Finite Group Databasebeta

← C103×#25317 #39930592

Subgroups — C103×#25317 #39930592

Order 26368.

690 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3140C211yesmaximal, characteristic
2C103×#3078C211yesmaximal, characteristic, complemented
3C2×#464×C103C211yesmaximal, characteristic
4C103×#2962C211yesmaximal, characteristic, complemented
5C103×#2064C211yesmaximal, characteristic, complemented
6C103×#2063C211yesmaximal, characteristic
7C103×#2047C211yesmaximal, characteristic, complemented
8C103×#2046C211yesmaximal, characteristic
9C103×#1979C211yesmaximal, characteristic, complemented
10C103×#1977C211yesmaximal, characteristic
11C103×#1967C211yesmaximal, characteristic
12C103×#1950C211yesmaximal, characteristic, complemented
13C103×#1931C211yesmaximal, characteristic
14C103×#1930C211yesmaximal, characteristic, complemented
15C4×#101×C103C211yesmaximal, characteristic, complemented
16C22×Q16×C103C2211yescharacteristic
17C22×SD16×C103C2211yescharacteristic
18#533×C103C2211yescharacteristic
19C2×#124×C103C2211yescharacteristic
20C2×C4×Q8×C103C2211yescharacteristic
21#489×C103—21no—
22#489×C103—21no—
23#488×C103—21no—
24#488×C103—21no—
25#479×C103—21no—
26#479×C103—21no—
27#477×C103—21no—
28#475×C103—21no—
29#464×C103—21no—
30#464×C103—21no—
31#464×C103—21no—
32#464×C103—21no—
33#446×C103—21no—
34#446×C103—21no—
35#446×C103—21no—
36C8×Q8×C103—21no—
37C2×#108×C103C2211yescharacteristic
38C2×#108×C103C2211yescharacteristic
39#428×C103C2211yescharacteristic
40#428×C103C2211yescharacteristic
41#424×C103C2211yescharacteristic
42#424×C103C2211yescharacteristic
43#423×C103C2211yescharacteristic
44C2×C4⋊C8×C103C2211yescharacteristic
45#419×C103C2211yescharacteristic
46#419×C103C2211yescharacteristic
47#419×C103C2211yescharacteristic
48#419×C103C2211yescharacteristic
49#418×C103C2211yescharacteristic
50#418×C103C2211yescharacteristic
51C2×#103×C103C2211yescharacteristic
52C2×#102×C103C2211yescharacteristic
53C2×#101×C103C2211yescharacteristic
54C2×#101×C103C2211yescharacteristic
55C2×#101×C103C2211yescharacteristic
56C2×#101×C103C2211yescharacteristic
57C2×#100×C103C2211yescharacteristic
58C2×#100×C103C2211yescharacteristic
59#405×C103C2211yescharacteristic
60#405×C103C2211yescharacteristic
61C4×M16×C103C2211yescharacteristic
62C4×M16×C103C2211yescharacteristic
63#343×C103C2211yescharacteristic
64#343×C103C2211yescharacteristic
65#341×C103C2211yescharacteristic
66#341×C103C2211yescharacteristic
67C22×Q8×C103C2311yescharacteristic
68C22×Q8×C103C2311yescharacteristic
69C22×D4×C103C2311yescharacteristic
70C2×Q16×C103—22no—
71C2×Q16×C103—21no—
72C2×Q16×C103—21no—
73C2×Q16×C103—41no—
74C2×SD16×C103—22no—
75C2×SD16×C103—21no—
76C2×SD16×C103—21no—
77C2×SD16×C103—41no—
78C2×M16×C103C2311yescharacteristic
79C2×M16×C103C2311yescharacteristic
80C2×M16×C103C2311yescharacteristic
81C2×M16×C103C2311yescharacteristic
82C2×M16×C103C2311yescharacteristic
83C2×M16×C103C2311yescharacteristic
84C22×C8×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C4⋊Q8×C103D411yescharacteristic
87C4⋊Q8×C103D411yescharacteristic
88#125×C103D411yescharacteristic
89#125×C103D411yescharacteristic
90#124×C103—21no—
91#124×C103—21no—
92#124×C103—21no—
93#124×C103—21no—
94C22⋊Q8×C103—21no—
95C22⋊Q8×C103—21no—
96C4×Q8×C103—21no—
97C4×Q8×C103—21no—
98C4×Q8×C103—21no—
99C4×Q8×C103—21no—
100C4×Q8×C103—21no—
101C4×Q8×C103—21no—
102#117×C103C2311yescharacteristic
103#117×C103C2311yescharacteristic
104C2×C4⋊C4×C103—21no—
105C2×C4⋊C4×C103C2311yescharacteristic
106C2×C22⋊C4×C103—21no—
107C2×C22⋊C4×C103—21no—
108C2×C42×C103—21no—
109C2×C42×C103C2311yescharacteristic
110#108×C103—41no—
111#108×C103—41no—
112#107×C103—21no—
113#107×C103—21no—
114#106×C103—21no—
115#106×C103—21no—
116C4⋊C8×C103—21no—
117C4⋊C8×C103—21no—
118C4⋊C8×C103—21no—
119C4⋊C8×C103—21no—
120C4⋊C8×C103—21no—
121C4⋊C8×C103—21no—
122C4⋊C8×C103D411yescharacteristic
123C4⋊C8×C103D411yescharacteristic
124C4⋊C8×C103D411yescharacteristic
125C4⋊C8×C103D411yescharacteristic
126#103×C103—21no—
127#103×C103—21no—
128#103×C103—21no—
129#103×C103—21no—
130#103×C103—21no—
131#103×C103—21no—
132#103×C103—21no—
133#103×C103—21no—
134#103×C103—21no—
135#103×C103—21no—
136#102×C103—21no—
137#102×C103—21no—
138#102×C103—21no—
139#102×C103—21no—
140#102×C103—21no—
141#102×C103—21no—
142#101×C103—22no—
143#101×C103—22no—
144#101×C103—22no—
145#101×C103—41no—
146#100×C103—22no—
147#100×C103—41no—
148#97×C103—21no—
149#97×C103—21no—
150#97×C103—21no—
151#97×C103—21no—
152C4×C8×C103—21no—
153C4×C8×C103—21no—
154C4×C8×C103—21no—
155C4×C8×C103—21no—
156C24×C103—21no—
157C2×Q8×C103—21no—
158C2×Q8×C103—21no—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×Q8×C103—21no—
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103—21no—
166C2×Q8×C103—21no—
167C2×Q8×C103—21no—
168C2×Q8×C103—21no—
169C2×Q8×C103—21no—
170C2×Q8×C103#4112yes—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—21no—
175C2×D4×C103—21no—
176C2×D4×C103—21no—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103#4111yescharacteristic
181C22×C4×C103#4111yescharacteristic
182C22×C4×C103C2411yescharacteristic
183Q16×C103—42no—
184Q16×C103—42no—
185SD16×C103—42no—
186SD16×C103—42no—
187M16×C103—21no—
188M16×C103—21no—
189M16×C103—21no—
190M16×C103—21no—
191M16×C103—21no—
192M16×C103—21no—
193M16×C103—21no—
194M16×C103—21no—
195M16×C103—21no—
196M16×C103—21no—
197M16×C103—21no—
198M16×C103#4112yes—
199C2×C8×C103—21no—
200C2×C8×C103—21no—
201C2×C8×C103—21no—
202C2×C8×C103—21no—
203C2×C8×C103—21no—
204C2×C8×C103—21no—
205C2×C8×C103—21no—
206C2×C8×C103—21no—
207C2×C8×C103—21no—
208C2×C8×C103—21no—
209C2×C8×C103C2×D411yescharacteristic
210C2×C8×C103C2×D411yescharacteristic
211C2×C8×C103C2×D411yescharacteristic
212C2×C8×C103C2×D411yescharacteristic
213C4⋊C4×C103—21no—
214C4⋊C4×C103—21no—
215C4⋊C4×C103—21no—
216C4⋊C4×C103—21no—
217C4⋊C4×C103—21no—
218C4⋊C4×C103—21no—
219C4⋊C4×C103—21no—
220C4⋊C4×C103—21no—
221C4⋊C4×C103—41no—
222C4⋊C4×C103—41no—
223C4⋊C4×C103C2×D411yescharacteristic
224C4⋊C4×C103C2×D411yescharacteristic
225C4⋊C4×C103C2×D411yescharacteristic
226C4⋊C4×C103C2×D411yescharacteristic
227C22⋊C4×C103—21no—
228C22⋊C4×C103—21no—
229C22⋊C4×C103—41no—
230C22⋊C4×C103—41no—
231C22⋊C4×C103—41no—
232C22⋊C4×C103—41no—
233C42×C103—21no—
234C42×C103—21no—
235C42×C103—41no—
236C42×C103—41no—
237C42×C103C2×D411yescharacteristic
238C42×C103C2×D411yescharacteristic
239C42×C103C2×D411yescharacteristic
240C42×C103C2×D411yescharacteristic
241C23×C103—41no—
242C23×C103—41no—
243C23×C103—41no—
244C23×C103—81no—
245C23×C103—81no—
246C23×C103C2×#4111yescharacteristic
247Q8×C103—22no—
248Q8×C103—22no—
249Q8×C103—42no—
250Q8×C103—41no—
251Q8×C103—41no—
252Q8×C103—41no—
253Q8×C103—41no—
254Q8×C103—41no—
255Q8×C103—41no—
256Q8×C103—81no—
257D4×C103—41no—
258D4×C103—41no—
259D4×C103—41no—
260D4×C103—41no—
261C2×C4×C103—21no—
262C2×C4×C103—21no—
263C2×C4×C103—21no—
264C2×C4×C103—21no—
265C2×C4×C103—22no—
266C2×C4×C103—41no—
267C2×C4×C103—41no—
268C2×C4×C103—41no—
269C2×C4×C103—41no—
270C2×C4×C103—41no—
271C2×C4×C103—41no—
272C2×C4×C103—41no—
273C2×C4×C103—41no—
274C2×C4×C103—81no—
275C2×C4×C103#12111yescharacteristic
276C2×C4×C103#12111yescharacteristic
277C2×C4×C103#12111yescharacteristic
278C2×C4×C103#12111yescharacteristic
279C2×C4×C103C22×D411yescharacteristic
280C2×C4×C103C22×D411yescharacteristic
281C2×C4×C103C2×#4111yescharacteristic
282C2×C4×C103C2×#4111yescharacteristic
283C2×C4×C103H(5,𝔽2)11yescharacteristic
284C2×C4×C1032−1+411yescharacteristic
285C8×C103—21no—
286C8×C103—21no—
287C8×C103—21no—
288C8×C103—21no—
289C8×C103—22no—
290C8×C103—41no—
291C8×C103—41no—
292C8×C103—41no—
293C8×C103—41no—
294C8×C103—41no—
295C22×C103—21no—
296C22×C103—21no—
297C22×C103—81no—
298C22×C103—81no—
299C22×C103—81no—
300C22×C103—161no—
301C22×C103—161no—
302C22×C103C2×#12111yescharacteristic
303C22×C103#52911yescharacteristic
304C22×C103#54211yescharacteristic
305C4×C103—21no—
306C4×C103—21no—
307C4×C103—21no—
308C4×C103—21no—
309C4×C103—42no—
310C4×C103—41no—
311C4×C103—41no—
312C4×C103—41no—
313C4×C103—41no—
314C4×C103—81no—
315C4×C103—81no—
316C4×C103#54611yescharacteristic
317C4×C103#54811yescharacteristic
318C4×C103#54811yescharacteristic
319C4×C103#55011yescharacteristic
320#25317C10311yesmaximal, characteristic, direct product factor, Sylow
321C2×C103—21no—
322C2×C103—21no—
323C2×C103—161no—
324C2×C103#242611yescharacteristic
325C2×C103#306711yescharacteristic
326C2×C103#306911yescharacteristic
327#3140C2×C10311yescharacteristic
328#3078C2×C10311yescharacteristic, complemented
329C2×#464C2×C10311yescharacteristic
330#2962C2×C10311yescharacteristic, complemented
331#2064C2×C10311yescharacteristic, complemented
332#2063C2×C10311yescharacteristic
333#2047C2×C10311yescharacteristic, complemented
334#2046C2×C10311yescharacteristic
335#1979C2×C10311yescharacteristic, complemented
336#1977C2×C10311yescharacteristic
337#1967C2×C10311yescharacteristic
338#1950C2×C10311yescharacteristic, complemented
339#1931C2×C10311yescharacteristic
340#1930C2×C10311yescharacteristic, complemented
341C4×#101C2×C10311yescharacteristic, complemented
342C103#2531711yescharacteristic, direct product factor, Sylow
343C22×Q16C22×C10311yescharacteristic
344C22×SD16C22×C10311yescharacteristic
345#533C22×C10311yescharacteristic
346C2×#124C22×C10311yescharacteristic
347C2×C4×Q8C22×C10311yescharacteristic
348#489—21no—
349#489—21no—
350#488—21no—
351#488—21no—
352#479—21no—
353#479—21no—
354#477—21no—
355#475—21no—
356#464—21no—
357#464—21no—
358#464—21no—
359#464—21no—
360#446—21no—
361#446—21no—
362#446—21no—
363C8×Q8—21no—
364C2×#108C22×C10311yescharacteristic
365C2×#108C22×C10311yescharacteristic
366#428C22×C10311yescharacteristic
367#428C22×C10311yescharacteristic
368#424C22×C10311yescharacteristic
369#424C22×C10311yescharacteristic
370#423C22×C10311yescharacteristic
371C2×C4⋊C8C22×C10311yescharacteristic
372#419C22×C10311yescharacteristic
373#419C22×C10311yescharacteristic
374#419C22×C10311yescharacteristic
375#419C22×C10311yescharacteristic
376#418C22×C10311yescharacteristic
377#418C22×C10311yescharacteristic
378C2×#103C22×C10311yescharacteristic
379C2×#102C22×C10311yescharacteristic
380C2×#101C22×C10311yescharacteristic
381C2×#101C22×C10311yescharacteristic
382C2×#101C22×C10311yescharacteristic
383C2×#101C22×C10311yescharacteristic
384C2×#100C22×C10311yescharacteristic
385C2×#100C22×C10311yescharacteristic
386#405C22×C10311yescharacteristic
387#405C22×C10311yescharacteristic
388C4×M16C22×C10311yescharacteristic
389C4×M16C22×C10311yescharacteristic
390#343C22×C10311yescharacteristic
391#343C22×C10311yescharacteristic
392#341C22×C10311yescharacteristic
393#341C22×C10311yescharacteristic
394C22×Q8C23×C10311yescharacteristic
395C22×Q8C23×C10311yescharacteristic
396C22×D4C23×C10311yescharacteristic
397C2×Q16—22no—
398C2×Q16—21no—
399C2×Q16—21no—
400C2×Q16—41no—
401C2×SD16—22no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—41no—
405C2×M16C23×C10311yescharacteristic
406C2×M16C23×C10311yescharacteristic
407C2×M16C23×C10311yescharacteristic
408C2×M16C23×C10311yescharacteristic
409C2×M16C23×C10311yescharacteristic
410C2×M16C23×C10311yescharacteristic
411C22×C8C23×C10311yescharacteristic
412C22×C8C23×C10311yescharacteristic
413C4⋊Q8D4×C10311yescharacteristic
414C4⋊Q8D4×C10311yescharacteristic
415#125D4×C10311yescharacteristic
416#125D4×C10311yescharacteristic
417#124—21no—
418#124—21no—
419#124—21no—
420#124—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429#117C23×C10311yescharacteristic
430#117C23×C10311yescharacteristic
431C2×C4⋊C4—21no—
432C2×C4⋊C4C23×C10311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—21no—
436C2×C42C23×C10311yescharacteristic
437#108—41no—
438#108—41no—
439#107—21no—
440#107—21no—
441#106—21no—
442#106—21no—
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8D4×C10311yescharacteristic
450C4⋊C8D4×C10311yescharacteristic
451C4⋊C8D4×C10311yescharacteristic
452C4⋊C8D4×C10311yescharacteristic
453#103—21no—
454#103—21no—
455#103—21no—
456#103—21no—
457#103—21no—
458#103—21no—
459#103—21no—
460#103—21no—
461#103—21no—
462#103—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—21no—
467#102—21no—
468#102—21no—
469#101—22no—
470#101—22no—
471#101—22no—
472#101—41no—
473#100—22no—
474#100—41no—
475#97—21no—
476#97—21no—
477#97—21no—
478#97—21no—
479C4×C8—21no—
480C4×C8—21no—
481C4×C8—21no—
482C4×C8—21no—
483C24—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8#41×C10312yes—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4#41×C10311yescharacteristic
508C22×C4#41×C10311yescharacteristic
509C22×C4C24×C10311yescharacteristic
510Q16—42no—
511Q16—42no—
512SD16—42no—
513SD16—42no—
514M16—21no—
515M16—21no—
516M16—21no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—21no—
523M16—21no—
524M16—21no—
525M16#41×C10312yes—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8C2×D4×C10311yescharacteristic
537C2×C8C2×D4×C10311yescharacteristic
538C2×C8C2×D4×C10311yescharacteristic
539C2×C8C2×D4×C10311yescharacteristic
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4C2×D4×C10311yescharacteristic
551C4⋊C4C2×D4×C10311yescharacteristic
552C4⋊C4C2×D4×C10311yescharacteristic
553C4⋊C4C2×D4×C10311yescharacteristic
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C42—21no—
561C42—21no—
562C42—41no—
563C42—41no—
564C42C2×D4×C10311yescharacteristic
565C42C2×D4×C10311yescharacteristic
566C42C2×D4×C10311yescharacteristic
567C42C2×D4×C10311yescharacteristic
568C23—41no—
569C23—41no—
570C23—41no—
571C23—81no—
572C23—81no—
573C23C2×#41×C10311yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—42no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—81no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—81no—
602C2×C4#121×C10311yescharacteristic
603C2×C4#121×C10311yescharacteristic
604C2×C4#121×C10311yescharacteristic
605C2×C4#121×C10311yescharacteristic
606C2×C4C22×D4×C10311yescharacteristic
607C2×C4C22×D4×C10311yescharacteristic
608C2×C4C2×#41×C10311yescharacteristic
609C2×C4C2×#41×C10311yescharacteristic
610C2×C4H(5,𝔽2)×C10311yescharacteristic
611C2×C42−1+4×C10311yescharacteristic
612C8—21no—
613C8—21no—
614C8—21no—
615C8—21no—
616C8—22no—
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C8—41no—
622C22—21no—
623C22—21no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22C2×#121×C10311yescharacteristic
630C22#529×C10311yescharacteristic
631C22#542×C10311yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4#546×C10311yescharacteristic
644C4#548×C10311yescharacteristic
645C4#548×C10311yescharacteristic
646C4#550×C10311yescharacteristic
647C2—21no—
648C2—21no—
649C2—161no—
650C2C103×#242611yescharacteristic
651C2C103×#306711yescharacteristic
652C2C103×#306911yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3078C2semidirect
4. C103×#2962C2semidirect
5. C103×#2064C2semidirect
7. C103×#2047C2semidirect
9. C103×#1979C2semidirect
12. C103×#1950C2semidirect
14. C103×#1930C2semidirect
15. C4×#101×C103C2semidirect
320. #25317C103direct (N × H)
328. #3078C2×C103semidirect
330. #2962C2×C103semidirect
331. #2064C2×C103semidirect
333. #2047C2×C103semidirect
335. #1979C2×C103semidirect
338. #1950C2×C103semidirect
340. #1930C2×C103semidirect
341. C4×#101C2×C103semidirect
342. C103#25317direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31402
C103×#30782
C2×#464×C1032
C103×#29622
C103×#20642
C103×#20632
C103×#20472
C103×#20462
C103×#19792
C103×#19772
C103×#19672
C103×#19502
C103×#19312
C103×#19302
C4×#101×C1032
#25317103