Finite Group Databasebeta

← C103×#9013 #39914288

Subgroups — C103×#9013 #39914288

Order 26368.

908 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C103C211yesmaximal, characteristic
2C103×#2315C211yesmaximal, characteristic
3C103×#1787C212yesmaximal, complemented
4C2×#323×C103C211yesmaximal, characteristic
5C103×#1294C212yesmaximal, complemented
6C23×Q8×C103C2211yescharacteristic
7C22×C22⋊C4×C103—21no—
8C22×C22⋊C4×C103—21no—
9C22×C22⋊C4×C103C2211yescharacteristic
10C2×#103×C103—24no—
11C2×C22⋊C8×C103C2212yes—
12#393×C103—22no—
13#393×C103C414yescomplemented
14#385×C103—24no—
15#380×C103—21no—
16#380×C103C2212yes—
17C2×#95×C103—21no—
18C2×#95×C103C2211yescharacteristic
19#323×C103—22no—
20C25×C103D411yescharacteristic
21C22×Q8×C103—21no—
22C22×Q8×C103—22no—
23C22×Q8×C103—22no—
24C22×Q8×C103—44no—
25C22×Q8×C103C2×C412yescomplemented
26C23×C4×C103—21no—
27C23×C4×C103—21no—
28C23×C4×C103—22no—
29C23×C4×C103D411yescharacteristic
30C23×C4×C103C2311yescharacteristic
31C22×C8×C103—22no—
32C2×C4⋊C4×C103—22no—
33C2×C4⋊C4×C103D414yes—
34C2×C22⋊C4×C103—22no—
35C2×C22⋊C4×C103—22no—
36C2×C22⋊C4×C103—22no—
37C2×C22⋊C4×C103—24no—
38C2×C22⋊C4×C103—22no—
39C2×C22⋊C4×C103—44no—
40C2×C22⋊C4×C103—42no—
41C2×C22⋊C4×C103—42no—
42C2×C22⋊C4×C103C2×C412yes—
43C2×C22⋊C4×C103D412yes—
44#103×C103—48no—
45C22⋊C8×C103—22no—
46C22⋊C8×C103—22no—
47#95×C103—22no—
48#95×C103—24no—
49#95×C103—21no—
50#95×C103—22no—
51#95×C103C2×C412yescomplemented
52C24×C103—21no—
53C24×C103—21no—
54C24×C103—21no—
55C24×C103—21no—
56C24×C103—42no—
57C24×C103—42no—
58C24×C103C22⋊C412yes—
59C24×C103SD1612yes—
60C24×C103Q1612yes—
61C24×C103C2×D411yescharacteristic
62C2×Q8×C103—28no—
63C2×Q8×C103—24no—
64C2×Q8×C103—44no—
65C2×Q8×C103—44no—
66C2×Q8×C103—44no—
67C2×Q8×C103—48no—
68C2×Q8×C103—42no—
69C22×C4×C103—24no—
70C22×C4×C103—22no—
71C22×C4×C103—21no—
72C22×C4×C103—21no—
73C22×C4×C103—22no—
74C22×C4×C103—24no—
75C22×C4×C103—42no—
76C22×C4×C103—42no—
77C22×C4×C103—41no—
78C22×C4×C103—41no—
79C22×C4×C103—42no—
80C22×C4×C103—42no—
81C22×C4×C103—44no—
82C22×C4×C103—42no—
83C22×C4×C103—41no—
84C22×C4×C103—41no—
85C22×C4×C103—82no—
86C22×C4×C103—82no—
87C22×C4×C103C22⋊C412yes—
88C22×C4×C103C22×C411yescharacteristic
89C22×C4×C103C2×D412yes—
90C22×C4×C103C2×D411yescharacteristic
91C22×C4×C103#4112yes—
92C2×C8×C103—44no—
93C2×C8×C103—42no—
94C4⋊C4×C103—44no—
95C4⋊C4×C103—82no—
96C22⋊C4×C103—24no—
97C22⋊C4×C103—24no—
98C22⋊C4×C103—48no—
99C22⋊C4×C103—44no—
100C22⋊C4×C103—42no—
101C22⋊C4×C103—42no—
102C23×C103—22no—
103C23×C103—22no—
104C23×C103—22no—
105C23×C103—22no—
106C23×C103—22no—
107C23×C103—22no—
108C23×C103—22no—
109C23×C103—22no—
110C23×C103—42no—
111C23×C103—42no—
112C23×C103—44no—
113C23×C103—44no—
114C23×C103—42no—
115C23×C103—42no—
116C23×C103—82no—
117C23×C103—82no—
118C23×C103—81no—
119C23×C103—81no—
120C23×C103#10314yescomplemented
121C23×C103C2×C22⋊C411yescharacteristic
122C23×C103#12011yescharacteristic
123C23×C103#12311yescharacteristic
124C23×C103C2×SD1611yescharacteristic
125C23×C103C2×Q1611yescharacteristic
126C23×C103AGL(1,ℤ/8)11yescharacteristic
127C23×C103#13711yescharacteristic
128Q8×C103—28no—
129Q8×C103—48no—
130Q8×C103—44no—
131C2×C4×C103—24no—
132C2×C4×C103—24no—
133C2×C4×C103—22no—
134C2×C4×C103—41no—
135C2×C4×C103—41no—
136C2×C4×C103—42no—
137C2×C4×C103—42no—
138C2×C4×C103—44no—
139C2×C4×C103—42no—
140C2×C4×C103—42no—
141C2×C4×C103—44no—
142C2×C4×C103—42no—
143C2×C4×C103—42no—
144C2×C4×C103—42no—
145C2×C4×C103—42no—
146C2×C4×C103—44no—
147C2×C4×C103—44no—
148C2×C4×C103—44no—
149C2×C4×C103—81no—
150C2×C4×C103—82no—
151C2×C4×C103—82no—
152C2×C4×C103—88no—
153C2×C4×C103C4×D412yes—
154C2×C4×C103#12112yes—
155C8×C103—82no—
156C22×C103—22no—
157C22×C103—22no—
158C22×C103—22no—
159C22×C103—22no—
160C22×C103—21no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103—21no—
164C22×C103—24no—
165C22×C103—44no—
166C22×C103—44no—
167C22×C103—44no—
168C22×C103—42no—
169C22×C103—42no—
170C22×C103—82no—
171C22×C103—82no—
172C22×C103—82no—
173C22×C103#38611yescharacteristic
174C22×C103C2×#10311yescharacteristic
175C22×C103#41711yescharacteristic
176C22×C103#45011yescharacteristic
177C22×C103#45111yescharacteristic
178C22×C103#45512yes—
179C22×C103B(4,𝔽2)12yes—
180C22×C103#48311yescharacteristic
181C22×C103#48411yescharacteristic
182C4×C103—22no—
183C4×C103—22no—
184C4×C103—42no—
185C4×C103—44no—
186C4×C103—82no—
187C4×C103—84no—
188#9013C10311yesmaximal, characteristic, direct product factor, Sylow
189C2×C103—21no—
190C2×C103—21no—
191C2×C103—21no—
192C2×C103—21no—
193C2×C103—44no—
194C2×C103#160112yes—
195C2×C103#160212yes—
196C2×C103#187211yescharacteristic
197C2×C103#188511yescharacteristic
198C2×C103#188911yescharacteristic
199C2×#393C2×C10311yescharacteristic
200#2315C2×C10311yescharacteristic
201#1787C2×C10312yescomplemented
202C2×#323C2×C10311yescharacteristic
203#1294C2×C10312yescomplemented
204C103#901311yescharacteristic, direct product factor, Sylow
205C23×Q8C22×C10311yescharacteristic
206C22×C22⋊C4—21no—
207C22×C22⋊C4—21no—
208C22×C22⋊C4C22×C10311yescharacteristic
209C2×#103—24no—
210C2×C22⋊C8C22×C10312yes—
211#393—22no—
212#393C4×C10314yescomplemented
213#385—24no—
214#380—21no—
215#380C22×C10312yes—
216C2×#95—21no—
217C2×#95C22×C10311yescharacteristic
218#323—22no—
219C25D4×C10311yescharacteristic
220C22×Q8—21no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—44no—
224C22×Q8C2×C4×C10312yescomplemented
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—22no—
228C23×C4D4×C10311yescharacteristic
229C23×C4C23×C10311yescharacteristic
230C22×C8—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4D4×C10314yes—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—44no—
239C2×C22⋊C4—42no—
240C2×C22⋊C4—42no—
241C2×C22⋊C4C2×C4×C10312yes—
242C2×C22⋊C4D4×C10312yes—
243#103—48no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246#95—22no—
247#95—24no—
248#95—21no—
249#95—22no—
250#95C2×C4×C10312yescomplemented
251C24—21no—
252C24—21no—
253C24—21no—
254C24—21no—
255C24—42no—
256C24—42no—
257C24C22⋊C4×C10312yes—
258C24SD16×C10312yes—
259C24Q16×C10312yes—
260C24C2×D4×C10311yescharacteristic
261C2×Q8—28no—
262C2×Q8—24no—
263C2×Q8—44no—
264C2×Q8—44no—
265C2×Q8—44no—
266C2×Q8—48no—
267C2×Q8—42no—
268C22×C4—24no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—44no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4C22⋊C4×C10312yes—
287C22×C4C22×C4×C10311yescharacteristic
288C22×C4C2×D4×C10312yes—
289C22×C4C2×D4×C10311yescharacteristic
290C22×C4#41×C10312yes—
291C2×C8—44no—
292C2×C8—42no—
293C4⋊C4—44no—
294C4⋊C4—82no—
295C22⋊C4—24no—
296C22⋊C4—24no—
297C22⋊C4—48no—
298C22⋊C4—44no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—22no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23—42no—
310C23—42no—
311C23—44no—
312C23—44no—
313C23—42no—
314C23—42no—
315C23—82no—
316C23—82no—
317C23—81no—
318C23—81no—
319C23#103×C10314yescomplemented
320C23C2×C22⋊C4×C10311yescharacteristic
321C23#120×C10311yescharacteristic
322C23#123×C10311yescharacteristic
323C23C2×SD16×C10311yescharacteristic
324C23C2×Q16×C10311yescharacteristic
325C23AGL(1,ℤ/8)×C10311yescharacteristic
326C23#137×C10311yescharacteristic
327Q8—28no—
328Q8—48no—
329Q8—44no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—81no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—88no—
352C2×C4C4×D4×C10312yes—
353C2×C4#121×C10312yes—
354C8—82no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—44no—
365C22—44no—
366C22—44no—
367C22—42no—
368C22—42no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22#386×C10311yescharacteristic
373C22C2×#103×C10311yescharacteristic
374C22#417×C10311yescharacteristic
375C22#450×C10311yescharacteristic
376C22#451×C10311yescharacteristic
377C22#455×C10312yes—
378C22B(4,𝔽2)×C10312yes—
379C22#483×C10311yescharacteristic
380C22#484×C10311yescharacteristic
381C4—22no—
382C4—22no—
383C4—42no—
384C4—44no—
385C4—82no—
386C4—84no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2—21no—
391C2—44no—
392C2C103×#160112yes—
393C2C103×#160212yes—
394C2C103×#187211yescharacteristic
395C2C103×#188511yescharacteristic
396C2C103×#188911yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
prime radicalC25×C103D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#1787C2semidirect
5. C103×#1294C2semidirect
13. #393×C103C4semidirect
25. C22×Q8×C103C2×C4semidirect
51. #95×C103C2×C4semidirect
120. C23×C103#103semidirect
188. #9013C103direct (N × H)
201. #1787C2×C103semidirect
203. #1294C2×C103semidirect
204. C103#9013direct (N × H)
212. #393C4×C103semidirect
224. C22×Q8C2×C4×C103semidirect
250. #95C2×C4×C103semidirect
319. C23#103×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1032
C103×#23152
C103×#17872
C2×#323×C1032
C103×#12942
#9013103