Finite Group Databasebeta

← C103×#19950 #39925225

Subgroups — C103×#19950 #39925225

Order 26368.

570 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3398C211yesmaximal, characteristic, complemented
2C103×#3381C211yesmaximal, characteristic, complemented
3C103×#3357C211yesmaximal, characteristic
4C103×#3340C211yesmaximal, characteristic
5C103×#1707C211yesmaximal, characteristic, complemented
6C103×#1696C211yesmaximal, characteristic, complemented
7C103×#1689C211yesmaximal, characteristic, complemented
8C103×#1672C211yesmaximal, characteristic, complemented
9C103×#1671C211yesmaximal, characteristic, complemented
10C103×#1646C211yesmaximal, characteristic
11C103×#1644C211yesmaximal, characteristic, complemented
12C103×#1638C211yesmaximal, characteristic, complemented
13C103×#1636C211yesmaximal, characteristic, complemented
14C103×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C103C211yesmaximal, characteristic, complemented
16#557×C103C2211yescharacteristic
17#556×C103C2211yescharacteristic
18#555×C103C2211yescharacteristic
19#554×C103C2211yescharacteristic
20#500×C103C2211yescharacteristic
21#499×C103—21no—
22#498×C103C2211yescharacteristic
23#498×C103C2211yescharacteristic
24#497×C103—21no—
25#494×C103C2211yescharacteristic
26#487×C103C2211yescharacteristic
27#487×C103C2211yescharacteristic
28#485×C103—21no—
29#485×C103—21no—
30#482×C103—21no—
31#480×C103—21no—
32#479×C103—21no—
33#478×C103—21no—
34#477×C103C2211yescharacteristic
35#477×C103C2211yescharacteristic
36#477×C103C2211yescharacteristic
37#476×C103C2211yescharacteristic
38#474×C103C2211yescharacteristic
39#474×C103C2211yescharacteristic
40#468×C103—21no—
41#465×C103—21no—
42#464×C103—21no—
43#462×C103—21no—
44#462×C103C2211yescharacteristic
45#461×C103C2211yescharacteristic
46#446×C103C2211yescharacteristic
47C8×Q8×C103C2211yescharacteristic
48#441×C103—21no—
49C4×SD16×C103—21no—
50C4×SD16×C103C2211yescharacteristic
51C4×SD16×C103C2211yescharacteristic
52#436×C103C2211yescharacteristic
53C8×D4×C103C2211yescharacteristic
54#428×C103—21no—
55#427×C103—21no—
56#334×C103C2211yescharacteristic
57#334×C103C2211yescharacteristic
58#333×C103C2211yescharacteristic
59#333×C103C2211yescharacteristic
60#332×C103C2211yescharacteristic
61#332×C103C2211yescharacteristic
62Q8⋊C8×C103C2211yescharacteristic
63Q8⋊C8×C103C2211yescharacteristic
64D4⋊C8×C103C2211yescharacteristic
65D4⋊C8×C103C2211yescharacteristic
66C82×C103C2211yescharacteristic
67C2×Q16×C103—21no—
68C2×Q16×C103—21no—
69C2×Q16×C103—21no—
70C2×SD16×C103—21no—
71C2×SD16×C103D411yescharacteristic
72C2×SD16×C103D411yescharacteristic
73C2×M16×C103—21no—
74C22×C8×C103—21no—
75C4⋊Q8×C103—21no—
76C4⋊Q8×C103C2311yescharacteristic
77C4⋊Q8×C103C2311yescharacteristic
78C4⋊Q8×C103C2311yescharacteristic
79C4⋊Q8×C103C2311yescharacteristic
80#126×C103—41no—
81#125×C103—21no—
82#125×C103—21no—
83#125×C103—41no—
84#124×C103—21no—
85#124×C103—41no—
86C22⋊Q8×C103—21no—
87C22⋊Q8×C103—21no—
88C22⋊Q8×C103—41no—
89#121×C103—21no—
90#121×C103—21no—
91C4×Q8×C103—21no—
92C4×Q8×C103—21no—
93C4×Q8×C103—21no—
94C4×Q8×C103C2311yescharacteristic
95C4×Q8×C103C2311yescharacteristic
96C4×D4×C103—21no—
97C4×D4×C103C2311yescharacteristic
98C4×D4×C103C2311yescharacteristic
99#117×C103—21no—
100#117×C103—21no—
101#117×C103—21no—
102C2×C4⋊C4×C103—21no—
103#107×C103—21no—
104#107×C103—21no—
105#107×C103—21no—
106#107×C103—21no—
107#107×C103—21no—
108#107×C103—21no—
109#107×C103—21no—
110#106×C103—21no—
111#106×C103—21no—
112#106×C103—21no—
113#106×C103—21no—
114#106×C103—21no—
115#106×C103D411yescharacteristic
116#106×C103D411yescharacteristic
117C4⋊C8×C103—21no—
118C4⋊C8×C103—21no—
119C4⋊C8×C103C2311yescharacteristic
120C4⋊C8×C103C2311yescharacteristic
121C4⋊C8×C103C2311yescharacteristic
122C4⋊C8×C103C2311yescharacteristic
123#103×C103—21no—
124#103×C103—21no—
125#103×C103—21no—
126#103×C103—21no—
127#103×C103—21no—
128#103×C103—41no—
129#103×C103—41no—
130#103×C103D411yescharacteristic
131#103×C103D411yescharacteristic
132#102×C103—21no—
133#102×C103—21no—
134#102×C103—21no—
135#102×C103D411yescharacteristic
136#102×C103D411yescharacteristic
137C22⋊C8×C103—21no—
138C22⋊C8×C103—21no—
139#97×C103—21no—
140C4×C8×C103—21no—
141C4×C8×C103C2311yescharacteristic
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144C2×Q8×C103—21no—
145C2×Q8×C103—21no—
146C2×Q8×C103—21no—
147C2×Q8×C103—21no—
148C2×Q8×C103C2×D411yescharacteristic
149C2×Q8×C103C2×D411yescharacteristic
150C2×D4×C103—41no—
151C2×D4×C103C2×D411yescharacteristic
152C2×D4×C103C2×D411yescharacteristic
153C22×C4×C103—21no—
154C22×C4×C103—21no—
155C22×C4×C103—41no—
156Q16×C103—42no—
157Q16×C103—81no—
158Q16×C103—81no—
159SD16×C103—22no—
160SD16×C103—22no—
161SD16×C103—81no—
162M16×C103—42no—
163C2×C8×C103—21no—
164C2×C8×C103—21no—
165C2×C8×C103—21no—
166C2×C8×C103—21no—
167C2×C8×C103—21no—
168C2×C8×C103—42no—
169C2×C8×C103C2×D411yescharacteristic
170C2×C8×C103C2×D411yescharacteristic
171C2×C8×C103C2×D411yescharacteristic
172C2×C8×C103C2×D411yescharacteristic
173C4⋊C4×C103—21no—
174C4⋊C4×C103—21no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—21no—
179C4⋊C4×C103—21no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—21no—
182C4⋊C4×C103—21no—
183C4⋊C4×C103—41no—
184C4⋊C4×C103—41no—
185C4⋊C4×C103—41no—
186C4⋊C4×C103—41no—
187C4⋊C4×C103—41no—
188C4⋊C4×C103—41no—
189C4⋊C4×C103C2×D411yescharacteristic
190C4⋊C4×C103C2×D411yescharacteristic
191C4⋊C4×C103C2×D411yescharacteristic
192C4⋊C4×C103C2×D411yescharacteristic
193C22⋊C4×C103—21no—
194C22⋊C4×C103—21no—
195C22⋊C4×C103—41no—
196C22⋊C4×C103—41no—
197C22⋊C4×C103—41no—
198C22⋊C4×C103—41no—
199C22⋊C4×C103—41no—
200C42×C103—21no—
201C42×C103—21no—
202C42×C103—41no—
203C42×C103—41no—
204C42×C103—41no—
205C42×C103C2411yescharacteristic
206C23×C103—21no—
207C23×C103—21no—
208Q8×C103—21no—
209Q8×C103—21no—
210Q8×C103—21no—
211Q8×C103—21no—
212Q8×C103—41no—
213Q8×C103—41no—
214Q8×C103—41no—
215Q8×C103—41no—
216Q8×C103—81no—
217Q8×C103—81no—
218D4×C103—21no—
219D4×C103—21no—
220D4×C103—21no—
221D4×C103—21no—
222D4×C103—161no—
223C2×C4×C103—21no—
224C2×C4×C103—21no—
225C2×C4×C103—21no—
226C2×C4×C103—21no—
227C2×C4×C103—21no—
228C2×C4×C103—21no—
229C2×C4×C103—41no—
230C2×C4×C103—41no—
231C2×C4×C103—41no—
232C2×C4×C103—41no—
233C2×C4×C103—41no—
234C2×C4×C103—41no—
235C2×C4×C103—41no—
236C2×C4×C103—41no—
237C2×C4×C103—161no—
238C2×C4×C103C22×D411yescharacteristic
239C2×C4×C103C22×D411yescharacteristic
240C2×C4×C103H(5,𝔽2)11yescharacteristic
241C8×C103—21no—
242C8×C103—21no—
243C8×C103—41no—
244C8×C103—41no—
245C8×C103—41no—
246C8×C103—41no—
247C8×C103—41no—
248C8×C103#13512yes—
249C8×C103#13712yes—
250C22×C103—41no—
251C22×C103—41no—
252C22×C103—41no—
253C22×C103—41no—
254C22×C103—41no—
255C22×C103—41no—
256C22×C103D4211yescharacteristic
257C4×C103—21no—
258C4×C103—41no—
259C4×C103—41no—
260C4×C103—41no—
261C4×C103—41no—
262C4×C103—41no—
263C4×C103—41no—
264C4×C103—81no—
265C4×C103—81no—
266C4×C103—81no—
267C4×C103—81no—
268C4×C103C2×#13511yescharacteristic
269C4×C103C2×#13711yescharacteristic
270C4×C103#57711yescharacteristic
271C4×C103#57811yescharacteristic
272#19950C10311yesmaximal, characteristic, direct product factor, Sylow
273C2×C103—81no—
274C2×C103—81no—
275C2×C103#327611yescharacteristic
276C2×C103#328411yescharacteristic
277C2×C103#329011yescharacteristic
278#3398C2×C10311yescharacteristic, complemented
279#3381C2×C10311yescharacteristic, complemented
280#3357C2×C10311yescharacteristic
281#3340C2×C10311yescharacteristic
282#1707C2×C10311yescharacteristic, complemented
283#1696C2×C10311yescharacteristic, complemented
284#1689C2×C10311yescharacteristic, complemented
285#1672C2×C10311yescharacteristic, complemented
286#1671C2×C10311yescharacteristic, complemented
287#1646C2×C10311yescharacteristic
288#1644C2×C10311yescharacteristic, complemented
289#1638C2×C10311yescharacteristic, complemented
290#1636C2×C10311yescharacteristic, complemented
291#1590C2×C10311yescharacteristic, complemented
292C8×SD16C2×C10311yescharacteristic, complemented
293C103#1995011yescharacteristic, direct product factor, Sylow
294#557C22×C10311yescharacteristic
295#556C22×C10311yescharacteristic
296#555C22×C10311yescharacteristic
297#554C22×C10311yescharacteristic
298#500C22×C10311yescharacteristic
299#499—21no—
300#498C22×C10311yescharacteristic
301#498C22×C10311yescharacteristic
302#497—21no—
303#494C22×C10311yescharacteristic
304#487C22×C10311yescharacteristic
305#487C22×C10311yescharacteristic
306#485—21no—
307#485—21no—
308#482—21no—
309#480—21no—
310#479—21no—
311#478—21no—
312#477C22×C10311yescharacteristic
313#477C22×C10311yescharacteristic
314#477C22×C10311yescharacteristic
315#476C22×C10311yescharacteristic
316#474C22×C10311yescharacteristic
317#474C22×C10311yescharacteristic
318#468—21no—
319#465—21no—
320#464—21no—
321#462—21no—
322#462C22×C10311yescharacteristic
323#461C22×C10311yescharacteristic
324#446C22×C10311yescharacteristic
325C8×Q8C22×C10311yescharacteristic
326#441—21no—
327C4×SD16—21no—
328C4×SD16C22×C10311yescharacteristic
329C4×SD16C22×C10311yescharacteristic
330#436C22×C10311yescharacteristic
331C8×D4C22×C10311yescharacteristic
332#428—21no—
333#427—21no—
334#334C22×C10311yescharacteristic
335#334C22×C10311yescharacteristic
336#333C22×C10311yescharacteristic
337#333C22×C10311yescharacteristic
338#332C22×C10311yescharacteristic
339#332C22×C10311yescharacteristic
340Q8⋊C8C22×C10311yescharacteristic
341Q8⋊C8C22×C10311yescharacteristic
342D4⋊C8C22×C10311yescharacteristic
343D4⋊C8C22×C10311yescharacteristic
344C82C22×C10311yescharacteristic
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×SD16—21no—
349C2×SD16D4×C10311yescharacteristic
350C2×SD16D4×C10311yescharacteristic
351C2×M16—21no—
352C22×C8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C10311yescharacteristic
355C4⋊Q8C23×C10311yescharacteristic
356C4⋊Q8C23×C10311yescharacteristic
357C4⋊Q8C23×C10311yescharacteristic
358#126—41no—
359#125—21no—
360#125—21no—
361#125—41no—
362#124—21no—
363#124—41no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367#121—21no—
368#121—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C23×C10311yescharacteristic
373C4×Q8C23×C10311yescharacteristic
374C4×D4—21no—
375C4×D4C23×C10311yescharacteristic
376C4×D4C23×C10311yescharacteristic
377#117—21no—
378#117—21no—
379#117—21no—
380C2×C4⋊C4—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106D4×C10311yescharacteristic
394#106D4×C10311yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C10311yescharacteristic
398C4⋊C8C23×C10311yescharacteristic
399C4⋊C8C23×C10311yescharacteristic
400C4⋊C8C23×C10311yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—41no—
407#103—41no—
408#103D4×C10311yescharacteristic
409#103D4×C10311yescharacteristic
410#102—21no—
411#102—21no—
412#102—21no—
413#102D4×C10311yescharacteristic
414#102D4×C10311yescharacteristic
415C22⋊C8—21no—
416C22⋊C8—21no—
417#97—21no—
418C4×C8—21no—
419C4×C8C23×C10311yescharacteristic
420C4×C8C23×C10311yescharacteristic
421C4×C8C23×C10311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C10311yescharacteristic
427C2×Q8C2×D4×C10311yescharacteristic
428C2×D4—41no—
429C2×D4C2×D4×C10311yescharacteristic
430C2×D4C2×D4×C10311yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434Q16—42no—
435Q16—81no—
436Q16—81no—
437SD16—22no—
438SD16—22no—
439SD16—81no—
440M16—42no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8C2×D4×C10311yescharacteristic
448C2×C8C2×D4×C10311yescharacteristic
449C2×C8C2×D4×C10311yescharacteristic
450C2×C8C2×D4×C10311yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C10311yescharacteristic
468C4⋊C4C2×D4×C10311yescharacteristic
469C4⋊C4C2×D4×C10311yescharacteristic
470C4⋊C4C2×D4×C10311yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—41no—
482C42—41no—
483C42C24×C10311yescharacteristic
484C23—21no—
485C23—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496D4—21no—
497D4—21no—
498D4—21no—
499D4—21no—
500D4—161no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—161no—
516C2×C4C22×D4×C10311yescharacteristic
517C2×C4C22×D4×C10311yescharacteristic
518C2×C4H(5,𝔽2)×C10311yescharacteristic
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8#135×C10312yes—
527C8#137×C10312yes—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22D42×C10311yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4C2×#135×C10311yescharacteristic
547C4C2×#137×C10311yescharacteristic
548C4#577×C10311yescharacteristic
549C4#578×C10311yescharacteristic
550C2—81no—
551C2—81no—
552C2C103×#327611yescharacteristic
553C2C103×#328411yescharacteristic
554C2C103×#329011yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
prime radical#555×C103C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3398C2semidirect
2. C103×#3381C2semidirect
5. C103×#1707C2semidirect
6. C103×#1696C2semidirect
7. C103×#1689C2semidirect
8. C103×#1672C2semidirect
9. C103×#1671C2semidirect
11. C103×#1644C2semidirect
12. C103×#1638C2semidirect
13. C103×#1636C2semidirect
14. C103×#1590C2semidirect
15. C8×SD16×C103C2semidirect
272. #19950C103direct (N × H)
278. #3398C2×C103semidirect
279. #3381C2×C103semidirect
282. #1707C2×C103semidirect
283. #1696C2×C103semidirect
284. #1689C2×C103semidirect
285. #1672C2×C103semidirect
286. #1671C2×C103semidirect
288. #1644C2×C103semidirect
289. #1638C2×C103semidirect
290. #1636C2×C103semidirect
291. #1590C2×C103semidirect
292. C8×SD16C2×C103semidirect
293. C103#19950direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#33982
C103×#33812
C103×#33572
C103×#33402
C103×#17072
C103×#16962
C103×#16892
C103×#16722
C103×#16712
C103×#16462
C103×#16442
C103×#16382
C103×#16362
C103×#15902
C8×SD16×C1032
#19950103