Finite Group Databasebeta

← C103×#26849 #39932124

Subgroups — C103×#26849 #39932124

Order 26368.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3137C211yesmaximal, characteristic
2C103×#3097C211yesmaximal, characteristic
3C103×#3082C211yesmaximal, characteristic, complemented
4C103×#2947C211yesmaximal, characteristic
5C103×#2064C211yesmaximal, characteristic, complemented
6C103×#2060C211yesmaximal, characteristic, complemented
7C103×#2052C211yesmaximal, characteristic
8C103×#2005C211yesmaximal, characteristic
9C103×#1956C211yesmaximal, characteristic, complemented
10C103×#1937C211yesmaximal, characteristic
11C103×#1930C211yesmaximal, characteristic, complemented
12C103×#1930C211yesmaximal, characteristic, complemented
13C103×#1886C211yesmaximal, characteristic, complemented
14C103×#1859C211yesmaximal, characteristic
15C103×#1772C211yesmaximal, characteristic, complemented
16C2×#137×C103C2211yescharacteristic
17#544×C103C2211yescharacteristic
18#536×C103C2211yescharacteristic
19C2×C4⋊Q8×C103C2211yescharacteristic
20#520×C103C2211yescharacteristic
21#519×C103C2211yescharacteristic
22#491×C103—21no—
23#489×C103—21no—
24#488×C103—21no—
25#487×C103—21no—
26#485×C103—21no—
27#485×C103—21no—
28#484×C103—21no—
29#483×C103—21no—
30#479×C103—21no—
31#479×C103—21no—
32#477×C103—21no—
33#475×C103—21no—
34#441×C103—21no—
35#440×C103—21no—
36C4×Q16×C103—21no—
37C4×SD16×C103—21no—
38C2×#108×C103C2211yescharacteristic
39#428×C103C2211yescharacteristic
40#428×C103C2211yescharacteristic
41#428×C103C2211yescharacteristic
42#427×C103C2211yescharacteristic
43#424×C103C2211yescharacteristic
44C2×#104×C103C2211yescharacteristic
45#419×C103C2211yescharacteristic
46#419×C103C2211yescharacteristic
47#419×C103C2211yescharacteristic
48#417×C103C2211yescharacteristic
49#416×C103C2211yescharacteristic
50C2×#103×C103C2211yescharacteristic
51C2×#103×C103C2211yescharacteristic
52C2×#103×C103C2211yescharacteristic
53C2×#103×C103C2211yescharacteristic
54C2×#101×C103C2211yescharacteristic
55C2×#101×C103C2211yescharacteristic
56#408×C103C2211yescharacteristic
57#405×C103C2211yescharacteristic
58#405×C103C2211yescharacteristic
59C2×C4×C8×C103C2211yescharacteristic
60#384×C103C2211yescharacteristic
61#343×C103C2211yescharacteristic
62#343×C103C2211yescharacteristic
63#341×C103C2211yescharacteristic
64#339×C103C2211yescharacteristic
65#339×C103C2211yescharacteristic
66#339×C103C2211yescharacteristic
67C2×#41×C103C2311yescharacteristic
68C22×Q8×C103C2311yescharacteristic
69C22×Q8×C103C2311yescharacteristic
70#137×C103—22no—
71#137×C103—22no—
72C2×Q16×C103—21no—
73C2×SD16×C103—21no—
74C2×M16×C103C2311yescharacteristic
75C2×M16×C103C2311yescharacteristic
76C2×M16×C103C2311yescharacteristic
77C2×M16×C103C2311yescharacteristic
78C22×C8×C103C2311yescharacteristic
79C22×C8×C103C2311yescharacteristic
80C4⋊Q8×C103—21no—
81C4⋊Q8×C103—21no—
82C4⋊Q8×C103—21no—
83C4⋊Q8×C103—22no—
84C4⋊Q8×C103—22no—
85#125×C103—21no—
86#125×C103—21no—
87#124×C103—21no—
88#123×C103—41no—
89C22⋊Q8×C103—21no—
90C22⋊Q8×C103—21no—
91C22⋊Q8×C103—41no—
92C4×Q8×C103—21no—
93C4×Q8×C103—21no—
94C4×Q8×C103—21no—
95C4×Q8×C103—21no—
96C4×Q8×C103—21no—
97C4×D4×C103—21no—
98C4×D4×C103—41no—
99#117×C103—21no—
100#117×C103—41no—
101#117×C103C2311yescharacteristic
102#117×C103C2311yescharacteristic
103#117×C103C2311yescharacteristic
104C2×C4⋊C4×C103—21no—
105C2×C4⋊C4×C103—41no—
106C2×C4⋊C4×C103—41no—
107C2×C4⋊C4×C103C2311yescharacteristic
108C2×C4⋊C4×C103C2311yescharacteristic
109C2×C42×C103C2311yescharacteristic
110#108×C103—22no—
111#107×C103—21no—
112#107×C103—21no—
113#107×C103—21no—
114#107×C103D411yescharacteristic
115#107×C103D411yescharacteristic
116#106×C103—21no—
117#106×C103—21no—
118#106×C103—21no—
119#106×C103D411yescharacteristic
120#106×C103D411yescharacteristic
121C4⋊C8×C103—21no—
122C4⋊C8×C103—21no—
123#104×C103—22no—
124#103×C103—21no—
125#103×C103—21no—
126#103×C103—21no—
127#103×C103—21no—
128#103×C103—21no—
129#103×C103—21no—
130#103×C103—21no—
131#103×C103—21no—
132#103×C103—21no—
133#103×C103—21no—
134#103×C103—21no—
135#103×C103—21no—
136#103×C103—21no—
137#103×C103—21no—
138#103×C103—21no—
139#103×C103D411yescharacteristic
140#103×C103D411yescharacteristic
141#102×C103—21no—
142#102×C103D411yescharacteristic
143#102×C103D411yescharacteristic
144#101×C103—22no—
145#101×C103—22no—
146C22⋊C8×C103—21no—
147C22⋊C8×C103—21no—
148#97×C103—21no—
149#97×C103—21no—
150C4×C8×C103—21no—
151C4×C8×C103—21no—
152C4×C8×C103—22no—
153#41×C103—21no—
154#41×C103—21no—
155#41×C103—21no—
156#41×C103—21no—
157C2×Q8×C103—21no—
158C2×Q8×C103—21no—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×Q8×C103—21no—
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103—21no—
166C2×Q8×C103—21no—
167C2×Q8×C103—21no—
168C2×Q8×C103—41no—
169C2×Q8×C103C2×D411yescharacteristic
170C2×Q8×C103#4112yes—
171C2×D4×C103—21no—
172C2×D4×C103C2×D411yescharacteristic
173C22×C4×C103—21no—
174C22×C4×C103—21no—
175C22×C4×C103—21no—
176C22×C4×C103—21no—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—41no—
180C22×C4×C103C2411yescharacteristic
181Q16×C103—24no—
182SD16×C103—24no—
183M16×C103—21no—
184M16×C103—21no—
185M16×C103—21no—
186M16×C103—21no—
187M16×C103—21no—
188M16×C103—21no—
189M16×C103—21no—
190M16×C103#4112yes—
191C2×C8×C103—21no—
192C2×C8×C103—21no—
193C2×C8×C103—21no—
194C2×C8×C103—21no—
195C2×C8×C103—21no—
196C2×C8×C103—21no—
197C2×C8×C103—21no—
198C2×C8×C103—21no—
199C2×C8×C103C2×D411yescharacteristic
200C2×C8×C103C2×D411yescharacteristic
201C2×C8×C103C2×D411yescharacteristic
202C2×C8×C103C2×D411yescharacteristic
203C4⋊C4×C103—21no—
204C4⋊C4×C103—21no—
205C4⋊C4×C103—21no—
206C4⋊C4×C103—21no—
207C4⋊C4×C103—41no—
208C4⋊C4×C103—44no—
209C4⋊C4×C103—41no—
210C4⋊C4×C103—41no—
211C4⋊C4×C103—41no—
212C4⋊C4×C103—41no—
213C4⋊C4×C103—41no—
214C4⋊C4×C103—41no—
215C4⋊C4×C103—41no—
216C4⋊C4×C103—82no—
217C4⋊C4×C103C2×D411yescharacteristic
218C4⋊C4×C103C2×D411yescharacteristic
219C4⋊C4×C103C2×D411yescharacteristic
220C4⋊C4×C103C2×D411yescharacteristic
221C4⋊C4×C103C2×D411yescharacteristic
222C4⋊C4×C103C2×D411yescharacteristic
223C22⋊C4×C103—21no—
224C22⋊C4×C103—21no—
225C22⋊C4×C103—21no—
226C22⋊C4×C103—41no—
227C22⋊C4×C103—41no—
228C22⋊C4×C103—41no—
229C42×C103—21no—
230C42×C103—21no—
231C42×C103—21no—
232C42×C103—21no—
233C42×C103—41no—
234C42×C103—41no—
235C42×C103—41no—
236C42×C103#4112yes—
237C23×C103—21no—
238C23×C103H(5,𝔽2)11yescharacteristic
239Q8×C103—22no—
240Q8×C103—21no—
241Q8×C103—21no—
242Q8×C103—22no—
243Q8×C103—41no—
244Q8×C103—41no—
245Q8×C103—41no—
246Q8×C103—41no—
247Q8×C103—41no—
248Q8×C103—41no—
249Q8×C103—161no—
250D4×C103—21no—
251D4×C103—21no—
252D4×C103—41no—
253D4×C103—41no—
254C2×C4×C103—22no—
255C2×C4×C103—22no—
256C2×C4×C103—22no—
257C2×C4×C103—21no—
258C2×C4×C103—21no—
259C2×C4×C103—21no—
260C2×C4×C103—21no—
261C2×C4×C103—21no—
262C2×C4×C103—21no—
263C2×C4×C103—21no—
264C2×C4×C103—22no—
265C2×C4×C103—41no—
266C2×C4×C103—41no—
267C2×C4×C103—41no—
268C2×C4×C103—41no—
269C2×C4×C103—41no—
270C2×C4×C103—41no—
271C2×C4×C103—41no—
272C2×C4×C103—41no—
273C2×C4×C103—41no—
274C2×C4×C103—81no—
275C2×C4×C103—81no—
276C2×C4×C103—161no—
277C2×C4×C103C22×D411yescharacteristic
278C2×C4×C103C22×D411yescharacteristic
279C2×C4×C103C2×#4111yescharacteristic
280C2×C4×C103C2×#4111yescharacteristic
281C2×C4×C103C2×#4111yescharacteristic
282C2×C4×C1032−1+411yescharacteristic
283C8×C103—22no—
284C8×C103—21no—
285C8×C103—21no—
286C8×C103—21no—
287C8×C103—21no—
288C8×C103—41no—
289C8×C103—41no—
290C8×C103—41no—
291C22×C103—21no—
292C22×C103—21no—
293C22×C103—41no—
294C22×C103—41no—
295C22×C103—41no—
296C22×C103#54211yescharacteristic
297C22×C103D4211yescharacteristic
298C22×C103#55111yescharacteristic
299C4×C103—24no—
300C4×C103—41no—
301C4×C103—42no—
302C4×C103—41no—
303C4×C103—41no—
304C4×C103—41no—
305C4×C103—41no—
306C4×C103—41no—
307C4×C103—41no—
308C4×C103—81no—
309C4×C103—81no—
310C4×C103—81no—
311C4×C103#52511yescharacteristic
312C4×C103#53211yescharacteristic
313C4×C103#54711yescharacteristic
314C4×C103#54811yescharacteristic
315#26849C10311yesmaximal, characteristic, direct product factor, Sylow
316C2×C103—21no—
317C2×C103—21no—
318C2×C103—81no—
319C2×C103#246111yescharacteristic
320C2×C103#329111yescharacteristic
321C2×C103#329311yescharacteristic
322#3137C2×C10311yescharacteristic
323#3097C2×C10311yescharacteristic
324#3082C2×C10311yescharacteristic, complemented
325#2947C2×C10311yescharacteristic
326#2064C2×C10311yescharacteristic, complemented
327#2060C2×C10311yescharacteristic, complemented
328#2052C2×C10311yescharacteristic
329#2005C2×C10311yescharacteristic
330#1956C2×C10311yescharacteristic, complemented
331#1937C2×C10311yescharacteristic
332#1930C2×C10311yescharacteristic, complemented
333#1930C2×C10311yescharacteristic, complemented
334#1886C2×C10311yescharacteristic, complemented
335#1859C2×C10311yescharacteristic
336#1772C2×C10311yescharacteristic, complemented
337C103#2684911yescharacteristic, direct product factor, Sylow
338C2×#137C22×C10311yescharacteristic
339#544C22×C10311yescharacteristic
340#536C22×C10311yescharacteristic
341C2×C4⋊Q8C22×C10311yescharacteristic
342#520C22×C10311yescharacteristic
343#519C22×C10311yescharacteristic
344#491—21no—
345#489—21no—
346#488—21no—
347#487—21no—
348#485—21no—
349#485—21no—
350#484—21no—
351#483—21no—
352#479—21no—
353#479—21no—
354#477—21no—
355#475—21no—
356#441—21no—
357#440—21no—
358C4×Q16—21no—
359C4×SD16—21no—
360C2×#108C22×C10311yescharacteristic
361#428C22×C10311yescharacteristic
362#428C22×C10311yescharacteristic
363#428C22×C10311yescharacteristic
364#427C22×C10311yescharacteristic
365#424C22×C10311yescharacteristic
366C2×#104C22×C10311yescharacteristic
367#419C22×C10311yescharacteristic
368#419C22×C10311yescharacteristic
369#419C22×C10311yescharacteristic
370#417C22×C10311yescharacteristic
371#416C22×C10311yescharacteristic
372C2×#103C22×C10311yescharacteristic
373C2×#103C22×C10311yescharacteristic
374C2×#103C22×C10311yescharacteristic
375C2×#103C22×C10311yescharacteristic
376C2×#101C22×C10311yescharacteristic
377C2×#101C22×C10311yescharacteristic
378#408C22×C10311yescharacteristic
379#405C22×C10311yescharacteristic
380#405C22×C10311yescharacteristic
381C2×C4×C8C22×C10311yescharacteristic
382#384C22×C10311yescharacteristic
383#343C22×C10311yescharacteristic
384#343C22×C10311yescharacteristic
385#341C22×C10311yescharacteristic
386#339C22×C10311yescharacteristic
387#339C22×C10311yescharacteristic
388#339C22×C10311yescharacteristic
389C2×#41C23×C10311yescharacteristic
390C22×Q8C23×C10311yescharacteristic
391C22×Q8C23×C10311yescharacteristic
392#137—22no—
393#137—22no—
394C2×Q16—21no—
395C2×SD16—21no—
396C2×M16C23×C10311yescharacteristic
397C2×M16C23×C10311yescharacteristic
398C2×M16C23×C10311yescharacteristic
399C2×M16C23×C10311yescharacteristic
400C22×C8C23×C10311yescharacteristic
401C22×C8C23×C10311yescharacteristic
402C4⋊Q8—21no—
403C4⋊Q8—21no—
404C4⋊Q8—21no—
405C4⋊Q8—22no—
406C4⋊Q8—22no—
407#125—21no—
408#125—21no—
409#124—21no—
410#123—41no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—41no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×D4—21no—
420C4×D4—41no—
421#117—21no—
422#117—41no—
423#117C23×C10311yescharacteristic
424#117C23×C10311yescharacteristic
425#117C23×C10311yescharacteristic
426C2×C4⋊C4—21no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4C23×C10311yescharacteristic
430C2×C4⋊C4C23×C10311yescharacteristic
431C2×C42C23×C10311yescharacteristic
432#108—22no—
433#107—21no—
434#107—21no—
435#107—21no—
436#107D4×C10311yescharacteristic
437#107D4×C10311yescharacteristic
438#106—21no—
439#106—21no—
440#106—21no—
441#106D4×C10311yescharacteristic
442#106D4×C10311yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445#104—22no—
446#103—21no—
447#103—21no—
448#103—21no—
449#103—21no—
450#103—21no—
451#103—21no—
452#103—21no—
453#103—21no—
454#103—21no—
455#103—21no—
456#103—21no—
457#103—21no—
458#103—21no—
459#103—21no—
460#103—21no—
461#103D4×C10311yescharacteristic
462#103D4×C10311yescharacteristic
463#102—21no—
464#102D4×C10311yescharacteristic
465#102D4×C10311yescharacteristic
466#101—22no—
467#101—22no—
468C22⋊C8—21no—
469C22⋊C8—21no—
470#97—21no—
471#97—21no—
472C4×C8—21no—
473C4×C8—21no—
474C4×C8—22no—
475#41—21no—
476#41—21no—
477#41—21no—
478#41—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—41no—
491C2×Q8C2×D4×C10311yescharacteristic
492C2×Q8#41×C10312yes—
493C2×D4—21no—
494C2×D4C2×D4×C10311yescharacteristic
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—41no—
502C22×C4C24×C10311yescharacteristic
503Q16—24no—
504SD16—24no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16—21no—
509M16—21no—
510M16—21no—
511M16—21no—
512M16#41×C10312yes—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8C2×D4×C10311yescharacteristic
522C2×C8C2×D4×C10311yescharacteristic
523C2×C8C2×D4×C10311yescharacteristic
524C2×C8C2×D4×C10311yescharacteristic
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—44no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—82no—
539C4⋊C4C2×D4×C10311yescharacteristic
540C4⋊C4C2×D4×C10311yescharacteristic
541C4⋊C4C2×D4×C10311yescharacteristic
542C4⋊C4C2×D4×C10311yescharacteristic
543C4⋊C4C2×D4×C10311yescharacteristic
544C4⋊C4C2×D4×C10311yescharacteristic
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42#41×C10312yes—
559C23—21no—
560C23H(5,𝔽2)×C10311yescharacteristic
561Q8—22no—
562Q8—21no—
563Q8—21no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570Q8—41no—
571Q8—161no—
572D4—21no—
573D4—21no—
574D4—41no—
575D4—41no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—161no—
599C2×C4C22×D4×C10311yescharacteristic
600C2×C4C22×D4×C10311yescharacteristic
601C2×C4C2×#41×C10311yescharacteristic
602C2×C4C2×#41×C10311yescharacteristic
603C2×C4C2×#41×C10311yescharacteristic
604C2×C42−1+4×C10311yescharacteristic
605C8—22no—
606C8—21no—
607C8—21no—
608C8—21no—
609C8—21no—
610C8—41no—
611C8—41no—
612C8—41no—
613C22—21no—
614C22—21no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22#542×C10311yescharacteristic
619C22D42×C10311yescharacteristic
620C22#551×C10311yescharacteristic
621C4—24no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4#525×C10311yescharacteristic
634C4#532×C10311yescharacteristic
635C4#547×C10311yescharacteristic
636C4#548×C10311yescharacteristic
637C2—21no—
638C2—21no—
639C2—81no—
640C2C103×#246111yescharacteristic
641C2C103×#329111yescharacteristic
642C2C103×#329311yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#41×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#3082C2semidirect
5. C103×#2064C2semidirect
6. C103×#2060C2semidirect
9. C103×#1956C2semidirect
11. C103×#1930C2semidirect
12. C103×#1930C2semidirect
13. C103×#1886C2semidirect
15. C103×#1772C2semidirect
315. #26849C103direct (N × H)
324. #3082C2×C103semidirect
326. #2064C2×C103semidirect
327. #2060C2×C103semidirect
330. #1956C2×C103semidirect
332. #1930C2×C103semidirect
333. #1930C2×C103semidirect
334. #1886C2×C103semidirect
336. #1772C2×C103semidirect
337. C103#26849direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31372
C103×#30972
C103×#30822
C103×#29472
C103×#20642
C103×#20602
C103×#20522
C103×#20052
C103×#19562
C103×#19372
C103×#19302
C103×#18862
C103×#18592
C103×#17722
#26849103