Finite Group Databasebeta

← C103×#33530 #39938805

Subgroups — C103×#33530 #39938805

Order 26368.

1132 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C103C211yesmaximal, characteristic, complemented
2C103×#3414C212yesmaximal, complemented
3C103×#3054C211yesmaximal, characteristic, complemented
4C103×#2191C214yesmaximal, complemented
5C103×#2190C214yesmaximal, complemented
6C103×#2145C212yesmaximal, complemented
7C2×#349×C103C211yesmaximal, characteristic, complemented
8C22×#41×C103—21no—
9#575×C103—24no—
10#575×C103—22no—
11#575×C103C2214yes—
12C2×#137×C103—22no—
13C2×AGL(1,ℤ/8)×C103—22no—
14C2×#135×C103—21no—
15C2×#135×C103C2212yes—
16C2×#135×C103C2211yescharacteristic, complemented
17C22×M16×C103C2211yescharacteristic
18#525×C103—21no—
19#510×C103—22no—
20#510×C103C2214yescomplemented
21#509×C103—22no—
22#509×C103C2214yescomplemented
23#508×C103—24no—
24C2×M32×C103C2212yescomplemented
25#470×C103C2212yescomplemented
26#469×C103C2212yescomplemented
27#468×C103—22no—
28#427×C103C2211yescharacteristic, complemented
29#416×C103—21no—
30#360×C103C2218yescomplemented
31#349×C103C2214yescomplemented
32C2×#41×C103—22no—
33C2×#41×C103—24no—
34C2×#41×C103—24no—
35C2×#41×C103—22no—
36C2×#41×C103—21no—
37C2×#41×C103—41no—
38C2×#41×C103—42no—
39C2×#41×C103—42no—
40C2×#41×C103—41no—
41C22×Q8×C103—21no—
42C22×D4×C103—21no—
43C22×D4×C103—41no—
44C23×C4×C103—41no—
45C23×C4×C103D411yescharacteristic
46#137×C103—28no—
47#137×C103—28no—
48AGL(1,ℤ/8)×C103—28no—
49AGL(1,ℤ/8)×C103—28no—
50#135×C103—24no—
51#135×C103—24no—
52#135×C103—22no—
53#135×C103—22no—
54#135×C103—22no—
55#135×C103—22no—
56#135×C103D414yescomplemented
57#135×C103C2314yes—
58C2×Q16×C103—21no—
59C2×Q16×C103D412yescomplemented
60C2×Q16×C103C2311yescharacteristic, complemented
61C2×SD16×C103—22no—
62C2×SD16×C103—22no—
63C2×SD16×C103—21no—
64C2×D8×C103—21no—
65C2×D8×C103D412yescomplemented
66C2×D8×C103C2311yescharacteristic, complemented
67C2×M16×C103—22no—
68C2×M16×C103—22no—
69C2×M16×C103D412yes—
70C2×M16×C103C2312yes—
71C22×C8×C103D411yescharacteristic
72C22×C8×C103C2311yescharacteristic
73#123×C103—41no—
74C22⋊Q8×C103—22no—
75#121×C103—22no—
76#120×C103—41no—
77C4×D4×C103—42no—
78#117×C103—21no—
79Q32×C103—24no—
80SD32×C103—24no—
81SD32×C103—24no—
82D16×C103—24no—
83M32×C103—22no—
84M32×C103C2314yescomplemented
85C2×C16×C103—22no—
86#107×C103—21no—
87#106×C103C2312yescomplemented
88#103×C103—22no—
89#102×C103—22no—
90C24×C103—41no—
91C24×C103D811yescharacteristic
92#41×C103—28no—
93#41×C103—24no—
94#41×C103—24no—
95#41×C103—44no—
96#41×C103—44no—
97#41×C103—44no—
98#41×C103—44no—
99#41×C103—44no—
100#41×C103—42no—
101#41×C103—42no—
102#41×C103—41no—
103#41×C103—41no—
104#41×C103—41no—
105#41×C103—41no—
106C2×Q8×C103—24no—
107C2×Q8×C103—22no—
108C2×Q8×C103—21no—
109C2×Q8×C103—41no—
110C2×Q8×C103—42no—
111C2×D4×C103—24no—
112C2×D4×C103—22no—
113C2×D4×C103—21no—
114C2×D4×C103—41no—
115C2×D4×C103—42no—
116C2×D4×C103—44no—
117C2×D4×C103—42no—
118C2×D4×C103—44no—
119C2×D4×C103—42no—
120C2×D4×C103—42no—
121C2×D4×C103—41no—
122C22×C4×C103—21no—
123C22×C4×C103—21no—
124C22×C4×C103—21no—
125C22×C4×C103—21no—
126C22×C4×C103—42no—
127C22×C4×C103—44no—
128C22×C4×C103—44no—
129C22×C4×C103—41no—
130C22×C4×C103—42no—
131C22×C4×C103—41no—
132C22×C4×C103D812yes—
133C22×C4×C103D811yescharacteristic
134C22×C4×C103C2×D412yes—
135C22×C4×C103C2×D411yescharacteristic
136Q16×C103—24no—
137Q16×C103—22no—
138Q16×C103—22no—
139Q16×C103C2×D414yes—
140SD16×C103—28no—
141SD16×C103—24no—
142SD16×C103—24no—
143SD16×C103—42no—
144D8×C103—24no—
145D8×C103—22no—
146D8×C103—22no—
147D8×C103C2×D414yes—
148M16×C103—24no—
149M16×C103—24no—
150C2×C8×C103—21no—
151C2×C8×C103—21no—
152C2×C8×C103C2×D412yes—
153C2×C8×C103C2×D411yescharacteristic
154C2×C8×C103C2×D412yes—
155C2×C8×C103C2×D412yes—
156C2×C8×C103C2411yescharacteristic
157C4⋊C4×C103—22no—
158C4⋊C4×C103—42no—
159C22⋊C4×C103—41no—
160C22⋊C4×C103—42no—
161C22⋊C4×C103—42no—
162C42×C103—41no—
163C16×C103—24no—
164C23×C103—21no—
165C23×C103—21no—
166C23×C103—44no—
167C23×C103—42no—
168C23×C103—41no—
169C23×C103—81no—
170C23×C103—84no—
171C23×C103C2×D812yes—
172C23×C103C2×D811yescharacteristic
173Q8×C103—24no—
174Q8×C103—44no—
175Q8×C103—42no—
176Q8×C103—41no—
177Q8×C103—41no—
178D4×C103—24no—
179D4×C103—44no—
180D4×C103—48no—
181D4×C103—44no—
182D4×C103—44no—
183D4×C103—41no—
184D4×C103—41no—
185D4×C103—42no—
186D4×C103—84no—
187D4×C103—81no—
188D4×C103—81no—
189C2×C4×C103—21no—
190C2×C4×C103—21no—
191C2×C4×C103—22no—
192C2×C4×C103—22no—
193C2×C4×C103—22no—
194C2×C4×C103—22no—
195C2×C4×C103—48no—
196C2×C4×C103—44no—
197C2×C4×C103—42no—
198C2×C4×C103—44no—
199C2×C4×C103—44no—
200C2×C4×C103—42no—
201C2×C4×C103—41no—
202C2×C4×C103—81no—
203C2×C4×C103—81no—
204C2×C4×C103#12011yescharacteristic
205C2×C4×C103#12011yescharacteristic
206C2×C4×C103C2×D812yes—
207C2×C4×C103C2×D811yescharacteristic
208C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
209C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C103C22×D411yescharacteristic
211C8×C103—22no—
212C8×C103#12012yes—
213C8×C103C22×D412yes—
214C22×C103—22no—
215C22×C103—41no—
216C22×C103—42no—
217C22×C103—42no—
218C22×C103—44no—
219C22×C103—81no—
220C22×C103—84no—
221C22×C103—82no—
222C22×C103—88no—
223C22×C103—81no—
224C22×C103#44711yescharacteristic
225C22×C103#44711yescharacteristic
226C22×C103C22×D811yescharacteristic
227C4×C103—22no—
228C4×C103—44no—
229C4×C103—82no—
230C4×C103—81no—
231C4×C103#44711yescharacteristic
232C4×C103#44711yescharacteristic
233C4×C103C2×#12011yescharacteristic
234C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
235#33530C10311yesmaximal, characteristic, direct product factor, Sylow
236C2×C103—21no—
237C2×C103—21no—
238C2×C103—21no—
239C2×C103—42no—
240C2×C103—84no—
241C2×C103—161no—
242C2×C103C2×#44711yescharacteristic
243C2×#575C2×C10311yescharacteristic, complemented
244#3414C2×C10312yescomplemented
245#3054C2×C10311yescharacteristic, complemented
246#2191C2×C10314yescomplemented
247#2190C2×C10314yescomplemented
248#2145C2×C10312yescomplemented
249C2×#349C2×C10311yescharacteristic, complemented
250C103#3353011yescharacteristic, direct product factor, Sylow
251C22×#41—21no—
252#575—24no—
253#575—22no—
254#575C22×C10314yes—
255C2×#137—22no—
256C2×AGL(1,ℤ/8)—22no—
257C2×#135—21no—
258C2×#135C22×C10312yes—
259C2×#135C22×C10311yescharacteristic, complemented
260C22×M16C22×C10311yescharacteristic
261#525—21no—
262#510—22no—
263#510C22×C10314yescomplemented
264#509—22no—
265#509C22×C10314yescomplemented
266#508—24no—
267C2×M32C22×C10312yescomplemented
268#470C22×C10312yescomplemented
269#469C22×C10312yescomplemented
270#468—22no—
271#427C22×C10311yescharacteristic, complemented
272#416—21no—
273#360C22×C10318yescomplemented
274#349C22×C10314yescomplemented
275C2×#41—22no—
276C2×#41—24no—
277C2×#41—22no—
278C2×#41—24no—
279C2×#41—21no—
280C2×#41—41no—
281C2×#41—42no—
282C2×#41—42no—
283C2×#41—41no—
284C22×Q8—21no—
285C22×D4—21no—
286C22×D4—41no—
287C23×C4—41no—
288C23×C4D4×C10311yescharacteristic
289#137—28no—
290#137—28no—
291AGL(1,ℤ/8)—28no—
292AGL(1,ℤ/8)—28no—
293#135—24no—
294#135—24no—
295#135—22no—
296#135—22no—
297#135—22no—
298#135—22no—
299#135D4×C10314yescomplemented
300#135C23×C10314yes—
301C2×Q16—21no—
302C2×Q16D4×C10312yescomplemented
303C2×Q16C23×C10311yescharacteristic, complemented
304C2×SD16—22no—
305C2×SD16—22no—
306C2×SD16—21no—
307C2×D8—21no—
308C2×D8D4×C10312yescomplemented
309C2×D8C23×C10311yescharacteristic, complemented
310C2×M16—22no—
311C2×M16—22no—
312C2×M16D4×C10312yes—
313C2×M16C23×C10312yes—
314C22×C8D4×C10311yescharacteristic
315C22×C8C23×C10311yescharacteristic
316#123—41no—
317C22⋊Q8—22no—
318#121—22no—
319#120—41no—
320C4×D4—42no—
321#117—21no—
322Q32—24no—
323SD32—24no—
324SD32—24no—
325D16—24no—
326M32—22no—
327M32C23×C10314yescomplemented
328C2×C16—22no—
329#107—21no—
330#106C23×C10312yescomplemented
331#103—22no—
332#102—22no—
333C24—41no—
334C24D8×C10311yescharacteristic
335#41—28no—
336#41—24no—
337#41—24no—
338#41—44no—
339#41—44no—
340#41—44no—
341#41—44no—
342#41—44no—
343#41—42no—
344#41—42no—
345#41—41no—
346#41—41no—
347#41—41no—
348#41—41no—
349C2×Q8—24no—
350C2×Q8—22no—
351C2×Q8—21no—
352C2×Q8—41no—
353C2×Q8—42no—
354C2×D4—24no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4—42no—
359C2×D4—44no—
360C2×D4—42no—
361C2×D4—44no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—41no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—42no—
370C22×C4—44no—
371C22×C4—44no—
372C22×C4—41no—
373C22×C4—42no—
374C22×C4—41no—
375C22×C4D8×C10312yes—
376C22×C4D8×C10311yescharacteristic
377C22×C4C2×D4×C10312yes—
378C22×C4C2×D4×C10311yescharacteristic
379Q16—24no—
380Q16—22no—
381Q16—22no—
382Q16C2×D4×C10314yes—
383SD16—28no—
384SD16—24no—
385SD16—24no—
386SD16—42no—
387D8—24no—
388D8—22no—
389D8—22no—
390D8C2×D4×C10314yes—
391M16—24no—
392M16—24no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8C2×D4×C10312yes—
396C2×C8C2×D4×C10311yescharacteristic
397C2×C8C2×D4×C10312yes—
398C2×C8C2×D4×C10312yes—
399C2×C8C24×C10311yescharacteristic
400C4⋊C4—22no—
401C4⋊C4—42no—
402C22⋊C4—41no—
403C22⋊C4—42no—
404C22⋊C4—42no—
405C42—41no—
406C16—24no—
407C23—21no—
408C23—21no—
409C23—44no—
410C23—42no—
411C23—41no—
412C23—81no—
413C23—84no—
414C23C2×D8×C10312yes—
415C23C2×D8×C10311yescharacteristic
416Q8—24no—
417Q8—44no—
418Q8—42no—
419Q8—41no—
420Q8—41no—
421D4—24no—
422D4—44no—
423D4—48no—
424D4—44no—
425D4—44no—
426D4—42no—
427D4—41no—
428D4—41no—
429D4—84no—
430D4—81no—
431D4—81no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—48no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4#120×C10311yescharacteristic
448C2×C4#120×C10311yescharacteristic
449C2×C4C2×D8×C10312yes—
450C2×C4C2×D8×C10311yescharacteristic
451C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
452C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
453C2×C4C22×D4×C10311yescharacteristic
454C8—22no—
455C8#120×C10312yes—
456C8C22×D4×C10312yes—
457C22—22no—
458C22—41no—
459C22—42no—
460C22—42no—
461C22—44no—
462C22—81no—
463C22—84no—
464C22—82no—
465C22—88no—
466C22—81no—
467C22#447×C10311yescharacteristic
468C22#447×C10311yescharacteristic
469C22C22×D8×C10311yescharacteristic
470C4—22no—
471C4—44no—
472C4—82no—
473C4—81no—
474C4#447×C10311yescharacteristic
475C4#447×C10311yescharacteristic
476C4C2×#120×C10311yescharacteristic
477C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
478C2—21no—
479C2—21no—
480C2—21no—
481C2—42no—
482C2—84no—
483C2—161no—
484C2C2×#447×C10311yescharacteristic
subgroupG/H
centerC4×C103#447
commutator, Frattini, cosocleC2×C8C24×C103
socleC2×C103C2×#447
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C4×C103 ◁ C22×M16×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C103C2semidirect
2. C103×#3414C2semidirect
3. C103×#3054C2semidirect
4. C103×#2191C2semidirect
5. C103×#2190C2semidirect
6. C103×#2145C2semidirect
7. C2×#349×C103C2semidirect
16. C2×#135×C103C22semidirect
20. #510×C103C22semidirect
22. #509×C103C22semidirect
24. C2×M32×C103C22semidirect
25. #470×C103C22semidirect
26. #469×C103C22semidirect
28. #427×C103C22semidirect
30. #360×C103C22semidirect
31. #349×C103C22semidirect
56. #135×C103D4semidirect
59. C2×Q16×C103D4semidirect
60. C2×Q16×C103C23semidirect
65. C2×D8×C103D4semidirect
66. C2×D8×C103C23semidirect
84. M32×C103C23semidirect
87. #106×C103C23semidirect
235. #33530C103direct (N × H)
243. C2×#575C2×C103semidirect
244. #3414C2×C103semidirect
245. #3054C2×C103semidirect
246. #2191C2×C103semidirect
247. #2190C2×C103semidirect
248. #2145C2×C103semidirect
249. C2×#349C2×C103semidirect
250. C103#33530direct (N × H)
259. C2×#135C22×C103semidirect
263. #510C22×C103semidirect
265. #509C22×C103semidirect
267. C2×M32C22×C103semidirect
268. #470C22×C103semidirect
269. #469C22×C103semidirect
271. #427C22×C103semidirect
273. #360C22×C103semidirect
274. #349C22×C103semidirect
299. #135D4×C103semidirect
302. C2×Q16D4×C103semidirect
303. C2×Q16C23×C103semidirect
308. C2×D8D4×C103semidirect
309. C2×D8C23×C103semidirect
327. M32C23×C103semidirect
330. #106C23×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1032
C103×#34142
C103×#30542
C103×#21912
C103×#21902
C103×#21452
C2×#349×C1032
#33530103