Finite Group Databasebeta

← C103×#19262 #39924537

Subgroups — C103×#19262 #39924537

Order 26368.

602 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×#3170C211yesmaximal, characteristic
2C103×#3078C212yesmaximal
3C2×C8×Q8×C103C211yesmaximal, characteristic
4C103×#1684C214yesmaximal, complemented
5C103×#1676C212yesmaximal, complemented
6C103×#1670C212yesmaximal, complemented
7C103×#1567C211yesmaximal, characteristic
8C103×#1550C212yesmaximal
9#533×C103C2212yes—
10C2×C4×Q8×C103C2211yescharacteristic
11#500×C103C2211yescharacteristic
12#494×C103C2211yescharacteristic
13#487×C103C2212yes—
14#479×C103—24no—
15#477×C103C2214yes—
16#475×C103C2214yes—
17#467×C103—21no—
18#467×C103—21no—
19C8×Q8×C103—21no—
20C8×Q8×C103—21no—
21C8×Q8×C103C2212yes—
22C8×Q8×C103C2212yes—
23C4×Q16×C103—21no—
24C4×Q16×C103—21no—
25#428×C103—22no—
26#423×C103C2212yes—
27C2×C4⋊C8×C103—21no—
28C2×C4⋊C8×C103C2211yescharacteristic
29#419×C103—22no—
30C2×C4×C8×C103—21no—
31C2×C4×C8×C103C2211yescharacteristic
32#335×C103C2212yes—
33#335×C103C2212yes—
34#333×C103C2214yes—
35#332×C103C2214yes—
36C22×Q8×C103D411yescharacteristic
37C2×Q16×C103—21no—
38C2×Q16×C103—21no—
39C2×M16×C103—22no—
40C22×C8×C103—21no—
41C22×C8×C103D411yescharacteristic
42C22×C8×C103D411yescharacteristic
43C4⋊Q8×C103C2312yes—
44C4⋊Q8×C103C2312yes—
45#125×C103—22no—
46C22⋊Q8×C103—22no—
47C22⋊Q8×C103—22no—
48C4×Q8×C103—21no—
49C4×Q8×C103—21no—
50C4×Q8×C103—22no—
51C4×Q8×C103—22no—
52C4×Q8×C103D412yes—
53C4×Q8×C103C2312yes—
54#117×C103—22no—
55C2×C4⋊C4×C103—21no—
56C2×C4⋊C4×C103D411yescharacteristic
57C2×C42×C103—21no—
58C2×C42×C103C2311yescharacteristic
59#107×C103—21no—
60#107×C103—21no—
61#107×C103—24no—
62#106×C103—24no—
63C4⋊C8×C103—22no—
64C4⋊C8×C103—22no—
65C4⋊C8×C103—21no—
66C4⋊C8×C103—22no—
67C4⋊C8×C103C2312yes—
68C4⋊C8×C103C2314yes—
69#103×C103—24no—
70#103×C103—24no—
71#103×C103—22no—
72#103×C103—22no—
73C4×C8×C103—22no—
74C4×C8×C103—22no—
75C4×C8×C103D411yescharacteristic
76C4×C8×C103D411yescharacteristic
77C4×C8×C103C2311yescharacteristic
78C4×C8×C103C2311yescharacteristic
79C2×Q8×C103—21no—
80C2×Q8×C103—22no—
81C2×Q8×C103—22no—
82C2×Q8×C103—22no—
83C2×Q8×C103Q1614yescomplemented
84C2×Q8×C103C2×D412yes—
85C22×C4×C103—21no—
86C22×C4×C103—21no—
87C22×C4×C103C2×D411yescharacteristic
88C22×C4×C103C2×D411yescharacteristic
89C22×C4×C103#4111yescharacteristic
90Q16×C103—42no—
91Q16×C103—42no—
92M16×C103—44no—
93C2×C8×C103—22no—
94C2×C8×C103—22no—
95C2×C8×C103—24no—
96C2×C8×C103—41no—
97C2×C8×C103—42no—
98C2×C8×C103C2×D411yescharacteristic
99C2×C8×C103C2×D411yescharacteristic
100C2×C8×C103C2×D411yescharacteristic
101C2×C8×C103C2×D411yescharacteristic
102C4⋊C4×C103—22no—
103C4⋊C4×C103—21no—
104C4⋊C4×C103—22no—
105C4⋊C4×C103—22no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—22no—
109C4⋊C4×C103—42no—
110C4⋊C4×C103—42no—
111C4⋊C4×C103C2×D412yes—
112C22⋊C4×C103—42no—
113C42×C103—22no—
114C42×C103—22no—
115C42×C103—42no—
116C42×C103C2×D411yescharacteristic
117C42×C103C2×D411yescharacteristic
118C42×C103#4111yescharacteristic
119C42×C103C2411yescharacteristic
120C23×C103#12111yescharacteristic
121Q8×C103—22no—
122Q8×C103—24no—
123Q8×C103—42no—
124Q8×C103—42no—
125Q8×C103—82no—
126Q8×C103C2×Q1614yes—
127C2×C4×C103—22no—
128C2×C4×C103—24no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—22no—
132C2×C4×C103—41no—
133C2×C4×C103—42no—
134C2×C4×C103—42no—
135C2×C4×C103—42no—
136C2×C4×C103#12111yescharacteristic
137C2×C4×C103#12111yescharacteristic
138C2×C4×C103#12111yescharacteristic
139C2×C4×C103C2×Q1612yes—
140C2×C4×C103#13512yes—
141C2×C4×C103C22×D411yescharacteristic
142C2×C4×C103C22×D411yescharacteristic
143C2×C4×C103C2×#4111yescharacteristic
144C8×C103—21no—
145C8×C103—21no—
146C8×C103—21no—
147C8×C103—44no—
148C8×C103—42no—
149C8×C103#13712yes—
150C22×C103—21no—
151C22×C103—21no—
152C22×C103#46712yes—
153C22×C103C2×#12111yescharacteristic
154C4×C103—21no—
155C4×C103—24no—
156C4×C103—21no—
157C4×C103—21no—
158C4×C103—42no—
159C4×C103—82no—
160C4×C103—82no—
161C4×C103#46712yes—
162C4×C103C22×Q1611yescharacteristic
163C4×C103C2×#13511yescharacteristic
164C4×C103C2×#13711yescharacteristic
165C4×C103#57511yescharacteristic
166#19262C10311yesmaximal, characteristic, direct product factor, Sylow
167C2×C103—22no—
168C2×C103#303711yescharacteristic
169C2×C103C2×#46711yescharacteristic
170C2×C103#306711yescharacteristic
171#3170C2×C10311yescharacteristic
172#3078C2×C10312yes—
173C2×C8×Q8C2×C10311yescharacteristic
174#1684C2×C10314yescomplemented
175#1676C2×C10312yescomplemented
176#1670C2×C10312yescomplemented
177#1567C2×C10311yescharacteristic
178#1550C2×C10312yes—
179C103#1926211yescharacteristic, direct product factor, Sylow
180#533C22×C10312yes—
181C2×C4×Q8C22×C10311yescharacteristic
182#500C22×C10311yescharacteristic
183#494C22×C10311yescharacteristic
184#487C22×C10312yes—
185#479—24no—
186#477C22×C10314yes—
187#475C22×C10314yes—
188#467—21no—
189#467—21no—
190C8×Q8—21no—
191C8×Q8—21no—
192C8×Q8C22×C10312yes—
193C8×Q8C22×C10312yes—
194C4×Q16—21no—
195C4×Q16—21no—
196#428—22no—
197#423C22×C10312yes—
198C2×C4⋊C8—21no—
199C2×C4⋊C8C22×C10311yescharacteristic
200#419—22no—
201C2×C4×C8—21no—
202C2×C4×C8C22×C10311yescharacteristic
203#335C22×C10312yes—
204#335C22×C10312yes—
205#333C22×C10314yes—
206#332C22×C10314yes—
207C22×Q8D4×C10311yescharacteristic
208C2×Q16—21no—
209C2×Q16—21no—
210C2×M16—22no—
211C22×C8—21no—
212C22×C8D4×C10311yescharacteristic
213C22×C8D4×C10311yescharacteristic
214C4⋊Q8C23×C10312yes—
215C4⋊Q8C23×C10312yes—
216#125—22no—
217C22⋊Q8—22no—
218C22⋊Q8—22no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—22no—
222C4×Q8—22no—
223C4×Q8D4×C10312yes—
224C4×Q8C23×C10312yes—
225#117—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C10311yescharacteristic
228C2×C42—21no—
229C2×C42C23×C10311yescharacteristic
230#107—21no—
231#107—21no—
232#107—24no—
233#106—24no—
234C4⋊C8—22no—
235C4⋊C8—22no—
236C4⋊C8—21no—
237C4⋊C8—22no—
238C4⋊C8C23×C10312yes—
239C4⋊C8C23×C10314yes—
240#103—24no—
241#103—24no—
242#103—22no—
243#103—22no—
244C4×C8—22no—
245C4×C8—22no—
246C4×C8D4×C10311yescharacteristic
247C4×C8D4×C10311yescharacteristic
248C4×C8C23×C10311yescharacteristic
249C4×C8C23×C10311yescharacteristic
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8Q16×C10314yescomplemented
255C2×Q8C2×D4×C10312yes—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4C2×D4×C10311yescharacteristic
259C22×C4C2×D4×C10311yescharacteristic
260C22×C4#41×C10311yescharacteristic
261Q16—42no—
262Q16—42no—
263M16—44no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—24no—
267C2×C8—41no—
268C2×C8—42no—
269C2×C8C2×D4×C10311yescharacteristic
270C2×C8C2×D4×C10311yescharacteristic
271C2×C8C2×D4×C10311yescharacteristic
272C2×C8C2×D4×C10311yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4C2×D4×C10312yes—
283C22⋊C4—42no—
284C42—22no—
285C42—22no—
286C42—42no—
287C42C2×D4×C10311yescharacteristic
288C42C2×D4×C10311yescharacteristic
289C42#41×C10311yescharacteristic
290C42C24×C10311yescharacteristic
291C23#121×C10311yescharacteristic
292Q8—24no—
293Q8—22no—
294Q8—42no—
295Q8—42no—
296Q8—82no—
297Q8C2×Q16×C10314yes—
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4#121×C10311yescharacteristic
308C2×C4#121×C10311yescharacteristic
309C2×C4#121×C10311yescharacteristic
310C2×C4C2×Q16×C10312yes—
311C2×C4#135×C10312yes—
312C2×C4C22×D4×C10311yescharacteristic
313C2×C4C22×D4×C10311yescharacteristic
314C2×C4C2×#41×C10311yescharacteristic
315C8—21no—
316C8—21no—
317C8—21no—
318C8—44no—
319C8—42no—
320C8#137×C10312yes—
321C22—21no—
322C22—21no—
323C22#467×C10312yes—
324C22C2×#121×C10311yescharacteristic
325C4—21no—
326C4—24no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—82no—
331C4—82no—
332C4#467×C10312yes—
333C4C22×Q16×C10311yescharacteristic
334C4C2×#135×C10311yescharacteristic
335C4C2×#137×C10311yescharacteristic
336C4#575×C10311yescharacteristic
337C2—22no—
338C2C103×#303711yescharacteristic
339C2C2×#467×C10311yescharacteristic
340C2C103×#306711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC23×C103#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1684C2semidirect
5. C103×#1676C2semidirect
6. C103×#1670C2semidirect
83. C2×Q8×C103Q16semidirect
166. #19262C103direct (N × H)
174. #1684C2×C103semidirect
175. #1676C2×C103semidirect
176. #1670C2×C103semidirect
179. C103#19262direct (N × H)
254. C2×Q8Q16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31702
C103×#30782
C2×C8×Q8×C1032
C103×#16842
C103×#16762
C103×#16702
C103×#15672
C103×#15502
#19262103