Finite Group Databasebeta

← C101×#12687 #38794838

Subgroups — C101×#12687 #38794838

Order 25856.

2508 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 2508 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C101C211yesmaximal, characteristic
2C2×AΣL(1,𝔽16)×C101C214yesmaximal, complemented
3C101×#1783C211yesmaximal, characteristic, complemented
4C101×#1781C211yesmaximal, characteristic, complemented
5C26×C101C411yescharacteristic, complemented
6C23×D4×C101—21no—
7C23×D4×C101C2211yescharacteristic
8C2×#120×C101—21no—
9C2×#120×C101—21no—
10C2×#120×C101—28no—
11C2×#120×C101C412yescomplemented
12C2×#120×C101C2212yes—
13C22×C22⋊C4×C101—21no—
14C22×C22⋊C4×C101C411yescharacteristic, complemented
15C2×#100×C101—21no—
16C2×#100×C101C2212yescomplemented
17C2×#99×C101—21no—
18C2×#99×C101C2212yescomplemented
19#407×C101—21no—
20#379×C101—21no—
21AΣL(1,𝔽16)×C101—28no—
22C25×C101—21no—
23C25×C101—21no—
24C25×C101—24no—
25C25×C101—48no—
26C25×C101—42no—
27C25×C101—42no—
28C25×C101C2×C411yescharacteristic
29C25×C101C2×C412yes—
30C25×C101D411yescharacteristic
31C22×D4×C101—28no—
32C22×D4×C101—22no—
33C22×D4×C101—22no—
34C22×D4×C101—24no—
35C22×D4×C101—42no—
36C22×D4×C101—42no—
37C22×D4×C101—48no—
38C22×D4×C101C2×C411yescharacteristic
39C22×D4×C101D411yescharacteristic
40C22×D4×C101D411yescharacteristic
41C22×D4×C101C2311yescharacteristic
42C23×C4×C101—21no—
43C23×C4×C101D411yescharacteristic
44C2×M16×C101—22no—
45#120×C101—28no—
46#120×C101—28no—
47#120×C101—24no—
48#120×C101—24no—
49#120×C101—24no—
50#120×C101D418yes—
51C2×C22⋊C4×C101—28no—
52C2×C22⋊C4×C101—21no—
53C2×C22⋊C4×C101—22no—
54C2×C22⋊C4×C101—22no—
55C2×C22⋊C4×C101—24no—
56C2×C22⋊C4×C101—22no—
57C2×C22⋊C4×C101—42no—
58C2×C22⋊C4×C101C2×C412yes—
59#100×C101—24no—
60#100×C101—42no—
61#99×C101—24no—
62#99×C101—42no—
63C22⋊C8×C101—42no—
64C24×C101—24no—
65C24×C101—28no—
66C24×C101—22no—
67C24×C101—22no—
68C24×C101—22no—
69C24×C101—22no—
70C24×C101—24no—
71C24×C101—22no—
72C24×C101—22no—
73C24×C101—22no—
74C24×C101—41no—
75C24×C101—44no—
76C24×C101—48no—
77C24×C101—42no—
78C24×C101—42no—
79C24×C101—44no—
80C24×C101—42no—
81C24×C101—48no—
82C24×C101—432no—
83C24×C101—416no—
84C24×C101—42no—
85C24×C101—44no—
86C24×C101—48no—
87C24×C101—416no—
88C24×C101—432no—
89C24×C101—48no—
90C24×C101—42no—
91C24×C101—42no—
92C24×C101C22⋊C411yescharacteristic
93C24×C101C22⋊C411yescharacteristic
94C24×C101C22⋊C411yescharacteristic
95C24×C101C22⋊C414yescomplemented
96C24×C101C22×C411yescharacteristic
97C24×C101C2×D411yescharacteristic
98C2×D4×C101—28no—
99C2×D4×C101—22no—
100C2×D4×C101—22no—
101C2×D4×C101—22no—
102C2×D4×C101—22no—
103C2×D4×C101—28no—
104C2×D4×C101—22no—
105C2×D4×C101—41no—
106C2×D4×C101—41no—
107C2×D4×C101—41no—
108C2×D4×C101—41no—
109C2×D4×C101—41no—
110C2×D4×C101—41no—
111C2×D4×C101—416no—
112C2×D4×C101—48no—
113C2×D4×C101—48no—
114C2×D4×C101—432no—
115C2×D4×C101C2×D414yes—
116C22×C4×C101—24no—
117C22×C4×C101—22no—
118C22×C4×C101—22no—
119C22×C4×C101—22no—
120C22×C4×C101—41no—
121C22×C4×C101—44no—
122C22×C4×C101—42no—
123C22×C4×C101C22⋊C411yescharacteristic
124C22×C4×C101C2×D411yescharacteristic
125M16×C101—42no—
126M16×C101—42no—
127C2×C8×C101—42no—
128C22⋊C4×C101—28no—
129C22⋊C4×C101—24no—
130C22⋊C4×C101—22no—
131C22⋊C4×C101—28no—
132C22⋊C4×C101—42no—
133C22⋊C4×C101—42no—
134C22⋊C4×C101—84no—
135C22⋊C4×C101C22⋊C414yescomplemented
136C23×C101—24no—
137C23×C101—21no—
138C23×C101—21no—
139C23×C101—216no—
140C23×C101—28no—
141C23×C101—28no—
142C23×C101—21no—
143C23×C101—24no—
144C23×C101—21no—
145C23×C101—21no—
146C23×C101—21no—
147C23×C101—21no—
148C23×C101—21no—
149C23×C101—21no—
150C23×C101—21no—
151C23×C101—21no—
152C23×C101—44no—
153C23×C101—42no—
154C23×C101—48no—
155C23×C101—44no—
156C23×C101—42no—
157C23×C101—48no—
158C23×C101—48no—
159C23×C101—48no—
160C23×C101—416no—
161C23×C101—44no—
162C23×C101—48no—
163C23×C101—44no—
164C23×C101—48no—
165C23×C101—48no—
166C23×C101—416no—
167C23×C101—48no—
168C23×C101—44no—
169C23×C101—42no—
170C23×C101—42no—
171C23×C101—48no—
172C23×C101—48no—
173C23×C101—416no—
174C23×C101—416no—
175C23×C101—464no—
176C23×C101—464no—
177C23×C101—48no—
178C23×C101—416no—
179C23×C101—48no—
180C23×C101—44no—
181C23×C101—42no—
182C23×C101—42no—
183C23×C101—44no—
184C23×C101—82no—
185C23×C101—84no—
186C23×C101#9912yes—
187C23×C101#9912yes—
188C23×C101C2×C22⋊C411yescharacteristic
189C23×C101C2×C22⋊C412yes—
190C23×C101#12012yes—
191D4×C101—44no—
192D4×C101—44no—
193D4×C101—44no—
194D4×C101—416no—
195D4×C101—416no—
196D4×C101—44no—
197C2×C4×C101—21no—
198C2×C4×C101—21no—
199C2×C4×C101—21no—
200C2×C4×C101—24no—
201C2×C4×C101—21no—
202C2×C4×C101—21no—
203C2×C4×C101—44no—
204C2×C4×C101—48no—
205C2×C4×C101—44no—
206C2×C4×C101—82no—
207C2×C4×C101—84no—
208C2×C4×C101#12012yes—
209C8×C101—82no—
210C22×C101—24no—
211C22×C101—24no—
212C22×C101—22no—
213C22×C101—22no—
214C22×C101—22no—
215C22×C101—28no—
216C22×C101—22no—
217C22×C101—22no—
218C22×C101—22no—
219C22×C101—42no—
220C22×C101—42no—
221C22×C101—42no—
222C22×C101—42no—
223C22×C101—44no—
224C22×C101—432no—
225C22×C101—416no—
226C22×C101—48no—
227C22×C101—42no—
228C22×C101—42no—
229C22×C101—48no—
230C22×C101—48no—
231C22×C101—416no—
232C22×C101—432no—
233C22×C101—42no—
234C22×C101—48no—
235C22×C101—42no—
236C22×C101—42no—
237C22×C101—44no—
238C22×C101—42no—
239C22×C101—41no—
240C22×C101—81no—
241C22×C101—88no—
242C22×C101—81no—
243C22×C101AΣL(1,𝔽16)14yescomplemented
244C22×C101#37911yescharacteristic
245C22×C101C2×#9911yescharacteristic
246C22×C101C2×#9911yescharacteristic
247C4×C101—22no—
248C4×C101—44no—
249C4×C101—41no—
250C4×C101—162no—
251#12687C10111yesmaximal, characteristic, direct product factor, Sylow
252C2×C101—21no—
253C2×C101—24no—
254C2×C101—21no—
255C2×C101—42no—
256C2×C101—48no—
257C2×C101—42no—
258C2×C101—42no—
259C2×C101—81no—
260C2×C101#178111yescharacteristic
261C2×C101C2×AΣL(1,𝔽16)12yes—
262C22×#120C2×C10111yescharacteristic
263C2×AΣL(1,𝔽16)C2×C10114yescomplemented
264#1783C2×C10111yescharacteristic, complemented
265#1781C2×C10111yescharacteristic, complemented
266C101#1268711yescharacteristic, direct product factor, Sylow
267C26C4×C10111yescharacteristic, complemented
268C23×D4—21no—
269C23×D4C22×C10111yescharacteristic
270C2×#120—21no—
271C2×#120—21no—
272C2×#120—28no—
273C2×#120C4×C10112yescomplemented
274C2×#120C22×C10112yes—
275C22×C22⋊C4—21no—
276C22×C22⋊C4C4×C10111yescharacteristic, complemented
277C2×#100—21no—
278C2×#100C22×C10112yescomplemented
279C2×#99—21no—
280C2×#99C22×C10112yescomplemented
281#407—21no—
282#379—21no—
283AΣL(1,𝔽16)—28no—
284C25—21no—
285C25—21no—
286C25—24no—
287C25—48no—
288C25—42no—
289C25—42no—
290C25C2×C4×C10111yescharacteristic
291C25C2×C4×C10112yes—
292C25D4×C10111yescharacteristic
293C22×D4—28no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—24no—
297C22×D4—42no—
298C22×D4—42no—
299C22×D4—48no—
300C22×D4C2×C4×C10111yescharacteristic
301C22×D4D4×C10111yescharacteristic
302C22×D4D4×C10111yescharacteristic
303C22×D4C23×C10111yescharacteristic
304C23×C4—21no—
305C23×C4D4×C10111yescharacteristic
306C2×M16—22no—
307#120—28no—
308#120—28no—
309#120—24no—
310#120—24no—
311#120—24no—
312#120D4×C10118yes—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4C2×C4×C10112yes—
321#100—24no—
322#100—42no—
323#99—24no—
324#99—42no—
325C22⋊C8—42no—
326C24—24no—
327C24—28no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—24no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—41no—
337C24—44no—
338C24—48no—
339C24—42no—
340C24—42no—
341C24—42no—
342C24—44no—
343C24—48no—
344C24—432no—
345C24—416no—
346C24—42no—
347C24—44no—
348C24—48no—
349C24—416no—
350C24—432no—
351C24—48no—
352C24—42no—
353C24—42no—
354C24C22⋊C4×C10111yescharacteristic
355C24C22⋊C4×C10111yescharacteristic
356C24C22⋊C4×C10111yescharacteristic
357C24C22⋊C4×C10114yescomplemented
358C24C22×C4×C10111yescharacteristic
359C24C2×D4×C10111yescharacteristic
360C2×D4—28no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—28no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—416no—
374C2×D4—48no—
375C2×D4—48no—
376C2×D4—432no—
377C2×D4C2×D4×C10114yes—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—44no—
384C22×C4—42no—
385C22×C4C22⋊C4×C10111yescharacteristic
386C22×C4C2×D4×C10111yescharacteristic
387M16—42no—
388M16—42no—
389C2×C8—42no—
390C22⋊C4—28no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—28no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—84no—
397C22⋊C4C22⋊C4×C10114yescomplemented
398C23—21no—
399C23—24no—
400C23—21no—
401C23—216no—
402C23—28no—
403C23—28no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—24no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—44no—
415C23—42no—
416C23—48no—
417C23—44no—
418C23—42no—
419C23—48no—
420C23—48no—
421C23—48no—
422C23—416no—
423C23—48no—
424C23—44no—
425C23—48no—
426C23—44no—
427C23—48no—
428C23—416no—
429C23—48no—
430C23—44no—
431C23—42no—
432C23—42no—
433C23—48no—
434C23—48no—
435C23—416no—
436C23—416no—
437C23—464no—
438C23—464no—
439C23—48no—
440C23—416no—
441C23—42no—
442C23—42no—
443C23—48no—
444C23—44no—
445C23—44no—
446C23—82no—
447C23—84no—
448C23#99×C10112yes—
449C23#99×C10112yes—
450C23C2×C22⋊C4×C10111yescharacteristic
451C23C2×C22⋊C4×C10112yes—
452C23#120×C10112yes—
453D4—44no—
454D4—44no—
455D4—44no—
456D4—416no—
457D4—416no—
458D4—44no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—24no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—82no—
469C2×C4—84no—
470C2×C4#120×C10112yes—
471C8—82no—
472C22—24no—
473C22—24no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—28no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—44no—
486C22—48no—
487C22—42no—
488C22—432no—
489C22—416no—
490C22—42no—
491C22—48no—
492C22—48no—
493C22—416no—
494C22—432no—
495C22—44no—
496C22—42no—
497C22—48no—
498C22—42no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—81no—
503C22—88no—
504C22—81no—
505C22AΣL(1,𝔽16)×C10114yescomplemented
506C22#379×C10111yescharacteristic
507C22C2×#99×C10111yescharacteristic
508C22C2×#99×C10111yescharacteristic
509C4—22no—
510C4—44no—
511C4—41no—
512C4—162no—
513C2—21no—
514C2—21no—
515C2—24no—
516C2—42no—
517C2—48no—
518C2—42no—
519C2—42no—
520C2—81no—
521C2C101×#178111yescharacteristic
522C2C2×AΣL(1,𝔽16)×C10112yes—
subgroupG/H
center, socleC22×C101C2×#99
commutatorC24C22×C4×C101
Frattini, cosocleC22×D4C23×C101
prime radicalC22×#120×C101C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C24×C101 ◁ C23×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×AΣL(1,𝔽16)×C101C2semidirect
3. C101×#1783C2semidirect
4. C101×#1781C2semidirect
5. C26×C101C4semidirect
11. C2×#120×C101C4semidirect
14. C22×C22⋊C4×C101C4semidirect
16. C2×#100×C101C22semidirect
18. C2×#99×C101C22semidirect
95. C24×C101C22⋊C4semidirect
135. C22⋊C4×C101C22⋊C4semidirect
243. C22×C101AΣL(1,𝔽16)semidirect
251. #12687C101direct (N × H)
263. C2×AΣL(1,𝔽16)C2×C101semidirect
264. #1783C2×C101semidirect
265. #1781C2×C101semidirect
266. C101#12687direct (N × H)
267. C26C4×C101semidirect
273. C2×#120C4×C101semidirect
276. C22×C22⋊C4C4×C101semidirect
278. C2×#100C22×C101semidirect
280. C2×#99C22×C101semidirect
357. C24C22⋊C4×C101semidirect
397. C22⋊C4C22⋊C4×C101semidirect
505. C22AΣL(1,𝔽16)×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1012
C2×AΣL(1,𝔽16)×C1012
C101×#17832
C101×#17812
#12687101