Finite Group Databasebeta

← C101×#17201 #38799352

Subgroups — C101×#17201 #38799352

Order 25856.

1270 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C101C211yesmaximal, characteristic
2C2×#393×C101C211yesmaximal, characteristic
3C101×#1446C212yesmaximal, complemented
4C101×#1445C212yesmaximal, complemented
5C101×#1442C212yesmaximal, complemented
6C101×#1442C212yesmaximal, complemented
7C101×#1440C211yesmaximal, characteristic
8C101×#1440C212yesmaximal
9C101×#1439C212yesmaximal
10C23×Q8×C101C2211yescharacteristic
11C22×C4⋊C4×C101C2211yescharacteristic
12C22×C4⋊C4×C101C2212yes—
13C22×C22⋊C4×C101C2211yescharacteristic
14C22×C22⋊C4×C101C2212yes—
15C22×C22⋊C4×C101C2212yes—
16C22×C22⋊C4×C101C2211yescharacteristic
17C22×C22⋊C4×C101C2211yescharacteristic
18#397×C101—24no—
19#393×C101—24no—
20C2×#95×C101C2211yescharacteristic
21C2×#95×C101C2212yes—
22C2×#95×C101C2212yes—
23C2×#95×C101C2212yes—
24C2×#95×C101C2212yes—
25C2×#95×C101C2211yescharacteristic
26C2×#95×C101C2212yes—
27C2×#95×C101C2212yes—
28C2×#95×C101C2212yes—
29C2×#95×C101C2212yes—
30C2×#95×C101C2212yes—
31C2×#95×C101C2212yes—
32C2×#95×C101C2212yes—
33C25×C101C2311yescharacteristic
34C22×Q8×C101—22no—
35C22×Q8×C101—24no—
36C22×Q8×C101—42no—
37C22×Q8×C101—41no—
38C22×Q8×C101—41no—
39C23×C4×C101C2312yes—
40C23×C4×C101C2312yes—
41C23×C4×C101C2312yes—
42C23×C4×C101C2312yes—
43C23×C4×C101C2311yescharacteristic
44C23×C4×C101C2311yescharacteristic
45C23×C4×C101C2312yes—
46C23×C4×C101C2312yes—
47C2×C4⋊C4×C101—22no—
48C2×C4⋊C4×C101—24no—
49C2×C4⋊C4×C101—42no—
50C2×C4⋊C4×C101—42no—
51C2×C4⋊C4×C101—41no—
52C2×C4⋊C4×C101—41no—
53C2×C22⋊C4×C101—24no—
54C2×C22⋊C4×C101—24no—
55C2×C22⋊C4×C101—24no—
56C2×C22⋊C4×C101—24no—
57C2×C22⋊C4×C101—41no—
58C2×C22⋊C4×C101—41no—
59C2×C22⋊C4×C101—41no—
60C2×C22⋊C4×C101—42no—
61C2×C22⋊C4×C101—42no—
62C2×C22⋊C4×C101—42no—
63C2×C22⋊C4×C101—42no—
64C2×C22⋊C4×C101—41no—
65C2×C22⋊C4×C101D414yes—
66#95×C101—22no—
67#95×C101—24no—
68#95×C101—24no—
69#95×C101—22no—
70#95×C101—24no—
71#95×C101—24no—
72#95×C101—42no—
73#95×C101—42no—
74#95×C101—42no—
75#95×C101—42no—
76#95×C101—42no—
77#95×C101—42no—
78#95×C101—42no—
79C24×C101—22no—
80C24×C101—22no—
81C24×C101—21no—
82C24×C101—21no—
83C24×C101—22no—
84C24×C101—22no—
85C24×C101—22no—
86C24×C101—22no—
87C24×C101C2×D412yes—
88C24×C101C2411yescharacteristic
89C2×Q8×C101—48no—
90C2×Q8×C101—44no—
91C2×Q8×C101—44no—
92C2×Q8×C101—48no—
93C2×Q8×C101—44no—
94C22×C4×C101—22no—
95C22×C4×C101—22no—
96C22×C4×C101—22no—
97C22×C4×C101—22no—
98C22×C4×C101—22no—
99C22×C4×C101—22no—
100C22×C4×C101—22no—
101C22×C4×C101—22no—
102C22×C4×C101—22no—
103C22×C4×C101—22no—
104C22×C4×C101—22no—
105C22×C4×C101—22no—
106C22×C4×C101—22no—
107C22×C4×C101—21no—
108C22×C4×C101—21no—
109C22×C4×C101—21no—
110C22×C4×C101—21no—
111C22×C4×C101—22no—
112C22×C4×C101—22no—
113C22×C4×C101—22no—
114C22×C4×C101—22no—
115C22×C4×C101—22no—
116C22×C4×C101—22no—
117C22×C4×C101—22no—
118C22×C4×C101—22no—
119C22×C4×C101—22no—
120C22×C4×C101—22no—
121C22×C4×C101—22no—
122C22×C4×C101—22no—
123C22×C4×C101—22no—
124C22×C4×C101—22no—
125C22×C4×C101—22no—
126C22×C4×C101—22no—
127C22×C4×C101—22no—
128C22×C4×C101—22no—
129C22×C4×C101—22no—
130C22×C4×C101—22no—
131C22×C4×C101—22no—
132C22×C4×C101—22no—
133C22×C4×C101—22no—
134C22×C4×C101—22no—
135C22×C4×C101—22no—
136C22×C4×C101—22no—
137C22×C4×C101—22no—
138C22×C4×C101—22no—
139C22×C4×C101—22no—
140C22×C4×C101—22no—
141C22×C4×C101—22no—
142C22×C4×C101C2×D412yes—
143C22×C4×C101C2×D412yes—
144C22×C4×C101#4114yes—
145C22×C4×C101#4114yes—
146C4⋊C4×C101—44no—
147C4⋊C4×C101—48no—
148C22⋊C4×C101—44no—
149C22⋊C4×C101—44no—
150C22⋊C4×C101—48no—
151C22⋊C4×C101—48no—
152C22⋊C4×C101—44no—
153C23×C101—22no—
154C23×C101—22no—
155C23×C101—22no—
156C23×C101—24no—
157C23×C101—24no—
158C23×C101—42no—
159C23×C101—42no—
160C23×C101—42no—
161C23×C101—42no—
162C23×C101—42no—
163C23×C101—42no—
164C23×C101—41no—
165C23×C101—41no—
166C23×C101—42no—
167C23×C101—42no—
168C23×C101—41no—
169C23×C101—42no—
170C23×C101—42no—
171C23×C101—42no—
172C23×C101—42no—
173C23×C101—41no—
174C23×C101C22×D411yescharacteristic
175C23×C101C2×#4112yes—
176C23×C101C2×#4112yes—
177C23×C101H(5,𝔽2)11yescharacteristic
178C23×C101H(5,𝔽2)11yescharacteristic
179C23×C101H(5,𝔽2)12yes—
180C23×C101H(5,𝔽2)12yes—
181C23×C1012−1+412yes—
182C23×C1012−1+412yes—
183Q8×C101—416no—
184C2×C4×C101—22no—
185C2×C4×C101—22no—
186C2×C4×C101—24no—
187C2×C4×C101—24no—
188C2×C4×C101—24no—
189C2×C4×C101—24no—
190C2×C4×C101—24no—
191C2×C4×C101—24no—
192C2×C4×C101—24no—
193C2×C4×C101—24no—
194C2×C4×C101—42no—
195C2×C4×C101—42no—
196C2×C4×C101—42no—
197C2×C4×C101—42no—
198C2×C4×C101—42no—
199C2×C4×C101—42no—
200C2×C4×C101—42no—
201C2×C4×C101—41no—
202C2×C4×C101—41no—
203C2×C4×C101—42no—
204C2×C4×C101—41no—
205C2×C4×C101—42no—
206C2×C4×C101—42no—
207C2×C4×C101—41no—
208C2×C4×C101—42no—
209C2×C4×C101—42no—
210C2×C4×C101—42no—
211C2×C4×C101—42no—
212C2×C4×C101—42no—
213C2×C4×C101—42no—
214C2×C4×C101—42no—
215C2×C4×C101—42no—
216C2×C4×C101—42no—
217C2×C4×C101—42no—
218C2×C4×C101—42no—
219C2×C4×C101—42no—
220C2×C4×C101—42no—
221C2×C4×C101—42no—
222C2×C4×C101—42no—
223C2×C4×C101—42no—
224C2×C4×C101—42no—
225C2×C4×C101—42no—
226C2×C4×C101—42no—
227C2×C4×C101—42no—
228C2×C4×C101—42no—
229C2×C4×C101—42no—
230C2×C4×C101—42no—
231C2×C4×C101—42no—
232C2×C4×C101—42no—
233C2×C4×C101—42no—
234C2×C4×C101—42no—
235C2×C4×C101—42no—
236C22×C101—42no—
237C22×C101—42no—
238C22×C101—44no—
239C22×C101—44no—
240C22×C101—42no—
241C22×C101—82no—
242C22×C101—82no—
243C22×C101—82no—
244C22×C101—82no—
245C22×C101#53411yescharacteristic
246C22×C101#53511yescharacteristic
247C22×C101#53611yescharacteristic
248C22×C101#53812yes—
249C22×C101#53812yes—
250C22×C101#54112yes—
251C22×C101#54212yes—
252C22×C101#54212yes—
253C22×C101#54212yes—
254C22×C101#54612yes—
255C22×C101#54712yes—
256C22×C101#55111yescharacteristic
257C22×C101#55111yescharacteristic
258C22×C101#55212yes—
259C22×C101#55912yes—
260C22×C101H(3,𝔽4)11yescharacteristic
261C22×C101#56212yes—
262C22×C101#56212yes—
263C22×C101#56212yes—
264C22×C101#56311yescharacteristic
265C22×C101#56312yes—
266C4×C101—42no—
267C4×C101—44no—
268C4×C101—42no—
269C4×C101—44no—
270C4×C101—82no—
271C4×C101—82no—
272C4×C101—82no—
273C4×C101—82no—
274#17201C10111yesmaximal, characteristic, direct product factor, Sylow
275C2×C101—82no—
276C2×C101#268411yescharacteristic
277C2×C101#269812yes—
278C2×C101#271012yes—
279C2×C101#271711yescharacteristic
280C2×C101#275112yes—
281C2×C101#275412yes—
282C2×C101#281611yescharacteristic
283C2×C101#283112yes—
284C2×C101#283212yes—
285C2×#397C2×C10111yescharacteristic
286C2×#393C2×C10111yescharacteristic
287#1446C2×C10112yescomplemented
288#1445C2×C10112yescomplemented
289#1442C2×C10112yescomplemented
290#1442C2×C10112yescomplemented
291#1440C2×C10112yes—
292#1440C2×C10111yescharacteristic
293#1439C2×C10112yes—
294C101#1720111yescharacteristic, direct product factor, Sylow
295C23×Q8C22×C10111yescharacteristic
296C22×C4⋊C4C22×C10111yescharacteristic
297C22×C4⋊C4C22×C10112yes—
298C22×C22⋊C4C22×C10112yes—
299C22×C22⋊C4C22×C10111yescharacteristic
300C22×C22⋊C4C22×C10112yes—
301C22×C22⋊C4C22×C10111yescharacteristic
302C22×C22⋊C4C22×C10111yescharacteristic
303#397—24no—
304#393—24no—
305C2×#95C22×C10112yes—
306C2×#95C22×C10111yescharacteristic
307C2×#95C22×C10111yescharacteristic
308C2×#95C22×C10112yes—
309C2×#95C22×C10112yes—
310C2×#95C22×C10112yes—
311C2×#95C22×C10112yes—
312C2×#95C22×C10112yes—
313C2×#95C22×C10112yes—
314C2×#95C22×C10112yes—
315C2×#95C22×C10112yes—
316C2×#95C22×C10112yes—
317C2×#95C22×C10112yes—
318C25C23×C10111yescharacteristic
319C22×Q8—22no—
320C22×Q8—24no—
321C22×Q8—42no—
322C22×Q8—41no—
323C22×Q8—41no—
324C23×C4C23×C10112yes—
325C23×C4C23×C10112yes—
326C23×C4C23×C10112yes—
327C23×C4C23×C10112yes—
328C23×C4C23×C10111yescharacteristic
329C23×C4C23×C10111yescharacteristic
330C23×C4C23×C10112yes—
331C23×C4C23×C10112yes—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—41no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4D4×C10114yes—
351#95—24no—
352#95—22no—
353#95—22no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95—42no—
364C24—22no—
365C24—22no—
366C24—21no—
367C24—21no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24C2×D4×C10112yes—
373C24C24×C10111yescharacteristic
374C2×Q8—48no—
375C2×Q8—44no—
376C2×Q8—44no—
377C2×Q8—48no—
378C2×Q8—44no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4C2×D4×C10112yes—
428C22×C4C2×D4×C10112yes—
429C22×C4#41×C10114yes—
430C22×C4#41×C10114yes—
431C4⋊C4—44no—
432C4⋊C4—48no—
433C22⋊C4—44no—
434C22⋊C4—44no—
435C22⋊C4—48no—
436C22⋊C4—48no—
437C22⋊C4—44no—
438C23—22no—
439C23—22no—
440C23—22no—
441C23—24no—
442C23—24no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—41no—
450C23—41no—
451C23—42no—
452C23—42no—
453C23—41no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—41no—
459C23C22×D4×C10111yescharacteristic
460C23C2×#41×C10112yes—
461C23C2×#41×C10112yes—
462C23H(5,𝔽2)×C10111yescharacteristic
463C23H(5,𝔽2)×C10111yescharacteristic
464C23H(5,𝔽2)×C10112yes—
465C23H(5,𝔽2)×C10112yes—
466C232−1+4×C10112yes—
467C232−1+4×C10112yes—
468Q8—416no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C22—42no—
522C22—44no—
523C22—44no—
524C22—42no—
525C22—42no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22#534×C10111yescharacteristic
531C22#535×C10111yescharacteristic
532C22#536×C10111yescharacteristic
533C22#538×C10112yes—
534C22#538×C10112yes—
535C22#541×C10112yes—
536C22#542×C10112yes—
537C22#542×C10112yes—
538C22#542×C10112yes—
539C22#546×C10112yes—
540C22#547×C10112yes—
541C22#551×C10111yescharacteristic
542C22#551×C10111yescharacteristic
543C22#552×C10112yes—
544C22#559×C10112yes—
545C22H(3,𝔽4)×C10111yescharacteristic
546C22#562×C10112yes—
547C22#562×C10112yes—
548C22#562×C10112yes—
549C22#563×C10112yes—
550C22#563×C10111yescharacteristic
551C4—42no—
552C4—44no—
553C4—42no—
554C4—44no—
555C4—82no—
556C4—82no—
557C4—82no—
558C4—82no—
559C2—82no—
560C2C101×#268411yescharacteristic
561C2C101×#269812yes—
562C2C101×#271012yes—
563C2C101×#271711yescharacteristic
564C2C101×#275112yes—
565C2C101×#275412yes—
566C2C101×#281611yescharacteristic
567C2C101×#283112yes—
568C2C101×#283212yes—
subgroupG/H
center, socleC24×C101C24
commutator, Frattini, cosocleC24C24×C101
prime radicalC25×C101C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#1446C2semidirect
4. C101×#1445C2semidirect
5. C101×#1442C2semidirect
6. C101×#1442C2semidirect
274. #17201C101direct (N × H)
287. #1446C2×C101semidirect
288. #1445C2×C101semidirect
289. #1442C2×C101semidirect
290. #1442C2×C101semidirect
294. C101#17201direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#397×C1012
C2×#393×C1012
C101×#14462
C101×#14452
C101×#14422
C101×#14402
C101×#14392
#17201101