Finite Group Databasebeta

← C103×#19482 #39924757

Subgroups — C103×#19482 #39924757

Order 26368.

626 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3206C211yesmaximal, characteristic, complemented
2C103×#3106C211yesmaximal, characteristic
3C103×#3079C211yesmaximal, characteristic, complemented
4C103×#2990C211yesmaximal, characteristic, complemented
5C103×#1704C212yesmaximal, complemented
6C103×#1686C212yesmaximal, complemented
7C103×#1683C212yesmaximal, complemented
8C103×#1665C212yesmaximal, complemented
9C103×#1574C211yesmaximal, characteristic, complemented
10C103×#1560C211yesmaximal, characteristic, complemented
11C103×#1546C211yesmaximal, characteristic, complemented
12#532×C103C2211yescharacteristic
13C2×C4⋊Q8×C103C2211yescharacteristic
14C4×#41×C103C2211yescharacteristic
15#492×C103C2212yes—
16#487×C103C2212yes—
17#482×C103—21no—
18#477×C103—21no—
19#477×C103C2211yescharacteristic
20#476×C103—21no—
21#476×C103C2211yescharacteristic
22#475×C103C2212yes—
23#474×C103C2212yes—
24#461×C103—21no—
25#461×C103—21no—
26#460×C103C2211yescharacteristic
27#459×C103C2211yescharacteristic
28#449×C103—21no—
29#448×C103—22no—
30#446×C103C2212yes—
31C4×SD16×C103—21no—
32C4×D8×C103—21no—
33#435×C103—22no—
34C8×D4×C103C2212yes—
35#432×C103—21no—
36#431×C103C2211yescharacteristic
37#431×C103C2211yescharacteristic
38#428×C103—21no—
39#423×C103C2211yescharacteristic
40#423×C103C2211yescharacteristic
41C2×C4⋊C8×C103—21no—
42#417×C103—21no—
43#335×C103C2212yes—
44#334×C103C2212yes—
45#333×C103C2212yes—
46#332×C103C2212yes—
47#332×C103C2212yes—
48#331×C103C2212yes—
49C2×#41×C103—21no—
50C2×#41×C103D411yescharacteristic
51C22×Q8×C103—21no—
52C2×SD16×C103—21no—
53C2×SD16×C103—22no—
54C2×SD16×C103—22no—
55C2×D8×C103—21no—
56C2×M16×C103—21no—
57C2×M16×C103—21no—
58C22×C8×C103—22no—
59C4⋊Q8×C103—21no—
60C4⋊Q8×C103—21no—
61C4⋊Q8×C103—21no—
62C4⋊Q8×C103C2312yes—
63C4⋊Q8×C103C2311yescharacteristic
64#127×C103C2311yescharacteristic
65#124×C103—21no—
66#121×C103—21no—
67#121×C103—21no—
68C4×Q8×C103D411yescharacteristic
69C4×Q8×C103C2311yescharacteristic
70C4×D4×C103—21no—
71C4×D4×C103—21no—
72C4×D4×C103—21no—
73C4×D4×C103—21no—
74C4×D4×C103D411yescharacteristic
75C4×D4×C103C2311yescharacteristic
76#117×C103—21no—
77#117×C103D411yescharacteristic
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—21no—
80C2×C42×C103—21no—
81C2×C42×C103C2311yescharacteristic
82#107×C103—22no—
83#107×C103—21no—
84#106×C103—22no—
85#106×C103—21no—
86C4⋊C8×C103—22no—
87C4⋊C8×C103—21no—
88C4⋊C8×C103—21no—
89C4⋊C8×C103D411yescharacteristic
90C4⋊C8×C103D411yescharacteristic
91C4⋊C8×C103C2312yes—
92C4⋊C8×C103C2312yes—
93C4⋊C8×C103C2311yescharacteristic
94C4⋊C8×C103C2311yescharacteristic
95#103×C103—22no—
96#103×C103—21no—
97#103×C103—22no—
98#103×C103—22no—
99#102×C103—22no—
100#102×C103—21no—
101#102×C103—21no—
102#102×C103—21no—
103C22⋊C8×C103—21no—
104C22⋊C8×C103—22no—
105C22⋊C8×C103D412yes—
106#97×C103—22no—
107C4×C8×C103—21no—
108C4×C8×C103C2312yes—
109#41×C103—22no—
110#41×C103—41no—
111#41×C103—82no—
112C2×Q8×C103—22no—
113C2×Q8×C103—21no—
114C2×Q8×C103—41no—
115C2×Q8×C103—81no—
116C2×Q8×C103—81no—
117C2×Q8×C103C2×D411yescharacteristic
118C2×D4×C103—21no—
119C2×D4×C103—21no—
120C2×D4×C103—21no—
121C2×D4×C103—21no—
122C2×D4×C103—41no—
123C2×D4×C103C2×D411yescharacteristic
124C22×C4×C103—21no—
125C22×C4×C103—21no—
126C22×C4×C103—21no—
127C22×C4×C103—41no—
128C22×C4×C103—41no—
129C22×C4×C103C2×D411yescharacteristic
130C22×C4×C103C2×D411yescharacteristic
131C22×C4×C103#4111yescharacteristic
132SD16×C103—42no—
133SD16×C103—82no—
134SD16×C103—82no—
135D8×C103—42no—
136M16×C103—42no—
137M16×C103—81no—
138C2×C8×C103—21no—
139C2×C8×C103—21no—
140C2×C8×C103—22no—
141C2×C8×C103—22no—
142C2×C8×C103—82no—
143C2×C8×C103C2×D412yes—
144C2×C8×C103C2×D412yes—
145C4⋊C4×C103—21no—
146C4⋊C4×C103—21no—
147C4⋊C4×C103—22no—
148C4⋊C4×C103—21no—
149C4⋊C4×C103—21no—
150C4⋊C4×C103—22no—
151C4⋊C4×C103—41no—
152C4⋊C4×C103—41no—
153C4⋊C4×C103C2×D411yescharacteristic
154C4⋊C4×C103C2×D411yescharacteristic
155C22⋊C4×C103—21no—
156C22⋊C4×C103—21no—
157C22⋊C4×C103—21no—
158C22⋊C4×C103—41no—
159C22⋊C4×C103—41no—
160C42×C103—21no—
161C42×C103—21no—
162C42×C103—21no—
163C42×C103C2×D411yescharacteristic
164C42×C103C2×D411yescharacteristic
165C42×C103#4111yescharacteristic
166C42×C103C2411yescharacteristic
167C23×C103—21no—
168C23×C103—41no—
169C23×C103#12111yescharacteristic
170Q8×C103—21no—
171Q8×C103—21no—
172Q8×C103—42no—
173Q8×C103—42no—
174Q8×C103—81no—
175Q8×C103—82no—
176D4×C103—21no—
177D4×C103—42no—
178D4×C103—41no—
179D4×C103—41no—
180D4×C103—41no—
181D4×C103—41no—
182D4×C103—81no—
183D4×C103—82no—
184D4×C103#13712yes—
185C2×C4×C103—21no—
186C2×C4×C103—21no—
187C2×C4×C103—21no—
188C2×C4×C103—21no—
189C2×C4×C103—22no—
190C2×C4×C103—21no—
191C2×C4×C103—21no—
192C2×C4×C103—21no—
193C2×C4×C103—42no—
194C2×C4×C103—41no—
195C2×C4×C103—41no—
196C2×C4×C103—42no—
197C2×C4×C103—41no—
198C2×C4×C103—42no—
199C2×C4×C103—82no—
200C2×C4×C103—82no—
201C2×C4×C103#12111yescharacteristic
202C2×C4×C103#12111yescharacteristic
203C2×C4×C103#12111yescharacteristic
204C2×C4×C103C22×D411yescharacteristic
205C2×C4×C103C22×D411yescharacteristic
206C2×C4×C103C2×#4111yescharacteristic
207C8×C103—22no—
208C8×C103—22no—
209C8×C103—41no—
210C8×C103—42no—
211C8×C103—41no—
212C8×C103—42no—
213C22×C103—21no—
214C22×C103—21no—
215C22×C103—22no—
216C22×C103—21no—
217C22×C103—41no—
218C22×C103—41no—
219C22×C103—81no—
220C22×C103—81no—
221C22×C103—81no—
222C22×C103C2×#12111yescharacteristic
223C4×C103—21no—
224C4×C103—21no—
225C4×C103—21no—
226C4×C103—41no—
227C4×C103—41no—
228C4×C103—41no—
229C4×C103—82no—
230C4×C103—81no—
231C4×C103#47112yes—
232C4×C103C2×#13711yescharacteristic
233C4×C103#57511yescharacteristic
234C4×C103#57611yescharacteristic
235C4×C103#57711yescharacteristic
236#19482C10311yesmaximal, characteristic, direct product factor, Sylow
237C2×C103—41no—
238C2×C103—42no—
239C2×C103—161no—
240C2×C103#304511yescharacteristic
241C2×C103#305611yescharacteristic
242C2×C103C2×#47111yescharacteristic
243#3206C2×C10311yescharacteristic, complemented
244#3106C2×C10311yescharacteristic
245#3079C2×C10311yescharacteristic, complemented
246#2990C2×C10311yescharacteristic, complemented
247#1704C2×C10312yescomplemented
248#1686C2×C10312yescomplemented
249#1683C2×C10312yescomplemented
250#1665C2×C10312yescomplemented
251#1574C2×C10311yescharacteristic, complemented
252#1560C2×C10311yescharacteristic, complemented
253#1546C2×C10311yescharacteristic, complemented
254C103#1948211yescharacteristic, direct product factor, Sylow
255#532C22×C10311yescharacteristic
256C2×C4⋊Q8C22×C10311yescharacteristic
257C4×#41C22×C10311yescharacteristic
258#492C22×C10312yes—
259#487C22×C10312yes—
260#482—21no—
261#477—21no—
262#477C22×C10311yescharacteristic
263#476—21no—
264#476C22×C10311yescharacteristic
265#475C22×C10312yes—
266#474C22×C10312yes—
267#461—21no—
268#461—21no—
269#460C22×C10311yescharacteristic
270#459C22×C10311yescharacteristic
271#449—21no—
272#448—22no—
273#446C22×C10312yes—
274C4×SD16—21no—
275C4×D8—21no—
276#435—22no—
277C8×D4C22×C10312yes—
278#432—21no—
279#431C22×C10311yescharacteristic
280#431C22×C10311yescharacteristic
281#428—21no—
282#423C22×C10311yescharacteristic
283#423C22×C10311yescharacteristic
284C2×C4⋊C8—21no—
285#417—21no—
286#335C22×C10312yes—
287#334C22×C10312yes—
288#333C22×C10312yes—
289#332C22×C10312yes—
290#332C22×C10312yes—
291#331C22×C10312yes—
292C2×#41—21no—
293C2×#41D4×C10311yescharacteristic
294C22×Q8—21no—
295C2×SD16—21no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×D8—21no—
299C2×M16—21no—
300C2×M16—21no—
301C22×C8—22no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8C23×C10312yes—
306C4⋊Q8C23×C10311yescharacteristic
307#127C23×C10311yescharacteristic
308#124—21no—
309#121—21no—
310#121—21no—
311C4×Q8D4×C10311yescharacteristic
312C4×Q8C23×C10311yescharacteristic
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4D4×C10311yescharacteristic
318C4×D4C23×C10311yescharacteristic
319#117—21no—
320#117D4×C10311yescharacteristic
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C42—21no—
324C2×C42C23×C10311yescharacteristic
325#107—22no—
326#107—21no—
327#106—22no—
328#106—21no—
329C4⋊C8—22no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8D4×C10311yescharacteristic
333C4⋊C8D4×C10311yescharacteristic
334C4⋊C8C23×C10312yes—
335C4⋊C8C23×C10312yes—
336C4⋊C8C23×C10311yescharacteristic
337C4⋊C8C23×C10311yescharacteristic
338#103—22no—
339#103—21no—
340#103—22no—
341#103—22no—
342#102—22no—
343#102—21no—
344#102—21no—
345#102—21no—
346C22⋊C8—21no—
347C22⋊C8—22no—
348C22⋊C8D4×C10312yes—
349#97—22no—
350C4×C8—21no—
351C4×C8C23×C10312yes—
352#41—22no—
353#41—41no—
354#41—82no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—41no—
358C2×Q8—81no—
359C2×Q8—81no—
360C2×Q8C2×D4×C10311yescharacteristic
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4C2×D4×C10311yescharacteristic
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4C2×D4×C10311yescharacteristic
373C22×C4C2×D4×C10311yescharacteristic
374C22×C4#41×C10311yescharacteristic
375SD16—42no—
376SD16—82no—
377SD16—82no—
378D8—42no—
379M16—42no—
380M16—81no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—82no—
386C2×C8C2×D4×C10312yes—
387C2×C8C2×D4×C10312yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C10311yescharacteristic
397C4⋊C4C2×D4×C10311yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42C2×D4×C10311yescharacteristic
407C42C2×D4×C10311yescharacteristic
408C42#41×C10311yescharacteristic
409C42C24×C10311yescharacteristic
410C23—21no—
411C23—41no—
412C23#121×C10311yescharacteristic
413Q8—21no—
414Q8—21no—
415Q8—42no—
416Q8—42no—
417Q8—81no—
418Q8—82no—
419D4—21no—
420D4—42no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—81no—
426D4—82no—
427D4#137×C10312yes—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4#121×C10311yescharacteristic
445C2×C4#121×C10311yescharacteristic
446C2×C4#121×C10311yescharacteristic
447C2×C4C22×D4×C10311yescharacteristic
448C2×C4C22×D4×C10311yescharacteristic
449C2×C4C2×#41×C10311yescharacteristic
450C8—22no—
451C8—22no—
452C8—41no—
453C8—42no—
454C8—41no—
455C8—42no—
456C22—21no—
457C22—21no—
458C22—22no—
459C22—21no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22C2×#121×C10311yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—82no—
473C4—81no—
474C4#471×C10312yes—
475C4C2×#137×C10311yescharacteristic
476C4#575×C10311yescharacteristic
477C4#576×C10311yescharacteristic
478C4#577×C10311yescharacteristic
479C2—41no—
480C2—42no—
481C2—161no—
482C2C103×#304511yescharacteristic
483C2C103×#305611yescharacteristic
484C2C2×#471×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3106C2
LCSG ▷ C42 ▷ 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×#3206C2semidirect
3. C103×#3079C2semidirect
4. C103×#2990C2semidirect
5. C103×#1704C2semidirect
6. C103×#1686C2semidirect
7. C103×#1683C2semidirect
8. C103×#1665C2semidirect
9. C103×#1574C2semidirect
10. C103×#1560C2semidirect
11. C103×#1546C2semidirect
236. #19482C103direct (N × H)
243. #3206C2×C103semidirect
245. #3079C2×C103semidirect
246. #2990C2×C103semidirect
247. #1704C2×C103semidirect
248. #1686C2×C103semidirect
249. #1683C2×C103semidirect
250. #1665C2×C103semidirect
251. #1574C2×C103semidirect
252. #1560C2×C103semidirect
253. #1546C2×C103semidirect
254. C103#19482direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32062
C103×#31062
C103×#30792
C103×#29902
C103×#17042
C103×#16862
C103×#16832
C103×#16652
C103×#15742
C103×#15602
C103×#15462
#19482103