Finite Group Databasebeta

← C113×#23972 #43291992

Subgroups — C113×#23972 #43291992

Order 28928.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C113C211yesmaximal, characteristic, complemented
2C2×#449×C113C211yesmaximal, characteristic, complemented
3C2×#417×C113C211yesmaximal, characteristic, complemented
4C113×#2407C211yesmaximal, characteristic, complemented
5C113×#2024C211yesmaximal, characteristic, complemented
6C113×#2023C211yesmaximal, characteristic, complemented
7C113×#2000C211yesmaximal, characteristic, complemented
8C113×#1999C211yesmaximal, characteristic, complemented
9C113×#1895C211yesmaximal, characteristic, complemented
10C113×#1879C211yesmaximal, characteristic, complemented
11C113×#1877C211yesmaximal, characteristic, complemented
12C113×#1874C211yesmaximal, characteristic, complemented
13C113×#1872C211yesmaximal, characteristic, complemented
14C113×#1870C211yesmaximal, characteristic, complemented
15C113×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C113—21no—
17C22×#41×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×D8×C113C2211yescharacteristic
20C22×M16×C113C2211yescharacteristic
21#547×C113—24no—
22#547×C113—24no—
23C2×C4⋊Q8×C113C2211yescharacteristic
24C2×#123×C113—21no—
25C2×#123×C113—21no—
26C2×C22⋊Q8×C113—21no—
27C2×C22⋊Q8×C113C2211yescharacteristic
28C2×#121×C113C2211yescharacteristic
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic
31C2×C4×D4×C113C2211yescharacteristic
32C2×C4×D4×C113C2211yescharacteristic
33C22×C4⋊C4×C113C2211yescharacteristic
34C22×C4⋊C4×C113C2211yescharacteristic
35#449×C113—24no—
36#417×C113—24no—
37C2×#103×C113C2211yescharacteristic
38C2×#103×C113C2211yescharacteristic
39C2×#103×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×C22⋊C8×C113C2211yescharacteristic
46C2×C22⋊C8×C113C2211yescharacteristic
47C2×C22⋊C8×C113C2211yescharacteristic
48#394×C113—21no—
49#392×C113—21no—
50#391×C113C2211yescharacteristic
51#390×C113C2211yescharacteristic
52#386×C113—21no—
53#385×C113—21no—
54#380×C113C2211yescharacteristic
55#340×C113C2211yescharacteristic
56#340×C113C2211yescharacteristic
57#340×C113C2211yescharacteristic
58#340×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#336×C113C2211yescharacteristic
62#336×C113C2211yescharacteristic
63C2×#41×C113—28no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—41no—
69C2×#41×C113—41no—
70C2×#41×C113—44no—
71C2×#41×C113—44no—
72C22×Q8×C113—21no—
73C22×Q8×C113C2311yescharacteristic
74C22×D4×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113D411yescharacteristic
79C22×D4×C113C2311yescharacteristic
80C22×D4×C113C2311yescharacteristic
81C23×C4×C113—21no—
82C23×C4×C113—21no—
83C23×C4×C113—21no—
84C23×C4×C113—21no—
85C23×C4×C113C2311yescharacteristic
86C23×C4×C113C2311yescharacteristic
87C2×SD16×C113—22no—
88C2×SD16×C113—22no—
89C2×SD16×C113—41no—
90C2×D8×C113—22no—
91C2×D8×C113—22no—
92C2×D8×C113—41no—
93C2×M16×C113—22no—
94C2×M16×C113—41no—
95C2×M16×C113—41no—
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98C22×C8×C113C2311yescharacteristic
99C22×C8×C113C2311yescharacteristic
100C4⋊Q8×C113—22no—
101C4⋊Q8×C113—22no—
102#123×C113—28no—
103#123×C113—28no—
104C22⋊Q8×C113—28no—
105C22⋊Q8×C113—22no—
106C22⋊Q8×C113—41no—
107#121×C113—22no—
108#121×C113—22no—
109#121×C113—22no—
110#121×C113—22no—
111#121×C113—41no—
112#121×C113D414yescomplemented
113C4×D4×C113—22no—
114C4×D4×C113—22no—
115C4×D4×C113—22no—
116C4×D4×C113—22no—
117C2×C4⋊C4×C113—21no—
118C2×C4⋊C4×C113—21no—
119C2×C4⋊C4×C113—22no—
120C2×C4⋊C4×C113—21no—
121C2×C4⋊C4×C113—22no—
122C2×C4⋊C4×C113—22no—
123C2×C4⋊C4×C113—21no—
124C2×C4⋊C4×C113D411yescharacteristic
125C2×C4⋊C4×C113D414yescomplemented
126C2×C4⋊C4×C113C2311yescharacteristic
127C2×C4⋊C4×C113C2311yescharacteristic
128C2×C4⋊C4×C113C2311yescharacteristic
129C2×C4⋊C4×C113C2311yescharacteristic
130C2×C4⋊C4×C113C2311yescharacteristic
131C2×C22⋊C4×C113—21no—
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×C113D411yescharacteristic
140C2×C22⋊C4×C113D411yescharacteristic
141C2×C42×C113C2311yescharacteristic
142#103×C113—22no—
143#103×C113—22no—
144#103×C113—22no—
145#102×C113—22no—
146#102×C113—22no—
147#102×C113—22no—
148#102×C113—41no—
149#102×C113—41no—
150C22⋊C8×C113—22no—
151C22⋊C8×C113—41no—
152C22⋊C8×C113—41no—
153#95×C113—21no—
154#95×C113—21no—
155#95×C113—21no—
156C24×C113—21no—
157C24×C113—21no—
158C24×C113C2×D411yescharacteristic
159C24×C113C2×D411yescharacteristic
160#41×C113—28no—
161#41×C113—44no—
162#41×C113—44no—
163#41×C113—44no—
164#41×C113—432no—
165C2×Q8×C113—24no—
166C2×Q8×C113—21no—
167C2×Q8×C113—21no—
168C2×Q8×C113—21no—
169C2×Q8×C113—21no—
170C2×Q8×C113—21no—
171C2×Q8×C113—42no—
172C2×Q8×C113—42no—
173C2×Q8×C113#4112yescomplemented
174C2×D4×C113—22no—
175C2×D4×C113—22no—
176C2×D4×C113—24no—
177C2×D4×C113—24no—
178C2×D4×C113—22no—
179C2×D4×C113—21no—
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—21no—
189C2×D4×C113—42no—
190C2×D4×C113—42no—
191C2×D4×C113—42no—
192C2×D4×C113—42no—
193C2×D4×C113—42no—
194C2×D4×C113—42no—
195C2×D4×C113—42no—
196C2×D4×C113—42no—
197C2×D4×C113—42no—
198C2×D4×C113—81no—
199C2×D4×C113C2×D412yes—
200C2×D4×C113#4112yescomplemented
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—24no—
206C22×C4×C113—24no—
207C22×C4×C113—24no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
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—42no—
221C22×C4×C113—42no—
222C22×C4×C113—42no—
223C22×C4×C113—42no—
224C22×C4×C113—42no—
225C22×C4×C113—42no—
226C22×C4×C113—42no—
227C22×C4×C113—42no—
228C22×C4×C113—42no—
229C22×C4×C113C2×D411yescharacteristic
230C22×C4×C113C2×D411yescharacteristic
231C22×C4×C113C2×D411yescharacteristic
232C22×C4×C113C2×D412yes—
233C22×C4×C113C2×D412yes—
234C22×C4×C113C2×D411yescharacteristic
235C22×C4×C113C2411yescharacteristic
236SD16×C113—44no—
237D8×C113—44no—
238M16×C113—44no—
239C2×C8×C113—21no—
240C2×C8×C113—21no—
241C2×C8×C113—21no—
242C2×C8×C113—21no—
243C2×C8×C113—21no—
244C2×C8×C113—21no—
245C2×C8×C113—21no—
246C2×C8×C113—21no—
247C2×C8×C113—21no—
248C2×C8×C113—21no—
249C2×C8×C113—21no—
250C2×C8×C113—21no—
251C4⋊C4×C113—24no—
252C4⋊C4×C113—24no—
253C4⋊C4×C113—24no—
254C4⋊C4×C113—22no—
255C4⋊C4×C113—21no—
256C4⋊C4×C113—21no—
257C4⋊C4×C113—21no—
258C4⋊C4×C113—21no—
259C4⋊C4×C113—21no—
260C4⋊C4×C113—21no—
261C4⋊C4×C113—21no—
262C4⋊C4×C113—42no—
263C4⋊C4×C113C2×D412yes—
264C4⋊C4×C113C2×D412yes—
265C4⋊C4×C113C2×D412yes—
266C22⋊C4×C113—24no—
267C22⋊C4×C113—24no—
268C22⋊C4×C113—22no—
269C22⋊C4×C113—24no—
270C22⋊C4×C113—22no—
271C22⋊C4×C113—42no—
272C22⋊C4×C113—42no—
273C22⋊C4×C113—42no—
274C22⋊C4×C113—81no—
275C22⋊C4×C113—81no—
276C42×C113—21no—
277C42×C113—21no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—21no—
281C23×C113—21no—
282C23×C113—21no—
283C23×C113—21no—
284C23×C113—21no—
285C23×C113—21no—
286C23×C113—21no—
287C23×C113—21no—
288C23×C113—21no—
289C23×C113—21no—
290C23×C113—22no—
291C23×C113—22no—
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—41no—
303C23×C113—41no—
304C23×C113#12012yes—
305C23×C113AGL(1,ℤ/8)12yes—
306C23×C113C22×D411yescharacteristic
307Q8×C113—22no—
308Q8×C113—22no—
309Q8×C113—48no—
310Q8×C113—41no—
311Q8×C113—41no—
312D4×C113—28no—
313D4×C113—22no—
314D4×C113—22no—
315D4×C113—22no—
316D4×C113—22no—
317D4×C113—48no—
318D4×C113—48no—
319D4×C113—48no—
320D4×C113—41no—
321D4×C113—41no—
322D4×C113—41no—
323D4×C113—41no—
324D4×C113—84no—
325C2×C4×C113—21no—
326C2×C4×C113—21no—
327C2×C4×C113—21no—
328C2×C4×C113—21no—
329C2×C4×C113—22no—
330C2×C4×C113—22no—
331C2×C4×C113—22no—
332C2×C4×C113—22no—
333C2×C4×C113—21no—
334C2×C4×C113—21no—
335C2×C4×C113—22no—
336C2×C4×C113—22no—
337C2×C4×C113—22no—
338C2×C4×C113—21no—
339C2×C4×C113—22no—
340C2×C4×C113—21no—
341C2×C4×C113—21no—
342C2×C4×C113—21no—
343C2×C4×C113—48no—
344C2×C4×C113—48no—
345C2×C4×C113—48no—
346C2×C4×C113—48no—
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—41no—
364C2×C4×C113—41no—
365C2×C4×C113#12012yes—
366C2×C4×C113AGL(1,ℤ/8)12yes—
367C2×C4×C113C22×D411yescharacteristic
368C2×C4×C113C22×D411yescharacteristic
369C2×C4×C113C2×#4111yescharacteristic
370C2×C4×C113C2×#4111yescharacteristic
371C2×C4×C113H(5,𝔽2)11yescharacteristic
372C2×C4×C113H(5,𝔽2)11yescharacteristic
373C8×C113—41no—
374C8×C113—41no—
375C8×C113—41no—
376C8×C113—41no—
377C22×C113—22no—
378C22×C113—22no—
379C22×C113—22no—
380C22×C113—22no—
381C22×C113—22no—
382C22×C113—22no—
383C22×C113—41no—
384C22×C113—41no—
385C22×C113—41no—
386C22×C113—41no—
387C22×C113—41no—
388C22×C113—41no—
389C22×C113—41no—
390C22×C113—41no—
391C22×C113—42no—
392C22×C113—42no—
393C22×C113—42no—
394C22×C113—42no—
395C22×C113—42no—
396C22×C113—42no—
397C22×C113—81no—
398C22×C113—81no—
399C22×C113—81no—
400C22×C113—81no—
401C22×C113—81no—
402C22×C113—81no—
403C22×C113—81no—
404C22×C113—81no—
405C22×C113C2×#12011yescharacteristic
406C22×C113#54611yescharacteristic
407C22×C113#54611yescharacteristic
408C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C113#57711yescharacteristic
411C22×C113#57811yescharacteristic
412C4×C113—22no—
413C4×C113—22no—
414C4×C113—41no—
415C4×C113—42no—
416C4×C113—42no—
417C4×C113—42no—
418C4×C113—42no—
419C4×C113—41no—
420C4×C113—81no—
421C4×C113—81no—
422C4×C113#52511yescharacteristic
423C4×C113#53511yescharacteristic
424C4×C113#54611yescharacteristic
425C4×C113#54611yescharacteristic
426#23972C11311yesmaximal, characteristic, direct product factor, Sylow
427C2×C113—42no—
428C2×C113—42no—
429C2×C113—82no—
430C2×C113—82no—
431C2×C113#240411yescharacteristic
432C2×C113#300311yescharacteristic
433C2×C113#301311yescharacteristic
434C2×C113#330611yescharacteristic
435C2×C113#330811yescharacteristic
436C2×C113#333011yescharacteristic
437C2×C113#333211yescharacteristic
438C2×#547C2×C11311yescharacteristic, complemented
439C2×#449C2×C11311yescharacteristic, complemented
440C2×#417C2×C11311yescharacteristic, complemented
441#2407C2×C11311yescharacteristic, complemented
442#2024C2×C11311yescharacteristic, complemented
443#2023C2×C11311yescharacteristic, complemented
444#2000C2×C11311yescharacteristic, complemented
445#1999C2×C11311yescharacteristic, complemented
446#1895C2×C11311yescharacteristic, complemented
447#1879C2×C11311yescharacteristic, complemented
448#1877C2×C11311yescharacteristic, complemented
449#1874C2×C11311yescharacteristic, complemented
450#1872C2×C11311yescharacteristic, complemented
451#1870C2×C11311yescharacteristic, complemented
452#1824C2×C11311yescharacteristic, complemented
453C113#2397211yescharacteristic, direct product factor, Sylow
454C22×#41—21no—
455C22×#41C22×C11311yescharacteristic
456C22×SD16C22×C11311yescharacteristic
457C22×D8C22×C11311yescharacteristic
458C22×M16C22×C11311yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C11311yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C11311yescharacteristic
466C2×#121C22×C11311yescharacteristic
467C2×#121C22×C11311yescharacteristic
468C2×#121C22×C11311yescharacteristic
469C2×C4×D4C22×C11311yescharacteristic
470C2×C4×D4C22×C11311yescharacteristic
471C22×C4⋊C4C22×C11311yescharacteristic
472C22×C4⋊C4C22×C11311yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C11311yescharacteristic
476C2×#103C22×C11311yescharacteristic
477C2×#103C22×C11311yescharacteristic
478C2×#102C22×C11311yescharacteristic
479C2×#102C22×C11311yescharacteristic
480C2×#102C22×C11311yescharacteristic
481C2×#102C22×C11311yescharacteristic
482C2×#102C22×C11311yescharacteristic
483C2×C22⋊C8C22×C11311yescharacteristic
484C2×C22⋊C8C22×C11311yescharacteristic
485C2×C22⋊C8C22×C11311yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C11311yescharacteristic
489#390C22×C11311yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C11311yescharacteristic
493#340C22×C11311yescharacteristic
494#340C22×C11311yescharacteristic
495#340C22×C11311yescharacteristic
496#340C22×C11311yescharacteristic
497#340C22×C11311yescharacteristic
498#340C22×C11311yescharacteristic
499#336C22×C11311yescharacteristic
500#336C22×C11311yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C11311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C11311yescharacteristic
517C22×D4C23×C11311yescharacteristic
518C22×D4C23×C11311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C11311yescharacteristic
524C23×C4C23×C11311yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C11311yescharacteristic
535C22×C8C23×C11311yescharacteristic
536C22×C8C23×C11311yescharacteristic
537C22×C8C23×C11311yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C11314yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C11311yescharacteristic
563C2×C4⋊C4D4×C11314yescomplemented
564C2×C4⋊C4C23×C11311yescharacteristic
565C2×C4⋊C4C23×C11311yescharacteristic
566C2×C4⋊C4C23×C11311yescharacteristic
567C2×C4⋊C4C23×C11311yescharacteristic
568C2×C4⋊C4C23×C11311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C11311yescharacteristic
578C2×C22⋊C4D4×C11311yescharacteristic
579C2×C42C23×C11311yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C11311yescharacteristic
597C24C2×D4×C11311yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C11312yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
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—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C11312yes—
638C2×D4#41×C11312yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
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—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C11311yescharacteristic
668C22×C4C2×D4×C11311yescharacteristic
669C22×C4C2×D4×C11311yescharacteristic
670C22×C4C2×D4×C11312yes—
671C22×C4C2×D4×C11312yes—
672C22×C4C2×D4×C11311yescharacteristic
673C22×C4C24×C11311yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C11312yes—
702C4⋊C4C2×D4×C11312yes—
703C4⋊C4C2×D4×C11312yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C11312yes—
743C23AGL(1,ℤ/8)×C11312yes—
744C23C22×D4×C11311yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
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—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C11312yes—
804C2×C4AGL(1,ℤ/8)×C11312yes—
805C2×C4C22×D4×C11311yescharacteristic
806C2×C4C22×D4×C11311yescharacteristic
807C2×C4C2×#41×C11311yescharacteristic
808C2×C4C2×#41×C11311yescharacteristic
809C2×C4H(5,𝔽2)×C11311yescharacteristic
810C2×C4H(5,𝔽2)×C11311yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C11311yescharacteristic
844C22#546×C11311yescharacteristic
845C22#546×C11311yescharacteristic
846C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
847C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
848C22#577×C11311yescharacteristic
849C22#578×C11311yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4#525×C11311yescharacteristic
861C4#535×C11311yescharacteristic
862C4#546×C11311yescharacteristic
863C4#546×C11311yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C113×#240411yescharacteristic
869C2C113×#300311yescharacteristic
870C2C113×#301311yescharacteristic
871C2C113×#330611yescharacteristic
872C2C113×#330811yescharacteristic
873C2C113×#333011yescharacteristic
874C2C113×#333211yescharacteristic
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×#547×C113C2semidirect
2. C2×#449×C113C2semidirect
3. C2×#417×C113C2semidirect
4. C113×#2407C2semidirect
5. C113×#2024C2semidirect
6. C113×#2023C2semidirect
7. C113×#2000C2semidirect
8. C113×#1999C2semidirect
9. C113×#1895C2semidirect
10. C113×#1879C2semidirect
11. C113×#1877C2semidirect
12. C113×#1874C2semidirect
13. C113×#1872C2semidirect
14. C113×#1870C2semidirect
15. C113×#1824C2semidirect
112. #121×C113D4semidirect
125. C2×C4⋊C4×C113D4semidirect
173. C2×Q8×C113#41semidirect
200. C2×D4×C113#41semidirect
426. #23972C113direct (N × H)
438. C2×#547C2×C113semidirect
439. C2×#449C2×C113semidirect
440. C2×#417C2×C113semidirect
441. #2407C2×C113semidirect
442. #2024C2×C113semidirect
443. #2023C2×C113semidirect
444. #2000C2×C113semidirect
445. #1999C2×C113semidirect
446. #1895C2×C113semidirect
447. #1879C2×C113semidirect
448. #1877C2×C113semidirect
449. #1874C2×C113semidirect
450. #1872C2×C113semidirect
451. #1870C2×C113semidirect
452. #1824C2×C113semidirect
453. C113#23972direct (N × H)
550. #121D4×C113semidirect
563. C2×C4⋊C4D4×C113semidirect
611. C2×Q8#41×C113semidirect
638. C2×D4#41×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1132
C2×#449×C1132
C2×#417×C1132
C113×#24072
C113×#20242
C113×#20232
C113×#20002
C113×#19992
C113×#18952
C113×#18792
C113×#18772
C113×#18742
C113×#18722
C113×#18702
C113×#18242
#23972113