Finite Group Databasebeta

← C113×#25140 #43293160

Subgroups — C113×#25140 #43293160

Order 28928.

1140 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C113C211yesmaximal, characteristic, complemented
2C113×#3055C211yesmaximal, characteristic, complemented
3C113×#3003C211yesmaximal, characteristic, complemented
4C2×#447×C113C211yesmaximal, characteristic, complemented
5C113×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C113C211yesmaximal, characteristic, complemented
7C113×#2063C211yesmaximal, characteristic, complemented
8C113×#2051C211yesmaximal, characteristic, complemented
9C113×#2045C211yesmaximal, characteristic, complemented
10C113×#2018C211yesmaximal, characteristic, complemented
11C113×#1978C211yesmaximal, characteristic, complemented
12C113×#1931C211yesmaximal, characteristic, complemented
13C113×#1907C211yesmaximal, characteristic, complemented
14C113×#1900C211yesmaximal, characteristic, complemented
15C113×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
20C22×D8×C113C2211yescharacteristic
21C22×D8×C113C2211yescharacteristic
22C2×#131×C113C2211yescharacteristic, complemented
23C22×M16×C113C2211yescharacteristic
24C22×M16×C113C2211yescharacteristic
25#525×C113C2211yescharacteristic
26C2×#121×C113C2211yescharacteristic
27#472×C113—24no—
28#469×C113—21no—
29#468×C113—21no—
30#466×C113—21no—
31#465×C113—21no—
32#450×C113—21no—
33#450×C113—21no—
34#447×C113—21no—
35#447×C113—21no—
36#447×C113—21no—
37#447×C113—21no—
38#447×C113—21no—
39#447×C113—21no—
40#436×C113—21no—
41#435×C113—21no—
42#435×C113—21no—
43C8×D4×C113—21no—
44C2×#108×C113C2211yescharacteristic, complemented
45C2×#108×C113C2211yescharacteristic, complemented
46#428×C113C2211yescharacteristic, complemented
47#424×C113C2211yescharacteristic, complemented
48#418×C113C2211yescharacteristic
49#418×C113C2211yescharacteristic
50#418×C113C2211yescharacteristic, complemented
51#417×C113C2211yescharacteristic, complemented
52C2×#102×C113C2211yescharacteristic
53C2×#102×C113C2211yescharacteristic
54C2×#100×C113—24no—
55C2×#100×C113C2211yescharacteristic
56C2×#100×C113C2211yescharacteristic
57C2×#100×C113C2211yescharacteristic
58C2×#100×C113C2211yescharacteristic
59C2×#100×C113C2211yescharacteristic, complemented
60C2×#100×C113C2211yescharacteristic, complemented
61#408×C113C2211yescharacteristic, complemented
62#407×C113C2211yescharacteristic
63C2×C22⋊C8×C113C2211yescharacteristic
64#405×C113C2211yescharacteristic, complemented
65#343×C113C2211yescharacteristic, complemented
66#343×C113C2211yescharacteristic, complemented
67#341×C113C2211yescharacteristic, complemented
68#341×C113C2211yescharacteristic, complemented
69C25×C113—21no—
70C2×#41×C113C2311yescharacteristic
71C22×D4×C113—22no—
72C22×D4×C113—22no—
73C22×D4×C113—21no—
74C22×D4×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113—21no—
79C22×D4×C113—41no—
80C22×D4×C113—41no—
81C22×D4×C113C2311yescharacteristic
82C22×D4×C113C2311yescharacteristic
83C22×D4×C113C2311yescharacteristic
84C23×C4×C113C2311yescharacteristic
85AGL(1,ℤ/8)×C113—22no—
86AGL(1,ℤ/8)×C113—22no—
87AGL(1,ℤ/8)×C113—22no—
88AGL(1,ℤ/8)×C113—41no—
89AGL(1,ℤ/8)×C113—41no—
90AGL(1,ℤ/8)×C113—41no—
91C2×SD16×C113—21no—
92C2×SD16×C113—21no—
93C2×SD16×C113—21no—
94C2×D8×C113—22no—
95C2×D8×C113—21no—
96C2×D8×C113—21no—
97C2×D8×C113—21no—
98C2×D8×C113—22no—
99C2×D8×C113—21no—
100C2×D8×C113—21no—
101C2×D8×C113—21no—
102C2×D8×C113—21no—
103C2×D8×C113—41no—
104C2×D8×C113—41no—
105#131×C113—22no—
106#131×C113—41no—
107C2×M16×C113—21no—
108C2×M16×C113—21no—
109C2×M16×C113—21no—
110C2×M16×C113—22no—
111C2×M16×C113—22no—
112C2×M16×C113—41no—
113C2×M16×C113—41no—
114C2×M16×C113C2311yescharacteristic
115C2×M16×C113C2311yescharacteristic
116C2×M16×C113C2311yescharacteristic
117C2×M16×C113C2311yescharacteristic
118C2×M16×C113C2311yescharacteristic
119C2×M16×C113C2311yescharacteristic
120C22×C8×C113—21no—
121C22×C8×C113—21no—
122C22×C8×C113—21no—
123C22×C8×C113C2311yescharacteristic
124C22×C8×C113C2311yescharacteristic
125#123×C113—21no—
126C22⋊Q8×C113D411yescharacteristic
127C22⋊Q8×C113D411yescharacteristic
128#121×C113—21no—
129#121×C113—21no—
130#121×C113—21no—
131#121×C113—21no—
132#121×C113D411yescharacteristic
133#121×C113D411yescharacteristic
134#120×C113—21no—
135C4×D4×C113—21no—
136C4×D4×C113—21no—
137#117×C113C2311yescharacteristic
138C2×C4⋊C4×C113C2311yescharacteristic
139C2×C22⋊C4×C113—21no—
140#108×C113—22no—
141#108×C113—41no—
142#107×C113—21no—
143#106×C113—21no—
144C4⋊C8×C113—21no—
145C4⋊C8×C113—21no—
146#103×C113—21no—
147#102×C113—21no—
148#102×C113—21no—
149#102×C113—21no—
150#102×C113—21no—
151#102×C113—21no—
152#102×C113—21no—
153#102×C113—21no—
154#102×C113—21no—
155#102×C113—21no—
156#102×C113—21no—
157#102×C113—21no—
158#100×C113—22no—
159#100×C113—22no—
160#100×C113—22no—
161#100×C113—22no—
162#100×C113—41no—
163#100×C113D414yescomplemented
164C22⋊C8×C113—21no—
165C22⋊C8×C113—21no—
166C22⋊C8×C113—21no—
167C22⋊C8×C113—21no—
168C22⋊C8×C113D411yescharacteristic
169C22⋊C8×C113D411yescharacteristic
170C22⋊C8×C113D411yescharacteristic
171C22⋊C8×C113D411yescharacteristic
172#97×C113—21no—
173C4×C8×C113—21no—
174C24×C113—24no—
175C24×C113—21no—
176C24×C113—21no—
177C24×C113—21no—
178C24×C113—42no—
179C24×C113—41no—
180C24×C113—41no—
181C24×C113—82no—
182C24×C113—82no—
183C24×C113#4111yescharacteristic
184#41×C113—21no—
185#41×C113—21no—
186#41×C113—21no—
187#41×C113—21no—
188C2×Q8×C113C2×D411yescharacteristic
189C2×D4×C113—24no—
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—21no—
205C2×D4×C113—21no—
206C2×D4×C113—21no—
207C2×D4×C113—21no—
208C2×D4×C113—21no—
209C2×D4×C113—42no—
210C2×D4×C113—42no—
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—41no—
219C2×D4×C113—41no—
220C2×D4×C113—41no—
221C2×D4×C113—41no—
222C2×D4×C113—82no—
223C2×D4×C113C2×D412yes—
224C2×D4×C113C2×D411yescharacteristic
225C2×D4×C113#4112yes—
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×C113C2×D411yescharacteristic
233C22×C4×C113C2×D411yescharacteristic
234C22×C4×C113C2×D411yescharacteristic
235C22×C4×C113C2×D411yescharacteristic
236C22×C4×C113#4111yescharacteristic
237C22×C4×C113C2411yescharacteristic
238SD16×C113—42no—
239SD16×C113—42no—
240SD16×C113—42no—
241D8×C113—42no—
242D8×C113—42no—
243D8×C113—42no—
244D8×C113—42no—
245D8×C113—42no—
246D8×C113—42no—
247D8×C113—42no—
248M16×C113—21no—
249M16×C113—21no—
250M16×C113—21no—
251M16×C113—21no—
252M16×C113—21no—
253M16×C113—21no—
254M16×C113—21no—
255M16×C113—21no—
256M16×C113—21no—
257M16×C113—21no—
258M16×C113—42no—
259M16×C113—42no—
260M16×C113—42no—
261M16×C113C2×D412yes—
262M16×C113C2×D412yes—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—21no—
270C2×C8×C113—21no—
271C2×C8×C113—21no—
272C2×C8×C113—21no—
273C2×C8×C113—42no—
274C2×C8×C113—42no—
275C2×C8×C113—42no—
276C2×C8×C113C2×D411yescharacteristic
277C2×C8×C113C2×D411yescharacteristic
278C2×C8×C113C2×D411yescharacteristic
279C2×C8×C113C2×D411yescharacteristic
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
283C4⋊C4×C113—21no—
284C4⋊C4×C113C2×D411yescharacteristic
285C4⋊C4×C113C2×D411yescharacteristic
286C22⋊C4×C113—21no—
287C22⋊C4×C113—21no—
288C22⋊C4×C113—21no—
289C22⋊C4×C113—21no—
290C22⋊C4×C113—21no—
291C22⋊C4×C113—41no—
292C22⋊C4×C113—41no—
293C42×C113—21no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—22no—
297C23×C113—21no—
298C23×C113—22no—
299C23×C113—22no—
300C23×C113—41no—
301C23×C113—44no—
302C23×C113—44no—
303C23×C113—41no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—41no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—81no—
311C23×C113—81no—
312C23×C113—81no—
313C23×C113—81no—
314C23×C113—82no—
315C23×C113—82no—
316C23×C113—82no—
317C23×C113—81no—
318C23×C113—81no—
319C23×C113—88no—
320C23×C113—88no—
321C23×C113—82no—
322C23×C113#12111yescharacteristic
323C23×C113#12111yescharacteristic
324C23×C113C2×#4111yescharacteristic
325Q8×C113—21no—
326Q8×C113—21no—
327D4×C113—21no—
328D4×C113—22no—
329D4×C113—22no—
330D4×C113—22no—
331D4×C113—21no—
332D4×C113—22no—
333D4×C113—44no—
334D4×C113—44no—
335D4×C113—41no—
336D4×C113—41no—
337D4×C113—42no—
338D4×C113—41no—
339D4×C113—41no—
340D4×C113—41no—
341D4×C113—41no—
342D4×C113—41no—
343D4×C113—41no—
344D4×C113—41no—
345D4×C113—41no—
346D4×C113—81no—
347D4×C113—82no—
348D4×C113—82no—
349C2×C4×C113—21no—
350C2×C4×C113—21no—
351C2×C4×C113—21no—
352C2×C4×C113—21no—
353C2×C4×C113—21no—
354C2×C4×C113—21no—
355C2×C4×C113—21no—
356C2×C4×C113—21no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—21no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
362C2×C4×C113—41no—
363C2×C4×C113—41no—
364C2×C4×C113—41no—
365C2×C4×C113—81no—
366C2×C4×C113#12111yescharacteristic
367C2×C4×C113#12111yescharacteristic
368C2×C4×C113C22×D411yescharacteristic
369C2×C4×C113C22×D411yescharacteristic
370C2×C4×C113C22×D411yescharacteristic
371C2×C4×C113C2×#4111yescharacteristic
372C2×C4×C113H(5,𝔽2)11yescharacteristic
373C2×C4×C113H(5,𝔽2)11yescharacteristic
374C8×C113—21no—
375C8×C113—21no—
376C8×C113—22no—
377C8×C113—22no—
378C8×C113—21no—
379C8×C113—21no—
380C8×C113—41no—
381C8×C113—41no—
382C8×C113—41no—
383C8×C113—41no—
384C22×C113—21no—
385C22×C113—21no—
386C22×C113—21no—
387C22×C113—21no—
388C22×C113—21no—
389C22×C113—21no—
390C22×C113—21no—
391C22×C113—42no—
392C22×C113—42no—
393C22×C113—41no—
394C22×C113—42no—
395C22×C113—42no—
396C22×C113—41no—
397C22×C113—41no—
398C22×C113—82no—
399C22×C113—82no—
400C22×C113—88no—
401C22×C113—82no—
402C22×C113—82no—
403C22×C113—88no—
404C22×C113—81no—
405C22×C113—81no—
406C22×C113—81no—
407C22×C113—81no—
408C22×C113—81no—
409C22×C113—81no—
410C22×C113—81no—
411C22×C113—161no—
412C22×C113—161no—
413C22×C113#47212yescomplemented
414C22×C113C2×#12111yescharacteristic
415C22×C113#52511yescharacteristic
416C22×C113#53811yescharacteristic
417C4×C113—21no—
418C4×C113—21no—
419C4×C113—41no—
420C4×C113—41no—
421C4×C113—41no—
422C4×C113—81no—
423C4×C113D4211yescharacteristic
424C4×C113D4211yescharacteristic
425C4×C113#54611yescharacteristic
426C4×C113#54611yescharacteristic
427#25140C11311yesmaximal, characteristic, direct product factor, Sylow
428C2×C113—21no—
429C2×C113—21no—
430C2×C113—22no—
431C2×C113—41no—
432C2×C113—81no—
433C2×C113—82no—
434C2×C113—82no—
435C2×C113—161no—
436C2×C113#242411yescharacteristic
437C2×C113C2×#47211yescharacteristic
438C2×C113#306811yescharacteristic
439C2×#472C2×C11311yescharacteristic, complemented
440#3055C2×C11311yescharacteristic, complemented
441#3003C2×C11311yescharacteristic, complemented
442C2×#447C2×C11311yescharacteristic, complemented
443#2933C2×C11311yescharacteristic, complemented
444C22×#100C2×C11311yescharacteristic, complemented
445#2063C2×C11311yescharacteristic, complemented
446#2051C2×C11311yescharacteristic, complemented
447#2045C2×C11311yescharacteristic, complemented
448#2018C2×C11311yescharacteristic, complemented
449#1978C2×C11311yescharacteristic, complemented
450#1931C2×C11311yescharacteristic, complemented
451#1907C2×C11311yescharacteristic, complemented
452#1900C2×C11311yescharacteristic, complemented
453#1855C2×C11311yescharacteristic, complemented
454C113#2514011yescharacteristic, direct product factor, Sylow
455C23×D4C22×C11311yescharacteristic
456C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
457C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
458C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
459C22×D8C22×C11311yescharacteristic
460C22×D8C22×C11311yescharacteristic
461C2×#131C22×C11311yescharacteristic, complemented
462C22×M16C22×C11311yescharacteristic
463C22×M16C22×C11311yescharacteristic
464#525C22×C11311yescharacteristic
465C2×#121C22×C11311yescharacteristic
466#472—24no—
467#469—21no—
468#468—21no—
469#466—21no—
470#465—21no—
471#450—21no—
472#450—21no—
473#447—21no—
474#447—21no—
475#447—21no—
476#447—21no—
477#447—21no—
478#447—21no—
479#436—21no—
480#435—21no—
481#435—21no—
482C8×D4—21no—
483C2×#108C22×C11311yescharacteristic, complemented
484C2×#108C22×C11311yescharacteristic, complemented
485#428C22×C11311yescharacteristic, complemented
486#424C22×C11311yescharacteristic, complemented
487#418C22×C11311yescharacteristic
488#418C22×C11311yescharacteristic
489#418C22×C11311yescharacteristic, complemented
490#417C22×C11311yescharacteristic, complemented
491C2×#102C22×C11311yescharacteristic
492C2×#102C22×C11311yescharacteristic
493C2×#100—24no—
494C2×#100C22×C11311yescharacteristic
495C2×#100C22×C11311yescharacteristic
496C2×#100C22×C11311yescharacteristic
497C2×#100C22×C11311yescharacteristic
498C2×#100C22×C11311yescharacteristic, complemented
499C2×#100C22×C11311yescharacteristic, complemented
500#408C22×C11311yescharacteristic, complemented
501#407C22×C11311yescharacteristic
502C2×C22⋊C8C22×C11311yescharacteristic
503#405C22×C11311yescharacteristic, complemented
504#343C22×C11311yescharacteristic, complemented
505#343C22×C11311yescharacteristic, complemented
506#341C22×C11311yescharacteristic, complemented
507#341C22×C11311yescharacteristic, complemented
508C25—21no—
509C2×#41C23×C11311yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C23×C11311yescharacteristic
521C22×D4C23×C11311yescharacteristic
522C22×D4C23×C11311yescharacteristic
523C23×C4C23×C11311yescharacteristic
524AGL(1,ℤ/8)—22no—
525AGL(1,ℤ/8)—22no—
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—41no—
528AGL(1,ℤ/8)—41no—
529AGL(1,ℤ/8)—41no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×SD16—21no—
533C2×D8—22no—
534C2×D8—21no—
535C2×D8—21no—
536C2×D8—21no—
537C2×D8—22no—
538C2×D8—21no—
539C2×D8—21no—
540C2×D8—21no—
541C2×D8—21no—
542C2×D8—41no—
543C2×D8—41no—
544#131—22no—
545#131—41no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16C23×C11311yescharacteristic
554C2×M16C23×C11311yescharacteristic
555C2×M16C23×C11311yescharacteristic
556C2×M16C23×C11311yescharacteristic
557C2×M16C23×C11311yescharacteristic
558C2×M16C23×C11311yescharacteristic
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8C23×C11311yescharacteristic
563C22×C8C23×C11311yescharacteristic
564#123—21no—
565C22⋊Q8D4×C11311yescharacteristic
566C22⋊Q8D4×C11311yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121D4×C11311yescharacteristic
572#121D4×C11311yescharacteristic
573#120—21no—
574C4×D4—21no—
575C4×D4—21no—
576#117C23×C11311yescharacteristic
577C2×C4⋊C4C23×C11311yescharacteristic
578C2×C22⋊C4—21no—
579#108—22no—
580#108—41no—
581#107—21no—
582#106—21no—
583C4⋊C8—21no—
584C4⋊C8—21no—
585#103—21no—
586#102—21no—
587#102—21no—
588#102—21no—
589#102—21no—
590#102—21no—
591#102—21no—
592#102—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—21no—
597#100—22no—
598#100—22no—
599#100—22no—
600#100—22no—
601#100—41no—
602#100D4×C11314yescomplemented
603C22⋊C8—21no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8D4×C11311yescharacteristic
608C22⋊C8D4×C11311yescharacteristic
609C22⋊C8D4×C11311yescharacteristic
610C22⋊C8D4×C11311yescharacteristic
611#97—21no—
612C4×C8—21no—
613C24—24no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—42no—
618C24—41no—
619C24—41no—
620C24—82no—
621C24—82no—
622C24#41×C11311yescharacteristic
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627C2×Q8C2×D4×C11311yescharacteristic
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—41no—
658C2×D4—41no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—82no—
662C2×D4C2×D4×C11312yes—
663C2×D4C2×D4×C11311yescharacteristic
664C2×D4#41×C11312yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4C2×D4×C11311yescharacteristic
672C22×C4C2×D4×C11311yescharacteristic
673C22×C4C2×D4×C11311yescharacteristic
674C22×C4C2×D4×C11311yescharacteristic
675C22×C4#41×C11311yescharacteristic
676C22×C4C24×C11311yescharacteristic
677SD16—42no—
678SD16—42no—
679SD16—42no—
680D8—42no—
681D8—42no—
682D8—42no—
683D8—42no—
684D8—42no—
685D8—42no—
686D8—42no—
687M16—21no—
688M16—21no—
689M16—21no—
690M16—21no—
691M16—21no—
692M16—21no—
693M16—21no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—42no—
698M16—42no—
699M16—42no—
700M16C2×D4×C11312yes—
701M16C2×D4×C11312yes—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—42no—
713C2×C8—42no—
714C2×C8—42no—
715C2×C8C2×D4×C11311yescharacteristic
716C2×C8C2×D4×C11311yescharacteristic
717C2×C8C2×D4×C11311yescharacteristic
718C2×C8C2×D4×C11311yescharacteristic
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4C2×D4×C11311yescharacteristic
724C4⋊C4C2×D4×C11311yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C42—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—44no—
741C23—44no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—82no—
754C23—82no—
755C23—82no—
756C23—81no—
757C23—81no—
758C23—88no—
759C23—88no—
760C23—82no—
761C23#121×C11311yescharacteristic
762C23#121×C11311yescharacteristic
763C23C2×#41×C11311yescharacteristic
764Q8—21no—
765Q8—21no—
766D4—21no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—21no—
771D4—22no—
772D4—44no—
773D4—44no—
774D4—41no—
775D4—41no—
776D4—42no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—81no—
786D4—82no—
787D4—82no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—81no—
805C2×C4#121×C11311yescharacteristic
806C2×C4#121×C11311yescharacteristic
807C2×C4C22×D4×C11311yescharacteristic
808C2×C4C22×D4×C11311yescharacteristic
809C2×C4C22×D4×C11311yescharacteristic
810C2×C4C2×#41×C11311yescharacteristic
811C2×C4H(5,𝔽2)×C11311yescharacteristic
812C2×C4H(5,𝔽2)×C11311yescharacteristic
813C8—21no—
814C8—21no—
815C8—22no—
816C8—22no—
817C8—21no—
818C8—21no—
819C8—41no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—88no—
842C22—88no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—161no—
851C22—161no—
852C22#472×C11312yescomplemented
853C22C2×#121×C11311yescharacteristic
854C22#525×C11311yescharacteristic
855C22#538×C11311yescharacteristic
856C4—21no—
857C4—21no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—81no—
862C4D42×C11311yescharacteristic
863C4D42×C11311yescharacteristic
864C4#546×C11311yescharacteristic
865C4#546×C11311yescharacteristic
866C2—21no—
867C2—21no—
868C2—22no—
869C2—41no—
870C2—81no—
871C2—82no—
872C2—82no—
873C2—161no—
874C2C113×#242411yescharacteristic
875C2C2×#472×C11311yescharacteristic
876C2C113×#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×#472×C113C2semidirect
2. C113×#3055C2semidirect
3. C113×#3003C2semidirect
4. C2×#447×C113C2semidirect
5. C113×#2933C2semidirect
6. C22×#100×C113C2semidirect
7. C113×#2063C2semidirect
8. C113×#2051C2semidirect
9. C113×#2045C2semidirect
10. C113×#2018C2semidirect
11. C113×#1978C2semidirect
12. C113×#1931C2semidirect
13. C113×#1907C2semidirect
14. C113×#1900C2semidirect
15. C113×#1855C2semidirect
19. C2×AGL(1,ℤ/8)×C113C22semidirect
22. C2×#131×C113C22semidirect
44. C2×#108×C113C22semidirect
45. C2×#108×C113C22semidirect
46. #428×C113C22semidirect
47. #424×C113C22semidirect
50. #418×C113C22semidirect
51. #417×C113C22semidirect
59. C2×#100×C113C22semidirect
60. C2×#100×C113C22semidirect
61. #408×C113C22semidirect
64. #405×C113C22semidirect
65. #343×C113C22semidirect
66. #343×C113C22semidirect
67. #341×C113C22semidirect
68. #341×C113C22semidirect
163. #100×C113D4semidirect
413. C22×C113#472semidirect
427. #25140C113direct (N × H)
439. C2×#472C2×C113semidirect
440. #3055C2×C113semidirect
441. #3003C2×C113semidirect
442. C2×#447C2×C113semidirect
443. #2933C2×C113semidirect
444. C22×#100C2×C113semidirect
445. #2063C2×C113semidirect
446. #2051C2×C113semidirect
447. #2045C2×C113semidirect
448. #2018C2×C113semidirect
449. #1978C2×C113semidirect
450. #1931C2×C113semidirect
451. #1907C2×C113semidirect
452. #1900C2×C113semidirect
453. #1855C2×C113semidirect
454. C113#25140direct (N × H)
458. C2×AGL(1,ℤ/8)C22×C113semidirect
461. C2×#131C22×C113semidirect
483. C2×#108C22×C113semidirect
484. C2×#108C22×C113semidirect
485. #428C22×C113semidirect
486. #424C22×C113semidirect
489. #418C22×C113semidirect
490. #417C22×C113semidirect
498. C2×#100C22×C113semidirect
499. C2×#100C22×C113semidirect
500. #408C22×C113semidirect
503. #405C22×C113semidirect
504. #343C22×C113semidirect
505. #343C22×C113semidirect
506. #341C22×C113semidirect
507. #341C22×C113semidirect
602. #100D4×C113semidirect
852. C22#472×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#472×C1132
C113×#30552
C113×#30032
C2×#447×C1132
C113×#29332
C22×#100×C1132
C113×#20632
C113×#20512
C113×#20452
C113×#20182
C113×#19782
C113×#19312
C113×#19072
C113×#19002
C113×#18552
#25140113