Finite Group Databasebeta

← C103×#19174 #39924449

Subgroups — C103×#19174 #39924449

Order 26368.

680 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3138C211yesmaximal, characteristic
2C103×#3104C211yesmaximal, characteristic, complemented
3C2×#460×C103C211yesmaximal, characteristic
4Q8×M16×C103C211yesmaximal, characteristic, complemented
5C103×#1702C212yesmaximal, complemented
6C103×#1698C212yesmaximal, complemented
7C103×#1682C212yesmaximal, complemented
8C103×#1678C212yesmaximal, complemented
9C103×#1565C211yesmaximal, characteristic, complemented
10C103×#1550C211yesmaximal, characteristic, complemented
11C103×#1545C211yesmaximal, characteristic
12C22×SD16×C103—21no—
13#533×C103C2211yescharacteristic
14C2×#127×C103C2211yescharacteristic
15C2×C4×Q8×C103C2211yescharacteristic
16#490×C103—22no—
17#486×C103C2212yes—
18#486×C103C2212yes—
19#484×C103—21no—
20#477×C103C2211yescharacteristic, complemented
21#477×C103C2211yescharacteristic, complemented
22#462×C103C2211yescharacteristic, complemented
23#462×C103C2211yescharacteristic, complemented
24#460×C103—21no—
25#460×C103—21no—
26#460×C103C2212yes—
27#460×C103C2212yes—
28#451×C103—21no—
29#446×C103—22no—
30#446×C103C2212yescomplemented
31C8×Q8×C103C2212yescomplemented
32C4×Q16×C103—21no—
33C4×Q16×C103—21no—
34#431×C103C2211yescharacteristic
35#423×C103—21no—
36#423×C103C2211yescharacteristic
37C2×C4⋊C8×C103C2211yescharacteristic
38#418×C103—21no—
39#418×C103—21no—
40C2×#102×C103—21no—
41C4×M16×C103—21no—
42C4×M16×C103C2211yescharacteristic
43#335×C103C2212yescomplemented
44#334×C103C2212yescomplemented
45#333×C103C2212yescomplemented
46#332×C103C2212yescomplemented
47#331×C103C2212yes—
48#331×C103C2212yes—
49C22×Q8×C103D411yescharacteristic
50C22×D4×C103—21no—
51C22×D4×C103—21no—
52C22×D4×C103—21no—
53C2×Q16×C103—21no—
54C2×Q16×C103—21no—
55C2×SD16×C103—22no—
56C2×SD16×C103—22no—
57C2×SD16×C103—44no—
58C2×M16×C103—21no—
59C2×M16×C103D411yescharacteristic
60C2×M16×C103D411yescharacteristic
61C22×C8×C103—21no—
62C4⋊Q8×C103C2311yescharacteristic
63C4⋊Q8×C103C2311yescharacteristic
64#127×C103—21no—
65#127×C103—21no—
66#127×C103—21no—
67#127×C103C2312yes—
68#125×C103—21no—
69C22⋊Q8×C103—21no—
70C22⋊Q8×C103—21no—
71C4×Q8×C103—21no—
72C4×Q8×C103—21no—
73C4×Q8×C103—21no—
74C4×Q8×C103—21no—
75C4×Q8×C103D411yescharacteristic
76C4×Q8×C103D411yescharacteristic
77C4×Q8×C103C2311yescharacteristic
78C4×Q8×C103C2311yescharacteristic
79#117×C103—21no—
80C2×C4⋊C4×C103—21no—
81C2×C4⋊C4×C103D411yescharacteristic
82C2×C42×C103—21no—
83C2×C42×C103C2311yescharacteristic
84#107×C103—21no—
85#107×C103—21no—
86C4⋊C8×C103—22no—
87C4⋊C8×C103—22no—
88C4⋊C8×C103—21no—
89C4⋊C8×C103—21no—
90C4⋊C8×C103C2312yes—
91C4⋊C8×C103C2312yes—
92C4⋊C8×C103C2311yescharacteristic
93C4⋊C8×C103C2311yescharacteristic
94#103×C103—21no—
95#103×C103—21no—
96#103×C103—21no—
97#103×C103—21no—
98#102×C103—22no—
99#102×C103—22no—
100#102×C103—22no—
101#102×C103—22no—
102#102×C103—22no—
103#102×C103—22no—
104C22⋊C8×C103—21no—
105#97×C103—22no—
106#97×C103D412yes—
107C4×C8×C103—22no—
108C4×C8×C103—21no—
109C4×C8×C103C2312yes—
110C24×C103—41no—
111C2×Q8×C103—21no—
112C2×Q8×C103—22no—
113C2×Q8×C103—21no—
114C2×Q8×C103—21no—
115C2×Q8×C103—41no—
116C2×Q8×C103C2×D411yescharacteristic
117C2×Q8×C103C2×D411yescharacteristic
118C2×D4×C103—22no—
119C2×D4×C103—22no—
120C2×D4×C103—22no—
121C2×D4×C103—42no—
122C2×D4×C103—42no—
123C2×D4×C103—41no—
124C2×D4×C103—41no—
125C2×D4×C103—41no—
126C2×D4×C103—42no—
127C2×D4×C103—42no—
128C2×D4×C103—82no—
129C22×C4×C103—21no—
130C22×C4×C103—21no—
131C22×C4×C103C2×D411yescharacteristic
132C22×C4×C103C2×D411yescharacteristic
133C22×C4×C103#4111yescharacteristic
134Q16×C103—42no—
135Q16×C103—42no—
136SD16×C103—44no—
137SD16×C103—44no—
138M16×C103—22no—
139M16×C103—22no—
140M16×C103—42no—
141C2×C8×C103—22no—
142C2×C8×C103—21no—
143C2×C8×C103—21no—
144C2×C8×C103—22no—
145C2×C8×C103—42no—
146C2×C8×C103C2×D412yes—
147C2×C8×C103C2×D412yes—
148C4⋊C4×C103—21no—
149C4⋊C4×C103—21no—
150C4⋊C4×C103—21no—
151C4⋊C4×C103—21no—
152C4⋊C4×C103—21no—
153C4⋊C4×C103—21no—
154C4⋊C4×C103—21no—
155C4⋊C4×C103—21no—
156C4⋊C4×C103—21no—
157C4⋊C4×C103—41no—
158C4⋊C4×C103—41no—
159C4⋊C4×C103C2×D411yescharacteristic
160C4⋊C4×C103C2×D411yescharacteristic
161C22⋊C4×C103—41no—
162C42×C103—21no—
163C42×C103—21no—
164C42×C103—21no—
165C42×C103—21no—
166C42×C103—41no—
167C42×C103C2×D411yescharacteristic
168C42×C103C2×D411yescharacteristic
169C42×C103#4111yescharacteristic
170C42×C103C2411yescharacteristic
171C23×C103—42no—
172C23×C103—82no—
173C23×C103—82no—
174C23×C103—82no—
175C23×C103#12111yescharacteristic
176Q8×C103—21no—
177Q8×C103—21no—
178Q8×C103—21no—
179Q8×C103—42no—
180Q8×C103—41no—
181Q8×C103—41no—
182Q8×C103—81no—
183Q8×C103AGL(1,ℤ/8)12yes—
184D4×C103—42no—
185D4×C103—42no—
186D4×C103—42no—
187D4×C103—42no—
188D4×C103—82no—
189D4×C103—82no—
190D4×C103—82no—
191D4×C103—82no—
192C2×C4×C103—21no—
193C2×C4×C103—21no—
194C2×C4×C103—21no—
195C2×C4×C103—21no—
196C2×C4×C103—21no—
197C2×C4×C103—21no—
198C2×C4×C103—41no—
199C2×C4×C103—42no—
200C2×C4×C103—41no—
201C2×C4×C103—41no—
202C2×C4×C103—81no—
203C2×C4×C103#12111yescharacteristic
204C2×C4×C103#12111yescharacteristic
205C2×C4×C103#12111yescharacteristic
206C2×C4×C103#13512yes—
207C2×C4×C103#13712yes—
208C2×C4×C103C22×D411yescharacteristic
209C2×C4×C103C22×D411yescharacteristic
210C2×C4×C103C2×#4111yescharacteristic
211C8×C103—22no—
212C8×C103—22no—
213C8×C103—42no—
214C8×C103—42no—
215C8×C103—41no—
216C8×C103—41no—
217C22×C103—21no—
218C22×C103—21no—
219C22×C103—82no—
220C22×C103—82no—
221C22×C103—82no—
222C22×C103—164no—
223C22×C103#46412yes—
224C22×C103C2×#12111yescharacteristic
225C4×C103—21no—
226C4×C103—22no—
227C4×C103—21no—
228C4×C103—21no—
229C4×C103—41no—
230C4×C103—41no—
231C4×C103—41no—
232C4×C103—81no—
233C4×C103—81no—
234C4×C103#46412yes—
235C4×C103C2×#13511yescharacteristic
236C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
237C4×C103C2×#13711yescharacteristic
238C4×C103#57511yescharacteristic
239#19174C10311yesmaximal, characteristic, direct product factor, Sylow
240C2×C103—22no—
241C2×C103—162no—
242C2×C103C2×#46411yescharacteristic
243C2×C103#305511yescharacteristic
244C2×C103#306811yescharacteristic
245#3138C2×C10311yescharacteristic
246#3104C2×C10311yescharacteristic, complemented
247C2×#460C2×C10311yescharacteristic
248Q8×M16C2×C10311yescharacteristic, complemented
249#1702C2×C10312yescomplemented
250#1698C2×C10312yescomplemented
251#1682C2×C10312yescomplemented
252#1678C2×C10312yescomplemented
253#1565C2×C10311yescharacteristic, complemented
254#1550C2×C10311yescharacteristic, complemented
255#1545C2×C10311yescharacteristic
256C103#1917411yescharacteristic, direct product factor, Sylow
257C22×SD16—21no—
258#533C22×C10311yescharacteristic
259C2×#127C22×C10311yescharacteristic
260C2×C4×Q8C22×C10311yescharacteristic
261#490—22no—
262#486C22×C10312yes—
263#486C22×C10312yes—
264#484—21no—
265#477C22×C10311yescharacteristic, complemented
266#477C22×C10311yescharacteristic, complemented
267#462C22×C10311yescharacteristic, complemented
268#462C22×C10311yescharacteristic, complemented
269#460—21no—
270#460—21no—
271#460C22×C10312yes—
272#460C22×C10312yes—
273#451—21no—
274#446—22no—
275#446C22×C10312yescomplemented
276C8×Q8C22×C10312yescomplemented
277C4×Q16—21no—
278C4×Q16—21no—
279#431C22×C10311yescharacteristic
280#423—21no—
281#423C22×C10311yescharacteristic
282C2×C4⋊C8C22×C10311yescharacteristic
283#418—21no—
284#418—21no—
285C2×#102—21no—
286C4×M16—21no—
287C4×M16C22×C10311yescharacteristic
288#335C22×C10312yescomplemented
289#334C22×C10312yescomplemented
290#333C22×C10312yescomplemented
291#332C22×C10312yescomplemented
292#331C22×C10312yes—
293#331C22×C10312yes—
294C22×Q8D4×C10311yescharacteristic
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C2×Q16—21no—
299C2×Q16—21no—
300C2×SD16—22no—
301C2×SD16—22no—
302C2×SD16—44no—
303C2×M16—21no—
304C2×M16D4×C10311yescharacteristic
305C2×M16D4×C10311yescharacteristic
306C22×C8—21no—
307C4⋊Q8C23×C10311yescharacteristic
308C4⋊Q8C23×C10311yescharacteristic
309#127—21no—
310#127—21no—
311#127—21no—
312#127C23×C10312yes—
313#125—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8D4×C10311yescharacteristic
321C4×Q8D4×C10311yescharacteristic
322C4×Q8C23×C10311yescharacteristic
323C4×Q8C23×C10311yescharacteristic
324#117—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4D4×C10311yescharacteristic
327C2×C42—21no—
328C2×C42C23×C10311yescharacteristic
329#107—21no—
330#107—21no—
331C4⋊C8—22no—
332C4⋊C8—22no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8C23×C10312yes—
336C4⋊C8C23×C10311yescharacteristic
337C4⋊C8C23×C10311yescharacteristic
338C4⋊C8C23×C10312yes—
339#103—21no—
340#103—21no—
341#103—21no—
342#103—21no—
343#102—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#102—22no—
349C22⋊C8—21no—
350#97—22no—
351#97D4×C10312yes—
352C4×C8—22no—
353C4×C8—21no—
354C4×C8C23×C10312yes—
355C24—41no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—41no—
361C2×Q8C2×D4×C10311yescharacteristic
362C2×Q8C2×D4×C10311yescharacteristic
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—82no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4C2×D4×C10311yescharacteristic
377C22×C4C2×D4×C10311yescharacteristic
378C22×C4#41×C10311yescharacteristic
379Q16—42no—
380Q16—42no—
381SD16—44no—
382SD16—44no—
383M16—22no—
384M16—22no—
385M16—42no—
386C2×C8—22no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C2×C8—42no—
391C2×C8C2×D4×C10312yes—
392C2×C8C2×D4×C10312yes—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4C2×D4×C10311yescharacteristic
405C4⋊C4C2×D4×C10311yescharacteristic
406C22⋊C4—41no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—41no—
412C42C2×D4×C10311yescharacteristic
413C42C2×D4×C10311yescharacteristic
414C42#41×C10311yescharacteristic
415C42C24×C10311yescharacteristic
416C23—42no—
417C23—82no—
418C23—82no—
419C23—82no—
420C23#121×C10311yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—21no—
424Q8—42no—
425Q8—41no—
426Q8—41no—
427Q8—81no—
428Q8AGL(1,ℤ/8)×C10312yes—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—42no—
433D4—82no—
434D4—82no—
435D4—82no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—81no—
448C2×C4#121×C10311yescharacteristic
449C2×C4#121×C10311yescharacteristic
450C2×C4#121×C10311yescharacteristic
451C2×C4#135×C10312yes—
452C2×C4#137×C10312yes—
453C2×C4C22×D4×C10311yescharacteristic
454C2×C4C22×D4×C10311yescharacteristic
455C2×C4C2×#41×C10311yescharacteristic
456C8—22no—
457C8—22no—
458C8—42no—
459C8—42no—
460C8—41no—
461C8—41no—
462C22—21no—
463C22—21no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22#464×C10312yes—
469C22C2×#121×C10311yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—81no—
479C4#464×C10312yes—
480C4C2×#135×C10311yescharacteristic
481C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
482C4C2×#137×C10311yescharacteristic
483C4#575×C10311yescharacteristic
484C2—22no—
485C2—162no—
486C2C2×#464×C10311yescharacteristic
487C2C103×#305511yescharacteristic
488C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC2×#127×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×#3104C2semidirect
4. Q8×M16×C103C2semidirect
5. C103×#1702C2semidirect
6. C103×#1698C2semidirect
7. C103×#1682C2semidirect
8. C103×#1678C2semidirect
9. C103×#1565C2semidirect
10. C103×#1550C2semidirect
20. #477×C103C22semidirect
21. #477×C103C22semidirect
22. #462×C103C22semidirect
23. #462×C103C22semidirect
30. #446×C103C22semidirect
31. C8×Q8×C103C22semidirect
43. #335×C103C22semidirect
44. #334×C103C22semidirect
45. #333×C103C22semidirect
46. #332×C103C22semidirect
239. #19174C103direct (N × H)
246. #3104C2×C103semidirect
248. Q8×M16C2×C103semidirect
249. #1702C2×C103semidirect
250. #1698C2×C103semidirect
251. #1682C2×C103semidirect
252. #1678C2×C103semidirect
253. #1565C2×C103semidirect
254. #1550C2×C103semidirect
256. C103#19174direct (N × H)
265. #477C22×C103semidirect
266. #477C22×C103semidirect
267. #462C22×C103semidirect
268. #462C22×C103semidirect
275. #446C22×C103semidirect
276. C8×Q8C22×C103semidirect
288. #335C22×C103semidirect
289. #334C22×C103semidirect
290. #333C22×C103semidirect
291. #332C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31382
C103×#31042
C2×#460×C1032
Q8×M16×C1032
C103×#17022
C103×#16982
C103×#16822
C103×#16782
C103×#15652
C103×#15502
C103×#15452
#19174103