Finite Group Databasebeta

← C103×#10164 #39915439

Subgroups — C103×#10164 #39915439

Order 26368.

498 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3227C211yesmaximal, characteristic
2C2×#500×C103C211yesmaximal, characteristic, complemented
3C103×#3141C211yesmaximal, characteristic
4C103×#1997C211yesmaximal, characteristic, complemented
5C103×#1548C211yesmaximal, characteristic, complemented
6C103×#1492C211yesmaximal, characteristic
7C103×#1278C211yesmaximal, characteristic, complemented
8#532×C103C2211yescharacteristic
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×C4⋊Q8×C103C2211yescharacteristic
11#500×C103—22no—
12#500×C103—22no—
13#498×C103—21no—
14#489×C103—22no—
15#487×C103—21no—
16#486×C103—21no—
17#486×C103—21no—
18#481×C103—22no—
19#476×C103—22no—
20#431×C103C2211yescharacteristic
21C2×#107×C103—22no—
22#423×C103C2211yescharacteristic
23#417×C103—22no—
24C4×M16×C103C2211yescharacteristic
25C2×C4×C8×C103C2211yescharacteristic
26#343×C103—22no—
27#333×C103—22no—
28D4⋊C8×C103—22no—
29C2×#41×C103—21no—
30C22×Q8×C103—21no—
31C22×Q8×C103—21no—
32C2×M16×C103—21no—
33C2×M16×C103D412yes—
34C22×C8×C103—21no—
35C4⋊Q8×C103—21no—
36C4⋊Q8×C103—21no—
37C4⋊Q8×C103—21no—
38C4⋊Q8×C103—21no—
39C4⋊Q8×C103—21no—
40C4⋊Q8×C103—21no—
41C4⋊Q8×C103—21no—
42C4⋊Q8×C103D411yescharacteristic
43C4⋊Q8×C103D412yes—
44#127×C103D411yescharacteristic
45#124×C103—21no—
46#121×C103—21no—
47#121×C103—21no—
48C4×D4×C103—21no—
49C4×D4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103D412yes—
54C2×C42×C103C2311yescharacteristic
55#107×C103—28no—
56#106×C103—24no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103—21no—
59C4⋊C8×C103D412yes—
60#103×C103—24no—
61#102×C103—24no—
62#102×C103—24no—
63C22⋊C8×C103—21no—
64#97×C103—21no—
65C4×C8×C103—21no—
66C4×C8×C103—21no—
67C4×C8×C103—21no—
68C4×C8×C103D412yes—
69#41×C103—42no—
70#41×C103—42no—
71C2×Q8×C103—21no—
72C2×Q8×C103—22no—
73C2×Q8×C103—41no—
74C2×Q8×C103—41no—
75C2×Q8×C103—41no—
76C2×Q8×C103—82no—
77C2×Q8×C103—82no—
78C2×D4×C103—21no—
79C2×D4×C103—21no—
80C2×D4×C103—21no—
81C2×D4×C103—41no—
82C22×C4×C103—22no—
83C22×C4×C103—41no—
84C22×C4×C103—41no—
85C22×C4×C103C2×D411yescharacteristic
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103#4111yescharacteristic
88M16×C103—22no—
89M16×C103—22no—
90M16×C103—42no—
91C2×C8×C103—24no—
92C2×C8×C103—22no—
93C2×C8×C103—22no—
94C2×C8×C103—22no—
95C2×C8×C103—41no—
96C4⋊C4×C103—22no—
97C4⋊C4×C103—22no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103—22no—
100C4⋊C4×C103—22no—
101C4⋊C4×C103—21no—
102C4⋊C4×C103—41no—
103C4⋊C4×C103—41no—
104C4⋊C4×C103—41no—
105C4⋊C4×C103—41no—
106C22⋊C4×C103—41no—
107C22⋊C4×C103—41no—
108C42×C103C2×D411yescharacteristic
109C42×C103C2×D411yescharacteristic
110C42×C103C2×D411yescharacteristic
111C42×C103C2×D411yescharacteristic
112C23×C103—41no—
113C23×C103#12111yescharacteristic
114Q8×C103—42no—
115Q8×C103—82no—
116Q8×C103—82no—
117Q8×C103—82no—
118Q8×C103—82no—
119D4×C103—42no—
120D4×C103—42no—
121D4×C103—42no—
122D4×C103—82no—
123C2×C4×C103—22no—
124C2×C4×C103—22no—
125C2×C4×C103—41no—
126C2×C4×C103—42no—
127C2×C4×C103—42no—
128C2×C4×C103—82no—
129C2×C4×C103—81no—
130C2×C4×C103—81no—
131C2×C4×C103—82no—
132C2×C4×C103#12011yescharacteristic
133C2×C4×C103#12011yescharacteristic
134C2×C4×C103#12011yescharacteristic
135C2×C4×C103#12111yescharacteristic
136C2×C4×C103#12111yescharacteristic
137C2×C4×C103#12711yescharacteristic
138C2×C4×C103#13512yes—
139C2×C4×C103#13712yes—
140C8×C103—24no—
141C8×C103—42no—
142C8×C103—42no—
143C8×C103—81no—
144C22×C103—21no—
145C22×C103—21no—
146C22×C103—81no—
147C22×C103—81no—
148C22×C103—81no—
149C22×C103#39211yescharacteristic
150C22×C103#46412yes—
151C4×C103—21no—
152C4×C103—21no—
153C4×C103—81no—
154C4×C103—82no—
155C4×C103—82no—
156C4×C103#45212yes—
157C4×C103#45612yes—
158C4×C103#47212yes—
159C4×C103#49511yescharacteristic
160C4×C103#49711yescharacteristic
161#10164C10311yesmaximal, characteristic, direct product factor, Sylow
162C2×C103—22no—
163C2×C103—161no—
164C2×C103#200511yescharacteristic
165C2×C103#201511yescharacteristic
166C2×C103#201811yescharacteristic
167#3227C2×C10311yescharacteristic
168C2×#500C2×C10311yescharacteristic, complemented
169#3141C2×C10311yescharacteristic
170#1997C2×C10311yescharacteristic, complemented
171#1548C2×C10311yescharacteristic, complemented
172#1492C2×C10311yescharacteristic
173#1278C2×C10311yescharacteristic, complemented
174C103#1016411yescharacteristic, direct product factor, Sylow
175#532C22×C10311yescharacteristic
176C2×C4⋊Q8C22×C10311yescharacteristic
177C2×C4⋊Q8C22×C10311yescharacteristic
178#500—22no—
179#500—22no—
180#498—21no—
181#489—22no—
182#487—21no—
183#486—21no—
184#486—21no—
185#481—22no—
186#476—22no—
187#431C22×C10311yescharacteristic
188C2×#107—22no—
189#423C22×C10311yescharacteristic
190#417—22no—
191C4×M16C22×C10311yescharacteristic
192C2×C4×C8C22×C10311yescharacteristic
193#343—22no—
194#333—22no—
195D4⋊C8—22no—
196C2×#41—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C2×M16—21no—
200C2×M16D4×C10312yes—
201C22×C8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8D4×C10312yes—
210C4⋊Q8D4×C10311yescharacteristic
211#127D4×C10311yescharacteristic
212#124—21no—
213#121—21no—
214#121—21no—
215C4×D4—21no—
216C4×D4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4D4×C10312yes—
221C2×C42C23×C10311yescharacteristic
222#107—28no—
223#106—24no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8D4×C10312yes—
227#103—24no—
228#102—24no—
229#102—24no—
230C22⋊C8—21no—
231#97—21no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8D4×C10312yes—
236#41—42no—
237#41—42no—
238C2×Q8—21no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—82no—
244C2×Q8—82no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—41no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C2×D4×C10311yescharacteristic
253C22×C4C2×D4×C10311yescharacteristic
254C22×C4#41×C10311yescharacteristic
255M16—22no—
256M16—22no—
257M16—42no—
258C2×C8—24no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—41no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C42C2×D4×C10311yescharacteristic
276C42C2×D4×C10311yescharacteristic
277C42C2×D4×C10311yescharacteristic
278C42C2×D4×C10311yescharacteristic
279C23—41no—
280C23#121×C10311yescharacteristic
281Q8—42no—
282Q8—82no—
283Q8—82no—
284Q8—82no—
285Q8—82no—
286D4—42no—
287D4—42no—
288D4—42no—
289D4—82no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4#120×C10311yescharacteristic
300C2×C4#120×C10311yescharacteristic
301C2×C4#120×C10311yescharacteristic
302C2×C4#121×C10311yescharacteristic
303C2×C4#121×C10311yescharacteristic
304C2×C4#127×C10311yescharacteristic
305C2×C4#135×C10312yes—
306C2×C4#137×C10312yes—
307C8—24no—
308C8—42no—
309C8—42no—
310C8—81no—
311C22—21no—
312C22—21no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22#392×C10311yescharacteristic
317C22#464×C10312yes—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—82no—
322C4—82no—
323C4#452×C10312yes—
324C4#456×C10312yes—
325C4#472×C10312yes—
326C4#495×C10311yescharacteristic
327C4#497×C10311yescharacteristic
328C2—22no—
329C2—161no—
330C2C103×#200511yescharacteristic
331C2C103×#201511yescharacteristic
332C2C103×#201811yescharacteristic
subgroupG/H
center, socleC22×C103#392
commutator, Frattini, cosocleC2×C42C23×C103
prime radical#532×C103C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#500×C103C2semidirect
4. C103×#1997C2semidirect
5. C103×#1548C2semidirect
7. C103×#1278C2semidirect
161. #10164C103direct (N × H)
168. C2×#500C2×C103semidirect
170. #1997C2×C103semidirect
171. #1548C2×C103semidirect
173. #1278C2×C103semidirect
174. C103#10164direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32272
C2×#500×C1032
C103×#31412
C103×#19972
C103×#15482
C103×#14922
C103×#12782
#10164103