Finite Group Databasebeta

← C101×#19741 #38801892

Subgroups — C101×#19741 #38801892

Order 25856.

704 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3228C211yesmaximal, characteristic, complemented
2C101×#3227C211yesmaximal, characteristic, complemented
3C101×#3226C211yesmaximal, characteristic, complemented
4C101×#3210C211yesmaximal, characteristic, complemented
5C101×#3209C211yesmaximal, characteristic, complemented
6C101×#3207C211yesmaximal, characteristic
7C101×#1723C211yesmaximal, characteristic, complemented
8C101×#1722C211yesmaximal, characteristic, complemented
9C101×#1720C211yesmaximal, characteristic, complemented
10C101×#1720C211yesmaximal, characteristic, complemented
11C101×#1717C211yesmaximal, characteristic, complemented
12C101×#1714C211yesmaximal, characteristic, complemented
13C101×#1709C211yesmaximal, characteristic, complemented
14C101×#1707C211yesmaximal, characteristic, complemented
15C101×#1454C211yesmaximal, characteristic, complemented
16#533×C101C2211yescharacteristic
17#532×C101C2211yescharacteristic
18#532×C101C2211yescharacteristic
19C2×C4⋊Q8×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#500×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#498×C101C2211yescharacteristic
25#498×C101C2211yescharacteristic
26#494×C101C2211yescharacteristic
27#494×C101C2211yescharacteristic
28#494×C101C2211yescharacteristic
29#493×C101C2211yescharacteristic
30#492×C101C2211yescharacteristic
31#492×C101C2211yescharacteristic
32#487×C101C2211yescharacteristic
33#487×C101C2211yescharacteristic
34#487×C101C2211yescharacteristic
35#487×C101C2211yescharacteristic
36#486×C101C2211yescharacteristic
37#486×C101C2211yescharacteristic
38#486×C101C2211yescharacteristic
39#486×C101C2211yescharacteristic
40#486×C101C2211yescharacteristic
41#486×C101C2211yescharacteristic
42#486×C101C2211yescharacteristic
43#486×C101C2211yescharacteristic
44#482×C101—22no—
45#481×C101—22no—
46#480×C101—22no—
47#478×C101—22no—
48#476×C101—22no—
49#474×C101—22no—
50#464×C101—22no—
51#463×C101—22no—
52#462×C101—22no—
53#452×C101—22no—
54#451×C101—22no—
55#449×C101—22no—
56#431×C101C2211yescharacteristic
57#431×C101C2211yescharacteristic
58#431×C101C2211yescharacteristic
59#322×C101C2211yescharacteristic
60#322×C101C2211yescharacteristic
61#322×C101C2211yescharacteristic
62C82×C101C2211yescharacteristic
63C2×#41×C101—21no—
64C2×#41×C101—21no—
65C22×Q8×C101—21no—
66C2×Q16×C101—22no—
67C2×Q16×C101—22no—
68C2×Q16×C101—22no—
69C2×SD16×C101—22no—
70C2×SD16×C101—22no—
71C2×D8×C101—22no—
72C4⋊Q8×C101—21no—
73C4⋊Q8×C101—21no—
74C4⋊Q8×C101—21no—
75C4⋊Q8×C101C2311yescharacteristic
76C4⋊Q8×C101C2311yescharacteristic
77C4⋊Q8×C101C2311yescharacteristic
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80C4⋊Q8×C101C2311yescharacteristic
81#127×C101C2311yescharacteristic
82#127×C101C2311yescharacteristic
83#125×C101—21no—
84#124×C101—21no—
85#124×C101—21no—
86C22⋊Q8×C101—21no—
87C22⋊Q8×C101—21no—
88#121×C101—21no—
89#121×C101—21no—
90#121×C101—21no—
91#121×C101—21no—
92C4×Q8×C101—21no—
93C4×Q8×C101—21no—
94C4×D4×C101—21no—
95C4×D4×C101—21no—
96C4×D4×C101—21no—
97C4×D4×C101—21no—
98#117×C101—21no—
99C2×C4⋊C4×C101—21no—
100C2×C4⋊C4×C101—21no—
101C2×C42×C101C2311yescharacteristic
102#107×C101—22no—
103#107×C101—22no—
104#107×C101—22no—
105#106×C101—22no—
106#106×C101—22no—
107#106×C101—22no—
108C4⋊C8×C101D412yes—
109C4⋊C8×C101D412yes—
110C4⋊C8×C101D412yes—
111#103×C101—22no—
112#103×C101—22no—
113#103×C101—22no—
114#103×C101—22no—
115#102×C101—22no—
116#102×C101—22no—
117#102×C101—22no—
118#102×C101—22no—
119#102×C101—22no—
120#102×C101—22no—
121#102×C101—22no—
122#102×C101—22no—
123C22⋊C8×C101D412yes—
124C22⋊C8×C101D412yes—
125C22⋊C8×C101D412yes—
126C4×C8×C101C2311yescharacteristic
127C4×C8×C101C2311yescharacteristic
128C4×C8×C101C2311yescharacteristic
129C4×C8×C101C2311yescharacteristic
130C4×C8×C101C2311yescharacteristic
131C4×C8×C101C2311yescharacteristic
132#41×C101—82no—
133#41×C101—82no—
134C2×Q8×C101—21no—
135C2×Q8×C101—21no—
136C2×Q8×C101—21no—
137C2×Q8×C101—21no—
138C2×Q8×C101—21no—
139C2×Q8×C101—21no—
140C2×Q8×C101—41no—
141C2×Q8×C101—82no—
142C2×D4×C101—21no—
143C2×D4×C101—21no—
144C2×D4×C101—21no—
145C2×D4×C101—21no—
146C2×D4×C101—21no—
147C2×D4×C101—21no—
148C2×D4×C101—41no—
149C2×D4×C101—41no—
150C22×C4×C101—41no—
151C22×C4×C101—41no—
152C22×C4×C101—41no—
153C22×C4×C101C2×D411yescharacteristic
154C22×C4×C101C2×D411yescharacteristic
155C22×C4×C101C2×D411yescharacteristic
156Q16×C101—82no—
157Q16×C101—82no—
158Q16×C101—82no—
159SD16×C101—82no—
160SD16×C101—82no—
161D8×C101—82no—
162C2×C8×C101C2×D412yes—
163C2×C8×C101C2×D412yes—
164C2×C8×C101C2×D412yes—
165C2×C8×C101C2×D412yes—
166C2×C8×C101C2×D412yes—
167C2×C8×C101C2×D412yes—
168C4⋊C4×C101—21no—
169C4⋊C4×C101—21no—
170C4⋊C4×C101—21no—
171C4⋊C4×C101—21no—
172C4⋊C4×C101—21no—
173C4⋊C4×C101—21no—
174C4⋊C4×C101—21no—
175C4⋊C4×C101—21no—
176C4⋊C4×C101—21no—
177C4⋊C4×C101—21no—
178C4⋊C4×C101—21no—
179C4⋊C4×C101—21no—
180C4⋊C4×C101—41no—
181C4⋊C4×C101—41no—
182C4⋊C4×C101—41no—
183C4⋊C4×C101—41no—
184C22⋊C4×C101—41no—
185C22⋊C4×C101—41no—
186C22⋊C4×C101—41no—
187C22⋊C4×C101—41no—
188C22⋊C4×C101—41no—
189C42×C101—41no—
190C42×C101C2×D411yescharacteristic
191C42×C101C2×D411yescharacteristic
192C42×C101C2×D411yescharacteristic
193C42×C101C2411yescharacteristic
194C23×C101—41no—
195C23×C101—41no—
196C23×C101#12711yescharacteristic
197Q8×C101—42no—
198Q8×C101—42no—
199Q8×C101—42no—
200Q8×C101—42no—
201Q8×C101—42no—
202Q8×C101—42no—
203Q8×C101—82no—
204D4×C101—42no—
205D4×C101—42no—
206D4×C101—42no—
207D4×C101—42no—
208D4×C101—42no—
209D4×C101—42no—
210D4×C101—82no—
211D4×C101—82no—
212C2×C4×C101—22no—
213C2×C4×C101—22no—
214C2×C4×C101—22no—
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—82no—
222C2×C4×C101—82no—
223C2×C4×C101—82no—
224C2×C4×C101#12711yescharacteristic
225C2×C4×C101#12711yescharacteristic
226C2×C4×C101#12711yescharacteristic
227C2×C4×C101C22×D411yescharacteristic
228C2×C4×C101C22×D411yescharacteristic
229C2×C4×C101C22×D411yescharacteristic
230C8×C101—22no—
231C8×C101—22no—
232C8×C101—22no—
233C8×C101—22no—
234C8×C101—22no—
235C8×C101—22no—
236C22×C101—21no—
237C22×C101—21no—
238C22×C101—21no—
239C22×C101—81no—
240C22×C101—81no—
241C22×C101—81no—
242C22×C101—81no—
243C22×C101—81no—
244C22×C101—81no—
245C22×C101C2×#12711yescharacteristic
246C4×C101—21no—
247C4×C101—21no—
248C4×C101—21no—
249C4×C101—81no—
250C4×C101—81no—
251C4×C101—81no—
252C4×C101—81no—
253C4×C101—81no—
254C4×C101—81no—
255C4×C101#57612yes—
256C4×C101#57712yes—
257C4×C101#57812yes—
258#19741C10111yesmaximal, characteristic, direct product factor, Sylow
259C2×C101—41no—
260C2×C101—161no—
261C2×C101—161no—
262C2×C101#315411yescharacteristic
263C2×C101#315511yescharacteristic
264C2×C101#315611yescharacteristic
265#3228C2×C10111yescharacteristic, complemented
266#3227C2×C10111yescharacteristic, complemented
267#3226C2×C10111yescharacteristic, complemented
268#3210C2×C10111yescharacteristic, complemented
269#3209C2×C10111yescharacteristic, complemented
270#3207C2×C10111yescharacteristic
271#1723C2×C10111yescharacteristic, complemented
272#1722C2×C10111yescharacteristic, complemented
273#1720C2×C10111yescharacteristic, complemented
274#1720C2×C10111yescharacteristic, complemented
275#1717C2×C10111yescharacteristic, complemented
276#1714C2×C10111yescharacteristic, complemented
277#1709C2×C10111yescharacteristic, complemented
278#1707C2×C10111yescharacteristic, complemented
279#1454C2×C10111yescharacteristic, complemented
280C101#1974111yescharacteristic, direct product factor, Sylow
281#533C22×C10111yescharacteristic
282#532C22×C10111yescharacteristic
283#532C22×C10111yescharacteristic
284C2×C4⋊Q8C22×C10111yescharacteristic
285#500C22×C10111yescharacteristic
286#500C22×C10111yescharacteristic
287#500C22×C10111yescharacteristic
288#498C22×C10111yescharacteristic
289#498C22×C10111yescharacteristic
290#498C22×C10111yescharacteristic
291#494C22×C10111yescharacteristic
292#494C22×C10111yescharacteristic
293#494C22×C10111yescharacteristic
294#493C22×C10111yescharacteristic
295#492C22×C10111yescharacteristic
296#492C22×C10111yescharacteristic
297#487C22×C10111yescharacteristic
298#487C22×C10111yescharacteristic
299#487C22×C10111yescharacteristic
300#487C22×C10111yescharacteristic
301#486C22×C10111yescharacteristic
302#486C22×C10111yescharacteristic
303#486C22×C10111yescharacteristic
304#486C22×C10111yescharacteristic
305#486C22×C10111yescharacteristic
306#486C22×C10111yescharacteristic
307#486C22×C10111yescharacteristic
308#486C22×C10111yescharacteristic
309#482—22no—
310#481—22no—
311#480—22no—
312#478—22no—
313#476—22no—
314#474—22no—
315#464—22no—
316#463—22no—
317#462—22no—
318#452—22no—
319#451—22no—
320#449—22no—
321#431C22×C10111yescharacteristic
322#431C22×C10111yescharacteristic
323#431C22×C10111yescharacteristic
324#322C22×C10111yescharacteristic
325#322C22×C10111yescharacteristic
326#322C22×C10111yescharacteristic
327C82C22×C10111yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C22×Q8—21no—
331C2×Q16—22no—
332C2×Q16—22no—
333C2×Q16—22no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×D8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8C23×C10111yescharacteristic
341C4⋊Q8C23×C10111yescharacteristic
342C4⋊Q8C23×C10111yescharacteristic
343C4⋊Q8C23×C10111yescharacteristic
344C4⋊Q8C23×C10111yescharacteristic
345C4⋊Q8C23×C10111yescharacteristic
346#127C23×C10111yescharacteristic
347#127C23×C10111yescharacteristic
348#125—21no—
349#124—21no—
350#124—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363#117—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C42C23×C10111yescharacteristic
367#107—22no—
368#107—22no—
369#107—22no—
370#106—22no—
371#106—22no—
372#106—22no—
373C4⋊C8D4×C10112yes—
374C4⋊C8D4×C10112yes—
375C4⋊C8D4×C10112yes—
376#103—22no—
377#103—22no—
378#103—22no—
379#103—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388C22⋊C8D4×C10112yes—
389C22⋊C8D4×C10112yes—
390C22⋊C8D4×C10112yes—
391C4×C8C23×C10111yescharacteristic
392C4×C8C23×C10111yescharacteristic
393C4×C8C23×C10111yescharacteristic
394C4×C8C23×C10111yescharacteristic
395C4×C8C23×C10111yescharacteristic
396C4×C8C23×C10111yescharacteristic
397#41—82no—
398#41—82no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—41no—
406C2×Q8—82no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—41no—
414C2×D4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4C2×D4×C10111yescharacteristic
419C22×C4C2×D4×C10111yescharacteristic
420C22×C4C2×D4×C10111yescharacteristic
421Q16—82no—
422Q16—82no—
423Q16—82no—
424SD16—82no—
425SD16—82no—
426D8—82no—
427C2×C8C2×D4×C10112yes—
428C2×C8C2×D4×C10112yes—
429C2×C8C2×D4×C10112yes—
430C2×C8C2×D4×C10112yes—
431C2×C8C2×D4×C10112yes—
432C2×C8C2×D4×C10112yes—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C42—41no—
455C42C2×D4×C10111yescharacteristic
456C42C2×D4×C10111yescharacteristic
457C42C2×D4×C10111yescharacteristic
458C42C24×C10111yescharacteristic
459C23—41no—
460C23—41no—
461C23#127×C10111yescharacteristic
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—42no—
466Q8—42no—
467Q8—42no—
468Q8—82no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—82no—
476D4—82no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4#127×C10111yescharacteristic
490C2×C4#127×C10111yescharacteristic
491C2×C4#127×C10111yescharacteristic
492C2×C4C22×D4×C10111yescharacteristic
493C2×C4C22×D4×C10111yescharacteristic
494C2×C4C22×D4×C10111yescharacteristic
495C8—22no—
496C8—22no—
497C8—22no—
498C8—22no—
499C8—22no—
500C8—22no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22C2×#127×C10111yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—81no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—81no—
519C4—81no—
520C4#576×C10112yes—
521C4#577×C10112yes—
522C4#578×C10112yes—
523C2—41no—
524C2—161no—
525C2—161no—
526C2C101×#315411yescharacteristic
527C2C101×#315511yescharacteristic
528C2C101×#315611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#127
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3207C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3228C2semidirect
2. C101×#3227C2semidirect
3. C101×#3226C2semidirect
4. C101×#3210C2semidirect
5. C101×#3209C2semidirect
7. C101×#1723C2semidirect
8. C101×#1722C2semidirect
9. C101×#1720C2semidirect
10. C101×#1720C2semidirect
11. C101×#1717C2semidirect
12. C101×#1714C2semidirect
13. C101×#1709C2semidirect
14. C101×#1707C2semidirect
15. C101×#1454C2semidirect
258. #19741C101direct (N × H)
265. #3228C2×C101semidirect
266. #3227C2×C101semidirect
267. #3226C2×C101semidirect
268. #3210C2×C101semidirect
269. #3209C2×C101semidirect
271. #1723C2×C101semidirect
272. #1722C2×C101semidirect
273. #1720C2×C101semidirect
274. #1720C2×C101semidirect
275. #1717C2×C101semidirect
276. #1714C2×C101semidirect
277. #1709C2×C101semidirect
278. #1707C2×C101semidirect
279. #1454C2×C101semidirect
280. C101#19741direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32282
C101×#32272
C101×#32262
C101×#32102
C101×#32092
C101×#32072
C101×#17232
C101×#17222
C101×#17202
C101×#17172
C101×#17142
C101×#17092
C101×#17072
C101×#14542
#19741101