Finite Group Databasebeta

← C101×#24457 #38806608

Subgroups — C101×#24457 #38806608

Order 25856.

1376 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C101C211yesmaximal, characteristic, complemented
2C2×#471×C101C211yesmaximal, characteristic, complemented
3C101×#3045C211yesmaximal, characteristic, complemented
4C2×#453×C101C211yesmaximal, characteristic, complemented
5C101×#3010C211yesmaximal, characteristic, complemented
6C101×#2897C211yesmaximal, characteristic, complemented
7C101×#2051C211yesmaximal, characteristic, complemented
8C101×#2046C211yesmaximal, characteristic, complemented
9C101×#2014C211yesmaximal, characteristic, complemented
10C101×#2002C211yesmaximal, characteristic, complemented
11C101×#1907C211yesmaximal, characteristic, complemented
12C101×#1882C211yesmaximal, characteristic, complemented
13C101×#1876C211yesmaximal, characteristic, complemented
14C101×#1866C211yesmaximal, characteristic, complemented
15C101×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C101C2211yescharacteristic
17C2×H(5,𝔽2)×C101C2211yescharacteristic
18#577×C101—24no—
19#577×C101—24no—
20C2×#137×C101—21no—
21C2×#137×C101C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C101—21no—
23C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
26C2×#135×C101—21no—
27C2×#135×C101C2211yescharacteristic
28C22×SD16×C101—21no—
29C22×SD16×C101C2211yescharacteristic
30C22×SD16×C101C2211yescharacteristic, complemented
31C2×#131×C101C2211yescharacteristic
32C2×#131×C101C2211yescharacteristic
33#535×C101C2211yescharacteristic, complemented
34C2×#127×C101C2211yescharacteristic
35#520×C101C2211yescharacteristic
36#471×C101—24no—
37#464×C101—21no—
38#463×C101—21no—
39#460×C101—21no—
40#459×C101—21no—
41#453×C101—24no—
42#449×C101—21no—
43#449×C101—21no—
44#448×C101—21no—
45#448×C101—21no—
46C2×#108×C101C2211yescharacteristic, complemented
47#424×C101C2211yescharacteristic, complemented
48C2×#104×C101C2211yescharacteristic
49C2×#104×C101C2211yescharacteristic
50C2×#104×C101C2211yescharacteristic, complemented
51#419×C101C2211yescharacteristic, complemented
52#418×C101—21no—
53#418×C101C2211yescharacteristic
54#417×C101—21no—
55#417×C101C2211yescharacteristic
56#417×C101C2211yescharacteristic, complemented
57#416×C101—21no—
58#416×C101C2211yescharacteristic
59C2×#102×C101—21no—
60C2×#102×C101C2211yescharacteristic
61C2×#102×C101C2211yescharacteristic, complemented
62C2×#101×C101C2211yescharacteristic, complemented
63C2×#100×C101C2211yescharacteristic
64C2×#100×C101C2211yescharacteristic, complemented
65#408×C101C2211yescharacteristic, complemented
66#391×C101C2211yescharacteristic, complemented
67#343×C101C2211yescharacteristic, complemented
68#341×C101C2211yescharacteristic, complemented
69#339×C101C2211yescharacteristic, complemented
70#336×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—41no—
78H(5,𝔽2)×C101D414yescomplemented
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
87C22×Q8×C101—21no—
88C22×Q8×C101—21no—
89C22×Q8×C101C2311yescharacteristic
90C22×D4×C101—21no—
91C22×D4×C101—21no—
92C22×D4×C101—41no—
93C22×D4×C101—41no—
94C22×D4×C101C2311yescharacteristic
95C22×D4×C101C2311yescharacteristic
96#137×C101—28no—
97#137×C101—22no—
98#137×C101D414yescomplemented
99AGL(1,ℤ/8)×C101—28no—
100AGL(1,ℤ/8)×C101—22no—
101AGL(1,ℤ/8)×C101—22no—
102AGL(1,ℤ/8)×C101—22no—
103AGL(1,ℤ/8)×C101—22no—
104AGL(1,ℤ/8)×C101—22no—
105AGL(1,ℤ/8)×C101—22no—
106#135×C101—28no—
107#135×C101—22no—
108#135×C101—22no—
109C2×Q16×C101—21no—
110C2×Q16×C101D411yescharacteristic, complemented
111C2×SD16×C101—28no—
112C2×SD16×C101—21no—
113C2×SD16×C101—22no—
114C2×SD16×C101—21no—
115C2×SD16×C101—22no—
116C2×SD16×C101—21no—
117C2×SD16×C101—21no—
118C2×SD16×C101—22no—
119C2×SD16×C101—21no—
120C2×SD16×C101—21no—
121C2×SD16×C101—21no—
122C2×SD16×C101—21no—
123C2×SD16×C101—41no—
124C2×SD16×C101D411yescharacteristic, complemented
125C2×SD16×C101D411yescharacteristic, complemented
126C2×D8×C101—21no—
127C2×D8×C101—21no—
128C2×D8×C101—21no—
129C2×D8×C101D411yescharacteristic, complemented
130#131×C101—22no—
131#131×C101—22no—
132#131×C101—22no—
133#131×C101—41no—
134C2×M16×C101—21no—
135C2×M16×C101—21no—
136C2×M16×C101C2311yescharacteristic
137C2×M16×C101C2311yescharacteristic
138C2×M16×C101C2311yescharacteristic
139C2×M16×C101C2311yescharacteristic
140C22×C8×C101—21no—
141C22×C8×C101—21no—
142C22×C8×C101C2311yescharacteristic
143C22×C8×C101C2311yescharacteristic
144#127×C101—22no—
145#127×C101—21no—
146#127×C101—41no—
147#124×C101—21no—
148#121×C101—21no—
149#121×C101—21no—
150#120×C101—41no—
151C4×Q8×C101—21no—
152C4×D4×C101—21no—
153C4×D4×C101—41no—
154#117×C101—21no—
155#117×C101C2311yescharacteristic
156C2×C4⋊C4×C101—21no—
157C2×C4⋊C4×C101C2311yescharacteristic
158C2×C42×C101C2311yescharacteristic
159#108×C101—22no—
160C4⋊C8×C101—21no—
161C4⋊C8×C101—21no—
162#104×C101—22no—
163#104×C101—22no—
164#104×C101—41no—
165#103×C101—21no—
166#103×C101—21no—
167#103×C101—21no—
168#103×C101—21no—
169#103×C101D411yescharacteristic, complemented
170#103×C101D411yescharacteristic, complemented
171#102×C101—21no—
172#102×C101—21no—
173#102×C101—21no—
174#102×C101—21no—
175#102×C101—21no—
176#102×C101—21no—
177#102×C101—21no—
178#102×C101—21no—
179#102×C101D411yescharacteristic, complemented
180#102×C101D411yescharacteristic, complemented
181#101×C101—22no—
182#100×C101—22no—
183#100×C101—22no—
184C22⋊C8×C101—21no—
185C22⋊C8×C101—21no—
186#95×C101—41no—
187C24×C101—21no—
188C24×C101—21no—
189C24×C101—41no—
190#41×C101—21no—
191#41×C101—21no—
192#41×C101—21no—
193#41×C101—21no—
194#41×C101—24no—
195#41×C101—24no—
196#41×C101—24no—
197#41×C101—21no—
198#41×C101—21no—
199#41×C101—21no—
200#41×C101—21no—
201#41×C101—42no—
202#41×C101—44no—
203#41×C101—42no—
204#41×C101—42no—
205#41×C101—42no—
206#41×C101—44no—
207#41×C101—42no—
208#41×C101C2×D412yes—
209#41×C101C2×D412yes—
210#41×C101C2×D412yes—
211#41×C101#4112yes—
212C2×Q8×C101—21no—
213C2×Q8×C101—24no—
214C2×Q8×C101—21no—
215C2×Q8×C101—21no—
216C2×Q8×C101—21no—
217C2×Q8×C101—21no—
218C2×Q8×C101—41no—
219C2×Q8×C101—42no—
220C2×Q8×C101—42no—
221C2×Q8×C101—42no—
222C2×Q8×C101C2×D412yes—
223C2×Q8×C101C2×D411yescharacteristic
224C2×Q8×C101C2×D411yescharacteristic
225C2×Q8×C101C2×D411yescharacteristic
226C2×D4×C101—21no—
227C2×D4×C101—21no—
228C2×D4×C101—24no—
229C2×D4×C101—24no—
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—21no—
239C2×D4×C101—21no—
240C2×D4×C101—21no—
241C2×D4×C101—21no—
242C2×D4×C101—42no—
243C2×D4×C101—42no—
244C2×D4×C101—41no—
245C2×D4×C101—41no—
246C2×D4×C101—41no—
247C2×D4×C101—41no—
248C2×D4×C101—44no—
249C2×D4×C101—44no—
250C2×D4×C101—41no—
251C2×D4×C101—44no—
252C2×D4×C101—82no—
253C2×D4×C101—82no—
254C2×D4×C101C2×D412yes—
255C2×D4×C101C2×D411yescharacteristic
256C2×D4×C101C2×D411yescharacteristic
257C2×D4×C101C2×D411yescharacteristic
258C22×C4×C101—21no—
259C22×C4×C101—21no—
260C22×C4×C101—21no—
261C22×C4×C101—21no—
262C22×C4×C101—21no—
263C22×C4×C101—21no—
264C22×C4×C101—41no—
265C22×C4×C101—41no—
266C22×C4×C101—41no—
267C22×C4×C101—41no—
268C22×C4×C101C2411yescharacteristic
269Q16×C101—24no—
270Q16×C101—22no—
271SD16×C101—24no—
272SD16×C101—24no—
273SD16×C101—24no—
274SD16×C101—22no—
275SD16×C101—22no—
276SD16×C101—24no—
277SD16×C101—42no—
278SD16×C101—42no—
279SD16×C101—42no—
280SD16×C101—42no—
281D8×C101—24no—
282D8×C101—22no—
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—42no—
294M16×C101C2×D412yes—
295C2×C8×C101—24no—
296C2×C8×C101—21no—
297C2×C8×C101—21no—
298C2×C8×C101—21no—
299C2×C8×C101—21no—
300C2×C8×C101—21no—
301C2×C8×C101—21no—
302C2×C8×C101—21no—
303C2×C8×C101—21no—
304C2×C8×C101—42no—
305C2×C8×C101C2×D411yescharacteristic
306C2×C8×C101C2×D411yescharacteristic
307C2×C8×C101C2×D411yescharacteristic
308C2×C8×C101C2×D411yescharacteristic
309C4⋊C4×C101—21no—
310C4⋊C4×C101—21no—
311C4⋊C4×C101—41no—
312C4⋊C4×C101C2×D411yescharacteristic
313C4⋊C4×C101C2×D411yescharacteristic
314C22⋊C4×C101—21no—
315C22⋊C4×C101—41no—
316C22⋊C4×C101—41no—
317C22⋊C4×C101—41no—
318C42×C101—21no—
319C42×C101—21no—
320C42×C101—21no—
321C42×C101—41no—
322C23×C101—21no—
323C23×C101—21no—
324C23×C101—21no—
325C23×C101—22no—
326C23×C101—44no—
327C23×C101—41no—
328C23×C101—41no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—81no—
333C23×C101—81no—
334C23×C101—81no—
335C23×C101—81no—
336C23×C101—161no—
337C23×C101—161no—
338C23×C101H(5,𝔽2)11yescharacteristic
339Q8×C101—21no—
340Q8×C101—21no—
341Q8×C101—22no—
342Q8×C101—21no—
343Q8×C101—22no—
344Q8×C101—21no—
345Q8×C101—44no—
346Q8×C101—41no—
347Q8×C101—41no—
348Q8×C101#12012yes—
349Q8×C101#12112yes—
350D4×C101—22no—
351D4×C101—22no—
352D4×C101—22no—
353D4×C101—22no—
354D4×C101—21no—
355D4×C101—22no—
356D4×C101—22no—
357D4×C101—21no—
358D4×C101—21no—
359D4×C101—21no—
360D4×C101—44no—
361D4×C101—44no—
362D4×C101—44no—
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—88no—
372D4×C101—161no—
373D4×C101—161no—
374D4×C101#12012yes—
375D4×C101#12112yes—
376C2×C4×C101—21no—
377C2×C4×C101—21no—
378C2×C4×C101—22no—
379C2×C4×C101—22no—
380C2×C4×C101—22no—
381C2×C4×C101—22no—
382C2×C4×C101—22no—
383C2×C4×C101—21no—
384C2×C4×C101—21no—
385C2×C4×C101—21no—
386C2×C4×C101—22no—
387C2×C4×C101—44no—
388C2×C4×C101—44no—
389C2×C4×C101—41no—
390C2×C4×C101—44no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—81no—
398C2×C4×C101—161no—
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—21no—
406C8×C101—22no—
407C8×C101—21no—
408C8×C101—21no—
409C8×C101—21no—
410C8×C101—41no—
411C8×C101—41no—
412C8×C101—41no—
413C22×C101—21no—
414C22×C101—21no—
415C22×C101—22no—
416C22×C101—22no—
417C22×C101—41no—
418C22×C101—41no—
419C22×C101—41no—
420C22×C101—41no—
421C22×C101—41no—
422C22×C101—42no—
423C22×C101—41no—
424C22×C101—41no—
425C22×C101—82no—
426C22×C101—82no—
427C22×C101—81no—
428C22×C101—81no—
429C22×C101—81no—
430C22×C101—81no—
431C22×C101—81no—
432C22×C101—161no—
433C22×C101—161no—
434C22×C101—164no—
435C22×C101#53411yescharacteristic
436C22×C101D4211yescharacteristic
437C22×C101#54611yescharacteristic
438C4×C101—22no—
439C4×C101—22no—
440C4×C101—42no—
441C4×C101—41no—
442C4×C101—42no—
443C4×C101—41no—
444C4×C101—41no—
445C4×C101—81no—
446C4×C101C2×#12011yescharacteristic
447C4×C101C2×#12111yescharacteristic
448C4×C101D4211yescharacteristic
449C4×C101#54611yescharacteristic
450#24457C10111yesmaximal, characteristic, direct product factor, Sylow
451C2×C101—21no—
452C2×C101—21no—
453C2×C101—42no—
454C2×C101—42no—
455C2×C101—81no—
456C2×C101—82no—
457C2×C101—161no—
458C2×C101#241011yescharacteristic
459C2×C101#328811yescharacteristic
460C2×C101#329111yescharacteristic
461C2×#577C2×C10111yescharacteristic, complemented
462C2×#471C2×C10111yescharacteristic, complemented
463#3045C2×C10111yescharacteristic, complemented
464C2×#453C2×C10111yescharacteristic, complemented
465#3010C2×C10111yescharacteristic, complemented
466#2897C2×C10111yescharacteristic, complemented
467#2051C2×C10111yescharacteristic, complemented
468#2046C2×C10111yescharacteristic, complemented
469#2014C2×C10111yescharacteristic, complemented
470#2002C2×C10111yescharacteristic, complemented
471#1907C2×C10111yescharacteristic, complemented
472#1882C2×C10111yescharacteristic, complemented
473#1876C2×C10111yescharacteristic, complemented
474#1866C2×C10111yescharacteristic, complemented
475#1793C2×C10111yescharacteristic, complemented
476C101#2445711yescharacteristic, direct product factor, Sylow
477C2×2−1+4C22×C10111yescharacteristic
478C2×H(5,𝔽2)C22×C10111yescharacteristic
479#577—24no—
480#577—24no—
481C2×#137—21no—
482C2×#137C22×C10111yescharacteristic
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
485C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
486C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
487C2×#135—21no—
488C2×#135C22×C10111yescharacteristic
489C22×SD16—21no—
490C22×SD16C22×C10111yescharacteristic
491C22×SD16C22×C10111yescharacteristic, complemented
492C2×#131C22×C10111yescharacteristic
493C2×#131C22×C10111yescharacteristic
494#535C22×C10111yescharacteristic, complemented
495C2×#127C22×C10111yescharacteristic
496#520C22×C10111yescharacteristic
497#471—24no—
498#464—21no—
499#463—21no—
500#460—21no—
501#459—21no—
502#453—24no—
503#449—21no—
504#449—21no—
505#448—21no—
506#448—21no—
507C2×#108C22×C10111yescharacteristic, complemented
508#424C22×C10111yescharacteristic, complemented
509C2×#104C22×C10111yescharacteristic
510C2×#104C22×C10111yescharacteristic
511C2×#104C22×C10111yescharacteristic, complemented
512#419C22×C10111yescharacteristic, complemented
513#418—21no—
514#418C22×C10111yescharacteristic
515#417—21no—
516#417C22×C10111yescharacteristic
517#417C22×C10111yescharacteristic, complemented
518#416—21no—
519#416C22×C10111yescharacteristic
520C2×#102—21no—
521C2×#102C22×C10111yescharacteristic
522C2×#102C22×C10111yescharacteristic, complemented
523C2×#101C22×C10111yescharacteristic, complemented
524C2×#100C22×C10111yescharacteristic
525C2×#100C22×C10111yescharacteristic, complemented
526#408C22×C10111yescharacteristic, complemented
527#391C22×C10111yescharacteristic, complemented
528#343C22×C10111yescharacteristic, complemented
529#341C22×C10111yescharacteristic, complemented
530#339C22×C10111yescharacteristic, complemented
531#336C22×C10111yescharacteristic, complemented
5322−1+4—22no—
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—41no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—41no—
539H(5,𝔽2)D4×C10114yescomplemented
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—41no—
545C2×#41C23×C10111yescharacteristic
546C2×#41C23×C10111yescharacteristic
547C2×#41C23×C10111yescharacteristic
548C22×Q8—21no—
549C22×Q8—21no—
550C22×Q8C23×C10111yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4—41no—
555C22×D4C23×C10111yescharacteristic
556C22×D4C23×C10111yescharacteristic
557#137—28no—
558#137—22no—
559#137D4×C10114yescomplemented
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567#135—28no—
568#135—22no—
569#135—22no—
570C2×Q16—21no—
571C2×Q16D4×C10111yescharacteristic, complemented
572C2×SD16—28no—
573C2×SD16—21no—
574C2×SD16—22no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16—21no—
581C2×SD16—21no—
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—41no—
585C2×SD16D4×C10111yescharacteristic, complemented
586C2×SD16D4×C10111yescharacteristic, complemented
587C2×D8—21no—
588C2×D8—21no—
589C2×D8—21no—
590C2×D8D4×C10111yescharacteristic, complemented
591#131—22no—
592#131—22no—
593#131—22no—
594#131—41no—
595C2×M16—21no—
596C2×M16—21no—
597C2×M16C23×C10111yescharacteristic
598C2×M16C23×C10111yescharacteristic
599C2×M16C23×C10111yescharacteristic
600C2×M16C23×C10111yescharacteristic
601C22×C8—21no—
602C22×C8—21no—
603C22×C8C23×C10111yescharacteristic
604C22×C8C23×C10111yescharacteristic
605#127—22no—
606#127—21no—
607#127—41no—
608#124—21no—
609#121—21no—
610#121—21no—
611#120—41no—
612C4×Q8—21no—
613C4×D4—21no—
614C4×D4—41no—
615#117—21no—
616#117C23×C10111yescharacteristic
617C2×C4⋊C4—21no—
618C2×C4⋊C4C23×C10111yescharacteristic
619C2×C42C23×C10111yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C10111yescharacteristic, complemented
631#103D4×C10111yescharacteristic, complemented
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C10111yescharacteristic, complemented
641#102D4×C10111yescharacteristic, complemented
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647#95—41no—
648C24—21no—
649C24—21no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—44no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41—44no—
668#41—42no—
669#41C2×D4×C10112yes—
670#41C2×D4×C10112yes—
671#41C2×D4×C10112yes—
672#41#41×C10112yes—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—41no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8C2×D4×C10112yes—
684C2×Q8C2×D4×C10111yescharacteristic
685C2×Q8C2×D4×C10111yescharacteristic
686C2×Q8C2×D4×C10111yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—41no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—41no—
712C2×D4—44no—
713C2×D4—82no—
714C2×D4—82no—
715C2×D4C2×D4×C10112yes—
716C2×D4C2×D4×C10111yescharacteristic
717C2×D4C2×D4×C10111yescharacteristic
718C2×D4C2×D4×C10111yescharacteristic
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4C24×C10111yescharacteristic
730Q16—24no—
731Q16—22no—
732SD16—24no—
733SD16—24no—
734SD16—24no—
735SD16—22no—
736SD16—22no—
737SD16—24no—
738SD16—42no—
739SD16—42no—
740SD16—42no—
741SD16—42no—
742D8—24no—
743D8—22no—
744D8—42no—
745D8—42no—
746M16—24no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—21no—
753M16—21no—
754M16—42no—
755M16C2×D4×C10112yes—
756C2×C8—24no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—42no—
766C2×C8C2×D4×C10111yescharacteristic
767C2×C8C2×D4×C10111yescharacteristic
768C2×C8C2×D4×C10111yescharacteristic
769C2×C8C2×D4×C10111yescharacteristic
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—41no—
773C4⋊C4C2×D4×C10111yescharacteristic
774C4⋊C4C2×D4×C10111yescharacteristic
775C22⋊C4—21no—
776C22⋊C4—41no—
777C22⋊C4—41no—
778C22⋊C4—41no—
779C42—21no—
780C42—21no—
781C42—21no—
782C42—41no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—81no—
797C23—161no—
798C23—161no—
799C23H(5,𝔽2)×C10111yescharacteristic
800Q8—21no—
801Q8—21no—
802Q8—22no—
803Q8—21no—
804Q8—22no—
805Q8—21no—
806Q8—44no—
807Q8—41no—
808Q8—41no—
809Q8#120×C10112yes—
810Q8#121×C10112yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—21no—
816D4—22no—
817D4—22no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—88no—
833D4—161no—
834D4—161no—
835D4#120×C10112yes—
836D4#121×C10112yes—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—41no—
851C2×C4—44no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—81no—
859C2×C4—161no—
860C2×C4C22×D4×C10111yescharacteristic
861C2×C4C22×D4×C10111yescharacteristic
862C2×C4C22×D4×C10111yescharacteristic
863C2×C4C22×D4×C10111yescharacteristic
864C2×C4C2×#41×C10111yescharacteristic
865C2×C4H(5,𝔽2)×C10111yescharacteristic
866C8—21no—
867C8—22no—
868C8—21no—
869C8—21no—
870C8—21no—
871C8—41no—
872C8—41no—
873C8—41no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—22no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—82no—
887C22—82no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—161no—
894C22—161no—
895C22—164no—
896C22#534×C10111yescharacteristic
897C22D42×C10111yescharacteristic
898C22#546×C10111yescharacteristic
899C4—22no—
900C4—22no—
901C4—42no—
902C4—41no—
903C4—42no—
904C4—41no—
905C4—41no—
906C4—81no—
907C4C2×#120×C10111yescharacteristic
908C4C2×#121×C10111yescharacteristic
909C4D42×C10111yescharacteristic
910C4#546×C10111yescharacteristic
911C2—21no—
912C2—21no—
913C2—42no—
914C2—42no—
915C2—81no—
916C2—82no—
917C2—161no—
918C2C101×#241011yescharacteristic
919C2C101×#328811yescharacteristic
920C2C101×#329111yescharacteristic
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. C2×#577×C101C2semidirect
2. C2×#471×C101C2semidirect
3. C101×#3045C2semidirect
4. C2×#453×C101C2semidirect
5. C101×#3010C2semidirect
6. C101×#2897C2semidirect
7. C101×#2051C2semidirect
8. C101×#2046C2semidirect
9. C101×#2014C2semidirect
10. C101×#2002C2semidirect
11. C101×#1907C2semidirect
12. C101×#1882C2semidirect
13. C101×#1876C2semidirect
14. C101×#1866C2semidirect
15. C101×#1793C2semidirect
30. C22×SD16×C101C22semidirect
33. #535×C101C22semidirect
46. C2×#108×C101C22semidirect
47. #424×C101C22semidirect
50. C2×#104×C101C22semidirect
51. #419×C101C22semidirect
56. #417×C101C22semidirect
61. C2×#102×C101C22semidirect
62. C2×#101×C101C22semidirect
64. C2×#100×C101C22semidirect
65. #408×C101C22semidirect
66. #391×C101C22semidirect
67. #343×C101C22semidirect
68. #341×C101C22semidirect
69. #339×C101C22semidirect
70. #336×C101C22semidirect
78. H(5,𝔽2)×C101D4semidirect
98. #137×C101D4semidirect
110. C2×Q16×C101D4semidirect
124. C2×SD16×C101D4semidirect
125. C2×SD16×C101D4semidirect
129. C2×D8×C101D4semidirect
169. #103×C101D4semidirect
170. #103×C101D4semidirect
179. #102×C101D4semidirect
180. #102×C101D4semidirect
450. #24457C101direct (N × H)
461. C2×#577C2×C101semidirect
462. C2×#471C2×C101semidirect
463. #3045C2×C101semidirect
464. C2×#453C2×C101semidirect
465. #3010C2×C101semidirect
466. #2897C2×C101semidirect
467. #2051C2×C101semidirect
468. #2046C2×C101semidirect
469. #2014C2×C101semidirect
470. #2002C2×C101semidirect
471. #1907C2×C101semidirect
472. #1882C2×C101semidirect
473. #1876C2×C101semidirect
474. #1866C2×C101semidirect
475. #1793C2×C101semidirect
476. C101#24457direct (N × H)
491. C22×SD16C22×C101semidirect
494. #535C22×C101semidirect
507. C2×#108C22×C101semidirect
508. #424C22×C101semidirect
511. C2×#104C22×C101semidirect
512. #419C22×C101semidirect
517. #417C22×C101semidirect
522. C2×#102C22×C101semidirect
523. C2×#101C22×C101semidirect
525. C2×#100C22×C101semidirect
526. #408C22×C101semidirect
527. #391C22×C101semidirect
528. #343C22×C101semidirect
529. #341C22×C101semidirect
530. #339C22×C101semidirect
531. #336C22×C101semidirect
539. H(5,𝔽2)D4×C101semidirect
559. #137D4×C101semidirect
571. C2×Q16D4×C101semidirect
585. C2×SD16D4×C101semidirect
586. C2×SD16D4×C101semidirect
590. C2×D8D4×C101semidirect
630. #103D4×C101semidirect
631. #103D4×C101semidirect
640. #102D4×C101semidirect
641. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1012
C2×#471×C1012
C101×#30452
C2×#453×C1012
C101×#30102
C101×#28972
C101×#20512
C101×#20462
C101×#20142
C101×#20022
C101×#19072
C101×#18822
C101×#18762
C101×#18662
C101×#17932
#24457101