Finite Group Databasebeta

← C113×#22443 #43290463

Subgroups — C113×#22443 #43290463

Order 28928.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic
2C2×#440×C113C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C113C211yesmaximal, characteristic, complemented
4C113×#2341C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
6C113×#1972C211yesmaximal, characteristic, complemented
7C113×#1970C211yesmaximal, characteristic, complemented
8C113×#1880C211yesmaximal, characteristic, complemented
9C113×#1880C211yesmaximal, characteristic, complemented
10C113×#1879C211yesmaximal, characteristic, complemented
11C113×#1879C211yesmaximal, characteristic, complemented
12C113×#1809C211yesmaximal, characteristic, complemented
13C113×#1788C211yesmaximal, characteristic, complemented
14C113×#1786C211yesmaximal, characteristic, complemented
15C113×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C113—24no—
19C2×AGL(1,ℤ/8)×C113—24no—
20C2×AGL(1,ℤ/8)×C113C418yescomplemented
21C22×SD16×C113C2211yescharacteristic
22C22×SD16×C113C2211yescharacteristic
23C22×D8×C113C2211yescharacteristic
24C22×D8×C113C2211yescharacteristic
25C22×M16×C113C2211yescharacteristic
26C2×C4×Q8×C113C2211yescharacteristic, complemented
27C2×C4×Q8×C113C2211yescharacteristic, complemented
28C2×C4×D4×C113C2211yescharacteristic
29C2×C4×D4×C113C2211yescharacteristic
30C22×C22⋊C4×C113—21no—
31#440×C113—24no—
32C4×SD16×C113—24no—
33C2×#107×C113C2211yescharacteristic, complemented
34C2×#106×C113C2211yescharacteristic, complemented
35C2×#103×C113C2211yescharacteristic, complemented
36C2×#103×C113C2211yescharacteristic, complemented
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic, complemented
42C2×#102×C113C2211yescharacteristic, complemented
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×#97×C113C2211yescharacteristic, complemented
45C2×C4×C8×C113C2211yescharacteristic, complemented
46#390×C113—21no—
47#390×C113—21no—
48#390×C113C2211yescharacteristic
49#390×C113C2211yescharacteristic
50#390×C113C2211yescharacteristic, complemented
51#390×C113C2211yescharacteristic, complemented
52#386×C113—21no—
53#386×C113—21no—
54#380×C113—21no—
55#380×C113C2211yescharacteristic
56#380×C113C2211yescharacteristic
57#379×C113—21no—
58C4×C22⋊C4×C113—21no—
59C4×C22⋊C4×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic, complemented
61#340×C113C2211yescharacteristic, complemented
62#336×C113C2211yescharacteristic, complemented
63#336×C113C2211yescharacteristic, complemented
64C25×C113—21no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—41no—
69C2×#41×C113—41no—
70C2×#41×C113C2×C414yescomplemented
71C22×Q8×C113C2311yescharacteristic
72C22×D4×C113—22no—
73C22×D4×C113—22no—
74C22×D4×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—22no—
77C22×D4×C113—41no—
78C22×D4×C113—41no—
79C22×D4×C113C2×C414yes—
80C22×D4×C113C2311yescharacteristic
81C22×D4×C113C2311yescharacteristic
82C22×D4×C113C2311yescharacteristic
83C23×C4×C113—21no—
84C23×C4×C113—21no—
85C23×C4×C113—21no—
86C23×C4×C113C2311yescharacteristic
87AGL(1,ℤ/8)×C113—232no—
88C2×SD16×C113—22no—
89C2×SD16×C113—22no—
90C2×SD16×C113C2×C414yes—
91C2×SD16×C113C2×C414yescomplemented
92C2×SD16×C113D414yes—
93C2×SD16×C113D414yes—
94C2×D8×C113—22no—
95C2×D8×C113—22no—
96C2×D8×C113—22no—
97C2×D8×C113—22no—
98C2×D8×C113C2×C414yes—
99C2×D8×C113C2×C414yescomplemented
100C2×M16×C113—22no—
101C2×M16×C113—22no—
102C2×M16×C113C2×C414yescomplemented
103C22×C8×C113C2311yescharacteristic
104C22×C8×C113C2311yescharacteristic
105C22×C8×C113C2311yescharacteristic
106C22×C8×C113C2311yescharacteristic
107C4×Q8×C113—22no—
108C4×Q8×C113—22no—
109C4×Q8×C113—41no—
110C4×Q8×C113—41no—
111C4×D4×C113—22no—
112C4×D4×C113—22no—
113C4×D4×C113—41no—
114C4×D4×C113—41no—
115C2×C4⋊C4×C113—21no—
116C2×C4⋊C4×C113—21no—
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
119C2×C4⋊C4×C113C2311yescharacteristic
120C2×C4⋊C4×C113C2311yescharacteristic
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×C113—21no—
129C2×C22⋊C4×C113—21no—
130C2×C22⋊C4×C113—21no—
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—44no—
134C2×C22⋊C4×C113D411yescharacteristic
135C2×C22⋊C4×C113D411yescharacteristic
136C2×C42×C113—21no—
137C2×C42×C113—21no—
138C2×C42×C113C2311yescharacteristic
139C2×C42×C113C2311yescharacteristic
140#107×C113—22no—
141#106×C113—22no—
142#103×C113—22no—
143#103×C113—22no—
144#102×C113—22no—
145#102×C113—22no—
146#102×C113—41no—
147#102×C113—41no—
148#102×C113—41no—
149#102×C113—41no—
150C22⋊C8×C113—22no—
151#97×C113—22no—
152C4×C8×C113—22no—
153#95×C113—21no—
154#95×C113—21no—
155#95×C113D411yescharacteristic
156#95×C113D411yescharacteristic
157C24×C113—21no—
158C24×C113—21no—
159C24×C113—21no—
160C24×C113—24no—
161C24×C113—42no—
162C24×C113—42no—
163C24×C113—42no—
164C24×C113—42no—
165C24×C113—81no—
166C24×C113—81no—
167C24×C113C2×D411yescharacteristic
168#41×C113—28no—
169#41×C113—44no—
170#41×C113—44no—
171#41×C113—44no—
172C2×Q8×C113—21no—
173C2×Q8×C113—21no—
174C2×Q8×C113—21no—
175C2×Q8×C113C22×C412yes—
176C2×Q8×C113C2×D412yes—
177C2×Q8×C113C2×D412yes—
178C2×D4×C113—28no—
179C2×D4×C113—24no—
180C2×D4×C113—24no—
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—21no—
190C2×D4×C113—21no—
191C2×D4×C113—21no—
192C2×D4×C113—21no—
193C2×D4×C113—21no—
194C2×D4×C113—44no—
195C2×D4×C113—44no—
196C2×D4×C113—44no—
197C2×D4×C113—42no—
198C2×D4×C113—42no—
199C2×D4×C113—42no—
200C2×D4×C113—42no—
201C2×D4×C113C22×C412yes—
202C2×D4×C113C22×C412yes—
203C2×D4×C113C22×C412yes—
204C2×D4×C113C2×D412yes—
205C2×D4×C113C2×D412yes—
206C22×C4×C113—21no—
207C22×C4×C113—21no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—24no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—42no—
217C22×C4×C113—42no—
218C22×C4×C113—42no—
219C22×C4×C113—42no—
220C22×C4×C113—42no—
221C22×C4×C113—42no—
222C22×C4×C113—81no—
223C22×C4×C113—81no—
224C22×C4×C113C22×C412yes—
225C22×C4×C113C2×D411yescharacteristic
226C22×C4×C113C2×D411yescharacteristic
227C22×C4×C113C2×D411yescharacteristic
228C22×C4×C113C2×D411yescharacteristic
229C22×C4×C113C2×D411yescharacteristic
230C22×C4×C113#4112yes—
231C22×C4×C113C2411yescharacteristic
232SD16×C113—28no—
233SD16×C113C22⋊C4116yescomplemented
234D8×C113—28no—
235D8×C113—28no—
236M16×C113—28no—
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—
245C2×C8×C113C22×C412yes—
246C2×C8×C113C22×C412yes—
247C2×C8×C113C2×D412yes—
248C2×C8×C113C2×D412yes—
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—21no—
257C4⋊C4×C113—42no—
258C4⋊C4×C113—42no—
259C22⋊C4×C113—22no—
260C22⋊C4×C113—41no—
261C22⋊C4×C113—42no—
262C22⋊C4×C113—42no—
263C22⋊C4×C113—42no—
264C22⋊C4×C113—42no—
265C22⋊C4×C113—42no—
266C22⋊C4×C113—42no—
267C22⋊C4×C113—42no—
268C22⋊C4×C113—81no—
269C22⋊C4×C113—81no—
270C22⋊C4×C113—81no—
271C22⋊C4×C113—81no—
272C22⋊C4×C113—81no—
273C42×C113—21no—
274C42×C113—21no—
275C42×C113—21no—
276C42×C113—21no—
277C42×C113—42no—
278C42×C113—42no—
279C23×C113—22no—
280C23×C113—22no—
281C23×C113—22no—
282C23×C113—21no—
283C23×C113—21no—
284C23×C113—21no—
285C23×C113—21no—
286C23×C113—21no—
287C23×C113—21no—
288C23×C113—22no—
289C23×C113—22no—
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—41no—
303C23×C113—41no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—41no—
307C23×C113—41no—
308C23×C113—84no—
309C23×C113—84no—
310C23×C113—84no—
311C23×C113—84no—
312C23×C113—84no—
313C23×C113C4×D412yes—
314C23×C113C22×D411yescharacteristic
315Q8×C113—22no—
316Q8×C113—22no—
317Q8×C113—22no—
318Q8×C113C2×C22⋊C414yescomplemented
319D4×C113—22no—
320D4×C113—22no—
321D4×C113—22no—
322D4×C113—22no—
323D4×C113—22no—
324D4×C113—22no—
325D4×C113—22no—
326D4×C113—48no—
327D4×C113—48no—
328D4×C113—41no—
329D4×C113—41no—
330D4×C113—41no—
331D4×C113—41no—
332D4×C113C2×C22⋊C414yes—
333C2×C4×C113—22no—
334C2×C4×C113—21no—
335C2×C4×C113—22no—
336C2×C4×C113—22no—
337C2×C4×C113—21no—
338C2×C4×C113—21no—
339C2×C4×C113—21no—
340C2×C4×C113—22no—
341C2×C4×C113—22no—
342C2×C4×C113—22no—
343C2×C4×C113—22no—
344C2×C4×C113—21no—
345C2×C4×C113—21no—
346C2×C4×C113—21no—
347C2×C4×C113—21no—
348C2×C4×C113—21no—
349C2×C4×C113—21no—
350C2×C4×C113—21no—
351C2×C4×C113—21no—
352C2×C4×C113—21no—
353C2×C4×C113—48no—
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—41no—
366C2×C4×C113—84no—
367C2×C4×C113—84no—
368C2×C4×C113C4×D412yes—
369C2×C4×C113AGL(1,ℤ/8)12yescomplemented
370C2×C4×C113C23×C411yescharacteristic
371C2×C4×C113C22×D411yescharacteristic
372C2×C4×C113C22×D411yescharacteristic
373C2×C4×C113C2×#4111yescharacteristic
374C2×C4×C113H(5,𝔽2)11yescharacteristic
375C2×C4×C113H(5,𝔽2)11yescharacteristic
376C8×C113—22no—
377C8×C113—41no—
378C8×C113—41no—
379C8×C113C2×C22⋊C414yescomplemented
380C22×C113—22no—
381C22×C113—24no—
382C22×C113—22no—
383C22×C113—22no—
384C22×C113—42no—
385C22×C113—42no—
386C22×C113—42no—
387C22×C113—41no—
388C22×C113—41no—
389C22×C113—42no—
390C22×C113—42no—
391C22×C113—41no—
392C22×C113—41no—
393C22×C113—42no—
394C22×C113—42no—
395C22×C113—42no—
396C22×C113—42no—
397C22×C113—42no—
398C22×C113—42no—
399C22×C113—42no—
400C22×C113—816no—
401C22×C113—81no—
402C22×C113—81no—
403C22×C113—81no—
404C22×C113—81no—
405C22×C113—81no—
406C22×C113—81no—
407C22×C113—81no—
408C22×C113—81no—
409C22×C113C2×C4×D411yescharacteristic
410C22×C113D4211yescharacteristic
411C22×C113D4211yescharacteristic
412C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C113#57511yescharacteristic
414C22×C113#57611yescharacteristic
415C22×C113#57711yescharacteristic
416C4×C113—22no—
417C4×C113—24no—
418C4×C113—22no—
419C4×C113—41no—
420C4×C113—41no—
421C4×C113—41no—
422C4×C113—81no—
423C4×C113—81no—
424C4×C113—81no—
425C4×C113—81no—
426C4×C113C22×C22⋊C411yescharacteristic
427C4×C113#51811yescharacteristic
428C4×C113#54611yescharacteristic
429C4×C113#54611yescharacteristic
430#22443C11311yesmaximal, characteristic, direct product factor, Sylow
431C2×C113—42no—
432C2×C113—44no—
433C2×C113—82no—
434C2×C113—82no—
435C2×C113D4×C22⋊C411yescharacteristic
436C2×C113C4×AGL(1,ℤ/8)11yescharacteristic
437C2×C113#294611yescharacteristic
438C2×C113#326511yescharacteristic
439C2×C113#326811yescharacteristic
440C2×C113#327411yescharacteristic
441C2×C113#327511yescharacteristic
442C22×AGL(1,ℤ/8)C2×C11311yescharacteristic
443C2×#440C2×C11311yescharacteristic, complemented
444C2×C4×SD16C2×C11311yescharacteristic, complemented
445#2341C2×C11311yescharacteristic, complemented
446D4×C22⋊C4C2×C11311yescharacteristic, complemented
447#1972C2×C11311yescharacteristic, complemented
448#1970C2×C11311yescharacteristic, complemented
449#1880C2×C11311yescharacteristic, complemented
450#1880C2×C11311yescharacteristic, complemented
451#1879C2×C11311yescharacteristic, complemented
452#1879C2×C11311yescharacteristic, complemented
453#1809C2×C11311yescharacteristic, complemented
454#1788C2×C11311yescharacteristic, complemented
455#1786C2×C11311yescharacteristic, complemented
456#1753C2×C11311yescharacteristic, complemented
457C113#2244311yescharacteristic, direct product factor, Sylow
458C22×#41C22×C11311yescharacteristic
459C23×D4C22×C11311yescharacteristic
460C2×AGL(1,ℤ/8)—24no—
461C2×AGL(1,ℤ/8)—24no—
462C2×AGL(1,ℤ/8)C4×C11318yescomplemented
463C22×SD16C22×C11311yescharacteristic
464C22×SD16C22×C11311yescharacteristic
465C22×D8C22×C11311yescharacteristic
466C22×D8C22×C11311yescharacteristic
467C22×M16C22×C11311yescharacteristic
468C2×C4×Q8C22×C11311yescharacteristic, complemented
469C2×C4×Q8C22×C11311yescharacteristic, complemented
470C2×C4×D4C22×C11311yescharacteristic
471C2×C4×D4C22×C11311yescharacteristic
472C22×C22⋊C4—21no—
473#440—24no—
474C4×SD16—24no—
475C2×#107C22×C11311yescharacteristic, complemented
476C2×#106C22×C11311yescharacteristic, complemented
477C2×#103C22×C11311yescharacteristic, complemented
478C2×#103C22×C11311yescharacteristic, complemented
479C2×#102C22×C11311yescharacteristic
480C2×#102C22×C11311yescharacteristic
481C2×#102C22×C11311yescharacteristic
482C2×#102C22×C11311yescharacteristic
483C2×#102C22×C11311yescharacteristic, complemented
484C2×#102C22×C11311yescharacteristic, complemented
485C2×C22⋊C8C22×C11311yescharacteristic
486C2×#97C22×C11311yescharacteristic, complemented
487C2×C4×C8C22×C11311yescharacteristic, complemented
488#390—21no—
489#390—21no—
490#390C22×C11311yescharacteristic
491#390C22×C11311yescharacteristic
492#390C22×C11311yescharacteristic, complemented
493#390C22×C11311yescharacteristic, complemented
494#386—21no—
495#386—21no—
496#380—21no—
497#380C22×C11311yescharacteristic
498#380C22×C11311yescharacteristic
499#379—21no—
500C4×C22⋊C4—21no—
501C4×C22⋊C4C22×C11311yescharacteristic
502#340C22×C11311yescharacteristic, complemented
503#340C22×C11311yescharacteristic, complemented
504#336C22×C11311yescharacteristic, complemented
505#336C22×C11311yescharacteristic, complemented
506C25—21no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41C2×C4×C11314yescomplemented
513C22×Q8C23×C11311yescharacteristic
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×C4×C11314yes—
522C22×D4C23×C11311yescharacteristic
523C22×D4C23×C11311yescharacteristic
524C22×D4C23×C11311yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C23×C11311yescharacteristic
529AGL(1,ℤ/8)—232no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16C2×C4×C11314yes—
533C2×SD16C2×C4×C11314yescomplemented
534C2×SD16D4×C11314yes—
535C2×SD16D4×C11314yes—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8C2×C4×C11314yes—
541C2×D8C2×C4×C11314yescomplemented
542C2×M16—22no—
543C2×M16—22no—
544C2×M16C2×C4×C11314yescomplemented
545C22×C8C23×C11311yescharacteristic
546C22×C8C23×C11311yescharacteristic
547C22×C8C23×C11311yescharacteristic
548C22×C8C23×C11311yescharacteristic
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—41no—
556C4×D4—41no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4C23×C11311yescharacteristic
560C2×C4⋊C4C23×C11311yescharacteristic
561C2×C4⋊C4C23×C11311yescharacteristic
562C2×C4⋊C4C23×C11311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
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—44no—
576C2×C22⋊C4D4×C11311yescharacteristic
577C2×C22⋊C4D4×C11311yescharacteristic
578C2×C42—21no—
579C2×C42—21no—
580C2×C42C23×C11311yescharacteristic
581C2×C42C23×C11311yescharacteristic
582#107—22no—
583#106—22no—
584#103—22no—
585#103—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590#102—41no—
591#102—41no—
592C22⋊C8—22no—
593#97—22no—
594C4×C8—22no—
595#95—21no—
596#95—21no—
597#95D4×C11311yescharacteristic
598#95D4×C11311yescharacteristic
599C24—21no—
600C24—21no—
601C24—21no—
602C24—24no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—81no—
608C24—81no—
609C24C2×D4×C11311yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8C22×C4×C11312yes—
618C2×Q8C2×D4×C11312yes—
619C2×Q8C2×D4×C11312yes—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4C22×C4×C11312yes—
644C2×D4C22×C4×C11312yes—
645C2×D4C22×C4×C11312yes—
646C2×D4C2×D4×C11312yes—
647C2×D4C2×D4×C11312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
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—81no—
665C22×C4—81no—
666C22×C4C22×C4×C11312yes—
667C22×C4C2×D4×C11311yescharacteristic
668C22×C4C2×D4×C11311yescharacteristic
669C22×C4C2×D4×C11311yescharacteristic
670C22×C4C2×D4×C11311yescharacteristic
671C22×C4C2×D4×C11311yescharacteristic
672C22×C4#41×C11312yes—
673C22×C4C24×C11311yescharacteristic
674SD16—28no—
675SD16C22⋊C4×C113116yescomplemented
676D8—28no—
677D8—28no—
678M16—28no—
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×C8C22×C4×C11312yes—
688C2×C8C22×C4×C11312yes—
689C2×C8C2×D4×C11312yes—
690C2×C8C2×D4×C11312yes—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—41no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—81no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—42no—
720C42—42no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—48no—
733C23—48no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23C4×D4×C11312yes—
756C23C22×D4×C11311yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C2×C22⋊C4×C11314yescomplemented
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊C4×C11314yes—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4C4×D4×C11312yes—
811C2×C4AGL(1,ℤ/8)×C11312yescomplemented
812C2×C4C23×C4×C11311yescharacteristic
813C2×C4C22×D4×C11311yescharacteristic
814C2×C4C22×D4×C11311yescharacteristic
815C2×C4C2×#41×C11311yescharacteristic
816C2×C4H(5,𝔽2)×C11311yescharacteristic
817C2×C4H(5,𝔽2)×C11311yescharacteristic
818C8—22no—
819C8—41no—
820C8—41no—
821C8C2×C22⋊C4×C11314yescomplemented
822C22—22no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—816no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22C2×C4×D4×C11311yescharacteristic
852C22D42×C11311yescharacteristic
853C22D42×C11311yescharacteristic
854C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
855C22#575×C11311yescharacteristic
856C22#576×C11311yescharacteristic
857C22#577×C11311yescharacteristic
858C4—22no—
859C4—24no—
860C4—22no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4C22×C22⋊C4×C11311yescharacteristic
869C4#518×C11311yescharacteristic
870C4#546×C11311yescharacteristic
871C4#546×C11311yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—82no—
876C2D4×C22⋊C4×C11311yescharacteristic
877C2C4×AGL(1,ℤ/8)×C11311yescharacteristic
878C2C113×#294611yescharacteristic
879C2C113×#326511yescharacteristic
880C2C113×#326811yescharacteristic
881C2C113×#327411yescharacteristic
882C2C113×#327511yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC22×AGL(1,ℤ/8)×C113C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C113C2semidirect
3. C2×C4×SD16×C113C2semidirect
4. C113×#2341C2semidirect
5. D4×C22⋊C4×C113C2semidirect
6. C113×#1972C2semidirect
7. C113×#1970C2semidirect
8. C113×#1880C2semidirect
9. C113×#1880C2semidirect
10. C113×#1879C2semidirect
11. C113×#1879C2semidirect
12. C113×#1809C2semidirect
13. C113×#1788C2semidirect
14. C113×#1786C2semidirect
15. C113×#1753C2semidirect
20. C2×AGL(1,ℤ/8)×C113C4semidirect
26. C2×C4×Q8×C113C22semidirect
27. C2×C4×Q8×C113C22semidirect
33. C2×#107×C113C22semidirect
34. C2×#106×C113C22semidirect
35. C2×#103×C113C22semidirect
36. C2×#103×C113C22semidirect
41. C2×#102×C113C22semidirect
42. C2×#102×C113C22semidirect
44. C2×#97×C113C22semidirect
45. C2×C4×C8×C113C22semidirect
50. #390×C113C22semidirect
51. #390×C113C22semidirect
60. #340×C113C22semidirect
61. #340×C113C22semidirect
62. #336×C113C22semidirect
63. #336×C113C22semidirect
70. C2×#41×C113C2×C4semidirect
91. C2×SD16×C113C2×C4semidirect
99. C2×D8×C113C2×C4semidirect
102. C2×M16×C113C2×C4semidirect
233. SD16×C113C22⋊C4semidirect
318. Q8×C113C2×C22⋊C4semidirect
369. C2×C4×C113AGL(1,ℤ/8)semidirect
379. C8×C113C2×C22⋊C4semidirect
430. #22443C113direct (N × H)
443. C2×#440C2×C113semidirect
444. C2×C4×SD16C2×C113semidirect
445. #2341C2×C113semidirect
446. D4×C22⋊C4C2×C113semidirect
447. #1972C2×C113semidirect
448. #1970C2×C113semidirect
449. #1880C2×C113semidirect
450. #1880C2×C113semidirect
451. #1879C2×C113semidirect
452. #1879C2×C113semidirect
453. #1809C2×C113semidirect
454. #1788C2×C113semidirect
455. #1786C2×C113semidirect
456. #1753C2×C113semidirect
457. C113#22443direct (N × H)
462. C2×AGL(1,ℤ/8)C4×C113semidirect
468. C2×C4×Q8C22×C113semidirect
469. C2×C4×Q8C22×C113semidirect
475. C2×#107C22×C113semidirect
476. C2×#106C22×C113semidirect
477. C2×#103C22×C113semidirect
478. C2×#103C22×C113semidirect
483. C2×#102C22×C113semidirect
484. C2×#102C22×C113semidirect
486. C2×#97C22×C113semidirect
487. C2×C4×C8C22×C113semidirect
492. #390C22×C113semidirect
493. #390C22×C113semidirect
502. #340C22×C113semidirect
503. #340C22×C113semidirect
504. #336C22×C113semidirect
505. #336C22×C113semidirect
512. C2×#41C2×C4×C113semidirect
533. C2×SD16C2×C4×C113semidirect
541. C2×D8C2×C4×C113semidirect
544. C2×M16C2×C4×C113semidirect
675. SD16C22⋊C4×C113semidirect
760. Q8C2×C22⋊C4×C113semidirect
811. C2×C4AGL(1,ℤ/8)×C113semidirect
821. C8C2×C22⋊C4×C113semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1132
C2×#440×C1132
C2×C4×SD16×C1132
C113×#23412
D4×C22⋊C4×C1132
C113×#19722
C113×#19702
C113×#18802
C113×#18792
C113×#18092
C113×#17882
C113×#17862
C113×#17532
#22443113