Finite Group Databasebeta

← C103×#9029 #39914304

Subgroups — C103×#9029 #39914304

Order 26368.

534 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2973C211yesmaximal, characteristic
2C103×#2398C211yesmaximal, characteristic
3C4×#100×C103C211yesmaximal, characteristic
4C103×#1491C212yesmaximal, complemented
5C103×#1300C212yesmaximal, complemented
6C2×C4×Q8×C103C2211yescharacteristic
7C2×C4×D4×C103C2211yescharacteristic
8#435×C103—24no—
9#432×C103C2212yes—
10C2×#100×C103—21no—
11#407×C103—21no—
12C2×C22⋊C8×C103—21no—
13C4×M16×C103C2212yes—
14#400×C103—21no—
15#397×C103C411yescharacteristic
16#397×C103C411yescharacteristic
17#394×C103—21no—
18#393×C103C411yescharacteristic
19#393×C103C411yescharacteristic
20C4×C22⋊C4×C103—21no—
21C4×C22⋊C4×C103—21no—
22#376×C103C2211yescharacteristic
23#343×C103—21no—
24Q8⋊C8×C103—24no—
25C22×Q8×C103C2×C411yescharacteristic
26C22×D4×C103D411yescharacteristic
27C23×C4×C103D411yescharacteristic
28C23×C4×C103D411yescharacteristic
29C2×M16×C103—22no—
30C2×M16×C103—22no—
31C22×C8×C103—22no—
32C4×Q8×C103—22no—
33C4×Q8×C103—22no—
34C4×D4×C103—22no—
35C4×D4×C103—22no—
36C2×C4⋊C4×C103—21no—
37C2×C4⋊C4×C103C2×C411yescharacteristic
38C2×C4⋊C4×C103D411yescharacteristic
39C2×C22⋊C4×C103—21no—
40C2×C22⋊C4×C103—21no—
41C2×C22⋊C4×C103—21no—
42C2×C22⋊C4×C103—21no—
43C2×C22⋊C4×C103C2×C411yescharacteristic
44C2×C22⋊C4×C103C2×C411yescharacteristic
45C2×C42×C103—21no—
46C2×C42×C103—21no—
47C2×C42×C103C2311yescharacteristic
48C4⋊C8×C103D414yes—
49#100×C103—24no—
50C22⋊C8×C103—22no—
51C22⋊C8×C103—22no—
52C22⋊C8×C103—22no—
53#97×C103—22no—
54#97×C103—22no—
55C4×C8×C103—22no—
56#95×C103—21no—
57#95×C103—21no—
58#95×C103—21no—
59#95×C103—21no—
60#95×C103—21no—
61#95×C103C2×C411yescharacteristic
62#95×C103C2×C411yescharacteristic
63C24×C103C22⋊C411yescharacteristic
64C24×C103C22⋊C411yescharacteristic
65C2×Q8×C103—22no—
66C2×Q8×C103—42no—
67C2×D4×C103—22no—
68C2×D4×C103—22no—
69C2×D4×C103—41no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103—21no—
73C22×C4×C103—21no—
74C22×C4×C103—21no—
75C22×C4×C103—21no—
76C22×C4×C103—21no—
77C22×C4×C103—21no—
78C22×C4×C103—42no—
79C22×C4×C103—42no—
80C22×C4×C103C22⋊C411yescharacteristic
81C22×C4×C103C22⋊C411yescharacteristic
82C22×C4×C103C22×C411yescharacteristic
83C22×C4×C103C2×D411yescharacteristic
84C22×C4×C103C2×D411yescharacteristic
85M16×C103—24no—
86M16×C103—42no—
87M16×C103—82no—
88C2×C8×C103—24no—
89C2×C8×C103—42no—
90C2×C8×C103—82no—
91C4⋊C4×C103—22no—
92C4⋊C4×C103—22no—
93C4⋊C4×C103—42no—
94C22⋊C4×C103—22no—
95C22⋊C4×C103—22no—
96C22⋊C4×C103—42no—
97C22⋊C4×C103—42no—
98C22⋊C4×C103—42no—
99C22⋊C4×C103—42no—
100C42×C103—42no—
101C42×C103—41no—
102C42×C103—41no—
103C42×C103C2×D412yes—
104C42×C103#4112yes—
105C23×C103—21no—
106C23×C103—21no—
107C23×C103—21no—
108C23×C103—21no—
109C23×C103—21no—
110C23×C103—41no—
111C23×C103—41no—
112C23×C103—41no—
113C23×C103—41no—
114C23×C103#10412yes—
115C23×C103C2×C22⋊C411yescharacteristic
116Q8×C103—24no—
117Q8×C103—42no—
118D4×C103—44no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—22no—
122C2×C4×C103—22no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—41no—
126C2×C4×C103—41no—
127C2×C4×C103—41no—
128C2×C4×C103—42no—
129C2×C4×C103—42no—
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×C103C4×D412yes—
144C2×C4×C103#12011yescharacteristic
145C2×C4×C103#12112yes—
146C2×C4×C103#12311yescharacteristic
147C8×C103—44no—
148C8×C103—44no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103—22no—
152C22×C103—42no—
153C22×C103—42no—
154C22×C103—41no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103—41no—
158C22×C103—41no—
159C22×C103—81no—
160C22×C103—81no—
161C22×C103#38611yescharacteristic
162C22×C103C2×#10411yescharacteristic
163C22×C103#42111yescharacteristic
164C4×C103—22no—
165C4×C103—21no—
166C4×C103—22no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103—42no—
170C4×C103—81no—
171C4×C103—81no—
172C4×C103—81no—
173C4×C103#45512yes—
174#9029C10311yesmaximal, characteristic, direct product factor, Sylow
175C2×C103—21no—
176C2×C103—21no—
177C2×C103—42no—
178C2×C103—81no—
179C2×C103#187111yescharacteristic
180C2×C103#188511yescharacteristic
181C2×C103#189111yescharacteristic
182#2973C2×C10311yescharacteristic
183#2398C2×C10311yescharacteristic
184C4×#100C2×C10311yescharacteristic
185#1491C2×C10312yescomplemented
186#1300C2×C10312yescomplemented
187C103#902911yescharacteristic, direct product factor, Sylow
188C2×C4×Q8C22×C10311yescharacteristic
189C2×C4×D4C22×C10311yescharacteristic
190#435—24no—
191#432C22×C10312yes—
192C2×#100—21no—
193#407—21no—
194C2×C22⋊C8—21no—
195C4×M16C22×C10312yes—
196#400—21no—
197#397C4×C10311yescharacteristic
198#397C4×C10311yescharacteristic
199#394—21no—
200#393C4×C10311yescharacteristic
201#393C4×C10311yescharacteristic
202C4×C22⋊C4—21no—
203C4×C22⋊C4—21no—
204#376C22×C10311yescharacteristic
205#343—21no—
206Q8⋊C8—24no—
207C22×Q8C2×C4×C10311yescharacteristic
208C22×D4D4×C10311yescharacteristic
209C23×C4D4×C10311yescharacteristic
210C23×C4D4×C10311yescharacteristic
211C2×M16—22no—
212C2×M16—22no—
213C22×C8—22no—
214C4×Q8—22no—
215C4×Q8—22no—
216C4×D4—22no—
217C4×D4—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×C4×C10311yescharacteristic
220C2×C4⋊C4D4×C10311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4C2×C4×C10311yescharacteristic
226C2×C22⋊C4C2×C4×C10311yescharacteristic
227C2×C42—21no—
228C2×C42—21no—
229C2×C42C23×C10311yescharacteristic
230C4⋊C8D4×C10314yes—
231#100—24no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235#97—22no—
236#97—22no—
237C4×C8—22no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95C2×C4×C10311yescharacteristic
244#95C2×C4×C10311yescharacteristic
245C24C22⋊C4×C10311yescharacteristic
246C24C22⋊C4×C10311yescharacteristic
247C2×Q8—22no—
248C2×Q8—42no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
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—42no—
262C22×C4C22⋊C4×C10311yescharacteristic
263C22×C4C22⋊C4×C10311yescharacteristic
264C22×C4C22×C4×C10311yescharacteristic
265C22×C4C2×D4×C10311yescharacteristic
266C22×C4C2×D4×C10311yescharacteristic
267M16—24no—
268M16—42no—
269M16—82no—
270C2×C8—24no—
271C2×C8—42no—
272C2×C8—82no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C42—42no—
283C42—41no—
284C42—41no—
285C42C2×D4×C10312yes—
286C42#41×C10312yes—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#104×C10312yes—
297C23C2×C22⋊C4×C10311yescharacteristic
298Q8—24no—
299Q8—42no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
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—81no—
324C2×C4—81no—
325C2×C4C4×D4×C10312yes—
326C2×C4#120×C10311yescharacteristic
327C2×C4#121×C10312yes—
328C2×C4#123×C10311yescharacteristic
329C8—44no—
330C8—44no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22#386×C10311yescharacteristic
344C22C2×#104×C10311yescharacteristic
345C22#421×C10311yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—42no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4#455×C10312yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2C103×#187111yescharacteristic
361C2C103×#188511yescharacteristic
362C2C103×#189111yescharacteristic
subgroupG/H
centerC2×C4×C103#120
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#386
prime radicalC22×D4×C103D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1491C2semidirect
5. C103×#1300C2semidirect
174. #9029C103direct (N × H)
185. #1491C2×C103semidirect
186. #1300C2×C103semidirect
187. C103#9029direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#29732
C103×#23982
C4×#100×C1032
C103×#14912
C103×#13002
#9029103