Finite Group Databasebeta

← C103×#18182 #39923457

Subgroups — C103×#18182 #39923457

Order 26368.

958 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3507C211yesmaximal, characteristic, complemented
2C103×#3110C211yesmaximal, characteristic, complemented
3C103×#3109C211yesmaximal, characteristic
4C103×#2398C211yesmaximal, characteristic, complemented
5C103×#1615C214yesmaximal, complemented
6C103×#1597C214yesmaximal, complemented
7C103×#1506C211yesmaximal, characteristic, complemented
8C103×#1505C211yesmaximal, characteristic, complemented
9C103×#1467C211yesmaximal, characteristic, complemented
10#559×C103—21no—
11#557×C103—21no—
12#556×C103—21no—
13#556×C103—22no—
14#554×C103—21no—
15#552×C103—22no—
16#539×C103C2214yes—
17#536×C103—21no—
18#533×C103C2211yescharacteristic
19#532×C103C2211yescharacteristic
20#529×C103—22no—
21#520×C103—21no—
22C2×C4×Q8×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24#484×C103C2212yes—
25#481×C103C2212yes—
26#476×C103—21no—
27#474×C103—21no—
28#461×C103—21no—
29#459×C103—21no—
30#450×C103C2212yes—
31#447×C103C2212yes—
32#442×C103—22no—
33#440×C103—22no—
34#432×C103C2211yescharacteristic
35#432×C103C2211yescharacteristic
36#400×C103C2212yes—
37#397×C103—21no—
38#394×C103C2212yes—
39#393×C103—21no—
40C4×C22⋊C4×C103—22no—
41#376×C103C2211yescharacteristic
42#328×C103C2214yes—
43#327×C103C2214yes—
44#324×C103C2214yes—
45C2×#41×C103—21no—
46C22×Q8×C103D411yescharacteristic
47C22×D4×C103C2311yescharacteristic
48C23×C4×C103—21no—
49C2×SD16×C103—22no—
50C2×D8×C103—22no—
51C4⋊Q8×C103—22no—
52C4⋊Q8×C103D411yescharacteristic
53C4⋊Q8×C103D411yescharacteristic
54C4⋊Q8×C103D411yescharacteristic
55#127×C103D411yescharacteristic
56#126×C103—24no—
57#126×C103—24no—
58#125×C103—22no—
59#125×C103—24no—
60#125×C103—21no—
61#124×C103—22no—
62#124×C103—22no—
63#124×C103—21no—
64#123×C103—24no—
65#123×C103—24no—
66C22⋊Q8×C103—22no—
67C22⋊Q8×C103—22no—
68C22⋊Q8×C103—24no—
69C22⋊Q8×C103—21no—
70C22⋊Q8×C103C2312yes—
71#121×C103—21no—
72#121×C103C2312yes—
73C4×Q8×C103—22no—
74C4×Q8×C103—22no—
75C4×Q8×C103—21no—
76C4×Q8×C103—21no—
77C4×Q8×C103—21no—
78C4×Q8×C103—21no—
79C4×Q8×C103—21no—
80C4×Q8×C103D412yes—
81C4×D4×C103—22no—
82C4×D4×C103—22no—
83C4×D4×C103—24no—
84C4×D4×C103—21no—
85C4×D4×C103—21no—
86C4×D4×C103—21no—
87C4×D4×C103—21no—
88C4×D4×C103—21no—
89C4×D4×C103D412yes—
90#117×C103—22no—
91#117×C103—24no—
92#117×C103—21no—
93C2×C4⋊C4×C103—22no—
94C2×C4⋊C4×C103D411yescharacteristic
95C2×C4⋊C4×C103C2311yescharacteristic
96C2×C4⋊C4×C103C2312yes—
97C2×C22⋊C4×C103—22no—
98C2×C22⋊C4×C103—22no—
99C2×C22⋊C4×C103—21no—
100C2×C42×C103—21no—
101C2×C42×C103D412yes—
102C2×C42×C103C2311yescharacteristic
103#107×C103—22no—
104#106×C103—22no—
105C4⋊C8×C103—21no—
106C4⋊C8×C103—21no—
107#103×C103—22no—
108#102×C103—22no—
109#102×C103—22no—
110#102×C103—22no—
111C22⋊C8×C103C2312yes—
112C22⋊C8×C103C2312yes—
113#97×C103—21no—
114#97×C103—21no—
115#95×C103—21no—
116#95×C103—22no—
117#95×C103—22no—
118#95×C103C2312yes—
119C24×C103—21no—
120#41×C103—44no—
121C2×Q8×C103—21no—
122C2×Q8×C103—21no—
123C2×Q8×C103—21no—
124C2×Q8×C103—21no—
125C2×Q8×C103—42no—
126C2×Q8×C103C2×D412yes—
127C2×D4×C103—22no—
128C2×D4×C103—21no—
129C2×D4×C103—21no—
130C2×D4×C103—21no—
131C2×D4×C103—21no—
132C2×D4×C103—42no—
133C2×D4×C103C2×D412yes—
134C22×C4×C103—24no—
135C22×C4×C103—22no—
136C22×C4×C103—21no—
137C22×C4×C103—22no—
138C22×C4×C103—44no—
139C22×C4×C103—41no—
140C22×C4×C103—41no—
141C22×C4×C103C2×D412yes—
142C22×C4×C103C2×D411yescharacteristic
143C22×C4×C103C2×D411yescharacteristic
144C22×C4×C103C2×D412yes—
145C22×C4×C103C2411yescharacteristic
146SD16×C103—44no—
147D8×C103—44no—
148C2×C8×C103—22no—
149C2×C8×C103—22no—
150C4⋊C4×C103—24no—
151C4⋊C4×C103—24no—
152C4⋊C4×C103—24no—
153C4⋊C4×C103—21no—
154C4⋊C4×C103—21no—
155C4⋊C4×C103—21no—
156C4⋊C4×C103—21no—
157C4⋊C4×C103—22no—
158C4⋊C4×C103—21no—
159C4⋊C4×C103—21no—
160C4⋊C4×C103—22no—
161C4⋊C4×C103—22no—
162C4⋊C4×C103—22no—
163C4⋊C4×C103—21no—
164C4⋊C4×C103—21no—
165C4⋊C4×C103C2×D412yes—
166C4⋊C4×C103C2×D412yes—
167C22⋊C4×C103—24no—
168C22⋊C4×C103—24no—
169C22⋊C4×C103—24no—
170C22⋊C4×C103—22no—
171C22⋊C4×C103—22no—
172C22⋊C4×C103—22no—
173C22⋊C4×C103—44no—
174C22⋊C4×C103—44no—
175C22⋊C4×C103—41no—
176C22⋊C4×C103—41no—
177C42×C103—24no—
178C42×C103—22no—
179C42×C103—22no—
180C42×C103—22no—
181C42×C103—42no—
182C42×C103C2×D411yescharacteristic
183C42×C103C2×D411yescharacteristic
184C42×C103C2×D411yescharacteristic
185C42×C103C2×D411yescharacteristic
186C23×C103—22no—
187C23×C103—22no—
188C23×C103—42no—
189C23×C103—41no—
190C23×C103—41no—
191C23×C103—42no—
192C23×C103C22×D411yescharacteristic
193Q8×C103—42no—
194Q8×C103—42no—
195Q8×C103—42no—
196Q8×C103—42no—
197Q8×C103—42no—
198D4×C103—22no—
199D4×C103—22no—
200D4×C103—42no—
201D4×C103—41no—
202D4×C103—41no—
203D4×C103—42no—
204D4×C103—44no—
205D4×C103—42no—
206C2×C4×C103—22no—
207C2×C4×C103—22no—
208C2×C4×C103—22no—
209C2×C4×C103—22no—
210C2×C4×C103—22no—
211C2×C4×C103—22no—
212C2×C4×C103—22no—
213C2×C4×C103—22no—
214C2×C4×C103—22no—
215C2×C4×C103—41no—
216C2×C4×C103—44no—
217C2×C4×C103—42no—
218C2×C4×C103—42no—
219C2×C4×C103—42no—
220C2×C4×C103—42no—
221C2×C4×C103—41no—
222C2×C4×C103—42no—
223C2×C4×C103—82no—
224C2×C4×C103—84no—
225C2×C4×C103—82no—
226C2×C4×C103#12011yescharacteristic
227C2×C4×C103#12011yescharacteristic
228C2×C4×C103#12011yescharacteristic
229C2×C4×C103#12011yescharacteristic
230C2×C4×C103C22×D411yescharacteristic
231C2×C4×C103C22×D411yescharacteristic
232C8×C103—42no—
233C8×C103—42no—
234C22×C103—21no—
235C22×C103—21no—
236C22×C103—44no—
237C22×C103—42no—
238C22×C103—42no—
239C22×C103—42no—
240C22×C103—42no—
241C22×C103—82no—
242C22×C103—81no—
243C22×C103—81no—
244C22×C103C2×#12011yescharacteristic
245C22×C103#57512yes—
246C4×C103—21no—
247C4×C103—21no—
248C4×C103—21no—
249C4×C103—21no—
250C4×C103—21no—
251C4×C103—42no—
252C4×C103—42no—
253C4×C103—42no—
254C4×C103—42no—
255C4×C103—42no—
256C4×C103—82no—
257C4×C103—81no—
258C4×C103#45412yes—
259#18182C10311yesmaximal, characteristic, direct product factor, Sylow
260C2×C103—22no—
261C2×C103—82no—
262C2×C103—82no—
263C2×C103#300511yescharacteristic
264C2×C103C2×#45411yescharacteristic
265C2×C103#302511yescharacteristic
266#3507C2×C10311yescharacteristic, complemented
267#3110C2×C10311yescharacteristic, complemented
268#3109C2×C10311yescharacteristic
269#2398C2×C10311yescharacteristic, complemented
270#1615C2×C10314yescomplemented
271#1597C2×C10314yescomplemented
272#1506C2×C10311yescharacteristic, complemented
273#1505C2×C10311yescharacteristic, complemented
274#1467C2×C10311yescharacteristic, complemented
275C103#1818211yescharacteristic, direct product factor, Sylow
276#559—21no—
277#557—21no—
278#556—21no—
279#556—22no—
280#554—21no—
281#552—22no—
282#539C22×C10314yes—
283#536—21no—
284#533C22×C10311yescharacteristic
285#532C22×C10311yescharacteristic
286#529—22no—
287#520—21no—
288C2×C4×Q8C22×C10311yescharacteristic
289C2×C4×D4C22×C10311yescharacteristic
290#484C22×C10312yes—
291#481C22×C10312yes—
292#476—21no—
293#474—21no—
294#461—21no—
295#459—21no—
296#450C22×C10312yes—
297#447C22×C10312yes—
298#442—22no—
299#440—22no—
300#432C22×C10311yescharacteristic
301#432C22×C10311yescharacteristic
302#400C22×C10312yes—
303#397—21no—
304#394C22×C10312yes—
305#393—21no—
306C4×C22⋊C4—22no—
307#376C22×C10311yescharacteristic
308#328C22×C10314yes—
309#327C22×C10314yes—
310#324C22×C10314yes—
311C2×#41—21no—
312C22×Q8D4×C10311yescharacteristic
313C22×D4C23×C10311yescharacteristic
314C23×C4—21no—
315C2×SD16—22no—
316C2×D8—22no—
317C4⋊Q8—22no—
318C4⋊Q8D4×C10311yescharacteristic
319C4⋊Q8D4×C10311yescharacteristic
320C4⋊Q8D4×C10311yescharacteristic
321#127D4×C10311yescharacteristic
322#126—24no—
323#126—24no—
324#125—22no—
325#125—24no—
326#125—21no—
327#124—22no—
328#124—22no—
329#124—21no—
330#123—24no—
331#123—24no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—24no—
335C22⋊Q8—21no—
336C22⋊Q8C23×C10312yes—
337#121—21no—
338#121C23×C10312yes—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8D4×C10312yes—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—24no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4D4×C10312yes—
356#117—22no—
357#117—24no—
358#117—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4D4×C10311yescharacteristic
361C2×C4⋊C4C23×C10311yescharacteristic
362C2×C4⋊C4C23×C10312yes—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C42—21no—
367C2×C42D4×C10312yes—
368C2×C42C23×C10311yescharacteristic
369#107—22no—
370#106—22no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373#103—22no—
374#102—22no—
375#102—22no—
376#102—22no—
377C22⋊C8C23×C10312yes—
378C22⋊C8C23×C10312yes—
379#97—21no—
380#97—21no—
381#95—21no—
382#95—22no—
383#95—22no—
384#95C23×C10312yes—
385C24—21no—
386#41—44no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—42no—
392C2×Q8C2×D4×C10312yes—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—42no—
399C2×D4C2×D4×C10312yes—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—44no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4C2×D4×C10312yes—
408C22×C4C2×D4×C10311yescharacteristic
409C22×C4C2×D4×C10311yescharacteristic
410C22×C4C2×D4×C10312yes—
411C22×C4C24×C10311yescharacteristic
412SD16—44no—
413D8—44no—
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4C2×D4×C10312yes—
432C4⋊C4C2×D4×C10312yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—44no—
440C22⋊C4—44no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C42—24no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—42no—
448C42C2×D4×C10311yescharacteristic
449C42C2×D4×C10311yescharacteristic
450C42C2×D4×C10311yescharacteristic
451C42C2×D4×C10311yescharacteristic
452C23—22no—
453C23—22no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23C22×D4×C10311yescharacteristic
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464D4—22no—
465D4—22no—
466D4—42no—
467D4—41no—
468D4—41no—
469D4—42no—
470D4—44no—
471D4—42no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—82no—
490C2×C4—84no—
491C2×C4—82no—
492C2×C4#120×C10311yescharacteristic
493C2×C4#120×C10311yescharacteristic
494C2×C4#120×C10311yescharacteristic
495C2×C4#120×C10311yescharacteristic
496C2×C4C22×D4×C10311yescharacteristic
497C2×C4C22×D4×C10311yescharacteristic
498C8—42no—
499C8—42no—
500C22—21no—
501C22—21no—
502C22—44no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—82no—
508C22—81no—
509C22—81no—
510C22C2×#120×C10311yescharacteristic
511C22#575×C10312yes—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—82no—
523C4—81no—
524C4#454×C10312yes—
525C2—22no—
526C2—82no—
527C2—82no—
528C2C103×#300511yescharacteristic
529C2C2×#454×C10311yescharacteristic
530C2C103×#302511yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3109C2
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
1. C103×#3507C2semidirect
2. C103×#3110C2semidirect
4. C103×#2398C2semidirect
5. C103×#1615C2semidirect
6. C103×#1597C2semidirect
7. C103×#1506C2semidirect
8. C103×#1505C2semidirect
9. C103×#1467C2semidirect
259. #18182C103direct (N × H)
266. #3507C2×C103semidirect
267. #3110C2×C103semidirect
269. #2398C2×C103semidirect
270. #1615C2×C103semidirect
271. #1597C2×C103semidirect
272. #1506C2×C103semidirect
273. #1505C2×C103semidirect
274. #1467C2×C103semidirect
275. C103#18182direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#35072
C103×#31102
C103×#31092
C103×#23982
C103×#16152
C103×#15972
C103×#15062
C103×#15052
C103×#14672
#18182103