Finite Group Databasebeta

← C113×#24244 #43292264

Subgroups — C113×#24244 #43292264

Order 28928.

1488 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×#463×C113C211yesmaximal, characteristic, complemented
3C2×#449×C113C211yesmaximal, characteristic, complemented
4C2×#448×C113C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C113C211yesmaximal, characteristic, complemented
6C113×#2535C211yesmaximal, characteristic, complemented
7C113×#2035C211yesmaximal, characteristic, complemented
8C113×#2034C211yesmaximal, characteristic, complemented
9C113×#2000C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1958C211yesmaximal, characteristic, complemented
12C113×#1954C211yesmaximal, characteristic, complemented
13C113×#1805C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×Q8×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×D8×C113C2211yescharacteristic
21#548×C113—24no—
22#548×C113—24no—
23C2×#124×C113—21no—
24C2×#124×C113C2211yescharacteristic
25C2×C22⋊Q8×C113—21no—
26C2×C22⋊Q8×C113C2211yescharacteristic
27C2×#121×C113—21no—
28C2×#121×C113C2211yescharacteristic
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic
31C2×C4×Q8×C113C2211yescharacteristic
32C2×C4×D4×C113—21no—
33C2×C4×D4×C113C2211yescharacteristic
34C2×C4×D4×C113C2211yescharacteristic
35#463×C113—24no—
36#449×C113—24no—
37#448×C113—24no—
38C4×SD16×C113—24no—
39C2×#106×C113C2211yescharacteristic
40C2×C4⋊C8×C113C2211yescharacteristic
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
54C2×C22⋊C8×C113C2211yescharacteristic
55C2×C4×C8×C113C2211yescharacteristic
56#397×C113—21no—
57#392×C113—21no—
58#386×C113—21no—
59#386×C113—21no—
60#382×C113C2211yescharacteristic
61#380×C113C2211yescharacteristic
62#380×C113C2211yescharacteristic
63#340×C113C2211yescharacteristic
64#340×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—22no—
72C22×Q8×C113—22no—
73C22×Q8×C113—21no—
74C22×Q8×C113—22no—
75C22×Q8×C113—22no—
76C22×Q8×C113—41no—
77C22×Q8×C113—41no—
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×C113—21no—
90C23×C4×C113C2311yescharacteristic
91C23×C4×C113C2311yescharacteristic
92C2×SD16×C113—22no—
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—22no—
96C2×SD16×C113—41no—
97C2×SD16×C113D414yescomplemented
98C2×D8×C113—22no—
99C2×D8×C113—22no—
100C2×D8×C113—41no—
101C22×C8×C113C2311yescharacteristic
102C22×C8×C113C2311yescharacteristic
103C22×C8×C113C2311yescharacteristic
104C22×C8×C113C2311yescharacteristic
105#124×C113—28no—
106#124×C113—22no—
107#124×C113D414yescomplemented
108C22⋊Q8×C113—28no—
109C22⋊Q8×C113—22no—
110C22⋊Q8×C113—22no—
111#121×C113—28no—
112#121×C113—22no—
113#121×C113—22no—
114#121×C113—22no—
115#121×C113—22no—
116#121×C113—41no—
117#121×C113—41no—
118C4×Q8×C113—22no—
119C4×Q8×C113D414yescomplemented
120C4×D4×C113—28no—
121C4×D4×C113—22no—
122C4×D4×C113—22no—
123C4×D4×C113—22no—
124C4×D4×C113—22no—
125C2×C4⋊C4×C113—21no—
126C2×C4⋊C4×C113—21no—
127C2×C4⋊C4×C113D411yescharacteristic
128C2×C4⋊C4×C113C2311yescharacteristic
129C2×C4⋊C4×C113C2311yescharacteristic
130C2×C4⋊C4×C113C2311yescharacteristic
131C2×C4⋊C4×C113C2311yescharacteristic
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—21no—
134C2×C22⋊C4×C113—21no—
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×C113D411yescharacteristic
142C2×C22⋊C4×C113D411yescharacteristic
143C2×C42×C113—21no—
144C2×C42×C113C2311yescharacteristic
145#106×C113—22no—
146C4⋊C8×C113—22no—
147#103×C113—22no—
148#103×C113—22no—
149#103×C113—22no—
150#103×C113—22no—
151#103×C113—22no—
152#103×C113—41no—
153#102×C113—22no—
154#102×C113—22no—
155#102×C113—22no—
156#102×C113—41no—
157C22⋊C8×C113—22no—
158C22⋊C8×C113—22no—
159C22⋊C8×C113—41no—
160C22⋊C8×C113—41no—
161C4×C8×C113—22no—
162#95×C113—21no—
163#95×C113—21no—
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—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—42no—
184C2×Q8×C113—42no—
185C2×Q8×C113—44no—
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—24no—
195C2×D4×C113—22no—
196C2×D4×C113—22no—
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—42no—
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×C113C2×D412yes—
219C2×D4×C113C2×D412yes—
220C22×C4×C113—21no—
221C22×C4×C113—24no—
222C22×C4×C113—24no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—21no—
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—21no—
239C22×C4×C113—21no—
240C22×C4×C113—42no—
241C22×C4×C113—42no—
242C22×C4×C113—42no—
243C22×C4×C113—42no—
244C22×C4×C113—42no—
245C22×C4×C113—81no—
246C22×C4×C113—81no—
247C22×C4×C113C2×D411yescharacteristic
248C22×C4×C113C2×D411yescharacteristic
249C22×C4×C113C2×D411yescharacteristic
250C22×C4×C113C2×D411yescharacteristic
251C22×C4×C113C2411yescharacteristic
252SD16×C113—28no—
253SD16×C113—44no—
254D8×C113—44no—
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×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113C2×D412yes—
267C4⋊C4×C113—24no—
268C4⋊C4×C113—24no—
269C4⋊C4×C113—22no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—21no—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113C2×D412yes—
278C22⋊C4×C113—24no—
279C22⋊C4×C113—24no—
280C22⋊C4×C113—24no—
281C22⋊C4×C113—24no—
282C22⋊C4×C113—22no—
283C22⋊C4×C113—22no—
284C22⋊C4×C113—42no—
285C22⋊C4×C113—42no—
286C22⋊C4×C113—42no—
287C22⋊C4×C113—81no—
288C22⋊C4×C113—81no—
289C42×C113—24no—
290C42×C113C2×D412yes—
291C42×C113C2×D412yes—
292C23×C113—21no—
293C23×C113—21no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—22no—
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#13512yes—
320C23×C113C22×D411yescharacteristic
321Q8×C113—22no—
322Q8×C113—22no—
323Q8×C113—22no—
324Q8×C113—22no—
325Q8×C113—22no—
326Q8×C113—48no—
327Q8×C113—41no—
328Q8×C113—41no—
329Q8×C113#12114yes—
330D4×C113—22no—
331D4×C113—22no—
332D4×C113—22no—
333D4×C113—22no—
334D4×C113—44no—
335D4×C113—48no—
336D4×C113—48no—
337D4×C113—41no—
338D4×C113—41no—
339D4×C113—41no—
340D4×C113—41no—
341D4×C113—84no—
342D4×C113—84no—
343C2×C4×C113—22no—
344C2×C4×C113—22no—
345C2×C4×C113—22no—
346C2×C4×C113—21no—
347C2×C4×C113—21no—
348C2×C4×C113—21no—
349C2×C4×C113—21no—
350C2×C4×C113—22no—
351C2×C4×C113—22no—
352C2×C4×C113—21no—
353C2×C4×C113—21no—
354C2×C4×C113—21no—
355C2×C4×C113—21no—
356C2×C4×C113—21no—
357C2×C4×C113—21no—
358C2×C4×C113—48no—
359C2×C4×C113—48no—
360C2×C4×C113—41no—
361C2×C4×C113—41no—
362C2×C4×C113—41no—
363C2×C4×C113—41no—
364C2×C4×C113—41no—
365C2×C4×C113—41no—
366C2×C4×C113—41no—
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—84no—
382C2×C4×C113#12012yes—
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—42no—
404C22×C113—41no—
405C22×C113—42no—
406C22×C113—41no—
407C22×C113—42no—
408C22×C113—41no—
409C22×C113—42no—
410C22×C113—42no—
411C22×C113—41no—
412C22×C113—41no—
413C22×C113—41no—
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×C113C2×#13511yescharacteristic
426C22×C113#57511yescharacteristic
427C22×C113#57711yescharacteristic
428C22×C113#57711yescharacteristic
429C4×C113—24no—
430C4×C113—22no—
431C4×C113—22no—
432C4×C113—41no—
433C4×C113—41no—
434C4×C113—42no—
435C4×C113—42no—
436C4×C113—81no—
437C4×C113—81no—
438C4×C113—81no—
439C4×C113C2×#12111yescharacteristic
440C4×C113#53511yescharacteristic
441C4×C113D4211yescharacteristic
442C4×C113#54611yescharacteristic
443#24244C11311yesmaximal, characteristic, direct product factor, Sylow
444C2×C113—42no—
445C2×C113—81no—
446C2×C113—82no—
447C2×C113—82no—
448C2×C113#240811yescharacteristic
449C2×C113#300211yescharacteristic
450C2×C113#301011yescharacteristic
451C2×C113#327511yescharacteristic
452C2×C113#328211yescharacteristic
453C2×C113#330111yescharacteristic
454C2×C113#332611yescharacteristic
455C2×#548C2×C11311yescharacteristic, complemented
456C2×#463C2×C11311yescharacteristic, complemented
457C2×#449C2×C11311yescharacteristic, complemented
458C2×#448C2×C11311yescharacteristic, complemented
459C2×C4×SD16C2×C11311yescharacteristic, complemented
460#2535C2×C11311yescharacteristic, complemented
461#2035C2×C11311yescharacteristic, complemented
462#2034C2×C11311yescharacteristic, complemented
463#2000C2×C11311yescharacteristic, complemented
464#1999C2×C11311yescharacteristic, complemented
465#1958C2×C11311yescharacteristic, complemented
466#1954C2×C11311yescharacteristic, complemented
467#1805C2×C11311yescharacteristic, complemented
468#1788C2×C11311yescharacteristic, complemented
469#1787C2×C11311yescharacteristic, complemented
470C113#2424411yescharacteristic, direct product factor, Sylow
471C22×#41C22×C11311yescharacteristic
472C23×Q8C22×C11311yescharacteristic
473C22×SD16C22×C11311yescharacteristic
474C22×SD16C22×C11311yescharacteristic
475C22×D8C22×C11311yescharacteristic
476#548—24no—
477#548—24no—
478C2×#124—21no—
479C2×#124C22×C11311yescharacteristic
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C22×C11311yescharacteristic
482C2×#121—21no—
483C2×#121C22×C11311yescharacteristic
484C2×#121C22×C11311yescharacteristic
485C2×#121C22×C11311yescharacteristic
486C2×C4×Q8C22×C11311yescharacteristic
487C2×C4×D4—21no—
488C2×C4×D4C22×C11311yescharacteristic
489C2×C4×D4C22×C11311yescharacteristic
490#463—24no—
491#449—24no—
492#448—24no—
493C4×SD16—24no—
494C2×#106C22×C11311yescharacteristic
495C2×C4⋊C8C22×C11311yescharacteristic
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
509C2×C22⋊C8C22×C11311yescharacteristic
510C2×C4×C8C22×C11311yescharacteristic
511#397—21no—
512#392—21no—
513#386—21no—
514#386—21no—
515#382C22×C11311yescharacteristic
516#380C22×C11311yescharacteristic
517#380C22×C11311yescharacteristic
518#340C22×C11311yescharacteristic
519#340C22×C11311yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—21no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—41no—
532C22×Q8—41no—
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×C4—21no—
545C23×C4C23×C11311yescharacteristic
546C23×C4C23×C11311yescharacteristic
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16D4×C11314yescomplemented
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C22×C8C23×C11311yescharacteristic
557C22×C8C23×C11311yescharacteristic
558C22×C8C23×C11311yescharacteristic
559C22×C8C23×C11311yescharacteristic
560#124—28no—
561#124—22no—
562#124D4×C11314yescomplemented
563C22⋊Q8—28no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566#121—28no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—41no—
572#121—41no—
573C4×Q8—22no—
574C4×Q8D4×C11314yescomplemented
575C4×D4—28no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4D4×C11311yescharacteristic
583C2×C4⋊C4C23×C11311yescharacteristic
584C2×C4⋊C4C23×C11311yescharacteristic
585C2×C4⋊C4C23×C11311yescharacteristic
586C2×C4⋊C4C23×C11311yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
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⋊C4D4×C11311yescharacteristic
597C2×C22⋊C4D4×C11311yescharacteristic
598C2×C42—21no—
599C2×C42C23×C11311yescharacteristic
600#106—22no—
601C4⋊C8—22no—
602#103—22no—
603#103—22no—
604#103—22no—
605#103—22no—
606#103—22no—
607#103—41no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—41no—
612C22⋊C8—22no—
613C22⋊C8—22no—
614C22⋊C8—41no—
615C22⋊C8—41no—
616C4×C8—22no—
617#95—21no—
618#95—21no—
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—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—42no—
639C2×Q8—42no—
640C2×Q8—44no—
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—24no—
650C2×D4—22no—
651C2×D4—22no—
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—42no—
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×D4C2×D4×C11312yes—
674C2×D4C2×D4×C11312yes—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
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—21no—
694C22×C4—21no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—81no—
701C22×C4—81no—
702C22×C4C2×D4×C11311yescharacteristic
703C22×C4C2×D4×C11311yescharacteristic
704C22×C4C2×D4×C11311yescharacteristic
705C22×C4C2×D4×C11311yescharacteristic
706C22×C4C24×C11311yescharacteristic
707SD16—28no—
708SD16—44no—
709D8—44no—
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×C8—21no—
720C2×C8—21no—
721C2×C8C2×D4×C11312yes—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4C2×D4×C11312yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42C2×D4×C11312yes—
746C42C2×D4×C11312yes—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—22no—
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#135×C11312yes—
775C23C22×D4×C11311yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—48no—
782Q8—41no—
783Q8—41no—
784Q8#121×C11314yes—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—44no—
790D4—48no—
791D4—48no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—84no—
797D4—84no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
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—84no—
837C2×C4#120×C11312yes—
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—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—42no—
868C22—41no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C11311yescharacteristic
878C22D42×C11311yescharacteristic
879C22#546×C11311yescharacteristic
880C22C2×#135×C11311yescharacteristic
881C22#575×C11311yescharacteristic
882C22#577×C11311yescharacteristic
883C22#577×C11311yescharacteristic
884C4—24no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4C2×#121×C11311yescharacteristic
895C4#535×C11311yescharacteristic
896C4D42×C11311yescharacteristic
897C4#546×C11311yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—82no—
902C2C113×#240811yescharacteristic
903C2C113×#300211yescharacteristic
904C2C113×#301011yescharacteristic
905C2C113×#327511yescharacteristic
906C2C113×#328211yescharacteristic
907C2C113×#330111yescharacteristic
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×#463×C113C2semidirect
3. C2×#449×C113C2semidirect
4. C2×#448×C113C2semidirect
5. C2×C4×SD16×C113C2semidirect
6. C113×#2535C2semidirect
7. C113×#2035C2semidirect
8. C113×#2034C2semidirect
9. C113×#2000C2semidirect
10. C113×#1999C2semidirect
11. C113×#1958C2semidirect
12. C113×#1954C2semidirect
13. C113×#1805C2semidirect
14. C113×#1788C2semidirect
15. C113×#1787C2semidirect
97. C2×SD16×C113D4semidirect
107. #124×C113D4semidirect
119. C4×Q8×C113D4semidirect
443. #24244C113direct (N × H)
455. C2×#548C2×C113semidirect
456. C2×#463C2×C113semidirect
457. C2×#449C2×C113semidirect
458. C2×#448C2×C113semidirect
459. C2×C4×SD16C2×C113semidirect
460. #2535C2×C113semidirect
461. #2035C2×C113semidirect
462. #2034C2×C113semidirect
463. #2000C2×C113semidirect
464. #1999C2×C113semidirect
465. #1958C2×C113semidirect
466. #1954C2×C113semidirect
467. #1805C2×C113semidirect
468. #1788C2×C113semidirect
469. #1787C2×C113semidirect
470. C113#24244direct (N × H)
552. C2×SD16D4×C113semidirect
562. #124D4×C113semidirect
574. C4×Q8D4×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×#463×C1132
C2×#449×C1132
C2×#448×C1132
C2×C4×SD16×C1132
C113×#25352
C113×#20352
C113×#20342
C113×#20002
C113×#19992
C113×#19582
C113×#19542
C113×#18052
C113×#17882
C113×#17872
#24244113