Finite Group Databasebeta

← C103×#8400 #39913675

Subgroups — C103×#8400 #39913675

Order 26368.

858 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3460C211yesmaximal, characteristic
2C103×#1871C212yesmaximal, complemented
3C103×#1870C211yesmaximal, characteristic, complemented
4C4×#99×C103C211yesmaximal, characteristic, complemented
5C103×#1501C212yesmaximal, complemented
6C22×M16×C103C2211yescharacteristic
7#544×C103C411yescharacteristic, complemented
8#542×C103—22no—
9#540×C103—22no—
10#538×C103—21no—
11#538×C103C412yescomplemented
12#537×C103C411yescharacteristic, complemented
13#535×C103—21no—
14#532×C103—22no—
15#529×C103—22no—
16#525×C103—21no—
17#525×C103C2212yes—
18C4×#41×C103—21no—
19C2×C4×D4×C103C2211yescharacteristic
20C2×#104×C103—22no—
21C2×#99×C103—21no—
22C2×C22⋊C8×C103—21no—
23C2×C22⋊C8×C103C2211yescharacteristic
24C4×C22⋊C4×C103C2212yes—
25#342×C103—21no—
26#339×C103—22no—
27#336×C103—21no—
28#328×C103—22no—
29#327×C103—22no—
30C2×#41×C103—21no—
31C2×#41×C103—21no—
32C2×#41×C103D412yes—
33C22×D4×C103D411yescharacteristic
34C23×C4×C103D411yescharacteristic
35C23×C4×C103C2311yescharacteristic
36C2×M16×C103—22no—
37C2×M16×C103—42no—
38C22×C8×C103—21no—
39C22×C8×C103—21no—
40C4⋊Q8×C103—22no—
41#127×C103—22no—
42#126×C103—22no—
43#126×C103—22no—
44#125×C103—22no—
45#124×C103—22no—
46#124×C103—22no—
47#124×C103—22no—
48#123×C103—22no—
49#123×C103—22no—
50#123×C103—22no—
51#123×C103—22no—
52C22⋊Q8×C103—21no—
53C22⋊Q8×C103—21no—
54C22⋊Q8×C103—22no—
55C22⋊Q8×C103C2×C412yes—
56C22⋊Q8×C103D412yes—
57#121×C103—21no—
58#121×C103—22no—
59#121×C103—22no—
60#121×C103—22no—
61#121×C103—22no—
62#121×C103—22no—
63#121×C103—21no—
64#121×C103C2×C412yes—
65#121×C103D412yes—
66#120×C103—22no—
67#120×C103—22no—
68C4×Q8×C103—21no—
69C4×Q8×C103—21no—
70C4×D4×C103—21no—
71C4×D4×C103—21no—
72C4×D4×C103—22no—
73C4×D4×C103—22no—
74C4×D4×C103—22no—
75C4×D4×C103—22no—
76C4×D4×C103—22no—
77C4×D4×C103—22no—
78#117×C103—22no—
79#117×C103—21no—
80#117×C103—21no—
81#117×C103D412yes—
82C2×C4⋊C4×C103C2×C411yescharacteristic
83C2×C22⋊C4×C103—22no—
84C2×C22⋊C4×C103C2×C411yescharacteristic
85C2×C22⋊C4×C103D411yescharacteristic
86C2×C42×C103—22no—
87C2×C42×C103—22no—
88C2×C42×C103D411yescharacteristic
89#104×C103—44no—
90#99×C103—24no—
91C22⋊C8×C103—22no—
92C22⋊C8×C103—42no—
93#95×C103—22no—
94C24×C103C22⋊C411yescharacteristic
95C24×C103C2×D411yescharacteristic
96#41×C103—42no—
97#41×C103—42no—
98#41×C103—42no—
99#41×C103—42no—
100#41×C103—81no—
101#41×C103—81no—
102C2×Q8×C103—21no—
103C2×Q8×C103—21no—
104C2×Q8×C103C22⋊C412yes—
105C2×D4×C103—21no—
106C2×D4×C103—22no—
107C2×D4×C103—22no—
108C2×D4×C103—22no—
109C2×D4×C103—22no—
110C2×D4×C103—21no—
111C2×D4×C103—22no—
112C2×D4×C103—22no—
113C2×D4×C103—22no—
114C2×D4×C103—41no—
115C2×D4×C103C22⋊C412yes—
116C22×C4×C103—22no—
117C22×C4×C103—22no—
118C22×C4×C103—22no—
119C22×C4×C103—21no—
120C22×C4×C103—21no—
121C22×C4×C103—41no—
122C22×C4×C103—41no—
123C22×C4×C103—41no—
124C22×C4×C103—41no—
125C22×C4×C103—42no—
126C22×C4×C103C22⋊C411yescharacteristic
127C22×C4×C103C22⋊C411yescharacteristic
128C22×C4×C103C22⋊C411yescharacteristic
129C22×C4×C103C22×C411yescharacteristic
130C22×C4×C103C2×D412yes—
131C22×C4×C103C2×D411yescharacteristic
132C22×C4×C103C2×D412yes—
133M16×C103—24no—
134M16×C103—42no—
135C2×C8×C103—22no—
136C2×C8×C103—41no—
137C2×C8×C103—41no—
138C2×C8×C103—41no—
139C2×C8×C103—41no—
140C2×C8×C103—41no—
141C4⋊C4×C103—21no—
142C4⋊C4×C103—21no—
143C4⋊C4×C103—22no—
144C4⋊C4×C103—21no—
145C4⋊C4×C103—21no—
146C4⋊C4×C103—22no—
147C4⋊C4×C103—22no—
148C4⋊C4×C103—22no—
149C4⋊C4×C103—22no—
150C4⋊C4×C103C22⋊C412yes—
151C4⋊C4×C103C22⋊C412yes—
152C22⋊C4×C103—22no—
153C22⋊C4×C103—22no—
154C22⋊C4×C103—22no—
155C22⋊C4×C103—22no—
156C22⋊C4×C103—22no—
157C22⋊C4×C103—22no—
158C22⋊C4×C103—22no—
159C22⋊C4×C103—22no—
160C22⋊C4×C103—22no—
161C22⋊C4×C103—22no—
162C22⋊C4×C103—22no—
163C22⋊C4×C103—24no—
164C22⋊C4×C103—42no—
165C42×C103—22no—
166C42×C103—22no—
167C42×C103—21no—
168C42×C103—21no—
169C42×C103—22no—
170C42×C103—42no—
171C42×C103—42no—
172C23×C103—21no—
173C23×C103—21no—
174C23×C103—21no—
175C23×C103—22no—
176C23×C103—21no—
177C23×C103—21no—
178C23×C103—41no—
179C23×C103—41no—
180C23×C103—41no—
181C23×C103—41no—
182C23×C103C2×C22⋊C411yescharacteristic
183C23×C103#12012yes—
184Q8×C103—42no—
185Q8×C103—42no—
186Q8×C103—81no—
187D4×C103—44no—
188D4×C103—42no—
189D4×C103—42no—
190D4×C103—42no—
191D4×C103—42no—
192D4×C103—82no—
193D4×C103—82no—
194D4×C103—82no—
195D4×C103—81no—
196D4×C103—82no—
197C2×C4×C103—21no—
198C2×C4×C103—21no—
199C2×C4×C103—22no—
200C2×C4×C103—21no—
201C2×C4×C103—22no—
202C2×C4×C103—21no—
203C2×C4×C103—21no—
204C2×C4×C103—22no—
205C2×C4×C103—22no—
206C2×C4×C103—22no—
207C2×C4×C103—21no—
208C2×C4×C103—41no—
209C2×C4×C103—42no—
210C2×C4×C103—44no—
211C2×C4×C103—41no—
212C2×C4×C103—42no—
213C2×C4×C103—41no—
214C2×C4×C103—42no—
215C2×C4×C103—41no—
216C2×C4×C103—41no—
217C2×C4×C103—44no—
218C2×C4×C103—81no—
219C2×C4×C103—82no—
220C2×C4×C103—82no—
221C2×C4×C103—82no—
222C2×C4×C103#10412yescomplemented
223C2×C4×C103C2×C22⋊C412yes—
224C2×C4×C103#12011yescharacteristic
225C2×C4×C103#12011yescharacteristic
226C8×C103—42no—
227C8×C103—81no—
228C22×C103—21no—
229C22×C103—21no—
230C22×C103—22no—
231C22×C103—22no—
232C22×C103—22no—
233C22×C103—42no—
234C22×C103—42no—
235C22×C103—41no—
236C22×C103—42no—
237C22×C103—41no—
238C22×C103—41no—
239C22×C103—42no—
240C22×C103—81no—
241C22×C103—81no—
242C22×C103—81no—
243C22×C103#37911yescharacteristic
244C22×C103C2×#10411yescharacteristic
245C22×C103#42111yescharacteristic
246C4×C103—22no—
247C4×C103—21no—
248C4×C103—22no—
249C4×C103—41no—
250C4×C103—42no—
251C4×C103—42no—
252C4×C103—41no—
253C4×C103—42no—
254C4×C103—84no—
255C4×C103B(4,𝔽2)11yescharacteristic
256C4×C103#45811yescharacteristic
257#8400C10311yesmaximal, characteristic, direct product factor, Sylow
258C2×C103—21no—
259C2×C103—21no—
260C2×C103—42no—
261C2×C103—82no—
262C2×C103—81no—
263C2×C103#178911yescharacteristic
264C2×C103#179011yescharacteristic
265C2×C103#179411yescharacteristic
266#3460C2×C10311yescharacteristic
267#1871C2×C10312yescomplemented
268#1870C2×C10311yescharacteristic, complemented
269C4×#99C2×C10311yescharacteristic, complemented
270#1501C2×C10312yescomplemented
271C103#840011yescharacteristic, direct product factor, Sylow
272C22×M16C22×C10311yescharacteristic
273#544C4×C10311yescharacteristic, complemented
274#542—22no—
275#540—22no—
276#538—21no—
277#538C4×C10312yescomplemented
278#537C4×C10311yescharacteristic, complemented
279#535—21no—
280#532—22no—
281#529—22no—
282#525—21no—
283#525C22×C10312yes—
284C4×#41—21no—
285C2×C4×D4C22×C10311yescharacteristic
286C2×#104—22no—
287C2×#99—21no—
288C2×C22⋊C8—21no—
289C2×C22⋊C8C22×C10311yescharacteristic
290C4×C22⋊C4C22×C10312yes—
291#342—21no—
292#339—22no—
293#336—21no—
294#328—22no—
295#327—22no—
296C2×#41—21no—
297C2×#41—21no—
298C2×#41D4×C10312yes—
299C22×D4D4×C10311yescharacteristic
300C23×C4D4×C10311yescharacteristic
301C23×C4C23×C10311yescharacteristic
302C2×M16—22no—
303C2×M16—42no—
304C22×C8—21no—
305C22×C8—21no—
306C4⋊Q8—22no—
307#127—22no—
308#126—22no—
309#126—22no—
310#125—22no—
311#124—22no—
312#124—22no—
313#124—22no—
314#123—22no—
315#123—22no—
316#123—22no—
317#123—22no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—22no—
321C22⋊Q8C2×C4×C10312yes—
322C22⋊Q8D4×C10312yes—
323#121—21no—
324#121—22no—
325#121—22no—
326#121—22no—
327#121—22no—
328#121—22no—
329#121—21no—
330#121C2×C4×C10312yes—
331#121D4×C10312yes—
332#120—22no—
333#120—22no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344#117—22no—
345#117—21no—
346#117—21no—
347#117D4×C10312yes—
348C2×C4⋊C4C2×C4×C10311yescharacteristic
349C2×C22⋊C4—22no—
350C2×C22⋊C4C2×C4×C10311yescharacteristic
351C2×C22⋊C4D4×C10311yescharacteristic
352C2×C42—22no—
353C2×C42—22no—
354C2×C42D4×C10311yescharacteristic
355#104—44no—
356#99—24no—
357C22⋊C8—22no—
358C22⋊C8—42no—
359#95—22no—
360C24C22⋊C4×C10311yescharacteristic
361C24C2×D4×C10311yescharacteristic
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—81no—
367#41—81no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8C22⋊C4×C10312yes—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—41no—
381C2×D4C22⋊C4×C10312yes—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—42no—
392C22×C4C22⋊C4×C10311yescharacteristic
393C22×C4C22⋊C4×C10311yescharacteristic
394C22×C4C22⋊C4×C10311yescharacteristic
395C22×C4C22×C4×C10311yescharacteristic
396C22×C4C2×D4×C10312yes—
397C22×C4C2×D4×C10311yescharacteristic
398C22×C4C2×D4×C10312yes—
399M16—24no—
400M16—42no—
401C2×C8—22no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4C22⋊C4×C10312yes—
417C4⋊C4C22⋊C4×C10312yes—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—24no—
430C22⋊C4—42no—
431C42—22no—
432C42—22no—
433C42—21no—
434C42—22no—
435C42—21no—
436C42—42no—
437C42—42no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—22no—
442C23—21no—
443C23—21no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23C2×C22⋊C4×C10311yescharacteristic
449C23#120×C10312yes—
450Q8—42no—
451Q8—42no—
452Q8—81no—
453D4—44no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—82no—
460D4—81no—
461D4—82no—
462D4—82no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—44no—
484C2×C4—81no—
485C2×C4—82no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4#104×C10312yescomplemented
489C2×C4C2×C22⋊C4×C10312yes—
490C2×C4#120×C10311yescharacteristic
491C2×C4#120×C10311yescharacteristic
492C8—42no—
493C8—81no—
494C22—21no—
495C22—21no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—41no—
503C22—42no—
504C22—42no—
505C22—41no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22#379×C10311yescharacteristic
510C22C2×#104×C10311yescharacteristic
511C22#421×C10311yescharacteristic
512C4—22no—
513C4—21no—
514C4—22no—
515C4—42no—
516C4—41no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—84no—
521C4B(4,𝔽2)×C10311yescharacteristic
522C4#458×C10311yescharacteristic
523C2—21no—
524C2—21no—
525C2—42no—
526C2—81no—
527C2—82no—
528C2C103×#178911yescharacteristic
529C2C103×#179011yescharacteristic
530C2C103×#179411yescharacteristic
subgroupG/H
centerC2×C4×C103#120
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
socleC22×C103#379
prime radicalC103×#3460C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1871C2semidirect
3. C103×#1870C2semidirect
4. C4×#99×C103C2semidirect
5. C103×#1501C2semidirect
7. #544×C103C4semidirect
11. #538×C103C4semidirect
12. #537×C103C4semidirect
222. C2×C4×C103#104semidirect
257. #8400C103direct (N × H)
267. #1871C2×C103semidirect
268. #1870C2×C103semidirect
269. C4×#99C2×C103semidirect
270. #1501C2×C103semidirect
271. C103#8400direct (N × H)
273. #544C4×C103semidirect
277. #538C4×C103semidirect
278. #537C4×C103semidirect
488. C2×C4#104×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34602
C103×#18712
C103×#18702
C4×#99×C1032
C103×#15012
#8400103