Finite Group Databasebeta

← C113×#24442 #43292462

Subgroups — C113×#24442 #43292462

Order 28928.

1570 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C113C211yesmaximal, characteristic
2C2×#470×C113C211yesmaximal, characteristic, complemented
3C2×#452×C113C211yesmaximal, characteristic, complemented
4C2×#450×C113C211yesmaximal, characteristic, complemented
5C2×#418×C113C211yesmaximal, characteristic, complemented
6C113×#2415C211yesmaximal, characteristic, complemented
7C113×#2042C211yesmaximal, characteristic, complemented
8C113×#2034C211yesmaximal, characteristic, complemented
9C113×#2015C211yesmaximal, characteristic, complemented
10C113×#2000C211yesmaximal, characteristic, complemented
11C113×#1877C211yesmaximal, characteristic, complemented
12C113×#1873C211yesmaximal, characteristic, complemented
13C113×#1870C211yesmaximal, characteristic, complemented
14C113×#1864C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C22×Q16×C113C2211yescharacteristic, complemented
19C22×SD16×C113C2211yescharacteristic
20C22×SD16×C113C2211yescharacteristic
21C22×M16×C113C2211yescharacteristic
22#546×C113—24no—
23#546×C113—24no—
24C2×#124×C113C2211yescharacteristic
25C2×#123×C113—21no—
26C2×C22⋊Q8×C113C2211yescharacteristic
27C2×C22⋊Q8×C113C2211yescharacteristic
28C2×C22⋊Q8×C113C2211yescharacteristic, complemented
29C2×#121×C113—21no—
30C2×#121×C113C2211yescharacteristic
31C2×#120×C113—21no—
32C2×C4×D4×C113C2211yescharacteristic
33C2×C4×D4×C113C2211yescharacteristic
34C2×#117×C113C2211yescharacteristic
35C22×C22⋊C4×C113—21no—
36#470×C113—24no—
37#452×C113—24no—
38#450×C113—24no—
39C2×#106×C113C2211yescharacteristic, complemented
40#418×C113—24no—
41C2×#103×C113C2211yescharacteristic, complemented
42C2×#103×C113C2211yescharacteristic, complemented
43C2×#103×C113C2211yescharacteristic, complemented
44C2×#103×C113C2211yescharacteristic, complemented
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×C22⋊C8×C113C2211yescharacteristic
52C2×C22⋊C8×C113C2211yescharacteristic, complemented
53C2×C22⋊C8×C113C2211yescharacteristic, complemented
54#397×C113—21no—
55#394×C113—21no—
56#391×C113C2211yescharacteristic, complemented
57#389×C113—21no—
58#389×C113C2211yescharacteristic, complemented
59#388×C113—21no—
60#380×C113C2211yescharacteristic, complemented
61#340×C113C2211yescharacteristic, complemented
62#340×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×Q8×C113C2311yescharacteristic
74C22×D4×C113—22no—
75C22×D4×C113—22no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113—21no—
79C22×D4×C113—22no—
80C22×D4×C113—41no—
81C22×D4×C113—41no—
82C22×D4×C113D414yes—
83C22×D4×C113D411yescharacteristic
84C22×D4×C113C2311yescharacteristic
85C22×D4×C113C2311yescharacteristic
86C23×C4×C113—21no—
87C23×C4×C113—21no—
88C23×C4×C113C2311yescharacteristic
89C23×C4×C113C2311yescharacteristic
90C2×Q16×C113—22no—
91C2×Q16×C113—22no—
92C2×Q16×C113—41no—
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—22no—
96C2×SD16×C113—22no—
97C2×SD16×C113—41no—
98C2×SD16×C113—41no—
99C2×M16×C113—22no—
100C2×M16×C113—22no—
101C2×M16×C113—41no—
102C22×C8×C113C2311yescharacteristic
103C22×C8×C113C2311yescharacteristic
104C22×C8×C113C2311yescharacteristic
105C22×C8×C113C2311yescharacteristic
106#124×C113—22no—
107#124×C113—22no—
108#123×C113—28no—
109C22⋊Q8×C113—22no—
110C22⋊Q8×C113—22no—
111C22⋊Q8×C113—22no—
112C22⋊Q8×C113—22no—
113C22⋊Q8×C113—41no—
114C22⋊Q8×C113D414yes—
115#121×C113—28no—
116#121×C113—22no—
117#121×C113—22no—
118#120×C113—28no—
119C4×D4×C113—22no—
120C4×D4×C113—22no—
121C4×D4×C113—22no—
122C4×D4×C113—22no—
123#117×C113—22no—
124#117×C113—41no—
125C2×C4⋊C4×C113—21no—
126C2×C4⋊C4×C113—21no—
127C2×C4⋊C4×C113—21no—
128C2×C4⋊C4×C113—21no—
129C2×C4⋊C4×C113D411yescharacteristic
130C2×C4⋊C4×C113C2311yescharacteristic
131C2×C4⋊C4×C113C2311yescharacteristic
132C2×C4⋊C4×C113C2311yescharacteristic
133C2×C4⋊C4×C113C2311yescharacteristic
134C2×C22⋊C4×C113—28no—
135C2×C22⋊C4×C113—21no—
136C2×C22⋊C4×C113—21no—
137C2×C22⋊C4×C113—21no—
138C2×C22⋊C4×C113—21no—
139C2×C22⋊C4×C113—21no—
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113—21no—
142C2×C22⋊C4×C113—21no—
143C2×C22⋊C4×C113—21no—
144C2×C22⋊C4×C113D411yescharacteristic
145C2×C22⋊C4×C113D411yescharacteristic
146C2×C42×C113—21no—
147C2×C42×C113C2311yescharacteristic
148#106×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—22no—
157#102×C113—22no—
158#102×C113D414yescomplemented
159C22⋊C8×C113—22no—
160C22⋊C8×C113—22no—
161C22⋊C8×C113—41no—
162#95×C113—21no—
163#95×C113—21no—
164#95×C113—21no—
165#95×C113—21no—
166C24×C113—21no—
167C24×C113—21no—
168C24×C113—24no—
169C24×C113—42no—
170C24×C113—42no—
171C24×C113—42no—
172C24×C113—42no—
173C24×C113—81no—
174C24×C113—81no—
175C24×C113C2×D411yescharacteristic
176C24×C113C2×D411yescharacteristic
177#41×C113—44no—
178#41×C113—44no—
179#41×C113—44no—
180#41×C113—44no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113—21no—
186C2×Q8×C113—21no—
187C2×Q8×C113—21no—
188C2×Q8×C113—21no—
189C2×Q8×C113—21no—
190C2×Q8×C113—21no—
191C2×Q8×C113—21no—
192C2×Q8×C113C2×D412yes—
193C2×D4×C113—28no—
194C2×D4×C113—24no—
195C2×D4×C113—22no—
196C2×D4×C113—24no—
197C2×D4×C113—24no—
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—44no—
207C2×D4×C113—44no—
208C2×D4×C113—44no—
209C2×D4×C113—41no—
210C2×D4×C113—41no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—42no—
215C2×D4×C113—81no—
216C2×D4×C113—81no—
217C2×D4×C113C2×D412yes—
218C2×D4×C113C2×D412yes—
219C2×D4×C113C2×D412yes—
220C2×D4×C113#4112yes—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—24no—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—24no—
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—42no—
240C22×C4×C113—42no—
241C22×C4×C113—81no—
242C22×C4×C113—81no—
243C22×C4×C113C2×D411yescharacteristic
244C22×C4×C113C2×D411yescharacteristic
245C22×C4×C113C2×D411yescharacteristic
246C22×C4×C113C2×D411yescharacteristic
247C22×C4×C113C2×D412yes—
248C22×C4×C113C2×D412yes—
249C22×C4×C113C2411yescharacteristic
250Q16×C113—44no—
251SD16×C113—44no—
252SD16×C113—44no—
253M16×C113—44no—
254C2×C8×C113—21no—
255C2×C8×C113—21no—
256C2×C8×C113—21no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C2×C8×C113—21no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113C2×D412yes—
266C4⋊C4×C113—24no—
267C4⋊C4×C113—22no—
268C4⋊C4×C113—21no—
269C4⋊C4×C113—21no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—42no—
275C4⋊C4×C113—42no—
276C4⋊C4×C113—42no—
277C4⋊C4×C113C2×D412yes—
278C4⋊C4×C113C2×D412yes—
279C22⋊C4×C113—24no—
280C22⋊C4×C113—24no—
281C22⋊C4×C113—24no—
282C22⋊C4×C113—24no—
283C22⋊C4×C113—22no—
284C22⋊C4×C113—24no—
285C22⋊C4×C113—22no—
286C22⋊C4×C113—42no—
287C22⋊C4×C113—42no—
288C22⋊C4×C113—42no—
289C22⋊C4×C113—42no—
290C42×C113—21no—
291C42×C113—21no—
292C42×C113—42no—
293C23×C113—22no—
294C23×C113—21no—
295C23×C113—22no—
296C23×C113—21no—
297C23×C113—22no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—21no—
301C23×C113—21no—
302C23×C113—22no—
303C23×C113—21no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
307C23×C113—21no—
308C23×C113—21no—
309C23×C113—21no—
310C23×C113—48no—
311C23×C113—48no—
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—84no—
323C23×C113—84no—
324C23×C113—84no—
325C23×C113—84no—
326C23×C113—84no—
327C23×C113#12012yes—
328C23×C113C22×D411yescharacteristic
329Q8×C113—22no—
330Q8×C113—22no—
331Q8×C113—41no—
332Q8×C113—41no—
333Q8×C113—41no—
334Q8×C113—41no—
335Q8×C113—41no—
336Q8×C113—41no—
337D4×C113—22no—
338D4×C113—22no—
339D4×C113—22no—
340D4×C113—22no—
341D4×C113—22no—
342D4×C113—48no—
343D4×C113—44no—
344D4×C113—48no—
345D4×C113—41no—
346D4×C113—41no—
347D4×C113—84no—
348D4×C113#12114yes—
349C2×C4×C113—21no—
350C2×C4×C113—21no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—22no—
354C2×C4×C113—22no—
355C2×C4×C113—21no—
356C2×C4×C113—21no—
357C2×C4×C113—22no—
358C2×C4×C113—21no—
359C2×C4×C113—22no—
360C2×C4×C113—22no—
361C2×C4×C113—21no—
362C2×C4×C113—21no—
363C2×C4×C113—21no—
364C2×C4×C113—21no—
365C2×C4×C113—21no—
366C2×C4×C113—21no—
367C2×C4×C113—48no—
368C2×C4×C113—41no—
369C2×C4×C113—41no—
370C2×C4×C113—41no—
371C2×C4×C113—41no—
372C2×C4×C113—41no—
373C2×C4×C113—41no—
374C2×C4×C113—41no—
375C2×C4×C113—41no—
376C2×C4×C113—41no—
377C2×C4×C113—41no—
378C2×C4×C113—41no—
379C2×C4×C113—41no—
380C2×C4×C113—41no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
383C2×C4×C113—41no—
384C2×C4×C113—41no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—84no—
388C2×C4×C113#12012yes—
389C2×C4×C113C22×D411yescharacteristic
390C2×C4×C113C22×D411yescharacteristic
391C2×C4×C113C22×D411yescharacteristic
392C2×C4×C113C2×#4111yescharacteristic
393C2×C4×C113H(5,𝔽2)11yescharacteristic
394C2×C4×C113H(5,𝔽2)11yescharacteristic
395C8×C113—22no—
396C8×C113—41no—
397C8×C113—41no—
398C8×C113—41no—
399C22×C113—22no—
400C22×C113—24no—
401C22×C113—22no—
402C22×C113—22no—
403C22×C113—42no—
404C22×C113—42no—
405C22×C113—41no—
406C22×C113—42no—
407C22×C113—41no—
408C22×C113—42no—
409C22×C113—41no—
410C22×C113—42no—
411C22×C113—41no—
412C22×C113—42no—
413C22×C113—41no—
414C22×C113—42no—
415C22×C113—41no—
416C22×C113—42no—
417C22×C113—41no—
418C22×C113—42no—
419C22×C113—41no—
420C22×C113—41no—
421C22×C113—41no—
422C22×C113—41no—
423C22×C113—816no—
424C22×C113—81no—
425C22×C113—81no—
426C22×C113—81no—
427C22×C113—81no—
428C22×C113C2×#12011yescharacteristic
429C22×C113D4211yescharacteristic
430C22×C113#54611yescharacteristic
431C22×C113#57511yescharacteristic
432C22×C113#57511yescharacteristic
433C22×C113#57711yescharacteristic
434C22×C113#57711yescharacteristic
435C4×C113—22no—
436C4×C113—41no—
437C4×C113—42no—
438C4×C113—41no—
439C4×C113—41no—
440C4×C113—42no—
441C4×C113—42no—
442C4×C113—81no—
443C4×C113—81no—
444C4×C113—81no—
445C4×C113C2×#12111yescharacteristic
446C4×C113#53411yescharacteristic
447C4×C113D4211yescharacteristic
448C4×C113#54611yescharacteristic
449#24442C11311yesmaximal, characteristic, direct product factor, Sylow
450C2×C113—42no—
451C2×C113—44no—
452C2×C113—81no—
453C2×C113—82no—
454C2×C113#241011yescharacteristic
455C2×C113#300511yescharacteristic
456C2×C113#300911yescharacteristic
457C2×C113#326711yescharacteristic
458C2×C113#327511yescharacteristic
459C2×C113#331111yescharacteristic
460C2×C113#332311yescharacteristic
461C2×#546C2×C11311yescharacteristic
462C2×#470C2×C11311yescharacteristic, complemented
463C2×#452C2×C11311yescharacteristic, complemented
464C2×#450C2×C11311yescharacteristic, complemented
465C2×#418C2×C11311yescharacteristic, complemented
466#2415C2×C11311yescharacteristic, complemented
467#2042C2×C11311yescharacteristic, complemented
468#2034C2×C11311yescharacteristic, complemented
469#2015C2×C11311yescharacteristic, complemented
470#2000C2×C11311yescharacteristic, complemented
471#1877C2×C11311yescharacteristic, complemented
472#1873C2×C11311yescharacteristic, complemented
473#1870C2×C11311yescharacteristic, complemented
474#1864C2×C11311yescharacteristic, complemented
475#1788C2×C11311yescharacteristic, complemented
476C113#2444211yescharacteristic, direct product factor, Sylow
477C22×#41C22×C11311yescharacteristic
478C23×D4C22×C11311yescharacteristic
479C22×Q16C22×C11311yescharacteristic, complemented
480C22×SD16C22×C11311yescharacteristic
481C22×SD16C22×C11311yescharacteristic
482C22×M16C22×C11311yescharacteristic
483#546—24no—
484#546—24no—
485C2×#124C22×C11311yescharacteristic
486C2×#123—21no—
487C2×C22⋊Q8C22×C11311yescharacteristic
488C2×C22⋊Q8C22×C11311yescharacteristic
489C2×C22⋊Q8C22×C11311yescharacteristic, complemented
490C2×#121—21no—
491C2×#121C22×C11311yescharacteristic
492C2×#120—21no—
493C2×C4×D4C22×C11311yescharacteristic
494C2×C4×D4C22×C11311yescharacteristic
495C2×#117C22×C11311yescharacteristic
496C22×C22⋊C4—21no—
497#470—24no—
498#452—24no—
499#450—24no—
500C2×#106C22×C11311yescharacteristic, complemented
501#418—24no—
502C2×#103C22×C11311yescharacteristic, complemented
503C2×#103C22×C11311yescharacteristic, complemented
504C2×#103C22×C11311yescharacteristic, complemented
505C2×#103C22×C11311yescharacteristic, complemented
506C2×#102C22×C11311yescharacteristic
507C2×#102C22×C11311yescharacteristic
508C2×#102C22×C11311yescharacteristic
509C2×#102C22×C11311yescharacteristic
510C2×#102C22×C11311yescharacteristic
511C2×#102C22×C11311yescharacteristic
512C2×C22⋊C8C22×C11311yescharacteristic
513C2×C22⋊C8C22×C11311yescharacteristic, complemented
514C2×C22⋊C8C22×C11311yescharacteristic, complemented
515#397—21no—
516#394—21no—
517#391C22×C11311yescharacteristic, complemented
518#389—21no—
519#389C22×C11311yescharacteristic, complemented
520#388—21no—
521#380C22×C11311yescharacteristic, complemented
522#340C22×C11311yescharacteristic, complemented
523#340C22×C11311yescharacteristic, complemented
524#336C22×C11311yescharacteristic, complemented
525#336C22×C11311yescharacteristic, complemented
526C25—21no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C22×Q8C23×C11311yescharacteristic
534C22×Q8C23×C11311yescharacteristic
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C11314yes—
544C22×D4D4×C11311yescharacteristic
545C22×D4C23×C11311yescharacteristic
546C22×D4C23×C11311yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C11311yescharacteristic
550C23×C4C23×C11311yescharacteristic
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C22×C8C23×C11311yescharacteristic
564C22×C8C23×C11311yescharacteristic
565C22×C8C23×C11311yescharacteristic
566C22×C8C23×C11311yescharacteristic
567#124—22no—
568#124—22no—
569#123—28no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C22⋊Q8D4×C11314yes—
576#121—28no—
577#121—22no—
578#121—22no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—41no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4D4×C11311yescharacteristic
591C2×C4⋊C4C23×C11311yescharacteristic
592C2×C4⋊C4C23×C11311yescharacteristic
593C2×C4⋊C4C23×C11311yescharacteristic
594C2×C4⋊C4C23×C11311yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C11311yescharacteristic
606C2×C22⋊C4D4×C11311yescharacteristic
607C2×C42—21no—
608C2×C42C23×C11311yescharacteristic
609#106—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—41no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102D4×C11314yescomplemented
620C22⋊C8—22no—
621C22⋊C8—22no—
622C22⋊C8—41no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—21no—
629C24—24no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×D4×C11311yescharacteristic
637C24C2×D4×C11311yescharacteristic
638#41—44no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C11312yes—
654C2×D4—28no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—41no—
671C2×D4—41no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×D4×C11312yes—
679C2×D4C2×D4×C11312yes—
680C2×D4C2×D4×C11312yes—
681C2×D4#41×C11312yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4C2×D4×C11311yescharacteristic
705C22×C4C2×D4×C11311yescharacteristic
706C22×C4C2×D4×C11311yescharacteristic
707C22×C4C2×D4×C11311yescharacteristic
708C22×C4C2×D4×C11312yes—
709C22×C4C2×D4×C11312yes—
710C22×C4C24×C11311yescharacteristic
711Q16—44no—
712SD16—44no—
713SD16—44no—
714M16—44no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8C2×D4×C11312yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4C2×D4×C11312yes—
739C4⋊C4C2×D4×C11312yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C42—21no—
752C42—21no—
753C42—42no—
754C23—22no—
755C23—21no—
756C23—22no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—48no—
772C23—48no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23#120×C11312yes—
789C23C22×D4×C11311yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—48no—
805D4—44no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4#121×C11314yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—84no—
849C2×C4#120×C11312yes—
850C2×C4C22×D4×C11311yescharacteristic
851C2×C4C22×D4×C11311yescharacteristic
852C2×C4C22×D4×C11311yescharacteristic
853C2×C4C2×#41×C11311yescharacteristic
854C2×C4H(5,𝔽2)×C11311yescharacteristic
855C2×C4H(5,𝔽2)×C11311yescharacteristic
856C8—22no—
857C8—41no—
858C8—41no—
859C8—41no—
860C22—22no—
861C22—24no—
862C22—22no—
863C22—22no—
864C22—41no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—41no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×#120×C11311yescharacteristic
890C22D42×C11311yescharacteristic
891C22#546×C11311yescharacteristic
892C22#575×C11311yescharacteristic
893C22#575×C11311yescharacteristic
894C22#577×C11311yescharacteristic
895C22#577×C11311yescharacteristic
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—42no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4C2×#121×C11311yescharacteristic
907C4#534×C11311yescharacteristic
908C4D42×C11311yescharacteristic
909C4#546×C11311yescharacteristic
910C2—42no—
911C2—44no—
912C2—81no—
913C2—82no—
914C2C113×#241011yescharacteristic
915C2C113×#300511yescharacteristic
916C2C113×#300911yescharacteristic
917C2C113×#326711yescharacteristic
918C2C113×#327511yescharacteristic
919C2C113×#331111yescharacteristic
920C2C113×#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×#470×C113C2semidirect
3. C2×#452×C113C2semidirect
4. C2×#450×C113C2semidirect
5. C2×#418×C113C2semidirect
6. C113×#2415C2semidirect
7. C113×#2042C2semidirect
8. C113×#2034C2semidirect
9. C113×#2015C2semidirect
10. C113×#2000C2semidirect
11. C113×#1877C2semidirect
12. C113×#1873C2semidirect
13. C113×#1870C2semidirect
14. C113×#1864C2semidirect
15. C113×#1788C2semidirect
18. C22×Q16×C113C22semidirect
28. C2×C22⋊Q8×C113C22semidirect
39. C2×#106×C113C22semidirect
41. C2×#103×C113C22semidirect
42. C2×#103×C113C22semidirect
43. C2×#103×C113C22semidirect
44. C2×#103×C113C22semidirect
52. C2×C22⋊C8×C113C22semidirect
53. C2×C22⋊C8×C113C22semidirect
56. #391×C113C22semidirect
58. #389×C113C22semidirect
60. #380×C113C22semidirect
61. #340×C113C22semidirect
62. #340×C113C22semidirect
63. #336×C113C22semidirect
64. #336×C113C22semidirect
158. #102×C113D4semidirect
449. #24442C113direct (N × H)
462. C2×#470C2×C113semidirect
463. C2×#452C2×C113semidirect
464. C2×#450C2×C113semidirect
465. C2×#418C2×C113semidirect
466. #2415C2×C113semidirect
467. #2042C2×C113semidirect
468. #2034C2×C113semidirect
469. #2015C2×C113semidirect
470. #2000C2×C113semidirect
471. #1877C2×C113semidirect
472. #1873C2×C113semidirect
473. #1870C2×C113semidirect
474. #1864C2×C113semidirect
475. #1788C2×C113semidirect
476. C113#24442direct (N × H)
479. C22×Q16C22×C113semidirect
489. C2×C22⋊Q8C22×C113semidirect
500. C2×#106C22×C113semidirect
502. C2×#103C22×C113semidirect
503. C2×#103C22×C113semidirect
504. C2×#103C22×C113semidirect
505. C2×#103C22×C113semidirect
513. C2×C22⋊C8C22×C113semidirect
514. C2×C22⋊C8C22×C113semidirect
517. #391C22×C113semidirect
519. #389C22×C113semidirect
521. #380C22×C113semidirect
522. #340C22×C113semidirect
523. #340C22×C113semidirect
524. #336C22×C113semidirect
525. #336C22×C113semidirect
619. #102D4×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×#470×C1132
C2×#452×C1132
C2×#450×C1132
C2×#418×C1132
C113×#24152
C113×#20422
C113×#20342
C113×#20152
C113×#20002
C113×#18772
C113×#18732
C113×#18702
C113×#18642
C113×#17882
#24442113