Finite Group Databasebeta

← C103×#9266 #39914541

Subgroups — C103×#9266 #39914541

Order 26368.

400 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3232C211yesmaximal, characteristic
2C103×#2968C211yesmaximal, characteristic
3C103×#1532C211yesmaximal, characteristic
4C2×#330×C103C211yesmaximal, characteristic, complemented
5C103×#1470C211yesmaximal, characteristic, complemented
6C103×#1302C211yesmaximal, characteristic, complemented
7C103×#1281C211yesmaximal, characteristic, complemented
8#529×C103C2211yescharacteristic
9C2×#125×C103C2211yescharacteristic
10#499×C103—21no—
11#488×C103—21no—
12#484×C103C411yescharacteristic
13#483×C103C411yescharacteristic
14#481×C103C411yescharacteristic
15#480×C103C411yescharacteristic
16#479×C103—21no—
17#478×C103—21no—
18#446×C103—21no—
19#435×C103—21no—
20#435×C103—21no—
21C8×D4×C103—21no—
22#433×C103—21no—
23#432×C103C2211yescharacteristic
24#431×C103C2211yescharacteristic
25#431×C103C2211yescharacteristic
26#405×C103—21no—
27C2×#97×C103C2211yescharacteristic
28C2×#97×C103C2211yescharacteristic
29#330×C103—21no—
30#330×C103—21no—
31#330×C103—21no—
32#329×C103—21no—
33#324×C103—21no—
34#324×C103—21no—
35C2×M16×C103—21no—
36C22×C8×C103—21no—
37C22×C8×C103—21no—
38C22×C8×C103—21no—
39#126×C103—21no—
40#125×C103—21no—
41#125×C103—21no—
42#125×C103—21no—
43#125×C103—21no—
44#125×C103D411yescharacteristic
45#124×C103D411yescharacteristic
46#123×C103—21no—
47C22⋊Q8×C103C2×C411yescharacteristic
48#121×C103C2×C411yescharacteristic
49C4×Q8×C103D411yescharacteristic
50C4×D4×C103—21no—
51C4×D4×C103D411yescharacteristic
52#117×C103—21no—
53C2×C4⋊C4×C103—21no—
54C2×C4⋊C4×C103—21no—
55C2×C4⋊C4×C103C2×C411yescharacteristic
56C2×C4⋊C4×C103C2×C411yescharacteristic
57C2×C42×C103C2311yescharacteristic
58#107×C103—21no—
59#107×C103—21no—
60#106×C103—21no—
61#106×C103—21no—
62C4⋊C8×C103—21no—
63C4⋊C8×C103—21no—
64C4⋊C8×C103—21no—
65C4⋊C8×C103—21no—
66C4⋊C8×C103—21no—
67#103×C103—21no—
68#103×C103—21no—
69#102×C103—21no—
70#102×C103—21no—
71C22⋊C8×C103—21no—
72C22⋊C8×C103—21no—
73C22⋊C8×C103—21no—
74C22⋊C8×C103C2×C411yescharacteristic
75C22⋊C8×C103C2×C411yescharacteristic
76C22⋊C8×C103D411yescharacteristic
77C22⋊C8×C103D411yescharacteristic
78#97×C103—21no—
79#97×C103—21no—
80#97×C103—21no—
81#97×C103—21no—
82#97×C103—21no—
83#97×C103D411yescharacteristic
84#97×C103D411yescharacteristic
85C4×C8×C103—21no—
86C4×C8×C103—21no—
87C4×C8×C103—21no—
88C2×Q8×C103C22⋊C411yescharacteristic
89C2×D4×C103—21no—
90C2×D4×C103C22⋊C411yescharacteristic
91C22×C4×C103—21no—
92C22×C4×C103—21no—
93C22×C4×C103—21no—
94C22×C4×C103C22×C411yescharacteristic
95C22×C4×C103C2×D411yescharacteristic
96C22×C4×C103#4111yescharacteristic
97M16×C103—42no—
98C2×C8×C103—21no—
99C2×C8×C103—22no—
100C2×C8×C103—21no—
101C2×C8×C103—21no—
102C2×C8×C103—21no—
103C2×C8×C103—21no—
104C2×C8×C103—21no—
105C2×C8×C103—42no—
106C2×C8×C103—42no—
107C2×C8×C103—41no—
108C2×C8×C103—41no—
109C2×C8×C103—41no—
110C4⋊C4×C103—21no—
111C4⋊C4×C103—21no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103—21no—
114C4⋊C4×C103—21no—
115C4⋊C4×C103—21no—
116C4⋊C4×C103—21no—
117C4⋊C4×C103—21no—
118C4⋊C4×C103—41no—
119C4⋊C4×C103—41no—
120C4⋊C4×C103—41no—
121C4⋊C4×C103—41no—
122C4⋊C4×C103C22⋊C411yescharacteristic
123C4⋊C4×C103C22⋊C411yescharacteristic
124C22⋊C4×C103—21no—
125C22⋊C4×C103—21no—
126C22⋊C4×C103—21no—
127C22⋊C4×C103—21no—
128C22⋊C4×C103—21no—
129C42×C103—21no—
130C42×C103C2×D411yescharacteristic
131C42×C103C2×D411yescharacteristic
132C42×C103C2×D411yescharacteristic
133C42×C103#4111yescharacteristic
134C23×C103—21no—
135C23×C103C4×D411yescharacteristic
136Q8×C103—41no—
137D4×C103—41no—
138D4×C103—41no—
139D4×C103—41no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—41no—
146C2×C4×C103—41no—
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×C103—81no—
154C2×C4×C103C2×C22⋊C411yescharacteristic
155C2×C4×C103C4×D411yescharacteristic
156C2×C4×C103#12011yescharacteristic
157C2×C4×C103#12111yescharacteristic
158C2×C4×C103#12111yescharacteristic
159C2×C4×C103#12311yescharacteristic
160C8×C103—22no—
161C8×C103—41no—
162C8×C103—41no—
163C8×C103—42no—
164C8×C103—41no—
165C8×C103—41no—
166C8×C103—41no—
167C8×C103—81no—
168C22×C103—21no—
169C22×C103—21no—
170C22×C103—41no—
171C22×C103—41no—
172C22×C103—41no—
173C22×C103#38611yescharacteristic
174C22×C103#44311yescharacteristic
175C22×C103#44411yescharacteristic
176C4×C103—21no—
177C4×C103—21no—
178C4×C103—21no—
179C4×C103—21no—
180C4×C103—21no—
181C4×C103—21no—
182C4×C103—41no—
183C4×C103—41no—
184C4×C103—41no—
185C4×C103—81no—
186C4×C103—81no—
187#9266C10311yesmaximal, characteristic, direct product factor, Sylow
188C2×C103—21no—
189C2×C103—21no—
190C2×C103—81no—
191C2×C103#187611yescharacteristic
192C2×C103#190611yescharacteristic
193C2×C103#191511yescharacteristic
194#3232C2×C10311yescharacteristic
195#2968C2×C10311yescharacteristic
196#1532C2×C10311yescharacteristic
197C2×#330C2×C10311yescharacteristic, complemented
198#1470C2×C10311yescharacteristic, complemented
199#1302C2×C10311yescharacteristic, complemented
200#1281C2×C10311yescharacteristic, complemented
201C103#926611yescharacteristic, direct product factor, Sylow
202#529C22×C10311yescharacteristic
203C2×#125C22×C10311yescharacteristic
204#499—21no—
205#488—21no—
206#484C4×C10311yescharacteristic
207#483C4×C10311yescharacteristic
208#481C4×C10311yescharacteristic
209#480C4×C10311yescharacteristic
210#479—21no—
211#478—21no—
212#446—21no—
213#435—21no—
214#435—21no—
215C8×D4—21no—
216#433—21no—
217#432C22×C10311yescharacteristic
218#431C22×C10311yescharacteristic
219#431C22×C10311yescharacteristic
220#405—21no—
221C2×#97C22×C10311yescharacteristic
222C2×#97C22×C10311yescharacteristic
223#330—21no—
224#330—21no—
225#330—21no—
226#329—21no—
227#324—21no—
228#324—21no—
229C2×M16—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233#126—21no—
234#125—21no—
235#125—21no—
236#125—21no—
237#125—21no—
238#125D4×C10311yescharacteristic
239#124D4×C10311yescharacteristic
240#123—21no—
241C22⋊Q8C2×C4×C10311yescharacteristic
242#121C2×C4×C10311yescharacteristic
243C4×Q8D4×C10311yescharacteristic
244C4×D4—21no—
245C4×D4D4×C10311yescharacteristic
246#117—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4C2×C4×C10311yescharacteristic
250C2×C4⋊C4C2×C4×C10311yescharacteristic
251C2×C42C23×C10311yescharacteristic
252#107—21no—
253#107—21no—
254#106—21no—
255#106—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264#102—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8C2×C4×C10311yescharacteristic
269C22⋊C8C2×C4×C10311yescharacteristic
270C22⋊C8D4×C10311yescharacteristic
271C22⋊C8D4×C10311yescharacteristic
272#97—21no—
273#97—21no—
274#97—21no—
275#97—21no—
276#97—21no—
277#97D4×C10311yescharacteristic
278#97D4×C10311yescharacteristic
279C4×C8—21no—
280C4×C8—21no—
281C4×C8—21no—
282C2×Q8C22⋊C4×C10311yescharacteristic
283C2×D4—21no—
284C2×D4C22⋊C4×C10311yescharacteristic
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×C4×C10311yescharacteristic
289C22×C4C2×D4×C10311yescharacteristic
290C22×C4#41×C10311yescharacteristic
291M16—42no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4C22⋊C4×C10311yescharacteristic
317C4⋊C4C22⋊C4×C10311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C42—21no—
324C42C2×D4×C10311yescharacteristic
325C42C2×D4×C10311yescharacteristic
326C42C2×D4×C10311yescharacteristic
327C42#41×C10311yescharacteristic
328C23—21no—
329C23C4×D4×C10311yescharacteristic
330Q8—41no—
331D4—41no—
332D4—41no—
333D4—41no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4C2×C22⋊C4×C10311yescharacteristic
349C2×C4C4×D4×C10311yescharacteristic
350C2×C4#120×C10311yescharacteristic
351C2×C4#121×C10311yescharacteristic
352C2×C4#121×C10311yescharacteristic
353C2×C4#123×C10311yescharacteristic
354C8—22no—
355C8—42no—
356C8—41no—
357C8—41no—
358C8—41no—
359C8—41no—
360C8—41no—
361C8—81no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22#386×C10311yescharacteristic
368C22#443×C10311yescharacteristic
369C22#444×C10311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C2—21no—
382C2—21no—
383C2—81no—
384C2C103×#187611yescharacteristic
385C2C103×#190611yescharacteristic
386C2C103×#191511yescharacteristic
subgroupG/H
center, socleC22×C103#386
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radical#121×C103C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#330×C103C2semidirect
5. C103×#1470C2semidirect
6. C103×#1302C2semidirect
7. C103×#1281C2semidirect
187. #9266C103direct (N × H)
197. C2×#330C2×C103semidirect
198. #1470C2×C103semidirect
199. #1302C2×C103semidirect
200. #1281C2×C103semidirect
201. C103#9266direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32322
C103×#29682
C103×#15322
C2×#330×C1032
C103×#14702
C103×#13022
C103×#12812
#9266103