Finite Group Databasebeta

← C103×#12996 #39918271

Subgroups — C103×#12996 #39918271

Order 26368.

512 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C103C211yesmaximal, characteristic
2C103×#2913C211yesmaximal, characteristic, complemented
3C103×#2140C211yesmaximal, characteristic, complemented
4C2×#357×C103C211yesmaximal, characteristic, complemented
5C2×#350×C103C211yesmaximal, characteristic, complemented
6C103×#1387C211yesmaximal, characteristic, complemented
7C103×#1382C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C103—21no—
9C22×D8×C103C2211yescharacteristic
10C2×#131×C103C2211yescharacteristic
11#520×C103—21no—
12C2×M32×C103C2211yescharacteristic
13C22×C16×C103C2211yescharacteristic
14#472×C103—22no—
15#472×C103C414yescomplemented
16C2×#108×C103C2211yescharacteristic
17#428×C103—21no—
18#428×C103—22no—
19#427×C103—21no—
20#427×C103C2211yescharacteristic
21C2×#107×C103—21no—
22C2×#107×C103C2211yescharacteristic
23C2×#100×C103—21no—
24#357×C103—22no—
25#357×C103—21no—
26#357×C103—21no—
27#350×C103—22no—
28C2×#41×C103D411yescharacteristic
29C22×D4×C103—21no—
30AGL(1,ℤ/8)×C103—24no—
31AGL(1,ℤ/8)×C103—42no—
32C2×SD16×C103—41no—
33C2×D8×C103—21no—
34C2×D8×C103—21no—
35C2×D8×C103—21no—
36C2×D8×C103—21no—
37C2×D8×C103—21no—
38C2×D8×C103—41no—
39C2×D8×C103C2×C412yescomplemented
40#131×C103—21no—
41#131×C103—21no—
42#131×C103C2×C412yes—
43#131×C103D412yes—
44C2×M16×C103—21no—
45C2×M16×C103—21no—
46C2×M16×C103D411yescharacteristic
47C22×C8×C103—21no—
48C22×C8×C103C2311yescharacteristic
49C4×Q8×C103—41no—
50C4×D4×C103—42no—
51C4×D4×C103—41no—
52#117×C103—22no—
53#117×C103—21no—
54C2×C4⋊C4×C103—22no—
55C2×C4⋊C4×C103—21no—
56M32×C103—21no—
57M32×C103—21no—
58C2×C16×C103—21no—
59C2×C16×C103—21no—
60C2×C16×C103—21no—
61C2×C16×C103—21no—
62#108×C103—21no—
63#108×C103C2×C412yescomplemented
64#107×C103—22no—
65#107×C103—21no—
66#107×C103D411yescharacteristic
67#107×C103D412yes—
68#107×C103D411yescharacteristic
69#106×C103—22no—
70#106×C103—21no—
71#100×C103—24no—
72C24×C103—41no—
73#41×C103—21no—
74#41×C103—21no—
75#41×C103C22⋊C412yes—
76#41×C103SD1612yes—
77C2×Q8×C103D811yescharacteristic
78C2×D4×C103—21no—
79C2×D4×C103—22no—
80C2×D4×C103—41no—
81C2×D4×C103—41no—
82C2×D4×C103—41no—
83C2×D4×C103—41no—
84C2×D4×C103—41no—
85C2×D4×C103D811yescharacteristic
86C22×C4×C103—21no—
87C22×C4×C103—42no—
88C22×C4×C103—41no—
89C22×C4×C103C2×D411yescharacteristic
90SD16×C103—44no—
91D8×C103—22no—
92D8×C103—22no—
93D8×C103—44no—
94D8×C103—41no—
95D8×C103—41no—
96M16×C103—21no—
97M16×C103—22no—
98M16×C103—22no—
99M16×C103—22no—
100M16×C103—41no—
101M16×C103C22⋊C412yes—
102C2×C8×C103—21no—
103C2×C8×C103—22no—
104C2×C8×C103—22no—
105C2×C8×C103—41no—
106C2×C8×C103C22×C411yescharacteristic
107C2×C8×C103C2×D411yescharacteristic
108C2×C8×C103C2×D411yescharacteristic
109C2×C8×C103C2×D411yescharacteristic
110C2×C8×C103#4111yescharacteristic
111C2×C8×C103#4111yescharacteristic
112C4⋊C4×C103—21no—
113C4⋊C4×C103—22no—
114C4⋊C4×C103—21no—
115C4⋊C4×C103—42no—
116C4⋊C4×C103—41no—
117C22⋊C4×C103—42no—
118C22⋊C4×C103—41no—
119C42×C103—42no—
120C42×C103—41no—
121C16×C103—41no—
122C16×C103—41no—
123C23×C103—21no—
124C23×C103—42no—
125C23×C103—81no—
126C23×C103—81no—
127C23×C103—161no—
128C23×C103—161no—
129C23×C103AGL(1,ℤ/8)11yescharacteristic
130Q8×C103—21no—
131Q8×C103#10212yes—
132D4×C103—22no—
133D4×C103—22no—
134D4×C103—21no—
135D4×C103—42no—
136D4×C103—42no—
137D4×C103—81no—
138D4×C103—81no—
139D4×C103#10212yes—
140C2×C4×C103—21no—
141C2×C4×C103—22no—
142C2×C4×C103—22no—
143C2×C4×C103—41no—
144C2×C4×C103—42no—
145C2×C4×C103—41no—
146C2×C4×C103—161no—
147C2×C4×C103—162no—
148C2×C4×C103C2×C22⋊C411yescharacteristic
149C2×C4×C103#12011yescharacteristic
150C2×C4×C103#12311yescharacteristic
151C2×C4×C103C2×D811yescharacteristic
152C2×C4×C103C2×SD1611yescharacteristic
153C2×C4×C103#13711yescharacteristic
154C8×C103—22no—
155C8×C103—42no—
156C8×C103C4×D411yescharacteristic
157C8×C103C4×D411yescharacteristic
158C8×C103#12111yescharacteristic
159C8×C103#12111yescharacteristic
160C22×C103—21no—
161C22×C103—21no—
162C22×C103—22no—
163C22×C103—41no—
164C22×C103—41no—
165C22×C103—82no—
166C22×C103—162no—
167C22×C103—162no—
168C22×C103—161no—
169C22×C103—161no—
170C22×C103#41711yescharacteristic
171C22×C103#44711yescharacteristic
172C22×C103#48111yescharacteristic
173C4×C103—22no—
174C4×C103—82no—
175C4×C103—81no—
176C4×C103—81no—
177C4×C103#38611yescharacteristic
178C4×C103C2×#10211yescharacteristic
179C4×C103#44811yescharacteristic
180C4×C103#48011yescharacteristic
181#12996C10311yesmaximal, characteristic, direct product factor, Sylow
182C2×C103—21no—
183C2×C103—21no—
184C2×C103—42no—
185C2×C103—162no—
186C2×C103#187411yescharacteristic
187C2×C103#219211yescharacteristic
188C2×C103#219311yescharacteristic
189C2×#472C2×C10311yescharacteristic
190#2913C2×C10311yescharacteristic, complemented
191#2140C2×C10311yescharacteristic, complemented
192C2×#357C2×C10311yescharacteristic, complemented
193C2×#350C2×C10311yescharacteristic, complemented
194#1387C2×C10311yescharacteristic, complemented
195#1382C2×C10311yescharacteristic, complemented
196C103#1299611yescharacteristic, direct product factor, Sylow
197C2×AGL(1,ℤ/8)—21no—
198C22×D8C22×C10311yescharacteristic
199C2×#131C22×C10311yescharacteristic
200#520—21no—
201C2×M32C22×C10311yescharacteristic
202C22×C16C22×C10311yescharacteristic
203#472—22no—
204#472C4×C10314yescomplemented
205C2×#108C22×C10311yescharacteristic
206#428—21no—
207#428—22no—
208#427—21no—
209#427C22×C10311yescharacteristic
210C2×#107—21no—
211C2×#107C22×C10311yescharacteristic
212C2×#100—21no—
213#357—22no—
214#357—21no—
215#357—21no—
216#350—22no—
217C2×#41D4×C10311yescharacteristic
218C22×D4—21no—
219AGL(1,ℤ/8)—24no—
220AGL(1,ℤ/8)—42no—
221C2×SD16—41no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—41no—
228C2×D8C2×C4×C10312yescomplemented
229#131—21no—
230#131—21no—
231#131C2×C4×C10312yes—
232#131D4×C10312yes—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16D4×C10311yescharacteristic
236C22×C8—21no—
237C22×C8C23×C10311yescharacteristic
238C4×Q8—41no—
239C4×D4—42no—
240C4×D4—41no—
241#117—22no—
242#117—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245M32—21no—
246M32—21no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251#108—21no—
252#108C2×C4×C10312yescomplemented
253#107—22no—
254#107—21no—
255#107D4×C10311yescharacteristic
256#107D4×C10312yes—
257#107D4×C10311yescharacteristic
258#106—22no—
259#106—21no—
260#100—24no—
261C24—41no—
262#41—21no—
263#41—21no—
264#41C22⋊C4×C10312yes—
265#41SD16×C10312yes—
266C2×Q8D8×C10311yescharacteristic
267C2×D4—21no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4D8×C10311yescharacteristic
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—41no—
278C22×C4C2×D4×C10311yescharacteristic
279SD16—44no—
280D8—22no—
281D8—22no—
282D8—44no—
283D8—41no—
284D8—41no—
285M16—21no—
286M16—22no—
287M16—22no—
288M16—22no—
289M16—41no—
290M16C22⋊C4×C10312yes—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8C22×C4×C10311yescharacteristic
296C2×C8C2×D4×C10311yescharacteristic
297C2×C8C2×D4×C10311yescharacteristic
298C2×C8C2×D4×C10311yescharacteristic
299C2×C8#41×C10311yescharacteristic
300C2×C8#41×C10311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C42—42no—
309C42—41no—
310C16—41no—
311C16—41no—
312C23—21no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—161no—
317C23—161no—
318C23AGL(1,ℤ/8)×C10311yescharacteristic
319Q8—21no—
320Q8#102×C10312yes—
321D4—22no—
322D4—22no—
323D4—21no—
324D4—42no—
325D4—42no—
326D4—81no—
327D4—81no—
328D4#102×C10312yes—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—161no—
336C2×C4—162no—
337C2×C4C2×C22⋊C4×C10311yescharacteristic
338C2×C4#120×C10311yescharacteristic
339C2×C4#123×C10311yescharacteristic
340C2×C4C2×D8×C10311yescharacteristic
341C2×C4C2×SD16×C10311yescharacteristic
342C2×C4#137×C10311yescharacteristic
343C8—22no—
344C8—42no—
345C8C4×D4×C10311yescharacteristic
346C8C4×D4×C10311yescharacteristic
347C8#121×C10311yescharacteristic
348C8#121×C10311yescharacteristic
349C22—21no—
350C22—21no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—82no—
355C22—162no—
356C22—162no—
357C22—161no—
358C22—161no—
359C22#417×C10311yescharacteristic
360C22#447×C10311yescharacteristic
361C22#481×C10311yescharacteristic
362C4—22no—
363C4—82no—
364C4—81no—
365C4—81no—
366C4#386×C10311yescharacteristic
367C4C2×#102×C10311yescharacteristic
368C4#448×C10311yescharacteristic
369C4#480×C10311yescharacteristic
370C2—21no—
371C2—21no—
372C2—42no—
373C2—162no—
374C2C103×#187411yescharacteristic
375C2C103×#219211yescharacteristic
376C2C103×#219311yescharacteristic
subgroupG/H
center, socleC22×C103#447
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
prime radicalC2×#472×C103C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×#131×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2913C2semidirect
3. C103×#2140C2semidirect
4. C2×#357×C103C2semidirect
5. C2×#350×C103C2semidirect
6. C103×#1387C2semidirect
7. C103×#1382C2semidirect
15. #472×C103C4semidirect
39. C2×D8×C103C2×C4semidirect
63. #108×C103C2×C4semidirect
181. #12996C103direct (N × H)
190. #2913C2×C103semidirect
191. #2140C2×C103semidirect
192. C2×#357C2×C103semidirect
193. C2×#350C2×C103semidirect
194. #1387C2×C103semidirect
195. #1382C2×C103semidirect
196. C103#12996direct (N × H)
204. #472C4×C103semidirect
228. C2×D8C2×C4×C103semidirect
252. #108C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#472×C1032
C103×#29132
C103×#21402
C2×#357×C1032
C2×#350×C1032
C103×#13872
C103×#13822
#12996103