Finite Group Databasebeta

← C103×#33595 #39938870

Subgroups — C103×#33595 #39938870

Order 26368.

706 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3414C211yesmaximal, characteristic, complemented
2C2×#509×C103C211yesmaximal, characteristic, complemented
3C103×#3155C211yesmaximal, characteristic, complemented
4C103×#2957C211yesmaximal, characteristic, complemented
5C103×#2213C214yesmaximal, complemented
6C103×#2212C214yesmaximal, complemented
7C103×#2153C211yesmaximal, characteristic, complemented
8C103×#2148C211yesmaximal, characteristic, complemented
9C2×#361×C103C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C103—21no—
11C2×#135×C103C2211yescharacteristic
12C2×#135×C103C2211yescharacteristic
13C22×D8×C103C2211yescharacteristic
14#568×C103—21no—
15#535×C103—21no—
16#510×C103—21no—
17#510×C103C2212yescomplemented
18#509×C103—22no—
19#509×C103—21no—
20#509×C103C2214yes—
21#509×C103C2212yescomplemented
22#508×C103—22no—
23C2×SD32×C103—21no—
24C2×D16×C103—21no—
25C2×M32×C103C2211yescharacteristic
26C2×M32×C103C2211yescharacteristic
27#496×C103—22no—
28#495×C103C2212yescomplemented
29#493×C103C2212yescomplemented
30#444×C103—22no—
31#443×C103C2214yescomplemented
32C2×#108×C103C2211yescharacteristic
33#421×C103—21no—
34#405×C103C2211yescharacteristic
35#364×C103C2214yescomplemented
36#362×C103C2212yescomplemented
37#361×C103C2214yescomplemented
38#361×C103C2212yescomplemented
39C2×#41×C103—21no—
40C2×#41×C103—21no—
41C22×D4×C103—21no—
42AGL(1,ℤ/8)×C103—42no—
43AGL(1,ℤ/8)×C103—42no—
44#135×C103—21no—
45#135×C103—21no—
46#135×C103—21no—
47#135×C103—21no—
48#135×C103—21no—
49#135×C103—21no—
50#135×C103D412yescomplemented
51#135×C103C2312yes—
52C2×Q16×C103D411yescharacteristic, complemented
53C2×Q16×C103C2311yescharacteristic
54C2×SD16×C103—22no—
55C2×SD16×C103—21no—
56C2×SD16×C103—21no—
57C2×D8×C103—21no—
58C2×D8×C103—21no—
59C2×D8×C103—22no—
60C2×D8×C103—21no—
61C2×D8×C103—21no—
62C2×D8×C103—21no—
63C2×D8×C103D411yescharacteristic, complemented
64C2×D8×C103C2311yescharacteristic
65C2×D8×C103C2312yes—
66#131×C103—24no—
67#131×C103—42no—
68C2×M16×C103—21no—
69C2×M16×C103—42no—
70C2×M16×C103D411yescharacteristic
71C22×C8×C103C2311yescharacteristic
72#127×C103—22no—
73#124×C103—22no—
74#121×C103—42no—
75#120×C103—42no—
76#117×C103D411yescharacteristic
77Q32×C103—22no—
78SD32×C103—24no—
79SD32×C103—22no—
80SD32×C103—22no—
81D16×C103—24no—
82D16×C103—22no—
83M32×C103—21no—
84M32×C103—21no—
85M32×C103C2312yes—
86M32×C103C2312yes—
87C2×C16×C103—21no—
88C2×C16×C103—21no—
89#108×C103—21no—
90#108×C103C2312yes—
91#104×C103—24no—
92#97×C103D412yes—
93C4×C8×C103C2312yes—
94C24×C103—41no—
95#41×C103—22no—
96#41×C103—22no—
97#41×C103—41no—
98#41×C103—41no—
99#41×C103—41no—
100#41×C103—41no—
101#41×C103—41no—
102#41×C103—41no—
103C2×Q8×C103—21no—
104C2×Q8×C103—21no—
105C2×D4×C103—21no—
106C2×D4×C103—22no—
107C2×D4×C103—21no—
108C2×D4×C103—44no—
109C2×D4×C103—41no—
110C2×D4×C103—41no—
111C2×D4×C103—41no—
112C2×D4×C103—41no—
113C2×D4×C103—41no—
114C2×D4×C103—41no—
115C2×D4×C103—41no—
116C22×C4×C103—41no—
117C22×C4×C103—41no—
118C22×C4×C103C2×D411yescharacteristic
119Q16×C103—21no—
120Q16×C103—21no—
121Q16×C103—21no—
122Q16×C103C2×D412yes—
123SD16×C103—22no—
124SD16×C103—22no—
125SD16×C103—41no—
126SD16×C103—41no—
127SD16×C103—44no—
128D8×C103—21no—
129D8×C103—22no—
130D8×C103—21no—
131D8×C103—22no—
132D8×C103—21no—
133D8×C103—41no—
134D8×C103—41no—
135D8×C103—44no—
136D8×C103C2×D412yes—
137M16×C103—22no—
138M16×C103—41no—
139M16×C103—44no—
140M16×C103D812yes—
141M16×C103D812yes—
142C2×C8×C103—41no—
143C2×C8×C103—44no—
144C2×C8×C103C2×D411yescharacteristic
145C2×C8×C103C2×D411yescharacteristic
146C2×C8×C103C2×D411yescharacteristic
147C2×C8×C103C2×D412yes—
148C2×C8×C103#4111yescharacteristic
149C2×C8×C103#4111yescharacteristic
150C2×C8×C103C2411yescharacteristic
151C4⋊C4×C103—21no—
152C22⋊C4×C103—21no—
153C22⋊C4×C103—44no—
154C42×C103C2×D412yes—
155C16×C103—22no—
156C16×C103—22no—
157C23×C103—41no—
158C23×C103—42no—
159C23×C103—41no—
160C23×C103—81no—
161C23×C103—81no—
162C23×C103—162no—
163C23×C103AGL(1,ℤ/8)11yescharacteristic
164Q8×C103—22no—
165Q8×C103—41no—
166Q8×C103—41no—
167Q8×C103—41no—
168D4×C103—22no—
169D4×C103—42no—
170D4×C103—42no—
171D4×C103—42no—
172D4×C103—41no—
173D4×C103—41no—
174D4×C103—42no—
175D4×C103—41no—
176D4×C103—81no—
177D4×C103—81no—
178D4×C103—81no—
179D4×C103—81no—
180D4×C103—164no—
181C2×C4×C103—22no—
182C2×C4×C103—41no—
183C2×C4×C103—42no—
184C2×C4×C103—42no—
185C2×C4×C103—41no—
186C2×C4×C103—81no—
187C2×C4×C103—81no—
188C2×C4×C103#12111yescharacteristic
189C2×C4×C103#12111yescharacteristic
190C2×C4×C103C2×D811yescharacteristic
191C2×C4×C103C2×D811yescharacteristic
192C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C103C22×D411yescharacteristic
194C8×C103—42no—
195C8×C103#12111yescharacteristic
196C8×C103#12111yescharacteristic
197C8×C103C2×D814yes—
198C8×C103C22×D411yescharacteristic
199C8×C103C2×#4111yescharacteristic
200C22×C103—41no—
201C22×C103—42no—
202C22×C103—82no—
203C22×C103—84no—
204C22×C103—81no—
205C22×C103—82no—
206C22×C103—161no—
207C22×C103—162no—
208C22×C103—162no—
209C22×C103#45911yescharacteristic
210C22×C103#45911yescharacteristic
211C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
212C4×C103—42no—
213C4×C103—42no—
214C4×C103—81no—
215C4×C103#45911yescharacteristic
216C4×C103#45911yescharacteristic
217C4×C103C2×#12111yescharacteristic
218C4×C103C22×D811yescharacteristic
219#33595C10311yesmaximal, characteristic, direct product factor, Sylow
220C2×C103—21no—
221C2×C103—21no—
222C2×C103—21no—
223C2×C103—82no—
224C2×C103—161no—
225C2×C103—162no—
226C2×C103C2×#45911yescharacteristic
227#3414C2×C10311yescharacteristic, complemented
228C2×#509C2×C10311yescharacteristic, complemented
229#3155C2×C10311yescharacteristic, complemented
230#2957C2×C10311yescharacteristic, complemented
231#2213C2×C10314yescomplemented
232#2212C2×C10314yescomplemented
233#2153C2×C10311yescharacteristic, complemented
234#2148C2×C10311yescharacteristic, complemented
235C2×#361C2×C10311yescharacteristic, complemented
236C103#3359511yescharacteristic, direct product factor, Sylow
237C2×AGL(1,ℤ/8)—21no—
238C2×#135C22×C10311yescharacteristic
239C2×#135C22×C10311yescharacteristic
240C22×D8C22×C10311yescharacteristic
241#568—21no—
242#535—21no—
243#510—21no—
244#510C22×C10312yescomplemented
245#509—22no—
246#509—21no—
247#509C22×C10314yes—
248#509C22×C10312yescomplemented
249#508—22no—
250C2×SD32—21no—
251C2×D16—21no—
252C2×M32C22×C10311yescharacteristic
253C2×M32C22×C10311yescharacteristic
254#496—22no—
255#495C22×C10312yescomplemented
256#493C22×C10312yescomplemented
257#444—22no—
258#443C22×C10314yescomplemented
259C2×#108C22×C10311yescharacteristic
260#421—21no—
261#405C22×C10311yescharacteristic
262#364C22×C10314yescomplemented
263#362C22×C10312yescomplemented
264#361C22×C10314yescomplemented
265#361C22×C10312yescomplemented
266C2×#41—21no—
267C2×#41—21no—
268C22×D4—21no—
269AGL(1,ℤ/8)—42no—
270AGL(1,ℤ/8)—42no—
271#135—21no—
272#135—21no—
273#135—21no—
274#135—21no—
275#135—21no—
276#135—21no—
277#135D4×C10312yescomplemented
278#135C23×C10312yes—
279C2×Q16D4×C10311yescharacteristic, complemented
280C2×Q16C23×C10311yescharacteristic
281C2×SD16—21no—
282C2×SD16—22no—
283C2×SD16—21no—
284C2×D8—21no—
285C2×D8—21no—
286C2×D8—21no—
287C2×D8—22no—
288C2×D8—21no—
289C2×D8—21no—
290C2×D8D4×C10311yescharacteristic, complemented
291C2×D8C23×C10312yes—
292C2×D8C23×C10311yescharacteristic
293#131—24no—
294#131—42no—
295C2×M16—21no—
296C2×M16—42no—
297C2×M16D4×C10311yescharacteristic
298C22×C8C23×C10311yescharacteristic
299#127—22no—
300#124—22no—
301#121—42no—
302#120—42no—
303#117D4×C10311yescharacteristic
304Q32—22no—
305SD32—24no—
306SD32—22no—
307SD32—22no—
308D16—24no—
309D16—22no—
310M32—21no—
311M32—21no—
312M32C23×C10312yes—
313M32C23×C10312yes—
314C2×C16—21no—
315C2×C16—21no—
316#108—21no—
317#108C23×C10312yes—
318#104—24no—
319#97D4×C10312yes—
320C4×C8C23×C10312yes—
321C24—41no—
322#41—22no—
323#41—22no—
324#41—41no—
325#41—41no—
326#41—41no—
327#41—41no—
328#41—41no—
329#41—41no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—44no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4C2×D4×C10311yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16C2×D4×C10312yes—
350SD16—22no—
351SD16—22no—
352SD16—41no—
353SD16—41no—
354SD16—44no—
355D8—21no—
356D8—22no—
357D8—21no—
358D8—22no—
359D8—21no—
360D8—41no—
361D8—41no—
362D8—44no—
363D8C2×D4×C10312yes—
364M16—22no—
365M16—41no—
366M16—44no—
367M16D8×C10312yes—
368M16D8×C10312yes—
369C2×C8—41no—
370C2×C8—44no—
371C2×C8C2×D4×C10311yescharacteristic
372C2×C8C2×D4×C10311yescharacteristic
373C2×C8C2×D4×C10311yescharacteristic
374C2×C8C2×D4×C10312yes—
375C2×C8#41×C10311yescharacteristic
376C2×C8#41×C10311yescharacteristic
377C2×C8C24×C10311yescharacteristic
378C4⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—44no—
381C42C2×D4×C10312yes—
382C16—22no—
383C16—22no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—81no—
388C23—81no—
389C23—162no—
390C23AGL(1,ℤ/8)×C10311yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—42no—
400D4—41no—
401D4—41no—
402D4—42no—
403D4—81no—
404D4—81no—
405D4—81no—
406D4—81no—
407D4—164no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4#121×C10311yescharacteristic
416C2×C4#121×C10311yescharacteristic
417C2×C4C2×D8×C10311yescharacteristic
418C2×C4C2×D8×C10311yescharacteristic
419C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
420C2×C4C22×D4×C10311yescharacteristic
421C8—42no—
422C8#121×C10311yescharacteristic
423C8#121×C10311yescharacteristic
424C8C2×D8×C10314yes—
425C8C22×D4×C10311yescharacteristic
426C8C2×#41×C10311yescharacteristic
427C22—41no—
428C22—42no—
429C22—82no—
430C22—84no—
431C22—81no—
432C22—82no—
433C22—161no—
434C22—162no—
435C22—162no—
436C22#459×C10311yescharacteristic
437C22#459×C10311yescharacteristic
438C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
439C4—42no—
440C4—42no—
441C4—81no—
442C4#459×C10311yescharacteristic
443C4#459×C10311yescharacteristic
444C4C2×#121×C10311yescharacteristic
445C4C22×D8×C10311yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—162no—
451C2—161no—
452C2C2×#459×C10311yescharacteristic
subgroupG/H
center, socleC2×C103C2×#459
commutator, Frattini, cosocleC2×C8C24×C103
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C22×C4×C103 ◁ #405×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3414C2semidirect
2. C2×#509×C103C2semidirect
3. C103×#3155C2semidirect
4. C103×#2957C2semidirect
5. C103×#2213C2semidirect
6. C103×#2212C2semidirect
7. C103×#2153C2semidirect
8. C103×#2148C2semidirect
9. C2×#361×C103C2semidirect
17. #510×C103C22semidirect
21. #509×C103C22semidirect
28. #495×C103C22semidirect
29. #493×C103C22semidirect
31. #443×C103C22semidirect
35. #364×C103C22semidirect
36. #362×C103C22semidirect
37. #361×C103C22semidirect
38. #361×C103C22semidirect
50. #135×C103D4semidirect
52. C2×Q16×C103D4semidirect
63. C2×D8×C103D4semidirect
219. #33595C103direct (N × H)
227. #3414C2×C103semidirect
228. C2×#509C2×C103semidirect
229. #3155C2×C103semidirect
230. #2957C2×C103semidirect
231. #2213C2×C103semidirect
232. #2212C2×C103semidirect
233. #2153C2×C103semidirect
234. #2148C2×C103semidirect
235. C2×#361C2×C103semidirect
236. C103#33595direct (N × H)
244. #510C22×C103semidirect
248. #509C22×C103semidirect
255. #495C22×C103semidirect
256. #493C22×C103semidirect
258. #443C22×C103semidirect
262. #364C22×C103semidirect
263. #362C22×C103semidirect
264. #361C22×C103semidirect
265. #361C22×C103semidirect
277. #135D4×C103semidirect
279. C2×Q16D4×C103semidirect
290. C2×D8D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34142
C2×#509×C1032
C103×#31552
C103×#29572
C103×#22132
C103×#22122
C103×#21532
C103×#21482
C2×#361×C1032
#33595103