Finite Group Databasebeta

← C113×#13996 #43282016

Subgroups — C113×#13996 #43282016

Order 28928.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C113C211yesmaximal, characteristic
2C2×#386×C113C211yesmaximal, characteristic
3C2×#386×C113C211yesmaximal, characteristic
4C2×#385×C113C211yesmaximal, characteristic, complemented
5C2×#381×C113C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
7C22×#95×C113C211yesmaximal, characteristic, complemented
8C113×#1445C212yesmaximal, complemented
9C113×#1439C212yesmaximal, complemented
10C113×#1437C212yesmaximal, complemented
11C113×C4⋊#95C212yesmaximal, complemented
12C23×D4×C113C2211yescharacteristic
13C24×C4×C113C2211yescharacteristic
14C24×C4×C113C2211yescharacteristic
15C24×C4×C113C2211yescharacteristic
16C2×#123×C113—24no—
17C2×#123×C113—24no—
18C2×#123×C113C418yescomplemented
19C22×C4⋊C4×C113C2212yes—
20C22×C4⋊C4×C113C2212yes—
21C22×C22⋊C4×C113C2211yescharacteristic
22C22×C22⋊C4×C113C2211yescharacteristic
23C22×C22⋊C4×C113C2212yes—
24C22×C22⋊C4×C113C2212yes—
25C22×C22⋊C4×C113C2211yescharacteristic
26C22×C22⋊C4×C113C2211yescharacteristic
27C22×C22⋊C4×C113C2211yescharacteristic
28C22×C42×C113C2212yes—
29#386×C113—24no—
30#386×C113—24no—
31#385×C113—24no—
32#381×C113—24no—
33C4×C22⋊C4×C113—24no—
34C2×#95×C113—24no—
35C2×#95×C113C2212yes—
36C2×#95×C113C2212yes—
37C2×#95×C113C2212yes—
38C2×#95×C113C2211yescharacteristic
39C2×#95×C113C2212yes—
40C2×#95×C113C2211yescharacteristic
41C2×#95×C113C2212yes—
42C2×#95×C113C2212yes—
43C2×#95×C113C2212yes—
44C25×C113C2311yescharacteristic
45C25×C113C2311yescharacteristic
46C22×D4×C113—22no—
47C22×D4×C113—22no—
48C22×D4×C113—22no—
49C22×D4×C113—22no—
50C22×D4×C113—22no—
51C22×D4×C113—22no—
52C22×D4×C113C2×C414yes—
53C23×C4×C113—22no—
54C23×C4×C113—22no—
55C23×C4×C113—22no—
56C23×C4×C113—22no—
57C23×C4×C113—22no—
58C23×C4×C113—22no—
59C23×C4×C113—22no—
60C23×C4×C113—22no—
61C23×C4×C113—22no—
62C23×C4×C113—24no—
63C23×C4×C113—24no—
64C23×C4×C113—22no—
65C23×C4×C113—22no—
66C23×C4×C113—42no—
67C23×C4×C113—42no—
68C23×C4×C113C2×C414yes—
69C23×C4×C113D414yes—
70C23×C4×C113C2311yescharacteristic
71C23×C4×C113C2311yescharacteristic
72C23×C4×C113C2312yes—
73C23×C4×C113C2311yescharacteristic
74C23×C4×C113C2312yes—
75C23×C4×C113C2311yescharacteristic
76C23×C4×C113C2312yes—
77C23×C4×C113C2312yes—
78C23×C4×C113C2311yescharacteristic
79#123×C113—232no—
80C2×C4⋊C4×C113—24no—
81C2×C4⋊C4×C113—24no—
82C2×C4⋊C4×C113—24no—
83C2×C4⋊C4×C113—24no—
84C2×C4⋊C4×C113—42no—
85C2×C4⋊C4×C113C2×C418yescomplemented
86C2×C22⋊C4×C113—22no—
87C2×C22⋊C4×C113—22no—
88C2×C22⋊C4×C113—24no—
89C2×C22⋊C4×C113—24no—
90C2×C22⋊C4×C113—22no—
91C2×C22⋊C4×C113—22no—
92C2×C22⋊C4×C113—22no—
93C2×C22⋊C4×C113—24no—
94C2×C22⋊C4×C113—22no—
95C2×C22⋊C4×C113—22no—
96C2×C22⋊C4×C113—24no—
97C2×C22⋊C4×C113—24no—
98C2×C22⋊C4×C113—42no—
99C2×C22⋊C4×C113—42no—
100C2×C22⋊C4×C113C2×C414yes—
101C2×C22⋊C4×C113C2×C418yescomplemented
102C2×C22⋊C4×C113D414yes—
103C2×C22⋊C4×C113D414yes—
104C2×C22⋊C4×C113D414yes—
105C2×C42×C113—24no—
106C2×C42×C113—24no—
107C2×C42×C113—42no—
108#95×C113—24no—
109#95×C113—24no—
110#95×C113—24no—
111#95×C113—24no—
112#95×C113—24no—
113#95×C113—24no—
114#95×C113—24no—
115#95×C113—22no—
116#95×C113—22no—
117C24×C113—22no—
118C24×C113—22no—
119C24×C113—22no—
120C24×C113—22no—
121C24×C113—21no—
122C24×C113—21no—
123C24×C113—21no—
124C24×C113—21no—
125C24×C113—22no—
126C24×C113—22no—
127C24×C113—21no—
128C24×C113—21no—
129C24×C113—22no—
130C24×C113—22no—
131C24×C113C22×C412yes—
132C24×C113C22×C412yes—
133C24×C113C2×D412yes—
134C24×C113C2×D412yes—
135C24×C113C2×D412yes—
136C24×C113C2×D412yes—
137C24×C113#4112yes—
138C24×C113#4112yes—
139C24×C113C2411yescharacteristic
140C2×D4×C113—28no—
141C2×D4×C113—28no—
142C2×D4×C113—28no—
143C2×D4×C113—44no—
144C2×D4×C113—44no—
145C2×D4×C113—44no—
146C2×D4×C113—44no—
147C22×C4×C113—21no—
148C22×C4×C113—22no—
149C22×C4×C113—22no—
150C22×C4×C113—21no—
151C22×C4×C113—22no—
152C22×C4×C113—22no—
153C22×C4×C113—22no—
154C22×C4×C113—28no—
155C22×C4×C113—28no—
156C22×C4×C113—28no—
157C22×C4×C113—28no—
158C22×C4×C113—28no—
159C22×C4×C113—22no—
160C22×C4×C113—22no—
161C22×C4×C113—21no—
162C22×C4×C113—22no—
163C22×C4×C113—21no—
164C22×C4×C113—21no—
165C22×C4×C113—22no—
166C22×C4×C113—22no—
167C22×C4×C113—22no—
168C22×C4×C113—22no—
169C22×C4×C113—22no—
170C22×C4×C113—21no—
171C22×C4×C113—21no—
172C22×C4×C113—22no—
173C22×C4×C113—22no—
174C22×C4×C113—22no—
175C22×C4×C113—22no—
176C22×C4×C113—22no—
177C22×C4×C113—21no—
178C22×C4×C113—22no—
179C22×C4×C113—22no—
180C22×C4×C113—21no—
181C22×C4×C113—21no—
182C22×C4×C113—22no—
183C22×C4×C113—22no—
184C22×C4×C113—22no—
185C22×C4×C113—22no—
186C22×C4×C113—22no—
187C22×C4×C113—28no—
188C22×C4×C113—21no—
189C22×C4×C113—21no—
190C22×C4×C113—21no—
191C22×C4×C113—21no—
192C22×C4×C113—21no—
193C22×C4×C113—21no—
194C22×C4×C113—22no—
195C22×C4×C113—22no—
196C22×C4×C113—22no—
197C22×C4×C113—22no—
198C22×C4×C113—44no—
199C22×C4×C113—48no—
200C22×C4×C113—48no—
201C22×C4×C113—48no—
202C22×C4×C113—48no—
203C22×C4×C113—44no—
204C22×C4×C113—44no—
205C22×C4×C113—44no—
206C22×C4×C113—44no—
207C22×C4×C113—44no—
208C22×C4×C113—44no—
209C22×C4×C113C22×C414yes—
210C22×C4×C113C22×C412yes—
211C22×C4×C113C22×C414yes—
212C22×C4×C113C2×D414yes—
213C22×C4×C113C2×D412yes—
214C22×C4×C113C2×D414yes—
215C22×C4×C113C2×D414yes—
216C22×C4×C113C2×D412yes—
217C22×C4×C113#4114yes—
218C22×C4×C113#4114yes—
219C4⋊C4×C113—216no—
220C4⋊C4×C113—48no—
221C22⋊C4×C113—28no—
222C22⋊C4×C113—216no—
223C22⋊C4×C113—48no—
224C22⋊C4×C113—44no—
225C22⋊C4×C113—44no—
226C22⋊C4×C113—44no—
227C22⋊C4×C113C22⋊C4116yescomplemented
228C42×C113—48no—
229C23×C113—24no—
230C23×C113—24no—
231C23×C113—22no—
232C23×C113—22no—
233C23×C113—24no—
234C23×C113—22no—
235C23×C113—22no—
236C23×C113—24no—
237C23×C113—24no—
238C23×C113—24no—
239C23×C113—24no—
240C23×C113—24no—
241C23×C113—24no—
242C23×C113—24no—
243C23×C113—24no—
244C23×C113—24no—
245C23×C113—22no—
246C23×C113—22no—
247C23×C113—22no—
248C23×C113—24no—
249C23×C113—24no—
250C23×C113—41no—
251C23×C113—41no—
252C23×C113—41no—
253C23×C113—41no—
254C23×C113—41no—
255C23×C113—42no—
256C23×C113—41no—
257C23×C113—41no—
258C23×C113—41no—
259C23×C113—42no—
260C23×C113—42no—
261C23×C113—42no—
262C23×C113—42no—
263C23×C113—42no—
264C23×C113—42no—
265C23×C113—42no—
266C23×C113—42no—
267C23×C113—42no—
268C23×C113C2×C22⋊C414yes—
269C23×C113C4×D414yes—
270C23×C113C4×D414yes—
271C23×C113#12114yes—
272C23×C113#12114yes—
273C23×C113#12414yes—
274C23×C113#12714yes—
275C23×C113C23×C411yescharacteristic
276C23×C113C22×D411yescharacteristic
277C23×C113C22×D411yescharacteristic
278C23×C113C22×D411yescharacteristic
279C23×C113C22×D411yescharacteristic
280C23×C113C2×#4111yescharacteristic
281C23×C113C2×#4111yescharacteristic
282C23×C113C2×#4112yes—
283C23×C113C2×#4112yes—
284C23×C113H(5,𝔽2)12yes—
285C23×C1132−1+412yes—
286D4×C113—416no—
287C2×C4×C113—24no—
288C2×C4×C113—24no—
289C2×C4×C113—22no—
290C2×C4×C113—22no—
291C2×C4×C113—24no—
292C2×C4×C113—24no—
293C2×C4×C113—24no—
294C2×C4×C113—24no—
295C2×C4×C113—24no—
296C2×C4×C113—24no—
297C2×C4×C113—24no—
298C2×C4×C113—22no—
299C2×C4×C113—24no—
300C2×C4×C113—24no—
301C2×C4×C113—22no—
302C2×C4×C113—22no—
303C2×C4×C113—24no—
304C2×C4×C113—22no—
305C2×C4×C113—22no—
306C2×C4×C113—24no—
307C2×C4×C113—22no—
308C2×C4×C113—24no—
309C2×C4×C113—24no—
310C2×C4×C113—24no—
311C2×C4×C113—24no—
312C2×C4×C113—416no—
313C2×C4×C113—416no—
314C2×C4×C113—42no—
315C2×C4×C113—42no—
316C2×C4×C113—41no—
317C2×C4×C113—41no—
318C2×C4×C113—42no—
319C2×C4×C113—41no—
320C2×C4×C113—42no—
321C2×C4×C113—42no—
322C2×C4×C113—42no—
323C2×C4×C113—41no—
324C2×C4×C113—42no—
325C2×C4×C113—42no—
326C2×C4×C113—42no—
327C2×C4×C113—42no—
328C2×C4×C113—42no—
329C2×C4×C113—42no—
330C2×C4×C113—42no—
331C2×C4×C113—42no—
332C2×C4×C113—416no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113—41no—
339C2×C4×C113—42no—
340C2×C4×C113—42no—
341C2×C4×C113—42no—
342C2×C4×C113—42no—
343C2×C4×C113C2×C22⋊C418yes—
344C2×C4×C113#12314yescomplemented
345C22×C113—24no—
346C22×C113—28no—
347C22×C113—28no—
348C22×C113—24no—
349C22×C113—24no—
350C22×C113—28no—
351C22×C113—28no—
352C22×C113—24no—
353C22×C113—24no—
354C22×C113—24no—
355C22×C113—42no—
356C22×C113—44no—
357C22×C113—44no—
358C22×C113—42no—
359C22×C113—42no—
360C22×C113—81no—
361C22×C113—81no—
362C22×C113—82no—
363C22×C113—82no—
364C22×C113—81no—
365C22×C113—81no—
366C22×C113#39018yes—
367C22×C113C22×C22⋊C411yescharacteristic
368C22×C113C2×C4×D411yescharacteristic
369C22×C113C2×C4×D411yescharacteristic
370C22×C113C4×#4112yes—
371C22×C113#52012yes—
372C22×C113C2×#12111yescharacteristic
373C22×C113C2×#12111yescharacteristic
374C22×C113C2×#12311yescharacteristic
375C22×C113#52511yescharacteristic
376C22×C113C2×#12411yescharacteristic
377C22×C113#52912yes—
378C22×C113C2×#12711yescharacteristic
379C22×C113#53411yescharacteristic
380C22×C113#53611yescharacteristic
381C22×C113#53912yes—
382C22×C113#54612yes—
383C22×C113#54612yes—
384C22×C113#54612yes—
385C22×C113#54712yes—
386C22×C113#54712yes—
387C22×C113#54712yes—
388C22×C113#55112yes—
389C22×C113#55212yes—
390C4×C113—28no—
391C4×C113—24no—
392C4×C113—42no—
393C4×C113—44no—
394C4×C113—44no—
395C4×C113—44no—
396C4×C113—42no—
397C4×C113—81no—
398C4×C113—81no—
399#13996C11311yesmaximal, characteristic, direct product factor, Sylow
400C2×C113—28no—
401C2×C113—82no—
402C2×C113C2×#39011yescharacteristic
403C2×C113C4×#12311yescharacteristic
404C2×C113#232211yescharacteristic
405C2×C113#233912yes—
406C2×C113#235912yes—
407C2×C113#241211yescharacteristic
408C2×C113#241311yescharacteristic
409C2×C113#242512yes—
410C2×C113#248812yes—
411C2×C113#250111yescharacteristic
412C2×C113#253911yescharacteristic
413C22×#123C2×C11311yescharacteristic
414C2×#386C2×C11311yescharacteristic
415C2×#386C2×C11311yescharacteristic
416C2×#385C2×C11311yescharacteristic, complemented
417C2×#381C2×C11311yescharacteristic, complemented
418C2×C4×C22⋊C4C2×C11311yescharacteristic, complemented
419C22×#95C2×C11311yescharacteristic, complemented
420#1445C2×C11312yescomplemented
421#1439C2×C11312yescomplemented
422#1437C2×C11312yescomplemented
423C4⋊#95C2×C11312yescomplemented
424C113#1399611yescharacteristic, direct product factor, Sylow
425C23×D4C22×C11311yescharacteristic
426C24×C4C22×C11311yescharacteristic
427C24×C4C22×C11311yescharacteristic
428C24×C4C22×C11311yescharacteristic
429C2×#123—24no—
430C2×#123—24no—
431C2×#123C4×C11318yescomplemented
432C22×C4⋊C4C22×C11312yes—
433C22×C4⋊C4C22×C11312yes—
434C22×C22⋊C4C22×C11311yescharacteristic
435C22×C22⋊C4C22×C11311yescharacteristic
436C22×C22⋊C4C22×C11312yes—
437C22×C22⋊C4C22×C11312yes—
438C22×C22⋊C4C22×C11311yescharacteristic
439C22×C22⋊C4C22×C11311yescharacteristic
440C22×C22⋊C4C22×C11311yescharacteristic
441C22×C42C22×C11312yes—
442#386—24no—
443#386—24no—
444#385—24no—
445#381—24no—
446C4×C22⋊C4—24no—
447C2×#95—24no—
448C2×#95C22×C11311yescharacteristic
449C2×#95C22×C11312yes—
450C2×#95C22×C11312yes—
451C2×#95C22×C11312yes—
452C2×#95C22×C11312yes—
453C2×#95C22×C11312yes—
454C2×#95C22×C11312yes—
455C2×#95C22×C11312yes—
456C2×#95C22×C11311yescharacteristic
457C25C23×C11311yescharacteristic
458C25C23×C11311yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C11314yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4C2×C4×C11314yes—
482C23×C4D4×C11314yes—
483C23×C4C23×C11311yescharacteristic
484C23×C4C23×C11311yescharacteristic
485C23×C4C23×C11312yes—
486C23×C4C23×C11311yescharacteristic
487C23×C4C23×C11312yes—
488C23×C4C23×C11311yescharacteristic
489C23×C4C23×C11312yes—
490C23×C4C23×C11312yes—
491C23×C4C23×C11311yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C11318yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C11314yes—
514C2×C22⋊C4C2×C4×C11318yescomplemented
515C2×C22⋊C4D4×C11314yes—
516C2×C22⋊C4D4×C11314yes—
517C2×C22⋊C4D4×C11314yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C11312yes—
545C24C22×C4×C11312yes—
546C24C2×D4×C11312yes—
547C24C2×D4×C11312yes—
548C24C2×D4×C11312yes—
549C24C2×D4×C11312yes—
550C24#41×C11312yes—
551C24#41×C11312yes—
552C24C24×C11311yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C11314yes—
623C22×C4C22×C4×C11312yes—
624C22×C4C22×C4×C11314yes—
625C22×C4C2×D4×C11314yes—
626C22×C4C2×D4×C11312yes—
627C22×C4C2×D4×C11314yes—
628C22×C4C2×D4×C11314yes—
629C22×C4C2×D4×C11312yes—
630C22×C4#41×C11314yes—
631C22×C4#41×C11314yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C113116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C11314yes—
682C23C4×D4×C11314yes—
683C23C4×D4×C11314yes—
684C23#121×C11314yes—
685C23#121×C11314yes—
686C23#124×C11314yes—
687C23#127×C11314yes—
688C23C23×C4×C11311yescharacteristic
689C23C22×D4×C11311yescharacteristic
690C23C22×D4×C11311yescharacteristic
691C23C22×D4×C11311yescharacteristic
692C23C22×D4×C11311yescharacteristic
693C23C2×#41×C11311yescharacteristic
694C23C2×#41×C11311yescharacteristic
695C23C2×#41×C11312yes—
696C23C2×#41×C11312yes—
697C23H(5,𝔽2)×C11312yes—
698C232−1+4×C11312yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—416no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C11318yes—
757C2×C4#123×C11314yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—28no—
766C22—28no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—82no—
777C22—82no—
778C22—81no—
779C22#390×C11318yes—
780C22C22×C22⋊C4×C11311yescharacteristic
781C22C2×C4×D4×C11311yescharacteristic
782C22C2×C4×D4×C11311yescharacteristic
783C22C4×#41×C11312yes—
784C22#520×C11312yes—
785C22C2×#121×C11311yescharacteristic
786C22C2×#121×C11311yescharacteristic
787C22C2×#123×C11311yescharacteristic
788C22#525×C11311yescharacteristic
789C22C2×#124×C11311yescharacteristic
790C22#529×C11312yes—
791C22C2×#127×C11311yescharacteristic
792C22#534×C11311yescharacteristic
793C22#536×C11311yescharacteristic
794C22#539×C11312yes—
795C22#546×C11312yes—
796C22#546×C11312yes—
797C22#546×C11312yes—
798C22#547×C11312yes—
799C22#547×C11312yes—
800C22#547×C11312yes—
801C22#551×C11312yes—
802C22#552×C11312yes—
803C4—28no—
804C4—24no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×#390×C11311yescharacteristic
815C2C4×#123×C11311yescharacteristic
816C2C113×#232211yescharacteristic
817C2C113×#233912yes—
818C2C113×#235912yes—
819C2C113×#241211yescharacteristic
820C2C113×#241311yescharacteristic
821C2C113×#242512yes—
822C2C113×#248812yes—
823C2C113×#250111yescharacteristic
824C2C113×#253911yescharacteristic
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
4. C2×#385×C113C2semidirect
5. C2×#381×C113C2semidirect
6. C2×C4×C22⋊C4×C113C2semidirect
7. C22×#95×C113C2semidirect
8. C113×#1445C2semidirect
9. C113×#1439C2semidirect
10. C113×#1437C2semidirect
11. C113×C4⋊#95C2semidirect
18. C2×#123×C113C4semidirect
85. C2×C4⋊C4×C113C2×C4semidirect
101. C2×C22⋊C4×C113C2×C4semidirect
227. C22⋊C4×C113C22⋊C4semidirect
344. C2×C4×C113#123semidirect
399. #13996C113direct (N × H)
416. C2×#385C2×C113semidirect
417. C2×#381C2×C113semidirect
418. C2×C4×C22⋊C4C2×C113semidirect
419. C22×#95C2×C113semidirect
420. #1445C2×C113semidirect
421. #1439C2×C113semidirect
422. #1437C2×C113semidirect
423. C4⋊#95C2×C113semidirect
424. C113#13996direct (N × H)
431. C2×#123C4×C113semidirect
498. C2×C4⋊C4C2×C4×C113semidirect
514. C2×C22⋊C4C2×C4×C113semidirect
640. C22⋊C4C22⋊C4×C113semidirect
757. C2×C4#123×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1132
C2×#386×C1132
C2×#385×C1132
C2×#381×C1132
C2×C4×C22⋊C4×C1132
C22×#95×C1132
C113×#14452
C113×#14392
C113×#14372
C113×C4⋊#952
#13996113