Finite Group Databasebeta

← C101×#12753 #38794904

Subgroups — C101×#12753 #38794904

Order 25856.

936 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3532C211yesmaximal, characteristic
2C101×#2127C211yesmaximal, characteristic, complemented
3C101×#2121C211yesmaximal, characteristic, complemented
4C2×AΣL(1,𝔽16)×C101C211yesmaximal, characteristic, complemented
5C101×#1913C211yesmaximal, characteristic, complemented
6C101×#1911C211yesmaximal, characteristic, complemented
7C101×#1889C211yesmaximal, characteristic, complemented
8H(3,𝔽4)×C101C411yescharacteristic, complemented
9#560×C101—21no—
10#560×C101C411yescharacteristic, complemented
11#551×C101—21no—
12#551×C101C411yescharacteristic, complemented
13#546×C101—21no—
14#546×C101—21no—
15#546×C101—21no—
16D42×C101—21no—
17D42×C101C411yescharacteristic, complemented
18#538×C101—21no—
19#538×C101—21no—
20#538×C101—21no—
21#535×C101—21no—
22#535×C101C2211yescharacteristic
23#534×C101—21no—
24#534×C101C2211yescharacteristic
25C2×#120×C101—21no—
26C2×#120×C101C2211yescharacteristic
27#518×C101C2211yescharacteristic, complemented
28#421×C101—21no—
29C2×#100×C101C2211yescharacteristic, complemented
30C2×#99×C101—21no—
31C2×#99×C101C2211yescharacteristic, complemented
32C2×#99×C101C2211yescharacteristic, complemented
33#379×C101—21no—
34#354×C101—21no—
35#353×C101—21no—
36#352×C101—21no—
37AΣL(1,𝔽16)×C101—21no—
38AΣL(1,𝔽16)×C101—21no—
39AΣL(1,𝔽16)×C101—21no—
40#342×C101—21no—
41#342×C101—21no—
42H(3,ℤ/4)×C101—21no—
43C25×C101D411yescharacteristic
44C2×#41×C101—21no—
45C2×#41×C101D411yescharacteristic
46C22×D4×C101—21no—
47C22×D4×C101—21no—
48C22×D4×C101—21no—
49C22×D4×C101—21no—
50C22×D4×C101—21no—
51C22×D4×C101D411yescharacteristic
52C22×D4×C101C2311yescharacteristic
53C2×M16×C101—21no—
54#127×C101—21no—
55#127×C101C2×C411yescharacteristic
56#127×C101D411yescharacteristic
57#126×C101—21no—
58#126×C101—21no—
59#126×C101—21no—
60#126×C101—21no—
61#124×C101—21no—
62#124×C101—21no—
63#124×C101—21no—
64#124×C101—21no—
65#124×C101—21no—
66#124×C101C2×C411yescharacteristic
67#124×C101D411yescharacteristic
68#123×C101—21no—
69#123×C101—21no—
70#123×C101—21no—
71#123×C101—21no—
72#123×C101—21no—
73#123×C101—21no—
74#123×C101—21no—
75#123×C101—21no—
76#123×C101C2×C411yescharacteristic
77#123×C101D411yescharacteristic
78C22⋊Q8×C101—21no—
79C22⋊Q8×C101—21no—
80C22⋊Q8×C101—21no—
81#121×C101—21no—
82#121×C101—21no—
83#121×C101—21no—
84#121×C101—21no—
85#121×C101—21no—
86#121×C101—21no—
87#121×C101—21no—
88#121×C101—21no—
89#121×C101—21no—
90#121×C101—21no—
91#121×C101—21no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95#121×C101—21no—
96#120×C101—21no—
97#120×C101—21no—
98#120×C101—21no—
99#120×C101—21no—
100#120×C101—21no—
101#120×C101—21no—
102#120×C101—21no—
103#120×C101—21no—
104#120×C101—21no—
105#120×C101—21no—
106#120×C101—21no—
107#120×C101—21no—
108#120×C101—21no—
109#120×C101—21no—
110#120×C101C2×C411yescharacteristic
111#120×C101C2×C411yescharacteristic
112#120×C101C2×C411yescharacteristic
113#120×C101D411yescharacteristic
114#120×C101D411yescharacteristic
115#120×C101D411yescharacteristic
116C4×D4×C101—21no—
117C4×D4×C101—21no—
118C4×D4×C101—21no—
119C4×D4×C101—21no—
120C4×D4×C101—21no—
121C4×D4×C101—21no—
122C4×D4×C101—42no—
123#117×C101—21no—
124#117×C101—21no—
125#117×C101D411yescharacteristic
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—42no—
136C2×C22⋊C4×C101D411yescharacteristic
137C2×C22⋊C4×C101D411yescharacteristic
138#104×C101—42no—
139#100×C101—21no—
140#100×C101—21no—
141#99×C101—21no—
142#99×C101—21no—
143#99×C101—21no—
144#99×C101—21no—
145#99×C101—42no—
146C24×C101—21no—
147C24×C101—21no—
148C24×C101—21no—
149C24×C101—41no—
150C24×C101—41no—
151C24×C101—82no—
152C24×C101C22⋊C411yescharacteristic
153C24×C101C22⋊C411yescharacteristic
154C24×C101C22⋊C411yescharacteristic, complemented
155C24×C101C2×D411yescharacteristic
156C24×C101C2×D411yescharacteristic
157#41×C101—41no—
158#41×C101—41no—
159#41×C101—82no—
160C2×Q8×C101—21no—
161C2×Q8×C101C22⋊C411yescharacteristic, complemented
162C2×D4×C101—21no—
163C2×D4×C101—21no—
164C2×D4×C101—21no—
165C2×D4×C101—21no—
166C2×D4×C101—21no—
167C2×D4×C101—21no—
168C2×D4×C101—21no—
169C2×D4×C101—21no—
170C2×D4×C101—21no—
171C2×D4×C101—21no—
172C2×D4×C101—21no—
173C2×D4×C101—21no—
174C2×D4×C101—21no—
175C2×D4×C101—21no—
176C2×D4×C101—21no—
177C2×D4×C101—21no—
178C2×D4×C101—21no—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—41no—
183C2×D4×C101—41no—
184C2×D4×C101—41no—
185C2×D4×C101—41no—
186C2×D4×C101—82no—
187C2×D4×C101—82no—
188C2×D4×C101—82no—
189C2×D4×C101—82no—
190C2×D4×C101—81no—
191C2×D4×C101—81no—
192C2×D4×C101C22⋊C411yescharacteristic, complemented
193C2×D4×C101C22×C411yescharacteristic
194C2×D4×C101C2×D411yescharacteristic
195C2×D4×C101C2×D411yescharacteristic
196C2×D4×C101C2×D411yescharacteristic
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—22no—
206C22×C4×C101—41no—
207C22×C4×C101—41no—
208C22×C4×C101—41no—
209C22×C4×C101C22⋊C411yescharacteristic, complemented
210C22×C4×C101C2×D411yescharacteristic
211M16×C101—41no—
212M16×C101—41no—
213C2×C8×C101—41no—
214C4⋊C4×C101—21no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101—21no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—21no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—41no—
224C22⋊C4×C101—21no—
225C22⋊C4×C101—21no—
226C22⋊C4×C101—21no—
227C22⋊C4×C101—21no—
228C22⋊C4×C101—21no—
229C22⋊C4×C101—21no—
230C22⋊C4×C101—21no—
231C22⋊C4×C101—21no—
232C22⋊C4×C101—21no—
233C22⋊C4×C101—21no—
234C22⋊C4×C101—21no—
235C22⋊C4×C101—21no—
236C22⋊C4×C101—21no—
237C22⋊C4×C101—21no—
238C22⋊C4×C101—21no—
239C22⋊C4×C101—21no—
240C22⋊C4×C101—21no—
241C22⋊C4×C101—21no—
242C22⋊C4×C101—21no—
243C22⋊C4×C101—21no—
244C22⋊C4×C101—21no—
245C22⋊C4×C101—21no—
246C22⋊C4×C101—21no—
247C22⋊C4×C101—21no—
248C22⋊C4×C101—21no—
249C22⋊C4×C101—22no—
250C22⋊C4×C101—41no—
251C22⋊C4×C101—41no—
252C22⋊C4×C101—41no—
253C22⋊C4×C101—41no—
254C22⋊C4×C101—41no—
255C22⋊C4×C101—41no—
256C22⋊C4×C101—84no—
257C22⋊C4×C101C22⋊C411yescharacteristic
258C22⋊C4×C101C22⋊C411yescharacteristic
259C22⋊C4×C101C22⋊C411yescharacteristic, complemented
260C22⋊C4×C101C22⋊C411yescharacteristic, complemented
261C42×C101—21no—
262C42×C101—21no—
263C42×C101—22no—
264C42×C101C22⋊C411yescharacteristic, complemented
265C42×C101C22⋊C411yescharacteristic, complemented
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—42no—
275C23×C101—41no—
276C23×C101—41no—
277C23×C101—42no—
278C23×C101—42no—
279C23×C101—42no—
280C23×C101—41no—
281C23×C101—44no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—81no—
285C23×C101—81no—
286C23×C101—81no—
287C23×C101—81no—
288C23×C101—81no—
289C23×C101—81no—
290C23×C101—81no—
291C23×C101—81no—
292C23×C101—81no—
293C23×C101—82no—
294C23×C101—82no—
295C23×C101—82no—
296C23×C101C2×C22⋊C411yescharacteristic
297C23×C101C2×C22⋊C411yescharacteristic
298C23×C101#12011yescharacteristic
299C23×C101#12011yescharacteristic
300C23×C101#12011yescharacteristic
301Q8×C101—41no—
302Q8×C101—81no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—42no—
309D4×C101—42no—
310D4×C101—42no—
311D4×C101—42no—
312D4×C101—41no—
313D4×C101—41no—
314D4×C101—41no—
315D4×C101—41no—
316D4×C101—81no—
317D4×C101—81no—
318D4×C101—81no—
319D4×C101—81no—
320D4×C101—81no—
321D4×C101—81no—
322D4×C101—81no—
323D4×C101—81no—
324D4×C101—81no—
325D4×C101—81no—
326D4×C101—81no—
327D4×C101—81no—
328D4×C101—81no—
329D4×C101—81no—
330C2×C4×C101—21no—
331C2×C4×C101—21no—
332C2×C4×C101—21no—
333C2×C4×C101—21no—
334C2×C4×C101—21no—
335C2×C4×C101—21no—
336C2×C4×C101—21no—
337C2×C4×C101—21no—
338C2×C4×C101—21no—
339C2×C4×C101—21no—
340C2×C4×C101—42no—
341C2×C4×C101—41no—
342C2×C4×C101—42no—
343C2×C4×C101—81no—
344C2×C4×C101—81no—
345C2×C4×C101—81no—
346C2×C4×C101—81no—
347C2×C4×C101—81no—
348C2×C4×C101—81no—
349C2×C4×C101—81no—
350C2×C4×C101—82no—
351C2×C4×C101—81no—
352C2×C4×C101—81no—
353C2×C4×C101—82no—
354C2×C4×C101—161no—
355C2×C4×C101—161no—
356C2×C4×C101C2×C22⋊C411yescharacteristic
357C2×C4×C101#12011yescharacteristic
358C8×C101—81no—
359C22×C101—22no—
360C22×C101—21no—
361C22×C101—21no—
362C22×C101—21no—
363C22×C101—21no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—42no—
370C22×C101—41no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—41no—
375C22×C101—41no—
376C22×C101—41no—
377C22×C101—42no—
378C22×C101—41no—
379C22×C101—42no—
380C22×C101—41no—
381C22×C101—41no—
382C22×C101—41no—
383C22×C101—81no—
384C22×C101—81no—
385C22×C101—81no—
386C22×C101—82no—
387C22×C101—82no—
388C22×C101—81no—
389C22×C101—84no—
390C22×C101—81no—
391C22×C101—161no—
392C22×C101—162no—
393C22×C101#37911yescharacteristic
394C22×C101B(4,𝔽2)11yescharacteristic
395C22×C101#45811yescharacteristic
396C4×C101—21no—
397C4×C101—21no—
398C4×C101—41no—
399C4×C101—41no—
400C4×C101—41no—
401C4×C101—41no—
402C4×C101—41no—
403C4×C101—41no—
404C4×C101—41no—
405C4×C101—41no—
406C4×C101—82no—
407C4×C101—161no—
408C4×C101—161no—
409#12753C10111yesmaximal, characteristic, direct product factor, Sylow
410C2×C101—21no—
411C2×C101—21no—
412C2×C101—21no—
413C2×C101—41no—
414C2×C101—41no—
415C2×C101—41no—
416C2×C101—42no—
417C2×C101—41no—
418C2×C101—81no—
419C2×C101—81no—
420C2×C101—81no—
421C2×C101#179011yescharacteristic
422#3532C2×C10111yescharacteristic
423#2127C2×C10111yescharacteristic, complemented
424#2121C2×C10111yescharacteristic, complemented
425C2×AΣL(1,𝔽16)C2×C10111yescharacteristic, complemented
426#1913C2×C10111yescharacteristic, complemented
427#1911C2×C10111yescharacteristic, complemented
428#1889C2×C10111yescharacteristic, complemented
429C101#1275311yescharacteristic, direct product factor, Sylow
430H(3,𝔽4)C4×C10111yescharacteristic, complemented
431#560—21no—
432#560C4×C10111yescharacteristic, complemented
433#551—21no—
434#551C4×C10111yescharacteristic, complemented
435#546—21no—
436#546—21no—
437#546—21no—
438D42—21no—
439D42C4×C10111yescharacteristic, complemented
440#538—21no—
441#538—21no—
442#538—21no—
443#535—21no—
444#535C22×C10111yescharacteristic
445#534—21no—
446#534C22×C10111yescharacteristic
447C2×#120—21no—
448C2×#120C22×C10111yescharacteristic
449#518C22×C10111yescharacteristic, complemented
450#421—21no—
451C2×#100C22×C10111yescharacteristic, complemented
452C2×#99—21no—
453C2×#99C22×C10111yescharacteristic, complemented
454C2×#99C22×C10111yescharacteristic, complemented
455#379—21no—
456#354—21no—
457#353—21no—
458#352—21no—
459AΣL(1,𝔽16)—21no—
460AΣL(1,𝔽16)—21no—
461AΣL(1,𝔽16)—21no—
462#342—21no—
463#342—21no—
464H(3,ℤ/4)—21no—
465C25D4×C10111yescharacteristic
466C2×#41—21no—
467C2×#41D4×C10111yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4D4×C10111yescharacteristic
474C22×D4C23×C10111yescharacteristic
475C2×M16—21no—
476#127—21no—
477#127C2×C4×C10111yescharacteristic
478#127D4×C10111yescharacteristic
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488#124C2×C4×C10111yescharacteristic
489#124D4×C10111yescharacteristic
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123C2×C4×C10111yescharacteristic
499#123D4×C10111yescharacteristic
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524#120—21no—
525#120—21no—
526#120—21no—
527#120—21no—
528#120—21no—
529#120—21no—
530#120—21no—
531#120—21no—
532#120C2×C4×C10111yescharacteristic
533#120C2×C4×C10111yescharacteristic
534#120C2×C4×C10111yescharacteristic
535#120D4×C10111yescharacteristic
536#120D4×C10111yescharacteristic
537#120D4×C10111yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—42no—
545#117—21no—
546#117—21no—
547#117D4×C10111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4D4×C10111yescharacteristic
559C2×C22⋊C4D4×C10111yescharacteristic
560#104—42no—
561#100—21no—
562#100—21no—
563#99—21no—
564#99—21no—
565#99—21no—
566#99—21no—
567#99—42no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—41no—
572C24—41no—
573C24—82no—
574C24C22⋊C4×C10111yescharacteristic
575C24C22⋊C4×C10111yescharacteristic
576C24C22⋊C4×C10111yescharacteristic, complemented
577C24C2×D4×C10111yescharacteristic
578C24C2×D4×C10111yescharacteristic
579#41—41no—
580#41—41no—
581#41—82no—
582C2×Q8—21no—
583C2×Q8C22⋊C4×C10111yescharacteristic, complemented
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C22⋊C4×C10111yescharacteristic, complemented
615C2×D4C22×C4×C10111yescharacteristic
616C2×D4C2×D4×C10111yescharacteristic
617C2×D4C2×D4×C10111yescharacteristic
618C2×D4C2×D4×C10111yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4C22⋊C4×C10111yescharacteristic, complemented
632C22×C4C2×D4×C10111yescharacteristic
633M16—41no—
634M16—41no—
635C2×C8—41no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—41no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—84no—
679C22⋊C4C22⋊C4×C10111yescharacteristic
680C22⋊C4C22⋊C4×C10111yescharacteristic
681C22⋊C4C22⋊C4×C10111yescharacteristic, complemented
682C22⋊C4C22⋊C4×C10111yescharacteristic, complemented
683C42—21no—
684C42—21no—
685C42—22no—
686C42C22⋊C4×C10111yescharacteristic, complemented
687C42C22⋊C4×C10111yescharacteristic, complemented
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—44no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23—82no—
718C23C2×C22⋊C4×C10111yescharacteristic
719C23C2×C22⋊C4×C10111yescharacteristic
720C23#120×C10111yescharacteristic
721C23#120×C10111yescharacteristic
722C23#120×C10111yescharacteristic
723Q8—41no—
724Q8—81no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—161no—
777C2×C4—161no—
778C2×C4C2×C22⋊C4×C10111yescharacteristic
779C2×C4#120×C10111yescharacteristic
780C8—81no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—82no—
809C22—82no—
810C22—81no—
811C22—84no—
812C22—81no—
813C22—161no—
814C22—162no—
815C22#379×C10111yescharacteristic
816C22B(4,𝔽2)×C10111yescharacteristic
817C22#458×C10111yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—161no—
830C4—161no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—41no—
835C2—41no—
836C2—41no—
837C2—42no—
838C2—41no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C101×#179011yescharacteristic
subgroupG/H
center, socleC2×C101#1790
commutatorC2×D4C22×C4×C101
Frattini, cosocleC22×D4C23×C101
prime radicalC101×#3532C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C23×C101 ◁ C22×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2127C2semidirect
3. C101×#2121C2semidirect
4. C2×AΣL(1,𝔽16)×C101C2semidirect
5. C101×#1913C2semidirect
6. C101×#1911C2semidirect
7. C101×#1889C2semidirect
8. H(3,𝔽4)×C101C4semidirect
10. #560×C101C4semidirect
12. #551×C101C4semidirect
17. D42×C101C4semidirect
27. #518×C101C22semidirect
29. C2×#100×C101C22semidirect
31. C2×#99×C101C22semidirect
32. C2×#99×C101C22semidirect
154. C24×C101C22⋊C4semidirect
161. C2×Q8×C101C22⋊C4semidirect
192. C2×D4×C101C22⋊C4semidirect
209. C22×C4×C101C22⋊C4semidirect
259. C22⋊C4×C101C22⋊C4semidirect
260. C22⋊C4×C101C22⋊C4semidirect
264. C42×C101C22⋊C4semidirect
265. C42×C101C22⋊C4semidirect
409. #12753C101direct (N × H)
423. #2127C2×C101semidirect
424. #2121C2×C101semidirect
425. C2×AΣL(1,𝔽16)C2×C101semidirect
426. #1913C2×C101semidirect
427. #1911C2×C101semidirect
428. #1889C2×C101semidirect
429. C101#12753direct (N × H)
430. H(3,𝔽4)C4×C101semidirect
432. #560C4×C101semidirect
434. #551C4×C101semidirect
439. D42C4×C101semidirect
449. #518C22×C101semidirect
451. C2×#100C22×C101semidirect
453. C2×#99C22×C101semidirect
454. C2×#99C22×C101semidirect
576. C24C22⋊C4×C101semidirect
583. C2×Q8C22⋊C4×C101semidirect
614. C2×D4C22⋊C4×C101semidirect
631. C22×C4C22⋊C4×C101semidirect
681. C22⋊C4C22⋊C4×C101semidirect
682. C22⋊C4C22⋊C4×C101semidirect
686. C42C22⋊C4×C101semidirect
687. C42C22⋊C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35322
C101×#21272
C101×#21212
C2×AΣL(1,𝔽16)×C1012
C101×#19132
C101×#19112
C101×#18892
#12753101