Finite Group Databasebeta

← C103×#18326 #39923601

Subgroups — C103×#18326 #39923601

Order 26368.

976 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C103C211yesmaximal, characteristic, complemented
2C103×#3193C212yesmaximal
3C103×#2591C211yesmaximal, characteristic
4C103×#1617C214yesmaximal, complemented
5C103×#1599C214yesmaximal, complemented
6C103×#1508C212yesmaximal, complemented
7C103×#1463C211yesmaximal, characteristic, complemented
8#544×C103—24no—
9#544×C103—22no—
10#544×C103C2214yes—
11C2×C4⋊Q8×C103—22no—
12C2×#125×C103—22no—
13C2×C22⋊Q8×C103—21no—
14C2×C22⋊Q8×C103C2212yes—
15C2×#121×C103C2211yescharacteristic
16C2×#117×C103—21no—
17C22×C4⋊C4×C103C2211yescharacteristic
18#484×C103C2214yes—
19#480×C103—22no—
20#468×C103—24no—
21#450×C103C2214yes—
22#448×C103—22no—
23#407×C103C2212yes—
24#400×C103C2212yes—
25#394×C103C2212yes—
26#388×C103—22no—
27#386×C103—21no—
28#386×C103—21no—
29C4×C22⋊C4×C103C2211yescharacteristic
30#328×C103C2218yes—
31#324×C103C2214yes—
32C22×Q8×C103—21no—
33C22×Q8×C103D412yes—
34C22×D4×C103—21no—
35C22×D4×C103C2311yescharacteristic
36C23×C4×C103D411yescharacteristic
37C23×C4×C103D411yescharacteristic
38C23×C4×C103C2311yescharacteristic
39C2×SD16×C103—24no—
40C2×M16×C103—22no—
41C4⋊Q8×C103—28no—
42C4⋊Q8×C103—28no—
43#125×C103—28no—
44#125×C103—28no—
45C22⋊Q8×C103—24no—
46C22⋊Q8×C103—24no—
47C22⋊Q8×C103—22no—
48C22⋊Q8×C103—22no—
49C22⋊Q8×C103D414yes—
50C22⋊Q8×C103C2314yes—
51#121×C103—22no—
52#121×C103—22no—
53#117×C103—24no—
54#117×C103—24no—
55C2×C4⋊C4×C103—21no—
56C2×C4⋊C4×C103—21no—
57C2×C4⋊C4×C103—21no—
58C2×C4⋊C4×C103—22no—
59C2×C4⋊C4×C103—22no—
60C2×C4⋊C4×C103—22no—
61C2×C4⋊C4×C103—22no—
62C2×C4⋊C4×C103D412yes—
63C2×C4⋊C4×C103D412yes—
64C2×C4⋊C4×C103C2311yescharacteristic
65C2×C4⋊C4×C103C2312yes—
66C2×C22⋊C4×C103—22no—
67C2×C22⋊C4×C103—21no—
68C2×C22⋊C4×C103—22no—
69C2×C22⋊C4×C103—21no—
70C2×C22⋊C4×C103—22no—
71C2×C42×C103—22no—
72C2×C42×C103—21no—
73#107×C103—24no—
74#103×C103—24no—
75#102×C103—24no—
76C22⋊C8×C103—22no—
77C22⋊C8×C103C2314yes—
78#95×C103—22no—
79#95×C103—22no—
80#95×C103C2312yes—
81C24×C103—21no—
82C24×C103C2×D411yescharacteristic
83C2×Q8×C103—24no—
84C2×Q8×C103—22no—
85C2×Q8×C103—82no—
86C2×Q8×C103—82no—
87C2×Q8×C103C2×D414yes—
88C2×D4×C103—22no—
89C2×D4×C103—44no—
90C2×D4×C103—41no—
91C2×D4×C103—41no—
92C2×D4×C103—81no—
93C22×C4×C103—21no—
94C22×C4×C103—21no—
95C22×C4×C103—24no—
96C22×C4×C103—22no—
97C22×C4×C103—22no—
98C22×C4×C103—21no—
99C22×C4×C103—21no—
100C22×C4×C103—21no—
101C22×C4×C103—22no—
102C22×C4×C103—81no—
103C22×C4×C103—81no—
104C22×C4×C103C2×D412yes—
105C22×C4×C103C2×D412yes—
106C22×C4×C103C2×D411yescharacteristic
107C22×C4×C103C2×D412yes—
108C22×C4×C103C2×D412yes—
109C22×C4×C103C2411yescharacteristic
110SD16×C103—84no—
111M16×C103—82no—
112C2×C8×C103—24no—
113C4⋊C4×C103—24no—
114C4⋊C4×C103—24no—
115C4⋊C4×C103—24no—
116C4⋊C4×C103—28no—
117C4⋊C4×C103—24no—
118C4⋊C4×C103—24no—
119C4⋊C4×C103—22no—
120C4⋊C4×C103—24no—
121C4⋊C4×C103—24no—
122C4⋊C4×C103—22no—
123C4⋊C4×C103C2×D414yes—
124C22⋊C4×C103—24no—
125C22⋊C4×C103—24no—
126C22⋊C4×C103—42no—
127C22⋊C4×C103—42no—
128C22⋊C4×C103—44no—
129C22⋊C4×C103—82no—
130C42×C103—28no—
131C42×C103—81no—
132C23×C103—22no—
133C23×C103—22no—
134C23×C103—41no—
135C23×C103—42no—
136C23×C103—42no—
137C23×C103—41no—
138C23×C103—42no—
139C23×C103#12011yescharacteristic
140C23×C103#12011yescharacteristic
141C23×C103C22×D411yescharacteristic
142Q8×C103—44no—
143Q8×C103—82no—
144Q8×C103—84no—
145D4×C103—44no—
146D4×C103—82no—
147D4×C103—82no—
148C2×C4×C103—24no—
149C2×C4×C103—24no—
150C2×C4×C103—22no—
151C2×C4×C103—22no—
152C2×C4×C103—24no—
153C2×C4×C103—24no—
154C2×C4×C103—22no—
155C2×C4×C103—41no—
156C2×C4×C103—42no—
157C2×C4×C103—42no—
158C2×C4×C103—41no—
159C2×C4×C103—42no—
160C2×C4×C103—44no—
161C2×C4×C103—44no—
162C2×C4×C103—42no—
163C2×C4×C103—42no—
164C2×C4×C103—42no—
165C2×C4×C103—42no—
166C2×C4×C103—41no—
167C2×C4×C103—42no—
168C2×C4×C103—81no—
169C2×C4×C103#12012yes—
170C2×C4×C103#13714yes—
171C2×C4×C103C22×D412yes—
172C8×C103—44no—
173C22×C103—21no—
174C22×C103—21no—
175C22×C103—21no—
176C22×C103—21no—
177C22×C103—21no—
178C22×C103—21no—
179C22×C103—21no—
180C22×C103—44no—
181C22×C103—84no—
182C22×C103—81no—
183C22×C103—81no—
184C22×C103—81no—
185C22×C103#45412yes—
186C22×C103C2×#12011yescharacteristic
187C22×C103C2×#13712yes—
188C4×C103—24no—
189C4×C103—22no—
190C4×C103—22no—
191C4×C103—44no—
192C4×C103—42no—
193C4×C103—44no—
194C4×C103—82no—
195C4×C103—81no—
196#18326C10311yesmaximal, characteristic, direct product factor, Sylow
197C2×C103—22no—
198C2×C103—22no—
199C2×C103—41no—
200C2×C103—161no—
201C2×C103#300411yescharacteristic
202C2×C103C2×#45411yescharacteristic
203C2×C103#302611yescharacteristic
204C2×#544C2×C10311yescharacteristic, complemented
205#3193C2×C10312yes—
206#2591C2×C10311yescharacteristic
207#1617C2×C10314yescomplemented
208#1599C2×C10314yescomplemented
209#1508C2×C10312yescomplemented
210#1463C2×C10311yescharacteristic, complemented
211C103#1832611yescharacteristic, direct product factor, Sylow
212#544—24no—
213#544—22no—
214#544C22×C10314yes—
215C2×C4⋊Q8—22no—
216C2×#125—22no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8C22×C10312yes—
219C2×#121C22×C10311yescharacteristic
220C2×#117—21no—
221C22×C4⋊C4C22×C10311yescharacteristic
222#484C22×C10314yes—
223#480—22no—
224#468—24no—
225#450C22×C10314yes—
226#448—22no—
227#407C22×C10312yes—
228#400C22×C10312yes—
229#394C22×C10312yes—
230#388—22no—
231#386—21no—
232#386—21no—
233C4×C22⋊C4C22×C10311yescharacteristic
234#328C22×C10318yes—
235#324C22×C10314yes—
236C22×Q8—21no—
237C22×Q8D4×C10312yes—
238C22×D4—21no—
239C22×D4C23×C10311yescharacteristic
240C23×C4D4×C10311yescharacteristic
241C23×C4D4×C10311yescharacteristic
242C23×C4C23×C10311yescharacteristic
243C2×SD16—24no—
244C2×M16—22no—
245C4⋊Q8—28no—
246C4⋊Q8—28no—
247#125—28no—
248#125—28no—
249C22⋊Q8—24no—
250C22⋊Q8—24no—
251C22⋊Q8—22no—
252C22⋊Q8—22no—
253C22⋊Q8D4×C10314yes—
254C22⋊Q8C23×C10314yes—
255#121—22no—
256#121—22no—
257#117—24no—
258#117—24no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4D4×C10312yes—
267C2×C4⋊C4D4×C10312yes—
268C2×C4⋊C4C23×C10311yescharacteristic
269C2×C4⋊C4C23×C10312yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C42—22no—
276C2×C42—21no—
277#107—24no—
278#103—24no—
279#102—24no—
280C22⋊C8—22no—
281C22⋊C8C23×C10314yes—
282#95—22no—
283#95—22no—
284#95C23×C10312yes—
285C24—21no—
286C24C2×D4×C10311yescharacteristic
287C2×Q8—24no—
288C2×Q8—22no—
289C2×Q8—82no—
290C2×Q8—82no—
291C2×Q8C2×D4×C10314yes—
292C2×D4—22no—
293C2×D4—44no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—81no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4C2×D4×C10312yes—
309C22×C4C2×D4×C10312yes—
310C22×C4C2×D4×C10311yescharacteristic
311C22×C4C2×D4×C10312yes—
312C22×C4C2×D4×C10312yes—
313C22×C4C24×C10311yescharacteristic
314SD16—84no—
315M16—82no—
316C2×C8—24no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—24no—
320C4⋊C4—28no—
321C4⋊C4—24no—
322C4⋊C4—24no—
323C4⋊C4—22no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—22no—
327C4⋊C4C2×D4×C10314yes—
328C22⋊C4—24no—
329C22⋊C4—24no—
330C22⋊C4—42no—
331C22⋊C4—42no—
332C22⋊C4—44no—
333C22⋊C4—82no—
334C42—28no—
335C42—81no—
336C23—22no—
337C23—22no—
338C23—41no—
339C23—42no—
340C23—42no—
341C23—41no—
342C23—42no—
343C23#120×C10311yescharacteristic
344C23#120×C10311yescharacteristic
345C23C22×D4×C10311yescharacteristic
346Q8—44no—
347Q8—82no—
348Q8—84no—
349D4—44no—
350D4—82no—
351D4—82no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—81no—
373C2×C4#120×C10312yes—
374C2×C4#137×C10314yes—
375C2×C4C22×D4×C10312yes—
376C8—44no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—44no—
385C22—84no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22#454×C10312yes—
390C22C2×#120×C10311yescharacteristic
391C22C2×#137×C10312yes—
392C4—24no—
393C4—22no—
394C4—22no—
395C4—44no—
396C4—42no—
397C4—44no—
398C4—82no—
399C4—81no—
400C2—22no—
401C2—22no—
402C2—41no—
403C2—161no—
404C2C103×#300411yescharacteristic
405C2C2×#454×C10311yescharacteristic
406C2C103×#302611yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#121×C103C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#544×C103C2semidirect
4. C103×#1617C2semidirect
5. C103×#1599C2semidirect
6. C103×#1508C2semidirect
7. C103×#1463C2semidirect
196. #18326C103direct (N × H)
204. C2×#544C2×C103semidirect
207. #1617C2×C103semidirect
208. #1599C2×C103semidirect
209. #1508C2×C103semidirect
210. #1463C2×C103semidirect
211. C103#18326direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#544×C1032
C103×#31932
C103×#25912
C103×#16172
C103×#15992
C103×#15082
C103×#14632
#18326103