Finite Group Databasebeta

← C101×#24460 #38806611

Subgroups — C101×#24460 #38806611

Order 25856.

1352 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C101C211yesmaximal, characteristic, complemented
2C2×#472×C101C211yesmaximal, characteristic, complemented
3C101×#3045C211yesmaximal, characteristic, complemented
4C2×#454×C101C211yesmaximal, characteristic, complemented
5C101×#3008C211yesmaximal, characteristic, complemented
6C101×#2898C211yesmaximal, characteristic, complemented
7C101×#2052C211yesmaximal, characteristic, complemented
8C101×#2046C211yesmaximal, characteristic, complemented
9C101×#2012C211yesmaximal, characteristic, complemented
10C101×#2004C211yesmaximal, characteristic, complemented
11C101×#1907C211yesmaximal, characteristic, complemented
12C101×#1883C211yesmaximal, characteristic, complemented
13C101×#1876C211yesmaximal, characteristic, complemented
14C101×#1866C211yesmaximal, characteristic, complemented
15C101×#1792C211yesmaximal, 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, complemented
26C2×#135×C101—21no—
27C2×#135×C101C2211yescharacteristic
28C22×SD16×C101—21no—
29C22×SD16×C101C2211yescharacteristic
30C22×D8×C101C2211yescharacteristic
31C2×#131×C101C2211yescharacteristic
32C2×#131×C101C2211yescharacteristic, complemented
33#535×C101C2211yescharacteristic
34C2×#124×C101C2211yescharacteristic, complemented
35#520×C101C2211yescharacteristic, complemented
36#472×C101—24no—
37#464×C101—21no—
38#463×C101—21no—
39#460×C101—21no—
40#459×C101—21no—
41#454×C101—24no—
42#449×C101—21no—
43#449×C101—21no—
44#447×C101—21no—
45#447×C101—21no—
46C2×#108×C101C2211yescharacteristic, complemented
47#424×C101C2211yescharacteristic, complemented
48C2×#104×C101C2211yescharacteristic
49C2×#104×C101C2211yescharacteristic
50C2×#104×C101C2211yescharacteristic, complemented
51#419×C101—21no—
52#419×C101C2211yescharacteristic, complemented
53#418×C101C2211yescharacteristic
54#417×C101—21no—
55#417×C101C2211yescharacteristic
56#417×C101C2211yescharacteristic
57#416×C101—21no—
58#416×C101C2211yescharacteristic
59C2×#103×C101—21no—
60C2×#103×C101C2211yescharacteristic, complemented
61C2×#102×C101C2211yescharacteristic, complemented
62C2×#101×C101C2211yescharacteristic, complemented
63C2×#100×C101C2211yescharacteristic
64C2×#100×C101C2211yescharacteristic, complemented
65#408×C101C2211yescharacteristic
66#390×C101C2211yescharacteristic
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—41no—
742−1+4×C101D414yescomplemented
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
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×C101C2311yescharacteristic
94C22×D4×C101C2311yescharacteristic
95#137×C101—28no—
96#137×C101—22no—
97#137×C101—22no—
98AGL(1,ℤ/8)×C101—28no—
99AGL(1,ℤ/8)×C101—22no—
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)×C101D414yescomplemented
105#135×C101—28no—
106#135×C101—22no—
107#135×C101—22no—
108C2×Q16×C101—21no—
109C2×Q16×C101D411yescharacteristic
110C2×SD16×C101—28no—
111C2×SD16×C101—21no—
112C2×SD16×C101—22no—
113C2×SD16×C101—21no—
114C2×SD16×C101—22no—
115C2×SD16×C101—21no—
116C2×SD16×C101—21no—
117C2×SD16×C101—21no—
118C2×SD16×C101—21no—
119C2×SD16×C101D411yescharacteristic
120C2×SD16×C101D411yescharacteristic
121C2×D8×C101—21no—
122C2×D8×C101—21no—
123C2×D8×C101—21no—
124C2×D8×C101—22no—
125C2×D8×C101—21no—
126C2×D8×C101—21no—
127C2×D8×C101—41no—
128C2×D8×C101D411yescharacteristic
129#131×C101—22no—
130#131×C101—22no—
131#131×C101—22no—
132#131×C101—41no—
133C2×M16×C101—21no—
134C2×M16×C101—21no—
135C2×M16×C101C2311yescharacteristic
136C2×M16×C101C2311yescharacteristic
137C2×M16×C101C2311yescharacteristic
138C2×M16×C101C2311yescharacteristic
139C22×C8×C101—21no—
140C22×C8×C101—21no—
141C22×C8×C101C2311yescharacteristic
142C22×C8×C101C2311yescharacteristic
143#127×C101—21no—
144#124×C101—22no—
145#124×C101—21no—
146#124×C101—41no—
147#121×C101—21no—
148#121×C101—21no—
149#120×C101—41no—
150C4×Q8×C101—21no—
151C4×D4×C101—21no—
152C4×D4×C101—41no—
153#117×C101—21no—
154#117×C101C2311yescharacteristic
155C2×C4⋊C4×C101—21no—
156C2×C4⋊C4×C101C2311yescharacteristic
157C2×C22⋊C4×C101—41no—
158C2×C22⋊C4×C101—41no—
159C2×C42×C101C2311yescharacteristic
160#108×C101—22no—
161C4⋊C8×C101—21no—
162C4⋊C8×C101—21no—
163#104×C101—22no—
164#104×C101—22no—
165#104×C101—41no—
166#103×C101—21no—
167#103×C101—21no—
168#103×C101—21no—
169#103×C101—21no—
170#103×C101—21no—
171#103×C101—21no—
172#103×C101D411yescharacteristic
173#103×C101D411yescharacteristic
174#102×C101—21no—
175#102×C101—21no—
176#102×C101—21no—
177#102×C101—21no—
178#102×C101—21no—
179#102×C101—21no—
180#102×C101D411yescharacteristic
181#102×C101D411yescharacteristic
182#101×C101—22no—
183#100×C101—22no—
184#100×C101—22no—
185C22⋊C8×C101—21no—
186C22⋊C8×C101—21no—
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—44no—
202#41×C101—42no—
203#41×C101—42no—
204#41×C101—42no—
205#41×C101—44no—
206#41×C101—42no—
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—24no—
215C2×Q8×C101—21no—
216C2×Q8×C101—21no—
217C2×Q8×C101—21no—
218C2×Q8×C101—21no—
219C2×Q8×C101—41no—
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—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—21no—
239C2×D4×C101—21no—
240C2×D4×C101—21no—
241C2×D4×C101—42no—
242C2×D4×C101—41no—
243C2×D4×C101—41no—
244C2×D4×C101—41no—
245C2×D4×C101—41no—
246C2×D4×C101—42no—
247C2×D4×C101—44no—
248C2×D4×C101—44no—
249C2×D4×C101—41no—
250C2×D4×C101—42no—
251C2×D4×C101C2×D412yes—
252C2×D4×C101C2×D411yescharacteristic
253C2×D4×C101C2×D411yescharacteristic
254C2×D4×C101C2×D411yescharacteristic
255C22×C4×C101—21no—
256C22×C4×C101—21no—
257C22×C4×C101—21no—
258C22×C4×C101—21no—
259C22×C4×C101—21no—
260C22×C4×C101—21no—
261C22×C4×C101—41no—
262C22×C4×C101—41no—
263C22×C4×C101—41no—
264C22×C4×C101—41no—
265C22×C4×C101C2411yescharacteristic
266Q16×C101—24no—
267Q16×C101—22no—
268SD16×C101—24no—
269SD16×C101—24no—
270SD16×C101—24no—
271SD16×C101—22no—
272SD16×C101—24no—
273SD16×C101—22no—
274SD16×C101—42no—
275SD16×C101—42no—
276D8×C101—24no—
277D8×C101—22no—
278D8×C101—42no—
279D8×C101—42no—
280D8×C101—42no—
281D8×C101—42no—
282M16×C101—24no—
283M16×C101—21no—
284M16×C101—21no—
285M16×C101—21no—
286M16×C101—21no—
287M16×C101—21no—
288M16×C101—21no—
289M16×C101—21no—
290M16×C101—42no—
291M16×C101C2×D412yes—
292C2×C8×C101—24no—
293C2×C8×C101—21no—
294C2×C8×C101—21no—
295C2×C8×C101—21no—
296C2×C8×C101—21no—
297C2×C8×C101—21no—
298C2×C8×C101—21no—
299C2×C8×C101—21no—
300C2×C8×C101—21no—
301C2×C8×C101—42no—
302C2×C8×C101C2×D411yescharacteristic
303C2×C8×C101C2×D411yescharacteristic
304C2×C8×C101C2×D411yescharacteristic
305C2×C8×C101C2×D411yescharacteristic
306C4⋊C4×C101—21no—
307C4⋊C4×C101—21no—
308C4⋊C4×C101—41no—
309C4⋊C4×C101C2×D411yescharacteristic
310C4⋊C4×C101C2×D411yescharacteristic
311C22⋊C4×C101—21no—
312C22⋊C4×C101—41no—
313C22⋊C4×C101—41no—
314C22⋊C4×C101—41no—
315C22⋊C4×C101—44no—
316C22⋊C4×C101—82no—
317C42×C101—21no—
318C42×C101—21no—
319C42×C101—21no—
320C42×C101—41no—
321C23×C101—21no—
322C23×C101—21no—
323C23×C101—21no—
324C23×C101—22no—
325C23×C101—44no—
326C23×C101—41no—
327C23×C101—41no—
328C23×C101—41no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—81no—
332C23×C101—81no—
333C23×C101—81no—
334C23×C101—81no—
335C23×C101—161no—
336C23×C101—161no—
337C23×C101H(5,𝔽2)11yescharacteristic
338Q8×C101—21no—
339Q8×C101—21no—
340Q8×C101—22no—
341Q8×C101—21no—
342Q8×C101—22no—
343Q8×C101—21no—
344Q8×C101—44no—
345Q8×C101—41no—
346Q8×C101—41no—
347Q8×C101#12012yes—
348Q8×C101#12112yes—
349D4×C101—22no—
350D4×C101—22no—
351D4×C101—22no—
352D4×C101—22no—
353D4×C101—22no—
354D4×C101—21no—
355D4×C101—21no—
356D4×C101—22no—
357D4×C101—21no—
358D4×C101—21no—
359D4×C101—44no—
360D4×C101—44no—
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—161no—
371D4×C101—161no—
372D4×C101#12012yes—
373D4×C101#12112yes—
374C2×C4×C101—21no—
375C2×C4×C101—21no—
376C2×C4×C101—22no—
377C2×C4×C101—22no—
378C2×C4×C101—22no—
379C2×C4×C101—22no—
380C2×C4×C101—22no—
381C2×C4×C101—21no—
382C2×C4×C101—21no—
383C2×C4×C101—21no—
384C2×C4×C101—44no—
385C2×C4×C101—44no—
386C2×C4×C101—44no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—81no—
396C2×C4×C101—161no—
397C2×C4×C101C22×D411yescharacteristic
398C2×C4×C101C22×D411yescharacteristic
399C2×C4×C101C22×D411yescharacteristic
400C2×C4×C101C22×D411yescharacteristic
401C2×C4×C101C2×#4111yescharacteristic
402C2×C4×C101H(5,𝔽2)11yescharacteristic
403C8×C101—21no—
404C8×C101—22no—
405C8×C101—21no—
406C8×C101—21no—
407C8×C101—21no—
408C8×C101—41no—
409C8×C101—41no—
410C8×C101—41no—
411C22×C101—21no—
412C22×C101—21no—
413C22×C101—22no—
414C22×C101—22no—
415C22×C101—41no—
416C22×C101—41no—
417C22×C101—41no—
418C22×C101—41no—
419C22×C101—41no—
420C22×C101—42no—
421C22×C101—41no—
422C22×C101—41no—
423C22×C101—82no—
424C22×C101—82no—
425C22×C101—81no—
426C22×C101—81no—
427C22×C101—81no—
428C22×C101—81no—
429C22×C101—81no—
430C22×C101—161no—
431C22×C101—161no—
432C22×C101—164no—
433C22×C101#53411yescharacteristic
434C22×C101D4211yescharacteristic
435C22×C101#54611yescharacteristic
436C4×C101—22no—
437C4×C101—22no—
438C4×C101—41no—
439C4×C101—42no—
440C4×C101—41no—
441C4×C101—41no—
442C4×C101—81no—
443C4×C101—81no—
444C4×C101C2×#12011yescharacteristic
445C4×C101C2×#12111yescharacteristic
446C4×C101D4211yescharacteristic
447C4×C101#54611yescharacteristic
448#24460C10111yesmaximal, characteristic, direct product factor, Sylow
449C2×C101—21no—
450C2×C101—21no—
451C2×C101—42no—
452C2×C101—42no—
453C2×C101—81no—
454C2×C101—82no—
455C2×C101—161no—
456C2×C101#241011yescharacteristic
457C2×C101#328811yescharacteristic
458C2×C101#329011yescharacteristic
459C2×#577C2×C10111yescharacteristic, complemented
460C2×#472C2×C10111yescharacteristic, complemented
461#3045C2×C10111yescharacteristic, complemented
462C2×#454C2×C10111yescharacteristic, complemented
463#3008C2×C10111yescharacteristic, complemented
464#2898C2×C10111yescharacteristic, complemented
465#2052C2×C10111yescharacteristic, complemented
466#2046C2×C10111yescharacteristic, complemented
467#2012C2×C10111yescharacteristic, complemented
468#2004C2×C10111yescharacteristic, complemented
469#1907C2×C10111yescharacteristic, complemented
470#1883C2×C10111yescharacteristic, complemented
471#1876C2×C10111yescharacteristic, complemented
472#1866C2×C10111yescharacteristic, complemented
473#1792C2×C10111yescharacteristic, complemented
474C101#2446011yescharacteristic, direct product factor, Sylow
475C2×2−1+4C22×C10111yescharacteristic
476C2×H(5,𝔽2)C22×C10111yescharacteristic
477#577—24no—
478#577—24no—
479C2×#137—21no—
480C2×#137C22×C10111yescharacteristic
481C2×AGL(1,ℤ/8)—21no—
482C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
483C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
484C2×AGL(1,ℤ/8)C22×C10111yescharacteristic, complemented
485C2×#135—21no—
486C2×#135C22×C10111yescharacteristic
487C22×SD16—21no—
488C22×SD16C22×C10111yescharacteristic
489C22×D8C22×C10111yescharacteristic
490C2×#131C22×C10111yescharacteristic
491C2×#131C22×C10111yescharacteristic, complemented
492#535C22×C10111yescharacteristic
493C2×#124C22×C10111yescharacteristic, complemented
494#520C22×C10111yescharacteristic, complemented
495#472—24no—
496#464—21no—
497#463—21no—
498#460—21no—
499#459—21no—
500#454—24no—
501#449—21no—
502#449—21no—
503#447—21no—
504#447—21no—
505C2×#108C22×C10111yescharacteristic, complemented
506#424C22×C10111yescharacteristic, complemented
507C2×#104C22×C10111yescharacteristic
508C2×#104C22×C10111yescharacteristic
509C2×#104C22×C10111yescharacteristic, complemented
510#419—21no—
511#419C22×C10111yescharacteristic, complemented
512#418C22×C10111yescharacteristic
513#417—21no—
514#417C22×C10111yescharacteristic
515#417C22×C10111yescharacteristic
516#416—21no—
517#416C22×C10111yescharacteristic
518C2×#103—21no—
519C2×#103C22×C10111yescharacteristic, complemented
520C2×#102C22×C10111yescharacteristic, complemented
521C2×#101C22×C10111yescharacteristic, complemented
522C2×#100C22×C10111yescharacteristic
523C2×#100C22×C10111yescharacteristic, complemented
524#408C22×C10111yescharacteristic
525#390C22×C10111yescharacteristic
526#343C22×C10111yescharacteristic, complemented
527#341C22×C10111yescharacteristic, complemented
528#339C22×C10111yescharacteristic, complemented
529#336C22×C10111yescharacteristic, complemented
5302−1+4—22no—
5312−1+4—22no—
5322−1+4—41no—
5332−1+4D4×C10114yescomplemented
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—41no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—41no—
543C2×#41C23×C10111yescharacteristic
544C2×#41C23×C10111yescharacteristic
545C2×#41C23×C10111yescharacteristic
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8C23×C10111yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4C23×C10111yescharacteristic
553C22×D4C23×C10111yescharacteristic
554#137—28no—
555#137—22no—
556#137—22no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)D4×C10114yescomplemented
564#135—28no—
565#135—22no—
566#135—22no—
567C2×Q16—21no—
568C2×Q16D4×C10111yescharacteristic
569C2×SD16—28no—
570C2×SD16—21no—
571C2×SD16—22no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16D4×C10111yescharacteristic
579C2×SD16D4×C10111yescharacteristic
580C2×D8—21no—
581C2×D8—22no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8—41no—
587C2×D8D4×C10111yescharacteristic
588#131—22no—
589#131—22no—
590#131—22no—
591#131—41no—
592C2×M16—21no—
593C2×M16—21no—
594C2×M16C23×C10111yescharacteristic
595C2×M16C23×C10111yescharacteristic
596C2×M16C23×C10111yescharacteristic
597C2×M16C23×C10111yescharacteristic
598C22×C8—21no—
599C22×C8—21no—
600C22×C8C23×C10111yescharacteristic
601C22×C8C23×C10111yescharacteristic
602#127—21no—
603#124—22no—
604#124—21no—
605#124—41no—
606#121—21no—
607#121—21no—
608#120—41no—
609C4×Q8—21no—
610C4×D4—21no—
611C4×D4—41no—
612#117—21no—
613#117C23×C10111yescharacteristic
614C2×C4⋊C4—21no—
615C2×C4⋊C4C23×C10111yescharacteristic
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C42C23×C10111yescharacteristic
619#108—22no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622#104—22no—
623#104—22no—
624#104—41no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#103D4×C10111yescharacteristic
632#103D4×C10111yescharacteristic
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102D4×C10111yescharacteristic
640#102D4×C10111yescharacteristic
641#101—22no—
642#100—22no—
643#100—22no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C24—21no—
647C24—21no—
648C24—41no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—24no—
654#41—24no—
655#41—24no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—44no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—44no—
665#41—42no—
666#41—42no—
667#41C2×D4×C10112yes—
668#41C2×D4×C10112yes—
669#41C2×D4×C10112yes—
670#41#41×C10112yes—
671C2×Q8—21no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8C2×D4×C10112yes—
682C2×Q8C2×D4×C10111yescharacteristic
683C2×Q8C2×D4×C10111yescharacteristic
684C2×Q8C2×D4×C10111yescharacteristic
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
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—42no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—41no—
709C2×D4—42no—
710C2×D4C2×D4×C10112yes—
711C2×D4C2×D4×C10111yescharacteristic
712C2×D4C2×D4×C10111yescharacteristic
713C2×D4C2×D4×C10111yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C24×C10111yescharacteristic
725Q16—24no—
726Q16—22no—
727SD16—24no—
728SD16—24no—
729SD16—24no—
730SD16—22no—
731SD16—24no—
732SD16—22no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—22no—
737D8—42no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—42no—
750M16C2×D4×C10112yes—
751C2×C8—24no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C10111yescharacteristic
762C2×C8C2×D4×C10111yescharacteristic
763C2×C8C2×D4×C10111yescharacteristic
764C2×C8C2×D4×C10111yescharacteristic
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—41no—
768C4⋊C4C2×D4×C10111yescharacteristic
769C4⋊C4C2×D4×C10111yescharacteristic
770C22⋊C4—21no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—44no—
775C22⋊C4—82no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—41no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—44no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—161no—
795C23—161no—
796C23H(5,𝔽2)×C10111yescharacteristic
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—22no—
802Q8—21no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8#120×C10112yes—
807Q8#121×C10112yes—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—21no—
814D4—21no—
815D4—22no—
816D4—21no—
817D4—21no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—161no—
830D4—161no—
831D4#120×C10112yes—
832D4#121×C10112yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—161no—
856C2×C4C22×D4×C10111yescharacteristic
857C2×C4C22×D4×C10111yescharacteristic
858C2×C4C22×D4×C10111yescharacteristic
859C2×C4C22×D4×C10111yescharacteristic
860C2×C4C2×#41×C10111yescharacteristic
861C2×C4H(5,𝔽2)×C10111yescharacteristic
862C8—21no—
863C8—22no—
864C8—21no—
865C8—21no—
866C8—21no—
867C8—41no—
868C8—41no—
869C8—41no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—161no—
890C22—161no—
891C22—164no—
892C22#534×C10111yescharacteristic
893C22D42×C10111yescharacteristic
894C22#546×C10111yescharacteristic
895C4—22no—
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—81no—
902C4—81no—
903C4C2×#120×C10111yescharacteristic
904C4C2×#121×C10111yescharacteristic
905C4D42×C10111yescharacteristic
906C4#546×C10111yescharacteristic
907C2—21no—
908C2—21no—
909C2—42no—
910C2—42no—
911C2—81no—
912C2—82no—
913C2—161no—
914C2C101×#241011yescharacteristic
915C2C101×#328811yescharacteristic
916C2C101×#329011yescharacteristic
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×#472×C101C2semidirect
3. C101×#3045C2semidirect
4. C2×#454×C101C2semidirect
5. C101×#3008C2semidirect
6. C101×#2898C2semidirect
7. C101×#2052C2semidirect
8. C101×#2046C2semidirect
9. C101×#2012C2semidirect
10. C101×#2004C2semidirect
11. C101×#1907C2semidirect
12. C101×#1883C2semidirect
13. C101×#1876C2semidirect
14. C101×#1866C2semidirect
15. C101×#1792C2semidirect
25. C2×AGL(1,ℤ/8)×C101C22semidirect
32. C2×#131×C101C22semidirect
34. C2×#124×C101C22semidirect
35. #520×C101C22semidirect
46. C2×#108×C101C22semidirect
47. #424×C101C22semidirect
50. C2×#104×C101C22semidirect
52. #419×C101C22semidirect
60. C2×#103×C101C22semidirect
61. C2×#102×C101C22semidirect
62. C2×#101×C101C22semidirect
64. C2×#100×C101C22semidirect
67. #343×C101C22semidirect
68. #341×C101C22semidirect
69. #339×C101C22semidirect
70. #336×C101C22semidirect
74. 2−1+4×C101D4semidirect
104. AGL(1,ℤ/8)×C101D4semidirect
448. #24460C101direct (N × H)
459. C2×#577C2×C101semidirect
460. C2×#472C2×C101semidirect
461. #3045C2×C101semidirect
462. C2×#454C2×C101semidirect
463. #3008C2×C101semidirect
464. #2898C2×C101semidirect
465. #2052C2×C101semidirect
466. #2046C2×C101semidirect
467. #2012C2×C101semidirect
468. #2004C2×C101semidirect
469. #1907C2×C101semidirect
470. #1883C2×C101semidirect
471. #1876C2×C101semidirect
472. #1866C2×C101semidirect
473. #1792C2×C101semidirect
474. C101#24460direct (N × H)
484. C2×AGL(1,ℤ/8)C22×C101semidirect
491. C2×#131C22×C101semidirect
493. C2×#124C22×C101semidirect
494. #520C22×C101semidirect
505. C2×#108C22×C101semidirect
506. #424C22×C101semidirect
509. C2×#104C22×C101semidirect
511. #419C22×C101semidirect
519. C2×#103C22×C101semidirect
520. C2×#102C22×C101semidirect
521. C2×#101C22×C101semidirect
523. C2×#100C22×C101semidirect
526. #343C22×C101semidirect
527. #341C22×C101semidirect
528. #339C22×C101semidirect
529. #336C22×C101semidirect
533. 2−1+4D4×C101semidirect
563. AGL(1,ℤ/8)D4×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×#472×C1012
C101×#30452
C2×#454×C1012
C101×#30082
C101×#28982
C101×#20522
C101×#20462
C101×#20122
C101×#20042
C101×#19072
C101×#18832
C101×#18762
C101×#18662
C101×#17922
#24460101