Finite Group Databasebeta

← C103×#19275 #39924550

Subgroups — C103×#19275 #39924550

Order 26368.

670 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#487×C103C211yesmaximal, characteristic, complemented
2C103×#3079C211yesmaximal, characteristic
3C103×#3039C211yesmaximal, characteristic
4C8×#41×C103C211yesmaximal, characteristic
5C103×#1680C214yesmaximal, complemented
6C103×#1679C214yesmaximal, complemented
7C103×#1566C211yesmaximal, characteristic, complemented
8C103×#1549C211yesmaximal, characteristic, complemented
9C103×#1546C211yesmaximal, characteristic, complemented
10C2×#137×C103—21no—
11C2×C4⋊Q8×C103C2211yescharacteristic
12C2×C4⋊Q8×C103C2211yescharacteristic
13C4×#41×C103C2211yescharacteristic
14#487×C103—21no—
15#487×C103—21no—
16#487×C103C2214yes—
17#477×C103—21no—
18#476×C103—21no—
19#475×C103C2212yes—
20#474×C103C2212yes—
21#462×C103—21no—
22#462×C103C2212yes—
23#461×C103—21no—
24#461×C103C2212yes—
25C8×Q8×C103C2212yes—
26C8×D4×C103—22no—
27C8×D4×C103C2212yes—
28#431×C103—21no—
29#431×C103C2211yescharacteristic
30#428×C103—21no—
31#423×C103C2211yescharacteristic
32#423×C103C2211yescharacteristic
33#419×C103—21no—
34#417×C103—21no—
35C2×#103×C103—22no—
36C2×C4×C8×C103—21no—
37C2×C4×C8×C103C2211yescharacteristic
38#334×C103C2214yes—
39#332×C103C2214yes—
40#332×C103C2214yes—
41C2×#41×C103D411yescharacteristic
42C22×Q8×C103—21no—
43C22×Q8×C103—21no—
44#137×C103—44no—
45C2×Q16×C103—22no—
46C2×SD16×C103—22no—
47C2×M16×C103—21no—
48C2×M16×C103—21no—
49C22×C8×C103—22no—
50C22×C8×C103D412yes—
51C4⋊Q8×C103—21no—
52C4⋊Q8×C103—21no—
53C4⋊Q8×C103—21no—
54C4⋊Q8×C103—21no—
55C4⋊Q8×C103—21no—
56C4⋊Q8×C103—21no—
57C4⋊Q8×C103C2312yes—
58C4⋊Q8×C103C2312yes—
59C4×Q8×C103D411yescharacteristic
60C4×Q8×C103C2311yescharacteristic
61C4×D4×C103—21no—
62C4×D4×C103—21no—
63C4×D4×C103D411yescharacteristic
64C4×D4×C103C2311yescharacteristic
65#117×C103—21no—
66#117×C103D411yescharacteristic
67C2×C4⋊C4×C103—21no—
68C2×C4⋊C4×C103—21no—
69C2×C4⋊C4×C103—21no—
70C2×C4⋊C4×C103—21no—
71C2×C42×C103—21no—
72C2×C42×C103C2311yescharacteristic
73#107×C103—22no—
74#106×C103—22no—
75C4⋊C8×C103—22no—
76C4⋊C8×C103—21no—
77C4⋊C8×C103—21no—
78C4⋊C8×C103C2312yes—
79C4⋊C8×C103C2312yes—
80C4⋊C8×C103C2312yes—
81#103×C103—22no—
82#103×C103—24no—
83#103×C103—24no—
84#103×C103—22no—
85#103×C103—22no—
86#102×C103—22no—
87C22⋊C8×C103—21no—
88C22⋊C8×C103—22no—
89C4×C8×C103—22no—
90C4×C8×C103—21no—
91C4×C8×C103D411yescharacteristic
92C4×C8×C103D411yescharacteristic
93C4×C8×C103C2312yes—
94#41×C103—22no—
95#41×C103SD1614yes—
96C2×Q8×C103—22no—
97C2×Q8×C103—22no—
98C2×Q8×C103—44no—
99C2×Q8×C103—41no—
100C2×Q8×C103—41no—
101C2×Q8×C103—42no—
102C2×Q8×C103—42no—
103C2×Q8×C103C2×D411yescharacteristic
104C2×D4×C103—21no—
105C2×D4×C103C2×D411yescharacteristic
106C22×C4×C103—21no—
107C22×C4×C103—21no—
108C22×C4×C103—21no—
109C22×C4×C103—41no—
110C22×C4×C103—41no—
111C22×C4×C103C2×D411yescharacteristic
112C22×C4×C103C2×D411yescharacteristic
113C22×C4×C103#4111yescharacteristic
114Q16×C103—44no—
115SD16×C103—44no—
116M16×C103—42no—
117M16×C103—42no—
118C2×C8×C103—22no—
119C2×C8×C103—22no—
120C2×C8×C103—22no—
121C2×C8×C103—42no—
122C2×C8×C103—44no—
123C2×C8×C103C2×D412yes—
124C2×C8×C103C2×D412yes—
125C4⋊C4×C103—21no—
126C4⋊C4×C103—21no—
127C4⋊C4×C103—22no—
128C4⋊C4×C103—22no—
129C4⋊C4×C103—22no—
130C4⋊C4×C103—22no—
131C4⋊C4×C103—41no—
132C4⋊C4×C103—41no—
133C4⋊C4×C103—41no—
134C4⋊C4×C103—41no—
135C4⋊C4×C103C2×D411yescharacteristic
136C4⋊C4×C103C2×D411yescharacteristic
137C22⋊C4×C103—21no—
138C22⋊C4×C103—21no—
139C22⋊C4×C103—21no—
140C42×C103—21no—
141C42×C103—21no—
142C42×C103—21no—
143C42×C103C2×D411yescharacteristic
144C42×C103C2×D411yescharacteristic
145C42×C103#4111yescharacteristic
146C42×C103C2411yescharacteristic
147C23×C103—21no—
148C23×C103#12111yescharacteristic
149Q8×C103—21no—
150Q8×C103—42no—
151Q8×C103—42no—
152Q8×C103—44no—
153Q8×C103—82no—
154Q8×C103—82no—
155Q8×C103C2×SD1612yes—
156D4×C103—24no—
157D4×C103—21no—
158D4×C103C2×SD1612yes—
159C2×C4×C103—21no—
160C2×C4×C103—22no—
161C2×C4×C103—24no—
162C2×C4×C103—22no—
163C2×C4×C103—21no—
164C2×C4×C103—21no—
165C2×C4×C103—42no—
166C2×C4×C103—42no—
167C2×C4×C103—42no—
168C2×C4×C103—42no—
169C2×C4×C103—82no—
170C2×C4×C103—82no—
171C2×C4×C103#12111yescharacteristic
172C2×C4×C103#12111yescharacteristic
173C2×C4×C103#12111yescharacteristic
174C2×C4×C103C2×SD1612yes—
175C2×C4×C103#13512yes—
176C2×C4×C103C22×D411yescharacteristic
177C2×C4×C103C22×D411yescharacteristic
178C2×C4×C103C2×#4111yescharacteristic
179C8×C103—22no—
180C8×C103—22no—
181C8×C103—42no—
182C8×C103—42no—
183C8×C103—42no—
184C22×C103—21no—
185C22×C103—21no—
186C22×C103—22no—
187C22×C103—41no—
188C22×C103—41no—
189C22×C103#46512yes—
190C22×C103C2×#12111yescharacteristic
191C4×C103—21no—
192C4×C103—22no—
193C4×C103—21no—
194C4×C103—41no—
195C4×C103—41no—
196C4×C103—82no—
197C4×C103—82no—
198C4×C103#46512yes—
199C4×C103#47312yes—
200C4×C103C22×SD1611yescharacteristic
201C4×C103C2×#13511yescharacteristic
202C4×C103#57512yes—
203#19275C10311yesmaximal, characteristic, direct product factor, Sylow
204C2×C103—22no—
205C2×C103—42no—
206C2×C103#304011yescharacteristic
207C2×C103C2×#46511yescharacteristic
208C2×C103C2×#47311yescharacteristic
209C2×#487C2×C10311yescharacteristic, complemented
210#3079C2×C10311yescharacteristic
211#3039C2×C10311yescharacteristic
212C8×#41C2×C10311yescharacteristic
213#1680C2×C10314yescomplemented
214#1679C2×C10314yescomplemented
215#1566C2×C10311yescharacteristic, complemented
216#1549C2×C10311yescharacteristic, complemented
217#1546C2×C10311yescharacteristic, complemented
218C103#1927511yescharacteristic, direct product factor, Sylow
219C2×#137—21no—
220C2×C4⋊Q8C22×C10311yescharacteristic
221C2×C4⋊Q8C22×C10311yescharacteristic
222C4×#41C22×C10311yescharacteristic
223#487—21no—
224#487—21no—
225#487C22×C10314yes—
226#477—21no—
227#476—21no—
228#475C22×C10312yes—
229#474C22×C10312yes—
230#462—21no—
231#462C22×C10312yes—
232#461—21no—
233#461C22×C10312yes—
234C8×Q8C22×C10312yes—
235C8×D4—22no—
236C8×D4C22×C10312yes—
237#431—21no—
238#431C22×C10311yescharacteristic
239#428—21no—
240#423C22×C10311yescharacteristic
241#423C22×C10311yescharacteristic
242#419—21no—
243#417—21no—
244C2×#103—22no—
245C2×C4×C8—21no—
246C2×C4×C8C22×C10311yescharacteristic
247#334C22×C10314yes—
248#332C22×C10314yes—
249#332C22×C10314yes—
250C2×#41D4×C10311yescharacteristic
251C22×Q8—21no—
252C22×Q8—21no—
253#137—44no—
254C2×Q16—22no—
255C2×SD16—22no—
256C2×M16—21no—
257C2×M16—21no—
258C22×C8—22no—
259C22×C8D4×C10312yes—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8C23×C10312yes—
267C4⋊Q8C23×C10312yes—
268C4×Q8D4×C10311yescharacteristic
269C4×Q8C23×C10311yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4D4×C10311yescharacteristic
273C4×D4C23×C10311yescharacteristic
274#117—21no—
275#117D4×C10311yescharacteristic
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C42—21no—
281C2×C42C23×C10311yescharacteristic
282#107—22no—
283#106—22no—
284C4⋊C8—22no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8C23×C10312yes—
288C4⋊C8C23×C10312yes—
289C4⋊C8C23×C10312yes—
290#103—22no—
291#103—24no—
292#103—24no—
293#103—22no—
294#103—22no—
295#102—22no—
296C22⋊C8—21no—
297C22⋊C8—22no—
298C4×C8—22no—
299C4×C8—21no—
300C4×C8D4×C10311yescharacteristic
301C4×C8D4×C10311yescharacteristic
302C4×C8C23×C10312yes—
303#41—22no—
304#41SD16×C10314yes—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—44no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—42no—
311C2×Q8—42no—
312C2×Q8C2×D4×C10311yescharacteristic
313C2×D4—21no—
314C2×D4C2×D4×C10311yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×D4×C10311yescharacteristic
321C22×C4C2×D4×C10311yescharacteristic
322C22×C4#41×C10311yescharacteristic
323Q16—44no—
324SD16—44no—
325M16—42no—
326M16—42no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—42no—
331C2×C8—44no—
332C2×C8C2×D4×C10312yes—
333C2×C8C2×D4×C10312yes—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4C2×D4×C10311yescharacteristic
345C4⋊C4C2×D4×C10311yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C42—21no—
350C42—21no—
351C42—21no—
352C42C2×D4×C10311yescharacteristic
353C42C2×D4×C10311yescharacteristic
354C42#41×C10311yescharacteristic
355C42C24×C10311yescharacteristic
356C23—21no—
357C23#121×C10311yescharacteristic
358Q8—21no—
359Q8—42no—
360Q8—42no—
361Q8—44no—
362Q8—82no—
363Q8—82no—
364Q8C2×SD16×C10312yes—
365D4—24no—
366D4—21no—
367D4C2×SD16×C10312yes—
368C2×C4—21no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4#121×C10311yescharacteristic
381C2×C4#121×C10311yescharacteristic
382C2×C4#121×C10311yescharacteristic
383C2×C4C2×SD16×C10312yes—
384C2×C4#135×C10312yes—
385C2×C4C22×D4×C10311yescharacteristic
386C2×C4C22×D4×C10311yescharacteristic
387C2×C4C2×#41×C10311yescharacteristic
388C8—22no—
389C8—22no—
390C8—42no—
391C8—42no—
392C8—42no—
393C22—21no—
394C22—21no—
395C22—22no—
396C22—41no—
397C22—41no—
398C22#465×C10312yes—
399C22C2×#121×C10311yescharacteristic
400C4—21no—
401C4—22no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—82no—
406C4—82no—
407C4#465×C10312yes—
408C4#473×C10312yes—
409C4C22×SD16×C10311yescharacteristic
410C4C2×#135×C10311yescharacteristic
411C4#575×C10312yes—
412C2—22no—
413C2—42no—
414C2C103×#304011yescharacteristic
415C2C2×#465×C10311yescharacteristic
416C2C2×#473×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC2×#41×C103D4
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. C2×#487×C103C2semidirect
5. C103×#1680C2semidirect
6. C103×#1679C2semidirect
7. C103×#1566C2semidirect
8. C103×#1549C2semidirect
9. C103×#1546C2semidirect
203. #19275C103direct (N × H)
209. C2×#487C2×C103semidirect
213. #1680C2×C103semidirect
214. #1679C2×C103semidirect
215. #1566C2×C103semidirect
216. #1549C2×C103semidirect
217. #1546C2×C103semidirect
218. C103#19275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#487×C1032
C103×#30792
C103×#30392
C8×#41×C1032
C103×#16802
C103×#16792
C103×#15662
C103×#15492
C103×#15462
#19275103