Finite Group Databasebeta

← C103×#8444 #39913719

Subgroups — C103×#8444 #39913719

Order 26368.

1116 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C103C211yesmaximal, characteristic
2C103×#1957C211yesmaximal, characteristic, complemented
3C103×#1803C211yesmaximal, characteristic, complemented
4C103×#1802C211yesmaximal, characteristic, complemented
5C2×#331×C103C211yesmaximal, characteristic, complemented
6C2×Q8⋊C8×C103C211yesmaximal, characteristic, complemented
7C2×D4⋊C8×C103C211yesmaximal, characteristic, complemented
8C22×#41×C103—21no—
9#550×C103—22no—
10#550×C103—22no—
11#550×C103—22no—
12#550×C103C414yescomplemented
13C2×#127×C103—21no—
14C2×#127×C103C2211yescharacteristic
15C2×#121×C103—22no—
16C2×#121×C103—21no—
17C2×C4×Q8×C103C2211yescharacteristic
18C2×C4×D4×C103—21no—
19C2×C4×D4×C103C2211yescharacteristic
20C2×C4⋊C8×C103C2211yescharacteristic
21C2×C4⋊C8×C103C2211yescharacteristic
22C2×#103×C103—21no—
23C2×#102×C103—22no—
24C2×#102×C103—21no—
25C2×C4×C8×C103C2211yescharacteristic
26#384×C103C2211yescharacteristic
27#340×C103—21no—
28#340×C103—21no—
29#331×C103—22no—
30Q8⋊C8×C103—22no—
31D4⋊C8×C103—22no—
32C2×#41×C103—24no—
33C2×#41×C103—24no—
34C2×#41×C103—42no—
35C2×#41×C103—42no—
36C2×#41×C103—42no—
37C2×#41×C103—42no—
38C22×Q8×C103D411yescharacteristic
39C22×D4×C103—22no—
40C22×D4×C103—22no—
41C22×D4×C103—21no—
42C22×D4×C103—21no—
43C22×D4×C103D411yescharacteristic
44C22×D4×C103D412yes—
45C23×C4×C103—22no—
46C23×C4×C103—21no—
47C22×C8×C103—21no—
48C22×C8×C103—21no—
49C22×C8×C103—21no—
50#127×C103—24no—
51#127×C103—24no—
52#127×C103—21no—
53#127×C103—21no—
54#127×C103C2×C412yes—
55#127×C103D412yes—
56#121×C103—24no—
57#121×C103—28no—
58#121×C103—28no—
59#121×C103—24no—
60C4×Q8×C103—21no—
61C4×Q8×C103—21no—
62C4×Q8×C103C2×C412yes—
63C4×Q8×C103D412yes—
64C4×D4×C103—24no—
65C4×D4×C103—24no—
66C4×D4×C103—21no—
67C4×D4×C103—21no—
68C4×D4×C103C2×C412yes—
69C4×D4×C103D412yes—
70C2×C4⋊C4×C103—21no—
71C2×C4⋊C4×C103—21no—
72C2×C4⋊C4×C103—21no—
73C2×C4⋊C4×C103—21no—
74C2×C4⋊C4×C103D411yescharacteristic
75C2×C4⋊C4×C103D411yescharacteristic
76C2×C22⋊C4×C103—22no—
77C2×C22⋊C4×C103—21no—
78C2×C42×C103—21no—
79C2×C42×C103C2311yescharacteristic
80C4⋊C8×C103—21no—
81C4⋊C8×C103—21no—
82C4⋊C8×C103—21no—
83C4⋊C8×C103—21no—
84#103×C103—42no—
85#102×C103—44no—
86#102×C103—42no—
87C4×C8×C103—21no—
88C4×C8×C103—21no—
89C24×C103—21no—
90C24×C103—22no—
91#41×C103—48no—
92#41×C103—48no—
93#41×C103—48no—
94#41×C103—48no—
95C2×Q8×C103—21no—
96C2×Q8×C103—21no—
97C2×Q8×C103—21no—
98C2×Q8×C103C22⋊C412yes—
99C2×Q8×C103D812yes—
100C2×Q8×C103SD1612yes—
101C2×D4×C103—28no—
102C2×D4×C103—28no—
103C2×D4×C103—22no—
104C2×D4×C103—22no—
105C2×D4×C103—21no—
106C2×D4×C103—22no—
107C2×D4×C103—22no—
108C2×D4×C103—22no—
109C2×D4×C103—21no—
110C2×D4×C103—21no—
111C2×D4×C103—21no—
112C2×D4×C103—21no—
113C2×D4×C103—44no—
114C2×D4×C103—44no—
115C2×D4×C103—42no—
116C2×D4×C103—42no—
117C2×D4×C103—41no—
118C2×D4×C103—41no—
119C2×D4×C103—41no—
120C2×D4×C103—41no—
121C2×D4×C103—41no—
122C2×D4×C103—41no—
123C2×D4×C103—41no—
124C2×D4×C103—41no—
125C2×D4×C103—82no—
126C2×D4×C103—82no—
127C2×D4×C103C22⋊C412yes—
128C2×D4×C103C22⋊C414yes—
129C22×C4×C103—21no—
130C22×C4×C103—28no—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—22no—
134C22×C4×C103—22no—
135C22×C4×C103—44no—
136C22×C4×C103—44no—
137C22×C4×C103—41no—
138C22×C4×C103—41no—
139C22×C4×C103—41no—
140C22×C4×C103—41no—
141C22×C4×C103—41no—
142C22×C4×C103C2×D411yescharacteristic
143C22×C4×C103C2×D411yescharacteristic
144C22×C4×C103C2×D411yescharacteristic
145C2×C8×C103—22no—
146C2×C8×C103—41no—
147C2×C8×C103—41no—
148C2×C8×C103—41no—
149C2×C8×C103—41no—
150C2×C8×C103—41no—
151C2×C8×C103—41no—
152C2×C8×C103—41no—
153C2×C8×C103—41no—
154C4⋊C4×C103—22no—
155C4⋊C4×C103—22no—
156C4⋊C4×C103—21no—
157C4⋊C4×C103—21no—
158C4⋊C4×C103—42no—
159C4⋊C4×C103—41no—
160C4⋊C4×C103—41no—
161C4⋊C4×C103—41no—
162C4⋊C4×C103—41no—
163C4⋊C4×C103C22⋊C412yes—
164C4⋊C4×C103C22⋊C412yes—
165C22⋊C4×C103—28no—
166C22⋊C4×C103—22no—
167C22⋊C4×C103—22no—
168C42×C103—22no—
169C42×C103—22no—
170C42×C103C22×C411yescharacteristic
171C42×C103C2×D411yescharacteristic
172C42×C103C2×D411yescharacteristic
173C42×C103C2×D411yescharacteristic
174C23×C103—24no—
175C23×C103—22no—
176C23×C103—42no—
177C23×C103—41no—
178C23×C103—41no—
179C23×C103—42no—
180C23×C103—42no—
181C23×C103—41no—
182C23×C103—41no—
183C23×C103—42no—
184C23×C103—42no—
185C23×C103—41no—
186C23×C103—42no—
187C23×C103—41no—
188C23×C103#12011yescharacteristic
189Q8×C103—22no—
190Q8×C103—22no—
191Q8×C103—22no—
192Q8×C103#10214yescomplemented
193D4×C103—22no—
194D4×C103—22no—
195D4×C103—44no—
196D4×C103—416no—
197D4×C103—42no—
198D4×C103—42no—
199D4×C103—42no—
200D4×C103—42no—
201D4×C103—42no—
202D4×C103—41no—
203D4×C103—42no—
204D4×C103—42no—
205D4×C103—41no—
206D4×C103—42no—
207D4×C103—82no—
208D4×C103—88no—
209C2×C4×C103—22no—
210C2×C4×C103—22no—
211C2×C4×C103—22no—
212C2×C4×C103—21no—
213C2×C4×C103—21no—
214C2×C4×C103—22no—
215C2×C4×C103—22no—
216C2×C4×C103—416no—
217C2×C4×C103—41no—
218C2×C4×C103—41no—
219C2×C4×C103—41no—
220C2×C4×C103—41no—
221C2×C4×C103—42no—
222C2×C4×C103—42no—
223C2×C4×C103—42no—
224C2×C4×C103—42no—
225C2×C4×C103—81no—
226C2×C4×C103—81no—
227C2×C4×C103—81no—
228C2×C4×C103C2×C22⋊C411yescharacteristic
229C2×C4×C103C2×C22⋊C411yescharacteristic
230C2×C4×C103C2×C22⋊C411yescharacteristic
231C2×C4×C103#12011yescharacteristic
232C2×C4×C103#12011yescharacteristic
233C2×C4×C103#12011yescharacteristic
234C2×C4×C103C2×D811yescharacteristic
235C2×C4×C103C2×SD1611yescharacteristic
236C2×C4×C103#13511yescharacteristic
237C2×C4×C103#13511yescharacteristic
238C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
239C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
240C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
241C2×C4×C103#13711yescharacteristic
242C8×C103—42no—
243C8×C103—81no—
244C8×C103—81no—
245C22×C103—44no—
246C22×C103—42no—
247C22×C103—44no—
248C22×C103—42no—
249C22×C103—42no—
250C22×C103—44no—
251C22×C103—81no—
252C22×C103—82no—
253C22×C103—81no—
254C22×C103—82no—
255C22×C103—81no—
256C22×C103—82no—
257C22×C103—81no—
258C22×C103—82no—
259C22×C103#37911yescharacteristic
260C22×C103#44711yescharacteristic
261C22×C103#44911yescharacteristic
262C22×C103#45011yescharacteristic
263C22×C103#45211yescharacteristic
264C22×C103#45311yescharacteristic
265C22×C103#45511yescharacteristic
266C4×C103—21no—
267C4×C103—21no—
268C4×C103—24no—
269C4×C103—42no—
270C4×C103—42no—
271C4×C103—161no—
272C4×C103C2×#10211yescharacteristic
273C4×C103#41611yescharacteristic
274C4×C103#41711yescharacteristic
275C4×C103#41811yescharacteristic
276C4×C103#44711yescharacteristic
277C4×C103#44911yescharacteristic
278C4×C103#45011yescharacteristic
279C4×C103#45211yescharacteristic
280#8444C10311yesmaximal, characteristic, direct product factor, Sylow
281C2×C103—84no—
282C2×C103—82no—
283C2×C103#162111yescharacteristic
284C2×C103#163111yescharacteristic
285C2×C103#164111yescharacteristic
286C2×C103#164211yescharacteristic
287C2×C103#178611yescharacteristic
288C2×C103#178811yescharacteristic
289C2×C103#179211yescharacteristic
290C2×#550C2×C10311yescharacteristic
291#1957C2×C10311yescharacteristic, complemented
292#1803C2×C10311yescharacteristic, complemented
293#1802C2×C10311yescharacteristic, complemented
294C2×#331C2×C10311yescharacteristic, complemented
295C2×Q8⋊C8C2×C10311yescharacteristic, complemented
296C2×D4⋊C8C2×C10311yescharacteristic, complemented
297C103#844411yescharacteristic, direct product factor, Sylow
298C22×#41—21no—
299#550—22no—
300#550—22no—
301#550—22no—
302#550C4×C10314yescomplemented
303C2×#127—21no—
304C2×#127C22×C10311yescharacteristic
305C2×#121—22no—
306C2×#121—21no—
307C2×C4×Q8C22×C10311yescharacteristic
308C2×C4×D4—21no—
309C2×C4×D4C22×C10311yescharacteristic
310C2×C4⋊C8C22×C10311yescharacteristic
311C2×C4⋊C8C22×C10311yescharacteristic
312C2×#103—21no—
313C2×#102—21no—
314C2×#102—22no—
315C2×C4×C8C22×C10311yescharacteristic
316#384C22×C10311yescharacteristic
317#340—21no—
318#340—21no—
319#331—22no—
320Q8⋊C8—22no—
321D4⋊C8—22no—
322C2×#41—24no—
323C2×#41—24no—
324C2×#41—42no—
325C2×#41—42no—
326C2×#41—42no—
327C2×#41—42no—
328C22×Q8D4×C10311yescharacteristic
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4D4×C10311yescharacteristic
334C22×D4D4×C10312yes—
335C23×C4—22no—
336C23×C4—21no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—21no—
340#127—24no—
341#127—24no—
342#127—21no—
343#127—21no—
344#127C2×C4×C10312yes—
345#127D4×C10312yes—
346#121—24no—
347#121—28no—
348#121—28no—
349#121—24no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8C2×C4×C10312yes—
353C4×Q8D4×C10312yes—
354C4×D4—24no—
355C4×D4—24no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4C2×C4×C10312yes—
359C4×D4D4×C10312yes—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4D4×C10311yescharacteristic
365C2×C4⋊C4D4×C10311yescharacteristic
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C42—21no—
369C2×C42C23×C10311yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374#103—42no—
375#102—44no—
376#102—42no—
377C4×C8—21no—
378C4×C8—21no—
379C24—21no—
380C24—22no—
381#41—48no—
382#41—48no—
383#41—48no—
384#41—48no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8C22⋊C4×C10312yes—
389C2×Q8D8×C10312yes—
390C2×Q8SD16×C10312yes—
391C2×D4—28no—
392C2×D4—28no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—44no—
404C2×D4—44no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—82no—
416C2×D4—82no—
417C2×D4C22⋊C4×C10312yes—
418C2×D4C22⋊C4×C10314yes—
419C22×C4—21no—
420C22×C4—28no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4C2×D4×C10311yescharacteristic
433C22×C4C2×D4×C10311yescharacteristic
434C22×C4C2×D4×C10311yescharacteristic
435C2×C8—22no—
436C2×C8—41no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C2×C8—41no—
443C2×C8—41no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—42no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4C22⋊C4×C10312yes—
454C4⋊C4C22⋊C4×C10312yes—
455C22⋊C4—28no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C42—22no—
459C42—22no—
460C42C22×C4×C10311yescharacteristic
461C42C2×D4×C10311yescharacteristic
462C42C2×D4×C10311yescharacteristic
463C42C2×D4×C10311yescharacteristic
464C23—22no—
465C23—24no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—42no—
475C23—41no—
476C23—42no—
477C23—41no—
478C23#120×C10311yescharacteristic
479Q8—22no—
480Q8—22no—
481Q8—22no—
482Q8#102×C10314yescomplemented
483D4—22no—
484D4—22no—
485D4—44no—
486D4—416no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—42no—
492D4—41no—
493D4—42no—
494D4—42no—
495D4—41no—
496D4—42no—
497D4—82no—
498D4—88no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—416no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4C2×C22⋊C4×C10311yescharacteristic
519C2×C4C2×C22⋊C4×C10311yescharacteristic
520C2×C4C2×C22⋊C4×C10311yescharacteristic
521C2×C4#120×C10311yescharacteristic
522C2×C4#120×C10311yescharacteristic
523C2×C4#120×C10311yescharacteristic
524C2×C4C2×D8×C10311yescharacteristic
525C2×C4C2×SD16×C10311yescharacteristic
526C2×C4#135×C10311yescharacteristic
527C2×C4#135×C10311yescharacteristic
528C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
529C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
530C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
531C2×C4#137×C10311yescharacteristic
532C8—42no—
533C8—81no—
534C8—81no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—44no—
539C22—44no—
540C22—42no—
541C22—81no—
542C22—82no—
543C22—81no—
544C22—82no—
545C22—81no—
546C22—82no—
547C22—81no—
548C22—82no—
549C22#379×C10311yescharacteristic
550C22#447×C10311yescharacteristic
551C22#449×C10311yescharacteristic
552C22#450×C10311yescharacteristic
553C22#452×C10311yescharacteristic
554C22#453×C10311yescharacteristic
555C22#455×C10311yescharacteristic
556C4—24no—
557C4—21no—
558C4—21no—
559C4—42no—
560C4—42no—
561C4—161no—
562C4C2×#102×C10311yescharacteristic
563C4#416×C10311yescharacteristic
564C4#417×C10311yescharacteristic
565C4#418×C10311yescharacteristic
566C4#447×C10311yescharacteristic
567C4#449×C10311yescharacteristic
568C4#450×C10311yescharacteristic
569C4#452×C10311yescharacteristic
570C2—82no—
571C2—84no—
572C2C103×#162111yescharacteristic
573C2C103×#163111yescharacteristic
574C2C103×#164111yescharacteristic
575C2C103×#164211yescharacteristic
576C2C103×#178611yescharacteristic
577C2C103×#178811yescharacteristic
578C2C103×#179211yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC2×#550×C103C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1957C2semidirect
3. C103×#1803C2semidirect
4. C103×#1802C2semidirect
5. C2×#331×C103C2semidirect
6. C2×Q8⋊C8×C103C2semidirect
7. C2×D4⋊C8×C103C2semidirect
12. #550×C103C4semidirect
192. Q8×C103#102semidirect
280. #8444C103direct (N × H)
291. #1957C2×C103semidirect
292. #1803C2×C103semidirect
293. #1802C2×C103semidirect
294. C2×#331C2×C103semidirect
295. C2×Q8⋊C8C2×C103semidirect
296. C2×D4⋊C8C2×C103semidirect
297. C103#8444direct (N × H)
302. #550C4×C103semidirect
482. Q8#102×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1032
C103×#19572
C103×#18032
C103×#18022
C2×#331×C1032
C2×Q8⋊C8×C1032
C2×D4⋊C8×C1032
#8444103