Finite Group Databasebeta

← C103×#19515 #39924790

Subgroups — C103×#19515 #39924790

Order 26368.

576 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3235C211yesmaximal, characteristic
2C103×#3230C211yesmaximal, characteristic, complemented
3C103×#3227C211yesmaximal, characteristic
4C103×#2981C211yesmaximal, characteristic
5C103×#1703C212yesmaximal, complemented
6C103×#1695C212yesmaximal, complemented
7C103×#1683C212yesmaximal, complemented
8C103×#1675C212yesmaximal, complemented
9C103×#1572C211yesmaximal, characteristic, complemented
10C103×#1558C211yesmaximal, characteristic, complemented
11C103×#1554C211yesmaximal, characteristic, complemented
12#533×C103C2211yescharacteristic
13#532×C103C2211yescharacteristic
14C2×C4⋊Q8×C103C2211yescharacteristic
15#501×C103—21no—
16#500×C103C2211yescharacteristic
17#500×C103C2211yescharacteristic
18#498×C103—21no—
19#490×C103—21no—
20#487×C103C2211yescharacteristic
21#487×C103C2211yescharacteristic
22#486×C103—21no—
23#484×C103—22no—
24#482×C103—22no—
25#481×C103—22no—
26#477×C103—22no—
27#476×C103C2212yes—
28#476×C103C2212yes—
29#476×C103C2212yes—
30#474×C103C2212yes—
31#436×C103C2212yes—
32#435×C103—22no—
33C8×D4×C103C2212yes—
34#432×C103C2211yescharacteristic
35#432×C103C2211yescharacteristic
36#431×C103C2211yescharacteristic
37#431×C103C2211yescharacteristic
38#408×C103—22no—
39#335×C103C2212yes—
40#334×C103C2212yes—
41#333×C103C2212yes—
42#333×C103C2212yes—
43#333×C103C2212yes—
44#332×C103C2212yes—
45C2×#41×C103—21no—
46C22×Q8×C103—21no—
47C2×M16×C103—22no—
48C22×C8×C103—22no—
49C4⋊Q8×C103—21no—
50C4⋊Q8×C103—21no—
51C4⋊Q8×C103—21no—
52C4⋊Q8×C103D411yescharacteristic
53C4⋊Q8×C103C2311yescharacteristic
54C4⋊Q8×C103C2311yescharacteristic
55C4⋊Q8×C103C2311yescharacteristic
56C4⋊Q8×C103C2311yescharacteristic
57#127×C103D411yescharacteristic
58#125×C103—21no—
59#124×C103—21no—
60C22⋊Q8×C103—21no—
61C22⋊Q8×C103—21no—
62#121×C103—21no—
63#121×C103D412yes—
64C4×Q8×C103—21no—
65C4×Q8×C103—21no—
66C4×D4×C103—21no—
67C4×D4×C103C2312yes—
68#117×C103—21no—
69C2×C4⋊C4×C103—21no—
70C2×C4⋊C4×C103—21no—
71C2×C42×C103C2311yescharacteristic
72#107×C103—22no—
73#107×C103—22no—
74#107×C103—22no—
75#106×C103—22no—
76#106×C103—22no—
77#106×C103—22no—
78C4⋊C8×C103D412yes—
79C4⋊C8×C103C2312yes—
80C4⋊C8×C103C2312yes—
81C4⋊C8×C103C2312yes—
82#103×C103—22no—
83#103×C103—22no—
84#102×C103—22no—
85#102×C103—22no—
86#102×C103—22no—
87#102×C103—22no—
88C22⋊C8×C103—21no—
89C22⋊C8×C103—21no—
90C22⋊C8×C103—21no—
91C22⋊C8×C103—22no—
92C22⋊C8×C103—22no—
93C22⋊C8×C103D412yes—
94#97×C103—21no—
95#97×C103—21no—
96C4×C8×C103—21no—
97C4×C8×C103C2311yescharacteristic
98C4×C8×C103C2311yescharacteristic
99#41×C103—82no—
100C2×Q8×C103—21no—
101C2×Q8×C103—21no—
102C2×Q8×C103—21no—
103C2×Q8×C103—21no—
104C2×Q8×C103—21no—
105C2×Q8×C103—41no—
106C2×Q8×C103—82no—
107C2×D4×C103—22no—
108C2×D4×C103—21no—
109C2×D4×C103—21no—
110C2×D4×C103C2×D412yes—
111C22×C4×C103—22no—
112C22×C4×C103—41no—
113C22×C4×C103C2×D411yescharacteristic
114C22×C4×C103C2×D411yescharacteristic
115C22×C4×C103#4111yescharacteristic
116M16×C103—82no—
117C2×C8×C103—22no—
118C2×C8×C103—22no—
119C2×C8×C103—22no—
120C2×C8×C103—82no—
121C2×C8×C103C2×D412yes—
122C2×C8×C103C2×D412yes—
123C4⋊C4×C103—21no—
124C4⋊C4×C103—21no—
125C4⋊C4×C103—21no—
126C4⋊C4×C103—21no—
127C4⋊C4×C103—21no—
128C4⋊C4×C103—21no—
129C4⋊C4×C103—21no—
130C4⋊C4×C103—21no—
131C4⋊C4×C103—21no—
132C4⋊C4×C103—41no—
133C4⋊C4×C103—41no—
134C4⋊C4×C103—41no—
135C4⋊C4×C103—41no—
136C4⋊C4×C103C2×D412yes—
137C22⋊C4×C103—22no—
138C22⋊C4×C103—22no—
139C22⋊C4×C103—41no—
140C42×C103—41no—
141C42×C103C2×D411yescharacteristic
142C42×C103C2×D411yescharacteristic
143C42×C103#4111yescharacteristic
144C42×C103C2411yescharacteristic
145C23×C103—22no—
146C23×C103#12111yescharacteristic
147Q8×C103—42no—
148Q8×C103—81no—
149Q8×C103—81no—
150Q8×C103—81no—
151Q8×C103—81no—
152Q8×C103—82no—
153D4×C103—24no—
154D4×C103—81no—
155D4×C103—81no—
156D4×C103—82no—
157C2×C4×C103—22no—
158C2×C4×C103—22no—
159C2×C4×C103—22no—
160C2×C4×C103—41no—
161C2×C4×C103—42no—
162C2×C4×C103—42no—
163C2×C4×C103—41no—
164C2×C4×C103—41no—
165C2×C4×C103—41no—
166C2×C4×C103—41no—
167C2×C4×C103—82no—
168C2×C4×C103#12111yescharacteristic
169C2×C4×C103#12111yescharacteristic
170C2×C4×C103#12111yescharacteristic
171C2×C4×C103C22×D411yescharacteristic
172C2×C4×C103C22×D411yescharacteristic
173C2×C4×C103C2×#4111yescharacteristic
174C8×C103—22no—
175C8×C103—22no—
176C8×C103—42no—
177C8×C103—42no—
178C8×C103—42no—
179C22×C103—21no—
180C22×C103—21no—
181C22×C103—21no—
182C22×C103—42no—
183C22×C103—42no—
184C22×C103—42no—
185C22×C103C2×#12111yescharacteristic
186C4×C103—21no—
187C4×C103—21no—
188C4×C103—21no—
189C4×C103—21no—
190C4×C103—42no—
191C4×C103—81no—
192C4×C103—81no—
193C4×C103—81no—
194C4×C103—81no—
195C4×C103#57712yes—
196C4×C103#57812yes—
197#19515C10311yesmaximal, characteristic, direct product factor, Sylow
198C2×C103—41no—
199C2×C103—82no—
200C2×C103#304211yescharacteristic
201C2×C103#305911yescharacteristic
202C2×C103#306811yescharacteristic
203#3235C2×C10311yescharacteristic
204#3230C2×C10311yescharacteristic, complemented
205#3227C2×C10311yescharacteristic
206#2981C2×C10311yescharacteristic
207#1703C2×C10312yescomplemented
208#1695C2×C10312yescomplemented
209#1683C2×C10312yescomplemented
210#1675C2×C10312yescomplemented
211#1572C2×C10311yescharacteristic, complemented
212#1558C2×C10311yescharacteristic, complemented
213#1554C2×C10311yescharacteristic, complemented
214C103#1951511yescharacteristic, direct product factor, Sylow
215#533C22×C10311yescharacteristic
216#532C22×C10311yescharacteristic
217C2×C4⋊Q8C22×C10311yescharacteristic
218#501—21no—
219#500C22×C10311yescharacteristic
220#500C22×C10311yescharacteristic
221#498—21no—
222#490—21no—
223#487C22×C10311yescharacteristic
224#487C22×C10311yescharacteristic
225#486—21no—
226#484—22no—
227#482—22no—
228#481—22no—
229#477—22no—
230#476C22×C10312yes—
231#476C22×C10312yes—
232#476C22×C10312yes—
233#474C22×C10312yes—
234#436C22×C10312yes—
235#435—22no—
236C8×D4C22×C10312yes—
237#432C22×C10311yescharacteristic
238#432C22×C10311yescharacteristic
239#431C22×C10311yescharacteristic
240#431C22×C10311yescharacteristic
241#408—22no—
242#335C22×C10312yes—
243#334C22×C10312yes—
244#333C22×C10312yes—
245#333C22×C10312yes—
246#333C22×C10312yes—
247#332C22×C10312yes—
248C2×#41—21no—
249C22×Q8—21no—
250C2×M16—22no—
251C22×C8—22no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8D4×C10311yescharacteristic
256C4⋊Q8C23×C10311yescharacteristic
257C4⋊Q8C23×C10311yescharacteristic
258C4⋊Q8C23×C10311yescharacteristic
259C4⋊Q8C23×C10311yescharacteristic
260#127D4×C10311yescharacteristic
261#125—21no—
262#124—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265#121—21no—
266#121D4×C10312yes—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×D4—21no—
270C4×D4C23×C10312yes—
271#117—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C42C23×C10311yescharacteristic
275#107—22no—
276#107—22no—
277#107—22no—
278#106—22no—
279#106—22no—
280#106—22no—
281C4⋊C8D4×C10312yes—
282C4⋊C8C23×C10312yes—
283C4⋊C8C23×C10312yes—
284C4⋊C8C23×C10312yes—
285#103—22no—
286#103—22no—
287#102—22no—
288#102—22no—
289#102—22no—
290#102—22no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—22no—
295C22⋊C8—22no—
296C22⋊C8D4×C10312yes—
297#97—21no—
298#97—21no—
299C4×C8—21no—
300C4×C8C23×C10311yescharacteristic
301C4×C8C23×C10311yescharacteristic
302#41—82no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—41no—
309C2×Q8—82no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4C2×D4×C10312yes—
314C22×C4—22no—
315C22×C4—41no—
316C22×C4C2×D4×C10311yescharacteristic
317C22×C4C2×D4×C10311yescharacteristic
318C22×C4#41×C10311yescharacteristic
319M16—82no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—82no—
324C2×C8C2×D4×C10312yes—
325C2×C8C2×D4×C10312yes—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4C2×D4×C10312yes—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—41no—
343C42—41no—
344C42C2×D4×C10311yescharacteristic
345C42C2×D4×C10311yescharacteristic
346C42#41×C10311yescharacteristic
347C42C24×C10311yescharacteristic
348C23—22no—
349C23#121×C10311yescharacteristic
350Q8—42no—
351Q8—81no—
352Q8—81no—
353Q8—81no—
354Q8—81no—
355Q8—82no—
356D4—24no—
357D4—81no—
358D4—81no—
359D4—82no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—82no—
371C2×C4#121×C10311yescharacteristic
372C2×C4#121×C10311yescharacteristic
373C2×C4#121×C10311yescharacteristic
374C2×C4C22×D4×C10311yescharacteristic
375C2×C4C22×D4×C10311yescharacteristic
376C2×C4C2×#41×C10311yescharacteristic
377C8—22no—
378C8—22no—
379C8—42no—
380C8—42no—
381C8—42no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22C2×#121×C10311yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4#577×C10312yes—
399C4#578×C10312yes—
400C2—41no—
401C2—82no—
402C2C103×#304211yescharacteristic
403C2C103×#305911yescharacteristic
404C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radical#532×C103C22
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
2. C103×#3230C2semidirect
5. C103×#1703C2semidirect
6. C103×#1695C2semidirect
7. C103×#1683C2semidirect
8. C103×#1675C2semidirect
9. C103×#1572C2semidirect
10. C103×#1558C2semidirect
11. C103×#1554C2semidirect
197. #19515C103direct (N × H)
204. #3230C2×C103semidirect
207. #1703C2×C103semidirect
208. #1695C2×C103semidirect
209. #1683C2×C103semidirect
210. #1675C2×C103semidirect
211. #1572C2×C103semidirect
212. #1558C2×C103semidirect
213. #1554C2×C103semidirect
214. C103#19515direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32352
C103×#32302
C103×#32272
C103×#29812
C103×#17032
C103×#16952
C103×#16832
C103×#16752
C103×#15722
C103×#15582
C103×#15542
#19515103