Finite Group Databasebeta

← C103×#9918 #39915193

Subgroups — C103×#9918 #39915193

Order 26368.

812 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C103C211yesmaximal, characteristic, complemented
2C103×#2617C211yesmaximal, characteristic
3C2×#397×C103C211yesmaximal, characteristic, complemented
4C103×#1823C211yesmaximal, characteristic, complemented
5C2×#327×C103C211yesmaximal, characteristic, complemented
6C2×#323×C103C211yesmaximal, characteristic, complemented
7C103×#1294C211yesmaximal, characteristic, complemented
8C2×#121×C103C2211yescharacteristic
9C2×#120×C103—21no—
10C22×C4⋊C4×C103C2211yescharacteristic
11C22×C22⋊C4×C103—21no—
12C22×C22⋊C4×C103C2211yescharacteristic
13#480×C103—22no—
14#480×C103—22no—
15C2×#107×C103—21no—
16C2×#102×C103—21no—
17C2×C22⋊C8×C103C2211yescharacteristic
18C2×C22⋊C8×C103C2211yescharacteristic
19#397×C103—21no—
20#397×C103—22no—
21#397×C103—22no—
22#394×C103—22no—
23#392×C103—21no—
24#386×C103—21no—
25#380×C103C2211yescharacteristic
26C2×#95×C103—21no—
27C2×#95×C103C2211yescharacteristic
28#340×C103—22no—
29#327×C103—22no—
30#323×C103—22no—
31C25×C103D411yescharacteristic
32C22×D4×C103—21no—
33C22×D4×C103—22no—
34C22×D4×C103D411yescharacteristic
35C23×C4×C103—21no—
36C23×C4×C103—21no—
37C23×C4×C103D411yescharacteristic
38C23×C4×C103C2311yescharacteristic
39C22×C8×C103—21no—
40C22×C8×C103—21no—
41#121×C103—21no—
42#121×C103—21no—
43#121×C103—21no—
44#121×C103—21no—
45#120×C103—42no—
46#120×C103—42no—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103—21no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103D411yescharacteristic
53C2×C4⋊C4×C103D412yes—
54C2×C4⋊C4×C103D412yescomplemented
55C2×C22⋊C4×C103—22no—
56C2×C22⋊C4×C103—24no—
57C2×C22⋊C4×C103—21no—
58C2×C22⋊C4×C103—21no—
59C2×C22⋊C4×C103—21no—
60C2×C22⋊C4×C103—21no—
61C2×C22⋊C4×C103—21no—
62C2×C22⋊C4×C103—21no—
63C2×C22⋊C4×C103—21no—
64C2×C22⋊C4×C103—21no—
65C2×C22⋊C4×C103—22no—
66C2×C22⋊C4×C103—42no—
67C2×C22⋊C4×C103—42no—
68#107×C103—24no—
69#102×C103—24no—
70C22⋊C8×C103—21no—
71C22⋊C8×C103—21no—
72C22⋊C8×C103—21no—
73C22⋊C8×C103D412yescomplemented
74#95×C103—24no—
75#95×C103—22no—
76#95×C103—21no—
77#95×C103—21no—
78#95×C103D412yescomplemented
79C24×C103—21no—
80C24×C103—21no—
81C24×C103—21no—
82C24×C103—21no—
83C24×C103—21no—
84C24×C103—21no—
85C24×C103—21no—
86C24×C103—42no—
87C24×C103—42no—
88C24×C103D812yes—
89C24×C103C2×D411yescharacteristic
90C2×D4×C103—21no—
91C2×D4×C103—21no—
92C2×D4×C103—42no—
93C2×D4×C103—44no—
94C2×D4×C103—41no—
95C2×D4×C103—41no—
96C2×D4×C103—41no—
97C2×D4×C103—41no—
98C2×D4×C103—41no—
99C2×D4×C103—41no—
100C2×D4×C103—82no—
101C2×D4×C103—82no—
102C22×C4×C103—21no—
103C22×C4×C103—22no—
104C22×C4×C103—22no—
105C22×C4×C103—21no—
106C22×C4×C103—21no—
107C22×C4×C103—22no—
108C22×C4×C103—21no—
109C22×C4×C103—42no—
110C22×C4×C103—42no—
111C22×C4×C103—42no—
112C22×C4×C103—42no—
113C22×C4×C103—41no—
114C22×C4×C103—41no—
115C22×C4×C103—41no—
116C22×C4×C103—41no—
117C22×C4×C103—41no—
118C22×C4×C103—41no—
119C22×C4×C103—41no—
120C22×C4×C103—41no—
121C22×C4×C103C2×D411yescharacteristic
122C22×C4×C103C2×D411yescharacteristic
123C22×C4×C103C2×D411yescharacteristic
124C22×C4×C103C2×D411yescharacteristic
125C22×C4×C103C2×D411yescharacteristic
126C22×C4×C103#4111yescharacteristic
127C2×C8×C103—22no—
128C2×C8×C103—42no—
129C2×C8×C103—42no—
130C2×C8×C103—41no—
131C4⋊C4×C103—22no—
132C4⋊C4×C103—21no—
133C4⋊C4×C103—22no—
134C4⋊C4×C103—21no—
135C4⋊C4×C103—42no—
136C4⋊C4×C103—41no—
137C4⋊C4×C103—41no—
138C22⋊C4×C103—48no—
139C22⋊C4×C103—44no—
140C22⋊C4×C103—41no—
141C22⋊C4×C103—41no—
142C22⋊C4×C103—41no—
143C22⋊C4×C103—41no—
144C22⋊C4×C103—41no—
145C22⋊C4×C103—41no—
146C22⋊C4×C103—41no—
147C22⋊C4×C103—41no—
148C22⋊C4×C103—82no—
149C23×C103—22no—
150C23×C103—22no—
151C23×C103—22no—
152C23×C103—22no—
153C23×C103—22no—
154C23×C103—44no—
155C23×C103—44no—
156C23×C103—42no—
157C23×C103—42no—
158C23×C103—41no—
159C23×C103—41no—
160C23×C103—41no—
161C23×C103—42no—
162C23×C103—42no—
163C23×C103—41no—
164C23×C103—41no—
165C23×C103—41no—
166C23×C103—41no—
167C23×C103—42no—
168C23×C103—42no—
169C23×C103—82no—
170C23×C103—82no—
171C23×C103—81no—
172C23×C103—81no—
173C23×C103#12011yescharacteristic
174C23×C103#12011yescharacteristic
175C23×C103#12111yescharacteristic
176C23×C103C2×D811yescharacteristic
177C23×C103#13511yescharacteristic
178C23×C103AGL(1,ℤ/8)11yescharacteristic
179C23×C103AGL(1,ℤ/8)11yescharacteristic
180D4×C103—42no—
181D4×C103—81no—
182D4×C103—88no—
183D4×C103—81no—
184D4×C103—81no—
185D4×C103—81no—
186D4×C103—81no—
187C2×C4×C103—22no—
188C2×C4×C103—22no—
189C2×C4×C103—41no—
190C2×C4×C103—41no—
191C2×C4×C103—41no—
192C2×C4×C103—41no—
193C2×C4×C103—42no—
194C2×C4×C103—42no—
195C2×C4×C103—42no—
196C2×C4×C103—41no—
197C2×C4×C103—41no—
198C2×C4×C103—42no—
199C2×C4×C103—42no—
200C2×C4×C103—42no—
201C2×C4×C103—42no—
202C2×C4×C103—41no—
203C2×C4×C103—42no—
204C2×C4×C103—41no—
205C2×C4×C103—42no—
206C2×C4×C103—42no—
207C2×C4×C103—42no—
208C2×C4×C103—82no—
209C2×C4×C103—82no—
210C2×C4×C103—81no—
211C2×C4×C103—81no—
212C2×C4×C103—81no—
213C2×C4×C103—81no—
214C2×C4×C103—81no—
215C2×C4×C103#12011yescharacteristic
216C2×C4×C103#12111yescharacteristic
217C2×C4×C103#12111yescharacteristic
218C2×C4×C103#12711yescharacteristic
219C8×C103—42no—
220C8×C103—81no—
221C22×C103—22no—
222C22×C103—22no—
223C22×C103—22no—
224C22×C103—22no—
225C22×C103—21no—
226C22×C103—21no—
227C22×C103—21no—
228C22×C103—21no—
229C22×C103—44no—
230C22×C103—44no—
231C22×C103—42no—
232C22×C103—82no—
233C22×C103—82no—
234C22×C103—82no—
235C22×C103—82no—
236C22×C103—81no—
237C22×C103—81no—
238C22×C103—82no—
239C22×C103—82no—
240C22×C103—81no—
241C22×C103—81no—
242C22×C103—81no—
243C22×C103#39211yescharacteristic
244C22×C103#44711yescharacteristic
245C22×C103#44711yescharacteristic
246C22×C103#44911yescharacteristic
247C22×C103#44911yescharacteristic
248C22×C103#45512yes—
249C22×C103#45812yes—
250C22×C103#46611yescharacteristic
251C22×C103#46911yescharacteristic
252C4×C103—21no—
253C4×C103—21no—
254C4×C103—21no—
255C4×C103—21no—
256C4×C103—82no—
257C4×C103—82no—
258C4×C103—82no—
259C4×C103—81no—
260C4×C103—81no—
261#9918C10311yesmaximal, characteristic, direct product factor, Sylow
262C2×C103—21no—
263C2×C103—21no—
264C2×C103—21no—
265C2×C103—21no—
266C2×C103—82no—
267C2×C103—161no—
268C2×C103#160712yes—
269C2×C103#161212yes—
270C2×C103#199911yescharacteristic
271C2×C103#200411yescharacteristic
272C2×C103#202211yescharacteristic
273C2×#480C2×C10311yescharacteristic, complemented
274#2617C2×C10311yescharacteristic
275C2×#397C2×C10311yescharacteristic, complemented
276#1823C2×C10311yescharacteristic, complemented
277C2×#327C2×C10311yescharacteristic, complemented
278C2×#323C2×C10311yescharacteristic, complemented
279#1294C2×C10311yescharacteristic, complemented
280C103#991811yescharacteristic, direct product factor, Sylow
281C2×#121C22×C10311yescharacteristic
282C2×#120—21no—
283C22×C4⋊C4C22×C10311yescharacteristic
284C22×C22⋊C4—21no—
285C22×C22⋊C4C22×C10311yescharacteristic
286#480—22no—
287#480—22no—
288C2×#107—21no—
289C2×#102—21no—
290C2×C22⋊C8C22×C10311yescharacteristic
291C2×C22⋊C8C22×C10311yescharacteristic
292#397—21no—
293#397—22no—
294#397—22no—
295#394—22no—
296#392—21no—
297#386—21no—
298#380C22×C10311yescharacteristic
299C2×#95—21no—
300C2×#95C22×C10311yescharacteristic
301#340—22no—
302#327—22no—
303#323—22no—
304C25D4×C10311yescharacteristic
305C22×D4—21no—
306C22×D4—22no—
307C22×D4D4×C10311yescharacteristic
308C23×C4—21no—
309C23×C4—21no—
310C23×C4D4×C10311yescharacteristic
311C23×C4C23×C10311yescharacteristic
312C22×C8—21no—
313C22×C8—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#120—42no—
319#120—42no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4D4×C10311yescharacteristic
326C2×C4⋊C4D4×C10312yes—
327C2×C4⋊C4D4×C10312yescomplemented
328C2×C22⋊C4—24no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341#107—24no—
342#102—24no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8D4×C10312yescomplemented
347#95—24no—
348#95—22no—
349#95—21no—
350#95—21no—
351#95D4×C10312yescomplemented
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—42no—
360C24—42no—
361C24D8×C10312yes—
362C24C2×D4×C10311yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—42no—
366C2×D4—44no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—82no—
374C2×D4—82no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4C2×D4×C10311yescharacteristic
395C22×C4C2×D4×C10311yescharacteristic
396C22×C4C2×D4×C10311yescharacteristic
397C22×C4C2×D4×C10311yescharacteristic
398C22×C4C2×D4×C10311yescharacteristic
399C22×C4#41×C10311yescharacteristic
400C2×C8—22no—
401C2×C8—42no—
402C2×C8—42no—
403C2×C8—41no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—42no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C22⋊C4—48no—
412C22⋊C4—44no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—82no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—44no—
428C23—42no—
429C23—42no—
430C23—44no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—42no—
435C23—42no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—42no—
441C23—42no—
442C23—82no—
443C23—81no—
444C23—81no—
445C23—82no—
446C23#120×C10311yescharacteristic
447C23#120×C10311yescharacteristic
448C23#121×C10311yescharacteristic
449C23C2×D8×C10311yescharacteristic
450C23#135×C10311yescharacteristic
451C23AGL(1,ℤ/8)×C10311yescharacteristic
452C23AGL(1,ℤ/8)×C10311yescharacteristic
453D4—42no—
454D4—81no—
455D4—88no—
456D4—81no—
457D4—81no—
458D4—81no—
459D4—81no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4#120×C10311yescharacteristic
489C2×C4#121×C10311yescharacteristic
490C2×C4#121×C10311yescharacteristic
491C2×C4#127×C10311yescharacteristic
492C8—42no—
493C8—81no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—44no—
503C22—42no—
504C22—44no—
505C22—82no—
506C22—82no—
507C22—82no—
508C22—81no—
509C22—81no—
510C22—82no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—82no—
515C22—82no—
516C22#392×C10311yescharacteristic
517C22#447×C10311yescharacteristic
518C22#447×C10311yescharacteristic
519C22#449×C10311yescharacteristic
520C22#449×C10311yescharacteristic
521C22#455×C10312yes—
522C22#458×C10312yes—
523C22#466×C10311yescharacteristic
524C22#469×C10311yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—82no—
530C4—82no—
531C4—81no—
532C4—81no—
533C4—82no—
534C2—21no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—82no—
539C2—161no—
540C2C103×#160712yes—
541C2C103×#161212yes—
542C2C103×#199911yescharacteristic
543C2C103×#200411yescharacteristic
544C2C103×#202211yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutator, Frattini, cosocleC23×C4C23×C103
prime radicalC103×#2617C2
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×#480×C103C2semidirect
3. C2×#397×C103C2semidirect
4. C103×#1823C2semidirect
5. C2×#327×C103C2semidirect
6. C2×#323×C103C2semidirect
7. C103×#1294C2semidirect
54. C2×C4⋊C4×C103D4semidirect
73. C22⋊C8×C103D4semidirect
78. #95×C103D4semidirect
261. #9918C103direct (N × H)
273. C2×#480C2×C103semidirect
275. C2×#397C2×C103semidirect
276. #1823C2×C103semidirect
277. C2×#327C2×C103semidirect
278. C2×#323C2×C103semidirect
279. #1294C2×C103semidirect
280. C103#9918direct (N × H)
327. C2×C4⋊C4D4×C103semidirect
346. C22⋊C8D4×C103semidirect
351. #95D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1032
C103×#26172
C2×#397×C1032
C103×#18232
C2×#327×C1032
C2×#323×C1032
C103×#12942
#9918103