Finite Group Databasebeta

← C103×#19170 #39924445

Subgroups — C103×#19170 #39924445

Order 26368.

766 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3151C211yesmaximal, characteristic
2C103×#3103C211yesmaximal, characteristic, complemented
3C2×#460×C103C211yesmaximal, characteristic, complemented
4Q8×M16×C103C211yesmaximal, characteristic, complemented
5C103×#1688C212yesmaximal, complemented
6C103×#1686C212yesmaximal, complemented
7C103×#1668C212yesmaximal, complemented
8C103×#1666C212yesmaximal, complemented
9C103×#1565C211yesmaximal, characteristic, complemented
10C103×#1547C211yesmaximal, characteristic, complemented
11C103×#1545C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C103—21no—
13C2×AGL(1,ℤ/8)×C103—21no—
14C22×SD16×C103—21no—
15#532×C103C2211yescharacteristic
16C2×#127×C103C2211yescharacteristic
17C2×C4×Q8×C103C2211yescharacteristic
18#496×C103—22no—
19#493×C103C2212yes—
20#492×C103C2212yes—
21#481×C103—21no—
22#475×C103C2211yescharacteristic, complemented
23#475×C103C2211yescharacteristic, complemented
24#460×C103—21no—
25#460×C103—21no—
26#460×C103C2212yes—
27#460×C103C2212yes—
28#460×C103C2211yescharacteristic, complemented
29#460×C103C2211yescharacteristic, complemented
30#448×C103—21no—
31#446×C103—22no—
32#446×C103C2212yescomplemented
33C8×Q8×C103C2212yescomplemented
34C4×SD16×C103—21no—
35C4×SD16×C103—21no—
36#431×C103C2211yescharacteristic
37#423×C103—21no—
38#423×C103C2211yescharacteristic
39C2×C4⋊C8×C103C2211yescharacteristic
40C2×#102×C103—21no—
41C4×M16×C103—21no—
42C4×M16×C103C2211yescharacteristic
43#335×C103C2212yescomplemented
44#334×C103C2212yescomplemented
45#332×C103C2212yescomplemented
46#331×C103C2212yes—
47#331×C103C2212yes—
48#331×C103C2212yescomplemented
49C2×#41×C103—21no—
50C22×Q8×C103D411yescharacteristic
51C22×D4×C103—21no—
52C22×D4×C103—21no—
53C22×D4×C103—21no—
54AGL(1,ℤ/8)×C103—44no—
55AGL(1,ℤ/8)×C103—44no—
56C2×SD16×C103—21no—
57C2×SD16×C103—21no—
58C2×SD16×C103—22no—
59C2×SD16×C103—22no—
60C2×SD16×C103—22no—
61C2×SD16×C103—22no—
62C2×SD16×C103—44no—
63C2×D8×C103—22no—
64C2×D8×C103—22no—
65C2×M16×C103—21no—
66C2×M16×C103D411yescharacteristic
67C2×M16×C103D411yescharacteristic
68C22×C8×C103—21no—
69C4⋊Q8×C103C2311yescharacteristic
70#127×C103—21no—
71#127×C103—21no—
72#127×C103—21no—
73#127×C103C2312yes—
74#127×C103C2311yescharacteristic
75#124×C103—21no—
76#121×C103—21no—
77#121×C103—21no—
78C4×Q8×C103—21no—
79C4×Q8×C103—21no—
80C4×Q8×C103D411yescharacteristic
81C4×Q8×C103D411yescharacteristic
82C4×Q8×C103C2311yescharacteristic
83C4×Q8×C103C2311yescharacteristic
84C4×D4×C103—21no—
85C4×D4×C103—21no—
86C2×C4⋊C4×C103—21no—
87C2×C4⋊C4×C103D411yescharacteristic
88C2×C42×C103—21no—
89C2×C42×C103C2311yescharacteristic
90#106×C103—21no—
91#106×C103—21no—
92C4⋊C8×C103—22no—
93C4⋊C8×C103—22no—
94C4⋊C8×C103—21no—
95C4⋊C8×C103—21no—
96C4⋊C8×C103C2312yes—
97C4⋊C8×C103C2312yes—
98C4⋊C8×C103C2311yescharacteristic
99C4⋊C8×C103C2311yescharacteristic
100#103×C103—21no—
101#103×C103—21no—
102#102×C103—22no—
103#102×C103—22no—
104#102×C103—21no—
105#102×C103—21no—
106C22⋊C8×C103—21no—
107#97×C103—22no—
108#97×C103D412yes—
109C4×C8×C103—22no—
110C4×C8×C103—21no—
111C4×C8×C103C2312yes—
112C24×C103—41no—
113#41×C103—42no—
114#41×C103—42no—
115C2×Q8×C103—21no—
116C2×Q8×C103—22no—
117C2×Q8×C103—21no—
118C2×Q8×C103—41no—
119C2×Q8×C103C2×D411yescharacteristic
120C2×Q8×C103C2×D411yescharacteristic
121C2×D4×C103—21no—
122C2×D4×C103—22no—
123C2×D4×C103—21no—
124C2×D4×C103—22no—
125C2×D4×C103—21no—
126C2×D4×C103—22no—
127C2×D4×C103—42no—
128C2×D4×C103—42no—
129C2×D4×C103—41no—
130C2×D4×C103—41no—
131C2×D4×C103—41no—
132C2×D4×C103—41no—
133C2×D4×C103—42no—
134C2×D4×C103—42no—
135C2×D4×C103—82no—
136C22×C4×C103—21no—
137C22×C4×C103—21no—
138C22×C4×C103—41no—
139C22×C4×C103C2×D411yescharacteristic
140C22×C4×C103C2×D411yescharacteristic
141C22×C4×C103#4111yescharacteristic
142SD16×C103—44no—
143SD16×C103—42no—
144SD16×C103—44no—
145SD16×C103—42no—
146SD16×C103—44no—
147SD16×C103—44no—
148D8×C103—44no—
149D8×C103—44no—
150M16×C103—22no—
151M16×C103—42no—
152M16×C103SD1614yescomplemented
153C2×C8×C103—22no—
154C2×C8×C103—21no—
155C2×C8×C103—21no—
156C2×C8×C103—22no—
157C2×C8×C103—42no—
158C2×C8×C103C2×D412yes—
159C2×C8×C103C2×D412yes—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—21no—
163C4⋊C4×C103—21no—
164C4⋊C4×C103—21no—
165C4⋊C4×C103—21no—
166C4⋊C4×C103—21no—
167C4⋊C4×C103C2×D411yescharacteristic
168C4⋊C4×C103C2×D411yescharacteristic
169C22⋊C4×C103—41no—
170C22⋊C4×C103—41no—
171C42×C103—21no—
172C42×C103—21no—
173C42×C103—21no—
174C42×C103—21no—
175C42×C103C2×D411yescharacteristic
176C42×C103C2×D411yescharacteristic
177C42×C103#4111yescharacteristic
178C42×C103C2411yescharacteristic
179C23×C103—41no—
180C23×C103—42no—
181C23×C103—82no—
182C23×C103—82no—
183C23×C103—82no—
184C23×C103#12111yescharacteristic
185Q8×C103—21no—
186Q8×C103—21no—
187Q8×C103—21no—
188Q8×C103—42no—
189Q8×C103—41no—
190Q8×C103—41no—
191Q8×C103AGL(1,ℤ/8)12yescomplemented
192D4×C103—41no—
193D4×C103—42no—
194D4×C103—41no—
195D4×C103—42no—
196D4×C103—42no—
197D4×C103—41no—
198D4×C103—41no—
199D4×C103—42no—
200D4×C103—81no—
201D4×C103—82no—
202D4×C103—82no—
203D4×C103—82no—
204D4×C103—82no—
205D4×C103—82no—
206C2×C4×C103—21no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—21no—
210C2×C4×C103—21no—
211C2×C4×C103—21no—
212C2×C4×C103—41no—
213C2×C4×C103—42no—
214C2×C4×C103—41no—
215C2×C4×C103—81no—
216C2×C4×C103—82no—
217C2×C4×C103#12111yescharacteristic
218C2×C4×C103#12111yescharacteristic
219C2×C4×C103#12111yescharacteristic
220C2×C4×C103C2×SD1612yes—
221C2×C4×C103AGL(1,ℤ/8)12yes—
222C2×C4×C103C22×D411yescharacteristic
223C2×C4×C103C22×D411yescharacteristic
224C2×C4×C103C2×#4111yescharacteristic
225C8×C103—22no—
226C8×C103—42no—
227C8×C103—42no—
228C8×C103—41no—
229C8×C103—41no—
230C8×C103C2×SD1614yescomplemented
231C22×C103—21no—
232C22×C103—21no—
233C22×C103—81no—
234C22×C103—82no—
235C22×C103—82no—
236C22×C103—81no—
237C22×C103—82no—
238C22×C103—81no—
239C22×C103—164no—
240C22×C103#46012yes—
241C22×C103C2×#12111yescharacteristic
242C4×C103—21no—
243C4×C103—22no—
244C4×C103—21no—
245C4×C103—21no—
246C4×C103—41no—
247C4×C103—41no—
248C4×C103—41no—
249C4×C103—81no—
250C4×C103#46012yes—
251C4×C103C22×SD1611yescharacteristic
252C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
253C4×C103C2×AGL(1,ℤ/8)11yescharacteristic
254C4×C103#57511yescharacteristic
255#19170C10311yesmaximal, characteristic, direct product factor, Sylow
256C2×C103—22no—
257C2×C103—161no—
258C2×C103—162no—
259C2×C103C2×#46011yescharacteristic
260C2×C103#305511yescharacteristic
261C2×C103#306811yescharacteristic
262#3151C2×C10311yescharacteristic
263#3103C2×C10311yescharacteristic, complemented
264C2×#460C2×C10311yescharacteristic, complemented
265Q8×M16C2×C10311yescharacteristic, complemented
266#1688C2×C10312yescomplemented
267#1686C2×C10312yescomplemented
268#1668C2×C10312yescomplemented
269#1666C2×C10312yescomplemented
270#1565C2×C10311yescharacteristic, complemented
271#1547C2×C10311yescharacteristic, complemented
272#1545C2×C10311yescharacteristic, complemented
273C103#1917011yescharacteristic, direct product factor, Sylow
274C2×AGL(1,ℤ/8)—21no—
275C2×AGL(1,ℤ/8)—21no—
276C22×SD16—21no—
277#532C22×C10311yescharacteristic
278C2×#127C22×C10311yescharacteristic
279C2×C4×Q8C22×C10311yescharacteristic
280#496—22no—
281#493C22×C10312yes—
282#492C22×C10312yes—
283#481—21no—
284#475C22×C10311yescharacteristic, complemented
285#475C22×C10311yescharacteristic, complemented
286#460—21no—
287#460—21no—
288#460C22×C10312yes—
289#460C22×C10312yes—
290#460C22×C10311yescharacteristic, complemented
291#460C22×C10311yescharacteristic, complemented
292#448—21no—
293#446—22no—
294#446C22×C10312yescomplemented
295C8×Q8C22×C10312yescomplemented
296C4×SD16—21no—
297C4×SD16—21no—
298#431C22×C10311yescharacteristic
299#423—21no—
300#423C22×C10311yescharacteristic
301C2×C4⋊C8C22×C10311yescharacteristic
302C2×#102—21no—
303C4×M16—21no—
304C4×M16C22×C10311yescharacteristic
305#335C22×C10312yescomplemented
306#334C22×C10312yescomplemented
307#332C22×C10312yescomplemented
308#331C22×C10312yes—
309#331C22×C10312yes—
310#331C22×C10312yescomplemented
311C2×#41—21no—
312C22×Q8D4×C10311yescharacteristic
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—21no—
316AGL(1,ℤ/8)—44no—
317AGL(1,ℤ/8)—44no—
318C2×SD16—22no—
319C2×SD16—22no—
320C2×SD16—21no—
321C2×SD16—21no—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—44no—
325C2×D8—22no—
326C2×D8—22no—
327C2×M16—21no—
328C2×M16D4×C10311yescharacteristic
329C2×M16D4×C10311yescharacteristic
330C22×C8—21no—
331C4⋊Q8C23×C10311yescharacteristic
332#127—21no—
333#127—21no—
334#127—21no—
335#127C23×C10312yes—
336#127C23×C10311yescharacteristic
337#124—21no—
338#121—21no—
339#121—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8D4×C10311yescharacteristic
343C4×Q8D4×C10311yescharacteristic
344C4×Q8C23×C10311yescharacteristic
345C4×Q8C23×C10311yescharacteristic
346C4×D4—21no—
347C4×D4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4D4×C10311yescharacteristic
350C2×C42—21no—
351C2×C42C23×C10311yescharacteristic
352#106—21no—
353#106—21no—
354C4⋊C8—22no—
355C4⋊C8—22no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8C23×C10312yes—
359C4⋊C8C23×C10311yescharacteristic
360C4⋊C8C23×C10311yescharacteristic
361C4⋊C8C23×C10312yes—
362#103—21no—
363#103—21no—
364#102—22no—
365#102—22no—
366#102—21no—
367#102—21no—
368C22⋊C8—21no—
369#97—22no—
370#97D4×C10312yes—
371C4×C8—22no—
372C4×C8—21no—
373C4×C8C23×C10312yes—
374C24—41no—
375#41—42no—
376#41—42no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—21no—
380C2×Q8—41no—
381C2×Q8C2×D4×C10311yescharacteristic
382C2×Q8C2×D4×C10311yescharacteristic
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—82no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—41no—
401C22×C4C2×D4×C10311yescharacteristic
402C22×C4C2×D4×C10311yescharacteristic
403C22×C4#41×C10311yescharacteristic
404SD16—44no—
405SD16—42no—
406SD16—44no—
407SD16—42no—
408SD16—44no—
409SD16—44no—
410D8—44no—
411D8—44no—
412M16—22no—
413M16—42no—
414M16SD16×C10314yescomplemented
415C2×C8—22no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—22no—
419C2×C8—42no—
420C2×C8C2×D4×C10312yes—
421C2×C8C2×D4×C10312yes—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4C2×D4×C10311yescharacteristic
430C4⋊C4C2×D4×C10311yescharacteristic
431C22⋊C4—41no—
432C22⋊C4—41no—
433C42—21no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42C2×D4×C10311yescharacteristic
438C42C2×D4×C10311yescharacteristic
439C42#41×C10311yescharacteristic
440C42C24×C10311yescharacteristic
441C23—41no—
442C23—42no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23#121×C10311yescharacteristic
447Q8—21no—
448Q8—21no—
449Q8—21no—
450Q8—42no—
451Q8—41no—
452Q8—41no—
453Q8AGL(1,ℤ/8)×C10312yescomplemented
454D4—41no—
455D4—42no—
456D4—41no—
457D4—42no—
458D4—42no—
459D4—41no—
460D4—41no—
461D4—42no—
462D4—82no—
463D4—81no—
464D4—82no—
465D4—82no—
466D4—82no—
467D4—82no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—81no—
478C2×C4—82no—
479C2×C4#121×C10311yescharacteristic
480C2×C4#121×C10311yescharacteristic
481C2×C4#121×C10311yescharacteristic
482C2×C4C2×SD16×C10312yes—
483C2×C4AGL(1,ℤ/8)×C10312yes—
484C2×C4C22×D4×C10311yescharacteristic
485C2×C4C22×D4×C10311yescharacteristic
486C2×C4C2×#41×C10311yescharacteristic
487C8—22no—
488C8—42no—
489C8—42no—
490C8—41no—
491C8—41no—
492C8C2×SD16×C10314yescomplemented
493C22—21no—
494C22—21no—
495C22—81no—
496C22—82no—
497C22—82no—
498C22—81no—
499C22—82no—
500C22—81no—
501C22—164no—
502C22#460×C10312yes—
503C22C2×#121×C10311yescharacteristic
504C4—21no—
505C4—22no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—81no—
512C4#460×C10312yes—
513C4C22×SD16×C10311yescharacteristic
514C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
515C4C2×AGL(1,ℤ/8)×C10311yescharacteristic
516C4#575×C10311yescharacteristic
517C2—22no—
518C2—162no—
519C2—161no—
520C2C2×#460×C10311yescharacteristic
521C2C103×#305511yescharacteristic
522C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3151C2
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×#3103C2semidirect
3. C2×#460×C103C2semidirect
4. Q8×M16×C103C2semidirect
5. C103×#1688C2semidirect
6. C103×#1686C2semidirect
7. C103×#1668C2semidirect
8. C103×#1666C2semidirect
9. C103×#1565C2semidirect
10. C103×#1547C2semidirect
11. C103×#1545C2semidirect
22. #475×C103C22semidirect
23. #475×C103C22semidirect
28. #460×C103C22semidirect
29. #460×C103C22semidirect
32. #446×C103C22semidirect
33. C8×Q8×C103C22semidirect
43. #335×C103C22semidirect
44. #334×C103C22semidirect
45. #332×C103C22semidirect
48. #331×C103C22semidirect
152. M16×C103SD16semidirect
191. Q8×C103AGL(1,ℤ/8)semidirect
230. C8×C103C2×SD16semidirect
255. #19170C103direct (N × H)
263. #3103C2×C103semidirect
264. C2×#460C2×C103semidirect
265. Q8×M16C2×C103semidirect
266. #1688C2×C103semidirect
267. #1686C2×C103semidirect
268. #1668C2×C103semidirect
269. #1666C2×C103semidirect
270. #1565C2×C103semidirect
271. #1547C2×C103semidirect
272. #1545C2×C103semidirect
273. C103#19170direct (N × H)
284. #475C22×C103semidirect
285. #475C22×C103semidirect
290. #460C22×C103semidirect
291. #460C22×C103semidirect
294. #446C22×C103semidirect
295. C8×Q8C22×C103semidirect
305. #335C22×C103semidirect
306. #334C22×C103semidirect
307. #332C22×C103semidirect
310. #331C22×C103semidirect
414. M16SD16×C103semidirect
453. Q8AGL(1,ℤ/8)×C103semidirect
492. C8C2×SD16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31512
C103×#31032
C2×#460×C1032
Q8×M16×C1032
C103×#16882
C103×#16862
C103×#16682
C103×#16662
C103×#15652
C103×#15472
C103×#15452
#19170103