Finite Group Databasebeta

← C103×#8938 #39914213

Subgroups — C103×#8938 #39914213

Order 26368.

628 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#431×C103C211yesmaximal, characteristic
2C4×C22⋊Q8×C103C211yesmaximal, characteristic
3C4×C22⋊C8×C103C211yesmaximal, characteristic
4C2×Q8⋊C8×C103C212yesmaximal, complemented
5C103×#1279C212yesmaximal, complemented
6C2×C22⋊Q8×C103C411yescharacteristic
7C2×C4×Q8×C103C2211yescharacteristic
8C22×C42×C103C2211yescharacteristic
9#431×C103—24no—
10C2×C4⋊C8×C103C2212yes—
11C2×C22⋊C8×C103—21no—
12C2×C22⋊C8×C103—21no—
13C2×C4×C8×C103—21no—
14C2×C4×C8×C103C2212yes—
15#391×C103C411yescharacteristic
16#389×C103C411yescharacteristic
17#387×C103—21no—
18#385×C103—21no—
19#380×C103C411yescharacteristic
20C4×C4⋊C4×C103—21no—
21C4×C4⋊C4×C103C2211yescharacteristic
22C4×C22⋊C4×C103—21no—
23#336×C103—21no—
24Q8⋊C8×C103—24no—
25C22×Q8×C103C2×C411yescharacteristic
26C23×C4×C103C2×C411yescharacteristic
27C23×C4×C103D411yescharacteristic
28C23×C4×C103D411yescharacteristic
29C22×C8×C103—22no—
30C22×C8×C103—22no—
31C22⋊Q8×C103—22no—
32C22⋊Q8×C103C814yescomplemented
33C4×Q8×C103—22no—
34C4×Q8×C103—22no—
35C2×C4⋊C4×C103—21no—
36C2×C4⋊C4×C103—21no—
37C2×C4⋊C4×C103—21no—
38C2×C4⋊C4×C103C2×C411yescharacteristic
39C2×C4⋊C4×C103C2×C411yescharacteristic
40C2×C4⋊C4×C103C2×C411yescharacteristic
41C2×C22⋊C4×C103—21no—
42C2×C22⋊C4×C103—21no—
43C2×C42×C103—22no—
44C2×C42×C103—22no—
45C2×C42×C103—21no—
46C2×C42×C103—21no—
47C2×C42×C103C2×C411yescharacteristic
48C2×C42×C103D411yescharacteristic
49C2×C42×C103D411yescharacteristic
50C2×C42×C103C2311yescharacteristic
51C4⋊C8×C103—22no—
52C4⋊C8×C103D414yes—
53C22⋊C8×C103—24no—
54C22⋊C8×C103—24no—
55C4×C8×C103—24no—
56C4×C8×C103—22no—
57C4×C8×C103—22no—
58#95×C103—21no—
59#95×C103—21no—
60#95×C103—21no—
61#95×C103—21no—
62#95×C103—21no—
63C24×C103C22⋊C411yescharacteristic
64C2×Q8×C103—21no—
65C2×Q8×C103—22no—
66C2×Q8×C103—22no—
67C2×Q8×C103C2×C812yes—
68C22×C4×C103—22no—
69C22×C4×C103—22no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103—22no—
73C22×C4×C103—21no—
74C22×C4×C103—22no—
75C22×C4×C103—21no—
76C22×C4×C103—22no—
77C22×C4×C103—22no—
78C22×C4×C103—21no—
79C22×C4×C103—21no—
80C22×C4×C103—41no—
81C22×C4×C103C22⋊C411yescharacteristic
82C22×C4×C103C22⋊C411yescharacteristic
83C22×C4×C103C22⋊C411yescharacteristic
84C22×C4×C103C2×C812yes—
85C22×C4×C103M1612yes—
86C22×C4×C103C22×C411yescharacteristic
87C22×C4×C103C2×D411yescharacteristic
88C22×C4×C103C2×D411yescharacteristic
89C2×C8×C103—24no—
90C2×C8×C103—24no—
91C2×C8×C103—42no—
92C2×C8×C103—42no—
93C2×C8×C103—42no—
94C2×C8×C103—42no—
95C4⋊C4×C103—24no—
96C4⋊C4×C103—21no—
97C4⋊C4×C103—22no—
98C4⋊C4×C103—22no—
99C4⋊C4×C103—42no—
100C4⋊C4×C103—42no—
101C4⋊C4×C103C2×C812yes—
102C22⋊C4×C103—24no—
103C22⋊C4×C103—42no—
104C42×C103—22no—
105C42×C103—21no—
106C42×C103—22no—
107C42×C103—21no—
108C42×C103—41no—
109C42×C103—41no—
110C42×C103—42no—
111C42×C103C2×D412yes—
112C42×C103#4112yes—
113C23×C103—21no—
114C23×C103—21no—
115C23×C103—21no—
116C23×C103—21no—
117C23×C103—21no—
118C23×C103—21no—
119C23×C103C22⋊C812yes—
120C23×C103C2×C22⋊C411yescharacteristic
121Q8×C103—24no—
122Q8×C103—42no—
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—24no—
130C2×C4×C103—24no—
131C2×C4×C103—21no—
132C2×C4×C103—22no—
133C2×C4×C103—22no—
134C2×C4×C103—21no—
135C2×C4×C103—21no—
136C2×C4×C103—44no—
137C2×C4×C103—41no—
138C2×C4×C103—41no—
139C2×C4×C103—41no—
140C2×C4×C103—41no—
141C2×C4×C103—42no—
142C2×C4×C103—42no—
143C2×C4×C103—41no—
144C2×C4×C103—41no—
145C2×C4×C103—41no—
146C2×C4×C103—41no—
147C2×C4×C103—41no—
148C2×C4×C103—41no—
149C2×C4×C103C22⋊C812yes—
150C2×C4×C103#10412yes—
151C2×C4×C103C4×D412yes—
152C2×C4×C103#12011yescharacteristic
153C2×C4×C103#12112yes—
154C2×C4×C103#12311yescharacteristic
155C2×C4×C103C22×C811yescharacteristic
156C2×C4×C103C2×M1611yescharacteristic
157C2×C4×C103#13112yes—
158C2×C4×C103#13512yes—
159C2×C4×C103#13712yes—
160C8×C103—44no—
161C8×C103—44no—
162C22×C103—22no—
163C22×C103—22no—
164C22×C103—22no—
165C22×C103—41no—
166C22×C103—41no—
167C22×C103—41no—
168C22×C103—41no—
169C22×C103#38611yescharacteristic
170C22×C103C2×C22⋊C811yescharacteristic
171C22×C103#40811yescharacteristic
172C22×C103#41611yescharacteristic
173C22×C103#41911yescharacteristic
174C22×C103C2×#10411yescharacteristic
175C22×C103#42111yescharacteristic
176C4×C103—22no—
177C4×C103—22no—
178C4×C103—22no—
179C4×C103—42no—
180C4×C103—41no—
181C4×C103—42no—
182C4×C103—81no—
183C4×C103—81no—
184C4×C103C8×D412yes—
185C4×C103#43512yes—
186C4×C103#45212yes—
187C4×C103#48512yes—
188#8938C10311yesmaximal, characteristic, direct product factor, Sylow
189C2×C103—42no—
190C2×C103#147611yescharacteristic
191C2×C103#147911yescharacteristic
192C2×C103#148211yescharacteristic
193C2×C103#148511yescharacteristic
194C2×C103#186911yescharacteristic
195C2×C103#187111yescharacteristic
196C2×C103#187311yescharacteristic
197C2×#431C2×C10311yescharacteristic
198C4×C22⋊Q8C2×C10311yescharacteristic
199C4×C22⋊C8C2×C10311yescharacteristic
200C2×Q8⋊C8C2×C10312yescomplemented
201#1279C2×C10312yescomplemented
202C103#893811yescharacteristic, direct product factor, Sylow
203C2×C22⋊Q8C4×C10311yescharacteristic
204C2×C4×Q8C22×C10311yescharacteristic
205C22×C42C22×C10311yescharacteristic
206#431—24no—
207C2×C4⋊C8C22×C10312yes—
208C2×C22⋊C8—21no—
209C2×C22⋊C8—21no—
210C2×C4×C8—21no—
211C2×C4×C8C22×C10312yes—
212#391C4×C10311yescharacteristic
213#389C4×C10311yescharacteristic
214#387—21no—
215#385—21no—
216#380C4×C10311yescharacteristic
217C4×C4⋊C4—21no—
218C4×C4⋊C4C22×C10311yescharacteristic
219C4×C22⋊C4—21no—
220#336—21no—
221Q8⋊C8—24no—
222C22×Q8C2×C4×C10311yescharacteristic
223C23×C4C2×C4×C10311yescharacteristic
224C23×C4D4×C10311yescharacteristic
225C23×C4D4×C10311yescharacteristic
226C22×C8—22no—
227C22×C8—22no—
228C22⋊Q8—22no—
229C22⋊Q8C8×C10314yescomplemented
230C4×Q8—22no—
231C4×Q8—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×C4×C10311yescharacteristic
236C2×C4⋊C4C2×C4×C10311yescharacteristic
237C2×C4⋊C4C2×C4×C10311yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42C2×C4×C10311yescharacteristic
245C2×C42D4×C10311yescharacteristic
246C2×C42D4×C10311yescharacteristic
247C2×C42C23×C10311yescharacteristic
248C4⋊C8—22no—
249C4⋊C8D4×C10314yes—
250C22⋊C8—24no—
251C22⋊C8—24no—
252C4×C8—24no—
253C4×C8—22no—
254C4×C8—22no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260C24C22⋊C4×C10311yescharacteristic
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8C2×C8×C10312yes—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4C22⋊C4×C10311yescharacteristic
279C22×C4C22⋊C4×C10311yescharacteristic
280C22×C4C22⋊C4×C10311yescharacteristic
281C22×C4C2×C8×C10312yes—
282C22×C4M16×C10312yes—
283C22×C4C22×C4×C10311yescharacteristic
284C22×C4C2×D4×C10311yescharacteristic
285C22×C4C2×D4×C10311yescharacteristic
286C2×C8—24no—
287C2×C8—24no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C4⋊C4—24no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4C2×C8×C10312yes—
299C22⋊C4—24no—
300C22⋊C4—42no—
301C42—22no—
302C42—21no—
303C42—22no—
304C42—21no—
305C42—41no—
306C42—41no—
307C42—42no—
308C42C2×D4×C10312yes—
309C42#41×C10312yes—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23C22⋊C8×C10312yes—
317C23C2×C22⋊C4×C10311yescharacteristic
318Q8—24no—
319Q8—42no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—44no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4C22⋊C8×C10312yes—
347C2×C4#104×C10312yes—
348C2×C4C4×D4×C10312yes—
349C2×C4#120×C10311yescharacteristic
350C2×C4#121×C10312yes—
351C2×C4#123×C10311yescharacteristic
352C2×C4C22×C8×C10311yescharacteristic
353C2×C4C2×M16×C10311yescharacteristic
354C2×C4#131×C10312yes—
355C2×C4#135×C10312yes—
356C2×C4#137×C10312yes—
357C8—44no—
358C8—44no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22#386×C10311yescharacteristic
367C22C2×C22⋊C8×C10311yescharacteristic
368C22#408×C10311yescharacteristic
369C22#416×C10311yescharacteristic
370C22#419×C10311yescharacteristic
371C22C2×#104×C10311yescharacteristic
372C22#421×C10311yescharacteristic
373C4—22no—
374C4—22no—
375C4—22no—
376C4—42no—
377C4—42no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4C8×D4×C10312yes—
382C4#435×C10312yes—
383C4#452×C10312yes—
384C4#485×C10312yes—
385C2—42no—
386C2C103×#147611yescharacteristic
387C2C103×#147911yescharacteristic
388C2C103×#148211yescharacteristic
389C2C103×#148511yescharacteristic
390C2C103×#186911yescharacteristic
391C2C103×#187111yescharacteristic
392C2C103×#187311yescharacteristic
subgroupG/H
centerC22×C4×C103C2×D4
commutatorC2×C4C22×C8×C103
Frattini, cosocleC2×C42C23×C103
socleC23×C103C2×C22⋊C4
prime radicalC24×C103C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊C8×C103C2semidirect
5. C103×#1279C2semidirect
32. C22⋊Q8×C103C8semidirect
188. #8938C103direct (N × H)
200. C2×Q8⋊C8C2×C103semidirect
201. #1279C2×C103semidirect
202. C103#8938direct (N × H)
229. C22⋊Q8C8×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#431×C1032
C4×C22⋊Q8×C1032
C4×C22⋊C8×C1032
C2×Q8⋊C8×C1032
C103×#12792
#8938103