Finite Group Databasebeta

← C113×#24218 #43292238

Subgroups — C113×#24218 #43292238

Order 28928.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C113C211yesmaximal, characteristic, complemented
2C2×#463×C113C211yesmaximal, characteristic, complemented
3C2×#459×C113C211yesmaximal, characteristic, complemented
4C2×#449×C113C211yesmaximal, characteristic, complemented
5C2×#447×C113C211yesmaximal, characteristic, complemented
6C113×#2324C211yesmaximal, characteristic, complemented
7C113×#2042C211yesmaximal, characteristic, complemented
8C113×#2041C211yesmaximal, characteristic, complemented
9C113×#2012C211yesmaximal, characteristic, complemented
10C113×#2011C211yesmaximal, characteristic, complemented
11C113×#1983C211yesmaximal, characteristic, complemented
12C113×#1982C211yesmaximal, characteristic, complemented
13C113×#1798C211yesmaximal, 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
21C22×D8×C113C2211yescharacteristic, complemented
22#535×C113—24no—
23#535×C113—24no—
24C2×#127×C113C2211yescharacteristic
25C2×#127×C113C2211yescharacteristic
26C2×#124×C113C2211yescharacteristic
27C2×#124×C113C2211yescharacteristic
28C2×#121×C113—21no—
29C2×#121×C113—21no—
30C2×#121×C113C2211yescharacteristic
31C2×#120×C113—21no—
32C2×#120×C113—21no—
33C2×C4×D4×C113C2211yescharacteristic, complemented
34C2×#117×C113C2211yescharacteristic
35#463×C113—24no—
36#459×C113—24no—
37#449×C113—24no—
38#447×C113—24no—
39C2×C4⋊C8×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×#102×C113C2211yescharacteristic, complemented
52C2×#102×C113C2211yescharacteristic, complemented
53C2×C22⋊C8×C113C2211yescharacteristic
54C2×C22⋊C8×C113C2211yescharacteristic
55#390×C113—21no—
56#390×C113C2211yescharacteristic, complemented
57#389×C113C2211yescharacteristic, complemented
58#388×C113—21no—
59#386×C113—21no—
60#385×C113—21no—
61#380×C113C2211yescharacteristic
62C4×C4⋊C4×C113C2211yescharacteristic, complemented
63#336×C113C2211yescharacteristic, complemented
64#336×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—21no—
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—22no—
83C22×D4×C113—22no—
84C22×D4×C113—41no—
85C22×D4×C113—41no—
86C22×D4×C113C2311yescharacteristic
87C22×D4×C113C2311yescharacteristic
88C22×D4×C113C2311yescharacteristic
89C22×D4×C113C2311yescharacteristic
90C23×C4×C113—21no—
91C23×C4×C113—21no—
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—22no—
101C2×D8×C113—22no—
102C2×D8×C113—41no—
103C2×D8×C113—41no—
104C2×D8×C113—41no—
105C22×C8×C113C2311yescharacteristic
106C22×C8×C113C2311yescharacteristic
107C22×C8×C113C2311yescharacteristic
108C22×C8×C113C2311yescharacteristic
109#127×C113—22no—
110#127×C113—22no—
111#127×C113—22no—
112#127×C113D414yescomplemented
113#124×C113—22no—
114#124×C113—22no—
115#124×C113—22no—
116#124×C113D414yescomplemented
117#121×C113—28no—
118#121×C113—28no—
119#121×C113—22no—
120#121×C113D414yescomplemented
121#120×C113—28no—
122#120×C113—28no—
123C4×D4×C113—22no—
124C4×D4×C113—22no—
125#117×C113—22no—
126#117×C113—22no—
127C2×C4⋊C4×C113—21no—
128C2×C4⋊C4×C113D411yescharacteristic
129C2×C4⋊C4×C113D411yescharacteristic
130C2×C4⋊C4×C113C2311yescharacteristic
131C2×C4⋊C4×C113C2311yescharacteristic
132C2×C4⋊C4×C113C2311yescharacteristic
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×C113—21no—
145C2×C42×C113C2311yescharacteristic
146C2×C42×C113C2311yescharacteristic
147C4⋊C8×C113—22no—
148C4⋊C8×C113—22no—
149#103×C113—22no—
150#103×C113—22no—
151#103×C113—41no—
152#102×C113—22no—
153#102×C113—22no—
154#102×C113—22no—
155#102×C113—22no—
156#102×C113—22no—
157#102×C113—22no—
158#102×C113—41no—
159#102×C113—41no—
160#102×C113—41no—
161C22⋊C8×C113—22no—
162C22⋊C8×C113—22no—
163#95×C113—21no—
164#95×C113—21no—
165#95×C113—21no—
166C24×C113—24no—
167C24×C113—21no—
168C24×C113—21no—
169C24×C113—21no—
170C24×C113—21no—
171C24×C113—42no—
172C24×C113—42no—
173C24×C113—81no—
174C24×C113—81no—
175C24×C113—81no—
176C24×C113—81no—
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—24no—
191C2×D4×C113—24no—
192C2×D4×C113—24no—
193C2×D4×C113—24no—
194C2×D4×C113—24no—
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—21no—
207C2×D4×C113—21no—
208C2×D4×C113—21no—
209C2×D4×C113—21no—
210C2×D4×C113—21no—
211C2×D4×C113—21no—
212C2×D4×C113—21no—
213C2×D4×C113—21no—
214C2×D4×C113—21no—
215C2×D4×C113—44no—
216C2×D4×C113—44no—
217C2×D4×C113—44no—
218C2×D4×C113—44no—
219C2×D4×C113—42no—
220C2×D4×C113—42no—
221C2×D4×C113—42no—
222C2×D4×C113—42no—
223C2×D4×C113—81no—
224C2×D4×C113—81no—
225C2×D4×C113—81no—
226C2×D4×C113—81no—
227C2×D4×C113—81no—
228C2×D4×C113—81no—
229C2×D4×C113—81no—
230C2×D4×C113—81no—
231C2×D4×C113—81no—
232C2×D4×C113—81no—
233C2×D4×C113C2×D412yes—
234C2×D4×C113C2×D412yes—
235C2×D4×C113C2×D412yes—
236C2×D4×C113C2×D412yes—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—21no—
240C22×C4×C113—21no—
241C22×C4×C113—24no—
242C22×C4×C113—21no—
243C22×C4×C113—21no—
244C22×C4×C113—21no—
245C22×C4×C113—21no—
246C22×C4×C113—42no—
247C22×C4×C113—42no—
248C22×C4×C113—42no—
249C22×C4×C113—81no—
250C22×C4×C113—81no—
251C22×C4×C113C2×D411yescharacteristic
252C22×C4×C113C2×D411yescharacteristic
253C22×C4×C113C2×D411yescharacteristic
254C22×C4×C113C2×D411yescharacteristic
255C22×C4×C113C2×D411yescharacteristic
256C22×C4×C113C2×D412yes—
257C22×C4×C113#4112yes—
258C22×C4×C113C2411yescharacteristic
259SD16×C113—44no—
260D8×C113—44no—
261D8×C113—44no—
262D8×C113—44no—
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×C113—21no—
274C2×C8×C113—21no—
275C4⋊C4×C113—22no—
276C4⋊C4×C113—22no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—81no—
283C4⋊C4×C113C2×D412yes—
284C22⋊C4×C113—24no—
285C22⋊C4×C113—24no—
286C22⋊C4×C113—24no—
287C22⋊C4×C113—24no—
288C22⋊C4×C113—22no—
289C22⋊C4×C113—22no—
290C22⋊C4×C113—24no—
291C22⋊C4×C113—42no—
292C22⋊C4×C113—81no—
293C22⋊C4×C113—81no—
294C22⋊C4×C113—81no—
295C42×C113—21no—
296C42×C113—21no—
297C42×C113—81no—
298C42×C113C2×D412yes—
299C42×C113C2×D412yes—
300C23×C113—21no—
301C23×C113—21no—
302C23×C113—21no—
303C23×C113—21no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—22no—
307C23×C113—22no—
308C23×C113—22no—
309C23×C113—22no—
310C23×C113—48no—
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—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—41no—
335C23×C113—84no—
336C23×C113—84no—
337C23×C113—84no—
338C23×C113—84no—
339C23×C113—84no—
340C23×C113—84no—
341C23×C113#12112yes—
342C23×C113C22×D411yescharacteristic
343Q8×C113—22no—
344Q8×C113—22no—
345Q8×C113—41no—
346Q8×C113—41no—
347D4×C113—22no—
348D4×C113—22no—
349D4×C113—22no—
350D4×C113—22no—
351D4×C113—22no—
352D4×C113—22no—
353D4×C113—22no—
354D4×C113—22no—
355D4×C113—48no—
356D4×C113—48no—
357D4×C113—41no—
358D4×C113—41no—
359D4×C113—41no—
360D4×C113—41no—
361D4×C113—41no—
362D4×C113—41no—
363D4×C113—41no—
364D4×C113—41no—
365D4×C113—84no—
366D4×C113—84no—
367D4×C113—84no—
368D4×C113—84no—
369D4×C113—84no—
370C2×C4×C113—21no—
371C2×C4×C113—21no—
372C2×C4×C113—21no—
373C2×C4×C113—21no—
374C2×C4×C113—21no—
375C2×C4×C113—21no—
376C2×C4×C113—22no—
377C2×C4×C113—22no—
378C2×C4×C113—22no—
379C2×C4×C113—22no—
380C2×C4×C113—21no—
381C2×C4×C113—21no—
382C2×C4×C113—22no—
383C2×C4×C113—22no—
384C2×C4×C113—21no—
385C2×C4×C113—21no—
386C2×C4×C113—21no—
387C2×C4×C113—21no—
388C2×C4×C113—48no—
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—41no—
398C2×C4×C113—41no—
399C2×C4×C113—84no—
400C2×C4×C113#12012yes—
401C2×C4×C113#12012yes—
402C2×C4×C113#12112yes—
403C2×C4×C113C22×D411yescharacteristic
404C2×C4×C113C22×D411yescharacteristic
405C2×C4×C113C22×D411yescharacteristic
406C2×C4×C113C2×#4111yescharacteristic
407C2×C4×C113H(5,𝔽2)11yescharacteristic
408C2×C4×C113H(5,𝔽2)11yescharacteristic
409C8×C113—41no—
410C8×C113—41no—
411C8×C113—41no—
412C8×C113—41no—
413C22×C113—22no—
414C22×C113—22no—
415C22×C113—22no—
416C22×C113—41no—
417C22×C113—41no—
418C22×C113—41no—
419C22×C113—41no—
420C22×C113—42no—
421C22×C113—42no—
422C22×C113—42no—
423C22×C113—42no—
424C22×C113—42no—
425C22×C113—42no—
426C22×C113—42no—
427C22×C113—42no—
428C22×C113—42no—
429C22×C113—42no—
430C22×C113—42no—
431C22×C113—42no—
432C22×C113—816no—
433C22×C113—81no—
434C22×C113—81no—
435C22×C113—81no—
436C22×C113—81no—
437C22×C113—81no—
438C22×C113—81no—
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×C113—81no—
448C22×C113—81no—
449C22×C113C2×#12011yescharacteristic
450C22×C113C2×#12111yescharacteristic
451C22×C113#53511yescharacteristic
452C22×C113#57611yescharacteristic
453C22×C113#57611yescharacteristic
454C22×C113#57611yescharacteristic
455C22×C113#57711yescharacteristic
456C4×C113—22no—
457C4×C113—22no—
458C4×C113—22no—
459C4×C113—42no—
460C4×C113—41no—
461C4×C113—41no—
462C4×C113—42no—
463C4×C113—81no—
464C4×C113—81no—
465C4×C113D4211yescharacteristic
466C4×C113D4211yescharacteristic
467C4×C113#54611yescharacteristic
468C4×C113#54611yescharacteristic
469#24218C11311yesmaximal, characteristic, direct product factor, Sylow
470C2×C113—42no—
471C2×C113—82no—
472C2×C113—82no—
473C2×C113—82no—
474C2×C113—82no—
475C2×C113#240811yescharacteristic
476C2×C113#300811yescharacteristic
477C2×C113#301211yescharacteristic
478C2×C113#304111yescharacteristic
479C2×C113#304511yescharacteristic
480C2×C113#322011yescharacteristic
481C2×C113#322411yescharacteristic
482C2×#535C2×C11311yescharacteristic, complemented
483C2×#463C2×C11311yescharacteristic, complemented
484C2×#459C2×C11311yescharacteristic, complemented
485C2×#449C2×C11311yescharacteristic, complemented
486C2×#447C2×C11311yescharacteristic, complemented
487#2324C2×C11311yescharacteristic, complemented
488#2042C2×C11311yescharacteristic, complemented
489#2041C2×C11311yescharacteristic, complemented
490#2012C2×C11311yescharacteristic, complemented
491#2011C2×C11311yescharacteristic, complemented
492#1983C2×C11311yescharacteristic, complemented
493#1982C2×C11311yescharacteristic, complemented
494#1798C2×C11311yescharacteristic, complemented
495#1788C2×C11311yescharacteristic, complemented
496#1786C2×C11311yescharacteristic, complemented
497C113#2421811yescharacteristic, direct product factor, Sylow
498C22×#41C22×C11311yescharacteristic
499C23×D4C22×C11311yescharacteristic
500C22×SD16C22×C11311yescharacteristic, complemented
501C22×D8C22×C11311yescharacteristic
502C22×D8C22×C11311yescharacteristic
503C22×D8C22×C11311yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127C22×C11311yescharacteristic
507C2×#127C22×C11311yescharacteristic
508C2×#124C22×C11311yescharacteristic
509C2×#124C22×C11311yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C11311yescharacteristic
513C2×#120—21no—
514C2×#120—21no—
515C2×C4×D4C22×C11311yescharacteristic, complemented
516C2×#117C22×C11311yescharacteristic
517#463—24no—
518#459—24no—
519#449—24no—
520#447—24no—
521C2×C4⋊C8C22×C11311yescharacteristic, complemented
522C2×C4⋊C8C22×C11311yescharacteristic, complemented
523C2×#103C22×C11311yescharacteristic, complemented
524C2×#103C22×C11311yescharacteristic, complemented
525C2×#103C22×C11311yescharacteristic, complemented
526C2×#102C22×C11311yescharacteristic
527C2×#102C22×C11311yescharacteristic
528C2×#102C22×C11311yescharacteristic
529C2×#102C22×C11311yescharacteristic
530C2×#102C22×C11311yescharacteristic
531C2×#102C22×C11311yescharacteristic
532C2×#102C22×C11311yescharacteristic, complemented
533C2×#102C22×C11311yescharacteristic, complemented
534C2×#102C22×C11311yescharacteristic, complemented
535C2×C22⋊C8C22×C11311yescharacteristic
536C2×C22⋊C8C22×C11311yescharacteristic
537#390—21no—
538#390C22×C11311yescharacteristic, complemented
539#389C22×C11311yescharacteristic, complemented
540#388—21no—
541#386—21no—
542#385—21no—
543#380C22×C11311yescharacteristic
544C4×C4⋊C4C22×C11311yescharacteristic, complemented
545#336C22×C11311yescharacteristic, complemented
546#336C22×C11311yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C11311yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4C23×C11311yescharacteristic
569C22×D4C23×C11311yescharacteristic
570C22×D4C23×C11311yescharacteristic
571C22×D4C23×C11311yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C11311yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C22×C8C23×C11311yescharacteristic
588C22×C8C23×C11311yescharacteristic
589C22×C8C23×C11311yescharacteristic
590C22×C8C23×C11311yescharacteristic
591#127—22no—
592#127—22no—
593#127—22no—
594#127D4×C11314yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124D4×C11314yescomplemented
599#121—28no—
600#121—28no—
601#121—22no—
602#121D4×C11314yescomplemented
603#120—28no—
604#120—28no—
605C4×D4—22no—
606C4×D4—22no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C11311yescharacteristic
611C2×C4⋊C4D4×C11311yescharacteristic
612C2×C4⋊C4C23×C11311yescharacteristic
613C2×C4⋊C4C23×C11311yescharacteristic
614C2×C4⋊C4C23×C11311yescharacteristic
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⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4D4×C11311yescharacteristic
625C2×C22⋊C4D4×C11311yescharacteristic
626C2×C42—21no—
627C2×C42C23×C11311yescharacteristic
628C2×C42C23×C11311yescharacteristic
629C4⋊C8—22no—
630C4⋊C8—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641#102—41no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—81no—
659C24C2×D4×C11311yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×D4×C11312yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
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—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4C2×D4×C11312yes—
716C2×D4C2×D4×C11312yes—
717C2×D4C2×D4×C11312yes—
718C2×D4C2×D4×C11312yes—
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—21no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C11311yescharacteristic
734C22×C4C2×D4×C11311yescharacteristic
735C22×C4C2×D4×C11311yescharacteristic
736C22×C4C2×D4×C11311yescharacteristic
737C22×C4C2×D4×C11311yescharacteristic
738C22×C4C2×D4×C11312yes—
739C22×C4#41×C11312yes—
740C22×C4C24×C11311yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744D8—44no—
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×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—81no—
765C4⋊C4C2×D4×C11312yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—81no—
780C42C2×D4×C11312yes—
781C42C2×D4×C11312yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
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—41no—
815C23—41no—
816C23—41no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23#121×C11312yes—
824C23C22×D4×C11311yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—48no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—84no—
882C2×C4#120×C11312yes—
883C2×C4#120×C11312yes—
884C2×C4#121×C11312yes—
885C2×C4C22×D4×C11311yescharacteristic
886C2×C4C22×D4×C11311yescharacteristic
887C2×C4C22×D4×C11311yescharacteristic
888C2×C4C2×#41×C11311yescharacteristic
889C2×C4H(5,𝔽2)×C11311yescharacteristic
890C2×C4H(5,𝔽2)×C11311yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C11311yescharacteristic
932C22C2×#121×C11311yescharacteristic
933C22#535×C11311yescharacteristic
934C22#576×C11311yescharacteristic
935C22#576×C11311yescharacteristic
936C22#576×C11311yescharacteristic
937C22#577×C11311yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—42no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—81no—
946C4—81no—
947C4D42×C11311yescharacteristic
948C4D42×C11311yescharacteristic
949C4#546×C11311yescharacteristic
950C4#546×C11311yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2C113×#240811yescharacteristic
957C2C113×#300811yescharacteristic
958C2C113×#301211yescharacteristic
959C2C113×#304111yescharacteristic
960C2C113×#304511yescharacteristic
961C2C113×#322011yescharacteristic
962C2C113×#322411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×#117×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#535×C113C2semidirect
2. C2×#463×C113C2semidirect
3. C2×#459×C113C2semidirect
4. C2×#449×C113C2semidirect
5. C2×#447×C113C2semidirect
6. C113×#2324C2semidirect
7. C113×#2042C2semidirect
8. C113×#2041C2semidirect
9. C113×#2012C2semidirect
10. C113×#2011C2semidirect
11. C113×#1983C2semidirect
12. C113×#1982C2semidirect
13. C113×#1798C2semidirect
14. C113×#1788C2semidirect
15. C113×#1786C2semidirect
18. C22×SD16×C113C22semidirect
21. C22×D8×C113C22semidirect
33. C2×C4×D4×C113C22semidirect
39. C2×C4⋊C8×C113C22semidirect
40. C2×C4⋊C8×C113C22semidirect
41. C2×#103×C113C22semidirect
42. C2×#103×C113C22semidirect
43. C2×#103×C113C22semidirect
50. C2×#102×C113C22semidirect
51. C2×#102×C113C22semidirect
52. C2×#102×C113C22semidirect
56. #390×C113C22semidirect
57. #389×C113C22semidirect
62. C4×C4⋊C4×C113C22semidirect
63. #336×C113C22semidirect
64. #336×C113C22semidirect
112. #127×C113D4semidirect
116. #124×C113D4semidirect
120. #121×C113D4semidirect
469. #24218C113direct (N × H)
482. C2×#535C2×C113semidirect
483. C2×#463C2×C113semidirect
484. C2×#459C2×C113semidirect
485. C2×#449C2×C113semidirect
486. C2×#447C2×C113semidirect
487. #2324C2×C113semidirect
488. #2042C2×C113semidirect
489. #2041C2×C113semidirect
490. #2012C2×C113semidirect
491. #2011C2×C113semidirect
492. #1983C2×C113semidirect
493. #1982C2×C113semidirect
494. #1798C2×C113semidirect
495. #1788C2×C113semidirect
496. #1786C2×C113semidirect
497. C113#24218direct (N × H)
500. C22×SD16C22×C113semidirect
503. C22×D8C22×C113semidirect
515. C2×C4×D4C22×C113semidirect
521. C2×C4⋊C8C22×C113semidirect
522. C2×C4⋊C8C22×C113semidirect
523. C2×#103C22×C113semidirect
524. C2×#103C22×C113semidirect
525. C2×#103C22×C113semidirect
532. C2×#102C22×C113semidirect
533. C2×#102C22×C113semidirect
534. C2×#102C22×C113semidirect
538. #390C22×C113semidirect
539. #389C22×C113semidirect
544. C4×C4⋊C4C22×C113semidirect
545. #336C22×C113semidirect
546. #336C22×C113semidirect
594. #127D4×C113semidirect
598. #124D4×C113semidirect
602. #121D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1132
C2×#463×C1132
C2×#459×C1132
C2×#449×C1132
C2×#447×C1132
C113×#23242
C113×#20422
C113×#20412
C113×#20122
C113×#20112
C113×#19832
C113×#19822
C113×#17982
C113×#17882
C113×#17862
#24218113