Finite Group Databasebeta

← C101×#24404 #38806555

Subgroups — C101×#24404 #38806555

Order 25856.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3484C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C101C211yesmaximal, characteristic, complemented
3C22×#99×C101C211yesmaximal, characteristic, complemented
4C101×#2410C212yesmaximal, complemented
5C101×#2403C211yesmaximal, characteristic, complemented
6C101×#2044C212yesmaximal, complemented
7C101×#2021C212yesmaximal, complemented
8C101×#1898C212yesmaximal, complemented
9C101×#1889C211yesmaximal, characteristic, complemented
10C101×#1867C211yesmaximal, characteristic, complemented
11C101×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C101C2211yescharacteristic
13C23×D4×C101C2211yescharacteristic
14C23×D4×C101C2211yescharacteristic, complemented
15#546×C101—22no—
16#546×C101—22no—
17D42×C101—22no—
18D42×C101—22no—
19#535×C101—21no—
20#534×C101—21no—
21#534×C101C2212yes—
22#525×C101—21no—
23C2×#121×C101—22no—
24C2×#120×C101—21no—
25C2×#120×C101—21no—
26C2×#120×C101C2211yescharacteristic
27C2×#120×C101C2212yes—
28C2×#120×C101C2212yescomplemented
29C2×#120×C101C2211yescharacteristic, complemented
30#518×C101C2211yescharacteristic
31C22×C22⋊C4×C101C2212yescomplemented
32B(4,𝔽2)×C101—24no—
33C2×#99×C101—24no—
34C2×#99×C101C2211yescharacteristic
35C2×#99×C101C2211yescharacteristic
36C2×#99×C101C2212yescomplemented
37C2×#99×C101C2212yescomplemented
38C2×#99×C101C2212yescomplemented
39#394×C101—22no—
40#392×C101—21no—
41#392×C101—21no—
42#392×C101—22no—
43#386×C101—21no—
44#386×C101—22no—
45#386×C101C2211yescharacteristic
46#386×C101C2211yescharacteristic, complemented
47#386×C101C2212yescomplemented
48#385×C101C2212yescomplemented
49#379×C101C2212yescomplemented
50#379×C101C2211yescharacteristic, complemented
51#342×C101C2212yescomplemented
52#342×C101C2212yescomplemented
53C25×C101D411yescharacteristic, complemented
54C25×C101C2311yescharacteristic
55C25×C101C2311yescharacteristic
56H(5,𝔽2)×C101—22no—
57H(5,𝔽2)×C101—22no—
58H(5,𝔽2)×C101—42no—
59C2×#41×C101—21no—
60C2×#41×C101—22no—
61C22×D4×C101—21no—
62C22×D4×C101—21no—
63C22×D4×C101—22no—
64C22×D4×C101—22no—
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—22no—
70C22×D4×C101—22no—
71C22×D4×C101—21no—
72C22×D4×C101—22no—
73C22×D4×C101—21no—
74C22×D4×C101—21no—
75C22×D4×C101—22no—
76C22×D4×C101—44no—
77C22×D4×C101—42no—
78C22×D4×C101D411yescharacteristic, complemented
79C22×D4×C101D411yescharacteristic, complemented
80C22×D4×C101D412yescomplemented
81C22×D4×C101D412yescomplemented
82C22×D4×C101C2312yes—
83C22×D4×C101C2311yescharacteristic
84C22×D4×C101C2311yescharacteristic
85C23×C4×C101—22no—
86C23×C4×C101D411yescharacteristic, complemented
87C23×C4×C101C2311yescharacteristic
88#127×C101—22no—
89#124×C101—22no—
90#123×C101—22no—
91#123×C101—22no—
92#123×C101—22no—
93C22⋊Q8×C101—21no—
94C22⋊Q8×C101—21no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—22no—
98#121×C101—22no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—22no—
102#121×C101—22no—
103#121×C101—48no—
104#120×C101—22no—
105#120×C101—22no—
106#120×C101—22no—
107#120×C101—22no—
108#120×C101—22no—
109#120×C101—22no—
110#120×C101—22no—
111#120×C101—22no—
112#120×C101—22no—
113#120×C101—22no—
114#120×C101—22no—
115#120×C101—24no—
116#120×C101—42no—
117#120×C101—42no—
118#120×C101—44no—
119C4×D4×C101—22no—
120C4×D4×C101—22no—
121C4×D4×C101—22no—
122C4×D4×C101—22no—
123#117×C101—21no—
124C2×C4⋊C4×C101—22no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—24no—
129C2×C22⋊C4×C101—22no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—22no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101—22no—
137C2×C22⋊C4×C101—22no—
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101—22no—
140C2×C22⋊C4×C101—42no—
141C2×C22⋊C4×C101D412yescomplemented
142C2×C22⋊C4×C101D412yescomplemented
143C2×C22⋊C4×C101C2312yes—
144C2×C22⋊C4×C101C2311yescharacteristic
145C2×C22⋊C4×C101C2311yescharacteristic
146C2×C22⋊C4×C101C2312yes—
147C2×C22⋊C4×C101C2312yes—
148#99×C101—22no—
149#99×C101—24no—
150#99×C101—24no—
151#99×C101—42no—
152#99×C101D414yescomplemented
153#95×C101—22no—
154#95×C101—21no—
155#95×C101—21no—
156#95×C101—22no—
157C24×C101—21no—
158C24×C101—21no—
159C24×C101—22no—
160C24×C101—21no—
161C24×C101—22no—
162C24×C101—21no—
163C24×C101—21no—
164C24×C101—21no—
165C24×C101—22no—
166C24×C101—21no—
167C24×C101—21no—
168C24×C101—22no—
169C24×C101—41no—
170C24×C101—42no—
171C24×C101—42no—
172C24×C101—42no—
173C24×C101—81no—
174C24×C101—81no—
175C24×C101—81no—
176C24×C101C2×D411yescharacteristic
177C24×C101C2×D412yes—
178C24×C101C2×D411yescharacteristic
179C24×C101C2×D412yes—
180C24×C101C2×D412yes—
181C24×C101C2×D411yescharacteristic
182C24×C101C2×D411yescharacteristic
183C24×C101C2411yescharacteristic
184#41×C101—44no—
185#41×C101—44no—
186#41×C101—42no—
187#41×C101—42no—
188C2×Q8×C101—21no—
189C2×D4×C101—22no—
190C2×D4×C101—22no—
191C2×D4×C101—22no—
192C2×D4×C101—24no—
193C2×D4×C101—21no—
194C2×D4×C101—28no—
195C2×D4×C101—22no—
196C2×D4×C101—22no—
197C2×D4×C101—22no—
198C2×D4×C101—22no—
199C2×D4×C101—22no—
200C2×D4×C101—21no—
201C2×D4×C101—22no—
202C2×D4×C101—22no—
203C2×D4×C101—22no—
204C2×D4×C101—22no—
205C2×D4×C101—21no—
206C2×D4×C101—22no—
207C2×D4×C101—22no—
208C2×D4×C101—22no—
209C2×D4×C101—22no—
210C2×D4×C101—22no—
211C2×D4×C101—22no—
212C2×D4×C101—22no—
213C2×D4×C101—22no—
214C2×D4×C101—22no—
215C2×D4×C101—41no—
216C2×D4×C101—41no—
217C2×D4×C101—42no—
218C2×D4×C101—44no—
219C2×D4×C101—44no—
220C2×D4×C101—44no—
221C2×D4×C101—44no—
222C2×D4×C101—44no—
223C2×D4×C101—44no—
224C2×D4×C101—44no—
225C2×D4×C101—44no—
226C2×D4×C101—44no—
227C2×D4×C101—42no—
228C2×D4×C101—42no—
229C2×D4×C101—44no—
230C2×D4×C101—42no—
231C2×D4×C101—41no—
232C2×D4×C101—42no—
233C2×D4×C101—41no—
234C2×D4×C101—42no—
235C2×D4×C101—44no—
236C2×D4×C101—42no—
237C2×D4×C101—42no—
238C2×D4×C101—42no—
239C2×D4×C101—44no—
240C2×D4×C101—42no—
241C2×D4×C101—82no—
242C2×D4×C101—82no—
243C2×D4×C101—81no—
244C2×D4×C101—81no—
245C2×D4×C101—82no—
246C2×D4×C101—82no—
247C2×D4×C101C2×D412yes—
248C2×D4×C101#4112yes—
249C22×C4×C101—21no—
250C22×C4×C101—22no—
251C22×C4×C101—21no—
252C22×C4×C101—21no—
253C22×C4×C101—21no—
254C22×C4×C101—22no—
255C22×C4×C101—22no—
256C22×C4×C101—21no—
257C22×C4×C101—21no—
258C22×C4×C101—22no—
259C22×C4×C101—22no—
260C22×C4×C101—21no—
261C22×C4×C101—21no—
262C22×C4×C101—42no—
263C22×C4×C101—41no—
264C22×C4×C101—44no—
265C22×C4×C101—44no—
266C22×C4×C101—82no—
267C22×C4×C101C2×D412yes—
268C22×C4×C101C2×D411yescharacteristic
269C22×C4×C101C2×D411yescharacteristic
270C22×C4×C101C2×D412yes—
271C22×C4×C101C2×D412yes—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—22no—
275C4⋊C4×C101—22no—
276C4⋊C4×C101—44no—
277C22⋊C4×C101—22no—
278C22⋊C4×C101—22no—
279C22⋊C4×C101—22no—
280C22⋊C4×C101—22no—
281C22⋊C4×C101—22no—
282C22⋊C4×C101—22no—
283C22⋊C4×C101—22no—
284C22⋊C4×C101—22no—
285C22⋊C4×C101—22no—
286C22⋊C4×C101—22no—
287C22⋊C4×C101—22no—
288C22⋊C4×C101—22no—
289C22⋊C4×C101—22no—
290C22⋊C4×C101—21no—
291C22⋊C4×C101—21no—
292C22⋊C4×C101—22no—
293C22⋊C4×C101—22no—
294C22⋊C4×C101—44no—
295C22⋊C4×C101—44no—
296C22⋊C4×C101—42no—
297C22⋊C4×C101—42no—
298C22⋊C4×C101—42no—
299C22⋊C4×C101—44no—
300C22⋊C4×C101—42no—
301C22⋊C4×C101—44no—
302C22⋊C4×C101—42no—
303C22⋊C4×C101—82no—
304C22⋊C4×C101—81no—
305C22⋊C4×C101C2×D414yescomplemented
306C42×C101—22no—
307C23×C101—21no—
308C23×C101—21no—
309C23×C101—21no—
310C23×C101—22no—
311C23×C101—22no—
312C23×C101—22no—
313C23×C101—24no—
314C23×C101—21no—
315C23×C101—21no—
316C23×C101—21no—
317C23×C101—22no—
318C23×C101—22no—
319C23×C101—24no—
320C23×C101—22no—
321C23×C101—21no—
322C23×C101—22no—
323C23×C101—21no—
324C23×C101—21no—
325C23×C101—22no—
326C23×C101—22no—
327C23×C101—41no—
328C23×C101—42no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—42no—
333C23×C101—41no—
334C23×C101—42no—
335C23×C101—42no—
336C23×C101—42no—
337C23×C101—41no—
338C23×C101—41no—
339C23×C101—41no—
340C23×C101—41no—
341C23×C101—42no—
342C23×C101—42no—
343C23×C101—41no—
344C23×C101—42no—
345C23×C101—41no—
346C23×C101—41no—
347C23×C101—42no—
348C23×C101—42no—
349C23×C101—42no—
350C23×C101—42no—
351C23×C101—41no—
352C23×C101—41no—
353C23×C101—41no—
354C23×C101—42no—
355C23×C101—42no—
356C23×C101—42no—
357C23×C101—81no—
358C23×C101—81no—
359C23×C101—82no—
360C23×C101—82no—
361C23×C101—82no—
362C23×C101—82no—
363C23×C101—84no—
364C23×C101—84no—
365C23×C101—81no—
366C23×C101—81no—
367C23×C101—84no—
368C23×C101—84no—
369C23×C101#12011yescharacteristic
370C23×C101#12012yes—
371C23×C101#12011yescharacteristic
372C23×C101#12112yescomplemented
373C23×C101C22×D411yescharacteristic
374C23×C101C22×D412yes—
375C23×C101C22×D411yescharacteristic
376C23×C101C2×#4111yescharacteristic
377C23×C101H(5,𝔽2)12yes—
378Q8×C101—42no—
379D4×C101—24no—
380D4×C101—24no—
381D4×C101—44no—
382D4×C101—42no—
383D4×C101—44no—
384D4×C101—48no—
385D4×C101—44no—
386D4×C101—44no—
387D4×C101—44no—
388D4×C101—42no—
389D4×C101—42no—
390D4×C101—42no—
391D4×C101—42no—
392D4×C101—42no—
393D4×C101—42no—
394D4×C101—44no—
395D4×C101—44no—
396D4×C101—82no—
397D4×C101—82no—
398D4×C101—82no—
399D4×C101—82no—
400D4×C101—88no—
401D4×C101—84no—
402D4×C101—84no—
403C2×C4×C101—21no—
404C2×C4×C101—21no—
405C2×C4×C101—22no—
406C2×C4×C101—24no—
407C2×C4×C101—22no—
408C2×C4×C101—22no—
409C2×C4×C101—22no—
410C2×C4×C101—21no—
411C2×C4×C101—21no—
412C2×C4×C101—21no—
413C2×C4×C101—24no—
414C2×C4×C101—22no—
415C2×C4×C101—22no—
416C2×C4×C101—42no—
417C2×C4×C101—42no—
418C2×C4×C101—44no—
419C2×C4×C101—42no—
420C2×C4×C101—42no—
421C2×C4×C101—41no—
422C2×C4×C101—42no—
423C2×C4×C101—42no—
424C2×C4×C101—41no—
425C2×C4×C101—42no—
426C2×C4×C101—42no—
427C2×C4×C101—42no—
428C2×C4×C101—41no—
429C2×C4×C101—41no—
430C2×C4×C101—42no—
431C2×C4×C101—41no—
432C2×C4×C101—41no—
433C2×C4×C101—41no—
434C2×C4×C101—41no—
435C2×C4×C101—42no—
436C2×C4×C101—81no—
437C2×C4×C101—81no—
438C2×C4×C101—88no—
439C2×C4×C101#12112yescomplemented
440C22×C101—21no—
441C22×C101—22no—
442C22×C101—21no—
443C22×C101—22no—
444C22×C101—21no—
445C22×C101—21no—
446C22×C101—21no—
447C22×C101—22no—
448C22×C101—22no—
449C22×C101—22no—
450C22×C101—21no—
451C22×C101—21no—
452C22×C101—22no—
453C22×C101—41no—
454C22×C101—41no—
455C22×C101—42no—
456C22×C101—44no—
457C22×C101—44no—
458C22×C101—42no—
459C22×C101—42no—
460C22×C101—42no—
461C22×C101—44no—
462C22×C101—42no—
463C22×C101—42no—
464C22×C101—42no—
465C22×C101—44no—
466C22×C101—41no—
467C22×C101—41no—
468C22×C101—42no—
469C22×C101—41no—
470C22×C101—42no—
471C22×C101—42no—
472C22×C101—41no—
473C22×C101—42no—
474C22×C101—41no—
475C22×C101—82no—
476C22×C101—81no—
477C22×C101—81no—
478C22×C101—81no—
479C22×C101—82no—
480C22×C101—84no—
481C22×C101—82no—
482C22×C101—82no—
483C22×C101—81no—
484C22×C101—82no—
485C22×C101—81no—
486C22×C101—81no—
487C22×C101—82no—
488C22×C101—84no—
489C22×C101—81no—
490C22×C101—81no—
491C22×C101—162no—
492C22×C101B(4,𝔽2)12yescomplemented
493C22×C101C2×#12011yescharacteristic
494C22×C101C2×#12111yescharacteristic
495C22×C101#53411yescharacteristic
496C22×C101D4212yes—
497C22×C101#54612yes—
498C4×C101—22no—
499C4×C101—44no—
500C4×C101—41no—
501C4×C101—42no—
502C4×C101—42no—
503C4×C101—42no—
504C4×C101—42no—
505C4×C101—82no—
506C4×C101—81no—
507C4×C101—81no—
508#24404C10111yesmaximal, characteristic, direct product factor, Sylow
509C2×C101—22no—
510C2×C101—21no—
511C2×C101—21no—
512C2×C101—22no—
513C2×C101—22no—
514C2×C101—42no—
515C2×C101—41no—
516C2×C101—42no—
517C2×C101—82no—
518C2×C101—81no—
519C2×C101—82no—
520C2×C101#241011yescharacteristic
521C2×C101C2×B(4,𝔽2)11yescharacteristic
522C2×C101#302611yescharacteristic
523#3484C2×C10111yescharacteristic, complemented
524C2×B(4,𝔽2)C2×C10111yescharacteristic, complemented
525C22×#99C2×C10111yescharacteristic, complemented
526#2410C2×C10112yescomplemented
527#2403C2×C10111yescharacteristic, complemented
528#2044C2×C10112yescomplemented
529#2021C2×C10112yescomplemented
530#1898C2×C10112yescomplemented
531#1889C2×C10111yescharacteristic, complemented
532#1867C2×C10111yescharacteristic, complemented
533#1790C2×C10111yescharacteristic, complemented
534C101#2440411yescharacteristic, direct product factor, Sylow
535C2×H(5,𝔽2)C22×C10111yescharacteristic
536C23×D4C22×C10111yescharacteristic
537C23×D4C22×C10111yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C10112yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C10111yescharacteristic
550C2×#120C22×C10112yes—
551C2×#120C22×C10112yescomplemented
552C2×#120C22×C10111yescharacteristic, complemented
553#518C22×C10111yescharacteristic
554C22×C22⋊C4C22×C10112yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C10111yescharacteristic
558C2×#99C22×C10111yescharacteristic
559C2×#99C22×C10112yescomplemented
560C2×#99C22×C10112yescomplemented
561C2×#99C22×C10112yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C10111yescharacteristic
569#386C22×C10111yescharacteristic, complemented
570#386C22×C10112yescomplemented
571#385C22×C10112yescomplemented
572#379C22×C10112yescomplemented
573#379C22×C10111yescharacteristic, complemented
574#342C22×C10112yescomplemented
575#342C22×C10112yescomplemented
576C25D4×C10111yescharacteristic, complemented
577C25C23×C10111yescharacteristic
578C25C23×C10111yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C10111yescharacteristic, complemented
602C22×D4D4×C10111yescharacteristic, complemented
603C22×D4D4×C10112yescomplemented
604C22×D4D4×C10112yescomplemented
605C22×D4C23×C10112yes—
606C22×D4C23×C10111yescharacteristic
607C22×D4C23×C10111yescharacteristic
608C23×C4—22no—
609C23×C4D4×C10111yescharacteristic, complemented
610C23×C4C23×C10111yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C10112yescomplemented
665C2×C22⋊C4D4×C10112yescomplemented
666C2×C22⋊C4C23×C10112yes—
667C2×C22⋊C4C23×C10111yescharacteristic
668C2×C22⋊C4C23×C10111yescharacteristic
669C2×C22⋊C4C23×C10112yes—
670C2×C22⋊C4C23×C10112yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C10114yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C10111yescharacteristic
700C24C2×D4×C10112yes—
701C24C2×D4×C10111yescharacteristic
702C24C2×D4×C10112yes—
703C24C2×D4×C10112yes—
704C24C2×D4×C10111yescharacteristic
705C24C2×D4×C10111yescharacteristic
706C24C24×C10111yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C10112yes—
771C2×D4#41×C10112yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C10112yes—
791C22×C4C2×D4×C10111yescharacteristic
792C22×C4C2×D4×C10111yescharacteristic
793C22×C4C2×D4×C10112yes—
794C22×C4C2×D4×C10112yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C10114yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C10111yescharacteristic
893C23#120×C10112yes—
894C23#120×C10111yescharacteristic
895C23#121×C10112yescomplemented
896C23C22×D4×C10111yescharacteristic
897C23C22×D4×C10112yes—
898C23C22×D4×C10111yescharacteristic
899C23C2×#41×C10111yescharacteristic
900C23H(5,𝔽2)×C10112yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C10112yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C10112yescomplemented
1016C22C2×#120×C10111yescharacteristic
1017C22C2×#121×C10111yescharacteristic
1018C22#534×C10111yescharacteristic
1019C22D42×C10112yes—
1020C22#546×C10112yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C101×#241011yescharacteristic
1043C2C2×B(4,𝔽2)×C10111yescharacteristic
1044C2C101×#302611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC24C24×C101
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C25×C101 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C101×#3484C2semidirect
2. C2×B(4,𝔽2)×C101C2semidirect
3. C22×#99×C101C2semidirect
4. C101×#2410C2semidirect
5. C101×#2403C2semidirect
6. C101×#2044C2semidirect
7. C101×#2021C2semidirect
8. C101×#1898C2semidirect
9. C101×#1889C2semidirect
10. C101×#1867C2semidirect
11. C101×#1790C2semidirect
14. C23×D4×C101C22semidirect
28. C2×#120×C101C22semidirect
29. C2×#120×C101C22semidirect
31. C22×C22⋊C4×C101C22semidirect
36. C2×#99×C101C22semidirect
37. C2×#99×C101C22semidirect
38. C2×#99×C101C22semidirect
46. #386×C101C22semidirect
47. #386×C101C22semidirect
48. #385×C101C22semidirect
49. #379×C101C22semidirect
50. #379×C101C22semidirect
51. #342×C101C22semidirect
52. #342×C101C22semidirect
53. C25×C101D4semidirect
78. C22×D4×C101D4semidirect
79. C22×D4×C101D4semidirect
80. C22×D4×C101D4semidirect
81. C22×D4×C101D4semidirect
86. C23×C4×C101D4semidirect
141. C2×C22⋊C4×C101D4semidirect
142. C2×C22⋊C4×C101D4semidirect
152. #99×C101D4semidirect
305. C22⋊C4×C101C2×D4semidirect
372. C23×C101#121semidirect
439. C2×C4×C101#121semidirect
492. C22×C101B(4,𝔽2)semidirect
508. #24404C101direct (N × H)
523. #3484C2×C101semidirect
524. C2×B(4,𝔽2)C2×C101semidirect
525. C22×#99C2×C101semidirect
526. #2410C2×C101semidirect
527. #2403C2×C101semidirect
528. #2044C2×C101semidirect
529. #2021C2×C101semidirect
530. #1898C2×C101semidirect
531. #1889C2×C101semidirect
532. #1867C2×C101semidirect
533. #1790C2×C101semidirect
534. C101#24404direct (N × H)
537. C23×D4C22×C101semidirect
551. C2×#120C22×C101semidirect
552. C2×#120C22×C101semidirect
554. C22×C22⋊C4C22×C101semidirect
559. C2×#99C22×C101semidirect
560. C2×#99C22×C101semidirect
561. C2×#99C22×C101semidirect
569. #386C22×C101semidirect
570. #386C22×C101semidirect
571. #385C22×C101semidirect
572. #379C22×C101semidirect
573. #379C22×C101semidirect
574. #342C22×C101semidirect
575. #342C22×C101semidirect
576. C25D4×C101semidirect
601. C22×D4D4×C101semidirect
602. C22×D4D4×C101semidirect
603. C22×D4D4×C101semidirect
604. C22×D4D4×C101semidirect
609. C23×C4D4×C101semidirect
664. C2×C22⋊C4D4×C101semidirect
665. C2×C22⋊C4D4×C101semidirect
675. #99D4×C101semidirect
828. C22⋊C4C2×D4×C101semidirect
895. C23#121×C101semidirect
962. C2×C4#121×C101semidirect
1015. C22B(4,𝔽2)×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34842
C2×B(4,𝔽2)×C1012
C22×#99×C1012
C101×#24102
C101×#24032
C101×#20442
C101×#20212
C101×#18982
C101×#18892
C101×#18672
C101×#17902
#24404101