Finite Group Databasebeta

← C101×#24405 #38806556

Subgroups — C101×#24405 #38806556

Order 25856.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3484C211yesmaximal, characteristic
2C2×#458×C101C211yesmaximal, characteristic, complemented
3C22×#99×C101C211yesmaximal, characteristic, complemented
4C101×#2412C212yesmaximal, complemented
5C101×#2405C211yesmaximal, characteristic, complemented
6C101×#2044C212yesmaximal, complemented
7C101×#2022C212yesmaximal, complemented
8C101×#1898C212yesmaximal, complemented
9C101×#1890C211yesmaximal, characteristic, complemented
10C101×#1867C211yesmaximal, characteristic, complemented
11C101×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C101C2211yescharacteristic
13C23×D4×C101C2211yescharacteristic
14#546×C101—22no—
15#546×C101—22no—
16D42×C101—22no—
17D42×C101—22no—
18#535×C101—21no—
19#534×C101—21no—
20#534×C101C2212yes—
21#525×C101—21no—
22C2×#123×C101C2211yescharacteristic
23C2×#123×C101C2212yescomplemented
24C2×#123×C101C2211yescharacteristic, complemented
25C2×#120×C101—21no—
26C2×#120×C101C2212yes—
27#518×C101C2211yescharacteristic
28C22×C22⋊C4×C101C2211yescharacteristic, complemented
29C22×C22⋊C4×C101C2212yescomplemented
30#458×C101—24no—
31C2×#99×C101—24no—
32C2×#99×C101C2211yescharacteristic
33C2×#99×C101C2211yescharacteristic
34C2×#99×C101C2212yescomplemented
35C2×#99×C101C2212yescomplemented
36C2×#99×C101C2212yescomplemented
37#397×C101—22no—
38#394×C101—21no—
39#394×C101—21no—
40#394×C101—22no—
41#386×C101—22no—
42#386×C101C2211yescharacteristic
43#386×C101C2211yescharacteristic, complemented
44#386×C101C2212yescomplemented
45#385×C101—21no—
46#385×C101C2212yescomplemented
47#381×C101C2212yescomplemented
48#380×C101—22no—
49#379×C101—21no—
50#379×C101C2211yescharacteristic, complemented
51#342×C101C2212yescomplemented
52#342×C101C2212yescomplemented
53C25×C101D411yescharacteristic
54C25×C101C2311yescharacteristic
55H(5,𝔽2)×C101—22no—
56H(5,𝔽2)×C101—22no—
57H(5,𝔽2)×C101—42no—
58C2×#41×C101—21no—
59C2×#41×C101—22no—
60C22×D4×C101—21no—
61C22×D4×C101—22no—
62C22×D4×C101—22no—
63C22×D4×C101—22no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—22no—
67C22×D4×C101—22no—
68C22×D4×C101—42no—
69C22×D4×C101D411yescharacteristic
70C22×D4×C101D411yescharacteristic
71C22×D4×C101D412yes—
72C22×D4×C101D412yes—
73C22×D4×C101C2312yes—
74C22×D4×C101C2311yescharacteristic
75C22×D4×C101C2311yescharacteristic
76C23×C4×C101—22no—
77C23×C4×C101D411yescharacteristic
78C23×C4×C101C2311yescharacteristic
79C23×C4×C101C2311yescharacteristic
80#127×C101—22no—
81#124×C101—22no—
82#123×C101—22no—
83#123×C101—22no—
84#123×C101—22no—
85#123×C101—22no—
86#123×C101—22no—
87#123×C101—24no—
88#123×C101—42no—
89#123×C101—42no—
90C22⋊Q8×C101—21no—
91C22⋊Q8×C101—21no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—22no—
95#121×C101—22no—
96#121×C101—22no—
97#121×C101—22no—
98#121×C101—22no—
99#121×C101—22no—
100#120×C101—22no—
101#120×C101—22no—
102#120×C101—22no—
103#120×C101—22no—
104#120×C101—22no—
105#120×C101—22no—
106#120×C101—22no—
107#120×C101—22no—
108#120×C101—22no—
109C4×D4×C101—22no—
110C4×D4×C101—22no—
111C4×D4×C101—22no—
112C4×D4×C101—22no—
113#117×C101—21no—
114C2×C4⋊C4×C101—22no—
115C2×C4⋊C4×C101—21no—
116C2×C4⋊C4×C101—21no—
117C2×C4⋊C4×C101—22no—
118C2×C22⋊C4×C101—21no—
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101—21no—
121C2×C22⋊C4×C101—24no—
122C2×C22⋊C4×C101—22no—
123C2×C22⋊C4×C101—22no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—22no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—22no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—22no—
135C2×C22⋊C4×C101—42no—
136C2×C22⋊C4×C101D412yes—
137C2×C22⋊C4×C101D412yes—
138C2×C22⋊C4×C101C2312yes—
139C2×C22⋊C4×C101C2311yescharacteristic
140C2×C22⋊C4×C101C2311yescharacteristic
141C2×C22⋊C4×C101C2312yes—
142C2×C22⋊C4×C101C2312yes—
143#99×C101—22no—
144#99×C101—24no—
145#99×C101—24no—
146#99×C101—42no—
147#99×C101D414yescomplemented
148#95×C101—22no—
149#95×C101—22no—
150#95×C101—22no—
151#95×C101—22no—
152#95×C101—21no—
153#95×C101—21no—
154C24×C101—21no—
155C24×C101—21no—
156C24×C101—22no—
157C24×C101—21no—
158C24×C101—21no—
159C24×C101—21no—
160C24×C101—22no—
161C24×C101—41no—
162C24×C101—42no—
163C24×C101—42no—
164C24×C101—81no—
165C24×C101—81no—
166C24×C101C2×D411yescharacteristic
167C24×C101C2×D412yes—
168C24×C101C2×D411yescharacteristic
169C24×C101C2×D412yes—
170C24×C101C2×D412yes—
171C24×C101C2×D411yescharacteristic
172C24×C101C2×D411yescharacteristic
173C24×C101C2411yescharacteristic
174#41×C101—44no—
175#41×C101—44no—
176#41×C101—42no—
177#41×C101—42no—
178C2×Q8×C101—21no—
179C2×D4×C101—22no—
180C2×D4×C101—22no—
181C2×D4×C101—22no—
182C2×D4×C101—21no—
183C2×D4×C101—22no—
184C2×D4×C101—22no—
185C2×D4×C101—22no—
186C2×D4×C101—22no—
187C2×D4×C101—22no—
188C2×D4×C101—21no—
189C2×D4×C101—22no—
190C2×D4×C101—22no—
191C2×D4×C101—22no—
192C2×D4×C101—22no—
193C2×D4×C101—21no—
194C2×D4×C101—22no—
195C2×D4×C101—22no—
196C2×D4×C101—22no—
197C2×D4×C101—22no—
198C2×D4×C101—22no—
199C2×D4×C101—22no—
200C2×D4×C101—22no—
201C2×D4×C101—22no—
202C2×D4×C101—22no—
203C2×D4×C101—41no—
204C2×D4×C101—41no—
205C2×D4×C101—44no—
206C2×D4×C101—44no—
207C2×D4×C101—44no—
208C2×D4×C101—44no—
209C2×D4×C101—44no—
210C2×D4×C101—44no—
211C2×D4×C101—42no—
212C2×D4×C101—42no—
213C2×D4×C101—44no—
214C2×D4×C101—82no—
215C2×D4×C101—82no—
216C2×D4×C101—82no—
217C2×D4×C101C2×D412yes—
218C2×D4×C101#4112yes—
219C22×C4×C101—21no—
220C22×C4×C101—22no—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—22no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—22no—
227C22×C4×C101—22no—
228C22×C4×C101—21no—
229C22×C4×C101—22no—
230C22×C4×C101—22no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—22no—
237C22×C4×C101—41no—
238C22×C4×C101—44no—
239C22×C4×C101—44no—
240C22×C4×C101—81no—
241C22×C4×C101—82no—
242C22×C4×C101C2×D412yes—
243C22×C4×C101C2×D411yescharacteristic
244C22×C4×C101C2×D411yescharacteristic
245C22×C4×C101C2×D412yes—
246C22×C4×C101C2×D412yes—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—22no—
250C4⋊C4×C101—22no—
251C4⋊C4×C101—44no—
252C4⋊C4×C101—42no—
253C4⋊C4×C101—42no—
254C4⋊C4×C101—82no—
255C22⋊C4×C101—22no—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—22no—
258C22⋊C4×C101—22no—
259C22⋊C4×C101—22no—
260C22⋊C4×C101—22no—
261C22⋊C4×C101—22no—
262C22⋊C4×C101—22no—
263C22⋊C4×C101—22no—
264C22⋊C4×C101—22no—
265C22⋊C4×C101—22no—
266C22⋊C4×C101—22no—
267C22⋊C4×C101—22no—
268C22⋊C4×C101—21no—
269C22⋊C4×C101—21no—
270C22⋊C4×C101—22no—
271C22⋊C4×C101—22no—
272C22⋊C4×C101—44no—
273C22⋊C4×C101—44no—
274C22⋊C4×C101—42no—
275C22⋊C4×C101—42no—
276C22⋊C4×C101—41no—
277C22⋊C4×C101—42no—
278C22⋊C4×C101—41no—
279C22⋊C4×C101—42no—
280C22⋊C4×C101—81no—
281C22⋊C4×C101—81no—
282C22⋊C4×C101—81no—
283C22⋊C4×C101—82no—
284C22⋊C4×C101C2×D414yescomplemented
285C42×C101—22no—
286C23×C101—21no—
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—22no—
290C23×C101—22no—
291C23×C101—22no—
292C23×C101—24no—
293C23×C101—21no—
294C23×C101—21no—
295C23×C101—21no—
296C23×C101—22no—
297C23×C101—22no—
298C23×C101—21no—
299C23×C101—22no—
300C23×C101—21no—
301C23×C101—21no—
302C23×C101—22no—
303C23×C101—22no—
304C23×C101—42no—
305C23×C101—41no—
306C23×C101—41no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—42no—
310C23×C101—42no—
311C23×C101—41no—
312C23×C101—42no—
313C23×C101—42no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—42no—
319C23×C101—42no—
320C23×C101—42no—
321C23×C101—42no—
322C23×C101—42no—
323C23×C101—81no—
324C23×C101—81no—
325C23×C101—82no—
326C23×C101—82no—
327C23×C101—84no—
328C23×C101—81no—
329C23×C101—81no—
330C23×C101—84no—
331C23×C101—84no—
332C23×C101#12011yescharacteristic
333C23×C101#12012yes—
334C23×C101#12011yescharacteristic
335C23×C101#12112yes—
336C23×C101C22×D411yescharacteristic
337C23×C101C22×D412yes—
338C23×C101C22×D411yescharacteristic
339C23×C101C2×#4111yescharacteristic
340C23×C101H(5,𝔽2)12yes—
341Q8×C101—42no—
342D4×C101—24no—
343D4×C101—24no—
344D4×C101—44no—
345D4×C101—42no—
346D4×C101—44no—
347D4×C101—44no—
348D4×C101—44no—
349D4×C101—42no—
350D4×C101—42no—
351D4×C101—42no—
352D4×C101—42no—
353D4×C101—42no—
354D4×C101—42no—
355D4×C101—44no—
356D4×C101—82no—
357D4×C101—82no—
358D4×C101—82no—
359D4×C101—82no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—22no—
363C2×C4×C101—22no—
364C2×C4×C101—22no—
365C2×C4×C101—21no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—24no—
369C2×C4×C101—22no—
370C2×C4×C101—22no—
371C2×C4×C101—42no—
372C2×C4×C101—42no—
373C2×C4×C101—44no—
374C2×C4×C101—42no—
375C2×C4×C101—42no—
376C2×C4×C101—42no—
377C2×C4×C101—42no—
378C2×C4×C101—42no—
379C2×C4×C101—41no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—41no—
383C2×C4×C101—42no—
384C2×C4×C101—42no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—42no—
388C2×C4×C101—42no—
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—42no—
396C2×C4×C101—42no—
397C2×C4×C101—42no—
398C2×C4×C101—81no—
399C2×C4×C101—81no—
400C2×C4×C101—88no—
401C2×C4×C101#12112yes—
402C22×C101—21no—
403C22×C101—22no—
404C22×C101—21no—
405C22×C101—22no—
406C22×C101—21no—
407C22×C101—21no—
408C22×C101—21no—
409C22×C101—22no—
410C22×C101—22no—
411C22×C101—22no—
412C22×C101—21no—
413C22×C101—21no—
414C22×C101—22no—
415C22×C101—41no—
416C22×C101—41no—
417C22×C101—42no—
418C22×C101—44no—
419C22×C101—44no—
420C22×C101—42no—
421C22×C101—42no—
422C22×C101—42no—
423C22×C101—42no—
424C22×C101—41no—
425C22×C101—41no—
426C22×C101—42no—
427C22×C101—41no—
428C22×C101—42no—
429C22×C101—41no—
430C22×C101—42no—
431C22×C101—41no—
432C22×C101—82no—
433C22×C101—81no—
434C22×C101—81no—
435C22×C101—81no—
436C22×C101—82no—
437C22×C101—84no—
438C22×C101—82no—
439C22×C101—82no—
440C22×C101—81no—
441C22×C101—84no—
442C22×C101—162no—
443C22×C101#45812yescomplemented
444C22×C101C2×#12011yescharacteristic
445C22×C101C2×#12111yescharacteristic
446C22×C101#53411yescharacteristic
447C22×C101D4212yes—
448C22×C101#54612yes—
449C4×C101—22no—
450C4×C101—44no—
451C4×C101—41no—
452C4×C101—42no—
453C4×C101—42no—
454C4×C101—42no—
455C4×C101—81no—
456C4×C101—81no—
457C4×C101—82no—
458C4×C101—81no—
459C4×C101—81no—
460#24405C10111yesmaximal, characteristic, direct product factor, Sylow
461C2×C101—22no—
462C2×C101—21no—
463C2×C101—21no—
464C2×C101—22no—
465C2×C101—22no—
466C2×C101—42no—
467C2×C101—41no—
468C2×C101—42no—
469C2×C101—81no—
470C2×C101—82no—
471C2×C101#241011yescharacteristic
472C2×C101C2×#45811yescharacteristic
473C2×C101#302611yescharacteristic
474#3484C2×C10111yescharacteristic
475C2×#458C2×C10111yescharacteristic, complemented
476C22×#99C2×C10111yescharacteristic, complemented
477#2412C2×C10112yescomplemented
478#2405C2×C10111yescharacteristic, complemented
479#2044C2×C10112yescomplemented
480#2022C2×C10112yescomplemented
481#1898C2×C10112yescomplemented
482#1890C2×C10111yescharacteristic, complemented
483#1867C2×C10111yescharacteristic, complemented
484#1790C2×C10111yescharacteristic, complemented
485C101#2440511yescharacteristic, direct product factor, Sylow
486C2×H(5,𝔽2)C22×C10111yescharacteristic
487C23×D4C22×C10111yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C10112yes—
495#525—21no—
496C2×#123C22×C10111yescharacteristic
497C2×#123C22×C10112yescomplemented
498C2×#123C22×C10111yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C10112yes—
501#518C22×C10111yescharacteristic
502C22×C22⋊C4C22×C10111yescharacteristic, complemented
503C22×C22⋊C4C22×C10112yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C10111yescharacteristic
507C2×#99C22×C10111yescharacteristic
508C2×#99C22×C10112yescomplemented
509C2×#99C22×C10112yescomplemented
510C2×#99C22×C10112yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C10111yescharacteristic
517#386C22×C10111yescharacteristic, complemented
518#386C22×C10112yescomplemented
519#385—21no—
520#385C22×C10112yescomplemented
521#381C22×C10112yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C10111yescharacteristic, complemented
525#342C22×C10112yescomplemented
526#342C22×C10112yescomplemented
527C25D4×C10111yescharacteristic
528C25C23×C10111yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C10111yescharacteristic
544C22×D4D4×C10111yescharacteristic
545C22×D4D4×C10112yes—
546C22×D4D4×C10112yes—
547C22×D4C23×C10112yes—
548C22×D4C23×C10111yescharacteristic
549C22×D4C23×C10111yescharacteristic
550C23×C4—22no—
551C23×C4D4×C10111yescharacteristic
552C23×C4C23×C10111yescharacteristic
553C23×C4C23×C10111yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C10112yes—
611C2×C22⋊C4D4×C10112yes—
612C2×C22⋊C4C23×C10112yes—
613C2×C22⋊C4C23×C10111yescharacteristic
614C2×C22⋊C4C23×C10111yescharacteristic
615C2×C22⋊C4C23×C10112yes—
616C2×C22⋊C4C23×C10112yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C10114yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C10111yescharacteristic
641C24C2×D4×C10112yes—
642C24C2×D4×C10111yescharacteristic
643C24C2×D4×C10112yes—
644C24C2×D4×C10112yes—
645C24C2×D4×C10111yescharacteristic
646C24C2×D4×C10111yescharacteristic
647C24C24×C10111yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C10112yes—
692C2×D4#41×C10112yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C10112yes—
717C22×C4C2×D4×C10111yescharacteristic
718C22×C4C2×D4×C10111yescharacteristic
719C22×C4C2×D4×C10112yes—
720C22×C4C2×D4×C10112yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C10114yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C10111yescharacteristic
807C23#120×C10112yes—
808C23#120×C10111yescharacteristic
809C23#121×C10112yes—
810C23C22×D4×C10111yescharacteristic
811C23C22×D4×C10112yes—
812C23C22×D4×C10111yescharacteristic
813C23C2×#41×C10111yescharacteristic
814C23H(5,𝔽2)×C10112yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C10112yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C10112yescomplemented
918C22C2×#120×C10111yescharacteristic
919C22C2×#121×C10111yescharacteristic
920C22#534×C10111yescharacteristic
921C22D42×C10112yes—
922C22#546×C10112yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C101×#241011yescharacteristic
945C2C2×#458×C10111yescharacteristic
946C2C101×#302611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC24C24×C101
prime radicalC101×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C25×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#458×C101C2semidirect
3. C22×#99×C101C2semidirect
4. C101×#2412C2semidirect
5. C101×#2405C2semidirect
6. C101×#2044C2semidirect
7. C101×#2022C2semidirect
8. C101×#1898C2semidirect
9. C101×#1890C2semidirect
10. C101×#1867C2semidirect
11. C101×#1790C2semidirect
23. C2×#123×C101C22semidirect
24. C2×#123×C101C22semidirect
28. C22×C22⋊C4×C101C22semidirect
29. C22×C22⋊C4×C101C22semidirect
34. C2×#99×C101C22semidirect
35. C2×#99×C101C22semidirect
36. C2×#99×C101C22semidirect
43. #386×C101C22semidirect
44. #386×C101C22semidirect
46. #385×C101C22semidirect
47. #381×C101C22semidirect
50. #379×C101C22semidirect
51. #342×C101C22semidirect
52. #342×C101C22semidirect
147. #99×C101D4semidirect
284. C22⋊C4×C101C2×D4semidirect
443. C22×C101#458semidirect
460. #24405C101direct (N × H)
475. C2×#458C2×C101semidirect
476. C22×#99C2×C101semidirect
477. #2412C2×C101semidirect
478. #2405C2×C101semidirect
479. #2044C2×C101semidirect
480. #2022C2×C101semidirect
481. #1898C2×C101semidirect
482. #1890C2×C101semidirect
483. #1867C2×C101semidirect
484. #1790C2×C101semidirect
485. C101#24405direct (N × H)
497. C2×#123C22×C101semidirect
498. C2×#123C22×C101semidirect
502. C22×C22⋊C4C22×C101semidirect
503. C22×C22⋊C4C22×C101semidirect
508. C2×#99C22×C101semidirect
509. C2×#99C22×C101semidirect
510. C2×#99C22×C101semidirect
517. #386C22×C101semidirect
518. #386C22×C101semidirect
520. #385C22×C101semidirect
521. #381C22×C101semidirect
524. #379C22×C101semidirect
525. #342C22×C101semidirect
526. #342C22×C101semidirect
621. #99D4×C101semidirect
758. C22⋊C4C2×D4×C101semidirect
917. C22#458×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34842
C2×#458×C1012
C22×#99×C1012
C101×#24122
C101×#24052
C101×#20442
C101×#20222
C101×#18982
C101×#18902
C101×#18672
C101×#17902
#24405101