Finite Group Databasebeta

← C103×#12705 #39917980

Subgroups — C103×#12705 #39917980

Order 26368.

1186 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3484C211yesmaximal, characteristic
2C103×#2121C214yesmaximal, complemented
3C103×#1783C211yesmaximal, characteristic, complemented
4C103×#1781C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C103C411yescharacteristic, complemented
6C23×D4×C103C2211yescharacteristic
7#546×C103—24no—
8D42×C103—24no—
9#535×C103—21no—
10#534×C103—21no—
11#534×C103C2212yes—
12#525×C103—21no—
13C2×#120×C103—21no—
14C2×#120×C103C412yescomplemented
15#518×C103C411yescharacteristic, complemented
16C2×#100×C103—21no—
17C2×#100×C103C2212yescomplemented
18C2×#99×C103—21no—
19C2×#99×C103C2212yescomplemented
20#407×C103—21no—
21#379×C103—21no—
22#352×C103—24no—
23AΣL(1,𝔽16)×C103—24no—
24C25×C103C2×C411yescharacteristic
25C25×C103D411yescharacteristic
26H(5,𝔽2)×C103—42no—
27H(5,𝔽2)×C103—42no—
28C2×#41×C103—21no—
29C2×#41×C103—22no—
30C22×D4×C103—21no—
31C22×D4×C103—22no—
32C22×D4×C103—22no—
33C22×D4×C103—22no—
34C22×D4×C103—24no—
35C22×D4×C103—42no—
36C22×D4×C103—42no—
37C22×D4×C103C2×C411yescharacteristic
38C22×D4×C103C2×C412yes—
39C22×D4×C103D411yescharacteristic
40C22×D4×C103D411yescharacteristic
41C22×D4×C103C2311yescharacteristic
42C23×C4×C103D411yescharacteristic
43C2×M16×C103—22no—
44#127×C103—22no—
45#124×C103—22no—
46#123×C103—22no—
47#123×C103—22no—
48#123×C103D414yes—
49C22⋊Q8×C103—22no—
50#121×C103—22no—
51#121×C103—24no—
52#121×C103—24no—
53#121×C103—24no—
54#120×C103—24no—
55#120×C103—22no—
56#120×C103—22no—
57#120×C103—22no—
58#120×C103—22no—
59#120×C103—24no—
60#120×C103D414yes—
61C4×D4×C103—24no—
62C4×D4×C103—24no—
63#117×C103—21no—
64C2×C22⋊C4×C103—22no—
65C2×C22⋊C4×C103—21no—
66C2×C22⋊C4×C103—22no—
67C2×C22⋊C4×C103—22no—
68C2×C22⋊C4×C103—42no—
69C2×C22⋊C4×C103C2×C412yes—
70#100×C103—24no—
71#100×C103—42no—
72#99×C103—24no—
73#99×C103—42no—
74C22⋊C8×C103—42no—
75C24×C103—21no—
76C24×C103—22no—
77C24×C103—22no—
78C24×C103—22no—
79C24×C103—41no—
80C24×C103—41no—
81C24×C103—41no—
82C24×C103—82no—
83C24×C103—82no—
84C24×C103C22⋊C411yescharacteristic
85C24×C103C22⋊C411yescharacteristic
86C24×C103C22⋊C411yescharacteristic
87C24×C103C22⋊C412yescomplemented
88C24×C103C22×C411yescharacteristic
89C24×C103C2×D411yescharacteristic
90#41×C103—42no—
91#41×C103—48no—
92#41×C103—42no—
93C2×Q8×C103—21no—
94C2×D4×C103—22no—
95C2×D4×C103—22no—
96C2×D4×C103—24no—
97C2×D4×C103—22no—
98C2×D4×C103—21no—
99C2×D4×C103—22no—
100C2×D4×C103—22no—
101C2×D4×C103—22no—
102C2×D4×C103—22no—
103C2×D4×C103—24no—
104C2×D4×C103—24no—
105C2×D4×C103—22no—
106C2×D4×C103—22no—
107C2×D4×C103—22no—
108C2×D4×C103—41no—
109C2×D4×C103—41no—
110C2×D4×C103—41no—
111C2×D4×C103—41no—
112C2×D4×C103—416no—
113C2×D4×C103—48no—
114C2×D4×C103—42no—
115C2×D4×C103—42no—
116C2×D4×C103—42no—
117C2×D4×C103—42no—
118C2×D4×C103—84no—
119C2×D4×C103—84no—
120C2×D4×C103C2×D414yes—
121C22×C4×C103—21no—
122C22×C4×C103—22no—
123C22×C4×C103—22no—
124C22×C4×C103—22no—
125C22×C4×C103—22no—
126C22×C4×C103—22no—
127C22×C4×C103—41no—
128C22×C4×C103—42no—
129C22×C4×C103C22⋊C411yescharacteristic
130C22×C4×C103C22⋊C412yescomplemented
131C22×C4×C103C2×D411yescharacteristic
132M16×C103—42no—
133M16×C103—42no—
134C2×C8×C103—42no—
135C4⋊C4×C103—22no—
136C4⋊C4×C103—24no—
137C22⋊C4×C103—24no—
138C22⋊C4×C103—22no—
139C22⋊C4×C103—24no—
140C22⋊C4×C103—22no—
141C22⋊C4×C103—24no—
142C22⋊C4×C103—24no—
143C22⋊C4×C103—42no—
144C22⋊C4×C103—42no—
145C22⋊C4×C103—84no—
146C22⋊C4×C103C22⋊C414yescomplemented
147C42×C103—22no—
148C23×C103—21no—
149C23×C103—21no—
150C23×C103—21no—
151C23×C103—21no—
152C23×C103—21no—
153C23×C103—21no—
154C23×C103—21no—
155C23×C103—21no—
156C23×C103—21no—
157C23×C103—21no—
158C23×C103—22no—
159C23×C103—21no—
160C23×C103—21no—
161C23×C103—42no—
162C23×C103—44no—
163C23×C103—44no—
164C23×C103—44no—
165C23×C103—44no—
166C23×C103—44no—
167C23×C103—42no—
168C23×C103—42no—
169C23×C103—82no—
170C23×C103—82no—
171C23×C103—82no—
172C23×C103—81no—
173C23×C103—81no—
174C23×C103—81no—
175C23×C103—81no—
176C23×C103—82no—
177C23×C103—82no—
178C23×C103—82no—
179C23×C103—82no—
180C23×C103—82no—
181C23×C103—82no—
182C23×C103—82no—
183C23×C103—82no—
184C23×C103#9912yes—
185C23×C103C2×C22⋊C412yes—
186C23×C103C2×C22⋊C411yescharacteristic
187C23×C103#12012yes—
188Q8×C103—42no—
189D4×C103—28no—
190D4×C103—44no—
191D4×C103—44no—
192D4×C103—44no—
193D4×C103—42no—
194D4×C103—44no—
195D4×C103—44no—
196D4×C103—48no—
197D4×C103—42no—
198D4×C103—42no—
199D4×C103—84no—
200D4×C103—84no—
201C2×C4×C103—21no—
202C2×C4×C103—21no—
203C2×C4×C103—21no—
204C2×C4×C103—21no—
205C2×C4×C103—24no—
206C2×C4×C103—22no—
207C2×C4×C103—44no—
208C2×C4×C103—44no—
209C2×C4×C103—42no—
210C2×C4×C103—42no—
211C2×C4×C103—82no—
212C2×C4×C103—82no—
213C2×C4×C103—82no—
214C2×C4×C103—84no—
215C2×C4×C103#9912yes—
216C2×C4×C103#12012yes—
217C8×C103—82no—
218C22×C103—22no—
219C22×C103—22no—
220C22×C103—22no—
221C22×C103—22no—
222C22×C103—22no—
223C22×C103—22no—
224C22×C103—41no—
225C22×C103—42no—
226C22×C103—42no—
227C22×C103—42no—
228C22×C103—42no—
229C22×C103—42no—
230C22×C103—41no—
231C22×C103—41no—
232C22×C103—41no—
233C22×C103—44no—
234C22×C103—42no—
235C22×C103—41no—
236C22×C103—42no—
237C22×C103—41no—
238C22×C103—81no—
239C22×C103—81no—
240C22×C103—81no—
241C22×C103—81no—
242C22×C103—81no—
243C22×C103—81no—
244C22×C103—88no—
245C22×C103—88no—
246C22×C103—162no—
247C22×C103—162no—
248C22×C103#37911yescharacteristic
249C22×C103C2×#9911yescharacteristic
250C22×C103C2×#9911yescharacteristic
251C4×C103—22no—
252C4×C103—22no—
253C4×C103—44no—
254C4×C103—42no—
255C4×C103—162no—
256#12705C10311yesmaximal, characteristic, direct product factor, Sylow
257C2×C103—21no—
258C2×C103—21no—
259C2×C103—21no—
260C2×C103—42no—
261C2×C103—42no—
262C2×C103—42no—
263C2×C103—42no—
264C2×C103—81no—
265C2×C103—82no—
266C2×C103#178111yescharacteristic
267#3484C2×C10311yescharacteristic
268#2121C2×C10314yescomplemented
269#1783C2×C10311yescharacteristic, complemented
270#1781C2×C10311yescharacteristic, complemented
271C103#1270511yescharacteristic, direct product factor, Sylow
272C2×H(5,𝔽2)C4×C10311yescharacteristic, complemented
273C23×D4C22×C10311yescharacteristic
274#546—24no—
275D42—24no—
276#535—21no—
277#534—21no—
278#534C22×C10312yes—
279#525—21no—
280C2×#120—21no—
281C2×#120C4×C10312yescomplemented
282#518C4×C10311yescharacteristic, complemented
283C2×#100—21no—
284C2×#100C22×C10312yescomplemented
285C2×#99—21no—
286C2×#99C22×C10312yescomplemented
287#407—21no—
288#379—21no—
289#352—24no—
290AΣL(1,𝔽16)—24no—
291C25C2×C4×C10311yescharacteristic
292C25D4×C10311yescharacteristic
293H(5,𝔽2)—42no—
294H(5,𝔽2)—42no—
295C2×#41—21no—
296C2×#41—22no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4C2×C4×C10311yescharacteristic
305C22×D4C2×C4×C10312yes—
306C22×D4D4×C10311yescharacteristic
307C22×D4D4×C10311yescharacteristic
308C22×D4C23×C10311yescharacteristic
309C23×C4D4×C10311yescharacteristic
310C2×M16—22no—
311#127—22no—
312#124—22no—
313#123—22no—
314#123—22no—
315#123D4×C10314yes—
316C22⋊Q8—22no—
317#121—22no—
318#121—24no—
319#121—24no—
320#121—24no—
321#120—24no—
322#120—22no—
323#120—22no—
324#120—22no—
325#120—22no—
326#120—24no—
327#120D4×C10314yes—
328C4×D4—24no—
329C4×D4—24no—
330#117—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4C2×C4×C10312yes—
337#100—24no—
338#100—42no—
339#99—24no—
340#99—42no—
341C22⋊C8—42no—
342C24—21no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—82no—
350C24—82no—
351C24C22⋊C4×C10311yescharacteristic
352C24C22⋊C4×C10311yescharacteristic
353C24C22⋊C4×C10311yescharacteristic
354C24C22⋊C4×C10312yescomplemented
355C24C22×C4×C10311yescharacteristic
356C24C2×D4×C10311yescharacteristic
357#41—42no—
358#41—48no—
359#41—42no—
360C2×Q8—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—416no—
380C2×D4—48no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—84no—
386C2×D4—84no—
387C2×D4C2×D4×C10314yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C22⋊C4×C10311yescharacteristic
397C22×C4C22⋊C4×C10312yescomplemented
398C22×C4C2×D4×C10311yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—84no—
413C22⋊C4C22⋊C4×C10314yescomplemented
414C42—22no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—42no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23—82no—
451C23#99×C10312yes—
452C23C2×C22⋊C4×C10312yes—
453C23C2×C22⋊C4×C10311yescharacteristic
454C23#120×C10312yes—
455Q8—42no—
456D4—28no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4#99×C10312yes—
483C2×C4#120×C10312yes—
484C8—82no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—88no—
512C22—88no—
513C22—162no—
514C22—162no—
515C22#379×C10311yescharacteristic
516C22C2×#99×C10311yescharacteristic
517C22C2×#99×C10311yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—162no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—82no—
532C2C103×#178111yescharacteristic
subgroupG/H
center, socleC2×C103#1781
commutatorC24C22×C4×C103
Frattini, cosocleC22×D4C23×C103
prime radicalC103×#3484C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C23×C103 ◁ C23×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2121C2semidirect
3. C103×#1783C2semidirect
4. C103×#1781C2semidirect
5. C2×H(5,𝔽2)×C103C4semidirect
14. C2×#120×C103C4semidirect
15. #518×C103C4semidirect
17. C2×#100×C103C22semidirect
19. C2×#99×C103C22semidirect
87. C24×C103C22⋊C4semidirect
130. C22×C4×C103C22⋊C4semidirect
146. C22⋊C4×C103C22⋊C4semidirect
256. #12705C103direct (N × H)
268. #2121C2×C103semidirect
269. #1783C2×C103semidirect
270. #1781C2×C103semidirect
271. C103#12705direct (N × H)
272. C2×H(5,𝔽2)C4×C103semidirect
281. C2×#120C4×C103semidirect
282. #518C4×C103semidirect
284. C2×#100C22×C103semidirect
286. C2×#99C22×C103semidirect
354. C24C22⋊C4×C103semidirect
397. C22×C4C22⋊C4×C103semidirect
413. C22⋊C4C22⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34842
C103×#21212
C103×#17832
C103×#17812
#12705103