Finite Group Databasebeta

← C103×#18833 #39924108

Subgroups — C103×#18833 #39924108

Order 26368.

894 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3511C211yesmaximal, characteristic
2C103×#3235C211yesmaximal, characteristic, complemented
3C103×#3229C211yesmaximal, characteristic, complemented
4C103×#3116C211yesmaximal, characteristic, complemented
5C103×#1654C212yesmaximal, complemented
6C103×#1652C212yesmaximal, complemented
7C103×#1638C212yesmaximal, complemented
8C103×#1635C212yesmaximal, complemented
9C103×#1556C211yesmaximal, characteristic, complemented
10C103×#1496C211yesmaximal, characteristic, complemented
11C103×#1488C211yesmaximal, characteristic, complemented
12#556×C103C2212yes—
13#555×C103—21no—
14#554×C103—21no—
15#553×C103—22no—
16#548×C103—22no—
17#547×C103C2212yes—
18#542×C103—22no—
19#537×C103—21no—
20#533×C103—21no—
21#533×C103C2211yescharacteristic
22#532×C103—21no—
23#532×C103C2211yescharacteristic
24C2×C4⋊Q8×C103C2211yescharacteristic
25#520×C103—21no—
26C4×#41×C103C2211yescharacteristic
27#501×C103—21no—
28#498×C103C2212yes—
29#490×C103—21no—
30#487×C103C2212yes—
31#485×C103—21no—
32#483×C103—22no—
33#482×C103—22no—
34#477×C103C2211yescharacteristic
35#476×C103C2212yes—
36#476×C103C2211yescharacteristic
37#475×C103—22no—
38#474×C103C2212yes—
39#462×C103C2211yescharacteristic
40#461×C103C2211yescharacteristic
41#452×C103—21no—
42#441×C103—21no—
43#440×C103—21no—
44#432×C103C2211yescharacteristic
45#432×C103C2211yescharacteristic
46#431×C103C2211yescharacteristic
47#332×C103C2212yes—
48#332×C103C2212yes—
49Q8⋊C8×C103C2212yes—
50D4⋊C8×C103C2212yes—
51D4⋊C8×C103C2212yes—
52D4⋊C8×C103C2212yes—
53C2×#41×C103—22no—
54C2×#41×C103—21no—
55C2×#41×C103D411yescharacteristic
56C22×Q8×C103—21no—
57C2×Q16×C103—21no—
58C2×SD16×C103—21no—
59C4⋊Q8×C103—21no—
60C4⋊Q8×C103—21no—
61C4⋊Q8×C103D412yes—
62C4⋊Q8×C103D411yescharacteristic
63C4⋊Q8×C103C2311yescharacteristic
64C4⋊Q8×C103C2311yescharacteristic
65C4⋊Q8×C103C2312yes—
66#127×C103D411yescharacteristic
67#126×C103—24no—
68#125×C103—22no—
69#125×C103—21no—
70#124×C103—24no—
71#124×C103—22no—
72#124×C103—21no—
73#123×C103—24no—
74C22⋊Q8×C103—22no—
75C22⋊Q8×C103—24no—
76C22⋊Q8×C103—22no—
77C22⋊Q8×C103—22no—
78C22⋊Q8×C103—21no—
79C22⋊Q8×C103—21no—
80#121×C103—22no—
81#121×C103—22no—
82#121×C103—24no—
83#121×C103—22no—
84#121×C103—21no—
85#121×C103D412yes—
86C4×Q8×C103—22no—
87C4×Q8×C103—22no—
88C4×Q8×C103—21no—
89C4×Q8×C103—21no—
90C4×Q8×C103D411yescharacteristic
91C4×Q8×C103C2311yescharacteristic
92C4×D4×C103—22no—
93C4×D4×C103—24no—
94C4×D4×C103—22no—
95C4×D4×C103—21no—
96C4×D4×C103—21no—
97C4×D4×C103—21no—
98C4×D4×C103D411yescharacteristic
99C4×D4×C103C2311yescharacteristic
100C4×D4×C103C2312yes—
101#117×C103—22no—
102#117×C103—22no—
103#117×C103—21no—
104#117×C103—21no—
105#117×C103D411yescharacteristic
106C2×C4⋊C4×C103—21no—
107C2×C4⋊C4×C103—22no—
108C2×C4⋊C4×C103D412yes—
109C2×C42×C103—21no—
110C2×C42×C103C2311yescharacteristic
111#107×C103—21no—
112#107×C103—22no—
113#106×C103—21no—
114#106×C103—24no—
115#106×C103—22no—
116C4⋊C8×C103—21no—
117C4⋊C8×C103C2311yescharacteristic
118C4⋊C8×C103C2311yescharacteristic
119C4⋊C8×C103C2312yes—
120#103×C103—21no—
121#103×C103—21no—
122#103×C103—21no—
123#103×C103—24no—
124#102×C103—21no—
125#102×C103—22no—
126#102×C103—22no—
127C22⋊C8×C103—21no—
128C22⋊C8×C103—21no—
129C22⋊C8×C103—21no—
130#97×C103—21no—
131#97×C103—21no—
132C4×C8×C103C2312yes—
133#41×C103—41no—
134#41×C103—41no—
135#41×C103—42no—
136#41×C103—42no—
137#41×C103—84no—
138C2×Q8×C103—21no—
139C2×Q8×C103—22no—
140C2×Q8×C103—22no—
141C2×Q8×C103—21no—
142C2×Q8×C103—21no—
143C2×Q8×C103—82no—
144C2×Q8×C103C2×D411yescharacteristic
145C2×D4×C103—21no—
146C2×D4×C103—22no—
147C2×D4×C103—24no—
148C2×D4×C103—21no—
149C2×D4×C103—21no—
150C2×D4×C103C2×D412yes—
151C2×D4×C103C2×D411yescharacteristic
152C22×C4×C103—24no—
153C22×C4×C103—22no—
154C22×C4×C103—21no—
155C22×C4×C103—21no—
156C22×C4×C103—21no—
157C22×C4×C103—22no—
158C22×C4×C103C2×D411yescharacteristic
159C22×C4×C103C2×D411yescharacteristic
160C22×C4×C103C2×D411yescharacteristic
161Q16×C103—42no—
162SD16×C103—42no—
163C2×C8×C103—22no—
164C2×C8×C103—22no—
165C2×C8×C103—21no—
166C2×C8×C103—21no—
167C4⋊C4×C103—24no—
168C4⋊C4×C103—24no—
169C4⋊C4×C103—22no—
170C4⋊C4×C103—22no—
171C4⋊C4×C103—21no—
172C4⋊C4×C103—21no—
173C4⋊C4×C103—22no—
174C4⋊C4×C103—21no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—21no—
179C4⋊C4×C103—41no—
180C4⋊C4×C103—41no—
181C4⋊C4×C103C2×D411yescharacteristic
182C4⋊C4×C103C2×D414yes—
183C4⋊C4×C103C2×D411yescharacteristic
184C4⋊C4×C103C2×D412yes—
185C22⋊C4×C103—24no—
186C22⋊C4×C103—24no—
187C22⋊C4×C103—24no—
188C22⋊C4×C103—21no—
189C22⋊C4×C103—21no—
190C22⋊C4×C103—22no—
191C22⋊C4×C103—21no—
192C22⋊C4×C103—22no—
193C22⋊C4×C103—41no—
194C42×C103—24no—
195C42×C103—21no—
196C42×C103—21no—
197C42×C103—21no—
198C42×C103—41no—
199C42×C103C2×D411yescharacteristic
200C42×C103C2×D411yescharacteristic
201C42×C103C2×D411yescharacteristic
202C42×C103C2411yescharacteristic
203C23×C103—21no—
204C23×C103—22no—
205C23×C103#12011yescharacteristic
206Q8×C103—21no—
207Q8×C103—21no—
208Q8×C103—42no—
209Q8×C103—42no—
210Q8×C103—44no—
211Q8×C103—41no—
212Q8×C103—41no—
213Q8×C103—82no—
214D4×C103—21no—
215D4×C103—21no—
216D4×C103—24no—
217D4×C103—42no—
218D4×C103—42no—
219D4×C103—42no—
220D4×C103—44no—
221D4×C103—84no—
222C2×C4×C103—21no—
223C2×C4×C103—21no—
224C2×C4×C103—22no—
225C2×C4×C103—21no—
226C2×C4×C103—21no—
227C2×C4×C103—22no—
228C2×C4×C103—21no—
229C2×C4×C103—24no—
230C2×C4×C103—41no—
231C2×C4×C103—42no—
232C2×C4×C103—42no—
233C2×C4×C103—42no—
234C2×C4×C103—42no—
235C2×C4×C103—42no—
236C2×C4×C103—41no—
237C2×C4×C103—41no—
238C2×C4×C103—82no—
239C2×C4×C103—84no—
240C2×C4×C103#12011yescharacteristic
241C2×C4×C103#12011yescharacteristic
242C2×C4×C103#12011yescharacteristic
243C2×C4×C103C22×D411yescharacteristic
244C2×C4×C103C22×D411yescharacteristic
245C2×C4×C103C22×D411yescharacteristic
246C8×C103—42no—
247C8×C103—41no—
248C8×C103—41no—
249C8×C103—42no—
250C22×C103—21no—
251C22×C103—21no—
252C22×C103—21no—
253C22×C103—41no—
254C22×C103—42no—
255C22×C103—41no—
256C22×C103—42no—
257C22×C103—41no—
258C22×C103—42no—
259C22×C103C2×#12011yescharacteristic
260C4×C103—21no—
261C4×C103—21no—
262C4×C103—21no—
263C4×C103—21no—
264C4×C103—41no—
265C4×C103—42no—
266C4×C103—41no—
267C4×C103—44no—
268C4×C103—41no—
269C4×C103—81no—
270C4×C103—81no—
271C4×C103#57511yescharacteristic
272C4×C103#57511yescharacteristic
273C4×C103#57712yes—
274#18833C10311yesmaximal, characteristic, direct product factor, Sylow
275C2×C103—41no—
276C2×C103—81no—
277C2×C103—82no—
278C2×C103#300511yescharacteristic
279C2×C103#300911yescharacteristic
280C2×C103#302011yescharacteristic
281#3511C2×C10311yescharacteristic
282#3235C2×C10311yescharacteristic, complemented
283#3229C2×C10311yescharacteristic, complemented
284#3116C2×C10311yescharacteristic, complemented
285#1654C2×C10312yescomplemented
286#1652C2×C10312yescomplemented
287#1638C2×C10312yescomplemented
288#1635C2×C10312yescomplemented
289#1556C2×C10311yescharacteristic, complemented
290#1496C2×C10311yescharacteristic, complemented
291#1488C2×C10311yescharacteristic, complemented
292C103#1883311yescharacteristic, direct product factor, Sylow
293#556C22×C10312yes—
294#555—21no—
295#554—21no—
296#553—22no—
297#548—22no—
298#547C22×C10312yes—
299#542—22no—
300#537—21no—
301#533—21no—
302#533C22×C10311yescharacteristic
303#532—21no—
304#532C22×C10311yescharacteristic
305C2×C4⋊Q8C22×C10311yescharacteristic
306#520—21no—
307C4×#41C22×C10311yescharacteristic
308#501—21no—
309#498C22×C10312yes—
310#490—21no—
311#487C22×C10312yes—
312#485—21no—
313#483—22no—
314#482—22no—
315#477C22×C10311yescharacteristic
316#476C22×C10311yescharacteristic
317#476C22×C10312yes—
318#475—22no—
319#474C22×C10312yes—
320#462C22×C10311yescharacteristic
321#461C22×C10311yescharacteristic
322#452—21no—
323#441—21no—
324#440—21no—
325#432C22×C10311yescharacteristic
326#432C22×C10311yescharacteristic
327#431C22×C10311yescharacteristic
328#332C22×C10312yes—
329#332C22×C10312yes—
330Q8⋊C8C22×C10312yes—
331D4⋊C8C22×C10312yes—
332D4⋊C8C22×C10312yes—
333D4⋊C8C22×C10312yes—
334C2×#41—22no—
335C2×#41—21no—
336C2×#41D4×C10311yescharacteristic
337C22×Q8—21no—
338C2×Q16—21no—
339C2×SD16—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8D4×C10312yes—
343C4⋊Q8D4×C10311yescharacteristic
344C4⋊Q8C23×C10311yescharacteristic
345C4⋊Q8C23×C10311yescharacteristic
346C4⋊Q8C23×C10312yes—
347#127D4×C10311yescharacteristic
348#126—24no—
349#125—22no—
350#125—21no—
351#124—24no—
352#124—22no—
353#124—21no—
354#123—24no—
355C22⋊Q8—22no—
356C22⋊Q8—24no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361#121—22no—
362#121—22no—
363#121—24no—
364#121—22no—
365#121—21no—
366#121D4×C10312yes—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8D4×C10311yescharacteristic
372C4×Q8C23×C10311yescharacteristic
373C4×D4—22no—
374C4×D4—24no—
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4D4×C10311yescharacteristic
380C4×D4C23×C10311yescharacteristic
381C4×D4C23×C10312yes—
382#117—22no—
383#117—22no—
384#117—21no—
385#117—21no—
386#117D4×C10311yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4D4×C10312yes—
390C2×C42—21no—
391C2×C42C23×C10311yescharacteristic
392#107—21no—
393#107—22no—
394#106—21no—
395#106—24no—
396#106—22no—
397C4⋊C8—21no—
398C4⋊C8C23×C10311yescharacteristic
399C4⋊C8C23×C10311yescharacteristic
400C4⋊C8C23×C10312yes—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—24no—
405#102—21no—
406#102—22no—
407#102—22no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411#97—21no—
412#97—21no—
413C4×C8C23×C10312yes—
414#41—41no—
415#41—41no—
416#41—42no—
417#41—42no—
418#41—84no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—82no—
425C2×Q8C2×D4×C10311yescharacteristic
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—24no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4C2×D4×C10312yes—
432C2×D4C2×D4×C10311yescharacteristic
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4C2×D4×C10311yescharacteristic
440C22×C4C2×D4×C10311yescharacteristic
441C22×C4C2×D4×C10311yescharacteristic
442Q16—42no—
443SD16—42no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—21no—
447C2×C8—21no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C10311yescharacteristic
463C4⋊C4C2×D4×C10314yes—
464C4⋊C4C2×D4×C10311yescharacteristic
465C4⋊C4C2×D4×C10312yes—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C42—24no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—41no—
480C42C2×D4×C10311yescharacteristic
481C42C2×D4×C10311yescharacteristic
482C42C2×D4×C10311yescharacteristic
483C42C24×C10311yescharacteristic
484C23—21no—
485C23—22no—
486C23#120×C10311yescharacteristic
487Q8—21no—
488Q8—21no—
489Q8—42no—
490Q8—42no—
491Q8—44no—
492Q8—41no—
493Q8—41no—
494Q8—82no—
495D4—21no—
496D4—21no—
497D4—24no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—44no—
502D4—84no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—24no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—84no—
521C2×C4#120×C10311yescharacteristic
522C2×C4#120×C10311yescharacteristic
523C2×C4#120×C10311yescharacteristic
524C2×C4C22×D4×C10311yescharacteristic
525C2×C4C22×D4×C10311yescharacteristic
526C2×C4C22×D4×C10311yescharacteristic
527C8—42no—
528C8—41no—
529C8—41no—
530C8—42no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—41no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22C2×#120×C10311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—42no—
547C4—41no—
548C4—44no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4#575×C10311yescharacteristic
553C4#575×C10311yescharacteristic
554C4#577×C10312yes—
555C2—41no—
556C2—81no—
557C2—82no—
558C2C103×#300511yescharacteristic
559C2C103×#300911yescharacteristic
560C2C103×#302011yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3511C2
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×#3235C2semidirect
3. C103×#3229C2semidirect
4. C103×#3116C2semidirect
5. C103×#1654C2semidirect
6. C103×#1652C2semidirect
7. C103×#1638C2semidirect
8. C103×#1635C2semidirect
9. C103×#1556C2semidirect
10. C103×#1496C2semidirect
11. C103×#1488C2semidirect
274. #18833C103direct (N × H)
282. #3235C2×C103semidirect
283. #3229C2×C103semidirect
284. #3116C2×C103semidirect
285. #1654C2×C103semidirect
286. #1652C2×C103semidirect
287. #1638C2×C103semidirect
288. #1635C2×C103semidirect
289. #1556C2×C103semidirect
290. #1496C2×C103semidirect
291. #1488C2×C103semidirect
292. C103#18833direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#35112
C103×#32352
C103×#32292
C103×#31162
C103×#16542
C103×#16522
C103×#16382
C103×#16352
C103×#15562
C103×#14962
C103×#14882
#18833103