Finite Group Databasebeta

← C103×#9218 #39914493

Subgroups — C103×#9218 #39914493

Order 26368.

522 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#462×C103C211yesmaximal, characteristic
2C2×C8×Q8×C103C211yesmaximal, characteristic
3C103×#1990C211yesmaximal, characteristic
4C103×#1803C211yesmaximal, characteristic
5C2×#332×C103C211yesmaximal, characteristic
6C103×#1296C211yesmaximal, characteristic
7C103×#1277C211yesmaximal, characteristic
8C22×Q16×C103—21no—
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×C4×Q8×C103C2211yescharacteristic
11#462×C103—22no—
12#462×C103C414yescomplemented
13C8×Q8×C103—22no—
14C8×Q8×C103—22no—
15C2×C4⋊C8×C103—21no—
16C2×C4⋊C8×C103C2211yescharacteristic
17C2×C4⋊C8×C103C2211yescharacteristic
18C2×C4⋊C8×C103C2211yescharacteristic
19C2×#103×C103—21no—
20C2×#103×C103—21no—
21C2×C4×C8×C103—21no—
22C2×C4×C8×C103C2211yescharacteristic
23#384×C103C2211yescharacteristic
24#340×C103—21no—
25#340×C103—21no—
26#340×C103—21no—
27#332×C103—22no—
28C22×Q8×C103—21no—
29C22×Q8×C103D411yescharacteristic
30C2×Q16×C103—24no—
31C2×Q16×C103—42no—
32C2×Q16×C103—42no—
33C22×C8×C103—21no—
34C22×C8×C103—21no—
35C22×C8×C103—21no—
36C22×C8×C103D411yescharacteristic
37C22×C8×C103D411yescharacteristic
38C4⋊Q8×C103—21no—
39C4⋊Q8×C103—21no—
40C4⋊Q8×C103—21no—
41C4⋊Q8×C103C2×C412yes—
42C4×Q8×C103—21no—
43C4×Q8×C103—21no—
44C4×Q8×C103C2×C412yes—
45C4×Q8×C103D412yes—
46C2×C4⋊C4×C103—21no—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103—21no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103D411yescharacteristic
53C2×C42×C103—21no—
54C2×C42×C103C2311yescharacteristic
55C4⋊C8×C103—24no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103—21no—
59C4⋊C8×C103—21no—
60C4⋊C8×C103C2×C412yes—
61C4⋊C8×C103D412yes—
62#103×C103—24no—
63#103×C103—42no—
64C4×C8×C103—24no—
65C4×C8×C103—21no—
66C4×C8×C103—21no—
67C2×Q8×C103—21no—
68C2×Q8×C103—21no—
69C2×Q8×C103—21no—
70C2×Q8×C103—22no—
71C2×Q8×C103—41no—
72C2×Q8×C103—41no—
73C2×Q8×C103—41no—
74C2×Q8×C103—41no—
75C2×Q8×C103—41no—
76C2×Q8×C103C22⋊C412yes—
77C2×Q8×C103D812yes—
78C2×Q8×C103SD1612yes—
79C22×C4×C103—21no—
80C22×C4×C103—21no—
81C22×C4×C103—41no—
82C22×C4×C103—41no—
83C22×C4×C103C2×D411yescharacteristic
84C22×C4×C103C2×D411yescharacteristic
85C22×C4×C103#4111yescharacteristic
86Q16×C103—48no—
87C2×C8×C103—21no—
88C2×C8×C103—21no—
89C2×C8×C103—22no—
90C2×C8×C103—21no—
91C2×C8×C103—22no—
92C2×C8×C103—21no—
93C2×C8×C103—21no—
94C2×C8×C103—41no—
95C2×C8×C103—41no—
96C2×C8×C103—41no—
97C2×C8×C103—41no—
98C2×C8×C103—41no—
99C2×C8×C103—41no—
100C2×C8×C103—41no—
101C2×C8×C103Q1612yescomplemented
102C4⋊C4×C103—22no—
103C4⋊C4×C103—21no—
104C4⋊C4×C103—22no—
105C4⋊C4×C103—22no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103—41no—
108C4⋊C4×C103—41no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103—41no—
111C4⋊C4×C103—41no—
112C4⋊C4×C103—41no—
113C4⋊C4×C103—81no—
114C4⋊C4×C103C22⋊C412yes—
115C42×C103—22no—
116C42×C103—22no—
117C42×C103C22×C411yescharacteristic
118C42×C103C2×D411yescharacteristic
119C42×C103C2×D411yescharacteristic
120C42×C103#4111yescharacteristic
121C23×C103#12111yescharacteristic
122Q8×C103—22no—
123Q8×C103—22no—
124Q8×C103—22no—
125Q8×C103—42no—
126Q8×C103—42no—
127Q8×C103—81no—
128Q8×C103—81no—
129Q8×C103#10214yes—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—22no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—22no—
136C2×C4×C103—41no—
137C2×C4×C103—41no—
138C2×C4×C103—42no—
139C2×C4×C103—81no—
140C2×C4×C103—81no—
141C2×C4×C103—81no—
142C2×C4×C103—81no—
143C2×C4×C103—81no—
144C2×C4×C103C2×C22⋊C411yescharacteristic
145C2×C4×C103C4×D411yescharacteristic
146C2×C4×C103C4×D411yescharacteristic
147C2×C4×C103#12011yescharacteristic
148C2×C4×C103#12111yescharacteristic
149C2×C4×C103#12311yescharacteristic
150C2×C4×C103C2×D811yescharacteristic
151C2×C4×C103C2×SD1611yescharacteristic
152C2×C4×C103C2×Q1611yescharacteristic
153C2×C4×C103#13511yescharacteristic
154C2×C4×C103#13511yescharacteristic
155C2×C4×C103#13511yescharacteristic
156C2×C4×C103#13711yescharacteristic
157C2×C4×C103#13711yescharacteristic
158C8×C103—22no—
159C8×C103—42no—
160C8×C103—41no—
161C8×C103—42no—
162C8×C103—81no—
163C22×C103#38611yescharacteristic
164C22×C103#46211yescharacteristic
165C22×C103#46411yescharacteristic
166C22×C103#46511yescharacteristic
167C22×C103#46611yescharacteristic
168C22×C103#47111yescharacteristic
169C22×C103#47311yescharacteristic
170C4×C103—24no—
171C4×C103—21no—
172C4×C103—21no—
173C4×C103—42no—
174C4×C103—82no—
175C4×C103—161no—
176C4×C103C2×#10211yescharacteristic
177C4×C103#41611yescharacteristic
178C4×C103C4×Q1611yescharacteristic
179C4×C103#44111yescharacteristic
180C4×C103#45111yescharacteristic
181C4×C103#45211yescharacteristic
182C4×C103#46511yescharacteristic
183C4×C103#46611yescharacteristic
184#9218C10311yesmaximal, characteristic, direct product factor, Sylow
185C2×C103#167211yescharacteristic
186C2×C103#167411yescharacteristic
187C2×C103#168011yescharacteristic
188C2×C103#168211yescharacteristic
189C2×C103#187811yescharacteristic
190C2×C103#189311yescharacteristic
191C2×C103#190811yescharacteristic
192C2×#462C2×C10311yescharacteristic
193C2×C8×Q8C2×C10311yescharacteristic
194#1990C2×C10311yescharacteristic
195#1803C2×C10311yescharacteristic
196C2×#332C2×C10311yescharacteristic
197#1296C2×C10311yescharacteristic
198#1277C2×C10311yescharacteristic
199C103#921811yescharacteristic, direct product factor, Sylow
200C22×Q16—21no—
201C2×C4⋊Q8C22×C10311yescharacteristic
202C2×C4×Q8C22×C10311yescharacteristic
203#462—22no—
204#462C4×C10314yescomplemented
205C8×Q8—22no—
206C8×Q8—22no—
207C2×C4⋊C8—21no—
208C2×C4⋊C8C22×C10311yescharacteristic
209C2×C4⋊C8C22×C10311yescharacteristic
210C2×C4⋊C8C22×C10311yescharacteristic
211C2×#103—21no—
212C2×#103—21no—
213C2×C4×C8—21no—
214C2×C4×C8C22×C10311yescharacteristic
215#384C22×C10311yescharacteristic
216#340—21no—
217#340—21no—
218#340—21no—
219#332—22no—
220C22×Q8—21no—
221C22×Q8D4×C10311yescharacteristic
222C2×Q16—24no—
223C2×Q16—42no—
224C2×Q16—42no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8D4×C10311yescharacteristic
229C22×C8D4×C10311yescharacteristic
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C2×C4×C10312yes—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8C2×C4×C10312yes—
237C4×Q8D4×C10312yes—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C10311yescharacteristic
245C2×C42—21no—
246C2×C42C23×C10311yescharacteristic
247C4⋊C8—24no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8C2×C4×C10312yes—
253C4⋊C8D4×C10312yes—
254#103—24no—
255#103—42no—
256C4×C8—24no—
257C4×C8—21no—
258C4×C8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8C22⋊C4×C10312yes—
269C2×Q8D8×C10312yes—
270C2×Q8SD16×C10312yes—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4C2×D4×C10311yescharacteristic
276C22×C4C2×D4×C10311yescharacteristic
277C22×C4#41×C10311yescharacteristic
278Q16—48no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8Q16×C10312yescomplemented
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—81no—
306C4⋊C4C22⋊C4×C10312yes—
307C42—22no—
308C42—22no—
309C42C22×C4×C10311yescharacteristic
310C42C2×D4×C10311yescharacteristic
311C42C2×D4×C10311yescharacteristic
312C42#41×C10311yescharacteristic
313C23#121×C10311yescharacteristic
314Q8—22no—
315Q8—22no—
316Q8—22no—
317Q8—42no—
318Q8—42no—
319Q8—81no—
320Q8—81no—
321Q8#102×C10314yes—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4C2×C22⋊C4×C10311yescharacteristic
337C2×C4C4×D4×C10311yescharacteristic
338C2×C4C4×D4×C10311yescharacteristic
339C2×C4#120×C10311yescharacteristic
340C2×C4#121×C10311yescharacteristic
341C2×C4#123×C10311yescharacteristic
342C2×C4C2×D8×C10311yescharacteristic
343C2×C4C2×SD16×C10311yescharacteristic
344C2×C4C2×Q16×C10311yescharacteristic
345C2×C4#135×C10311yescharacteristic
346C2×C4#135×C10311yescharacteristic
347C2×C4#135×C10311yescharacteristic
348C2×C4#137×C10311yescharacteristic
349C2×C4#137×C10311yescharacteristic
350C8—22no—
351C8—42no—
352C8—41no—
353C8—42no—
354C8—81no—
355C22#386×C10311yescharacteristic
356C22#462×C10311yescharacteristic
357C22#464×C10311yescharacteristic
358C22#465×C10311yescharacteristic
359C22#466×C10311yescharacteristic
360C22#471×C10311yescharacteristic
361C22#473×C10311yescharacteristic
362C4—24no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—82no—
367C4—161no—
368C4C2×#102×C10311yescharacteristic
369C4#416×C10311yescharacteristic
370C4C4×Q16×C10311yescharacteristic
371C4#441×C10311yescharacteristic
372C4#451×C10311yescharacteristic
373C4#452×C10311yescharacteristic
374C4#465×C10311yescharacteristic
375C4#466×C10311yescharacteristic
376C2C103×#167211yescharacteristic
377C2C103×#167411yescharacteristic
378C2C103×#168011yescharacteristic
379C2C103×#168211yescharacteristic
380C2C103×#187811yescharacteristic
381C2C103×#189311yescharacteristic
382C2C103×#190811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103#121
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
12. #462×C103C4semidirect
101. C2×C8×C103Q16semidirect
184. #9218C103direct (N × H)
199. C103#9218direct (N × H)
204. #462C4×C103semidirect
293. C2×C8Q16×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#462×C1032
C2×C8×Q8×C1032
C103×#19902
C103×#18032
C2×#332×C1032
C103×#12962
C103×#12772
#9218103