Finite Group Databasebeta

← C103×#19093 #39924368

Subgroups — C103×#19093 #39924368

Order 26368.

782 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3563C211yesmaximal, characteristic
2C103×#3240C211yesmaximal, characteristic
3C103×#3237C211yesmaximal, characteristic, complemented
4C103×#3236C211yesmaximal, characteristic, complemented
5C103×#1664C212yesmaximal, complemented
6C103×#1664C212yesmaximal, complemented
7C103×#1663C212yesmaximal, complemented
8C103×#1663C212yesmaximal, complemented
9C103×#1537C211yesmaximal, characteristic, complemented
10C103×#1535C211yesmaximal, characteristic
11C103×#1534C211yesmaximal, characteristic, complemented
12#564×C103C2212yes—
13#563×C103C2212yes—
14#557×C103—21no—
15#554×C103—21no—
16#552×C103—21no—
17#552×C103—22no—
18#552×C103—21no—
19#544×C103—21no—
20#544×C103—21no—
21#541×C103—21no—
22#541×C103—22no—
23#539×C103—21no—
24#533×C103C2211yescharacteristic
25#533×C103C2211yescharacteristic
26#529×C103C2211yescharacteristic
27C2×#125×C103C2211yescharacteristic
28#501×C103C2212yes—
29#501×C103C2212yes—
30#501×C103C2211yescharacteristic
31#501×C103C2211yescharacteristic
32#491×C103C2212yes—
33#491×C103C2212yes—
34#489×C103C2211yescharacteristic
35#489×C103C2211yescharacteristic
36#485×C103—21no—
37#485×C103—22no—
38#484×C103—21no—
39#483×C103—21no—
40#482×C103—21no—
41#479×C103—22no—
42#479×C103—21no—
43#478×C103—21no—
44#477×C103—21no—
45#475×C103—21no—
46#432×C103C2211yescharacteristic
47#432×C103C2211yescharacteristic
48#432×C103C2211yescharacteristic
49#330×C103C2212yes—
50#330×C103C2212yes—
51#330×C103C2212yes—
52#330×C103C2212yes—
53#330×C103C2212yes—
54#329×C103C2212yes—
55C4⋊Q8×C103—22no—
56C4⋊Q8×C103—21no—
57C4⋊Q8×C103—22no—
58C4⋊Q8×C103D411yescharacteristic
59C4⋊Q8×C103D411yescharacteristic
60C4⋊Q8×C103C2311yescharacteristic
61C4⋊Q8×C103C2311yescharacteristic
62#126×C103—22no—
63#126×C103—22no—
64#126×C103—22no—
65#126×C103—22no—
66#126×C103—21no—
67#125×C103—22no—
68#125×C103—22no—
69#125×C103—21no—
70#125×C103—22no—
71#125×C103—22no—
72#125×C103—22no—
73#125×C103—22no—
74#125×C103—22no—
75#125×C103—22no—
76#125×C103—21no—
77#125×C103—21no—
78#125×C103—21no—
79#125×C103D412yes—
80#125×C103C2312yes—
81#125×C103C2312yes—
82#125×C103C2311yescharacteristic
83#124×C103C2311yescharacteristic
84#123×C103—22no—
85#123×C103—22no—
86#123×C103—21no—
87C22⋊Q8×C103—22no—
88C22⋊Q8×C103—21no—
89C22⋊Q8×C103—21no—
90C22⋊Q8×C103—22no—
91C22⋊Q8×C103—21no—
92C22⋊Q8×C103—21no—
93C22⋊Q8×C103—22no—
94C22⋊Q8×C103—22no—
95C22⋊Q8×C103—21no—
96C22⋊Q8×C103—21no—
97C22⋊Q8×C103D411yescharacteristic
98#121×C103D411yescharacteristic
99C4×Q8×C103—21no—
100C4×Q8×C103—22no—
101C4×Q8×C103—21no—
102C4×Q8×C103—21no—
103C4×Q8×C103—21no—
104C4×Q8×C103—21no—
105C4×Q8×C103—21no—
106C4×Q8×C103D411yescharacteristic
107C4×D4×C103—22no—
108C4×D4×C103—21no—
109C4×D4×C103D411yescharacteristic
110#117×C103—22no—
111#117×C103—21no—
112#117×C103—22no—
113#117×C103—21no—
114#117×C103—21no—
115#117×C103D412yes—
116C2×C4⋊C4×C103—21no—
117C2×C4⋊C4×C103—21no—
118C2×C4⋊C4×C103—21no—
119C2×C4⋊C4×C103D411yescharacteristic
120C2×C4⋊C4×C103D411yescharacteristic
121C2×C42×C103C2311yescharacteristic
122#107×C103—22no—
123#107×C103—21no—
124#107×C103—21no—
125#107×C103—22no—
126#106×C103—22no—
127#106×C103—21no—
128#106×C103—21no—
129#106×C103—22no—
130C4⋊C8×C103—21no—
131C4⋊C8×C103—21no—
132C4⋊C8×C103—21no—
133#103×C103—21no—
134#103×C103—21no—
135#103×C103—22no—
136#103×C103—22no—
137#103×C103—22no—
138#103×C103—22no—
139#102×C103—21no—
140#102×C103—21no—
141C22⋊C8×C103—21no—
142C22⋊C8×C103—21no—
143C22⋊C8×C103—21no—
144#97×C103C2311yescharacteristic
145#97×C103C2311yescharacteristic
146#97×C103C2312yes—
147#97×C103C2312yes—
148C2×Q8×C103—22no—
149C2×Q8×C103—21no—
150C2×Q8×C103—21no—
151C2×Q8×C103—21no—
152C2×Q8×C103—21no—
153C2×Q8×C103C2×D411yescharacteristic
154C2×D4×C103—21no—
155C2×D4×C103C2×D411yescharacteristic
156C22×C4×C103—21no—
157C22×C4×C103—22no—
158C22×C4×C103—21no—
159C22×C4×C103—21no—
160C22×C4×C103C2×D411yescharacteristic
161C22×C4×C103C2×D411yescharacteristic
162C22×C4×C103C2×D411yescharacteristic
163C2×C8×C103—21no—
164C2×C8×C103—21no—
165C2×C8×C103—22no—
166C2×C8×C103—22no—
167C4⋊C4×C103—22no—
168C4⋊C4×C103—22no—
169C4⋊C4×C103—22no—
170C4⋊C4×C103—22no—
171C4⋊C4×C103—22no—
172C4⋊C4×C103—22no—
173C4⋊C4×C103—22no—
174C4⋊C4×C103—22no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—22no—
178C4⋊C4×C103—22no—
179C4⋊C4×C103—21no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—21no—
182C4⋊C4×C103—21no—
183C4⋊C4×C103—22no—
184C4⋊C4×C103—22no—
185C4⋊C4×C103—21no—
186C4⋊C4×C103—21no—
187C4⋊C4×C103—22no—
188C4⋊C4×C103—22no—
189C4⋊C4×C103—21no—
190C4⋊C4×C103—21no—
191C4⋊C4×C103—21no—
192C4⋊C4×C103—21no—
193C4⋊C4×C103—41no—
194C4⋊C4×C103—41no—
195C4⋊C4×C103C2×D412yes—
196C4⋊C4×C103C2×D412yes—
197C4⋊C4×C103C2×D412yes—
198C4⋊C4×C103C2×D412yes—
199C4⋊C4×C103C2×D411yescharacteristic
200C4⋊C4×C103C2×D411yescharacteristic
201C22⋊C4×C103—22no—
202C22⋊C4×C103—22no—
203C22⋊C4×C103—22no—
204C22⋊C4×C103—21no—
205C22⋊C4×C103—22no—
206C22⋊C4×C103—21no—
207C22⋊C4×C103—21no—
208C22⋊C4×C103—21no—
209C22⋊C4×C103—21no—
210C22⋊C4×C103—41no—
211C42×C103—22no—
212C42×C103—22no—
213C42×C103—22no—
214C42×C103—22no—
215C42×C103—21no—
216C42×C103—41no—
217C42×C103C2×D411yescharacteristic
218C42×C103C2×D411yescharacteristic
219C42×C103C2×D411yescharacteristic
220C42×C103C2411yescharacteristic
221C23×C103—21no—
222C23×C103#12011yescharacteristic
223Q8×C103—41no—
224Q8×C103—42no—
225Q8×C103—42no—
226Q8×C103—42no—
227Q8×C103—81no—
228Q8×C103—82no—
229D4×C103—41no—
230D4×C103—42no—
231C2×C4×C103—22no—
232C2×C4×C103—21no—
233C2×C4×C103—21no—
234C2×C4×C103—21no—
235C2×C4×C103—22no—
236C2×C4×C103—22no—
237C2×C4×C103—22no—
238C2×C4×C103—41no—
239C2×C4×C103—41no—
240C2×C4×C103—41no—
241C2×C4×C103—42no—
242C2×C4×C103—42no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—81no—
246C2×C4×C103—82no—
247C2×C4×C103#12011yescharacteristic
248C2×C4×C103#12011yescharacteristic
249C2×C4×C103#12011yescharacteristic
250C2×C4×C103C22×D411yescharacteristic
251C2×C4×C103C22×D411yescharacteristic
252C2×C4×C103C22×D411yescharacteristic
253C8×C103—42no—
254C8×C103—42no—
255C8×C103—41no—
256C8×C103—41no—
257C22×C103—21no—
258C22×C103—21no—
259C22×C103—21no—
260C22×C103—41no—
261C22×C103—41no—
262C22×C103—41no—
263C22×C103C2×#12011yescharacteristic
264C4×C103—21no—
265C4×C103—21no—
266C4×C103—21no—
267C4×C103—21no—
268C4×C103—21no—
269C4×C103—21no—
270C4×C103—41no—
271C4×C103—42no—
272C4×C103—41no—
273C4×C103—42no—
274C4×C103—42no—
275C4×C103—42no—
276C4×C103—41no—
277C4×C103—81no—
278C4×C103—81no—
279#19093C10311yesmaximal, characteristic, direct product factor, Sylow
280C2×C103—41no—
281C2×C103—81no—
282C2×C103#302011yescharacteristic
283C2×C103#302011yescharacteristic
284C2×C103#302211yescharacteristic
285#3563C2×C10311yescharacteristic
286#3240C2×C10311yescharacteristic
287#3237C2×C10311yescharacteristic, complemented
288#3236C2×C10311yescharacteristic, complemented
289#1664C2×C10312yescomplemented
290#1664C2×C10312yescomplemented
291#1663C2×C10312yescomplemented
292#1663C2×C10312yescomplemented
293#1537C2×C10311yescharacteristic, complemented
294#1535C2×C10311yescharacteristic
295#1534C2×C10311yescharacteristic, complemented
296C103#1909311yescharacteristic, direct product factor, Sylow
297#564C22×C10312yes—
298#563C22×C10312yes—
299#557—21no—
300#554—21no—
301#552—21no—
302#552—22no—
303#552—21no—
304#544—21no—
305#544—21no—
306#541—21no—
307#541—22no—
308#539—21no—
309#533C22×C10311yescharacteristic
310#533C22×C10311yescharacteristic
311#529C22×C10311yescharacteristic
312C2×#125C22×C10311yescharacteristic
313#501C22×C10311yescharacteristic
314#501C22×C10311yescharacteristic
315#501C22×C10312yes—
316#501C22×C10312yes—
317#491C22×C10312yes—
318#491C22×C10312yes—
319#489C22×C10311yescharacteristic
320#489C22×C10311yescharacteristic
321#485—21no—
322#485—22no—
323#484—21no—
324#483—21no—
325#482—21no—
326#479—22no—
327#479—21no—
328#478—21no—
329#477—21no—
330#475—21no—
331#432C22×C10311yescharacteristic
332#432C22×C10311yescharacteristic
333#432C22×C10311yescharacteristic
334#330C22×C10312yes—
335#330C22×C10312yes—
336#330C22×C10312yes—
337#330C22×C10312yes—
338#330C22×C10312yes—
339#329C22×C10312yes—
340C4⋊Q8—22no—
341C4⋊Q8—21no—
342C4⋊Q8—22no—
343C4⋊Q8D4×C10311yescharacteristic
344C4⋊Q8D4×C10311yescharacteristic
345C4⋊Q8C23×C10311yescharacteristic
346C4⋊Q8C23×C10311yescharacteristic
347#126—22no—
348#126—22no—
349#126—22no—
350#126—22no—
351#126—21no—
352#125—22no—
353#125—22no—
354#125—21no—
355#125—22no—
356#125—22no—
357#125—22no—
358#125—22no—
359#125—22no—
360#125—22no—
361#125—21no—
362#125—21no—
363#125—21no—
364#125D4×C10312yes—
365#125C23×C10312yes—
366#125C23×C10311yescharacteristic
367#125C23×C10312yes—
368#124C23×C10311yescharacteristic
369#123—22no—
370#123—22no—
371#123—21no—
372C22⋊Q8—22no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8D4×C10311yescharacteristic
383#121D4×C10311yescharacteristic
384C4×Q8—21no—
385C4×Q8—22no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8D4×C10311yescharacteristic
392C4×D4—22no—
393C4×D4—21no—
394C4×D4D4×C10311yescharacteristic
395#117—22no—
396#117—21no—
397#117—22no—
398#117—21no—
399#117—21no—
400#117D4×C10312yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4D4×C10311yescharacteristic
405C2×C4⋊C4D4×C10311yescharacteristic
406C2×C42C23×C10311yescharacteristic
407#107—22no—
408#107—21no—
409#107—21no—
410#107—22no—
411#106—22no—
412#106—21no—
413#106—21no—
414#106—22no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418#103—21no—
419#103—21no—
420#103—22no—
421#103—22no—
422#103—22no—
423#103—22no—
424#102—21no—
425#102—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429#97C23×C10312yes—
430#97C23×C10312yes—
431#97C23×C10311yescharacteristic
432#97C23×C10311yescharacteristic
433C2×Q8—22no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C10311yescharacteristic
439C2×D4—21no—
440C2×D4C2×D4×C10311yescharacteristic
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C2×D4×C10311yescharacteristic
446C22×C4C2×D4×C10311yescharacteristic
447C22×C4C2×D4×C10311yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C10312yes—
481C4⋊C4C2×D4×C10312yes—
482C4⋊C4C2×D4×C10312yes—
483C4⋊C4C2×D4×C10312yes—
484C4⋊C4C2×D4×C10311yescharacteristic
485C4⋊C4C2×D4×C10311yescharacteristic
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—22no—
500C42—21no—
501C42—41no—
502C42C2×D4×C10311yescharacteristic
503C42C2×D4×C10311yescharacteristic
504C42C2×D4×C10311yescharacteristic
505C42C24×C10311yescharacteristic
506C23—21no—
507C23#120×C10311yescharacteristic
508Q8—41no—
509Q8—42no—
510Q8—42no—
511Q8—42no—
512Q8—81no—
513Q8—82no—
514D4—41no—
515D4—42no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4—82no—
532C2×C4#120×C10311yescharacteristic
533C2×C4#120×C10311yescharacteristic
534C2×C4#120×C10311yescharacteristic
535C2×C4C22×D4×C10311yescharacteristic
536C2×C4C22×D4×C10311yescharacteristic
537C2×C4C22×D4×C10311yescharacteristic
538C8—42no—
539C8—42no—
540C8—41no—
541C8—41no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22C2×#120×C10311yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—42no—
557C4—41no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—41no—
562C4—81no—
563C4—81no—
564C2—41no—
565C2—81no—
566C2C103×#302011yescharacteristic
567C2C103×#302011yescharacteristic
568C2C103×#302211yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC42C24×C103
prime radical#121×C103D4
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
3. C103×#3237C2semidirect
4. C103×#3236C2semidirect
5. C103×#1664C2semidirect
6. C103×#1664C2semidirect
7. C103×#1663C2semidirect
8. C103×#1663C2semidirect
9. C103×#1537C2semidirect
11. C103×#1534C2semidirect
279. #19093C103direct (N × H)
287. #3237C2×C103semidirect
288. #3236C2×C103semidirect
289. #1664C2×C103semidirect
290. #1664C2×C103semidirect
291. #1663C2×C103semidirect
292. #1663C2×C103semidirect
293. #1537C2×C103semidirect
295. #1534C2×C103semidirect
296. C103#19093direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#35632
C103×#32402
C103×#32372
C103×#32362
C103×#16642
C103×#16632
C103×#15372
C103×#15352
C103×#15342
#19093103