Finite Group Databasebeta

← C103×#20032 #39925307

Subgroups — C103×#20032 #39925307

Order 26368.

654 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3384C211yesmaximal, characteristic, complemented
2C103×#3358C211yesmaximal, characteristic
3C103×#3299C211yesmaximal, characteristic, complemented
4C103×#3278C211yesmaximal, characteristic, complemented
5C103×#1714C211yesmaximal, characteristic, complemented
6C103×#1703C211yesmaximal, characteristic, complemented
7C103×#1702C211yesmaximal, characteristic, complemented
8C103×#1672C211yesmaximal, characteristic, complemented
9C103×#1665C211yesmaximal, characteristic, complemented
10C103×#1649C211yesmaximal, characteristic, complemented
11C103×#1649C211yesmaximal, characteristic, complemented
12C103×#1631C211yesmaximal, characteristic, complemented
13C103×#1622C211yesmaximal, characteristic, complemented
14C103×#1587C211yesmaximal, characteristic, complemented
15C103×#1586C211yesmaximal, characteristic, complemented
16C2×#137×C103—21no—
17#554×C103C2211yescharacteristic
18#550×C103C2211yescharacteristic
19D4×Q8×C103C2211yescharacteristic
20D4×Q8×C103C2211yescharacteristic
21#501×C103—21no—
22#500×C103C2211yescharacteristic
23#498×C103C2211yescharacteristic
24#492×C103C2211yescharacteristic
25#492×C103C2211yescharacteristic
26#487×C103C2211yescharacteristic
27#486×C103—21no—
28#486×C103C2211yescharacteristic
29#484×C103—21no—
30#478×C103—21no—
31#477×C103C2211yescharacteristic
32#476×C103—21no—
33#476×C103C2211yescharacteristic
34#474×C103—21no—
35#474×C103C2211yescharacteristic
36#474×C103C2211yescharacteristic
37#468×C103—21no—
38#467×C103—21no—
39#462×C103C2211yescharacteristic
40#462×C103C2211yescharacteristic
41#460×C103C2211yescharacteristic
42#459×C103—21no—
43#459×C103C2211yescharacteristic
44#452×C103—21no—
45#451×C103—21no—
46#448×C103—21no—
47#446×C103C2211yescharacteristic
48C8×Q8×C103C2211yescharacteristic
49#442×C103—21no—
50C4×Q16×C103C2211yescharacteristic
51C4×D8×C103—21no—
52C4×D8×C103C2211yescharacteristic
53#436×C103C2211yescharacteristic
54C8×D4×C103C2211yescharacteristic
55C2×#103×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
66#322×C103C2211yescharacteristic
67C2×#41×C103—21no—
68C22×Q8×C103—21no—
69C22×Q8×C103—21no—
70#137×C103—44no—
71C2×Q16×C103—21no—
72C2×Q16×C103—21no—
73C2×Q16×C103D411yescharacteristic
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103—21no—
77C2×SD16×C103—41no—
78C2×D8×C103—21no—
79C2×D8×C103D411yescharacteristic
80C2×M16×C103—21no—
81C22×C8×C103—21no—
82C4⋊Q8×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—
90C22⋊Q8×C103—21no—
91C22⋊Q8×C103—21no—
92C22⋊Q8×C103—21no—
93C22⋊Q8×C103—41no—
94C22⋊Q8×C103—41no—
95C22⋊Q8×C103—41no—
96#121×C103—21no—
97#121×C103—41no—
98C4×Q8×C103C2311yescharacteristic
99C4×Q8×C103C2311yescharacteristic
100C4×D4×C103—21no—
101C4×D4×C103—21no—
102C4×D4×C103—21no—
103C4×D4×C103—21no—
104C4×D4×C103C2311yescharacteristic
105C4×D4×C103C2311yescharacteristic
106C2×C4⋊C4×C103—21no—
107#107×C103—21no—
108#107×C103—21no—
109#107×C103—21no—
110#107×C103—41no—
111#107×C103D411yescharacteristic
112#107×C103D411yescharacteristic
113#106×C103—21no—
114#106×C103—21no—
115#106×C103—21no—
116C4⋊C8×C103—21no—
117C4⋊C8×C103—21no—
118C4⋊C8×C103C2311yescharacteristic
119C4⋊C8×C103C2311yescharacteristic
120C4⋊C8×C103C2311yescharacteristic
121C4⋊C8×C103C2311yescharacteristic
122#103×C103—21no—
123#103×C103—21no—
124#103×C103—21no—
125#103×C103—21no—
126#103×C103—21no—
127#103×C103D411yescharacteristic
128#103×C103D411yescharacteristic
129#102×C103—21no—
130#102×C103—21no—
131#102×C103—21no—
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—
140#97×C103—21no—
141C4×C8×C103—21no—
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144C4×C8×C103C2311yescharacteristic
145#41×C103—42no—
146#41×C103—81no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
149C2×Q8×C103—21no—
150C2×Q8×C103—41no—
151C2×Q8×C103—41no—
152C2×Q8×C103—42no—
153C2×Q8×C103—42no—
154C2×Q8×C103—81no—
155C2×Q8×C103—81no—
156C2×Q8×C103C2×D411yescharacteristic
157C2×Q8×C103C2×D411yescharacteristic
158C2×D4×C103—21no—
159C2×D4×C103—21no—
160C2×D4×C103—21no—
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—
170C22×C4×C103—41no—
171Q16×C103—22no—
172Q16×C103—42no—
173Q16×C103—81no—
174SD16×C103—42no—
175SD16×C103—42no—
176SD16×C103—81no—
177SD16×C103—82no—
178D8×C103—22no—
179D8×C103—42no—
180M16×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—81no—
187C2×C8×C103C2×D411yescharacteristic
188C2×C8×C103C2×D411yescharacteristic
189C2×C8×C103C2×D411yescharacteristic
190C2×C8×C103C2×D411yescharacteristic
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—21no—
198C4⋊C4×C103—21no—
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—
212C22⋊C4×C103—41no—
213C42×C103—21no—
214C42×C103—21no—
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—82no—
227Q8×C103—81no—
228Q8×C103—82no—
229Q8×C103AGL(1,ℤ/8)12yes—
230D4×C103—21no—
231D4×C103—21no—
232D4×C103—21no—
233D4×C103—41no—
234D4×C103—41no—
235D4×C103—41no—
236D4×C103—41no—
237D4×C103—82no—
238D4×C103—81no—
239D4×C103—161no—
240D4×C103#13712yescomplemented
241C2×C4×C103—21no—
242C2×C4×C103—21no—
243C2×C4×C103—21no—
244C2×C4×C103—21no—
245C2×C4×C103—21no—
246C2×C4×C103—21no—
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—41no—
254C2×C4×C103—82no—
255C2×C4×C103—82no—
256C2×C4×C103—82no—
257C2×C4×C103—161no—
258C2×C4×C103C22×D411yescharacteristic
259C2×C4×C103C22×D411yescharacteristic
260C2×C4×C103H(5,𝔽2)11yescharacteristic
261C8×C103—22no—
262C8×C103—21no—
263C8×C103—21no—
264C8×C103—21no—
265C8×C103—21no—
266C8×C103—41no—
267C8×C103—41no—
268C8×C103—41no—
269C8×C103—41no—
270C22×C103—22no—
271C22×C103—41no—
272C22×C103—41no—
273C22×C103—41no—
274C22×C103—41no—
275C22×C103—41no—
276C22×C103—81no—
277C22×C103—81no—
278C22×C103—81no—
279C22×C103D4211yescharacteristic
280C4×C103—22no—
281C4×C103—21no—
282C4×C103—41no—
283C4×C103—41no—
284C4×C103—41no—
285C4×C103—41no—
286C4×C103—41no—
287C4×C103—81no—
288C4×C103—81no—
289C4×C103—81no—
290C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C103C2×#13711yescharacteristic
292C4×C103#57611yescharacteristic
293C4×C103#57811yescharacteristic
294#20032C10311yesmaximal, characteristic, direct product factor, Sylow
295C2×C103—42no—
296C2×C103—81no—
297C2×C103—161no—
298C2×C103#326411yescharacteristic
299C2×C103#327011yescharacteristic
300C2×C103#329111yescharacteristic
301#3384C2×C10311yescharacteristic, complemented
302#3358C2×C10311yescharacteristic
303#3299C2×C10311yescharacteristic, complemented
304#3278C2×C10311yescharacteristic, complemented
305#1714C2×C10311yescharacteristic, complemented
306#1703C2×C10311yescharacteristic, complemented
307#1702C2×C10311yescharacteristic, complemented
308#1672C2×C10311yescharacteristic, complemented
309#1665C2×C10311yescharacteristic, complemented
310#1649C2×C10311yescharacteristic, complemented
311#1649C2×C10311yescharacteristic, complemented
312#1631C2×C10311yescharacteristic, complemented
313#1622C2×C10311yescharacteristic, complemented
314#1587C2×C10311yescharacteristic, complemented
315#1586C2×C10311yescharacteristic, complemented
316C103#2003211yescharacteristic, direct product factor, Sylow
317C2×#137—21no—
318#554C22×C10311yescharacteristic
319#550C22×C10311yescharacteristic
320D4×Q8C22×C10311yescharacteristic
321D4×Q8C22×C10311yescharacteristic
322#501—21no—
323#500C22×C10311yescharacteristic
324#498C22×C10311yescharacteristic
325#492C22×C10311yescharacteristic
326#492C22×C10311yescharacteristic
327#487C22×C10311yescharacteristic
328#486—21no—
329#486C22×C10311yescharacteristic
330#484—21no—
331#478—21no—
332#477C22×C10311yescharacteristic
333#476—21no—
334#476C22×C10311yescharacteristic
335#474—21no—
336#474C22×C10311yescharacteristic
337#474C22×C10311yescharacteristic
338#468—21no—
339#467—21no—
340#462C22×C10311yescharacteristic
341#462C22×C10311yescharacteristic
342#460C22×C10311yescharacteristic
343#459—21no—
344#459C22×C10311yescharacteristic
345#452—21no—
346#451—21no—
347#448—21no—
348#446C22×C10311yescharacteristic
349C8×Q8C22×C10311yescharacteristic
350#442—21no—
351C4×Q16C22×C10311yescharacteristic
352C4×D8—21no—
353C4×D8C22×C10311yescharacteristic
354#436C22×C10311yescharacteristic
355C8×D4C22×C10311yescharacteristic
356C2×#103—21no—
357#334C22×C10311yescharacteristic
358#334C22×C10311yescharacteristic
359#333C22×C10311yescharacteristic
360#332C22×C10311yescharacteristic
361#332C22×C10311yescharacteristic
362#331C22×C10311yescharacteristic
363Q8⋊C8C22×C10311yescharacteristic
364Q8⋊C8C22×C10311yescharacteristic
365D4⋊C8C22×C10311yescharacteristic
366D4⋊C8C22×C10311yescharacteristic
367#322C22×C10311yescharacteristic
368C2×#41—21no—
369C22×Q8—21no—
370C22×Q8—21no—
371#137—44no—
372C2×Q16—21no—
373C2×Q16—21no—
374C2×Q16D4×C10311yescharacteristic
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—41no—
379C2×D8—21no—
380C2×D8D4×C10311yescharacteristic
381C2×M16—21no—
382C22×C8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—21no—
385C4⋊Q8C23×C10311yescharacteristic
386C4⋊Q8C23×C10311yescharacteristic
387C4⋊Q8C23×C10311yescharacteristic
388#127—21no—
389#127C23×C10311yescharacteristic
390#125—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—41no—
395C22⋊Q8—41no—
396C22⋊Q8—41no—
397#121—21no—
398#121—41no—
399C4×Q8C23×C10311yescharacteristic
400C4×Q8C23×C10311yescharacteristic
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C10311yescharacteristic
406C4×D4C23×C10311yescharacteristic
407C2×C4⋊C4—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107—41no—
412#107D4×C10311yescharacteristic
413#107D4×C10311yescharacteristic
414#106—21no—
415#106—21no—
416#106—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C10311yescharacteristic
420C4⋊C8C23×C10311yescharacteristic
421C4⋊C8C23×C10311yescharacteristic
422C4⋊C8C23×C10311yescharacteristic
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103D4×C10311yescharacteristic
429#103D4×C10311yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102D4×C10311yescharacteristic
438#102D4×C10311yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C10311yescharacteristic
444C4×C8C23×C10311yescharacteristic
445C4×C8C23×C10311yescharacteristic
446#41—42no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—81no—
457C2×Q8C2×D4×C10311yescharacteristic
458C2×Q8C2×D4×C10311yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C10311yescharacteristic
465C2×D4C2×D4×C10311yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—22no—
473Q16—42no—
474Q16—81no—
475SD16—42no—
476SD16—42no—
477SD16—81no—
478SD16—82no—
479D8—22no—
480D8—42no—
481M16—42no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—81no—
488C2×C8C2×D4×C10311yescharacteristic
489C2×C8C2×D4×C10311yescharacteristic
490C2×C8C2×D4×C10311yescharacteristic
491C2×C8C2×D4×C10311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C10311yescharacteristic
505C4⋊C4C2×D4×C10311yescharacteristic
506C4⋊C4C2×D4×C10311yescharacteristic
507C4⋊C4C2×D4×C10311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42C24×C10311yescharacteristic
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—82no—
528Q8—81no—
529Q8—82no—
530Q8AGL(1,ℤ/8)×C10312yes—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—82no—
539D4—81no—
540D4—161no—
541D4#137×C10312yescomplemented
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—161no—
559C2×C4C22×D4×C10311yescharacteristic
560C2×C4C22×D4×C10311yescharacteristic
561C2×C4H(5,𝔽2)×C10311yescharacteristic
562C8—22no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22D42×C10311yescharacteristic
581C4—22no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
592C4C2×#137×C10311yescharacteristic
593C4#576×C10311yescharacteristic
594C4#578×C10311yescharacteristic
595C2—42no—
596C2—81no—
597C2—161no—
598C2C103×#326411yescharacteristic
599C2C103×#327011yescharacteristic
600C2C103×#329111yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3358C2
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×#3384C2semidirect
3. C103×#3299C2semidirect
4. C103×#3278C2semidirect
5. C103×#1714C2semidirect
6. C103×#1703C2semidirect
7. C103×#1702C2semidirect
8. C103×#1672C2semidirect
9. C103×#1665C2semidirect
10. C103×#1649C2semidirect
11. C103×#1649C2semidirect
12. C103×#1631C2semidirect
13. C103×#1622C2semidirect
14. C103×#1587C2semidirect
15. C103×#1586C2semidirect
240. D4×C103#137semidirect
294. #20032C103direct (N × H)
301. #3384C2×C103semidirect
303. #3299C2×C103semidirect
304. #3278C2×C103semidirect
305. #1714C2×C103semidirect
306. #1703C2×C103semidirect
307. #1702C2×C103semidirect
308. #1672C2×C103semidirect
309. #1665C2×C103semidirect
310. #1649C2×C103semidirect
311. #1649C2×C103semidirect
312. #1631C2×C103semidirect
313. #1622C2×C103semidirect
314. #1587C2×C103semidirect
315. #1586C2×C103semidirect
316. C103#20032direct (N × H)
541. D4#137×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33842
C103×#33582
C103×#32992
C103×#32782
C103×#17142
C103×#17032
C103×#17022
C103×#16722
C103×#16652
C103×#16492
C103×#16312
C103×#16222
C103×#15872
C103×#15862
#20032103