Finite Group Databasebeta

← C101×#24474 #38806625

Subgroups — C101×#24474 #38806625

Order 25856.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3586C211yesmaximal, characteristic
2C101×#3069C211yesmaximal, characteristic, complemented
3C101×#3039C211yesmaximal, characteristic, complemented
4C101×#3022C211yesmaximal, characteristic, complemented
5C2×#456×C101C211yesmaximal, characteristic, complemented
6C101×#2901C211yesmaximal, characteristic, complemented
7C101×#2050C211yesmaximal, characteristic, complemented
8C101×#2049C211yesmaximal, characteristic, complemented
9C101×#2009C211yesmaximal, characteristic, complemented
10C101×#2005C211yesmaximal, characteristic, complemented
11C101×#1906C211yesmaximal, characteristic, complemented
12C101×#1902C211yesmaximal, characteristic, complemented
13C101×#1902C211yesmaximal, characteristic, complemented
14C101×#1861C211yesmaximal, characteristic, complemented
15C101×#1796C211yesmaximal, characteristic, complemented
16#585×C101C2211yescharacteristic
17C2×2−1+4×C101C2211yescharacteristic
18#578×C101—22no—
19#578×C101—22no—
20#577×C101—22no—
21#577×C101—22no—
22#575×C101—22no—
23#575×C101C2211yescharacteristic
24#575×C101C2211yescharacteristic
25C2×#137×C101—22no—
26C2×#137×C101C2211yescharacteristic
27C2×#137×C101C2211yescharacteristic
28C2×#137×C101C2211yescharacteristic
29C2×#137×C101C2211yescharacteristic
30C2×#137×C101C2211yescharacteristic, complemented
31#568×C101C2211yescharacteristic
32#568×C101C2211yescharacteristic
33#536×C101C2211yescharacteristic
34C2×C4⋊Q8×C101C2211yescharacteristic, complemented
35C4×#41×C101C2211yescharacteristic
36#473×C101—22no—
37#471×C101—22no—
38#462×C101—22no—
39#461×C101—22no—
40#456×C101—22no—
41#456×C101—22no—
42#456×C101—22no—
43#455×C101—22no—
44#430×C101C2211yescharacteristic, complemented
45#423×C101C2211yescharacteristic, complemented
46#421×C101—22no—
47#421×C101C2211yescharacteristic
48#421×C101C2211yescharacteristic
49#421×C101C2211yescharacteristic
50#421×C101C2211yescharacteristic
51C2×#104×C101—22no—
52C2×#104×C101C2211yescharacteristic
53C2×#104×C101C2211yescharacteristic
54C2×#104×C101C2211yescharacteristic, complemented
55#419×C101C2211yescharacteristic, complemented
56#419×C101C2211yescharacteristic, complemented
57#419×C101C2211yescharacteristic, complemented
58#413×C101C2211yescharacteristic
59#413×C101C2211yescharacteristic, complemented
60C2×#101×C101C2211yescharacteristic, complemented
61C2×#101×C101C2211yescharacteristic, complemented
62#410×C101C2211yescharacteristic, complemented
63#344×C101C2211yescharacteristic, complemented
64#344×C101C2211yescharacteristic, complemented
65#339×C101C2211yescharacteristic, complemented
66#338×C101C2211yescharacteristic, complemented
672−1+4×C101—22no—
682−1+4×C101—22no—
692−1+4×C101—21no—
702−1+4×C101—21no—
712−1+4×C101—22no—
722−1+4×C101—41no—
732−1+4×C101D412yes—
74H(5,𝔽2)×C101—21no—
75H(5,𝔽2)×C101—21no—
76H(5,𝔽2)×C101—41no—
77H(5,𝔽2)×C101D412yes—
78C2×#41×C101—22no—
79C2×#41×C101—22no—
80C2×#41×C101—21no—
81C2×#41×C101—21no—
82C2×#41×C101—41no—
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×Q8×C101C2311yescharacteristic
92#137×C101—24no—
93#137×C101—24no—
94#137×C101—24no—
95#137×C101—22no—
96#137×C101—22no—
97#137×C101—21no—
98#137×C101—22no—
99#137×C101—21no—
100#137×C101—21no—
101#137×C101—22no—
102#137×C101—22no—
103#137×C101—22no—
104#137×C101—22no—
105#137×C101—22no—
106#137×C101—22no—
107#137×C101—41no—
108#137×C101D412yes—
109AGL(1,ℤ/8)×C101—24no—
110AGL(1,ℤ/8)×C101—21no—
111AGL(1,ℤ/8)×C101—21no—
112AGL(1,ℤ/8)×C101—21no—
113AGL(1,ℤ/8)×C101D412yes—
114#135×C101—24no—
115#135×C101—24no—
116#135×C101—22no—
117#135×C101—22no—
118C2×Q16×C101—24no—
119C2×Q16×C101—21no—
120C2×Q16×C101—21no—
121C2×Q16×C101—21no—
122C2×Q16×C101—21no—
123C2×Q16×C101D412yes—
124C2×SD16×C101—24no—
125C2×SD16×C101—21no—
126C2×SD16×C101—21no—
127C2×SD16×C101—21no—
128C2×SD16×C101—21no—
129C2×SD16×C101D412yes—
130#131×C101—22no—
131#131×C101—22no—
132#131×C101—22no—
133#131×C101—41no—
134C2×M16×C101—22no—
135C2×M16×C101—22no—
136C2×M16×C101C2311yescharacteristic
137C2×M16×C101C2311yescharacteristic
138C2×M16×C101C2311yescharacteristic
139C2×M16×C101C2311yescharacteristic
140C2×M16×C101C2311yescharacteristic
141C2×M16×C101C2311yescharacteristic
142C4⋊Q8×C101—21no—
143C4⋊Q8×C101—22no—
144C4⋊Q8×C101—21no—
145C4⋊Q8×C101—21no—
146#124×C101—21no—
147#123×C101—41no—
148C22⋊Q8×C101—41no—
149C4×Q8×C101—21no—
150C4×D4×C101—21no—
151C4×D4×C101—41no—
152#117×C101—21no—
153#117×C101C2311yescharacteristic
154#117×C101C2311yescharacteristic
155C2×C4⋊C4×C101—41no—
156C2×C42×C101—21no—
157C2×C42×C101C2311yescharacteristic
158#108×C101—22no—
159C4⋊C8×C101—22no—
160#104×C101—22no—
161#104×C101—22no—
162#104×C101—22no—
163#104×C101—22no—
164#104×C101—21no—
165#104×C101—21no—
166#104×C101—21no—
167#104×C101—21no—
168#104×C101D412yes—
169#104×C101D412yes—
170#103×C101—22no—
171#103×C101—22no—
172#103×C101—41no—
173#101×C101—21no—
174#101×C101—21no—
175#101×C101—22no—
176#101×C101—22no—
177#100×C101—21no—
178#100×C101—21no—
179#99×C101—41no—
180#41×C101—21no—
181#41×C101—21no—
182#41×C101—21no—
183#41×C101—21no—
184#41×C101—24no—
185#41×C101—22no—
186#41×C101—22no—
187#41×C101—22no—
188#41×C101—22no—
189#41×C101—21no—
190#41×C101—21no—
191#41×C101—21no—
192#41×C101—21no—
193#41×C101—21no—
194#41×C101—21no—
195#41×C101—21no—
196#41×C101—21no—
197#41×C101—42no—
198#41×C101—42no—
199#41×C101—42no—
200#41×C101—42no—
201#41×C101—42no—
202#41×C101—44no—
203#41×C101—42no—
204#41×C101—41no—
205#41×C101—41no—
206#41×C101—44no—
207#41×C101—42no—
208#41×C101C2×D412yes—
209#41×C101C2×D412yes—
210#41×C101C2×D412yes—
211#41×C101C2×D412yes—
212C2×Q8×C101—21no—
213C2×Q8×C101—24no—
214C2×Q8×C101—22no—
215C2×Q8×C101—22no—
216C2×Q8×C101—21no—
217C2×Q8×C101—21no—
218C2×Q8×C101—21no—
219C2×Q8×C101—21no—
220C2×Q8×C101—21no—
221C2×Q8×C101—21no—
222C2×Q8×C101—21no—
223C2×Q8×C101—21no—
224C2×Q8×C101—21no—
225C2×Q8×C101—21no—
226C2×Q8×C101—41no—
227C2×Q8×C101—42no—
228C2×Q8×C101—42no—
229C2×Q8×C101—41no—
230C2×Q8×C101—42no—
231C2×Q8×C101C2×D411yescharacteristic
232C2×Q8×C101C2×D411yescharacteristic
233C2×Q8×C101C2×D412yes—
234C2×Q8×C101C2×D411yescharacteristic
235C2×Q8×C101#4111yescharacteristic
236C2×D4×C101—21no—
237C2×D4×C101—21no—
238C2×D4×C101—22no—
239C2×D4×C101—22no—
240C2×D4×C101—21no—
241C2×D4×C101—21no—
242C2×D4×C101—42no—
243C2×D4×C101—41no—
244C2×D4×C101—42no—
245C2×D4×C101—42no—
246C2×D4×C101—41no—
247C2×D4×C101C2×D411yescharacteristic
248C2×D4×C101C2×D411yescharacteristic
249C2×D4×C101C2×D411yescharacteristic
250C2×D4×C101#4111yescharacteristic
251C22×C4×C101—21no—
252C22×C4×C101—21no—
253C22×C4×C101—21no—
254C22×C4×C101—21no—
255C22×C4×C101—21no—
256C22×C4×C101—21no—
257C22×C4×C101—21no—
258C22×C4×C101—42no—
259C22×C4×C101—41no—
260C22×C4×C101—41no—
261C22×C4×C101—41no—
262C22×C4×C101C2411yescharacteristic
263Q16×C101—24no—
264Q16×C101—22no—
265Q16×C101—22no—
266Q16×C101—24no—
267Q16×C101—42no—
268Q16×C101—42no—
269Q16×C101—42no—
270SD16×C101—24no—
271SD16×C101—22no—
272SD16×C101—22no—
273SD16×C101—22no—
274SD16×C101—22no—
275SD16×C101—24no—
276SD16×C101—42no—
277SD16×C101—42no—
278SD16×C101—42no—
279D8×C101—22no—
280D8×C101—22no—
281M16×C101—24no—
282M16×C101—21no—
283M16×C101—21no—
284M16×C101—21no—
285M16×C101—21no—
286M16×C101—21no—
287M16×C101—21no—
288M16×C101—21no—
289M16×C101—21no—
290M16×C101—21no—
291M16×C101—21no—
292M16×C101—42no—
293M16×C101C2×D412yes—
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—42no—
302C2×C8×C101C2×D412yes—
303C4⋊C4×C101—21no—
304C4⋊C4×C101—21no—
305C4⋊C4×C101—42no—
306C4⋊C4×C101—42no—
307C4⋊C4×C101—41no—
308C4⋊C4×C101—42no—
309C22⋊C4×C101—21no—
310C22⋊C4×C101—21no—
311C22⋊C4×C101—41no—
312C22⋊C4×C101—42no—
313C42×C101—21no—
314C42×C101—21no—
315C42×C101—21no—
316C42×C101—41no—
317C42×C101C2×D411yescharacteristic
318C42×C101C2×D411yescharacteristic
319C23×C101—21no—
320C23×C101—21no—
321C23×C101—21no—
322C23×C101—21no—
323C23×C101—42no—
324C23×C101H(5,𝔽2)11yescharacteristic
325Q8×C101—21no—
326Q8×C101—21no—
327Q8×C101—21no—
328Q8×C101—22no—
329Q8×C101—21no—
330Q8×C101—21no—
331Q8×C101—21no—
332Q8×C101—22no—
333Q8×C101—42no—
334Q8×C101—44no—
335Q8×C101—41no—
336Q8×C101—41no—
337Q8×C101—41no—
338Q8×C101—41no—
339Q8×C101—41no—
340Q8×C101—41no—
341Q8×C101#12012yes—
342Q8×C101#12112yes—
343D4×C101—22no—
344D4×C101—22no—
345D4×C101—22no—
346D4×C101—22no—
347D4×C101—21no—
348D4×C101—21no—
349D4×C101—21no—
350D4×C101—21no—
351D4×C101—21no—
352D4×C101—21no—
353D4×C101—42no—
354D4×C101—42no—
355D4×C101—42no—
356D4×C101—44no—
357D4×C101—41no—
358D4×C101—41no—
359D4×C101—41no—
360D4×C101—41no—
361D4×C101#12012yes—
362D4×C101#12112yes—
363C2×C4×C101—21no—
364C2×C4×C101—21no—
365C2×C4×C101—21no—
366C2×C4×C101—22no—
367C2×C4×C101—22no—
368C2×C4×C101—22no—
369C2×C4×C101—22no—
370C2×C4×C101—21no—
371C2×C4×C101—21no—
372C2×C4×C101—22no—
373C2×C4×C101—21no—
374C2×C4×C101—42no—
375C2×C4×C101—42no—
376C2×C4×C101—42no—
377C2×C4×C101—42no—
378C2×C4×C101—44no—
379C2×C4×C101—44no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—41no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—82no—
392C2×C4×C101C22×D411yescharacteristic
393C2×C4×C101C22×D411yescharacteristic
394C2×C4×C101C22×D411yescharacteristic
395C2×C4×C101C22×D411yescharacteristic
396C2×C4×C101C2×#4111yescharacteristic
397C2×C4×C101H(5,𝔽2)11yescharacteristic
398C8×C101—22no—
399C8×C101—22no—
400C8×C101—22no—
401C8×C101—41no—
402C8×C101—41no—
403C8×C101—41no—
404C22×C101—22no—
405C22×C101—22no—
406C22×C101—41no—
407C22×C101—41no—
408C22×C101—41no—
409C22×C101—81no—
410C22×C101—81no—
411C22×C101—81no—
412C22×C101—81no—
413C22×C101—162no—
414C22×C101#53411yescharacteristic
415C22×C101D4211yescharacteristic
416C22×C101#54611yescharacteristic
417C4×C101—22no—
418C4×C101—22no—
419C4×C101—22no—
420C4×C101—41no—
421C4×C101—41no—
422C4×C101—42no—
423C4×C101—41no—
424C4×C101—81no—
425C4×C101—81no—
426C4×C101—81no—
427C4×C101C2×#12011yescharacteristic
428C4×C101C2×#12111yescharacteristic
429C4×C101D4211yescharacteristic
430C4×C101#54611yescharacteristic
431#24474C10111yesmaximal, characteristic, direct product factor, Sylow
432C2×C101—21no—
433C2×C101—21no—
434C2×C101—21no—
435C2×C101—42no—
436C2×C101—42no—
437C2×C101—81no—
438C2×C101—81no—
439C2×C101#241011yescharacteristic
440#3586C2×C10111yescharacteristic
441#3069C2×C10111yescharacteristic, complemented
442#3039C2×C10111yescharacteristic, complemented
443#3022C2×C10111yescharacteristic, complemented
444C2×#456C2×C10111yescharacteristic, complemented
445#2901C2×C10111yescharacteristic, complemented
446#2050C2×C10111yescharacteristic, complemented
447#2049C2×C10111yescharacteristic, complemented
448#2009C2×C10111yescharacteristic, complemented
449#2005C2×C10111yescharacteristic, complemented
450#1906C2×C10111yescharacteristic, complemented
451#1902C2×C10111yescharacteristic, complemented
452#1902C2×C10111yescharacteristic, complemented
453#1861C2×C10111yescharacteristic, complemented
454#1796C2×C10111yescharacteristic, complemented
455C101#2447411yescharacteristic, direct product factor, Sylow
456#585C22×C10111yescharacteristic
457C2×2−1+4C22×C10111yescharacteristic
458#578—22no—
459#578—22no—
460#577—22no—
461#577—22no—
462#575—22no—
463#575C22×C10111yescharacteristic
464#575C22×C10111yescharacteristic
465C2×#137—22no—
466C2×#137C22×C10111yescharacteristic
467C2×#137C22×C10111yescharacteristic
468C2×#137C22×C10111yescharacteristic
469C2×#137C22×C10111yescharacteristic
470C2×#137C22×C10111yescharacteristic, complemented
471#568C22×C10111yescharacteristic
472#568C22×C10111yescharacteristic
473#536C22×C10111yescharacteristic
474C2×C4⋊Q8C22×C10111yescharacteristic, complemented
475C4×#41C22×C10111yescharacteristic
476#473—22no—
477#471—22no—
478#462—22no—
479#461—22no—
480#456—22no—
481#456—22no—
482#456—22no—
483#455—22no—
484#430C22×C10111yescharacteristic, complemented
485#423C22×C10111yescharacteristic, complemented
486#421—22no—
487#421C22×C10111yescharacteristic
488#421C22×C10111yescharacteristic
489#421C22×C10111yescharacteristic
490#421C22×C10111yescharacteristic
491C2×#104—22no—
492C2×#104C22×C10111yescharacteristic
493C2×#104C22×C10111yescharacteristic
494C2×#104C22×C10111yescharacteristic, complemented
495#419C22×C10111yescharacteristic, complemented
496#419C22×C10111yescharacteristic, complemented
497#419C22×C10111yescharacteristic, complemented
498#413C22×C10111yescharacteristic
499#413C22×C10111yescharacteristic, complemented
500C2×#101C22×C10111yescharacteristic, complemented
501C2×#101C22×C10111yescharacteristic, complemented
502#410C22×C10111yescharacteristic, complemented
503#344C22×C10111yescharacteristic, complemented
504#344C22×C10111yescharacteristic, complemented
505#339C22×C10111yescharacteristic, complemented
506#338C22×C10111yescharacteristic, complemented
5072−1+4—22no—
5082−1+4—22no—
5092−1+4—21no—
5102−1+4—21no—
5112−1+4—22no—
5122−1+4—41no—
5132−1+4D4×C10112yes—
514H(5,𝔽2)—21no—
515H(5,𝔽2)—21no—
516H(5,𝔽2)—41no—
517H(5,𝔽2)D4×C10112yes—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C10111yescharacteristic
525C2×#41C23×C10111yescharacteristic
526C2×#41C23×C10111yescharacteristic
527C2×#41C23×C10111yescharacteristic
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C10111yescharacteristic
531C22×Q8C23×C10111yescharacteristic
532#137—24no—
533#137—24no—
534#137—24no—
535#137—22no—
536#137—22no—
537#137—21no—
538#137—22no—
539#137—21no—
540#137—21no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—41no—
548#137D4×C10112yes—
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)D4×C10112yes—
554#135—24no—
555#135—24no—
556#135—22no—
557#135—22no—
558C2×Q16—24no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C10112yes—
564C2×SD16—24no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16D4×C10112yes—
570#131—22no—
571#131—22no—
572#131—22no—
573#131—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16C23×C10111yescharacteristic
577C2×M16C23×C10111yescharacteristic
578C2×M16C23×C10111yescharacteristic
579C2×M16C23×C10111yescharacteristic
580C2×M16C23×C10111yescharacteristic
581C2×M16C23×C10111yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586#124—21no—
587#123—41no—
588C22⋊Q8—41no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C10111yescharacteristic
594#117C23×C10111yescharacteristic
595C2×C4⋊C4—41no—
596C2×C42—21no—
597C2×C42C23×C10111yescharacteristic
598#108—22no—
599C4⋊C8—22no—
600#104—22no—
601#104—22no—
602#104—22no—
603#104—22no—
604#104—21no—
605#104—21no—
606#104—21no—
607#104—21no—
608#104D4×C10112yes—
609#104D4×C10112yes—
610#103—22no—
611#103—22no—
612#103—41no—
613#101—21no—
614#101—21no—
615#101—22no—
616#101—22no—
617#100—21no—
618#100—21no—
619#99—41no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—24no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—41no—
645#41—41no—
646#41—44no—
647#41—42no—
648#41C2×D4×C10112yes—
649#41C2×D4×C10112yes—
650#41C2×D4×C10112yes—
651#41C2×D4×C10112yes—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—41no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8C2×D4×C10111yescharacteristic
672C2×Q8C2×D4×C10111yescharacteristic
673C2×Q8C2×D4×C10112yes—
674C2×Q8C2×D4×C10111yescharacteristic
675C2×Q8#41×C10111yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4C2×D4×C10111yescharacteristic
688C2×D4C2×D4×C10111yescharacteristic
689C2×D4C2×D4×C10111yescharacteristic
690C2×D4#41×C10111yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C10111yescharacteristic
703Q16—24no—
704Q16—22no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710SD16—24no—
711SD16—22no—
712SD16—22no—
713SD16—22no—
714SD16—22no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719D8—22no—
720D8—22no—
721M16—24no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—42no—
733M16C2×D4×C10112yes—
734M16C2×D4×C10112yes—
735C2×C8—24no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—42no—
742C2×C8C2×D4×C10112yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—42no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—41no—
757C42C2×D4×C10111yescharacteristic
758C42C2×D4×C10111yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—42no—
764C23H(5,𝔽2)×C10111yescharacteristic
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—22no—
773Q8—42no—
774Q8—44no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C10112yes—
782Q8#121×C10112yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4#120×C10112yes—
802D4#121×C10112yes—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—82no—
832C2×C4C22×D4×C10111yescharacteristic
833C2×C4C22×D4×C10111yescharacteristic
834C2×C4C22×D4×C10111yescharacteristic
835C2×C4C22×D4×C10111yescharacteristic
836C2×C4C2×#41×C10111yescharacteristic
837C2×C4H(5,𝔽2)×C10111yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—162no—
854C22#534×C10111yescharacteristic
855C22D42×C10111yescharacteristic
856C22#546×C10111yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4C2×#120×C10111yescharacteristic
868C4C2×#121×C10111yescharacteristic
869C4D42×C10111yescharacteristic
870C4#546×C10111yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—42no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2C101×#241011yescharacteristic
subgroupG/H
center, socleC2×C101#2410
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3586C2
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
2. C101×#3069C2semidirect
3. C101×#3039C2semidirect
4. C101×#3022C2semidirect
5. C2×#456×C101C2semidirect
6. C101×#2901C2semidirect
7. C101×#2050C2semidirect
8. C101×#2049C2semidirect
9. C101×#2009C2semidirect
10. C101×#2005C2semidirect
11. C101×#1906C2semidirect
12. C101×#1902C2semidirect
13. C101×#1902C2semidirect
14. C101×#1861C2semidirect
15. C101×#1796C2semidirect
30. C2×#137×C101C22semidirect
34. C2×C4⋊Q8×C101C22semidirect
44. #430×C101C22semidirect
45. #423×C101C22semidirect
54. C2×#104×C101C22semidirect
55. #419×C101C22semidirect
56. #419×C101C22semidirect
57. #419×C101C22semidirect
59. #413×C101C22semidirect
60. C2×#101×C101C22semidirect
61. C2×#101×C101C22semidirect
62. #410×C101C22semidirect
63. #344×C101C22semidirect
64. #344×C101C22semidirect
65. #339×C101C22semidirect
66. #338×C101C22semidirect
431. #24474C101direct (N × H)
441. #3069C2×C101semidirect
442. #3039C2×C101semidirect
443. #3022C2×C101semidirect
444. C2×#456C2×C101semidirect
445. #2901C2×C101semidirect
446. #2050C2×C101semidirect
447. #2049C2×C101semidirect
448. #2009C2×C101semidirect
449. #2005C2×C101semidirect
450. #1906C2×C101semidirect
451. #1902C2×C101semidirect
452. #1902C2×C101semidirect
453. #1861C2×C101semidirect
454. #1796C2×C101semidirect
455. C101#24474direct (N × H)
470. C2×#137C22×C101semidirect
474. C2×C4⋊Q8C22×C101semidirect
484. #430C22×C101semidirect
485. #423C22×C101semidirect
494. C2×#104C22×C101semidirect
495. #419C22×C101semidirect
496. #419C22×C101semidirect
497. #419C22×C101semidirect
499. #413C22×C101semidirect
500. C2×#101C22×C101semidirect
501. C2×#101C22×C101semidirect
502. #410C22×C101semidirect
503. #344C22×C101semidirect
504. #344C22×C101semidirect
505. #339C22×C101semidirect
506. #338C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35862
C101×#30692
C101×#30392
C101×#30222
C2×#456×C1012
C101×#29012
C101×#20502
C101×#20492
C101×#20092
C101×#20052
C101×#19062
C101×#19022
C101×#18612
C101×#17962
#24474101