Finite Group Databasebeta

← C103×#21067 #39926342

Subgroups — C103×#21067 #39926342

Order 26368.

1126 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#107×C103C211yesmaximal, characteristic, complemented
2C2×#417×C103C211yesmaximal, characteristic
3C2×#416×C103C211yesmaximal, characteristic
4C103×#2311C211yesmaximal, characteristic
5C103×#2274C211yesmaximal, characteristic, complemented
6C103×#1928C214yesmaximal, complemented
7C103×#1925C214yesmaximal, complemented
8C103×#1736C211yesmaximal, characteristic, complemented
9C103×#1729C211yesmaximal, characteristic, complemented
10C22×#41×C103C2211yescharacteristic
11C22×M16×C103C2211yescharacteristic
12C23×C8×C103C2211yescharacteristic
13C2×#117×C103C2211yescharacteristic
14C2×#117×C103C2211yescharacteristic
15C22×C4⋊C4×C103C2211yescharacteristic
16C22×C4⋊C4×C103C2211yescharacteristic
17C2×#107×C103—24no—
18C2×#107×C103C2214yes—
19#417×C103—24no—
20#416×C103C418yescomplemented
21C2×#103×C103C2212yes—
22C2×#103×C103C2212yes—
23C2×#102×C103C2212yes—
24C2×#102×C103C2212yes—
25#391×C103C2212yes—
26#390×C103C2212yes—
27#386×C103—22no—
28#380×C103—22no—
29C4×C4⋊C4×C103—22no—
30C4×C4⋊C4×C103C2214yes—
31C4×C22⋊C4×C103—22no—
32#340×C103C2214yes—
33#336×C103C2214yes—
34C2×#41×C103—22no—
35C2×#41×C103—22no—
36C2×#41×C103—22no—
37C2×#41×C103—22no—
38C2×#41×C103—22no—
39C2×#41×C103C2×C414yes—
40C22×Q8×C103C2311yescharacteristic
41C22×D4×C103—21no—
42C22×D4×C103C2311yescharacteristic
43C23×C4×C103—21no—
44C23×C4×C103—21no—
45C23×C4×C103—21no—
46C23×C4×C103C2311yescharacteristic
47C2×M16×C103—22no—
48C2×M16×C103—22no—
49C2×M16×C103—22no—
50C22×C8×C103—22no—
51C22×C8×C103—22no—
52C22×C8×C103C2×C414yes—
53C22×C8×C103C2312yes—
54C22×C8×C103C2312yes—
55#117×C103—22no—
56#117×C103—22no—
57#117×C103—22no—
58#117×C103C2×C414yes—
59C2×C4⋊C4×C103—21no—
60C2×C4⋊C4×C103—22no—
61C2×C4⋊C4×C103—22no—
62C2×C4⋊C4×C103—22no—
63C2×C4⋊C4×C103—21no—
64C2×C4⋊C4×C103D412yes—
65C2×C4⋊C4×C103D414yes—
66C2×C4⋊C4×C103C2312yes—
67C2×C4⋊C4×C103C2312yes—
68C2×C4⋊C4×C103C2312yes—
69C2×C22⋊C4×C103—21no—
70C2×C22⋊C4×C103—24no—
71C2×C22⋊C4×C103D412yes—
72C2×C42×C103—21no—
73C2×C42×C103—24no—
74C2×C42×C103C2312yes—
75#107×C103—28no—
76#103×C103—24no—
77#103×C103C2×C418yescomplemented
78#102×C103—24no—
79#102×C103C2×C418yescomplemented
80#95×C103—24no—
81#95×C103—24no—
82C24×C103—21no—
83C24×C103C2×D411yescharacteristic
84#41×C103—28no—
85#41×C103—28no—
86#41×C103—44no—
87#41×C103—44no—
88C2×Q8×C103—21no—
89C2×Q8×C103—21no—
90C2×Q8×C103—21no—
91C2×Q8×C103—21no—
92C2×Q8×C103—21no—
93C2×Q8×C103C22×C412yes—
94C2×D4×C103—24no—
95C2×D4×C103—21no—
96C2×D4×C103—21no—
97C2×D4×C103—21no—
98C2×D4×C103—21no—
99C2×D4×C103—21no—
100C2×D4×C103—42no—
101C2×D4×C103—42no—
102C2×D4×C103C22×C412yes—
103C22×C4×C103—21no—
104C22×C4×C103—22no—
105C22×C4×C103—22no—
106C22×C4×C103—24no—
107C22×C4×C103—24no—
108C22×C4×C103—22no—
109C22×C4×C103—42no—
110C22×C4×C103—42no—
111C22×C4×C103—42no—
112C22×C4×C103—82no—
113C22×C4×C103—82no—
114C22×C4×C103C22×C412yes—
115C22×C4×C103C2×D414yes—
116C22×C4×C103C2×D411yescharacteristic
117C22×C4×C103C2×D412yes—
118C22×C4×C103#4112yes—
119C22×C4×C103#4112yes—
120C22×C4×C103#4112yes—
121C22×C4×C103#4112yes—
122C22×C4×C103C2411yescharacteristic
123M16×C103—44no—
124C2×C8×C103—28no—
125C2×C8×C103—22no—
126C2×C8×C103—22no—
127C2×C8×C103—22no—
128C2×C8×C103—22no—
129C2×C8×C103—22no—
130C2×C8×C103C22×C414yes—
131C4⋊C4×C103—24no—
132C4⋊C4×C103—24no—
133C4⋊C4×C103—22no—
134C4⋊C4×C103—22no—
135C4⋊C4×C103—22no—
136C4⋊C4×C103—22no—
137C4⋊C4×C103—42no—
138C4⋊C4×C103C22×C414yes—
139C4⋊C4×C103C2×D414yes—
140C22⋊C4×C103—24no—
141C22⋊C4×C103—24no—
142C22⋊C4×C103—84no—
143C42×C103—24no—
144C42×C103—22no—
145C42×C103—22no—
146C42×C103—84no—
147C23×C103—22no—
148C23×C103—22no—
149C23×C103—22no—
150C23×C103—41no—
151C23×C103—41no—
152C23×C103—42no—
153C23×C103—42no—
154C23×C103C4×D412yes—
155C23×C103#12112yes—
156C23×C103#12312yes—
157C23×C103C22×D411yescharacteristic
158Q8×C103—22no—
159Q8×C103—22no—
160Q8×C103—41no—
161Q8×C103—41no—
162D4×C103—22no—
163D4×C103—22no—
164D4×C103—48no—
165D4×C103—41no—
166D4×C103—41no—
167C2×C4×C103—24no—
168C2×C4×C103—22no—
169C2×C4×C103—24no—
170C2×C4×C103—24no—
171C2×C4×C103—24no—
172C2×C4×C103—24no—
173C2×C4×C103—41no—
174C2×C4×C103—41no—
175C2×C4×C103—42no—
176C2×C4×C103—44no—
177C2×C4×C103—42no—
178C2×C4×C103—48no—
179C2×C4×C103—42no—
180C2×C4×C103—44no—
181C2×C4×C103—84no—
182C2×C4×C103—84no—
183C2×C4×C103#11714yes—
184C2×C4×C103C4×D414yes—
185C2×C4×C103C4×D412yes—
186C2×C4×C103#12112yes—
187C2×C4×C103#12312yes—
188C2×C4×C103#12414yes—
189C2×C4×C103#12614yes—
190C2×C4×C103C23×C411yescharacteristic
191C2×C4×C103C22×D411yescharacteristic
192C2×C4×C103C2×#4111yescharacteristic
193C2×C4×C103C2×#4111yescharacteristic
194C2×C4×C103C2×#4111yescharacteristic
195C2×C4×C103C2×#4111yescharacteristic
196C8×C103—24no—
197C8×C103—42no—
198C22×C103—24no—
199C22×C103—24no—
200C22×C103—22no—
201C22×C103—22no—
202C22×C103—44no—
203C22×C103—42no—
204C22×C103—82no—
205C22×C103—81no—
206C22×C103—81no—
207C22×C103#38814yes—
208C22×C103C2×C4×D411yescharacteristic
209C22×C103C2×#12111yescharacteristic
210C22×C103C2×#12311yescharacteristic
211C22×C103#57612yes—
212C22×C103#57812yes—
213C4×C103—44no—
214C4×C103—44no—
215C4×C103—44no—
216C4×C103—42no—
217C4×C103—82no—
218C4×C103#38814yes—
219C4×C103C2×#11711yescharacteristic
220C4×C103C2×C4×D411yescharacteristic
221C4×C103C2×#12411yescharacteristic
222C4×C103C2×#12611yescharacteristic
223#21067C10311yesmaximal, characteristic, direct product factor, Sylow
224C2×C103—24no—
225C2×C103—82no—
226C2×C103C2×#38811yescharacteristic
227C2×C103#295112yes—
228C2×C103#304111yescharacteristic
229C2×C103#304411yescharacteristic
230C2×C103#309812yes—
231C22×#107C2×C10311yescharacteristic, complemented
232C2×#417C2×C10311yescharacteristic
233C2×#416C2×C10311yescharacteristic
234#2311C2×C10311yescharacteristic
235#2274C2×C10311yescharacteristic, complemented
236#1928C2×C10314yescomplemented
237#1925C2×C10314yescomplemented
238#1736C2×C10311yescharacteristic, complemented
239#1729C2×C10311yescharacteristic, complemented
240C103#2106711yescharacteristic, direct product factor, Sylow
241C22×#41C22×C10311yescharacteristic
242C22×M16C22×C10311yescharacteristic
243C23×C8C22×C10311yescharacteristic
244C2×#117C22×C10311yescharacteristic
245C2×#117C22×C10311yescharacteristic
246C22×C4⋊C4C22×C10311yescharacteristic
247C22×C4⋊C4C22×C10311yescharacteristic
248C2×#107—24no—
249C2×#107C22×C10314yes—
250#417—24no—
251#416C4×C10318yescomplemented
252C2×#103C22×C10312yes—
253C2×#103C22×C10312yes—
254C2×#102C22×C10312yes—
255C2×#102C22×C10312yes—
256#391C22×C10312yes—
257#390C22×C10312yes—
258#386—22no—
259#380—22no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4C22×C10314yes—
262C4×C22⋊C4—22no—
263#340C22×C10314yes—
264#336C22×C10314yes—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—22no—
269C2×#41—22no—
270C2×#41C2×C4×C10314yes—
271C22×Q8C23×C10311yescharacteristic
272C22×D4—21no—
273C22×D4C23×C10311yescharacteristic
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4C23×C10311yescharacteristic
278C2×M16—22no—
279C2×M16—22no—
280C2×M16—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8C2×C4×C10314yes—
284C22×C8C23×C10312yes—
285C22×C8C23×C10312yes—
286#117—22no—
287#117—22no—
288#117—22no—
289#117C2×C4×C10314yes—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4D4×C10312yes—
296C2×C4⋊C4D4×C10314yes—
297C2×C4⋊C4C23×C10312yes—
298C2×C4⋊C4C23×C10312yes—
299C2×C4⋊C4C23×C10312yes—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4D4×C10312yes—
303C2×C42—21no—
304C2×C42—24no—
305C2×C42C23×C10312yes—
306#107—28no—
307#103—24no—
308#103C2×C4×C10318yescomplemented
309#102—24no—
310#102C2×C4×C10318yescomplemented
311#95—24no—
312#95—24no—
313C24—21no—
314C24C2×D4×C10311yescharacteristic
315#41—28no—
316#41—28no—
317#41—44no—
318#41—44no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8C22×C4×C10312yes—
325C2×D4—24no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4C22×C4×C10312yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—82no—
344C22×C4—82no—
345C22×C4C22×C4×C10312yes—
346C22×C4C2×D4×C10314yes—
347C22×C4C2×D4×C10311yescharacteristic
348C22×C4C2×D4×C10312yes—
349C22×C4#41×C10312yes—
350C22×C4#41×C10312yes—
351C22×C4#41×C10312yes—
352C22×C4#41×C10312yes—
353C22×C4C24×C10311yescharacteristic
354M16—44no—
355C2×C8—28no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8C22×C4×C10314yes—
362C4⋊C4—24no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—42no—
369C4⋊C4C22×C4×C10314yes—
370C4⋊C4C2×D4×C10314yes—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—84no—
374C42—24no—
375C42—22no—
376C42—22no—
377C42—84no—
378C23—22no—
379C23—22no—
380C23—22no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23C4×D4×C10312yes—
386C23#121×C10312yes—
387C23#123×C10312yes—
388C23C22×D4×C10311yescharacteristic
389Q8—22no—
390Q8—22no—
391Q8—41no—
392Q8—41no—
393D4—22no—
394D4—22no—
395D4—48no—
396D4—41no—
397D4—41no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—48no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—84no—
413C2×C4—84no—
414C2×C4#117×C10314yes—
415C2×C4C4×D4×C10312yes—
416C2×C4C4×D4×C10314yes—
417C2×C4#121×C10312yes—
418C2×C4#123×C10312yes—
419C2×C4#124×C10314yes—
420C2×C4#126×C10314yes—
421C2×C4C23×C4×C10311yescharacteristic
422C2×C4C22×D4×C10311yescharacteristic
423C2×C4C2×#41×C10311yescharacteristic
424C2×C4C2×#41×C10311yescharacteristic
425C2×C4C2×#41×C10311yescharacteristic
426C2×C4C2×#41×C10311yescharacteristic
427C8—24no—
428C8—42no—
429C22—22no—
430C22—22no—
431C22—24no—
432C22—24no—
433C22—42no—
434C22—44no—
435C22—81no—
436C22—81no—
437C22—82no—
438C22#388×C10314yes—
439C22C2×C4×D4×C10311yescharacteristic
440C22C2×#121×C10311yescharacteristic
441C22C2×#123×C10311yescharacteristic
442C22#576×C10312yes—
443C22#578×C10312yes—
444C4—44no—
445C4—42no—
446C4—44no—
447C4—44no—
448C4—82no—
449C4#388×C10314yes—
450C4C2×#117×C10311yescharacteristic
451C4C2×C4×D4×C10311yescharacteristic
452C4C2×#124×C10311yescharacteristic
453C4C2×#126×C10311yescharacteristic
454C2—24no—
455C2—82no—
456C2C2×#388×C10311yescharacteristic
457C2C103×#295112yes—
458C2C103×#304111yescharacteristic
459C2C103×#304411yescharacteristic
460C2C103×#309812yes—
subgroupG/H
center, socleC23×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC22×#41×C103C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×#117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#107×C103C2semidirect
5. C103×#2274C2semidirect
6. C103×#1928C2semidirect
7. C103×#1925C2semidirect
8. C103×#1736C2semidirect
9. C103×#1729C2semidirect
20. #416×C103C4semidirect
77. #103×C103C2×C4semidirect
79. #102×C103C2×C4semidirect
223. #21067C103direct (N × H)
231. C22×#107C2×C103semidirect
235. #2274C2×C103semidirect
236. #1928C2×C103semidirect
237. #1925C2×C103semidirect
238. #1736C2×C103semidirect
239. #1729C2×C103semidirect
240. C103#21067direct (N × H)
251. #416C4×C103semidirect
308. #103C2×C4×C103semidirect
310. #102C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#107×C1032
C2×#417×C1032
C2×#416×C1032
C103×#23112
C103×#22742
C103×#19282
C103×#19252
C103×#17362
C103×#17292
#21067103