Finite Group Databasebeta

← C103×#24586 #39929861

Subgroups — C103×#24586 #39929861

Order 26368.

762 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C103C211yesmaximal, characteristic
2C2×#427×C103C211yesmaximal, characteristic
3C103×#2499C211yesmaximal, characteristic
4C103×#2346C211yesmaximal, characteristic
5C103×#2085C211yesmaximal, characteristic, complemented
6C103×#2084C211yesmaximal, characteristic, complemented
7C103×#2068C211yesmaximal, characteristic, complemented
8C103×#2066C211yesmaximal, characteristic, complemented
9C103×#1949C211yesmaximal, characteristic, complemented
10C103×#1947C211yesmaximal, characteristic, complemented
11C103×#1928C211yesmaximal, characteristic, complemented
12C103×#1927C211yesmaximal, characteristic, complemented
13C103×#1892C211yesmaximal, characteristic
14C103×#1850C211yesmaximal, characteristic
15C103×#1825C211yesmaximal, characteristic
16C23×C8×C103C2211yescharacteristic
17C2×C22⋊Q8×C103C2211yescharacteristic
18C2×#117×C103C2211yescharacteristic
19C2×#117×C103C2211yescharacteristic
20#485×C103—24no—
21#427×C103—24no—
22C2×#107×C103C2211yescharacteristic
23C2×#107×C103C2211yescharacteristic
24C2×#107×C103C2211yescharacteristic
25C2×#106×C103C2211yescharacteristic
26C2×#106×C103C2211yescharacteristic
27C2×#106×C103C2211yescharacteristic
28C2×C4⋊C8×C103C2211yescharacteristic
29C2×C4⋊C8×C103C2211yescharacteristic
30C2×#103×C103C2211yescharacteristic
31C2×#103×C103C2211yescharacteristic
32C2×#103×C103C2211yescharacteristic
33C2×#103×C103C2211yescharacteristic
34C2×C22⋊C8×C103C2211yescharacteristic
35#397×C103—21no—
36#397×C103—21no—
37#391×C103C2211yescharacteristic
38#391×C103C2211yescharacteristic
39#389×C103C2211yescharacteristic
40#389×C103C2211yescharacteristic
41#388×C103—21no—
42#388×C103—21no—
43#387×C103—21no—
44#387×C103—21no—
45#384×C103C2211yescharacteristic
46#382×C103—21no—
47#382×C103C2211yescharacteristic
48#380×C103C2211yescharacteristic
49C4×C4⋊C4×C103C2211yescharacteristic
50C4×C4⋊C4×C103C2211yescharacteristic
51C4×C22⋊C4×C103C2211yescharacteristic
52#376×C103—21no—
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×Q8×C103C2311yescharacteristic
62C23×C4×C103C2311yescharacteristic
63C22×C8×C103—22no—
64C22×C8×C103—22no—
65C22×C8×C103—22no—
66C22×C8×C103C2311yescharacteristic
67C22×C8×C103C2311yescharacteristic
68C22×C8×C103C2311yescharacteristic
69C22×C8×C103C2311yescharacteristic
70C22⋊Q8×C103—22no—
71C22⋊Q8×C103—22no—
72#117×C103—22no—
73#117×C103—22no—
74#117×C103—22no—
75#117×C103D414yes—
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×C103C2311yescharacteristic
82C2×C4⋊C4×C103C2311yescharacteristic
83C2×C4⋊C4×C103C2311yescharacteristic
84C2×C4⋊C4×C103C2311yescharacteristic
85C2×C4⋊C4×C103C2311yescharacteristic
86C2×C4⋊C4×C103C2311yescharacteristic
87C2×C4⋊C4×C103C2311yescharacteristic
88C2×C22⋊C4×C103—21no—
89C2×C22⋊C4×C103—21no—
90C2×C22⋊C4×C103—21no—
91C2×C22⋊C4×C103—21no—
92C2×C22⋊C4×C103D411yescharacteristic
93C2×C22⋊C4×C103D411yescharacteristic
94C2×C42×C103—21no—
95C2×C42×C103—21no—
96C2×C42×C103—21no—
97C2×C42×C103—21no—
98C2×C42×C103C2311yescharacteristic
99C2×C42×C103C2311yescharacteristic
100#107×C103—22no—
101#107×C103—22no—
102#107×C103—22no—
103#106×C103—22no—
104#106×C103—22no—
105#106×C103—22no—
106C4⋊C8×C103—22no—
107C4⋊C8×C103—22no—
108#103×C103—22no—
109#103×C103—22no—
110#103×C103—22no—
111#103×C103—22no—
112C22⋊C8×C103—22no—
113#95×C103—21no—
114#95×C103—21no—
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×C103C2×D411yescharacteristic
127C2×Q8×C103—21no—
128C2×Q8×C103—21no—
129C2×Q8×C103—21no—
130C2×Q8×C103—21no—
131C2×Q8×C103—21no—
132C2×Q8×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—21no—
139C22×C4×C103—21no—
140C22×C4×C103—21no—
141C22×C4×C103—21no—
142C22×C4×C103—21no—
143C22×C4×C103—21no—
144C22×C4×C103—21no—
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D411yescharacteristic
147C22×C4×C103C2×D411yescharacteristic
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2×D412yes—
150C22×C4×C103C2×D411yescharacteristic
151C22×C4×C103#4112yes—
152C22×C4×C103C2411yescharacteristic
153C2×C8×C103—28no—
154C2×C8×C103—21no—
155C2×C8×C103—21no—
156C2×C8×C103—21no—
157C2×C8×C103—21no—
158C2×C8×C103—21no—
159C2×C8×C103—21no—
160C2×C8×C103—21no—
161C2×C8×C103—21no—
162C2×C8×C103—21no—
163C2×C8×C103—21no—
164C2×C8×C103#4112yes—
165C2×C8×C103#4112yes—
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—21no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—42no—
179C4⋊C4×C103—42no—
180C4⋊C4×C103—42no—
181C4⋊C4×C103—81no—
182C4⋊C4×C103—81no—
183C4⋊C4×C103C2×D412yes—
184C4⋊C4×C103C2×D412yes—
185C22⋊C4×C103—24no—
186C22⋊C4×C103—22no—
187C22⋊C4×C103—41no—
188C22⋊C4×C103—42no—
189C22⋊C4×C103—42no—
190C22⋊C4×C103—81no—
191C42×C103—24no—
192C42×C103—21no—
193C42×C103—21no—
194C42×C103—21no—
195C42×C103—21no—
196C42×C103—42no—
197C42×C103—42no—
198C42×C103—42no—
199C23×C103—21no—
200C23×C103—21no—
201C23×C103—21no—
202C23×C103—21no—
203C23×C103—21no—
204C23×C103—21no—
205C23×C103#12112yes—
206C23×C103C22×D411yescharacteristic
207Q8×C103—41no—
208Q8×C103—41no—
209Q8×C103—41no—
210Q8×C103—41no—
211C2×C4×C103—21no—
212C2×C4×C103—21no—
213C2×C4×C103—21no—
214C2×C4×C103—21no—
215C2×C4×C103—22no—
216C2×C4×C103—22no—
217C2×C4×C103—22no—
218C2×C4×C103—22no—
219C2×C4×C103—22no—
220C2×C4×C103—22no—
221C2×C4×C103—21no—
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—21no—
229C2×C4×C103—21no—
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—41no—
247C2×C4×C103—41no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103#12112yes—
253C2×C4×C103#13512yes—
254C2×C4×C103C22×D411yescharacteristic
255C2×C4×C103C2×#4111yescharacteristic
256C2×C4×C103C2×#4111yescharacteristic
257C2×C4×C103C2×#4111yescharacteristic
258C2×C4×C1032−1+411yescharacteristic
259C2×C4×C1032−1+411yescharacteristic
260C8×C103—22no—
261C8×C103—22no—
262C8×C103—41no—
263C8×C103—41no—
264C22×C103—22no—
265C22×C103—22no—
266C22×C103—22no—
267C22×C103—41no—
268C22×C103—41no—
269C22×C103—41no—
270C22×C103—41no—
271C22×C103C2×#12111yescharacteristic
272C22×C103#54711yescharacteristic
273C22×C103#54711yescharacteristic
274C22×C103C2×#13511yescharacteristic
275C22×C103#57511yescharacteristic
276C22×C103#57711yescharacteristic
277C22×C103#57811yescharacteristic
278C4×C103—22no—
279C4×C103—22no—
280C4×C103—41no—
281C4×C103—41no—
282C4×C103—41no—
283C4×C103—42no—
284C4×C103—42no—
285C4×C103—81no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103—81no—
289C4×C103—81no—
290C4×C103—81no—
291C4×C103#52511yescharacteristic
292C4×C103#53611yescharacteristic
293C4×C103#55211yescharacteristic
294C4×C103#55211yescharacteristic
295#24586C10311yesmaximal, characteristic, direct product factor, Sylow
296C2×C103—42no—
297C2×C103#241311yescharacteristic
298C2×C103#303511yescharacteristic
299C2×C103#304611yescharacteristic
300C2×C103#333611yescharacteristic
301C2×C103#334011yescharacteristic
302C2×C103#334811yescharacteristic
303C2×C103#334911yescharacteristic
304C2×#485C2×C10311yescharacteristic
305C2×#427C2×C10311yescharacteristic
306#2499C2×C10311yescharacteristic
307#2346C2×C10311yescharacteristic
308#2085C2×C10311yescharacteristic, complemented
309#2084C2×C10311yescharacteristic, complemented
310#2068C2×C10311yescharacteristic, complemented
311#2066C2×C10311yescharacteristic, complemented
312#1949C2×C10311yescharacteristic, complemented
313#1947C2×C10311yescharacteristic, complemented
314#1928C2×C10311yescharacteristic, complemented
315#1927C2×C10311yescharacteristic, complemented
316#1892C2×C10311yescharacteristic
317#1850C2×C10311yescharacteristic
318#1825C2×C10311yescharacteristic
319C103#2458611yescharacteristic, direct product factor, Sylow
320C23×C8C22×C10311yescharacteristic
321C2×C22⋊Q8C22×C10311yescharacteristic
322C2×#117C22×C10311yescharacteristic
323C2×#117C22×C10311yescharacteristic
324#485—24no—
325#427—24no—
326C2×#107C22×C10311yescharacteristic
327C2×#107C22×C10311yescharacteristic
328C2×#107C22×C10311yescharacteristic
329C2×#106C22×C10311yescharacteristic
330C2×#106C22×C10311yescharacteristic
331C2×#106C22×C10311yescharacteristic
332C2×C4⋊C8C22×C10311yescharacteristic
333C2×C4⋊C8C22×C10311yescharacteristic
334C2×#103C22×C10311yescharacteristic
335C2×#103C22×C10311yescharacteristic
336C2×#103C22×C10311yescharacteristic
337C2×#103C22×C10311yescharacteristic
338C2×C22⋊C8C22×C10311yescharacteristic
339#397—21no—
340#397—21no—
341#391C22×C10311yescharacteristic
342#391C22×C10311yescharacteristic
343#389C22×C10311yescharacteristic
344#389C22×C10311yescharacteristic
345#388—21no—
346#388—21no—
347#387—21no—
348#387—21no—
349#384C22×C10311yescharacteristic
350#382—21no—
351#382C22×C10311yescharacteristic
352#380C22×C10311yescharacteristic
353C4×C4⋊C4C22×C10311yescharacteristic
354C4×C4⋊C4C22×C10311yescharacteristic
355C4×C22⋊C4C22×C10311yescharacteristic
356#376—21no—
357#340C22×C10311yescharacteristic
358#340C22×C10311yescharacteristic
359#340C22×C10311yescharacteristic
360#340C22×C10311yescharacteristic
361#340C22×C10311yescharacteristic
362#340C22×C10311yescharacteristic
363#336C22×C10311yescharacteristic
364#336C22×C10311yescharacteristic
365C22×Q8C23×C10311yescharacteristic
366C23×C4C23×C10311yescharacteristic
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8C23×C10311yescharacteristic
371C22×C8C23×C10311yescharacteristic
372C22×C8C23×C10311yescharacteristic
373C22×C8C23×C10311yescharacteristic
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376#117—22no—
377#117—22no—
378#117—22no—
379#117D4×C10314yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C23×C10311yescharacteristic
386C2×C4⋊C4C23×C10311yescharacteristic
387C2×C4⋊C4C23×C10311yescharacteristic
388C2×C4⋊C4C23×C10311yescharacteristic
389C2×C4⋊C4C23×C10311yescharacteristic
390C2×C4⋊C4C23×C10311yescharacteristic
391C2×C4⋊C4C23×C10311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4D4×C10311yescharacteristic
397C2×C22⋊C4D4×C10311yescharacteristic
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42C23×C10311yescharacteristic
403C2×C42C23×C10311yescharacteristic
404#107—22no—
405#107—22no—
406#107—22no—
407#106—22no—
408#106—22no—
409#106—22no—
410C4⋊C8—22no—
411C4⋊C8—22no—
412#103—22no—
413#103—22no—
414#103—22no—
415#103—22no—
416C22⋊C8—22no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95D4×C10311yescharacteristic
429#95D4×C10311yescharacteristic
430C24C2×D4×C10311yescharacteristic
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4C2×D4×C10311yescharacteristic
450C22×C4C2×D4×C10311yescharacteristic
451C22×C4C2×D4×C10311yescharacteristic
452C22×C4C2×D4×C10311yescharacteristic
453C22×C4C2×D4×C10312yes—
454C22×C4C2×D4×C10311yescharacteristic
455C22×C4#41×C10312yes—
456C22×C4C24×C10311yescharacteristic
457C2×C8—28no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8#41×C10312yes—
469C2×C8#41×C10312yes—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4C2×D4×C10312yes—
488C4⋊C4C2×D4×C10312yes—
489C22⋊C4—24no—
490C22⋊C4—22no—
491C22⋊C4—41no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—81no—
495C42—24no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—42no—
501C42—42no—
502C42—42no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23#121×C10312yes—
510C23C22×D4×C10311yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
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—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4#121×C10312yes—
557C2×C4#135×C10312yes—
558C2×C4C22×D4×C10311yescharacteristic
559C2×C4C2×#41×C10311yescharacteristic
560C2×C4C2×#41×C10311yescharacteristic
561C2×C4C2×#41×C10311yescharacteristic
562C2×C42−1+4×C10311yescharacteristic
563C2×C42−1+4×C10311yescharacteristic
564C8—22no—
565C8—22no—
566C8—41no—
567C8—41no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×#121×C10311yescharacteristic
576C22#547×C10311yescharacteristic
577C22#547×C10311yescharacteristic
578C22C2×#135×C10311yescharacteristic
579C22#575×C10311yescharacteristic
580C22#577×C10311yescharacteristic
581C22#578×C10311yescharacteristic
582C4—22no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4#525×C10311yescharacteristic
596C4#536×C10311yescharacteristic
597C4#552×C10311yescharacteristic
598C4#552×C10311yescharacteristic
599C2—42no—
600C2C103×#241311yescharacteristic
601C2C103×#303511yescharacteristic
602C2C103×#304611yescharacteristic
603C2C103×#333611yescharacteristic
604C2C103×#334011yescharacteristic
605C2C103×#334811yescharacteristic
606C2C103×#334911yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C22⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
5. C103×#2085C2semidirect
6. C103×#2084C2semidirect
7. C103×#2068C2semidirect
8. C103×#2066C2semidirect
9. C103×#1949C2semidirect
10. C103×#1947C2semidirect
11. C103×#1928C2semidirect
12. C103×#1927C2semidirect
295. #24586C103direct (N × H)
308. #2085C2×C103semidirect
309. #2084C2×C103semidirect
310. #2068C2×C103semidirect
311. #2066C2×C103semidirect
312. #1949C2×C103semidirect
313. #1947C2×C103semidirect
314. #1928C2×C103semidirect
315. #1927C2×C103semidirect
319. C103#24586direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#485×C1032
C2×#427×C1032
C103×#24992
C103×#23462
C103×#20852
C103×#20842
C103×#20682
C103×#20662
C103×#19492
C103×#19472
C103×#19282
C103×#19272
C103×#18922
C103×#18502
C103×#18252
#24586103