Finite Group Databasebeta

← C101×#24472 #38806623

Subgroups — C101×#24472 #38806623

Order 25856.

1372 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3585C211yesmaximal, characteristic, complemented
2C101×#3068C211yesmaximal, characteristic, complemented
3C101×#3038C211yesmaximal, characteristic, complemented
4C101×#3021C211yesmaximal, characteristic, complemented
5C2×#453×C101C211yesmaximal, characteristic, complemented
6C101×#2901C211yesmaximal, characteristic, complemented
7C101×#2050C211yesmaximal, characteristic, complemented
8C101×#2048C211yesmaximal, characteristic, complemented
9C101×#2008C211yesmaximal, characteristic, complemented
10C101×#2002C211yesmaximal, characteristic, complemented
11C101×#1906C211yesmaximal, characteristic, complemented
12C101×#1903C211yesmaximal, characteristic, complemented
13C101×#1903C211yesmaximal, characteristic, complemented
14C101×#1861C211yesmaximal, characteristic, complemented
15C101×#1795C211yesmaximal, characteristic, complemented
16#585×C101C2211yescharacteristic
17C2×H(5,𝔽2)×C101C2211yescharacteristic
18#577×C101—22no—
19#577×C101—22no—
20#576×C101—22no—
21#576×C101—22no—
22#575×C101—22no—
23#575×C101C2211yescharacteristic
24#575×C101C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C101—22no—
26C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C101C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C101C2211yescharacteristic, complemented
31#568×C101C2211yescharacteristic
32#568×C101C2211yescharacteristic, complemented
33#535×C101C2211yescharacteristic, complemented
34C2×#127×C101C2211yescharacteristic, complemented
35C4×#41×C101C2211yescharacteristic, complemented
36#472×C101—22no—
37#471×C101—22no—
38#460×C101—22no—
39#459×C101—22no—
40#454×C101—22no—
41#453×C101—22no—
42#453×C101—22no—
43#453×C101—22no—
44#430×C101C2211yescharacteristic, complemented
45#423×C101C2211yescharacteristic, complemented
46#421×C101—22no—
47#421×C101C2211yescharacteristic
48#421×C101C2211yescharacteristic
49#421×C101C2211yescharacteristic, complemented
50#421×C101C2211yescharacteristic, complemented
51C2×#104×C101—22no—
52C2×#104×C101C2211yescharacteristic
53C2×#104×C101C2211yescharacteristic, complemented
54C2×#104×C101C2211yescharacteristic, complemented
55#418×C101C2211yescharacteristic, complemented
56#418×C101C2211yescharacteristic, complemented
57#418×C101C2211yescharacteristic, complemented
58#413×C101C2211yescharacteristic, complemented
59#413×C101C2211yescharacteristic, complemented
60C2×#100×C101C2211yescharacteristic, complemented
61C2×#100×C101C2211yescharacteristic, complemented
62#410×C101C2211yescharacteristic, complemented
63#344×C101C2211yescharacteristic, complemented
64#344×C101C2211yescharacteristic, complemented
65#339×C101C2211yescharacteristic, complemented
66#338×C101C2211yescharacteristic, complemented
672−1+4×C101—21no—
682−1+4×C101—21no—
692−1+4×C101D412yescomplemented
70H(5,𝔽2)×C101—22no—
71H(5,𝔽2)×C101—21no—
72H(5,𝔽2)×C101—22no—
73H(5,𝔽2)×C101—21no—
74H(5,𝔽2)×C101—22no—
75H(5,𝔽2)×C101—41no—
76H(5,𝔽2)×C101—41no—
77H(5,𝔽2)×C101D412yescomplemented
78C2×#41×C101—22no—
79C2×#41×C101—22no—
80C2×#41×C101—21no—
81C2×#41×C101—21no—
82C2×#41×C101—41no—
83C2×#41×C101C2311yescharacteristic
84C2×#41×C101C2311yescharacteristic
85C2×#41×C101C2311yescharacteristic
86C2×#41×C101C2311yescharacteristic
87C22×D4×C101—21no—
88C22×D4×C101—21no—
89C22×D4×C101—41no—
90C22×D4×C101—41no—
91C22×D4×C101C2311yescharacteristic
92C22×D4×C101C2311yescharacteristic
93#137×C101—24no—
94#137×C101—21no—
95#137×C101—21no—
96#137×C101—21no—
97#137×C101D412yescomplemented
98AGL(1,ℤ/8)×C101—24no—
99AGL(1,ℤ/8)×C101—24no—
100AGL(1,ℤ/8)×C101—24no—
101AGL(1,ℤ/8)×C101—22no—
102AGL(1,ℤ/8)×C101—22no—
103AGL(1,ℤ/8)×C101—21no—
104AGL(1,ℤ/8)×C101—22no—
105AGL(1,ℤ/8)×C101—21no—
106AGL(1,ℤ/8)×C101—21no—
107AGL(1,ℤ/8)×C101—22no—
108AGL(1,ℤ/8)×C101—22no—
109AGL(1,ℤ/8)×C101—22no—
110AGL(1,ℤ/8)×C101—22no—
111AGL(1,ℤ/8)×C101—22no—
112AGL(1,ℤ/8)×C101—22no—
113AGL(1,ℤ/8)×C101—41no—
114AGL(1,ℤ/8)×C101D412yescomplemented
115#135×C101—24no—
116#135×C101—24no—
117#135×C101—22no—
118#135×C101—22no—
119C2×SD16×C101—24no—
120C2×SD16×C101—21no—
121C2×SD16×C101—21no—
122C2×SD16×C101—21no—
123C2×SD16×C101—21no—
124C2×SD16×C101D412yescomplemented
125C2×D8×C101—24no—
126C2×D8×C101—21no—
127C2×D8×C101—21no—
128C2×D8×C101—21no—
129C2×D8×C101—21no—
130C2×D8×C101D412yescomplemented
131#131×C101—22no—
132#131×C101—22no—
133#131×C101—22no—
134#131×C101—41no—
135C2×M16×C101—22no—
136C2×M16×C101—22no—
137C2×M16×C101C2311yescharacteristic
138C2×M16×C101C2311yescharacteristic
139C2×M16×C101C2311yescharacteristic
140C2×M16×C101C2311yescharacteristic
141C2×M16×C101C2311yescharacteristic
142C2×M16×C101C2311yescharacteristic
143#127×C101—21no—
144#127×C101—22no—
145#127×C101—21no—
146#127×C101—21no—
147#124×C101—21no—
148#121×C101—41no—
149#120×C101—41no—
150C4×Q8×C101—21no—
151C4×D4×C101—21no—
152C4×D4×C101—41no—
153#117×C101—21no—
154#117×C101C2311yescharacteristic
155#117×C101C2311yescharacteristic
156C2×C42×C101—21no—
157C2×C42×C101C2311yescharacteristic
158#108×C101—22no—
159C4⋊C8×C101—22no—
160#104×C101—22no—
161#104×C101—22no—
162#104×C101—22no—
163#104×C101—22no—
164#104×C101—21no—
165#104×C101—21no—
166#104×C101—21no—
167#104×C101—21no—
168#104×C101D412yescomplemented
169#104×C101D412yescomplemented
170#102×C101—22no—
171#102×C101—22no—
172#102×C101—41no—
173#101×C101—21no—
174#101×C101—21no—
175#100×C101—21no—
176#100×C101—21no—
177#100×C101—22no—
178#100×C101—22no—
179#99×C101—41no—
180C24×C101—21no—
181C24×C101—21no—
182C24×C101—41no—
183#41×C101—21no—
184#41×C101—21no—
185#41×C101—21no—
186#41×C101—21no—
187#41×C101—24no—
188#41×C101—22no—
189#41×C101—22no—
190#41×C101—22no—
191#41×C101—22no—
192#41×C101—21no—
193#41×C101—21no—
194#41×C101—21no—
195#41×C101—21no—
196#41×C101—21no—
197#41×C101—21no—
198#41×C101—21no—
199#41×C101—21no—
200#41×C101—42no—
201#41×C101—42no—
202#41×C101—42no—
203#41×C101—42no—
204#41×C101—42no—
205#41×C101—42no—
206#41×C101—41no—
207#41×C101—41no—
208#41×C101—42no—
209#41×C101C2×D412yes—
210#41×C101C2×D412yes—
211#41×C101C2×D412yes—
212#41×C101C2×D412yes—
213C2×Q8×C101—22no—
214C2×Q8×C101—22no—
215C2×Q8×C101—41no—
216C2×Q8×C101C2×D411yescharacteristic
217C2×Q8×C101C2×D411yescharacteristic
218C2×Q8×C101C2×D411yescharacteristic
219C2×Q8×C101#4111yescharacteristic
220C2×D4×C101—21no—
221C2×D4×C101—21no—
222C2×D4×C101—24no—
223C2×D4×C101—22no—
224C2×D4×C101—22no—
225C2×D4×C101—21no—
226C2×D4×C101—21no—
227C2×D4×C101—21no—
228C2×D4×C101—21no—
229C2×D4×C101—21no—
230C2×D4×C101—21no—
231C2×D4×C101—21no—
232C2×D4×C101—21no—
233C2×D4×C101—21no—
234C2×D4×C101—21no—
235C2×D4×C101—21no—
236C2×D4×C101—21no—
237C2×D4×C101—21no—
238C2×D4×C101—42no—
239C2×D4×C101—41no—
240C2×D4×C101—41no—
241C2×D4×C101—42no—
242C2×D4×C101—42no—
243C2×D4×C101—42no—
244C2×D4×C101—42no—
245C2×D4×C101—41no—
246C2×D4×C101—44no—
247C2×D4×C101—42no—
248C2×D4×C101—42no—
249C2×D4×C101—44no—
250C2×D4×C101—42no—
251C2×D4×C101—42no—
252C2×D4×C101—84no—
253C2×D4×C101C2×D411yescharacteristic
254C2×D4×C101C2×D411yescharacteristic
255C2×D4×C101C2×D412yes—
256C2×D4×C101C2×D411yescharacteristic
257C2×D4×C101#4111yescharacteristic
258C22×C4×C101—21no—
259C22×C4×C101—21no—
260C22×C4×C101—21no—
261C22×C4×C101—21no—
262C22×C4×C101—21no—
263C22×C4×C101—41no—
264C22×C4×C101—42no—
265C22×C4×C101—41no—
266C22×C4×C101C2411yescharacteristic
267Q16×C101—22no—
268Q16×C101—22no—
269SD16×C101—24no—
270SD16×C101—22no—
271SD16×C101—22no—
272SD16×C101—22no—
273SD16×C101—24no—
274SD16×C101—22no—
275SD16×C101—42no—
276SD16×C101—42no—
277SD16×C101—42no—
278D8×C101—24no—
279D8×C101—22no—
280D8×C101—22no—
281D8×C101—24no—
282D8×C101—42no—
283D8×C101—42no—
284D8×C101—42no—
285M16×C101—24no—
286M16×C101—21no—
287M16×C101—21no—
288M16×C101—21no—
289M16×C101—21no—
290M16×C101—21no—
291M16×C101—21no—
292M16×C101—21no—
293M16×C101—21no—
294M16×C101—21no—
295M16×C101—21no—
296M16×C101—42no—
297M16×C101C2×D412yes—
298M16×C101C2×D412yes—
299C2×C8×C101—24no—
300C2×C8×C101—21no—
301C2×C8×C101—21no—
302C2×C8×C101—21no—
303C2×C8×C101—21no—
304C2×C8×C101—21no—
305C2×C8×C101—42no—
306C2×C8×C101C2×D412yes—
307C4⋊C4×C101—21no—
308C4⋊C4×C101—21no—
309C4⋊C4×C101—41no—
310C22⋊C4×C101—21no—
311C22⋊C4×C101—21no—
312C22⋊C4×C101—41no—
313C22⋊C4×C101—42no—
314C42×C101—21no—
315C42×C101—21no—
316C42×C101—21no—
317C42×C101—41no—
318C42×C101C2×D411yescharacteristic
319C42×C101C2×D411yescharacteristic
320C23×C101—21no—
321C23×C101—21no—
322C23×C101—21no—
323C23×C101—22no—
324C23×C101—21no—
325C23×C101—42no—
326C23×C101—44no—
327C23×C101—41no—
328C23×C101—41no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—82no—
333C23×C101—82no—
334C23×C101—162no—
335C23×C101H(5,𝔽2)11yescharacteristic
336Q8×C101—21no—
337Q8×C101—21no—
338Q8×C101—21no—
339Q8×C101—21no—
340Q8×C101—21no—
341Q8×C101—21no—
342Q8×C101—42no—
343Q8×C101#12012yes—
344Q8×C101#12112yes—
345D4×C101—22no—
346D4×C101—22no—
347D4×C101—22no—
348D4×C101—22no—
349D4×C101—21no—
350D4×C101—21no—
351D4×C101—22no—
352D4×C101—21no—
353D4×C101—21no—
354D4×C101—21no—
355D4×C101—21no—
356D4×C101—22no—
357D4×C101—42no—
358D4×C101—42no—
359D4×C101—44no—
360D4×C101—42no—
361D4×C101—44no—
362D4×C101—41no—
363D4×C101—41no—
364D4×C101—41no—
365D4×C101—41no—
366D4×C101—41no—
367D4×C101—41no—
368D4×C101—41no—
369D4×C101—41no—
370D4×C101—41no—
371D4×C101—41no—
372D4×C101—84no—
373D4×C101—84no—
374D4×C101—162no—
375D4×C101#12012yes—
376D4×C101#12112yes—
377C2×C4×C101—21no—
378C2×C4×C101—21no—
379C2×C4×C101—21no—
380C2×C4×C101—22no—
381C2×C4×C101—22no—
382C2×C4×C101—22no—
383C2×C4×C101—22no—
384C2×C4×C101—21no—
385C2×C4×C101—21no—
386C2×C4×C101—21no—
387C2×C4×C101—42no—
388C2×C4×C101—42no—
389C2×C4×C101—42no—
390C2×C4×C101—42no—
391C2×C4×C101—44no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—82no—
399C2×C4×C101C22×D411yescharacteristic
400C2×C4×C101C22×D411yescharacteristic
401C2×C4×C101C22×D411yescharacteristic
402C2×C4×C101C22×D411yescharacteristic
403C2×C4×C101C2×#4111yescharacteristic
404C2×C4×C101H(5,𝔽2)11yescharacteristic
405C8×C101—22no—
406C8×C101—22no—
407C8×C101—22no—
408C8×C101—41no—
409C8×C101—41no—
410C8×C101—41no—
411C22×C101—22no—
412C22×C101—22no—
413C22×C101—41no—
414C22×C101—41no—
415C22×C101—42no—
416C22×C101—41no—
417C22×C101—81no—
418C22×C101—81no—
419C22×C101—82no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101—82no—
423C22×C101—82no—
424C22×C101—82no—
425C22×C101—81no—
426C22×C101—161no—
427C22×C101—161no—
428C22×C101—162no—
429C22×C101—164no—
430C22×C101#53411yescharacteristic
431C22×C101D4211yescharacteristic
432C22×C101#54611yescharacteristic
433C4×C101—22no—
434C4×C101—22no—
435C4×C101—22no—
436C4×C101—41no—
437C4×C101—41no—
438C4×C101—41no—
439C4×C101—81no—
440C4×C101—81no—
441C4×C101C2×#12011yescharacteristic
442C4×C101C2×#12111yescharacteristic
443C4×C101D4211yescharacteristic
444C4×C101#54611yescharacteristic
445#24472C10111yesmaximal, characteristic, direct product factor, Sylow
446C2×C101—21no—
447C2×C101—21no—
448C2×C101—21no—
449C2×C101—42no—
450C2×C101—42no—
451C2×C101—82no—
452C2×C101—81no—
453C2×C101—81no—
454C2×C101—161no—
455C2×C101#241011yescharacteristic
456#3585C2×C10111yescharacteristic, complemented
457#3068C2×C10111yescharacteristic, complemented
458#3038C2×C10111yescharacteristic, complemented
459#3021C2×C10111yescharacteristic, complemented
460C2×#453C2×C10111yescharacteristic, complemented
461#2901C2×C10111yescharacteristic, complemented
462#2050C2×C10111yescharacteristic, complemented
463#2048C2×C10111yescharacteristic, complemented
464#2008C2×C10111yescharacteristic, complemented
465#2002C2×C10111yescharacteristic, complemented
466#1906C2×C10111yescharacteristic, complemented
467#1903C2×C10111yescharacteristic, complemented
468#1903C2×C10111yescharacteristic, complemented
469#1861C2×C10111yescharacteristic, complemented
470#1795C2×C10111yescharacteristic, complemented
471C101#2447211yescharacteristic, direct product factor, Sylow
472#585C22×C10111yescharacteristic
473C2×H(5,𝔽2)C22×C10111yescharacteristic
474#577—22no—
475#577—22no—
476#576—22no—
477#576—22no—
478#575—22no—
479#575C22×C10111yescharacteristic
480#575C22×C10111yescharacteristic
481C2×AGL(1,ℤ/8)—22no—
482C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
483C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
484C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
485C2×AGL(1,ℤ/8)C22×C10111yescharacteristic, complemented
486C2×AGL(1,ℤ/8)C22×C10111yescharacteristic, complemented
487#568C22×C10111yescharacteristic
488#568C22×C10111yescharacteristic, complemented
489#535C22×C10111yescharacteristic, complemented
490C2×#127C22×C10111yescharacteristic, complemented
491C4×#41C22×C10111yescharacteristic, complemented
492#472—22no—
493#471—22no—
494#460—22no—
495#459—22no—
496#454—22no—
497#453—22no—
498#453—22no—
499#453—22no—
500#430C22×C10111yescharacteristic, complemented
501#423C22×C10111yescharacteristic, complemented
502#421—22no—
503#421C22×C10111yescharacteristic
504#421C22×C10111yescharacteristic
505#421C22×C10111yescharacteristic, complemented
506#421C22×C10111yescharacteristic, complemented
507C2×#104—22no—
508C2×#104C22×C10111yescharacteristic
509C2×#104C22×C10111yescharacteristic, complemented
510C2×#104C22×C10111yescharacteristic, complemented
511#418C22×C10111yescharacteristic, complemented
512#418C22×C10111yescharacteristic, complemented
513#418C22×C10111yescharacteristic, complemented
514#413C22×C10111yescharacteristic, complemented
515#413C22×C10111yescharacteristic, complemented
516C2×#100C22×C10111yescharacteristic, complemented
517C2×#100C22×C10111yescharacteristic, complemented
518#410C22×C10111yescharacteristic, complemented
519#344C22×C10111yescharacteristic, complemented
520#344C22×C10111yescharacteristic, complemented
521#339C22×C10111yescharacteristic, complemented
522#338C22×C10111yescharacteristic, complemented
5232−1+4—21no—
5242−1+4—21no—
5252−1+4D4×C10112yescomplemented
526H(5,𝔽2)—22no—
527H(5,𝔽2)—21no—
528H(5,𝔽2)—22no—
529H(5,𝔽2)—21no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—41no—
532H(5,𝔽2)—41no—
533H(5,𝔽2)D4×C10112yescomplemented
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—41no—
539C2×#41C23×C10111yescharacteristic
540C2×#41C23×C10111yescharacteristic
541C2×#41C23×C10111yescharacteristic
542C2×#41C23×C10111yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4C23×C10111yescharacteristic
548C22×D4C23×C10111yescharacteristic
549#137—24no—
550#137—21no—
551#137—21no—
552#137—21no—
553#137D4×C10112yescomplemented
554AGL(1,ℤ/8)—24no—
555AGL(1,ℤ/8)—24no—
556AGL(1,ℤ/8)—24no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—21no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—21no—
562AGL(1,ℤ/8)—21no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567AGL(1,ℤ/8)—22no—
568AGL(1,ℤ/8)—22no—
569AGL(1,ℤ/8)—41no—
570AGL(1,ℤ/8)D4×C10112yescomplemented
571#135—24no—
572#135—24no—
573#135—22no—
574#135—22no—
575C2×SD16—24no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16D4×C10112yescomplemented
581C2×D8—24no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8D4×C10112yescomplemented
587#131—22no—
588#131—22no—
589#131—22no—
590#131—41no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16C23×C10111yescharacteristic
594C2×M16C23×C10111yescharacteristic
595C2×M16C23×C10111yescharacteristic
596C2×M16C23×C10111yescharacteristic
597C2×M16C23×C10111yescharacteristic
598C2×M16C23×C10111yescharacteristic
599#127—22no—
600#127—21no—
601#127—21no—
602#127—21no—
603#124—21no—
604#121—41no—
605#120—41no—
606C4×Q8—21no—
607C4×D4—21no—
608C4×D4—41no—
609#117—21no—
610#117C23×C10111yescharacteristic
611#117C23×C10111yescharacteristic
612C2×C42—21no—
613C2×C42C23×C10111yescharacteristic
614#108—22no—
615C4⋊C8—22no—
616#104—22no—
617#104—22no—
618#104—22no—
619#104—22no—
620#104—21no—
621#104—21no—
622#104—21no—
623#104—21no—
624#104D4×C10112yescomplemented
625#104D4×C10112yescomplemented
626#102—22no—
627#102—22no—
628#102—41no—
629#101—21no—
630#101—21no—
631#100—21no—
632#100—21no—
633#100—22no—
634#100—22no—
635#99—41no—
636C24—21no—
637C24—21no—
638C24—41no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—24no—
644#41—22no—
645#41—22no—
646#41—22no—
647#41—22no—
648#41—21no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—42no—
657#41—42no—
658#41—42no—
659#41—42no—
660#41—42no—
661#41—42no—
662#41—41no—
663#41—41no—
664#41—42no—
665#41C2×D4×C10112yes—
666#41C2×D4×C10112yes—
667#41C2×D4×C10112yes—
668#41C2×D4×C10112yes—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—41no—
672C2×Q8C2×D4×C10111yescharacteristic
673C2×Q8C2×D4×C10111yescharacteristic
674C2×Q8C2×D4×C10111yescharacteristic
675C2×Q8#41×C10111yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—42no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—44no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—84no—
709C2×D4C2×D4×C10111yescharacteristic
710C2×D4C2×D4×C10111yescharacteristic
711C2×D4C2×D4×C10112yes—
712C2×D4C2×D4×C10111yescharacteristic
713C2×D4#41×C10111yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—41no—
720C22×C4—42no—
721C22×C4—41no—
722C22×C4C24×C10111yescharacteristic
723Q16—22no—
724Q16—22no—
725SD16—24no—
726SD16—22no—
727SD16—22no—
728SD16—22no—
729SD16—24no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734D8—24no—
735D8—22no—
736D8—22no—
737D8—24no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—42no—
753M16C2×D4×C10112yes—
754M16C2×D4×C10112yes—
755C2×C8—24no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—42no—
762C2×C8C2×D4×C10112yes—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—41no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—41no—
769C22⋊C4—42no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—41no—
774C42C2×D4×C10111yescharacteristic
775C42C2×D4×C10111yescharacteristic
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—42no—
782C23—44no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—82no—
789C23—82no—
790C23—162no—
791C23H(5,𝔽2)×C10111yescharacteristic
792Q8—21no—
793Q8—21no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—42no—
799Q8#120×C10112yes—
800Q8#121×C10112yes—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—21no—
806D4—21no—
807D4—22no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—22no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—42no—
817D4—44no—
818D4—41no—
819D4—41no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—84no—
829D4—84no—
830D4—162no—
831D4#120×C10112yes—
832D4#121×C10112yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—82no—
855C2×C4C22×D4×C10111yescharacteristic
856C2×C4C22×D4×C10111yescharacteristic
857C2×C4C22×D4×C10111yescharacteristic
858C2×C4C22×D4×C10111yescharacteristic
859C2×C4C2×#41×C10111yescharacteristic
860C2×C4H(5,𝔽2)×C10111yescharacteristic
861C8—22no—
862C8—22no—
863C8—22no—
864C8—41no—
865C8—41no—
866C8—41no—
867C22—22no—
868C22—22no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—81no—
874C22—81no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—81no—
882C22—161no—
883C22—161no—
884C22—162no—
885C22—164no—
886C22#534×C10111yescharacteristic
887C22D42×C10111yescharacteristic
888C22#546×C10111yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C4C2×#120×C10111yescharacteristic
898C4C2×#121×C10111yescharacteristic
899C4D42×C10111yescharacteristic
900C4#546×C10111yescharacteristic
901C2—21no—
902C2—21no—
903C2—21no—
904C2—42no—
905C2—42no—
906C2—82no—
907C2—81no—
908C2—81no—
909C2—161no—
910C2C101×#241011yescharacteristic
subgroupG/H
center, socleC2×C101#2410
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3585C2semidirect
2. C101×#3068C2semidirect
3. C101×#3038C2semidirect
4. C101×#3021C2semidirect
5. C2×#453×C101C2semidirect
6. C101×#2901C2semidirect
7. C101×#2050C2semidirect
8. C101×#2048C2semidirect
9. C101×#2008C2semidirect
10. C101×#2002C2semidirect
11. C101×#1906C2semidirect
12. C101×#1903C2semidirect
13. C101×#1903C2semidirect
14. C101×#1861C2semidirect
15. C101×#1795C2semidirect
29. C2×AGL(1,ℤ/8)×C101C22semidirect
30. C2×AGL(1,ℤ/8)×C101C22semidirect
32. #568×C101C22semidirect
33. #535×C101C22semidirect
34. C2×#127×C101C22semidirect
35. C4×#41×C101C22semidirect
44. #430×C101C22semidirect
45. #423×C101C22semidirect
49. #421×C101C22semidirect
50. #421×C101C22semidirect
53. C2×#104×C101C22semidirect
54. C2×#104×C101C22semidirect
55. #418×C101C22semidirect
56. #418×C101C22semidirect
57. #418×C101C22semidirect
58. #413×C101C22semidirect
59. #413×C101C22semidirect
60. C2×#100×C101C22semidirect
61. C2×#100×C101C22semidirect
62. #410×C101C22semidirect
63. #344×C101C22semidirect
64. #344×C101C22semidirect
65. #339×C101C22semidirect
66. #338×C101C22semidirect
69. 2−1+4×C101D4semidirect
77. H(5,𝔽2)×C101D4semidirect
97. #137×C101D4semidirect
114. AGL(1,ℤ/8)×C101D4semidirect
124. C2×SD16×C101D4semidirect
130. C2×D8×C101D4semidirect
168. #104×C101D4semidirect
169. #104×C101D4semidirect
445. #24472C101direct (N × H)
456. #3585C2×C101semidirect
457. #3068C2×C101semidirect
458. #3038C2×C101semidirect
459. #3021C2×C101semidirect
460. C2×#453C2×C101semidirect
461. #2901C2×C101semidirect
462. #2050C2×C101semidirect
463. #2048C2×C101semidirect
464. #2008C2×C101semidirect
465. #2002C2×C101semidirect
466. #1906C2×C101semidirect
467. #1903C2×C101semidirect
468. #1903C2×C101semidirect
469. #1861C2×C101semidirect
470. #1795C2×C101semidirect
471. C101#24472direct (N × H)
485. C2×AGL(1,ℤ/8)C22×C101semidirect
486. C2×AGL(1,ℤ/8)C22×C101semidirect
488. #568C22×C101semidirect
489. #535C22×C101semidirect
490. C2×#127C22×C101semidirect
491. C4×#41C22×C101semidirect
500. #430C22×C101semidirect
501. #423C22×C101semidirect
505. #421C22×C101semidirect
506. #421C22×C101semidirect
509. C2×#104C22×C101semidirect
510. C2×#104C22×C101semidirect
511. #418C22×C101semidirect
512. #418C22×C101semidirect
513. #418C22×C101semidirect
514. #413C22×C101semidirect
515. #413C22×C101semidirect
516. C2×#100C22×C101semidirect
517. C2×#100C22×C101semidirect
518. #410C22×C101semidirect
519. #344C22×C101semidirect
520. #344C22×C101semidirect
521. #339C22×C101semidirect
522. #338C22×C101semidirect
525. 2−1+4D4×C101semidirect
533. H(5,𝔽2)D4×C101semidirect
553. #137D4×C101semidirect
570. AGL(1,ℤ/8)D4×C101semidirect
580. C2×SD16D4×C101semidirect
586. C2×D8D4×C101semidirect
624. #104D4×C101semidirect
625. #104D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35852
C101×#30682
C101×#30382
C101×#30212
C2×#453×C1012
C101×#29012
C101×#20502
C101×#20482
C101×#20082
C101×#20022
C101×#19062
C101×#19032
C101×#18612
C101×#17952
#24472101