Finite Group Databasebeta

← C103×#8466 #39913741

Subgroups — C103×#8466 #39913741

Order 26368.

798 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3494C211yesmaximal, characteristic
2C103×#1964C211yesmaximal, characteristic, complemented
3C103×#1826C211yesmaximal, characteristic, complemented
4C103×#1825C211yesmaximal, characteristic, complemented
5C103×#1513C211yesmaximal, characteristic, complemented
6C103×#1501C211yesmaximal, characteristic, complemented
7C103×#1471C211yesmaximal, characteristic, complemented
8#555×C103—21no—
9#553×C103—21no—
10#553×C103—21no—
11#551×C103—22no—
12#547×C103—21no—
13#546×C103—22no—
14#544×C103C411yescharacteristic, complemented
15#542×C103—21no—
16#540×C103—21no—
17#535×C103C411yescharacteristic, complemented
18#532×C103—21no—
19#529×C103—21no—
20#525×C103C2211yescharacteristic
21C2×#121×C103C2211yescharacteristic
22#520×C103C411yescharacteristic, complemented
23#518×C103C411yescharacteristic, complemented
24C2×#117×C103C2211yescharacteristic
25C2×#99×C103—22no—
26#407×C103C2211yescharacteristic
27C2×C22⋊C8×C103C2211yescharacteristic
28#380×C103C2211yescharacteristic
29C4×C22⋊C4×C103C2211yescharacteristic
30#340×C103—21no—
31#340×C103—21no—
32#339×C103—21no—
33#339×C103—21no—
34#328×C103—21no—
35#328×C103—21no—
36#327×C103—21no—
37#327×C103—21no—
38#323×C103—22no—
39C2×#41×C103—22no—
40C2×#41×C103C2×C411yescharacteristic
41C22×D4×C103C2×C411yescharacteristic
42C22×D4×C103D412yes—
43C23×C4×C103C2311yescharacteristic
44C2×M16×C103—21no—
45C22×C8×C103—21no—
46C4⋊Q8×C103—21no—
47C4⋊Q8×C103—21no—
48#127×C103—21no—
49#126×C103—22no—
50#126×C103—22no—
51#125×C103—21no—
52#125×C103—21no—
53#124×C103—22no—
54#124×C103—22no—
55#124×C103—21no—
56#123×C103—22no—
57#123×C103—22no—
58#123×C103—22no—
59#123×C103—22no—
60#123×C103—21no—
61C22⋊Q8×C103—22no—
62C22⋊Q8×C103—22no—
63C22⋊Q8×C103D411yescharacteristic
64C22⋊Q8×C103D411yescharacteristic
65#121×C103—22no—
66#121×C103—22no—
67#121×C103—22no—
68#121×C103—21no—
69#121×C103—21no—
70#121×C103—21no—
71#121×C103—21no—
72#121×C103—21no—
73#121×C103—21no—
74#121×C103D411yescharacteristic
75#121×C103D411yescharacteristic
76#120×C103—22no—
77#120×C103—21no—
78C4×Q8×C103—21no—
79C4×D4×C103—22no—
80C4×D4×C103—22no—
81C4×D4×C103—21no—
82C4×D4×C103—22no—
83C4×D4×C103—21no—
84C4×D4×C103—21no—
85C4×D4×C103—21no—
86C4×D4×C103—21no—
87C4×D4×C103—21no—
88C4×D4×C103—21no—
89#117×C103—22no—
90#117×C103—21no—
91#117×C103—21no—
92#117×C103—21no—
93#117×C103C2×C411yescharacteristic
94#117×C103C2×C411yescharacteristic
95#117×C103C2×C411yescharacteristic
96#117×C103D411yescharacteristic
97#117×C103D411yescharacteristic
98C2×C4⋊C4×C103—21no—
99C2×C4⋊C4×C103—21no—
100C2×C4⋊C4×C103C2×C411yescharacteristic
101C2×C4⋊C4×C103D411yescharacteristic
102C2×C4⋊C4×C103D411yescharacteristic
103C2×C22⋊C4×C103—22no—
104C2×C22⋊C4×C103—21no—
105C2×C22⋊C4×C103—21no—
106C2×C22⋊C4×C103—21no—
107C2×C22⋊C4×C103D412yes—
108C2×C42×C103—21no—
109C2×C42×C103—21no—
110#99×C103—44no—
111C22⋊C8×C103—21no—
112C22⋊C8×C103—21no—
113C22⋊C8×C103—21no—
114C22⋊C8×C103—21no—
115#95×C103—21no—
116#95×C103—21no—
117C24×C103C22⋊C412yes—
118C24×C103C2×D411yescharacteristic
119#41×C103—42no—
120#41×C103—82no—
121#41×C103—82no—
122C2×Q8×C103—22no—
123C2×Q8×C103C22⋊C411yescharacteristic
124C2×D4×C103—21no—
125C2×D4×C103—21no—
126C2×D4×C103—22no—
127C2×D4×C103—22no—
128C2×D4×C103—22no—
129C2×D4×C103—21no—
130C2×D4×C103—22no—
131C2×D4×C103—21no—
132C2×D4×C103—21no—
133C2×D4×C103—42no—
134C2×D4×C103—42no—
135C2×D4×C103—42no—
136C2×D4×C103C22⋊C411yescharacteristic
137C22×C4×C103—21no—
138C22×C4×C103—22no—
139C22×C4×C103—22no—
140C22×C4×C103—22no—
141C22×C4×C103—21no—
142C22×C4×C103—21no—
143C22×C4×C103—42no—
144C22×C4×C103—41no—
145C22×C4×C103—41no—
146C22×C4×C103C22⋊C412yes—
147C22×C4×C103C22×C411yescharacteristic
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2×D411yescharacteristic
150C22×C4×C103C2×D411yescharacteristic
151C22×C4×C103C2×D411yescharacteristic
152C22×C4×C103C2×D411yescharacteristic
153M16×C103—42no—
154C2×C8×C103—42no—
155C2×C8×C103—41no—
156C2×C8×C103—41no—
157C4⋊C4×C103—22no—
158C4⋊C4×C103—22no—
159C4⋊C4×C103—22no—
160C4⋊C4×C103—22no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—21no—
163C4⋊C4×C103—21no—
164C4⋊C4×C103—21no—
165C4⋊C4×C103—21no—
166C4⋊C4×C103—21no—
167C4⋊C4×C103—42no—
168C4⋊C4×C103C22⋊C411yescharacteristic
169C4⋊C4×C103C22⋊C411yescharacteristic
170C4⋊C4×C103C22⋊C411yescharacteristic
171C4⋊C4×C103C22⋊C411yescharacteristic
172C4⋊C4×C103C22⋊C411yescharacteristic
173C4⋊C4×C103C22⋊C411yescharacteristic
174C22⋊C4×C103—22no—
175C22⋊C4×C103—22no—
176C22⋊C4×C103—22no—
177C22⋊C4×C103—22no—
178C22⋊C4×C103—22no—
179C22⋊C4×C103—21no—
180C22⋊C4×C103—21no—
181C22⋊C4×C103—21no—
182C22⋊C4×C103—21no—
183C22⋊C4×C103—21no—
184C22⋊C4×C103—21no—
185C22⋊C4×C103—21no—
186C22⋊C4×C103—22no—
187C22⋊C4×C103—22no—
188C22⋊C4×C103—21no—
189C22⋊C4×C103—21no—
190C22⋊C4×C103—22no—
191C22⋊C4×C103—41no—
192C22⋊C4×C103—42no—
193C42×C103—22no—
194C42×C103—21no—
195C42×C103—21no—
196C42×C103—21no—
197C42×C103—21no—
198C42×C103—21no—
199C42×C103—42no—
200C23×C103—21no—
201C23×C103—21no—
202C23×C103—22no—
203C23×C103—21no—
204C23×C103—41no—
205C23×C103—41no—
206C23×C103—42no—
207C23×C103—42no—
208C23×C103—42no—
209C23×C103C2×C22⋊C411yescharacteristic
210C23×C103#12011yescharacteristic
211C23×C103#12011yescharacteristic
212Q8×C103—41no—
213Q8×C103—82no—
214D4×C103—41no—
215D4×C103—42no—
216D4×C103—42no—
217D4×C103—42no—
218D4×C103—41no—
219D4×C103—42no—
220D4×C103—41no—
221D4×C103—42no—
222D4×C103—81no—
223D4×C103—82no—
224D4×C103—82no—
225D4×C103—82no—
226C2×C4×C103—22no—
227C2×C4×C103—22no—
228C2×C4×C103—22no—
229C2×C4×C103—21no—
230C2×C4×C103—21no—
231C2×C4×C103—21no—
232C2×C4×C103—21no—
233C2×C4×C103—21no—
234C2×C4×C103—21no—
235C2×C4×C103—21no—
236C2×C4×C103—22no—
237C2×C4×C103—41no—
238C2×C4×C103—41no—
239C2×C4×C103—41no—
240C2×C4×C103—41no—
241C2×C4×C103—41no—
242C2×C4×C103—42no—
243C2×C4×C103—42no—
244C2×C4×C103—42no—
245C2×C4×C103—81no—
246C2×C4×C103—82no—
247C2×C4×C103—82no—
248C2×C4×C103—82no—
249C2×C4×C103—81no—
250C2×C4×C103—81no—
251C2×C4×C103—81no—
252C2×C4×C103—81no—
253C2×C4×C103—81no—
254C2×C4×C103C2×C22⋊C411yescharacteristic
255C2×C4×C103C2×C22⋊C411yescharacteristic
256C2×C4×C103#12011yescharacteristic
257C2×C4×C103#12011yescharacteristic
258C8×C103—81no—
259C8×C103—81no—
260C22×C103—21no—
261C22×C103—21no—
262C22×C103—21no—
263C22×C103—21no—
264C22×C103—21no—
265C22×C103—21no—
266C22×C103—21no—
267C22×C103—21no—
268C22×C103—41no—
269C22×C103—42no—
270C22×C103—42no—
271C22×C103—41no—
272C22×C103—41no—
273C22×C103—42no—
274C22×C103—81no—
275C22×C103—81no—
276C22×C103—162no—
277C22×C103#37911yescharacteristic
278C22×C103#45311yescharacteristic
279C22×C103#45511yescharacteristic
280C4×C103—21no—
281C4×C103—21no—
282C4×C103—21no—
283C4×C103—41no—
284C4×C103—41no—
285C4×C103—42no—
286C4×C103—41no—
287C4×C103—41no—
288C4×C103—41no—
289C4×C103—41no—
290C4×C103—41no—
291C4×C103—82no—
292C4×C103—161no—
293C4×C103#41012yes—
294#8466C10311yesmaximal, characteristic, direct product factor, Sylow
295C2×C103—21no—
296C2×C103—21no—
297C2×C103—41no—
298C2×C103—41no—
299C2×C103—81no—
300C2×C103—82no—
301C2×C103#178211yescharacteristic
302C2×C103#179211yescharacteristic
303C2×C103#179411yescharacteristic
304#3494C2×C10311yescharacteristic
305#1964C2×C10311yescharacteristic, complemented
306#1826C2×C10311yescharacteristic, complemented
307#1825C2×C10311yescharacteristic, complemented
308#1513C2×C10311yescharacteristic, complemented
309#1501C2×C10311yescharacteristic, complemented
310#1471C2×C10311yescharacteristic, complemented
311C103#846611yescharacteristic, direct product factor, Sylow
312#555—21no—
313#553—21no—
314#553—21no—
315#551—22no—
316#547—21no—
317#546—22no—
318#544C4×C10311yescharacteristic, complemented
319#542—21no—
320#540—21no—
321#535C4×C10311yescharacteristic, complemented
322#532—21no—
323#529—21no—
324#525C22×C10311yescharacteristic
325C2×#121C22×C10311yescharacteristic
326#520C4×C10311yescharacteristic, complemented
327#518C4×C10311yescharacteristic, complemented
328C2×#117C22×C10311yescharacteristic
329C2×#99—22no—
330#407C22×C10311yescharacteristic
331C2×C22⋊C8C22×C10311yescharacteristic
332#380C22×C10311yescharacteristic
333C4×C22⋊C4C22×C10311yescharacteristic
334#340—21no—
335#340—21no—
336#339—21no—
337#339—21no—
338#328—21no—
339#328—21no—
340#327—21no—
341#327—21no—
342#323—22no—
343C2×#41—22no—
344C2×#41C2×C4×C10311yescharacteristic
345C22×D4C2×C4×C10311yescharacteristic
346C22×D4D4×C10312yes—
347C23×C4C23×C10311yescharacteristic
348C2×M16—21no—
349C22×C8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352#127—21no—
353#126—22no—
354#126—22no—
355#125—21no—
356#125—21no—
357#124—22no—
358#124—22no—
359#124—21no—
360#123—22no—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8D4×C10311yescharacteristic
368C22⋊Q8D4×C10311yescharacteristic
369#121—22no—
370#121—22no—
371#121—22no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—21no—
377#121—21no—
378#121D4×C10311yescharacteristic
379#121D4×C10311yescharacteristic
380#120—22no—
381#120—21no—
382C4×Q8—21no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#117—22no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117C2×C4×C10311yescharacteristic
398#117C2×C4×C10311yescharacteristic
399#117C2×C4×C10311yescharacteristic
400#117D4×C10311yescharacteristic
401#117D4×C10311yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4C2×C4×C10311yescharacteristic
405C2×C4⋊C4D4×C10311yescharacteristic
406C2×C4⋊C4D4×C10311yescharacteristic
407C2×C22⋊C4—22no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4D4×C10312yes—
412C2×C42—21no—
413C2×C42—21no—
414#99—44no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419#95—21no—
420#95—21no—
421C24C22⋊C4×C10312yes—
422C24C2×D4×C10311yescharacteristic
423#41—42no—
424#41—82no—
425#41—82no—
426C2×Q8—22no—
427C2×Q8C22⋊C4×C10311yescharacteristic
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4C22⋊C4×C10311yescharacteristic
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4C22⋊C4×C10312yes—
451C22×C4C22×C4×C10311yescharacteristic
452C22×C4C2×D4×C10311yescharacteristic
453C22×C4C2×D4×C10311yescharacteristic
454C22×C4C2×D4×C10311yescharacteristic
455C22×C4C2×D4×C10311yescharacteristic
456C22×C4C2×D4×C10311yescharacteristic
457M16—42no—
458C2×C8—42no—
459C2×C8—41no—
460C2×C8—41no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4C22⋊C4×C10311yescharacteristic
473C4⋊C4C22⋊C4×C10311yescharacteristic
474C4⋊C4C22⋊C4×C10311yescharacteristic
475C4⋊C4C22⋊C4×C10311yescharacteristic
476C4⋊C4C22⋊C4×C10311yescharacteristic
477C4⋊C4C22⋊C4×C10311yescharacteristic
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C22⋊C4—42no—
497C42—22no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—42no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—21no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23C2×C22⋊C4×C10311yescharacteristic
514C23#120×C10311yescharacteristic
515C23#120×C10311yescharacteristic
516Q8—41no—
517Q8—82no—
518D4—41no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—42no—
524D4—41no—
525D4—42no—
526D4—82no—
527D4—81no—
528D4—82no—
529D4—82no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4C2×C22⋊C4×C10311yescharacteristic
559C2×C4C2×C22⋊C4×C10311yescharacteristic
560C2×C4#120×C10311yescharacteristic
561C2×C4#120×C10311yescharacteristic
562C8—81no—
563C8—81no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—42no—
574C22—41no—
575C22—42no—
576C22—42no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—162no—
581C22#379×C10311yescharacteristic
582C22#453×C10311yescharacteristic
583C22#455×C10311yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—82no—
596C4—161no—
597C4#410×C10312yes—
598C2—21no—
599C2—21no—
600C2—41no—
601C2—41no—
602C2—82no—
603C2—81no—
604C2C103×#178211yescharacteristic
605C2C103×#179211yescharacteristic
606C2C103×#179411yescharacteristic
subgroupG/H
center, socleC22×C103#379
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
prime radicalC103×#3494C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1964C2semidirect
3. C103×#1826C2semidirect
4. C103×#1825C2semidirect
5. C103×#1513C2semidirect
6. C103×#1501C2semidirect
7. C103×#1471C2semidirect
14. #544×C103C4semidirect
17. #535×C103C4semidirect
22. #520×C103C4semidirect
23. #518×C103C4semidirect
294. #8466C103direct (N × H)
305. #1964C2×C103semidirect
306. #1826C2×C103semidirect
307. #1825C2×C103semidirect
308. #1513C2×C103semidirect
309. #1501C2×C103semidirect
310. #1471C2×C103semidirect
311. C103#8466direct (N × H)
318. #544C4×C103semidirect
321. #535C4×C103semidirect
326. #520C4×C103semidirect
327. #518C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34942
C103×#19642
C103×#18262
C103×#18252
C103×#15132
C103×#15012
C103×#14712
#8466103