Finite Group Databasebeta

← C103×#8979 #39914254

Subgroups — C103×#8979 #39914254

Order 26368.

660 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C103C211yesmaximal, characteristic
2Q8×C4⋊C4×C103C211yesmaximal, characteristic, complemented
3C103×#1982C211yesmaximal, characteristic
4C103×#1957C211yesmaximal, characteristic
5C2×Q8⋊C8×C103C211yesmaximal, characteristic, complemented
6C103×#1296C211yesmaximal, characteristic, complemented
7C103×#1279C211yesmaximal, characteristic, complemented
8C22×SD16×C103—21no—
9C2×#127×C103C2211yescharacteristic
10C2×C4×Q8×C103—21no—
11C2×C4×Q8×C103C2211yescharacteristic
12#460×C103—22no—
13#460×C103C414yescomplemented
14C2×C4⋊C8×C103C2211yescharacteristic
15C2×C4⋊C8×C103C2211yescharacteristic
16C2×#102×C103—21no—
17C2×#102×C103—22no—
18C2×#102×C103—21no—
19C2×#102×C103—21no—
20C2×C4×C8×C103C2211yescharacteristic
21#389×C103—21no—
22#389×C103—22no—
23#384×C103—21no—
24#384×C103C2211yescharacteristic
25C4×C4⋊C4×C103—21no—
26C4×C4⋊C4×C103C2211yescharacteristic
27Q8⋊C8×C103—22no—
28C22×Q8×C103D411yescharacteristic
29C22×D4×C103—21no—
30C22×D4×C103—21no—
31C22×D4×C103—21no—
32C2×SD16×C103—24no—
33C2×SD16×C103—42no—
34C2×SD16×C103—42no—
35C22×C8×C103—21no—
36C22×C8×C103—21no—
37C22×C8×C103—21no—
38#127×C103—21no—
39#127×C103—21no—
40#127×C103—21no—
41#127×C103C2×C412yes—
42C4×Q8×C103—21no—
43C4×Q8×C103—21no—
44C4×Q8×C103—42no—
45C4×Q8×C103—42no—
46C4×Q8×C103C2×C412yes—
47C4×Q8×C103D412yes—
48C2×C4⋊C4×C103—21no—
49C2×C4⋊C4×C103—22no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103—22no—
53C2×C4⋊C4×C103D411yescharacteristic
54C2×C4⋊C4×C103D411yescharacteristic
55C2×C4⋊C4×C103D411yescharacteristic
56C2×C4⋊C4×C103D412yes—
57C2×C42×C103—21no—
58C2×C42×C103—22no—
59C2×C42×C103—21no—
60C2×C42×C103C2311yescharacteristic
61C4⋊C8×C103—21no—
62C4⋊C8×C103—21no—
63C4⋊C8×C103—21no—
64C4⋊C8×C103C2×C412yes—
65#102×C103—24no—
66#102×C103—42no—
67#102×C103—44no—
68#102×C103—42no—
69C4×C8×C103—21no—
70C4×C8×C103—21no—
71#95×C103—22no—
72#95×C103—21no—
73C24×C103—41no—
74C2×Q8×C103—21no—
75C2×Q8×C103—21no—
76C2×Q8×C103—21no—
77C2×Q8×C103C22⋊C412yes—
78C2×Q8×C103D812yes—
79C2×Q8×C103SD1612yes—
80C2×D4×C103—22no—
81C2×D4×C103—22no—
82C2×D4×C103—22no—
83C2×D4×C103—42no—
84C2×D4×C103—42no—
85C2×D4×C103—41no—
86C2×D4×C103—41no—
87C2×D4×C103—41no—
88C2×D4×C103—41no—
89C2×D4×C103—41no—
90C2×D4×C103—41no—
91C2×D4×C103—41no—
92C2×D4×C103—41no—
93C2×D4×C103—41no—
94C2×D4×C103—41no—
95C2×D4×C103—41no—
96C22×C4×C103—21no—
97C22×C4×C103—21no—
98C22×C4×C103—21no—
99C22×C4×C103—21no—
100C22×C4×C103—22no—
101C22×C4×C103C2×D411yescharacteristic
102C22×C4×C103C2×D411yescharacteristic
103C22×C4×C103C2×D411yescharacteristic
104SD16×C103—48no—
105C2×C8×C103—22no—
106C2×C8×C103—22no—
107C2×C8×C103—41no—
108C2×C8×C103—41no—
109C2×C8×C103—41no—
110C2×C8×C103—41no—
111C2×C8×C103—41no—
112C2×C8×C103—41no—
113C2×C8×C103—41no—
114C4⋊C4×C103—22no—
115C4⋊C4×C103—22no—
116C4⋊C4×C103—21no—
117C4⋊C4×C103—21no—
118C4⋊C4×C103—21no—
119C4⋊C4×C103—21no—
120C4⋊C4×C103—42no—
121C4⋊C4×C103—44no—
122C4⋊C4×C103—41no—
123C4⋊C4×C103—41no—
124C4⋊C4×C103—41no—
125C4⋊C4×C103—41no—
126C4⋊C4×C103—82no—
127C4⋊C4×C103C22⋊C412yes—
128C4⋊C4×C103SD1612yescomplemented
129C42×C103—22no—
130C42×C103—22no—
131C42×C103—44no—
132C42×C103—41no—
133C42×C103—41no—
134C42×C103C22×C411yescharacteristic
135C42×C103C2×D411yescharacteristic
136C42×C103#4111yescharacteristic
137C42×C103#4111yescharacteristic
138C23×C103—42no—
139C23×C103—81no—
140C23×C103—81no—
141C23×C103—81no—
142C23×C103—81no—
143C23×C103—81no—
144C23×C103—81no—
145C23×C103#12011yescharacteristic
146Q8×C103—22no—
147Q8×C103—22no—
148Q8×C103—22no—
149Q8×C103#10214yescomplemented
150D4×C103—44no—
151D4×C103—42no—
152D4×C103—42no—
153D4×C103—42no—
154D4×C103—42no—
155D4×C103—82no—
156D4×C103—81no—
157D4×C103—81no—
158D4×C103—81no—
159D4×C103—81no—
160C2×C4×C103—22no—
161C2×C4×C103—22no—
162C2×C4×C103—22no—
163C2×C4×C103—21no—
164C2×C4×C103—21no—
165C2×C4×C103—22no—
166C2×C4×C103—22no—
167C2×C4×C103—41no—
168C2×C4×C103—41no—
169C2×C4×C103—41no—
170C2×C4×C103—41no—
171C2×C4×C103—42no—
172C2×C4×C103—41no—
173C2×C4×C103—41no—
174C2×C4×C103—42no—
175C2×C4×C103—42no—
176C2×C4×C103—41no—
177C2×C4×C103C2×C22⋊C411yescharacteristic
178C2×C4×C103C4×D411yescharacteristic
179C2×C4×C103C4×D411yescharacteristic
180C2×C4×C103#12111yescharacteristic
181C2×C4×C103#12111yescharacteristic
182C2×C4×C103#12311yescharacteristic
183C2×C4×C103C2×D811yescharacteristic
184C2×C4×C103C2×SD1611yescharacteristic
185C2×C4×C103C2×SD1611yescharacteristic
186C2×C4×C103#13511yescharacteristic
187C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C103#13711yescharacteristic
190C2×C4×C103#13711yescharacteristic
191C8×C103—42no—
192C8×C103—42no—
193C8×C103—81no—
194C22×C103—82no—
195C22×C103—82no—
196C22×C103—82no—
197C22×C103—161no—
198C22×C103—161no—
199C22×C103—161no—
200C22×C103—161no—
201C22×C103#38611yescharacteristic
202C22×C103#44711yescharacteristic
203C22×C103#44811yescharacteristic
204C22×C103#44811yescharacteristic
205C22×C103#44911yescharacteristic
206C22×C103#45311yescharacteristic
207C22×C103#45411yescharacteristic
208C4×C103—24no—
209C4×C103—21no—
210C4×C103—21no—
211C4×C103—42no—
212C4×C103—42no—
213C4×C103—81no—
214C4×C103—82no—
215C4×C103C2×#10211yescharacteristic
216C4×C103#41711yescharacteristic
217C4×C103C4×SD1611yescharacteristic
218C4×C103#44011yescharacteristic
219C4×C103#46011yescharacteristic
220C4×C103#46411yescharacteristic
221C4×C103#48011yescharacteristic
222C4×C103#48111yescharacteristic
223#8979C10311yesmaximal, characteristic, direct product factor, Sylow
224C2×C103—162no—
225C2×C103#162111yescharacteristic
226C2×C103#162311yescharacteristic
227C2×C103#162611yescharacteristic
228C2×C103#162711yescharacteristic
229C2×C103#187411yescharacteristic
230C2×C103#188011yescharacteristic
231C2×C103#188311yescharacteristic
232C2×#460C2×C10311yescharacteristic
233Q8×C4⋊C4C2×C10311yescharacteristic, complemented
234#1982C2×C10311yescharacteristic
235#1957C2×C10311yescharacteristic
236C2×Q8⋊C8C2×C10311yescharacteristic, complemented
237#1296C2×C10311yescharacteristic, complemented
238#1279C2×C10311yescharacteristic, complemented
239C103#897911yescharacteristic, direct product factor, Sylow
240C22×SD16—21no—
241C2×#127C22×C10311yescharacteristic
242C2×C4×Q8—21no—
243C2×C4×Q8C22×C10311yescharacteristic
244#460—22no—
245#460C4×C10314yescomplemented
246C2×C4⋊C8C22×C10311yescharacteristic
247C2×C4⋊C8C22×C10311yescharacteristic
248C2×#102—21no—
249C2×#102—22no—
250C2×#102—21no—
251C2×#102—21no—
252C2×C4×C8C22×C10311yescharacteristic
253#389—21no—
254#389—22no—
255#384—21no—
256#384C22×C10311yescharacteristic
257C4×C4⋊C4—21no—
258C4×C4⋊C4C22×C10311yescharacteristic
259Q8⋊C8—22no—
260C22×Q8D4×C10311yescharacteristic
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C2×SD16—24no—
265C2×SD16—42no—
266C2×SD16—42no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270#127—21no—
271#127—21no—
272#127—21no—
273#127C2×C4×C10312yes—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×Q8—42no—
277C4×Q8—42no—
278C4×Q8C2×C4×C10312yes—
279C4×Q8D4×C10312yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4D4×C10311yescharacteristic
286C2×C4⋊C4D4×C10311yescharacteristic
287C2×C4⋊C4D4×C10311yescharacteristic
288C2×C4⋊C4D4×C10312yes—
289C2×C42—21no—
290C2×C42—22no—
291C2×C42—21no—
292C2×C42C23×C10311yescharacteristic
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8C2×C4×C10312yes—
297#102—24no—
298#102—42no—
299#102—44no—
300#102—42no—
301C4×C8—21no—
302C4×C8—21no—
303#95—22no—
304#95—21no—
305C24—41no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8C22⋊C4×C10312yes—
310C2×Q8D8×C10312yes—
311C2×Q8SD16×C10312yes—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4C2×D4×C10311yescharacteristic
334C22×C4C2×D4×C10311yescharacteristic
335C22×C4C2×D4×C10311yescharacteristic
336SD16—48no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—42no—
353C4⋊C4—44no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—82no—
359C4⋊C4C22⋊C4×C10312yes—
360C4⋊C4SD16×C10312yescomplemented
361C42—22no—
362C42—22no—
363C42—44no—
364C42—41no—
365C42—41no—
366C42C22×C4×C10311yescharacteristic
367C42C2×D4×C10311yescharacteristic
368C42#41×C10311yescharacteristic
369C42#41×C10311yescharacteristic
370C23—42no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—81no—
375C23—81no—
376C23—81no—
377C23#120×C10311yescharacteristic
378Q8—22no—
379Q8—22no—
380Q8—22no—
381Q8#102×C10314yescomplemented
382D4—44no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—42no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4C2×C22⋊C4×C10311yescharacteristic
410C2×C4C4×D4×C10311yescharacteristic
411C2×C4C4×D4×C10311yescharacteristic
412C2×C4#121×C10311yescharacteristic
413C2×C4#121×C10311yescharacteristic
414C2×C4#123×C10311yescharacteristic
415C2×C4C2×D8×C10311yescharacteristic
416C2×C4C2×SD16×C10311yescharacteristic
417C2×C4C2×SD16×C10311yescharacteristic
418C2×C4#135×C10311yescharacteristic
419C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
420C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
421C2×C4#137×C10311yescharacteristic
422C2×C4#137×C10311yescharacteristic
423C8—42no—
424C8—42no—
425C8—81no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22—161no—
430C22—161no—
431C22—161no—
432C22—161no—
433C22#386×C10311yescharacteristic
434C22#447×C10311yescharacteristic
435C22#448×C10311yescharacteristic
436C22#448×C10311yescharacteristic
437C22#449×C10311yescharacteristic
438C22#453×C10311yescharacteristic
439C22#454×C10311yescharacteristic
440C4—24no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—81no—
446C4—82no—
447C4C2×#102×C10311yescharacteristic
448C4#417×C10311yescharacteristic
449C4C4×SD16×C10311yescharacteristic
450C4#440×C10311yescharacteristic
451C4#460×C10311yescharacteristic
452C4#464×C10311yescharacteristic
453C4#480×C10311yescharacteristic
454C4#481×C10311yescharacteristic
455C2—162no—
456C2C103×#162111yescharacteristic
457C2C103×#162311yescharacteristic
458C2C103×#162611yescharacteristic
459C2C103×#162711yescharacteristic
460C2C103×#187411yescharacteristic
461C2C103×#188011yescharacteristic
462C2C103×#188311yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC2×#127×C103C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C4⋊C4×C103C2semidirect
5. C2×Q8⋊C8×C103C2semidirect
6. C103×#1296C2semidirect
7. C103×#1279C2semidirect
13. #460×C103C4semidirect
128. C4⋊C4×C103SD16semidirect
149. Q8×C103#102semidirect
223. #8979C103direct (N × H)
233. Q8×C4⋊C4C2×C103semidirect
236. C2×Q8⋊C8C2×C103semidirect
237. #1296C2×C103semidirect
238. #1279C2×C103semidirect
239. C103#8979direct (N × H)
245. #460C4×C103semidirect
360. C4⋊C4SD16×C103semidirect
381. Q8#102×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1032
Q8×C4⋊C4×C1032
C103×#19822
C103×#19572
C2×Q8⋊C8×C1032
C103×#12962
C103×#12792
#8979103