Finite Group Databasebeta

← C103×#25458 #39930733

Subgroups — C103×#25458 #39930733

Order 26368.

754 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#499×C103C211yesmaximal, characteristic, complemented
2C2×#478×C103C211yesmaximal, characteristic
3C103×#2566C211yesmaximal, characteristic
4C103×#2370C211yesmaximal, characteristic, complemented
5C103×#2085C211yesmaximal, characteristic, complemented
6C103×#2083C211yesmaximal, characteristic, complemented
7C103×#2065C211yesmaximal, characteristic
8C103×#2065C211yesmaximal, characteristic
9C103×#1989C211yesmaximal, characteristic, complemented
10C103×#1949C211yesmaximal, characteristic, complemented
11C103×#1948C211yesmaximal, characteristic, complemented
12C103×#1939C211yesmaximal, characteristic, complemented
13C103×#1925C211yesmaximal, characteristic
14C103×#1925C211yesmaximal, characteristic
15C4×#102×C103C211yesmaximal, characteristic
16C2×#125×C103C2211yescharacteristic
17C2×#125×C103C2211yescharacteristic
18C2×C4×D4×C103C2211yescharacteristic
19#499×C103—24no—
20#478×C103—24no—
21C2×#107×C103C2211yescharacteristic
22C2×#107×C103C2211yescharacteristic
23C2×#107×C103C2211yescharacteristic
24C2×#106×C103C2211yescharacteristic
25C2×#106×C103C2211yescharacteristic
26C2×#106×C103C2211yescharacteristic
27C2×C4⋊C8×C103C2211yescharacteristic
28C2×C4⋊C8×C103C2211yescharacteristic
29C2×C4⋊C8×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×C4×C8×C103C2211yescharacteristic
35#396×C103—21no—
36#396×C103—21no—
37#390×C103C2211yescharacteristic
38#390×C103C2211yescharacteristic
39#389×C103—21no—
40#389×C103C2211yescharacteristic
41#389×C103C2211yescharacteristic
42#387×C103—21no—
43#387×C103—21no—
44#385×C103—21no—
45#385×C103—21no—
46#384×C103C2211yescharacteristic
47#382×C103C2211yescharacteristic
48C4×C4⋊C4×C103—21no—
49C4×C4⋊C4×C103C2211yescharacteristic
50C4×C4⋊C4×C103C2211yescharacteristic
51C4×C4⋊C4×C103C2211yescharacteristic
52C4×C4⋊C4×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#336×C103C2211yescharacteristic
60#336×C103C2211yescharacteristic
61C22×D4×C103C2311yescharacteristic
62C23×C4×C103—21no—
63C22×C8×C103C2311yescharacteristic
64C22×C8×C103C2311yescharacteristic
65C22×C8×C103C2311yescharacteristic
66C22×C8×C103C2311yescharacteristic
67#125×C103—22no—
68#125×C103—22no—
69#125×C103—22no—
70#125×C103D414yes—
71C4×D4×C103—22no—
72C4×D4×C103—22no—
73C2×C4⋊C4×C103—21no—
74C2×C4⋊C4×C103—21no—
75C2×C4⋊C4×C103—21no—
76C2×C4⋊C4×C103—21no—
77C2×C4⋊C4×C103—21no—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—21no—
80C2×C4⋊C4×C103—21no—
81C2×C4⋊C4×C103D411yescharacteristic
82C2×C4⋊C4×C103D411yescharacteristic
83C2×C4⋊C4×C103C2311yescharacteristic
84C2×C4⋊C4×C103C2311yescharacteristic
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×C42×C103—21no—
96C2×C42×C103—21no—
97C2×C42×C103—21no—
98C2×C42×C103C2311yescharacteristic
99C2×C42×C103C2311yescharacteristic
100C2×C42×C103C2311yescharacteristic
101#107×C103—22no—
102#107×C103—22no—
103#107×C103—22no—
104#106×C103—22no—
105#106×C103—22no—
106#106×C103—22no—
107C4⋊C8×C103—22no—
108C4⋊C8×C103—22no—
109C4⋊C8×C103—22no—
110#102×C103—22no—
111#102×C103—22no—
112#102×C103—22no—
113#102×C103Q814yes—
114C4×C8×C103—22no—
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×C103D411yescharacteristic
123#95×C103D411yescharacteristic
124C24×C103—21no—
125C2×D4×C103—21no—
126C2×D4×C103—21no—
127C2×D4×C103—21no—
128C2×D4×C103—21no—
129C2×D4×C103—21no—
130C2×D4×C103C2×Q812yes—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—21no—
136C22×C4×C103—21no—
137C22×C4×C103—21no—
138C22×C4×C103—42no—
139C22×C4×C103—81no—
140C22×C4×C103—81no—
141C22×C4×C103C2×D411yescharacteristic
142C22×C4×C103C2×D411yescharacteristic
143C22×C4×C103C2×D411yescharacteristic
144C22×C4×C103C2×D411yescharacteristic
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D411yescharacteristic
147C22×C4×C103C2411yescharacteristic
148C2×C8×C103—21no—
149C2×C8×C103—21no—
150C2×C8×C103—21no—
151C2×C8×C103—21no—
152C2×C8×C103—21no—
153C2×C8×C103—21no—
154C2×C8×C103—21no—
155C2×C8×C103—21no—
156C2×C8×C103—21no—
157C2×C8×C103—21no—
158C2×C8×C103C2×Q812yes—
159C2×C8×C103#4112yes—
160C4⋊C4×C103—24no—
161C4⋊C4×C103—24no—
162C4⋊C4×C103—22no—
163C4⋊C4×C103—21no—
164C4⋊C4×C103—21no—
165C4⋊C4×C103—21no—
166C4⋊C4×C103—21no—
167C4⋊C4×C103—21no—
168C4⋊C4×C103—21no—
169C4⋊C4×C103—21no—
170C4⋊C4×C103—21no—
171C4⋊C4×C103—21no—
172C4⋊C4×C103—21no—
173C4⋊C4×C103—21no—
174C4⋊C4×C103—41no—
175C4⋊C4×C103—42no—
176C4⋊C4×C103—42no—
177C4⋊C4×C103—42no—
178C4⋊C4×C103—81no—
179C4⋊C4×C103—81no—
180C4⋊C4×C103—81no—
181C4⋊C4×C103C2×D412yes—
182C4⋊C4×C103C2×D412yes—
183C4⋊C4×C103C2×Q812yes—
184C22⋊C4×C103—42no—
185C22⋊C4×C103—42no—
186C22⋊C4×C103—42no—
187C22⋊C4×C103—81no—
188C22⋊C4×C103—81no—
189C42×C103—21no—
190C42×C103—21no—
191C42×C103—21no—
192C42×C103—21no—
193C42×C103—42no—
194C42×C103—81no—
195C42×C103—81no—
196C42×C103C2×D412yes—
197C42×C103#4112yes—
198C23×C103—22no—
199C23×C103—41no—
200C23×C103—41no—
201C23×C103—41no—
202C23×C103—41no—
203C23×C103—41no—
204C23×C103—41no—
205C23×C103C22×D411yescharacteristic
206D4×C103—22no—
207D4×C103—22no—
208D4×C103—41no—
209D4×C103—41no—
210C2×C4×C103—21no—
211C2×C4×C103—21no—
212C2×C4×C103—21no—
213C2×C4×C103—21no—
214C2×C4×C103—21no—
215C2×C4×C103—21no—
216C2×C4×C103—22no—
217C2×C4×C103—22no—
218C2×C4×C103—21no—
219C2×C4×C103—21no—
220C2×C4×C103—21no—
221C2×C4×C103—22no—
222C2×C4×C103—21no—
223C2×C4×C103—21no—
224C2×C4×C103—21no—
225C2×C4×C103—21no—
226C2×C4×C103—21no—
227C2×C4×C103—21no—
228C2×C4×C103—41no—
229C2×C4×C103—41no—
230C2×C4×C103—41no—
231C2×C4×C103—41no—
232C2×C4×C103—41no—
233C2×C4×C103—41no—
234C2×C4×C103—41no—
235C2×C4×C103—41no—
236C2×C4×C103—41no—
237C2×C4×C103—41no—
238C2×C4×C103—41no—
239C2×C4×C103—41no—
240C2×C4×C103—41no—
241C2×C4×C103—41no—
242C2×C4×C103—41no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—84no—
247C2×C4×C103#12112yes—
248C2×C4×C103#12112yes—
249C2×C4×C103#13512yes—
250C2×C4×C103C22×D411yescharacteristic
251C2×C4×C103C22×Q811yescharacteristic
252C2×C4×C103C2×#4111yescharacteristic
253C2×C4×C103C2×#4111yescharacteristic
254C2×C4×C1032−1+411yescharacteristic
255C2×C4×C1032−1+411yescharacteristic
256C8×C103—22no—
257C8×C103—22no—
258C8×C103—41no—
259C8×C103—41no—
260C22×C103—42no—
261C22×C103—42no—
262C22×C103—42no—
263C22×C103—81no—
264C22×C103—81no—
265C22×C103—81no—
266C22×C103—81no—
267C22×C103C2×#12111yescharacteristic
268C22×C103#54711yescharacteristic
269C22×C103D4×Q811yescharacteristic
270C22×C103C2×#13511yescharacteristic
271C22×C103#57511yescharacteristic
272C22×C103#57611yescharacteristic
273C22×C103#57711yescharacteristic
274C4×C103—22no—
275C4×C103—22no—
276C4×C103—22no—
277C4×C103—41no—
278C4×C103—41no—
279C4×C103—41no—
280C4×C103—42no—
281C4×C103—42no—
282C4×C103—42no—
283C4×C103—81no—
284C4×C103—81no—
285C4×C103—81no—
286C4×C103—81no—
287C4×C103#53311yescharacteristic
288C4×C103#54111yescharacteristic
289C4×C103#54811yescharacteristic
290C4×C103D4×Q811yescharacteristic
291#25458C10311yesmaximal, characteristic, direct product factor, Sylow
292C2×C103—82no—
293C2×C103#242911yescharacteristic
294C2×C103#303511yescharacteristic
295C2×C103#304511yescharacteristic
296C2×C103#333711yescharacteristic
297C2×C103#335511yescharacteristic
298C2×C103#338011yescharacteristic
299C2×C103#338811yescharacteristic
300C2×#499C2×C10311yescharacteristic, complemented
301C2×#478C2×C10311yescharacteristic
302#2566C2×C10311yescharacteristic
303#2370C2×C10311yescharacteristic, complemented
304#2085C2×C10311yescharacteristic, complemented
305#2083C2×C10311yescharacteristic, complemented
306#2065C2×C10311yescharacteristic
307#2065C2×C10311yescharacteristic
308#1989C2×C10311yescharacteristic, complemented
309#1949C2×C10311yescharacteristic, complemented
310#1948C2×C10311yescharacteristic, complemented
311#1939C2×C10311yescharacteristic, complemented
312#1925C2×C10311yescharacteristic
313#1925C2×C10311yescharacteristic
314C4×#102C2×C10311yescharacteristic
315C103#2545811yescharacteristic, direct product factor, Sylow
316C2×#125C22×C10311yescharacteristic
317C2×#125C22×C10311yescharacteristic
318C2×C4×D4C22×C10311yescharacteristic
319#499—24no—
320#478—24no—
321C2×#107C22×C10311yescharacteristic
322C2×#107C22×C10311yescharacteristic
323C2×#107C22×C10311yescharacteristic
324C2×#106C22×C10311yescharacteristic
325C2×#106C22×C10311yescharacteristic
326C2×#106C22×C10311yescharacteristic
327C2×C4⋊C8C22×C10311yescharacteristic
328C2×C4⋊C8C22×C10311yescharacteristic
329C2×C4⋊C8C22×C10311yescharacteristic
330C2×#102C22×C10311yescharacteristic
331C2×#102C22×C10311yescharacteristic
332C2×#102C22×C10311yescharacteristic
333C2×#102C22×C10311yescharacteristic
334C2×C4×C8C22×C10311yescharacteristic
335#396—21no—
336#396—21no—
337#390C22×C10311yescharacteristic
338#390C22×C10311yescharacteristic
339#389—21no—
340#389C22×C10311yescharacteristic
341#389C22×C10311yescharacteristic
342#387—21no—
343#387—21no—
344#385—21no—
345#385—21no—
346#384C22×C10311yescharacteristic
347#382C22×C10311yescharacteristic
348C4×C4⋊C4—21no—
349C4×C4⋊C4C22×C10311yescharacteristic
350C4×C4⋊C4C22×C10311yescharacteristic
351C4×C4⋊C4C22×C10311yescharacteristic
352C4×C4⋊C4C22×C10311yescharacteristic
353#340C22×C10311yescharacteristic
354#340C22×C10311yescharacteristic
355#340C22×C10311yescharacteristic
356#340C22×C10311yescharacteristic
357#340C22×C10311yescharacteristic
358#340C22×C10311yescharacteristic
359#336C22×C10311yescharacteristic
360#336C22×C10311yescharacteristic
361C22×D4C23×C10311yescharacteristic
362C23×C4—21no—
363C22×C8C23×C10311yescharacteristic
364C22×C8C23×C10311yescharacteristic
365C22×C8C23×C10311yescharacteristic
366C22×C8C23×C10311yescharacteristic
367#125—22no—
368#125—22no—
369#125—22no—
370#125D4×C10314yes—
371C4×D4—22no—
372C4×D4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4D4×C10311yescharacteristic
382C2×C4⋊C4D4×C10311yescharacteristic
383C2×C4⋊C4C23×C10311yescharacteristic
384C2×C4⋊C4C23×C10311yescharacteristic
385C2×C4⋊C4C23×C10311yescharacteristic
386C2×C4⋊C4C23×C10311yescharacteristic
387C2×C4⋊C4C23×C10311yescharacteristic
388C2×C4⋊C4C23×C10311yescharacteristic
389C2×C4⋊C4C23×C10311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C10311yescharacteristic
399C2×C42C23×C10311yescharacteristic
400C2×C42C23×C10311yescharacteristic
401#107—22no—
402#107—22no—
403#107—22no—
404#106—22no—
405#106—22no—
406#106—22no—
407C4⋊C8—22no—
408C4⋊C8—22no—
409C4⋊C8—22no—
410#102—22no—
411#102—22no—
412#102—22no—
413#102Q8×C10314yes—
414C4×C8—22no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95D4×C10311yescharacteristic
423#95D4×C10311yescharacteristic
424C24—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4C2×Q8×C10312yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—81no—
440C22×C4—81no—
441C22×C4C2×D4×C10311yescharacteristic
442C22×C4C2×D4×C10311yescharacteristic
443C22×C4C2×D4×C10311yescharacteristic
444C22×C4C2×D4×C10311yescharacteristic
445C22×C4C2×D4×C10311yescharacteristic
446C22×C4C2×D4×C10311yescharacteristic
447C22×C4C24×C10311yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C2×Q8×C10312yes—
459C2×C8#41×C10312yes—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4C2×D4×C10312yes—
482C4⋊C4C2×D4×C10312yes—
483C4⋊C4C2×Q8×C10312yes—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—81no—
495C42—81no—
496C42C2×D4×C10312yes—
497C42#41×C10312yes—
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23C22×D4×C10311yescharacteristic
506D4—22no—
507D4—22no—
508D4—41no—
509D4—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—84no—
547C2×C4#121×C10312yes—
548C2×C4#121×C10312yes—
549C2×C4#135×C10312yes—
550C2×C4C22×D4×C10311yescharacteristic
551C2×C4C22×Q8×C10311yescharacteristic
552C2×C4C2×#41×C10311yescharacteristic
553C2×C4C2×#41×C10311yescharacteristic
554C2×C42−1+4×C10311yescharacteristic
555C2×C42−1+4×C10311yescharacteristic
556C8—22no—
557C8—22no—
558C8—41no—
559C8—41no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22C2×#121×C10311yescharacteristic
568C22#547×C10311yescharacteristic
569C22D4×Q8×C10311yescharacteristic
570C22C2×#135×C10311yescharacteristic
571C22#575×C10311yescharacteristic
572C22#576×C10311yescharacteristic
573C22#577×C10311yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—42no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4#533×C10311yescharacteristic
588C4#541×C10311yescharacteristic
589C4#548×C10311yescharacteristic
590C4D4×Q8×C10311yescharacteristic
591C2—82no—
592C2C103×#242911yescharacteristic
593C2C103×#303511yescharacteristic
594C2C103×#304511yescharacteristic
595C2C103×#333711yescharacteristic
596C2C103×#335511yescharacteristic
597C2C103×#338011yescharacteristic
598C2C103×#338811yescharacteristic
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
1. C2×#499×C103C2semidirect
4. C103×#2370C2semidirect
5. C103×#2085C2semidirect
6. C103×#2083C2semidirect
9. C103×#1989C2semidirect
10. C103×#1949C2semidirect
11. C103×#1948C2semidirect
12. C103×#1939C2semidirect
291. #25458C103direct (N × H)
300. C2×#499C2×C103semidirect
303. #2370C2×C103semidirect
304. #2085C2×C103semidirect
305. #2083C2×C103semidirect
308. #1989C2×C103semidirect
309. #1949C2×C103semidirect
310. #1948C2×C103semidirect
311. #1939C2×C103semidirect
315. C103#25458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#499×C1032
C2×#478×C1032
C103×#25662
C103×#23702
C103×#20852
C103×#20832
C103×#20652
C103×#19892
C103×#19492
C103×#19482
C103×#19392
C103×#19252
C4×#102×C1032
#25458103