Finite Group Databasebeta

← C103×#13398 #39918673

Subgroups — C103×#13398 #39918673

Order 26368.

458 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C103C211yesmaximal, characteristic
2C2×#365×C103C211yesmaximal, characteristic, complemented
3C2×#361×C103C211yesmaximal, characteristic, complemented
4C2×#361×C103C211yesmaximal, characteristic, complemented
5C2×#349×C103C211yesmaximal, characteristic, complemented
6C103×#1811C211yesmaximal, characteristic, complemented
7C103×#1383C211yesmaximal, characteristic, complemented
8C22×D8×C103C2211yescharacteristic
9C22×M16×C103C2211yescharacteristic
10C2×#121×C103—21no—
11C2×M32×C103C2211yescharacteristic
12C2×M32×C103C2211yescharacteristic
13#469×C103—22no—
14#469×C103—22no—
15C2×#108×C103C2211yescharacteristic
16C2×#108×C103C2211yescharacteristic
17C2×#106×C103C2211yescharacteristic
18C2×#102×C103—21no—
19#407×C103—21no—
20#365×C103—22no—
21#361×C103—22no—
22#361×C103—22no—
23#349×C103—22no—
24#341×C103—21no—
25C22×D4×C103—21no—
26C22×D4×C103—41no—
27C23×C4×C103D411yescharacteristic
28C2×D8×C103—21no—
29C2×D8×C103—21no—
30C2×D8×C103—21no—
31C2×D8×C103—21no—
32C2×D8×C103—21no—
33C2×D8×C103D412yes—
34C2×M16×C103—21no—
35C2×M16×C103—21no—
36C2×M16×C103—21no—
37C2×M16×C103—21no—
38C2×M16×C103—21no—
39C2×M16×C103—21no—
40C2×M16×C103—21no—
41C2×M16×C103—21no—
42C22×C8×C103D411yescharacteristic
43C22×C8×C103C2311yescharacteristic
44#121×C103—24no—
45#121×C103—42no—
46C2×C4⋊C4×C103—21no—
47C2×C22⋊C4×C103—41no—
48M32×C103—21no—
49M32×C103—21no—
50M32×C103—21no—
51M32×C103D412yescomplemented
52C2×C16×C103—21no—
53C2×C16×C103—21no—
54#108×C103—21no—
55#108×C103—21no—
56#108×C103—21no—
57#108×C103—21no—
58#106×C103—21no—
59#106×C103D412yes—
60#102×C103—24no—
61C22⋊C8×C103—42no—
62C24×C103—41no—
63C24×C103SD1611yescharacteristic
64C2×D4×C103—22no—
65C2×D4×C103—44no—
66C2×D4×C103—41no—
67C2×D4×C103—41no—
68C2×D4×C103—41no—
69C2×D4×C103—41no—
70C2×D4×C103—41no—
71C2×D4×C103—84no—
72C22×C4×C103—21no—
73C22×C4×C103—21no—
74C22×C4×C103—21no—
75C22×C4×C103—21no—
76C22×C4×C103—21no—
77C22×C4×C103—21no—
78C22×C4×C103—41no—
79C22×C4×C103SD1611yescharacteristic
80C22×C4×C103C2×D411yescharacteristic
81D8×C103—22no—
82D8×C103—22no—
83D8×C103—41no—
84D8×C103—41no—
85M16×C103—41no—
86M16×C103—41no—
87M16×C103—41no—
88M16×C103—41no—
89M16×C103—41no—
90M16×C103—41no—
91M16×C103—41no—
92M16×C103—41no—
93C2×C8×C103—21no—
94C2×C8×C103—21no—
95C2×C8×C103—21no—
96C2×C8×C103—41no—
97C2×C8×C103—41no—
98C2×C8×C103C2×D411yescharacteristic
99C2×C8×C103C2×D411yescharacteristic
100C2×C8×C103C2×D411yescharacteristic
101C2×C8×C103#4111yescharacteristic
102C2×C8×C103#4111yescharacteristic
103C2×C8×C103#4111yescharacteristic
104C4⋊C4×C103—22no—
105C4⋊C4×C103—41no—
106C22⋊C4×C103—44no—
107C16×C103—22no—
108C16×C103—41no—
109C23×C103—21no—
110C23×C103—21no—
111C23×C103—21no—
112C23×C103—42no—
113C23×C103—42no—
114C23×C103—82no—
115C23×C103—82no—
116C23×C103—81no—
117C23×C103—81no—
118C23×C103C2×SD1611yescharacteristic
119D4×C103—42no—
120D4×C103—42no—
121D4×C103—88no—
122D4×C103—81no—
123D4×C103—81no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—41no—
128C2×C4×C103—41no—
129C2×C4×C103—41no—
130C2×C4×C103—41no—
131C2×C4×C103—42no—
132C2×C4×C103—82no—
133C2×C4×C103#12011yescharacteristic
134C2×C4×C103#12111yescharacteristic
135C2×C4×C103#12311yescharacteristic
136C2×C4×C103#13511yescharacteristic
137C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
139C8×C103—41no—
140C8×C103—81no—
141C8×C103—81no—
142C8×C103#12111yescharacteristic
143C8×C103#12111yescharacteristic
144C8×C103#12311yescharacteristic
145C8×C103#12411yescharacteristic
146C22×C103—22no—
147C22×C103—42no—
148C22×C103—42no—
149C22×C103—41no—
150C22×C103—81no—
151C22×C103—82no—
152C22×C103—82no—
153C22×C103—82no—
154C22×C103—162no—
155C22×C103—162no—
156C22×C103#45011yescharacteristic
157C22×C103#46511yescharacteristic
158C22×C103#48111yescharacteristic
159C4×C103—41no—
160C4×C103—82no—
161C4×C103#39411yescharacteristic
162C4×C103#44911yescharacteristic
163C4×C103#46911yescharacteristic
164C4×C103#48211yescharacteristic
165#13398C10311yesmaximal, characteristic, direct product factor, Sylow
166C2×C103—21no—
167C2×C103—21no—
168C2×C103—81no—
169C2×C103—162no—
170C2×C103#203411yescharacteristic
171C2×C103#223812yes—
172C2×#469C2×C10311yescharacteristic
173C2×#365C2×C10311yescharacteristic, complemented
174C2×#361C2×C10311yescharacteristic, complemented
175C2×#361C2×C10311yescharacteristic, complemented
176C2×#349C2×C10311yescharacteristic, complemented
177#1811C2×C10311yescharacteristic, complemented
178#1383C2×C10311yescharacteristic, complemented
179C103#1339811yescharacteristic, direct product factor, Sylow
180C22×D8C22×C10311yescharacteristic
181C22×M16C22×C10311yescharacteristic
182C2×#121—21no—
183C2×M32C22×C10311yescharacteristic
184C2×M32C22×C10311yescharacteristic
185#469—22no—
186#469—22no—
187C2×#108C22×C10311yescharacteristic
188C2×#108C22×C10311yescharacteristic
189C2×#106C22×C10311yescharacteristic
190C2×#102—21no—
191#407—21no—
192#365—22no—
193#361—22no—
194#361—22no—
195#349—22no—
196#341—21no—
197C22×D4—21no—
198C22×D4—41no—
199C23×C4D4×C10311yescharacteristic
200C2×D8—21no—
201C2×D8—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8D4×C10312yes—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—21no—
211C2×M16—21no—
212C2×M16—21no—
213C2×M16—21no—
214C22×C8D4×C10311yescharacteristic
215C22×C8C23×C10311yescharacteristic
216#121—24no—
217#121—42no—
218C2×C4⋊C4—21no—
219C2×C22⋊C4—41no—
220M32—21no—
221M32—21no—
222M32—21no—
223M32D4×C10312yescomplemented
224C2×C16—21no—
225C2×C16—21no—
226#108—21no—
227#108—21no—
228#108—21no—
229#108—21no—
230#106—21no—
231#106D4×C10312yes—
232#102—24no—
233C22⋊C8—42no—
234C24—41no—
235C24SD16×C10311yescharacteristic
236C2×D4—22no—
237C2×D4—44no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—84no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4SD16×C10311yescharacteristic
252C22×C4C2×D4×C10311yescharacteristic
253D8—22no—
254D8—22no—
255D8—41no—
256D8—41no—
257M16—41no—
258M16—41no—
259M16—41no—
260M16—41no—
261M16—41no—
262M16—41no—
263M16—41no—
264M16—41no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
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—22no—
277C4⋊C4—41no—
278C22⋊C4—44no—
279C16—22no—
280C16—41no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—42no—
285C23—42no—
286C23—82no—
287C23—82no—
288C23—81no—
289C23—81no—
290C23C2×SD16×C10311yescharacteristic
291D4—42no—
292D4—42no—
293D4—88no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4#120×C10311yescharacteristic
306C2×C4#121×C10311yescharacteristic
307C2×C4#123×C10311yescharacteristic
308C2×C4#135×C10311yescharacteristic
309C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
310C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
311C8—41no—
312C8—81no—
313C8—81no—
314C8#121×C10311yescharacteristic
315C8#121×C10311yescharacteristic
316C8#123×C10311yescharacteristic
317C8#124×C10311yescharacteristic
318C22—22no—
319C22—42no—
320C22—42no—
321C22—41no—
322C22—81no—
323C22—82no—
324C22—82no—
325C22—82no—
326C22—162no—
327C22—162no—
328C22#450×C10311yescharacteristic
329C22#465×C10311yescharacteristic
330C22#481×C10311yescharacteristic
331C4—41no—
332C4—82no—
333C4#394×C10311yescharacteristic
334C4#449×C10311yescharacteristic
335C4#469×C10311yescharacteristic
336C4#482×C10311yescharacteristic
337C2—21no—
338C2—21no—
339C2—81no—
340C2—162no—
341C2C103×#203411yescharacteristic
342C2C103×#223812yes—
subgroupG/H
center, socleC22×C103#481
commutator, Frattini, cosocleC22×C8C23×C103
prime radicalC2×#469×C103C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C22×M16×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#365×C103C2semidirect
3. C2×#361×C103C2semidirect
4. C2×#361×C103C2semidirect
5. C2×#349×C103C2semidirect
6. C103×#1811C2semidirect
7. C103×#1383C2semidirect
51. M32×C103D4semidirect
165. #13398C103direct (N × H)
173. C2×#365C2×C103semidirect
174. C2×#361C2×C103semidirect
175. C2×#361C2×C103semidirect
176. C2×#349C2×C103semidirect
177. #1811C2×C103semidirect
178. #1383C2×C103semidirect
179. C103#13398direct (N × H)
223. M32D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1032
C2×#365×C1032
C2×#361×C1032
C2×#349×C1032
C103×#18112
C103×#13832
#13398103