Finite Group Databasebeta

← C113×#24050 #43292070

Subgroups — C113×#24050 #43292070

Order 28928.

1450 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C113C211yesmaximal, characteristic
2C2×#485×C113C211yesmaximal, characteristic, complemented
3C2×#418×C113C211yesmaximal, characteristic, complemented
4C113×#2485C211yesmaximal, characteristic, complemented
5C113×#2042C211yesmaximal, characteristic, complemented
6C113×#2042C211yesmaximal, characteristic, complemented
7C113×#2034C211yesmaximal, characteristic, complemented
8C113×#2033C211yesmaximal, characteristic, complemented
9C113×#1894C211yesmaximal, characteristic, complemented
10C113×#1870C211yesmaximal, characteristic, complemented
11C113×#1864C211yesmaximal, characteristic, complemented
12C113×#1862C211yesmaximal, characteristic, complemented
13C113×#1788C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C22×M16×C113C2211yescharacteristic
19#546×C113—24no—
20#546×C113—24no—
21C2×#124×C113C2211yescharacteristic
22C2×#123×C113—21no—
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×#121×C113—21no—
25C2×#121×C113C2211yescharacteristic
26C2×#120×C113—21no—
27C2×C4×D4×C113C2211yescharacteristic
28C2×C4×D4×C113C2211yescharacteristic
29C2×#117×C113C2211yescharacteristic
30C22×C22⋊C4×C113—21no—
31#485×C113—24no—
32C2×#107×C113C2211yescharacteristic, complemented
33C2×#106×C113C2211yescharacteristic, complemented
34#418×C113—24no—
35C2×#103×C113C2211yescharacteristic, complemented
36C2×#103×C113C2211yescharacteristic, complemented
37C2×#103×C113C2211yescharacteristic, complemented
38C2×#103×C113C2211yescharacteristic, complemented
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×C22⋊C8×C113C2211yescharacteristic
48C2×C22⋊C8×C113C2211yescharacteristic, complemented
49C2×C22⋊C8×C113C2211yescharacteristic, complemented
50#397×C113—21no—
51#394×C113—21no—
52#389×C113C2211yescharacteristic, complemented
53#389×C113C2211yescharacteristic, complemented
54#388×C113—21no—
55#387×C113—21no—
56#380×C113C2211yescharacteristic
57#380×C113C2211yescharacteristic, complemented
58#380×C113C2211yescharacteristic, complemented
59#340×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#336×C113C2211yescharacteristic, complemented
62#336×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—41no—
69C2×#41×C113—41no—
70C22×Q8×C113C2311yescharacteristic
71C22×D4×C113—22no—
72C22×D4×C113—22no—
73C22×D4×C113—21no—
74C22×D4×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—22no—
77C22×D4×C113—41no—
78C22×D4×C113—41no—
79C22×D4×C113D414yes—
80C22×D4×C113D411yescharacteristic
81C22×D4×C113C2311yescharacteristic
82C22×D4×C113C2311yescharacteristic
83C23×C4×C113—21no—
84C23×C4×C113—21no—
85C23×C4×C113C2311yescharacteristic
86C23×C4×C113C2311yescharacteristic
87C2×M16×C113—22no—
88C2×M16×C113—41no—
89C2×M16×C113—41no—
90C22×C8×C113C2311yescharacteristic
91C22×C8×C113C2311yescharacteristic
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94#124×C113—22no—
95#124×C113—22no—
96#123×C113—28no—
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113D414yes—
99#121×C113—28no—
100#121×C113—22no—
101#121×C113—22no—
102#120×C113—28no—
103C4×D4×C113—22no—
104C4×D4×C113—22no—
105C4×D4×C113—22no—
106C4×D4×C113—22no—
107#117×C113—22no—
108#117×C113—22no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113—21no—
112C2×C4⋊C4×C113D411yescharacteristic
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C22⋊C4×C113—28no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113D411yescharacteristic
129C2×C22⋊C4×C113D411yescharacteristic
130C2×C42×C113—21no—
131C2×C42×C113C2311yescharacteristic
132#107×C113—22no—
133#106×C113—22no—
134#103×C113—22no—
135#103×C113—22no—
136#103×C113—41no—
137#103×C113—41no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—22no—
143#102×C113—22no—
144#102×C113—41no—
145#102×C113—41no—
146C22⋊C8×C113—22no—
147C22⋊C8×C113—41no—
148C22⋊C8×C113—41no—
149#95×C113—21no—
150#95×C113—21no—
151#95×C113—21no—
152#95×C113—21no—
153#95×C113—21no—
154C24×C113—21no—
155C24×C113—21no—
156C24×C113—24no—
157C24×C113—42no—
158C24×C113—42no—
159C24×C113—42no—
160C24×C113—42no—
161C24×C113—81no—
162C24×C113—81no—
163C24×C113C2×D411yescharacteristic
164C24×C113C2×D411yescharacteristic
165#41×C113—44no—
166#41×C113—44no—
167#41×C113—44no—
168#41×C113—44no—
169C2×Q8×C113—21no—
170C2×Q8×C113—21no—
171C2×Q8×C113—21no—
172C2×Q8×C113—21no—
173C2×Q8×C113—21no—
174C2×Q8×C113C2×D412yes—
175C2×D4×C113—28no—
176C2×D4×C113—24no—
177C2×D4×C113—22no—
178C2×D4×C113—24no—
179C2×D4×C113—24no—
180C2×D4×C113—21no—
181C2×D4×C113—21no—
182C2×D4×C113—21no—
183C2×D4×C113—21no—
184C2×D4×C113—21no—
185C2×D4×C113—21no—
186C2×D4×C113—21no—
187C2×D4×C113—21no—
188C2×D4×C113—44no—
189C2×D4×C113—44no—
190C2×D4×C113—44no—
191C2×D4×C113—41no—
192C2×D4×C113—41no—
193C2×D4×C113—42no—
194C2×D4×C113—42no—
195C2×D4×C113—42no—
196C2×D4×C113—42no—
197C2×D4×C113—81no—
198C2×D4×C113—81no—
199C2×D4×C113C2×D412yes—
200C2×D4×C113C2×D412yes—
201C2×D4×C113#4112yes—
202C2×D4×C113#4112yes—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—24no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—24no—
211C22×C4×C113—21no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—42no—
222C22×C4×C113—42no—
223C22×C4×C113—81no—
224C22×C4×C113—81no—
225C22×C4×C113C2×D411yescharacteristic
226C22×C4×C113C2×D411yescharacteristic
227C22×C4×C113C2×D411yescharacteristic
228C22×C4×C113C2×D411yescharacteristic
229C22×C4×C113C2×D412yes—
230C22×C4×C113C2×D412yes—
231C22×C4×C113C2411yescharacteristic
232M16×C113—44no—
233C2×C8×C113—21no—
234C2×C8×C113—21no—
235C2×C8×C113—21no—
236C2×C8×C113—21no—
237C2×C8×C113—21no—
238C2×C8×C113—21no—
239C2×C8×C113—21no—
240C2×C8×C113—21no—
241C2×C8×C113—21no—
242C2×C8×C113—21no—
243C2×C8×C113—21no—
244C2×C8×C113—21no—
245C4⋊C4×C113—24no—
246C4⋊C4×C113—22no—
247C4⋊C4×C113—21no—
248C4⋊C4×C113—21no—
249C4⋊C4×C113—21no—
250C4⋊C4×C113—21no—
251C4⋊C4×C113—21no—
252C4⋊C4×C113—21no—
253C4⋊C4×C113—21no—
254C4⋊C4×C113—21no—
255C4⋊C4×C113—21no—
256C4⋊C4×C113—42no—
257C4⋊C4×C113—81no—
258C4⋊C4×C113C2×D412yes—
259C22⋊C4×C113—24no—
260C22⋊C4×C113—24no—
261C22⋊C4×C113—24no—
262C22⋊C4×C113—24no—
263C22⋊C4×C113—22no—
264C22⋊C4×C113—24no—
265C22⋊C4×C113—22no—
266C22⋊C4×C113—42no—
267C22⋊C4×C113—42no—
268C22⋊C4×C113—81no—
269C22⋊C4×C113—81no—
270C42×C113—21no—
271C42×C113—21no—
272C42×C113—42no—
273C23×C113—22no—
274C23×C113—21no—
275C23×C113—21no—
276C23×C113—22no—
277C23×C113—22no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—21no—
281C23×C113—21no—
282C23×C113—22no—
283C23×C113—21no—
284C23×C113—21no—
285C23×C113—21no—
286C23×C113—21no—
287C23×C113—21no—
288C23×C113—21no—
289C23×C113—21no—
290C23×C113—48no—
291C23×C113—48no—
292C23×C113—41no—
293C23×C113—41no—
294C23×C113—41no—
295C23×C113—41no—
296C23×C113—41no—
297C23×C113—41no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113—41no—
302C23×C113—84no—
303C23×C113—84no—
304C23×C113—84no—
305C23×C113—84no—
306C23×C113—84no—
307C23×C113#12012yes—
308C23×C113C22×D411yescharacteristic
309Q8×C113—22no—
310Q8×C113—22no—
311Q8×C113—41no—
312Q8×C113—41no—
313D4×C113—22no—
314D4×C113—22no—
315D4×C113—22no—
316D4×C113—22no—
317D4×C113—22no—
318D4×C113—48no—
319D4×C113—44no—
320D4×C113—48no—
321D4×C113—41no—
322D4×C113—41no—
323D4×C113—84no—
324D4×C113#12314yes—
325C2×C4×C113—21no—
326C2×C4×C113—21no—
327C2×C4×C113—22no—
328C2×C4×C113—22no—
329C2×C4×C113—22no—
330C2×C4×C113—22no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—22no—
334C2×C4×C113—21no—
335C2×C4×C113—22no—
336C2×C4×C113—21no—
337C2×C4×C113—21no—
338C2×C4×C113—21no—
339C2×C4×C113—21no—
340C2×C4×C113—21no—
341C2×C4×C113—21no—
342C2×C4×C113—48no—
343C2×C4×C113—41no—
344C2×C4×C113—41no—
345C2×C4×C113—41no—
346C2×C4×C113—41no—
347C2×C4×C113—41no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—41no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
353C2×C4×C113—41no—
354C2×C4×C113—41no—
355C2×C4×C113—41no—
356C2×C4×C113—41no—
357C2×C4×C113—41no—
358C2×C4×C113—41no—
359C2×C4×C113—41no—
360C2×C4×C113—41no—
361C2×C4×C113—41no—
362C2×C4×C113—41no—
363C2×C4×C113—84no—
364C2×C4×C113#12012yes—
365C2×C4×C113C22×D411yescharacteristic
366C2×C4×C113C22×D411yescharacteristic
367C2×C4×C113C2×#4111yescharacteristic
368C2×C4×C113C2×#4111yescharacteristic
369C2×C4×C113H(5,𝔽2)11yescharacteristic
370C2×C4×C113H(5,𝔽2)11yescharacteristic
371C8×C113—41no—
372C8×C113—41no—
373C8×C113—41no—
374C8×C113—41no—
375C22×C113—22no—
376C22×C113—24no—
377C22×C113—22no—
378C22×C113—22no—
379C22×C113—42no—
380C22×C113—42no—
381C22×C113—41no—
382C22×C113—42no—
383C22×C113—41no—
384C22×C113—42no—
385C22×C113—41no—
386C22×C113—42no—
387C22×C113—41no—
388C22×C113—42no—
389C22×C113—41no—
390C22×C113—42no—
391C22×C113—41no—
392C22×C113—42no—
393C22×C113—41no—
394C22×C113—42no—
395C22×C113—41no—
396C22×C113—41no—
397C22×C113—41no—
398C22×C113—41no—
399C22×C113—816no—
400C22×C113—81no—
401C22×C113—81no—
402C22×C113—81no—
403C22×C113—81no—
404C22×C113C2×#12011yescharacteristic
405C22×C113#54611yescharacteristic
406C22×C113#54611yescharacteristic
407C22×C113#57511yescharacteristic
408C22×C113#57511yescharacteristic
409C22×C113#57611yescharacteristic
410C22×C113#57711yescharacteristic
411C4×C113—22no—
412C4×C113—41no—
413C4×C113—42no—
414C4×C113—41no—
415C4×C113—41no—
416C4×C113—42no—
417C4×C113—81no—
418C4×C113—81no—
419C4×C113—81no—
420C4×C113—81no—
421C4×C113C2×#12311yescharacteristic
422C4×C113#53411yescharacteristic
423C4×C113#54611yescharacteristic
424C4×C113#54611yescharacteristic
425#24050C11311yesmaximal, characteristic, direct product factor, Sylow
426C2×C113—42no—
427C2×C113—44no—
428C2×C113—81no—
429C2×C113—82no—
430C2×C113#240511yescharacteristic
431C2×C113#300511yescharacteristic
432C2×C113#301211yescharacteristic
433C2×C113#331111yescharacteristic
434C2×C113#331911yescharacteristic
435C2×C113#332211yescharacteristic
436C2×C113#332311yescharacteristic
437C2×#546C2×C11311yescharacteristic
438C2×#485C2×C11311yescharacteristic, complemented
439C2×#418C2×C11311yescharacteristic, complemented
440#2485C2×C11311yescharacteristic, complemented
441#2042C2×C11311yescharacteristic, complemented
442#2042C2×C11311yescharacteristic, complemented
443#2034C2×C11311yescharacteristic, complemented
444#2033C2×C11311yescharacteristic, complemented
445#1894C2×C11311yescharacteristic, complemented
446#1870C2×C11311yescharacteristic, complemented
447#1864C2×C11311yescharacteristic, complemented
448#1862C2×C11311yescharacteristic, complemented
449#1788C2×C11311yescharacteristic, complemented
450#1788C2×C11311yescharacteristic, complemented
451#1786C2×C11311yescharacteristic, complemented
452C113#2405011yescharacteristic, direct product factor, Sylow
453C22×#41C22×C11311yescharacteristic
454C23×D4C22×C11311yescharacteristic
455C22×M16C22×C11311yescharacteristic
456#546—24no—
457#546—24no—
458C2×#124C22×C11311yescharacteristic
459C2×#123—21no—
460C2×C22⋊Q8C22×C11311yescharacteristic
461C2×#121—21no—
462C2×#121C22×C11311yescharacteristic
463C2×#120—21no—
464C2×C4×D4C22×C11311yescharacteristic
465C2×C4×D4C22×C11311yescharacteristic
466C2×#117C22×C11311yescharacteristic
467C22×C22⋊C4—21no—
468#485—24no—
469C2×#107C22×C11311yescharacteristic, complemented
470C2×#106C22×C11311yescharacteristic, complemented
471#418—24no—
472C2×#103C22×C11311yescharacteristic, complemented
473C2×#103C22×C11311yescharacteristic, complemented
474C2×#103C22×C11311yescharacteristic, complemented
475C2×#103C22×C11311yescharacteristic, complemented
476C2×#102C22×C11311yescharacteristic
477C2×#102C22×C11311yescharacteristic
478C2×#102C22×C11311yescharacteristic
479C2×#102C22×C11311yescharacteristic
480C2×#102C22×C11311yescharacteristic
481C2×#102C22×C11311yescharacteristic
482C2×#102C22×C11311yescharacteristic
483C2×#102C22×C11311yescharacteristic
484C2×C22⋊C8C22×C11311yescharacteristic
485C2×C22⋊C8C22×C11311yescharacteristic, complemented
486C2×C22⋊C8C22×C11311yescharacteristic, complemented
487#397—21no—
488#394—21no—
489#389C22×C11311yescharacteristic, complemented
490#389C22×C11311yescharacteristic, complemented
491#388—21no—
492#387—21no—
493#380C22×C11311yescharacteristic
494#380C22×C11311yescharacteristic, complemented
495#380C22×C11311yescharacteristic, complemented
496#340C22×C11311yescharacteristic, complemented
497#340C22×C11311yescharacteristic, complemented
498#336C22×C11311yescharacteristic, complemented
499#336C22×C11311yescharacteristic, complemented
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C22×Q8C23×C11311yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C11314yes—
517C22×D4D4×C11311yescharacteristic
518C22×D4C23×C11311yescharacteristic
519C22×D4C23×C11311yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C11311yescharacteristic
523C23×C4C23×C11311yescharacteristic
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8C23×C11311yescharacteristic
528C22×C8C23×C11311yescharacteristic
529C22×C8C23×C11311yescharacteristic
530C22×C8C23×C11311yescharacteristic
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C11314yes—
536#121—28no—
537#121—22no—
538#121—22no—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—22no—
545#117—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C11311yescharacteristic
550C2×C4⋊C4C23×C11311yescharacteristic
551C2×C4⋊C4C23×C11311yescharacteristic
552C2×C4⋊C4C23×C11311yescharacteristic
553C2×C4⋊C4C23×C11311yescharacteristic
554C2×C4⋊C4C23×C11311yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C11311yescharacteristic
566C2×C22⋊C4D4×C11311yescharacteristic
567C2×C42—21no—
568C2×C42C23×C11311yescharacteristic
569#107—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—41no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—41no—
585C22⋊C8—41no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24—21no—
592C24—21no—
593C24—24no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×D4×C11311yescharacteristic
601C24C2×D4×C11311yescharacteristic
602#41—44no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C11312yes—
612C2×D4—28no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C2×D4×C11312yes—
637C2×D4C2×D4×C11312yes—
638C2×D4#41×C11312yes—
639C2×D4#41×C11312yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×D4×C11311yescharacteristic
663C22×C4C2×D4×C11311yescharacteristic
664C22×C4C2×D4×C11311yescharacteristic
665C22×C4C2×D4×C11311yescharacteristic
666C22×C4C2×D4×C11312yes—
667C22×C4C2×D4×C11312yes—
668C22×C4C24×C11311yescharacteristic
669M16—44no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C11312yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—22no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—48no—
728C23—48no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23#120×C11312yes—
745C23C22×D4×C11311yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—44no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#123×C11314yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4#120×C11312yes—
802C2×C4C22×D4×C11311yescharacteristic
803C2×C4C22×D4×C11311yescharacteristic
804C2×C4C2×#41×C11311yescharacteristic
805C2×C4C2×#41×C11311yescharacteristic
806C2×C4H(5,𝔽2)×C11311yescharacteristic
807C2×C4H(5,𝔽2)×C11311yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#120×C11311yescharacteristic
842C22#546×C11311yescharacteristic
843C22#546×C11311yescharacteristic
844C22#575×C11311yescharacteristic
845C22#575×C11311yescharacteristic
846C22#576×C11311yescharacteristic
847C22#577×C11311yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×#123×C11311yescharacteristic
859C4#534×C11311yescharacteristic
860C4#546×C11311yescharacteristic
861C4#546×C11311yescharacteristic
862C2—42no—
863C2—44no—
864C2—81no—
865C2—82no—
866C2C113×#240511yescharacteristic
867C2C113×#300511yescharacteristic
868C2C113×#301211yescharacteristic
869C2C113×#331111yescharacteristic
870C2C113×#331911yescharacteristic
871C2C113×#332211yescharacteristic
872C2C113×#332311yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#546×C113C2
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
2. C2×#485×C113C2semidirect
3. C2×#418×C113C2semidirect
4. C113×#2485C2semidirect
5. C113×#2042C2semidirect
6. C113×#2042C2semidirect
7. C113×#2034C2semidirect
8. C113×#2033C2semidirect
9. C113×#1894C2semidirect
10. C113×#1870C2semidirect
11. C113×#1864C2semidirect
12. C113×#1862C2semidirect
13. C113×#1788C2semidirect
14. C113×#1788C2semidirect
15. C113×#1786C2semidirect
32. C2×#107×C113C22semidirect
33. C2×#106×C113C22semidirect
35. C2×#103×C113C22semidirect
36. C2×#103×C113C22semidirect
37. C2×#103×C113C22semidirect
38. C2×#103×C113C22semidirect
48. C2×C22⋊C8×C113C22semidirect
49. C2×C22⋊C8×C113C22semidirect
52. #389×C113C22semidirect
53. #389×C113C22semidirect
57. #380×C113C22semidirect
58. #380×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
425. #24050C113direct (N × H)
438. C2×#485C2×C113semidirect
439. C2×#418C2×C113semidirect
440. #2485C2×C113semidirect
441. #2042C2×C113semidirect
442. #2042C2×C113semidirect
443. #2034C2×C113semidirect
444. #2033C2×C113semidirect
445. #1894C2×C113semidirect
446. #1870C2×C113semidirect
447. #1864C2×C113semidirect
448. #1862C2×C113semidirect
449. #1788C2×C113semidirect
450. #1788C2×C113semidirect
451. #1786C2×C113semidirect
452. C113#24050direct (N × H)
469. C2×#107C22×C113semidirect
470. C2×#106C22×C113semidirect
472. C2×#103C22×C113semidirect
473. C2×#103C22×C113semidirect
474. C2×#103C22×C113semidirect
475. C2×#103C22×C113semidirect
485. C2×C22⋊C8C22×C113semidirect
486. C2×C22⋊C8C22×C113semidirect
489. #389C22×C113semidirect
490. #389C22×C113semidirect
494. #380C22×C113semidirect
495. #380C22×C113semidirect
496. #340C22×C113semidirect
497. #340C22×C113semidirect
498. #336C22×C113semidirect
499. #336C22×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×#485×C1132
C2×#418×C1132
C113×#24852
C113×#20422
C113×#20342
C113×#20332
C113×#18942
C113×#18702
C113×#18642
C113×#18622
C113×#17882
C113×#17862
#24050113