Finite Group Databasebeta

← C101×#24462 #38806613

Subgroups — C101×#24462 #38806613

Order 25856.

1302 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C101C211yesmaximal, characteristic
2C2×#473×C101C211yesmaximal, characteristic, complemented
3C101×#3046C211yesmaximal, characteristic, complemented
4C2×#456×C101C211yesmaximal, characteristic, complemented
5C101×#3011C211yesmaximal, characteristic, complemented
6C101×#2898C211yesmaximal, characteristic, complemented
7C101×#2052C211yesmaximal, characteristic, complemented
8C101×#2047C211yesmaximal, characteristic, complemented
9C101×#2016C211yesmaximal, characteristic, complemented
10C101×#2005C211yesmaximal, characteristic, complemented
11C101×#1908C211yesmaximal, characteristic, complemented
12C101×#1882C211yesmaximal, characteristic, complemented
13C101×#1876C211yesmaximal, characteristic, complemented
14C101×#1866C211yesmaximal, characteristic, complemented
15C101×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C101C2211yescharacteristic
17C2×2−1+4×C101C2211yescharacteristic
18#578×C101—24no—
19#578×C101—24no—
20C2×#137×C101—21no—
21C2×#137×C101—21no—
22C2×#137×C101C2211yescharacteristic
23C2×#137×C101C2211yescharacteristic
24C2×#137×C101C2211yescharacteristic
25C2×#137×C101C2211yescharacteristic
26C2×#135×C101—21no—
27C2×#135×C101C2211yescharacteristic
28C22×Q16×C101—21no—
29C22×Q16×C101C2211yescharacteristic
30C22×Q16×C101C2211yescharacteristic
31C2×#131×C101C2211yescharacteristic
32C2×#131×C101C2211yescharacteristic
33#536×C101C2211yescharacteristic
34C2×C4⋊Q8×C101C2211yescharacteristic
35#520×C101C2211yescharacteristic
36#473×C101—24no—
37#464×C101—21no—
38#463×C101—21no—
39#462×C101—21no—
40#461×C101—21no—
41#456×C101—24no—
42#452×C101—21no—
43#452×C101—21no—
44#451×C101—21no—
45#451×C101—21no—
46C2×#108×C101C2211yescharacteristic
47#424×C101C2211yescharacteristic
48C2×#104×C101C2211yescharacteristic
49C2×#104×C101C2211yescharacteristic
50C2×#104×C101C2211yescharacteristic
51#419×C101—21no—
52#419×C101C2211yescharacteristic
53#419×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
61C2×#103×C101C2211yescharacteristic
62C2×#101×C101C2211yescharacteristic
63C2×#101×C101C2211yescharacteristic
64C2×#101×C101C2211yescharacteristic
65#408×C101C2211yescharacteristic
66#391×C101C2211yescharacteristic
67#343×C101C2211yescharacteristic
68#341×C101C2211yescharacteristic
69#339×C101C2211yescharacteristic
70#336×C101C2211yescharacteristic
712−1+4×C101—22no—
722−1+4×C101—22no—
732−1+4×C101—22no—
742−1+4×C101—22no—
752−1+4×C101—22no—
762−1+4×C101—41no—
772−1+4×C101—41no—
782−1+4×C101D414yes—
79C2×#41×C101—21no—
80C2×#41×C101—21no—
81C2×#41×C101—21no—
82C2×#41×C101—21no—
83C2×#41×C101—41no—
84C2×#41×C101—41no—
85C2×#41×C101C2311yescharacteristic
86C2×#41×C101C2311yescharacteristic
87C2×#41×C101C2311yescharacteristic
88C22×Q8×C101—21no—
89C22×Q8×C101—21no—
90C22×Q8×C101—21no—
91C22×Q8×C101—21no—
92C22×Q8×C101C2311yescharacteristic
93C22×Q8×C101C2311yescharacteristic
94C22×Q8×C101C2311yescharacteristic
95#137×C101—28no—
96#137×C101—28no—
97#137×C101—22no—
98#137×C101—22no—
99#137×C101—22no—
100#137×C101—22no—
101#137×C101—22no—
102#137×C101—22no—
103#137×C101—22no—
104#137×C101D414yes—
105#135×C101—28no—
106#135×C101—22no—
107#135×C101—22no—
108C2×Q16×C101—28no—
109C2×Q16×C101—21no—
110C2×Q16×C101—21no—
111C2×Q16×C101—22no—
112C2×Q16×C101—22no—
113C2×Q16×C101—21no—
114C2×Q16×C101—21no—
115C2×Q16×C101—22no—
116C2×Q16×C101—21no—
117C2×Q16×C101—21no—
118C2×Q16×C101—21no—
119C2×Q16×C101—21no—
120C2×Q16×C101—41no—
121C2×Q16×C101D411yescharacteristic
122C2×SD16×C101—21no—
123C2×SD16×C101—21no—
124C2×SD16×C101—21no—
125C2×SD16×C101—21no—
126C2×SD16×C101D411yescharacteristic
127C2×SD16×C101D411yescharacteristic
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
143C4⋊Q8×C101—22no—
144C4⋊Q8×C101—21no—
145C4⋊Q8×C101—41no—
146#124×C101—21no—
147#123×C101—41no—
148C22⋊Q8×C101—21no—
149C22⋊Q8×C101—21no—
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×C101—41no—
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×C101—21no—
170#103×C101—21no—
171#103×C101—21no—
172#103×C101—21no—
173#103×C101—21no—
174#103×C101—21no—
175#103×C101D411yescharacteristic
176#103×C101D411yescharacteristic
177#102×C101—21no—
178#102×C101—21no—
179#102×C101D411yescharacteristic
180#102×C101D411yescharacteristic
181#101×C101—22no—
182#101×C101—22no—
183#101×C101—22no—
184C22⋊C8×C101—21no—
185C22⋊C8×C101—21no—
186#95×C101—41no—
187#41×C101—21no—
188#41×C101—21no—
189#41×C101—21no—
190#41×C101—21no—
191#41×C101—24no—
192#41×C101—24no—
193#41×C101—24no—
194#41×C101—21no—
195#41×C101—21no—
196#41×C101—21no—
197#41×C101—21no—
198#41×C101—44no—
199#41×C101—42no—
200#41×C101—42no—
201#41×C101—42no—
202#41×C101—44no—
203#41×C101—44no—
204#41×C101—42no—
205#41×C101—44no—
206#41×C101—42no—
207#41×C101C2×D412yes—
208#41×C101C2×D412yes—
209#41×C101C2×D412yes—
210#41×C101#4112yes—
211C2×Q8×C101—21no—
212C2×Q8×C101—21no—
213C2×Q8×C101—24no—
214C2×Q8×C101—24no—
215C2×Q8×C101—24no—
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—21no—
227C2×Q8×C101—21no—
228C2×Q8×C101—21no—
229C2×Q8×C101—21no—
230C2×Q8×C101—41no—
231C2×Q8×C101—41no—
232C2×Q8×C101—42no—
233C2×Q8×C101—42no—
234C2×Q8×C101—42no—
235C2×Q8×C101—42no—
236C2×Q8×C101—42no—
237C2×Q8×C101C2×D412yes—
238C2×Q8×C101C2×D412yes—
239C2×Q8×C101C2×D411yescharacteristic
240C2×Q8×C101C2×D411yescharacteristic
241C2×Q8×C101C2×D411yescharacteristic
242C2×D4×C101—21no—
243C2×D4×C101—21no—
244C2×D4×C101—21no—
245C2×D4×C101—41no—
246C2×D4×C101—41no—
247C2×D4×C101C2×D411yescharacteristic
248C2×D4×C101C2×D411yescharacteristic
249C2×D4×C101C2×D411yescharacteristic
250C22×C4×C101—21no—
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—41no—
259C22×C4×C101—41no—
260C22×C4×C101—41no—
261C22×C4×C101—41no—
262C22×C4×C101—41no—
263C22×C4×C101C2411yescharacteristic
264Q16×C101—24no—
265Q16×C101—24no—
266Q16×C101—24no—
267Q16×C101—22no—
268Q16×C101—24no—
269Q16×C101—42no—
270Q16×C101—42no—
271Q16×C101—42no—
272Q16×C101—42no—
273SD16×C101—24no—
274SD16×C101—22no—
275SD16×C101—24no—
276SD16×C101—22no—
277SD16×C101—42no—
278SD16×C101—42no—
279D8×C101—22no—
280M16×C101—24no—
281M16×C101—21no—
282M16×C101—21no—
283M16×C101—21no—
284M16×C101—21no—
285M16×C101—21no—
286M16×C101—21no—
287M16×C101—21no—
288M16×C101—42no—
289M16×C101C2×D412yes—
290C2×C8×C101—24no—
291C2×C8×C101—21no—
292C2×C8×C101—21no—
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—42no—
300C2×C8×C101C2×D411yescharacteristic
301C2×C8×C101C2×D411yescharacteristic
302C2×C8×C101C2×D411yescharacteristic
303C2×C8×C101C2×D411yescharacteristic
304C4⋊C4×C101—21no—
305C4⋊C4×C101—21no—
306C4⋊C4×C101—41no—
307C4⋊C4×C101—41no—
308C4⋊C4×C101—41no—
309C4⋊C4×C101—44no—
310C4⋊C4×C101C2×D411yescharacteristic
311C4⋊C4×C101C2×D411yescharacteristic
312C22⋊C4×C101—21no—
313C22⋊C4×C101—41no—
314C22⋊C4×C101—41no—
315C22⋊C4×C101—41no—
316C42×C101—21no—
317C42×C101—21no—
318C42×C101—21no—
319C42×C101—41no—
320C23×C101—21no—
321C23×C101—21no—
322C23×C101—21no—
323C23×C101H(5,𝔽2)11yescharacteristic
324Q8×C101—21no—
325Q8×C101—21no—
326Q8×C101—22no—
327Q8×C101—22no—
328Q8×C101—21no—
329Q8×C101—22no—
330Q8×C101—22no—
331Q8×C101—21no—
332Q8×C101—44no—
333Q8×C101—44no—
334Q8×C101—41no—
335Q8×C101—41no—
336Q8×C101—41no—
337Q8×C101—41no—
338Q8×C101—41no—
339Q8×C101—41no—
340Q8×C101—41no—
341Q8×C101—41no—
342Q8×C101#12012yes—
343Q8×C101#12112yes—
344D4×C101—22no—
345D4×C101—22no—
346D4×C101—22no—
347D4×C101—22no—
348D4×C101—21no—
349D4×C101—21no—
350D4×C101—21no—
351D4×C101—21no—
352D4×C101—44no—
353D4×C101—44no—
354D4×C101—41no—
355D4×C101—41no—
356D4×C101#12012yes—
357D4×C101#12112yes—
358C2×C4×C101—21no—
359C2×C4×C101—21no—
360C2×C4×C101—22no—
361C2×C4×C101—22no—
362C2×C4×C101—22no—
363C2×C4×C101—22no—
364C2×C4×C101—22no—
365C2×C4×C101—22no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—21no—
369C2×C4×C101—22no—
370C2×C4×C101—44no—
371C2×C4×C101—44no—
372C2×C4×C101—44no—
373C2×C4×C101—41no—
374C2×C4×C101—44no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—41no—
379C2×C4×C101—41no—
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—81no—
387C2×C4×C101—161no—
388C2×C4×C101C22×D411yescharacteristic
389C2×C4×C101C22×D411yescharacteristic
390C2×C4×C101C22×D411yescharacteristic
391C2×C4×C101C22×D411yescharacteristic
392C2×C4×C101C2×#4111yescharacteristic
393C2×C4×C101H(5,𝔽2)11yescharacteristic
394C8×C101—21no—
395C8×C101—22no—
396C8×C101—21no—
397C8×C101—21no—
398C8×C101—21no—
399C8×C101—41no—
400C8×C101—41no—
401C8×C101—41no—
402C22×C101—21no—
403C22×C101—21no—
404C22×C101—22no—
405C22×C101—22no—
406C22×C101—41no—
407C22×C101—41no—
408C22×C101—41no—
409C22×C101—41no—
410C22×C101—41no—
411C22×C101—41no—
412C22×C101—41no—
413C22×C101#53411yescharacteristic
414C22×C101D4211yescharacteristic
415C22×C101#54611yescharacteristic
416C4×C101—22no—
417C4×C101—22no—
418C4×C101—42no—
419C4×C101—42no—
420C4×C101—41no—
421C4×C101—42no—
422C4×C101—41no—
423C4×C101—41no—
424C4×C101—81no—
425C4×C101—81no—
426C4×C101C2×#12011yescharacteristic
427C4×C101C2×#12111yescharacteristic
428C4×C101D4211yescharacteristic
429C4×C101#54611yescharacteristic
430#24462C10111yesmaximal, characteristic, direct product factor, Sylow
431C2×C101—21no—
432C2×C101—21no—
433C2×C101—42no—
434C2×C101—42no—
435C2×C101—81no—
436C2×C101#241011yescharacteristic
437C2×C101#328911yescharacteristic
438C2×C101#329311yescharacteristic
439C2×#578C2×C10111yescharacteristic
440C2×#473C2×C10111yescharacteristic, complemented
441#3046C2×C10111yescharacteristic, complemented
442C2×#456C2×C10111yescharacteristic, complemented
443#3011C2×C10111yescharacteristic, complemented
444#2898C2×C10111yescharacteristic, complemented
445#2052C2×C10111yescharacteristic, complemented
446#2047C2×C10111yescharacteristic, complemented
447#2016C2×C10111yescharacteristic, complemented
448#2005C2×C10111yescharacteristic, complemented
449#1908C2×C10111yescharacteristic, complemented
450#1882C2×C10111yescharacteristic, complemented
451#1876C2×C10111yescharacteristic, complemented
452#1866C2×C10111yescharacteristic, complemented
453#1793C2×C10111yescharacteristic, complemented
454C101#2446211yescharacteristic, direct product factor, Sylow
455C2×2−1+4C22×C10111yescharacteristic
456C2×2−1+4C22×C10111yescharacteristic
457#578—24no—
458#578—24no—
459C2×#137—21no—
460C2×#137—21no—
461C2×#137C22×C10111yescharacteristic
462C2×#137C22×C10111yescharacteristic
463C2×#137C22×C10111yescharacteristic
464C2×#137C22×C10111yescharacteristic
465C2×#135—21no—
466C2×#135C22×C10111yescharacteristic
467C22×Q16—21no—
468C22×Q16C22×C10111yescharacteristic
469C22×Q16C22×C10111yescharacteristic
470C2×#131C22×C10111yescharacteristic
471C2×#131C22×C10111yescharacteristic
472#536C22×C10111yescharacteristic
473C2×C4⋊Q8C22×C10111yescharacteristic
474#520C22×C10111yescharacteristic
475#473—24no—
476#464—21no—
477#463—21no—
478#462—21no—
479#461—21no—
480#456—24no—
481#452—21no—
482#452—21no—
483#451—21no—
484#451—21no—
485C2×#108C22×C10111yescharacteristic
486#424C22×C10111yescharacteristic
487C2×#104C22×C10111yescharacteristic
488C2×#104C22×C10111yescharacteristic
489C2×#104C22×C10111yescharacteristic
490#419—21no—
491#419C22×C10111yescharacteristic
492#419C22×C10111yescharacteristic
493#417—21no—
494#417C22×C10111yescharacteristic
495#417C22×C10111yescharacteristic
496#416—21no—
497#416C22×C10111yescharacteristic
498C2×#103—21no—
499C2×#103C22×C10111yescharacteristic
500C2×#103C22×C10111yescharacteristic
501C2×#101C22×C10111yescharacteristic
502C2×#101C22×C10111yescharacteristic
503C2×#101C22×C10111yescharacteristic
504#408C22×C10111yescharacteristic
505#391C22×C10111yescharacteristic
506#343C22×C10111yescharacteristic
507#341C22×C10111yescharacteristic
508#339C22×C10111yescharacteristic
509#336C22×C10111yescharacteristic
5102−1+4—22no—
5112−1+4—22no—
5122−1+4—22no—
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—41no—
5162−1+4—41no—
5172−1+4D4×C10114yes—
518C2×#41—21no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C10111yescharacteristic
525C2×#41C23×C10111yescharacteristic
526C2×#41C23×C10111yescharacteristic
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8C23×C10111yescharacteristic
532C22×Q8C23×C10111yescharacteristic
533C22×Q8C23×C10111yescharacteristic
534#137—28no—
535#137—28no—
536#137—22no—
537#137—22no—
538#137—22no—
539#137—22no—
540#137—22no—
541#137—22no—
542#137—22no—
543#137D4×C10114yes—
544#135—28no—
545#135—22no—
546#135—22no—
547C2×Q16—28no—
548C2×Q16—21no—
549C2×Q16—21no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—21no—
554C2×Q16—21no—
555C2×Q16—21no—
556C2×Q16—21no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16—41no—
560C2×Q16D4×C10111yescharacteristic
561C2×SD16—21no—
562C2×SD16—21no—
563C2×SD16—21no—
564C2×SD16—21no—
565C2×SD16D4×C10111yescharacteristic
566C2×SD16D4×C10111yescharacteristic
567C2×D8D4×C10111yescharacteristic
568#131—22no—
569#131—22no—
570#131—22no—
571#131—41no—
572C2×M16—21no—
573C2×M16—21no—
574C2×M16C23×C10111yescharacteristic
575C2×M16C23×C10111yescharacteristic
576C2×M16C23×C10111yescharacteristic
577C2×M16C23×C10111yescharacteristic
578C22×C8—21no—
579C22×C8—21no—
580C22×C8C23×C10111yescharacteristic
581C22×C8C23×C10111yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—41no—
585#124—21no—
586#123—41no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C10111yescharacteristic
594C2×C4⋊C4—21no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4C23×C10111yescharacteristic
597C2×C42C23×C10111yescharacteristic
598#108—22no—
599C4⋊C8—21no—
600C4⋊C8—21no—
601#104—22no—
602#104—22no—
603#104—41no—
604#103—21no—
605#103—21no—
606#103—21no—
607#103—21no—
608#103—21no—
609#103—21no—
610#103—21no—
611#103—21no—
612#103—21no—
613#103—21no—
614#103D4×C10111yescharacteristic
615#103D4×C10111yescharacteristic
616#102—21no—
617#102—21no—
618#102D4×C10111yescharacteristic
619#102D4×C10111yescharacteristic
620#101—22no—
621#101—22no—
622#101—22no—
623C22⋊C8—21no—
624C22⋊C8—21no—
625#95—41no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—24no—
631#41—24no—
632#41—24no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—44no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—44no—
642#41—44no—
643#41—42no—
644#41—44no—
645#41—42no—
646#41C2×D4×C10112yes—
647#41C2×D4×C10112yes—
648#41C2×D4×C10112yes—
649#41#41×C10112yes—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—21no—
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—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—41no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8C2×D4×C10112yes—
677C2×Q8C2×D4×C10112yes—
678C2×Q8C2×D4×C10111yescharacteristic
679C2×Q8C2×D4×C10111yescharacteristic
680C2×Q8C2×D4×C10111yescharacteristic
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4C2×D4×C10111yescharacteristic
687C2×D4C2×D4×C10111yescharacteristic
688C2×D4C2×D4×C10111yescharacteristic
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C10111yescharacteristic
703Q16—24no—
704Q16—24no—
705Q16—24no—
706Q16—22no—
707Q16—24no—
708Q16—42no—
709Q16—42no—
710Q16—42no—
711Q16—42no—
712SD16—24no—
713SD16—22no—
714SD16—24no—
715SD16—22no—
716SD16—42no—
717SD16—42no—
718D8—22no—
719M16—24no—
720M16—21no—
721M16—21no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—42no—
728M16C2×D4×C10112yes—
729C2×C8—24no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—42no—
739C2×C8C2×D4×C10111yescharacteristic
740C2×C8C2×D4×C10111yescharacteristic
741C2×C8C2×D4×C10111yescharacteristic
742C2×C8C2×D4×C10111yescharacteristic
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—41no—
746C4⋊C4—41no—
747C4⋊C4—41no—
748C4⋊C4—44no—
749C4⋊C4C2×D4×C10111yescharacteristic
750C4⋊C4C2×D4×C10111yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—41no—
753C22⋊C4—41no—
754C22⋊C4—41no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—41no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23H(5,𝔽2)×C10111yescharacteristic
763Q8—21no—
764Q8—21no—
765Q8—22no—
766Q8—22no—
767Q8—21no—
768Q8—22no—
769Q8—22no—
770Q8—21no—
771Q8—44no—
772Q8—44no—
773Q8—41no—
774Q8—41no—
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—44no—
792D4—44no—
793D4—41no—
794D4—41no—
795D4#120×C10112yes—
796D4#121×C10112yes—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—41no—
813C2×C4—44no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—81no—
826C2×C4—161no—
827C2×C4C22×D4×C10111yescharacteristic
828C2×C4C22×D4×C10111yescharacteristic
829C2×C4C22×D4×C10111yescharacteristic
830C2×C4C22×D4×C10111yescharacteristic
831C2×C4C2×#41×C10111yescharacteristic
832C2×C4H(5,𝔽2)×C10111yescharacteristic
833C8—21no—
834C8—22no—
835C8—21no—
836C8—21no—
837C8—21no—
838C8—41no—
839C8—41no—
840C8—41no—
841C22—21no—
842C22—21no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22#534×C10111yescharacteristic
853C22D42×C10111yescharacteristic
854C22#546×C10111yescharacteristic
855C4—22no—
856C4—22no—
857C4—42no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—41no—
863C4—81no—
864C4—81no—
865C4C2×#120×C10111yescharacteristic
866C4C2×#121×C10111yescharacteristic
867C4D42×C10111yescharacteristic
868C4#546×C10111yescharacteristic
869C2—21no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—81no—
874C2C101×#241011yescharacteristic
875C2C101×#328911yescharacteristic
876C2C101×#329311yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#578×C101C2
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
2. C2×#473×C101C2semidirect
3. C101×#3046C2semidirect
4. C2×#456×C101C2semidirect
5. C101×#3011C2semidirect
6. C101×#2898C2semidirect
7. C101×#2052C2semidirect
8. C101×#2047C2semidirect
9. C101×#2016C2semidirect
10. C101×#2005C2semidirect
11. C101×#1908C2semidirect
12. C101×#1882C2semidirect
13. C101×#1876C2semidirect
14. C101×#1866C2semidirect
15. C101×#1793C2semidirect
430. #24462C101direct (N × H)
440. C2×#473C2×C101semidirect
441. #3046C2×C101semidirect
442. C2×#456C2×C101semidirect
443. #3011C2×C101semidirect
444. #2898C2×C101semidirect
445. #2052C2×C101semidirect
446. #2047C2×C101semidirect
447. #2016C2×C101semidirect
448. #2005C2×C101semidirect
449. #1908C2×C101semidirect
450. #1882C2×C101semidirect
451. #1876C2×C101semidirect
452. #1866C2×C101semidirect
453. #1793C2×C101semidirect
454. C101#24462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#578×C1012
C2×#473×C1012
C101×#30462
C2×#456×C1012
C101×#30112
C101×#28982
C101×#20522
C101×#20472
C101×#20162
C101×#20052
C101×#19082
C101×#18822
C101×#18762
C101×#18662
C101×#17932
#24462101