Finite Group Databasebeta

← C103×#18400 #39923675

Subgroups — C103×#18400 #39923675

Order 26368.

978 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×#3493C211yesmaximal, characteristic, complemented
2C103×#3211C212yesmaximal, complemented
3C103×#2610C211yesmaximal, characteristic, complemented
4C103×#1606C212yesmaximal, complemented
5C103×#1605C211yesmaximal, characteristic, complemented
6C103×#1604C211yesmaximal, characteristic, complemented
7C103×#1600C212yesmaximal, complemented
8C103×#1599C211yesmaximal, characteristic, complemented
9C103×#1598C211yesmaximal, characteristic, complemented
10C103×#1500C212yesmaximal, complemented
11C103×#1458C211yesmaximal, characteristic, complemented
12#556×C103—22no—
13#555×C103—22no—
14#553×C103—22no—
15#552×C103—22no—
16#544×C103C2211yescharacteristic
17#538×C103—21no—
18#538×C103C2212yes—
19#537×C103C2211yescharacteristic
20#529×C103—21no—
21#529×C103C2212yes—
22C2×#124×C103C2211yescharacteristic
23#525×C103—21no—
24#520×C103—21no—
25C2×#117×C103C2211yescharacteristic
26#495×C103—22no—
27#488×C103—22no—
28#464×C103—22no—
29#463×C103—22no—
30#451×C103C2212yes—
31#450×C103C2212yes—
32#448×C103C2212yes—
33#447×C103C2212yes—
34#431×C103C2212yes—
35#395×C103C2211yescharacteristic
36#394×C103C2211yescharacteristic
37#393×C103C2211yescharacteristic
38#392×C103C2211yescharacteristic
39#390×C103—21no—
40#388×C103—21no—
41#388×C103—21no—
42#386×C103—21no—
43#376×C103C2211yescharacteristic
44#328×C103C2212yes—
45#328×C103C2212yes—
46#327×C103C2212yes—
47#327×C103C2212yes—
48#324×C103C2211yescharacteristic
49#324×C103C2211yescharacteristic
50#323×C103C2212yes—
51C2×#41×C103—21no—
52C22×Q8×C103C2311yescharacteristic
53C22×D4×C103—21no—
54C22×D4×C103C2311yescharacteristic
55C23×C4×C103D411yescharacteristic
56C2×Q16×C103—22no—
57C2×SD16×C103—22no—
58C2×SD16×C103—22no—
59C2×D8×C103—22no—
60C4⋊Q8×C103—22no—
61#126×C103—22no—
62#126×C103—22no—
63#126×C103—22no—
64#126×C103—22no—
65#125×C103—21no—
66#125×C103—22no—
67#125×C103D412yescomplemented
68#124×C103—21no—
69#124×C103—22no—
70#124×C103—22no—
71#124×C103—22no—
72#124×C103—22no—
73#124×C103D412yescomplemented
74#123×C103—22no—
75#123×C103—22no—
76#123×C103—22no—
77C22⋊Q8×C103—21no—
78C22⋊Q8×C103—21no—
79C22⋊Q8×C103—21no—
80C22⋊Q8×C103—22no—
81C22⋊Q8×C103C2312yes—
82#121×C103—21no—
83#121×C103—21no—
84#121×C103—22no—
85#121×C103—22no—
86#121×C103—22no—
87#121×C103—21no—
88#121×C103C2312yes—
89#120×C103—22no—
90C4×Q8×C103—22no—
91C4×Q8×C103—21no—
92C4×Q8×C103D412yescomplemented
93C4×D4×C103—22no—
94C4×D4×C103—22no—
95C4×D4×C103—22no—
96C4×D4×C103—21no—
97C4×D4×C103—22no—
98C4×D4×C103—22no—
99C4×D4×C103D412yescomplemented
100#117×C103—22no—
101#117×C103—22no—
102#117×C103—21no—
103#117×C103—22no—
104#117×C103—22no—
105#117×C103—22no—
106C2×C4⋊C4×C103—22no—
107C2×C4⋊C4×C103—21no—
108C2×C4⋊C4×C103D411yescharacteristic
109C2×C4⋊C4×C103C2311yescharacteristic
110C2×C22⋊C4×C103—21no—
111C2×C22⋊C4×C103—21no—
112C2×C22⋊C4×C103—21no—
113C2×C22⋊C4×C103—21no—
114C2×C22⋊C4×C103—21no—
115C2×C22⋊C4×C103—21no—
116C2×C22⋊C4×C103D411yescharacteristic
117C2×C22⋊C4×C103C2311yescharacteristic
118C2×C42×C103—21no—
119C2×C42×C103D411yescharacteristic
120C2×C42×C103C2311yescharacteristic
121C4⋊C8×C103—22no—
122#103×C103—22no—
123#103×C103—22no—
124#102×C103—22no—
125#102×C103—22no—
126C22⋊C8×C103C2312yes—
127C22⋊C8×C103C2312yes—
128C4×C8×C103—22no—
129#95×C103—21no—
130#95×C103—21no—
131#95×C103—21no—
132#95×C103C2311yescharacteristic
133#95×C103C2311yescharacteristic
134C24×C103—21no—
135C24×C103C2×D411yescharacteristic
136#41×C103—42no—
137#41×C103—42no—
138C2×Q8×C103—21no—
139C2×Q8×C103—21no—
140C2×Q8×C103—22no—
141C2×Q8×C103—81no—
142C2×Q8×C103C2×D412yes—
143C2×D4×C103—21no—
144C2×D4×C103—22no—
145C2×D4×C103—22no—
146C2×D4×C103—22no—
147C2×D4×C103—21no—
148C2×D4×C103—22no—
149C2×D4×C103—42no—
150C2×D4×C103—42no—
151C2×D4×C103—81no—
152C2×D4×C103—81no—
153C2×D4×C103C2×D412yes—
154C22×C4×C103—22no—
155C22×C4×C103—21no—
156C22×C4×C103—22no—
157C22×C4×C103—21no—
158C22×C4×C103—21no—
159C22×C4×C103—22no—
160C22×C4×C103—22no—
161C22×C4×C103—21no—
162C22×C4×C103—21no—
163C22×C4×C103—41no—
164C22×C4×C103C2×D411yescharacteristic
165C22×C4×C103C2×D411yescharacteristic
166C22×C4×C103C2×D411yescharacteristic
167C22×C4×C103C2×D411yescharacteristic
168C22×C4×C103C2×D411yescharacteristic
169C22×C4×C103C2411yescharacteristic
170Q16×C103—82no—
171SD16×C103—82no—
172SD16×C103—82no—
173D8×C103—82no—
174C2×C8×C103—22no—
175C2×C8×C103—22no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—22no—
178C4⋊C4×C103—21no—
179C4⋊C4×C103—22no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—21no—
182C4⋊C4×C103—22no—
183C4⋊C4×C103—22no—
184C4⋊C4×C103—22no—
185C4⋊C4×C103—22no—
186C4⋊C4×C103—22no—
187C4⋊C4×C103—22no—
188C4⋊C4×C103—81no—
189C4⋊C4×C103C2×D412yes—
190C4⋊C4×C103C2×D412yes—
191C22⋊C4×C103—22no—
192C22⋊C4×C103—22no—
193C22⋊C4×C103—22no—
194C22⋊C4×C103—22no—
195C22⋊C4×C103—22no—
196C22⋊C4×C103—22no—
197C22⋊C4×C103—22no—
198C22⋊C4×C103—22no—
199C22⋊C4×C103—22no—
200C22⋊C4×C103—22no—
201C22⋊C4×C103—22no—
202C22⋊C4×C103—42no—
203C22⋊C4×C103—41no—
204C22⋊C4×C103—41no—
205C22⋊C4×C103—42no—
206C22⋊C4×C103—42no—
207C22⋊C4×C103—81no—
208C22⋊C4×C103—81no—
209C42×C103—22no—
210C42×C103—22no—
211C42×C103—21no—
212C42×C103—21no—
213C42×C103—22no—
214C42×C103—42no—
215C42×C103C2×D412yes—
216C42×C103C2×D412yes—
217C23×C103—21no—
218C23×C103—22no—
219C23×C103—21no—
220C23×C103—21no—
221C23×C103—41no—
222C23×C103—41no—
223C23×C103—41no—
224C23×C103—41no—
225C23×C103—41no—
226C23×C103—41no—
227C23×C103—41no—
228C23×C103—41no—
229C23×C103—41no—
230C23×C103C22×D411yescharacteristic
231Q8×C103—42no—
232Q8×C103—42no—
233Q8×C103—42no—
234Q8×C103—42no—
235Q8×C103—81no—
236D4×C103—42no—
237D4×C103—42no—
238D4×C103—42no—
239D4×C103—42no—
240D4×C103—42no—
241D4×C103—42no—
242D4×C103—82no—
243D4×C103—81no—
244D4×C103—82no—
245D4×C103—84no—
246C2×C4×C103—21no—
247C2×C4×C103—21no—
248C2×C4×C103—21no—
249C2×C4×C103—21no—
250C2×C4×C103—22no—
251C2×C4×C103—21no—
252C2×C4×C103—22no—
253C2×C4×C103—21no—
254C2×C4×C103—22no—
255C2×C4×C103—22no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103—42no—
259C2×C4×C103—42no—
260C2×C4×C103—44no—
261C2×C4×C103—41no—
262C2×C4×C103—41no—
263C2×C4×C103—41no—
264C2×C4×C103—41no—
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—82no—
272C2×C4×C103—82no—
273C2×C4×C103#12011yescharacteristic
274C2×C4×C103#12011yescharacteristic
275C2×C4×C103#12012yes—
276C2×C4×C103#13512yes—
277C2×C4×C103C22×D412yes—
278C8×C103—42no—
279C8×C103—42no—
280C22×C103—21no—
281C22×C103—21no—
282C22×C103—42no—
283C22×C103—41no—
284C22×C103—42no—
285C22×C103—42no—
286C22×C103—41no—
287C22×C103—42no—
288C22×C103—41no—
289C22×C103—81no—
290C22×C103—81no—
291C22×C103—81no—
292C22×C103—81no—
293C22×C103—81no—
294C22×C103—81no—
295C22×C103—81no—
296C22×C103—81no—
297C22×C103C2×#12011yescharacteristic
298C22×C103C2×#13511yescharacteristic
299C22×C103#57511yescharacteristic
300C4×C103—22no—
301C4×C103—21no—
302C4×C103—21no—
303C4×C103—22no—
304C4×C103—22no—
305C4×C103—42no—
306C4×C103—42no—
307C4×C103—41no—
308C4×C103—42no—
309C4×C103—41no—
310C4×C103—42no—
311C4×C103—81no—
312C4×C103—81no—
313#18400C10311yesmaximal, characteristic, direct product factor, Sylow
314C2×C103—21no—
315C2×C103—21no—
316C2×C103—82no—
317C2×C103—81no—
318C2×C103—161no—
319C2×C103#300211yescharacteristic
320C2×C103#301811yescharacteristic
321C2×C103#302711yescharacteristic
322#3493C2×C10311yescharacteristic, complemented
323#3211C2×C10312yescomplemented
324#2610C2×C10311yescharacteristic, complemented
325#1606C2×C10312yescomplemented
326#1605C2×C10311yescharacteristic, complemented
327#1604C2×C10311yescharacteristic, complemented
328#1600C2×C10312yescomplemented
329#1599C2×C10311yescharacteristic, complemented
330#1598C2×C10311yescharacteristic, complemented
331#1500C2×C10312yescomplemented
332#1458C2×C10311yescharacteristic, complemented
333C103#1840011yescharacteristic, direct product factor, Sylow
334#556—22no—
335#555—22no—
336#553—22no—
337#552—22no—
338#544C22×C10311yescharacteristic
339#538—21no—
340#538C22×C10312yes—
341#537C22×C10311yescharacteristic
342#529—21no—
343#529C22×C10312yes—
344C2×#124C22×C10311yescharacteristic
345#525—21no—
346#520—21no—
347C2×#117C22×C10311yescharacteristic
348#495—22no—
349#488—22no—
350#464—22no—
351#463—22no—
352#451C22×C10312yes—
353#450C22×C10312yes—
354#448C22×C10312yes—
355#447C22×C10312yes—
356#431C22×C10312yes—
357#395C22×C10311yescharacteristic
358#394C22×C10311yescharacteristic
359#393C22×C10311yescharacteristic
360#392C22×C10311yescharacteristic
361#390—21no—
362#388—21no—
363#388—21no—
364#386—21no—
365#376C22×C10311yescharacteristic
366#328C22×C10312yes—
367#328C22×C10312yes—
368#327C22×C10312yes—
369#327C22×C10312yes—
370#324C22×C10311yescharacteristic
371#324C22×C10311yescharacteristic
372#323C22×C10312yes—
373C2×#41—21no—
374C22×Q8C23×C10311yescharacteristic
375C22×D4—21no—
376C22×D4C23×C10311yescharacteristic
377C23×C4D4×C10311yescharacteristic
378C2×Q16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×D8—22no—
382C4⋊Q8—22no—
383#126—22no—
384#126—22no—
385#126—22no—
386#126—22no—
387#125—21no—
388#125—22no—
389#125D4×C10312yescomplemented
390#124—21no—
391#124—22no—
392#124—22no—
393#124—22no—
394#124—22no—
395#124D4×C10312yescomplemented
396#123—22no—
397#123—22no—
398#123—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8C23×C10312yes—
404#121—21no—
405#121—21no—
406#121—22no—
407#121—22no—
408#121—22no—
409#121—21no—
410#121C23×C10312yes—
411#120—22no—
412C4×Q8—22no—
413C4×Q8—21no—
414C4×Q8D4×C10312yescomplemented
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4D4×C10312yescomplemented
422#117—22no—
423#117—22no—
424#117—21no—
425#117—22no—
426#117—22no—
427#117—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4D4×C10311yescharacteristic
431C2×C4⋊C4C23×C10311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C10311yescharacteristic
439C2×C22⋊C4C23×C10311yescharacteristic
440C2×C42—21no—
441C2×C42D4×C10311yescharacteristic
442C2×C42C23×C10311yescharacteristic
443C4⋊C8—22no—
444#103—22no—
445#103—22no—
446#102—22no—
447#102—22no—
448C22⋊C8C23×C10312yes—
449C22⋊C8C23×C10312yes—
450C4×C8—22no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95C23×C10311yescharacteristic
455#95C23×C10311yescharacteristic
456C24—21no—
457C24C2×D4×C10311yescharacteristic
458#41—42no—
459#41—42no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—81no—
464C2×Q8C2×D4×C10312yes—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4C2×D4×C10312yes—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4C2×D4×C10311yescharacteristic
487C22×C4C2×D4×C10311yescharacteristic
488C22×C4C2×D4×C10311yescharacteristic
489C22×C4C2×D4×C10311yescharacteristic
490C22×C4C2×D4×C10311yescharacteristic
491C22×C4C24×C10311yescharacteristic
492Q16—82no—
493SD16—82no—
494SD16—82no—
495D8—82no—
496C2×C8—22no—
497C2×C8—22no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—81no—
511C4⋊C4C2×D4×C10312yes—
512C4⋊C4C2×D4×C10312yes—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—42no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42—21no—
535C42—22no—
536C42—42no—
537C42C2×D4×C10312yes—
538C42C2×D4×C10312yes—
539C23—21no—
540C23—22no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C22×D4×C10311yescharacteristic
553Q8—42no—
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—81no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—82no—
565D4—81no—
566D4—82no—
567D4—84no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—44no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4#120×C10311yescharacteristic
596C2×C4#120×C10311yescharacteristic
597C2×C4#120×C10312yes—
598C2×C4#135×C10312yes—
599C2×C4C22×D4×C10312yes—
600C8—42no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—42no—
605C22—41no—
606C22—42no—
607C22—42no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22C2×#120×C10311yescharacteristic
620C22C2×#135×C10311yescharacteristic
621C22#575×C10311yescharacteristic
622C4—22no—
623C4—21no—
624C4—21no—
625C4—22no—
626C4—22no—
627C4—42no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—81no—
634C4—81no—
635C2—21no—
636C2—21no—
637C2—81no—
638C2—82no—
639C2—161no—
640C2C103×#300211yescharacteristic
641C2C103×#301811yescharacteristic
642C2C103×#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×#3493C2semidirect
2. C103×#3211C2semidirect
3. C103×#2610C2semidirect
4. C103×#1606C2semidirect
5. C103×#1605C2semidirect
6. C103×#1604C2semidirect
7. C103×#1600C2semidirect
8. C103×#1599C2semidirect
9. C103×#1598C2semidirect
10. C103×#1500C2semidirect
11. C103×#1458C2semidirect
67. #125×C103D4semidirect
73. #124×C103D4semidirect
92. C4×Q8×C103D4semidirect
99. C4×D4×C103D4semidirect
313. #18400C103direct (N × H)
322. #3493C2×C103semidirect
323. #3211C2×C103semidirect
324. #2610C2×C103semidirect
325. #1606C2×C103semidirect
326. #1605C2×C103semidirect
327. #1604C2×C103semidirect
328. #1600C2×C103semidirect
329. #1599C2×C103semidirect
330. #1598C2×C103semidirect
331. #1500C2×C103semidirect
332. #1458C2×C103semidirect
333. C103#18400direct (N × H)
389. #125D4×C103semidirect
395. #124D4×C103semidirect
414. C4×Q8D4×C103semidirect
421. C4×D4D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34932
C103×#32112
C103×#26102
C103×#16062
C103×#16052
C103×#16042
C103×#16002
C103×#15992
C103×#15982
C103×#15002
C103×#14582
#18400103