Finite Group Databasebeta

← C101×#26197 #38808348

Subgroups — C101×#26197 #38808348

Order 25856.

742 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3097C211yesmaximal, characteristic, complemented
2C101×#3046C211yesmaximal, characteristic
3C101×#2952C211yesmaximal, characteristic
4C101×#2912C211yesmaximal, characteristic, complemented
5C101×#2096C211yesmaximal, characteristic, complemented
6C101×#2090C211yesmaximal, characteristic, complemented
7C101×#2079C211yesmaximal, characteristic, complemented
8C101×#2038C211yesmaximal, characteristic, complemented
9C101×#1930C211yesmaximal, characteristic, complemented
10C101×#1922C211yesmaximal, characteristic, complemented
11C101×#1908C211yesmaximal, characteristic, complemented
12C101×#1882C211yesmaximal, characteristic, complemented
13C101×#1876C211yesmaximal, characteristic
14C101×#1859C211yesmaximal, characteristic, complemented
15C101×#1859C211yesmaximal, characteristic, complemented
16C2×#137×C101C2211yescharacteristic
17C2×#135×C101C2211yescharacteristic
18C2×#131×C101C2211yescharacteristic
19#536×C101C2211yescharacteristic
20#520×C101C2211yescharacteristic
21#520×C101C2211yescharacteristic
22#520×C101C2211yescharacteristic
23#485×C101—21no—
24#485×C101—21no—
25#484×C101—21no—
26#483×C101—21no—
27#464×C101—21no—
28#463×C101—21no—
29#462×C101—21no—
30#461×C101—21no—
31#442×C101—21no—
32#441×C101—21no—
33C4×SD16×C101—21no—
34C4×SD16×C101—21no—
35#428×C101—21no—
36#428×C101—21no—
37#428×C101C2211yescharacteristic
38#428×C101C2211yescharacteristic
39#428×C101C2211yescharacteristic
40#427×C101—21no—
41#427×C101C2211yescharacteristic
42C2×#106×C101—21no—
43C2×#106×C101C2211yescharacteristic
44C2×#106×C101C2211yescharacteristic
45#424×C101C2211yescharacteristic
46C2×#104×C101C2211yescharacteristic
47C2×#104×C101C2211yescharacteristic
48#419×C101C2211yescharacteristic
49#417×C101C2211yescharacteristic
50#417×C101C2211yescharacteristic
51#417×C101C2211yescharacteristic
52C2×#103×C101C2211yescharacteristic
53C2×#103×C101C2211yescharacteristic
54C2×#101×C101C2211yescharacteristic
55#408×C101C2211yescharacteristic
56#405×C101C2211yescharacteristic
57#391×C101C2211yescharacteristic
58#384×C101C2211yescharacteristic
59#343×C101C2211yescharacteristic
60#343×C101C2211yescharacteristic
61#343×C101C2211yescharacteristic
62#341×C101C2211yescharacteristic
63#341×C101C2211yescharacteristic
64#339×C101C2211yescharacteristic
65#339×C101C2211yescharacteristic
66#336×C101C2211yescharacteristic
67C2×#41×C101C2311yescharacteristic
68C2×#41×C101C2311yescharacteristic
69C22×Q8×C101C2311yescharacteristic
70#137×C101—22no—
71#137×C101—22no—
72#135×C101—22no—
73#135×C101—22no—
74C2×Q16×C101—21no—
75C2×Q16×C101D411yescharacteristic
76C2×SD16×C101—21no—
77C2×SD16×C101D411yescharacteristic
78C2×SD16×C101D411yescharacteristic
79C2×D8×C101D411yescharacteristic
80#131×C101—22no—
81#131×C101—22no—
82C2×M16×C101—21no—
83C2×M16×C101C2311yescharacteristic
84C2×M16×C101C2311yescharacteristic
85C2×M16×C101C2311yescharacteristic
86C2×M16×C101C2311yescharacteristic
87C22×C8×C101—21no—
88C22×C8×C101C2311yescharacteristic
89C22×C8×C101C2311yescharacteristic
90C4⋊Q8×C101—21no—
91#124×C101—21no—
92#123×C101—41no—
93C22⋊Q8×C101—21no—
94C22⋊Q8×C101—21no—
95C4×Q8×C101—21no—
96C4×Q8×C101—21no—
97C4×Q8×C101—21no—
98C4×D4×C101—21no—
99C4×D4×C101—21no—
100C4×D4×C101—21no—
101C4×D4×C101—41no—
102C4×D4×C101—41no—
103C4×D4×C101—41no—
104#117×C101—21no—
105#117×C101—21no—
106#117×C101—21no—
107#117×C101C2311yescharacteristic
108#117×C101C2311yescharacteristic
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—41no—
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C42×C101C2311yescharacteristic
117#107×C101—21no—
118#107×C101—21no—
119#107×C101—21no—
120#107×C101D411yescharacteristic
121#107×C101D411yescharacteristic
122#106×C101—21no—
123#106×C101—21no—
124#106×C101—21no—
125#106×C101—21no—
126#106×C101—21no—
127#106×C101—21no—
128#106×C101—21no—
129#106×C101D411yescharacteristic
130#106×C101D411yescharacteristic
131C4⋊C8×C101—21no—
132C4⋊C8×C101—21no—
133#104×C101—22no—
134#104×C101—22no—
135#103×C101—21no—
136#103×C101—21no—
137#103×C101—21no—
138#103×C101—21no—
139#103×C101—21no—
140#103×C101—21no—
141#103×C101—21no—
142#103×C101—21no—
143#103×C101—21no—
144#102×C101—21no—
145#102×C101—21no—
146#102×C101—21no—
147#101×C101—22no—
148C22⋊C8×C101—21no—
149C22⋊C8×C101—21no—
150#97×C101—21no—
151C4×C8×C101—21no—
152#95×C101—41no—
153#41×C101—21no—
154#41×C101—21no—
155#41×C101—21no—
156#41×C101—21no—
157#41×C101—21no—
158#41×C101—21no—
159#41×C101#4112yes—
160#41×C101#4112yes—
161C2×Q8×C101—21no—
162C2×Q8×C101—21no—
163C2×Q8×C101—21no—
164C2×Q8×C101—21no—
165C2×Q8×C101—21no—
166C2×Q8×C101—21no—
167C2×Q8×C101C2×D411yescharacteristic
168C2×Q8×C101C2×D411yescharacteristic
169C2×D4×C101—21no—
170C2×D4×C101—21no—
171C2×D4×C101C2×D411yescharacteristic
172C2×D4×C101C2×D411yescharacteristic
173C22×C4×C101—21no—
174C22×C4×C101—21no—
175C22×C4×C101—21no—
176C22×C4×C101—21no—
177C22×C4×C101—21no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—41no—
181C22×C4×C101—41no—
182C22×C4×C101—41no—
183C22×C4×C101C2411yescharacteristic
184Q16×C101—22no—
185Q16×C101—42no—
186SD16×C101—22no—
187SD16×C101—22no—
188SD16×C101—42no—
189D8×C101—22no—
190M16×C101—24no—
191M16×C101—21no—
192M16×C101—21no—
193M16×C101—21no—
194M16×C101—21no—
195M16×C101—21no—
196M16×C101—21no—
197M16×C101—21no—
198M16×C101#4112yes—
199C2×C8×C101—24no—
200C2×C8×C101—21no—
201C2×C8×C101—21no—
202C2×C8×C101—21no—
203C2×C8×C101—21no—
204C2×C8×C101—21no—
205C2×C8×C101—21no—
206C2×C8×C101—21no—
207C2×C8×C101—21no—
208C2×C8×C101C2×D411yescharacteristic
209C2×C8×C101C2×D411yescharacteristic
210C2×C8×C101C2×D411yescharacteristic
211C2×C8×C101C2×D411yescharacteristic
212C4⋊C4×C101—21no—
213C4⋊C4×C101—21no—
214C4⋊C4×C101—21no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—41no—
219C4⋊C4×C101—41no—
220C4⋊C4×C101—41no—
221C4⋊C4×C101—41no—
222C4⋊C4×C101—41no—
223C4⋊C4×C101—82no—
224C4⋊C4×C101C2×D411yescharacteristic
225C4⋊C4×C101C2×D411yescharacteristic
226C4⋊C4×C101C2×D411yescharacteristic
227C4⋊C4×C101C2×D411yescharacteristic
228C22⋊C4×C101—21no—
229C22⋊C4×C101—21no—
230C22⋊C4×C101—41no—
231C22⋊C4×C101—41no—
232C22⋊C4×C101—41no—
233C22⋊C4×C101—41no—
234C22⋊C4×C101—41no—
235C42×C101—21no—
236C42×C101—21no—
237C42×C101—21no—
238C42×C101—21no—
239C42×C101—41no—
240C42×C101—41no—
241C42×C101—41no—
242C23×C101—21no—
243C23×C101—21no—
244C23×C101H(5,𝔽2)11yescharacteristic
245Q8×C101—21no—
246Q8×C101—21no—
247Q8×C101—21no—
248Q8×C101—41no—
249Q8×C101—41no—
250Q8×C101—41no—
251Q8×C101—41no—
252Q8×C101#12312yes—
253D4×C101—22no—
254D4×C101—22no—
255D4×C101—21no—
256D4×C101—21no—
257D4×C101—21no—
258D4×C101—41no—
259D4×C101—41no—
260D4×C101#12312yes—
261C2×C4×C101—21no—
262C2×C4×C101—22no—
263C2×C4×C101—22no—
264C2×C4×C101—22no—
265C2×C4×C101—21no—
266C2×C4×C101—21no—
267C2×C4×C101—21no—
268C2×C4×C101—21no—
269C2×C4×C101—21no—
270C2×C4×C101—41no—
271C2×C4×C101—41no—
272C2×C4×C101—41no—
273C2×C4×C101—41no—
274C2×C4×C101—41no—
275C2×C4×C101—41no—
276C2×C4×C101—41no—
277C2×C4×C101—41no—
278C2×C4×C101—41no—
279C2×C4×C101—41no—
280C2×C4×C101—81no—
281C2×C4×C101—81no—
282C2×C4×C101—81no—
283C2×C4×C101—161no—
284C2×C4×C101—161no—
285C2×C4×C101—161no—
286C2×C4×C101C22×D411yescharacteristic
287C2×C4×C101C22×D411yescharacteristic
288C2×C4×C101C2×#4111yescharacteristic
289C2×C4×C101C2×#4111yescharacteristic
290C2×C4×C101C2×#4111yescharacteristic
291C2×C4×C1012−1+411yescharacteristic
292C8×C101—21no—
293C8×C101—21no—
294C8×C101—21no—
295C8×C101—22no—
296C8×C101—21no—
297C8×C101—41no—
298C8×C101—41no—
299C8×C101—41no—
300C22×C101—21no—
301C22×C101—21no—
302C22×C101—22no—
303C22×C101—41no—
304C22×C101—41no—
305C22×C101—41no—
306C22×C101—41no—
307C22×C101—41no—
308C22×C101#53911yescharacteristic
309C22×C101D4211yescharacteristic
310C22×C101#55311yescharacteristic
311C4×C101—22no—
312C4×C101—42no—
313C4×C101—41no—
314C4×C101—41no—
315C4×C101—41no—
316C4×C101—41no—
317C4×C101—41no—
318C4×C101—81no—
319C4×C101—81no—
320C4×C101—81no—
321C4×C101—81no—
322C4×C101C2×#12311yescharacteristic
323C4×C101#52511yescharacteristic
324C4×C101#54711yescharacteristic
325C4×C101#54811yescharacteristic
326#26197C10111yesmaximal, characteristic, direct product factor, Sylow
327C2×C101—21no—
328C2×C101—21no—
329C2×C101—42no—
330C2×C101—81no—
331C2×C101#244311yescharacteristic
332C2×C101#328911yescharacteristic
333C2×C101#329111yescharacteristic
334#3097C2×C10111yescharacteristic, complemented
335#3046C2×C10111yescharacteristic
336#2952C2×C10111yescharacteristic
337#2912C2×C10111yescharacteristic, complemented
338#2096C2×C10111yescharacteristic, complemented
339#2090C2×C10111yescharacteristic, complemented
340#2079C2×C10111yescharacteristic, complemented
341#2038C2×C10111yescharacteristic, complemented
342#1930C2×C10111yescharacteristic, complemented
343#1922C2×C10111yescharacteristic, complemented
344#1908C2×C10111yescharacteristic, complemented
345#1882C2×C10111yescharacteristic, complemented
346#1876C2×C10111yescharacteristic
347#1859C2×C10111yescharacteristic, complemented
348#1859C2×C10111yescharacteristic, complemented
349C101#2619711yescharacteristic, direct product factor, Sylow
350C2×#137C22×C10111yescharacteristic
351C2×#135C22×C10111yescharacteristic
352C2×#131C22×C10111yescharacteristic
353#536C22×C10111yescharacteristic
354#520C22×C10111yescharacteristic
355#520C22×C10111yescharacteristic
356#520C22×C10111yescharacteristic
357#485—21no—
358#485—21no—
359#484—21no—
360#483—21no—
361#464—21no—
362#463—21no—
363#462—21no—
364#461—21no—
365#442—21no—
366#441—21no—
367C4×SD16—21no—
368C4×SD16—21no—
369#428—21no—
370#428—21no—
371#428C22×C10111yescharacteristic
372#428C22×C10111yescharacteristic
373#428C22×C10111yescharacteristic
374#427—21no—
375#427C22×C10111yescharacteristic
376C2×#106—21no—
377C2×#106C22×C10111yescharacteristic
378C2×#106C22×C10111yescharacteristic
379#424C22×C10111yescharacteristic
380C2×#104C22×C10111yescharacteristic
381C2×#104C22×C10111yescharacteristic
382#419C22×C10111yescharacteristic
383#417C22×C10111yescharacteristic
384#417C22×C10111yescharacteristic
385#417C22×C10111yescharacteristic
386C2×#103C22×C10111yescharacteristic
387C2×#103C22×C10111yescharacteristic
388C2×#101C22×C10111yescharacteristic
389#408C22×C10111yescharacteristic
390#405C22×C10111yescharacteristic
391#391C22×C10111yescharacteristic
392#384C22×C10111yescharacteristic
393#343C22×C10111yescharacteristic
394#343C22×C10111yescharacteristic
395#343C22×C10111yescharacteristic
396#341C22×C10111yescharacteristic
397#341C22×C10111yescharacteristic
398#339C22×C10111yescharacteristic
399#339C22×C10111yescharacteristic
400#336C22×C10111yescharacteristic
401C2×#41C23×C10111yescharacteristic
402C2×#41C23×C10111yescharacteristic
403C22×Q8C23×C10111yescharacteristic
404#137—22no—
405#137—22no—
406#135—22no—
407#135—22no—
408C2×Q16—21no—
409C2×Q16D4×C10111yescharacteristic
410C2×SD16—21no—
411C2×SD16D4×C10111yescharacteristic
412C2×SD16D4×C10111yescharacteristic
413C2×D8D4×C10111yescharacteristic
414#131—22no—
415#131—22no—
416C2×M16—21no—
417C2×M16C23×C10111yescharacteristic
418C2×M16C23×C10111yescharacteristic
419C2×M16C23×C10111yescharacteristic
420C2×M16C23×C10111yescharacteristic
421C22×C8—21no—
422C22×C8C23×C10111yescharacteristic
423C22×C8C23×C10111yescharacteristic
424C4⋊Q8—21no—
425#124—21no—
426#123—41no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—41no—
436C4×D4—41no—
437C4×D4—41no—
438#117—21no—
439#117—21no—
440#117—21no—
441#117C23×C10111yescharacteristic
442#117C23×C10111yescharacteristic
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4C23×C10111yescharacteristic
448C2×C4⋊C4C23×C10111yescharacteristic
449C2×C4⋊C4C23×C10111yescharacteristic
450C2×C42C23×C10111yescharacteristic
451#107—21no—
452#107—21no—
453#107—21no—
454#107D4×C10111yescharacteristic
455#107D4×C10111yescharacteristic
456#106—21no—
457#106—21no—
458#106—21no—
459#106—21no—
460#106—21no—
461#106—21no—
462#106—21no—
463#106D4×C10111yescharacteristic
464#106D4×C10111yescharacteristic
465C4⋊C8—21no—
466C4⋊C8—21no—
467#104—22no—
468#104—22no—
469#103—21no—
470#103—21no—
471#103—21no—
472#103—21no—
473#103—21no—
474#103—21no—
475#103—21no—
476#103—21no—
477#103—21no—
478#102—21no—
479#102—21no—
480#102—21no—
481#101—22no—
482C22⋊C8—21no—
483C22⋊C8—21no—
484#97—21no—
485C4×C8—21no—
486#95—41no—
487#41—21no—
488#41—21no—
489#41—21no—
490#41—21no—
491#41—21no—
492#41—21no—
493#41#41×C10112yes—
494#41#41×C10112yes—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C2×D4×C10111yescharacteristic
502C2×Q8C2×D4×C10111yescharacteristic
503C2×D4—21no—
504C2×D4—21no—
505C2×D4C2×D4×C10111yescharacteristic
506C2×D4C2×D4×C10111yescharacteristic
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4C24×C10111yescharacteristic
518Q16—22no—
519Q16—42no—
520SD16—22no—
521SD16—22no—
522SD16—42no—
523D8—22no—
524M16—24no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16#41×C10112yes—
533C2×C8—24no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8C2×D4×C10111yescharacteristic
543C2×C8C2×D4×C10111yescharacteristic
544C2×C8C2×D4×C10111yescharacteristic
545C2×C8C2×D4×C10111yescharacteristic
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—82no—
558C4⋊C4C2×D4×C10111yescharacteristic
559C4⋊C4C2×D4×C10111yescharacteristic
560C4⋊C4C2×D4×C10111yescharacteristic
561C4⋊C4C2×D4×C10111yescharacteristic
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—41no—
574C42—41no—
575C42—41no—
576C23—21no—
577C23—21no—
578C23H(5,𝔽2)×C10111yescharacteristic
579Q8—21no—
580Q8—21no—
581Q8—21no—
582Q8—41no—
583Q8—41no—
584Q8—41no—
585Q8—41no—
586Q8#123×C10112yes—
587D4—22no—
588D4—22no—
589D4—21no—
590D4—21no—
591D4—21no—
592D4—41no—
593D4—41no—
594D4#123×C10112yes—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—161no—
618C2×C4—161no—
619C2×C4—161no—
620C2×C4C22×D4×C10111yescharacteristic
621C2×C4C22×D4×C10111yescharacteristic
622C2×C4C2×#41×C10111yescharacteristic
623C2×C4C2×#41×C10111yescharacteristic
624C2×C4C2×#41×C10111yescharacteristic
625C2×C42−1+4×C10111yescharacteristic
626C8—21no—
627C8—21no—
628C8—21no—
629C8—22no—
630C8—21no—
631C8—41no—
632C8—41no—
633C8—41no—
634C22—21no—
635C22—21no—
636C22—22no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22#539×C10111yescharacteristic
643C22D42×C10111yescharacteristic
644C22#553×C10111yescharacteristic
645C4—22no—
646C4—42no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4C2×#123×C10111yescharacteristic
657C4#525×C10111yescharacteristic
658C4#547×C10111yescharacteristic
659C4#548×C10111yescharacteristic
660C2—21no—
661C2—21no—
662C2—42no—
663C2—81no—
664C2C101×#244311yescharacteristic
665C2C101×#328911yescharacteristic
666C2C101×#329111yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#135×C101C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3097C2semidirect
4. C101×#2912C2semidirect
5. C101×#2096C2semidirect
6. C101×#2090C2semidirect
7. C101×#2079C2semidirect
8. C101×#2038C2semidirect
9. C101×#1930C2semidirect
10. C101×#1922C2semidirect
11. C101×#1908C2semidirect
12. C101×#1882C2semidirect
14. C101×#1859C2semidirect
15. C101×#1859C2semidirect
326. #26197C101direct (N × H)
334. #3097C2×C101semidirect
337. #2912C2×C101semidirect
338. #2096C2×C101semidirect
339. #2090C2×C101semidirect
340. #2079C2×C101semidirect
341. #2038C2×C101semidirect
342. #1930C2×C101semidirect
343. #1922C2×C101semidirect
344. #1908C2×C101semidirect
345. #1882C2×C101semidirect
347. #1859C2×C101semidirect
348. #1859C2×C101semidirect
349. C101#26197direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#30972
C101×#30462
C101×#29522
C101×#29122
C101×#20962
C101×#20902
C101×#20792
C101×#20382
C101×#19302
C101×#19222
C101×#19082
C101×#18822
C101×#18762
C101×#18592
#26197101