Finite Group Databasebeta

← C103×#18243 #39923518

Subgroups — C103×#18243 #39923518

Order 26368.

928 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3561C211yesmaximal, characteristic
2C103×#3117C211yesmaximal, characteristic, complemented
3C103×#3104C211yesmaximal, characteristic, complemented
4C103×#2632C211yesmaximal, characteristic, complemented
5C103×#1618C212yesmaximal, complemented
6C103×#1614C212yesmaximal, complemented
7C103×#1606C212yesmaximal, complemented
8C103×#1602C212yesmaximal, complemented
9C103×#1521C211yesmaximal, characteristic, complemented
10C103×#1515C211yesmaximal, characteristic, complemented
11C103×#1469C211yesmaximal, characteristic, complemented
12#563×C103—21no—
13#562×C103—21no—
14#556×C103—21no—
15#551×C103—22no—
16D4×Q8×C103—21no—
17#548×C103—21no—
18#546×C103—21no—
19#543×C103C2212yes—
20#542×C103—21no—
21#542×C103—22no—
22#538×C103C2212yes—
23#536×C103—21no—
24#533×C103C2211yescharacteristic
25#529×C103C2211yescharacteristic
26C2×#124×C103C2211yescharacteristic
27C2×C4×Q8×C103C2211yescharacteristic
28#484×C103C2212yes—
29#484×C103C2211yescharacteristic
30#481×C103C2211yescharacteristic
31#479×C103—21no—
32#477×C103—21no—
33#464×C103—21no—
34#462×C103—21no—
35#451×C103C2212yes—
36#451×C103C2211yescharacteristic
37#448×C103C2211yescharacteristic
38#441×C103—21no—
39#440×C103—21no—
40C4×Q16×C103—22no—
41#432×C103C2211yescharacteristic
42#431×C103C2211yescharacteristic
43#399×C103C2212yes—
44#395×C103—21no—
45#394×C103—21no—
46#393×C103C2212yes—
47#388×C103—22no—
48#383×C103C2211yescharacteristic
49#328×C103C2212yes—
50#328×C103C2212yes—
51#328×C103C2212yes—
52#327×C103C2212yes—
53#323×C103C2212yes—
54#323×C103C2212yes—
55C2×#41×C103—21no—
56C22×Q8×C103—21no—
57C22×Q8×C103D411yescharacteristic
58C22×Q8×C103C2311yescharacteristic
59C22×D4×C103D411yescharacteristic
60C2×Q16×C103—22no—
61C2×Q16×C103—21no—
62C2×SD16×C103—21no—
63C4⋊Q8×C103—21no—
64C4⋊Q8×C103—22no—
65C4⋊Q8×C103D411yescharacteristic
66C4⋊Q8×C103D411yescharacteristic
67#126×C103—22no—
68#126×C103—22no—
69#126×C103—22no—
70#126×C103—21no—
71#125×C103—21no—
72#125×C103D411yescharacteristic
73#124×C103—21no—
74#124×C103—22no—
75#124×C103—22no—
76#124×C103—21no—
77#124×C103—21no—
78#124×C103—21no—
79#124×C103—21no—
80#124×C103D411yescharacteristic
81#123×C103—22no—
82#123×C103—22no—
83#123×C103—22no—
84#123×C103—21no—
85#123×C103—22no—
86C22⋊Q8×C103—22no—
87C22⋊Q8×C103—21no—
88C22⋊Q8×C103—22no—
89C22⋊Q8×C103—22no—
90C22⋊Q8×C103—22no—
91C22⋊Q8×C103—21no—
92C22⋊Q8×C103—22no—
93C22⋊Q8×C103—22no—
94C22⋊Q8×C103—22no—
95C22⋊Q8×C103C2311yescharacteristic
96C22⋊Q8×C103C2312yes—
97#121×C103—21no—
98#121×C103—22no—
99#121×C103—22no—
100#121×C103C2311yescharacteristic
101#120×C103—22no—
102C4×Q8×C103—21no—
103C4×Q8×C103—21no—
104C4×Q8×C103—21no—
105C4×Q8×C103—21no—
106C4×Q8×C103—21no—
107C4×Q8×C103—21no—
108C4×Q8×C103D412yes—
109C4×Q8×C103D411yescharacteristic
110C4×D4×C103—21no—
111C4×D4×C103—22no—
112C4×D4×C103—21no—
113C4×D4×C103—22no—
114C4×D4×C103D411yescharacteristic
115#117×C103—22no—
116#117×C103—21no—
117#117×C103—21no—
118C2×C4⋊C4×C103—21no—
119C2×C4⋊C4×C103—22no—
120C2×C4⋊C4×C103C2311yescharacteristic
121C2×C22⋊C4×C103—22no—
122C2×C22⋊C4×C103—22no—
123C2×C22⋊C4×C103—22no—
124C2×C22⋊C4×C103D412yes—
125C2×C22⋊C4×C103C2312yes—
126C2×C42×C103—21no—
127C2×C42×C103C2311yescharacteristic
128#107×C103—22no—
129#107×C103—21no—
130#106×C103—21no—
131C4⋊C8×C103—21no—
132C4⋊C8×C103—21no—
133#103×C103—22no—
134#103×C103—21no—
135#103×C103—22no—
136#103×C103—21no—
137#103×C103—21no—
138#102×C103—21no—
139C22⋊C8×C103C2312yes—
140C22⋊C8×C103C2311yescharacteristic
141C22⋊C8×C103C2311yescharacteristic
142#97×C103—21no—
143C4×C8×C103—21no—
144#95×C103—21no—
145#95×C103—21no—
146#95×C103—22no—
147#95×C103C2312yes—
148C24×C103C2×D412yes—
149#41×C103—82no—
150C2×Q8×C103—22no—
151C2×Q8×C103—21no—
152C2×Q8×C103—21no—
153C2×Q8×C103—21no—
154C2×Q8×C103—21no—
155C2×Q8×C103—21no—
156C2×Q8×C103—42no—
157C2×Q8×C103—81no—
158C2×Q8×C103—82no—
159C2×Q8×C103C2×D411yescharacteristic
160C2×Q8×C103C2×D412yes—
161C2×D4×C103—21no—
162C2×D4×C103—22no—
163C2×D4×C103—22no—
164C2×D4×C103—21no—
165C2×D4×C103—21no—
166C2×D4×C103—81no—
167C2×D4×C103C2×D411yescharacteristic
168C22×C4×C103—21no—
169C22×C4×C103—22no—
170C22×C4×C103—22no—
171C22×C4×C103—22no—
172C22×C4×C103—21no—
173C22×C4×C103—22no—
174C22×C4×C103—21no—
175C22×C4×C103C2×D411yescharacteristic
176C22×C4×C103C2×D412yes—
177C22×C4×C103C2×D411yescharacteristic
178C22×C4×C103C2411yescharacteristic
179Q16×C103—42no—
180Q16×C103—44no—
181SD16×C103—42no—
182C2×C8×C103—22no—
183C2×C8×C103—21no—
184C2×C8×C103—21no—
185C4⋊C4×C103—22no—
186C4⋊C4×C103—22no—
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—21no—
194C4⋊C4×C103—21no—
195C4⋊C4×C103—22no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—22no—
198C4⋊C4×C103—21no—
199C4⋊C4×C103—21no—
200C4⋊C4×C103—41no—
201C4⋊C4×C103—41no—
202C4⋊C4×C103—82no—
203C4⋊C4×C103C2×D411yescharacteristic
204C4⋊C4×C103C2×D411yescharacteristic
205C4⋊C4×C103C2×D412yes—
206C22⋊C4×C103—22no—
207C22⋊C4×C103—22no—
208C22⋊C4×C103—22no—
209C22⋊C4×C103—22no—
210C22⋊C4×C103—22no—
211C22⋊C4×C103—21no—
212C22⋊C4×C103—22no—
213C22⋊C4×C103—22no—
214C22⋊C4×C103—22no—
215C22⋊C4×C103—21no—
216C22⋊C4×C103—21no—
217C22⋊C4×C103—21no—
218C22⋊C4×C103—22no—
219C22⋊C4×C103—22no—
220C22⋊C4×C103—21no—
221C22⋊C4×C103—44no—
222C22⋊C4×C103—82no—
223C42×C103—22no—
224C42×C103—22no—
225C42×C103—21no—
226C42×C103—41no—
227C42×C103—41no—
228C42×C103C2×D411yescharacteristic
229C42×C103C2×D411yescharacteristic
230C42×C103C2×D411yescharacteristic
231C42×C103C2×D411yescharacteristic
232C23×C103—22no—
233C23×C103—21no—
234C23×C103—24no—
235C23×C103—42no—
236C23×C103—42no—
237C23×C103C22×D411yescharacteristic
238Q8×C103—22no—
239Q8×C103—22no—
240Q8×C103—41no—
241Q8×C103—42no—
242Q8×C103—41no—
243Q8×C103—41no—
244Q8×C103—42no—
245Q8×C103—42no—
246Q8×C103—81no—
247Q8×C103—82no—
248D4×C103—41no—
249D4×C103—42no—
250D4×C103—42no—
251D4×C103—81no—
252D4×C103—82no—
253D4×C103—82no—
254C2×C4×C103—22no—
255C2×C4×C103—22no—
256C2×C4×C103—21no—
257C2×C4×C103—22no—
258C2×C4×C103—21no—
259C2×C4×C103—22no—
260C2×C4×C103—22no—
261C2×C4×C103—21no—
262C2×C4×C103—41no—
263C2×C4×C103—41no—
264C2×C4×C103—42no—
265C2×C4×C103—41no—
266C2×C4×C103—41no—
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—82no—
275C2×C4×C103—82no—
276C2×C4×C103#12011yescharacteristic
277C2×C4×C103#12011yescharacteristic
278C2×C4×C103#12011yescharacteristic
279C2×C4×C103#12011yescharacteristic
280C2×C4×C103C22×D411yescharacteristic
281C2×C4×C103C22×D411yescharacteristic
282C8×C103—41no—
283C8×C103—41no—
284C8×C103—42no—
285C22×C103—21no—
286C22×C103—21no—
287C22×C103—41no—
288C22×C103—42no—
289C22×C103—41no—
290C22×C103—42no—
291C22×C103—42no—
292C22×C103—41no—
293C22×C103—84no—
294C22×C103C2×#12011yescharacteristic
295C22×C103#57812yes—
296C4×C103—21no—
297C4×C103—21no—
298C4×C103—21no—
299C4×C103—21no—
300C4×C103—21no—
301C4×C103—21no—
302C4×C103—41no—
303C4×C103—41no—
304C4×C103—42no—
305C4×C103—42no—
306C4×C103—42no—
307C4×C103—41no—
308C4×C103—42no—
309C4×C103—82no—
310C4×C103—81no—
311#18243C10311yesmaximal, characteristic, direct product factor, Sylow
312C2×C103—22no—
313C2×C103—81no—
314C2×C103—82no—
315C2×C103#301111yescharacteristic
316C2×C103#301911yescharacteristic
317C2×C103#302511yescharacteristic
318#3561C2×C10311yescharacteristic
319#3117C2×C10311yescharacteristic, complemented
320#3104C2×C10311yescharacteristic, complemented
321#2632C2×C10311yescharacteristic, complemented
322#1618C2×C10312yescomplemented
323#1614C2×C10312yescomplemented
324#1606C2×C10312yescomplemented
325#1602C2×C10312yescomplemented
326#1521C2×C10311yescharacteristic, complemented
327#1515C2×C10311yescharacteristic, complemented
328#1469C2×C10311yescharacteristic, complemented
329C103#1824311yescharacteristic, direct product factor, Sylow
330#563—21no—
331#562—21no—
332#556—21no—
333#551—22no—
334D4×Q8—21no—
335#548—21no—
336#546—21no—
337#543C22×C10312yes—
338#542—21no—
339#542—22no—
340#538C22×C10312yes—
341#536—21no—
342#533C22×C10311yescharacteristic
343#529C22×C10311yescharacteristic
344C2×#124C22×C10311yescharacteristic
345C2×C4×Q8C22×C10311yescharacteristic
346#484C22×C10312yes—
347#484C22×C10311yescharacteristic
348#481C22×C10311yescharacteristic
349#479—21no—
350#477—21no—
351#464—21no—
352#462—21no—
353#451C22×C10312yes—
354#451C22×C10311yescharacteristic
355#448C22×C10311yescharacteristic
356#441—21no—
357#440—21no—
358C4×Q16—22no—
359#432C22×C10311yescharacteristic
360#431C22×C10311yescharacteristic
361#399C22×C10312yes—
362#395—21no—
363#394—21no—
364#393C22×C10312yes—
365#388—22no—
366#383C22×C10311yescharacteristic
367#328C22×C10312yes—
368#328C22×C10312yes—
369#328C22×C10312yes—
370#327C22×C10312yes—
371#323C22×C10312yes—
372#323C22×C10312yes—
373C2×#41—21no—
374C22×Q8—21no—
375C22×Q8D4×C10311yescharacteristic
376C22×Q8C23×C10311yescharacteristic
377C22×D4D4×C10311yescharacteristic
378C2×Q16—22no—
379C2×Q16—21no—
380C2×SD16—21no—
381C4⋊Q8—21no—
382C4⋊Q8—22no—
383C4⋊Q8D4×C10311yescharacteristic
384C4⋊Q8D4×C10311yescharacteristic
385#126—22no—
386#126—22no—
387#126—22no—
388#126—21no—
389#125—21no—
390#125D4×C10311yescharacteristic
391#124—21no—
392#124—22no—
393#124—22no—
394#124—21no—
395#124—21no—
396#124—21no—
397#124—21no—
398#124D4×C10311yescharacteristic
399#123—22no—
400#123—22no—
401#123—22no—
402#123—21no—
403#123—22no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—21no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8C23×C10311yescharacteristic
414C22⋊Q8C23×C10312yes—
415#121—21no—
416#121—22no—
417#121—22no—
418#121C23×C10311yescharacteristic
419#120—22no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8D4×C10311yescharacteristic
427C4×Q8D4×C10312yes—
428C4×D4—21no—
429C4×D4—22no—
430C4×D4—21no—
431C4×D4—22no—
432C4×D4D4×C10311yescharacteristic
433#117—22no—
434#117—21no—
435#117—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4C23×C10311yescharacteristic
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4D4×C10312yes—
443C2×C22⋊C4C23×C10312yes—
444C2×C42—21no—
445C2×C42C23×C10311yescharacteristic
446#107—22no—
447#107—21no—
448#106—21no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451#103—22no—
452#103—21no—
453#103—22no—
454#103—21no—
455#103—21no—
456#102—21no—
457C22⋊C8C23×C10312yes—
458C22⋊C8C23×C10311yescharacteristic
459C22⋊C8C23×C10311yescharacteristic
460#97—21no—
461C4×C8—21no—
462#95—21no—
463#95—21no—
464#95—22no—
465#95C23×C10312yes—
466C24C2×D4×C10312yes—
467#41—82no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—42no—
475C2×Q8—81no—
476C2×Q8—82no—
477C2×Q8C2×D4×C10311yescharacteristic
478C2×Q8C2×D4×C10312yes—
479C2×D4—21no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—81no—
485C2×D4C2×D4×C10311yescharacteristic
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4C2×D4×C10311yescharacteristic
494C22×C4C2×D4×C10312yes—
495C22×C4C2×D4×C10311yescharacteristic
496C22×C4C24×C10311yescharacteristic
497Q16—42no—
498Q16—44no—
499SD16—42no—
500C2×C8—22no—
501C2×C8—21no—
502C2×C8—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—82no—
521C4⋊C4C2×D4×C10311yescharacteristic
522C4⋊C4C2×D4×C10311yescharacteristic
523C4⋊C4C2×D4×C10312yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—44no—
540C22⋊C4—82no—
541C42—22no—
542C42—22no—
543C42—21no—
544C42—41no—
545C42—41no—
546C42C2×D4×C10311yescharacteristic
547C42C2×D4×C10311yescharacteristic
548C42C2×D4×C10311yescharacteristic
549C42C2×D4×C10311yescharacteristic
550C23—22no—
551C23—21no—
552C23—24no—
553C23—42no—
554C23—42no—
555C23C22×D4×C10311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—42no—
560Q8—41no—
561Q8—41no—
562Q8—42no—
563Q8—42no—
564Q8—81no—
565Q8—82no—
566D4—41no—
567D4—42no—
568D4—42no—
569D4—81no—
570D4—82no—
571D4—82no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4#120×C10311yescharacteristic
595C2×C4#120×C10311yescharacteristic
596C2×C4#120×C10311yescharacteristic
597C2×C4#120×C10311yescharacteristic
598C2×C4C22×D4×C10311yescharacteristic
599C2×C4C22×D4×C10311yescharacteristic
600C8—41no—
601C8—41no—
602C8—42no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—42no—
607C22—41no—
608C22—42no—
609C22—42no—
610C22—41no—
611C22—84no—
612C22C2×#120×C10311yescharacteristic
613C22#578×C10312yes—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—42no—
624C4—42no—
625C4—41no—
626C4—42no—
627C4—82no—
628C4—81no—
629C2—22no—
630C2—82no—
631C2—81no—
632C2C103×#301111yescharacteristic
633C2C103×#301911yescharacteristic
634C2C103×#302511yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3561C2
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
2. C103×#3117C2semidirect
3. C103×#3104C2semidirect
4. C103×#2632C2semidirect
5. C103×#1618C2semidirect
6. C103×#1614C2semidirect
7. C103×#1606C2semidirect
8. C103×#1602C2semidirect
9. C103×#1521C2semidirect
10. C103×#1515C2semidirect
11. C103×#1469C2semidirect
311. #18243C103direct (N × H)
319. #3117C2×C103semidirect
320. #3104C2×C103semidirect
321. #2632C2×C103semidirect
322. #1618C2×C103semidirect
323. #1614C2×C103semidirect
324. #1606C2×C103semidirect
325. #1602C2×C103semidirect
326. #1521C2×C103semidirect
327. #1515C2×C103semidirect
328. #1469C2×C103semidirect
329. C103#18243direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#35612
C103×#31172
C103×#31042
C103×#26322
C103×#16182
C103×#16142
C103×#16062
C103×#16022
C103×#15212
C103×#15152
C103×#14692
#18243103