Finite Group Databasebeta

← C103×#9025 #39914300

Subgroups — C103×#9025 #39914300

Order 26368.

768 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C103C211yesmaximal, characteristic
2C103×#2315C211yesmaximal, characteristic
3C103×#1823C212yesmaximal, complemented
4C2×#323×C103C211yesmaximal, characteristic
5C103×#1294C212yesmaximal, complemented
6C22×C4⋊C4×C103C2211yescharacteristic
7C22×C22⋊C4×C103—21no—
8C22×C22⋊C4×C103—21no—
9C22×C22⋊C4×C103C2211yescharacteristic
10C2×C22⋊C8×C103C2212yes—
11#397×C103—22no—
12#397×C103C414yescomplemented
13#385×C103—24no—
14#380×C103—21no—
15#380×C103C2212yes—
16C2×#95×C103—21no—
17C2×#95×C103C2211yescharacteristic
18#340×C103—24no—
19#323×C103—22no—
20C25×C103D411yescharacteristic
21C23×C4×C103—21no—
22C23×C4×C103—21no—
23C23×C4×C103—22no—
24C23×C4×C103D411yescharacteristic
25C23×C4×C103C2311yescharacteristic
26C22×C8×C103—22no—
27C2×C4⋊C4×C103—22no—
28C2×C4⋊C4×C103—22no—
29C2×C4⋊C4×C103—21no—
30C2×C4⋊C4×C103—22no—
31C2×C4⋊C4×C103C2×C412yescomplemented
32C2×C4⋊C4×C103D414yes—
33C2×C22⋊C4×C103—22no—
34C2×C22⋊C4×C103—22no—
35C2×C22⋊C4×C103—22no—
36C2×C22⋊C4×C103—24no—
37C2×C22⋊C4×C103—22no—
38C2×C22⋊C4×C103—42no—
39C2×C22⋊C4×C103—42no—
40C2×C22⋊C4×C103—42no—
41C2×C22⋊C4×C103—42no—
42C2×C22⋊C4×C103C2×C412yes—
43C2×C22⋊C4×C103D412yes—
44C22⋊C8×C103—22no—
45C22⋊C8×C103—22no—
46#95×C103—22no—
47#95×C103—24no—
48#95×C103—21no—
49#95×C103—22no—
50#95×C103C2×C412yescomplemented
51C24×C103—21no—
52C24×C103—21no—
53C24×C103—21no—
54C24×C103—21no—
55C24×C103—42no—
56C24×C103—42no—
57C24×C103C22⋊C412yes—
58C24×C103D812yes—
59C24×C103SD1612yes—
60C24×C103C2×D411yescharacteristic
61C22×C4×C103—21no—
62C22×C4×C103—21no—
63C22×C4×C103—22no—
64C22×C4×C103—22no—
65C22×C4×C103—24no—
66C22×C4×C103—42no—
67C22×C4×C103—42no—
68C22×C4×C103—44no—
69C22×C4×C103—42no—
70C22×C4×C103—42no—
71C22×C4×C103—41no—
72C22×C4×C103—41no—
73C22×C4×C103—41no—
74C22×C4×C103—41no—
75C22×C4×C103—41no—
76C22×C4×C103—41no—
77C22×C4×C103—41no—
78C22×C4×C103—41no—
79C22×C4×C103—82no—
80C22×C4×C103—82no—
81C22×C4×C103C22⋊C412yes—
82C22×C4×C103C22×C411yescharacteristic
83C22×C4×C103C2×D412yes—
84C22×C4×C103C2×D411yescharacteristic
85C22×C4×C103#4112yes—
86C2×C8×C103—44no—
87C2×C8×C103—42no—
88C4⋊C4×C103—24no—
89C4⋊C4×C103—44no—
90C4⋊C4×C103—42no—
91C4⋊C4×C103—82no—
92C22⋊C4×C103—24no—
93C22⋊C4×C103—24no—
94C22⋊C4×C103—44no—
95C22⋊C4×C103—48no—
96C22⋊C4×C103—42no—
97C22⋊C4×C103—42no—
98C23×C103—22no—
99C23×C103—22no—
100C23×C103—22no—
101C23×C103—22no—
102C23×C103—22no—
103C23×C103—22no—
104C23×C103—22no—
105C23×C103—22no—
106C23×C103—42no—
107C23×C103—42no—
108C23×C103—44no—
109C23×C103—44no—
110C23×C103—42no—
111C23×C103—42no—
112C23×C103—82no—
113C23×C103—82no—
114C23×C103—81no—
115C23×C103—81no—
116C23×C103#10214yes—
117C23×C103C2×C22⋊C411yescharacteristic
118C23×C103#12011yescharacteristic
119C23×C103#12311yescharacteristic
120C23×C103C2×D811yescharacteristic
121C23×C103C2×SD1611yescharacteristic
122C23×C103AGL(1,ℤ/8)11yescharacteristic
123C23×C103#13711yescharacteristic
124C2×C4×C103—24no—
125C2×C4×C103—22no—
126C2×C4×C103—41no—
127C2×C4×C103—41no—
128C2×C4×C103—42no—
129C2×C4×C103—42no—
130C2×C4×C103—42no—
131C2×C4×C103—42no—
132C2×C4×C103—42no—
133C2×C4×C103—42no—
134C2×C4×C103—42no—
135C2×C4×C103—42no—
136C2×C4×C103—42no—
137C2×C4×C103—44no—
138C2×C4×C103—44no—
139C2×C4×C103—44no—
140C2×C4×C103—81no—
141C2×C4×C103—82no—
142C2×C4×C103—82no—
143C2×C4×C103—88no—
144C2×C4×C103—81no—
145C2×C4×C103—81no—
146C2×C4×C103—81no—
147C2×C4×C103—81no—
148C2×C4×C103C4×D412yes—
149C2×C4×C103#12112yes—
150C8×C103—82no—
151C22×C103—22no—
152C22×C103—22no—
153C22×C103—22no—
154C22×C103—22no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—21no—
159C22×C103—24no—
160C22×C103—44no—
161C22×C103—44no—
162C22×C103—44no—
163C22×C103—42no—
164C22×C103—42no—
165C22×C103—82no—
166C22×C103—82no—
167C22×C103—82no—
168C22×C103#38611yescharacteristic
169C22×C103C2×#10211yescharacteristic
170C22×C103#41711yescharacteristic
171C22×C103#44711yescharacteristic
172C22×C103#44811yescharacteristic
173C22×C103#45512yes—
174C22×C103#45812yes—
175C22×C103#48011yescharacteristic
176C22×C103#48111yescharacteristic
177C4×C103—22no—
178C4×C103—22no—
179C4×C103—42no—
180C4×C103—82no—
181C4×C103—84no—
182C4×C103—82no—
183#9025C10311yesmaximal, characteristic, direct product factor, Sylow
184C2×C103—21no—
185C2×C103—21no—
186C2×C103—21no—
187C2×C103—21no—
188C2×C103—44no—
189C2×C103#160712yes—
190C2×C103#160812yes—
191C2×C103#187411yescharacteristic
192C2×C103#188511yescharacteristic
193C2×C103#189011yescharacteristic
194C2×#397C2×C10311yescharacteristic
195#2315C2×C10311yescharacteristic
196#1823C2×C10312yescomplemented
197C2×#323C2×C10311yescharacteristic
198#1294C2×C10312yescomplemented
199C103#902511yescharacteristic, direct product factor, Sylow
200C22×C4⋊C4C22×C10311yescharacteristic
201C22×C22⋊C4—21no—
202C22×C22⋊C4—21no—
203C22×C22⋊C4C22×C10311yescharacteristic
204C2×C22⋊C8C22×C10312yes—
205#397—22no—
206#397C4×C10314yescomplemented
207#385—24no—
208#380—21no—
209#380C22×C10312yes—
210C2×#95—21no—
211C2×#95C22×C10311yescharacteristic
212#340—24no—
213#323—22no—
214C25D4×C10311yescharacteristic
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—22no—
218C23×C4D4×C10311yescharacteristic
219C23×C4C23×C10311yescharacteristic
220C22×C8—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4C2×C4×C10312yescomplemented
226C2×C4⋊C4D4×C10314yes—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—24no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—42no—
233C2×C22⋊C4—42no—
234C2×C22⋊C4—42no—
235C2×C22⋊C4—42no—
236C2×C22⋊C4C2×C4×C10312yes—
237C2×C22⋊C4D4×C10312yes—
238C22⋊C8—22no—
239C22⋊C8—22no—
240#95—22no—
241#95—24no—
242#95—21no—
243#95—22no—
244#95C2×C4×C10312yescomplemented
245C24—21no—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—42no—
250C24—42no—
251C24C22⋊C4×C10312yes—
252C24D8×C10312yes—
253C24SD16×C10312yes—
254C24C2×D4×C10311yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—44no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—82no—
274C22×C4—82no—
275C22×C4C22⋊C4×C10312yes—
276C22×C4C22×C4×C10311yescharacteristic
277C22×C4C2×D4×C10312yes—
278C22×C4C2×D4×C10311yescharacteristic
279C22×C4#41×C10312yes—
280C2×C8—44no—
281C2×C8—42no—
282C4⋊C4—24no—
283C4⋊C4—44no—
284C4⋊C4—42no—
285C4⋊C4—82no—
286C22⋊C4—24no—
287C22⋊C4—24no—
288C22⋊C4—44no—
289C22⋊C4—48no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—42no—
301C23—42no—
302C23—44no—
303C23—44no—
304C23—42no—
305C23—42no—
306C23—82no—
307C23—82no—
308C23—81no—
309C23—81no—
310C23#102×C10314yes—
311C23C2×C22⋊C4×C10311yescharacteristic
312C23#120×C10311yescharacteristic
313C23#123×C10311yescharacteristic
314C23C2×D8×C10311yescharacteristic
315C23C2×SD16×C10311yescharacteristic
316C23AGL(1,ℤ/8)×C10311yescharacteristic
317C23#137×C10311yescharacteristic
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—81no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—88no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4C4×D4×C10312yes—
343C2×C4#121×C10312yes—
344C8—82no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—24no—
354C22—44no—
355C22—44no—
356C22—44no—
357C22—42no—
358C22—42no—
359C22—82no—
360C22—82no—
361C22—82no—
362C22#386×C10311yescharacteristic
363C22C2×#102×C10311yescharacteristic
364C22#417×C10311yescharacteristic
365C22#447×C10311yescharacteristic
366C22#448×C10311yescharacteristic
367C22#455×C10312yes—
368C22#458×C10312yes—
369C22#480×C10311yescharacteristic
370C22#481×C10311yescharacteristic
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—84no—
376C4—82no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2C103×#160712yes—
383C2C103×#160812yes—
384C2C103×#187411yescharacteristic
385C2C103×#188511yescharacteristic
386C2C103×#189011yescharacteristic
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×#1823C2semidirect
5. C103×#1294C2semidirect
12. #397×C103C4semidirect
31. C2×C4⋊C4×C103C2×C4semidirect
50. #95×C103C2×C4semidirect
183. #9025C103direct (N × H)
196. #1823C2×C103semidirect
198. #1294C2×C103semidirect
199. C103#9025direct (N × H)
206. #397C4×C103semidirect
225. C2×C4⋊C4C2×C4×C103semidirect
244. #95C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1032
C103×#23152
C103×#18232
C2×#323×C1032
C103×#12942
#9025103