Finite Group Databasebeta

← C103×#9233 #39914508

Subgroups — C103×#9233 #39914508

Order 26368.

724 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3100C211yesmaximal, characteristic
2C42×D4×C103C211yesmaximal, characteristic, complemented
3C103×#1962C211yesmaximal, characteristic, complemented
4C103×#1502C211yesmaximal, characteristic, complemented
5C103×#1486C211yesmaximal, characteristic, complemented
6C103×#1303C211yesmaximal, characteristic, complemented
7C103×#1276C211yesmaximal, characteristic, complemented
8#532×C103C2211yescharacteristic
9C2×C4×D4×C103—21no—
10C2×C4×D4×C103C2211yescharacteristic
11C22×C42×C103—21no—
12#480×C103—21no—
13#474×C103C412yescomplemented
14#459×C103C412yescomplemented
15#447×C103—21no—
16C4×D8×C103—22no—
17#431×C103C2211yescharacteristic
18#431×C103C2211yescharacteristic
19#423×C103C2211yescharacteristic
20C2×#104×C103—21no—
21C2×#104×C103—21no—
22C4×C4⋊C4×C103—21no—
23C4×C4⋊C4×C103C2211yescharacteristic
24C4×C22⋊C4×C103—21no—
25C4×C22⋊C4×C103—22no—
26C43×C103C2211yescharacteristic
27#327×C103—22no—
28D4⋊C8×C103—22no—
29C2×#41×C103—21no—
30C22×D4×C103D411yescharacteristic
31C23×C4×C103—22no—
32C23×C4×C103—21no—
33C2×D8×C103—22no—
34C2×M16×C103—21no—
35C4⋊Q8×C103C2×C411yescharacteristic, complemented
36#127×C103C2×C411yescharacteristic, complemented
37#124×C103—21no—
38#121×C103—21no—
39#121×C103—21no—
40C4×D4×C103—28no—
41C4×D4×C103—21no—
42C4×D4×C103—21no—
43C4×D4×C103—21no—
44C4×D4×C103—21no—
45C4×D4×C103C2×C412yes—
46C4×D4×C103D412yes—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103D411yescharacteristic
49C2×C22⋊C4×C103—22no—
50C2×C22⋊C4×C103—21no—
51C2×C42×C103—21no—
52C2×C42×C103—22no—
53C2×C42×C103—21no—
54C2×C42×C103—21no—
55C2×C42×C103—42no—
56C2×C42×C103—42no—
57C2×C42×C103D411yescharacteristic
58C2×C42×C103D411yescharacteristic
59C2×C42×C103C2311yescharacteristic
60#107×C103—22no—
61C4⋊C8×C103—21no—
62C4⋊C8×C103—21no—
63C4⋊C8×C103—21no—
64C4⋊C8×C103C2×C412yescomplemented
65#104×C103—42no—
66#104×C103—42no—
67#102×C103—22no—
68#102×C103—22no—
69C22⋊C8×C103—21no—
70C22⋊C8×C103—21no—
71C4×C8×C103—21no—
72C4×C8×C103—21no—
73#95×C103—22no—
74#95×C103D412yes—
75C24×C103—21no—
76#41×C103—41no—
77#41×C103—41no—
78#41×C103—41no—
79#41×C103—41no—
80C2×Q8×C103—21no—
81C2×D4×C103—24no—
82C2×D4×C103—21no—
83C2×D4×C103—21no—
84C2×D4×C103—21no—
85C2×D4×C103—21no—
86C2×D4×C103—41no—
87C2×D4×C103C22⋊C412yes—
88C22×C4×C103—21no—
89C22×C4×C103—28no—
90C22×C4×C103—21no—
91C22×C4×C103—21no—
92C22×C4×C103—22no—
93C22×C4×C103—22no—
94C22×C4×C103—22no—
95C22×C4×C103—44no—
96C22×C4×C103—44no—
97C22×C4×C103—41no—
98C22×C4×C103—41no—
99C22×C4×C103—41no—
100C22×C4×C103—41no—
101C22×C4×C103—41no—
102C22×C4×C103C2×D411yescharacteristic
103C22×C4×C103C2×D411yescharacteristic
104C22×C4×C103C2×D411yescharacteristic
105D8×C103—44no—
106M16×C103—41no—
107M16×C103—41no—
108C2×C8×C103—22no—
109C2×C8×C103—41no—
110C2×C8×C103—41no—
111C4⋊C4×C103—24no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103—21no—
114C4⋊C4×C103—21no—
115C4⋊C4×C103C22⋊C412yes—
116C22⋊C4×C103—28no—
117C22⋊C4×C103—22no—
118C22⋊C4×C103—22no—
119C22⋊C4×C103—41no—
120C22⋊C4×C103—41no—
121C42×C103—24no—
122C42×C103—21no—
123C42×C103—21no—
124C42×C103—21no—
125C42×C103—42no—
126C42×C103—44no—
127C42×C103—41no—
128C42×C103—41no—
129C42×C103D812yescomplemented
130C42×C103C22×C411yescharacteristic
131C42×C103C2×D411yescharacteristic
132C42×C103#4111yescharacteristic
133C42×C103#4111yescharacteristic
134C23×C103—24no—
135C23×C103—22no—
136C23×C103—42no—
137C23×C103—41no—
138C23×C103—41no—
139C23×C103—41no—
140C23×C103#12011yescharacteristic
141Q8×C103—41no—
142Q8×C103—41no—
143D4×C103—24no—
144D4×C103—22no—
145D4×C103—42no—
146D4×C103—41no—
147D4×C103—41no—
148D4×C103—81no—
149D4×C103—81no—
150D4×C103—81no—
151D4×C103#10414yescomplemented
152C2×C4×C103—22no—
153C2×C4×C103—22no—
154C2×C4×C103—22no—
155C2×C4×C103—22no—
156C2×C4×C103—22no—
157C2×C4×C103—24no—
158C2×C4×C103—22no—
159C2×C4×C103—41no—
160C2×C4×C103—416no—
161C2×C4×C103—41no—
162C2×C4×C103—42no—
163C2×C4×C103—42no—
164C2×C4×C103—41no—
165C2×C4×C103—41no—
166C2×C4×C103—41no—
167C2×C4×C103—42no—
168C2×C4×C103—42no—
169C2×C4×C103—42no—
170C2×C4×C103—42no—
171C2×C4×C103—41no—
172C2×C4×C103—81no—
173C2×C4×C103—81no—
174C2×C4×C103C2×C22⋊C411yescharacteristic
175C2×C4×C103C4×D411yescharacteristic
176C2×C4×C103C4×D411yescharacteristic
177C2×C4×C103#12111yescharacteristic
178C2×C4×C103#12111yescharacteristic
179C2×C4×C103#12311yescharacteristic
180C2×C4×C103C2×D811yescharacteristic
181C2×C4×C103#13511yescharacteristic
182C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
184C8×C103—42no—
185C8×C103—81no—
186C8×C103—81no—
187C22×C103—21no—
188C22×C103—21no—
189C22×C103—24no—
190C22×C103—44no—
191C22×C103—44no—
192C22×C103—42no—
193C22×C103—42no—
194C22×C103—81no—
195C22×C103—81no—
196C22×C103—81no—
197C22×C103#38611yescharacteristic
198C22×C103#44711yescharacteristic
199C22×C103#44911yescharacteristic
200C4×C103—24no—
201C4×C103—21no—
202C4×C103—21no—
203C4×C103—21no—
204C4×C103—42no—
205C4×C103—44no—
206C4×C103—42no—
207C4×C103—81no—
208C4×C103C2×#10412yes—
209C4×C103C4×D811yescharacteristic
210C4×C103#44211yescharacteristic
211C4×C103#45911yescharacteristic
212C4×C103#46311yescharacteristic
213#9233C10311yesmaximal, characteristic, direct product factor, Sylow
214C2×C103—21no—
215C2×C103—21no—
216C2×C103—44no—
217C2×C103—161no—
218C2×C103#187911yescharacteristic
219C2×C103#189611yescharacteristic
220C2×C103#190611yescharacteristic
221#3100C2×C10311yescharacteristic
222C42×D4C2×C10311yescharacteristic, complemented
223#1962C2×C10311yescharacteristic, complemented
224#1502C2×C10311yescharacteristic, complemented
225#1486C2×C10311yescharacteristic, complemented
226#1303C2×C10311yescharacteristic, complemented
227#1276C2×C10311yescharacteristic, complemented
228C103#923311yescharacteristic, direct product factor, Sylow
229#532C22×C10311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4C22×C10311yescharacteristic
232C22×C42—21no—
233#480—21no—
234#474C4×C10312yescomplemented
235#459C4×C10312yescomplemented
236#447—21no—
237C4×D8—22no—
238#431C22×C10311yescharacteristic
239#431C22×C10311yescharacteristic
240#423C22×C10311yescharacteristic
241C2×#104—21no—
242C2×#104—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4C22×C10311yescharacteristic
245C4×C22⋊C4—21no—
246C4×C22⋊C4—22no—
247C43C22×C10311yescharacteristic
248#327—22no—
249D4⋊C8—22no—
250C2×#41—21no—
251C22×D4D4×C10311yescharacteristic
252C23×C4—22no—
253C23×C4—21no—
254C2×D8—22no—
255C2×M16—21no—
256C4⋊Q8C2×C4×C10311yescharacteristic, complemented
257#127C2×C4×C10311yescharacteristic, complemented
258#124—21no—
259#121—21no—
260#121—21no—
261C4×D4—28no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4C2×C4×C10312yes—
267C4×D4D4×C10312yes—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C10311yescharacteristic
270C2×C22⋊C4—22no—
271C2×C22⋊C4—21no—
272C2×C42—21no—
273C2×C42—22no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—42no—
277C2×C42—42no—
278C2×C42D4×C10311yescharacteristic
279C2×C42D4×C10311yescharacteristic
280C2×C42C23×C10311yescharacteristic
281#107—22no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8C2×C4×C10312yescomplemented
286#104—42no—
287#104—42no—
288#102—22no—
289#102—22no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C4×C8—21no—
293C4×C8—21no—
294#95—22no—
295#95D4×C10312yes—
296C24—21no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—21no—
302C2×D4—24no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4C22⋊C4×C10312yes—
309C22×C4—21no—
310C22×C4—28no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—44no—
317C22×C4—44no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4C2×D4×C10311yescharacteristic
324C22×C4C2×D4×C10311yescharacteristic
325C22×C4C2×D4×C10311yescharacteristic
326D8—44no—
327M16—41no—
328M16—41no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C4⋊C4—24no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊C4×C10312yes—
337C22⋊C4—28no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—24no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—42no—
347C42—44no—
348C42—41no—
349C42—41no—
350C42D8×C10312yescomplemented
351C42C22×C4×C10311yescharacteristic
352C42C2×D4×C10311yescharacteristic
353C42#41×C10311yescharacteristic
354C42#41×C10311yescharacteristic
355C23—24no—
356C23—22no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23#120×C10311yescharacteristic
362Q8—41no—
363Q8—41no—
364D4—24no—
365D4—22no—
366D4—42no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4#104×C10314yescomplemented
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—416no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C2×C22⋊C4×C10311yescharacteristic
396C2×C4C4×D4×C10311yescharacteristic
397C2×C4C4×D4×C10311yescharacteristic
398C2×C4#121×C10311yescharacteristic
399C2×C4#121×C10311yescharacteristic
400C2×C4#123×C10311yescharacteristic
401C2×C4C2×D8×C10311yescharacteristic
402C2×C4#135×C10311yescharacteristic
403C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
404C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
405C8—42no—
406C8—81no—
407C8—81no—
408C22—21no—
409C22—21no—
410C22—24no—
411C22—44no—
412C22—44no—
413C22—42no—
414C22—42no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22#386×C10311yescharacteristic
419C22#447×C10311yescharacteristic
420C22#449×C10311yescharacteristic
421C4—24no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—44no—
426C4—42no—
427C4—42no—
428C4—81no—
429C4C2×#104×C10312yes—
430C4C4×D8×C10311yescharacteristic
431C4#442×C10311yescharacteristic
432C4#459×C10311yescharacteristic
433C4#463×C10311yescharacteristic
434C2—21no—
435C2—21no—
436C2—44no—
437C2—161no—
438C2C103×#187911yescharacteristic
439C2C103×#189611yescharacteristic
440C2C103×#190611yescharacteristic
subgroupG/H
centerC2×C4×C103#121
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#386
prime radicalC103×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C42×D4×C103C2semidirect
3. C103×#1962C2semidirect
4. C103×#1502C2semidirect
5. C103×#1486C2semidirect
6. C103×#1303C2semidirect
7. C103×#1276C2semidirect
13. #474×C103C4semidirect
14. #459×C103C4semidirect
35. C4⋊Q8×C103C2×C4semidirect
36. #127×C103C2×C4semidirect
64. C4⋊C8×C103C2×C4semidirect
129. C42×C103D8semidirect
151. D4×C103#104semidirect
213. #9233C103direct (N × H)
222. C42×D4C2×C103semidirect
223. #1962C2×C103semidirect
224. #1502C2×C103semidirect
225. #1486C2×C103semidirect
226. #1303C2×C103semidirect
227. #1276C2×C103semidirect
228. C103#9233direct (N × H)
234. #474C4×C103semidirect
235. #459C4×C103semidirect
256. C4⋊Q8C2×C4×C103semidirect
257. #127C2×C4×C103semidirect
285. C4⋊C8C2×C4×C103semidirect
350. C42D8×C103semidirect
372. D4#104×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31002
C42×D4×C1032
C103×#19622
C103×#15022
C103×#14862
C103×#13032
C103×#12762
#9233103