Finite Group Databasebeta

← C103×#10073 #39915348

Subgroups — C103×#10073 #39915348

Order 26368.

566 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#487×C103C211yesmaximal, characteristic
2C2×#475×C103C211yesmaximal, characteristic
3C103×#2567C211yesmaximal, characteristic
4C103×#1981C211yesmaximal, characteristic
5C2×#333×C103C211yesmaximal, characteristic
6C2×Q8⋊C8×C103C211yesmaximal, characteristic
7C103×#1279C211yesmaximal, characteristic
8C2×C4⋊Q8×C103C2211yescharacteristic
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×C4×Q8×C103C2211yescharacteristic
11#487×C103—22no—
12#487×C103—22no—
13#475×C103—22no—
14#475×C103—22no—
15C2×#106×C103—21no—
16C2×C4⋊C8×C103C2211yescharacteristic
17C2×C4⋊C8×C103C2211yescharacteristic
18C2×#103×C103—21no—
19C2×#103×C103—22no—
20C2×#103×C103—22no—
21C2×C4×C8×C103C2211yescharacteristic
22#395×C103—22no—
23#391×C103—21no—
24#389×C103—22no—
25#384×C103—21no—
26C4×C4⋊C4×C103C2211yescharacteristic
27#333×C103—22no—
28Q8⋊C8×C103—22no—
29C22×Q8×C103—21no—
30C22×Q8×C103D411yescharacteristic
31C22×Q8×C103D412yes—
32C22×C8×C103—21no—
33C22×C8×C103—21no—
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×C103D412yes—
43C4×Q8×C103—21no—
44C4×Q8×C103—21no—
45C4×Q8×C103—21no—
46C4×Q8×C103—21no—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103—21no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103—24no—
53C2×C4⋊C4×C103D411yescharacteristic
54C2×C4⋊C4×C103D412yes—
55C2×C42×C103—21no—
56C2×C42×C103—21no—
57C2×C42×C103C2311yescharacteristic
58#106×C103—24no—
59C4⋊C8×C103—21no—
60C4⋊C8×C103—21no—
61C4⋊C8×C103—21no—
62C4⋊C8×C103D412yes—
63#103×C103—24no—
64#103×C103—28no—
65#103×C103—44no—
66C4×C8×C103—21no—
67C4×C8×C103D412yes—
68#95×C103—24no—
69#95×C103—21no—
70C2×Q8×C103—21no—
71C2×Q8×C103—21no—
72C2×Q8×C103—22no—
73C2×Q8×C103—21no—
74C2×Q8×C103—22no—
75C2×Q8×C103—22no—
76C2×Q8×C103—21no—
77C2×Q8×C103—21no—
78C2×Q8×C103—44no—
79C2×Q8×C103—41no—
80C2×Q8×C103—42no—
81C2×Q8×C103—42no—
82C2×Q8×C103Q1612yes—
83C22×C4×C103—21no—
84C22×C4×C103—22no—
85C22×C4×C103—22no—
86C22×C4×C103—21no—
87C22×C4×C103—41no—
88C22×C4×C103C2×D411yescharacteristic
89C22×C4×C103C2×D411yescharacteristic
90C22×C4×C103C2×D411yescharacteristic
91C2×C8×C103—22no—
92C2×C8×C103—22no—
93C2×C8×C103—42no—
94C2×C8×C103—41no—
95C2×C8×C103—41no—
96C2×C8×C103—41no—
97C2×C8×C103—42no—
98C4⋊C4×C103—22no—
99C4⋊C4×C103—22no—
100C4⋊C4×C103—22no—
101C4⋊C4×C103—21no—
102C4⋊C4×C103—21no—
103C4⋊C4×C103—41no—
104C4⋊C4×C103—41no—
105C4⋊C4×C103—41no—
106C4⋊C4×C103—41no—
107C4⋊C4×C103—41no—
108C4⋊C4×C103—41no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103—41no—
111C4⋊C4×C103—84no—
112C4⋊C4×C103SD1614yes—
113C42×C103—41no—
114C42×C103—41no—
115C42×C103—41no—
116C42×C103—41no—
117C42×C103C2×D411yescharacteristic
118C42×C103C2×D411yescharacteristic
119C42×C103C2×D411yescharacteristic
120C42×C103#4111yescharacteristic
121C23×C103#12011yescharacteristic
122Q8×C103—22no—
123Q8×C103—22no—
124Q8×C103—44no—
125Q8×C103—41no—
126Q8×C103—41no—
127Q8×C103—44no—
128Q8×C103—82no—
129Q8×C103—81no—
130Q8×C103—81no—
131C2×C4×C103—22no—
132C2×C4×C103—24no—
133C2×C4×C103—22no—
134C2×C4×C103—41no—
135C2×C4×C103—42no—
136C2×C4×C103—41no—
137C2×C4×C103—42no—
138C2×C4×C103—41no—
139C2×C4×C103—42no—
140C2×C4×C103—42no—
141C2×C4×C103—42no—
142C2×C4×C103—44no—
143C2×C4×C103—82no—
144C2×C4×C103#12011yescharacteristic
145C2×C4×C103#12011yescharacteristic
146C2×C4×C103#12111yescharacteristic
147C2×C4×C103#12111yescharacteristic
148C2×C4×C103#12111yescharacteristic
149C2×C4×C103#12711yescharacteristic
150C2×C4×C103C2×SD1612yes—
151C2×C4×C103C2×Q1611yescharacteristic
152C2×C4×C103#13511yescharacteristic
153C2×C4×C103#13711yescharacteristic
154C2×C4×C103#13711yescharacteristic
155C2×C4×C103#13712yes—
156C8×C103—42no—
157C8×C103—42no—
158C8×C103—81no—
159C22×C103#39211yescharacteristic
160C22×C103#44812yes—
161C22×C103#45111yescharacteristic
162C22×C103#45211yescharacteristic
163C22×C103#45512yes—
164C4×C103—21no—
165C4×C103—21no—
166C4×C103—44no—
167C4×C103—42no—
168C4×C103—81no—
169C4×C103—82no—
170C4×C103—82no—
171C4×C103#45111yescharacteristic
172C4×C103#45211yescharacteristic
173C4×C103#46112yes—
174C4×C103#46711yescharacteristic
175C4×C103#47011yescharacteristic
176C4×C103#49211yescharacteristic
177C4×C103#49711yescharacteristic
178#10073C10311yesmaximal, characteristic, direct product factor, Sylow
179C2×C103#164312yes—
180C2×C103#164512yes—
181C2×C103#200111yescharacteristic
182C2×C103#200411yescharacteristic
183C2×C103#201311yescharacteristic
184C2×#487C2×C10311yescharacteristic
185C2×#475C2×C10311yescharacteristic
186#2567C2×C10311yescharacteristic
187#1981C2×C10311yescharacteristic
188C2×#333C2×C10311yescharacteristic
189C2×Q8⋊C8C2×C10311yescharacteristic
190#1279C2×C10311yescharacteristic
191C103#1007311yescharacteristic, direct product factor, Sylow
192C2×C4⋊Q8C22×C10311yescharacteristic
193C2×C4⋊Q8C22×C10311yescharacteristic
194C2×C4×Q8C22×C10311yescharacteristic
195#487—22no—
196#487—22no—
197#475—22no—
198#475—22no—
199C2×#106—21no—
200C2×C4⋊C8C22×C10311yescharacteristic
201C2×C4⋊C8C22×C10311yescharacteristic
202C2×#103—21no—
203C2×#103—22no—
204C2×#103—22no—
205C2×C4×C8C22×C10311yescharacteristic
206#395—22no—
207#391—21no—
208#389—22no—
209#384—21no—
210C4×C4⋊C4C22×C10311yescharacteristic
211#333—22no—
212Q8⋊C8—22no—
213C22×Q8—21no—
214C22×Q8D4×C10311yescharacteristic
215C22×Q8D4×C10312yes—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8D4×C10312yes—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4D4×C10311yescharacteristic
238C2×C4⋊C4D4×C10312yes—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42C23×C10311yescharacteristic
242#106—24no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8D4×C10312yes—
247#103—24no—
248#103—28no—
249#103—44no—
250C4×C8—21no—
251C4×C8D4×C10312yes—
252#95—24no—
253#95—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—44no—
263C2×Q8—41no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8Q16×C10312yes—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4C2×D4×C10311yescharacteristic
273C22×C4C2×D4×C10311yescharacteristic
274C22×C4C2×D4×C10311yescharacteristic
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—42no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—42no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—84no—
296C4⋊C4SD16×C10314yes—
297C42—41no—
298C42—41no—
299C42—41no—
300C42—41no—
301C42C2×D4×C10311yescharacteristic
302C42C2×D4×C10311yescharacteristic
303C42C2×D4×C10311yescharacteristic
304C42#41×C10311yescharacteristic
305C23#120×C10311yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—44no—
309Q8—41no—
310Q8—41no—
311Q8—44no—
312Q8—82no—
313Q8—81no—
314Q8—81no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—44no—
327C2×C4—82no—
328C2×C4#120×C10311yescharacteristic
329C2×C4#120×C10311yescharacteristic
330C2×C4#121×C10311yescharacteristic
331C2×C4#121×C10311yescharacteristic
332C2×C4#121×C10311yescharacteristic
333C2×C4#127×C10311yescharacteristic
334C2×C4C2×SD16×C10312yes—
335C2×C4C2×Q16×C10311yescharacteristic
336C2×C4#135×C10311yescharacteristic
337C2×C4#137×C10311yescharacteristic
338C2×C4#137×C10311yescharacteristic
339C2×C4#137×C10312yes—
340C8—42no—
341C8—42no—
342C8—81no—
343C22#392×C10311yescharacteristic
344C22#448×C10312yes—
345C22#451×C10311yescharacteristic
346C22#452×C10311yescharacteristic
347C22#455×C10312yes—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—44no—
352C4—82no—
353C4—81no—
354C4—82no—
355C4#451×C10311yescharacteristic
356C4#452×C10311yescharacteristic
357C4#461×C10312yes—
358C4#467×C10311yescharacteristic
359C4#470×C10311yescharacteristic
360C4#492×C10311yescharacteristic
361C4#497×C10311yescharacteristic
362C2C103×#164312yes—
363C2C103×#164512yes—
364C2C103×#200111yescharacteristic
365C2C103×#200411yescharacteristic
366C2C103×#201311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103#120
commutator, Frattini, cosocleC2×C42C23×C103
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
178. #10073C103direct (N × H)
191. C103#10073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#487×C1032
C2×#475×C1032
C103×#25672
C103×#19812
C2×#333×C1032
C2×Q8⋊C8×C1032
C103×#12792
#10073103