Finite Group Databasebeta

← C103×#10059 #39915334

Subgroups — C103×#10059 #39915334

Order 26368.

570 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#487×C103C211yesmaximal, characteristic
2C2×#477×C103C211yesmaximal, characteristic
3C103×#2546C211yesmaximal, characteristic
4C103×#1987C211yesmaximal, characteristic
5C2×#332×C103C211yesmaximal, characteristic
6C2×Q8⋊C8×C103C211yesmaximal, characteristic
7C103×#1279C211yesmaximal, characteristic
8C2×C4⋊Q8×C103—21no—
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×C4⋊Q8×C103C2211yescharacteristic
11C2×C4×Q8×C103C2211yescharacteristic
12#487×C103—22no—
13#487×C103—22no—
14#477×C103—22no—
15#477×C103—22no—
16C2×#107×C103—21no—
17C2×C4⋊C8×C103C2211yescharacteristic
18C2×C4⋊C8×C103C2211yescharacteristic
19C2×#103×C103—21no—
20C2×#103×C103—22no—
21C2×C4×C8×C103C2211yescharacteristic
22#398×C103—22no—
23#391×C103—21no—
24#389×C103—22no—
25C4×C4⋊C4×C103C2211yescharacteristic
26#340×C103—22no—
27#332×C103—22no—
28Q8⋊C8×C103—22no—
29C22×Q8×C103—21no—
30C22×Q8×C103—21no—
31C22×Q8×C103D411yescharacteristic
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×C103—42no—
43C4⋊Q8×C103—42no—
44C4⋊Q8×C103D412yes—
45C4×Q8×C103—21no—
46C4×Q8×C103—21no—
47C4×Q8×C103—21no—
48C4×Q8×C103—21no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—24no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103—21no—
54C2×C4⋊C4×C103D411yescharacteristic
55C2×C4⋊C4×C103D412yes—
56C2×C4⋊C4×C103D412yes—
57C2×C42×C103—21no—
58C2×C42×C103—21no—
59C2×C42×C103C2311yescharacteristic
60#107×C103—24no—
61C4⋊C8×C103—21no—
62C4⋊C8×C103—21no—
63C4⋊C8×C103—21no—
64C4⋊C8×C103D412yes—
65#103×C103—24no—
66#103×C103—28no—
67C4×C8×C103—21no—
68C4×C8×C103D412yes—
69#95×C103—24no—
70#95×C103—21no—
71C2×Q8×C103—21no—
72C2×Q8×C103—21no—
73C2×Q8×C103—22no—
74C2×Q8×C103—21no—
75C2×Q8×C103—21no—
76C2×Q8×C103—21no—
77C2×Q8×C103—44no—
78C2×Q8×C103—41no—
79C2×Q8×C103—41no—
80C2×Q8×C103—41no—
81C2×Q8×C103—41no—
82C2×Q8×C103—41no—
83C2×Q8×C103—41no—
84C2×Q8×C103—41no—
85C2×Q8×C103SD1612yes—
86C22×C4×C103—22no—
87C22×C4×C103—21no—
88C22×C4×C103—21no—
89C22×C4×C103—22no—
90C22×C4×C103—41no—
91C22×C4×C103C2×D411yescharacteristic
92C22×C4×C103C2×D411yescharacteristic
93C22×C4×C103C2×D411yescharacteristic
94C2×C8×C103—22no—
95C2×C8×C103—22no—
96C2×C8×C103—42no—
97C2×C8×C103—41no—
98C2×C8×C103—41no—
99C2×C8×C103—41no—
100C2×C8×C103—42no—
101C4⋊C4×C103—22no—
102C4⋊C4×C103—22no—
103C4⋊C4×C103—22no—
104C4⋊C4×C103—21no—
105C4⋊C4×C103—22no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—48no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103—41no—
111C4⋊C4×C103—41no—
112C4⋊C4×C103—41no—
113C4⋊C4×C103—41no—
114C4⋊C4×C103—41no—
115C4⋊C4×C103Q1614yes—
116C42×C103—41no—
117C42×C103—41no—
118C42×C103—41no—
119C42×C103—41no—
120C42×C103C2×D411yescharacteristic
121C42×C103C2×D411yescharacteristic
122C42×C103C2×D411yescharacteristic
123C42×C103#4111yescharacteristic
124C23×C103#12011yescharacteristic
125Q8×C103—22no—
126Q8×C103—22no—
127Q8×C103—44no—
128Q8×C103—41no—
129Q8×C103—41no—
130Q8×C103—82no—
131Q8×C103—81no—
132Q8×C103—81no—
133Q8×C103—81no—
134Q8×C103—81no—
135C2×C4×C103—22no—
136C2×C4×C103—22no—
137C2×C4×C103—24no—
138C2×C4×C103—41no—
139C2×C4×C103—42no—
140C2×C4×C103—41no—
141C2×C4×C103—42no—
142C2×C4×C103—41no—
143C2×C4×C103—42no—
144C2×C4×C103—42no—
145C2×C4×C103—42no—
146C2×C4×C103—42no—
147C2×C4×C103—42no—
148C2×C4×C103—82no—
149C2×C4×C103#12011yescharacteristic
150C2×C4×C103#12011yescharacteristic
151C2×C4×C103#12111yescharacteristic
152C2×C4×C103#12111yescharacteristic
153C2×C4×C103#12111yescharacteristic
154C2×C4×C103#12711yescharacteristic
155C2×C4×C103C2×SD1611yescharacteristic
156C2×C4×C103C2×Q1612yes—
157C2×C4×C103#13511yescharacteristic
158C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C103#13711yescharacteristic
160C2×C4×C103#13712yes—
161C8×C103—42no—
162C8×C103—42no—
163C8×C103—81no—
164C22×C103#39211yescharacteristic
165C22×C103#45011yescharacteristic
166C22×C103#45112yes—
167C22×C103#45211yescharacteristic
168C22×C103#45412yes—
169C4×C103—21no—
170C4×C103—21no—
171C4×C103—44no—
172C4×C103—42no—
173C4×C103—82no—
174C4×C103—81no—
175C4×C103—82no—
176C4×C103#44811yescharacteristic
177C4×C103#44911yescharacteristic
178C4×C103#46212yes—
179C4×C103#46511yescharacteristic
180C4×C103#46811yescharacteristic
181C4×C103#49411yescharacteristic
182C4×C103#49711yescharacteristic
183#10059C10311yesmaximal, characteristic, direct product factor, Sylow
184C2×C103#163612yes—
185C2×C103#163712yes—
186C2×C103#200011yescharacteristic
187C2×C103#200311yescharacteristic
188C2×C103#201611yescharacteristic
189C2×#487C2×C10311yescharacteristic
190C2×#477C2×C10311yescharacteristic
191#2546C2×C10311yescharacteristic
192#1987C2×C10311yescharacteristic
193C2×#332C2×C10311yescharacteristic
194C2×Q8⋊C8C2×C10311yescharacteristic
195#1279C2×C10311yescharacteristic
196C103#1005911yescharacteristic, direct product factor, Sylow
197C2×C4⋊Q8—21no—
198C2×C4⋊Q8C22×C10311yescharacteristic
199C2×C4⋊Q8C22×C10311yescharacteristic
200C2×C4×Q8C22×C10311yescharacteristic
201#487—22no—
202#487—22no—
203#477—22no—
204#477—22no—
205C2×#107—21no—
206C2×C4⋊C8C22×C10311yescharacteristic
207C2×C4⋊C8C22×C10311yescharacteristic
208C2×#103—21no—
209C2×#103—22no—
210C2×C4×C8C22×C10311yescharacteristic
211#398—22no—
212#391—21no—
213#389—22no—
214C4×C4⋊C4C22×C10311yescharacteristic
215#340—22no—
216#332—22no—
217Q8⋊C8—22no—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8D4×C10311yescharacteristic
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—42no—
232C4⋊Q8—42no—
233C4⋊Q8D4×C10312yes—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4D4×C10311yescharacteristic
244C2×C4⋊C4D4×C10312yes—
245C2×C4⋊C4D4×C10312yes—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42C23×C10311yescharacteristic
249#107—24no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8D4×C10312yes—
254#103—24no—
255#103—28no—
256C4×C8—21no—
257C4×C8D4×C10312yes—
258#95—24no—
259#95—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—44no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8SD16×C10312yes—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—41no—
280C22×C4C2×D4×C10311yescharacteristic
281C22×C4C2×D4×C10311yescharacteristic
282C22×C4C2×D4×C10311yescharacteristic
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—42no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—42no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—48no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4Q16×C10314yes—
305C42—41no—
306C42—41no—
307C42—41no—
308C42—41no—
309C42C2×D4×C10311yescharacteristic
310C42C2×D4×C10311yescharacteristic
311C42C2×D4×C10311yescharacteristic
312C42#41×C10311yescharacteristic
313C23#120×C10311yescharacteristic
314Q8—22no—
315Q8—22no—
316Q8—44no—
317Q8—41no—
318Q8—41no—
319Q8—82no—
320Q8—81no—
321Q8—81no—
322Q8—81no—
323Q8—81no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4#120×C10311yescharacteristic
339C2×C4#120×C10311yescharacteristic
340C2×C4#121×C10311yescharacteristic
341C2×C4#121×C10311yescharacteristic
342C2×C4#121×C10311yescharacteristic
343C2×C4#127×C10311yescharacteristic
344C2×C4C2×SD16×C10311yescharacteristic
345C2×C4C2×Q16×C10312yes—
346C2×C4#135×C10311yescharacteristic
347C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
348C2×C4#137×C10311yescharacteristic
349C2×C4#137×C10312yes—
350C8—42no—
351C8—42no—
352C8—81no—
353C22#392×C10311yescharacteristic
354C22#450×C10311yescharacteristic
355C22#451×C10312yes—
356C22#452×C10311yescharacteristic
357C22#454×C10312yes—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—81no—
364C4—82no—
365C4#448×C10311yescharacteristic
366C4#449×C10311yescharacteristic
367C4#462×C10312yes—
368C4#465×C10311yescharacteristic
369C4#468×C10311yescharacteristic
370C4#494×C10311yescharacteristic
371C4#497×C10311yescharacteristic
372C2C103×#163612yes—
373C2C103×#163712yes—
374C2C103×#200011yescharacteristic
375C2C103×#200311yescharacteristic
376C2C103×#201611yescharacteristic
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
183. #10059C103direct (N × H)
196. C103#10059direct (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×#477×C1032
C103×#25462
C103×#19872
C2×#332×C1032
C2×Q8⋊C8×C1032
C103×#12792
#10059103