Finite Group Databasebeta

← C103×#11872 #39917147

Subgroups — C103×#11872 #39917147

Order 26368.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3060C211yesmaximal, characteristic
2C103×#2115C211yesmaximal, characteristic, complemented
3C103×#1813C211yesmaximal, characteristic, complemented
4C103×#1342C212yesmaximal, complemented
5C103×#1341C212yesmaximal, complemented
6C2×#135×C103C411yescharacteristic
7C2×#131×C103C2211yescharacteristic
8#537×C103—21no—
9C2×M32×C103—21no—
10#470×C103C411yescharacteristic
11#470×C103C2211yescharacteristic
12#469×C103C411yescharacteristic
13#469×C103C2211yescharacteristic
14#465×C103—21no—
15#465×C103—21no—
16C2×#108×C103—21no—
17C2×#106×C103C411yescharacteristic
18#417×C103—21no—
19#413×C103—21no—
20#349×C103—21no—
21#349×C103C2212yes—
22#338×C103C2212yes—
23C2×#41×C103—21no—
24C2×#41×C103D411yescharacteristic
25#135×C103—41no—
26#135×C103—41no—
27C2×Q16×C103C2×C411yescharacteristic
28C2×SD16×C103—21no—
29C2×D8×C103C2×C411yescharacteristic
30#131×C103—41no—
31#131×C103—41no—
32C2×M16×C103—22no—
33C2×M16×C103C2×C411yescharacteristic
34C2×M16×C103D411yescharacteristic
35C2×M16×C103C2311yescharacteristic
36C22×C8×C103C2×C411yescharacteristic
37C22×C8×C103D411yescharacteristic
38C22×C8×C103D411yescharacteristic
39C22⋊Q8×C103—21no—
40C22⋊Q8×C103—21no—
41C22⋊Q8×C103—41no—
42#121×C103—21no—
43#121×C103—21no—
44#121×C103—41no—
45#121×C103—41no—
46#121×C103—41no—
47C2×C4⋊C4×C103—21no—
48M32×C103—22no—
49M32×C103—41no—
50C2×C16×C103—41no—
51#108×C103—41no—
52#108×C103—41no—
53#106×C103—21no—
54#106×C103C2×C411yescharacteristic
55#106×C103C2×C411yescharacteristic
56#103×C103—21no—
57#103×C103—21no—
58#102×C103—21no—
59#102×C103—21no—
60#101×C103—41no—
61#100×C103—41no—
62#41×C103—41no—
63#41×C103—41no—
64#41×C103—42no—
65#41×C103—42no—
66C2×Q8×C103—21no—
67C2×Q8×C103D811yescharacteristic
68C2×D4×C103—21no—
69C2×D4×C103—41no—
70C2×D4×C103—41no—
71C2×D4×C103—41no—
72C2×D4×C103D811yescharacteristic
73C2×D4×C103SD1611yescharacteristic
74C2×D4×C103SD1611yescharacteristic
75C22×C4×C103—41no—
76C22×C4×C103—41no—
77C22×C4×C103C22⋊C411yescharacteristic
78C22×C4×C103C22⋊C411yescharacteristic
79C22×C4×C103C2×D411yescharacteristic
80Q16×C103—41no—
81SD16×C103—41no—
82SD16×C103—41no—
83D8×C103—41no—
84M16×C103—41no—
85M16×C103—41no—
86M16×C103—41no—
87M16×C103—42no—
88M16×C103—42no—
89C2×C8×C103—21no—
90C2×C8×C103—21no—
91C2×C8×C103—21no—
92C2×C8×C103—21no—
93C2×C8×C103—21no—
94C2×C8×C103—21no—
95C2×C8×C103—42no—
96C2×C8×C103C22⋊C411yescharacteristic
97C2×C8×C103C22⋊C411yescharacteristic
98C2×C8×C103C22×C411yescharacteristic
99C2×C8×C103C2×D411yescharacteristic
100C4⋊C4×C103—21no—
101C4⋊C4×C103—21no—
102C4⋊C4×C103—41no—
103C4⋊C4×C103—41no—
104C4⋊C4×C103—41no—
105C22⋊C4×C103—41no—
106C22⋊C4×C103—41no—
107C22⋊C4×C103—41no—
108C22⋊C4×C103—41no—
109C16×C103—42no—
110C23×C103—41no—
111C23×C103#10211yescharacteristic
112C23×C103#10211yescharacteristic
113C23×C103C2×SD1611yescharacteristic
114Q8×C103—41no—
115Q8×C103—41no—
116Q8×C103—41no—
117D4×C103—41no—
118D4×C103—41no—
119D4×C103—41no—
120D4×C103—41no—
121D4×C103—41no—
122D4×C103—82no—
123D4×C103—161no—
124D4×C103—161no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—41no—
132C2×C4×C103—41no—
133C2×C4×C103—41no—
134C2×C4×C103—82no—
135C2×C4×C103—161no—
136C2×C4×C103#10211yescharacteristic
137C2×C4×C103#10211yescharacteristic
138C2×C4×C103C2×C22⋊C411yescharacteristic
139C2×C4×C103C2×D811yescharacteristic
140C8×C103—21no—
141C8×C103—21no—
142C8×C103—21no—
143C8×C103—82no—
144C8×C103#9911yescharacteristic
145C8×C103#9911yescharacteristic
146C22×C103—21no—
147C22×C103—21no—
148C22×C103—21no—
149C22×C103—41no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103—81no—
153C22×C103—81no—
154C22×C103—81no—
155C22×C103C2×#10211yescharacteristic
156C4×C103—21no—
157C4×C103—21no—
158C4×C103—21no—
159C4×C103—81no—
160C4×C103—81no—
161C4×C103—81no—
162C4×C103C2×#9911yescharacteristic
163C4×C103#42111yescharacteristic
164#11872C10311yesmaximal, characteristic, direct product factor, Sylow
165C2×C103—21no—
166C2×C103—41no—
167C2×C103—41no—
168C2×C103—41no—
169C2×C103—161no—
170C2×C103#151911yescharacteristic
171#3060C2×C10311yescharacteristic
172#2115C2×C10311yescharacteristic, complemented
173#1813C2×C10311yescharacteristic, complemented
174#1342C2×C10312yescomplemented
175#1341C2×C10312yescomplemented
176C103#1187211yescharacteristic, direct product factor, Sylow
177C2×#135C4×C10311yescharacteristic
178C2×#131C22×C10311yescharacteristic
179#537—21no—
180C2×M32—21no—
181#470C4×C10311yescharacteristic
182#470C22×C10311yescharacteristic
183#469C4×C10311yescharacteristic
184#469C22×C10311yescharacteristic
185#465—21no—
186#465—21no—
187C2×#108—21no—
188C2×#106C4×C10311yescharacteristic
189#417—21no—
190#413—21no—
191#349—21no—
192#349C22×C10312yes—
193#338C22×C10312yes—
194C2×#41—21no—
195C2×#41D4×C10311yescharacteristic
196#135—41no—
197#135—41no—
198C2×Q16C2×C4×C10311yescharacteristic
199C2×SD16—21no—
200C2×D8C2×C4×C10311yescharacteristic
201#131—41no—
202#131—41no—
203C2×M16—22no—
204C2×M16C2×C4×C10311yescharacteristic
205C2×M16D4×C10311yescharacteristic
206C2×M16C23×C10311yescharacteristic
207C22×C8C2×C4×C10311yescharacteristic
208C22×C8D4×C10311yescharacteristic
209C22×C8D4×C10311yescharacteristic
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—41no—
213#121—21no—
214#121—21no—
215#121—41no—
216#121—41no—
217#121—41no—
218C2×C4⋊C4—21no—
219M32—22no—
220M32—41no—
221C2×C16—41no—
222#108—41no—
223#108—41no—
224#106—21no—
225#106C2×C4×C10311yescharacteristic
226#106C2×C4×C10311yescharacteristic
227#103—21no—
228#103—21no—
229#102—21no—
230#102—21no—
231#101—41no—
232#100—41no—
233#41—41no—
234#41—41no—
235#41—42no—
236#41—42no—
237C2×Q8—21no—
238C2×Q8D8×C10311yescharacteristic
239C2×D4—21no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4D8×C10311yescharacteristic
244C2×D4SD16×C10311yescharacteristic
245C2×D4SD16×C10311yescharacteristic
246C22×C4—41no—
247C22×C4—41no—
248C22×C4C22⋊C4×C10311yescharacteristic
249C22×C4C22⋊C4×C10311yescharacteristic
250C22×C4C2×D4×C10311yescharacteristic
251Q16—41no—
252SD16—41no—
253SD16—41no—
254D8—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258M16—42no—
259M16—42no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—42no—
267C2×C8C22⋊C4×C10311yescharacteristic
268C2×C8C22⋊C4×C10311yescharacteristic
269C2×C8C22×C4×C10311yescharacteristic
270C2×C8C2×D4×C10311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C16—42no—
281C23—41no—
282C23#102×C10311yescharacteristic
283C23#102×C10311yescharacteristic
284C23C2×SD16×C10311yescharacteristic
285Q8—41no—
286Q8—41no—
287Q8—41no—
288D4—41no—
289D4—41no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—82no—
294D4—161no—
295D4—161no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—82no—
306C2×C4—161no—
307C2×C4#102×C10311yescharacteristic
308C2×C4#102×C10311yescharacteristic
309C2×C4C2×C22⋊C4×C10311yescharacteristic
310C2×C4C2×D8×C10311yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8—82no—
315C8#99×C10311yescharacteristic
316C8#99×C10311yescharacteristic
317C22—21no—
318C22—21no—
319C22—21no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22C2×#102×C10311yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4C2×#99×C10311yescharacteristic
334C4#421×C10311yescharacteristic
335C2—21no—
336C2—41no—
337C2—41no—
338C2—41no—
339C2—161no—
340C2C103×#151911yescharacteristic
subgroupG/H
center, socleC2×C103#1519
commutatorC2×C8C22×C4×C103
Frattini, cosocleC2×M16C23×C103
prime radicalC103×#3060C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C2×C4×C103 ◁ C2×#131×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2115C2semidirect
3. C103×#1813C2semidirect
4. C103×#1342C2semidirect
5. C103×#1341C2semidirect
164. #11872C103direct (N × H)
172. #2115C2×C103semidirect
173. #1813C2×C103semidirect
174. #1342C2×C103semidirect
175. #1341C2×C103semidirect
176. C103#11872direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#30602
C103×#21152
C103×#18132
C103×#13422
C103×#13412
#11872103