Finite Group Databasebeta

← C101×#25563 #38807714

Subgroups — C101×#25563 #38807714

Order 25856.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3490C211yesmaximal, characteristic, complemented
2C101×#2410C212yesmaximal, complemented
3C101×#2405C211yesmaximal, characteristic, complemented
4C101×#2062C211yesmaximal, characteristic, complemented
5C101×#2044C211yesmaximal, characteristic, complemented
6C101×#2029C211yesmaximal, characteristic, complemented
7C101×#2021C211yesmaximal, characteristic, complemented
8C101×#1898C212yesmaximal, complemented
9C101×#1889C212yesmaximal, complemented
10C101×#1867C212yesmaximal, complemented
11C2×#342×C101C211yesmaximal, characteristic, complemented
12C23×D4×C101C2211yescharacteristic
13#551×C101—22no—
14#551×C101—22no—
15#546×C101—22no—
16#546×C101—22no—
17#543×C101C2211yescharacteristic
18#538×C101—21no—
19#538×C101—21no—
20#534×C101C2211yescharacteristic
21#525×C101—21no—
22#525×C101—21no—
23C2×#123×C101—21no—
24C2×#121×C101—22no—
25C2×#120×C101C2212yes—
26C2×#120×C101C2212yes—
27#518×C101C2212yes—
28C22×C22⋊C4×C101C2211yescharacteristic
29C22×C22⋊C4×C101C2212yes—
30C2×#99×C101C2212yes—
31C2×#99×C101C2212yes—
32#394×C101—21no—
33#394×C101—21no—
34#394×C101—22no—
35#392×C101—22no—
36#386×C101—21no—
37#386×C101—22no—
38#386×C101C2212yes—
39#385×C101C2211yescharacteristic
40#385×C101C2211yescharacteristic
41#385×C101C2212yes—
42#379×C101C2211yescharacteristic
43#379×C101C2212yes—
44#379×C101C2211yescharacteristic
45#379×C101C2211yescharacteristic
46#342×C101C2212yes—
47#342×C101C2212yes—
48#342×C101C2212yes—
49#342×C101C2211yescharacteristic
50#342×C101C2211yescharacteristic
51C25×C101C2311yescharacteristic
52C25×C101C2311yescharacteristic
53C2×#41×C101—21no—
54C2×#41×C101—21no—
55C22×D4×C101—22no—
56C22×D4×C101—21no—
57C22×D4×C101—22no—
58C22×D4×C101—21no—
59C22×D4×C101—22no—
60C22×D4×C101—44no—
61C22×D4×C101D412yescomplemented
62C22×D4×C101D412yescomplemented
63C22×D4×C101C2312yes—
64C23×C4×C101—22no—
65C23×C4×C101D411yescharacteristic, complemented
66C23×C4×C101D411yescharacteristic, complemented
67C23×C4×C101C2311yescharacteristic
68#126×C101—22no—
69#126×C101—22no—
70#124×C101—22no—
71#124×C101—22no—
72#123×C101—22no—
73#123×C101—22no—
74#123×C101—22no—
75#123×C101—22no—
76#123×C101—22no—
77#123×C101—44no—
78C22⋊Q8×C101—21no—
79C22⋊Q8×C101—21no—
80C22⋊Q8×C101—21no—
81C22⋊Q8×C101—21no—
82C22⋊Q8×C101—22no—
83C22⋊Q8×C101—22no—
84#121×C101—21no—
85#121×C101—21no—
86#121×C101—22no—
87#121×C101—22no—
88#121×C101—21no—
89#121×C101—21no—
90#121×C101—48no—
91#120×C101—22no—
92#120×C101—22no—
93#120×C101—22no—
94#120×C101—22no—
95#120×C101—22no—
96#120×C101—24no—
97#120×C101—42no—
98C4×D4×C101—22no—
99C4×D4×C101—22no—
100C4×D4×C101—22no—
101C4×D4×C101—22no—
102C4×D4×C101—22no—
103C4×D4×C101—22no—
104#117×C101—21no—
105#117×C101—21no—
106#117×C101—22no—
107C2×C4⋊C4×C101—22no—
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—21no—
110C2×C22⋊C4×C101—22no—
111C2×C22⋊C4×C101—22no—
112C2×C22⋊C4×C101—22no—
113C2×C22⋊C4×C101—24no—
114C2×C22⋊C4×C101—22no—
115C2×C22⋊C4×C101—22no—
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101—22no—
118C2×C22⋊C4×C101—22no—
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101—21no—
121C2×C22⋊C4×C101—21no—
122C2×C22⋊C4×C101—22no—
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—42no—
126C2×C22⋊C4×C101D411yescharacteristic, complemented
127C2×C22⋊C4×C101D411yescharacteristic, complemented
128C2×C22⋊C4×C101D412yescomplemented
129C2×C22⋊C4×C101D412yescomplemented
130C2×C22⋊C4×C101C2311yescharacteristic
131C2×C22⋊C4×C101C2311yescharacteristic
132C2×C22⋊C4×C101C2312yes—
133C2×C22⋊C4×C101C2311yescharacteristic
134C2×C22⋊C4×C101C2311yescharacteristic
135C2×C22⋊C4×C101C2312yes—
136C2×C22⋊C4×C101C2312yes—
137#99×C101—24no—
138#99×C101—42no—
139#95×C101—22no—
140#95×C101—21no—
141#95×C101—21no—
142#95×C101—22no—
143C24×C101—22no—
144C24×C101—21no—
145C24×C101—21no—
146C24×C101—21no—
147C24×C101—22no—
148C24×C101—22no—
149C24×C101—21no—
150C24×C101—21no—
151C24×C101—42no—
152C24×C101—42no—
153C24×C101—81no—
154C24×C101—81no—
155C24×C101C2×D412yes—
156C24×C101C2×D411yescharacteristic
157C24×C101C2×D412yes—
158C24×C101C2×D412yes—
159C24×C101C2×D411yescharacteristic
160C24×C101C2411yescharacteristic
161#41×C101—82no—
162#41×C101—82no—
163C2×Q8×C101—21no—
164C2×Q8×C101—21no—
165C2×D4×C101—28no—
166C2×D4×C101—24no—
167C2×D4×C101—22no—
168C2×D4×C101—22no—
169C2×D4×C101—22no—
170C2×D4×C101—22no—
171C2×D4×C101—22no—
172C2×D4×C101—22no—
173C2×D4×C101—22no—
174C2×D4×C101—22no—
175C2×D4×C101—21no—
176C2×D4×C101—21no—
177C2×D4×C101—22no—
178C2×D4×C101—22no—
179C2×D4×C101—44no—
180C2×D4×C101—42no—
181C2×D4×C101—44no—
182C2×D4×C101—42no—
183C2×D4×C101—44no—
184C2×D4×C101—42no—
185C2×D4×C101—44no—
186C2×D4×C101—42no—
187C2×D4×C101—41no—
188C2×D4×C101—41no—
189C2×D4×C101—44no—
190C2×D4×C101—44no—
191C2×D4×C101—82no—
192C2×D4×C101—82no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—22no—
196C22×C4×C101—21no—
197C22×C4×C101—22no—
198C22×C4×C101—22no—
199C22×C4×C101—22no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—22no—
205C22×C4×C101—42no—
206C22×C4×C101—44no—
207C22×C4×C101—42no—
208C22×C4×C101—44no—
209C22×C4×C101—81no—
210C22×C4×C101—82no—
211C22×C4×C101C2×D412yes—
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2×D412yes—
214C22×C4×C101C2×D411yescharacteristic
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2×D412yes—
217C22×C4×C101C2×D411yescharacteristic
218C4⋊C4×C101—22no—
219C4⋊C4×C101—22no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—21no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—21no—
224C4⋊C4×C101—22no—
225C4⋊C4×C101—22no—
226C4⋊C4×C101—44no—
227C4⋊C4×C101—42no—
228C4⋊C4×C101—42no—
229C22⋊C4×C101—22no—
230C22⋊C4×C101—22no—
231C22⋊C4×C101—22no—
232C22⋊C4×C101—22no—
233C22⋊C4×C101—22no—
234C22⋊C4×C101—22no—
235C22⋊C4×C101—22no—
236C22⋊C4×C101—22no—
237C22⋊C4×C101—22no—
238C22⋊C4×C101—22no—
239C22⋊C4×C101—22no—
240C22⋊C4×C101—22no—
241C22⋊C4×C101—22no—
242C22⋊C4×C101—22no—
243C22⋊C4×C101—22no—
244C22⋊C4×C101—22no—
245C22⋊C4×C101—22no—
246C22⋊C4×C101—21no—
247C22⋊C4×C101—22no—
248C22⋊C4×C101—21no—
249C22⋊C4×C101—44no—
250C22⋊C4×C101—44no—
251C22⋊C4×C101—44no—
252C22⋊C4×C101—44no—
253C22⋊C4×C101—42no—
254C22⋊C4×C101—42no—
255C22⋊C4×C101—42no—
256C22⋊C4×C101—81no—
257C22⋊C4×C101—81no—
258C22⋊C4×C101—82no—
259C22⋊C4×C101—81no—
260C22⋊C4×C101#4114yescomplemented
261C42×C101—22no—
262C42×C101—22no—
263C23×C101—21no—
264C23×C101—21no—
265C23×C101—22no—
266C23×C101—22no—
267C23×C101—22no—
268C23×C101—24no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—22no—
272C23×C101—22no—
273C23×C101—22no—
274C23×C101—24no—
275C23×C101—22no—
276C23×C101—22no—
277C23×C101—22no—
278C23×C101—41no—
279C23×C101—41no—
280C23×C101—42no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—42no—
285C23×C101—42no—
286C23×C101—41no—
287C23×C101—41no—
288C23×C101—42no—
289C23×C101—41no—
290C23×C101—42no—
291C23×C101—42no—
292C23×C101—42no—
293C23×C101—42no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—42no—
298C23×C101—42no—
299C23×C101—84no—
300C23×C101—84no—
301C23×C101—82no—
302C23×C101—82no—
303C23×C101—82no—
304C23×C101—82no—
305C23×C101#12012yes—
306C23×C101#12011yescharacteristic
307C23×C101#12011yescharacteristic
308C23×C101C22×D411yescharacteristic
309C23×C101C22×D412yes—
310C23×C101C2×#4112yes—
311C23×C101H(5,𝔽2)11yescharacteristic
312C23×C1012−1+411yescharacteristic
313Q8×C101—81no—
314Q8×C101—81no—
315D4×C101—44no—
316D4×C101—48no—
317D4×C101—44no—
318D4×C101—42no—
319D4×C101—42no—
320D4×C101—42no—
321D4×C101—42no—
322D4×C101—44no—
323D4×C101—44no—
324D4×C101—82no—
325D4×C101—82no—
326D4×C101—81no—
327D4×C101—81no—
328D4×C101—88no—
329C2×C4×C101—24no—
330C2×C4×C101—22no—
331C2×C4×C101—22no—
332C2×C4×C101—21no—
333C2×C4×C101—21no—
334C2×C4×C101—22no—
335C2×C4×C101—22no—
336C2×C4×C101—21no—
337C2×C4×C101—21no—
338C2×C4×C101—24no—
339C2×C4×C101—22no—
340C2×C4×C101—22no—
341C2×C4×C101—42no—
342C2×C4×C101—41no—
343C2×C4×C101—42no—
344C2×C4×C101—42no—
345C2×C4×C101—42no—
346C2×C4×C101—41no—
347C2×C4×C101—42no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—42no—
351C2×C4×C101—41no—
352C2×C4×C101—41no—
353C2×C4×C101—42no—
354C2×C4×C101—41no—
355C2×C4×C101—41no—
356C2×C4×C101—42no—
357C2×C4×C101—41no—
358C2×C4×C101—41no—
359C2×C4×C101—42no—
360C2×C4×C101—41no—
361C2×C4×C101—41no—
362C2×C4×C101—42no—
363C2×C4×C101—81no—
364C2×C4×C101—81no—
365C2×C4×C101—82no—
366C2×C4×C101—82no—
367C2×C4×C101—88no—
368C22×C101—21no—
369C22×C101—21no—
370C22×C101—22no—
371C22×C101—21no—
372C22×C101—22no—
373C22×C101—21no—
374C22×C101—21no—
375C22×C101—22no—
376C22×C101—21no—
377C22×C101—22no—
378C22×C101—21no—
379C22×C101—22no—
380C22×C101—42no—
381C22×C101—41no—
382C22×C101—41no—
383C22×C101—44no—
384C22×C101—42no—
385C22×C101—42no—
386C22×C101—44no—
387C22×C101—44no—
388C22×C101—42no—
389C22×C101—42no—
390C22×C101—44no—
391C22×C101—42no—
392C22×C101—42no—
393C22×C101—42no—
394C22×C101—42no—
395C22×C101—82no—
396C22×C101—81no—
397C22×C101—81no—
398C22×C101—82no—
399C22×C101—82no—
400C22×C101—82no—
401C22×C101—82no—
402C22×C101—81no—
403C22×C101—81no—
404C22×C101—82no—
405C22×C101—81no—
406C22×C101—81no—
407C22×C101B(4,𝔽2)12yes—
408C22×C101C2×#12011yescharacteristic
409C22×C101#53211yescharacteristic
410C22×C101#53711yescharacteristic
411C22×C101#54612yes—
412C22×C101#54712yes—
413C4×C101—44no—
414C4×C101—42no—
415C4×C101—42no—
416C4×C101—41no—
417C4×C101—41no—
418C4×C101—42no—
419C4×C101—41no—
420C4×C101—41no—
421C4×C101—42no—
422C4×C101—81no—
423C4×C101—81no—
424C4×C101—82no—
425#25563C10111yesmaximal, characteristic, direct product factor, Sylow
426C2×C101—22no—
427C2×C101—21no—
428C2×C101—21no—
429C2×C101—22no—
430C2×C101—22no—
431C2×C101—41no—
432C2×C101—42no—
433C2×C101—82no—
434C2×C101—82no—
435C2×C101#243011yescharacteristic
436C2×C101C2×B(4,𝔽2)11yescharacteristic
437C2×C101#302611yescharacteristic
438#3490C2×C10111yescharacteristic, complemented
439#2410C2×C10112yescomplemented
440#2405C2×C10111yescharacteristic, complemented
441#2062C2×C10111yescharacteristic, complemented
442#2044C2×C10111yescharacteristic, complemented
443#2029C2×C10111yescharacteristic, complemented
444#2021C2×C10111yescharacteristic, complemented
445#1898C2×C10112yescomplemented
446#1889C2×C10112yescomplemented
447#1867C2×C10112yescomplemented
448C2×#342C2×C10111yescharacteristic, complemented
449C101#2556311yescharacteristic, direct product factor, Sylow
450C23×D4C22×C10111yescharacteristic
451#551—22no—
452#551—22no—
453#546—22no—
454#546—22no—
455#543C22×C10111yescharacteristic
456#538—21no—
457#538—21no—
458#534C22×C10111yescharacteristic
459#525—21no—
460#525—21no—
461C2×#123—21no—
462C2×#121—22no—
463C2×#120C22×C10112yes—
464C2×#120C22×C10112yes—
465#518C22×C10112yes—
466C22×C22⋊C4C22×C10111yescharacteristic
467C22×C22⋊C4C22×C10112yes—
468C2×#99C22×C10112yes—
469C2×#99C22×C10112yes—
470#394—21no—
471#394—21no—
472#394—22no—
473#392—22no—
474#386—21no—
475#386—22no—
476#386C22×C10112yes—
477#385C22×C10112yes—
478#385C22×C10111yescharacteristic
479#385C22×C10111yescharacteristic
480#379C22×C10111yescharacteristic
481#379C22×C10112yes—
482#379C22×C10111yescharacteristic
483#379C22×C10111yescharacteristic
484#342C22×C10112yes—
485#342C22×C10111yescharacteristic
486#342C22×C10112yes—
487#342C22×C10112yes—
488#342C22×C10111yescharacteristic
489C25C23×C10111yescharacteristic
490C25C23×C10111yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C10112yescomplemented
500C22×D4D4×C10112yescomplemented
501C22×D4C23×C10112yes—
502C23×C4—22no—
503C23×C4D4×C10111yescharacteristic, complemented
504C23×C4D4×C10111yescharacteristic, complemented
505C23×C4C23×C10111yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C10111yescharacteristic, complemented
565C2×C22⋊C4D4×C10111yescharacteristic, complemented
566C2×C22⋊C4D4×C10112yescomplemented
567C2×C22⋊C4D4×C10112yescomplemented
568C2×C22⋊C4C23×C10112yes—
569C2×C22⋊C4C23×C10111yescharacteristic
570C2×C22⋊C4C23×C10111yescharacteristic
571C2×C22⋊C4C23×C10111yescharacteristic
572C2×C22⋊C4C23×C10111yescharacteristic
573C2×C22⋊C4C23×C10112yes—
574C2×C22⋊C4C23×C10112yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C10112yes—
594C24C2×D4×C10111yescharacteristic
595C24C2×D4×C10112yes—
596C24C2×D4×C10112yes—
597C24C2×D4×C10111yescharacteristic
598C24C24×C10111yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C10112yes—
650C22×C4C2×D4×C10111yescharacteristic
651C22×C4C2×D4×C10112yes—
652C22×C4C2×D4×C10111yescharacteristic
653C22×C4C2×D4×C10111yescharacteristic
654C22×C4C2×D4×C10112yes—
655C22×C4C2×D4×C10111yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C10114yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C10112yes—
744C23#120×C10111yescharacteristic
745C23#120×C10111yescharacteristic
746C23C22×D4×C10111yescharacteristic
747C23C22×D4×C10112yes—
748C23C2×#41×C10112yes—
749C23H(5,𝔽2)×C10111yescharacteristic
750C232−1+4×C10111yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22B(4,𝔽2)×C10112yes—
846C22C2×#120×C10111yescharacteristic
847C22#532×C10111yescharacteristic
848C22#537×C10111yescharacteristic
849C22#546×C10112yes—
850C22#547×C10112yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C101×#243011yescharacteristic
873C2C2×B(4,𝔽2)×C10111yescharacteristic
874C2C101×#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×#3490C2semidirect
2. C101×#2410C2semidirect
3. C101×#2405C2semidirect
4. C101×#2062C2semidirect
5. C101×#2044C2semidirect
6. C101×#2029C2semidirect
7. C101×#2021C2semidirect
8. C101×#1898C2semidirect
9. C101×#1889C2semidirect
10. C101×#1867C2semidirect
11. C2×#342×C101C2semidirect
61. C22×D4×C101D4semidirect
62. C22×D4×C101D4semidirect
65. C23×C4×C101D4semidirect
66. C23×C4×C101D4semidirect
126. C2×C22⋊C4×C101D4semidirect
127. C2×C22⋊C4×C101D4semidirect
128. C2×C22⋊C4×C101D4semidirect
129. C2×C22⋊C4×C101D4semidirect
260. C22⋊C4×C101#41semidirect
425. #25563C101direct (N × H)
438. #3490C2×C101semidirect
439. #2410C2×C101semidirect
440. #2405C2×C101semidirect
441. #2062C2×C101semidirect
442. #2044C2×C101semidirect
443. #2029C2×C101semidirect
444. #2021C2×C101semidirect
445. #1898C2×C101semidirect
446. #1889C2×C101semidirect
447. #1867C2×C101semidirect
448. C2×#342C2×C101semidirect
449. C101#25563direct (N × H)
499. C22×D4D4×C101semidirect
500. C22×D4D4×C101semidirect
503. C23×C4D4×C101semidirect
504. C23×C4D4×C101semidirect
564. C2×C22⋊C4D4×C101semidirect
565. C2×C22⋊C4D4×C101semidirect
566. C2×C22⋊C4D4×C101semidirect
567. C2×C22⋊C4D4×C101semidirect
698. 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×#34902
C101×#24102
C101×#24052
C101×#20622
C101×#20442
C101×#20292
C101×#20212
C101×#18982
C101×#18892
C101×#18672
C2×#342×C1012
#25563101