Finite Group Databasebeta

← C103×#9073 #39914348

Subgroups — C103×#9073 #39914348

Order 26368.

610 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#431×C103C211yesmaximal, characteristic
2C4×C22⋊Q8×C103C211yesmaximal, characteristic
3C103×#1797C211yesmaximal, characteristic
4C2×Q8⋊C8×C103C212yesmaximal, complemented
5C103×#1279C212yesmaximal, complemented
6C2×C22⋊Q8×C103C411yescharacteristic
7C2×C4×Q8×C103C2211yescharacteristic
8C22×C42×C103C2211yescharacteristic
9#431×C103—24no—
10C2×C4⋊C8×C103—21no—
11C2×C4⋊C8×C103C2212yes—
12C2×C22⋊C8×C103—21no—
13C2×C22⋊C8×C103—21no—
14C2×C4×C8×C103C2212yes—
15#391×C103C411yescharacteristic
16#389×C103C411yescharacteristic
17#387×C103—21no—
18#385×C103—21no—
19#380×C103C411yescharacteristic
20C4×C4⋊C4×C103—21no—
21C4×C4⋊C4×C103C2211yescharacteristic
22C4×C22⋊C4×C103—21no—
23#336×C103—21no—
24Q8⋊C8×C103—24no—
25C22×Q8×C103C2×C411yescharacteristic
26C23×C4×C103C2×C411yescharacteristic
27C23×C4×C103D411yescharacteristic
28C23×C4×C103D411yescharacteristic
29C22×C8×C103—22no—
30C22×C8×C103—22no—
31C22⋊Q8×C103—22no—
32C22⋊Q8×C103C814yescomplemented
33C4×Q8×C103—22no—
34C4×Q8×C103—22no—
35C2×C4⋊C4×C103—21no—
36C2×C4⋊C4×C103—21no—
37C2×C4⋊C4×C103—21no—
38C2×C4⋊C4×C103C2×C411yescharacteristic
39C2×C4⋊C4×C103C2×C411yescharacteristic
40C2×C4⋊C4×C103C2×C411yescharacteristic
41C2×C22⋊C4×C103—21no—
42C2×C22⋊C4×C103—21no—
43C2×C42×C103—22no—
44C2×C42×C103—22no—
45C2×C42×C103—21no—
46C2×C42×C103—21no—
47C2×C42×C103C2×C411yescharacteristic
48C2×C42×C103D411yescharacteristic
49C2×C42×C103D411yescharacteristic
50C2×C42×C103C2311yescharacteristic
51C4⋊C8×C103—24no—
52C4⋊C8×C103—22no—
53C4⋊C8×C103—22no—
54C22⋊C8×C103—24no—
55C22⋊C8×C103—42no—
56C4×C8×C103—22no—
57C4×C8×C103D414yes—
58#95×C103—21no—
59#95×C103—21no—
60#95×C103—21no—
61#95×C103—21no—
62#95×C103—21no—
63C24×C103C22⋊C411yescharacteristic
64C2×Q8×C103—21no—
65C2×Q8×C103—22no—
66C2×Q8×C103—22no—
67C2×Q8×C103C2×C812yes—
68C22×C4×C103—22no—
69C22×C4×C103—22no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103—21no—
73C22×C4×C103—22no—
74C22×C4×C103—21no—
75C22×C4×C103—21no—
76C22×C4×C103—21no—
77C22×C4×C103—22no—
78C22×C4×C103—21no—
79C22×C4×C103—21no—
80C22×C4×C103—41no—
81C22×C4×C103—41no—
82C22×C4×C103C22⋊C411yescharacteristic
83C22×C4×C103C22⋊C411yescharacteristic
84C22×C4×C103C22⋊C411yescharacteristic
85C22×C4×C103C2×C812yes—
86C22×C4×C103M1612yes—
87C22×C4×C103C22×C411yescharacteristic
88C22×C4×C103C2×D411yescharacteristic
89C22×C4×C103C2×D411yescharacteristic
90C2×C8×C103—24no—
91C2×C8×C103—42no—
92C2×C8×C103—42no—
93C2×C8×C103—42no—
94C2×C8×C103—42no—
95C2×C8×C103—42no—
96C4⋊C4×C103—24no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—22no—
99C4⋊C4×C103—22no—
100C4⋊C4×C103—42no—
101C4⋊C4×C103—41no—
102C4⋊C4×C103—41no—
103C4⋊C4×C103C2×C812yes—
104C22⋊C4×C103—24no—
105C22⋊C4×C103—42no—
106C42×C103—22no—
107C42×C103—21no—
108C42×C103—22no—
109C42×C103—21no—
110C42×C103—42no—
111C42×C103—41no—
112C42×C103—41no—
113C42×C103C2×D412yes—
114C42×C103#4112yes—
115C23×C103—21no—
116C23×C103—21no—
117C23×C103—21no—
118C23×C103—21no—
119C23×C103—21no—
120C23×C103—21no—
121C23×C103C22⋊C812yes—
122C23×C103C2×C22⋊C411yescharacteristic
123Q8×C103—24no—
124Q8×C103—42no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—24no—
130C2×C4×C103—24no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—22no—
134C2×C4×C103—22no—
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103—21no—
139C2×C4×C103—42no—
140C2×C4×C103—42no—
141C2×C4×C103—41no—
142C2×C4×C103—41no—
143C2×C4×C103—41no—
144C2×C4×C103—41no—
145C2×C4×C103—42no—
146C2×C4×C103—42no—
147C2×C4×C103—41no—
148C2×C4×C103—41no—
149C2×C4×C103—41no—
150C2×C4×C103—41no—
151C2×C4×C103—41no—
152C2×C4×C103—41no—
153C2×C4×C103C22⋊C812yes—
154C2×C4×C103C4×D412yes—
155C2×C4×C103#12011yescharacteristic
156C2×C4×C103#12112yes—
157C2×C4×C103#12311yescharacteristic
158C2×C4×C103C22×C811yescharacteristic
159C2×C4×C103C2×M1611yescharacteristic
160C2×C4×C103#13112yes—
161C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C103#13712yes—
163C2×C4×C103#13711yescharacteristic
164C8×C103—44no—
165C8×C103—82no—
166C22×C103—22no—
167C22×C103—22no—
168C22×C103—22no—
169C22×C103—41no—
170C22×C103—41no—
171C22×C103—41no—
172C22×C103—41no—
173C22×C103#38611yescharacteristic
174C22×C103C2×C22⋊C811yescharacteristic
175C22×C103#40811yescharacteristic
176C22×C103#41711yescharacteristic
177C22×C103#41911yescharacteristic
178C22×C103#42111yescharacteristic
179C22×C103#42111yescharacteristic
180C4×C103—22no—
181C4×C103—21no—
182C4×C103—21no—
183C4×C103—42no—
184C4×C103—41no—
185C4×C103—41no—
186C4×C103—42no—
187C4×C103—81no—
188C4×C103—81no—
189C4×C103C8×D412yes—
190C4×C103#43512yes—
191C4×C103#46812yes—
192C4×C103#47012yes—
193#9073C10311yesmaximal, characteristic, direct product factor, Sylow
194C2×C103—42no—
195C2×C103#147711yescharacteristic
196C2×C103#147911yescharacteristic
197C2×C103#149511yescharacteristic
198C2×C103#149711yescharacteristic
199C2×C103#186911yescharacteristic
200C2×C103#189411yescharacteristic
201C2×C103#189711yescharacteristic
202C2×#431C2×C10311yescharacteristic
203C4×C22⋊Q8C2×C10311yescharacteristic
204#1797C2×C10311yescharacteristic
205C2×Q8⋊C8C2×C10312yescomplemented
206#1279C2×C10312yescomplemented
207C103#907311yescharacteristic, direct product factor, Sylow
208C2×C22⋊Q8C4×C10311yescharacteristic
209C2×C4×Q8C22×C10311yescharacteristic
210C22×C42C22×C10311yescharacteristic
211#431—24no—
212C2×C4⋊C8—21no—
213C2×C4⋊C8C22×C10312yes—
214C2×C22⋊C8—21no—
215C2×C22⋊C8—21no—
216C2×C4×C8C22×C10312yes—
217#391C4×C10311yescharacteristic
218#389C4×C10311yescharacteristic
219#387—21no—
220#385—21no—
221#380C4×C10311yescharacteristic
222C4×C4⋊C4—21no—
223C4×C4⋊C4C22×C10311yescharacteristic
224C4×C22⋊C4—21no—
225#336—21no—
226Q8⋊C8—24no—
227C22×Q8C2×C4×C10311yescharacteristic
228C23×C4C2×C4×C10311yescharacteristic
229C23×C4D4×C10311yescharacteristic
230C23×C4D4×C10311yescharacteristic
231C22×C8—22no—
232C22×C8—22no—
233C22⋊Q8—22no—
234C22⋊Q8C8×C10314yescomplemented
235C4×Q8—22no—
236C4×Q8—22no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×C4×C10311yescharacteristic
241C2×C4⋊C4C2×C4×C10311yescharacteristic
242C2×C4⋊C4C2×C4×C10311yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C2×C4×C10311yescharacteristic
250C2×C42D4×C10311yescharacteristic
251C2×C42D4×C10311yescharacteristic
252C2×C42C23×C10311yescharacteristic
253C4⋊C8—24no—
254C4⋊C8—22no—
255C4⋊C8—22no—
256C22⋊C8—24no—
257C22⋊C8—42no—
258C4×C8—22no—
259C4×C8D4×C10314yes—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265C24C22⋊C4×C10311yescharacteristic
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8C2×C8×C10312yes—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C22⋊C4×C10311yescharacteristic
285C22×C4C22⋊C4×C10311yescharacteristic
286C22×C4C22⋊C4×C10311yescharacteristic
287C22×C4C2×C8×C10312yes—
288C22×C4M16×C10312yes—
289C22×C4C22×C4×C10311yescharacteristic
290C22×C4C2×D4×C10311yescharacteristic
291C22×C4C2×D4×C10311yescharacteristic
292C2×C8—24no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C4⋊C4—24no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4C2×C8×C10312yes—
306C22⋊C4—24no—
307C22⋊C4—42no—
308C42—22no—
309C42—21no—
310C42—22no—
311C42—21no—
312C42—42no—
313C42—41no—
314C42—41no—
315C42C2×D4×C10312yes—
316C42#41×C10312yes—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23C22⋊C8×C10312yes—
324C23C2×C22⋊C4×C10311yescharacteristic
325Q8—24no—
326Q8—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4C22⋊C8×C10312yes—
356C2×C4C4×D4×C10312yes—
357C2×C4#120×C10311yescharacteristic
358C2×C4#121×C10312yes—
359C2×C4#123×C10311yescharacteristic
360C2×C4C22×C8×C10311yescharacteristic
361C2×C4C2×M16×C10311yescharacteristic
362C2×C4#131×C10312yes—
363C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
364C2×C4#137×C10312yes—
365C2×C4#137×C10311yescharacteristic
366C8—44no—
367C8—82no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22#386×C10311yescharacteristic
376C22C2×C22⋊C8×C10311yescharacteristic
377C22#408×C10311yescharacteristic
378C22#417×C10311yescharacteristic
379C22#419×C10311yescharacteristic
380C22#421×C10311yescharacteristic
381C22#421×C10311yescharacteristic
382C4—22no—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—42no—
387C4—41no—
388C4—41no—
389C4—81no—
390C4—81no—
391C4C8×D4×C10312yes—
392C4#435×C10312yes—
393C4#468×C10312yes—
394C4#470×C10312yes—
395C2—42no—
396C2C103×#147711yescharacteristic
397C2C103×#147911yescharacteristic
398C2C103×#149511yescharacteristic
399C2C103×#149711yescharacteristic
400C2C103×#186911yescharacteristic
401C2C103×#189411yescharacteristic
402C2C103×#189711yescharacteristic
subgroupG/H
centerC22×C4×C103C2×D4
commutatorC2×C4C22×C8×C103
Frattini, cosocleC2×C42C23×C103
socleC23×C103C2×C22⋊C4
prime radicalC24×C103C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊C8×C103C2semidirect
5. C103×#1279C2semidirect
32. C22⋊Q8×C103C8semidirect
193. #9073C103direct (N × H)
205. C2×Q8⋊C8C2×C103semidirect
206. #1279C2×C103semidirect
207. C103#9073direct (N × H)
234. C22⋊Q8C8×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#431×C1032
C4×C22⋊Q8×C1032
C103×#17972
C2×Q8⋊C8×C1032
C103×#12792
#9073103