Finite Group Databasebeta

← C101×#9259 #38791410

Subgroups — C101×#9259 #38791410

Order 25856.

966 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C101C211yesmaximal, characteristic
2D4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
3C101×#1964C211yesmaximal, characteristic, complemented
4C101×#1786C211yesmaximal, characteristic, complemented
5C101×#1519C211yesmaximal, characteristic, complemented
6C101×#1289C211yesmaximal, characteristic, complemented
7C101×#1282C211yesmaximal, characteristic, complemented
8C23×D4×C101C2211yescharacteristic
9C22×D8×C101C412yescomplemented
10C2×#121×C101C2211yescharacteristic
11C2×C4×D4×C101—21no—
12C22×C22⋊C4×C101—21no—
13#447×C101—21no—
14#447×C101—22no—
15#447×C101—21no—
16C2×#102×C101—22no—
17C2×#102×C101C412yescomplemented
18C2×#99×C101—21no—
19C2×#99×C101—21no—
20C2×C22⋊C8×C101C2211yescharacteristic
21C2×C22⋊C8×C101C2211yescharacteristic
22#390×C101—21no—
23#386×C101—22no—
24#380×C101C2211yescharacteristic
25#380×C101C2211yescharacteristic
26#379×C101—21no—
27C4×C22⋊C4×C101C2211yescharacteristic
28#327×C101—22no—
29C25×C101—21no—
30C22×D4×C101—21no—
31C22×D4×C101—21no—
32C22×D4×C101—21no—
33C22×D4×C101—21no—
34C22×D4×C101—44no—
35C22×D4×C101C2×C412yes—
36C22×D4×C101C2×C411yescharacteristic, complemented
37C22×D4×C101D411yescharacteristic
38C22×D4×C101D412yes—
39C22×D4×C101D411yescharacteristic
40C23×C4×C101—22no—
41C23×C4×C101C2311yescharacteristic
42C2×D8×C101—22no—
43C2×D8×C101—22no—
44C2×D8×C101—44no—
45C22×C8×C101—21no—
46C22×C8×C101C2×C412yescomplemented
47#121×C101—21no—
48#121×C101—21no—
49#121×C101—21no—
50#121×C101—21no—
51C4×D4×C101—44no—
52C2×C4⋊C4×C101—21no—
53C2×C4⋊C4×C101—21no—
54C2×C4⋊C4×C101C2×C411yescharacteristic, complemented
55C2×C22⋊C4×C101—22no—
56C2×C22⋊C4×C101—22no—
57C2×C22⋊C4×C101—21no—
58C2×C22⋊C4×C101—21no—
59C2×C22⋊C4×C101—21no—
60C2×C22⋊C4×C101—22no—
61C2×C22⋊C4×C101—42no—
62C2×C22⋊C4×C101—42no—
63C2×C22⋊C4×C101D411yescharacteristic
64C2×C22⋊C4×C101D411yescharacteristic
65C2×C42×C101—21no—
66#102×C101—22no—
67#102×C101—22no—
68#102×C101—44no—
69#99×C101—42no—
70#99×C101—42no—
71C22⋊C8×C101—21no—
72C22⋊C8×C101—21no—
73C22⋊C8×C101—21no—
74C22⋊C8×C101—21no—
75#95×C101—21no—
76#95×C101—21no—
77#95×C101D412yes—
78C24×C101—21no—
79C24×C101—21no—
80C24×C101—22no—
81C24×C101—22no—
82C24×C101—21no—
83C24×C101—44no—
84C24×C101—41no—
85C24×C101—41no—
86C24×C101—41no—
87C24×C101—41no—
88C24×C101—82no—
89C24×C101C2×D411yescharacteristic
90C2×D4×C101—24no—
91C2×D4×C101—24no—
92C2×D4×C101—24no—
93C2×D4×C101—21no—
94C2×D4×C101—22no—
95C2×D4×C101—21no—
96C2×D4×C101—22no—
97C2×D4×C101—21no—
98C2×D4×C101—21no—
99C2×D4×C101—42no—
100C2×D4×C101—42no—
101C2×D4×C101—42no—
102C2×D4×C101—42no—
103C2×D4×C101—44no—
104C2×D4×C101—44no—
105C2×D4×C101—44no—
106C2×D4×C101—41no—
107C2×D4×C101—41no—
108C2×D4×C101—41no—
109C2×D4×C101—41no—
110C2×D4×C101—41no—
111C2×D4×C101—41no—
112C2×D4×C101C22⋊C412yes—
113C2×D4×C101C22⋊C412yes—
114C22×C4×C101—21no—
115C22×C4×C101—21no—
116C22×C4×C101—21no—
117C22×C4×C101—22no—
118C22×C4×C101—42no—
119C22×C4×C101—44no—
120C22×C4×C101—44no—
121C22×C4×C101—41no—
122C22×C4×C101—82no—
123C22×C4×C101C22×C411yescharacteristic
124C22×C4×C101C2×D411yescharacteristic
125C22×C4×C101C2×D411yescharacteristic
126C22×C4×C101C2×D411yescharacteristic
127C22×C4×C101#4111yescharacteristic
128C22×C4×C101#4111yescharacteristic
129D8×C101—44no—
130D8×C101—44no—
131C2×C8×C101—22no—
132C2×C8×C101—42no—
133C2×C8×C101—42no—
134C2×C8×C101—41no—
135C4⋊C4×C101—21no—
136C4⋊C4×C101—21no—
137C4⋊C4×C101—42no—
138C4⋊C4×C101—42no—
139C22⋊C4×C101—21no—
140C22⋊C4×C101—21no—
141C22⋊C4×C101—21no—
142C22⋊C4×C101—44no—
143C22⋊C4×C101—44no—
144C22⋊C4×C101—41no—
145C22⋊C4×C101—41no—
146C22⋊C4×C101—41no—
147C22⋊C4×C101—41no—
148C22⋊C4×C101—41no—
149C22⋊C4×C101—41no—
150C22⋊C4×C101—82no—
151C22⋊C4×C101D812yescomplemented
152C42×C101—42no—
153C23×C101—24no—
154C23×C101—22no—
155C23×C101—22no—
156C23×C101—41no—
157C23×C101—41no—
158C23×C101—44no—
159C23×C101—44no—
160C23×C101—42no—
161C23×C101—42no—
162C23×C101—42no—
163C23×C101—41no—
164C23×C101—41no—
165C23×C101—42no—
166C23×C101—42no—
167C23×C101—41no—
168C23×C101—41no—
169C23×C101—42no—
170C23×C101—42no—
171C23×C101—41no—
172C23×C101—41no—
173C23×C101—41no—
174C23×C101—82no—
175C23×C101—82no—
176C23×C101—81no—
177C23×C101—81no—
178C23×C101—84no—
179C23×C101—84no—
180C23×C101—84no—
181C23×C101—84no—
182C23×C101C4×D411yescharacteristic
183C23×C101#12011yescharacteristic
184C23×C101#12111yescharacteristic
185C23×C101C2×D811yescharacteristic
186C23×C101#13511yescharacteristic
187C23×C101AGL(1,ℤ/8)11yescharacteristic
188C23×C101AGL(1,ℤ/8)11yescharacteristic
189D4×C101—24no—
190D4×C101—22no—
191D4×C101—22no—
192D4×C101—22no—
193D4×C101—44no—
194D4×C101—44no—
195D4×C101—42no—
196D4×C101—42no—
197D4×C101—81no—
198D4×C101—81no—
199D4×C101—81no—
200D4×C101—81no—
201D4×C101—81no—
202D4×C101#9914yescomplemented
203C2×C4×C101—22no—
204C2×C4×C101—22no—
205C2×C4×C101—22no—
206C2×C4×C101—22no—
207C2×C4×C101—41no—
208C2×C4×C101—41no—
209C2×C4×C101—41no—
210C2×C4×C101—41no—
211C2×C4×C101—41no—
212C2×C4×C101—41no—
213C2×C4×C101—42no—
214C2×C4×C101—41no—
215C2×C4×C101—42no—
216C2×C4×C101—41no—
217C2×C4×C101—41no—
218C2×C4×C101—41no—
219C2×C4×C101—42no—
220C2×C4×C101—41no—
221C2×C4×C101—88no—
222C2×C4×C101—81no—
223C2×C4×C101—81no—
224C2×C4×C101—81no—
225C2×C4×C101C2×C22⋊C411yescharacteristic
226C2×C4×C101C4×D411yescharacteristic
227C2×C4×C101#12111yescharacteristic
228C2×C4×C101#12311yescharacteristic
229C8×C101—42no—
230C8×C101—81no—
231C22×C101—21no—
232C22×C101—21no—
233C22×C101—21no—
234C22×C101—21no—
235C22×C101—21no—
236C22×C101—21no—
237C22×C101—24no—
238C22×C101—41no—
239C22×C101—41no—
240C22×C101—41no—
241C22×C101—41no—
242C22×C101—44no—
243C22×C101—44no—
244C22×C101—42no—
245C22×C101—42no—
246C22×C101—42no—
247C22×C101—42no—
248C22×C101—42no—
249C22×C101—84no—
250C22×C101—84no—
251C22×C101—84no—
252C22×C101—84no—
253C22×C101—82no—
254C22×C101—82no—
255C22×C101—81no—
256C22×C101—81no—
257C22×C101—81no—
258C22×C101—161no—
259C22×C101—161no—
260C22×C101#38611yescharacteristic
261C22×C101C4×D811yescharacteristic
262C22×C101#44211yescharacteristic
263C22×C101#44711yescharacteristic
264C22×C101#44911yescharacteristic
265C22×C101#45911yescharacteristic
266C22×C101#46311yescharacteristic
267C4×C101—21no—
268C4×C101—21no—
269C4×C101—21no—
270C4×C101—42no—
271C4×C101—81no—
272C4×C101—82no—
273C4×C101—81no—
274C4×C101—161no—
275C4×C101C2×#9912yes—
276#9259C10111yesmaximal, characteristic, direct product factor, Sylow
277C2×C101—21no—
278C2×C101—21no—
279C2×C101—21no—
280C2×C101—21no—
281C2×C101—21no—
282C2×C101—21no—
283C2×C101—44no—
284C2×C101—82no—
285C2×C101—161no—
286C2×C101#187911yescharacteristic
287C2×C101#189811yescharacteristic
288C2×C101#190411yescharacteristic
289C2×#447C2×C10111yescharacteristic
290D4×C22⋊C4C2×C10111yescharacteristic, complemented
291#1964C2×C10111yescharacteristic, complemented
292#1786C2×C10111yescharacteristic, complemented
293#1519C2×C10111yescharacteristic, complemented
294#1289C2×C10111yescharacteristic, complemented
295#1282C2×C10111yescharacteristic, complemented
296C101#925911yescharacteristic, direct product factor, Sylow
297C23×D4C22×C10111yescharacteristic
298C22×D8C4×C10112yescomplemented
299C2×#121C22×C10111yescharacteristic
300C2×C4×D4—21no—
301C22×C22⋊C4—21no—
302#447—21no—
303#447—22no—
304#447—21no—
305C2×#102—22no—
306C2×#102C4×C10112yescomplemented
307C2×#99—21no—
308C2×#99—21no—
309C2×C22⋊C8C22×C10111yescharacteristic
310C2×C22⋊C8C22×C10111yescharacteristic
311#390—21no—
312#386—22no—
313#380C22×C10111yescharacteristic
314#380C22×C10111yescharacteristic
315#379—21no—
316C4×C22⋊C4C22×C10111yescharacteristic
317#327—22no—
318C25—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—44no—
324C22×D4C2×C4×C10112yes—
325C22×D4C2×C4×C10111yescharacteristic, complemented
326C22×D4D4×C10111yescharacteristic
327C22×D4D4×C10112yes—
328C22×D4D4×C10111yescharacteristic
329C23×C4—22no—
330C23×C4C23×C10111yescharacteristic
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—44no—
334C22×C8—21no—
335C22×C8C2×C4×C10112yescomplemented
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C2×C4×C10111yescharacteristic, complemented
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4D4×C10111yescharacteristic
353C2×C22⋊C4D4×C10111yescharacteristic
354C2×C42—21no—
355#102—22no—
356#102—22no—
357#102—44no—
358#99—42no—
359#99—42no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364#95—21no—
365#95—21no—
366#95D4×C10112yes—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—44no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—82no—
378C24C2×D4×C10111yescharacteristic
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4C22⋊C4×C10112yes—
402C2×D4C22⋊C4×C10112yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—44no—
409C22×C4—44no—
410C22×C4—41no—
411C22×C4—82no—
412C22×C4C22×C4×C10111yescharacteristic
413C22×C4C2×D4×C10111yescharacteristic
414C22×C4C2×D4×C10111yescharacteristic
415C22×C4C2×D4×C10111yescharacteristic
416C22×C4#41×C10111yescharacteristic
417C22×C4#41×C10111yescharacteristic
418D8—44no—
419D8—44no—
420C2×C8—22no—
421C2×C8—42no—
422C2×C8—42no—
423C2×C8—41no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—44no—
432C22⋊C4—44no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—82no—
440C22⋊C4D8×C10112yescomplemented
441C42—42no—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—44no—
448C23—44no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—41no—
453C23—41no—
454C23—42no—
455C23—42no—
456C23—41no—
457C23—41no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—82no—
464C23—82no—
465C23—81no—
466C23—81no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23C4×D4×C10111yescharacteristic
472C23#120×C10111yescharacteristic
473C23#121×C10111yescharacteristic
474C23C2×D8×C10111yescharacteristic
475C23#135×C10111yescharacteristic
476C23AGL(1,ℤ/8)×C10111yescharacteristic
477C23AGL(1,ℤ/8)×C10111yescharacteristic
478D4—24no—
479D4—22no—
480D4—22no—
481D4—22no—
482D4—44no—
483D4—44no—
484D4—42no—
485D4—42no—
486D4—81no—
487D4—81no—
488D4—81no—
489D4—81no—
490D4—81no—
491D4#99×C10114yescomplemented
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—88no—
511C2×C4—81no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4C2×C22⋊C4×C10111yescharacteristic
515C2×C4C4×D4×C10111yescharacteristic
516C2×C4#121×C10111yescharacteristic
517C2×C4#123×C10111yescharacteristic
518C8—42no—
519C8—81no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—24no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—44no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—84no—
539C22—84no—
540C22—84no—
541C22—84no—
542C22—82no—
543C22—82no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—161no—
548C22—161no—
549C22#386×C10111yescharacteristic
550C22C4×D8×C10111yescharacteristic
551C22#442×C10111yescharacteristic
552C22#447×C10111yescharacteristic
553C22#449×C10111yescharacteristic
554C22#459×C10111yescharacteristic
555C22#463×C10111yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—42no—
560C4—82no—
561C4—81no—
562C4—81no—
563C4—161no—
564C4C2×#99×C10112yes—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2—21no—
571C2—44no—
572C2—82no—
573C2—161no—
574C2C101×#187911yescharacteristic
575C2C101×#189811yescharacteristic
576C2C101×#190411yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC22×C4C22×C4×C101
Frattini, cosocleC23×C4C23×C101
prime radicalC2×#447×C101C2
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. D4×C22⋊C4×C101C2semidirect
3. C101×#1964C2semidirect
4. C101×#1786C2semidirect
5. C101×#1519C2semidirect
6. C101×#1289C2semidirect
7. C101×#1282C2semidirect
9. C22×D8×C101C4semidirect
17. C2×#102×C101C4semidirect
36. C22×D4×C101C2×C4semidirect
46. C22×C8×C101C2×C4semidirect
54. C2×C4⋊C4×C101C2×C4semidirect
151. C22⋊C4×C101D8semidirect
202. D4×C101#99semidirect
276. #9259C101direct (N × H)
290. D4×C22⋊C4C2×C101semidirect
291. #1964C2×C101semidirect
292. #1786C2×C101semidirect
293. #1519C2×C101semidirect
294. #1289C2×C101semidirect
295. #1282C2×C101semidirect
296. C101#9259direct (N × H)
298. C22×D8C4×C101semidirect
306. C2×#102C4×C101semidirect
325. C22×D4C2×C4×C101semidirect
335. C22×C8C2×C4×C101semidirect
343. C2×C4⋊C4C2×C4×C101semidirect
440. C22⋊C4D8×C101semidirect
491. D4#99×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1012
D4×C22⋊C4×C1012
C101×#19642
C101×#17862
C101×#15192
C101×#12892
C101×#12822
#9259101