Finite Group Databasebeta

← C101×#24140 #38806291

Subgroups — C101×#24140 #38806291

Order 25856.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3505C211yesmaximal, characteristic, complemented
2C101×#2848C211yesmaximal, characteristic, complemented
3C101×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C101C211yesmaximal, characteristic, complemented
5C101×#2044C212yesmaximal, complemented
6C101×#2021C212yesmaximal, complemented
7C101×#1996C211yesmaximal, characteristic, complemented
8C101×#1964C211yesmaximal, characteristic, complemented
9C101×#1889C212yesmaximal, complemented
10C101×#1867C212yesmaximal, complemented
11C101×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C101C2211yescharacteristic
13#553×C101—21no—
14#553×C101—22no—
15#552×C101—21no—
16#551×C101—22no—
17#548×C101—21no—
18#546×C101—21no—
19#539×C101—21no—
20#538×C101—21no—
21#534×C101C2212yes—
22#529×C101—21no—
23#525×C101—21no—
24C2×C22⋊Q8×C101—21no—
25C2×C22⋊Q8×C101C2211yescharacteristic
26C2×#121×C101—21no—
27C2×#121×C101C2211yescharacteristic
28C2×#120×C101C2211yescharacteristic
29C2×#120×C101C2212yes—
30#518×C101C2212yes—
31C2×C4×D4×C101—21no—
32C2×C4×D4×C101C2211yescharacteristic
33C2×#99×C101C2212yes—
34C2×#99×C101C2212yes—
35C2×#99×C101C2212yes—
36#386×C101—21no—
37#386×C101—22no—
38#386×C101C2211yescharacteristic
39#386×C101C2212yes—
40#385×C101—21no—
41#385×C101—22no—
42#385×C101C2211yescharacteristic
43#385×C101C2212yes—
44#380×C101—21no—
45#380×C101—21no—
46#380×C101C2211yescharacteristic
47#380×C101C2211yescharacteristic
48#379×C101C2211yescharacteristic
49#379×C101C2212yes—
50C4×C22⋊C4×C101—21no—
51C4×C22⋊C4×C101C2211yescharacteristic
52#342×C101C2212yes—
53#342×C101C2212yes—
54#342×C101C2212yes—
55C25×C101C2311yescharacteristic
56C2×#41×C101—21no—
57C22×Q8×C101D411yescharacteristic, complemented
58C22×D4×C101—21no—
59C22×D4×C101—22no—
60C22×D4×C101D411yescharacteristic, complemented
61C22×D4×C101C2311yescharacteristic
62C22×D4×C101C2312yes—
63C23×C4×C101—21no—
64C23×C4×C101—21no—
65C23×C4×C101—21no—
66C23×C4×C101—21no—
67C23×C4×C101—21no—
68C23×C4×C101—21no—
69C23×C4×C101—44no—
70C23×C4×C101D411yescharacteristic, complemented
71C23×C4×C101C2311yescharacteristic
72C23×C4×C101C2311yescharacteristic
73#126×C101—22no—
74#126×C101—22no—
75#126×C101—22no—
76#125×C101—21no—
77#125×C101—22no—
78#124×C101—21no—
79#124×C101—22no—
80#123×C101—22no—
81#123×C101—22no—
82#123×C101—22no—
83#123×C101—22no—
84#123×C101—22no—
85C22⋊Q8×C101—21no—
86C22⋊Q8×C101—22no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×C101—21no—
91C22⋊Q8×C101—44no—
92#121×C101—21no—
93#121×C101—22no—
94#121×C101—21no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—21no—
98#121×C101—22no—
99#121×C101—22no—
100#121×C101—44no—
101#120×C101—22no—
102#120×C101—22no—
103#120×C101—22no—
104#120×C101—22no—
105#120×C101—24no—
106#120×C101—42no—
107C4×Q8×C101—21no—
108C4×D4×C101—22no—
109C4×D4×C101—21no—
110C4×D4×C101—21no—
111C4×D4×C101—21no—
112C4×D4×C101—21no—
113C4×D4×C101—21no—
114C4×D4×C101—22no—
115C4×D4×C101—22no—
116C4×D4×C101—22no—
117C4×D4×C101—22no—
118C4×D4×C101—44no—
119#117×C101—21no—
120#117×C101—22no—
121#117×C101—22no—
122C2×C4⋊C4×C101—21no—
123C2×C4⋊C4×C101—21no—
124C2×C4⋊C4×C101—21no—
125C2×C4⋊C4×C101—22no—
126C2×C4⋊C4×C101D411yescharacteristic, complemented
127C2×C4⋊C4×C101D411yescharacteristic, complemented
128C2×C4⋊C4×C101D411yescharacteristic, complemented
129C2×C4⋊C4×C101D412yescomplemented
130C2×C22⋊C4×C101—22no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—22no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—22no—
136C2×C22⋊C4×C101—22no—
137C2×C22⋊C4×C101—21no—
138C2×C22⋊C4×C101—22no—
139C2×C22⋊C4×C101D411yescharacteristic, complemented
140C2×C22⋊C4×C101D412yescomplemented
141C2×C22⋊C4×C101C2312yes—
142C2×C22⋊C4×C101C2311yescharacteristic
143C2×C22⋊C4×C101C2312yes—
144C2×C22⋊C4×C101C2311yescharacteristic
145C2×C22⋊C4×C101C2312yes—
146C2×C22⋊C4×C101C2311yescharacteristic
147C2×C42×C101—21no—
148C2×C42×C101D411yescharacteristic, complemented
149#99×C101—24no—
150#99×C101—42no—
151#99×C101—42no—
152#95×C101—21no—
153#95×C101—21no—
154#95×C101—21no—
155#95×C101—22no—
156#95×C101—22no—
157#95×C101—21no—
158#95×C101—21no—
159C24×C101—21no—
160C24×C101—21no—
161C24×C101—21no—
162C24×C101—21no—
163C24×C101—21no—
164C24×C101—21no—
165C24×C101—42no—
166C24×C101—42no—
167C24×C101C2×D412yes—
168C24×C101C2×D411yescharacteristic
169C24×C101#4112yescomplemented
170C24×C101C2411yescharacteristic
171#41×C101—82no—
172C2×Q8×C101—21no—
173C2×Q8×C101—21no—
174C2×Q8×C101—42no—
175C2×D4×C101—24no—
176C2×D4×C101—21no—
177C2×D4×C101—22no—
178C2×D4×C101—21no—
179C2×D4×C101—22no—
180C2×D4×C101—22no—
181C2×D4×C101—21no—
182C2×D4×C101—21no—
183C2×D4×C101—22no—
184C2×D4×C101—21no—
185C2×D4×C101—22no—
186C2×D4×C101—21no—
187C2×D4×C101—22no—
188C2×D4×C101—22no—
189C2×D4×C101—22no—
190C2×D4×C101—21no—
191C2×D4×C101—21no—
192C2×D4×C101—42no—
193C2×D4×C101—42no—
194C2×D4×C101—42no—
195C2×D4×C101—44no—
196C2×D4×C101—44no—
197C2×D4×C101—44no—
198C22×C4×C101—24no—
199C22×C4×C101—24no—
200C22×C4×C101—24no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—22no—
206C22×C4×C101—22no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—22no—
211C22×C4×C101—22no—
212C22×C4×C101—42no—
213C22×C4×C101—42no—
214C22×C4×C101—42no—
215C22×C4×C101—42no—
216C22×C4×C101—42no—
217C22×C4×C101—42no—
218C22×C4×C101—42no—
219C22×C4×C101—42no—
220C22×C4×C101—42no—
221C22×C4×C101—42no—
222C22×C4×C101—42no—
223C22×C4×C101—42no—
224C22×C4×C101—41no—
225C22×C4×C101—41no—
226C22×C4×C101—41no—
227C22×C4×C101—41no—
228C22×C4×C101C2×D411yescharacteristic
229C22×C4×C101C2×D412yes—
230C22×C4×C101C2×D411yescharacteristic
231C22×C4×C101C2×D411yescharacteristic
232C22×C4×C101C2×D411yescharacteristic
233C22×C4×C101C2×D411yescharacteristic
234C22×C4×C101C2×D412yes—
235C22×C4×C101C2×D411yescharacteristic
236C22×C4×C101C2×D412yes—
237C22×C4×C101C2×D411yescharacteristic
238C22×C4×C101C2×D411yescharacteristic
239C22×C4×C101C2×D411yescharacteristic
240C4⋊C4×C101—22no—
241C4⋊C4×C101—22no—
242C4⋊C4×C101—22no—
243C4⋊C4×C101—22no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—22no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—22no—
251C4⋊C4×C101—21no—
252C4⋊C4×C101—42no—
253C4⋊C4×C101—42no—
254C4⋊C4×C101—42no—
255C4⋊C4×C101—44no—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—22no—
258C22⋊C4×C101—24no—
259C22⋊C4×C101—22no—
260C22⋊C4×C101—22no—
261C22⋊C4×C101—22no—
262C22⋊C4×C101—22no—
263C22⋊C4×C101—21no—
264C22⋊C4×C101—22no—
265C22⋊C4×C101—21no—
266C22⋊C4×C101—22no—
267C22⋊C4×C101—21no—
268C22⋊C4×C101—22no—
269C22⋊C4×C101—21no—
270C22⋊C4×C101—21no—
271C22⋊C4×C101—22no—
272C22⋊C4×C101—22no—
273C22⋊C4×C101—22no—
274C22⋊C4×C101—21no—
275C22⋊C4×C101—22no—
276C22⋊C4×C101—22no—
277C22⋊C4×C101—21no—
278C22⋊C4×C101—44no—
279C22⋊C4×C101—42no—
280C22⋊C4×C101—44no—
281C22⋊C4×C101—44no—
282C22⋊C4×C101—42no—
283C22⋊C4×C101—42no—
284C22⋊C4×C101—44no—
285C22⋊C4×C101#4112yescomplemented
286C42×C101—22no—
287C42×C101—22no—
288C42×C101—21no—
289C42×C101—21no—
290C42×C101—42no—
291C23×C101—22no—
292C23×C101—22no—
293C23×C101—22no—
294C23×C101—22no—
295C23×C101—22no—
296C23×C101—22no—
297C23×C101—22no—
298C23×C101—22no—
299C23×C101—22no—
300C23×C101—21no—
301C23×C101—22no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—22no—
305C23×C101—22no—
306C23×C101—41no—
307C23×C101—44no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—44no—
316C23×C101—44no—
317C23×C101—44no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—42no—
321C23×C101—42no—
322C23×C101—41no—
323C23×C101—41no—
324C23×C101—41no—
325C23×C101—41no—
326C23×C101C22×D411yescharacteristic
327C23×C101C22×D411yescharacteristic
328C23×C101C22×D411yescharacteristic
329C23×C101C2×#4111yescharacteristic
330C23×C101C2×#4111yescharacteristic
331C23×C101H(5,𝔽2)11yescharacteristic
332C23×C1012−1+411yescharacteristic
333Q8×C101—42no—
334Q8×C101—81no—
335D4×C101—48no—
336D4×C101—42no—
337D4×C101—42no—
338D4×C101—41no—
339D4×C101—41no—
340D4×C101—41no—
341D4×C101—42no—
342D4×C101—42no—
343D4×C101—41no—
344D4×C101—42no—
345D4×C101—81no—
346D4×C101—82no—
347D4×C101—82no—
348D4×C101—88no—
349C2×C4×C101—22no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—21no—
356C2×C4×C101—22no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—22no—
360C2×C4×C101—22no—
361C2×C4×C101—21no—
362C2×C4×C101—22no—
363C2×C4×C101—21no—
364C2×C4×C101—22no—
365C2×C4×C101—22no—
366C2×C4×C101—41no—
367C2×C4×C101—41no—
368C2×C4×C101—41no—
369C2×C4×C101—44no—
370C2×C4×C101—44no—
371C2×C4×C101—44no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—44no—
379C2×C4×C101—42no—
380C2×C4×C101—41no—
381C2×C4×C101—42no—
382C2×C4×C101—41no—
383C2×C4×C101—42no—
384C2×C4×C101—41no—
385C2×C4×C101—42no—
386C2×C4×C101—42no—
387C2×C4×C101—42no—
388C2×C4×C101—41no—
389C2×C4×C101—42no—
390C2×C4×C101—41no—
391C2×C4×C101—42no—
392C2×C4×C101—42no—
393C2×C4×C101—81no—
394C2×C4×C101—82no—
395C2×C4×C101—82no—
396C2×C4×C101#12011yescharacteristic
397C2×C4×C101#12011yescharacteristic
398C2×C4×C101#12011yescharacteristic
399C2×C4×C101#12011yescharacteristic
400C22×C101—21no—
401C22×C101—21no—
402C22×C101—21no—
403C22×C101—21no—
404C22×C101—21no—
405C22×C101—21no—
406C22×C101—24no—
407C22×C101—24no—
408C22×C101—24no—
409C22×C101—41no—
410C22×C101—41no—
411C22×C101—41no—
412C22×C101—41no—
413C22×C101—42no—
414C22×C101—42no—
415C22×C101—42no—
416C22×C101—42no—
417C22×C101—42no—
418C22×C101—42no—
419C22×C101—42no—
420C22×C101—42no—
421C22×C101—42no—
422C22×C101—42no—
423C22×C101—42no—
424C22×C101—42no—
425C22×C101—42no—
426C22×C101—41no—
427C22×C101—42no—
428C22×C101—41no—
429C22×C101—42no—
430C22×C101—42no—
431C22×C101—41no—
432C22×C101—82no—
433C22×C101—81no—
434C22×C101—82no—
435C22×C101C2×#12011yescharacteristic
436C22×C101#52511yescharacteristic
437C22×C101#53711yescharacteristic
438C22×C101#54611yescharacteristic
439C22×C101#54711yescharacteristic
440C22×C101#54811yescharacteristic
441C22×C101#55011yescharacteristic
442C4×C101—21no—
443C4×C101—21no—
444C4×C101—21no—
445C4×C101—42no—
446C4×C101—41no—
447C4×C101—42no—
448C4×C101—42no—
449C4×C101—41no—
450C4×C101—42no—
451C4×C101—41no—
452C4×C101—42no—
453C4×C101—82no—
454C4×C101—81no—
455C4×C101—82no—
456C4×C101B(4,𝔽2)12yes—
457#24140C10111yesmaximal, characteristic, direct product factor, Sylow
458C2×C101—21no—
459C2×C101—21no—
460C2×C101—21no—
461C2×C101—21no—
462C2×C101—21no—
463C2×C101—21no—
464C2×C101—44no—
465C2×C101—81no—
466C2×C101—82no—
467C2×C101#240711yescharacteristic
468C2×C101C2×B(4,𝔽2)11yescharacteristic
469C2×C101#302511yescharacteristic
470#3505C2×C10111yescharacteristic, complemented
471#2848C2×C10111yescharacteristic, complemented
472#2847C2×C10111yescharacteristic, complemented
473C4×#120C2×C10111yescharacteristic, complemented
474#2044C2×C10112yescomplemented
475#2021C2×C10112yescomplemented
476#1996C2×C10111yescharacteristic, complemented
477#1964C2×C10111yescharacteristic, complemented
478#1889C2×C10112yescomplemented
479#1867C2×C10112yescomplemented
480#1799C2×C10111yescharacteristic, complemented
481C101#2414011yescharacteristic, direct product factor, Sylow
482C24×C4C22×C10111yescharacteristic
483#553—21no—
484#553—22no—
485#552—21no—
486#551—22no—
487#548—21no—
488#546—21no—
489#539—21no—
490#538—21no—
491#534C22×C10112yes—
492#529—21no—
493#525—21no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8C22×C10111yescharacteristic
496C2×#121—21no—
497C2×#121C22×C10111yescharacteristic
498C2×#120C22×C10111yescharacteristic
499C2×#120C22×C10112yes—
500#518C22×C10112yes—
501C2×C4×D4—21no—
502C2×C4×D4C22×C10111yescharacteristic
503C2×#99C22×C10112yes—
504C2×#99C22×C10112yes—
505C2×#99C22×C10112yes—
506#386—22no—
507#386—21no—
508#386C22×C10112yes—
509#386C22×C10111yescharacteristic
510#385—22no—
511#385—21no—
512#385C22×C10112yes—
513#385C22×C10111yescharacteristic
514#380—21no—
515#380—21no—
516#380C22×C10111yescharacteristic
517#380C22×C10111yescharacteristic
518#379C22×C10112yes—
519#379C22×C10111yescharacteristic
520C4×C22⋊C4—21no—
521C4×C22⋊C4C22×C10111yescharacteristic
522#342C22×C10112yes—
523#342C22×C10112yes—
524#342C22×C10112yes—
525C25C23×C10111yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C10111yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C10111yescharacteristic, complemented
531C22×D4C23×C10111yescharacteristic
532C22×D4C23×C10112yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C10111yescharacteristic, complemented
541C23×C4C23×C10111yescharacteristic
542C23×C4C23×C10111yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C10111yescharacteristic, complemented
597C2×C4⋊C4D4×C10111yescharacteristic, complemented
598C2×C4⋊C4D4×C10111yescharacteristic, complemented
599C2×C4⋊C4D4×C10112yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C10111yescharacteristic, complemented
610C2×C22⋊C4D4×C10112yescomplemented
611C2×C22⋊C4C23×C10112yes—
612C2×C22⋊C4C23×C10111yescharacteristic
613C2×C22⋊C4C23×C10112yes—
614C2×C22⋊C4C23×C10111yescharacteristic
615C2×C22⋊C4C23×C10112yes—
616C2×C22⋊C4C23×C10111yescharacteristic
617C2×C42—21no—
618C2×C42D4×C10111yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C10112yes—
638C24C2×D4×C10111yescharacteristic
639C24#41×C10112yescomplemented
640C24C24×C10111yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C10111yescharacteristic
699C22×C4C2×D4×C10112yes—
700C22×C4C2×D4×C10111yescharacteristic
701C22×C4C2×D4×C10111yescharacteristic
702C22×C4C2×D4×C10111yescharacteristic
703C22×C4C2×D4×C10111yescharacteristic
704C22×C4C2×D4×C10112yes—
705C22×C4C2×D4×C10111yescharacteristic
706C22×C4C2×D4×C10112yes—
707C22×C4C2×D4×C10111yescharacteristic
708C22×C4C2×D4×C10111yescharacteristic
709C22×C4C2×D4×C10111yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—44no—
755C22⋊C4#41×C10112yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C10111yescharacteristic
797C23C22×D4×C10111yescharacteristic
798C23C22×D4×C10111yescharacteristic
799C23C2×#41×C10111yescharacteristic
800C23C2×#41×C10111yescharacteristic
801C23H(5,𝔽2)×C10111yescharacteristic
802C232−1+4×C10111yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C10111yescharacteristic
867C2×C4#120×C10111yescharacteristic
868C2×C4#120×C10111yescharacteristic
869C2×C4#120×C10111yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C10111yescharacteristic
906C22#525×C10111yescharacteristic
907C22#537×C10111yescharacteristic
908C22#546×C10111yescharacteristic
909C22#547×C10111yescharacteristic
910C22#548×C10111yescharacteristic
911C22#550×C10111yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4B(4,𝔽2)×C10112yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C101×#240711yescharacteristic
937C2C2×B(4,𝔽2)×C10111yescharacteristic
938C2C101×#302511yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC24C24×C101
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3505C2semidirect
2. C101×#2848C2semidirect
3. C101×#2847C2semidirect
4. C4×#120×C101C2semidirect
5. C101×#2044C2semidirect
6. C101×#2021C2semidirect
7. C101×#1996C2semidirect
8. C101×#1964C2semidirect
9. C101×#1889C2semidirect
10. C101×#1867C2semidirect
11. C101×#1799C2semidirect
57. C22×Q8×C101D4semidirect
60. C22×D4×C101D4semidirect
70. C23×C4×C101D4semidirect
126. C2×C4⋊C4×C101D4semidirect
127. C2×C4⋊C4×C101D4semidirect
128. C2×C4⋊C4×C101D4semidirect
129. C2×C4⋊C4×C101D4semidirect
139. C2×C22⋊C4×C101D4semidirect
140. C2×C22⋊C4×C101D4semidirect
148. C2×C42×C101D4semidirect
169. C24×C101#41semidirect
285. C22⋊C4×C101#41semidirect
457. #24140C101direct (N × H)
470. #3505C2×C101semidirect
471. #2848C2×C101semidirect
472. #2847C2×C101semidirect
473. C4×#120C2×C101semidirect
474. #2044C2×C101semidirect
475. #2021C2×C101semidirect
476. #1996C2×C101semidirect
477. #1964C2×C101semidirect
478. #1889C2×C101semidirect
479. #1867C2×C101semidirect
480. #1799C2×C101semidirect
481. C101#24140direct (N × H)
527. C22×Q8D4×C101semidirect
530. C22×D4D4×C101semidirect
540. C23×C4D4×C101semidirect
596. C2×C4⋊C4D4×C101semidirect
597. C2×C4⋊C4D4×C101semidirect
598. C2×C4⋊C4D4×C101semidirect
599. C2×C4⋊C4D4×C101semidirect
609. C2×C22⋊C4D4×C101semidirect
610. C2×C22⋊C4D4×C101semidirect
618. C2×C42D4×C101semidirect
639. C24#41×C101semidirect
755. C22⋊C4#41×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35052
C101×#28482
C101×#28472
C4×#120×C1012
C101×#20442
C101×#20212
C101×#19962
C101×#19642
C101×#18892
C101×#18672
C101×#17992
#24140101