Finite Group Databasebeta

← C103×#19767 #39925042

Subgroups — C103×#19767 #39925042

Order 26368.

658 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3392C211yesmaximal, characteristic, complemented
2C103×#3386C211yesmaximal, characteristic, complemented
3C103×#3298C211yesmaximal, characteristic, complemented
4C103×#3284C211yesmaximal, characteristic
5C103×#1714C211yesmaximal, characteristic, complemented
6C103×#1686C211yesmaximal, characteristic, complemented
7C103×#1680C211yesmaximal, characteristic, complemented
8C103×#1673C211yesmaximal, characteristic, complemented
9C103×#1665C211yesmaximal, characteristic, complemented
10C103×#1654C211yesmaximal, characteristic, complemented
11C103×#1653C211yesmaximal, characteristic, complemented
12C103×#1642C211yesmaximal, characteristic, complemented
13C103×#1627C211yesmaximal, characteristic, complemented
14C103×#1582C211yesmaximal, characteristic, complemented
15C103×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C103—21no—
17#557×C103C2211yescharacteristic
18#550×C103C2211yescharacteristic
19D4×Q8×C103C2211yescharacteristic
20#547×C103C2211yescharacteristic
21#501×C103—21no—
22#500×C103C2211yescharacteristic
23#498×C103C2211yescharacteristic
24#492×C103—21no—
25#492×C103C2211yescharacteristic
26#492×C103C2211yescharacteristic
27#487×C103C2211yescharacteristic
28#486×C103C2211yescharacteristic
29#483×C103—21no—
30#478×C103—21no—
31#477×C103—21no—
32#475×C103C2211yescharacteristic
33#475×C103C2211yescharacteristic
34#474×C103C2211yescharacteristic
35#465×C103—21no—
36#465×C103—21no—
37#462×C103C2211yescharacteristic
38#461×C103—21no—
39#461×C103C2211yescharacteristic
40#461×C103C2211yescharacteristic
41#460×C103—21no—
42#460×C103C2211yescharacteristic
43#459×C103C2211yescharacteristic
44#452×C103—21no—
45#449×C103—21no—
46#448×C103—21no—
47#446×C103C2211yescharacteristic
48C8×Q8×C103C2211yescharacteristic
49#440×C103—21no—
50C4×SD16×C103—21no—
51C4×SD16×C103C2211yescharacteristic
52C4×SD16×C103C2211yescharacteristic
53C8×D4×C103C2211yescharacteristic
54C8×D4×C103C2211yescharacteristic
55C2×#103×C103—21no—
56#335×C103C2211yescharacteristic
57#334×C103C2211yescharacteristic
58#332×C103C2211yescharacteristic
59#332×C103C2211yescharacteristic
60#332×C103C2211yescharacteristic
61#331×C103C2211yescharacteristic
62Q8⋊C8×C103C2211yescharacteristic
63Q8⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66#322×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C22×Q8×C103—21no—
70#135×C103—44no—
71C2×Q16×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—21no—
78C2×SD16×C103—21no—
79C2×SD16×C103D411yescharacteristic
80C2×SD16×C103D411yescharacteristic
81C2×D8×C103—21no—
82C22×C8×C103—21no—
83C22×C8×C103—21no—
84C4⋊Q8×C103—21no—
85C4⋊Q8×C103—21no—
86C4⋊Q8×C103C2311yescharacteristic
87C4⋊Q8×C103C2311yescharacteristic
88C4⋊Q8×C103C2311yescharacteristic
89#127×C103—21no—
90#127×C103C2311yescharacteristic
91#125×C103—21no—
92#125×C103—41no—
93#123×C103—41no—
94C22⋊Q8×C103—21no—
95C22⋊Q8×C103—21no—
96C22⋊Q8×C103—41no—
97#121×C103—21no—
98#121×C103—21no—
99#121×C103—41no—
100C4×Q8×C103—21no—
101C4×Q8×C103—21no—
102C4×Q8×C103C2311yescharacteristic
103C4×Q8×C103C2311yescharacteristic
104C4×D4×C103—21no—
105C4×D4×C103—21no—
106C4×D4×C103C2311yescharacteristic
107C4×D4×C103C2311yescharacteristic
108C2×C4⋊C4×C103—21no—
109#107×C103—21no—
110#107×C103—21no—
111#107×C103—21no—
112#106×C103—21no—
113#106×C103—21no—
114#106×C103—41no—
115#106×C103D411yescharacteristic
116#106×C103D411yescharacteristic
117C4⋊C8×C103—21no—
118C4⋊C8×C103—21no—
119C4⋊C8×C103C2311yescharacteristic
120C4⋊C8×C103C2311yescharacteristic
121C4⋊C8×C103C2311yescharacteristic
122C4⋊C8×C103C2311yescharacteristic
123#103×C103—21no—
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×C103D411yescharacteristic
131#103×C103D411yescharacteristic
132#102×C103—21no—
133#102×C103—21no—
134#102×C103—21no—
135#102×C103—41no—
136#102×C103D411yescharacteristic
137#102×C103D411yescharacteristic
138C22⋊C8×C103—21no—
139C22⋊C8×C103—21no—
140#97×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×C103—41no—
153C2×Q8×C103—42no—
154C2×Q8×C103—81no—
155C2×Q8×C103C2×D411yescharacteristic
156C2×Q8×C103C2×D411yescharacteristic
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—21no—
160C2×D4×C103—41no—
161C2×D4×C103—41no—
162C2×D4×C103—41no—
163C2×D4×C103C2×D411yescharacteristic
164C2×D4×C103C2×D411yescharacteristic
165C22×C4×C103—21no—
166C22×C4×C103—21no—
167C22×C4×C103—41no—
168C22×C4×C103—41no—
169C22×C4×C103—41no—
170Q16×C103—42no—
171SD16×C103—41no—
172SD16×C103—42no—
173SD16×C103—42no—
174SD16×C103—81no—
175SD16×C103—81no—
176SD16×C103—81no—
177SD16×C103—81no—
178SD16×C103—81no—
179SD16×C103SD1614yescomplemented
180D8×C103—42no—
181C2×C8×C103—21no—
182C2×C8×C103—21no—
183C2×C8×C103—21no—
184C2×C8×C103—21no—
185C2×C8×C103—21no—
186C2×C8×C103—42no—
187C2×C8×C103—81no—
188C2×C8×C103C2×D411yescharacteristic
189C2×C8×C103C2×D411yescharacteristic
190C2×C8×C103C2×D411yescharacteristic
191C2×C8×C103C2×D411yescharacteristic
192C4⋊C4×C103—21no—
193C4⋊C4×C103—21no—
194C4⋊C4×C103—21no—
195C4⋊C4×C103—21no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—21no—
198C4⋊C4×C103—21no—
199C4⋊C4×C103—21no—
200C4⋊C4×C103—41no—
201C4⋊C4×C103—41no—
202C4⋊C4×C103—41no—
203C4⋊C4×C103—41no—
204C4⋊C4×C103—41no—
205C4⋊C4×C103C2×D411yescharacteristic
206C4⋊C4×C103C2×D411yescharacteristic
207C4⋊C4×C103C2×D411yescharacteristic
208C4⋊C4×C103C2×D411yescharacteristic
209C22⋊C4×C103—21no—
210C22⋊C4×C103—21no—
211C22⋊C4×C103—41no—
212C22⋊C4×C103—41no—
213C22⋊C4×C103—41no—
214C42×C103—21no—
215C42×C103—21no—
216C42×C103—41no—
217C42×C103C2411yescharacteristic
218C23×C103—21no—
219C23×C103—21no—
220C23×C103—41no—
221Q8×C103—21no—
222Q8×C103—21no—
223Q8×C103—21no—
224Q8×C103—41no—
225Q8×C103—41no—
226Q8×C103—41no—
227Q8×C103—41no—
228Q8×C103—41no—
229Q8×C103—41no—
230Q8×C103—82no—
231Q8×C103C2×SD1612yes—
232D4×C103—21no—
233D4×C103—21no—
234D4×C103—21no—
235D4×C103—41no—
236D4×C103—41no—
237D4×C103—41no—
238D4×C103—41no—
239D4×C103—82no—
240D4×C103—81no—
241D4×C103—82no—
242D4×C103—161no—
243D4×C103C2×SD1612yes—
244C2×C4×C103—21no—
245C2×C4×C103—21no—
246C2×C4×C103—21no—
247C2×C4×C103—21no—
248C2×C4×C103—21no—
249C2×C4×C103—21no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—41no—
254C2×C4×C103—41no—
255C2×C4×C103—41no—
256C2×C4×C103—41no—
257C2×C4×C103—82no—
258C2×C4×C103—82no—
259C2×C4×C103—82no—
260C2×C4×C103C22×D411yescharacteristic
261C2×C4×C103C22×D411yescharacteristic
262C2×C4×C103H(5,𝔽2)11yescharacteristic
263C8×C103—21no—
264C8×C103—21no—
265C8×C103—21no—
266C8×C103—41no—
267C8×C103—41no—
268C8×C103—41no—
269C8×C103—41no—
270C8×C103—41no—
271C8×C103C2×SD1612yes—
272C22×C103—22no—
273C22×C103—41no—
274C22×C103—41no—
275C22×C103—41no—
276C22×C103—41no—
277C22×C103—41no—
278C22×C103—81no—
279C22×C103—81no—
280C22×C103—81no—
281C22×C103D4211yescharacteristic
282C4×C103—22no—
283C4×C103—21no—
284C4×C103—41no—
285C4×C103—41no—
286C4×C103—41no—
287C4×C103—41no—
288C4×C103—41no—
289C4×C103—81no—
290C4×C103—81no—
291C4×C103—81no—
292C4×C103C22×SD1611yescharacteristic
293C4×C103#57511yescharacteristic
294C4×C103#57611yescharacteristic
295C4×C103#57711yescharacteristic
296#19767C10311yesmaximal, characteristic, direct product factor, Sylow
297C2×C103—42no—
298C2×C103—81no—
299C2×C103—161no—
300C2×C103#326811yescharacteristic
301C2×C103D4×SD1611yescharacteristic
302C2×C103#328911yescharacteristic
303#3392C2×C10311yescharacteristic, complemented
304#3386C2×C10311yescharacteristic, complemented
305#3298C2×C10311yescharacteristic, complemented
306#3284C2×C10311yescharacteristic
307#1714C2×C10311yescharacteristic, complemented
308#1686C2×C10311yescharacteristic, complemented
309#1680C2×C10311yescharacteristic, complemented
310#1673C2×C10311yescharacteristic, complemented
311#1665C2×C10311yescharacteristic, complemented
312#1654C2×C10311yescharacteristic, complemented
313#1653C2×C10311yescharacteristic, complemented
314#1642C2×C10311yescharacteristic, complemented
315#1627C2×C10311yescharacteristic, complemented
316#1582C2×C10311yescharacteristic, complemented
317SD16⋊C8C2×C10311yescharacteristic, complemented
318C103#1976711yescharacteristic, direct product factor, Sylow
319C2×#135—21no—
320#557C22×C10311yescharacteristic
321#550C22×C10311yescharacteristic
322D4×Q8C22×C10311yescharacteristic
323#547C22×C10311yescharacteristic
324#501—21no—
325#500C22×C10311yescharacteristic
326#498C22×C10311yescharacteristic
327#492—21no—
328#492C22×C10311yescharacteristic
329#492C22×C10311yescharacteristic
330#487C22×C10311yescharacteristic
331#486C22×C10311yescharacteristic
332#483—21no—
333#478—21no—
334#477—21no—
335#475C22×C10311yescharacteristic
336#475C22×C10311yescharacteristic
337#474C22×C10311yescharacteristic
338#465—21no—
339#465—21no—
340#462C22×C10311yescharacteristic
341#461—21no—
342#461C22×C10311yescharacteristic
343#461C22×C10311yescharacteristic
344#460—21no—
345#460C22×C10311yescharacteristic
346#459C22×C10311yescharacteristic
347#452—21no—
348#449—21no—
349#448—21no—
350#446C22×C10311yescharacteristic
351C8×Q8C22×C10311yescharacteristic
352#440—21no—
353C4×SD16—21no—
354C4×SD16C22×C10311yescharacteristic
355C4×SD16C22×C10311yescharacteristic
356C8×D4C22×C10311yescharacteristic
357C8×D4C22×C10311yescharacteristic
358C2×#103—21no—
359#335C22×C10311yescharacteristic
360#334C22×C10311yescharacteristic
361#332C22×C10311yescharacteristic
362#332C22×C10311yescharacteristic
363#332C22×C10311yescharacteristic
364#331C22×C10311yescharacteristic
365Q8⋊C8C22×C10311yescharacteristic
366Q8⋊C8C22×C10311yescharacteristic
367D4⋊C8C22×C10311yescharacteristic
368D4⋊C8C22×C10311yescharacteristic
369#322C22×C10311yescharacteristic
370C2×#41—21no—
371C2×#41—21no—
372C22×Q8—21no—
373#135—44no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16D4×C10311yescharacteristic
383C2×SD16D4×C10311yescharacteristic
384C2×D8—21no—
385C22×C8—21no—
386C22×C8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8C23×C10311yescharacteristic
390C4⋊Q8C23×C10311yescharacteristic
391C4⋊Q8C23×C10311yescharacteristic
392#127—21no—
393#127C23×C10311yescharacteristic
394#125—21no—
395#125—41no—
396#123—41no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—41no—
400#121—21no—
401#121—21no—
402#121—41no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8C23×C10311yescharacteristic
406C4×Q8C23×C10311yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4C23×C10311yescharacteristic
410C4×D4C23×C10311yescharacteristic
411C2×C4⋊C4—21no—
412#107—21no—
413#107—21no—
414#107—21no—
415#106—21no—
416#106—21no—
417#106—41no—
418#106D4×C10311yescharacteristic
419#106D4×C10311yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8C23×C10311yescharacteristic
423C4⋊C8C23×C10311yescharacteristic
424C4⋊C8C23×C10311yescharacteristic
425C4⋊C8C23×C10311yescharacteristic
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103D4×C10311yescharacteristic
434#103D4×C10311yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—41no—
439#102D4×C10311yescharacteristic
440#102D4×C10311yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444C4×C8—21no—
445C4×C8C23×C10311yescharacteristic
446C4×C8C23×C10311yescharacteristic
447C4×C8C23×C10311yescharacteristic
448#41—42no—
449#41—42no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—41no—
456C2×Q8—42no—
457C2×Q8—81no—
458C2×Q8C2×D4×C10311yescharacteristic
459C2×Q8C2×D4×C10311yescharacteristic
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C10311yescharacteristic
467C2×D4C2×D4×C10311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—42no—
474SD16—41no—
475SD16—42no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482SD16SD16×C10314yescomplemented
483D8—42no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—42no—
490C2×C8—81no—
491C2×C8C2×D4×C10311yescharacteristic
492C2×C8C2×D4×C10311yescharacteristic
493C2×C8C2×D4×C10311yescharacteristic
494C2×C8C2×D4×C10311yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C10311yescharacteristic
509C4⋊C4C2×D4×C10311yescharacteristic
510C4⋊C4C2×D4×C10311yescharacteristic
511C4⋊C4C2×D4×C10311yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C42—21no—
518C42—21no—
519C42—41no—
520C42C24×C10311yescharacteristic
521C23—21no—
522C23—21no—
523C23—41no—
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—82no—
534Q8C2×SD16×C10312yes—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—82no—
543D4—81no—
544D4—82no—
545D4—161no—
546D4C2×SD16×C10312yes—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4C22×D4×C10311yescharacteristic
564C2×C4C22×D4×C10311yescharacteristic
565C2×C4H(5,𝔽2)×C10311yescharacteristic
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8C2×SD16×C10312yes—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22D42×C10311yescharacteristic
585C4—22no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4C22×SD16×C10311yescharacteristic
596C4#575×C10311yescharacteristic
597C4#576×C10311yescharacteristic
598C4#577×C10311yescharacteristic
599C2—42no—
600C2—81no—
601C2—161no—
602C2C103×#326811yescharacteristic
603C2D4×SD16×C10311yescharacteristic
604C2C103×#328911yescharacteristic
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×#3386C2semidirect
3. C103×#3298C2semidirect
5. C103×#1714C2semidirect
6. C103×#1686C2semidirect
7. C103×#1680C2semidirect
8. C103×#1673C2semidirect
9. C103×#1665C2semidirect
10. C103×#1654C2semidirect
11. C103×#1653C2semidirect
12. C103×#1642C2semidirect
13. C103×#1627C2semidirect
14. C103×#1582C2semidirect
15. C103×SD16⋊C8C2semidirect
179. SD16×C103SD16semidirect
296. #19767C103direct (N × H)
303. #3392C2×C103semidirect
304. #3386C2×C103semidirect
305. #3298C2×C103semidirect
307. #1714C2×C103semidirect
308. #1686C2×C103semidirect
309. #1680C2×C103semidirect
310. #1673C2×C103semidirect
311. #1665C2×C103semidirect
312. #1654C2×C103semidirect
313. #1653C2×C103semidirect
314. #1642C2×C103semidirect
315. #1627C2×C103semidirect
316. #1582C2×C103semidirect
317. SD16⋊C8C2×C103semidirect
318. C103#19767direct (N × H)
482. SD16SD16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33922
C103×#33862
C103×#32982
C103×#32842
C103×#17142
C103×#16862
C103×#16802
C103×#16732
C103×#16652
C103×#16542
C103×#16532
C103×#16422
C103×#16272
C103×#15822
C103×SD16⋊C82
#19767103