Finite Group Databasebeta

← C113×#23881 #43291901

Subgroups — C113×#23881 #43291901

Order 28928.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C113C211yesmaximal, characteristic, complemented
2C113×#3489C211yesmaximal, characteristic, complemented
3C2×#456×C113C211yesmaximal, characteristic, complemented
4C2×#454×C113C211yesmaximal, characteristic, complemented
5C113×#3005C211yesmaximal, characteristic, complemented
6C113×#2432C211yesmaximal, characteristic, complemented
7C113×#2007C211yesmaximal, characteristic, complemented
8C113×#2006C211yesmaximal, characteristic, complemented
9C113×#2005C211yesmaximal, characteristic, complemented
10C113×#2003C211yesmaximal, characteristic, complemented
11C113×#1901C211yesmaximal, characteristic, complemented
12C113×#1883C211yesmaximal, characteristic, complemented
13C113×#1882C211yesmaximal, characteristic, complemented
14C113×#1871C211yesmaximal, characteristic, complemented
15C113×#1789C211yesmaximal, characteristic, complemented
16C2×2−1+4×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C22×#41×C113C2211yescharacteristic
19#575×C113—24no—
20#575×C113—24no—
21C2×#137×C113—21no—
22C2×#137×C113C2211yescharacteristic
23C2×#137×C113C2211yescharacteristic
24C2×#137×C113C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C113—21no—
26C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
29C2×#135×C113—21no—
30C2×#135×C113—21no—
31C22×M16×C113C2211yescharacteristic
32D4×Q8×C113—21no—
33#548×C113—21no—
34#547×C113—21no—
35#547×C113—22no—
36#546×C113—21no—
37#546×C113—22no—
38#537×C113—21no—
39#537×C113C2211yescharacteristic
40#536×C113—21no—
41#536×C113C2211yescharacteristic
42C2×C4⋊Q8×C113C2211yescharacteristic, complemented
43C2×#124×C113C2211yescharacteristic, complemented
44#525×C113—21no—
45#525×C113C2211yescharacteristic
46C2×C22⋊Q8×C113—21no—
47C2×C22⋊Q8×C113C2211yescharacteristic
48#520×C113C2211yescharacteristic
49#456×C113—24no—
50#454×C113—24no—
51#452×C113—21no—
52#452×C113—21no—
53#449×C113—21no—
54#449×C113—21no—
55C2×#104×C113C2211yescharacteristic
56C2×#104×C113C2211yescharacteristic
57C2×#104×C113C2211yescharacteristic
58C2×#104×C113C2211yescharacteristic
59C2×#104×C113C2211yescharacteristic, complemented
60C2×#104×C113C2211yescharacteristic, complemented
61#419×C113C2211yescharacteristic, complemented
62#418×C113C2211yescharacteristic, complemented
63C2×#101×C113C2211yescharacteristic, complemented
64C2×#101×C113C2211yescharacteristic, complemented
65#407×C113C2211yescharacteristic
66#394×C113—22no—
67#391×C113C2211yescharacteristic, complemented
68#390×C113C2211yescharacteristic, complemented
69#385×C113—22no—
70C4×C22⋊C4×C113C2211yescharacteristic
71#343×C113C2211yescharacteristic, complemented
72#343×C113C2211yescharacteristic, complemented
73#339×C113C2211yescharacteristic, complemented
74#339×C113C2211yescharacteristic, complemented
752−1+4×C113—22no—
762−1+4×C113—22no—
772−1+4×C113—41no—
782−1+4×C113—41no—
79C2×#41×C113—21no—
80C2×#41×C113—21no—
81C2×#41×C113—21no—
82C2×#41×C113—22no—
83C2×#41×C113—21no—
84C2×#41×C113—22no—
85C2×#41×C113—22no—
86C2×#41×C113—22no—
87C2×#41×C113—22no—
88C2×#41×C113—21no—
89C2×#41×C113—21no—
90C2×#41×C113—21no—
91C2×#41×C113—21no—
92C2×#41×C113—41no—
93C2×#41×C113—41no—
94C2×#41×C113—41no—
95C2×#41×C113—41no—
96C2×#41×C113D411yescharacteristic
97C2×#41×C113D411yescharacteristic
98C2×#41×C113C2311yescharacteristic
99C2×#41×C113C2311yescharacteristic
100C2×#41×C113C2311yescharacteristic
101C22×Q8×C113—21no—
102C22×Q8×C113—21no—
103C22×Q8×C113D411yescharacteristic
104C22×Q8×C113C2311yescharacteristic
105C22×Q8×C113C2311yescharacteristic
106C22×D4×C113—21no—
107C22×D4×C113—21no—
108C22×D4×C113D411yescharacteristic
109C22×D4×C113C2311yescharacteristic
110C23×C4×C113—21no—
111C23×C4×C113—21no—
112C23×C4×C113C2311yescharacteristic
113#137×C113—28no—
114#137×C113—22no—
115#137×C113—22no—
116#137×C113—22no—
117#137×C113—22no—
118#137×C113—41no—
119#137×C113D414yescomplemented
120AGL(1,ℤ/8)×C113—28no—
121AGL(1,ℤ/8)×C113—22no—
122AGL(1,ℤ/8)×C113—22no—
123AGL(1,ℤ/8)×C113—22no—
124AGL(1,ℤ/8)×C113—22no—
125AGL(1,ℤ/8)×C113—41no—
126AGL(1,ℤ/8)×C113D414yescomplemented
127#135×C113—28no—
128#135×C113—28no—
129C2×Q16×C113—21no—
130C2×Q16×C113—21no—
131C2×Q16×C113—21no—
132C2×SD16×C113—21no—
133C2×SD16×C113—21no—
134C2×SD16×C113—21no—
135C2×SD16×C113—21no—
136C2×SD16×C113—21no—
137C2×SD16×C113—21no—
138C2×D8×C113—21no—
139C2×D8×C113—21no—
140C2×D8×C113—21no—
141C2×M16×C113—21no—
142C2×M16×C113—22no—
143C2×M16×C113—22no—
144C2×M16×C113C2311yescharacteristic
145C2×M16×C113C2311yescharacteristic
146C2×M16×C113C2311yescharacteristic
147C2×M16×C113C2311yescharacteristic
148C22×C8×C113—21no—
149C4⋊Q8×C113—22no—
150C4⋊Q8×C113—21no—
151C4⋊Q8×C113—22no—
152C4⋊Q8×C113—41no—
153#124×C113—22no—
154#124×C113—21no—
155#124×C113—22no—
156#124×C113—41no—
157#123×C113—22no—
158#123×C113—22no—
159#123×C113—22no—
160#123×C113—21no—
161#123×C113—22no—
162C22⋊Q8×C113—22no—
163C22⋊Q8×C113—22no—
164C22⋊Q8×C113—22no—
165C22⋊Q8×C113—21no—
166C22⋊Q8×C113—21no—
167C22⋊Q8×C113—21no—
168C22⋊Q8×C113—21no—
169C22⋊Q8×C113—21no—
170C22⋊Q8×C113—21no—
171C22⋊Q8×C113—21no—
172C22⋊Q8×C113—21no—
173C22⋊Q8×C113D411yescharacteristic
174C22⋊Q8×C113D411yescharacteristic
175#121×C113—22no—
176#121×C113—22no—
177#121×C113—22no—
178#121×C113—21no—
179#121×C113—21no—
180#121×C113—22no—
181#121×C113D411yescharacteristic
182#121×C113D411yescharacteristic
183#120×C113—22no—
184#120×C113—21no—
185C4×Q8×C113—21no—
186C4×D4×C113—22no—
187C4×D4×C113—22no—
188C4×D4×C113—21no—
189C4×D4×C113—22no—
190C4×D4×C113—21no—
191C4×D4×C113—21no—
192#117×C113—21no—
193#117×C113C2311yescharacteristic
194C2×C4⋊C4×C113—22no—
195C2×C4⋊C4×C113—21no—
196C2×C4⋊C4×C113—22no—
197C2×C4⋊C4×C113D412yes—
198C2×C4⋊C4×C113C2311yescharacteristic
199C2×C22⋊C4×C113—22no—
200C2×C22⋊C4×C113—21no—
201C2×C22⋊C4×C113—22no—
202C2×C22⋊C4×C113—22no—
203C2×C22⋊C4×C113D412yes—
204C2×C42×C113C2311yescharacteristic
205C2×C42×C113C2311yescharacteristic
206#104×C113—22no—
207#104×C113—22no—
208#104×C113—22no—
209#104×C113—22no—
210#104×C113—41no—
211#104×C113—41no—
212#103×C113—21no—
213#103×C113—21no—
214#102×C113—21no—
215#102×C113—21no—
216#101×C113—22no—
217#101×C113—22no—
218C22⋊C8×C113—21no—
219C22⋊C8×C113—21no—
220#95×C113—21no—
221#95×C113—22no—
222C24×C113—21no—
223C24×C113—21no—
224C24×C113C2×D411yescharacteristic
225#41×C113—21no—
226#41×C113—21no—
227#41×C113—24no—
228#41×C113—24no—
229#41×C113—22no—
230#41×C113—22no—
231#41×C113—21no—
232#41×C113—21no—
233#41×C113—21no—
234#41×C113—21no—
235#41×C113—21no—
236#41×C113—21no—
237#41×C113—21no—
238#41×C113—21no—
239#41×C113—42no—
240#41×C113—42no—
241#41×C113—41no—
242#41×C113—41no—
243#41×C113—42no—
244#41×C113—42no—
245#41×C113—42no—
246#41×C113—42no—
247#41×C113—42no—
248#41×C113—42no—
249#41×C113—44no—
250#41×C113—44no—
251#41×C113—42no—
252#41×C113—42no—
253#41×C113—42no—
254#41×C113—42no—
255#41×C113—42no—
256#41×C113—42no—
257#41×C113C2×D412yes—
258#41×C113C2×D412yes—
259C2×Q8×C113—22no—
260C2×Q8×C113—21no—
261C2×Q8×C113—21no—
262C2×Q8×C113—21no—
263C2×Q8×C113—21no—
264C2×Q8×C113—21no—
265C2×Q8×C113—21no—
266C2×Q8×C113—21no—
267C2×Q8×C113—21no—
268C2×Q8×C113—22no—
269C2×Q8×C113—21no—
270C2×Q8×C113—21no—
271C2×Q8×C113—21no—
272C2×Q8×C113—21no—
273C2×Q8×C113—41no—
274C2×Q8×C113—42no—
275C2×Q8×C113—42no—
276C2×Q8×C113—42no—
277C2×Q8×C113—42no—
278C2×Q8×C113C2×D411yescharacteristic
279C2×Q8×C113C2×D411yescharacteristic
280C2×Q8×C113C2×D412yes—
281C2×Q8×C113C2×D411yescharacteristic
282C2×D4×C113—21no—
283C2×D4×C113—22no—
284C2×D4×C113—22no—
285C2×D4×C113—21no—
286C2×D4×C113—21no—
287C2×D4×C113—21no—
288C2×D4×C113—21no—
289C2×D4×C113—21no—
290C2×D4×C113—22no—
291C2×D4×C113—21no—
292C2×D4×C113—21no—
293C2×D4×C113—21no—
294C2×D4×C113—21no—
295C2×D4×C113—21no—
296C2×D4×C113—21no—
297C2×D4×C113—21no—
298C2×D4×C113—41no—
299C2×D4×C113—42no—
300C2×D4×C113—42no—
301C2×D4×C113—42no—
302C2×D4×C113—42no—
303C2×D4×C113—41no—
304C2×D4×C113—41no—
305C2×D4×C113C2×D411yescharacteristic
306C2×D4×C113C2×D411yescharacteristic
307C2×D4×C113C2×D412yes—
308C2×D4×C113C2×D411yescharacteristic
309C22×C4×C113—21no—
310C22×C4×C113—21no—
311C22×C4×C113—21no—
312C22×C4×C113—21no—
313C22×C4×C113—21no—
314C22×C4×C113—22no—
315C22×C4×C113—22no—
316C22×C4×C113—21no—
317C22×C4×C113—21no—
318C22×C4×C113—21no—
319C22×C4×C113—22no—
320C22×C4×C113—21no—
321C22×C4×C113—21no—
322C22×C4×C113—21no—
323C22×C4×C113—21no—
324C22×C4×C113—21no—
325C22×C4×C113—42no—
326C22×C4×C113—42no—
327C22×C4×C113—42no—
328C22×C4×C113—42no—
329C22×C4×C113—41no—
330C22×C4×C113—41no—
331C22×C4×C113C2×D412yes—
332C22×C4×C113C2×D411yescharacteristic
333C22×C4×C113C2×D411yescharacteristic
334C22×C4×C113C2×D411yescharacteristic
335C22×C4×C113C2×D411yescharacteristic
336C22×C4×C113C2×D411yescharacteristic
337C22×C4×C113C2×D412yes—
338C22×C4×C113C2411yescharacteristic
339Q16×C113—24no—
340Q16×C113—24no—
341Q16×C113—42no—
342SD16×C113—24no—
343SD16×C113—24no—
344SD16×C113—24no—
345SD16×C113—24no—
346SD16×C113—42no—
347SD16×C113—42no—
348D8×C113—24no—
349D8×C113—24no—
350D8×C113—42no—
351M16×C113—24no—
352M16×C113—21no—
353M16×C113—21no—
354M16×C113—21no—
355M16×C113—21no—
356M16×C113—21no—
357M16×C113—21no—
358M16×C113C2×D412yes—
359M16×C113C2×D412yes—
360C2×C8×C113—24no—
361C2×C8×C113—21no—
362C2×C8×C113—21no—
363C2×C8×C113—21no—
364C2×C8×C113—21no—
365C4⋊C4×C113—22no—
366C4⋊C4×C113—22no—
367C4⋊C4×C113—22no—
368C4⋊C4×C113—22no—
369C4⋊C4×C113—21no—
370C4⋊C4×C113—22no—
371C4⋊C4×C113—22no—
372C4⋊C4×C113—21no—
373C4⋊C4×C113—21no—
374C4⋊C4×C113—21no—
375C4⋊C4×C113—44no—
376C4⋊C4×C113C2×D411yescharacteristic
377C4⋊C4×C113C2×D411yescharacteristic
378C22⋊C4×C113—22no—
379C22⋊C4×C113—22no—
380C22⋊C4×C113—22no—
381C22⋊C4×C113—22no—
382C22⋊C4×C113—22no—
383C22⋊C4×C113—21no—
384C22⋊C4×C113—22no—
385C22⋊C4×C113—22no—
386C22⋊C4×C113—21no—
387C22⋊C4×C113—21no—
388C22⋊C4×C113—21no—
389C22⋊C4×C113—21no—
390C22⋊C4×C113—44no—
391C22⋊C4×C113—44no—
392C22⋊C4×C113—42no—
393C42×C113—22no—
394C42×C113—21no—
395C42×C113—21no—
396C42×C113—21no—
397C42×C113—21no—
398C42×C113—21no—
399C23×C113—21no—
400C23×C113—21no—
401C23×C113—21no—
402C23×C113—21no—
403C23×C113—21no—
404C23×C113—22no—
405C23×C113—41no—
406C23×C113—41no—
407C23×C113—42no—
408C23×C113—42no—
409C23×C113—42no—
410C23×C113—42no—
411C23×C113—41no—
412C23×C113—41no—
413C23×C113—81no—
414C23×C113#12011yescharacteristic
415C23×C113#12011yescharacteristic
416C23×C113C22×D411yescharacteristic
417Q8×C113—21no—
418Q8×C113—21no—
419Q8×C113—22no—
420Q8×C113—21no—
421Q8×C113—21no—
422Q8×C113—22no—
423Q8×C113—21no—
424Q8×C113—42no—
425Q8×C113—44no—
426Q8×C113—41no—
427Q8×C113—41no—
428Q8×C113—41no—
429Q8×C113—41no—
430Q8×C113—41no—
431Q8×C113—41no—
432Q8×C113#12012yes—
433D4×C113—22no—
434D4×C113—22no—
435D4×C113—21no—
436D4×C113—22no—
437D4×C113—21no—
438D4×C113—21no—
439D4×C113—21no—
440D4×C113—22no—
441D4×C113—21no—
442D4×C113—42no—
443D4×C113—42no—
444D4×C113—42no—
445D4×C113—42no—
446D4×C113—44no—
447D4×C113—44no—
448D4×C113—44no—
449D4×C113—41no—
450D4×C113—41no—
451D4×C113—41no—
452D4×C113—41no—
453D4×C113—41no—
454D4×C113—41no—
455D4×C113—81no—
456D4×C113—82no—
457D4×C113#12012yes—
458C2×C4×C113—21no—
459C2×C4×C113—21no—
460C2×C4×C113—21no—
461C2×C4×C113—21no—
462C2×C4×C113—21no—
463C2×C4×C113—21no—
464C2×C4×C113—21no—
465C2×C4×C113—21no—
466C2×C4×C113—21no—
467C2×C4×C113—21no—
468C2×C4×C113—21no—
469C2×C4×C113—22no—
470C2×C4×C113—22no—
471C2×C4×C113—22no—
472C2×C4×C113—21no—
473C2×C4×C113—22no—
474C2×C4×C113—21no—
475C2×C4×C113—21no—
476C2×C4×C113—22no—
477C2×C4×C113—21no—
478C2×C4×C113—22no—
479C2×C4×C113—22no—
480C2×C4×C113—22no—
481C2×C4×C113—42no—
482C2×C4×C113—42no—
483C2×C4×C113—42no—
484C2×C4×C113—44no—
485C2×C4×C113—44no—
486C2×C4×C113—44no—
487C2×C4×C113—41no—
488C2×C4×C113—44no—
489C2×C4×C113—41no—
490C2×C4×C113—41no—
491C2×C4×C113—41no—
492C2×C4×C113—41no—
493C2×C4×C113—41no—
494C2×C4×C113—41no—
495C2×C4×C113—41no—
496C2×C4×C113—42no—
497C2×C4×C113—41no—
498C2×C4×C113—41no—
499C2×C4×C113—41no—
500C2×C4×C113—82no—
501C2×C4×C113#12011yescharacteristic
502C2×C4×C113#12011yescharacteristic
503C2×C4×C113C22×D411yescharacteristic
504C2×C4×C113C22×D411yescharacteristic
505C2×C4×C113C22×D411yescharacteristic
506C2×C4×C113C22×D411yescharacteristic
507C2×C4×C113H(5,𝔽2)11yescharacteristic
508C2×C4×C113H(5,𝔽2)11yescharacteristic
509C8×C113—22no—
510C8×C113—22no—
511C8×C113—41no—
512C8×C113—41no—
513C22×C113—21no—
514C22×C113—21no—
515C22×C113—21no—
516C22×C113—21no—
517C22×C113—22no—
518C22×C113—21no—
519C22×C113—21no—
520C22×C113—21no—
521C22×C113—21no—
522C22×C113—44no—
523C22×C113—41no—
524C22×C113—41no—
525C22×C113—41no—
526C22×C113—41no—
527C22×C113—42no—
528C22×C113—41no—
529C22×C113—41no—
530C22×C113—41no—
531C22×C113—41no—
532C22×C113—81no—
533C22×C113—81no—
534C22×C113—82no—
535C22×C113—84no—
536C22×C113—81no—
537C22×C113—81no—
538C22×C113C2×#12011yescharacteristic
539C22×C113D4211yescharacteristic
540C22×C113D4211yescharacteristic
541C4×C113—21no—
542C4×C113—21no—
543C4×C113—22no—
544C4×C113—42no—
545C4×C113—42no—
546C4×C113—41no—
547C4×C113—42no—
548C4×C113—41no—
549C4×C113—42no—
550C4×C113—41no—
551C4×C113—41no—
552C4×C113—81no—
553C4×C113C2×#12011yescharacteristic
554C4×C113#53411yescharacteristic
555C4×C113D4211yescharacteristic
556C4×C113D4211yescharacteristic
557#23881C11311yesmaximal, characteristic, direct product factor, Sylow
558C2×C113—21no—
559C2×C113—21no—
560C2×C113—41no—
561C2×C113—41no—
562C2×C113—42no—
563C2×C113—81no—
564C2×C113—82no—
565C2×C113—81no—
566C2×C113#240311yescharacteristic
567C2×C113#301811yescharacteristic
568C2×C113#302011yescharacteristic
569C2×#575C2×C11311yescharacteristic, complemented
570#3489C2×C11311yescharacteristic, complemented
571C2×#456C2×C11311yescharacteristic, complemented
572C2×#454C2×C11311yescharacteristic, complemented
573#3005C2×C11311yescharacteristic, complemented
574#2432C2×C11311yescharacteristic, complemented
575#2007C2×C11311yescharacteristic, complemented
576#2006C2×C11311yescharacteristic, complemented
577#2005C2×C11311yescharacteristic, complemented
578#2003C2×C11311yescharacteristic, complemented
579#1901C2×C11311yescharacteristic, complemented
580#1883C2×C11311yescharacteristic, complemented
581#1882C2×C11311yescharacteristic, complemented
582#1871C2×C11311yescharacteristic, complemented
583#1789C2×C11311yescharacteristic, complemented
584C113#2388111yescharacteristic, direct product factor, Sylow
585C2×2−1+4C22×C11311yescharacteristic
586C22×#41C22×C11311yescharacteristic
587C22×#41C22×C11311yescharacteristic
588#575—24no—
589#575—24no—
590C2×#137—21no—
591C2×#137C22×C11311yescharacteristic
592C2×#137C22×C11311yescharacteristic
593C2×#137C22×C11311yescharacteristic, complemented
594C2×AGL(1,ℤ/8)—21no—
595C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
596C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
597C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
598C2×#135—21no—
599C2×#135—21no—
600C22×M16C22×C11311yescharacteristic
601D4×Q8—21no—
602#548—21no—
603#547—21no—
604#547—22no—
605#546—21no—
606#546—22no—
607#537—21no—
608#537C22×C11311yescharacteristic
609#536—21no—
610#536C22×C11311yescharacteristic
611C2×C4⋊Q8C22×C11311yescharacteristic, complemented
612C2×#124C22×C11311yescharacteristic, complemented
613#525—21no—
614#525C22×C11311yescharacteristic
615C2×C22⋊Q8—21no—
616C2×C22⋊Q8C22×C11311yescharacteristic
617#520C22×C11311yescharacteristic
618#456—24no—
619#454—24no—
620#452—21no—
621#452—21no—
622#449—21no—
623#449—21no—
624C2×#104C22×C11311yescharacteristic
625C2×#104C22×C11311yescharacteristic
626C2×#104C22×C11311yescharacteristic
627C2×#104C22×C11311yescharacteristic
628C2×#104C22×C11311yescharacteristic, complemented
629C2×#104C22×C11311yescharacteristic, complemented
630#419C22×C11311yescharacteristic, complemented
631#418C22×C11311yescharacteristic, complemented
632C2×#101C22×C11311yescharacteristic, complemented
633C2×#101C22×C11311yescharacteristic, complemented
634#407C22×C11311yescharacteristic
635#394—22no—
636#391C22×C11311yescharacteristic, complemented
637#390C22×C11311yescharacteristic, complemented
638#385—22no—
639C4×C22⋊C4C22×C11311yescharacteristic
640#343C22×C11311yescharacteristic, complemented
641#343C22×C11311yescharacteristic, complemented
642#339C22×C11311yescharacteristic, complemented
643#339C22×C11311yescharacteristic, complemented
6442−1+4—22no—
6452−1+4—22no—
6462−1+4—41no—
6472−1+4—41no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—21no—
651C2×#41—22no—
652C2×#41—21no—
653C2×#41—22no—
654C2×#41—22no—
655C2×#41—22no—
656C2×#41—22no—
657C2×#41—21no—
658C2×#41—21no—
659C2×#41—21no—
660C2×#41—21no—
661C2×#41—41no—
662C2×#41—41no—
663C2×#41—41no—
664C2×#41—41no—
665C2×#41D4×C11311yescharacteristic
666C2×#41D4×C11311yescharacteristic
667C2×#41C23×C11311yescharacteristic
668C2×#41C23×C11311yescharacteristic
669C2×#41C23×C11311yescharacteristic
670C22×Q8—21no—
671C22×Q8—21no—
672C22×Q8D4×C11311yescharacteristic
673C22×Q8C23×C11311yescharacteristic
674C22×Q8C23×C11311yescharacteristic
675C22×D4—21no—
676C22×D4—21no—
677C22×D4D4×C11311yescharacteristic
678C22×D4C23×C11311yescharacteristic
679C23×C4—21no—
680C23×C4—21no—
681C23×C4C23×C11311yescharacteristic
682#137—28no—
683#137—22no—
684#137—22no—
685#137—22no—
686#137—22no—
687#137—41no—
688#137D4×C11314yescomplemented
689AGL(1,ℤ/8)—28no—
690AGL(1,ℤ/8)—22no—
691AGL(1,ℤ/8)—22no—
692AGL(1,ℤ/8)—22no—
693AGL(1,ℤ/8)—22no—
694AGL(1,ℤ/8)—41no—
695AGL(1,ℤ/8)D4×C11314yescomplemented
696#135—28no—
697#135—28no—
698C2×Q16—21no—
699C2×Q16—21no—
700C2×Q16—21no—
701C2×SD16—21no—
702C2×SD16—21no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×SD16—21no—
707C2×D8—21no—
708C2×D8—21no—
709C2×D8—21no—
710C2×M16—21no—
711C2×M16—22no—
712C2×M16—22no—
713C2×M16C23×C11311yescharacteristic
714C2×M16C23×C11311yescharacteristic
715C2×M16C23×C11311yescharacteristic
716C2×M16C23×C11311yescharacteristic
717C22×C8—21no—
718C4⋊Q8—22no—
719C4⋊Q8—21no—
720C4⋊Q8—22no—
721C4⋊Q8—41no—
722#124—22no—
723#124—21no—
724#124—22no—
725#124—41no—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—21no—
730#123—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8D4×C11311yescharacteristic
743C22⋊Q8D4×C11311yescharacteristic
744#121—22no—
745#121—22no—
746#121—22no—
747#121—21no—
748#121—21no—
749#121—22no—
750#121D4×C11311yescharacteristic
751#121D4×C11311yescharacteristic
752#120—22no—
753#120—21no—
754C4×Q8—21no—
755C4×D4—22no—
756C4×D4—22no—
757C4×D4—21no—
758C4×D4—22no—
759C4×D4—21no—
760C4×D4—21no—
761#117—21no—
762#117C23×C11311yescharacteristic
763C2×C4⋊C4—22no—
764C2×C4⋊C4—21no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4D4×C11312yes—
767C2×C4⋊C4C23×C11311yescharacteristic
768C2×C22⋊C4—22no—
769C2×C22⋊C4—21no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4D4×C11312yes—
773C2×C42C23×C11311yescharacteristic
774C2×C42C23×C11311yescharacteristic
775#104—22no—
776#104—22no—
777#104—22no—
778#104—22no—
779#104—41no—
780#104—41no—
781#103—21no—
782#103—21no—
783#102—21no—
784#102—21no—
785#101—22no—
786#101—22no—
787C22⋊C8—21no—
788C22⋊C8—21no—
789#95—21no—
790#95—22no—
791C24—21no—
792C24—21no—
793C24C2×D4×C11311yescharacteristic
794#41—21no—
795#41—21no—
796#41—24no—
797#41—24no—
798#41—22no—
799#41—22no—
800#41—21no—
801#41—21no—
802#41—21no—
803#41—21no—
804#41—21no—
805#41—21no—
806#41—21no—
807#41—21no—
808#41—42no—
809#41—42no—
810#41—41no—
811#41—41no—
812#41—42no—
813#41—42no—
814#41—42no—
815#41—42no—
816#41—42no—
817#41—42no—
818#41—44no—
819#41—44no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41C2×D4×C11312yes—
827#41C2×D4×C11312yes—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8C2×D4×C11311yescharacteristic
848C2×Q8C2×D4×C11311yescharacteristic
849C2×Q8C2×D4×C11312yes—
850C2×Q8C2×D4×C11311yescharacteristic
851C2×D4—21no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4C2×D4×C11311yescharacteristic
875C2×D4C2×D4×C11311yescharacteristic
876C2×D4C2×D4×C11312yes—
877C2×D4C2×D4×C11311yescharacteristic
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4C2×D4×C11312yes—
901C22×C4C2×D4×C11311yescharacteristic
902C22×C4C2×D4×C11311yescharacteristic
903C22×C4C2×D4×C11311yescharacteristic
904C22×C4C2×D4×C11311yescharacteristic
905C22×C4C2×D4×C11311yescharacteristic
906C22×C4C2×D4×C11312yes—
907C22×C4C24×C11311yescharacteristic
908Q16—24no—
909Q16—24no—
910Q16—42no—
911SD16—24no—
912SD16—24no—
913SD16—24no—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917D8—24no—
918D8—24no—
919D8—42no—
920M16—24no—
921M16—21no—
922M16—21no—
923M16—21no—
924M16—21no—
925M16—21no—
926M16—21no—
927M16C2×D4×C11312yes—
928M16C2×D4×C11312yes—
929C2×C8—24no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—44no—
945C4⋊C4C2×D4×C11311yescharacteristic
946C4⋊C4C2×D4×C11311yescharacteristic
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—21no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—42no—
962C42—22no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—81no—
983C23#120×C11311yescharacteristic
984C23#120×C11311yescharacteristic
985C23C22×D4×C11311yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—22no—
989Q8—21no—
990Q8—21no—
991Q8—22no—
992Q8—21no—
993Q8—42no—
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8#120×C11312yes—
1002D4—22no—
1003D4—22no—
1004D4—21no—
1005D4—22no—
1006D4—21no—
1007D4—21no—
1008D4—21no—
1009D4—22no—
1010D4—21no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—44no—
1015D4—42no—
1016D4—44no—
1017D4—44no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—81no—
1025D4—82no—
1026D4#120×C11312yes—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—82no—
1070C2×C4#120×C11311yescharacteristic
1071C2×C4#120×C11311yescharacteristic
1072C2×C4C22×D4×C11311yescharacteristic
1073C2×C4C22×D4×C11311yescharacteristic
1074C2×C4C22×D4×C11311yescharacteristic
1075C2×C4C22×D4×C11311yescharacteristic
1076C2×C4H(5,𝔽2)×C11311yescharacteristic
1077C2×C4H(5,𝔽2)×C11311yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×#120×C11311yescharacteristic
1108C22D42×C11311yescharacteristic
1109C22D42×C11311yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—81no—
1122C4C2×#120×C11311yescharacteristic
1123C4#534×C11311yescharacteristic
1124C4D42×C11311yescharacteristic
1125C4D42×C11311yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2C113×#240311yescharacteristic
1135C2C113×#301811yescharacteristic
1136C2C113×#302011yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C113C2semidirect
2. C113×#3489C2semidirect
3. C2×#456×C113C2semidirect
4. C2×#454×C113C2semidirect
5. C113×#3005C2semidirect
6. C113×#2432C2semidirect
7. C113×#2007C2semidirect
8. C113×#2006C2semidirect
9. C113×#2005C2semidirect
10. C113×#2003C2semidirect
11. C113×#1901C2semidirect
12. C113×#1883C2semidirect
13. C113×#1882C2semidirect
14. C113×#1871C2semidirect
15. C113×#1789C2semidirect
24. C2×#137×C113C22semidirect
28. C2×AGL(1,ℤ/8)×C113C22semidirect
42. C2×C4⋊Q8×C113C22semidirect
43. C2×#124×C113C22semidirect
59. C2×#104×C113C22semidirect
60. C2×#104×C113C22semidirect
61. #419×C113C22semidirect
62. #418×C113C22semidirect
63. C2×#101×C113C22semidirect
64. C2×#101×C113C22semidirect
67. #391×C113C22semidirect
68. #390×C113C22semidirect
71. #343×C113C22semidirect
72. #343×C113C22semidirect
73. #339×C113C22semidirect
74. #339×C113C22semidirect
119. #137×C113D4semidirect
126. AGL(1,ℤ/8)×C113D4semidirect
557. #23881C113direct (N × H)
569. C2×#575C2×C113semidirect
570. #3489C2×C113semidirect
571. C2×#456C2×C113semidirect
572. C2×#454C2×C113semidirect
573. #3005C2×C113semidirect
574. #2432C2×C113semidirect
575. #2007C2×C113semidirect
576. #2006C2×C113semidirect
577. #2005C2×C113semidirect
578. #2003C2×C113semidirect
579. #1901C2×C113semidirect
580. #1883C2×C113semidirect
581. #1882C2×C113semidirect
582. #1871C2×C113semidirect
583. #1789C2×C113semidirect
584. C113#23881direct (N × H)
593. C2×#137C22×C113semidirect
597. C2×AGL(1,ℤ/8)C22×C113semidirect
611. C2×C4⋊Q8C22×C113semidirect
612. C2×#124C22×C113semidirect
628. C2×#104C22×C113semidirect
629. C2×#104C22×C113semidirect
630. #419C22×C113semidirect
631. #418C22×C113semidirect
632. C2×#101C22×C113semidirect
633. C2×#101C22×C113semidirect
636. #391C22×C113semidirect
637. #390C22×C113semidirect
640. #343C22×C113semidirect
641. #343C22×C113semidirect
642. #339C22×C113semidirect
643. #339C22×C113semidirect
688. #137D4×C113semidirect
695. AGL(1,ℤ/8)D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1132
C113×#34892
C2×#456×C1132
C2×#454×C1132
C113×#30052
C113×#24322
C113×#20072
C113×#20062
C113×#20052
C113×#20032
C113×#19012
C113×#18832
C113×#18822
C113×#18712
C113×#17892
#23881113