Finite Group Databasebeta

← C103×#13392 #39918667

Subgroups — C103×#13392 #39918667

Order 26368.

386 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3067C211yesmaximal, characteristic
2C2×#368×C103C211yesmaximal, characteristic, complemented
3C103×#2148C211yesmaximal, characteristic, complemented
4C2×#359×C103C211yesmaximal, characteristic, complemented
5C2×#350×C103C211yesmaximal, characteristic, complemented
6C103×#1813C211yesmaximal, characteristic, complemented
7C103×#1385C211yesmaximal, characteristic, complemented
8#575×C103—21no—
9C2×#135×C103C2211yescharacteristic
10C2×#131×C103C2211yescharacteristic
11C2×M32×C103C2211yescharacteristic
12C22×C16×C103C2211yescharacteristic
13#473×C103—21no—
14#472×C103—21no—
15#471×C103—22no—
16C2×#108×C103C2211yescharacteristic
17C2×#108×C103C2211yescharacteristic
18C2×#108×C103C2211yescharacteristic
19#413×C103—21no—
20#413×C103—21no—
21#368×C103—22no—
22#362×C103—21no—
23#361×C103—21no—
24#359×C103—22no—
25#350×C103—22no—
26#338×C103—21no—
27C2×#41×C103—21no—
28C2×#41×C103D411yescharacteristic
29#137×C103—22no—
30#137×C103—41no—
31AGL(1,ℤ/8)×C103—22no—
32AGL(1,ℤ/8)×C103—41no—
33#135×C103—21no—
34#135×C103—21no—
35#135×C103—21no—
36#135×C103—21no—
37#135×C103—42no—
38C2×Q16×C103D411yescharacteristic
39C2×SD16×C103—21no—
40C2×D8×C103D411yescharacteristic
41#131×C103—21no—
42#131×C103—21no—
43#131×C103—21no—
44#131×C103—21no—
45C2×M16×C103—21no—
46C2×M16×C103—21no—
47C2×M16×C103—21no—
48C2×M16×C103—21no—
49C2×M16×C103D411yescharacteristic
50C22×C8×C103—21no—
51C22×C8×C103C2311yescharacteristic
52M32×C103—21no—
53M32×C103—21no—
54C2×C16×C103—21no—
55C2×C16×C103—21no—
56C2×C16×C103—21no—
57C2×C16×C103D412yes—
58#108×C103—21no—
59#108×C103—21no—
60#108×C103—21no—
61#108×C103—21no—
62#108×C103—21no—
63#108×C103D412yes—
64#101×C103—22no—
65#101×C103—41no—
66#100×C103—22no—
67#100×C103—41no—
68#41×C103—21no—
69#41×C103—21no—
70#41×C103—21no—
71#41×C103—21no—
72#41×C103—41no—
73#41×C103—41no—
74#41×C103—41no—
75#41×C103—41no—
76C2×Q8×C103—21no—
77C2×Q8×C103D811yescharacteristic
78C2×D4×C103—21no—
79C2×D4×C103—21no—
80C2×D4×C103—41no—
81C2×D4×C103D811yescharacteristic
82C22×C4×C103—21no—
83C22×C4×C103—41no—
84C22×C4×C103C2×D411yescharacteristic
85Q16×C103—21no—
86Q16×C103—21no—
87Q16×C103—42no—
88SD16×C103—42no—
89SD16×C103—42no—
90SD16×C103—41no—
91SD16×C103—41no—
92D8×C103—21no—
93D8×C103—21no—
94D8×C103—42no—
95M16×C103—21no—
96M16×C103—22no—
97M16×C103—21no—
98M16×C103—41no—
99M16×C103—41no—
100M16×C103—41no—
101M16×C103—41no—
102M16×C103—41no—
103M16×C103—41no—
104M16×C103—41no—
105C2×C8×C103—21no—
106C2×C8×C103—41no—
107C2×C8×C103—41no—
108C2×C8×C103—41no—
109C2×C8×C103—41no—
110C2×C8×C103—41no—
111C2×C8×C103C2×D411yescharacteristic
112C2×C8×C103C2×D411yescharacteristic
113C2×C8×C103C2×D411yescharacteristic
114C2×C8×C103#4111yescharacteristic
115C2×C8×C103#4111yescharacteristic
116C2×C8×C103#4111yescharacteristic
117C16×C103—22no—
118C16×C103—41no—
119C23×C103—21no—
120C23×C103—41no—
121C23×C103#13711yescharacteristic
122Q8×C103—21no—
123Q8×C103—21no—
124Q8×C103—41no—
125Q8×C103—41no—
126D4×C103—21no—
127D4×C103—21no—
128D4×C103—41no—
129D4×C103—41no—
130D4×C103—41no—
131D4×C103—41no—
132D4×C103—81no—
133D4×C103—81no—
134C2×C4×C103—21no—
135C2×C4×C103—41no—
136C2×C4×C103—41no—
137C2×C4×C103—41no—
138C2×C4×C103—81no—
139C2×C4×C103—81no—
140C2×C4×C103#12011yescharacteristic
141C2×C4×C103#12111yescharacteristic
142C2×C4×C103#12311yescharacteristic
143C2×C4×C103C2×D811yescharacteristic
144C2×C4×C103#13511yescharacteristic
145C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
146C8×C103—41no—
147C8×C103—42no—
148C8×C103—81no—
149C8×C103—81no—
150C8×C103#12111yescharacteristic
151C8×C103#12111yescharacteristic
152C8×C103#12311yescharacteristic
153C8×C103#12411yescharacteristic
154C22×C103—41no—
155C22×C103—41no—
156C22×C103—81no—
157C22×C103—81no—
158C22×C103—161no—
159C22×C103#45211yescharacteristic
160C22×C103#46811yescharacteristic
161C22×C103#48011yescharacteristic
162C4×C103—41no—
163C4×C103—81no—
164C4×C103#39411yescharacteristic
165C4×C103#44711yescharacteristic
166C4×C103#46611yescharacteristic
167C4×C103#48211yescharacteristic
168#13392C10311yesmaximal, characteristic, direct product factor, Sylow
169C2×C103—21no—
170C2×C103—21no—
171C2×C103—21no—
172C2×C103—81no—
173C2×C103—161no—
174C2×C103#203311yescharacteristic
175#3067C2×C10311yescharacteristic
176C2×#368C2×C10311yescharacteristic, complemented
177#2148C2×C10311yescharacteristic, complemented
178C2×#359C2×C10311yescharacteristic, complemented
179C2×#350C2×C10311yescharacteristic, complemented
180#1813C2×C10311yescharacteristic, complemented
181#1385C2×C10311yescharacteristic, complemented
182C103#1339211yescharacteristic, direct product factor, Sylow
183#575—21no—
184C2×#135C22×C10311yescharacteristic
185C2×#131C22×C10311yescharacteristic
186C2×M32C22×C10311yescharacteristic
187C22×C16C22×C10311yescharacteristic
188#473—21no—
189#472—21no—
190#471—22no—
191C2×#108C22×C10311yescharacteristic
192C2×#108C22×C10311yescharacteristic
193C2×#108C22×C10311yescharacteristic
194#413—21no—
195#413—21no—
196#368—22no—
197#362—21no—
198#361—21no—
199#359—22no—
200#350—22no—
201#338—21no—
202C2×#41—21no—
203C2×#41D4×C10311yescharacteristic
204#137—22no—
205#137—41no—
206AGL(1,ℤ/8)—22no—
207AGL(1,ℤ/8)—41no—
208#135—21no—
209#135—21no—
210#135—21no—
211#135—21no—
212#135—42no—
213C2×Q16D4×C10311yescharacteristic
214C2×SD16—21no—
215C2×D8D4×C10311yescharacteristic
216#131—21no—
217#131—21no—
218#131—21no—
219#131—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16D4×C10311yescharacteristic
225C22×C8—21no—
226C22×C8C23×C10311yescharacteristic
227M32—21no—
228M32—21no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16D4×C10312yes—
233#108—21no—
234#108—21no—
235#108—21no—
236#108—21no—
237#108—21no—
238#108D4×C10312yes—
239#101—22no—
240#101—41no—
241#100—22no—
242#100—41no—
243#41—21no—
244#41—21no—
245#41—21no—
246#41—21no—
247#41—41no—
248#41—41no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×Q8D8×C10311yescharacteristic
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4D8×C10311yescharacteristic
257C22×C4—21no—
258C22×C4—41no—
259C22×C4C2×D4×C10311yescharacteristic
260Q16—21no—
261Q16—21no—
262Q16—42no—
263SD16—42no—
264SD16—42no—
265SD16—41no—
266SD16—41no—
267D8—21no—
268D8—21no—
269D8—42no—
270M16—21no—
271M16—22no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—41no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C10311yescharacteristic
287C2×C8C2×D4×C10311yescharacteristic
288C2×C8C2×D4×C10311yescharacteristic
289C2×C8#41×C10311yescharacteristic
290C2×C8#41×C10311yescharacteristic
291C2×C8#41×C10311yescharacteristic
292C16—22no—
293C16—41no—
294C23—21no—
295C23—41no—
296C23#137×C10311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—41no—
300Q8—41no—
301D4—21no—
302D4—21no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#120×C10311yescharacteristic
316C2×C4#121×C10311yescharacteristic
317C2×C4#123×C10311yescharacteristic
318C2×C4C2×D8×C10311yescharacteristic
319C2×C4#135×C10311yescharacteristic
320C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
321C8—41no—
322C8—42no—
323C8—81no—
324C8—81no—
325C8#121×C10311yescharacteristic
326C8#121×C10311yescharacteristic
327C8#123×C10311yescharacteristic
328C8#124×C10311yescharacteristic
329C22—41no—
330C22—41no—
331C22—81no—
332C22—81no—
333C22—161no—
334C22#452×C10311yescharacteristic
335C22#468×C10311yescharacteristic
336C22#480×C10311yescharacteristic
337C4—41no—
338C4—81no—
339C4#394×C10311yescharacteristic
340C4#447×C10311yescharacteristic
341C4#466×C10311yescharacteristic
342C4#482×C10311yescharacteristic
343C2—21no—
344C2—21no—
345C2—21no—
346C2—81no—
347C2—161no—
348C2C103×#203311yescharacteristic
subgroupG/H
centerC4×C103#482
commutator, Frattini, cosocleC22×C8C23×C103
socleC2×C103#2033
prime radicalC103×#3067C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C4×C103 ◁ C2×#131×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#368×C103C2semidirect
3. C103×#2148C2semidirect
4. C2×#359×C103C2semidirect
5. C2×#350×C103C2semidirect
6. C103×#1813C2semidirect
7. C103×#1385C2semidirect
168. #13392C103direct (N × H)
176. C2×#368C2×C103semidirect
177. #2148C2×C103semidirect
178. C2×#359C2×C103semidirect
179. C2×#350C2×C103semidirect
180. #1813C2×C103semidirect
181. #1385C2×C103semidirect
182. C103#13392direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#30672
C2×#368×C1032
C103×#21482
C2×#359×C1032
C2×#350×C1032
C103×#18132
C103×#13852
#13392103