Finite Group Databasebeta

← C101×#18352 #38800503

Subgroups — C101×#18352 #38800503

Order 25856.

996 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3501C211yesmaximal, characteristic, complemented
2C101×#3193C212yesmaximal, complemented
3C101×#2635C211yesmaximal, characteristic
4C101×#1617C212yesmaximal, complemented
5C101×#1614C212yesmaximal, complemented
6C101×#1599C212yesmaximal, complemented
7C101×#1596C212yesmaximal, complemented
8C101×#1511C212yesmaximal, complemented
9C101×#1465C211yesmaximal, characteristic, complemented
10#554×C101—24no—
11#554×C101—22no—
12D4×Q8×C101—22no—
13#544×C101C2212yes—
14#543×C101—21no—
15#543×C101C2212yes—
16#533×C101—21no—
17C2×C22⋊Q8×C101—21no—
18C2×C22⋊Q8×C101C2212yes—
19C2×#121×C101C2211yescharacteristic
20#518×C101—21no—
21C2×C4×D4×C101C2211yescharacteristic
22#484×C101C2214yes—
23#480×C101—22no—
24#468×C101—24no—
25#450×C101C2214yes—
26#448×C101—22no—
27#407×C101C2212yes—
28#400×C101C2211yescharacteristic
29#399×C101C2211yescharacteristic
30#394×C101—21no—
31#394×C101C2211yescharacteristic
32#392×C101—21no—
33#392×C101C2211yescharacteristic
34#388×C101—21no—
35#386×C101—21no—
36#381×C101C2211yescharacteristic
37#328×C101C2214yes—
38#328×C101C2214yes—
39#324×C101C2212yes—
40#323×C101C2212yes—
41C22×Q8×C101—21no—
42C22×Q8×C101D412yescomplemented
43C22×D4×C101—21no—
44C22×D4×C101—21no—
45C22×D4×C101D411yescharacteristic
46C22×D4×C101C2311yescharacteristic
47C23×C4×C101D411yescharacteristic
48C23×C4×C101C2311yescharacteristic
49C2×SD16×C101—24no—
50C2×M16×C101—22no—
51C4⋊Q8×C101—21no—
52C4⋊Q8×C101—21no—
53C4⋊Q8×C101—24no—
54#125×C101—22no—
55#125×C101—24no—
56C22⋊Q8×C101—22no—
57C22⋊Q8×C101—22no—
58C22⋊Q8×C101—24no—
59C22⋊Q8×C101—24no—
60C22⋊Q8×C101—24no—
61C22⋊Q8×C101—22no—
62C22⋊Q8×C101—22no—
63C22⋊Q8×C101—22no—
64C22⋊Q8×C101—22no—
65C22⋊Q8×C101—24no—
66C22⋊Q8×C101D414yescomplemented
67C22⋊Q8×C101C2314yes—
68#121×C101—22no—
69#121×C101—22no—
70C4×Q8×C101—22no—
71C4×Q8×C101—22no—
72C4×D4×C101—24no—
73C4×D4×C101—24no—
74C4×D4×C101—22no—
75C4×D4×C101—22no—
76#117×C101—22no—
77C2×C4⋊C4×C101—21no—
78C2×C4⋊C4×C101—22no—
79C2×C4⋊C4×C101—22no—
80C2×C4⋊C4×C101—21no—
81C2×C4⋊C4×C101D412yescomplemented
82C2×C4⋊C4×C101C2311yescharacteristic
83C2×C4⋊C4×C101C2311yescharacteristic
84C2×C22⋊C4×C101—22no—
85C2×C22⋊C4×C101—22no—
86C2×C22⋊C4×C101—21no—
87C2×C22⋊C4×C101—21no—
88C2×C22⋊C4×C101—21no—
89C2×C22⋊C4×C101—21no—
90C2×C22⋊C4×C101—21no—
91C2×C22⋊C4×C101—21no—
92C2×C22⋊C4×C101D411yescharacteristic
93C2×C22⋊C4×C101C2311yescharacteristic
94C2×C42×C101D411yescharacteristic
95#107×C101—24no—
96#103×C101—24no—
97#102×C101—24no—
98C22⋊C8×C101—22no—
99C22⋊C8×C101C2314yes—
100#95×C101—21no—
101#95×C101—21no—
102#95×C101—21no—
103#95×C101C2311yescharacteristic
104#95×C101C2311yescharacteristic
105C24×C101—21no—
106C24×C101C2×D411yescharacteristic
107C24×C101C2×D411yescharacteristic
108C2×Q8×C101—22no—
109C2×Q8×C101—22no—
110C2×Q8×C101—22no—
111C2×Q8×C101—82no—
112C2×Q8×C101—82no—
113C2×Q8×C101C2×D414yes—
114C2×D4×C101—22no—
115C2×D4×C101—22no—
116C2×D4×C101—22no—
117C2×D4×C101—22no—
118C2×D4×C101—42no—
119C2×D4×C101—42no—
120C2×D4×C101—81no—
121C2×D4×C101—81no—
122C2×D4×C101—81no—
123C2×D4×C101—81no—
124C2×D4×C101—81no—
125C22×C4×C101—22no—
126C22×C4×C101—22no—
127C22×C4×C101—22no—
128C22×C4×C101—22no—
129C22×C4×C101—21no—
130C22×C4×C101—21no—
131C22×C4×C101—21no—
132C22×C4×C101—21no—
133C22×C4×C101—21no—
134C22×C4×C101—81no—
135C22×C4×C101—81no—
136C22×C4×C101C2×D411yescharacteristic
137C22×C4×C101C2×D411yescharacteristic
138C22×C4×C101C2×D411yescharacteristic
139C22×C4×C101C2×D411yescharacteristic
140C22×C4×C101C2×D412yes—
141C22×C4×C101C2×D412yes—
142C22×C4×C101C2411yescharacteristic
143SD16×C101—84no—
144M16×C101—82no—
145C2×C8×C101—24no—
146C4⋊C4×C101—22no—
147C4⋊C4×C101—24no—
148C4⋊C4×C101—22no—
149C4⋊C4×C101—22no—
150C4⋊C4×C101—24no—
151C4⋊C4×C101—22no—
152C4⋊C4×C101—24no—
153C4⋊C4×C101—22no—
154C4⋊C4×C101—24no—
155C4⋊C4×C101—22no—
156C4⋊C4×C101—22no—
157C4⋊C4×C101—81no—
158C4⋊C4×C101C2×D414yes—
159C22⋊C4×C101—24no—
160C22⋊C4×C101—24no—
161C22⋊C4×C101—22no—
162C22⋊C4×C101—24no—
163C22⋊C4×C101—22no—
164C22⋊C4×C101—41no—
165C22⋊C4×C101—41no—
166C22⋊C4×C101—42no—
167C22⋊C4×C101—81no—
168C22⋊C4×C101—81no—
169C22⋊C4×C101—81no—
170C22⋊C4×C101—81no—
171C42×C101—24no—
172C42×C101—21no—
173C42×C101—21no—
174C23×C101—21no—
175C23×C101—21no—
176C23×C101—21no—
177C23×C101—21no—
178C23×C101—41no—
179C23×C101—41no—
180C23×C101—41no—
181C23×C101—41no—
182C23×C101—41no—
183C23×C101—41no—
184C23×C101—41no—
185C23×C101—41no—
186C23×C101—41no—
187C23×C101—41no—
188C23×C101—41no—
189C23×C101#12012yes—
190C23×C101#13712yes—
191C23×C101C22×D411yescharacteristic
192Q8×C101—44no—
193Q8×C101—44no—
194Q8×C101—82no—
195Q8×C101—82no—
196D4×C101—28no—
197D4×C101—44no—
198D4×C101—84no—
199D4×C101—84no—
200C2×C4×C101—21no—
201C2×C4×C101—21no—
202C2×C4×C101—21no—
203C2×C4×C101—24no—
204C2×C4×C101—24no—
205C2×C4×C101—21no—
206C2×C4×C101—42no—
207C2×C4×C101—41no—
208C2×C4×C101—42no—
209C2×C4×C101—41no—
210C2×C4×C101—42no—
211C2×C4×C101—41no—
212C2×C4×C101—41no—
213C2×C4×C101—41no—
214C2×C4×C101—41no—
215C2×C4×C101—41no—
216C2×C4×C101—41no—
217C2×C4×C101—41no—
218C2×C4×C101—41no—
219C2×C4×C101—41no—
220C2×C4×C101—41no—
221C2×C4×C101—41no—
222C2×C4×C101—81no—
223C2×C4×C101—82no—
224C2×C4×C101—82no—
225C2×C4×C101—82no—
226C2×C4×C101—82no—
227C2×C4×C101#12011yescharacteristic
228C2×C4×C101#12011yescharacteristic
229C2×C4×C101#13712yes—
230C2×C4×C101C22×D412yes—
231C8×C101—44no—
232C22×C101—21no—
233C22×C101—21no—
234C22×C101—22no—
235C22×C101—22no—
236C22×C101—22no—
237C22×C101—22no—
238C22×C101—42no—
239C22×C101—41no—
240C22×C101—41no—
241C22×C101—81no—
242C22×C101—81no—
243C22×C101—81no—
244C22×C101—81no—
245C22×C101—81no—
246C22×C101—81no—
247C22×C101—81no—
248C22×C101—81no—
249C22×C101—81no—
250C22×C101—81no—
251C22×C101C2×#12011yescharacteristic
252C22×C101C2×#13711yescharacteristic
253C22×C101C2×#13711yescharacteristic
254C4×C101—22no—
255C4×C101—22no—
256C4×C101—21no—
257C4×C101—21no—
258C4×C101—41no—
259C4×C101—44no—
260C4×C101—41no—
261C4×C101—44no—
262C4×C101—81no—
263C4×C101—81no—
264C4×C101—81no—
265#18352C10111yesmaximal, characteristic, direct product factor, Sylow
266C2×C101—21no—
267C2×C101—21no—
268C2×C101—42no—
269C2×C101—42no—
270C2×C101—161no—
271C2×C101#300411yescharacteristic
272C2×C101#302111yescharacteristic
273C2×C101#302611yescharacteristic
274#3501C2×C10111yescharacteristic, complemented
275#3193C2×C10112yescomplemented
276#2635C2×C10111yescharacteristic
277#1617C2×C10112yescomplemented
278#1614C2×C10112yescomplemented
279#1599C2×C10112yescomplemented
280#1596C2×C10112yescomplemented
281#1511C2×C10112yescomplemented
282#1465C2×C10111yescharacteristic, complemented
283C101#1835211yescharacteristic, direct product factor, Sylow
284#554—24no—
285#554—22no—
286D4×Q8—22no—
287#544C22×C10112yes—
288#543—21no—
289#543C22×C10112yes—
290#533—21no—
291C2×C22⋊Q8—21no—
292C2×C22⋊Q8C22×C10112yes—
293C2×#121C22×C10111yescharacteristic
294#518—21no—
295C2×C4×D4C22×C10111yescharacteristic
296#484C22×C10114yes—
297#480—22no—
298#468—24no—
299#450C22×C10114yes—
300#448—22no—
301#407C22×C10112yes—
302#400C22×C10111yescharacteristic
303#399C22×C10111yescharacteristic
304#394—21no—
305#394C22×C10111yescharacteristic
306#392—21no—
307#392C22×C10111yescharacteristic
308#388—21no—
309#386—21no—
310#381C22×C10111yescharacteristic
311#328C22×C10114yes—
312#328C22×C10114yes—
313#324C22×C10112yes—
314#323C22×C10112yes—
315C22×Q8—21no—
316C22×Q8D4×C10112yescomplemented
317C22×D4—21no—
318C22×D4—21no—
319C22×D4D4×C10111yescharacteristic
320C22×D4C23×C10111yescharacteristic
321C23×C4D4×C10111yescharacteristic
322C23×C4C23×C10111yescharacteristic
323C2×SD16—24no—
324C2×M16—22no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—24no—
328#125—22no—
329#125—24no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—24no—
340C22⋊Q8D4×C10114yescomplemented
341C22⋊Q8C23×C10114yes—
342#121—22no—
343#121—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—22no—
349C4×D4—22no—
350#117—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4D4×C10112yescomplemented
356C2×C4⋊C4C23×C10111yescharacteristic
357C2×C4⋊C4C23×C10111yescharacteristic
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4D4×C10111yescharacteristic
367C2×C22⋊C4C23×C10111yescharacteristic
368C2×C42D4×C10111yescharacteristic
369#107—24no—
370#103—24no—
371#102—24no—
372C22⋊C8—22no—
373C22⋊C8C23×C10114yes—
374#95—21no—
375#95—21no—
376#95—21no—
377#95C23×C10111yescharacteristic
378#95C23×C10111yescharacteristic
379C24—21no—
380C24C2×D4×C10111yescharacteristic
381C24C2×D4×C10111yescharacteristic
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—82no—
386C2×Q8—82no—
387C2×Q8C2×D4×C10114yes—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—81no—
395C2×D4—81no—
396C2×D4—81no—
397C2×D4—81no—
398C2×D4—81no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—81no—
409C22×C4—81no—
410C22×C4C2×D4×C10111yescharacteristic
411C22×C4C2×D4×C10111yescharacteristic
412C22×C4C2×D4×C10111yescharacteristic
413C22×C4C2×D4×C10111yescharacteristic
414C22×C4C2×D4×C10112yes—
415C22×C4C2×D4×C10112yes—
416C22×C4C24×C10111yescharacteristic
417SD16—84no—
418M16—82no—
419C2×C8—24no—
420C4⋊C4—22no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—24no—
427C4⋊C4—22no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—81no—
432C4⋊C4C2×D4×C10114yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—22no—
436C22⋊C4—24no—
437C22⋊C4—22no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—42no—
441C22⋊C4—81no—
442C22⋊C4—81no—
443C22⋊C4—81no—
444C22⋊C4—81no—
445C42—24no—
446C42—21no—
447C42—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23#120×C10112yes—
464C23#137×C10112yes—
465C23C22×D4×C10111yescharacteristic
466Q8—44no—
467Q8—44no—
468Q8—82no—
469Q8—82no—
470D4—28no—
471D4—44no—
472D4—84no—
473D4—84no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—81no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4#120×C10111yescharacteristic
502C2×C4#120×C10111yescharacteristic
503C2×C4#137×C10112yes—
504C2×C4C22×D4×C10112yes—
505C8—44no—
506C22—21no—
507C22—21no—
508C22—22no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—42no—
513C22—41no—
514C22—41no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22C2×#120×C10111yescharacteristic
526C22C2×#137×C10111yescharacteristic
527C22C2×#137×C10111yescharacteristic
528C4—22no—
529C4—22no—
530C4—21no—
531C4—21no—
532C4—41no—
533C4—44no—
534C4—41no—
535C4—44no—
536C4—81no—
537C4—81no—
538C4—81no—
539C2—21no—
540C2—21no—
541C2—42no—
542C2—42no—
543C2—161no—
544C2C101×#300411yescharacteristic
545C2C101×#302111yescharacteristic
546C2C101×#302611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#2635C2
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
1. C101×#3501C2semidirect
2. C101×#3193C2semidirect
4. C101×#1617C2semidirect
5. C101×#1614C2semidirect
6. C101×#1599C2semidirect
7. C101×#1596C2semidirect
8. C101×#1511C2semidirect
9. C101×#1465C2semidirect
42. C22×Q8×C101D4semidirect
66. C22⋊Q8×C101D4semidirect
81. C2×C4⋊C4×C101D4semidirect
265. #18352C101direct (N × H)
274. #3501C2×C101semidirect
275. #3193C2×C101semidirect
277. #1617C2×C101semidirect
278. #1614C2×C101semidirect
279. #1599C2×C101semidirect
280. #1596C2×C101semidirect
281. #1511C2×C101semidirect
282. #1465C2×C101semidirect
283. C101#18352direct (N × H)
316. C22×Q8D4×C101semidirect
340. C22⋊Q8D4×C101semidirect
355. C2×C4⋊C4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35012
C101×#31932
C101×#26352
C101×#16172
C101×#16142
C101×#15992
C101×#15962
C101×#15112
C101×#14652
#18352101