Finite Group Databasebeta

← C101×#25192 #38807343

Subgroups — C101×#25192 #38807343

Order 25856.

1054 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3062C211yesmaximal, characteristic, complemented
2C101×#3045C211yesmaximal, characteristic, complemented
3C2×#453×C101C211yesmaximal, characteristic, complemented
4C101×#3012C211yesmaximal, characteristic, complemented
5C2×#444×C101C211yesmaximal, characteristic, complemented
6C101×#2897C211yesmaximal, characteristic, complemented
7C101×#2063C211yesmaximal, characteristic, complemented
8C101×#2051C211yesmaximal, characteristic, complemented
9C101×#2040C211yesmaximal, characteristic, complemented
10C101×#2002C211yesmaximal, characteristic, complemented
11C101×#1961C211yesmaximal, characteristic, complemented
12C101×#1938C211yesmaximal, characteristic, complemented
13C101×#1907C211yesmaximal, characteristic, complemented
14C101×#1907C211yesmaximal, characteristic, complemented
15C101×#1860C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C101C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
20C2×#135×C101C2211yescharacteristic
21C2×#131×C101C2211yescharacteristic
22C2×#131×C101C2211yescharacteristic, complemented
23#537×C101C2211yescharacteristic
24#535×C101C2211yescharacteristic, complemented
25C2×#127×C101C2211yescharacteristic
26#520×C101C2211yescharacteristic
27#469×C101—21no—
28#468×C101—21no—
29#466×C101—21no—
30#465×C101—21no—
31#464×C101—21no—
32#463×C101—21no—
33#460×C101—21no—
34#459×C101—21no—
35#453×C101—24no—
36#452×C101—21no—
37#450×C101—21no—
38#449×C101—21no—
39#447×C101—21no—
40#444×C101—24no—
41C2×#108×C101C2211yescharacteristic, complemented
42#428×C101C2211yescharacteristic, complemented
43#424×C101C2211yescharacteristic, complemented
44C2×#104×C101C2211yescharacteristic
45C2×#104×C101C2211yescharacteristic
46C2×#104×C101C2211yescharacteristic, complemented
47#418×C101—21no—
48#418×C101C2211yescharacteristic
49#417×C101—21no—
50#417×C101C2211yescharacteristic
51#417×C101C2211yescharacteristic
52#417×C101C2211yescharacteristic, complemented
53#416×C101—21no—
54#416×C101C2211yescharacteristic
55C2×#102×C101—21no—
56C2×#102×C101C2211yescharacteristic
57C2×#102×C101C2211yescharacteristic
58C2×#102×C101C2211yescharacteristic, complemented
59C2×#102×C101C2211yescharacteristic, complemented
60C2×#100×C101C2211yescharacteristic
61C2×#100×C101C2211yescharacteristic, complemented
62#408×C101C2211yescharacteristic
63C2×#97×C101C2211yescharacteristic, complemented
64#382×C101C2211yescharacteristic, complemented
65#343×C101C2211yescharacteristic, complemented
66#343×C101C2211yescharacteristic, complemented
67#341×C101C2211yescharacteristic, complemented
68#339×C101C2211yescharacteristic, complemented
69H(5,𝔽2)×C101—22no—
70H(5,𝔽2)×C101—22no—
71H(5,𝔽2)×C101—22no—
72H(5,𝔽2)×C101—41no—
73C2×#41×C101—21no—
74C2×#41×C101—21no—
75C2×#41×C101C2311yescharacteristic
76C2×#41×C101C2311yescharacteristic
77C2×#41×C101C2311yescharacteristic
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101—41no—
81C22×D4×C101—41no—
82C22×D4×C101C2311yescharacteristic
83C22×D4×C101C2311yescharacteristic
84AGL(1,ℤ/8)×C101—22no—
85AGL(1,ℤ/8)×C101—22no—
86AGL(1,ℤ/8)×C101—22no—
87AGL(1,ℤ/8)×C101—22no—
88AGL(1,ℤ/8)×C101—41no—
89AGL(1,ℤ/8)×C101—41no—
90#135×C101—22no—
91#135×C101—22no—
92C2×Q16×C101D411yescharacteristic, complemented
93C2×SD16×C101—21no—
94C2×SD16×C101—21no—
95C2×SD16×C101—21no—
96C2×SD16×C101D411yescharacteristic, complemented
97C2×SD16×C101D411yescharacteristic, complemented
98C2×D8×C101—21no—
99C2×D8×C101—21no—
100C2×D8×C101—21no—
101C2×D8×C101D411yescharacteristic, complemented
102#131×C101—22no—
103#131×C101—22no—
104#131×C101—41no—
105#131×C101—41no—
106C2×M16×C101—21no—
107C2×M16×C101—21no—
108C2×M16×C101C2311yescharacteristic
109C2×M16×C101C2311yescharacteristic
110C2×M16×C101C2311yescharacteristic
111C2×M16×C101C2311yescharacteristic
112C22×C8×C101—21no—
113C22×C8×C101—21no—
114C22×C8×C101C2311yescharacteristic
115C22×C8×C101C2311yescharacteristic
116#127×C101—21no—
117#127×C101—22no—
118#127×C101—22no—
119#124×C101—21no—
120C22⋊Q8×C101—21no—
121C22⋊Q8×C101—21no—
122#121×C101—21no—
123#121×C101—21no—
124#121×C101—21no—
125#121×C101—21no—
126#121×C101—41no—
127#120×C101—41no—
128C4×Q8×C101—21no—
129C4×D4×C101—21no—
130C4×D4×C101—41no—
131#117×C101—21no—
132#117×C101C2311yescharacteristic
133C2×C4⋊C4×C101—21no—
134C2×C4⋊C4×C101C2311yescharacteristic
135C2×C4⋊C4×C101C2311yescharacteristic
136C2×C42×C101C2311yescharacteristic
137#108×C101—22no—
138#107×C101—21no—
139#106×C101—21no—
140C4⋊C8×C101—21no—
141C4⋊C8×C101—21no—
142#104×C101—22no—
143#104×C101—22no—
144#104×C101D414yescomplemented
145#103×C101—21no—
146#103×C101—21no—
147#103×C101—21no—
148#103×C101D411yescharacteristic, complemented
149#103×C101D411yescharacteristic, complemented
150#102×C101—21no—
151#102×C101—21no—
152#102×C101—21no—
153#102×C101—21no—
154#102×C101—21no—
155#102×C101—21no—
156#102×C101—21no—
157#102×C101—21no—
158#102×C101—21no—
159#102×C101—21no—
160#102×C101—21no—
161#102×C101—21no—
162#102×C101—21no—
163#102×C101D411yescharacteristic, complemented
164#102×C101D411yescharacteristic, complemented
165#100×C101—22no—
166#100×C101—41no—
167C22⋊C8×C101—21no—
168C22⋊C8×C101—21no—
169#97×C101—22no—
170#95×C101—41no—
171C24×C101—21no—
172C24×C101—21no—
173C24×C101—41no—
174#41×C101—21no—
175#41×C101—21no—
176#41×C101—24no—
177#41×C101—21no—
178#41×C101—21no—
179#41×C101—21no—
180#41×C101—21no—
181#41×C101—21no—
182#41×C101—21no—
183#41×C101—21no—
184#41×C101—21no—
185#41×C101—42no—
186#41×C101—42no—
187#41×C101—42no—
188#41×C101C2×D412yes—
189#41×C101#4112yes—
190C2×Q8×C101C2×D411yescharacteristic
191C2×Q8×C101C2×D411yescharacteristic
192C2×Q8×C101C2×D411yescharacteristic
193C2×D4×C101—21no—
194C2×D4×C101—24no—
195C2×D4×C101—21no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—21no—
207C2×D4×C101—21no—
208C2×D4×C101—42no—
209C2×D4×C101—41no—
210C2×D4×C101—41no—
211C2×D4×C101—44no—
212C2×D4×C101—41no—
213C2×D4×C101—41no—
214C2×D4×C101—42no—
215C2×D4×C101—44no—
216C2×D4×C101—44no—
217C2×D4×C101—42no—
218C2×D4×C101—41no—
219C2×D4×C101—82no—
220C2×D4×C101—82no—
221C2×D4×C101C2×D411yescharacteristic
222C2×D4×C101C2×D411yescharacteristic
223C2×D4×C101C2×D411yescharacteristic
224C2×D4×C101#4112yes—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—21no—
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—41no—
232C22×C4×C101—41no—
233C22×C4×C101C2411yescharacteristic
234Q16×C101—22no—
235SD16×C101—22no—
236SD16×C101—22no—
237SD16×C101—42no—
238SD16×C101—42no—
239SD16×C101—42no—
240D8×C101—22no—
241D8×C101—42no—
242D8×C101—42no—
243D8×C101—42no—
244M16×C101—21no—
245M16×C101—21no—
246M16×C101—21no—
247M16×C101—21no—
248M16×C101—21no—
249M16×C101—21no—
250M16×C101—21no—
251M16×C101—42no—
252M16×C101—42no—
253M16×C101C2×D412yes—
254C2×C8×C101—21no—
255C2×C8×C101—21no—
256C2×C8×C101—21no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C2×C8×C101—21no—
262C2×C8×C101—42no—
263C2×C8×C101—42no—
264C2×C8×C101C2×D411yescharacteristic
265C2×C8×C101C2×D411yescharacteristic
266C2×C8×C101C2×D411yescharacteristic
267C2×C8×C101C2×D411yescharacteristic
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—41no—
273C4⋊C4×C101—41no—
274C4⋊C4×C101C2×D411yescharacteristic
275C4⋊C4×C101C2×D411yescharacteristic
276C22⋊C4×C101—21no—
277C22⋊C4×C101—41no—
278C22⋊C4×C101—41no—
279C22⋊C4×C101—41no—
280C22⋊C4×C101—41no—
281C22⋊C4×C101—41no—
282C42×C101—21no—
283C42×C101—21no—
284C42×C101—41no—
285C42×C101C2×D412yes—
286C23×C101—21no—
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—22no—
290C23×C101—44no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—81no—
297C23×C101—81no—
298C23×C101—81no—
299C23×C101—81no—
300C23×C101—161no—
301C23×C101—161no—
302C23×C101H(5,𝔽2)11yescharacteristic
303Q8×C101—21no—
304Q8×C101—21no—
305Q8×C101—21no—
306Q8×C101—21no—
307Q8×C101—21no—
308Q8×C101#12112yes—
309D4×C101—22no—
310D4×C101—22no—
311D4×C101—21no—
312D4×C101—21no—
313D4×C101—22no—
314D4×C101—21no—
315D4×C101—21no—
316D4×C101—21no—
317D4×C101—22no—
318D4×C101—44no—
319D4×C101—44no—
320D4×C101—41no—
321D4×C101—41no—
322D4×C101—41no—
323D4×C101—41no—
324D4×C101—41no—
325D4×C101—41no—
326D4×C101—41no—
327D4×C101—41no—
328D4×C101—41no—
329D4×C101—41no—
330D4×C101—88no—
331D4×C101—161no—
332D4×C101—161no—
333D4×C101—161no—
334D4×C101#12112yes—
335C2×C4×C101—21no—
336C2×C4×C101—22no—
337C2×C4×C101—22no—
338C2×C4×C101—21no—
339C2×C4×C101—21no—
340C2×C4×C101—21no—
341C2×C4×C101—21no—
342C2×C4×C101—22no—
343C2×C4×C101—44no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—41no—
351C2×C4×C101—41no—
352C2×C4×C101—81no—
353C2×C4×C101—81no—
354C2×C4×C101—161no—
355C2×C4×C101C22×D411yescharacteristic
356C2×C4×C101C22×D411yescharacteristic
357C2×C4×C101C22×D411yescharacteristic
358C2×C4×C101C2×#4111yescharacteristic
359C2×C4×C101C2×#4111yescharacteristic
360C2×C4×C101H(5,𝔽2)11yescharacteristic
361C8×C101—21no—
362C8×C101—21no—
363C8×C101—21no—
364C8×C101—21no—
365C8×C101—22no—
366C8×C101—41no—
367C8×C101—41no—
368C8×C101—41no—
369C22×C101—21no—
370C22×C101—21no—
371C22×C101—22no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—41no—
375C22×C101—42no—
376C22×C101—41no—
377C22×C101—41no—
378C22×C101—41no—
379C22×C101—41no—
380C22×C101—41no—
381C22×C101—82no—
382C22×C101—82no—
383C22×C101—81no—
384C22×C101—81no—
385C22×C101—81no—
386C22×C101—81no—
387C22×C101—81no—
388C22×C101—161no—
389C22×C101—161no—
390C22×C101—164no—
391C22×C101#53811yescharacteristic
392C22×C101D4211yescharacteristic
393C22×C101#54611yescharacteristic
394C4×C101—22no—
395C4×C101—42no—
396C4×C101—41no—
397C4×C101—41no—
398C4×C101—41no—
399C4×C101—41no—
400C4×C101—81no—
401C4×C101—81no—
402C4×C101C2×#12111yescharacteristic
403C4×C101#52511yescharacteristic
404C4×C101D4211yescharacteristic
405C4×C101#54611yescharacteristic
406#25192C10111yesmaximal, characteristic, direct product factor, Sylow
407C2×C101—21no—
408C2×C101—21no—
409C2×C101—42no—
410C2×C101—81no—
411C2×C101—81no—
412C2×C101—82no—
413C2×C101—161no—
414C2×C101#242411yescharacteristic
415C2×C101#328811yescharacteristic
416C2×C101#328811yescharacteristic
417#3062C2×C10111yescharacteristic, complemented
418#3045C2×C10111yescharacteristic, complemented
419C2×#453C2×C10111yescharacteristic, complemented
420#3012C2×C10111yescharacteristic, complemented
421C2×#444C2×C10111yescharacteristic, complemented
422#2897C2×C10111yescharacteristic, complemented
423#2063C2×C10111yescharacteristic, complemented
424#2051C2×C10111yescharacteristic, complemented
425#2040C2×C10111yescharacteristic, complemented
426#2002C2×C10111yescharacteristic, complemented
427#1961C2×C10111yescharacteristic, complemented
428#1938C2×C10111yescharacteristic, complemented
429#1907C2×C10111yescharacteristic, complemented
430#1907C2×C10111yescharacteristic, complemented
431#1860C2×C10111yescharacteristic, complemented
432C101#2519211yescharacteristic, direct product factor, Sylow
433C2×H(5,𝔽2)C22×C10111yescharacteristic
434C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
435C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
436C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
437C2×#135C22×C10111yescharacteristic
438C2×#131C22×C10111yescharacteristic
439C2×#131C22×C10111yescharacteristic, complemented
440#537C22×C10111yescharacteristic
441#535C22×C10111yescharacteristic, complemented
442C2×#127C22×C10111yescharacteristic
443#520C22×C10111yescharacteristic
444#469—21no—
445#468—21no—
446#466—21no—
447#465—21no—
448#464—21no—
449#463—21no—
450#460—21no—
451#459—21no—
452#453—24no—
453#452—21no—
454#450—21no—
455#449—21no—
456#447—21no—
457#444—24no—
458C2×#108C22×C10111yescharacteristic, complemented
459#428C22×C10111yescharacteristic, complemented
460#424C22×C10111yescharacteristic, complemented
461C2×#104C22×C10111yescharacteristic
462C2×#104C22×C10111yescharacteristic
463C2×#104C22×C10111yescharacteristic, complemented
464#418—21no—
465#418C22×C10111yescharacteristic
466#417—21no—
467#417C22×C10111yescharacteristic
468#417C22×C10111yescharacteristic
469#417C22×C10111yescharacteristic, complemented
470#416—21no—
471#416C22×C10111yescharacteristic
472C2×#102—21no—
473C2×#102C22×C10111yescharacteristic
474C2×#102C22×C10111yescharacteristic
475C2×#102C22×C10111yescharacteristic, complemented
476C2×#102C22×C10111yescharacteristic, complemented
477C2×#100C22×C10111yescharacteristic
478C2×#100C22×C10111yescharacteristic, complemented
479#408C22×C10111yescharacteristic
480C2×#97C22×C10111yescharacteristic, complemented
481#382C22×C10111yescharacteristic, complemented
482#343C22×C10111yescharacteristic, complemented
483#343C22×C10111yescharacteristic, complemented
484#341C22×C10111yescharacteristic, complemented
485#339C22×C10111yescharacteristic, complemented
486H(5,𝔽2)—22no—
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—41no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41C23×C10111yescharacteristic
493C2×#41C23×C10111yescharacteristic
494C2×#41C23×C10111yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C10111yescharacteristic
500C22×D4C23×C10111yescharacteristic
501AGL(1,ℤ/8)—22no—
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—41no—
506AGL(1,ℤ/8)—41no—
507#135—22no—
508#135—22no—
509C2×Q16D4×C10111yescharacteristic, complemented
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16D4×C10111yescharacteristic, complemented
514C2×SD16D4×C10111yescharacteristic, complemented
515C2×D8—21no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8D4×C10111yescharacteristic, complemented
519#131—22no—
520#131—22no—
521#131—41no—
522#131—41no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16C23×C10111yescharacteristic
526C2×M16C23×C10111yescharacteristic
527C2×M16C23×C10111yescharacteristic
528C2×M16C23×C10111yescharacteristic
529C22×C8—21no—
530C22×C8—21no—
531C22×C8C23×C10111yescharacteristic
532C22×C8C23×C10111yescharacteristic
533#127—21no—
534#127—22no—
535#127—22no—
536#124—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—41no—
544#120—41no—
545C4×Q8—21no—
546C4×D4—21no—
547C4×D4—41no—
548#117—21no—
549#117C23×C10111yescharacteristic
550C2×C4⋊C4—21no—
551C2×C4⋊C4C23×C10111yescharacteristic
552C2×C4⋊C4C23×C10111yescharacteristic
553C2×C42C23×C10111yescharacteristic
554#108—22no—
555#107—21no—
556#106—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559#104—22no—
560#104—22no—
561#104D4×C10114yescomplemented
562#103—21no—
563#103—21no—
564#103—21no—
565#103D4×C10111yescharacteristic, complemented
566#103D4×C10111yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102D4×C10111yescharacteristic, complemented
581#102D4×C10111yescharacteristic, complemented
582#100—22no—
583#100—41no—
584C22⋊C8—21no—
585C22⋊C8—21no—
586#97—22no—
587#95—41no—
588C24—21no—
589C24—21no—
590C24—41no—
591#41—21no—
592#41—21no—
593#41—24no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41C2×D4×C10112yes—
606#41#41×C10112yes—
607C2×Q8C2×D4×C10111yescharacteristic
608C2×Q8C2×D4×C10111yescharacteristic
609C2×Q8C2×D4×C10111yescharacteristic
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—44no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—41no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C10111yescharacteristic
639C2×D4C2×D4×C10111yescharacteristic
640C2×D4C2×D4×C10111yescharacteristic
641C2×D4#41×C10112yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C10111yescharacteristic
651Q16—22no—
652SD16—22no—
653SD16—22no—
654SD16—42no—
655SD16—42no—
656SD16—42no—
657D8—22no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16—42no—
670M16C2×D4×C10112yes—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8C2×D4×C10111yescharacteristic
682C2×C8C2×D4×C10111yescharacteristic
683C2×C8C2×D4×C10111yescharacteristic
684C2×C8C2×D4×C10111yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4C2×D4×C10111yescharacteristic
692C4⋊C4C2×D4×C10111yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—41no—
702C42C2×D4×C10112yes—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—161no—
718C23—161no—
719C23H(5,𝔽2)×C10111yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8#121×C10112yes—
726D4—22no—
727D4—22no—
728D4—21no—
729D4—21no—
730D4—22no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—22no—
735D4—44no—
736D4—44no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—88no—
748D4—161no—
749D4—161no—
750D4—161no—
751D4#121×C10112yes—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—161no—
772C2×C4C22×D4×C10111yescharacteristic
773C2×C4C22×D4×C10111yescharacteristic
774C2×C4C22×D4×C10111yescharacteristic
775C2×C4C2×#41×C10111yescharacteristic
776C2×C4C2×#41×C10111yescharacteristic
777C2×C4H(5,𝔽2)×C10111yescharacteristic
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—161no—
806C22—161no—
807C22—164no—
808C22#538×C10111yescharacteristic
809C22D42×C10111yescharacteristic
810C22#546×C10111yescharacteristic
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4C2×#121×C10111yescharacteristic
820C4#525×C10111yescharacteristic
821C4D42×C10111yescharacteristic
822C4#546×C10111yescharacteristic
823C2—21no—
824C2—21no—
825C2—42no—
826C2—81no—
827C2—81no—
828C2—82no—
829C2—161no—
830C2C101×#242411yescharacteristic
831C2C101×#328811yescharacteristic
832C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3062C2semidirect
2. C101×#3045C2semidirect
3. C2×#453×C101C2semidirect
4. C101×#3012C2semidirect
5. C2×#444×C101C2semidirect
6. C101×#2897C2semidirect
7. C101×#2063C2semidirect
8. C101×#2051C2semidirect
9. C101×#2040C2semidirect
10. C101×#2002C2semidirect
11. C101×#1961C2semidirect
12. C101×#1938C2semidirect
13. C101×#1907C2semidirect
14. C101×#1907C2semidirect
15. C101×#1860C2semidirect
22. C2×#131×C101C22semidirect
24. #535×C101C22semidirect
41. C2×#108×C101C22semidirect
42. #428×C101C22semidirect
43. #424×C101C22semidirect
46. C2×#104×C101C22semidirect
52. #417×C101C22semidirect
58. C2×#102×C101C22semidirect
59. C2×#102×C101C22semidirect
61. C2×#100×C101C22semidirect
63. C2×#97×C101C22semidirect
64. #382×C101C22semidirect
65. #343×C101C22semidirect
66. #343×C101C22semidirect
67. #341×C101C22semidirect
68. #339×C101C22semidirect
92. C2×Q16×C101D4semidirect
96. C2×SD16×C101D4semidirect
97. C2×SD16×C101D4semidirect
101. C2×D8×C101D4semidirect
144. #104×C101D4semidirect
148. #103×C101D4semidirect
149. #103×C101D4semidirect
163. #102×C101D4semidirect
164. #102×C101D4semidirect
406. #25192C101direct (N × H)
417. #3062C2×C101semidirect
418. #3045C2×C101semidirect
419. C2×#453C2×C101semidirect
420. #3012C2×C101semidirect
421. C2×#444C2×C101semidirect
422. #2897C2×C101semidirect
423. #2063C2×C101semidirect
424. #2051C2×C101semidirect
425. #2040C2×C101semidirect
426. #2002C2×C101semidirect
427. #1961C2×C101semidirect
428. #1938C2×C101semidirect
429. #1907C2×C101semidirect
430. #1907C2×C101semidirect
431. #1860C2×C101semidirect
432. C101#25192direct (N × H)
439. C2×#131C22×C101semidirect
441. #535C22×C101semidirect
458. C2×#108C22×C101semidirect
459. #428C22×C101semidirect
460. #424C22×C101semidirect
463. C2×#104C22×C101semidirect
469. #417C22×C101semidirect
475. C2×#102C22×C101semidirect
476. C2×#102C22×C101semidirect
478. C2×#100C22×C101semidirect
480. C2×#97C22×C101semidirect
481. #382C22×C101semidirect
482. #343C22×C101semidirect
483. #343C22×C101semidirect
484. #341C22×C101semidirect
485. #339C22×C101semidirect
509. C2×Q16D4×C101semidirect
513. C2×SD16D4×C101semidirect
514. C2×SD16D4×C101semidirect
518. C2×D8D4×C101semidirect
561. #104D4×C101semidirect
565. #103D4×C101semidirect
566. #103D4×C101semidirect
580. #102D4×C101semidirect
581. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30622
C101×#30452
C2×#453×C1012
C101×#30122
C2×#444×C1012
C101×#28972
C101×#20632
C101×#20512
C101×#20402
C101×#20022
C101×#19612
C101×#19382
C101×#19072
C101×#18602
#25192101