Finite Group Databasebeta

← C101×#24295 #38806446

Subgroups — C101×#24295 #38806446

Order 25856.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C101C211yesmaximal, characteristic, complemented
2C101×#3067C211yesmaximal, characteristic, complemented
3C101×#3057C211yesmaximal, characteristic, complemented
4C101×#3020C211yesmaximal, characteristic, complemented
5C101×#3019C211yesmaximal, characteristic, complemented
6C101×#2955C211yesmaximal, characteristic, complemented
7C101×#2049C211yesmaximal, characteristic, complemented
8C101×#2048C211yesmaximal, characteristic, complemented
9C101×#2009C211yesmaximal, characteristic, complemented
10C101×#2008C211yesmaximal, characteristic, complemented
11C101×#1977C211yesmaximal, characteristic, complemented
12C101×#1976C211yesmaximal, characteristic, complemented
13C101×#1814C211yesmaximal, characteristic, complemented
14C101×#1796C211yesmaximal, characteristic, complemented
15C101×#1795C211yesmaximal, characteristic, complemented
16C2×2−1+4×C101C2211yescharacteristic
17C2×H(5,𝔽2)×C101C2211yescharacteristic
18#577×C101—22no—
19#577×C101—22no—
20#577×C101—22no—
21#577×C101—22no—
22#575×C101C2211yescharacteristic
23#575×C101C2211yescharacteristic
24#575×C101C2211yescharacteristic, complemented
25C2×#137×C101—21no—
26C2×#137×C101C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C101—21no—
28C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
29C2×#135×C101—21no—
30C2×#135×C101C2211yescharacteristic
31C22×SD16×C101—21no—
32C22×SD16×C101C2211yescharacteristic
33C2×#131×C101C2211yescharacteristic
34C2×#131×C101C2211yescharacteristic, complemented
35#536×C101C2211yescharacteristic, complemented
36#535×C101C2211yescharacteristic
37#473×C101—21no—
38#472×C101—21no—
39#471×C101—21no—
40#471×C101—21no—
41#468×C101—22no—
42#465×C101—22no—
43#456×C101—22no—
44#455×C101—22no—
45#454×C101—22no—
46#453×C101—22no—
47#444×C101—22no—
48#443×C101—22no—
49#430×C101C2211yescharacteristic, complemented
50C2×#108×C101C2211yescharacteristic, complemented
51#427×C101C2211yescharacteristic, complemented
52#421×C101C2211yescharacteristic
53#421×C101C2211yescharacteristic
54#421×C101C2211yescharacteristic
55#421×C101C2211yescharacteristic
56#421×C101C2211yescharacteristic, complemented
57#421×C101C2211yescharacteristic, complemented
58#419×C101C2211yescharacteristic, complemented
59#419×C101C2211yescharacteristic, complemented
60#418×C101C2211yescharacteristic
61#418×C101C2211yescharacteristic
62#413×C101C2211yescharacteristic
63#413×C101C2211yescharacteristic, complemented
64C2×#101×C101C2211yescharacteristic, complemented
65C2×#100×C101C2211yescharacteristic
66#410×C101C2211yescharacteristic
67#410×C101C2211yescharacteristic, complemented
68#405×C101C2211yescharacteristic, complemented
69#344×C101C2211yescharacteristic, complemented
70#344×C101C2211yescharacteristic, complemented
712−1+4×C101—22no—
722−1+4×C101—22no—
732−1+4×C101—22no—
742−1+4×C101—41no—
75H(5,𝔽2)×C101—22no—
76H(5,𝔽2)×C101—22no—
77H(5,𝔽2)×C101—22no—
78H(5,𝔽2)×C101—41no—
79C2×#41×C101—21no—
80C2×#41×C101—21no—
81C2×#41×C101—21no—
82C2×#41×C101—21no—
83C2×#41×C101—41no—
84C2×#41×C101C2311yescharacteristic
85C2×#41×C101C2311yescharacteristic
86C2×#41×C101C2311yescharacteristic
87C2×#41×C101C2311yescharacteristic
88C22×Q8×C101—21no—
89C22×Q8×C101—21no—
90C22×Q8×C101C2311yescharacteristic
91C22×D4×C101—21no—
92C22×D4×C101—21no—
93C22×D4×C101—41no—
94C22×D4×C101C2311yescharacteristic
95#137×C101—24no—
96#137×C101—24no—
97#137×C101—22no—
98#137×C101—21no—
99#137×C101—21no—
100#137×C101—21no—
101#137×C101—21no—
102#137×C101—21no—
103#137×C101—22no—
104#137×C101D412yes—
105AGL(1,ℤ/8)×C101—24no—
106AGL(1,ℤ/8)×C101—24no—
107AGL(1,ℤ/8)×C101—22no—
108AGL(1,ℤ/8)×C101—21no—
109AGL(1,ℤ/8)×C101—21no—
110AGL(1,ℤ/8)×C101—21no—
111AGL(1,ℤ/8)×C101—21no—
112AGL(1,ℤ/8)×C101—21no—
113AGL(1,ℤ/8)×C101—22no—
114AGL(1,ℤ/8)×C101D412yes—
115#135×C101—24no—
116#135×C101—24no—
117#135×C101—22no—
118#135×C101—21no—
119#135×C101—21no—
120#135×C101—21no—
121#135×C101—21no—
122#135×C101—41no—
123#135×C101—41no—
124C2×Q16×C101—21no—
125C2×Q16×C101D411yescharacteristic, complemented
126C2×SD16×C101—24no—
127C2×SD16×C101—24no—
128C2×SD16×C101—21no—
129C2×SD16×C101—21no—
130C2×SD16×C101—21no—
131C2×SD16×C101—21no—
132C2×SD16×C101—21no—
133C2×SD16×C101—21no—
134C2×SD16×C101D412yes—
135C2×SD16×C101D412yes—
136C2×SD16×C101D411yescharacteristic, complemented
137C2×SD16×C101D411yescharacteristic, complemented
138C2×D8×C101—21no—
139C2×D8×C101D411yescharacteristic, complemented
140#131×C101—21no—
141#131×C101—21no—
142#131×C101—21no—
143#131×C101—21no—
144#131×C101—21no—
145#131×C101—21no—
146#131×C101D412yescomplemented
147#131×C101D412yescomplemented
148C2×M16×C101—21no—
149C2×M16×C101—21no—
150C2×M16×C101C2311yescharacteristic
151C2×M16×C101C2311yescharacteristic
152C2×M16×C101C2311yescharacteristic
153C2×M16×C101C2311yescharacteristic
154C2×M16×C101C2311yescharacteristic
155C22×C8×C101—21no—
156C22×C8×C101—21no—
157C22×C8×C101C2311yescharacteristic
158C4⋊Q8×C101—21no—
159#127×C101—21no—
160#124×C101—21no—
161#124×C101—21no—
162#123×C101—41no—
163C22⋊Q8×C101—22no—
164#121×C101—22no—
165#120×C101—41no—
166#117×C101C2311yescharacteristic
167#117×C101C2311yescharacteristic
168#117×C101C2311yescharacteristic
169#108×C101—22no—
170#108×C101—21no—
171#108×C101—21no—
172#107×C101—21no—
173#106×C101—21no—
174#104×C101—22no—
175#104×C101—22no—
176#104×C101—22no—
177#104×C101—22no—
178#104×C101—22no—
179#104×C101—22no—
180#103×C101—22no—
181#103×C101—41no—
182#102×C101—22no—
183#102×C101—41no—
184#101×C101—21no—
185#101×C101—21no—
186#101×C101—22no—
187#100×C101—21no—
188#100×C101—21no—
189#100×C101—22no—
190#99×C101—41no—
191#99×C101—41no—
192#97×C101—21no—
193C4×C8×C101—21no—
194C24×C101—21no—
195C24×C101—41no—
196#41×C101—21no—
197#41×C101—21no—
198#41×C101—24no—
199#41×C101—24no—
200#41×C101—21no—
201#41×C101—21no—
202#41×C101—21no—
203#41×C101—21no—
204#41×C101—21no—
205#41×C101—21no—
206#41×C101—21no—
207#41×C101—21no—
208#41×C101—21no—
209#41×C101—21no—
210#41×C101—21no—
211#41×C101—21no—
212#41×C101—42no—
213#41×C101—44no—
214#41×C101—42no—
215#41×C101—42no—
216#41×C101—42no—
217#41×C101—44no—
218#41×C101—42no—
219#41×C101—42no—
220#41×C101C2×D412yes—
221#41×C101C2×D412yes—
222C2×Q8×C101—21no—
223C2×Q8×C101—24no—
224C2×Q8×C101—21no—
225C2×Q8×C101—21no—
226C2×Q8×C101—21no—
227C2×Q8×C101—21no—
228C2×Q8×C101—41no—
229C2×Q8×C101—42no—
230C2×Q8×C101—42no—
231C2×Q8×C101—42no—
232C2×Q8×C101C2×D411yescharacteristic
233C2×Q8×C101C2×D411yescharacteristic
234C2×Q8×C101C2×D412yes—
235C2×Q8×C101C2×D411yescharacteristic
236C2×Q8×C101#4111yescharacteristic
237C2×D4×C101—21no—
238C2×D4×C101—24no—
239C2×D4×C101—21no—
240C2×D4×C101—21no—
241C2×D4×C101—21no—
242C2×D4×C101—21no—
243C2×D4×C101—21no—
244C2×D4×C101—21no—
245C2×D4×C101—21no—
246C2×D4×C101—21no—
247C2×D4×C101—42no—
248C2×D4×C101—41no—
249C2×D4×C101—41no—
250C2×D4×C101—42no—
251C2×D4×C101—44no—
252C2×D4×C101—44no—
253C2×D4×C101—41no—
254C2×D4×C101—42no—
255C2×D4×C101—42no—
256C2×D4×C101C2×D411yescharacteristic
257C2×D4×C101C2×D411yescharacteristic
258C2×D4×C101C2×D412yes—
259C2×D4×C101C2×D411yescharacteristic
260C2×D4×C101#4111yescharacteristic
261C22×C4×C101—21no—
262C22×C4×C101—21no—
263C22×C4×C101—21no—
264C22×C4×C101—21no—
265C22×C4×C101—21no—
266C22×C4×C101—41no—
267C22×C4×C101—41no—
268C22×C4×C101—41no—
269C22×C4×C101C2411yescharacteristic
270Q16×C101—24no—
271Q16×C101—22no—
272Q16×C101—21no—
273Q16×C101—21no—
274Q16×C101—41no—
275Q16×C101—41no—
276SD16×C101—24no—
277SD16×C101—24no—
278SD16×C101—22no—
279SD16×C101—22no—
280SD16×C101—22no—
281SD16×C101—22no—
282SD16×C101—21no—
283SD16×C101—21no—
284SD16×C101—22no—
285SD16×C101—22no—
286SD16×C101—21no—
287SD16×C101—21no—
288SD16×C101—41no—
289SD16×C101—41no—
290SD16×C101—41no—
291SD16×C101—41no—
292D8×C101—24no—
293D8×C101—22no—
294D8×C101—21no—
295D8×C101—21no—
296D8×C101—41no—
297D8×C101—41no—
298M16×C101—21no—
299M16×C101—21no—
300M16×C101—22no—
301M16×C101—22no—
302M16×C101—21no—
303M16×C101—21no—
304M16×C101—21no—
305M16×C101—21no—
306M16×C101—21no—
307M16×C101—21no—
308M16×C101—41no—
309M16×C101—41no—
310M16×C101C2×D412yes—
311M16×C101C2×D412yes—
312C2×C8×C101—21no—
313C2×C8×C101—21no—
314C2×C8×C101—22no—
315C2×C8×C101—22no—
316C2×C8×C101—21no—
317C2×C8×C101—21no—
318C2×C8×C101—21no—
319C2×C8×C101—41no—
320C2×C8×C101—41no—
321C2×C8×C101C2×D411yescharacteristic
322C2×C8×C101C2×D411yescharacteristic
323C2×C8×C101C2×D411yescharacteristic
324C2×C8×C101C2×D411yescharacteristic
325C2×C8×C101C2×D411yescharacteristic
326C2×C8×C101C2×D411yescharacteristic
327C4⋊C4×C101—21no—
328C4⋊C4×C101—21no—
329C4⋊C4×C101—21no—
330C4⋊C4×C101—42no—
331C22⋊C4×C101—21no—
332C22⋊C4×C101—21no—
333C22⋊C4×C101—21no—
334C22⋊C4×C101—42no—
335C22⋊C4×C101—42no—
336C42×C101—21no—
337C42×C101—21no—
338C42×C101—21no—
339C23×C101—21no—
340C23×C101—21no—
341C23×C101—22no—
342C23×C101—21no—
343C23×C101—21no—
344C23×C101—44no—
345C23×C101—41no—
346C23×C101—41no—
347C23×C101—161no—
348C23×C101—162no—
349C23×C101H(5,𝔽2)11yescharacteristic
350Q8×C101—21no—
351Q8×C101—21no—
352Q8×C101—22no—
353Q8×C101—21no—
354Q8×C101—21no—
355Q8×C101—21no—
356Q8×C101—21no—
357Q8×C101—21no—
358Q8×C101—22no—
359Q8×C101—44no—
360Q8×C101—41no—
361Q8×C101—41no—
362Q8×C101#12112yes—
363D4×C101—22no—
364D4×C101—22no—
365D4×C101—21no—
366D4×C101—22no—
367D4×C101—21no—
368D4×C101—21no—
369D4×C101—21no—
370D4×C101—21no—
371D4×C101—21no—
372D4×C101—21no—
373D4×C101—22no—
374D4×C101—44no—
375D4×C101—44no—
376D4×C101—44no—
377D4×C101—41no—
378D4×C101—41no—
379D4×C101—41no—
380D4×C101—41no—
381D4×C101—41no—
382D4×C101—41no—
383D4×C101—41no—
384D4×C101—41no—
385D4×C101—162no—
386D4×C101#12112yes—
387C2×C4×C101—21no—
388C2×C4×C101—22no—
389C2×C4×C101—22no—
390C2×C4×C101—21no—
391C2×C4×C101—22no—
392C2×C4×C101—21no—
393C2×C4×C101—21no—
394C2×C4×C101—44no—
395C2×C4×C101—44no—
396C2×C4×C101—44no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—41no—
400C2×C4×C101—41no—
401C2×C4×C101—41no—
402C2×C4×C101—41no—
403C2×C4×C101—41no—
404C2×C4×C101—41no—
405C2×C4×C101—41no—
406C2×C4×C101—41no—
407C2×C4×C101—41no—
408C2×C4×C101C22×D411yescharacteristic
409C2×C4×C101C22×D411yescharacteristic
410C2×C4×C101C22×D411yescharacteristic
411C2×C4×C101C22×D411yescharacteristic
412C2×C4×C101C2×#4111yescharacteristic
413C2×C4×C101H(5,𝔽2)11yescharacteristic
414C8×C101—22no—
415C8×C101—22no—
416C8×C101—41no—
417C8×C101—41no—
418C8×C101—41no—
419C8×C101#12011yescharacteristic
420C8×C101#12011yescharacteristic
421C8×C101#12011yescharacteristic
422C8×C101#12011yescharacteristic
423C22×C101—22no—
424C22×C101—41no—
425C22×C101—42no—
426C22×C101—42no—
427C22×C101—41no—
428C22×C101—42no—
429C22×C101—41no—
430C22×C101—41no—
431C22×C101—82no—
432C22×C101—81no—
433C22×C101—81no—
434C22×C101—82no—
435C22×C101—161no—
436C22×C101—164no—
437C22×C101#53511yescharacteristic
438C22×C101D4211yescharacteristic
439C22×C101#54611yescharacteristic
440C4×C101—22no—
441C4×C101—41no—
442C4×C101—42no—
443C4×C101—41no—
444C4×C101—41no—
445C4×C101—81no—
446C4×C101—81no—
447C4×C101—81no—
448C4×C101C2×#12011yescharacteristic
449C4×C101C2×#12111yescharacteristic
450C4×C101D4211yescharacteristic
451C4×C101#54611yescharacteristic
452#24295C10111yesmaximal, characteristic, direct product factor, Sylow
453C2×C101—21no—
454C2×C101—21no—
455C2×C101—21no—
456C2×C101—42no—
457C2×C101—81no—
458C2×C101—81no—
459C2×C101—82no—
460C2×C101—81no—
461C2×C101#240811yescharacteristic
462C2×#577C2×C10111yescharacteristic, complemented
463#3067C2×C10111yescharacteristic, complemented
464#3057C2×C10111yescharacteristic, complemented
465#3020C2×C10111yescharacteristic, complemented
466#3019C2×C10111yescharacteristic, complemented
467#2955C2×C10111yescharacteristic, complemented
468#2049C2×C10111yescharacteristic, complemented
469#2048C2×C10111yescharacteristic, complemented
470#2009C2×C10111yescharacteristic, complemented
471#2008C2×C10111yescharacteristic, complemented
472#1977C2×C10111yescharacteristic, complemented
473#1976C2×C10111yescharacteristic, complemented
474#1814C2×C10111yescharacteristic, complemented
475#1796C2×C10111yescharacteristic, complemented
476#1795C2×C10111yescharacteristic, complemented
477C101#2429511yescharacteristic, direct product factor, Sylow
478C2×2−1+4C22×C10111yescharacteristic
479C2×H(5,𝔽2)C22×C10111yescharacteristic
480#577—22no—
481#577—22no—
482#577—22no—
483#577—22no—
484#575C22×C10111yescharacteristic
485#575C22×C10111yescharacteristic
486#575C22×C10111yescharacteristic, complemented
487C2×#137—21no—
488C2×#137C22×C10111yescharacteristic
489C2×AGL(1,ℤ/8)—21no—
490C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
491C2×#135—21no—
492C2×#135C22×C10111yescharacteristic
493C22×SD16—21no—
494C22×SD16C22×C10111yescharacteristic
495C2×#131C22×C10111yescharacteristic
496C2×#131C22×C10111yescharacteristic, complemented
497#536C22×C10111yescharacteristic, complemented
498#535C22×C10111yescharacteristic
499#473—21no—
500#472—21no—
501#471—21no—
502#471—21no—
503#468—22no—
504#465—22no—
505#456—22no—
506#455—22no—
507#454—22no—
508#453—22no—
509#444—22no—
510#443—22no—
511#430C22×C10111yescharacteristic, complemented
512C2×#108C22×C10111yescharacteristic, complemented
513#427C22×C10111yescharacteristic, complemented
514#421C22×C10111yescharacteristic
515#421C22×C10111yescharacteristic
516#421C22×C10111yescharacteristic
517#421C22×C10111yescharacteristic
518#421C22×C10111yescharacteristic, complemented
519#421C22×C10111yescharacteristic, complemented
520#419C22×C10111yescharacteristic, complemented
521#419C22×C10111yescharacteristic, complemented
522#418C22×C10111yescharacteristic
523#418C22×C10111yescharacteristic
524#413C22×C10111yescharacteristic
525#413C22×C10111yescharacteristic, complemented
526C2×#101C22×C10111yescharacteristic, complemented
527C2×#100C22×C10111yescharacteristic
528#410C22×C10111yescharacteristic
529#410C22×C10111yescharacteristic, complemented
530#405C22×C10111yescharacteristic, complemented
531#344C22×C10111yescharacteristic, complemented
532#344C22×C10111yescharacteristic, complemented
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C10111yescharacteristic
547C2×#41C23×C10111yescharacteristic
548C2×#41C23×C10111yescharacteristic
549C2×#41C23×C10111yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C10111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C10111yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C10112yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C10112yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C10111yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C10112yes—
597C2×SD16D4×C10112yes—
598C2×SD16D4×C10111yescharacteristic, complemented
599C2×SD16D4×C10111yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C10111yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C10112yescomplemented
609#131D4×C10112yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C10111yescharacteristic
613C2×M16C23×C10111yescharacteristic
614C2×M16C23×C10111yescharacteristic
615C2×M16C23×C10111yescharacteristic
616C2×M16C23×C10111yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C10111yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C10111yescharacteristic
629#117C23×C10111yescharacteristic
630#117C23×C10111yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C10112yes—
683#41C2×D4×C10112yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C10111yescharacteristic
695C2×Q8C2×D4×C10111yescharacteristic
696C2×Q8C2×D4×C10112yes—
697C2×Q8C2×D4×C10111yescharacteristic
698C2×Q8#41×C10111yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C10111yescharacteristic
719C2×D4C2×D4×C10111yescharacteristic
720C2×D4C2×D4×C10112yes—
721C2×D4C2×D4×C10111yescharacteristic
722C2×D4#41×C10111yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C10111yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C10112yes—
773M16C2×D4×C10112yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C10111yescharacteristic
784C2×C8C2×D4×C10111yescharacteristic
785C2×C8C2×D4×C10111yescharacteristic
786C2×C8C2×D4×C10111yescharacteristic
787C2×C8C2×D4×C10111yescharacteristic
788C2×C8C2×D4×C10111yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C10111yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—21no—
816Q8—21no—
817Q8—21no—
818Q8—21no—
819Q8—21no—
820Q8—22no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C10112yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—22no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C10112yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C10111yescharacteristic
871C2×C4C22×D4×C10111yescharacteristic
872C2×C4C22×D4×C10111yescharacteristic
873C2×C4C22×D4×C10111yescharacteristic
874C2×C4C2×#41×C10111yescharacteristic
875C2×C4H(5,𝔽2)×C10111yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C10111yescharacteristic
882C8#120×C10111yescharacteristic
883C8#120×C10111yescharacteristic
884C8#120×C10111yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22#535×C10111yescharacteristic
900C22D42×C10111yescharacteristic
901C22#546×C10111yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C10111yescharacteristic
911C4C2×#121×C10111yescharacteristic
912C4D42×C10111yescharacteristic
913C4#546×C10111yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2C101×#240811yescharacteristic
subgroupG/H
center, socleC2×C101#2408
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. C2×#577×C101C2semidirect
2. C101×#3067C2semidirect
3. C101×#3057C2semidirect
4. C101×#3020C2semidirect
5. C101×#3019C2semidirect
6. C101×#2955C2semidirect
7. C101×#2049C2semidirect
8. C101×#2048C2semidirect
9. C101×#2009C2semidirect
10. C101×#2008C2semidirect
11. C101×#1977C2semidirect
12. C101×#1976C2semidirect
13. C101×#1814C2semidirect
14. C101×#1796C2semidirect
15. C101×#1795C2semidirect
24. #575×C101C22semidirect
34. C2×#131×C101C22semidirect
35. #536×C101C22semidirect
49. #430×C101C22semidirect
50. C2×#108×C101C22semidirect
51. #427×C101C22semidirect
56. #421×C101C22semidirect
57. #421×C101C22semidirect
58. #419×C101C22semidirect
59. #419×C101C22semidirect
63. #413×C101C22semidirect
64. C2×#101×C101C22semidirect
67. #410×C101C22semidirect
68. #405×C101C22semidirect
69. #344×C101C22semidirect
70. #344×C101C22semidirect
125. C2×Q16×C101D4semidirect
136. C2×SD16×C101D4semidirect
137. C2×SD16×C101D4semidirect
139. C2×D8×C101D4semidirect
146. #131×C101D4semidirect
147. #131×C101D4semidirect
452. #24295C101direct (N × H)
462. C2×#577C2×C101semidirect
463. #3067C2×C101semidirect
464. #3057C2×C101semidirect
465. #3020C2×C101semidirect
466. #3019C2×C101semidirect
467. #2955C2×C101semidirect
468. #2049C2×C101semidirect
469. #2048C2×C101semidirect
470. #2009C2×C101semidirect
471. #2008C2×C101semidirect
472. #1977C2×C101semidirect
473. #1976C2×C101semidirect
474. #1814C2×C101semidirect
475. #1796C2×C101semidirect
476. #1795C2×C101semidirect
477. C101#24295direct (N × H)
486. #575C22×C101semidirect
496. C2×#131C22×C101semidirect
497. #536C22×C101semidirect
511. #430C22×C101semidirect
512. C2×#108C22×C101semidirect
513. #427C22×C101semidirect
518. #421C22×C101semidirect
519. #421C22×C101semidirect
520. #419C22×C101semidirect
521. #419C22×C101semidirect
525. #413C22×C101semidirect
526. C2×#101C22×C101semidirect
529. #410C22×C101semidirect
530. #405C22×C101semidirect
531. #344C22×C101semidirect
532. #344C22×C101semidirect
587. C2×Q16D4×C101semidirect
598. C2×SD16D4×C101semidirect
599. C2×SD16D4×C101semidirect
601. C2×D8D4×C101semidirect
608. #131D4×C101semidirect
609. #131D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1012
C101×#30672
C101×#30572
C101×#30202
C101×#30192
C101×#29552
C101×#20492
C101×#20482
C101×#20092
C101×#20082
C101×#19772
C101×#19762
C101×#18142
C101×#17962
C101×#17952
#24295101