Finite Group Databasebeta

← C101×#25180 #38807331

Subgroups — C101×#25180 #38807331

Order 25856.

1074 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C101C211yesmaximal, characteristic, complemented
2C101×#3041C211yesmaximal, characteristic, complemented
3C2×#453×C101C211yesmaximal, characteristic, complemented
4C101×#3008C211yesmaximal, characteristic, complemented
5C101×#2946C211yesmaximal, characteristic, complemented
6C101×#2897C211yesmaximal, characteristic, complemented
7C101×#2063C211yesmaximal, characteristic, complemented
8C101×#2051C211yesmaximal, characteristic, complemented
9C101×#2037C211yesmaximal, characteristic, complemented
10C101×#2011C211yesmaximal, characteristic, complemented
11C101×#1978C211yesmaximal, characteristic, complemented
12C101×#1929C211yesmaximal, characteristic, complemented
13C101×#1887C211yesmaximal, characteristic, complemented
14C101×#1883C211yesmaximal, characteristic, complemented
15C101×#1866C211yesmaximal, 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
20C22×D8×C101C2211yescharacteristic
21C22×D8×C101C2211yescharacteristic, complemented
22C2×#131×C101C2211yescharacteristic
23#535×C101C2211yescharacteristic
24C2×#127×C101C2211yescharacteristic
25#520×C101C2211yescharacteristic
26#518×C101C2211yescharacteristic, complemented
27#472×C101—24no—
28#463×C101—21no—
29#463×C101—21no—
30#459×C101—21no—
31#459×C101—21no—
32#453×C101—24no—
33#449×C101—21no—
34#449×C101—21no—
35#447×C101—21no—
36#447×C101—21no—
37#442×C101—21no—
38#440×C101—21no—
39C4×SD16×C101—21no—
40C4×D8×C101—21no—
41C2×#108×C101C2211yescharacteristic, complemented
42C2×#108×C101C2211yescharacteristic, complemented
43#428×C101C2211yescharacteristic, complemented
44#424×C101C2211yescharacteristic, complemented
45C2×#104×C101C2211yescharacteristic
46C2×#104×C101C2211yescharacteristic
47#418×C101—21no—
48#418×C101C2211yescharacteristic
49#418×C101C2211yescharacteristic
50#418×C101C2211yescharacteristic, complemented
51#417×C101—21no—
52#417×C101C2211yescharacteristic
53#416×C101—21no—
54#416×C101C2211yescharacteristic
55#416×C101C2211yescharacteristic
56C2×#102×C101—21no—
57C2×#102×C101C2211yescharacteristic
58C2×#102×C101C2211yescharacteristic, complemented
59C2×#100×C101C2211yescharacteristic
60C2×#100×C101C2211yescharacteristic, complemented
61C2×#100×C101C2211yescharacteristic, complemented
62#408×C101C2211yescharacteristic
63#405×C101C2211yescharacteristic, complemented
64#390×C101C2211yescharacteristic, complemented
65#343×C101C2211yescharacteristic, complemented
66#339×C101C2211yescharacteristic, complemented
67#339×C101C2211yescharacteristic, complemented
68#336×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
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101—41no—
80C22×D4×C101—41no—
81C22×D4×C101C2311yescharacteristic
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)×C101D414yescomplemented
90C2×SD16×C101—21no—
91C2×SD16×C101—21no—
92C2×SD16×C101—21no—
93C2×D8×C101—21no—
94C2×D8×C101—21no—
95C2×D8×C101—21no—
96C2×D8×C101—22no—
97C2×D8×C101—22no—
98C2×D8×C101—21no—
99C2×D8×C101—21no—
100C2×D8×C101—21no—
101C2×D8×C101—21no—
102C2×D8×C101—41no—
103C2×D8×C101—41no—
104#131×C101—22no—
105#131×C101—41no—
106C2×M16×C101—21no—
107C2×M16×C101C2311yescharacteristic
108C2×M16×C101C2311yescharacteristic
109C2×M16×C101C2311yescharacteristic
110C2×M16×C101C2311yescharacteristic
111C22×C8×C101—21no—
112C22×C8×C101C2311yescharacteristic
113C22×C8×C101C2311yescharacteristic
114#127×C101—22no—
115#127×C101—21no—
116#127×C101—22no—
117#124×C101—21no—
118#121×C101—21no—
119#121×C101—21no—
120#120×C101—41no—
121C4×Q8×C101—21no—
122C4×D4×C101—21no—
123C4×D4×C101—21no—
124C4×D4×C101—21no—
125C4×D4×C101—21no—
126C4×D4×C101—21no—
127C4×D4×C101—41no—
128#117×C101—21no—
129#117×C101C2311yescharacteristic
130#117×C101C2311yescharacteristic
131C2×C4⋊C4×C101—21no—
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C22⋊C4×C101—41no—
134C2×C22⋊C4×C101—41no—
135C2×C42×C101C2311yescharacteristic
136#108×C101—22no—
137#108×C101—41no—
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#103×C101—21no—
145#103×C101D411yescharacteristic, complemented
146#103×C101D411yescharacteristic, complemented
147#103×C101D411yescharacteristic, complemented
148#103×C101D411yescharacteristic, complemented
149#102×C101—21no—
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×C101D411yescharacteristic, complemented
161#102×C101D411yescharacteristic, complemented
162#102×C101D411yescharacteristic, complemented
163#102×C101D411yescharacteristic, complemented
164#100×C101—22no—
165#100×C101—22no—
166#100×C101—22no—
167C22⋊C8×C101—21no—
168C22⋊C8×C101—21no—
169#97×C101—21no—
170C4×C8×C101—21no—
171C24×C101—21no—
172C24×C101—21no—
173C24×C101—21no—
174C24×C101—41no—
175#41×C101—21no—
176#41×C101—21no—
177#41×C101—24no—
178#41×C101—21no—
179#41×C101—21no—
180#41×C101—21no—
181#41×C101—21no—
182#41×C101—42no—
183#41×C101—42no—
184#41×C101—42no—
185#41×C101C2×D412yes—
186#41×C101#4112yes—
187C2×Q8×C101C2×D411yescharacteristic
188C2×Q8×C101C2×D411yescharacteristic
189C2×D4×C101—21no—
190C2×D4×C101—24no—
191C2×D4×C101—21no—
192C2×D4×C101—21no—
193C2×D4×C101—21no—
194C2×D4×C101—21no—
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—41no—
212C2×D4×C101—41no—
213C2×D4×C101—42no—
214C2×D4×C101—44no—
215C2×D4×C101—44no—
216C2×D4×C101—42no—
217C2×D4×C101—44no—
218C2×D4×C101—82no—
219C2×D4×C101—82no—
220C2×D4×C101C2×D412yes—
221C2×D4×C101C2×D411yescharacteristic
222C2×D4×C101C2×D411yescharacteristic
223C2×D4×C101#4112yes—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—41no—
229C22×C4×C101—41no—
230C22×C4×C101—41no—
231C22×C4×C101—41no—
232C22×C4×C101C2411yescharacteristic
233SD16×C101—24no—
234SD16×C101—42no—
235SD16×C101—42no—
236D8×C101—24no—
237D8×C101—42no—
238D8×C101—42no—
239D8×C101—42no—
240D8×C101—42no—
241D8×C101—42no—
242D8×C101—42no—
243M16×C101—21no—
244M16×C101—21no—
245M16×C101—21no—
246M16×C101—21no—
247M16×C101—21no—
248M16×C101—21no—
249M16×C101—21no—
250M16×C101—42no—
251M16×C101C2×D412yes—
252C2×C8×C101—21no—
253C2×C8×C101—21no—
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—42no—
261C2×C8×C101C2×D411yescharacteristic
262C2×C8×C101C2×D411yescharacteristic
263C2×C8×C101C2×D411yescharacteristic
264C2×C8×C101C2×D411yescharacteristic
265C4⋊C4×C101—21no—
266C4⋊C4×C101—21no—
267C4⋊C4×C101—41no—
268C4⋊C4×C101C2×D411yescharacteristic
269C4⋊C4×C101C2×D411yescharacteristic
270C4⋊C4×C101C2×D411yescharacteristic
271C4⋊C4×C101C2×D411yescharacteristic
272C22⋊C4×C101—21no—
273C22⋊C4×C101—21no—
274C22⋊C4×C101—41no—
275C22⋊C4×C101—41no—
276C22⋊C4×C101—41no—
277C22⋊C4×C101—41no—
278C22⋊C4×C101—41no—
279C22⋊C4×C101—82no—
280C42×C101—21no—
281C42×C101—21no—
282C42×C101—21no—
283C42×C101—21no—
284C42×C101—41no—
285C23×C101—21no—
286C23×C101—21no—
287C23×C101—22no—
288C23×C101—22no—
289C23×C101—44no—
290C23×C101—41no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—81no—
298C23×C101—81no—
299C23×C101—81no—
300C23×C101—81no—
301C23×C101—81no—
302C23×C101—81no—
303C23×C101—161no—
304C23×C101—161no—
305C23×C101H(5,𝔽2)11yescharacteristic
306Q8×C101—21no—
307Q8×C101—21no—
308Q8×C101—21no—
309Q8×C101#12112yes—
310D4×C101—22no—
311D4×C101—22no—
312D4×C101—22no—
313D4×C101—21no—
314D4×C101—22no—
315D4×C101—22no—
316D4×C101—21no—
317D4×C101—21no—
318D4×C101—22no—
319D4×C101—44no—
320D4×C101—44no—
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—41no—
331D4×C101—88no—
332D4×C101—161no—
333D4×C101—161no—
334D4×C101#12112yes—
335C2×C4×C101—21no—
336C2×C4×C101—22no—
337C2×C4×C101—22no—
338C2×C4×C101—22no—
339C2×C4×C101—21no—
340C2×C4×C101—21no—
341C2×C4×C101—21no—
342C2×C4×C101—21no—
343C2×C4×C101—21no—
344C2×C4×C101—44no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—81no—
351C2×C4×C101—161no—
352C2×C4×C101—161no—
353C2×C4×C101—161no—
354C2×C4×C101C22×D411yescharacteristic
355C2×C4×C101C22×D411yescharacteristic
356C2×C4×C101C22×D411yescharacteristic
357C2×C4×C101C2×#4111yescharacteristic
358C2×C4×C101C2×#4111yescharacteristic
359C2×C4×C101H(5,𝔽2)11yescharacteristic
360C8×C101—22no—
361C8×C101—21no—
362C8×C101—21no—
363C8×C101—21no—
364C8×C101—21no—
365C8×C101—41no—
366C8×C101—41no—
367C8×C101—41no—
368C22×C101—21no—
369C22×C101—21no—
370C22×C101—22no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—42no—
375C22×C101—42no—
376C22×C101—41no—
377C22×C101—41no—
378C22×C101—82no—
379C22×C101—82no—
380C22×C101—82no—
381C22×C101—81no—
382C22×C101—81no—
383C22×C101—81no—
384C22×C101—81no—
385C22×C101—81no—
386C22×C101—81no—
387C22×C101—81no—
388C22×C101—161no—
389C22×C101—161no—
390C22×C101—161no—
391C22×C101—164no—
392C22×C101#53811yescharacteristic
393C22×C101D4211yescharacteristic
394C22×C101#54611yescharacteristic
395C4×C101—22no—
396C4×C101—42no—
397C4×C101—41no—
398C4×C101—41no—
399C4×C101—41no—
400C4×C101—41no—
401C4×C101—41no—
402C4×C101—81no—
403C4×C101C2×#12111yescharacteristic
404C4×C101#52511yescharacteristic
405C4×C101D4211yescharacteristic
406C4×C101#54611yescharacteristic
407#25180C10111yesmaximal, characteristic, direct product factor, Sylow
408C2×C101—21no—
409C2×C101—21no—
410C2×C101—42no—
411C2×C101—81no—
412C2×C101—82no—
413C2×C101—82no—
414C2×C101—161no—
415C2×C101#242411yescharacteristic
416C2×C101#328811yescharacteristic
417C2×C101#329211yescharacteristic
418C2×#472C2×C10111yescharacteristic, complemented
419#3041C2×C10111yescharacteristic, complemented
420C2×#453C2×C10111yescharacteristic, complemented
421#3008C2×C10111yescharacteristic, complemented
422#2946C2×C10111yescharacteristic, complemented
423#2897C2×C10111yescharacteristic, complemented
424#2063C2×C10111yescharacteristic, complemented
425#2051C2×C10111yescharacteristic, complemented
426#2037C2×C10111yescharacteristic, complemented
427#2011C2×C10111yescharacteristic, complemented
428#1978C2×C10111yescharacteristic, complemented
429#1929C2×C10111yescharacteristic, complemented
430#1887C2×C10111yescharacteristic, complemented
431#1883C2×C10111yescharacteristic, complemented
432#1866C2×C10111yescharacteristic, complemented
433C101#2518011yescharacteristic, direct product factor, Sylow
434C2×H(5,𝔽2)C22×C10111yescharacteristic
435C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
436C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
437C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
438C22×D8C22×C10111yescharacteristic
439C22×D8C22×C10111yescharacteristic, complemented
440C2×#131C22×C10111yescharacteristic
441#535C22×C10111yescharacteristic
442C2×#127C22×C10111yescharacteristic
443#520C22×C10111yescharacteristic
444#518C22×C10111yescharacteristic, complemented
445#472—24no—
446#463—21no—
447#463—21no—
448#459—21no—
449#459—21no—
450#453—24no—
451#449—21no—
452#449—21no—
453#447—21no—
454#447—21no—
455#442—21no—
456#440—21no—
457C4×SD16—21no—
458C4×D8—21no—
459C2×#108C22×C10111yescharacteristic, complemented
460C2×#108C22×C10111yescharacteristic, complemented
461#428C22×C10111yescharacteristic, complemented
462#424C22×C10111yescharacteristic, complemented
463C2×#104C22×C10111yescharacteristic
464C2×#104C22×C10111yescharacteristic
465#418—21no—
466#418C22×C10111yescharacteristic
467#418C22×C10111yescharacteristic
468#418C22×C10111yescharacteristic, complemented
469#417—21no—
470#417C22×C10111yescharacteristic
471#416—21no—
472#416C22×C10111yescharacteristic
473#416C22×C10111yescharacteristic
474C2×#102—21no—
475C2×#102C22×C10111yescharacteristic
476C2×#102C22×C10111yescharacteristic, complemented
477C2×#100C22×C10111yescharacteristic
478C2×#100C22×C10111yescharacteristic, complemented
479C2×#100C22×C10111yescharacteristic, complemented
480#408C22×C10111yescharacteristic
481#405C22×C10111yescharacteristic, complemented
482#390C22×C10111yescharacteristic, complemented
483#343C22×C10111yescharacteristic, complemented
484#339C22×C10111yescharacteristic, complemented
485#339C22×C10111yescharacteristic, complemented
486#336C22×C10111yescharacteristic, complemented
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C10111yescharacteristic
494C2×#41C23×C10111yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C10111yescharacteristic
500C22×D4C23×C10111yescharacteristic
501C22×D4C23×C10111yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)D4×C10114yescomplemented
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×D8—21no—
512C2×D8—22no—
513C2×D8—21no—
514C2×D8—21no—
515C2×D8—22no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8—21no—
520C2×D8—41no—
521C2×D8—41no—
522#131—22no—
523#131—41no—
524C2×M16—21no—
525C2×M16C23×C10111yescharacteristic
526C2×M16C23×C10111yescharacteristic
527C2×M16C23×C10111yescharacteristic
528C2×M16C23×C10111yescharacteristic
529C22×C8—21no—
530C22×C8C23×C10111yescharacteristic
531C22×C8C23×C10111yescharacteristic
532#127—22no—
533#127—21no—
534#127—22no—
535#124—21no—
536#121—21no—
537#121—21no—
538#120—41no—
539C4×Q8—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—41no—
546#117—21no—
547#117C23×C10111yescharacteristic
548#117C23×C10111yescharacteristic
549C2×C4⋊C4—21no—
550C2×C4⋊C4C23×C10111yescharacteristic
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C42C23×C10111yescharacteristic
554#108—22no—
555#108—41no—
556#107—21no—
557#106—21no—
558C4⋊C8—21no—
559C4⋊C8—21no—
560#104—22no—
561#104—22no—
562#103—21no—
563#103D4×C10111yescharacteristic, complemented
564#103D4×C10111yescharacteristic, complemented
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#102D4×C10111yescharacteristic, complemented
579#102D4×C10111yescharacteristic, complemented
580#102D4×C10111yescharacteristic, complemented
581#102D4×C10111yescharacteristic, complemented
582#100—22no—
583#100—22no—
584#100—22no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587#97—21no—
588C4×C8—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—41no—
593#41—21no—
594#41—21no—
595#41—24no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41C2×D4×C10112yes—
604#41#41×C10112yes—
605C2×Q8C2×D4×C10111yescharacteristic
606C2×Q8C2×D4×C10111yescharacteristic
607C2×D4—21no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
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—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—44no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C10112yes—
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—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C10111yescharacteristic
651SD16—24no—
652SD16—42no—
653SD16—42no—
654D8—24no—
655D8—42no—
656D8—42no—
657D8—42no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16C2×D4×C10112yes—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8C2×D4×C10111yescharacteristic
680C2×C8C2×D4×C10111yescharacteristic
681C2×C8C2×D4×C10111yescharacteristic
682C2×C8C2×D4×C10111yescharacteristic
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—41no—
686C4⋊C4C2×D4×C10111yescharacteristic
687C4⋊C4C2×D4×C10111yescharacteristic
688C4⋊C4C2×D4×C10111yescharacteristic
689C4⋊C4C2×D4×C10111yescharacteristic
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—82no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—41no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—161no—
722C23—161no—
723C23H(5,𝔽2)×C10111yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C10112yes—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—21no—
732D4—22no—
733D4—22no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4#121×C10112yes—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—44no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—81no—
769C2×C4—161no—
770C2×C4—161no—
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—22no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—42no—
794C22—41no—
795C22—41no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—161no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22#538×C10111yescharacteristic
811C22D42×C10111yescharacteristic
812C22#546×C10111yescharacteristic
813C4—22no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—81no—
821C4C2×#121×C10111yescharacteristic
822C4#525×C10111yescharacteristic
823C4D42×C10111yescharacteristic
824C4#546×C10111yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C101×#242411yescharacteristic
833C2C101×#328811yescharacteristic
834C2C101×#329211yescharacteristic
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×#472×C101C2semidirect
2. C101×#3041C2semidirect
3. C2×#453×C101C2semidirect
4. C101×#3008C2semidirect
5. C101×#2946C2semidirect
6. C101×#2897C2semidirect
7. C101×#2063C2semidirect
8. C101×#2051C2semidirect
9. C101×#2037C2semidirect
10. C101×#2011C2semidirect
11. C101×#1978C2semidirect
12. C101×#1929C2semidirect
13. C101×#1887C2semidirect
14. C101×#1883C2semidirect
15. C101×#1866C2semidirect
21. C22×D8×C101C22semidirect
26. #518×C101C22semidirect
41. C2×#108×C101C22semidirect
42. C2×#108×C101C22semidirect
43. #428×C101C22semidirect
44. #424×C101C22semidirect
50. #418×C101C22semidirect
58. C2×#102×C101C22semidirect
60. C2×#100×C101C22semidirect
61. C2×#100×C101C22semidirect
63. #405×C101C22semidirect
64. #390×C101C22semidirect
65. #343×C101C22semidirect
66. #339×C101C22semidirect
67. #339×C101C22semidirect
68. #336×C101C22semidirect
89. AGL(1,ℤ/8)×C101D4semidirect
145. #103×C101D4semidirect
146. #103×C101D4semidirect
147. #103×C101D4semidirect
148. #103×C101D4semidirect
160. #102×C101D4semidirect
161. #102×C101D4semidirect
162. #102×C101D4semidirect
163. #102×C101D4semidirect
407. #25180C101direct (N × H)
418. C2×#472C2×C101semidirect
419. #3041C2×C101semidirect
420. C2×#453C2×C101semidirect
421. #3008C2×C101semidirect
422. #2946C2×C101semidirect
423. #2897C2×C101semidirect
424. #2063C2×C101semidirect
425. #2051C2×C101semidirect
426. #2037C2×C101semidirect
427. #2011C2×C101semidirect
428. #1978C2×C101semidirect
429. #1929C2×C101semidirect
430. #1887C2×C101semidirect
431. #1883C2×C101semidirect
432. #1866C2×C101semidirect
433. C101#25180direct (N × H)
439. C22×D8C22×C101semidirect
444. #518C22×C101semidirect
459. C2×#108C22×C101semidirect
460. C2×#108C22×C101semidirect
461. #428C22×C101semidirect
462. #424C22×C101semidirect
468. #418C22×C101semidirect
476. C2×#102C22×C101semidirect
478. C2×#100C22×C101semidirect
479. C2×#100C22×C101semidirect
481. #405C22×C101semidirect
482. #390C22×C101semidirect
483. #343C22×C101semidirect
484. #339C22×C101semidirect
485. #339C22×C101semidirect
486. #336C22×C101semidirect
507. AGL(1,ℤ/8)D4×C101semidirect
563. #103D4×C101semidirect
564. #103D4×C101semidirect
565. #103D4×C101semidirect
566. #103D4×C101semidirect
578. #102D4×C101semidirect
579. #102D4×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
C2×#472×C1012
C101×#30412
C2×#453×C1012
C101×#30082
C101×#29462
C101×#28972
C101×#20632
C101×#20512
C101×#20372
C101×#20112
C101×#19782
C101×#19292
C101×#18872
C101×#18832
C101×#18662
#25180101