Finite Group Databasebeta

← C103×#8921 #39914196

Subgroups — C103×#8921 #39914196

Order 26368.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2366C211yesmaximal, characteristic
2C103×#1957C211yesmaximal, characteristic
3C103×#1948C211yesmaximal, characteristic, complemented
4C103×#1947C211yesmaximal, characteristic, complemented
5C2×#331×C103C211yesmaximal, characteristic
6C103×#1279C211yesmaximal, characteristic, complemented
7C103×#1279C211yesmaximal, characteristic, complemented
8C2×#127×C103C2211yescharacteristic
9C2×C4×D4×C103—21no—
10C2×C4×D4×C103—21no—
11C2×#107×C103—21no—
12C2×#106×C103—21no—
13C2×C4⋊C8×C103C2211yescharacteristic
14C2×C4⋊C8×C103C2211yescharacteristic
15C2×#102×C103—22no—
16C2×C4×C8×C103C2211yescharacteristic
17#390×C103—21no—
18#390×C103—21no—
19#386×C103—22no—
20#384×C103C2211yescharacteristic
21C4×C4⋊C4×C103C2211yescharacteristic
22C4×C4⋊C4×C103C2211yescharacteristic
23#340×C103—21no—
24#340×C103—21no—
25#331×C103C414yescomplemented
26C22×D4×C103—21no—
27C22×D4×C103—21no—
28C22×D4×C103D412yes—
29C23×C4×C103—22no—
30C22×C8×C103—21no—
31C22×C8×C103—21no—
32C22×C8×C103—21no—
33#127×C103—21no—
34#127×C103—21no—
35#127×C103C2×C412yes—
36#127×C103Q812yes—
37C4×D4×C103—42no—
38C4×D4×C103—42no—
39C4×D4×C103—42no—
40C4×D4×C103—42no—
41C2×C4⋊C4×C103—21no—
42C2×C4⋊C4×C103—21no—
43C2×C4⋊C4×C103—21no—
44C2×C4⋊C4×C103D411yescharacteristic
45C2×C4⋊C4×C103D411yescharacteristic
46C2×C4⋊C4×C103D411yescharacteristic
47C2×C4⋊C4×C103D411yescharacteristic
48C2×C22⋊C4×C103—22no—
49C2×C22⋊C4×C103—22no—
50C2×C22⋊C4×C103—22no—
51C2×C42×C103—21no—
52C2×C42×C103—21no—
53C2×C42×C103C2311yescharacteristic
54#107×C103—42no—
55#106×C103—42no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103C2×C412yescomplemented
59C4⋊C8×C103C2×C412yescomplemented
60#102×C103—44no—
61C4×C8×C103—21no—
62C4×C8×C103—21no—
63#95×C103—21no—
64#95×C103—21no—
65C24×C103—22no—
66C2×D4×C103—22no—
67C2×D4×C103—22no—
68C2×D4×C103—22no—
69C2×D4×C103—22no—
70C2×D4×C103—22no—
71C2×D4×C103—42no—
72C2×D4×C103—42no—
73C2×D4×C103—41no—
74C2×D4×C103—41no—
75C2×D4×C103—41no—
76C2×D4×C103—41no—
77C2×D4×C103—41no—
78C2×D4×C103—41no—
79C2×D4×C103—41no—
80C2×D4×C103—41no—
81C2×D4×C103C4⋊C414yes—
82C22×C4×C103—21no—
83C22×C4×C103—21no—
84C22×C4×C103—21no—
85C22×C4×C103—21no—
86C22×C4×C103—44no—
87C22×C4×C103—44no—
88C22×C4×C103—41no—
89C22×C4×C103—82no—
90C22×C4×C103C2×D411yescharacteristic
91C22×C4×C103C2×D411yescharacteristic
92C22×C4×C103C2×D411yescharacteristic
93C2×C8×C103—22no—
94C2×C8×C103—22no—
95C2×C8×C103—22no—
96C2×C8×C103—41no—
97C2×C8×C103—41no—
98C2×C8×C103—41no—
99C2×C8×C103—41no—
100C2×C8×C103—41no—
101C2×C8×C103—41no—
102C4⋊C4×C103—21no—
103C4⋊C4×C103—21no—
104C4⋊C4×C103—21no—
105C4⋊C4×C103—21no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103—21no—
108C4⋊C4×C103—42no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103—41no—
111C4⋊C4×C103—41no—
112C4⋊C4×C103—41no—
113C4⋊C4×C103D812yes—
114C4⋊C4×C103SD1612yes—
115C22⋊C4×C103—44no—
116C22⋊C4×C103—44no—
117C22⋊C4×C103—82no—
118C42×C103—41no—
119C42×C103—41no—
120C42×C103—41no—
121C42×C103—41no—
122C42×C103C22×C411yescharacteristic
123C42×C103C2×Q811yescharacteristic
124C42×C103#4111yescharacteristic
125C42×C103#4111yescharacteristic
126C23×C103—24no—
127C23×C103—42no—
128C23×C103—42no—
129C23×C103—42no—
130C23×C103—42no—
131C23×C103—42no—
132C23×C103—42no—
133C23×C103#12011yescharacteristic
134D4×C103—44no—
135D4×C103—42no—
136D4×C103—42no—
137D4×C103—42no—
138D4×C103—42no—
139D4×C103—42no—
140D4×C103—42no—
141D4×C103—42no—
142D4×C103—42no—
143D4×C103—82no—
144C2×C4×C103—21no—
145C2×C4×C103—21no—
146C2×C4×C103—22no—
147C2×C4×C103—22no—
148C2×C4×C103—41no—
149C2×C4×C103—41no—
150C2×C4×C103—41no—
151C2×C4×C103—41no—
152C2×C4×C103—41no—
153C2×C4×C103—41no—
154C2×C4×C103—41no—
155C2×C4×C103—41no—
156C2×C4×C103—41no—
157C2×C4×C103—41no—
158C2×C4×C103—88no—
159C2×C4×C103—81no—
160C2×C4×C103—81no—
161C2×C4×C103—81no—
162C2×C4×C103C2×C4⋊C411yescharacteristic
163C2×C4×C103C4×D411yescharacteristic
164C2×C4×C103C4×D411yescharacteristic
165C2×C4×C103C22⋊Q811yescharacteristic
166C2×C4×C103C22⋊Q811yescharacteristic
167C2×C4×C103#12311yescharacteristic
168C2×C4×C103C2×D811yescharacteristic
169C2×C4×C103C2×SD1611yescharacteristic
170C2×C4×C103#13511yescharacteristic
171C2×C4×C103#13511yescharacteristic
172C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C103#13711yescharacteristic
176C8×C103—42no—
177C8×C103—42no—
178C8×C103—42no—
179C22×C103—44no—
180C22×C103—44no—
181C22×C103—44no—
182C22×C103—82no—
183C22×C103—82no—
184C22×C103—82no—
185C22×C103—82no—
186C22×C103#38511yescharacteristic
187C22×C103#44711yescharacteristic
188C22×C103#44911yescharacteristic
189C22×C103#45011yescharacteristic
190C22×C103#45211yescharacteristic
191C22×C103#45311yescharacteristic
192C22×C103#45511yescharacteristic
193C4×C103—21no—
194C4×C103—21no—
195C4×C103—42no—
196C4×C103—42no—
197C4×C103—81no—
198C4×C103—81no—
199C4×C103—161no—
200C4×C103C4×D811yescharacteristic
201C4×C103C4×SD1611yescharacteristic
202C4×C103#44011yescharacteristic
203C4×C103#44211yescharacteristic
204C4×C103#47411yescharacteristic
205C4×C103#47611yescharacteristic
206C4×C103#47811yescharacteristic
207C4×C103#47811yescharacteristic
208#8921C10311yesmaximal, characteristic, direct product factor, Sylow
209C2×C103—84no—
210C2×C103#162111yescharacteristic
211C2×C103#163111yescharacteristic
212C2×C103#163911yescharacteristic
213C2×C103#164011yescharacteristic
214C2×C103#185611yescharacteristic
215C2×C103#186211yescharacteristic
216C2×C103#186411yescharacteristic
217#2366C2×C10311yescharacteristic
218#1957C2×C10311yescharacteristic
219#1948C2×C10311yescharacteristic, complemented
220#1947C2×C10311yescharacteristic, complemented
221C2×#331C2×C10311yescharacteristic
222#1279C2×C10311yescharacteristic, complemented
223#1279C2×C10311yescharacteristic, complemented
224C103#892111yescharacteristic, direct product factor, Sylow
225C2×#127C22×C10311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×#107—21no—
229C2×#106—21no—
230C2×C4⋊C8C22×C10311yescharacteristic
231C2×C4⋊C8C22×C10311yescharacteristic
232C2×#102—22no—
233C2×C4×C8C22×C10311yescharacteristic
234#390—21no—
235#390—21no—
236#386—22no—
237#384C22×C10311yescharacteristic
238C4×C4⋊C4C22×C10311yescharacteristic
239C4×C4⋊C4C22×C10311yescharacteristic
240#340—21no—
241#340—21no—
242#331C4×C10314yescomplemented
243C22×D4—21no—
244C22×D4—21no—
245C22×D4D4×C10312yes—
246C23×C4—22no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250#127—21no—
251#127—21no—
252#127C2×C4×C10312yes—
253#127Q8×C10312yes—
254C4×D4—42no—
255C4×D4—42no—
256C4×D4—42no—
257C4×D4—42no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C10311yescharacteristic
262C2×C4⋊C4D4×C10311yescharacteristic
263C2×C4⋊C4D4×C10311yescharacteristic
264C2×C4⋊C4D4×C10311yescharacteristic
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42C23×C10311yescharacteristic
271#107—42no—
272#106—42no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8C2×C4×C10312yescomplemented
276C4⋊C8C2×C4×C10312yescomplemented
277#102—44no—
278C4×C8—21no—
279C4×C8—21no—
280#95—21no—
281#95—21no—
282C24—22no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4C4⋊C4×C10314yes—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—44no—
304C22×C4—44no—
305C22×C4—41no—
306C22×C4—82no—
307C22×C4C2×D4×C10311yescharacteristic
308C22×C4C2×D4×C10311yescharacteristic
309C22×C4C2×D4×C10311yescharacteristic
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—42no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4D8×C10312yes—
331C4⋊C4SD16×C10312yes—
332C22⋊C4—44no—
333C22⋊C4—44no—
334C22⋊C4—82no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42—41no—
339C42C22×C4×C10311yescharacteristic
340C42C2×Q8×C10311yescharacteristic
341C42#41×C10311yescharacteristic
342C42#41×C10311yescharacteristic
343C23—24no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23#120×C10311yescharacteristic
351D4—44no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—42no—
360D4—82no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—88no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4C2×C4⋊C4×C10311yescharacteristic
380C2×C4C4×D4×C10311yescharacteristic
381C2×C4C4×D4×C10311yescharacteristic
382C2×C4C22⋊Q8×C10311yescharacteristic
383C2×C4C22⋊Q8×C10311yescharacteristic
384C2×C4#123×C10311yescharacteristic
385C2×C4C2×D8×C10311yescharacteristic
386C2×C4C2×SD16×C10311yescharacteristic
387C2×C4#135×C10311yescharacteristic
388C2×C4#135×C10311yescharacteristic
389C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
390C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
391C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
392C2×C4#137×C10311yescharacteristic
393C8—42no—
394C8—42no—
395C8—42no—
396C22—44no—
397C22—44no—
398C22—44no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—82no—
403C22#385×C10311yescharacteristic
404C22#447×C10311yescharacteristic
405C22#449×C10311yescharacteristic
406C22#450×C10311yescharacteristic
407C22#452×C10311yescharacteristic
408C22#453×C10311yescharacteristic
409C22#455×C10311yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—42no—
414C4—81no—
415C4—81no—
416C4—161no—
417C4C4×D8×C10311yescharacteristic
418C4C4×SD16×C10311yescharacteristic
419C4#440×C10311yescharacteristic
420C4#442×C10311yescharacteristic
421C4#474×C10311yescharacteristic
422C4#476×C10311yescharacteristic
423C4#478×C10311yescharacteristic
424C4#478×C10311yescharacteristic
425C2—84no—
426C2C103×#162111yescharacteristic
427C2C103×#163111yescharacteristic
428C2C103×#163911yescharacteristic
429C2C103×#164011yescharacteristic
430C2C103×#185611yescharacteristic
431C2C103×#186211yescharacteristic
432C2C103×#186411yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC2×#127×C103C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#1948C2semidirect
4. C103×#1947C2semidirect
6. C103×#1279C2semidirect
7. C103×#1279C2semidirect
25. #331×C103C4semidirect
58. C4⋊C8×C103C2×C4semidirect
59. C4⋊C8×C103C2×C4semidirect
208. #8921C103direct (N × H)
219. #1948C2×C103semidirect
220. #1947C2×C103semidirect
222. #1279C2×C103semidirect
223. #1279C2×C103semidirect
224. C103#8921direct (N × H)
242. #331C4×C103semidirect
275. C4⋊C8C2×C4×C103semidirect
276. C4⋊C8C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#23662
C103×#19572
C103×#19482
C103×#19472
C2×#331×C1032
C103×#12792
#8921103