Finite Group Databasebeta

← C103×#10501 #39915776

Subgroups — C103×#10501 #39915776

Order 26368.

440 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3206C211yesmaximal, characteristic
2C103×#1997C211yesmaximal, characteristic, complemented
3C103×#1981C211yesmaximal, characteristic, complemented
4C103×#1980C211yesmaximal, characteristic
5C103×#1565C211yesmaximal, characteristic, complemented
6C103×#1547C211yesmaximal, characteristic
7C103×#1303C211yesmaximal, characteristic, complemented
8#532×C103C2211yescharacteristic
9C2×C4⋊Q8×C103C2211yescharacteristic
10#492×C103—21no—
11#487×C103—21no—
12#461×C103—21no—
13#461×C103—21no—
14#448×C103—22no—
15#431×C103C2211yescharacteristic
16#423×C103C2211yescharacteristic
17C2×C4⋊C8×C103C2211yescharacteristic
18C2×#104×C103—21no—
19C2×#104×C103—21no—
20C2×#103×C103—22no—
21C4×M16×C103C2211yescharacteristic
22C4×C4⋊C4×C103C2211yescharacteristic
23#343×C103—21no—
24#343×C103—21no—
25#335×C103—21no—
26#334×C103—21no—
27#332×C103—21no—
28#331×C103—21no—
29C2×#41×C103—21no—
30C22×Q8×C103D412yes—
31C2×SD16×C103—22no—
32C2×SD16×C103—22no—
33C2×M16×C103—21no—
34C2×M16×C103D411yescharacteristic
35C2×M16×C103D411yescharacteristic
36C22×C8×C103—21no—
37C4⋊Q8×C103—21no—
38C4⋊Q8×C103—21no—
39C4⋊Q8×C103—21no—
40C4⋊Q8×C103—21no—
41C4⋊Q8×C103D411yescharacteristic
42#127×C103D411yescharacteristic
43#124×C103—21no—
44#121×C103—21no—
45#121×C103—21no—
46C4×D4×C103—21no—
47C4×D4×C103—21no—
48C2×C4⋊C4×C103—21no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C42×C103—21no—
52C2×C42×C103C2311yescharacteristic
53C4⋊C8×C103—21no—
54C4⋊C8×C103—21no—
55C4⋊C8×C103—21no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103D411yescharacteristic
58C4⋊C8×C103D411yescharacteristic
59#104×C103—42no—
60#104×C103—42no—
61#103×C103—22no—
62#103×C103—22no—
63#103×C103—44no—
64C22⋊C8×C103—21no—
65#97×C103—21no—
66C4×C8×C103—21no—
67C4×C8×C103—21no—
68#95×C103—21no—
69#41×C103—41no—
70#41×C103—41no—
71#41×C103—41no—
72#41×C103—41no—
73C2×Q8×C103—22no—
74C2×Q8×C103—21no—
75C2×Q8×C103—22no—
76C2×Q8×C103—42no—
77C2×Q8×C103—42no—
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
88SD16×C103—82no—
89SD16×C103—82no—
90M16×C103—21no—
91M16×C103—21no—
92M16×C103—21no—
93M16×C103—41no—
94M16×C103—41no—
95M16×C103SD1612yescomplemented
96C2×C8×C103—21no—
97C2×C8×C103—21no—
98C2×C8×C103—21no—
99C2×C8×C103—21no—
100C2×C8×C103—42no—
101C2×C8×C103—41no—
102C2×C8×C103—41no—
103C4⋊C4×C103—22no—
104C4⋊C4×C103—21no—
105C4⋊C4×C103—21no—
106C4⋊C4×C103—41no—
107C4⋊C4×C103—41no—
108C4⋊C4×C103—41no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103—41no—
111C22⋊C4×C103—41no—
112C22⋊C4×C103—41no—
113C42×C103—41no—
114C42×C103—41no—
115C42×C103C2×D411yescharacteristic
116C42×C103C2×D411yescharacteristic
117C42×C103#4111yescharacteristic
118C42×C103#4111yescharacteristic
119C23×C103—41no—
120C23×C103#12111yescharacteristic
121Q8×C103—44no—
122Q8×C103—42no—
123Q8×C103—42no—
124Q8×C103—41no—
125Q8×C103—41no—
126D4×C103—41no—
127D4×C103—41no—
128D4×C103—41no—
129D4×C103—41no—
130D4×C103—81no—
131D4×C103—81no—
132D4×C103—81no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—41no—
136C2×C4×C103—42no—
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—82no—
144C2×C4×C103#12011yescharacteristic
145C2×C4×C103#12111yescharacteristic
146C2×C4×C103#12111yescharacteristic
147C2×C4×C103#12311yescharacteristic
148C2×C4×C103#12311yescharacteristic
149C2×C4×C103#12411yescharacteristic
150C2×C4×C103C2×SD1611yescharacteristic
151C2×C4×C103#13511yescharacteristic
152C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C103#13711yescharacteristic
154C8×C103—22no—
155C8×C103—41no—
156C8×C103—41no—
157C8×C103—41no—
158C8×C103—81no—
159C8×C103—81no—
160C22×C103—21no—
161C22×C103—21no—
162C22×C103—81no—
163C22×C103—81no—
164C22×C103—81no—
165C22×C103#39411yescharacteristic
166C22×C103#46011yescharacteristic
167C22×C103#46411yescharacteristic
168C4×C103—21no—
169C4×C103—21no—
170C4×C103—21no—
171C4×C103—82no—
172C4×C103—81no—
173C4×C103—82no—
174C4×C103#45311yescharacteristic
175C4×C103#45511yescharacteristic
176C4×C103#46111yescharacteristic
177C4×C103#46311yescharacteristic
178C4×C103#46511yescharacteristic
179C4×C103#46811yescharacteristic
180#10501C10311yesmaximal, characteristic, direct product factor, Sylow
181C2×C103—21no—
182C2×C103—21no—
183C2×C103—161no—
184C2×C103#203711yescharacteristic
185C2×C103#204911yescharacteristic
186C2×C103#205511yescharacteristic
187#3206C2×C10311yescharacteristic
188#1997C2×C10311yescharacteristic, complemented
189#1981C2×C10311yescharacteristic, complemented
190#1980C2×C10311yescharacteristic
191#1565C2×C10311yescharacteristic, complemented
192#1547C2×C10311yescharacteristic
193#1303C2×C10311yescharacteristic, complemented
194C103#1050111yescharacteristic, direct product factor, Sylow
195#532C22×C10311yescharacteristic
196C2×C4⋊Q8C22×C10311yescharacteristic
197#492—21no—
198#487—21no—
199#461—21no—
200#461—21no—
201#448—22no—
202#431C22×C10311yescharacteristic
203#423C22×C10311yescharacteristic
204C2×C4⋊C8C22×C10311yescharacteristic
205C2×#104—21no—
206C2×#104—21no—
207C2×#103—22no—
208C4×M16C22×C10311yescharacteristic
209C4×C4⋊C4C22×C10311yescharacteristic
210#343—21no—
211#343—21no—
212#335—21no—
213#334—21no—
214#332—21no—
215#331—21no—
216C2×#41—21no—
217C22×Q8D4×C10312yes—
218C2×SD16—22no—
219C2×SD16—22no—
220C2×M16—21no—
221C2×M16D4×C10311yescharacteristic
222C2×M16D4×C10311yescharacteristic
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C10311yescharacteristic
229#127D4×C10311yescharacteristic
230#124—21no—
231#121—21no—
232#121—21no—
233C4×D4—21no—
234C4×D4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42—21no—
239C2×C42C23×C10311yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8D4×C10311yescharacteristic
245C4⋊C8D4×C10311yescharacteristic
246#104—42no—
247#104—42no—
248#103—22no—
249#103—22no—
250#103—44no—
251C22⋊C8—21no—
252#97—21no—
253C4×C8—21no—
254C4×C8—21no—
255#95—21no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C2×D4×C10311yescharacteristic
273C22×C4C2×D4×C10311yescharacteristic
274C22×C4#41×C10311yescharacteristic
275SD16—82no—
276SD16—82no—
277M16—21no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16SD16×C10312yescomplemented
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—42no—
288C2×C8—41no—
289C2×C8—41no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C42—41no—
301C42—41no—
302C42C2×D4×C10311yescharacteristic
303C42C2×D4×C10311yescharacteristic
304C42#41×C10311yescharacteristic
305C42#41×C10311yescharacteristic
306C23—41no—
307C23#121×C10311yescharacteristic
308Q8—44no—
309Q8—42no—
310Q8—42no—
311Q8—41no—
312Q8—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4—81no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4#120×C10311yescharacteristic
332C2×C4#121×C10311yescharacteristic
333C2×C4#121×C10311yescharacteristic
334C2×C4#123×C10311yescharacteristic
335C2×C4#123×C10311yescharacteristic
336C2×C4#124×C10311yescharacteristic
337C2×C4C2×SD16×C10311yescharacteristic
338C2×C4#135×C10311yescharacteristic
339C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
340C2×C4#137×C10311yescharacteristic
341C8—22no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#394×C10311yescharacteristic
353C22#460×C10311yescharacteristic
354C22#464×C10311yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—82no—
359C4—82no—
360C4—81no—
361C4#453×C10311yescharacteristic
362C4#455×C10311yescharacteristic
363C4#461×C10311yescharacteristic
364C4#463×C10311yescharacteristic
365C4#465×C10311yescharacteristic
366C4#468×C10311yescharacteristic
367C2—21no—
368C2—21no—
369C2—161no—
370C2C103×#203711yescharacteristic
371C2C103×#204911yescharacteristic
372C2C103×#205511yescharacteristic
subgroupG/H
center, socleC22×C103#394
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. C103×#1997C2semidirect
3. C103×#1981C2semidirect
5. C103×#1565C2semidirect
7. C103×#1303C2semidirect
95. M16×C103SD16semidirect
180. #10501C103direct (N × H)
188. #1997C2×C103semidirect
189. #1981C2×C103semidirect
191. #1565C2×C103semidirect
193. #1303C2×C103semidirect
194. C103#10501direct (N × H)
282. M16SD16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#32062
C103×#19972
C103×#19812
C103×#19802
C103×#15652
C103×#15472
C103×#13032
#10501103