Finite Group Databasebeta

← C103×#18426 #39923701

Subgroups — C103×#18426 #39923701

Order 26368.

1168 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3558C211yesmaximal, characteristic, complemented
2C103×#3217C211yesmaximal, characteristic, complemented
3C103×#3205C211yesmaximal, characteristic, complemented
4C103×#2657C211yesmaximal, characteristic, complemented
5C103×#1600C214yesmaximal, complemented
6C103×#1595C214yesmaximal, complemented
7C103×#1505C211yesmaximal, characteristic, complemented
8C103×#1500C211yesmaximal, characteristic, complemented
9C103×#1469C211yesmaximal, characteristic, complemented
10#562×C103—21no—
11H(3,𝔽4)×C103—21no—
12#559×C103—21no—
13#548×C103—21no—
14#546×C103—21no—
15#546×C103—22no—
16D42×C103—21no—
17#542×C103—21no—
18#538×C103—22no—
19#538×C103C2212yes—
20#535×C103—21no—
21#534×C103C2212yes—
22#532×C103C2211yescharacteristic
23C2×#127×C103—21no—
24C2×#127×C103C2211yescharacteristic, complemented
25#529×C103C2211yescharacteristic
26C2×#124×C103—21no—
27C2×#124×C103C2211yescharacteristic
28#496×C103—21no—
29#493×C103—21no—
30#490×C103—21no—
31#486×C103—21no—
32#460×C103—21no—
33#459×C103—21no—
34#459×C103—22no—
35#450×C103C2212yescomplemented
36#447×C103C2212yes—
37#447×C103C2214yescomplemented
38#432×C103C2211yescharacteristic, complemented
39#431×C103C2211yescharacteristic, complemented
40#392×C103—22no—
41#392×C103C2214yescomplemented
42#376×C103C2211yescharacteristic, complemented
43#328×C103C2212yescomplemented
44#327×C103C2212yes—
45#327×C103C2214yescomplemented
46#323×C103C2214yescomplemented
47C2×#41×C103—21no—
48C2×#41×C103—21no—
49C22×Q8×C103D411yescharacteristic
50C22×D4×C103—21no—
51C22×D4×C103—22no—
52C22×D4×C103—24no—
53C22×D4×C103—21no—
54C22×D4×C103—21no—
55C22×D4×C103D411yescharacteristic
56C22×D4×C103C2312yes—
57C2×SD16×C103—22no—
58C2×D8×C103—22no—
59C2×D8×C103—24no—
60C4⋊Q8×C103D411yescharacteristic, complemented
61#127×C103—21no—
62#127×C103—21no—
63#127×C103—21no—
64#127×C103—21no—
65#127×C103—21no—
66#127×C103—44no—
67#127×C103D411yescharacteristic, complemented
68#126×C103—22no—
69#126×C103—21no—
70#125×C103D411yescharacteristic, complemented
71#124×C103—21no—
72#124×C103—22no—
73#124×C103—22no—
74#124×C103—22no—
75#124×C103—21no—
76#124×C103—21no—
77#124×C103—21no—
78#124×C103—21no—
79#124×C103—21no—
80#124×C103—44no—
81#124×C103D411yescharacteristic, complemented
82#123×C103—22no—
83#123×C103—21no—
84#123×C103—22no—
85#123×C103—22no—
86#123×C103—22no—
87C22⋊Q8×C103—22no—
88C22⋊Q8×C103—21no—
89C22⋊Q8×C103—22no—
90C22⋊Q8×C103C2311yescharacteristic
91#121×C103—22no—
92#121×C103—22no—
93#121×C103—22no—
94#121×C103—21no—
95#121×C103—22no—
96#121×C103—21no—
97#121×C103—22no—
98#121×C103C2311yescharacteristic
99#121×C103C2312yes—
100#120×C103—22no—
101#120×C103—22no—
102#120×C103—22no—
103#120×C103—22no—
104#120×C103—22no—
105C4×Q8×C103—21no—
106C4×Q8×C103D411yescharacteristic, complemented
107C4×D4×C103—22no—
108C4×D4×C103—21no—
109C4×D4×C103—21no—
110C4×D4×C103—22no—
111C4×D4×C103—21no—
112C4×D4×C103D411yescharacteristic, complemented
113C4×D4×C103D412yescomplemented
114#117×C103—21no—
115C2×C22⋊C4×C103—22no—
116C2×C22⋊C4×C103—24no—
117C2×C22⋊C4×C103D412yes—
118C2×C22⋊C4×C103C2312yes—
119C2×C42×C103—21no—
120C2×C42×C103C2311yescharacteristic
121C4⋊C8×C103—21no—
122C4⋊C8×C103—21no—
123#102×C103—22no—
124#102×C103—24no—
125#102×C103—22no—
126C22⋊C8×C103C2312yes—
127C22⋊C8×C103C2312yes—
128#97×C103—21no—
129C4×C8×C103—21no—
130#95×C103—21no—
131#95×C103C2312yes—
132C24×C103—22no—
133C24×C103—22no—
134C24×C103C2×D412yes—
135#41×C103—82no—
136#41×C103—82no—
137C2×Q8×C103—21no—
138C2×Q8×C103—21no—
139C2×Q8×C103—21no—
140C2×Q8×C103—42no—
141C2×Q8×C103C2×D411yescharacteristic
142C2×D4×C103—22no—
143C2×D4×C103—21no—
144C2×D4×C103—22no—
145C2×D4×C103—22no—
146C2×D4×C103—22no—
147C2×D4×C103—22no—
148C2×D4×C103—22no—
149C2×D4×C103—21no—
150C2×D4×C103—21no—
151C2×D4×C103—21no—
152C2×D4×C103—21no—
153C2×D4×C103—22no—
154C2×D4×C103—22no—
155C2×D4×C103—42no—
156C2×D4×C103—42no—
157C2×D4×C103—42no—
158C2×D4×C103—48no—
159C2×D4×C103—41no—
160C2×D4×C103—41no—
161C2×D4×C103—41no—
162C2×D4×C103—41no—
163C2×D4×C103—82no—
164C2×D4×C103—82no—
165C2×D4×C103—82no—
166C2×D4×C103—84no—
167C2×D4×C103—84no—
168C2×D4×C103—84no—
169C2×D4×C103C2×D411yescharacteristic
170C2×D4×C103C2×D412yes—
171C22×C4×C103—22no—
172C22×C4×C103—22no—
173C22×C4×C103—22no—
174C22×C4×C103—21no—
175C22×C4×C103—22no—
176C22×C4×C103C2×D411yescharacteristic
177C22×C4×C103C2×D411yescharacteristic
178C22×C4×C103C2×D412yes—
179C22×C4×C103C2411yescharacteristic
180SD16×C103—82no—
181D8×C103—84no—
182D8×C103—82no—
183C2×C8×C103—22no—
184C2×C8×C103—22no—
185C4⋊C4×C103—22no—
186C4⋊C4×C103—22no—
187C4⋊C4×C103—21no—
188C4⋊C4×C103—21no—
189C4⋊C4×C103—21no—
190C4⋊C4×C103—21no—
191C4⋊C4×C103—21no—
192C4⋊C4×C103C2×D412yes—
193C4⋊C4×C103C2×D411yescharacteristic
194C4⋊C4×C103C2×D411yescharacteristic
195C22⋊C4×C103—22no—
196C22⋊C4×C103—22no—
197C22⋊C4×C103—22no—
198C22⋊C4×C103—22no—
199C22⋊C4×C103—22no—
200C22⋊C4×C103—21no—
201C22⋊C4×C103—21no—
202C22⋊C4×C103—22no—
203C22⋊C4×C103—22no—
204C22⋊C4×C103—21no—
205C22⋊C4×C103—21no—
206C22⋊C4×C103—22no—
207C22⋊C4×C103—22no—
208C22⋊C4×C103—22no—
209C22⋊C4×C103—21no—
210C22⋊C4×C103—22no—
211C22⋊C4×C103—48no—
212C42×C103—24no—
213C42×C103—22no—
214C42×C103—21no—
215C42×C103C2×D411yescharacteristic
216C42×C103C2×D411yescharacteristic
217C42×C103C2×D411yescharacteristic
218C42×C103C2×D411yescharacteristic
219C23×C103—22no—
220C23×C103—21no—
221C23×C103—22no—
222C23×C103—24no—
223C23×C103—42no—
224C23×C103—42no—
225C23×C103—42no—
226C23×C103—42no—
227C23×C103—44no—
228C23×C103—42no—
229C23×C103—44no—
230C23×C103—82no—
231C23×C103—82no—
232C23×C103—82no—
233C23×C103C22×D411yescharacteristic
234Q8×C103—41no—
235Q8×C103—42no—
236Q8×C103—81no—
237Q8×C103—81no—
238D4×C103—42no—
239D4×C103—41no—
240D4×C103—44no—
241D4×C103—42no—
242D4×C103—42no—
243D4×C103—42no—
244D4×C103—44no—
245D4×C103—42no—
246D4×C103—42no—
247D4×C103—81no—
248D4×C103—81no—
249D4×C103—82no—
250D4×C103—82no—
251D4×C103—82no—
252D4×C103—82no—
253D4×C103—82no—
254D4×C103—82no—
255D4×C103—82no—
256D4×C103—82no—
257D4×C103—816no—
258D4×C103—82no—
259C2×C4×C103—22no—
260C2×C4×C103—22no—
261C2×C4×C103—24no—
262C2×C4×C103—21no—
263C2×C4×C103—22no—
264C2×C4×C103—22no—
265C2×C4×C103—21no—
266C2×C4×C103—21no—
267C2×C4×C103—41no—
268C2×C4×C103—42no—
269C2×C4×C103—42no—
270C2×C4×C103—42no—
271C2×C4×C103—42no—
272C2×C4×C103—82no—
273C2×C4×C103—82no—
274C2×C4×C103—82no—
275C2×C4×C103#12011yescharacteristic
276C2×C4×C103#12011yescharacteristic
277C2×C4×C103#12011yescharacteristic
278C2×C4×C103#12011yescharacteristic
279C2×C4×C103C22×D411yescharacteristic
280C2×C4×C103C22×D411yescharacteristic
281C8×C103—42no—
282C8×C103—42no—
283C22×C103—21no—
284C22×C103—21no—
285C22×C103—42no—
286C22×C103—42no—
287C22×C103—41no—
288C22×C103—41no—
289C22×C103—42no—
290C22×C103—42no—
291C22×C103—42no—
292C22×C103—41no—
293C22×C103—42no—
294C22×C103—84no—
295C22×C103—84no—
296C22×C103—84no—
297C22×C103—82no—
298C22×C103—82no—
299C22×C103—82no—
300C22×C103—164no—
301C22×C103C2×#12011yescharacteristic
302C22×C103#57612yes—
303C4×C103—21no—
304C4×C103—21no—
305C4×C103—21no—
306C4×C103—21no—
307C4×C103—21no—
308C4×C103—44no—
309C4×C103—41no—
310C4×C103—42no—
311C4×C103—41no—
312C4×C103—42no—
313C4×C103—41no—
314C4×C103#45312yes—
315#18426C10311yesmaximal, characteristic, direct product factor, Sylow
316C2×C103—22no—
317C2×C103—82no—
318C2×C103—82no—
319C2×C103—81no—
320C2×C103—162no—
321C2×C103#300811yescharacteristic
322C2×C103C2×#45311yescharacteristic
323C2×C103#302711yescharacteristic
324#3558C2×C10311yescharacteristic, complemented
325#3217C2×C10311yescharacteristic, complemented
326#3205C2×C10311yescharacteristic, complemented
327#2657C2×C10311yescharacteristic, complemented
328#1600C2×C10314yescomplemented
329#1595C2×C10314yescomplemented
330#1505C2×C10311yescharacteristic, complemented
331#1500C2×C10311yescharacteristic, complemented
332#1469C2×C10311yescharacteristic, complemented
333C103#1842611yescharacteristic, direct product factor, Sylow
334#562—21no—
335H(3,𝔽4)—21no—
336#559—21no—
337#548—21no—
338#546—21no—
339#546—22no—
340D42—21no—
341#542—21no—
342#538—22no—
343#538C22×C10312yes—
344#535—21no—
345#534C22×C10312yes—
346#532C22×C10311yescharacteristic
347C2×#127—21no—
348C2×#127C22×C10311yescharacteristic, complemented
349#529C22×C10311yescharacteristic
350C2×#124—21no—
351C2×#124C22×C10311yescharacteristic
352#496—21no—
353#493—21no—
354#490—21no—
355#486—21no—
356#460—21no—
357#459—22no—
358#459—21no—
359#450C22×C10312yescomplemented
360#447C22×C10312yes—
361#447C22×C10314yescomplemented
362#432C22×C10311yescharacteristic, complemented
363#431C22×C10311yescharacteristic, complemented
364#392—22no—
365#392C22×C10314yescomplemented
366#376C22×C10311yescharacteristic, complemented
367#328C22×C10312yescomplemented
368#327C22×C10312yes—
369#327C22×C10314yescomplemented
370#323C22×C10314yescomplemented
371C2×#41—21no—
372C2×#41—21no—
373C22×Q8D4×C10311yescharacteristic
374C22×D4—21no—
375C22×D4—22no—
376C22×D4—24no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4D4×C10311yescharacteristic
380C22×D4C23×C10312yes—
381C2×SD16—22no—
382C2×D8—22no—
383C2×D8—24no—
384C4⋊Q8D4×C10311yescharacteristic, complemented
385#127—21no—
386#127—21no—
387#127—21no—
388#127—21no—
389#127—21no—
390#127—44no—
391#127D4×C10311yescharacteristic, complemented
392#126—22no—
393#126—21no—
394#125D4×C10311yescharacteristic, complemented
395#124—21no—
396#124—22no—
397#124—22no—
398#124—22no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#124—21no—
404#124—44no—
405#124D4×C10311yescharacteristic, complemented
406#123—22no—
407#123—21no—
408#123—22no—
409#123—22no—
410#123—22no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8C23×C10311yescharacteristic
415#121—22no—
416#121—22no—
417#121—22no—
418#121—21no—
419#121—22no—
420#121—21no—
421#121—22no—
422#121C23×C10311yescharacteristic
423#121C23×C10312yes—
424#120—22no—
425#120—22no—
426#120—22no—
427#120—22no—
428#120—22no—
429C4×Q8—21no—
430C4×Q8D4×C10311yescharacteristic, complemented
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—22no—
435C4×D4—21no—
436C4×D4D4×C10311yescharacteristic, complemented
437C4×D4D4×C10312yescomplemented
438#117—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4D4×C10312yes—
442C2×C22⋊C4C23×C10312yes—
443C2×C42—21no—
444C2×C42C23×C10311yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—21no—
447#102—22no—
448#102—24no—
449#102—22no—
450C22⋊C8C23×C10312yes—
451C22⋊C8C23×C10312yes—
452#97—21no—
453C4×C8—21no—
454#95—21no—
455#95C23×C10312yes—
456C24—22no—
457C24—22no—
458C24C2×D4×C10312yes—
459#41—82no—
460#41—82no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8C2×D4×C10311yescharacteristic
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—48no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—82no—
488C2×D4—82no—
489C2×D4—82no—
490C2×D4—84no—
491C2×D4—84no—
492C2×D4—84no—
493C2×D4C2×D4×C10311yescharacteristic
494C2×D4C2×D4×C10312yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4C2×D4×C10311yescharacteristic
501C22×C4C2×D4×C10311yescharacteristic
502C22×C4C2×D4×C10312yes—
503C22×C4C24×C10311yescharacteristic
504SD16—82no—
505D8—84no—
506D8—82no—
507C2×C8—22no—
508C2×C8—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4C2×D4×C10312yes—
517C4⋊C4C2×D4×C10311yescharacteristic
518C4⋊C4C2×D4×C10311yescharacteristic
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—22no—
535C22⋊C4—48no—
536C42—24no—
537C42—22no—
538C42—21no—
539C42C2×D4×C10311yescharacteristic
540C42C2×D4×C10311yescharacteristic
541C42C2×D4×C10311yescharacteristic
542C42C2×D4×C10311yescharacteristic
543C23—22no—
544C23—21no—
545C23—22no—
546C23—24no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—44no—
552C23—42no—
553C23—44no—
554C23—82no—
555C23—82no—
556C23—82no—
557C23C22×D4×C10311yescharacteristic
558Q8—41no—
559Q8—42no—
560Q8—81no—
561Q8—81no—
562D4—42no—
563D4—41no—
564D4—44no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—44no—
569D4—42no—
570D4—42no—
571D4—81no—
572D4—81no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—82no—
579D4—82no—
580D4—82no—
581D4—816no—
582D4—82no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4#120×C10311yescharacteristic
600C2×C4#120×C10311yescharacteristic
601C2×C4#120×C10311yescharacteristic
602C2×C4#120×C10311yescharacteristic
603C2×C4C22×D4×C10311yescharacteristic
604C2×C4C22×D4×C10311yescharacteristic
605C8—42no—
606C8—42no—
607C22—21no—
608C22—21no—
609C22—42no—
610C22—42no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—42no—
618C22—84no—
619C22—84no—
620C22—84no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—164no—
625C22C2×#120×C10311yescharacteristic
626C22#576×C10312yes—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—44no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—42no—
637C4—41no—
638C4#453×C10312yes—
639C2—22no—
640C2—82no—
641C2—81no—
642C2—82no—
643C2—162no—
644C2C103×#300811yescharacteristic
645C2C2×#453×C10311yescharacteristic
646C2C103×#302711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3558C2semidirect
2. C103×#3217C2semidirect
3. C103×#3205C2semidirect
4. C103×#2657C2semidirect
5. C103×#1600C2semidirect
6. C103×#1595C2semidirect
7. C103×#1505C2semidirect
8. C103×#1500C2semidirect
9. C103×#1469C2semidirect
24. C2×#127×C103C22semidirect
35. #450×C103C22semidirect
37. #447×C103C22semidirect
38. #432×C103C22semidirect
39. #431×C103C22semidirect
41. #392×C103C22semidirect
42. #376×C103C22semidirect
43. #328×C103C22semidirect
45. #327×C103C22semidirect
46. #323×C103C22semidirect
60. C4⋊Q8×C103D4semidirect
67. #127×C103D4semidirect
70. #125×C103D4semidirect
81. #124×C103D4semidirect
106. C4×Q8×C103D4semidirect
112. C4×D4×C103D4semidirect
113. C4×D4×C103D4semidirect
315. #18426C103direct (N × H)
324. #3558C2×C103semidirect
325. #3217C2×C103semidirect
326. #3205C2×C103semidirect
327. #2657C2×C103semidirect
328. #1600C2×C103semidirect
329. #1595C2×C103semidirect
330. #1505C2×C103semidirect
331. #1500C2×C103semidirect
332. #1469C2×C103semidirect
333. C103#18426direct (N × H)
348. C2×#127C22×C103semidirect
359. #450C22×C103semidirect
361. #447C22×C103semidirect
362. #432C22×C103semidirect
363. #431C22×C103semidirect
365. #392C22×C103semidirect
366. #376C22×C103semidirect
367. #328C22×C103semidirect
369. #327C22×C103semidirect
370. #323C22×C103semidirect
384. C4⋊Q8D4×C103semidirect
391. #127D4×C103semidirect
394. #125D4×C103semidirect
405. #124D4×C103semidirect
430. C4×Q8D4×C103semidirect
436. C4×D4D4×C103semidirect
437. C4×D4D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35582
C103×#32172
C103×#32052
C103×#26572
C103×#16002
C103×#15952
C103×#15052
C103×#15002
C103×#14692
#18426103