Finite Group Databasebeta

← C103×#25315 #39930590

Subgroups — C103×#25315 #39930590

Order 26368.

732 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3138C211yesmaximal, characteristic
2C103×#3078C211yesmaximal, characteristic, complemented
3C2×#460×C103C211yesmaximal, characteristic
4C103×#2962C211yesmaximal, characteristic, complemented
5C103×#2063C212yesmaximal, complemented
6C103×#2046C212yesmaximal, complemented
7C103×#1977C212yesmaximal, complemented
8C103×#1965C211yesmaximal, characteristic
9C103×#1950C211yesmaximal, characteristic, complemented
10C103×#1931C212yesmaximal, complemented
11C4×#101×C103C211yesmaximal, characteristic, complemented
12C22×SD16×C103C2212yes—
13#533×C103C2211yescharacteristic
14C2×#127×C103C2211yescharacteristic
15C2×C4×Q8×C103C2211yescharacteristic
16#490×C103—22no—
17#486×C103—21no—
18#486×C103—21no—
19#479×C103—22no—
20#477×C103—21no—
21#475×C103—21no—
22#460×C103—21no—
23#460×C103—22no—
24#460×C103—21no—
25#446×C103—22no—
26#446×C103—21no—
27C8×Q8×C103—21no—
28C2×#108×C103C2212yes—
29#428×C103C2212yes—
30#424×C103C2212yes—
31#423×C103C2211yescharacteristic
32C2×C4⋊C8×C103C2211yescharacteristic
33#419×C103C2212yes—
34#418×C103C2212yes—
35#418×C103C2212yes—
36C2×#102×C103C2212yes—
37C2×#101×C103C2211yescharacteristic
38C2×#101×C103C2211yescharacteristic
39C2×#100×C103C2212yes—
40C2×#100×C103C2212yes—
41#405×C103C2212yes—
42C4×M16×C103C2211yescharacteristic
43C4×M16×C103C2211yescharacteristic
44#343×C103C2211yescharacteristic
45#343×C103C2211yescharacteristic
46#341×C103C2212yes—
47C22×Q8×C103C2311yescharacteristic
48C22×D4×C103—21no—
49C22×D4×C103—21no—
50C22×D4×C103C2312yes—
51C2×SD16×C103—24no—
52C2×SD16×C103—22no—
53C2×SD16×C103—22no—
54C2×SD16×C103—42no—
55C2×M16×C103C2311yescharacteristic
56C2×M16×C103C2312yes—
57C2×M16×C103C2311yescharacteristic
58C2×M16×C103C2311yescharacteristic
59C2×M16×C103C2311yescharacteristic
60C22×C8×C103C2312yes—
61C4⋊Q8×C103D411yescharacteristic
62C4⋊Q8×C103D411yescharacteristic
63#127×C103—21no—
64#127×C103—21no—
65#127×C103—21no—
66#127×C103—21no—
67#125×C103D412yes—
68C22⋊Q8×C103—21no—
69C22⋊Q8×C103—21no—
70C4×Q8×C103—21no—
71C4×Q8×C103—21no—
72C4×Q8×C103—21no—
73C4×Q8×C103—21no—
74C4×Q8×C103—21no—
75C4×Q8×C103—21no—
76#117×C103C2312yes—
77C2×C4⋊C4×C103—21no—
78C2×C4⋊C4×C103C2311yescharacteristic
79C2×C42×C103—21no—
80C2×C42×C103C2311yescharacteristic
81#108×C103—42no—
82#107×C103—22no—
83#106×C103—22no—
84C4⋊C8×C103—22no—
85C4⋊C8×C103—22no—
86C4⋊C8×C103—21no—
87C4⋊C8×C103—21no—
88C4⋊C8×C103D411yescharacteristic
89C4⋊C8×C103D411yescharacteristic
90C4⋊C8×C103D412yes—
91#103×C103—22no—
92#103×C103—22no—
93#102×C103—22no—
94#102×C103—22no—
95#102×C103—22no—
96#102×C103—22no—
97#102×C103—22no—
98#102×C103—22no—
99#101×C103—22no—
100#101×C103—22no—
101#100×C103—24no—
102#100×C103—42no—
103#97×C103—22no—
104#97×C103—21no—
105#97×C103—21no—
106C4×C8×C103—22no—
107C4×C8×C103—21no—
108C4×C8×C103—21no—
109C24×C103—22no—
110C2×Q8×C103—21no—
111C2×Q8×C103—21no—
112C2×Q8×C103—21no—
113C2×Q8×C103—21no—
114C2×Q8×C103—21no—
115C2×Q8×C103—21no—
116C2×Q8×C103—21no—
117C2×Q8×C103#4112yes—
118C2×D4×C103—22no—
119C2×D4×C103—22no—
120C2×D4×C103—22no—
121C2×D4×C103—22no—
122C2×D4×C103—22no—
123C2×D4×C103—22no—
124C2×D4×C103—41no—
125C2×D4×C103—41no—
126C2×D4×C103—41no—
127C2×D4×C103—41no—
128C2×D4×C103—82no—
129C2×D4×C103—82no—
130C22×C4×C103—21no—
131C22×C4×C103—21no—
132C22×C4×C103#4111yescharacteristic
133C22×C4×C103#4111yescharacteristic
134C22×C4×C103C2411yescharacteristic
135SD16×C103—44no—
136SD16×C103—44no—
137M16×C103—21no—
138M16×C103—22no—
139M16×C103—21no—
140M16×C103—21no—
141M16×C103—21no—
142M16×C103—21no—
143M16×C103—22no—
144M16×C103—21no—
145M16×C103—21no—
146M16×C103#4112yes—
147C2×C8×C103—21no—
148C2×C8×C103—22no—
149C2×C8×C103—22no—
150C2×C8×C103—21no—
151C2×C8×C103—21no—
152C2×C8×C103—21no—
153C2×C8×C103—22no—
154C2×C8×C103C2×D412yes—
155C2×C8×C103C2×D412yes—
156C4⋊C4×C103—22no—
157C4⋊C4×C103—22no—
158C4⋊C4×C103—21no—
159C4⋊C4×C103—21no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—41no—
163C4⋊C4×C103—41no—
164C4⋊C4×C103C2×D412yes—
165C4⋊C4×C103C2×D412yes—
166C22⋊C4×C103—22no—
167C42×C103—22no—
168C42×C103—41no—
169C42×C103—41no—
170C42×C103C2×D411yescharacteristic
171C42×C103C2×D411yescharacteristic
172C42×C103C2×D411yescharacteristic
173C42×C103C2×D411yescharacteristic
174C23×C103—42no—
175C23×C103—42no—
176C23×C103—42no—
177C23×C103—82no—
178C23×C103—82no—
179C23×C103C2×#4111yescharacteristic
180Q8×C103—22no—
181Q8×C103—22no—
182Q8×C103—41no—
183Q8×C103—41no—
184Q8×C103—42no—
185Q8×C103—81no—
186D4×C103—42no—
187D4×C103—42no—
188D4×C103—42no—
189D4×C103—42no—
190D4×C103—82no—
191D4×C103—82no—
192D4×C103—82no—
193D4×C103—82no—
194C2×C4×C103—22no—
195C2×C4×C103—22no—
196C2×C4×C103—22no—
197C2×C4×C103—22no—
198C2×C4×C103—41no—
199C2×C4×C103—41no—
200C2×C4×C103—41no—
201C2×C4×C103—41no—
202C2×C4×C103—81no—
203C2×C4×C103#12111yescharacteristic
204C2×C4×C103#12111yescharacteristic
205C2×C4×C103#12111yescharacteristic
206C2×C4×C103#12111yescharacteristic
207C2×C4×C103C22×D411yescharacteristic
208C2×C4×C103C22×D411yescharacteristic
209C2×C4×C103C2×#4111yescharacteristic
210C2×C4×C103C2×#4111yescharacteristic
211C2×C4×C103H(5,𝔽2)11yescharacteristic
212C2×C4×C1032−1+411yescharacteristic
213C8×C103—22no—
214C8×C103—22no—
215C8×C103—22no—
216C8×C103—41no—
217C8×C103—41no—
218C8×C103—41no—
219C8×C103—42no—
220C22×C103—21no—
221C22×C103—21no—
222C22×C103—82no—
223C22×C103—82no—
224C22×C103—82no—
225C22×C103—162no—
226C22×C103—162no—
227C22×C103C2×#12111yescharacteristic
228C22×C103#52911yescharacteristic
229C22×C103#54211yescharacteristic
230C4×C103—21no—
231C4×C103—21no—
232C4×C103—21no—
233C4×C103—42no—
234C4×C103—42no—
235C4×C103—42no—
236C4×C103—81no—
237C4×C103#47112yes—
238C4×C103#54611yescharacteristic
239C4×C103#54811yescharacteristic
240C4×C103#54811yescharacteristic
241C4×C103#55011yescharacteristic
242#25315C10311yesmaximal, characteristic, direct product factor, Sylow
243C2×C103—21no—
244C2×C103—21no—
245C2×C103—162no—
246C2×C103#242611yescharacteristic
247C2×C103C2×#47111yescharacteristic
248C2×C103#306811yescharacteristic
249#3138C2×C10311yescharacteristic
250#3078C2×C10311yescharacteristic, complemented
251C2×#460C2×C10311yescharacteristic
252#2962C2×C10311yescharacteristic, complemented
253#2063C2×C10312yescomplemented
254#2046C2×C10312yescomplemented
255#1977C2×C10312yescomplemented
256#1965C2×C10311yescharacteristic
257#1950C2×C10311yescharacteristic, complemented
258#1931C2×C10312yescomplemented
259C4×#101C2×C10311yescharacteristic, complemented
260C103#2531511yescharacteristic, direct product factor, Sylow
261C22×SD16C22×C10312yes—
262#533C22×C10311yescharacteristic
263C2×#127C22×C10311yescharacteristic
264C2×C4×Q8C22×C10311yescharacteristic
265#490—22no—
266#486—21no—
267#486—21no—
268#479—22no—
269#477—21no—
270#475—21no—
271#460—21no—
272#460—22no—
273#460—21no—
274#446—22no—
275#446—21no—
276C8×Q8—21no—
277C2×#108C22×C10312yes—
278#428C22×C10312yes—
279#424C22×C10312yes—
280#423C22×C10311yescharacteristic
281C2×C4⋊C8C22×C10311yescharacteristic
282#419C22×C10312yes—
283#418C22×C10312yes—
284#418C22×C10312yes—
285C2×#102C22×C10312yes—
286C2×#101C22×C10311yescharacteristic
287C2×#101C22×C10311yescharacteristic
288C2×#100C22×C10312yes—
289C2×#100C22×C10312yes—
290#405C22×C10312yes—
291C4×M16C22×C10311yescharacteristic
292C4×M16C22×C10311yescharacteristic
293#343C22×C10311yescharacteristic
294#343C22×C10311yescharacteristic
295#341C22×C10312yes—
296C22×Q8C23×C10311yescharacteristic
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C23×C10312yes—
300C2×SD16—24no—
301C2×SD16—22no—
302C2×SD16—22no—
303C2×SD16—42no—
304C2×M16C23×C10311yescharacteristic
305C2×M16C23×C10312yes—
306C2×M16C23×C10311yescharacteristic
307C2×M16C23×C10311yescharacteristic
308C2×M16C23×C10311yescharacteristic
309C22×C8C23×C10312yes—
310C4⋊Q8D4×C10311yescharacteristic
311C4⋊Q8D4×C10311yescharacteristic
312#127—21no—
313#127—21no—
314#127—21no—
315#127—21no—
316#125D4×C10312yes—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325#117C23×C10312yes—
326C2×C4⋊C4—21no—
327C2×C4⋊C4C23×C10311yescharacteristic
328C2×C42—21no—
329C2×C42C23×C10311yescharacteristic
330#108—42no—
331#107—22no—
332#106—22no—
333C4⋊C8—22no—
334C4⋊C8—22no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337C4⋊C8D4×C10311yescharacteristic
338C4⋊C8D4×C10311yescharacteristic
339C4⋊C8D4×C10312yes—
340#103—22no—
341#103—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#101—22no—
349#101—22no—
350#100—24no—
351#100—42no—
352#97—22no—
353#97—21no—
354#97—21no—
355C4×C8—22no—
356C4×C8—21no—
357C4×C8—21no—
358C24—22no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8#41×C10312yes—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—82no—
378C2×D4—82no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4#41×C10311yescharacteristic
382C22×C4#41×C10311yescharacteristic
383C22×C4C24×C10311yescharacteristic
384SD16—44no—
385SD16—44no—
386M16—21no—
387M16—22no—
388M16—21no—
389M16—21no—
390M16—21no—
391M16—21no—
392M16—22no—
393M16—21no—
394M16—21no—
395M16#41×C10312yes—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8C2×D4×C10312yes—
404C2×C8C2×D4×C10312yes—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4C2×D4×C10312yes—
414C4⋊C4C2×D4×C10312yes—
415C22⋊C4—22no—
416C42—22no—
417C42—41no—
418C42—41no—
419C42C2×D4×C10311yescharacteristic
420C42C2×D4×C10311yescharacteristic
421C42C2×D4×C10311yescharacteristic
422C42C2×D4×C10311yescharacteristic
423C23—42no—
424C23—42no—
425C23—42no—
426C23—82no—
427C23—82no—
428C23C2×#41×C10311yescharacteristic
429Q8—22no—
430Q8—22no—
431Q8—42no—
432Q8—41no—
433Q8—41no—
434Q8—81no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4—82no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—81no—
452C2×C4#121×C10311yescharacteristic
453C2×C4#121×C10311yescharacteristic
454C2×C4#121×C10311yescharacteristic
455C2×C4#121×C10311yescharacteristic
456C2×C4C22×D4×C10311yescharacteristic
457C2×C4C22×D4×C10311yescharacteristic
458C2×C4C2×#41×C10311yescharacteristic
459C2×C4C2×#41×C10311yescharacteristic
460C2×C4H(5,𝔽2)×C10311yescharacteristic
461C2×C42−1+4×C10311yescharacteristic
462C8—22no—
463C8—22no—
464C8—22no—
465C8—41no—
466C8—41no—
467C8—41no—
468C8—42no—
469C22—21no—
470C22—21no—
471C22—82no—
472C22—82no—
473C22—82no—
474C22—162no—
475C22—162no—
476C22C2×#121×C10311yescharacteristic
477C22#529×C10311yescharacteristic
478C22#542×C10311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—81no—
486C4#471×C10312yes—
487C4#546×C10311yescharacteristic
488C4#548×C10311yescharacteristic
489C4#548×C10311yescharacteristic
490C4#550×C10311yescharacteristic
491C2—21no—
492C2—21no—
493C2—162no—
494C2C103×#242611yescharacteristic
495C2C2×#471×C10311yescharacteristic
496C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#127×C103C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3078C2semidirect
4. C103×#2962C2semidirect
5. C103×#2063C2semidirect
6. C103×#2046C2semidirect
7. C103×#1977C2semidirect
9. C103×#1950C2semidirect
10. C103×#1931C2semidirect
11. C4×#101×C103C2semidirect
242. #25315C103direct (N × H)
250. #3078C2×C103semidirect
252. #2962C2×C103semidirect
253. #2063C2×C103semidirect
254. #2046C2×C103semidirect
255. #1977C2×C103semidirect
257. #1950C2×C103semidirect
258. #1931C2×C103semidirect
259. C4×#101C2×C103semidirect
260. C103#25315direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31382
C103×#30782
C2×#460×C1032
C103×#29622
C103×#20632
C103×#20462
C103×#19772
C103×#19652
C103×#19502
C103×#19312
C4×#101×C1032
#25315103