Finite Group Databasebeta

← C113×#24245 #43292265

Subgroups — C113×#24245 #43292265

Order 28928.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C113C211yesmaximal, characteristic, complemented
2C2×#463×C113C211yesmaximal, characteristic, complemented
3C2×#449×C113C211yesmaximal, characteristic, complemented
4C2×#447×C113C211yesmaximal, characteristic, complemented
5C2×C4×D8×C113C211yesmaximal, characteristic, complemented
6C113×#2535C211yesmaximal, characteristic, complemented
7C113×#2036C211yesmaximal, characteristic, complemented
8C113×#2033C211yesmaximal, characteristic, complemented
9C113×#2000C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1958C211yesmaximal, characteristic, complemented
12C113×#1954C211yesmaximal, characteristic, complemented
13C113×#1804C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic, complemented
19C22×D8×C113C2211yescharacteristic
20C22×D8×C113C2211yescharacteristic
21#546×C113—24no—
22#546×C113—24no—
23C2×#124×C113C2211yescharacteristic
24C2×#123×C113—21no—
25C2×C22⋊Q8×C113C2211yescharacteristic
26C2×#121×C113—21no—
27C2×#121×C113C2211yescharacteristic
28C2×#121×C113C2211yescharacteristic
29C2×#121×C113C2211yescharacteristic, complemented
30C2×#120×C113—21no—
31C2×C4×D4×C113C2211yescharacteristic
32C2×C4×D4×C113C2211yescharacteristic
33C2×C4×D4×C113C2211yescharacteristic, complemented
34C22×C22⋊C4×C113—21no—
35#463×C113—24no—
36#449×C113—24no—
37#447×C113—24no—
38C4×D8×C113—24no—
39C2×#107×C113C2211yescharacteristic, complemented
40C2×C4⋊C8×C113C2211yescharacteristic, complemented
41C2×#103×C113C2211yescharacteristic, complemented
42C2×#103×C113C2211yescharacteristic, complemented
43C2×#103×C113C2211yescharacteristic, complemented
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic, complemented
51C2×C22⋊C8×C113C2211yescharacteristic
52C2×C22⋊C8×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic, complemented
54C2×C22⋊C8×C113C2211yescharacteristic, complemented
55C2×C4×C8×C113C2211yescharacteristic, complemented
56#397×C113—21no—
57#392×C113—21no—
58#386×C113—21no—
59#386×C113—21no—
60#382×C113C2211yescharacteristic, complemented
61#380×C113C2211yescharacteristic
62#380×C113C2211yescharacteristic, complemented
63#340×C113C2211yescharacteristic, complemented
64#340×C113C2211yescharacteristic, complemented
65C25×C113—21no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—41no—
71C2×#41×C113—41no—
72C22×Q8×C113C2311yescharacteristic
73C22×D4×C113—21no—
74C22×D4×C113—21no—
75C22×D4×C113—22no—
76C22×D4×C113—22no—
77C22×D4×C113—22no—
78C22×D4×C113—22no—
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—41no—
83C22×D4×C113—41no—
84C22×D4×C113D411yescharacteristic
85C22×D4×C113C2311yescharacteristic
86C22×D4×C113C2311yescharacteristic
87C22×D4×C113C2311yescharacteristic
88C23×C4×C113—21no—
89C23×C4×C113—21no—
90C23×C4×C113—21no—
91C23×C4×C113C2311yescharacteristic
92C23×C4×C113C2311yescharacteristic
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—41no—
96C2×D8×C113—22no—
97C2×D8×C113—22no—
98C2×D8×C113—22no—
99C2×D8×C113—22no—
100C2×D8×C113—41no—
101C2×D8×C113D414yescomplemented
102C22×C8×C113C2311yescharacteristic
103C22×C8×C113C2311yescharacteristic
104C22×C8×C113C2311yescharacteristic
105C22×C8×C113C2311yescharacteristic
106#124×C113—22no—
107#124×C113D414yescomplemented
108#123×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—
118#120×C113—28no—
119C4×D4×C113—22no—
120C4×D4×C113—22no—
121C4×D4×C113—22no—
122C4×D4×C113—22no—
123C4×D4×C113—22no—
124C4×D4×C113D414yescomplemented
125C2×C4⋊C4×C113—21no—
126C2×C4⋊C4×C113D411yescharacteristic
127C2×C4⋊C4×C113C2311yescharacteristic
128C2×C4⋊C4×C113C2311yescharacteristic
129C2×C4⋊C4×C113C2311yescharacteristic
130C2×C4⋊C4×C113C2311yescharacteristic
131C2×C22⋊C4×C113—28no—
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×C113—21no—
142C2×C22⋊C4×C113D411yescharacteristic
143C2×C22⋊C4×C113D411yescharacteristic
144C2×C42×C113C2311yescharacteristic
145#107×C113—22no—
146C4⋊C8×C113—22no—
147#103×C113—22no—
148#103×C113—22no—
149#103×C113—41no—
150#102×C113—22no—
151#102×C113—22no—
152#102×C113—22no—
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—24no—
168C24×C113—21no—
169C24×C113—21no—
170C24×C113—42no—
171C24×C113—42no—
172C24×C113—42no—
173C24×C113—42no—
174C24×C113—81no—
175C24×C113—81no—
176C24×C113C2×D411yescharacteristic
177C24×C113C2×D411yescharacteristic
178#41×C113—44no—
179#41×C113—44no—
180#41×C113—44no—
181#41×C113—44no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113—21no—
186C2×Q8×C113—21no—
187C2×Q8×C113C2×D412yes—
188C2×D4×C113—24no—
189C2×D4×C113—24no—
190C2×D4×C113—22no—
191C2×D4×C113—24no—
192C2×D4×C113—22no—
193C2×D4×C113—21no—
194C2×D4×C113—21no—
195C2×D4×C113—21no—
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—41no—
207C2×D4×C113—42no—
208C2×D4×C113—42no—
209C2×D4×C113—44no—
210C2×D4×C113—44no—
211C2×D4×C113—44no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—44no—
215C2×D4×C113—42no—
216C2×D4×C113—42no—
217C2×D4×C113—42no—
218C2×D4×C113—42no—
219C2×D4×C113—81no—
220C2×D4×C113—81no—
221C2×D4×C113—81no—
222C2×D4×C113—81no—
223C2×D4×C113C2×D412yes—
224C2×D4×C113C2×D412yes—
225C2×D4×C113C2×D412yes—
226C2×D4×C113C2×D412yes—
227C2×D4×C113#4112yes—
228C22×C4×C113—24no—
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—21no—
241C22×C4×C113—21no—
242C22×C4×C113—21no—
243C22×C4×C113—24no—
244C22×C4×C113—21no—
245C22×C4×C113—21no—
246C22×C4×C113—21no—
247C22×C4×C113—42no—
248C22×C4×C113—42no—
249C22×C4×C113—42no—
250C22×C4×C113—81no—
251C22×C4×C113—81no—
252C22×C4×C113—81no—
253C22×C4×C113—81no—
254C22×C4×C113C2×D411yescharacteristic
255C22×C4×C113C2×D411yescharacteristic
256C22×C4×C113C2×D411yescharacteristic
257C22×C4×C113C2×D411yescharacteristic
258C22×C4×C113C2411yescharacteristic
259SD16×C113—44no—
260D8×C113—28no—
261D8×C113—44no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—21no—
270C2×C8×C113—21no—
271C2×C8×C113—21no—
272C2×C8×C113—21no—
273C2×C8×C113C2×D412yes—
274C4⋊C4×C113—24no—
275C4⋊C4×C113—22no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
283C4⋊C4×C113C2×D412yes—
284C22⋊C4×C113—24no—
285C22⋊C4×C113—24no—
286C22⋊C4×C113—22no—
287C22⋊C4×C113—24no—
288C22⋊C4×C113—24no—
289C22⋊C4×C113—24no—
290C22⋊C4×C113—22no—
291C22⋊C4×C113—42no—
292C22⋊C4×C113—42no—
293C22⋊C4×C113—42no—
294C22⋊C4×C113—81no—
295C22⋊C4×C113—81no—
296C42×C113C2×D412yes—
297C42×C113C2×D412yes—
298C23×C113—21no—
299C23×C113—22no—
300C23×C113—21no—
301C23×C113—22no—
302C23×C113—21no—
303C23×C113—22no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
307C23×C113—22no—
308C23×C113—21no—
309C23×C113—22no—
310C23×C113—21no—
311C23×C113—21no—
312C23×C113—21no—
313C23×C113—21no—
314C23×C113—21no—
315C23×C113—21no—
316C23×C113—48no—
317C23×C113—48no—
318C23×C113—41no—
319C23×C113—41no—
320C23×C113—41no—
321C23×C113—41no—
322C23×C113—41no—
323C23×C113—41no—
324C23×C113—41no—
325C23×C113—41no—
326C23×C113—41no—
327C23×C113—41no—
328C23×C113—41no—
329C23×C113—41no—
330C23×C113—41no—
331C23×C113—41no—
332C23×C113—41no—
333C23×C113—41no—
334C23×C113—84no—
335C23×C113—84no—
336C23×C113—84no—
337C23×C113—84no—
338C23×C113—84no—
339C23×C113#13512yes—
340C23×C113C22×D411yescharacteristic
341Q8×C113—22no—
342Q8×C113—22no—
343Q8×C113—41no—
344Q8×C113—41no—
345D4×C113—22no—
346D4×C113—22no—
347D4×C113—22no—
348D4×C113—22no—
349D4×C113—22no—
350D4×C113—22no—
351D4×C113—22no—
352D4×C113—44no—
353D4×C113—48no—
354D4×C113—48no—
355D4×C113—41no—
356D4×C113—41no—
357D4×C113—41no—
358D4×C113—41no—
359D4×C113—84no—
360D4×C113—84no—
361D4×C113—84no—
362D4×C113#12114yes—
363C2×C4×C113—21no—
364C2×C4×C113—21no—
365C2×C4×C113—21no—
366C2×C4×C113—21no—
367C2×C4×C113—22no—
368C2×C4×C113—21no—
369C2×C4×C113—22no—
370C2×C4×C113—21no—
371C2×C4×C113—21no—
372C2×C4×C113—21no—
373C2×C4×C113—21no—
374C2×C4×C113—21no—
375C2×C4×C113—48no—
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—41no—
384C2×C4×C113—41no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—41no—
388C2×C4×C113—41no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—41no—
393C2×C4×C113—41no—
394C2×C4×C113—41no—
395C2×C4×C113—41no—
396C2×C4×C113—41no—
397C2×C4×C113—84no—
398C2×C4×C113—84no—
399C2×C4×C113#12012yes—
400C2×C4×C113#12012yes—
401C2×C4×C113C22×D411yescharacteristic
402C2×C4×C113C22×D411yescharacteristic
403C2×C4×C113C22×D411yescharacteristic
404C2×C4×C113C2×#4111yescharacteristic
405C2×C4×C113H(5,𝔽2)11yescharacteristic
406C2×C4×C113H(5,𝔽2)11yescharacteristic
407C8×C113—22no—
408C8×C113—41no—
409C8×C113—41no—
410C8×C113—41no—
411C22×C113—24no—
412C22×C113—22no—
413C22×C113—22no—
414C22×C113—22no—
415C22×C113—41no—
416C22×C113—42no—
417C22×C113—42no—
418C22×C113—41no—
419C22×C113—41no—
420C22×C113—42no—
421C22×C113—42no—
422C22×C113—42no—
423C22×C113—41no—
424C22×C113—42no—
425C22×C113—41no—
426C22×C113—42no—
427C22×C113—42no—
428C22×C113—41no—
429C22×C113—42no—
430C22×C113—41no—
431C22×C113—42no—
432C22×C113—41no—
433C22×C113—42no—
434C22×C113—42no—
435C22×C113—41no—
436C22×C113—41no—
437C22×C113—41no—
438C22×C113—816no—
439C22×C113—81no—
440C22×C113—81no—
441C22×C113—81no—
442C22×C113—81no—
443C22×C113—81no—
444C22×C113—81no—
445C22×C113—81no—
446C22×C113—81no—
447C22×C113C2×#12011yescharacteristic
448C22×C113D4211yescharacteristic
449C22×C113#54611yescharacteristic
450C22×C113C2×#13511yescharacteristic
451C22×C113#57511yescharacteristic
452C22×C113#57611yescharacteristic
453C22×C113#57611yescharacteristic
454C4×C113—22no—
455C4×C113—22no—
456C4×C113—41no—
457C4×C113—41no—
458C4×C113—42no—
459C4×C113—42no—
460C4×C113—81no—
461C4×C113—81no—
462C4×C113—81no—
463C4×C113C2×#12111yescharacteristic
464C4×C113#53511yescharacteristic
465C4×C113D4211yescharacteristic
466C4×C113#54611yescharacteristic
467#24245C11311yesmaximal, characteristic, direct product factor, Sylow
468C2×C113—42no—
469C2×C113—44no—
470C2×C113—81no—
471C2×C113—82no—
472C2×C113—82no—
473C2×C113#240811yescharacteristic
474C2×C113#300211yescharacteristic
475C2×C113#300811yescharacteristic
476C2×C113#327311yescharacteristic
477C2×C113#328011yescharacteristic
478C2×C113#329711yescharacteristic
479C2×C113#332211yescharacteristic
480C2×#546C2×C11311yescharacteristic, complemented
481C2×#463C2×C11311yescharacteristic, complemented
482C2×#449C2×C11311yescharacteristic, complemented
483C2×#447C2×C11311yescharacteristic, complemented
484C2×C4×D8C2×C11311yescharacteristic, complemented
485#2535C2×C11311yescharacteristic, complemented
486#2036C2×C11311yescharacteristic, complemented
487#2033C2×C11311yescharacteristic, complemented
488#2000C2×C11311yescharacteristic, complemented
489#1999C2×C11311yescharacteristic, complemented
490#1958C2×C11311yescharacteristic, complemented
491#1954C2×C11311yescharacteristic, complemented
492#1804C2×C11311yescharacteristic, complemented
493#1788C2×C11311yescharacteristic, complemented
494#1786C2×C11311yescharacteristic, complemented
495C113#2424511yescharacteristic, direct product factor, Sylow
496C22×#41C22×C11311yescharacteristic
497C23×D4C22×C11311yescharacteristic
498C22×SD16C22×C11311yescharacteristic, complemented
499C22×D8C22×C11311yescharacteristic
500C22×D8C22×C11311yescharacteristic
501#546—24no—
502#546—24no—
503C2×#124C22×C11311yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C22×C11311yescharacteristic
506C2×#121—21no—
507C2×#121C22×C11311yescharacteristic
508C2×#121C22×C11311yescharacteristic
509C2×#121C22×C11311yescharacteristic, complemented
510C2×#120—21no—
511C2×C4×D4C22×C11311yescharacteristic
512C2×C4×D4C22×C11311yescharacteristic
513C2×C4×D4C22×C11311yescharacteristic, complemented
514C22×C22⋊C4—21no—
515#463—24no—
516#449—24no—
517#447—24no—
518C4×D8—24no—
519C2×#107C22×C11311yescharacteristic, complemented
520C2×C4⋊C8C22×C11311yescharacteristic, complemented
521C2×#103C22×C11311yescharacteristic, complemented
522C2×#103C22×C11311yescharacteristic, complemented
523C2×#103C22×C11311yescharacteristic, complemented
524C2×#102C22×C11311yescharacteristic
525C2×#102C22×C11311yescharacteristic
526C2×#102C22×C11311yescharacteristic
527C2×#102C22×C11311yescharacteristic
528C2×#102C22×C11311yescharacteristic
529C2×#102C22×C11311yescharacteristic
530C2×#102C22×C11311yescharacteristic, complemented
531C2×C22⋊C8C22×C11311yescharacteristic
532C2×C22⋊C8C22×C11311yescharacteristic
533C2×C22⋊C8C22×C11311yescharacteristic, complemented
534C2×C22⋊C8C22×C11311yescharacteristic, complemented
535C2×C4×C8C22×C11311yescharacteristic, complemented
536#397—21no—
537#392—21no—
538#386—21no—
539#386—21no—
540#382C22×C11311yescharacteristic, complemented
541#380C22×C11311yescharacteristic
542#380C22×C11311yescharacteristic, complemented
543#340C22×C11311yescharacteristic, complemented
544#340C22×C11311yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C11311yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C11311yescharacteristic
565C22×D4C23×C11311yescharacteristic
566C22×D4C23×C11311yescharacteristic
567C22×D4C23×C11311yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C11311yescharacteristic
572C23×C4C23×C11311yescharacteristic
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—41no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8D4×C11314yescomplemented
582C22×C8C23×C11311yescharacteristic
583C22×C8C23×C11311yescharacteristic
584C22×C8C23×C11311yescharacteristic
585C22×C8C23×C11311yescharacteristic
586#124—22no—
587#124D4×C11314yescomplemented
588#123—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591#121—28no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—41no—
598#120—28no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4D4×C11314yescomplemented
605C2×C4⋊C4—21no—
606C2×C4⋊C4D4×C11311yescharacteristic
607C2×C4⋊C4C23×C11311yescharacteristic
608C2×C4⋊C4C23×C11311yescharacteristic
609C2×C4⋊C4C23×C11311yescharacteristic
610C2×C4⋊C4C23×C11311yescharacteristic
611C2×C22⋊C4—28no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C11311yescharacteristic
623C2×C22⋊C4D4×C11311yescharacteristic
624C2×C42C23×C11311yescharacteristic
625#107—22no—
626C4⋊C8—22no—
627#103—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636#102—41no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—41no—
640C22⋊C8—41no—
641C4×C8—22no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C11311yescharacteristic
657C24C2×D4×C11311yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C11312yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C11312yes—
704C2×D4C2×D4×C11312yes—
705C2×D4C2×D4×C11312yes—
706C2×D4C2×D4×C11312yes—
707C2×D4#41×C11312yes—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4—81no—
734C22×C4C2×D4×C11311yescharacteristic
735C22×C4C2×D4×C11311yescharacteristic
736C22×C4C2×D4×C11311yescharacteristic
737C22×C4C2×D4×C11311yescharacteristic
738C22×C4C24×C11311yescharacteristic
739SD16—44no—
740D8—28no—
741D8—44no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8C2×D4×C11312yes—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4C2×D4×C11312yes—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42C2×D4×C11312yes—
777C42C2×D4×C11312yes—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#135×C11312yes—
820C23C22×D4×C11311yescharacteristic
821Q8—22no—
822Q8—22no—
823Q8—41no—
824Q8—41no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—44no—
833D4—48no—
834D4—48no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#121×C11314yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4#120×C11312yes—
880C2×C4#120×C11312yes—
881C2×C4C22×D4×C11311yescharacteristic
882C2×C4C22×D4×C11311yescharacteristic
883C2×C4C22×D4×C11311yescharacteristic
884C2×C4C2×#41×C11311yescharacteristic
885C2×C4H(5,𝔽2)×C11311yescharacteristic
886C2×C4H(5,𝔽2)×C11311yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—41no—
906C22—41no—
907C22—42no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—41no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C11311yescharacteristic
928C22D42×C11311yescharacteristic
929C22#546×C11311yescharacteristic
930C22C2×#135×C11311yescharacteristic
931C22#575×C11311yescharacteristic
932C22#576×C11311yescharacteristic
933C22#576×C11311yescharacteristic
934C4—22no—
935C4—22no—
936C4—41no—
937C4—41no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×#121×C11311yescharacteristic
944C4#535×C11311yescharacteristic
945C4D42×C11311yescharacteristic
946C4#546×C11311yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2C113×#240811yescharacteristic
953C2C113×#300211yescharacteristic
954C2C113×#300811yescharacteristic
955C2C113×#327311yescharacteristic
956C2C113×#328011yescharacteristic
957C2C113×#329711yescharacteristic
958C2C113×#332211yescharacteristic
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×#546×C113C2semidirect
2. C2×#463×C113C2semidirect
3. C2×#449×C113C2semidirect
4. C2×#447×C113C2semidirect
5. C2×C4×D8×C113C2semidirect
6. C113×#2535C2semidirect
7. C113×#2036C2semidirect
8. C113×#2033C2semidirect
9. C113×#2000C2semidirect
10. C113×#1999C2semidirect
11. C113×#1958C2semidirect
12. C113×#1954C2semidirect
13. C113×#1804C2semidirect
14. C113×#1788C2semidirect
15. C113×#1786C2semidirect
18. C22×SD16×C113C22semidirect
29. C2×#121×C113C22semidirect
33. C2×C4×D4×C113C22semidirect
39. C2×#107×C113C22semidirect
40. C2×C4⋊C8×C113C22semidirect
41. C2×#103×C113C22semidirect
42. C2×#103×C113C22semidirect
43. C2×#103×C113C22semidirect
50. C2×#102×C113C22semidirect
53. C2×C22⋊C8×C113C22semidirect
54. C2×C22⋊C8×C113C22semidirect
55. C2×C4×C8×C113C22semidirect
60. #382×C113C22semidirect
62. #380×C113C22semidirect
63. #340×C113C22semidirect
64. #340×C113C22semidirect
101. C2×D8×C113D4semidirect
107. #124×C113D4semidirect
124. C4×D4×C113D4semidirect
467. #24245C113direct (N × H)
480. C2×#546C2×C113semidirect
481. C2×#463C2×C113semidirect
482. C2×#449C2×C113semidirect
483. C2×#447C2×C113semidirect
484. C2×C4×D8C2×C113semidirect
485. #2535C2×C113semidirect
486. #2036C2×C113semidirect
487. #2033C2×C113semidirect
488. #2000C2×C113semidirect
489. #1999C2×C113semidirect
490. #1958C2×C113semidirect
491. #1954C2×C113semidirect
492. #1804C2×C113semidirect
493. #1788C2×C113semidirect
494. #1786C2×C113semidirect
495. C113#24245direct (N × H)
498. C22×SD16C22×C113semidirect
509. C2×#121C22×C113semidirect
513. C2×C4×D4C22×C113semidirect
519. C2×#107C22×C113semidirect
520. C2×C4⋊C8C22×C113semidirect
521. C2×#103C22×C113semidirect
522. C2×#103C22×C113semidirect
523. C2×#103C22×C113semidirect
530. C2×#102C22×C113semidirect
533. C2×C22⋊C8C22×C113semidirect
534. C2×C22⋊C8C22×C113semidirect
535. C2×C4×C8C22×C113semidirect
540. #382C22×C113semidirect
542. #380C22×C113semidirect
543. #340C22×C113semidirect
544. #340C22×C113semidirect
581. C2×D8D4×C113semidirect
587. #124D4×C113semidirect
604. C4×D4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1132
C2×#463×C1132
C2×#449×C1132
C2×#447×C1132
C2×C4×D8×C1132
C113×#25352
C113×#20362
C113×#20332
C113×#20002
C113×#19992
C113×#19582
C113×#19542
C113×#18042
C113×#17882
C113×#17862
#24245113