Finite Group Databasebeta

← C103×#9241 #39914516

Subgroups — C103×#9241 #39914516

Order 26368.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C103C211yesmaximal, characteristic
2C103×#2880C211yesmaximal, characteristic, complemented
3C103×#1789C211yesmaximal, characteristic, complemented
4C103×#1507C211yesmaximal, characteristic, complemented
5C103×#1471C211yesmaximal, characteristic, complemented
6C103×#1293C211yesmaximal, characteristic, complemented
7C103×#1282C211yesmaximal, characteristic, complemented
8C22×#41×C103C2211yescharacteristic
9C22×SD16×C103C411yescharacteristic, complemented
10C22×D8×C103C411yescharacteristic, complemented
11C2×#131×C103—21no—
12C2×#121×C103C2211yescharacteristic
13#449×C103—21no—
14#449×C103—21no—
15#449×C103—21no—
16#449×C103—21no—
17C2×#104×C103—21no—
18C2×#104×C103—21no—
19C2×#103×C103C411yescharacteristic, complemented
20C2×#102×C103C411yescharacteristic, complemented
21#408×C103—21no—
22#408×C103—22no—
23#407×C103—21no—
24#407×C103C2211yescharacteristic
25#407×C103C2211yescharacteristic
26C2×C22⋊C8×C103—21no—
27C2×C22⋊C8×C103C2211yescharacteristic
28C2×C22⋊C8×C103C2211yescharacteristic
29C4×C22⋊C4×C103C2211yescharacteristic
30#327×C103—22no—
31#323×C103—21no—
32#323×C103—21no—
33C2×#41×C103—21no—
34C2×#41×C103—21no—
35C2×#41×C103—42no—
36C2×#41×C103—42no—
37C2×#41×C103D411yescharacteristic
38C2×#41×C103D411yescharacteristic
39C2×#41×C103D411yescharacteristic
40C2×#41×C103D411yescharacteristic
41C22×Q8×C103C2×C411yescharacteristic
42C22×D4×C103—21no—
43C22×D4×C103—21no—
44C22×D4×C103C2×C411yescharacteristic
45C22×D4×C103C2×C411yescharacteristic
46C23×C4×C103—21no—
47C23×C4×C103C2311yescharacteristic
48C2×SD16×C103—21no—
49C2×SD16×C103—21no—
50C2×SD16×C103—42no—
51C2×D8×C103—21no—
52C2×D8×C103—21no—
53C2×D8×C103—42no—
54#131×C103—42no—
55#131×C103—42no—
56C2×M16×C103—22no—
57C2×M16×C103—21no—
58C2×M16×C103—21no—
59C22×C8×C103—22no—
60C22×C8×C103—21no—
61C22×C8×C103C2×C411yescharacteristic
62C22×C8×C103C2×C411yescharacteristic
63#121×C103—21no—
64#121×C103—21no—
65#121×C103—21no—
66#121×C103—21no—
67C2×C4⋊C4×C103C2×C411yescharacteristic
68C2×C22⋊C4×C103—21no—
69C2×C22⋊C4×C103—21no—
70C2×C42×C103—21no—
71#104×C103—42no—
72#104×C103—42no—
73#103×C103—21no—
74#103×C103—21no—
75#102×C103—21no—
76#102×C103—21no—
77C22⋊C8×C103—22no—
78C22⋊C8×C103—22no—
79C22⋊C8×C103—21no—
80C22⋊C8×C103—21no—
81C22⋊C8×C103—21no—
82C22⋊C8×C103—21no—
83C22⋊C8×C103—21no—
84C22⋊C8×C103—21no—
85C22⋊C8×C103D411yescharacteristic
86C22⋊C8×C103D411yescharacteristic
87C22⋊C8×C103D412yes—
88#95×C103—21no—
89C24×C103—21no—
90C24×C103—21no—
91C24×C103#4111yescharacteristic
92#41×C103—22no—
93#41×C103—22no—
94#41×C103—22no—
95#41×C103—22no—
96#41×C103—41no—
97#41×C103—41no—
98#41×C103—41no—
99#41×C103—41no—
100#41×C103—44no—
101#41×C103—44no—
102C2×Q8×C103—21no—
103C2×Q8×C103—22no—
104C2×Q8×C103—41no—
105C2×Q8×C103C22⋊C411yescharacteristic
106C2×Q8×C103C22⋊C411yescharacteristic
107C2×D4×C103—21no—
108C2×D4×C103—22no—
109C2×D4×C103—21no—
110C2×D4×C103—21no—
111C2×D4×C103—21no—
112C2×D4×C103—21no—
113C2×D4×C103—21no—
114C2×D4×C103—21no—
115C2×D4×C103—41no—
116C2×D4×C103—41no—
117C2×D4×C103—41no—
118C2×D4×C103—44no—
119C2×D4×C103—41no—
120C2×D4×C103—41no—
121C2×D4×C103—82no—
122C2×D4×C103C22⋊C411yescharacteristic
123C2×D4×C103C22⋊C411yescharacteristic
124C22×C4×C103—21no—
125C22×C4×C103—21no—
126C22×C4×C103—21no—
127C22×C4×C103—21no—
128C22×C4×C103—21no—
129C22×C4×C103—21no—
130C22×C4×C103—41no—
131C22×C4×C103—41no—
132C22×C4×C103—44no—
133C22×C4×C103—41no—
134C22×C4×C103C22×C411yescharacteristic
135C22×C4×C103C2×D411yescharacteristic
136C22×C4×C103C2×D411yescharacteristic
137C22×C4×C103C2×D411yescharacteristic
138C22×C4×C103C2×D411yescharacteristic
139C22×C4×C103#4111yescharacteristic
140SD16×C103—42no—
141SD16×C103—42no—
142D8×C103—42no—
143D8×C103—42no—
144M16×C103—44no—
145M16×C103—41no—
146M16×C103—41no—
147M16×C103—41no—
148M16×C103—41no—
149C2×C8×C103—21no—
150C2×C8×C103—21no—
151C2×C8×C103—21no—
152C2×C8×C103—22no—
153C2×C8×C103—21no—
154C2×C8×C103—44no—
155C2×C8×C103—41no—
156C2×C8×C103—41no—
157C2×C8×C103—41no—
158C2×C8×C103—41no—
159C2×C8×C103—41no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C22⋊C4×C103—22no—
163C22⋊C4×C103—41no—
164C22⋊C4×C103—41no—
165C22⋊C4×C103—41no—
166C42×C103—41no—
167C42×C103—41no—
168C23×C103—21no—
169C23×C103—21no—
170C23×C103—21no—
171C23×C103—21no—
172C23×C103—41no—
173C23×C103—41no—
174C23×C103—42no—
175C23×C103—41no—
176C23×C103—41no—
177C23×C103—41no—
178C23×C103—41no—
179C23×C103—41no—
180C23×C103—81no—
181C23×C103—81no—
182C23×C103—81no—
183C23×C103C4×D411yescharacteristic
184C23×C103#12111yescharacteristic
185C23×C103#12311yescharacteristic
186Q8×C103—21no—
187Q8×C103—21no—
188Q8×C103—21no—
189Q8×C103—42no—
190Q8×C103#9912yes—
191D4×C103—24no—
192D4×C103—21no—
193D4×C103—21no—
194D4×C103—21no—
195D4×C103—42no—
196D4×C103—42no—
197D4×C103—42no—
198D4×C103—42no—
199D4×C103—41no—
200D4×C103—41no—
201D4×C103—81no—
202D4×C103—82no—
203D4×C103—82no—
204D4×C103#9912yes—
205C2×C4×C103—24no—
206C2×C4×C103—21no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—21no—
210C2×C4×C103—21no—
211C2×C4×C103—21no—
212C2×C4×C103—21no—
213C2×C4×C103—21no—
214C2×C4×C103—41no—
215C2×C4×C103—41no—
216C2×C4×C103—41no—
217C2×C4×C103—42no—
218C2×C4×C103—42no—
219C2×C4×C103—42no—
220C2×C4×C103—42no—
221C2×C4×C103—42no—
222C2×C4×C103—41no—
223C2×C4×C103—81no—
224C2×C4×C103—81no—
225C2×C4×C103—81no—
226C2×C4×C103C2×C22⋊C411yescharacteristic
227C2×C4×C103C4×D411yescharacteristic
228C2×C4×C103#12011yescharacteristic
229C2×C4×C103#12111yescharacteristic
230C8×C103—41no—
231C8×C103—42no—
232C8×C103—41no—
233C8×C103—41no—
234C8×C103—41no—
235C8×C103—81no—
236C22×C103—21no—
237C22×C103—21no—
238C22×C103—21no—
239C22×C103—21no—
240C22×C103—21no—
241C22×C103—21no—
242C22×C103—22no—
243C22×C103—21no—
244C22×C103—21no—
245C22×C103—41no—
246C22×C103—41no—
247C22×C103—41no—
248C22×C103—41no—
249C22×C103—41no—
250C22×C103—81no—
251C22×C103—81no—
252C22×C103—82no—
253C22×C103—82no—
254C22×C103—81no—
255C22×C103—81no—
256C22×C103—81no—
257C22×C103—161no—
258C22×C103—161no—
259C22×C103#38611yescharacteristic
260C22×C103#44311yescharacteristic
261C22×C103#44411yescharacteristic
262C4×C103—21no—
263C4×C103—21no—
264C4×C103—22no—
265C4×C103—21no—
266C4×C103—41no—
267C4×C103—82no—
268C4×C103—81no—
269C4×C103C2×#9911yescharacteristic
270C4×C103C2×#9911yescharacteristic
271#9241C10311yesmaximal, characteristic, direct product factor, Sylow
272C2×C103—21no—
273C2×C103—21no—
274C2×C103—41no—
275C2×C103—41no—
276C2×C103—42no—
277C2×C103—81no—
278C2×C103—161no—
279C2×C103#187611yescharacteristic
280C2×C103#189811yescharacteristic
281C2×C103#190311yescharacteristic
282C2×#449C2×C10311yescharacteristic
283#2880C2×C10311yescharacteristic, complemented
284#1789C2×C10311yescharacteristic, complemented
285#1507C2×C10311yescharacteristic, complemented
286#1471C2×C10311yescharacteristic, complemented
287#1293C2×C10311yescharacteristic, complemented
288#1282C2×C10311yescharacteristic, complemented
289C103#924111yescharacteristic, direct product factor, Sylow
290C22×#41C22×C10311yescharacteristic
291C22×SD16C4×C10311yescharacteristic, complemented
292C22×D8C4×C10311yescharacteristic, complemented
293C2×#131—21no—
294C2×#121C22×C10311yescharacteristic
295#449—21no—
296#449—21no—
297#449—21no—
298#449—21no—
299C2×#104—21no—
300C2×#104—21no—
301C2×#103C4×C10311yescharacteristic, complemented
302C2×#102C4×C10311yescharacteristic, complemented
303#408—21no—
304#408—22no—
305#407—21no—
306#407C22×C10311yescharacteristic
307#407C22×C10311yescharacteristic
308C2×C22⋊C8—21no—
309C2×C22⋊C8C22×C10311yescharacteristic
310C2×C22⋊C8C22×C10311yescharacteristic
311C4×C22⋊C4C22×C10311yescharacteristic
312#327—22no—
313#323—21no—
314#323—21no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41D4×C10311yescharacteristic
320C2×#41D4×C10311yescharacteristic
321C2×#41D4×C10311yescharacteristic
322C2×#41D4×C10311yescharacteristic
323C22×Q8C2×C4×C10311yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×C4×C10311yescharacteristic
327C22×D4C2×C4×C10311yescharacteristic
328C23×C4—21no—
329C23×C4C23×C10311yescharacteristic
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—42no—
333C2×D8—21no—
334C2×D8—21no—
335C2×D8—42no—
336#131—42no—
337#131—42no—
338C2×M16—22no—
339C2×M16—21no—
340C2×M16—21no—
341C22×C8—22no—
342C22×C8—21no—
343C22×C8C2×C4×C10311yescharacteristic
344C22×C8C2×C4×C10311yescharacteristic
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349C2×C4⋊C4C2×C4×C10311yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353#104—42no—
354#104—42no—
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8D4×C10311yescharacteristic
368C22⋊C8D4×C10311yescharacteristic
369C22⋊C8D4×C10312yes—
370#95—21no—
371C24—21no—
372C24—21no—
373C24#41×C10311yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8C22⋊C4×C10311yescharacteristic
388C2×Q8C22⋊C4×C10311yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—44no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—82no—
404C2×D4C22⋊C4×C10311yescharacteristic
405C2×D4C22⋊C4×C10311yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—41no—
416C22×C4C22×C4×C10311yescharacteristic
417C22×C4C2×D4×C10311yescharacteristic
418C22×C4C2×D4×C10311yescharacteristic
419C22×C4C2×D4×C10311yescharacteristic
420C22×C4C2×D4×C10311yescharacteristic
421C22×C4#41×C10311yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—44no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C42—41no—
449C42—41no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23C4×D4×C10311yescharacteristic
466C23#121×C10311yescharacteristic
467C23#123×C10311yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#99×C10312yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4#99×C10312yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4C2×C22⋊C4×C10311yescharacteristic
509C2×C4C4×D4×C10311yescharacteristic
510C2×C4#120×C10311yescharacteristic
511C2×C4#121×C10311yescharacteristic
512C8—41no—
513C8—42no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—81no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22#386×C10311yescharacteristic
542C22#443×C10311yescharacteristic
543C22#444×C10311yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—81no—
551C4C2×#99×C10311yescharacteristic
552C4C2×#99×C10311yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2C103×#187611yescharacteristic
561C2C103×#189811yescharacteristic
562C2C103×#190311yescharacteristic
subgroupG/H
center, socleC22×C103#386
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
prime radicalC2×#449×C103C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2880C2semidirect
3. C103×#1789C2semidirect
4. C103×#1507C2semidirect
5. C103×#1471C2semidirect
6. C103×#1293C2semidirect
7. C103×#1282C2semidirect
9. C22×SD16×C103C4semidirect
10. C22×D8×C103C4semidirect
19. C2×#103×C103C4semidirect
20. C2×#102×C103C4semidirect
271. #9241C103direct (N × H)
283. #2880C2×C103semidirect
284. #1789C2×C103semidirect
285. #1507C2×C103semidirect
286. #1471C2×C103semidirect
287. #1293C2×C103semidirect
288. #1282C2×C103semidirect
289. C103#9241direct (N × H)
291. C22×SD16C4×C103semidirect
292. C22×D8C4×C103semidirect
301. C2×#103C4×C103semidirect
302. C2×#102C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1032
C103×#28802
C103×#17892
C103×#15072
C103×#14712
C103×#12932
C103×#12822
#9241103