Finite Group Databasebeta

← C103×#29347 #39934622

Subgroups — C103×#29347 #39934622

Order 26368.

738 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2862C211yesmaximal, characteristic
2C4×C4⋊Q8×C103C211yesmaximal, characteristic
3C103×#2072C212yesmaximal
4C103×#2024C212yesmaximal
5C103×#1987C212yesmaximal
6C103×#1981C212yesmaximal
7C103×#1933C214yesmaximal
8C4×C4⋊C8×C103C211yesmaximal, characteristic
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×C4⋊Q8×C103C2211yescharacteristic
11C2×C4⋊Q8×C103C2211yescharacteristic
12C2×C4×Q8×C103—21no—
13C2×C4⋊C8×C103C2212yes—
14C2×#103×C103C2214yes—
15C2×#103×C103C2214yes—
16C2×C4×C8×C103C2212yes—
17#391×C103—21no—
18#391×C103—21no—
19#391×C103—21no—
20#391×C103C2212yes—
21#391×C103C2212yes—
22#389×C103—21no—
23#389×C103C2212yes—
24#384×C103C2211yescharacteristic
25#382×C103—21no—
26#382×C103—21no—
27C4×C4⋊C4×C103—21no—
28C4×C4⋊C4×C103C2212yes—
29C43×C103C2211yescharacteristic
30#340×C103C2214yes—
31#340×C103C2214yes—
32#336×C103C2212yes—
33C22×Q8×C103—21no—
34C22×Q8×C103—21no—
35C22×Q8×C103C2312yes—
36C22×C8×C103C2314yes—
37C4⋊Q8×C103—24no—
38C4⋊Q8×C103—24no—
39C4⋊Q8×C103—24no—
40C4×Q8×C103—44no—
41C2×C4⋊C4×C103—21no—
42C2×C4⋊C4×C103—21no—
43C2×C4⋊C4×C103—21no—
44C2×C4⋊C4×C103—21no—
45C2×C4⋊C4×C103—21no—
46C2×C4⋊C4×C103—22no—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103C2312yes—
49C2×C4⋊C4×C103C2312yes—
50C2×C4⋊C4×C103C2312yes—
51C2×C42×C103—22no—
52C2×C42×C103D411yescharacteristic
53C2×C42×C103D411yescharacteristic
54C2×C42×C103D411yescharacteristic
55C2×C42×C103D411yescharacteristic
56C2×C42×C103C2311yescharacteristic
57C2×C42×C103C2311yescharacteristic
58C2×C42×C103C2311yescharacteristic
59C4⋊C8×C103—24no—
60#103×C103—28no—
61#103×C103—44no—
62C4×C8×C103—42no—
63#95×C103—22no—
64#95×C103—22no—
65#95×C103—22no—
66#95×C103—22no—
67#95×C103—22no—
68#95×C103—22no—
69C2×Q8×C103—24no—
70C2×Q8×C103—24no—
71C2×Q8×C103—24no—
72C2×Q8×C103—22no—
73C2×Q8×C103—22no—
74C2×Q8×C103—42no—
75C2×Q8×C103—42no—
76C2×Q8×C103—42no—
77C2×Q8×C103—42no—
78C2×Q8×C103—42no—
79C22×C4×C103—22no—
80C22×C4×C103—22no—
81C22×C4×C103—22no—
82C22×C4×C103—22no—
83C22×C4×C103C2×D411yescharacteristic
84C22×C4×C103C2×D411yescharacteristic
85C22×C4×C103C2×D411yescharacteristic
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103C2×D411yescharacteristic
88C22×C4×C103C2×D411yescharacteristic
89C22×C4×C103C2411yescharacteristic
90C2×C8×C103—24no—
91C2×C8×C103—24no—
92C2×C8×C103—24no—
93C4⋊C4×C103—24no—
94C4⋊C4×C103—22no—
95C4⋊C4×C103—24no—
96C4⋊C4×C103—22no—
97C4⋊C4×C103—22no—
98C4⋊C4×C103—42no—
99C4⋊C4×C103—42no—
100C4⋊C4×C103—42no—
101C4⋊C4×C103—42no—
102C4⋊C4×C103—44no—
103C4⋊C4×C103—42no—
104C4⋊C4×C103#4114yes—
105C42×C103—22no—
106C42×C103—21no—
107C42×C103—21no—
108C42×C103—41no—
109C42×C103—41no—
110C42×C103—44no—
111C42×C103SD1614yes—
112C42×C103Q1614yes—
113C42×C103#4114yes—
114C23×C103C22×D411yescharacteristic
115Q8×C103—48no—
116Q8×C103—44no—
117Q8×C103—44no—
118Q8×C103—84no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
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—24no—
130C2×C4×C103—42no—
131C2×C4×C103—42no—
132C2×C4×C103—42no—
133C2×C4×C103—42no—
134C2×C4×C103—42no—
135C2×C4×C103—42no—
136C2×C4×C103—42no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103—42no—
140C2×C4×C103—42no—
141C2×C4×C103#12412yes—
142C2×C4×C103#12412yes—
143C2×C4×C103C2×SD1612yes—
144C2×C4×C103C2×SD1612yes—
145C2×C4×C103C2×SD1612yes—
146C2×C4×C103C2×Q1612yes—
147C2×C4×C103C2×Q1612yes—
148C2×C4×C103C2×Q1612yes—
149C2×C4×C103C2×#4112yes—
150C2×C4×C103C2×#4112yes—
151C2×C4×C103H(5,𝔽2)11yescharacteristic
152C2×C4×C1032−1+411yescharacteristic
153C8×C103—44no—
154C22×C103#52511yescharacteristic
155C22×C103C2×#12411yescharacteristic
156C22×C103#53711yescharacteristic
157C22×C103C22×SD1611yescharacteristic
158C22×C103C22×Q1611yescharacteristic
159C22×C103#57511yescharacteristic
160C22×C103#57511yescharacteristic
161C4×C103—22no—
162C4×C103—22no—
163C4×C103—22no—
164C4×C103—22no—
165C4×C103—22no—
166C4×C103—44no—
167C4×C103—82no—
168C4×C103—82no—
169C4×C103—82no—
170C4×C103#48714yes—
171C4×C103#55612yes—
172C4×C103#55912yes—
173#29347C10311yesmaximal, characteristic, direct product factor, Sylow
174C2×C103#259211yescharacteristic
175C2×C103#310111yescharacteristic
176C2×C103#310411yescharacteristic
177C2×C103C2×#48711yescharacteristic
178C2×C103#314011yescharacteristic
179C2×C103#324611yescharacteristic
180C2×C103#324911yescharacteristic
181#2862C2×C10311yescharacteristic
182C4×C4⋊Q8C2×C10311yescharacteristic
183#2072C2×C10312yes—
184#2024C2×C10312yes—
185#1987C2×C10312yes—
186#1981C2×C10312yes—
187#1933C2×C10314yes—
188C4×C4⋊C8C2×C10311yescharacteristic
189C103#2934711yescharacteristic, direct product factor, Sylow
190C2×C4⋊Q8C22×C10311yescharacteristic
191C2×C4⋊Q8C22×C10311yescharacteristic
192C2×C4⋊Q8C22×C10311yescharacteristic
193C2×C4×Q8—21no—
194C2×C4⋊C8C22×C10312yes—
195C2×#103C22×C10314yes—
196C2×#103C22×C10314yes—
197C2×C4×C8C22×C10312yes—
198#391—21no—
199#391—21no—
200#391—21no—
201#391C22×C10312yes—
202#391C22×C10312yes—
203#389—21no—
204#389C22×C10312yes—
205#384C22×C10311yescharacteristic
206#382—21no—
207#382—21no—
208C4×C4⋊C4—21no—
209C4×C4⋊C4C22×C10312yes—
210C43C22×C10311yescharacteristic
211#340C22×C10314yes—
212#340C22×C10314yes—
213#336C22×C10312yes—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8C23×C10312yes—
217C22×C8C23×C10314yes—
218C4⋊Q8—24no—
219C4⋊Q8—24no—
220C4⋊Q8—24no—
221C4×Q8—44no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C23×C10312yes—
230C2×C4⋊C4C23×C10312yes—
231C2×C4⋊C4C23×C10312yes—
232C2×C42—22no—
233C2×C42D4×C10311yescharacteristic
234C2×C42D4×C10311yescharacteristic
235C2×C42D4×C10311yescharacteristic
236C2×C42D4×C10311yescharacteristic
237C2×C42C23×C10311yescharacteristic
238C2×C42C23×C10311yescharacteristic
239C2×C42C23×C10311yescharacteristic
240C4⋊C8—24no—
241#103—28no—
242#103—44no—
243C4×C8—42no—
244#95—22no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95—22no—
249#95—22no—
250C2×Q8—24no—
251C2×Q8—24no—
252C2×Q8—24no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×Q8—42no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4C2×D4×C10311yescharacteristic
265C22×C4C2×D4×C10311yescharacteristic
266C22×C4C2×D4×C10311yescharacteristic
267C22×C4C2×D4×C10311yescharacteristic
268C22×C4C2×D4×C10311yescharacteristic
269C22×C4C2×D4×C10311yescharacteristic
270C22×C4C24×C10311yescharacteristic
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—24no—
274C4⋊C4—24no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—44no—
284C4⋊C4—42no—
285C4⋊C4#41×C10314yes—
286C42—22no—
287C42—21no—
288C42—21no—
289C42—41no—
290C42—41no—
291C42—44no—
292C42SD16×C10314yes—
293C42Q16×C10314yes—
294C42#41×C10314yes—
295C23C22×D4×C10311yescharacteristic
296Q8—48no—
297Q8—44no—
298Q8—44no—
299Q8—84no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—24no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4#124×C10312yes—
323C2×C4#124×C10312yes—
324C2×C4C2×SD16×C10312yes—
325C2×C4C2×SD16×C10312yes—
326C2×C4C2×SD16×C10312yes—
327C2×C4C2×Q16×C10312yes—
328C2×C4C2×Q16×C10312yes—
329C2×C4C2×Q16×C10312yes—
330C2×C4C2×#41×C10312yes—
331C2×C4C2×#41×C10312yes—
332C2×C4H(5,𝔽2)×C10311yescharacteristic
333C2×C42−1+4×C10311yescharacteristic
334C8—44no—
335C22#525×C10311yescharacteristic
336C22C2×#124×C10311yescharacteristic
337C22#537×C10311yescharacteristic
338C22C22×SD16×C10311yescharacteristic
339C22C22×Q16×C10311yescharacteristic
340C22#575×C10311yescharacteristic
341C22#575×C10311yescharacteristic
342C4—22no—
343C4—22no—
344C4—22no—
345C4—22no—
346C4—22no—
347C4—44no—
348C4—82no—
349C4—82no—
350C4—82no—
351C4#487×C10314yes—
352C4#556×C10312yes—
353C4#559×C10312yes—
354C2C103×#259211yescharacteristic
355C2C103×#310111yescharacteristic
356C2C103×#310411yescharacteristic
357C2C2×#487×C10311yescharacteristic
358C2C103×#314011yescharacteristic
359C2C103×#324611yescharacteristic
360C2C103×#324911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C43×C103 ◁ G

Complements

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

NH ≅ G/Ntype
173. #29347C103direct (N × H)
189. C103#29347direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#28622
C4×C4⋊Q8×C1032
C103×#20722
C103×#20242
C103×#19872
C103×#19812
C103×#19332
C4×C4⋊C8×C1032
#29347103