Finite Group Databasebeta

← C103×#9914 #39915189

Subgroups — C103×#9914 #39915189

Order 26368.

1356 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C103C211yesmaximal, characteristic, complemented
2C103×#2617C211yesmaximal, characteristic, complemented
3C2×#392×C103C211yesmaximal, characteristic, complemented
4C103×#1786C211yesmaximal, characteristic, complemented
5C2×#327×C103C211yesmaximal, characteristic, complemented
6C2×#323×C103C211yesmaximal, characteristic, complemented
7C103×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C103—21no—
9C23×D4×C103C2211yescharacteristic
10C22×D8×C103—21no—
11C2×#121×C103C2211yescharacteristic
12C2×#120×C103—21no—
13C22×C22⋊C4×C103—21no—
14C22×C22⋊C4×C103C2211yescharacteristic
15#447×C103—22no—
16#447×C103—22no—
17C2×#102×C103—21no—
18C2×#102×C103—22no—
19C2×C22⋊C8×C103C2211yescharacteristic
20C2×C22⋊C8×C103C2211yescharacteristic
21#397×C103—21no—
22#394×C103—22no—
23#392×C103—21no—
24#392×C103—22no—
25#392×C103—22no—
26#386×C103—21no—
27#380×C103C2211yescharacteristic
28C2×#95×C103C2211yescharacteristic
29#327×C103—22no—
30#323×C103—22no—
31C25×C103—21no—
32C25×C103D411yescharacteristic
33C22×D4×C103—24no—
34C22×D4×C103—21no—
35C22×D4×C103—22no—
36C22×D4×C103—21no—
37C22×D4×C103—21no—
38C22×D4×C103—21no—
39C22×D4×C103—21no—
40C22×D4×C103—21no—
41C22×D4×C103—44no—
42C22×D4×C103—44no—
43C22×D4×C103—44no—
44C22×D4×C103—42no—
45C22×D4×C103—42no—
46C22×D4×C103D412yescomplemented
47C22×D4×C103D411yescharacteristic, complemented
48C23×C4×C103—21no—
49C23×C4×C103D411yescharacteristic
50C23×C4×C103C2311yescharacteristic
51C2×D8×C103—24no—
52C2×D8×C103—44no—
53C22×C8×C103—21no—
54C22×C8×C103—21no—
55#121×C103—21no—
56#121×C103—21no—
57#121×C103—21no—
58#121×C103—21no—
59#120×C103—42no—
60#120×C103—42no—
61C2×C4⋊C4×C103D411yescharacteristic, complemented
62C2×C4⋊C4×C103D412yescomplemented
63C2×C22⋊C4×C103—24no—
64C2×C22⋊C4×C103—22no—
65C2×C22⋊C4×C103—21no—
66C2×C22⋊C4×C103—21no—
67C2×C22⋊C4×C103—21no—
68C2×C22⋊C4×C103—21no—
69C2×C22⋊C4×C103—21no—
70C2×C22⋊C4×C103—21no—
71C2×C22⋊C4×C103—21no—
72C2×C22⋊C4×C103—21no—
73C2×C22⋊C4×C103—22no—
74C2×C22⋊C4×C103—44no—
75#102×C103—24no—
76#102×C103—44no—
77C22⋊C8×C103—21no—
78C22⋊C8×C103—21no—
79C22⋊C8×C103—21no—
80C22⋊C8×C103D412yescomplemented
81#95×C103—22no—
82#95×C103—21no—
83#95×C103—21no—
84#95×C103D412yescomplemented
85C24×C103—24no—
86C24×C103—21no—
87C24×C103—22no—
88C24×C103—21no—
89C24×C103—21no—
90C24×C103—21no—
91C24×C103—21no—
92C24×C103—21no—
93C24×C103—21no—
94C24×C103—42no—
95C24×C103—42no—
96C24×C103—42no—
97C24×C103—42no—
98C24×C103—42no—
99C24×C103—41no—
100C24×C103—41no—
101C24×C103—41no—
102C24×C103—41no—
103C24×C103—41no—
104C24×C103—41no—
105C24×C103D812yescomplemented
106C24×C103C2×D411yescharacteristic
107C2×D4×C103—24no—
108C2×D4×C103—24no—
109C2×D4×C103—22no—
110C2×D4×C103—21no—
111C2×D4×C103—22no—
112C2×D4×C103—21no—
113C2×D4×C103—42no—
114C2×D4×C103—42no—
115C2×D4×C103—48no—
116C2×D4×C103—42no—
117C2×D4×C103—44no—
118C2×D4×C103—44no—
119C2×D4×C103—44no—
120C2×D4×C103—44no—
121C2×D4×C103—48no—
122C2×D4×C103—48no—
123C2×D4×C103—416no—
124C2×D4×C103—416no—
125C2×D4×C103—44no—
126C2×D4×C103—41no—
127C2×D4×C103—41no—
128C2×D4×C103—41no—
129C2×D4×C103—41no—
130C2×D4×C103—41no—
131C2×D4×C103—41no—
132C2×D4×C103—41no—
133C2×D4×C103—41no—
134C2×D4×C103—82no—
135C2×D4×C103—82no—
136C22×C4×C103—24no—
137C22×C4×C103—22no—
138C22×C4×C103—21no—
139C22×C4×C103—21no—
140C22×C4×C103—21no—
141C22×C4×C103—22no—
142C22×C4×C103—21no—
143C22×C4×C103—42no—
144C22×C4×C103—42no—
145C22×C4×C103—41no—
146C22×C4×C103—41no—
147C22×C4×C103—42no—
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2×D411yescharacteristic
150C22×C4×C103C2×D411yescharacteristic
151C22×C4×C103C2×D411yescharacteristic
152C22×C4×C103C2×D411yescharacteristic
153C22×C4×C103#4111yescharacteristic
154D8×C103—48no—
155C2×C8×C103—22no—
156C2×C8×C103—42no—
157C2×C8×C103—42no—
158C2×C8×C103—41no—
159C4⋊C4×C103—21no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—42no—
162C22⋊C4×C103—48no—
163C22⋊C4×C103—44no—
164C22⋊C4×C103—41no—
165C22⋊C4×C103—41no—
166C22⋊C4×C103—41no—
167C22⋊C4×C103—41no—
168C22⋊C4×C103—41no—
169C22⋊C4×C103—41no—
170C22⋊C4×C103—41no—
171C22⋊C4×C103—41no—
172C22⋊C4×C103—82no—
173C23×C103—22no—
174C23×C103—22no—
175C23×C103—24no—
176C23×C103—22no—
177C23×C103—22no—
178C23×C103—22no—
179C23×C103—44no—
180C23×C103—42no—
181C23×C103—44no—
182C23×C103—44no—
183C23×C103—44no—
184C23×C103—42no—
185C23×C103—42no—
186C23×C103—42no—
187C23×C103—42no—
188C23×C103—44no—
189C23×C103—44no—
190C23×C103—44no—
191C23×C103—41no—
192C23×C103—42no—
193C23×C103—42no—
194C23×C103—41no—
195C23×C103—41no—
196C23×C103—42no—
197C23×C103—42no—
198C23×C103—44no—
199C23×C103—42no—
200C23×C103—41no—
201C23×C103—41no—
202C23×C103—41no—
203C23×C103—41no—
204C23×C103—42no—
205C23×C103—42no—
206C23×C103—82no—
207C23×C103—82no—
208C23×C103—81no—
209C23×C103—81no—
210C23×C103—82no—
211C23×C103—82no—
212C23×C103—82no—
213C23×C103—82no—
214C23×C103—82no—
215C23×C103—81no—
216C23×C103—81no—
217C23×C103—82no—
218C23×C103—81no—
219C23×C103—81no—
220C23×C103#12011yescharacteristic
221C23×C103#12011yescharacteristic
222C23×C103#12111yescharacteristic
223C23×C103C2×D811yescharacteristic
224C23×C103#13511yescharacteristic
225C23×C103AGL(1,ℤ/8)11yescharacteristic
226C23×C103AGL(1,ℤ/8)11yescharacteristic
227D4×C103—24no—
228D4×C103—24no—
229D4×C103—42no—
230D4×C103—44no—
231D4×C103—42no—
232D4×C103—44no—
233D4×C103—42no—
234D4×C103—432no—
235D4×C103—81no—
236D4×C103—88no—
237D4×C103—81no—
238D4×C103—81no—
239D4×C103—81no—
240D4×C103—81no—
241C2×C4×C103—22no—
242C2×C4×C103—22no—
243C2×C4×C103—24no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—44no—
249C2×C4×C103—44no—
250C2×C4×C103—42no—
251C2×C4×C103—42no—
252C2×C4×C103—42no—
253C2×C4×C103—41no—
254C2×C4×C103—41no—
255C2×C4×C103—42no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103—42no—
259C2×C4×C103—42no—
260C2×C4×C103—42no—
261C2×C4×C103—81no—
262C2×C4×C103#12011yescharacteristic
263C2×C4×C103#12111yescharacteristic
264C2×C4×C103#12111yescharacteristic
265C2×C4×C103#12711yescharacteristic
266C8×C103—42no—
267C8×C103—81no—
268C22×C103—22no—
269C22×C103—22no—
270C22×C103—22no—
271C22×C103—22no—
272C22×C103—21no—
273C22×C103—21no—
274C22×C103—21no—
275C22×C103—21no—
276C22×C103—44no—
277C22×C103—44no—
278C22×C103—44no—
279C22×C103—44no—
280C22×C103—42no—
281C22×C103—44no—
282C22×C103—82no—
283C22×C103—82no—
284C22×C103—82no—
285C22×C103—82no—
286C22×C103—84no—
287C22×C103—82no—
288C22×C103—84no—
289C22×C103—84no—
290C22×C103—82no—
291C22×C103—84no—
292C22×C103—82no—
293C22×C103—81no—
294C22×C103—82no—
295C22×C103—81no—
296C22×C103—82no—
297C22×C103—82no—
298C22×C103—81no—
299C22×C103—81no—
300C22×C103—81no—
301C22×C103#39211yescharacteristic
302C22×C103#44711yescharacteristic
303C22×C103#44711yescharacteristic
304C22×C103#44911yescharacteristic
305C22×C103#44911yescharacteristic
306C22×C103#45312yes—
307C22×C103B(4,𝔽2)12yes—
308C22×C103#46611yescharacteristic
309C22×C103#46911yescharacteristic
310C4×C103—21no—
311C4×C103—21no—
312C4×C103—21no—
313C4×C103—21no—
314C4×C103—44no—
315C4×C103—82no—
316C4×C103—81no—
317C4×C103—81no—
318#9914C10311yesmaximal, characteristic, direct product factor, Sylow
319C2×C103—21no—
320C2×C103—21no—
321C2×C103—21no—
322C2×C103—21no—
323C2×C103—82no—
324C2×C103—84no—
325C2×C103—161no—
326C2×C103#159512yes—
327C2×C103#160012yes—
328C2×C103#199911yescharacteristic
329C2×C103#200211yescharacteristic
330C2×C103#202111yescharacteristic
331C2×#447C2×C10311yescharacteristic, complemented
332#2617C2×C10311yescharacteristic, complemented
333C2×#392C2×C10311yescharacteristic, complemented
334#1786C2×C10311yescharacteristic, complemented
335C2×#327C2×C10311yescharacteristic, complemented
336C2×#323C2×C10311yescharacteristic, complemented
337#1294C2×C10311yescharacteristic, complemented
338C103#991411yescharacteristic, direct product factor, Sylow
339C23×D4—21no—
340C23×D4C22×C10311yescharacteristic
341C22×D8—21no—
342C2×#121C22×C10311yescharacteristic
343C2×#120—21no—
344C22×C22⋊C4—21no—
345C22×C22⋊C4C22×C10311yescharacteristic
346#447—22no—
347#447—22no—
348C2×#102—21no—
349C2×#102—22no—
350C2×C22⋊C8C22×C10311yescharacteristic
351C2×C22⋊C8C22×C10311yescharacteristic
352#397—21no—
353#394—22no—
354#392—21no—
355#392—22no—
356#392—22no—
357#386—21no—
358#380C22×C10311yescharacteristic
359C2×#95C22×C10311yescharacteristic
360#327—22no—
361#323—22no—
362C25—21no—
363C25D4×C10311yescharacteristic
364C22×D4—24no—
365C22×D4—21no—
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4D4×C10311yescharacteristic, complemented
378C22×D4D4×C10312yescomplemented
379C23×C4—21no—
380C23×C4D4×C10311yescharacteristic
381C23×C4C23×C10311yescharacteristic
382C2×D8—24no—
383C2×D8—44no—
384C22×C8—21no—
385C22×C8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#120—42no—
391#120—42no—
392C2×C4⋊C4D4×C10311yescharacteristic, complemented
393C2×C4⋊C4D4×C10312yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—44no—
406#102—24no—
407#102—44no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C10312yescomplemented
412#95—22no—
413#95—21no—
414#95—21no—
415#95D4×C10312yescomplemented
416C24—24no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24D8×C10312yescomplemented
437C24C2×D4×C10311yescharacteristic
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—48no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—82no—
466C2×D4—82no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4C2×D4×C10311yescharacteristic
480C22×C4C2×D4×C10311yescharacteristic
481C22×C4C2×D4×C10311yescharacteristic
482C22×C4C2×D4×C10311yescharacteristic
483C22×C4C2×D4×C10311yescharacteristic
484C22×C4#41×C10311yescharacteristic
485D8—48no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—41no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—44no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—44no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—44no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—82no—
538C23—81no—
539C23—81no—
540C23—82no—
541C23—82no—
542C23—82no—
543C23—82no—
544C23—82no—
545C23—82no—
546C23—81no—
547C23—81no—
548C23—82no—
549C23—81no—
550C23—81no—
551C23#120×C10311yescharacteristic
552C23#120×C10311yescharacteristic
553C23#121×C10311yescharacteristic
554C23C2×D8×C10311yescharacteristic
555C23#135×C10311yescharacteristic
556C23AGL(1,ℤ/8)×C10311yescharacteristic
557C23AGL(1,ℤ/8)×C10311yescharacteristic
558D4—24no—
559D4—24no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—432no—
566D4—81no—
567D4—88no—
568D4—81no—
569D4—81no—
570D4—81no—
571D4—81no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—81no—
593C2×C4#120×C10311yescharacteristic
594C2×C4#121×C10311yescharacteristic
595C2×C4#121×C10311yescharacteristic
596C2×C4#127×C10311yescharacteristic
597C8—42no—
598C8—81no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—42no—
611C22—44no—
612C22—44no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—84no—
618C22—82no—
619C22—84no—
620C22—82no—
621C22—81no—
622C22—82no—
623C22—81no—
624C22—84no—
625C22—82no—
626C22—84no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—82no—
631C22—82no—
632C22#392×C10311yescharacteristic
633C22#447×C10311yescharacteristic
634C22#447×C10311yescharacteristic
635C22#449×C10311yescharacteristic
636C22#449×C10311yescharacteristic
637C22#453×C10312yes—
638C22B(4,𝔽2)×C10312yes—
639C22#466×C10311yescharacteristic
640C22#469×C10311yescharacteristic
641C4—21no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—44no—
646C4—81no—
647C4—81no—
648C4—82no—
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—82no—
654C2—84no—
655C2—161no—
656C2C103×#159512yes—
657C2C103×#160012yes—
658C2C103×#199911yescharacteristic
659C2C103×#200211yescharacteristic
660C2C103×#202111yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutator, Frattini, cosocleC23×C4C23×C103
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#447×C103C2semidirect
2. C103×#2617C2semidirect
3. C2×#392×C103C2semidirect
4. C103×#1786C2semidirect
5. C2×#327×C103C2semidirect
6. C2×#323×C103C2semidirect
7. C103×#1294C2semidirect
46. C22×D4×C103D4semidirect
47. C22×D4×C103D4semidirect
61. C2×C4⋊C4×C103D4semidirect
62. C2×C4⋊C4×C103D4semidirect
80. C22⋊C8×C103D4semidirect
84. #95×C103D4semidirect
105. C24×C103D8semidirect
318. #9914C103direct (N × H)
331. C2×#447C2×C103semidirect
332. #2617C2×C103semidirect
333. C2×#392C2×C103semidirect
334. #1786C2×C103semidirect
335. C2×#327C2×C103semidirect
336. C2×#323C2×C103semidirect
337. #1294C2×C103semidirect
338. C103#9914direct (N × H)
377. C22×D4D4×C103semidirect
378. C22×D4D4×C103semidirect
392. C2×C4⋊C4D4×C103semidirect
393. C2×C4⋊C4D4×C103semidirect
411. C22⋊C8D4×C103semidirect
415. #95D4×C103semidirect
436. C24D8×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1032
C103×#26172
C2×#392×C1032
C103×#17862
C2×#327×C1032
C2×#323×C1032
C103×#12942
#9914103