Finite Group Databasebeta

← C103×#13234 #39918509

Subgroups — C103×#13234 #39918509

Order 26368.

464 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3058C211yesmaximal, characteristic
2C103×#2134C212yesmaximal, complemented
3C103×#2122C212yesmaximal, complemented
4C103×#1813C211yesmaximal, characteristic, complemented
5C103×#1757C211yesmaximal, characteristic, complemented
6C22×D8×C103C411yescharacteristic, complemented
7C2×#131×C103C2211yescharacteristic
8#535×C103C2212yes—
9#469×C103—21no—
10#469×C103—21no—
11#466×C103—21no—
12#466×C103—21no—
13C2×#108×C103—21no—
14#427×C103C411yescharacteristic, complemented
15#418×C103C412yescomplemented
16#413×C103C2212yes—
17#413×C103C2211yescharacteristic
18#410×C103C2211yescharacteristic
19#405×C103—21no—
20#355×C103—24no—
21AΣL(1,𝔽16)×C103—24no—
22#344×C103—21no—
23#338×C103—21no—
24C2×#41×C103C2311yescharacteristic
25C22×D4×C103C2×C412yes—
26C2×D8×C103—21no—
27C2×D8×C103—21no—
28C2×D8×C103—41no—
29C2×D8×C103—41no—
30#131×C103—41no—
31#131×C103—41no—
32C2×M16×C103—21no—
33C2×M16×C103—22no—
34C2×M16×C103C2×C411yescharacteristic
35C2×M16×C103D411yescharacteristic
36C2×M16×C103D411yescharacteristic
37C22×C8×C103C2×C411yescharacteristic
38C22×C8×C103D411yescharacteristic
39C22×C8×C103D411yescharacteristic
40#127×C103—22no—
41#124×C103—22no—
42#121×C103—22no—
43#121×C103—22no—
44#120×C103—22no—
45#120×C103—22no—
46#117×C103—21no—
47#117×C103C2×C412yes—
48#108×C103—41no—
49#108×C103—41no—
50#107×C103—21no—
51#106×C103—21no—
52#102×C103—22no—
53#102×C103—22no—
54#101×C103—22no—
55#101×C103D412yes—
56#100×C103—21no—
57#100×C103—22no—
58#99×C103—21no—
59#99×C103D412yes—
60#97×C103—41no—
61C4×C8×C103—41no—
62C24×C103—22no—
63#41×C103—41no—
64#41×C103—41no—
65C2×Q8×C103C2×D411yescharacteristic
66C2×D4×C103—22no—
67C2×D4×C103—22no—
68C2×D4×C103—42no—
69C2×D4×C103—42no—
70C2×D4×C103—42no—
71C2×D4×C103—42no—
72C2×D4×C103C2×D411yescharacteristic
73C2×D4×C103#4111yescharacteristic
74C2×D4×C103#4111yescharacteristic
75C22×C4×C103C22×C411yescharacteristic
76C22×C4×C103C2×D411yescharacteristic
77C22×C4×C103C2×D411yescharacteristic
78D8×C103—42no—
79D8×C103—41no—
80D8×C103—41no—
81M16×C103—22no—
82M16×C103—41no—
83M16×C103—41no—
84M16×C103—41no—
85M16×C103—41no—
86M16×C103—42no—
87M16×C103—42no—
88C2×C8×C103—21no—
89C2×C8×C103—21no—
90C2×C8×C103—21no—
91C2×C8×C103—21no—
92C2×C8×C103—21no—
93C2×C8×C103—21no—
94C2×C8×C103—41no—
95C2×C8×C103—42no—
96C2×C8×C103C22⋊C411yescharacteristic
97C2×C8×C103C22⋊C411yescharacteristic
98C2×C8×C103C22⋊C411yescharacteristic
99C2×C8×C103C22⋊C411yescharacteristic
100C4⋊C4×C103—22no—
101C4⋊C4×C103—41no—
102C22⋊C4×C103—22no—
103C22⋊C4×C103—22no—
104C22⋊C4×C103—42no—
105C22⋊C4×C103—42no—
106C42×C103—22no—
107C42×C103—41no—
108C23×C103—42no—
109C23×C103—82no—
110C23×C103—162no—
111C23×C103C4×D411yescharacteristic
112C23×C103#12111yescharacteristic
113C23×C103#12411yescharacteristic
114Q8×C103—41no—
115D4×C103—41no—
116D4×C103—41no—
117D4×C103—41no—
118D4×C103—42no—
119D4×C103—42no—
120D4×C103—82no—
121D4×C103—162no—
122D4×C103—162no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—42no—
130C2×C4×C103—42no—
131C2×C4×C103C2×C22⋊C411yescharacteristic
132C2×C4×C103C4×D411yescharacteristic
133C2×C4×C103#12111yescharacteristic
134C2×C4×C103#12711yescharacteristic
135C8×C103—21no—
136C8×C103—21no—
137C8×C103—21no—
138C8×C103—42no—
139C8×C103—82no—
140C8×C103#9911yescharacteristic
141C8×C103#9911yescharacteristic
142C22×C103—21no—
143C22×C103—21no—
144C22×C103—21no—
145C22×C103—41no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103—82no—
149C22×C103—82no—
150C22×C103—82no—
151C22×C103—164no—
152C22×C103#39011yescharacteristic
153C4×C103—21no—
154C4×C103—21no—
155C4×C103—21no—
156C4×C103—82no—
157C4×C103—82no—
158C4×C103C2×#9911yescharacteristic
159C4×C103#41011yescharacteristic
160#13234C10311yesmaximal, characteristic, direct product factor, Sylow
161C2×C103—21no—
162C2×C103—41no—
163C2×C103—41no—
164C2×C103—41no—
165C2×C103—162no—
166C2×C103#196411yescharacteristic
167#3058C2×C10311yescharacteristic
168#2134C2×C10312yescomplemented
169#2122C2×C10312yescomplemented
170#1813C2×C10311yescharacteristic, complemented
171#1757C2×C10311yescharacteristic, complemented
172C103#1323411yescharacteristic, direct product factor, Sylow
173C22×D8C4×C10311yescharacteristic, complemented
174C2×#131C22×C10311yescharacteristic
175#535C22×C10312yes—
176#469—21no—
177#469—21no—
178#466—21no—
179#466—21no—
180C2×#108—21no—
181#427C4×C10311yescharacteristic, complemented
182#418C4×C10312yescomplemented
183#413C22×C10312yes—
184#413C22×C10311yescharacteristic
185#410C22×C10311yescharacteristic
186#405—21no—
187#355—24no—
188AΣL(1,𝔽16)—24no—
189#344—21no—
190#338—21no—
191C2×#41C23×C10311yescharacteristic
192C22×D4C2×C4×C10312yes—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—41no—
196C2×D8—41no—
197#131—41no—
198#131—41no—
199C2×M16—21no—
200C2×M16—22no—
201C2×M16C2×C4×C10311yescharacteristic
202C2×M16D4×C10311yescharacteristic
203C2×M16D4×C10311yescharacteristic
204C22×C8C2×C4×C10311yescharacteristic
205C22×C8D4×C10311yescharacteristic
206C22×C8D4×C10311yescharacteristic
207#127—22no—
208#124—22no—
209#121—22no—
210#121—22no—
211#120—22no—
212#120—22no—
213#117—21no—
214#117C2×C4×C10312yes—
215#108—41no—
216#108—41no—
217#107—21no—
218#106—21no—
219#102—22no—
220#102—22no—
221#101—22no—
222#101D4×C10312yes—
223#100—21no—
224#100—22no—
225#99—21no—
226#99D4×C10312yes—
227#97—41no—
228C4×C8—41no—
229C24—22no—
230#41—41no—
231#41—41no—
232C2×Q8C2×D4×C10311yescharacteristic
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4C2×D4×C10311yescharacteristic
240C2×D4#41×C10311yescharacteristic
241C2×D4#41×C10311yescharacteristic
242C22×C4C22×C4×C10311yescharacteristic
243C22×C4C2×D4×C10311yescharacteristic
244C22×C4C2×D4×C10311yescharacteristic
245D8—42no—
246D8—41no—
247D8—41no—
248M16—22no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—42no—
254M16—42no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—41no—
262C2×C8—42no—
263C2×C8C22⋊C4×C10311yescharacteristic
264C2×C8C22⋊C4×C10311yescharacteristic
265C2×C8C22⋊C4×C10311yescharacteristic
266C2×C8C22⋊C4×C10311yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—41no—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42—22no—
274C42—41no—
275C23—42no—
276C23—82no—
277C23—162no—
278C23C4×D4×C10311yescharacteristic
279C23#121×C10311yescharacteristic
280C23#124×C10311yescharacteristic
281Q8—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—42no—
286D4—42no—
287D4—82no—
288D4—162no—
289D4—162no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4C2×C22⋊C4×C10311yescharacteristic
299C2×C4C4×D4×C10311yescharacteristic
300C2×C4#121×C10311yescharacteristic
301C2×C4#127×C10311yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—42no—
306C8—82no—
307C8#99×C10311yescharacteristic
308C8#99×C10311yescharacteristic
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—82no—
316C22—82no—
317C22—82no—
318C22—164no—
319C22#390×C10311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—82no—
324C4—82no—
325C4C2×#99×C10311yescharacteristic
326C4#410×C10311yescharacteristic
327C2—21no—
328C2—41no—
329C2—41no—
330C2—41no—
331C2—162no—
332C2C103×#196411yescharacteristic
subgroupG/H
center, socleC2×C103#1964
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×#41C23×C103
prime radicalC103×#3058C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C2×C4×C103 ◁ C2×#131×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2134C2semidirect
3. C103×#2122C2semidirect
4. C103×#1813C2semidirect
5. C103×#1757C2semidirect
6. C22×D8×C103C4semidirect
14. #427×C103C4semidirect
15. #418×C103C4semidirect
160. #13234C103direct (N × H)
168. #2134C2×C103semidirect
169. #2122C2×C103semidirect
170. #1813C2×C103semidirect
171. #1757C2×C103semidirect
172. C103#13234direct (N × H)
173. C22×D8C4×C103semidirect
181. #427C4×C103semidirect
182. #418C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#30582
C103×#21342
C103×#21222
C103×#18132
C103×#17572
#13234103