Finite Group Databasebeta

← C103×#11266 #39916541

Subgroups — C103×#11266 #39916541

Order 26368.

560 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#430×C103C211yesmaximal, characteristic
2C2×#344×C103C211yesmaximal, characteristic
3C2×#344×C103C211yesmaximal, characteristic
4C103×#1742C211yesmaximal, characteristic
5C103×#1738C211yesmaximal, characteristic
6C103×#1738C211yesmaximal, characteristic
7C2×#338×C103C211yesmaximal, characteristic
8C22×M16×C103C2211yescharacteristic
9C22×M16×C103C2211yescharacteristic
10C22×M16×C103C2211yescharacteristic
11C22×M16×C103C2211yescharacteristic
12C22×M16×C103C2211yescharacteristic
13C22×M16×C103C2211yescharacteristic
14C2×#117×C103C2211yescharacteristic
15#430×C103—22no—
16#430×C103—22no—
17C2×#108×C103—22no—
18#344×C103—22no—
19#344×C103—22no—
20#343×C103—22no—
21#341×C103—22no—
22#341×C103C414yescomplemented
23#338×C103—22no—
24C23×C4×C103C2311yescharacteristic
25C2×M16×C103—21no—
26C2×M16×C103—21no—
27C2×M16×C103—21no—
28C2×M16×C103—21no—
29C2×M16×C103—21no—
30C2×M16×C103—21no—
31C2×M16×C103—21no—
32C2×M16×C103—21no—
33C2×M16×C103—21no—
34C2×M16×C103—21no—
35C2×M16×C103—21no—
36C2×M16×C103—21no—
37C2×M16×C103—21no—
38C2×M16×C103—21no—
39C2×M16×C103—21no—
40C2×M16×C103—21no—
41C2×M16×C103—21no—
42C2×M16×C103—21no—
43C2×M16×C103—21no—
44C2×M16×C103—21no—
45C2×M16×C103—21no—
46C2×M16×C103—21no—
47C2×M16×C103—21no—
48C2×M16×C103—21no—
49C2×M16×C103—21no—
50C2×M16×C103—21no—
51C2×M16×C103—21no—
52C2×M16×C103—21no—
53C2×M16×C103—21no—
54C2×M16×C103C2×C412yes—
55C2×M16×C103C2×C412yes—
56C2×M16×C103D412yes—
57C2×M16×C103D412yes—
58C2×M16×C103D412yes—
59C2×M16×C103D412yes—
60C2×M16×C103Q812yes—
61C22×C8×C103—21no—
62C22×C8×C103—21no—
63C22×C8×C103—21no—
64C22×C8×C103—21no—
65C22×C8×C103—21no—
66C22×C8×C103C2×C412yes—
67#117×C103—21no—
68#117×C103—21no—
69#117×C103—21no—
70#117×C103—21no—
71C2×C4⋊C4×C103—21no—
72C2×C22⋊C4×C103Q812yes—
73C2×C42×C103—21no—
74#108×C103—28no—
75C24×C103C2×Q811yescharacteristic
76C22×C4×C103—22no—
77C22×C4×C103C22×C411yescharacteristic
78C22×C4×C103C2×D411yescharacteristic
79C22×C4×C103C2×D411yescharacteristic
80C22×C4×C103C2×D411yescharacteristic
81C22×C4×C103C2×D411yescharacteristic
82C22×C4×C103C2×Q811yescharacteristic
83C22×C4×C103#4111yescharacteristic
84C22×C4×C103#4111yescharacteristic
85C22×C4×C103#4111yescharacteristic
86C22×C4×C103#4111yescharacteristic
87C22×C4×C103#4111yescharacteristic
88C22×C4×C103#4111yescharacteristic
89C22×C4×C103#4111yescharacteristic
90C22×C4×C103#4111yescharacteristic
91M16×C103—22no—
92M16×C103—22no—
93M16×C103—22no—
94M16×C103—22no—
95M16×C103—22no—
96M16×C103—22no—
97M16×C103—22no—
98M16×C103—22no—
99M16×C103—22no—
100M16×C103—22no—
101M16×C103—22no—
102M16×C103—41no—
103M16×C103—41no—
104M16×C103—41no—
105M16×C103—41no—
106M16×C103—41no—
107M16×C103—41no—
108M16×C103—41no—
109M16×C103—41no—
110M16×C103—41no—
111M16×C103—41no—
112M16×C103—41no—
113M16×C103—41no—
114M16×C103C4⋊C414yes—
115C2×C8×C103—22no—
116C2×C8×C103—22no—
117C2×C8×C103—22no—
118C2×C8×C103—22no—
119C2×C8×C103—22no—
120C2×C8×C103—22no—
121C2×C8×C103—22no—
122C2×C8×C103—22no—
123C2×C8×C103—22no—
124C2×C8×C103—22no—
125C2×C8×C103—41no—
126C2×C8×C103—41no—
127C2×C8×C103—41no—
128C2×C8×C103—41no—
129C2×C8×C103—41no—
130C2×C8×C103—41no—
131C2×C8×C103—41no—
132C2×C8×C103—41no—
133C4⋊C4×C103—41no—
134C4⋊C4×C103—41no—
135C22⋊C4×C103—22no—
136C22⋊C4×C103—22no—
137C42×C103—41no—
138C42×C103—41no—
139C23×C103—81no—
140C23×C103C4×Q811yescharacteristic
141C23×C103C22⋊Q811yescharacteristic
142C23×C103C22⋊Q811yescharacteristic
143C23×C103C22⋊Q811yescharacteristic
144C23×C103#12511yescharacteristic
145C23×C103#12511yescharacteristic
146C23×C103C4⋊Q811yescharacteristic
147C2×C4×C103—42no—
148C2×C4×C103—82no—
149C2×C4×C103C2×C4⋊C411yescharacteristic
150C2×C4×C103#11711yescharacteristic
151C2×C4×C103#11711yescharacteristic
152C2×C4×C103C4×D411yescharacteristic
153C2×C4×C103C4×D411yescharacteristic
154C2×C4×C103C4×D411yescharacteristic
155C2×C4×C103#12011yescharacteristic
156C2×C4×C103#12111yescharacteristic
157C2×C4×C103#12111yescharacteristic
158C2×C4×C103#12111yescharacteristic
159C2×C4×C103C22⋊Q811yescharacteristic
160C2×C4×C103C22⋊Q811yescharacteristic
161C2×C4×C103#12311yescharacteristic
162C2×C4×C103#12311yescharacteristic
163C2×C4×C103#12311yescharacteristic
164C2×C4×C103#12311yescharacteristic
165C2×C4×C103#12311yescharacteristic
166C2×C4×C103#12411yescharacteristic
167C2×C4×C103#12411yescharacteristic
168C2×C4×C103#12411yescharacteristic
169C2×C4×C103#12411yescharacteristic
170C2×C4×C103#12511yescharacteristic
171C2×C4×C103#12511yescharacteristic
172C2×C4×C103#12511yescharacteristic
173C2×C4×C103#12611yescharacteristic
174C2×C4×C103#12611yescharacteristic
175C2×C4×C103#12611yescharacteristic
176C2×C4×C103#12611yescharacteristic
177C8×C103—24no—
178C8×C103—42no—
179C8×C103—42no—
180C8×C103—42no—
181C8×C103—42no—
182C8×C103—42no—
183C22×C103—41no—
184C22×C103—41no—
185C22×C103—41no—
186C22×C103—41no—
187C22×C103—41no—
188C22×C103—41no—
189C22×C103—41no—
190C22×C103#38711yescharacteristic
191C22×C103#38711yescharacteristic
192C22×C103#38911yescharacteristic
193C22×C103#39311yescharacteristic
194C22×C103#39811yescharacteristic
195C22×C103#39811yescharacteristic
196C22×C103#40011yescharacteristic
197C4×C103—82no—
198C4×C103#38211yescharacteristic
199C4×C103#38511yescharacteristic
200C4×C103#38811yescharacteristic
201C4×C103#38811yescharacteristic
202C4×C103#39411yescharacteristic
203C4×C103#39711yescharacteristic
204C4×C103#40011yescharacteristic
205C4×C103#40011yescharacteristic
206#11266C10311yesmaximal, characteristic, direct product factor, Sylow
207C2×C103—21no—
208C2×C103—21no—
209C2×C103—21no—
210C2×C103—21no—
211C2×C103—21no—
212C2×C103—21no—
213C2×C103—21no—
214C2×C103#144211yescharacteristic
215C2×#430C2×C10311yescharacteristic
216C2×#344C2×C10311yescharacteristic
217C2×#344C2×C10311yescharacteristic
218#1742C2×C10311yescharacteristic
219#1738C2×C10311yescharacteristic
220#1738C2×C10311yescharacteristic
221C2×#338C2×C10311yescharacteristic
222C103#1126611yescharacteristic, direct product factor, Sylow
223C22×M16C22×C10311yescharacteristic
224C22×M16C22×C10311yescharacteristic
225C22×M16C22×C10311yescharacteristic
226C22×M16C22×C10311yescharacteristic
227C22×M16C22×C10311yescharacteristic
228C22×M16C22×C10311yescharacteristic
229C2×#117C22×C10311yescharacteristic
230#430—22no—
231#430—22no—
232C2×#108—22no—
233#344—22no—
234#344—22no—
235#343—22no—
236#341—22no—
237#341C4×C10314yescomplemented
238#338—22no—
239C23×C4C23×C10311yescharacteristic
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16C2×C4×C10312yes—
270C2×M16C2×C4×C10312yes—
271C2×M16D4×C10312yes—
272C2×M16D4×C10312yes—
273C2×M16D4×C10312yes—
274C2×M16D4×C10312yes—
275C2×M16Q8×C10312yes—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8C2×C4×C10312yes—
282#117—21no—
283#117—21no—
284#117—21no—
285#117—21no—
286C2×C4⋊C4—21no—
287C2×C22⋊C4Q8×C10312yes—
288C2×C42—21no—
289#108—28no—
290C24C2×Q8×C10311yescharacteristic
291C22×C4—22no—
292C22×C4C22×C4×C10311yescharacteristic
293C22×C4C2×D4×C10311yescharacteristic
294C22×C4C2×D4×C10311yescharacteristic
295C22×C4C2×D4×C10311yescharacteristic
296C22×C4C2×D4×C10311yescharacteristic
297C22×C4C2×Q8×C10311yescharacteristic
298C22×C4#41×C10311yescharacteristic
299C22×C4#41×C10311yescharacteristic
300C22×C4#41×C10311yescharacteristic
301C22×C4#41×C10311yescharacteristic
302C22×C4#41×C10311yescharacteristic
303C22×C4#41×C10311yescharacteristic
304C22×C4#41×C10311yescharacteristic
305C22×C4#41×C10311yescharacteristic
306M16—22no—
307M16—22no—
308M16—22no—
309M16—22no—
310M16—22no—
311M16—22no—
312M16—22no—
313M16—22no—
314M16—22no—
315M16—22no—
316M16—22no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—41no—
327M16—41no—
328M16—41no—
329M16C4⋊C4×C10314yes—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C42—41no—
353C42—41no—
354C23—81no—
355C23C4×Q8×C10311yescharacteristic
356C23C22⋊Q8×C10311yescharacteristic
357C23C22⋊Q8×C10311yescharacteristic
358C23C22⋊Q8×C10311yescharacteristic
359C23#125×C10311yescharacteristic
360C23#125×C10311yescharacteristic
361C23C4⋊Q8×C10311yescharacteristic
362C2×C4—42no—
363C2×C4—82no—
364C2×C4C2×C4⋊C4×C10311yescharacteristic
365C2×C4#117×C10311yescharacteristic
366C2×C4#117×C10311yescharacteristic
367C2×C4C4×D4×C10311yescharacteristic
368C2×C4C4×D4×C10311yescharacteristic
369C2×C4C4×D4×C10311yescharacteristic
370C2×C4#120×C10311yescharacteristic
371C2×C4#121×C10311yescharacteristic
372C2×C4#121×C10311yescharacteristic
373C2×C4#121×C10311yescharacteristic
374C2×C4C22⋊Q8×C10311yescharacteristic
375C2×C4C22⋊Q8×C10311yescharacteristic
376C2×C4#123×C10311yescharacteristic
377C2×C4#123×C10311yescharacteristic
378C2×C4#123×C10311yescharacteristic
379C2×C4#123×C10311yescharacteristic
380C2×C4#123×C10311yescharacteristic
381C2×C4#124×C10311yescharacteristic
382C2×C4#124×C10311yescharacteristic
383C2×C4#124×C10311yescharacteristic
384C2×C4#124×C10311yescharacteristic
385C2×C4#125×C10311yescharacteristic
386C2×C4#125×C10311yescharacteristic
387C2×C4#125×C10311yescharacteristic
388C2×C4#126×C10311yescharacteristic
389C2×C4#126×C10311yescharacteristic
390C2×C4#126×C10311yescharacteristic
391C2×C4#126×C10311yescharacteristic
392C8—24no—
393C8—42no—
394C8—42no—
395C8—42no—
396C8—42no—
397C8—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22#387×C10311yescharacteristic
406C22#387×C10311yescharacteristic
407C22#389×C10311yescharacteristic
408C22#393×C10311yescharacteristic
409C22#398×C10311yescharacteristic
410C22#398×C10311yescharacteristic
411C22#400×C10311yescharacteristic
412C4—82no—
413C4#382×C10311yescharacteristic
414C4#385×C10311yescharacteristic
415C4#388×C10311yescharacteristic
416C4#388×C10311yescharacteristic
417C4#394×C10311yescharacteristic
418C4#397×C10311yescharacteristic
419C4#400×C10311yescharacteristic
420C4#400×C10311yescharacteristic
421C2—21no—
422C2—21no—
423C2—21no—
424C2—21no—
425C2—21no—
426C2—21no—
427C2—21no—
428C2C103×#144211yescharacteristic
subgroupG/H
centerC4×C103#388
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
socleC2×C103#1442
prime radicalC24×C103C2×Q8
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
22. #341×C103C4semidirect
206. #11266C103direct (N × H)
222. C103#11266direct (N × H)
237. #341C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#430×C1032
C2×#344×C1032
C103×#17422
C103×#17382
C2×#338×C1032
#11266103