Finite Group Databasebeta

← C103×#19982 #39925257

Subgroups — C103×#19982 #39925257

Order 26368.

654 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3392C211yesmaximal, characteristic, complemented
2C103×#3381C211yesmaximal, characteristic, complemented
3C103×#3335C211yesmaximal, characteristic, complemented
4C103×#3284C211yesmaximal, characteristic
5C103×#1705C211yesmaximal, characteristic, complemented
6C103×#1672C211yesmaximal, characteristic, complemented
7C103×#1671C211yesmaximal, characteristic, complemented
8C103×#1666C211yesmaximal, characteristic, complemented
9C103×#1665C211yesmaximal, characteristic, complemented
10C103×#1654C211yesmaximal, characteristic, complemented
11C103×#1653C211yesmaximal, characteristic, complemented
12C103×#1631C211yesmaximal, characteristic, complemented
13C103×#1622C211yesmaximal, characteristic, complemented
14C8×SD16×C103C211yesmaximal, characteristic, complemented
15C8×SD16×C103C211yesmaximal, characteristic, complemented
16C2×#135×C103—21no—
17#557×C103C2211yescharacteristic
18#554×C103C2211yescharacteristic
19#550×C103C2211yescharacteristic
20#547×C103C2211yescharacteristic
21#499×C103—21no—
22#498×C103C2211yescharacteristic
23#498×C103C2211yescharacteristic
24#498×C103C2211yescharacteristic
25#492×C103—21no—
26#492×C103C2211yescharacteristic
27#492×C103C2211yescharacteristic
28#492×C103C2211yescharacteristic
29#483×C103—21no—
30#481×C103—21no—
31#479×C103—21no—
32#478×C103—21no—
33#477×C103C2211yescharacteristic
34#476×C103C2211yescharacteristic
35#475×C103C2211yescharacteristic
36#474×C103C2211yescharacteristic
37#465×C103—21no—
38#465×C103—21no—
39#462×C103C2211yescharacteristic
40#461×C103—21no—
41#461×C103C2211yescharacteristic
42#460×C103—21no—
43#460×C103C2211yescharacteristic
44#459×C103C2211yescharacteristic
45#452×C103—21no—
46#449×C103—21no—
47C8×Q8×C103C2211yescharacteristic
48C8×Q8×C103C2211yescharacteristic
49C4×SD16×C103—21no—
50C4×SD16×C103—21no—
51C4×SD16×C103C2211yescharacteristic
52C4×SD16×C103C2211yescharacteristic
53C8×D4×C103C2211yescharacteristic
54C8×D4×C103C2211yescharacteristic
55C2×#106×C103—21no—
56#334×C103C2211yescharacteristic
57#334×C103C2211yescharacteristic
58#333×C103C2211yescharacteristic
59#332×C103C2211yescharacteristic
60#332×C103C2211yescharacteristic
61#331×C103C2211yescharacteristic
62Q8⋊C8×C103C2211yescharacteristic
63Q8⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66C82×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69#135×C103—44no—
70C2×Q16×C103—21no—
71C2×SD16×C103—21no—
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103—21no—
77C2×SD16×C103—41no—
78C2×SD16×C103D411yescharacteristic
79C2×SD16×C103D411yescharacteristic
80C2×D8×C103—21no—
81C22×C8×C103—21no—
82C22×C8×C103—21no—
83C4⋊Q8×C103—21no—
84C4⋊Q8×C103C2311yescharacteristic
85C4⋊Q8×C103C2311yescharacteristic
86C4⋊Q8×C103C2311yescharacteristic
87#127×C103—21no—
88#127×C103C2311yescharacteristic
89#125×C103—21no—
90#125×C103—21no—
91#125×C103—41no—
92#123×C103—41no—
93C22⋊Q8×C103—21no—
94C22⋊Q8×C103—21no—
95C22⋊Q8×C103—41no—
96#121×C103—21no—
97#121×C103—21no—
98#121×C103—41no—
99C4×Q8×C103—21no—
100C4×Q8×C103—21no—
101C4×Q8×C103C2311yescharacteristic
102C4×Q8×C103C2311yescharacteristic
103C4×D4×C103—21no—
104C4×D4×C103—21no—
105C4×D4×C103C2311yescharacteristic
106C4×D4×C103C2311yescharacteristic
107C2×C4⋊C4×C103—21no—
108C2×C4⋊C4×C103—21no—
109#107×C103—21no—
110#107×C103—21no—
111#106×C103—21no—
112#106×C103—21no—
113#106×C103—21no—
114#106×C103—21no—
115#106×C103—21no—
116#106×C103—21no—
117#106×C103—41no—
118#106×C103D411yescharacteristic
119#106×C103D411yescharacteristic
120C4⋊C8×C103—21no—
121C4⋊C8×C103—21no—
122C4⋊C8×C103C2311yescharacteristic
123C4⋊C8×C103C2311yescharacteristic
124C4⋊C8×C103C2311yescharacteristic
125C4⋊C8×C103C2311yescharacteristic
126#103×C103—21no—
127#103×C103—21no—
128#103×C103—21no—
129#103×C103—21no—
130#103×C103D411yescharacteristic
131#103×C103D411yescharacteristic
132#102×C103—21no—
133#102×C103—21no—
134#102×C103—21no—
135#102×C103—21no—
136#102×C103D411yescharacteristic
137#102×C103D411yescharacteristic
138C22⋊C8×C103—21no—
139C22⋊C8×C103—21no—
140C4×C8×C103—21no—
141C4×C8×C103—21no—
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144C4×C8×C103C2311yescharacteristic
145#41×C103—42no—
146#41×C103—42no—
147#41×C103—81no—
148#41×C103—81no—
149C2×Q8×C103—21no—
150C2×Q8×C103—21no—
151C2×Q8×C103—21no—
152C2×Q8×C103C2×D411yescharacteristic
153C2×Q8×C103C2×D411yescharacteristic
154C2×D4×C103—21no—
155C2×D4×C103—21no—
156C2×D4×C103—21no—
157C2×D4×C103—41no—
158C2×D4×C103—41no—
159C2×D4×C103—41no—
160C2×D4×C103C2×D411yescharacteristic
161C2×D4×C103C2×D411yescharacteristic
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—41no—
165C22×C4×C103—41no—
166C22×C4×C103—41no—
167Q16×C103—42no—
168SD16×C103—22no—
169SD16×C103—42no—
170SD16×C103—42no—
171SD16×C103—81no—
172SD16×C103—81no—
173SD16×C103—82no—
174SD16×C103—81no—
175SD16×C103—81no—
176SD16×C103SD1614yescomplemented
177D8×C103—42no—
178C2×C8×C103—21no—
179C2×C8×C103—21no—
180C2×C8×C103—21no—
181C2×C8×C103—21no—
182C2×C8×C103—21no—
183C2×C8×C103—42no—
184C2×C8×C103—42no—
185C2×C8×C103C2×D411yescharacteristic
186C2×C8×C103C2×D411yescharacteristic
187C2×C8×C103C2×D411yescharacteristic
188C2×C8×C103C2×D411yescharacteristic
189C4⋊C4×C103—21no—
190C4⋊C4×C103—21no—
191C4⋊C4×C103—21no—
192C4⋊C4×C103—21no—
193C4⋊C4×C103—21no—
194C4⋊C4×C103—21no—
195C4⋊C4×C103—21no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—41no—
198C4⋊C4×C103—41no—
199C4⋊C4×C103—41no—
200C4⋊C4×C103—41no—
201C4⋊C4×C103—41no—
202C4⋊C4×C103—41no—
203C4⋊C4×C103C2×D411yescharacteristic
204C4⋊C4×C103C2×D411yescharacteristic
205C4⋊C4×C103C2×D411yescharacteristic
206C4⋊C4×C103C2×D411yescharacteristic
207C22⋊C4×C103—21no—
208C22⋊C4×C103—21no—
209C22⋊C4×C103—41no—
210C22⋊C4×C103—41no—
211C22⋊C4×C103—41no—
212C42×C103—21no—
213C42×C103—21no—
214C42×C103—41no—
215C42×C103C2411yescharacteristic
216C23×C103—21no—
217C23×C103—21no—
218C23×C103—41no—
219Q8×C103—21no—
220Q8×C103—21no—
221Q8×C103—21no—
222Q8×C103—41no—
223Q8×C103—41no—
224Q8×C103—41no—
225Q8×C103—41no—
226Q8×C103—81no—
227Q8×C103C2×SD1612yes—
228D4×C103—21no—
229D4×C103—21no—
230D4×C103—21no—
231D4×C103—41no—
232D4×C103—41no—
233D4×C103—41no—
234D4×C103—41no—
235D4×C103—82no—
236D4×C103—81no—
237D4×C103—82no—
238D4×C103—161no—
239D4×C103C2×SD1612yes—
240C2×C4×C103—21no—
241C2×C4×C103—21no—
242C2×C4×C103—21no—
243C2×C4×C103—21no—
244C2×C4×C103—21no—
245C2×C4×C103—21no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—82no—
254C2×C4×C103—82no—
255C2×C4×C103—161no—
256C2×C4×C103C22×D411yescharacteristic
257C2×C4×C103C22×D411yescharacteristic
258C2×C4×C103H(5,𝔽2)11yescharacteristic
259C8×C103—22no—
260C8×C103—21no—
261C8×C103—21no—
262C8×C103—41no—
263C8×C103—41no—
264C8×C103—41no—
265C8×C103—41no—
266C8×C103C2×SD1612yes—
267C8×C103#13512yescomplemented
268C22×C103—22no—
269C22×C103—41no—
270C22×C103—41no—
271C22×C103—41no—
272C22×C103—41no—
273C22×C103—41no—
274C22×C103—81no—
275C22×C103—81no—
276C22×C103—81no—
277C22×C103D4211yescharacteristic
278C4×C103—22no—
279C4×C103—21no—
280C4×C103—41no—
281C4×C103—41no—
282C4×C103—41no—
283C4×C103—41no—
284C4×C103—41no—
285C4×C103—81no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103C22×SD1611yescharacteristic
289C4×C103C2×#13511yescharacteristic
290C4×C103#57711yescharacteristic
291C4×C103#57711yescharacteristic
292#19982C10311yesmaximal, characteristic, direct product factor, Sylow
293C2×C103—42no—
294C2×C103—81no—
295C2×C103—161no—
296C2×C103D4×SD1611yescharacteristic
297C2×C103#328411yescharacteristic
298C2×C103#329111yescharacteristic
299#3392C2×C10311yescharacteristic, complemented
300#3381C2×C10311yescharacteristic, complemented
301#3335C2×C10311yescharacteristic, complemented
302#3284C2×C10311yescharacteristic
303#1705C2×C10311yescharacteristic, complemented
304#1672C2×C10311yescharacteristic, complemented
305#1671C2×C10311yescharacteristic, complemented
306#1666C2×C10311yescharacteristic, complemented
307#1665C2×C10311yescharacteristic, complemented
308#1654C2×C10311yescharacteristic, complemented
309#1653C2×C10311yescharacteristic, complemented
310#1631C2×C10311yescharacteristic, complemented
311#1622C2×C10311yescharacteristic, complemented
312C8×SD16C2×C10311yescharacteristic, complemented
313C8×SD16C2×C10311yescharacteristic, complemented
314C103#1998211yescharacteristic, direct product factor, Sylow
315C2×#135—21no—
316#557C22×C10311yescharacteristic
317#554C22×C10311yescharacteristic
318#550C22×C10311yescharacteristic
319#547C22×C10311yescharacteristic
320#499—21no—
321#498C22×C10311yescharacteristic
322#498C22×C10311yescharacteristic
323#498C22×C10311yescharacteristic
324#492—21no—
325#492C22×C10311yescharacteristic
326#492C22×C10311yescharacteristic
327#492C22×C10311yescharacteristic
328#483—21no—
329#481—21no—
330#479—21no—
331#478—21no—
332#477C22×C10311yescharacteristic
333#476C22×C10311yescharacteristic
334#475C22×C10311yescharacteristic
335#474C22×C10311yescharacteristic
336#465—21no—
337#465—21no—
338#462C22×C10311yescharacteristic
339#461—21no—
340#461C22×C10311yescharacteristic
341#460—21no—
342#460C22×C10311yescharacteristic
343#459C22×C10311yescharacteristic
344#452—21no—
345#449—21no—
346C8×Q8C22×C10311yescharacteristic
347C8×Q8C22×C10311yescharacteristic
348C4×SD16—21no—
349C4×SD16—21no—
350C4×SD16C22×C10311yescharacteristic
351C4×SD16C22×C10311yescharacteristic
352C8×D4C22×C10311yescharacteristic
353C8×D4C22×C10311yescharacteristic
354C2×#106—21no—
355#334C22×C10311yescharacteristic
356#334C22×C10311yescharacteristic
357#333C22×C10311yescharacteristic
358#332C22×C10311yescharacteristic
359#332C22×C10311yescharacteristic
360#331C22×C10311yescharacteristic
361Q8⋊C8C22×C10311yescharacteristic
362Q8⋊C8C22×C10311yescharacteristic
363D4⋊C8C22×C10311yescharacteristic
364D4⋊C8C22×C10311yescharacteristic
365C82C22×C10311yescharacteristic
366C2×#41—21no—
367C2×#41—21no—
368#135—44no—
369C2×Q16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—41no—
377C2×SD16D4×C10311yescharacteristic
378C2×SD16D4×C10311yescharacteristic
379C2×D8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C4⋊Q8—21no—
383C4⋊Q8C23×C10311yescharacteristic
384C4⋊Q8C23×C10311yescharacteristic
385C4⋊Q8C23×C10311yescharacteristic
386#127—21no—
387#127C23×C10311yescharacteristic
388#125—21no—
389#125—21no—
390#125—41no—
391#123—41no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—41no—
395#121—21no—
396#121—21no—
397#121—41no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8C23×C10311yescharacteristic
401C4×Q8C23×C10311yescharacteristic
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C23×C10311yescharacteristic
405C4×D4C23×C10311yescharacteristic
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408#107—21no—
409#107—21no—
410#106—21no—
411#106—21no—
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416#106—41no—
417#106D4×C10311yescharacteristic
418#106D4×C10311yescharacteristic
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8C23×C10311yescharacteristic
422C4⋊C8C23×C10311yescharacteristic
423C4⋊C8C23×C10311yescharacteristic
424C4⋊C8C23×C10311yescharacteristic
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103D4×C10311yescharacteristic
430#103D4×C10311yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102D4×C10311yescharacteristic
436#102D4×C10311yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C4×C8—21no—
440C4×C8—21no—
441C4×C8C23×C10311yescharacteristic
442C4×C8C23×C10311yescharacteristic
443C4×C8C23×C10311yescharacteristic
444#41—42no—
445#41—42no—
446#41—81no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×D4×C10311yescharacteristic
452C2×Q8C2×D4×C10311yescharacteristic
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C2×D4×C10311yescharacteristic
460C2×D4C2×D4×C10311yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466Q16—42no—
467SD16—22no—
468SD16—42no—
469SD16—42no—
470SD16—81no—
471SD16—81no—
472SD16—82no—
473SD16—81no—
474SD16—81no—
475SD16SD16×C10314yescomplemented
476D8—42no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
483C2×C8—42no—
484C2×C8C2×D4×C10311yescharacteristic
485C2×C8C2×D4×C10311yescharacteristic
486C2×C8C2×D4×C10311yescharacteristic
487C2×C8C2×D4×C10311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C10311yescharacteristic
503C4⋊C4C2×D4×C10311yescharacteristic
504C4⋊C4C2×D4×C10311yescharacteristic
505C4⋊C4C2×D4×C10311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42C24×C10311yescharacteristic
515C23—21no—
516C23—21no—
517C23—41no—
518Q8—21no—
519Q8—21no—
520Q8—21no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—81no—
526Q8C2×SD16×C10312yes—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—82no—
535D4—81no—
536D4—82no—
537D4—161no—
538D4C2×SD16×C10312yes—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4—161no—
555C2×C4C22×D4×C10311yescharacteristic
556C2×C4C22×D4×C10311yescharacteristic
557C2×C4H(5,𝔽2)×C10311yescharacteristic
558C8—22no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8C2×SD16×C10312yes—
566C8#135×C10312yescomplemented
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C10311yescharacteristic
577C4—22no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C22×SD16×C10311yescharacteristic
588C4C2×#135×C10311yescharacteristic
589C4#577×C10311yescharacteristic
590C4#577×C10311yescharacteristic
591C2—42no—
592C2—81no—
593C2—161no—
594C2D4×SD16×C10311yescharacteristic
595C2C103×#328411yescharacteristic
596C2C103×#329111yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3284C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3392C2semidirect
2. C103×#3381C2semidirect
3. C103×#3335C2semidirect
5. C103×#1705C2semidirect
6. C103×#1672C2semidirect
7. C103×#1671C2semidirect
8. C103×#1666C2semidirect
9. C103×#1665C2semidirect
10. C103×#1654C2semidirect
11. C103×#1653C2semidirect
12. C103×#1631C2semidirect
13. C103×#1622C2semidirect
14. C8×SD16×C103C2semidirect
15. C8×SD16×C103C2semidirect
176. SD16×C103SD16semidirect
267. C8×C103#135semidirect
292. #19982C103direct (N × H)
299. #3392C2×C103semidirect
300. #3381C2×C103semidirect
301. #3335C2×C103semidirect
303. #1705C2×C103semidirect
304. #1672C2×C103semidirect
305. #1671C2×C103semidirect
306. #1666C2×C103semidirect
307. #1665C2×C103semidirect
308. #1654C2×C103semidirect
309. #1653C2×C103semidirect
310. #1631C2×C103semidirect
311. #1622C2×C103semidirect
312. C8×SD16C2×C103semidirect
313. C8×SD16C2×C103semidirect
314. C103#19982direct (N × H)
475. SD16SD16×C103semidirect
566. C8#135×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33922
C103×#33812
C103×#33352
C103×#32842
C103×#17052
C103×#16722
C103×#16712
C103×#16662
C103×#16652
C103×#16542
C103×#16532
C103×#16312
C103×#16222
C8×SD16×C1032
#19982103