Finite Group Databasebeta

← C101×#9520 #38791671

Subgroups — C101×#9520 #38791671

Order 25856.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3003C211yesmaximal, characteristic
2C101×#2976C211yesmaximal, characteristic, complemented
3C101×#1786C211yesmaximal, characteristic, complemented
4C101×#1783C211yesmaximal, characteristic, complemented
5C101×#1513C211yesmaximal, characteristic, complemented
6C101×#1305C211yesmaximal, characteristic, complemented
7C101×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C101C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C101—21no—
10#525×C101C2211yescharacteristic
11#450×C101—21no—
12#450×C101C412yescomplemented
13#447×C101—21no—
14#447×C101C412yescomplemented
15#436×C101—21no—
16#435×C101—21no—
17#435×C101—21no—
18C8×D4×C101—21no—
19#433×C101—21no—
20#418×C101—21no—
21C2×#102×C101—21no—
22C2×#102×C101—21no—
23C2×#100×C101—21no—
24C2×#100×C101—21no—
25#408×C101—21no—
26#407×C101C2211yescharacteristic
27#407×C101C2211yescharacteristic
28#407×C101C2211yescharacteristic
29C2×C22⋊C8×C101C2211yescharacteristic
30#380×C101C2211yescharacteristic
31#328×C101—21no—
32#327×C101—21no—
33C25×C101—21no—
34C2×#41×C101D411yescharacteristic
35C22×D4×C101—21no—
36C22×D4×C101—21no—
37C22×D4×C101—21no—
38C22×D4×C101—21no—
39C22×D4×C101—21no—
40C22×D4×C101—42no—
41C22×D4×C101—42no—
42C22×D4×C101C2×C412yes—
43C23×C4×C101C2311yescharacteristic
44AGL(1,ℤ/8)×C101—42no—
45AGL(1,ℤ/8)×C101—42no—
46C2×SD16×C101—22no—
47C2×D8×C101—22no—
48C2×M16×C101—21no—
49C2×M16×C101—21no—
50C2×M16×C101—21no—
51C2×M16×C101D411yescharacteristic
52C2×M16×C101D411yescharacteristic
53C22×C8×C101—21no—
54C22×C8×C101D411yescharacteristic
55C22×C8×C101D411yescharacteristic
56#123×C101—21no—
57C22⋊Q8×C101C2×C411yescharacteristic
58C22⋊Q8×C101D411yescharacteristic
59#121×C101C2×C411yescharacteristic
60#121×C101D411yescharacteristic
61#120×C101—21no—
62C4×D4×C101—21no—
63C4×D4×C101—21no—
64#117×C101D411yescharacteristic
65C2×C4⋊C4×C101—21no—
66C2×C22⋊C4×C101—21no—
67C4⋊C8×C101—21no—
68C4⋊C8×C101—21no—
69#102×C101—22no—
70#102×C101—22no—
71#102×C101—42no—
72#102×C101—42no—
73#100×C101—42no—
74#100×C101—42no—
75C22⋊C8×C101—21no—
76C22⋊C8×C101—21no—
77C22⋊C8×C101—21no—
78C22⋊C8×C101—21no—
79C22⋊C8×C101—21no—
80C22⋊C8×C101—21no—
81C22⋊C8×C101—21no—
82C22⋊C8×C101—21no—
83C22⋊C8×C101—21no—
84C22⋊C8×C101C2×C412yes—
85#97×C101—21no—
86C4×C8×C101—21no—
87#95×C101—21no—
88C24×C101—22no—
89C24×C101—44no—
90C24×C101—41no—
91C24×C101—41no—
92C24×C101—81no—
93C24×C101—81no—
94C24×C101—82no—
95C24×C101#4111yescharacteristic
96#41×C101—41no—
97#41×C101—41no—
98C2×Q8×C101C22⋊C411yescharacteristic
99C2×D4×C101—22no—
100C2×D4×C101—22no—
101C2×D4×C101—22no—
102C2×D4×C101—22no—
103C2×D4×C101—22no—
104C2×D4×C101—22no—
105C2×D4×C101—21no—
106C2×D4×C101—21no—
107C2×D4×C101—21no—
108C2×D4×C101—22no—
109C2×D4×C101—22no—
110C2×D4×C101—41no—
111C2×D4×C101—41no—
112C2×D4×C101—41no—
113C2×D4×C101—41no—
114C2×D4×C101—41no—
115C2×D4×C101—41no—
116C2×D4×C101—44no—
117C2×D4×C101—44no—
118C2×D4×C101—44no—
119C2×D4×C101—41no—
120C2×D4×C101—41no—
121C2×D4×C101C22⋊C411yescharacteristic
122C22×C4×C101—21no—
123C22×C4×C101—41no—
124C22×C4×C101—41no—
125C22×C4×C101—41no—
126C22×C4×C101C22×C411yescharacteristic
127C22×C4×C101C2×D411yescharacteristic
128C22×C4×C101C2×D411yescharacteristic
129C22×C4×C101C2×D411yescharacteristic
130C22×C4×C101C2×D411yescharacteristic
131C22×C4×C101#4111yescharacteristic
132SD16×C101—44no—
133D8×C101—44no—
134M16×C101—41no—
135M16×C101—41no—
136M16×C101—41no—
137M16×C101—41no—
138M16×C101—41no—
139M16×C101—41no—
140M16×C101—81no—
141C2×C8×C101—22no—
142C2×C8×C101—21no—
143C2×C8×C101—21no—
144C2×C8×C101—21no—
145C2×C8×C101—21no—
146C2×C8×C101—41no—
147C2×C8×C101—41no—
148C2×C8×C101—41no—
149C2×C8×C101—81no—
150C4⋊C4×C101—21no—
151C4⋊C4×C101—21no—
152C4⋊C4×C101—41no—
153C4⋊C4×C101—41no—
154C4⋊C4×C101C22⋊C411yescharacteristic
155C4⋊C4×C101C22⋊C411yescharacteristic
156C22⋊C4×C101—21no—
157C22⋊C4×C101—21no—
158C22⋊C4×C101—21no—
159C22⋊C4×C101—21no—
160C22⋊C4×C101—21no—
161C22⋊C4×C101—81no—
162C42×C101—21no—
163C23×C101—21no—
164C23×C101—21no—
165C23×C101—24no—
166C23×C101—21no—
167C23×C101—41no—
168C23×C101—41no—
169C23×C101—42no—
170C23×C101—42no—
171C23×C101—42no—
172C23×C101—42no—
173C23×C101—42no—
174C23×C101—42no—
175C23×C101—82no—
176C23×C101—82no—
177C23×C101—82no—
178C23×C101—81no—
179C23×C101—81no—
180C23×C101—82no—
181C23×C101—88no—
182C23×C101—88no—
183C23×C101—81no—
184C23×C101—81no—
185C23×C101C4×D411yescharacteristic
186C23×C101#12111yescharacteristic
187C23×C101#12311yescharacteristic
188Q8×C101—41no—
189D4×C101—24no—
190D4×C101—24no—
191D4×C101—41no—
192D4×C101—42no—
193D4×C101—42no—
194D4×C101—42no—
195D4×C101—42no—
196D4×C101—41no—
197D4×C101—41no—
198D4×C101—42no—
199D4×C101—42no—
200D4×C101—81no—
201D4×C101—81no—
202C2×C4×C101—21no—
203C2×C4×C101—21no—
204C2×C4×C101—21no—
205C2×C4×C101—21no—
206C2×C4×C101—21no—
207C2×C4×C101—21no—
208C2×C4×C101—21no—
209C2×C4×C101—21no—
210C2×C4×C101—21no—
211C2×C4×C101—41no—
212C2×C4×C101—41no—
213C2×C4×C101—41no—
214C2×C4×C101—41no—
215C2×C4×C101—41no—
216C2×C4×C101—81no—
217C2×C4×C101—81no—
218C2×C4×C101—81no—
219C2×C4×C101C2×C22⋊C411yescharacteristic
220C2×C4×C101C4×D411yescharacteristic
221C2×C4×C101#12011yescharacteristic
222C2×C4×C101#12111yescharacteristic
223C8×C101—42no—
224C8×C101—41no—
225C8×C101—41no—
226C8×C101—41no—
227C8×C101—41no—
228C8×C101—81no—
229C22×C101—21no—
230C22×C101—21no—
231C22×C101—21no—
232C22×C101—21no—
233C22×C101—21no—
234C22×C101—21no—
235C22×C101—21no—
236C22×C101—21no—
237C22×C101—42no—
238C22×C101—42no—
239C22×C101—41no—
240C22×C101—44no—
241C22×C101—41no—
242C22×C101—41no—
243C22×C101—82no—
244C22×C101—82no—
245C22×C101—82no—
246C22×C101—82no—
247C22×C101—84no—
248C22×C101—84no—
249C22×C101—84no—
250C22×C101—84no—
251C22×C101—82no—
252C22×C101—82no—
253C22×C101#38611yescharacteristic
254C22×C101#47111yescharacteristic
255C22×C101#47211yescharacteristic
256C4×C101—21no—
257C4×C101—21no—
258C4×C101—21no—
259C4×C101—41no—
260C4×C101—41no—
261C4×C101—41no—
262C4×C101—161no—
263C4×C101B(4,𝔽2)11yescharacteristic
264C4×C101B(4,𝔽2)11yescharacteristic
265#9520C10111yesmaximal, characteristic, direct product factor, Sylow
266C2×C101—21no—
267C2×C101—21no—
268C2×C101—41no—
269C2×C101—41no—
270C2×C101—81no—
271C2×C101—84no—
272C2×C101#188911yescharacteristic
273C2×C101#190311yescharacteristic
274C2×C101#190711yescharacteristic
275#3003C2×C10111yescharacteristic
276#2976C2×C10111yescharacteristic, complemented
277#1786C2×C10111yescharacteristic, complemented
278#1783C2×C10111yescharacteristic, complemented
279#1513C2×C10111yescharacteristic, complemented
280#1305C2×C10111yescharacteristic, complemented
281#1293C2×C10111yescharacteristic, complemented
282C101#952011yescharacteristic, direct product factor, Sylow
283C23×D4C22×C10111yescharacteristic
284C2×AGL(1,ℤ/8)—21no—
285#525C22×C10111yescharacteristic
286#450—21no—
287#450C4×C10112yescomplemented
288#447—21no—
289#447C4×C10112yescomplemented
290#436—21no—
291#435—21no—
292#435—21no—
293C8×D4—21no—
294#433—21no—
295#418—21no—
296C2×#102—21no—
297C2×#102—21no—
298C2×#100—21no—
299C2×#100—21no—
300#408—21no—
301#407C22×C10111yescharacteristic
302#407C22×C10111yescharacteristic
303#407C22×C10111yescharacteristic
304C2×C22⋊C8C22×C10111yescharacteristic
305#380C22×C10111yescharacteristic
306#328—21no—
307#327—21no—
308C25—21no—
309C2×#41D4×C10111yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C10112yes—
318C23×C4C23×C10111yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C10111yescharacteristic
327C2×M16D4×C10111yescharacteristic
328C22×C8—21no—
329C22×C8D4×C10111yescharacteristic
330C22×C8D4×C10111yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C10111yescharacteristic
333C22⋊Q8D4×C10111yescharacteristic
334#121C2×C4×C10111yescharacteristic
335#121D4×C10111yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C10111yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C10112yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C10111yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C10111yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C10111yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C10111yescharacteristic
402C22×C4C2×D4×C10111yescharacteristic
403C22×C4C2×D4×C10111yescharacteristic
404C22×C4C2×D4×C10111yescharacteristic
405C22×C4C2×D4×C10111yescharacteristic
406C22×C4#41×C10111yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C10111yescharacteristic
430C4⋊C4C22⋊C4×C10111yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C10111yescharacteristic
461C23#121×C10111yescharacteristic
462C23#123×C10111yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C10111yescharacteristic
495C2×C4C4×D4×C10111yescharacteristic
496C2×C4#120×C10111yescharacteristic
497C2×C4#121×C10111yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22#386×C10111yescharacteristic
529C22#471×C10111yescharacteristic
530C22#472×C10111yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4B(4,𝔽2)×C10111yescharacteristic
539C4B(4,𝔽2)×C10111yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C101×#188911yescharacteristic
547C2C101×#190311yescharacteristic
548C2C101×#190711yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC22×C4C22×C4×C101
Frattini, cosocleC23×C4C23×C101
prime radicalC101×#3003C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2976C2semidirect
3. C101×#1786C2semidirect
4. C101×#1783C2semidirect
5. C101×#1513C2semidirect
6. C101×#1305C2semidirect
7. C101×#1293C2semidirect
12. #450×C101C4semidirect
14. #447×C101C4semidirect
265. #9520C101direct (N × H)
276. #2976C2×C101semidirect
277. #1786C2×C101semidirect
278. #1783C2×C101semidirect
279. #1513C2×C101semidirect
280. #1305C2×C101semidirect
281. #1293C2×C101semidirect
282. C101#9520direct (N × H)
287. #450C4×C101semidirect
289. #447C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30032
C101×#29762
C101×#17862
C101×#17832
C101×#15132
C101×#13052
C101×#12932
#9520101