Finite Group Databasebeta

← C103×#18461 #39923736

Subgroups — C103×#18461 #39923736

Order 26368.

880 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3563C211yesmaximal, characteristic, complemented
2C103×#3215C211yesmaximal, characteristic, complemented
3C103×#3211C211yesmaximal, characteristic
4C103×#2820C211yesmaximal, characteristic, complemented
5C103×#1605C212yesmaximal, complemented
6C103×#1603C212yesmaximal, complemented
7C103×#1599C212yesmaximal, complemented
8C103×#1597C212yesmaximal
9C103×#1518C211yesmaximal, characteristic, complemented
10C103×#1512C211yesmaximal, characteristic, complemented
11C103×#1470C211yesmaximal, characteristic, complemented
12#564×C103—21no—
13#563×C103—21no—
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×C103C2212yes—
21#541×C103—21no—
22#541×C103—22no—
23#539×C103C2212yes—
24#533×C103C2211yescharacteristic
25#529×C103C2211yescharacteristic
26C2×#125×C103C2211yescharacteristic
27C2×#124×C103C2211yescharacteristic
28#497×C103—21no—
29#495×C103—21no—
30#489×C103—21no—
31#488×C103—21no—
32#464×C103—21no—
33#464×C103—22no—
34#463×C103—21no—
35#451×C103C2211yescharacteristic
36#451×C103C2212yes—
37#450×C103C2211yescharacteristic
38#450×C103C2212yes—
39#448×C103C2211yescharacteristic
40#447×C103C2211yescharacteristic
41#432×C103C2211yescharacteristic
42#431×C103C2211yescharacteristic
43#399×C103—21no—
44#397×C103—21no—
45#396×C103—22no—
46#395×C103C2212yes—
47#394×C103C2212yes—
48#382×C103C2211yescharacteristic
49#328×C103C2212yes—
50#328×C103C2212yes—
51#328×C103C2212yes—
52#327×C103C2212yes—
53#324×C103C2212yes—
54#324×C103C2212yes—
55C22×Q8×C103C2311yescharacteristic
56C22×D4×C103C2311yescharacteristic
57C2×Q16×C103—21no—
58C2×Q16×C103—22no—
59C2×SD16×C103—21no—
60C2×SD16×C103—22no—
61C2×SD16×C103—21no—
62C2×D8×C103—21no—
63C4⋊Q8×C103—21no—
64C4⋊Q8×C103—22no—
65C4⋊Q8×C103—22no—
66C4⋊Q8×C103D411yescharacteristic
67C4⋊Q8×C103D411yescharacteristic
68#126×C103—22no—
69#126×C103—22no—
70#126×C103—22no—
71#126×C103—22no—
72#126×C103—21no—
73#125×C103—22no—
74#125×C103—22no—
75#125×C103—22no—
76#125×C103—22no—
77#125×C103—21no—
78#125×C103—22no—
79#125×C103—22no—
80#125×C103—22no—
81#125×C103—22no—
82#125×C103—21no—
83#125×C103—21no—
84#125×C103—21no—
85#125×C103—21no—
86#125×C103—21no—
87#125×C103D411yescharacteristic
88#124×C103—21no—
89#124×C103—21no—
90#124×C103—21no—
91#124×C103—21no—
92#124×C103D411yescharacteristic
93#123×C103—22no—
94#123×C103—21no—
95#123×C103—22no—
96C22⋊Q8×C103—21no—
97C22⋊Q8×C103—21no—
98C22⋊Q8×C103—22no—
99C22⋊Q8×C103—22no—
100C22⋊Q8×C103—22no—
101C22⋊Q8×C103—21no—
102C22⋊Q8×C103—22no—
103C22⋊Q8×C103C2311yescharacteristic
104C22⋊Q8×C103C2312yes—
105#121×C103C2311yescharacteristic
106C4×Q8×C103—21no—
107C4×Q8×C103—22no—
108C4×Q8×C103—21no—
109C4×Q8×C103—21no—
110C4×Q8×C103D411yescharacteristic
111C4×Q8×C103D412yes—
112C4×D4×C103—21no—
113C4×D4×C103—22no—
114C4×D4×C103D411yescharacteristic
115#117×C103—22no—
116#117×C103—21no—
117#117×C103—21no—
118#117×C103—22no—
119#117×C103—21no—
120C2×C4⋊C4×C103—21no—
121C2×C4⋊C4×C103—21no—
122C2×C4⋊C4×C103—22no—
123C2×C4⋊C4×C103D412yes—
124C2×C4⋊C4×C103D411yescharacteristic
125C2×C4⋊C4×C103D411yescharacteristic
126C2×C4⋊C4×C103C2312yes—
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103—21no—
129C2×C22⋊C4×C103—22no—
130C2×C22⋊C4×C103—22no—
131C2×C42×C103C2311yescharacteristic
132C4⋊C8×C103—21no—
133C4⋊C8×C103—21no—
134#103×C103—21no—
135#103×C103—21no—
136#103×C103—22no—
137#102×C103—21no—
138#102×C103—21no—
139#102×C103—22no—
140C22⋊C8×C103C2311yescharacteristic
141C22⋊C8×C103C2311yescharacteristic
142C22⋊C8×C103C2312yes—
143#97×C103—21no—
144C4×C8×C103—21no—
145#95×C103—21no—
146#95×C103—22no—
147#95×C103C2312yes—
148C24×C103—21no—
149C2×Q8×C103—22no—
150C2×Q8×C103—21no—
151C2×Q8×C103—21no—
152C2×Q8×C103—21no—
153C2×Q8×C103—81no—
154C2×Q8×C103C2×D412yes—
155C2×Q8×C103C2×D411yescharacteristic
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—81no—
160C2×D4×C103C2×D411yescharacteristic
161C22×C4×C103—22no—
162C22×C4×C103—21no—
163C22×C4×C103—22no—
164C22×C4×C103—21no—
165C22×C4×C103C2×D412yes—
166C22×C4×C103C2×D411yescharacteristic
167C22×C4×C103C2×D412yes—
168C22×C4×C103C2×D411yescharacteristic
169C22×C4×C103C2411yescharacteristic
170Q16×C103—81no—
171Q16×C103—82no—
172SD16×C103—81no—
173SD16×C103—81no—
174SD16×C103—82no—
175D8×C103—81no—
176C2×C8×C103—21no—
177C2×C8×C103—21no—
178C2×C8×C103—22no—
179C4⋊C4×C103—22no—
180C4⋊C4×C103—22no—
181C4⋊C4×C103—22no—
182C4⋊C4×C103—22no—
183C4⋊C4×C103—22no—
184C4⋊C4×C103—22no—
185C4⋊C4×C103—22no—
186C4⋊C4×C103—22no—
187C4⋊C4×C103—21no—
188C4⋊C4×C103—21no—
189C4⋊C4×C103—21no—
190C4⋊C4×C103—22no—
191C4⋊C4×C103—21no—
192C4⋊C4×C103—22no—
193C4⋊C4×C103—21no—
194C4⋊C4×C103—21no—
195C4⋊C4×C103—21no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—21no—
198C4⋊C4×C103—21no—
199C4⋊C4×C103—22no—
200C4⋊C4×C103—22no—
201C4⋊C4×C103—22no—
202C4⋊C4×C103—21no—
203C4⋊C4×C103—22no—
204C4⋊C4×C103—81no—
205C4⋊C4×C103—82no—
206C4⋊C4×C103C2×D411yescharacteristic
207C4⋊C4×C103C2×D411yescharacteristic
208C4⋊C4×C103C2×D412yes—
209C22⋊C4×C103—22no—
210C22⋊C4×C103—22no—
211C22⋊C4×C103—22no—
212C22⋊C4×C103—22no—
213C22⋊C4×C103—21no—
214C22⋊C4×C103—21no—
215C22⋊C4×C103—21no—
216C22⋊C4×C103—21no—
217C22⋊C4×C103—21no—
218C22⋊C4×C103—41no—
219C22⋊C4×C103—41no—
220C22⋊C4×C103—41no—
221C22⋊C4×C103—41no—
222C22⋊C4×C103—82no—
223C22⋊C4×C103—82no—
224C42×C103—22no—
225C42×C103—22no—
226C42×C103—22no—
227C42×C103—22no—
228C42×C103—21no—
229C42×C103C2×D411yescharacteristic
230C42×C103C2×D411yescharacteristic
231C42×C103C2×D411yescharacteristic
232C42×C103C2×D411yescharacteristic
233C23×C103—21no—
234C23×C103—42no—
235C23×C103—42no—
236C23×C103—41no—
237C23×C103—41no—
238C23×C103—41no—
239C23×C103C22×D411yescharacteristic
240Q8×C103—41no—
241Q8×C103—42no—
242Q8×C103—42no—
243Q8×C103—41no—
244Q8×C103—41no—
245Q8×C103—42no—
246Q8×C103—82no—
247D4×C103—41no—
248D4×C103—41no—
249D4×C103—41no—
250D4×C103—42no—
251D4×C103—41no—
252D4×C103—41no—
253C2×C4×C103—21no—
254C2×C4×C103—21no—
255C2×C4×C103—22no—
256C2×C4×C103—21no—
257C2×C4×C103—21no—
258C2×C4×C103—22no—
259C2×C4×C103—21no—
260C2×C4×C103—22no—
261C2×C4×C103—22no—
262C2×C4×C103—22no—
263C2×C4×C103—22no—
264C2×C4×C103—41no—
265C2×C4×C103—41no—
266C2×C4×C103—42no—
267C2×C4×C103—42no—
268C2×C4×C103—42no—
269C2×C4×C103—42no—
270C2×C4×C103—42no—
271C2×C4×C103—41no—
272C2×C4×C103—42no—
273C2×C4×C103—82no—
274C2×C4×C103#12011yescharacteristic
275C2×C4×C103#12011yescharacteristic
276C2×C4×C103#12011yescharacteristic
277C2×C4×C103#12011yescharacteristic
278C2×C4×C103C22×D411yescharacteristic
279C2×C4×C103C22×D411yescharacteristic
280C8×C103—41no—
281C8×C103—41no—
282C8×C103—42no—
283C22×C103—21no—
284C22×C103—21no—
285C22×C103—41no—
286C22×C103—41no—
287C22×C103—41no—
288C22×C103—82no—
289C22×C103—82no—
290C22×C103—81no—
291C22×C103—81no—
292C22×C103—81no—
293C22×C103C2×#12011yescharacteristic
294C22×C103#57711yescharacteristic
295C22×C103#57811yescharacteristic
296C4×C103—21no—
297C4×C103—21no—
298C4×C103—21no—
299C4×C103—21no—
300C4×C103—21no—
301C4×C103—21no—
302C4×C103—42no—
303C4×C103—41no—
304C4×C103—41no—
305C4×C103—42no—
306C4×C103—42no—
307C4×C103—42no—
308C4×C103—41no—
309C4×C103—82no—
310C4×C103—81no—
311#18461C10311yesmaximal, characteristic, direct product factor, Sylow
312C2×C103—21no—
313C2×C103—21no—
314C2×C103—81no—
315C2×C103—161no—
316C2×C103#301311yescharacteristic
317C2×C103#302011yescharacteristic
318C2×C103#302711yescharacteristic
319#3563C2×C10311yescharacteristic, complemented
320#3215C2×C10311yescharacteristic, complemented
321#3211C2×C10311yescharacteristic
322#2820C2×C10311yescharacteristic, complemented
323#1605C2×C10312yescomplemented
324#1603C2×C10312yescomplemented
325#1599C2×C10312yescomplemented
326#1597C2×C10312yes—
327#1518C2×C10311yescharacteristic, complemented
328#1512C2×C10311yescharacteristic, complemented
329#1470C2×C10311yescharacteristic, complemented
330C103#1846111yescharacteristic, direct product factor, Sylow
331#564—21no—
332#563—21no—
333#557—21no—
334#554—21no—
335#552—21no—
336#552—22no—
337#552—21no—
338#544—21no—
339#544C22×C10312yes—
340#541—21no—
341#541—22no—
342#539C22×C10312yes—
343#533C22×C10311yescharacteristic
344#529C22×C10311yescharacteristic
345C2×#125C22×C10311yescharacteristic
346C2×#124C22×C10311yescharacteristic
347#497—21no—
348#495—21no—
349#489—21no—
350#488—21no—
351#464—21no—
352#464—22no—
353#463—21no—
354#451C22×C10312yes—
355#451C22×C10311yescharacteristic
356#450C22×C10312yes—
357#450C22×C10311yescharacteristic
358#448C22×C10311yescharacteristic
359#447C22×C10311yescharacteristic
360#432C22×C10311yescharacteristic
361#431C22×C10311yescharacteristic
362#399—21no—
363#397—21no—
364#396—22no—
365#395C22×C10312yes—
366#394C22×C10312yes—
367#382C22×C10311yescharacteristic
368#328C22×C10312yes—
369#328C22×C10312yes—
370#328C22×C10312yes—
371#327C22×C10312yes—
372#324C22×C10312yes—
373#324C22×C10312yes—
374C22×Q8C23×C10311yescharacteristic
375C22×D4C23×C10311yescharacteristic
376C2×Q16—21no—
377C2×Q16—22no—
378C2×SD16—21no—
379C2×SD16—22no—
380C2×SD16—21no—
381C2×D8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385C4⋊Q8D4×C10311yescharacteristic
386C4⋊Q8D4×C10311yescharacteristic
387#126—22no—
388#126—22no—
389#126—22no—
390#126—22no—
391#126—21no—
392#125—22no—
393#125—22no—
394#125—22no—
395#125—22no—
396#125—21no—
397#125—22no—
398#125—22no—
399#125—22no—
400#125—22no—
401#125—21no—
402#125—21no—
403#125—21no—
404#125—21no—
405#125—21no—
406#125D4×C10311yescharacteristic
407#124—21no—
408#124—21no—
409#124—21no—
410#124—21no—
411#124D4×C10311yescharacteristic
412#123—22no—
413#123—21no—
414#123—22no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—21no—
421C22⋊Q8—22no—
422C22⋊Q8C23×C10311yescharacteristic
423C22⋊Q8C23×C10312yes—
424#121C23×C10311yescharacteristic
425C4×Q8—21no—
426C4×Q8—22no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8D4×C10311yescharacteristic
430C4×Q8D4×C10312yes—
431C4×D4—21no—
432C4×D4—22no—
433C4×D4D4×C10311yescharacteristic
434#117—22no—
435#117—21no—
436#117—21no—
437#117—22no—
438#117—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4D4×C10312yes—
443C2×C4⋊C4D4×C10311yescharacteristic
444C2×C4⋊C4D4×C10311yescharacteristic
445C2×C4⋊C4C23×C10312yes—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C42C23×C10311yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—21no—
453#103—21no—
454#103—21no—
455#103—22no—
456#102—21no—
457#102—21no—
458#102—22no—
459C22⋊C8C23×C10312yes—
460C22⋊C8C23×C10311yescharacteristic
461C22⋊C8C23×C10311yescharacteristic
462#97—21no—
463C4×C8—21no—
464#95—21no—
465#95—22no—
466#95C23×C10312yes—
467C24—21no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—81no—
473C2×Q8C2×D4×C10312yes—
474C2×Q8C2×D4×C10311yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—81no—
479C2×D4C2×D4×C10311yescharacteristic
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4C2×D4×C10312yes—
485C22×C4C2×D4×C10311yescharacteristic
486C22×C4C2×D4×C10312yes—
487C22×C4C2×D4×C10311yescharacteristic
488C22×C4C24×C10311yescharacteristic
489Q16—81no—
490Q16—82no—
491SD16—81no—
492SD16—81no—
493SD16—82no—
494D8—81no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—81no—
524C4⋊C4—82no—
525C4⋊C4C2×D4×C10311yescharacteristic
526C4⋊C4C2×D4×C10311yescharacteristic
527C4⋊C4C2×D4×C10312yes—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—82no—
542C22⋊C4—82no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—21no—
548C42C2×D4×C10311yescharacteristic
549C42C2×D4×C10311yescharacteristic
550C42C2×D4×C10311yescharacteristic
551C42C2×D4×C10311yescharacteristic
552C23—21no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23C22×D4×C10311yescharacteristic
559Q8—41no—
560Q8—42no—
561Q8—42no—
562Q8—41no—
563Q8—41no—
564Q8—42no—
565Q8—82no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—42no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—82no—
593C2×C4#120×C10311yescharacteristic
594C2×C4#120×C10311yescharacteristic
595C2×C4#120×C10311yescharacteristic
596C2×C4#120×C10311yescharacteristic
597C2×C4C22×D4×C10311yescharacteristic
598C2×C4C22×D4×C10311yescharacteristic
599C8—41no—
600C8—41no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—82no—
608C22—82no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22C2×#120×C10311yescharacteristic
613C22#577×C10311yescharacteristic
614C22#578×C10311yescharacteristic
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—41no—
628C4—82no—
629C4—81no—
630C2—21no—
631C2—21no—
632C2—81no—
633C2—161no—
634C2C103×#301311yescharacteristic
635C2C103×#302011yescharacteristic
636C2C103×#302711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radical#447×C103C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3563C2semidirect
2. C103×#3215C2semidirect
4. C103×#2820C2semidirect
5. C103×#1605C2semidirect
6. C103×#1603C2semidirect
7. C103×#1599C2semidirect
9. C103×#1518C2semidirect
10. C103×#1512C2semidirect
11. C103×#1470C2semidirect
311. #18461C103direct (N × H)
319. #3563C2×C103semidirect
320. #3215C2×C103semidirect
322. #2820C2×C103semidirect
323. #1605C2×C103semidirect
324. #1603C2×C103semidirect
325. #1599C2×C103semidirect
327. #1518C2×C103semidirect
328. #1512C2×C103semidirect
329. #1470C2×C103semidirect
330. C103#18461direct (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×#32152
C103×#32112
C103×#28202
C103×#16052
C103×#16032
C103×#15992
C103×#15972
C103×#15182
C103×#15122
C103×#14702
#18461103