Finite Group Databasebeta

← C103×#13393 #39918668

Subgroups — C103×#13393 #39918668

Order 26368.

412 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C103C211yesmaximal, characteristic
2C2×#368×C103C211yesmaximal, characteristic, complemented
3C2×#361×C103C211yesmaximal, characteristic, complemented
4C2×#357×C103C211yesmaximal, characteristic, complemented
5C103×#2113C211yesmaximal, characteristic, complemented
6C103×#1816C211yesmaximal, characteristic, complemented
7C103×#1387C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C103—21no—
9C22×D8×C103C2211yescharacteristic
10C2×#131×C103C2211yescharacteristic
11C2×M32×C103C2211yescharacteristic
12C22×C16×C103C2211yescharacteristic
13#472×C103—22no—
14#472×C103—22no—
15C2×#108×C103C2211yescharacteristic
16C2×#108×C103C2211yescharacteristic
17C2×#107×C103C2211yescharacteristic
18#417×C103—21no—
19C2×#100×C103—21no—
20#368×C103—22no—
21#361×C103—22no—
22#357×C103—22no—
23C22⋊C16×C103—22no—
24#343×C103—21no—
25C2×#41×C103D411yescharacteristic
26C22×D4×C103—21no—
27AGL(1,ℤ/8)×C103—24no—
28AGL(1,ℤ/8)×C103—42no—
29C2×SD16×C103—41no—
30C2×D8×C103—21no—
31C2×D8×C103—21no—
32C2×D8×C103—21no—
33C2×D8×C103—21no—
34C2×D8×C103—21no—
35C2×D8×C103—41no—
36C2×D8×C103D412yes—
37#131×C103—21no—
38#131×C103—21no—
39#131×C103—21no—
40#131×C103—21no—
41C2×M16×C103—21no—
42C2×M16×C103—21no—
43C2×M16×C103—21no—
44C2×M16×C103D411yescharacteristic
45C22×C8×C103—21no—
46C22×C8×C103C2311yescharacteristic
47C2×C4⋊C4×C103—21no—
48M32×C103—21no—
49M32×C103—21no—
50C2×C16×C103—21no—
51C2×C16×C103—21no—
52C2×C16×C103—21no—
53C2×C16×C103D412yes—
54#108×C103—21no—
55#108×C103—21no—
56#108×C103—21no—
57#108×C103D412yes—
58#107×C103—21no—
59#107×C103—21no—
60#103×C103—41no—
61#102×C103—41no—
62#100×C103—24no—
63C24×C103—41no—
64#41×C103—21no—
65#41×C103—21no—
66#41×C103—21no—
67#41×C103—21no—
68C2×Q8×C103D811yescharacteristic
69C2×D4×C103—21no—
70C2×D4×C103—22no—
71C2×D4×C103—41no—
72C2×D4×C103—41no—
73C2×D4×C103—41no—
74C2×D4×C103—41no—
75C2×D4×C103—41no—
76C2×D4×C103D811yescharacteristic
77C22×C4×C103—21no—
78C22×C4×C103—41no—
79C22×C4×C103C2×D411yescharacteristic
80SD16×C103—44no—
81D8×C103—22no—
82D8×C103—22no—
83D8×C103—44no—
84D8×C103—41no—
85D8×C103—41no—
86M16×C103—21no—
87M16×C103—22no—
88M16×C103—21no—
89M16×C103—41no—
90M16×C103—41no—
91M16×C103—41no—
92M16×C103—41no—
93M16×C103—41no—
94C2×C8×C103—21no—
95C2×C8×C103—41no—
96C2×C8×C103—41no—
97C2×C8×C103—41no—
98C2×C8×C103—41no—
99C2×C8×C103C2×D411yescharacteristic
100C2×C8×C103C2×D411yescharacteristic
101C2×C8×C103C2×D411yescharacteristic
102C2×C8×C103#4111yescharacteristic
103C2×C8×C103#4111yescharacteristic
104C2×C8×C103#4111yescharacteristic
105C4⋊C4×C103—41no—
106C4⋊C4×C103—41no—
107C16×C103—22no—
108C16×C103—41no—
109C23×C103—21no—
110C23×C103—42no—
111C23×C103—81no—
112C23×C103—81no—
113C23×C103—161no—
114C23×C103—161no—
115C23×C103#13511yescharacteristic
116Q8×C103—21no—
117Q8×C103—21no—
118D4×C103—21no—
119D4×C103—21no—
120D4×C103—41no—
121D4×C103—41no—
122D4×C103—42no—
123D4×C103—42no—
124D4×C103—81no—
125D4×C103—81no—
126C2×C4×C103—21no—
127C2×C4×C103—41no—
128C2×C4×C103—41no—
129C2×C4×C103—81no—
130C2×C4×C103—161no—
131C2×C4×C103#12011yescharacteristic
132C2×C4×C103#12111yescharacteristic
133C2×C4×C103#12311yescharacteristic
134C2×C4×C103C2×D811yescharacteristic
135C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C103#13711yescharacteristic
137C8×C103—41no—
138C8×C103—42no—
139C8×C103—81no—
140C8×C103#12111yescharacteristic
141C8×C103#12111yescharacteristic
142C8×C103#12311yescharacteristic
143C8×C103#12411yescharacteristic
144C22×C103—21no—
145C22×C103—21no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103—41no—
149C22×C103—82no—
150C22×C103—162no—
151C22×C103—162no—
152C22×C103—161no—
153C22×C103—161no—
154C22×C103#45211yescharacteristic
155C22×C103#46611yescharacteristic
156C22×C103#48211yescharacteristic
157C4×C103—41no—
158C4×C103—161no—
159C4×C103#39411yescharacteristic
160C4×C103#44711yescharacteristic
161C4×C103#46811yescharacteristic
162C4×C103#48011yescharacteristic
163#13393C10311yesmaximal, characteristic, direct product factor, Sylow
164C2×C103—21no—
165C2×C103—21no—
166C2×C103—81no—
167C2×C103—162no—
168C2×C103#203311yescharacteristic
169C2×C103#222111yescharacteristic
170C2×C103#222311yescharacteristic
171C2×#472C2×C10311yescharacteristic
172C2×#368C2×C10311yescharacteristic, complemented
173C2×#361C2×C10311yescharacteristic, complemented
174C2×#357C2×C10311yescharacteristic, complemented
175#2113C2×C10311yescharacteristic, complemented
176#1816C2×C10311yescharacteristic, complemented
177#1387C2×C10311yescharacteristic, complemented
178C103#1339311yescharacteristic, direct product factor, Sylow
179C2×AGL(1,ℤ/8)—21no—
180C22×D8C22×C10311yescharacteristic
181C2×#131C22×C10311yescharacteristic
182C2×M32C22×C10311yescharacteristic
183C22×C16C22×C10311yescharacteristic
184#472—22no—
185#472—22no—
186C2×#108C22×C10311yescharacteristic
187C2×#108C22×C10311yescharacteristic
188C2×#107C22×C10311yescharacteristic
189#417—21no—
190C2×#100—21no—
191#368—22no—
192#361—22no—
193#357—22no—
194C22⋊C16—22no—
195#343—21no—
196C2×#41D4×C10311yescharacteristic
197C22×D4—21no—
198AGL(1,ℤ/8)—24no—
199AGL(1,ℤ/8)—42no—
200C2×SD16—41no—
201C2×D8—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—41no—
207C2×D8D4×C10312yes—
208#131—21no—
209#131—21no—
210#131—21no—
211#131—21no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16D4×C10311yescharacteristic
216C22×C8—21no—
217C22×C8C23×C10311yescharacteristic
218C2×C4⋊C4—21no—
219M32—21no—
220M32—21no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—21no—
224C2×C16D4×C10312yes—
225#108—21no—
226#108—21no—
227#108—21no—
228#108D4×C10312yes—
229#107—21no—
230#107—21no—
231#103—41no—
232#102—41no—
233#100—24no—
234C24—41no—
235#41—21no—
236#41—21no—
237#41—21no—
238#41—21no—
239C2×Q8D8×C10311yescharacteristic
240C2×D4—21no—
241C2×D4—22no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4D8×C10311yescharacteristic
248C22×C4—21no—
249C22×C4—41no—
250C22×C4C2×D4×C10311yescharacteristic
251SD16—44no—
252D8—22no—
253D8—22no—
254D8—44no—
255D8—41no—
256D8—41no—
257M16—21no—
258M16—22no—
259M16—21no—
260M16—41no—
261M16—41no—
262M16—41no—
263M16—41no—
264M16—41no—
265C2×C8—21no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8C2×D4×C10311yescharacteristic
271C2×C8C2×D4×C10311yescharacteristic
272C2×C8C2×D4×C10311yescharacteristic
273C2×C8#41×C10311yescharacteristic
274C2×C8#41×C10311yescharacteristic
275C2×C8#41×C10311yescharacteristic
276C4⋊C4—41no—
277C4⋊C4—41no—
278C16—22no—
279C16—41no—
280C23—21no—
281C23—42no—
282C23—81no—
283C23—81no—
284C23—161no—
285C23—161no—
286C23#135×C10311yescharacteristic
287Q8—21no—
288Q8—21no—
289D4—21no—
290D4—21no—
291D4—41no—
292D4—41no—
293D4—42no—
294D4—42no—
295D4—81no—
296D4—81no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—161no—
302C2×C4#120×C10311yescharacteristic
303C2×C4#121×C10311yescharacteristic
304C2×C4#123×C10311yescharacteristic
305C2×C4C2×D8×C10311yescharacteristic
306C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
307C2×C4#137×C10311yescharacteristic
308C8—41no—
309C8—42no—
310C8—81no—
311C8#121×C10311yescharacteristic
312C8#121×C10311yescharacteristic
313C8#123×C10311yescharacteristic
314C8#124×C10311yescharacteristic
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—82no—
321C22—162no—
322C22—162no—
323C22—161no—
324C22—161no—
325C22#452×C10311yescharacteristic
326C22#466×C10311yescharacteristic
327C22#482×C10311yescharacteristic
328C4—41no—
329C4—161no—
330C4#394×C10311yescharacteristic
331C4#447×C10311yescharacteristic
332C4#468×C10311yescharacteristic
333C4#480×C10311yescharacteristic
334C2—21no—
335C2—21no—
336C2—81no—
337C2—162no—
338C2C103×#203311yescharacteristic
339C2C103×#222111yescharacteristic
340C2C103×#222311yescharacteristic
subgroupG/H
center, socleC22×C103#466
commutator, Frattini, cosocleC22×C8C23×C103
prime radicalC2×#472×C103C2
LCSG ▷ C22×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. C2×#368×C103C2semidirect
3. C2×#361×C103C2semidirect
4. C2×#357×C103C2semidirect
5. C103×#2113C2semidirect
6. C103×#1816C2semidirect
7. C103×#1387C2semidirect
163. #13393C103direct (N × H)
172. C2×#368C2×C103semidirect
173. C2×#361C2×C103semidirect
174. C2×#357C2×C103semidirect
175. #2113C2×C103semidirect
176. #1816C2×C103semidirect
177. #1387C2×C103semidirect
178. C103#13393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#472×C1032
C2×#368×C1032
C2×#361×C1032
C2×#357×C1032
C103×#21132
C103×#18162
C103×#13872
#13393103