Finite Group Databasebeta

← C103×#9887 #39915162

Subgroups — C103×#9887 #39915162

Order 26368.

598 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2851C211yesmaximal, characteristic
2C103×#1749C211yesmaximal, characteristic
3C103×C4⋊#95C211yesmaximal, characteristic
4C103×#1294C212yesmaximal
5C103×#1294C212yesmaximal
6C2×#125×C103C411yescharacteristic, complemented
7C22×C4⋊C4×C103—21no—
8C22×C42×C103C2211yescharacteristic
9C2×C22⋊C8×C103C2212yes—
10C2×#97×C103—21no—
11#389×C103C411yescharacteristic, complemented
12#389×C103C411yescharacteristic, complemented
13#387×C103—21no—
14#387×C103—21no—
15#385×C103—21no—
16#385×C103—21no—
17#382×C103C411yescharacteristic, complemented
18#380×C103C2211yescharacteristic
19#380×C103C2211yescharacteristic
20C2×#95×C103—21no—
21C2×#95×C103C2212yes—
22#336×C103—21no—
23C23×C4×C103—22no—
24C23×C4×C103D411yescharacteristic
25C23×C4×C103D411yescharacteristic
26C23×C4×C103C2311yescharacteristic
27C22×C8×C103—22no—
28#125×C103—42no—
29C2×C4⋊C4×C103—24no—
30C2×C4⋊C4×C103—21no—
31C2×C4⋊C4×C103—21no—
32C2×C4⋊C4×C103—21no—
33C2×C4⋊C4×C103—21no—
34C2×C4⋊C4×C103—42no—
35C2×C4⋊C4×C103—42no—
36C2×C4⋊C4×C103C2×C411yescharacteristic
37C2×C4⋊C4×C103C2×C411yescharacteristic
38C2×C4⋊C4×C103C2×C411yescharacteristic
39C2×C4⋊C4×C103C2×C411yescharacteristic
40C2×C22⋊C4×C103—21no—
41C2×C22⋊C4×C103—21no—
42C2×C42×C103—42no—
43C2×C42×C103C2×C411yescharacteristic
44C2×C42×C103C2×C411yescharacteristic
45C2×C42×C103D411yescharacteristic
46C2×C42×C103D411yescharacteristic
47C22⋊C8×C103—22no—
48C22⋊C8×C103Q814yes—
49#97×C103—42no—
50#95×C103—21no—
51#95×C103—21no—
52#95×C103—21no—
53#95×C103—21no—
54#95×C103—21no—
55#95×C103—21no—
56#95×C103—24no—
57#95×C103—42no—
58C24×C103C2×D411yescharacteristic
59C22×C4×C103—21no—
60C22×C4×C103—21no—
61C22×C4×C103—22no—
62C22×C4×C103—22no—
63C22×C4×C103—21no—
64C22×C4×C103—21no—
65C22×C4×C103—24no—
66C22×C4×C103—21no—
67C22×C4×C103—21no—
68C22×C4×C103—21no—
69C22×C4×C103—21no—
70C22×C4×C103—41no—
71C22×C4×C103—41no—
72C22×C4×C103—41no—
73C22×C4×C103—41no—
74C22×C4×C103—42no—
75C22×C4×C103—42no—
76C22×C4×C103—42no—
77C22×C4×C103—42no—
78C22×C4×C103—42no—
79C22×C4×C103—42no—
80C22×C4×C103C22⋊C411yescharacteristic
81C22×C4×C103C22⋊C411yescharacteristic
82C22×C4×C103C22⋊C411yescharacteristic
83C22×C4×C103C22⋊C411yescharacteristic
84C22×C4×C103C22×C411yescharacteristic
85C22×C4×C103C2×D411yescharacteristic
86C22×C4×C103C2×Q812yes—
87C22×C4×C103#4112yes—
88C2×C8×C103—24no—
89C2×C8×C103—42no—
90C2×C8×C103—42no—
91C4⋊C4×C103—41no—
92C4⋊C4×C103—41no—
93C4⋊C4×C103—41no—
94C4⋊C4×C103—41no—
95C4⋊C4×C103—42no—
96C4⋊C4×C103—48no—
97C4⋊C4×C103—42no—
98C4⋊C4×C103—42no—
99C4⋊C4×C103—42no—
100C22⋊C4×C103—41no—
101C22⋊C4×C103—41no—
102C22⋊C4×C103—41no—
103C22⋊C4×C103—41no—
104C42×C103—22no—
105C42×C103—22no—
106C42×C103—41no—
107C42×C103—41no—
108C23×C103—21no—
109C23×C103—21no—
110C23×C103—21no—
111C23×C103—21no—
112C23×C103C2×C22⋊C411yescharacteristic
113C23×C103#12411yescharacteristic
114C23×C103C4⋊Q811yescharacteristic
115C23×C103AGL(1,ℤ/8)11yescharacteristic
116C23×C103AGL(1,ℤ/8)11yescharacteristic
117C23×C103#13711yescharacteristic
118C23×C103#13711yescharacteristic
119C2×C4×C103—24no—
120C2×C4×C103—24no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
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—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—42no—
136C2×C4×C103—42no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103—44no—
140C2×C4×C103—44no—
141C2×C4×C103—44no—
142C2×C4×C103—41no—
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×C103—41no—
150C2×C4×C103—41no—
151C2×C4×C103—41no—
152C2×C4×C103—41no—
153C2×C4×C103—41no—
154C2×C4×C103—82no—
155C2×C4×C103—82no—
156C2×C4×C103—82no—
157C2×C4×C103—82no—
158C2×C4×C103#9912yes—
159C2×C4×C103#10412yes—
160C2×C4×C103C4×Q812yes—
161C2×C4×C103C22⋊Q812yes—
162C8×C103—44no—
163C22×C103—21no—
164C22×C103—21no—
165C22×C103—21no—
166C22×C103—21no—
167C22×C103—21no—
168C22×C103—21no—
169C22×C103—21no—
170C22×C103—21no—
171C22×C103—21no—
172C22×C103—21no—
173C22×C103—21no—
174C22×C103—21no—
175C22×C103#39111yescharacteristic
176C22×C103C2×#9911yescharacteristic
177C22×C103#41011yescharacteristic
178C22×C103#41711yescharacteristic
179C22×C103#41711yescharacteristic
180C22×C103C2×#10411yescharacteristic
181C22×C103#42111yescharacteristic
182C22×C103#49011yescharacteristic
183C22×C103#49111yescharacteristic
184C22×C103#50111yescharacteristic
185C22×C103#50111yescharacteristic
186C4×C103—22no—
187C4×C103—22no—
188C4×C103—22no—
189C4×C103—22no—
190C4×C103—41no—
191C4×C103—41no—
192C4×C103—84no—
193C4×C103—81no—
194C4×C103—81no—
195C4×C103—81no—
196C4×C103—81no—
197#9887C10311yesmaximal, characteristic, direct product factor, Sylow
198C2×C103—21no—
199C2×C103—21no—
200C2×C103—21no—
201C2×C103—21no—
202C2×C103#150411yescharacteristic
203C2×C103#150911yescharacteristic
204C2×C103#151211yescharacteristic
205C2×C103#151311yescharacteristic
206C2×C103#198611yescharacteristic
207C2×C103#199211yescharacteristic
208C2×C103#199611yescharacteristic
209#2851C2×C10311yescharacteristic
210#1749C2×C10311yescharacteristic
211C4⋊#95C2×C10311yescharacteristic
212#1294C2×C10312yes—
213#1294C2×C10312yes—
214C103#988711yescharacteristic, direct product factor, Sylow
215C2×#125C4×C10311yescharacteristic, complemented
216C22×C4⋊C4—21no—
217C22×C42C22×C10311yescharacteristic
218C2×C22⋊C8C22×C10312yes—
219C2×#97—21no—
220#389C4×C10311yescharacteristic, complemented
221#389C4×C10311yescharacteristic, complemented
222#387—21no—
223#387—21no—
224#385—21no—
225#385—21no—
226#382C4×C10311yescharacteristic, complemented
227#380C22×C10311yescharacteristic
228#380C22×C10311yescharacteristic
229C2×#95—21no—
230C2×#95C22×C10312yes—
231#336—21no—
232C23×C4—22no—
233C23×C4D4×C10311yescharacteristic
234C23×C4D4×C10311yescharacteristic
235C23×C4C23×C10311yescharacteristic
236C22×C8—22no—
237#125—42no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4C2×C4×C10311yescharacteristic
246C2×C4⋊C4C2×C4×C10311yescharacteristic
247C2×C4⋊C4C2×C4×C10311yescharacteristic
248C2×C4⋊C4C2×C4×C10311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C42—42no—
252C2×C42C2×C4×C10311yescharacteristic
253C2×C42C2×C4×C10311yescharacteristic
254C2×C42D4×C10311yescharacteristic
255C2×C42D4×C10311yescharacteristic
256C22⋊C8—22no—
257C22⋊C8Q8×C10314yes—
258#97—42no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—24no—
266#95—42no—
267C24C2×D4×C10311yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—24no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C22⋊C4×C10311yescharacteristic
290C22×C4C22⋊C4×C10311yescharacteristic
291C22×C4C22⋊C4×C10311yescharacteristic
292C22×C4C22⋊C4×C10311yescharacteristic
293C22×C4C22×C4×C10311yescharacteristic
294C22×C4C2×D4×C10311yescharacteristic
295C22×C4C2×Q8×C10312yes—
296C22×C4#41×C10312yes—
297C2×C8—24no—
298C2×C8—42no—
299C2×C8—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—48no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C42—22no—
314C42—22no—
315C42—41no—
316C42—41no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C22⋊C4×C10311yescharacteristic
322C23#124×C10311yescharacteristic
323C23C4⋊Q8×C10311yescharacteristic
324C23AGL(1,ℤ/8)×C10311yescharacteristic
325C23AGL(1,ℤ/8)×C10311yescharacteristic
326C23#137×C10311yescharacteristic
327C23#137×C10311yescharacteristic
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4#99×C10312yes—
368C2×C4#104×C10312yes—
369C2×C4C4×Q8×C10312yes—
370C2×C4C22⋊Q8×C10312yes—
371C8—44no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22#391×C10311yescharacteristic
385C22C2×#99×C10311yescharacteristic
386C22#410×C10311yescharacteristic
387C22#417×C10311yescharacteristic
388C22#417×C10311yescharacteristic
389C22C2×#104×C10311yescharacteristic
390C22#421×C10311yescharacteristic
391C22#490×C10311yescharacteristic
392C22#491×C10311yescharacteristic
393C22#501×C10311yescharacteristic
394C22#501×C10311yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—41no—
400C4—41no—
401C4—84no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—81no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2C103×#150411yescharacteristic
411C2C103×#150911yescharacteristic
412C2C103×#151211yescharacteristic
413C2C103×#151311yescharacteristic
414C2C103×#198611yescharacteristic
415C2C103×#199211yescharacteristic
416C2C103×#199611yescharacteristic
subgroupG/H
center, socleC23×C103C2×C22⋊C4
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#125×C103C4semidirect
11. #389×C103C4semidirect
12. #389×C103C4semidirect
17. #382×C103C4semidirect
197. #9887C103direct (N × H)
214. C103#9887direct (N × H)
215. C2×#125C4×C103semidirect
220. #389C4×C103semidirect
221. #389C4×C103semidirect
226. #382C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#28512
C103×#17492
C103×C4⋊#952
C103×#12942
#9887103