Finite Group Databasebeta

← C103×#9520 #39914795

Subgroups — C103×#9520 #39914795

Order 26368.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3003C211yesmaximal, characteristic
2C103×#2976C211yesmaximal, characteristic, complemented
3C103×#1786C211yesmaximal, characteristic, complemented
4C103×#1783C211yesmaximal, characteristic, complemented
5C103×#1513C211yesmaximal, characteristic, complemented
6C103×#1305C211yesmaximal, characteristic, complemented
7C103×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C103C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C103—21no—
10#525×C103C2211yescharacteristic
11#450×C103—21no—
12#450×C103C412yescomplemented
13#447×C103—21no—
14#447×C103C412yescomplemented
15#436×C103—21no—
16#435×C103—21no—
17#435×C103—21no—
18C8×D4×C103—21no—
19#433×C103—21no—
20#418×C103—21no—
21C2×#102×C103—21no—
22C2×#102×C103—21no—
23C2×#100×C103—21no—
24C2×#100×C103—21no—
25#408×C103—21no—
26#407×C103C2211yescharacteristic
27#407×C103C2211yescharacteristic
28#407×C103C2211yescharacteristic
29C2×C22⋊C8×C103C2211yescharacteristic
30#380×C103C2211yescharacteristic
31#328×C103—21no—
32#327×C103—21no—
33C25×C103—21no—
34C2×#41×C103D411yescharacteristic
35C22×D4×C103—21no—
36C22×D4×C103—21no—
37C22×D4×C103—21no—
38C22×D4×C103—21no—
39C22×D4×C103—21no—
40C22×D4×C103—42no—
41C22×D4×C103—42no—
42C22×D4×C103C2×C412yes—
43C23×C4×C103C2311yescharacteristic
44AGL(1,ℤ/8)×C103—42no—
45AGL(1,ℤ/8)×C103—42no—
46C2×SD16×C103—22no—
47C2×D8×C103—22no—
48C2×M16×C103—21no—
49C2×M16×C103—21no—
50C2×M16×C103—21no—
51C2×M16×C103D411yescharacteristic
52C2×M16×C103D411yescharacteristic
53C22×C8×C103—21no—
54C22×C8×C103D411yescharacteristic
55C22×C8×C103D411yescharacteristic
56#123×C103—21no—
57C22⋊Q8×C103C2×C411yescharacteristic
58C22⋊Q8×C103D411yescharacteristic
59#121×C103C2×C411yescharacteristic
60#121×C103D411yescharacteristic
61#120×C103—21no—
62C4×D4×C103—21no—
63C4×D4×C103—21no—
64#117×C103D411yescharacteristic
65C2×C4⋊C4×C103—21no—
66C2×C22⋊C4×C103—21no—
67C4⋊C8×C103—21no—
68C4⋊C8×C103—21no—
69#102×C103—22no—
70#102×C103—22no—
71#102×C103—42no—
72#102×C103—42no—
73#100×C103—42no—
74#100×C103—42no—
75C22⋊C8×C103—21no—
76C22⋊C8×C103—21no—
77C22⋊C8×C103—21no—
78C22⋊C8×C103—21no—
79C22⋊C8×C103—21no—
80C22⋊C8×C103—21no—
81C22⋊C8×C103—21no—
82C22⋊C8×C103—21no—
83C22⋊C8×C103—21no—
84C22⋊C8×C103C2×C412yes—
85#97×C103—21no—
86C4×C8×C103—21no—
87#95×C103—21no—
88C24×C103—22no—
89C24×C103—44no—
90C24×C103—41no—
91C24×C103—41no—
92C24×C103—81no—
93C24×C103—81no—
94C24×C103—82no—
95C24×C103#4111yescharacteristic
96#41×C103—41no—
97#41×C103—41no—
98C2×Q8×C103C22⋊C411yescharacteristic
99C2×D4×C103—22no—
100C2×D4×C103—22no—
101C2×D4×C103—22no—
102C2×D4×C103—22no—
103C2×D4×C103—22no—
104C2×D4×C103—22no—
105C2×D4×C103—21no—
106C2×D4×C103—21no—
107C2×D4×C103—21no—
108C2×D4×C103—22no—
109C2×D4×C103—22no—
110C2×D4×C103—41no—
111C2×D4×C103—41no—
112C2×D4×C103—41no—
113C2×D4×C103—41no—
114C2×D4×C103—41no—
115C2×D4×C103—41no—
116C2×D4×C103—44no—
117C2×D4×C103—44no—
118C2×D4×C103—44no—
119C2×D4×C103—41no—
120C2×D4×C103—41no—
121C2×D4×C103C22⋊C411yescharacteristic
122C22×C4×C103—21no—
123C22×C4×C103—41no—
124C22×C4×C103—41no—
125C22×C4×C103—41no—
126C22×C4×C103C22×C411yescharacteristic
127C22×C4×C103C2×D411yescharacteristic
128C22×C4×C103C2×D411yescharacteristic
129C22×C4×C103C2×D411yescharacteristic
130C22×C4×C103C2×D411yescharacteristic
131C22×C4×C103#4111yescharacteristic
132SD16×C103—44no—
133D8×C103—44no—
134M16×C103—41no—
135M16×C103—41no—
136M16×C103—41no—
137M16×C103—41no—
138M16×C103—41no—
139M16×C103—41no—
140M16×C103—81no—
141C2×C8×C103—22no—
142C2×C8×C103—21no—
143C2×C8×C103—21no—
144C2×C8×C103—21no—
145C2×C8×C103—21no—
146C2×C8×C103—41no—
147C2×C8×C103—41no—
148C2×C8×C103—41no—
149C2×C8×C103—81no—
150C4⋊C4×C103—21no—
151C4⋊C4×C103—21no—
152C4⋊C4×C103—41no—
153C4⋊C4×C103—41no—
154C4⋊C4×C103C22⋊C411yescharacteristic
155C4⋊C4×C103C22⋊C411yescharacteristic
156C22⋊C4×C103—21no—
157C22⋊C4×C103—21no—
158C22⋊C4×C103—21no—
159C22⋊C4×C103—21no—
160C22⋊C4×C103—21no—
161C22⋊C4×C103—81no—
162C42×C103—21no—
163C23×C103—21no—
164C23×C103—21no—
165C23×C103—24no—
166C23×C103—21no—
167C23×C103—41no—
168C23×C103—41no—
169C23×C103—42no—
170C23×C103—42no—
171C23×C103—42no—
172C23×C103—42no—
173C23×C103—42no—
174C23×C103—42no—
175C23×C103—82no—
176C23×C103—82no—
177C23×C103—82no—
178C23×C103—81no—
179C23×C103—81no—
180C23×C103—82no—
181C23×C103—88no—
182C23×C103—88no—
183C23×C103—81no—
184C23×C103—81no—
185C23×C103C4×D411yescharacteristic
186C23×C103#12111yescharacteristic
187C23×C103#12311yescharacteristic
188Q8×C103—41no—
189D4×C103—24no—
190D4×C103—24no—
191D4×C103—41no—
192D4×C103—42no—
193D4×C103—42no—
194D4×C103—42no—
195D4×C103—42no—
196D4×C103—41no—
197D4×C103—41no—
198D4×C103—42no—
199D4×C103—42no—
200D4×C103—81no—
201D4×C103—81no—
202C2×C4×C103—21no—
203C2×C4×C103—21no—
204C2×C4×C103—21no—
205C2×C4×C103—21no—
206C2×C4×C103—21no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—21no—
210C2×C4×C103—21no—
211C2×C4×C103—41no—
212C2×C4×C103—41no—
213C2×C4×C103—41no—
214C2×C4×C103—41no—
215C2×C4×C103—41no—
216C2×C4×C103—81no—
217C2×C4×C103—81no—
218C2×C4×C103—81no—
219C2×C4×C103C2×C22⋊C411yescharacteristic
220C2×C4×C103C4×D411yescharacteristic
221C2×C4×C103#12011yescharacteristic
222C2×C4×C103#12111yescharacteristic
223C8×C103—42no—
224C8×C103—41no—
225C8×C103—41no—
226C8×C103—41no—
227C8×C103—41no—
228C8×C103—81no—
229C22×C103—21no—
230C22×C103—21no—
231C22×C103—21no—
232C22×C103—21no—
233C22×C103—21no—
234C22×C103—21no—
235C22×C103—21no—
236C22×C103—21no—
237C22×C103—42no—
238C22×C103—42no—
239C22×C103—41no—
240C22×C103—44no—
241C22×C103—41no—
242C22×C103—41no—
243C22×C103—82no—
244C22×C103—82no—
245C22×C103—82no—
246C22×C103—82no—
247C22×C103—84no—
248C22×C103—84no—
249C22×C103—84no—
250C22×C103—84no—
251C22×C103—82no—
252C22×C103—82no—
253C22×C103#38611yescharacteristic
254C22×C103#47111yescharacteristic
255C22×C103#47211yescharacteristic
256C4×C103—21no—
257C4×C103—21no—
258C4×C103—21no—
259C4×C103—41no—
260C4×C103—41no—
261C4×C103—41no—
262C4×C103—161no—
263C4×C103B(4,𝔽2)11yescharacteristic
264C4×C103B(4,𝔽2)11yescharacteristic
265#9520C10311yesmaximal, characteristic, direct product factor, Sylow
266C2×C103—21no—
267C2×C103—21no—
268C2×C103—41no—
269C2×C103—41no—
270C2×C103—81no—
271C2×C103—84no—
272C2×C103#188911yescharacteristic
273C2×C103#190311yescharacteristic
274C2×C103#190711yescharacteristic
275#3003C2×C10311yescharacteristic
276#2976C2×C10311yescharacteristic, complemented
277#1786C2×C10311yescharacteristic, complemented
278#1783C2×C10311yescharacteristic, complemented
279#1513C2×C10311yescharacteristic, complemented
280#1305C2×C10311yescharacteristic, complemented
281#1293C2×C10311yescharacteristic, complemented
282C103#952011yescharacteristic, direct product factor, Sylow
283C23×D4C22×C10311yescharacteristic
284C2×AGL(1,ℤ/8)—21no—
285#525C22×C10311yescharacteristic
286#450—21no—
287#450C4×C10312yescomplemented
288#447—21no—
289#447C4×C10312yescomplemented
290#436—21no—
291#435—21no—
292#435—21no—
293C8×D4—21no—
294#433—21no—
295#418—21no—
296C2×#102—21no—
297C2×#102—21no—
298C2×#100—21no—
299C2×#100—21no—
300#408—21no—
301#407C22×C10311yescharacteristic
302#407C22×C10311yescharacteristic
303#407C22×C10311yescharacteristic
304C2×C22⋊C8C22×C10311yescharacteristic
305#380C22×C10311yescharacteristic
306#328—21no—
307#327—21no—
308C25—21no—
309C2×#41D4×C10311yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C10312yes—
318C23×C4C23×C10311yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C10311yescharacteristic
327C2×M16D4×C10311yescharacteristic
328C22×C8—21no—
329C22×C8D4×C10311yescharacteristic
330C22×C8D4×C10311yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C10311yescharacteristic
333C22⋊Q8D4×C10311yescharacteristic
334#121C2×C4×C10311yescharacteristic
335#121D4×C10311yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C10311yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C10312yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C10311yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C10311yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C10311yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C10311yescharacteristic
402C22×C4C2×D4×C10311yescharacteristic
403C22×C4C2×D4×C10311yescharacteristic
404C22×C4C2×D4×C10311yescharacteristic
405C22×C4C2×D4×C10311yescharacteristic
406C22×C4#41×C10311yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C10311yescharacteristic
430C4⋊C4C22⋊C4×C10311yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C10311yescharacteristic
461C23#121×C10311yescharacteristic
462C23#123×C10311yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C10311yescharacteristic
495C2×C4C4×D4×C10311yescharacteristic
496C2×C4#120×C10311yescharacteristic
497C2×C4#121×C10311yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22#386×C10311yescharacteristic
529C22#471×C10311yescharacteristic
530C22#472×C10311yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4B(4,𝔽2)×C10311yescharacteristic
539C4B(4,𝔽2)×C10311yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C103×#188911yescharacteristic
547C2C103×#190311yescharacteristic
548C2C103×#190711yescharacteristic
subgroupG/H
center, socleC22×C103#386
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
prime radicalC103×#3003C2
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×#2976C2semidirect
3. C103×#1786C2semidirect
4. C103×#1783C2semidirect
5. C103×#1513C2semidirect
6. C103×#1305C2semidirect
7. C103×#1293C2semidirect
12. #450×C103C4semidirect
14. #447×C103C4semidirect
265. #9520C103direct (N × H)
276. #2976C2×C103semidirect
277. #1786C2×C103semidirect
278. #1783C2×C103semidirect
279. #1513C2×C103semidirect
280. #1305C2×C103semidirect
281. #1293C2×C103semidirect
282. C103#9520direct (N × H)
287. #450C4×C103semidirect
289. #447C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#30032
C103×#29762
C103×#17862
C103×#17832
C103×#15132
C103×#13052
C103×#12932
#9520103