7. C113×#1442C2semidirect
8. C113×#1439C2semidirect
9. C113×#1439C2semidirect
10. C113×#1438C2semidirect
11. C113×#1438C2semidirect
68. C22×D4×C113D4semidirect
73. C23×C4×C113D4semidirect
112. C2×C22⋊C4×C113D4semidirect
119. #95×C113D4semidirect
455. #16260C113direct (N × H)
470. C22×#121C2×C113semidirect
471. C2×#394C2×C113semidirect
472. C2×#392C2×C113semidirect
473. C2×#392C2×C113semidirect
474. C2×#386C2×C113semidirect
475. C2×#380C2×C113semidirect
476. #1442C2×C113semidirect
477. #1439C2×C113semidirect
478. #1439C2×C113semidirect
479. #1438C2×C113semidirect
480. #1438C2×C113semidirect
481. C113#16260direct (N × H)
538. C22×D4D4×C113semidirect
543. C23×C4D4×C113semidirect
582. C2×C22⋊C4D4×C113semidirect
589. #95D4×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1132
C2×#394×C1132
C2×#392×C1132
C2×#386×C1132
C2×#380×C1132
C113×#14422
C113×#14392
C113×#14382
#16260113