Finite Group Databasebeta

← C113×#24275 #43292295

Subgroups — C113×#24275 #43292295

Order 28928.

1614 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic, complemented
2C2×#466×C113C211yesmaximal, characteristic, complemented
3C2×#465×C113C211yesmaximal, characteristic, complemented
4C2×#435×C113C211yesmaximal, characteristic, complemented
5C113×#2408C211yesmaximal, characteristic, complemented
6C113×#2407C211yesmaximal, characteristic, complemented
7C113×#2055C211yesmaximal, characteristic, complemented
8C113×#2054C211yesmaximal, characteristic, complemented
9C113×#2000C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1973C211yesmaximal, characteristic, complemented
12C113×#1972C211yesmaximal, characteristic, complemented
13C113×#1809C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1786C211yesmaximal, 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)×C113—24no—
21C22×SD16×C113C2211yescharacteristic
22C22×SD16×C113C2211yescharacteristic
23C22×D8×C113C2211yescharacteristic
24C22×D8×C113C2211yescharacteristic
25C22×M16×C113C2211yescharacteristic
26C23×C8×C113C2211yescharacteristic, complemented
27C2×C22⋊Q8×C113C2211yescharacteristic, complemented
28C2×#121×C113C2211yescharacteristic
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic, complemented
31C2×#120×C113—21no—
32C2×C4×D4×C113C2211yescharacteristic
33#466×C113—24no—
34#465×C113—24no—
35#435×C113—24no—
36C2×#107×C113C2211yescharacteristic, complemented
37C2×#106×C113C2211yescharacteristic, complemented
38C2×C4⋊C8×C113C2211yescharacteristic, complemented
39C2×#103×C113C2211yescharacteristic, complemented
40C2×#103×C113C2211yescharacteristic, complemented
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic, complemented
46C2×#102×C113C2211yescharacteristic, complemented
47C2×C22⋊C8×C113C2211yescharacteristic
48C2×C22⋊C8×C113C2211yescharacteristic, complemented
49C2×#97×C113C2211yescharacteristic, complemented
50#394×C113—21no—
51#394×C113—21no—
52#392×C113—21no—
53#392×C113—21no—
54#391×C113C2211yescharacteristic, complemented
55#390×C113C2211yescharacteristic
56#390×C113C2211yescharacteristic
57#390×C113C2211yescharacteristic, complemented
58#386×C113—21no—
59#385×C113—21no—
60#380×C113C2211yescharacteristic
61#380×C113C2211yescharacteristic
62#379×C113—21no—
63#340×C113C2211yescharacteristic, complemented
64#340×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—22no—
74C22×D4×C113—22no—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113—21no—
79C22×D4×C113—22no—
80C22×D4×C113—21no—
81C22×D4×C113—22no—
82C22×D4×C113—41no—
83C22×D4×C113—41no—
84C22×D4×C113D411yescharacteristic
85C22×D4×C113C2311yescharacteristic
86C22×D4×C113C2311yescharacteristic
87C22×D4×C113C2311yescharacteristic
88C23×C4×C113—21no—
89C23×C4×C113C2311yescharacteristic
90C23×C4×C113C2311yescharacteristic
91AGL(1,ℤ/8)×C113—232no—
92C2×SD16×C113—22no—
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—22no—
96C2×SD16×C113—22no—
97C2×SD16×C113D414yescomplemented
98C2×D8×C113—22no—
99C2×D8×C113—22no—
100C2×D8×C113—22no—
101C2×D8×C113—22no—
102C2×D8×C113—22no—
103C2×D8×C113D414yescomplemented
104C2×M16×C113—22no—
105C2×M16×C113—22no—
106C2×M16×C113D414yescomplemented
107C22×C8×C113—22no—
108C22×C8×C113—22no—
109C22×C8×C113—22no—
110C22×C8×C113C2311yescharacteristic
111C22×C8×C113C2311yescharacteristic
112C22×C8×C113C2311yescharacteristic
113C22×C8×C113C2311yescharacteristic
114C22⋊Q8×C113—22no—
115C22⋊Q8×C113—41no—
116#121×C113—22no—
117#121×C113—22no—
118#121×C113—22no—
119#121×C113—41no—
120#121×C113—41no—
121#121×C113—41no—
122#120×C113—44no—
123C4×D4×C113—22no—
124C4×D4×C113—22no—
125C2×C4⋊C4×C113—21no—
126C2×C4⋊C4×C113D411yescharacteristic
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×C113—21no—
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113—21no—
142C2×C22⋊C4×C113—21no—
143C2×C22⋊C4×C113D411yescharacteristic
144C2×C22⋊C4×C113D411yescharacteristic
145C2×C42×C113C2311yescharacteristic
146#107×C113—22no—
147#106×C113—22no—
148C4⋊C8×C113—22no—
149#103×C113—22no—
150#103×C113—41no—
151#102×C113—22no—
152#102×C113—22no—
153#102×C113—22no—
154#102×C113—41no—
155#102×C113—41no—
156#102×C113—41no—
157C22⋊C8×C113—22no—
158C22⋊C8×C113—22no—
159#97×C113—22no—
160#95×C113—21no—
161#95×C113—21no—
162#95×C113—21no—
163#95×C113—21no—
164C24×C113—21no—
165C24×C113—21no—
166C24×C113—21no—
167C24×C113—42no—
168C24×C113—42no—
169C24×C113—42no—
170C24×C113—42no—
171C24×C113—42no—
172C24×C113—81no—
173C24×C113—81no—
174C24×C113C2×D411yescharacteristic
175C24×C113C2×D411yescharacteristic
176#41×C113—28no—
177#41×C113—44no—
178#41×C113—44no—
179#41×C113—44no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113C2×D412yes—
186C2×D4×C113—28no—
187C2×D4×C113—22no—
188C2×D4×C113—22no—
189C2×D4×C113—21no—
190C2×D4×C113—21no—
191C2×D4×C113—21no—
192C2×D4×C113—21no—
193C2×D4×C113—21no—
194C2×D4×C113—21no—
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—44no—
205C2×D4×C113—44no—
206C2×D4×C113—41no—
207C2×D4×C113—42no—
208C2×D4×C113—42no—
209C2×D4×C113—42no—
210C2×D4×C113—44no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—42no—
215C2×D4×C113—42no—
216C2×D4×C113—42no—
217C2×D4×C113—42no—
218C2×D4×C113—42no—
219C2×D4×C113—42no—
220C2×D4×C113—81no—
221C2×D4×C113—81no—
222C2×D4×C113—81no—
223C2×D4×C113C2×D412yes—
224C2×D4×C113C2×D412yes—
225C2×D4×C113C2×D412yes—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
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—21no—
240C22×C4×C113—21no—
241C22×C4×C113—42no—
242C22×C4×C113—42no—
243C22×C4×C113—42no—
244C22×C4×C113C2×D411yescharacteristic
245C22×C4×C113C2×D411yescharacteristic
246C22×C4×C113C2×D411yescharacteristic
247C22×C4×C113C2×D411yescharacteristic
248C22×C4×C113C2×D412yes—
249C22×C4×C113#4112yes—
250C22×C4×C113C2411yescharacteristic
251SD16×C113—28no—
252SD16×C113—28no—
253D8×C113—28no—
254D8×C113—28no—
255M16×C113—28no—
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—44no—
265C2×C8×C113C2×D412yes—
266C2×C8×C113C2×D412yes—
267C2×C8×C113C2×D412yes—
268C2×C8×C113C2×D412yes—
269C4⋊C4×C113—22no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—21no—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—42no—
279C22⋊C4×C113—22no—
280C22⋊C4×C113—22no—
281C22⋊C4×C113—42no—
282C22⋊C4×C113—42no—
283C22⋊C4×C113—42no—
284C22⋊C4×C113—42no—
285C22⋊C4×C113—42no—
286C22⋊C4×C113—42no—
287C22⋊C4×C113—42no—
288C22⋊C4×C113—42no—
289C22⋊C4×C113—81no—
290C22⋊C4×C113—81no—
291C22⋊C4×C113—81no—
292C22⋊C4×C113—81no—
293C42×C113—21no—
294C42×C113—21no—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—21no—
301C23×C113—21no—
302C23×C113—21no—
303C23×C113—21no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
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—84no—
330C23×C113—84no—
331C23×C113—84no—
332C23×C113—84no—
333C23×C113—84no—
334C23×C113—84no—
335C23×C113#12112yes—
336C23×C113AGL(1,ℤ/8)12yescomplemented
337C23×C113C22×D411yescharacteristic
338Q8×C113—22no—
339Q8×C113—22no—
340Q8×C113—41no—
341Q8×C113—41no—
342D4×C113—22no—
343D4×C113—22no—
344D4×C113—22no—
345D4×C113—22no—
346D4×C113—22no—
347D4×C113—22no—
348D4×C113—48no—
349D4×C113—44no—
350D4×C113—48no—
351D4×C113—41no—
352D4×C113—41no—
353D4×C113—41no—
354D4×C113—41no—
355D4×C113—41no—
356D4×C113—41no—
357D4×C113—84no—
358D4×C113—84no—
359D4×C113—84no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
362C2×C4×C113—22no—
363C2×C4×C113—22no—
364C2×C4×C113—22no—
365C2×C4×C113—22no—
366C2×C4×C113—21no—
367C2×C4×C113—21no—
368C2×C4×C113—21no—
369C2×C4×C113—21no—
370C2×C4×C113—21no—
371C2×C4×C113—22no—
372C2×C4×C113—21no—
373C2×C4×C113—21no—
374C2×C4×C113—21no—
375C2×C4×C113—21no—
376C2×C4×C113—48no—
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—41no—
388C2×C4×C113—41no—
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#12112yes—
396C2×C4×C113C22×D411yescharacteristic
397C2×C4×C113C22×D411yescharacteristic
398C2×C4×C113C22×D411yescharacteristic
399C2×C4×C113C2×#4111yescharacteristic
400C2×C4×C113H(5,𝔽2)11yescharacteristic
401C2×C4×C113H(5,𝔽2)11yescharacteristic
402C8×C113—22no—
403C8×C113—41no—
404C8×C113—41no—
405C8×C113#12014yescomplemented
406C22×C113—22no—
407C22×C113—22no—
408C22×C113—22no—
409C22×C113—22no—
410C22×C113—22no—
411C22×C113—22no—
412C22×C113—41no—
413C22×C113—41no—
414C22×C113—41no—
415C22×C113—41no—
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—816no—
430C22×C113—81no—
431C22×C113—81no—
432C22×C113—81no—
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×C113C2×#12111yescharacteristic
443C22×C113D4211yescharacteristic
444C22×C113D4211yescharacteristic
445C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C113#57511yescharacteristic
447C22×C113#57611yescharacteristic
448C22×C113#57711yescharacteristic
449C4×C113—22no—
450C4×C113—41no—
451C4×C113—42no—
452C4×C113—41no—
453C4×C113—41no—
454C4×C113—81no—
455C4×C113—81no—
456C4×C113—81no—
457C4×C113—81no—
458C4×C113C2×#12011yescharacteristic
459C4×C113#53511yescharacteristic
460C4×C113#54611yescharacteristic
461C4×C113#54611yescharacteristic
462#24275C11311yesmaximal, characteristic, direct product factor, Sylow
463C2×C113—42no—
464C2×C113—42no—
465C2×C113—82no—
466C2×C113—82no—
467C2×C113—82no—
468C2×C113#240811yescharacteristic
469C2×C113#305511yescharacteristic
470C2×C113#306211yescharacteristic
471C2×C113#326411yescharacteristic
472C2×C113#326511yescharacteristic
473C2×C113#326711yescharacteristic
474C2×C113#326811yescharacteristic
475C22×AGL(1,ℤ/8)C2×C11311yescharacteristic, complemented
476C2×#466C2×C11311yescharacteristic, complemented
477C2×#465C2×C11311yescharacteristic, complemented
478C2×#435C2×C11311yescharacteristic, complemented
479#2408C2×C11311yescharacteristic, complemented
480#2407C2×C11311yescharacteristic, complemented
481#2055C2×C11311yescharacteristic, complemented
482#2054C2×C11311yescharacteristic, complemented
483#2000C2×C11311yescharacteristic, complemented
484#1999C2×C11311yescharacteristic, complemented
485#1973C2×C11311yescharacteristic, complemented
486#1972C2×C11311yescharacteristic, complemented
487#1809C2×C11311yescharacteristic, complemented
488#1788C2×C11311yescharacteristic, complemented
489#1786C2×C11311yescharacteristic, complemented
490C113#2427511yescharacteristic, direct product factor, Sylow
491C22×#41C22×C11311yescharacteristic
492C23×D4C22×C11311yescharacteristic
493C2×AGL(1,ℤ/8)—24no—
494C2×AGL(1,ℤ/8)—24no—
495C2×AGL(1,ℤ/8)—24no—
496C22×SD16C22×C11311yescharacteristic
497C22×SD16C22×C11311yescharacteristic
498C22×D8C22×C11311yescharacteristic
499C22×D8C22×C11311yescharacteristic
500C22×M16C22×C11311yescharacteristic
501C23×C8C22×C11311yescharacteristic, complemented
502C2×C22⋊Q8C22×C11311yescharacteristic, complemented
503C2×#121C22×C11311yescharacteristic
504C2×#121C22×C11311yescharacteristic
505C2×#121C22×C11311yescharacteristic, complemented
506C2×#120—21no—
507C2×C4×D4C22×C11311yescharacteristic
508#466—24no—
509#465—24no—
510#435—24no—
511C2×#107C22×C11311yescharacteristic, complemented
512C2×#106C22×C11311yescharacteristic, complemented
513C2×C4⋊C8C22×C11311yescharacteristic, complemented
514C2×#103C22×C11311yescharacteristic, complemented
515C2×#103C22×C11311yescharacteristic, complemented
516C2×#102C22×C11311yescharacteristic
517C2×#102C22×C11311yescharacteristic
518C2×#102C22×C11311yescharacteristic
519C2×#102C22×C11311yescharacteristic
520C2×#102C22×C11311yescharacteristic, complemented
521C2×#102C22×C11311yescharacteristic, complemented
522C2×C22⋊C8C22×C11311yescharacteristic
523C2×C22⋊C8C22×C11311yescharacteristic, complemented
524C2×#97C22×C11311yescharacteristic, complemented
525#394—21no—
526#394—21no—
527#392—21no—
528#392—21no—
529#391C22×C11311yescharacteristic, complemented
530#390C22×C11311yescharacteristic
531#390C22×C11311yescharacteristic
532#390C22×C11311yescharacteristic, complemented
533#386—21no—
534#385—21no—
535#380C22×C11311yescharacteristic
536#380C22×C11311yescharacteristic
537#379—21no—
538#340C22×C11311yescharacteristic, complemented
539#340C22×C11311yescharacteristic, complemented
540C25—21no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—41no—
546C2×#41—41no—
547C22×Q8C23×C11311yescharacteristic
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—22no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—41no—
558C22×D4—41no—
559C22×D4D4×C11311yescharacteristic
560C22×D4C23×C11311yescharacteristic
561C22×D4C23×C11311yescharacteristic
562C22×D4C23×C11311yescharacteristic
563C23×C4—21no—
564C23×C4C23×C11311yescharacteristic
565C23×C4C23×C11311yescharacteristic
566AGL(1,ℤ/8)—232no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16D4×C11314yescomplemented
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8D4×C11314yescomplemented
579C2×M16—22no—
580C2×M16—22no—
581C2×M16D4×C11314yescomplemented
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—22no—
585C22×C8C23×C11311yescharacteristic
586C22×C8C23×C11311yescharacteristic
587C22×C8C23×C11311yescharacteristic
588C22×C8C23×C11311yescharacteristic
589C22⋊Q8—22no—
590C22⋊Q8—41no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#121—41no—
597#120—44no—
598C4×D4—22no—
599C4×D4—22no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4D4×C11311yescharacteristic
602C2×C4⋊C4C23×C11311yescharacteristic
603C2×C4⋊C4C23×C11311yescharacteristic
604C2×C4⋊C4C23×C11311yescharacteristic
605C2×C4⋊C4C23×C11311yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4D4×C11311yescharacteristic
619C2×C22⋊C4D4×C11311yescharacteristic
620C2×C42C23×C11311yescharacteristic
621#107—22no—
622#106—22no—
623C4⋊C8—22no—
624#103—22no—
625#103—41no—
626#102—22no—
627#102—22no—
628#102—22no—
629#102—41no—
630#102—41no—
631#102—41no—
632C22⋊C8—22no—
633C22⋊C8—22no—
634#97—22no—
635#95—21no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—42no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24C2×D4×C11311yescharacteristic
650C24C2×D4×C11311yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C11312yes—
661C2×D4—28no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4C2×D4×C11312yes—
699C2×D4C2×D4×C11312yes—
700C2×D4C2×D4×C11312yes—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4C2×D4×C11311yescharacteristic
720C22×C4C2×D4×C11311yescharacteristic
721C22×C4C2×D4×C11311yescharacteristic
722C22×C4C2×D4×C11311yescharacteristic
723C22×C4C2×D4×C11312yes—
724C22×C4#41×C11312yes—
725C22×C4C24×C11311yescharacteristic
726SD16—28no—
727SD16—28no—
728D8—28no—
729D8—28no—
730M16—28no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—44no—
740C2×C8C2×D4×C11312yes—
741C2×C8C2×D4×C11312yes—
742C2×C8C2×D4×C11312yes—
743C2×C8C2×D4×C11312yes—
744C4⋊C4—22no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—81no—
766C22⋊C4—81no—
767C22⋊C4—81no—
768C42—21no—
769C42—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—48no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23#121×C11312yes—
811C23AGL(1,ℤ/8)×C11312yescomplemented
812C23C22×D4×C11311yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—41no—
816Q8—41no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—48no—
824D4—44no—
825D4—48no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—48no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4#121×C11312yes—
871C2×C4C22×D4×C11311yescharacteristic
872C2×C4C22×D4×C11311yescharacteristic
873C2×C4C22×D4×C11311yescharacteristic
874C2×C4C2×#41×C11311yescharacteristic
875C2×C4H(5,𝔽2)×C11311yescharacteristic
876C2×C4H(5,𝔽2)×C11311yescharacteristic
877C8—22no—
878C8—41no—
879C8—41no—
880C8#120×C11314yescomplemented
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—816no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#121×C11311yescharacteristic
918C22D42×C11311yescharacteristic
919C22D42×C11311yescharacteristic
920C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
921C22#575×C11311yescharacteristic
922C22#576×C11311yescharacteristic
923C22#577×C11311yescharacteristic
924C4—22no—
925C4—41no—
926C4—41no—
927C4—41no—
928C4—42no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4C2×#120×C11311yescharacteristic
934C4#535×C11311yescharacteristic
935C4#546×C11311yescharacteristic
936C4#546×C11311yescharacteristic
937C2—42no—
938C2—42no—
939C2—82no—
940C2—82no—
941C2—82no—
942C2C113×#240811yescharacteristic
943C2C113×#305511yescharacteristic
944C2C113×#306211yescharacteristic
945C2C113×#326411yescharacteristic
946C2C113×#326511yescharacteristic
947C2C113×#326711yescharacteristic
948C2C113×#326811yescharacteristic
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. C22×AGL(1,ℤ/8)×C113C2semidirect
2. C2×#466×C113C2semidirect
3. C2×#465×C113C2semidirect
4. C2×#435×C113C2semidirect
5. C113×#2408C2semidirect
6. C113×#2407C2semidirect
7. C113×#2055C2semidirect
8. C113×#2054C2semidirect
9. C113×#2000C2semidirect
10. C113×#1999C2semidirect
11. C113×#1973C2semidirect
12. C113×#1972C2semidirect
13. C113×#1809C2semidirect
14. C113×#1788C2semidirect
15. C113×#1786C2semidirect
26. C23×C8×C113C22semidirect
27. C2×C22⋊Q8×C113C22semidirect
30. C2×#121×C113C22semidirect
36. C2×#107×C113C22semidirect
37. C2×#106×C113C22semidirect
38. C2×C4⋊C8×C113C22semidirect
39. C2×#103×C113C22semidirect
40. C2×#103×C113C22semidirect
45. C2×#102×C113C22semidirect
46. C2×#102×C113C22semidirect
48. C2×C22⋊C8×C113C22semidirect
49. C2×#97×C113C22semidirect
54. #391×C113C22semidirect
57. #390×C113C22semidirect
63. #340×C113C22semidirect
64. #340×C113C22semidirect
97. C2×SD16×C113D4semidirect
103. C2×D8×C113D4semidirect
106. C2×M16×C113D4semidirect
336. C23×C113AGL(1,ℤ/8)semidirect
405. C8×C113#120semidirect
462. #24275C113direct (N × H)
475. C22×AGL(1,ℤ/8)C2×C113semidirect
476. C2×#466C2×C113semidirect
477. C2×#465C2×C113semidirect
478. C2×#435C2×C113semidirect
479. #2408C2×C113semidirect
480. #2407C2×C113semidirect
481. #2055C2×C113semidirect
482. #2054C2×C113semidirect
483. #2000C2×C113semidirect
484. #1999C2×C113semidirect
485. #1973C2×C113semidirect
486. #1972C2×C113semidirect
487. #1809C2×C113semidirect
488. #1788C2×C113semidirect
489. #1786C2×C113semidirect
490. C113#24275direct (N × H)
501. C23×C8C22×C113semidirect
502. C2×C22⋊Q8C22×C113semidirect
505. C2×#121C22×C113semidirect
511. C2×#107C22×C113semidirect
512. C2×#106C22×C113semidirect
513. C2×C4⋊C8C22×C113semidirect
514. C2×#103C22×C113semidirect
515. C2×#103C22×C113semidirect
520. C2×#102C22×C113semidirect
521. C2×#102C22×C113semidirect
523. C2×C22⋊C8C22×C113semidirect
524. C2×#97C22×C113semidirect
529. #391C22×C113semidirect
532. #390C22×C113semidirect
538. #340C22×C113semidirect
539. #340C22×C113semidirect
572. C2×SD16D4×C113semidirect
578. C2×D8D4×C113semidirect
581. C2×M16D4×C113semidirect
811. C23AGL(1,ℤ/8)×C113semidirect
880. C8#120×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×#466×C1132
C2×#465×C1132
C2×#435×C1132
C113×#24082
C113×#24072
C113×#20552
C113×#20542
C113×#20002
C113×#19992
C113×#19732
C113×#19722
C113×#18092
C113×#17882
C113×#17862
#24275113