Finite Group Databasebeta

← C113×#24402 #43292422

Subgroups — C113×#24402 #43292422

Order 28928.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C113C211yesmaximal, characteristic, complemented
2C2×#472×C113C211yesmaximal, characteristic, complemented
3C2×#471×C113C211yesmaximal, characteristic, complemented
4C113×#3006C211yesmaximal, characteristic, complemented
5C2×#449×C113C211yesmaximal, characteristic, complemented
6C113×#2880C211yesmaximal, characteristic, complemented
7C113×#2052C211yesmaximal, characteristic, complemented
8C113×#2051C211yesmaximal, characteristic, complemented
9C113×#2019C211yesmaximal, characteristic, complemented
10C113×#2018C211yesmaximal, characteristic, complemented
11C113×#1908C211yesmaximal, characteristic, complemented
12C113×#1907C211yesmaximal, characteristic, complemented
13C113×#1900C211yesmaximal, characteristic, complemented
14C113×#1855C211yesmaximal, characteristic, complemented
15C113×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18#575×C113—24no—
19#575×C113—24no—
20C2×#137×C113—21no—
21C2×#137×C113C2211yescharacteristic
22C2×#137×C113C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C113—21no—
24C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
28C2×#135×C113—21no—
29C2×#135×C113—21no—
30C22×SD16×C113C2211yescharacteristic, complemented
31C22×D8×C113C2211yescharacteristic, complemented
32C2×#131×C113C2211yescharacteristic
33C2×#131×C113C2211yescharacteristic
34C22×M16×C113C2211yescharacteristic
35C2×#121×C113C2211yescharacteristic
36#472×C113—24no—
37#471×C113—24no—
38#449×C113—21no—
39#449×C113—21no—
40#449×C113—21no—
41#449×C113—21no—
42#449×C113—21no—
43#449×C113—21no—
44#448×C113—21no—
45#447×C113—21no—
46C2×#108×C113C2211yescharacteristic, complemented
47C2×#108×C113C2211yescharacteristic, complemented
48#417×C113C2211yescharacteristic
49#417×C113C2211yescharacteristic
50C2×#103×C113C2211yescharacteristic, complemented
51C2×#102×C113C2211yescharacteristic, complemented
52C2×#101×C113C2211yescharacteristic, complemented
53C2×#101×C113C2211yescharacteristic, complemented
54C2×#100×C113C2211yescharacteristic, complemented
55C2×#100×C113C2211yescharacteristic, complemented
56C2×#100×C113C2211yescharacteristic, complemented
57C2×#100×C113C2211yescharacteristic, complemented
58#408×C113—21no—
59#408×C113—21no—
60#408×C113C2211yescharacteristic
61#408×C113C2211yescharacteristic
62#407×C113—21no—
63#407×C113C2211yescharacteristic
64#407×C113C2211yescharacteristic
65C2×C22⋊C8×C113—21no—
66C2×C22⋊C8×C113C2211yescharacteristic
67#343×C113C2211yescharacteristic, complemented
68#343×C113C2211yescharacteristic, complemented
69#341×C113C2211yescharacteristic, complemented
70#341×C113C2211yescharacteristic, complemented
71C2×#41×C113—21no—
72C2×#41×C113—21no—
73C2×#41×C113—22no—
74C2×#41×C113—22no—
75C2×#41×C113—22no—
76C2×#41×C113—22no—
77C2×#41×C113—21no—
78C2×#41×C113—21no—
79C2×#41×C113—21no—
80C2×#41×C113—21no—
81C2×#41×C113—41no—
82C2×#41×C113—41no—
83C2×#41×C113—41no—
84C2×#41×C113—41no—
85C2×#41×C113D411yescharacteristic
86C2×#41×C113D411yescharacteristic
87C2×#41×C113C2311yescharacteristic
88C2×#41×C113C2311yescharacteristic
89C22×Q8×C113D411yescharacteristic
90C22×Q8×C113C2311yescharacteristic
91C22×D4×C113—21no—
92C22×D4×C113—21no—
93C22×D4×C113—21no—
94C22×D4×C113D411yescharacteristic
95C22×D4×C113C2311yescharacteristic
96C22×D4×C113C2311yescharacteristic
97C23×C4×C113—21no—
98C23×C4×C113—21no—
99C23×C4×C113C2311yescharacteristic
100#137×C113—28no—
101#137×C113—22no—
102#137×C113—22no—
103#137×C113—22no—
104#137×C113D414yescomplemented
105AGL(1,ℤ/8)×C113—28no—
106AGL(1,ℤ/8)×C113—22no—
107AGL(1,ℤ/8)×C113—22no—
108AGL(1,ℤ/8)×C113—22no—
109AGL(1,ℤ/8)×C113—22no—
110AGL(1,ℤ/8)×C113—22no—
111AGL(1,ℤ/8)×C113—41no—
112AGL(1,ℤ/8)×C113—41no—
113AGL(1,ℤ/8)×C113D414yescomplemented
114#135×C113—28no—
115#135×C113—28no—
116C2×Q16×C113—21no—
117C2×Q16×C113—21no—
118C2×SD16×C113—21no—
119C2×SD16×C113—21no—
120C2×SD16×C113—21no—
121C2×SD16×C113—21no—
122C2×SD16×C113—22no—
123C2×SD16×C113—21no—
124C2×SD16×C113—21no—
125C2×SD16×C113—21no—
126C2×SD16×C113—21no—
127C2×SD16×C113—41no—
128C2×D8×C113—21no—
129C2×D8×C113—21no—
130C2×D8×C113—22no—
131C2×D8×C113—21no—
132C2×D8×C113—21no—
133C2×D8×C113—21no—
134C2×D8×C113—21no—
135C2×D8×C113—41no—
136#131×C113—22no—
137#131×C113—22no—
138#131×C113—41no—
139#131×C113—41no—
140C2×M16×C113—21no—
141C2×M16×C113—22no—
142C2×M16×C113—22no—
143C2×M16×C113—21no—
144C2×M16×C113—21no—
145C2×M16×C113C2311yescharacteristic
146C2×M16×C113C2311yescharacteristic
147C2×M16×C113C2311yescharacteristic
148C2×M16×C113C2311yescharacteristic
149C2×M16×C113C2311yescharacteristic
150C2×M16×C113C2311yescharacteristic
151C22×C8×C113—21no—
152C22×C8×C113—21no—
153C22×C8×C113—21no—
154C22×C8×C113C2311yescharacteristic
155C22×C8×C113C2311yescharacteristic
156#121×C113—21no—
157#121×C113—21no—
158#121×C113—21no—
159#121×C113—21no—
160C2×C4⋊C4×C113C2311yescharacteristic
161C2×C22⋊C4×C113—21no—
162#108×C113—22no—
163#108×C113—22no—
164#103×C113—21no—
165#103×C113—21no—
166#103×C113—21no—
167#103×C113—21no—
168#102×C113—21no—
169#102×C113—21no—
170#102×C113—21no—
171#102×C113—21no—
172#101×C113—22no—
173#101×C113—41no—
174#100×C113—22no—
175#100×C113—22no—
176#100×C113—22no—
177#100×C113—41no—
178C22⋊C8×C113—21no—
179C22⋊C8×C113—21no—
180C22⋊C8×C113—21no—
181C22⋊C8×C113—21no—
182C22⋊C8×C113—21no—
183C22⋊C8×C113—21no—
184C22⋊C8×C113—21no—
185C22⋊C8×C113—21no—
186C22⋊C8×C113D411yescharacteristic
187C22⋊C8×C113D411yescharacteristic
188C22⋊C8×C113D411yescharacteristic
189C22⋊C8×C113D411yescharacteristic
190C24×C113—21no—
191C24×C113—21no—
192C24×C113—21no—
193C24×C113#4111yescharacteristic
194#41×C113—21no—
195#41×C113—21no—
196#41×C113—24no—
197#41×C113—24no—
198#41×C113—22no—
199#41×C113—22no—
200#41×C113—21no—
201#41×C113—21no—
202#41×C113—21no—
203#41×C113—21no—
204#41×C113—42no—
205#41×C113—42no—
206#41×C113—41no—
207#41×C113—41no—
208#41×C113—42no—
209#41×C113—42no—
210#41×C113—42no—
211#41×C113—42no—
212#41×C113—42no—
213#41×C113—42no—
214#41×C113—42no—
215#41×C113—42no—
216#41×C113C2×D412yes—
217#41×C113C2×D412yes—
218C2×Q8×C113—21no—
219C2×Q8×C113—21no—
220C2×Q8×C113—22no—
221C2×Q8×C113—21no—
222C2×Q8×C113—21no—
223C2×Q8×C113—21no—
224C2×Q8×C113—21no—
225C2×Q8×C113—41no—
226C2×Q8×C113C2×D412yes—
227C2×Q8×C113C2×D411yescharacteristic
228C2×Q8×C113C2×D411yescharacteristic
229C2×D4×C113—21no—
230C2×D4×C113—22no—
231C2×D4×C113—21no—
232C2×D4×C113—21no—
233C2×D4×C113—21no—
234C2×D4×C113—21no—
235C2×D4×C113—21no—
236C2×D4×C113—21no—
237C2×D4×C113—21no—
238C2×D4×C113—21no—
239C2×D4×C113—21no—
240C2×D4×C113—21no—
241C2×D4×C113—21no—
242C2×D4×C113—21no—
243C2×D4×C113—21no—
244C2×D4×C113—21no—
245C2×D4×C113—21no—
246C2×D4×C113—41no—
247C2×D4×C113—42no—
248C2×D4×C113—42no—
249C2×D4×C113—42no—
250C2×D4×C113—42no—
251C2×D4×C113—41no—
252C2×D4×C113—41no—
253C2×D4×C113—41no—
254C2×D4×C113—41no—
255C2×D4×C113—82no—
256C2×D4×C113C2×D412yes—
257C2×D4×C113C2×D411yescharacteristic
258C2×D4×C113C2×D411yescharacteristic
259C22×C4×C113—21no—
260C22×C4×C113—21no—
261C22×C4×C113—21no—
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—41no—
275C22×C4×C113—41no—
276C22×C4×C113C2×D411yescharacteristic
277C22×C4×C113C2×D411yescharacteristic
278C22×C4×C113C2×D411yescharacteristic
279C22×C4×C113C2×D411yescharacteristic
280C22×C4×C113#4111yescharacteristic
281C22×C4×C113C2411yescharacteristic
282Q16×C113—24no—
283Q16×C113—24no—
284SD16×C113—24no—
285SD16×C113—24no—
286SD16×C113—24no—
287SD16×C113—24no—
288SD16×C113—42no—
289SD16×C113—42no—
290SD16×C113—42no—
291SD16×C113—42no—
292D8×C113—24no—
293D8×C113—24no—
294D8×C113—42no—
295D8×C113—42no—
296D8×C113—42no—
297D8×C113—42no—
298M16×C113—24no—
299M16×C113—21no—
300M16×C113—21no—
301M16×C113—21no—
302M16×C113—21no—
303M16×C113—21no—
304M16×C113—21no—
305M16×C113—21no—
306M16×C113—21no—
307M16×C113—21no—
308M16×C113—21no—
309M16×C113—42no—
310M16×C113—42no—
311M16×C113C2×D412yes—
312M16×C113C2×D412yes—
313C2×C8×C113—24no—
314C2×C8×C113—21no—
315C2×C8×C113—21no—
316C2×C8×C113—21no—
317C2×C8×C113—21no—
318C2×C8×C113—21no—
319C2×C8×C113—21no—
320C2×C8×C113—21no—
321C2×C8×C113—21no—
322C2×C8×C113—21no—
323C2×C8×C113—21no—
324C2×C8×C113—42no—
325C2×C8×C113—42no—
326C2×C8×C113C2×D411yescharacteristic
327C2×C8×C113C2×D411yescharacteristic
328C2×C8×C113C2×D411yescharacteristic
329C2×C8×C113C2×D411yescharacteristic
330C4⋊C4×C113—21no—
331C4⋊C4×C113—21no—
332C22⋊C4×C113—41no—
333C22⋊C4×C113—41no—
334C23×C113—21no—
335C23×C113—21no—
336C23×C113—21no—
337C23×C113—21no—
338C23×C113—22no—
339C23×C113—41no—
340C23×C113—41no—
341C23×C113—42no—
342C23×C113—42no—
343C23×C113—41no—
344C23×C113—41no—
345C23×C113—41no—
346C23×C113—41no—
347C23×C113—41no—
348C23×C113—81no—
349C23×C113—81no—
350C23×C113—81no—
351C23×C113—81no—
352C23×C113—81no—
353C23×C113#12111yescharacteristic
354C23×C113#12111yescharacteristic
355C23×C113C2×#4111yescharacteristic
356Q8×C113—21no—
357Q8×C113—21no—
358Q8×C113—22no—
359Q8×C113—21no—
360Q8×C113—22no—
361Q8×C113—42no—
362Q8×C113—41no—
363Q8×C113—41no—
364Q8×C113#12012yes—
365D4×C113—22no—
366D4×C113—22no—
367D4×C113—21no—
368D4×C113—22no—
369D4×C113—21no—
370D4×C113—21no—
371D4×C113—22no—
372D4×C113—42no—
373D4×C113—42no—
374D4×C113—42no—
375D4×C113—44no—
376D4×C113—44no—
377D4×C113—41no—
378D4×C113—41no—
379D4×C113—41no—
380D4×C113—41no—
381D4×C113—41no—
382D4×C113—41no—
383D4×C113—41no—
384D4×C113—41no—
385D4×C113—82no—
386D4×C113—82no—
387D4×C113#12012yes—
388C2×C4×C113—21no—
389C2×C4×C113—21no—
390C2×C4×C113—21no—
391C2×C4×C113—21no—
392C2×C4×C113—21no—
393C2×C4×C113—21no—
394C2×C4×C113—21no—
395C2×C4×C113—22no—
396C2×C4×C113—22no—
397C2×C4×C113—21no—
398C2×C4×C113—21no—
399C2×C4×C113—21no—
400C2×C4×C113—21no—
401C2×C4×C113—21no—
402C2×C4×C113—22no—
403C2×C4×C113—42no—
404C2×C4×C113—42no—
405C2×C4×C113—42no—
406C2×C4×C113—44no—
407C2×C4×C113—44no—
408C2×C4×C113—41no—
409C2×C4×C113—41no—
410C2×C4×C113—41no—
411C2×C4×C113—41no—
412C2×C4×C113—41no—
413C2×C4×C113—81no—
414C2×C4×C113#12111yescharacteristic
415C2×C4×C113#12111yescharacteristic
416C2×C4×C113C22×D411yescharacteristic
417C2×C4×C113C22×D411yescharacteristic
418C2×C4×C113C22×D411yescharacteristic
419C2×C4×C113C22×D411yescharacteristic
420C2×C4×C113H(5,𝔽2)11yescharacteristic
421C2×C4×C113H(5,𝔽2)11yescharacteristic
422C8×C113—22no—
423C8×C113—22no—
424C8×C113—21no—
425C8×C113—21no—
426C8×C113—21no—
427C8×C113—21no—
428C8×C113—41no—
429C8×C113—41no—
430C8×C113—41no—
431C8×C113—41no—
432C22×C113—21no—
433C22×C113—21no—
434C22×C113—21no—
435C22×C113—21no—
436C22×C113—22no—
437C22×C113—21no—
438C22×C113—21no—
439C22×C113—21no—
440C22×C113—21no—
441C22×C113—41no—
442C22×C113—41no—
443C22×C113—41no—
444C22×C113—42no—
445C22×C113—41no—
446C22×C113—41no—
447C22×C113—81no—
448C22×C113—81no—
449C22×C113—82no—
450C22×C113—82no—
451C22×C113—84no—
452C22×C113—81no—
453C22×C113—81no—
454C22×C113—81no—
455C22×C113—81no—
456C22×C113—81no—
457C22×C113—161no—
458C22×C113—161no—
459C22×C113C2×#12111yescharacteristic
460C22×C113#54611yescharacteristic
461C22×C113#54611yescharacteristic
462C4×C113—21no—
463C4×C113—21no—
464C4×C113—22no—
465C4×C113—41no—
466C4×C113—42no—
467C4×C113—81no—
468C4×C113C2×#12011yescharacteristic
469C4×C113#53411yescharacteristic
470C4×C113D4211yescharacteristic
471C4×C113D4211yescharacteristic
472#24402C11311yesmaximal, characteristic, direct product factor, Sylow
473C2×C113—21no—
474C2×C113—21no—
475C2×C113—41no—
476C2×C113—41no—
477C2×C113—42no—
478C2×C113—81no—
479C2×C113—82no—
480C2×C113—161no—
481C2×C113#241011yescharacteristic
482C2×C113#306711yescharacteristic
483C2×C113#306811yescharacteristic
484C2×#575C2×C11311yescharacteristic, complemented
485C2×#472C2×C11311yescharacteristic, complemented
486C2×#471C2×C11311yescharacteristic, complemented
487#3006C2×C11311yescharacteristic, complemented
488C2×#449C2×C11311yescharacteristic, complemented
489#2880C2×C11311yescharacteristic, complemented
490#2052C2×C11311yescharacteristic, complemented
491#2051C2×C11311yescharacteristic, complemented
492#2019C2×C11311yescharacteristic, complemented
493#2018C2×C11311yescharacteristic, complemented
494#1908C2×C11311yescharacteristic, complemented
495#1907C2×C11311yescharacteristic, complemented
496#1900C2×C11311yescharacteristic, complemented
497#1855C2×C11311yescharacteristic, complemented
498#1785C2×C11311yescharacteristic, complemented
499C113#2440211yescharacteristic, direct product factor, Sylow
500C22×#41C22×C11311yescharacteristic
501C22×#41C22×C11311yescharacteristic
502#575—24no—
503#575—24no—
504C2×#137—21no—
505C2×#137C22×C11311yescharacteristic
506C2×#137C22×C11311yescharacteristic
507C2×AGL(1,ℤ/8)—21no—
508C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
509C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
510C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
511C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
512C2×#135—21no—
513C2×#135—21no—
514C22×SD16C22×C11311yescharacteristic, complemented
515C22×D8C22×C11311yescharacteristic, complemented
516C2×#131C22×C11311yescharacteristic
517C2×#131C22×C11311yescharacteristic
518C22×M16C22×C11311yescharacteristic
519C2×#121C22×C11311yescharacteristic
520#472—24no—
521#471—24no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#449—21no—
528#448—21no—
529#447—21no—
530C2×#108C22×C11311yescharacteristic, complemented
531C2×#108C22×C11311yescharacteristic, complemented
532#417C22×C11311yescharacteristic
533#417C22×C11311yescharacteristic
534C2×#103C22×C11311yescharacteristic, complemented
535C2×#102C22×C11311yescharacteristic, complemented
536C2×#101C22×C11311yescharacteristic, complemented
537C2×#101C22×C11311yescharacteristic, complemented
538C2×#100C22×C11311yescharacteristic, complemented
539C2×#100C22×C11311yescharacteristic, complemented
540C2×#100C22×C11311yescharacteristic, complemented
541C2×#100C22×C11311yescharacteristic, complemented
542#408—21no—
543#408—21no—
544#408C22×C11311yescharacteristic
545#408C22×C11311yescharacteristic
546#407—21no—
547#407C22×C11311yescharacteristic
548#407C22×C11311yescharacteristic
549C2×C22⋊C8—21no—
550C2×C22⋊C8C22×C11311yescharacteristic
551#343C22×C11311yescharacteristic, complemented
552#343C22×C11311yescharacteristic, complemented
553#341C22×C11311yescharacteristic, complemented
554#341C22×C11311yescharacteristic, complemented
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C11311yescharacteristic
570C2×#41D4×C11311yescharacteristic
571C2×#41C23×C11311yescharacteristic
572C2×#41C23×C11311yescharacteristic
573C22×Q8D4×C11311yescharacteristic
574C22×Q8C23×C11311yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C11311yescharacteristic
579C22×D4C23×C11311yescharacteristic
580C22×D4C23×C11311yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C11311yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C11314yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C11314yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C11311yescharacteristic
630C2×M16C23×C11311yescharacteristic
631C2×M16C23×C11311yescharacteristic
632C2×M16C23×C11311yescharacteristic
633C2×M16C23×C11311yescharacteristic
634C2×M16C23×C11311yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C11311yescharacteristic
639C22×C8C23×C11311yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C11311yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C11311yescharacteristic
671C22⋊C8D4×C11311yescharacteristic
672C22⋊C8D4×C11311yescharacteristic
673C22⋊C8D4×C11311yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C11311yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C11312yes—
701#41C2×D4×C11312yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C11312yes—
711C2×Q8C2×D4×C11311yescharacteristic
712C2×Q8C2×D4×C11311yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
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—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C11312yes—
741C2×D4C2×D4×C11311yescharacteristic
742C2×D4C2×D4×C11311yescharacteristic
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C11311yescharacteristic
761C22×C4C2×D4×C11311yescharacteristic
762C22×C4C2×D4×C11311yescharacteristic
763C22×C4C2×D4×C11311yescharacteristic
764C22×C4#41×C11311yescharacteristic
765C22×C4C24×C11311yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C11312yes—
796M16C2×D4×C11312yes—
797C2×C8—24no—
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×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C11311yescharacteristic
811C2×C8C2×D4×C11311yescharacteristic
812C2×C8C2×D4×C11311yescharacteristic
813C2×C8C2×D4×C11311yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C11311yescharacteristic
838C23#121×C11311yescharacteristic
839C23C2×#41×C11311yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C11312yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C11312yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C11311yescharacteristic
899C2×C4#121×C11311yescharacteristic
900C2×C4C22×D4×C11311yescharacteristic
901C2×C4C22×D4×C11311yescharacteristic
902C2×C4C22×D4×C11311yescharacteristic
903C2×C4C22×D4×C11311yescharacteristic
904C2×C4H(5,𝔽2)×C11311yescharacteristic
905C2×C4H(5,𝔽2)×C11311yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—42no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C11311yescharacteristic
944C22#546×C11311yescharacteristic
945C22#546×C11311yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×#120×C11311yescharacteristic
953C4#534×C11311yescharacteristic
954C4D42×C11311yescharacteristic
955C4D42×C11311yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C113×#241011yescharacteristic
965C2C113×#306711yescharacteristic
966C2C113×#306811yescharacteristic
subgroupG/H
center, socleC22×C113C2×#121
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. C2×#472×C113C2semidirect
3. C2×#471×C113C2semidirect
4. C113×#3006C2semidirect
5. C2×#449×C113C2semidirect
6. C113×#2880C2semidirect
7. C113×#2052C2semidirect
8. C113×#2051C2semidirect
9. C113×#2019C2semidirect
10. C113×#2018C2semidirect
11. C113×#1908C2semidirect
12. C113×#1907C2semidirect
13. C113×#1900C2semidirect
14. C113×#1855C2semidirect
15. C113×#1785C2semidirect
30. C22×SD16×C113C22semidirect
31. C22×D8×C113C22semidirect
46. C2×#108×C113C22semidirect
47. C2×#108×C113C22semidirect
50. C2×#103×C113C22semidirect
51. C2×#102×C113C22semidirect
52. C2×#101×C113C22semidirect
53. C2×#101×C113C22semidirect
54. C2×#100×C113C22semidirect
55. C2×#100×C113C22semidirect
56. C2×#100×C113C22semidirect
57. C2×#100×C113C22semidirect
67. #343×C113C22semidirect
68. #343×C113C22semidirect
69. #341×C113C22semidirect
70. #341×C113C22semidirect
104. #137×C113D4semidirect
113. AGL(1,ℤ/8)×C113D4semidirect
472. #24402C113direct (N × H)
484. C2×#575C2×C113semidirect
485. C2×#472C2×C113semidirect
486. C2×#471C2×C113semidirect
487. #3006C2×C113semidirect
488. C2×#449C2×C113semidirect
489. #2880C2×C113semidirect
490. #2052C2×C113semidirect
491. #2051C2×C113semidirect
492. #2019C2×C113semidirect
493. #2018C2×C113semidirect
494. #1908C2×C113semidirect
495. #1907C2×C113semidirect
496. #1900C2×C113semidirect
497. #1855C2×C113semidirect
498. #1785C2×C113semidirect
499. C113#24402direct (N × H)
514. C22×SD16C22×C113semidirect
515. C22×D8C22×C113semidirect
530. C2×#108C22×C113semidirect
531. C2×#108C22×C113semidirect
534. C2×#103C22×C113semidirect
535. C2×#102C22×C113semidirect
536. C2×#101C22×C113semidirect
537. C2×#101C22×C113semidirect
538. C2×#100C22×C113semidirect
539. C2×#100C22×C113semidirect
540. C2×#100C22×C113semidirect
541. C2×#100C22×C113semidirect
551. #343C22×C113semidirect
552. #343C22×C113semidirect
553. #341C22×C113semidirect
554. #341C22×C113semidirect
588. #137D4×C113semidirect
597. 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
C2×#472×C1132
C2×#471×C1132
C113×#30062
C2×#449×C1132
C113×#28802
C113×#20522
C113×#20512
C113×#20192
C113×#20182
C113×#19082
C113×#19072
C113×#19002
C113×#18552
C113×#17852
#24402113