Finite Group Databasebeta

← C103×#27069 #39932344

Subgroups — C103×#27069 #39932344

Order 26368.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2513C211yesmaximal, characteristic
2C103×#2365C211yesmaximal, characteristic, complemented
3C103×#2097C211yesmaximal, characteristic, complemented
4C103×#2055C211yesmaximal, characteristic
5C103×#2043C211yesmaximal, characteristic, complemented
6C103×#2013C211yesmaximal, characteristic
7C103×#1968C211yesmaximal, characteristic
8C103×#1928C211yesmaximal, characteristic, complemented
9C103×#1925C211yesmaximal, characteristic
10C103×#1920C211yesmaximal, characteristic, complemented
11C103×#1916C211yesmaximal, characteristic, complemented
12C103×#1880C211yesmaximal, characteristic
13C103×#1880C211yesmaximal, characteristic
14C103×#1805C211yesmaximal, characteristic, complemented
15C4×#103×C103C211yesmaximal, characteristic, complemented
16C22×SD16×C103C2211yescharacteristic
17C22×SD16×C103C2211yescharacteristic
18C2×C4⋊Q8×C103C2211yescharacteristic
19C2×C4×Q8×C103C2211yescharacteristic
20C2×C4×Q8×C103C2211yescharacteristic
21C2×#107×C103C2211yescharacteristic
22C2×#106×C103C2211yescharacteristic
23C2×C4⋊C8×C103C2211yescharacteristic
24C2×#103×C103C2211yescharacteristic
25C2×#103×C103C2211yescharacteristic
26C2×#103×C103C2211yescharacteristic
27C2×#103×C103C2211yescharacteristic
28C2×#103×C103C2211yescharacteristic
29C2×#103×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×C4×C8×C103C2211yescharacteristic
33#397×C103—21no—
34#397×C103—21no—
35#391×C103C2211yescharacteristic
36#391×C103C2211yescharacteristic
37#390×C103C2211yescharacteristic
38#390×C103C2211yescharacteristic
39#390×C103C2211yescharacteristic
40#389×C103—21no—
41#389×C103C2211yescharacteristic
42#388×C103—21no—
43#388×C103—21no—
44#387×C103—21no—
45#387×C103—21no—
46#382×C103C2211yescharacteristic
47C4×C4⋊C4×C103—21no—
48C4×C4⋊C4×C103C2211yescharacteristic
49C4×C4⋊C4×C103C2211yescharacteristic
50C4×C4⋊C4×C103C2211yescharacteristic
51#340×C103C2211yescharacteristic
52#340×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#336×C103C2211yescharacteristic
56#336×C103C2211yescharacteristic
57#336×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59C22×Q8×C103C2311yescharacteristic
60C22×Q8×C103C2311yescharacteristic
61C22×D4×C103C2311yescharacteristic
62C2×SD16×C103—22no—
63C2×SD16×C103—22no—
64C2×SD16×C103—22no—
65C2×SD16×C103—41no—
66C2×SD16×C103—41no—
67C2×SD16×C103—41no—
68C22×C8×C103C2311yescharacteristic
69C22×C8×C103C2311yescharacteristic
70C22×C8×C103C2311yescharacteristic
71C22×C8×C103C2311yescharacteristic
72C4⋊Q8×C103—22no—
73C4⋊Q8×C103—22no—
74C4×Q8×C103—22no—
75C4×Q8×C103—22no—
76C4×Q8×C103—41no—
77C4×Q8×C103—41no—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—21no—
80C2×C4⋊C4×C103—21no—
81C2×C4⋊C4×C103—21no—
82C2×C4⋊C4×C103—21no—
83C2×C4⋊C4×C103D411yescharacteristic
84C2×C4⋊C4×C103D411yescharacteristic
85C2×C4⋊C4×C103C2311yescharacteristic
86C2×C4⋊C4×C103C2311yescharacteristic
87C2×C4⋊C4×C103C2311yescharacteristic
88C2×C4⋊C4×C103C2311yescharacteristic
89C2×C4⋊C4×C103C2311yescharacteristic
90C2×C22⋊C4×C103—21no—
91C2×C22⋊C4×C103—21no—
92C2×C22⋊C4×C103—21no—
93C2×C22⋊C4×C103—21no—
94C2×C22⋊C4×C103—21no—
95C2×C22⋊C4×C103—21no—
96C2×C42×C103—21no—
97C2×C42×C103—21no—
98C2×C42×C103—21no—
99C2×C42×C103—21no—
100C2×C42×C103C2311yescharacteristic
101C2×C42×C103C2311yescharacteristic
102C2×C42×C103C2311yescharacteristic
103#107×C103—41no—
104#106×C103—22no—
105C4⋊C8×C103—41no—
106#103×C103—22no—
107#103×C103—22no—
108#103×C103—22no—
109#103×C103—41no—
110#103×C103—41no—
111#103×C103—41no—
112#102×C103—22no—
113#102×C103—41no—
114C4×C8×C103—41no—
115#95×C103—21no—
116#95×C103—21no—
117#95×C103—21no—
118#95×C103—21no—
119#95×C103—21no—
120#95×C103—21no—
121#95×C103—21no—
122#95×C103—21no—
123#95×C103—21no—
124#95×C103D411yescharacteristic
125#95×C103D411yescharacteristic
126C24×C103—21no—
127C2×Q8×C103—21no—
128C2×Q8×C103—21no—
129C2×Q8×C103—21no—
130C2×Q8×C103—21no—
131C2×Q8×C103—21no—
132C2×Q8×C103—21no—
133C2×Q8×C103—21no—
134C2×Q8×C103—21no—
135C2×Q8×C103—21no—
136C2×Q8×C103—21no—
137C2×Q8×C103#4112yes—
138C2×Q8×C103#4112yes—
139C2×D4×C103—21no—
140C2×D4×C103—21no—
141C2×D4×C103—21no—
142C2×D4×C103—21no—
143C2×D4×C103—21no—
144C2×D4×C103—21no—
145C22×C4×C103—21no—
146C22×C4×C103—21no—
147C22×C4×C103—21no—
148C22×C4×C103—21no—
149C22×C4×C103—21no—
150C22×C4×C103—21no—
151C22×C4×C103—21no—
152C22×C4×C103C2×D411yescharacteristic
153C22×C4×C103C2×D411yescharacteristic
154C22×C4×C103C2×D411yescharacteristic
155C22×C4×C103C2×D411yescharacteristic
156C22×C4×C103C2×D411yescharacteristic
157C22×C4×C103C2×D411yescharacteristic
158C22×C4×C103C2411yescharacteristic
159SD16×C103—44no—
160SD16×C103—44no—
161C2×C8×C103—21no—
162C2×C8×C103—21no—
163C2×C8×C103—21no—
164C2×C8×C103—21no—
165C2×C8×C103—21no—
166C2×C8×C103—21no—
167C2×C8×C103—21no—
168C2×C8×C103—21no—
169C2×C8×C103—21no—
170C2×C8×C103—21no—
171C2×C8×C103—21no—
172C2×C8×C103#4112yes—
173C4⋊C4×C103—24no—
174C4⋊C4×C103—24no—
175C4⋊C4×C103—22no—
176C4⋊C4×C103—22no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—21no—
179C4⋊C4×C103—21no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—21no—
182C4⋊C4×C103—21no—
183C4⋊C4×C103—21no—
184C4⋊C4×C103—21no—
185C4⋊C4×C103—21no—
186C4⋊C4×C103—42no—
187C4⋊C4×C103—42no—
188C4⋊C4×C103—81no—
189C4⋊C4×C103#4112yes—
190C22⋊C4×C103—42no—
191C22⋊C4×C103—42no—
192C22⋊C4×C103—81no—
193C22⋊C4×C103—81no—
194C22⋊C4×C103—81no—
195C22⋊C4×C103—81no—
196C42×C103—21no—
197C42×C103—21no—
198C42×C103—21no—
199C42×C103—21no—
200C42×C103—21no—
201C42×C103—21no—
202C42×C103—42no—
203C42×C103—42no—
204C42×C103—42no—
205C42×C103—81no—
206C23×C103—41no—
207C23×C103—41no—
208C23×C103—41no—
209C23×C103—41no—
210C23×C103—41no—
211C23×C103—41no—
212C23×C103—41no—
213C23×C103C22×D411yescharacteristic
214Q8×C103—22no—
215Q8×C103—22no—
216Q8×C103—22no—
217Q8×C103—22no—
218Q8×C103—41no—
219Q8×C103—41no—
220Q8×C103—41no—
221Q8×C103—41no—
222D4×C103—41no—
223D4×C103—41no—
224D4×C103—41no—
225D4×C103—41no—
226C2×C4×C103—21no—
227C2×C4×C103—21no—
228C2×C4×C103—21no—
229C2×C4×C103—21no—
230C2×C4×C103—21no—
231C2×C4×C103—22no—
232C2×C4×C103—22no—
233C2×C4×C103—21no—
234C2×C4×C103—21no—
235C2×C4×C103—21no—
236C2×C4×C103—22no—
237C2×C4×C103—21no—
238C2×C4×C103—21no—
239C2×C4×C103—21no—
240C2×C4×C103—21no—
241C2×C4×C103—21no—
242C2×C4×C103—21no—
243C2×C4×C103—21no—
244C2×C4×C103—21no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
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—41no—
255C2×C4×C103—41no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103—41no—
259C2×C4×C103—41no—
260C2×C4×C103—41no—
261C2×C4×C103—41no—
262C2×C4×C103—41no—
263C2×C4×C103#13512yes—
264C2×C4×C103#13712yes—
265C2×C4×C103C2×#4111yescharacteristic
266C2×C4×C103C2×#4111yescharacteristic
267C2×C4×C103C2×#4111yescharacteristic
268C2×C4×C103C2×#4111yescharacteristic
269C2×C4×C103H(5,𝔽2)11yescharacteristic
270C2×C4×C103H(5,𝔽2)11yescharacteristic
271C8×C103—22no—
272C8×C103—41no—
273C8×C103—41no—
274C8×C103—41no—
275C22×C103—81no—
276C22×C103—81no—
277C22×C103—81no—
278C22×C103—81no—
279C22×C103—81no—
280C22×C103—81no—
281C22×C103—81no—
282C22×C103#52511yescharacteristic
283C22×C103#54611yescharacteristic
284C22×C103#55011yescharacteristic
285C22×C103C2×#13511yescharacteristic
286C22×C103C2×#13711yescharacteristic
287C22×C103#57711yescharacteristic
288C22×C103#57711yescharacteristic
289C4×C103—22no—
290C4×C103—22no—
291C4×C103—41no—
292C4×C103—42no—
293C4×C103—42no—
294C4×C103—41no—
295C4×C103—41no—
296C4×C103—42no—
297C4×C103—41no—
298C4×C103—81no—
299C4×C103—81no—
300C4×C103—81no—
301C4×C103—81no—
302C4×C103#52911yescharacteristic
303C4×C103#53811yescharacteristic
304C4×C103#55111yescharacteristic
305C4×C103#55311yescharacteristic
306#27069C10311yesmaximal, characteristic, direct product factor, Sylow
307C2×C103—161no—
308C2×C103#246711yescharacteristic
309C2×C103#310811yescharacteristic
310C2×C103#312611yescharacteristic
311C2×C103#330311yescharacteristic
312C2×C103#332011yescharacteristic
313C2×C103#339411yescharacteristic
314C2×C103#340011yescharacteristic
315#2513C2×C10311yescharacteristic
316#2365C2×C10311yescharacteristic, complemented
317#2097C2×C10311yescharacteristic, complemented
318#2055C2×C10311yescharacteristic
319#2043C2×C10311yescharacteristic, complemented
320#2013C2×C10311yescharacteristic
321#1968C2×C10311yescharacteristic
322#1928C2×C10311yescharacteristic, complemented
323#1925C2×C10311yescharacteristic
324#1920C2×C10311yescharacteristic, complemented
325#1916C2×C10311yescharacteristic, complemented
326#1880C2×C10311yescharacteristic
327#1880C2×C10311yescharacteristic
328#1805C2×C10311yescharacteristic, complemented
329C4×#103C2×C10311yescharacteristic, complemented
330C103#2706911yescharacteristic, direct product factor, Sylow
331C22×SD16C22×C10311yescharacteristic
332C22×SD16C22×C10311yescharacteristic
333C2×C4⋊Q8C22×C10311yescharacteristic
334C2×C4×Q8C22×C10311yescharacteristic
335C2×C4×Q8C22×C10311yescharacteristic
336C2×#107C22×C10311yescharacteristic
337C2×#106C22×C10311yescharacteristic
338C2×C4⋊C8C22×C10311yescharacteristic
339C2×#103C22×C10311yescharacteristic
340C2×#103C22×C10311yescharacteristic
341C2×#103C22×C10311yescharacteristic
342C2×#103C22×C10311yescharacteristic
343C2×#103C22×C10311yescharacteristic
344C2×#103C22×C10311yescharacteristic
345C2×#102C22×C10311yescharacteristic
346C2×#102C22×C10311yescharacteristic
347C2×C4×C8C22×C10311yescharacteristic
348#397—21no—
349#397—21no—
350#391C22×C10311yescharacteristic
351#391C22×C10311yescharacteristic
352#390C22×C10311yescharacteristic
353#390C22×C10311yescharacteristic
354#390C22×C10311yescharacteristic
355#389—21no—
356#389C22×C10311yescharacteristic
357#388—21no—
358#388—21no—
359#387—21no—
360#387—21no—
361#382C22×C10311yescharacteristic
362C4×C4⋊C4—21no—
363C4×C4⋊C4C22×C10311yescharacteristic
364C4×C4⋊C4C22×C10311yescharacteristic
365C4×C4⋊C4C22×C10311yescharacteristic
366#340C22×C10311yescharacteristic
367#340C22×C10311yescharacteristic
368#340C22×C10311yescharacteristic
369#340C22×C10311yescharacteristic
370#336C22×C10311yescharacteristic
371#336C22×C10311yescharacteristic
372#336C22×C10311yescharacteristic
373#336C22×C10311yescharacteristic
374C22×Q8C23×C10311yescharacteristic
375C22×Q8C23×C10311yescharacteristic
376C22×D4C23×C10311yescharacteristic
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—41no—
381C2×SD16—41no—
382C2×SD16—41no—
383C22×C8C23×C10311yescharacteristic
384C22×C8C23×C10311yescharacteristic
385C22×C8C23×C10311yescharacteristic
386C22×C8C23×C10311yescharacteristic
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—41no—
392C4×Q8—41no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C10311yescharacteristic
399C2×C4⋊C4D4×C10311yescharacteristic
400C2×C4⋊C4C23×C10311yescharacteristic
401C2×C4⋊C4C23×C10311yescharacteristic
402C2×C4⋊C4C23×C10311yescharacteristic
403C2×C4⋊C4C23×C10311yescharacteristic
404C2×C4⋊C4C23×C10311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C23×C10311yescharacteristic
416C2×C42C23×C10311yescharacteristic
417C2×C42C23×C10311yescharacteristic
418#107—41no—
419#106—22no—
420C4⋊C8—41no—
421#103—22no—
422#103—22no—
423#103—22no—
424#103—41no—
425#103—41no—
426#103—41no—
427#102—22no—
428#102—41no—
429C4×C8—41no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95D4×C10311yescharacteristic
440#95D4×C10311yescharacteristic
441C24—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8#41×C10312yes—
453C2×Q8#41×C10312yes—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4C2×D4×C10311yescharacteristic
468C22×C4C2×D4×C10311yescharacteristic
469C22×C4C2×D4×C10311yescharacteristic
470C22×C4C2×D4×C10311yescharacteristic
471C22×C4C2×D4×C10311yescharacteristic
472C22×C4C2×D4×C10311yescharacteristic
473C22×C4C24×C10311yescharacteristic
474SD16—44no—
475SD16—44no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8#41×C10312yes—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—22no—
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—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—81no—
504C4⋊C4#41×C10312yes—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—42no—
519C42—42no—
520C42—81no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C22×D4×C10311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4#135×C10312yes—
579C2×C4#137×C10312yes—
580C2×C4C2×#41×C10311yescharacteristic
581C2×C4C2×#41×C10311yescharacteristic
582C2×C4C2×#41×C10311yescharacteristic
583C2×C4C2×#41×C10311yescharacteristic
584C2×C4H(5,𝔽2)×C10311yescharacteristic
585C2×C4H(5,𝔽2)×C10311yescharacteristic
586C8—22no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#525×C10311yescharacteristic
598C22#546×C10311yescharacteristic
599C22#550×C10311yescharacteristic
600C22C2×#135×C10311yescharacteristic
601C22C2×#137×C10311yescharacteristic
602C22#577×C10311yescharacteristic
603C22#577×C10311yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4#529×C10311yescharacteristic
618C4#538×C10311yescharacteristic
619C4#551×C10311yescharacteristic
620C4#553×C10311yescharacteristic
621C2—161no—
622C2C103×#246711yescharacteristic
623C2C103×#310811yescharacteristic
624C2C103×#312611yescharacteristic
625C2C103×#330311yescharacteristic
626C2C103×#332011yescharacteristic
627C2C103×#339411yescharacteristic
628C2C103×#340011yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C4⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2365C2semidirect
3. C103×#2097C2semidirect
5. C103×#2043C2semidirect
8. C103×#1928C2semidirect
10. C103×#1920C2semidirect
11. C103×#1916C2semidirect
14. C103×#1805C2semidirect
15. C4×#103×C103C2semidirect
306. #27069C103direct (N × H)
316. #2365C2×C103semidirect
317. #2097C2×C103semidirect
319. #2043C2×C103semidirect
322. #1928C2×C103semidirect
324. #1920C2×C103semidirect
325. #1916C2×C103semidirect
328. #1805C2×C103semidirect
329. C4×#103C2×C103semidirect
330. C103#27069direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#25132
C103×#23652
C103×#20972
C103×#20552
C103×#20432
C103×#20132
C103×#19682
C103×#19282
C103×#19252
C103×#19202
C103×#19162
C103×#18802
C103×#18052
C4×#103×C1032
#27069103