Finite Group Databasebeta

← C113×#23857 #43291877

Subgroups — C113×#23857 #43291877

Order 28928.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C113C211yesmaximal, characteristic, complemented
2C2×#550×C113C211yesmaximal, characteristic, complemented
3C2×#452×C113C211yesmaximal, characteristic, complemented
4C2×#449×C113C211yesmaximal, characteristic, complemented
5C2×#449×C113C211yesmaximal, characteristic, complemented
6C113×#2407C211yesmaximal, characteristic, complemented
7C113×#2014C211yesmaximal, characteristic, complemented
8C113×#2011C211yesmaximal, characteristic, complemented
9C113×#2000C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1893C211yesmaximal, characteristic, complemented
12C113×#1880C211yesmaximal, characteristic, complemented
13C113×#1878C211yesmaximal, characteristic, complemented
14C113×#1869C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C22×#41×C113C2211yescharacteristic
19C2×#135×C113—24no—
20C2×#135×C113—24no—
21C2×#135×C113—24no—
22C22×Q16×C113C2211yescharacteristic
23C22×SD16×C113C2211yescharacteristic
24C22×SD16×C113C2211yescharacteristic
25C22×SD16×C113C2211yescharacteristic
26C22×D8×C113C2211yescharacteristic
27C22×D8×C113C2211yescharacteristic
28C23×C8×C113C2211yescharacteristic
29#550×C113—24no—
30#550×C113—24no—
31C2×#127×C113—21no—
32C2×#127×C113C2211yescharacteristic
33C2×C22⋊Q8×C113C2211yescharacteristic
34C2×#121×C113—21no—
35C2×#121×C113—21no—
36C2×#121×C113C2211yescharacteristic
37C2×#121×C113C2211yescharacteristic
38C2×#121×C113C2211yescharacteristic
39C2×C4×Q8×C113C2211yescharacteristic
40C2×C4×D4×C113—21no—
41C2×C4×D4×C113C2211yescharacteristic
42#452×C113—24no—
43#449×C113—24no—
44#449×C113—24no—
45C2×#103×C113C2211yescharacteristic
46C2×#103×C113C2211yescharacteristic
47C2×#103×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×#102×C113C2211yescharacteristic
52C2×#102×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54C2×C22⋊C8×C113C2211yescharacteristic
55C2×C22⋊C8×C113C2211yescharacteristic
56#394×C113—21no—
57#392×C113—21no—
58#391×C113C2211yescharacteristic
59#390×C113C2211yescharacteristic
60#386×C113—21no—
61#385×C113—21no—
62#380×C113C2211yescharacteristic
63#340×C113C2211yescharacteristic
64#340×C113C2211yescharacteristic
65#336×C113C2211yescharacteristic
66#336×C113C2211yescharacteristic
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—22no—
71C2×#41×C113—22no—
72C2×#41×C113—22no—
73C2×#41×C113—22no—
74C2×#41×C113—22no—
75C2×#41×C113—22no—
76C2×#41×C113—22no—
77C2×#41×C113—22no—
78C2×#41×C113—41no—
79C2×#41×C113—41no—
80C2×#41×C113—41no—
81C2×#41×C113—41no—
82C2×#41×C113—41no—
83C2×#41×C113—41no—
84C2×#41×C113D414yescomplemented
85C22×Q8×C113C2311yescharacteristic
86C22×Q8×C113C2311yescharacteristic
87C22×D4×C113—21no—
88C22×D4×C113—21no—
89C22×D4×C113—21no—
90C22×D4×C113—21no—
91C22×D4×C113—21no—
92C22×D4×C113—21no—
93C22×D4×C113—21no—
94C22×D4×C113—21no—
95C22×D4×C113D411yescharacteristic
96C22×D4×C113C2311yescharacteristic
97C22×D4×C113C2311yescharacteristic
98C22×D4×C113C2311yescharacteristic
99C23×C4×C113—21no—
100C23×C4×C113—21no—
101C23×C4×C113—21no—
102C23×C4×C113C2311yescharacteristic
103C23×C4×C113C2311yescharacteristic
104#135×C113—232no—
105C2×Q16×C113—22no—
106C2×Q16×C113—22no—
107C2×Q16×C113D414yescomplemented
108C2×SD16×C113—22no—
109C2×SD16×C113—22no—
110C2×SD16×C113—22no—
111C2×SD16×C113—22no—
112C2×SD16×C113—22no—
113C2×SD16×C113—22no—
114C2×SD16×C113—22no—
115C2×SD16×C113—41no—
116C2×SD16×C113D414yescomplemented
117C2×D8×C113—22no—
118C2×D8×C113—22no—
119C2×D8×C113—22no—
120C2×D8×C113—22no—
121C2×D8×C113—22no—
122C2×D8×C113—41no—
123C22×C8×C113—22no—
124C22×C8×C113—22no—
125C22×C8×C113—22no—
126C22×C8×C113C2311yescharacteristic
127C22×C8×C113C2311yescharacteristic
128C22×C8×C113C2311yescharacteristic
129C22×C8×C113C2311yescharacteristic
130#127×C113—28no—
131#127×C113—22no—
132#127×C113—22no—
133C22⋊Q8×C113—22no—
134C22⋊Q8×C113—41no—
135#121×C113—28no—
136#121×C113—28no—
137#121×C113—22no—
138#121×C113—22no—
139#121×C113—22no—
140#121×C113—22no—
141#121×C113—41no—
142#121×C113D414yescomplemented
143C4×Q8×C113—22no—
144C4×Q8×C113—22no—
145C4×D4×C113—28no—
146C4×D4×C113—22no—
147C4×D4×C113—22no—
148C2×C4⋊C4×C113—21no—
149C2×C4⋊C4×C113—21no—
150C2×C4⋊C4×C113D411yescharacteristic
151C2×C4⋊C4×C113C2311yescharacteristic
152C2×C4⋊C4×C113C2311yescharacteristic
153C2×C4⋊C4×C113C2311yescharacteristic
154C2×C22⋊C4×C113—21no—
155C2×C22⋊C4×C113—21no—
156C2×C22⋊C4×C113—21no—
157C2×C22⋊C4×C113—21no—
158C2×C22⋊C4×C113—21no—
159C2×C22⋊C4×C113—21no—
160C2×C22⋊C4×C113—21no—
161C2×C22⋊C4×C113D411yescharacteristic
162C2×C22⋊C4×C113D411yescharacteristic
163C2×C42×C113—21no—
164C2×C42×C113C2311yescharacteristic
165#103×C113—22no—
166#103×C113—22no—
167#103×C113—22no—
168#102×C113—22no—
169#102×C113—22no—
170#102×C113—22no—
171#102×C113—41no—
172#102×C113—41no—
173C22⋊C8×C113—22no—
174C22⋊C8×C113—22no—
175C22⋊C8×C113—22no—
176#95×C113—21no—
177#95×C113—21no—
178#95×C113—21no—
179C24×C113—21no—
180C24×C113—21no—
181C24×C113—21no—
182C24×C113C2×D411yescharacteristic
183C24×C113C2×D411yescharacteristic
184#41×C113—28no—
185#41×C113—28no—
186#41×C113—44no—
187#41×C113—44no—
188#41×C113—44no—
189#41×C113—44no—
190#41×C113—44no—
191#41×C113—44no—
192#41×C113—44no—
193#41×C113—44no—
194#41×C113—44no—
195#41×C113—44no—
196C2×Q8×C113—21no—
197C2×Q8×C113—21no—
198C2×Q8×C113—21no—
199C2×Q8×C113—21no—
200C2×Q8×C113—21no—
201C2×Q8×C113—21no—
202C2×Q8×C113—21no—
203C2×Q8×C113—21no—
204C2×Q8×C113C2×D412yes—
205C2×Q8×C113C2×D412yes—
206C2×Q8×C113C2×D412yes—
207C2×Q8×C113C2×D412yes—
208C2×D4×C113—24no—
209C2×D4×C113—24no—
210C2×D4×C113—22no—
211C2×D4×C113—24no—
212C2×D4×C113—24no—
213C2×D4×C113—24no—
214C2×D4×C113—24no—
215C2×D4×C113—22no—
216C2×D4×C113—21no—
217C2×D4×C113—21no—
218C2×D4×C113—21no—
219C2×D4×C113—21no—
220C2×D4×C113—21no—
221C2×D4×C113—21no—
222C2×D4×C113—21no—
223C2×D4×C113—21no—
224C2×D4×C113—21no—
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—21no—
228C2×D4×C113—21no—
229C2×D4×C113—21no—
230C2×D4×C113—21no—
231C2×D4×C113—41no—
232C2×D4×C113—42no—
233C2×D4×C113—42no—
234C2×D4×C113—42no—
235C2×D4×C113—42no—
236C2×D4×C113—42no—
237C2×D4×C113—42no—
238C2×D4×C113—42no—
239C2×D4×C113—42no—
240C2×D4×C113—42no—
241C2×D4×C113—42no—
242C2×D4×C113—42no—
243C2×D4×C113—81no—
244C2×D4×C113—81no—
245C2×D4×C113—81no—
246C2×D4×C113—81no—
247C2×D4×C113—81no—
248C2×D4×C113—81no—
249C2×D4×C113—81no—
250C2×D4×C113C2×D412yes—
251C2×D4×C113C2×D412yes—
252C2×D4×C113C2×D412yes—
253C22×C4×C113—21no—
254C22×C4×C113—21no—
255C22×C4×C113—21no—
256C22×C4×C113—21no—
257C22×C4×C113—21no—
258C22×C4×C113—24no—
259C22×C4×C113—21no—
260C22×C4×C113—21no—
261C22×C4×C113—24no—
262C22×C4×C113—21no—
263C22×C4×C113—21no—
264C22×C4×C113—21no—
265C22×C4×C113—21no—
266C22×C4×C113—21no—
267C22×C4×C113—21no—
268C22×C4×C113—21no—
269C22×C4×C113—21no—
270C22×C4×C113—42no—
271C22×C4×C113—42no—
272C22×C4×C113—42no—
273C22×C4×C113—42no—
274C22×C4×C113—42no—
275C22×C4×C113—42no—
276C22×C4×C113—42no—
277C22×C4×C113C2×D411yescharacteristic
278C22×C4×C113C2×D411yescharacteristic
279C22×C4×C113C2×D411yescharacteristic
280C22×C4×C113C2×D412yes—
281C22×C4×C113C2×D412yes—
282C22×C4×C113C2×D411yescharacteristic
283C22×C4×C113C2411yescharacteristic
284Q16×C113—28no—
285SD16×C113—28no—
286SD16×C113—28no—
287SD16×C113—44no—
288D8×C113—28no—
289D8×C113—44no—
290C2×C8×C113—28no—
291C2×C8×C113—21no—
292C2×C8×C113—21no—
293C2×C8×C113—21no—
294C2×C8×C113—21no—
295C2×C8×C113—21no—
296C2×C8×C113—21no—
297C2×C8×C113—21no—
298C2×C8×C113—21no—
299C2×C8×C113—21no—
300C2×C8×C113—21no—
301C2×C8×C113C2×D412yes—
302C2×C8×C113C2×D412yes—
303C4⋊C4×C113—24no—
304C4⋊C4×C113—22no—
305C4⋊C4×C113—21no—
306C4⋊C4×C113—21no—
307C4⋊C4×C113—21no—
308C4⋊C4×C113—21no—
309C4⋊C4×C113—21no—
310C4⋊C4×C113—42no—
311C4⋊C4×C113C2×D412yes—
312C22⋊C4×C113—24no—
313C22⋊C4×C113—22no—
314C22⋊C4×C113—24no—
315C22⋊C4×C113—22no—
316C22⋊C4×C113—42no—
317C22⋊C4×C113—42no—
318C22⋊C4×C113—42no—
319C22⋊C4×C113—81no—
320C22⋊C4×C113—81no—
321C42×C113—24no—
322C42×C113—21no—
323C42×C113—21no—
324C23×C113—21no—
325C23×C113—21no—
326C23×C113—21no—
327C23×C113—21no—
328C23×C113—21no—
329C23×C113—21no—
330C23×C113—21no—
331C23×C113—22no—
332C23×C113—22no—
333C23×C113—21no—
334C23×C113—22no—
335C23×C113—21no—
336C23×C113—21no—
337C23×C113—21no—
338C23×C113—21no—
339C23×C113—21no—
340C23×C113—41no—
341C23×C113—41no—
342C23×C113—41no—
343C23×C113—41no—
344C23×C113—41no—
345C23×C113—41no—
346C23×C113—41no—
347C23×C113—41no—
348C23×C113—41no—
349C23×C113—41no—
350C23×C113—41no—
351C23×C113—41no—
352C23×C113—41no—
353C23×C113—41no—
354C23×C113—41no—
355C23×C113—41no—
356C23×C113—41no—
357C23×C113—41no—
358C23×C113#12012yes—
359C23×C113C22×D411yescharacteristic
360Q8×C113—22no—
361Q8×C113—22no—
362Q8×C113—22no—
363Q8×C113—22no—
364Q8×C113—22no—
365Q8×C113—41no—
366Q8×C113—41no—
367Q8×C113#12014yes—
368D4×C113—22no—
369D4×C113—22no—
370D4×C113—22no—
371D4×C113—22no—
372D4×C113—22no—
373D4×C113—22no—
374D4×C113—44no—
375D4×C113—48no—
376D4×C113—48no—
377D4×C113—48no—
378D4×C113—48no—
379D4×C113—41no—
380D4×C113—41no—
381D4×C113—41no—
382D4×C113—41no—
383D4×C113—41no—
384D4×C113—41no—
385D4×C113—84no—
386D4×C113—84no—
387D4×C113—84no—
388D4×C113—84no—
389C2×C4×C113—21no—
390C2×C4×C113—22no—
391C2×C4×C113—21no—
392C2×C4×C113—21no—
393C2×C4×C113—22no—
394C2×C4×C113—22no—
395C2×C4×C113—21no—
396C2×C4×C113—22no—
397C2×C4×C113—22no—
398C2×C4×C113—22no—
399C2×C4×C113—22no—
400C2×C4×C113—21no—
401C2×C4×C113—22no—
402C2×C4×C113—21no—
403C2×C4×C113—21no—
404C2×C4×C113—22no—
405C2×C4×C113—21no—
406C2×C4×C113—21no—
407C2×C4×C113—21no—
408C2×C4×C113—48no—
409C2×C4×C113—48no—
410C2×C4×C113—48no—
411C2×C4×C113—41no—
412C2×C4×C113—41no—
413C2×C4×C113—41no—
414C2×C4×C113—41no—
415C2×C4×C113—41no—
416C2×C4×C113—41no—
417C2×C4×C113—41no—
418C2×C4×C113—41no—
419C2×C4×C113—41no—
420C2×C4×C113—41no—
421C2×C4×C113—41no—
422C2×C4×C113—41no—
423C2×C4×C113—41no—
424C2×C4×C113—41no—
425C2×C4×C113#12012yes—
426C2×C4×C113#13512yescomplemented
427C2×C4×C113C22×D411yescharacteristic
428C2×C4×C113C22×D411yescharacteristic
429C2×C4×C113C22×D411yescharacteristic
430C2×C4×C113C22×D411yescharacteristic
431C2×C4×C113H(5,𝔽2)11yescharacteristic
432C2×C4×C113H(5,𝔽2)11yescharacteristic
433C8×C113—22no—
434C8×C113—22no—
435C8×C113—41no—
436C8×C113—41no—
437C22×C113—22no—
438C22×C113—22no—
439C22×C113—22no—
440C22×C113—41no—
441C22×C113—41no—
442C22×C113—41no—
443C22×C113—41no—
444C22×C113—42no—
445C22×C113—42no—
446C22×C113—42no—
447C22×C113—41no—
448C22×C113—41no—
449C22×C113—42no—
450C22×C113—42no—
451C22×C113—41no—
452C22×C113—42no—
453C22×C113—42no—
454C22×C113—41no—
455C22×C113—42no—
456C22×C113—41no—
457C22×C113—41no—
458C22×C113—42no—
459C22×C113—41no—
460C22×C113—81no—
461C22×C113—81no—
462C22×C113—81no—
463C22×C113—81no—
464C22×C113—81no—
465C22×C113—81no—
466C22×C113—81no—
467C22×C113—81no—
468C22×C113—81no—
469C22×C113—81no—
470C22×C113—81no—
471C22×C113—81no—
472C22×C113C2×#12011yescharacteristic
473C22×C113D4211yescharacteristic
474C22×C113D4211yescharacteristic
475C22×C113C2×#13511yescharacteristic
476C22×C113#57511yescharacteristic
477C22×C113#57611yescharacteristic
478C22×C113#57711yescharacteristic
479C4×C113—22no—
480C4×C113—24no—
481C4×C113—22no—
482C4×C113—41no—
483C4×C113—42no—
484C4×C113—41no—
485C4×C113—42no—
486C4×C113—81no—
487C4×C113—81no—
488C4×C113C2×#12011yescharacteristic
489C4×C113#53411yescharacteristic
490C4×C113D4211yescharacteristic
491C4×C113D4211yescharacteristic
492#23857C11311yesmaximal, characteristic, direct product factor, Sylow
493C2×C113—42no—
494C2×C113—81no—
495C2×C113—82no—
496C2×C113—82no—
497C2×C113—82no—
498C2×C113#240311yescharacteristic
499C2×C113#300211yescharacteristic
500C2×C113#301211yescharacteristic
501C2×C113#326811yescharacteristic
502C2×C113#327111yescharacteristic
503C2×C113#328411yescharacteristic
504C2×C113#328711yescharacteristic
505C22×#135C2×C11311yescharacteristic, complemented
506C2×#550C2×C11311yescharacteristic, complemented
507C2×#452C2×C11311yescharacteristic, complemented
508C2×#449C2×C11311yescharacteristic, complemented
509C2×#449C2×C11311yescharacteristic, complemented
510#2407C2×C11311yescharacteristic, complemented
511#2014C2×C11311yescharacteristic, complemented
512#2011C2×C11311yescharacteristic, complemented
513#2000C2×C11311yescharacteristic, complemented
514#1999C2×C11311yescharacteristic, complemented
515#1893C2×C11311yescharacteristic, complemented
516#1880C2×C11311yescharacteristic, complemented
517#1878C2×C11311yescharacteristic, complemented
518#1869C2×C11311yescharacteristic, complemented
519#1788C2×C11311yescharacteristic, complemented
520C113#2385711yescharacteristic, direct product factor, Sylow
521C22×#41C22×C11311yescharacteristic
522C22×#41C22×C11311yescharacteristic
523C22×#41C22×C11311yescharacteristic
524C2×#135—24no—
525C2×#135—24no—
526C2×#135—24no—
527C22×Q16C22×C11311yescharacteristic
528C22×SD16C22×C11311yescharacteristic
529C22×SD16C22×C11311yescharacteristic
530C22×SD16C22×C11311yescharacteristic
531C22×D8C22×C11311yescharacteristic
532C22×D8C22×C11311yescharacteristic
533C23×C8C22×C11311yescharacteristic
534#550—24no—
535#550—24no—
536C2×#127—21no—
537C2×#127C22×C11311yescharacteristic
538C2×C22⋊Q8C22×C11311yescharacteristic
539C2×#121—21no—
540C2×#121—21no—
541C2×#121C22×C11311yescharacteristic
542C2×#121C22×C11311yescharacteristic
543C2×#121C22×C11311yescharacteristic
544C2×C4×Q8C22×C11311yescharacteristic
545C2×C4×D4—21no—
546C2×C4×D4C22×C11311yescharacteristic
547#452—24no—
548#449—24no—
549#449—24no—
550C2×#103C22×C11311yescharacteristic
551C2×#103C22×C11311yescharacteristic
552C2×#103C22×C11311yescharacteristic
553C2×#102C22×C11311yescharacteristic
554C2×#102C22×C11311yescharacteristic
555C2×#102C22×C11311yescharacteristic
556C2×#102C22×C11311yescharacteristic
557C2×#102C22×C11311yescharacteristic
558C2×C22⋊C8C22×C11311yescharacteristic
559C2×C22⋊C8C22×C11311yescharacteristic
560C2×C22⋊C8C22×C11311yescharacteristic
561#394—21no—
562#392—21no—
563#391C22×C11311yescharacteristic
564#390C22×C11311yescharacteristic
565#386—21no—
566#385—21no—
567#380C22×C11311yescharacteristic
568#340C22×C11311yescharacteristic
569#340C22×C11311yescharacteristic
570#336C22×C11311yescharacteristic
571#336C22×C11311yescharacteristic
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—41no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C11314yescomplemented
590C22×Q8C23×C11311yescharacteristic
591C22×Q8C23×C11311yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4D4×C11311yescharacteristic
601C22×D4C23×C11311yescharacteristic
602C22×D4C23×C11311yescharacteristic
603C22×D4C23×C11311yescharacteristic
604C23×C4—21no—
605C23×C4—21no—
606C23×C4—21no—
607C23×C4C23×C11311yescharacteristic
608C23×C4C23×C11311yescharacteristic
609#135—232no—
610C2×Q16—22no—
611C2×Q16—22no—
612C2×Q16D4×C11314yescomplemented
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—41no—
621C2×SD16D4×C11314yescomplemented
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—41no—
628C22×C8—22no—
629C22×C8—22no—
630C22×C8—22no—
631C22×C8C23×C11311yescharacteristic
632C22×C8C23×C11311yescharacteristic
633C22×C8C23×C11311yescharacteristic
634C22×C8C23×C11311yescharacteristic
635#127—28no—
636#127—22no—
637#127—22no—
638C22⋊Q8—22no—
639C22⋊Q8—41no—
640#121—28no—
641#121—28no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121—22no—
646#121—41no—
647#121D4×C11314yescomplemented
648C4×Q8—22no—
649C4×Q8—22no—
650C4×D4—28no—
651C4×D4—22no—
652C4×D4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4D4×C11311yescharacteristic
656C2×C4⋊C4C23×C11311yescharacteristic
657C2×C4⋊C4C23×C11311yescharacteristic
658C2×C4⋊C4C23×C11311yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4D4×C11311yescharacteristic
667C2×C22⋊C4D4×C11311yescharacteristic
668C2×C42—21no—
669C2×C42C23×C11311yescharacteristic
670#103—22no—
671#103—22no—
672#103—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681#95—21no—
682#95—21no—
683#95—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×D4×C11311yescharacteristic
688C24C2×D4×C11311yescharacteristic
689#41—28no—
690#41—28no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700#41—44no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8C2×D4×C11312yes—
710C2×Q8C2×D4×C11312yes—
711C2×Q8C2×D4×C11312yes—
712C2×Q8C2×D4×C11312yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×D4×C11312yes—
756C2×D4C2×D4×C11312yes—
757C2×D4C2×D4×C11312yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2×D4×C11311yescharacteristic
783C22×C4C2×D4×C11311yescharacteristic
784C22×C4C2×D4×C11311yescharacteristic
785C22×C4C2×D4×C11312yes—
786C22×C4C2×D4×C11312yes—
787C22×C4C2×D4×C11311yescharacteristic
788C22×C4C24×C11311yescharacteristic
789Q16—28no—
790SD16—28no—
791SD16—28no—
792SD16—44no—
793D8—28no—
794D8—44no—
795C2×C8—28no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×D4×C11312yes—
807C2×C8C2×D4×C11312yes—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4C2×D4×C11312yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C42—24no—
827C42—21no—
828C42—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23#120×C11312yes—
864C23C22×D4×C11311yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8#120×C11314yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4#120×C11312yes—
931C2×C4#135×C11312yescomplemented
932C2×C4C22×D4×C11311yescharacteristic
933C2×C4C22×D4×C11311yescharacteristic
934C2×C4C22×D4×C11311yescharacteristic
935C2×C4C22×D4×C11311yescharacteristic
936C2×C4H(5,𝔽2)×C11311yescharacteristic
937C2×C4H(5,𝔽2)×C11311yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×#120×C11311yescharacteristic
978C22D42×C11311yescharacteristic
979C22D42×C11311yescharacteristic
980C22C2×#135×C11311yescharacteristic
981C22#575×C11311yescharacteristic
982C22#576×C11311yescharacteristic
983C22#577×C11311yescharacteristic
984C4—22no—
985C4—24no—
986C4—22no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×#120×C11311yescharacteristic
994C4#534×C11311yescharacteristic
995C4D42×C11311yescharacteristic
996C4D42×C11311yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2C113×#240311yescharacteristic
1003C2C113×#300211yescharacteristic
1004C2C113×#301211yescharacteristic
1005C2C113×#326811yescharacteristic
1006C2C113×#327111yescharacteristic
1007C2C113×#328411yescharacteristic
1008C2C113×#328711yescharacteristic
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×#135×C113C2semidirect
2. C2×#550×C113C2semidirect
3. C2×#452×C113C2semidirect
4. C2×#449×C113C2semidirect
5. C2×#449×C113C2semidirect
6. C113×#2407C2semidirect
7. C113×#2014C2semidirect
8. C113×#2011C2semidirect
9. C113×#2000C2semidirect
10. C113×#1999C2semidirect
11. C113×#1893C2semidirect
12. C113×#1880C2semidirect
13. C113×#1878C2semidirect
14. C113×#1869C2semidirect
15. C113×#1788C2semidirect
84. C2×#41×C113D4semidirect
107. C2×Q16×C113D4semidirect
116. C2×SD16×C113D4semidirect
142. #121×C113D4semidirect
426. C2×C4×C113#135semidirect
492. #23857C113direct (N × H)
505. C22×#135C2×C113semidirect
506. C2×#550C2×C113semidirect
507. C2×#452C2×C113semidirect
508. C2×#449C2×C113semidirect
509. C2×#449C2×C113semidirect
510. #2407C2×C113semidirect
511. #2014C2×C113semidirect
512. #2011C2×C113semidirect
513. #2000C2×C113semidirect
514. #1999C2×C113semidirect
515. #1893C2×C113semidirect
516. #1880C2×C113semidirect
517. #1878C2×C113semidirect
518. #1869C2×C113semidirect
519. #1788C2×C113semidirect
520. C113#23857direct (N × H)
589. C2×#41D4×C113semidirect
612. C2×Q16D4×C113semidirect
621. C2×SD16D4×C113semidirect
647. #121D4×C113semidirect
931. C2×C4#135×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1132
C2×#550×C1132
C2×#452×C1132
C2×#449×C1132
C113×#24072
C113×#20142
C113×#20112
C113×#20002
C113×#19992
C113×#18932
C113×#18802
C113×#18782
C113×#18692
C113×#17882
#23857113