Finite Group Databasebeta

← C103×#18702 #39923977

Subgroups — C103×#18702 #39923977

Order 26368.

868 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3550C211yesmaximal, characteristic
2C103×#3255C211yesmaximal, characteristic, complemented
3C103×#3254C211yesmaximal, characteristic
4C103×#3160C211yesmaximal, characteristic, complemented
5C103×#1652C212yesmaximal, complemented
6C103×#1651C212yesmaximal, complemented
7C103×#1650C212yesmaximal, complemented
8C103×#1649C212yesmaximal, complemented
9C103×#1561C211yesmaximal, characteristic, complemented
10C103×#1493C211yesmaximal, characteristic, complemented
11C103×#1492C211yesmaximal, characteristic
12#563×C103—22no—
13#559×C103—21no—
14Q82×C103—21no—
15#556×C103—21no—
16#556×C103C2212yes—
17D4×Q8×C103—21no—
18D4×Q8×C103C2212yes—
19#542×C103—22no—
20#542×C103—22no—
21#536×C103—22no—
22#533×C103C2211yescharacteristic
23#533×C103C2211yescharacteristic
24#533×C103C2211yescharacteristic
25#532×C103C2211yescharacteristic
26#500×C103C2211yescharacteristic
27#500×C103C2211yescharacteristic
28#499×C103—22no—
29#498×C103C2211yescharacteristic
30#498×C103C2211yescharacteristic
31#477×C103—21no—
32#475×C103—21no—
33#475×C103C2212yes—
34#474×C103C2212yes—
35#470×C103—22no—
36#468×C103—22no—
37#462×C103—21no—
38#462×C103C2212yes—
39#461×C103C2212yes—
40#460×C103—21no—
41#427×C103—22no—
42#423×C103C2211yescharacteristic
43#423×C103C2211yescharacteristic
44C2×C4×C8×C103C2211yescharacteristic
45#332×C103C2212yes—
46#332×C103C2212yes—
47Q8⋊C8×C103C2212yes—
48Q8⋊C8×C103C2212yes—
49D4⋊C8×C103C2212yes—
50D4⋊C8×C103C2212yes—
51C2×#41×C103—21no—
52C22×Q8×C103—22no—
53C2×Q16×C103—22no—
54C2×SD16×C103—22no—
55C2×M16×C103—21no—
56C2×M16×C103—21no—
57C22×C8×C103—21no—
58C4⋊Q8×C103—24no—
59C4⋊Q8×C103—22no—
60C4⋊Q8×C103—22no—
61C4⋊Q8×C103D411yescharacteristic
62C4⋊Q8×C103D411yescharacteristic
63C4⋊Q8×C103D411yescharacteristic
64C4⋊Q8×C103C2311yescharacteristic
65C4⋊Q8×C103C2311yescharacteristic
66C4⋊Q8×C103C2311yescharacteristic
67C4⋊Q8×C103C2311yescharacteristic
68#127×C103D411yescharacteristic
69#126×C103—24no—
70#126×C103—24no—
71#125×C103—21no—
72#125×C103—21no—
73#125×C103D412yes—
74#124×C103—24no—
75#124×C103—22no—
76#124×C103—22no—
77#124×C103—21no—
78#123×C103—24no—
79#123×C103—24no—
80C22⋊Q8×C103—24no—
81C22⋊Q8×C103—22no—
82C22⋊Q8×C103—21no—
83C22⋊Q8×C103—21no—
84C22⋊Q8×C103—21no—
85C22⋊Q8×C103—22no—
86C22⋊Q8×C103—24no—
87C22⋊Q8×C103—21no—
88C22⋊Q8×C103—21no—
89C22⋊Q8×C103D412yes—
90#121×C103—21no—
91#121×C103D412yes—
92C4×Q8×C103—22no—
93C4×Q8×C103—22no—
94C4×Q8×C103—21no—
95C4×Q8×C103—21no—
96C4×Q8×C103—21no—
97C4×Q8×C103—21no—
98C4×Q8×C103—21no—
99C4×Q8×C103C2312yes—
100C4×D4×C103—22no—
101C4×D4×C103—22no—
102C4×D4×C103—21no—
103C4×D4×C103C2312yes—
104#117×C103—21no—
105#117×C103—22no—
106#117×C103—21no—
107#117×C103D412yes—
108C2×C42×C103C2311yescharacteristic
109#107×C103—22no—
110#107×C103—22no—
111#107×C103—22no—
112#106×C103—22no—
113#106×C103—22no—
114#106×C103—22no—
115C4⋊C8×C103—21no—
116C4⋊C8×C103—21no—
117C4⋊C8×C103C2312yes—
118C4⋊C8×C103C2312yes—
119#103×C103—22no—
120#103×C103—22no—
121#103×C103—22no—
122#102×C103—22no—
123C4×C8×C103—21no—
124C4×C8×C103C2311yescharacteristic
125C4×C8×C103C2311yescharacteristic
126#41×C103—81no—
127#41×C103—81no—
128C2×Q8×C103—24no—
129C2×Q8×C103—21no—
130C2×Q8×C103—21no—
131C2×Q8×C103—21no—
132C2×Q8×C103—21no—
133C2×Q8×C103—21no—
134C2×Q8×C103—21no—
135C2×Q8×C103—82no—
136C2×Q8×C103—82no—
137C2×Q8×C103C2×D412yes—
138C2×D4×C103—22no—
139C2×D4×C103—21no—
140C2×D4×C103—21no—
141C2×D4×C103C2×D412yes—
142C22×C4×C103—24no—
143C22×C4×C103—22no—
144C22×C4×C103C2×D411yescharacteristic
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D411yescharacteristic
147Q16×C103—82no—
148SD16×C103—82no—
149M16×C103—81no—
150M16×C103—81no—
151C2×C8×C103—24no—
152C2×C8×C103—21no—
153C2×C8×C103—21no—
154C2×C8×C103—22no—
155C2×C8×C103—22no—
156C4⋊C4×C103—24no—
157C4⋊C4×C103—24no—
158C4⋊C4×C103—21no—
159C4⋊C4×C103—21no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—22no—
163C4⋊C4×C103—22no—
164C4⋊C4×C103—22no—
165C4⋊C4×C103—21no—
166C4⋊C4×C103—21no—
167C4⋊C4×C103—22no—
168C4⋊C4×C103—21no—
169C4⋊C4×C103—21no—
170C4⋊C4×C103—21no—
171C4⋊C4×C103—21no—
172C4⋊C4×C103—41no—
173C4⋊C4×C103—41no—
174C4⋊C4×C103C2×D412yes—
175C4⋊C4×C103C2×D412yes—
176C4⋊C4×C103C2×D412yes—
177C4⋊C4×C103C2×D412yes—
178C22⋊C4×C103—24no—
179C22⋊C4×C103—24no—
180C22⋊C4×C103—24no—
181C22⋊C4×C103—22no—
182C22⋊C4×C103—22no—
183C22⋊C4×C103—22no—
184C22⋊C4×C103—22no—
185C22⋊C4×C103—41no—
186C42×C103—24no—
187C42×C103—22no—
188C42×C103—22no—
189C42×C103—41no—
190C42×C103C2×D411yescharacteristic
191C42×C103C2×D411yescharacteristic
192C42×C103C2×D411yescharacteristic
193C42×C103C2411yescharacteristic
194C23×C103—22no—
195C23×C103#12011yescharacteristic
196Q8×C103—22no—
197Q8×C103—22no—
198Q8×C103—41no—
199Q8×C103—41no—
200Q8×C103—41no—
201Q8×C103—41no—
202Q8×C103—42no—
203Q8×C103—41no—
204Q8×C103—41no—
205Q8×C103—41no—
206Q8×C103—41no—
207Q8×C103—81no—
208Q8×C103—84no—
209D4×C103—22no—
210D4×C103—22no—
211D4×C103—42no—
212D4×C103—81no—
213D4×C103—82no—
214C2×C4×C103—21no—
215C2×C4×C103—21no—
216C2×C4×C103—21no—
217C2×C4×C103—21no—
218C2×C4×C103—22no—
219C2×C4×C103—22no—
220C2×C4×C103—22no—
221C2×C4×C103—22no—
222C2×C4×C103—22no—
223C2×C4×C103—22no—
224C2×C4×C103—42no—
225C2×C4×C103—42no—
226C2×C4×C103—41no—
227C2×C4×C103—41no—
228C2×C4×C103—84no—
229C2×C4×C103#12011yescharacteristic
230C2×C4×C103#12011yescharacteristic
231C2×C4×C103#12011yescharacteristic
232C2×C4×C103C22×D411yescharacteristic
233C2×C4×C103C22×D411yescharacteristic
234C2×C4×C103C22×D411yescharacteristic
235C8×C103—22no—
236C8×C103—22no—
237C8×C103—42no—
238C8×C103—42no—
239C22×C103—21no—
240C22×C103—21no—
241C22×C103—21no—
242C22×C103—42no—
243C22×C103—42no—
244C22×C103—42no—
245C22×C103C2×#12011yescharacteristic
246C4×C103—21no—
247C4×C103—21no—
248C4×C103—21no—
249C4×C103—42no—
250C4×C103—42no—
251C4×C103—42no—
252C4×C103—42no—
253C4×C103—42no—
254C4×C103—81no—
255C4×C103—81no—
256C4×C103#45612yes—
257C4×C103#57611yescharacteristic
258C4×C103#57711yescharacteristic
259C4×C103#57711yescharacteristic
260C4×C103#57811yescharacteristic
261#18702C10311yesmaximal, characteristic, direct product factor, Sylow
262C2×C103—41no—
263C2×C103—82no—
264C2×C103#301211yescharacteristic
265C2×C103#301311yescharacteristic
266C2×C103C2×#45611yescharacteristic
267#3550C2×C10311yescharacteristic
268#3255C2×C10311yescharacteristic, complemented
269#3254C2×C10311yescharacteristic
270#3160C2×C10311yescharacteristic, complemented
271#1652C2×C10312yescomplemented
272#1651C2×C10312yescomplemented
273#1650C2×C10312yescomplemented
274#1649C2×C10312yescomplemented
275#1561C2×C10311yescharacteristic, complemented
276#1493C2×C10311yescharacteristic, complemented
277#1492C2×C10311yescharacteristic
278C103#1870211yescharacteristic, direct product factor, Sylow
279#563—22no—
280#559—21no—
281Q82—21no—
282#556—21no—
283#556C22×C10312yes—
284D4×Q8—21no—
285D4×Q8C22×C10312yes—
286#542—22no—
287#542—22no—
288#536—22no—
289#533C22×C10311yescharacteristic
290#533C22×C10311yescharacteristic
291#533C22×C10311yescharacteristic
292#532C22×C10311yescharacteristic
293#500C22×C10311yescharacteristic
294#500C22×C10311yescharacteristic
295#499—22no—
296#498C22×C10311yescharacteristic
297#498C22×C10311yescharacteristic
298#477—21no—
299#475—21no—
300#475C22×C10312yes—
301#474C22×C10312yes—
302#470—22no—
303#468—22no—
304#462—21no—
305#462C22×C10312yes—
306#461C22×C10312yes—
307#460—21no—
308#427—22no—
309#423C22×C10311yescharacteristic
310#423C22×C10311yescharacteristic
311C2×C4×C8C22×C10311yescharacteristic
312#332C22×C10312yes—
313#332C22×C10312yes—
314Q8⋊C8C22×C10312yes—
315Q8⋊C8C22×C10312yes—
316D4⋊C8C22×C10312yes—
317D4⋊C8C22×C10312yes—
318C2×#41—21no—
319C22×Q8—22no—
320C2×Q16—22no—
321C2×SD16—22no—
322C2×M16—21no—
323C2×M16—21no—
324C22×C8—21no—
325C4⋊Q8—24no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8D4×C10311yescharacteristic
329C4⋊Q8D4×C10311yescharacteristic
330C4⋊Q8D4×C10311yescharacteristic
331C4⋊Q8C23×C10311yescharacteristic
332C4⋊Q8C23×C10311yescharacteristic
333C4⋊Q8C23×C10311yescharacteristic
334C4⋊Q8C23×C10311yescharacteristic
335#127D4×C10311yescharacteristic
336#126—24no—
337#126—24no—
338#125—21no—
339#125—21no—
340#125D4×C10312yes—
341#124—24no—
342#124—22no—
343#124—22no—
344#124—21no—
345#123—24no—
346#123—24no—
347C22⋊Q8—24no—
348C22⋊Q8—22no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8D4×C10312yes—
357#121—21no—
358#121D4×C10312yes—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8C23×C10312yes—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—21no—
370C4×D4C23×C10312yes—
371#117—21no—
372#117—22no—
373#117—21no—
374#117D4×C10312yes—
375C2×C42C23×C10311yescharacteristic
376#107—22no—
377#107—22no—
378#107—22no—
379#106—22no—
380#106—22no—
381#106—22no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8C23×C10312yes—
385C4⋊C8C23×C10312yes—
386#103—22no—
387#103—22no—
388#103—22no—
389#102—22no—
390C4×C8—21no—
391C4×C8C23×C10311yescharacteristic
392C4×C8C23×C10311yescharacteristic
393#41—81no—
394#41—81no—
395C2×Q8—24no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—82no—
403C2×Q8—82no—
404C2×Q8C2×D4×C10312yes—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4C2×D4×C10312yes—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4C2×D4×C10311yescharacteristic
412C22×C4C2×D4×C10311yescharacteristic
413C22×C4C2×D4×C10311yescharacteristic
414Q16—82no—
415SD16—82no—
416M16—81no—
417M16—81no—
418C2×C8—24no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—22no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4C2×D4×C10312yes—
442C4⋊C4C2×D4×C10312yes—
443C4⋊C4C2×D4×C10312yes—
444C4⋊C4C2×D4×C10312yes—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—41no—
453C42—24no—
454C42—22no—
455C42—22no—
456C42—41no—
457C42C2×D4×C10311yescharacteristic
458C42C2×D4×C10311yescharacteristic
459C42C2×D4×C10311yescharacteristic
460C42C24×C10311yescharacteristic
461C23—22no—
462C23#120×C10311yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—42no—
466Q8—41no—
467Q8—41no—
468Q8—41no—
469Q8—41no—
470Q8—41no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—81no—
475Q8—84no—
476D4—22no—
477D4—22no—
478D4—42no—
479D4—81no—
480D4—82no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—84no—
496C2×C4#120×C10311yescharacteristic
497C2×C4#120×C10311yescharacteristic
498C2×C4#120×C10311yescharacteristic
499C2×C4C22×D4×C10311yescharacteristic
500C2×C4C22×D4×C10311yescharacteristic
501C2×C4C22×D4×C10311yescharacteristic
502C8—22no—
503C8—22no—
504C8—42no—
505C8—42no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22C2×#120×C10311yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—81no—
522C4—81no—
523C4#456×C10312yes—
524C4#576×C10311yescharacteristic
525C4#577×C10311yescharacteristic
526C4#577×C10311yescharacteristic
527C4#578×C10311yescharacteristic
528C2—41no—
529C2—82no—
530C2C103×#301211yescharacteristic
531C2C103×#301311yescharacteristic
532C2C2×#456×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC42C24×C103
prime radical#532×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×#3255C2semidirect
4. C103×#3160C2semidirect
5. C103×#1652C2semidirect
6. C103×#1651C2semidirect
7. C103×#1650C2semidirect
8. C103×#1649C2semidirect
9. C103×#1561C2semidirect
10. C103×#1493C2semidirect
261. #18702C103direct (N × H)
268. #3255C2×C103semidirect
270. #3160C2×C103semidirect
271. #1652C2×C103semidirect
272. #1651C2×C103semidirect
273. #1650C2×C103semidirect
274. #1649C2×C103semidirect
275. #1561C2×C103semidirect
276. #1493C2×C103semidirect
278. C103#18702direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#35502
C103×#32552
C103×#32542
C103×#31602
C103×#16522
C103×#16512
C103×#16502
C103×#16492
C103×#15612
C103×#14932
C103×#14922
#18702103