Finite Group Databasebeta

← C113×#24455 #43292475

Subgroups — C113×#24455 #43292475

Order 28928.

1480 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C113C211yesmaximal, characteristic, complemented
2C2×#469×C113C211yesmaximal, characteristic, complemented
3C2×#449×C113C211yesmaximal, characteristic, complemented
4C2×#448×C113C211yesmaximal, characteristic, complemented
5C2×#419×C113C211yesmaximal, characteristic, complemented
6C113×#2414C211yesmaximal, characteristic, complemented
7C113×#2042C211yesmaximal, characteristic, complemented
8C113×#2035C211yesmaximal, characteristic, complemented
9C113×#2012C211yesmaximal, characteristic, complemented
10C113×#2000C211yesmaximal, characteristic, complemented
11C113×#1880C211yesmaximal, characteristic, complemented
12C113×#1875C211yesmaximal, characteristic, complemented
13C113×#1870C211yesmaximal, characteristic, complemented
14C113×#1865C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×Q8×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×D8×C113C2211yescharacteristic
21C22×M16×C113C2211yescharacteristic
22#548×C113—24no—
23#548×C113—24no—
24C2×#124×C113—21no—
25C2×#124×C113C2211yescharacteristic
26C2×C22⋊Q8×C113—21no—
27C2×C22⋊Q8×C113C2211yescharacteristic
28C2×#121×C113—21no—
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic
31C2×#121×C113C2211yescharacteristic
32C2×C4×Q8×C113C2211yescharacteristic
33C2×C4×D4×C113—21no—
34C2×C4×D4×C113C2211yescharacteristic
35C2×#117×C113C2211yescharacteristic
36#469×C113—24no—
37#449×C113—24no—
38#448×C113—24no—
39C2×#106×C113C2211yescharacteristic
40#419×C113—24no—
41C2×#103×C113C2211yescharacteristic
42C2×#103×C113C2211yescharacteristic
43C2×#103×C113C2211yescharacteristic
44C2×#103×C113C2211yescharacteristic
45C2×#103×C113C2211yescharacteristic
46C2×#103×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×C22⋊C8×C113C2211yescharacteristic
52C2×C22⋊C8×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54#394×C113—21no—
55#392×C113—21no—
56#390×C113—21no—
57#390×C113C2211yescharacteristic
58#389×C113C2211yescharacteristic
59#388×C113—21no—
60#380×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic
62#340×C113C2211yescharacteristic
63#336×C113C2211yescharacteristic
64#336×C113C2211yescharacteristic
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—41no—
70C2×#41×C113—41no—
71C22×Q8×C113—21no—
72C22×Q8×C113—22no—
73C22×Q8×C113—22no—
74C22×Q8×C113—22no—
75C22×Q8×C113—41no—
76C22×Q8×C113—41no—
77C22×Q8×C113D414yescomplemented
78C22×Q8×C113C2311yescharacteristic
79C22×Q8×C113C2311yescharacteristic
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—21no—
83C22×D4×C113—21no—
84C22×D4×C113D411yescharacteristic
85C22×D4×C113C2311yescharacteristic
86C22×D4×C113C2311yescharacteristic
87C23×C4×C113—21no—
88C23×C4×C113—21no—
89C23×C4×C113C2311yescharacteristic
90C23×C4×C113C2311yescharacteristic
91C2×SD16×C113—22no—
92C2×SD16×C113—22no—
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—41no—
96C2×SD16×C113—41no—
97C2×D8×C113—22no—
98C2×D8×C113—22no—
99C2×D8×C113—41no—
100C2×M16×C113—22no—
101C2×M16×C113—22no—
102C2×M16×C113—41no—
103C22×C8×C113C2311yescharacteristic
104C22×C8×C113C2311yescharacteristic
105C22×C8×C113C2311yescharacteristic
106C22×C8×C113C2311yescharacteristic
107#124×C113—28no—
108#124×C113—22no—
109#124×C113—22no—
110C22⋊Q8×C113—28no—
111C22⋊Q8×C113—22no—
112C22⋊Q8×C113—22no—
113#121×C113—28no—
114#121×C113—22no—
115#121×C113—22no—
116#121×C113—22no—
117#121×C113—22no—
118#121×C113—41no—
119#121×C113D414yescomplemented
120C4×Q8×C113—22no—
121C4×Q8×C113—22no—
122C4×D4×C113—28no—
123C4×D4×C113—22no—
124C4×D4×C113—22no—
125#117×C113—22no—
126#117×C113—41no—
127C2×C4⋊C4×C113—21no—
128C2×C4⋊C4×C113—21no—
129C2×C4⋊C4×C113—21no—
130C2×C4⋊C4×C113D411yescharacteristic
131C2×C4⋊C4×C113C2311yescharacteristic
132C2×C4⋊C4×C113C2311yescharacteristic
133C2×C4⋊C4×C113C2311yescharacteristic
134C2×C4⋊C4×C113C2311yescharacteristic
135C2×C22⋊C4×C113—21no—
136C2×C22⋊C4×C113—21no—
137C2×C22⋊C4×C113—21no—
138C2×C22⋊C4×C113—21no—
139C2×C22⋊C4×C113—21no—
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113—21no—
142C2×C22⋊C4×C113—21no—
143C2×C22⋊C4×C113—21no—
144C2×C22⋊C4×C113—21no—
145C2×C22⋊C4×C113D411yescharacteristic
146C2×C22⋊C4×C113D411yescharacteristic
147C2×C42×C113—21no—
148C2×C42×C113—21no—
149C2×C42×C113C2311yescharacteristic
150#106×C113—22no—
151#103×C113—22no—
152#103×C113—22no—
153#103×C113—22no—
154#103×C113—22no—
155#103×C113—22no—
156#103×C113D414yescomplemented
157#102×C113—22no—
158#102×C113—22no—
159#102×C113—22no—
160#102×C113—41no—
161C22⋊C8×C113—22no—
162C22⋊C8×C113—22no—
163C22⋊C8×C113—41no—
164#95×C113—21no—
165#95×C113—21no—
166C24×C113—21no—
167C24×C113—21no—
168C24×C113C2×D411yescharacteristic
169C24×C113C2×D411yescharacteristic
170#41×C113—44no—
171#41×C113—44no—
172#41×C113—44no—
173#41×C113—44no—
174C2×Q8×C113—24no—
175C2×Q8×C113—21no—
176C2×Q8×C113—21no—
177C2×Q8×C113—21no—
178C2×Q8×C113—21no—
179C2×Q8×C113—28no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—42no—
185C2×Q8×C113—42no—
186C2×Q8×C113—44no—
187C2×Q8×C113—44no—
188C2×Q8×C113—44no—
189C2×Q8×C113C2×D412yes—
190C2×Q8×C113C2×D412yes—
191C2×Q8×C113C2×D412yes—
192C2×Q8×C113#4112yes—
193C2×D4×C113—24no—
194C2×D4×C113—22no—
195C2×D4×C113—24no—
196C2×D4×C113—21no—
197C2×D4×C113—21no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—21no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—21no—
207C2×D4×C113—41no—
208C2×D4×C113—41no—
209C2×D4×C113—42no—
210C2×D4×C113—42no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—42no—
215C2×D4×C113—42no—
216C2×D4×C113—81no—
217C2×D4×C113—81no—
218C2×D4×C113—81no—
219C2×D4×C113C2×D412yes—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—24no—
226C22×C4×C113—24no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
230C22×C4×C113—21no—
231C22×C4×C113—21no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—21no—
237C22×C4×C113—21no—
238C22×C4×C113—42no—
239C22×C4×C113—42no—
240C22×C4×C113—42no—
241C22×C4×C113—42no—
242C22×C4×C113C2×D411yescharacteristic
243C22×C4×C113C2×D411yescharacteristic
244C22×C4×C113C2×D411yescharacteristic
245C22×C4×C113C2×D411yescharacteristic
246C22×C4×C113C2×D412yes—
247C22×C4×C113C2×D412yes—
248C22×C4×C113C2411yescharacteristic
249SD16×C113—44no—
250SD16×C113—44no—
251D8×C113—44no—
252M16×C113—44no—
253C2×C8×C113—21no—
254C2×C8×C113—21no—
255C2×C8×C113—21no—
256C2×C8×C113—21no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C2×C8×C113—21no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113C2×D412yes—
265C4⋊C4×C113—24no—
266C4⋊C4×C113—24no—
267C4⋊C4×C113—22no—
268C4⋊C4×C113—21no—
269C4⋊C4×C113—21no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—81no—
275C4⋊C4×C113C2×D412yes—
276C4⋊C4×C113C2×D412yes—
277C22⋊C4×C113—24no—
278C22⋊C4×C113—24no—
279C22⋊C4×C113—24no—
280C22⋊C4×C113—22no—
281C22⋊C4×C113—24no—
282C22⋊C4×C113—22no—
283C22⋊C4×C113—42no—
284C22⋊C4×C113—42no—
285C22⋊C4×C113—42no—
286C22⋊C4×C113—42no—
287C22⋊C4×C113—81no—
288C22⋊C4×C113—81no—
289C42×C113—24no—
290C42×C113—21no—
291C42×C113—21no—
292C42×C113—42no—
293C23×C113—21no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—22no—
301C23×C113—21no—
302C23×C113—21no—
303C23×C113—21no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—41no—
311C23×C113—41no—
312C23×C113—41no—
313C23×C113—41no—
314C23×C113—41no—
315C23×C113—41no—
316C23×C113—41no—
317C23×C113—41no—
318C23×C113—41no—
319C23×C113—41no—
320C23×C113#12012yes—
321C23×C113C22×D411yescharacteristic
322Q8×C113—22no—
323Q8×C113—22no—
324Q8×C113—22no—
325Q8×C113—22no—
326Q8×C113—22no—
327Q8×C113—48no—
328Q8×C113—41no—
329Q8×C113—41no—
330Q8×C113#12114yes—
331D4×C113—22no—
332D4×C113—22no—
333D4×C113—48no—
334D4×C113—44no—
335D4×C113—48no—
336D4×C113—41no—
337D4×C113—41no—
338D4×C113—41no—
339D4×C113—41no—
340D4×C113—41no—
341D4×C113—41no—
342D4×C113—84no—
343D4×C113—84no—
344C2×C4×C113—22no—
345C2×C4×C113—21no—
346C2×C4×C113—22no—
347C2×C4×C113—21no—
348C2×C4×C113—22no—
349C2×C4×C113—22no—
350C2×C4×C113—22no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—21no—
354C2×C4×C113—21no—
355C2×C4×C113—22no—
356C2×C4×C113—22no—
357C2×C4×C113—21no—
358C2×C4×C113—22no—
359C2×C4×C113—21no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
362C2×C4×C113—21no—
363C2×C4×C113—21no—
364C2×C4×C113—21no—
365C2×C4×C113—48no—
366C2×C4×C113—48no—
367C2×C4×C113—41no—
368C2×C4×C113—41no—
369C2×C4×C113—41no—
370C2×C4×C113—41no—
371C2×C4×C113—41no—
372C2×C4×C113—41no—
373C2×C4×C113—41no—
374C2×C4×C113—41no—
375C2×C4×C113—41no—
376C2×C4×C113—41no—
377C2×C4×C113—41no—
378C2×C4×C113—41no—
379C2×C4×C113—41no—
380C2×C4×C113—41no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
383C2×C4×C113#12012yes—
384C2×C4×C113C22×D411yescharacteristic
385C2×C4×C113C22×D411yescharacteristic
386C2×C4×C113C22×D411yescharacteristic
387C2×C4×C113C2×#4111yescharacteristic
388C2×C4×C113H(5,𝔽2)11yescharacteristic
389C2×C4×C113H(5,𝔽2)11yescharacteristic
390C8×C113—22no—
391C8×C113—41no—
392C8×C113—41no—
393C8×C113—41no—
394C22×C113—22no—
395C22×C113—22no—
396C22×C113—22no—
397C22×C113—41no—
398C22×C113—41no—
399C22×C113—41no—
400C22×C113—41no—
401C22×C113—42no—
402C22×C113—41no—
403C22×C113—41no—
404C22×C113—42no—
405C22×C113—41no—
406C22×C113—42no—
407C22×C113—41no—
408C22×C113—41no—
409C22×C113—41no—
410C22×C113—41no—
411C22×C113—81no—
412C22×C113—81no—
413C22×C113—81no—
414C22×C113—81no—
415C22×C113—81no—
416C22×C113—81no—
417C22×C113—81no—
418C22×C113—81no—
419C22×C113—81no—
420C22×C113—81no—
421C22×C113—81no—
422C22×C113C2×#12011yescharacteristic
423C22×C113D4211yescharacteristic
424C22×C113#54611yescharacteristic
425C22×C113#57511yescharacteristic
426C22×C113#57511yescharacteristic
427C22×C113#57711yescharacteristic
428C22×C113#57711yescharacteristic
429C4×C113—22no—
430C4×C113—24no—
431C4×C113—41no—
432C4×C113—42no—
433C4×C113—41no—
434C4×C113—42no—
435C4×C113—41no—
436C4×C113—42no—
437C4×C113—81no—
438C4×C113—81no—
439C4×C113C2×#12111yescharacteristic
440C4×C113#53411yescharacteristic
441C4×C113D4211yescharacteristic
442C4×C113#54611yescharacteristic
443#24455C11311yesmaximal, characteristic, direct product factor, Sylow
444C2×C113—42no—
445C2×C113—81no—
446C2×C113—82no—
447C2×C113—161no—
448C2×C113#241011yescharacteristic
449C2×C113#300511yescharacteristic
450C2×C113#301011yescharacteristic
451C2×C113#327111yescharacteristic
452C2×C113#327511yescharacteristic
453C2×C113#332111yescharacteristic
454C2×C113#332611yescharacteristic
455C2×#548C2×C11311yescharacteristic, complemented
456C2×#469C2×C11311yescharacteristic, complemented
457C2×#449C2×C11311yescharacteristic, complemented
458C2×#448C2×C11311yescharacteristic, complemented
459C2×#419C2×C11311yescharacteristic, complemented
460#2414C2×C11311yescharacteristic, complemented
461#2042C2×C11311yescharacteristic, complemented
462#2035C2×C11311yescharacteristic, complemented
463#2012C2×C11311yescharacteristic, complemented
464#2000C2×C11311yescharacteristic, complemented
465#1880C2×C11311yescharacteristic, complemented
466#1875C2×C11311yescharacteristic, complemented
467#1870C2×C11311yescharacteristic, complemented
468#1865C2×C11311yescharacteristic, complemented
469#1788C2×C11311yescharacteristic, complemented
470C113#2445511yescharacteristic, direct product factor, Sylow
471C22×#41C22×C11311yescharacteristic
472C23×Q8C22×C11311yescharacteristic
473C22×SD16C22×C11311yescharacteristic
474C22×SD16C22×C11311yescharacteristic
475C22×D8C22×C11311yescharacteristic
476C22×M16C22×C11311yescharacteristic
477#548—24no—
478#548—24no—
479C2×#124—21no—
480C2×#124C22×C11311yescharacteristic
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8C22×C11311yescharacteristic
483C2×#121—21no—
484C2×#121C22×C11311yescharacteristic
485C2×#121C22×C11311yescharacteristic
486C2×#121C22×C11311yescharacteristic
487C2×C4×Q8C22×C11311yescharacteristic
488C2×C4×D4—21no—
489C2×C4×D4C22×C11311yescharacteristic
490C2×#117C22×C11311yescharacteristic
491#469—24no—
492#449—24no—
493#448—24no—
494C2×#106C22×C11311yescharacteristic
495#419—24no—
496C2×#103C22×C11311yescharacteristic
497C2×#103C22×C11311yescharacteristic
498C2×#103C22×C11311yescharacteristic
499C2×#103C22×C11311yescharacteristic
500C2×#103C22×C11311yescharacteristic
501C2×#103C22×C11311yescharacteristic
502C2×#102C22×C11311yescharacteristic
503C2×#102C22×C11311yescharacteristic
504C2×#102C22×C11311yescharacteristic
505C2×#102C22×C11311yescharacteristic
506C2×C22⋊C8C22×C11311yescharacteristic
507C2×C22⋊C8C22×C11311yescharacteristic
508C2×C22⋊C8C22×C11311yescharacteristic
509#394—21no—
510#392—21no—
511#390—21no—
512#390C22×C11311yescharacteristic
513#389C22×C11311yescharacteristic
514#388—21no—
515#380C22×C11311yescharacteristic
516#340C22×C11311yescharacteristic
517#340C22×C11311yescharacteristic
518#336C22×C11311yescharacteristic
519#336C22×C11311yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C22×Q8—21no—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—41no—
531C22×Q8—41no—
532C22×Q8D4×C11314yescomplemented
533C22×Q8C23×C11311yescharacteristic
534C22×Q8C23×C11311yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4D4×C11311yescharacteristic
540C22×D4C23×C11311yescharacteristic
541C22×D4C23×C11311yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C23×C11311yescharacteristic
545C23×C4C23×C11311yescharacteristic
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8C23×C11311yescharacteristic
559C22×C8C23×C11311yescharacteristic
560C22×C8C23×C11311yescharacteristic
561C22×C8C23×C11311yescharacteristic
562#124—28no—
563#124—22no—
564#124—22no—
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568#121—28no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—41no—
574#121D4×C11314yescomplemented
575C4×Q8—22no—
576C4×Q8—22no—
577C4×D4—28no—
578C4×D4—22no—
579C4×D4—22no—
580#117—22no—
581#117—41no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4D4×C11311yescharacteristic
586C2×C4⋊C4C23×C11311yescharacteristic
587C2×C4⋊C4C23×C11311yescharacteristic
588C2×C4⋊C4C23×C11311yescharacteristic
589C2×C4⋊C4C23×C11311yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4D4×C11311yescharacteristic
601C2×C22⋊C4D4×C11311yescharacteristic
602C2×C42—21no—
603C2×C42—21no—
604C2×C42C23×C11311yescharacteristic
605#106—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103D4×C11314yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—41no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C11311yescharacteristic
624C24C2×D4×C11311yescharacteristic
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—24no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—28no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—42no—
640C2×Q8—42no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8C2×D4×C11312yes—
645C2×Q8C2×D4×C11312yes—
646C2×Q8C2×D4×C11312yes—
647C2×Q8#41×C11312yes—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—41no—
663C2×D4—41no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4C2×D4×C11312yes—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×D4×C11311yescharacteristic
698C22×C4C2×D4×C11311yescharacteristic
699C22×C4C2×D4×C11311yescharacteristic
700C22×C4C2×D4×C11311yescharacteristic
701C22×C4C2×D4×C11312yes—
702C22×C4C2×D4×C11312yes—
703C22×C4C24×C11311yescharacteristic
704SD16—44no—
705SD16—44no—
706D8—44no—
707M16—44no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8C2×D4×C11312yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—22no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—81no—
730C4⋊C4C2×D4×C11312yes—
731C4⋊C4C2×D4×C11312yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—22no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23#120×C11312yes—
776C23C22×D4×C11311yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—22no—
782Q8—48no—
783Q8—41no—
784Q8—41no—
785Q8#121×C11314yes—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—44no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4#120×C11312yes—
839C2×C4C22×D4×C11311yescharacteristic
840C2×C4C22×D4×C11311yescharacteristic
841C2×C4C22×D4×C11311yescharacteristic
842C2×C4C2×#41×C11311yescharacteristic
843C2×C4H(5,𝔽2)×C11311yescharacteristic
844C2×C4H(5,𝔽2)×C11311yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—42no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C11311yescharacteristic
878C22D42×C11311yescharacteristic
879C22#546×C11311yescharacteristic
880C22#575×C11311yescharacteristic
881C22#575×C11311yescharacteristic
882C22#577×C11311yescharacteristic
883C22#577×C11311yescharacteristic
884C4—22no—
885C4—24no—
886C4—41no—
887C4—42no—
888C4—41no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×#121×C11311yescharacteristic
895C4#534×C11311yescharacteristic
896C4D42×C11311yescharacteristic
897C4#546×C11311yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—161no—
902C2C113×#241011yescharacteristic
903C2C113×#300511yescharacteristic
904C2C113×#301011yescharacteristic
905C2C113×#327111yescharacteristic
906C2C113×#327511yescharacteristic
907C2C113×#332111yescharacteristic
908C2C113×#332611yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#548×C113C2semidirect
2. C2×#469×C113C2semidirect
3. C2×#449×C113C2semidirect
4. C2×#448×C113C2semidirect
5. C2×#419×C113C2semidirect
6. C113×#2414C2semidirect
7. C113×#2042C2semidirect
8. C113×#2035C2semidirect
9. C113×#2012C2semidirect
10. C113×#2000C2semidirect
11. C113×#1880C2semidirect
12. C113×#1875C2semidirect
13. C113×#1870C2semidirect
14. C113×#1865C2semidirect
15. C113×#1788C2semidirect
77. C22×Q8×C113D4semidirect
119. #121×C113D4semidirect
156. #103×C113D4semidirect
443. #24455C113direct (N × H)
455. C2×#548C2×C113semidirect
456. C2×#469C2×C113semidirect
457. C2×#449C2×C113semidirect
458. C2×#448C2×C113semidirect
459. C2×#419C2×C113semidirect
460. #2414C2×C113semidirect
461. #2042C2×C113semidirect
462. #2035C2×C113semidirect
463. #2012C2×C113semidirect
464. #2000C2×C113semidirect
465. #1880C2×C113semidirect
466. #1875C2×C113semidirect
467. #1870C2×C113semidirect
468. #1865C2×C113semidirect
469. #1788C2×C113semidirect
470. C113#24455direct (N × H)
532. C22×Q8D4×C113semidirect
574. #121D4×C113semidirect
611. #103D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1132
C2×#469×C1132
C2×#449×C1132
C2×#448×C1132
C2×#419×C1132
C113×#24142
C113×#20422
C113×#20352
C113×#20122
C113×#20002
C113×#18802
C113×#18752
C113×#18702
C113×#18652
C113×#17882
#24455113