Finite Group Databasebeta

← C103×#11897 #39917172

Subgroups — C103×#11897 #39917172

Order 26368.

452 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2580C211yesmaximal, characteristic
2C103×#1799C211yesmaximal, characteristic
3C103×#1459C211yesmaximal, characteristic
4C103×#1352C212yesmaximal, complemented
5C103×#1351C212yesmaximal, complemented
6C2×C4×Q8×C103C411yescharacteristic, complemented
7C2×C4×D4×C103C2211yescharacteristic
8C2×#99×C103—21no—
9C2×C22⋊C8×C103—21no—
10#399×C103C411yescharacteristic, complemented
11#399×C103C2211yescharacteristic
12#393×C103C411yescharacteristic, complemented
13#393×C103C2211yescharacteristic
14#390×C103—21no—
15#389×C103—21no—
16#385×C103—21no—
17#385×C103—21no—
18#382×C103C411yescharacteristic, complemented
19#380×C103—21no—
20#342×C103C2212yes—
21#324×C103—21no—
22#323×C103C2212yes—
23C22×Q8×C103C2×C411yescharacteristic
24C22×D4×C103D411yescharacteristic
25C23×C4×C103D411yescharacteristic
26C23×C4×C103D411yescharacteristic
27C22×C8×C103—41no—
28C4×Q8×C103—41no—
29C4×Q8×C103—41no—
30C4×D4×C103—41no—
31C4×D4×C103—41no—
32C2×C4⋊C4×C103—21no—
33C2×C4⋊C4×C103—21no—
34C2×C4⋊C4×C103—21no—
35C2×C4⋊C4×C103—21no—
36C2×C4⋊C4×C103—41no—
37C2×C4⋊C4×C103C2×C411yescharacteristic
38C2×C4⋊C4×C103D411yescharacteristic
39C2×C22⋊C4×C103—21no—
40C2×C22⋊C4×C103—21no—
41C2×C22⋊C4×C103—22no—
42C2×C22⋊C4×C103—21no—
43C2×C22⋊C4×C103—21no—
44C2×C22⋊C4×C103C2×C411yescharacteristic
45C2×C22⋊C4×C103C2311yescharacteristic
46C2×C42×C103—21no—
47C2×C42×C103C2×C411yescharacteristic
48#99×C103—42no—
49C22⋊C8×C103—22no—
50C22⋊C8×C103—41no—
51#95×C103—21no—
52#95×C103—21no—
53#95×C103—21no—
54#95×C103—41no—
55#95×C103C2×C411yescharacteristic
56#95×C103C2×C411yescharacteristic
57C24×C103C22⋊C411yescharacteristic
58C24×C103C2×D411yescharacteristic
59C2×Q8×C103—42no—
60C2×Q8×C103—41no—
61C2×D4×C103—41no—
62C2×D4×C103—41no—
63C2×D4×C103SD1612yes—
64C2×D4×C103Q1612yes—
65C22×C4×C103—21no—
66C22×C4×C103—21no—
67C22×C4×C103—21no—
68C22×C4×C103—21no—
69C22×C4×C103—21no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103—21no—
73C22×C4×C103—42no—
74C22×C4×C103—81no—
75C22×C4×C103—81no—
76C22×C4×C103C22⋊C411yescharacteristic
77C22×C4×C103C22⋊C411yescharacteristic
78C22×C4×C103C22⋊C411yescharacteristic
79C22×C4×C103C22×C411yescharacteristic
80C22×C4×C103C2×D411yescharacteristic
81C2×C8×C103—42no—
82C2×C8×C103—82no—
83C4⋊C4×C103—41no—
84C4⋊C4×C103—41no—
85C4⋊C4×C103—42no—
86C4⋊C4×C103—41no—
87C4⋊C4×C103—41no—
88C4⋊C4×C103—81no—
89C4⋊C4×C103—81no—
90C4⋊C4×C103—82no—
91C22⋊C4×C103—41no—
92C22⋊C4×C103—41no—
93C22⋊C4×C103—42no—
94C22⋊C4×C103—42no—
95C22⋊C4×C103—42no—
96C22⋊C4×C103—42no—
97C22⋊C4×C103—81no—
98C22⋊C4×C103—81no—
99C42×C103—21no—
100C42×C103—21no—
101C42×C103—42no—
102C23×C103—21no—
103C23×C103—21no—
104C23×C103—21no—
105C23×C103—21no—
106C23×C103—41no—
107C23×C103—41no—
108C23×C103—41no—
109C23×C103—41no—
110C23×C103#10312yes—
111C23×C103C2×C22⋊C411yescharacteristic
112C23×C103C2×SD1611yescharacteristic
113C23×C103C2×Q1611yescharacteristic
114Q8×C103—42no—
115Q8×C103—42no—
116D4×C103—42no—
117D4×C103—42no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—22no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—41no—
125C2×C4×C103—42no—
126C2×C4×C103—42no—
127C2×C4×C103—41no—
128C2×C4×C103—41no—
129C2×C4×C103—41no—
130C2×C4×C103—41no—
131C2×C4×C103—41no—
132C2×C4×C103—41no—
133C2×C4×C103—41no—
134C2×C4×C103—41no—
135C2×C4×C103—41no—
136C2×C4×C103—41no—
137C2×C4×C103—41no—
138C2×C4×C103—41no—
139C2×C4×C103—41no—
140C2×C4×C103—41no—
141C2×C4×C103—81no—
142C2×C4×C103—81no—
143C2×C4×C103—82no—
144C2×C4×C103—82no—
145C2×C4×C103—82no—
146C2×C4×C103#9911yescharacteristic
147C2×C4×C103#9911yescharacteristic
148C2×C4×C103#10312yes—
149C8×C103—82no—
150C22×C103—21no—
151C22×C103—21no—
152C22×C103—21no—
153C22×C103—22no—
154C22×C103—21no—
155C22×C103—42no—
156C22×C103—41no—
157C22×C103—41no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—81no—
163C22×C103—81no—
164C22×C103C2×#9911yescharacteristic
165C22×C103C2×#10311yescharacteristic
166C22×C103#42111yescharacteristic
167C4×C103—21no—
168C4×C103—21no—
169C4×C103—22no—
170C4×C103—42no—
171C4×C103—41no—
172C4×C103—41no—
173C4×C103—41no—
174C4×C103—81no—
175C4×C103—81no—
176C4×C103—81no—
177C4×C103—162no—
178#11897C10311yesmaximal, characteristic, direct product factor, Sylow
179C2×C103—21no—
180C2×C103—21no—
181C2×C103—41no—
182C2×C103—42no—
183C2×C103—41no—
184C2×C103#152011yescharacteristic
185C2×C103#212011yescharacteristic
186C2×C103#212711yescharacteristic
187#2580C2×C10311yescharacteristic
188#1799C2×C10311yescharacteristic
189#1459C2×C10311yescharacteristic
190#1352C2×C10312yescomplemented
191#1351C2×C10312yescomplemented
192C103#1189711yescharacteristic, direct product factor, Sylow
193C2×C4×Q8C4×C10311yescharacteristic, complemented
194C2×C4×D4C22×C10311yescharacteristic
195C2×#99—21no—
196C2×C22⋊C8—21no—
197#399C4×C10311yescharacteristic, complemented
198#399C22×C10311yescharacteristic
199#393C4×C10311yescharacteristic, complemented
200#393C22×C10311yescharacteristic
201#390—21no—
202#389—21no—
203#385—21no—
204#385—21no—
205#382C4×C10311yescharacteristic, complemented
206#380—21no—
207#342C22×C10312yes—
208#324—21no—
209#323C22×C10312yes—
210C22×Q8C2×C4×C10311yescharacteristic
211C22×D4D4×C10311yescharacteristic
212C23×C4D4×C10311yescharacteristic
213C23×C4D4×C10311yescharacteristic
214C22×C8—41no—
215C4×Q8—41no—
216C4×Q8—41no—
217C4×D4—41no—
218C4×D4—41no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4C2×C4×C10311yescharacteristic
225C2×C4⋊C4D4×C10311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4C2×C4×C10311yescharacteristic
232C2×C22⋊C4C23×C10311yescharacteristic
233C2×C42—21no—
234C2×C42C2×C4×C10311yescharacteristic
235#99—42no—
236C22⋊C8—22no—
237C22⋊C8—41no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—41no—
242#95C2×C4×C10311yescharacteristic
243#95C2×C4×C10311yescharacteristic
244C24C22⋊C4×C10311yescharacteristic
245C24C2×D4×C10311yescharacteristic
246C2×Q8—42no—
247C2×Q8—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4SD16×C10312yes—
251C2×D4Q16×C10312yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4C22⋊C4×C10311yescharacteristic
264C22×C4C22⋊C4×C10311yescharacteristic
265C22×C4C22⋊C4×C10311yescharacteristic
266C22×C4C22×C4×C10311yescharacteristic
267C22×C4C2×D4×C10311yescharacteristic
268C2×C8—42no—
269C2×C8—82no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—82no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—81no—
285C22⋊C4—81no—
286C42—21no—
287C42—21no—
288C42—42no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#103×C10312yes—
298C23C2×C22⋊C4×C10311yescharacteristic
299C23C2×SD16×C10311yescharacteristic
300C23C2×Q16×C10311yescharacteristic
301Q8—42no—
302Q8—42no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4#99×C10311yescharacteristic
334C2×C4#99×C10311yescharacteristic
335C2×C4#103×C10312yes—
336C8—82no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×#99×C10311yescharacteristic
352C22C2×#103×C10311yescharacteristic
353C22#421×C10311yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—42no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—162no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—42no—
369C2—41no—
370C2C103×#152011yescharacteristic
371C2C103×#212011yescharacteristic
372C2C103×#212711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#99
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C22⋊C4C23×C103
prime radicalC22×D4×C103D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1352C2semidirect
5. C103×#1351C2semidirect
6. C2×C4×Q8×C103C4semidirect
10. #399×C103C4semidirect
12. #393×C103C4semidirect
18. #382×C103C4semidirect
178. #11897C103direct (N × H)
190. #1352C2×C103semidirect
191. #1351C2×C103semidirect
192. C103#11897direct (N × H)
193. C2×C4×Q8C4×C103semidirect
197. #399C4×C103semidirect
199. #393C4×C103semidirect
205. #382C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#25802
C103×#17992
C103×#14592
C103×#13522
C103×#13512
#11897103