Finite Group Databasebeta

← C103×#8894 #39914169

Subgroups — C103×#8894 #39914169

Order 26368.

602 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊C4×C103C211yesmaximal, characteristic
2C103×#1948C211yesmaximal, characteristic, complemented
3C103×#1834C211yesmaximal, characteristic, complemented
4C103×#1802C211yesmaximal, characteristic
5C2×D4⋊C8×C103C211yesmaximal, characteristic
6C103×#1296C211yesmaximal, characteristic, complemented
7C103×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D4×C103—21no—
9C2×C4×D4×C103C2211yescharacteristic
10C22×C4⋊C4×C103—21no—
11C2×#106×C103—21no—
12C2×C4⋊C8×C103C2211yescharacteristic
13C2×C4⋊C8×C103C2211yescharacteristic
14C2×#102×C103—21no—
15C2×C4×C8×C103C2211yescharacteristic
16#389×C103—21no—
17#385×C103—22no—
18#384×C103C2211yescharacteristic
19#384×C103C2211yescharacteristic
20#380×C103—21no—
21C4×C4⋊C4×C103C2211yescharacteristic
22#340×C103—21no—
23#340×C103—21no—
24#340×C103—22no—
25D4⋊C8×C103C414yescomplemented
26C22×D4×C103D411yescharacteristic
27C23×C4×C103—21no—
28C23×C4×C103—22no—
29C22×C8×C103—21no—
30C22×C8×C103—21no—
31C22×C8×C103—21no—
32C4×D4×C103—21no—
33C4×D4×C103—21no—
34C4×D4×C103—42no—
35C4×D4×C103—42no—
36C4×D4×C103C2×C412yes—
37C4×D4×C103Q812yes—
38C2×C4⋊C4×C103—22no—
39C2×C4⋊C4×C103—21no—
40C2×C4⋊C4×C103—21no—
41C2×C4⋊C4×C103—21no—
42C2×C4⋊C4×C103—21no—
43C2×C4⋊C4×C103—21no—
44C2×C4⋊C4×C103—42no—
45C2×C4⋊C4×C103—42no—
46C2×C4⋊C4×C103D411yescharacteristic
47C2×C4⋊C4×C103D411yescharacteristic
48C2×C4⋊C4×C103D411yescharacteristic
49C2×C4⋊C4×C103D412yes—
50C2×C22⋊C4×C103—21no—
51C2×C22⋊C4×C103—22no—
52C2×C42×C103—21no—
53C2×C42×C103C2311yescharacteristic
54#106×C103—42no—
55C4⋊C8×C103—21no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103C2×C412yescomplemented
59#102×C103—42no—
60C4×C8×C103—21no—
61C4×C8×C103C2×C412yescomplemented
62#95×C103—22no—
63#95×C103—21no—
64C24×C103—21no—
65C2×D4×C103—21no—
66C2×D4×C103—21no—
67C2×D4×C103—21no—
68C2×D4×C103C4⋊C412yes—
69C2×D4×C103SD1612yes—
70C2×D4×C103SD1612yes—
71C22×C4×C103—21no—
72C22×C4×C103—21no—
73C22×C4×C103—22no—
74C22×C4×C103—22no—
75C22×C4×C103—21no—
76C22×C4×C103—22no—
77C22×C4×C103—44no—
78C22×C4×C103—41no—
79C22×C4×C103—41no—
80C22×C4×C103—41no—
81C22×C4×C103—41no—
82C22×C4×C103—44no—
83C22×C4×C103—41no—
84C22×C4×C103—82no—
85C22×C4×C103C2×D411yescharacteristic
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103C2×D411yescharacteristic
88C2×C8×C103—22no—
89C2×C8×C103—22no—
90C2×C8×C103—41no—
91C2×C8×C103—41no—
92C2×C8×C103—41no—
93C2×C8×C103—41no—
94C2×C8×C103—41no—
95C2×C8×C103—41no—
96C2×C8×C103—41no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103—21no—
100C4⋊C4×C103—21no—
101C4⋊C4×C103—42no—
102C4⋊C4×C103—44no—
103C4⋊C4×C103—42no—
104C4⋊C4×C103—41no—
105C4⋊C4×C103—41no—
106C4⋊C4×C103—41no—
107C4⋊C4×C103—41no—
108C4⋊C4×C103—41no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103—41no—
111C4⋊C4×C103—41no—
112C4⋊C4×C103C4⋊C412yes—
113C4⋊C4×C103D812yes—
114C22⋊C4×C103—22no—
115C22⋊C4×C103—22no—
116C22⋊C4×C103—44no—
117C42×C103—41no—
118C42×C103—41no—
119C42×C103C22×C411yescharacteristic
120C42×C103C2×Q811yescharacteristic
121C42×C103#4111yescharacteristic
122C42×C103#4111yescharacteristic
123C23×C103—22no—
124C23×C103—22no—
125C23×C103—22no—
126C23×C103—41no—
127C23×C103—41no—
128C23×C103—41no—
129C23×C103—41no—
130C23×C103#12011yescharacteristic
131D4×C103—22no—
132D4×C103—22no—
133D4×C103—22no—
134D4×C103#10614yescomplemented
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103—22no—
138C2×C4×C103—22no—
139C2×C4×C103—41no—
140C2×C4×C103—41no—
141C2×C4×C103—41no—
142C2×C4×C103—41no—
143C2×C4×C103—42no—
144C2×C4×C103—42no—
145C2×C4×C103—42no—
146C2×C4×C103—42no—
147C2×C4×C103—42no—
148C2×C4×C103—41no—
149C2×C4×C103—42no—
150C2×C4×C103—41no—
151C2×C4×C103—41no—
152C2×C4×C103—42no—
153C2×C4×C103—88no—
154C2×C4×C103—81no—
155C2×C4×C103—81no—
156C2×C4×C103—81no—
157C2×C4×C103C2×C4⋊C411yescharacteristic
158C2×C4×C103C4×D411yescharacteristic
159C2×C4×C103C4×D411yescharacteristic
160C2×C4×C103C22⋊Q811yescharacteristic
161C2×C4×C103C22⋊Q811yescharacteristic
162C2×C4×C103#12311yescharacteristic
163C2×C4×C103C2×D811yescharacteristic
164C2×C4×C103C2×SD1611yescharacteristic
165C2×C4×C103C2×SD1611yescharacteristic
166C2×C4×C103#13511yescharacteristic
167C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C103#13711yescharacteristic
170C2×C4×C103#13711yescharacteristic
171C8×C103—42no—
172C8×C103—42no—
173C8×C103—81no—
174C22×C103—24no—
175C22×C103—42no—
176C22×C103—42no—
177C22×C103—42no—
178C22×C103—42no—
179C22×C103—42no—
180C22×C103—42no—
181C22×C103#38511yescharacteristic
182C22×C103#44711yescharacteristic
183C22×C103#44811yescharacteristic
184C22×C103#45011yescharacteristic
185C22×C103#45211yescharacteristic
186C22×C103#45411yescharacteristic
187C22×C103#45511yescharacteristic
188C4×C103—21no—
189C4×C103—21no—
190C4×C103—42no—
191C4×C103—42no—
192C4×C103—81no—
193C4×C103—82no—
194C4×C103—161no—
195C4×C103C2×#10611yescharacteristic
196C4×C103#42811yescharacteristic
197C4×C103C4×D811yescharacteristic
198C4×C103#44011yescharacteristic
199C4×C103#47411yescharacteristic
200C4×C103#47811yescharacteristic
201C4×C103#48111yescharacteristic
202C4×C103#48311yescharacteristic
203#8894C10311yesmaximal, characteristic, direct product factor, Sylow
204C2×C103—44no—
205C2×C103#162711yescharacteristic
206C2×C103#163511yescharacteristic
207C2×C103#163911yescharacteristic
208C2×C103#164311yescharacteristic
209C2×C103#185311yescharacteristic
210C2×C103#186011yescharacteristic
211C2×C103#186211yescharacteristic
212D4×C4⋊C4C2×C10311yescharacteristic
213#1948C2×C10311yescharacteristic, complemented
214#1834C2×C10311yescharacteristic, complemented
215#1802C2×C10311yescharacteristic
216C2×D4⋊C8C2×C10311yescharacteristic
217#1296C2×C10311yescharacteristic, complemented
218#1279C2×C10311yescharacteristic, complemented
219C103#889411yescharacteristic, direct product factor, Sylow
220C2×C4×D4—21no—
221C2×C4×D4C22×C10311yescharacteristic
222C22×C4⋊C4—21no—
223C2×#106—21no—
224C2×C4⋊C8C22×C10311yescharacteristic
225C2×C4⋊C8C22×C10311yescharacteristic
226C2×#102—21no—
227C2×C4×C8C22×C10311yescharacteristic
228#389—21no—
229#385—22no—
230#384C22×C10311yescharacteristic
231#384C22×C10311yescharacteristic
232#380—21no—
233C4×C4⋊C4C22×C10311yescharacteristic
234#340—21no—
235#340—22no—
236#340—21no—
237D4⋊C8C4×C10314yescomplemented
238C22×D4D4×C10311yescharacteristic
239C23×C4—21no—
240C23×C4—22no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—42no—
247C4×D4—42no—
248C4×D4C2×C4×C10312yes—
249C4×D4Q8×C10312yes—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4D4×C10311yescharacteristic
259C2×C4⋊C4D4×C10311yescharacteristic
260C2×C4⋊C4D4×C10311yescharacteristic
261C2×C4⋊C4D4×C10312yes—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C42—21no—
265C2×C42C23×C10311yescharacteristic
266#106—42no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8C2×C4×C10312yescomplemented
271#102—42no—
272C4×C8—21no—
273C4×C8C2×C4×C10312yescomplemented
274#95—22no—
275#95—21no—
276C24—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4C4⋊C4×C10312yes—
281C2×D4SD16×C10312yes—
282C2×D4SD16×C10312yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—44no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—44no—
295C22×C4—41no—
296C22×C4—82no—
297C22×C4C2×D4×C10311yescharacteristic
298C22×C4C2×D4×C10311yescharacteristic
299C22×C4C2×D4×C10311yescharacteristic
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—42no—
314C4⋊C4—44no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4C4⋊C4×C10312yes—
325C4⋊C4D8×C10312yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—44no—
329C42—41no—
330C42—41no—
331C42C22×C4×C10311yescharacteristic
332C42C2×Q8×C10311yescharacteristic
333C42#41×C10311yescharacteristic
334C42#41×C10311yescharacteristic
335C23—22no—
336C23—22no—
337C23—22no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23#120×C10311yescharacteristic
343D4—22no—
344D4—22no—
345D4—22no—
346D4#106×C10314yescomplemented
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—88no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4C2×C4⋊C4×C10311yescharacteristic
370C2×C4C4×D4×C10311yescharacteristic
371C2×C4C4×D4×C10311yescharacteristic
372C2×C4C22⋊Q8×C10311yescharacteristic
373C2×C4C22⋊Q8×C10311yescharacteristic
374C2×C4#123×C10311yescharacteristic
375C2×C4C2×D8×C10311yescharacteristic
376C2×C4C2×SD16×C10311yescharacteristic
377C2×C4C2×SD16×C10311yescharacteristic
378C2×C4#135×C10311yescharacteristic
379C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
380C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
381C2×C4#137×C10311yescharacteristic
382C2×C4#137×C10311yescharacteristic
383C8—42no—
384C8—42no—
385C8—81no—
386C22—24no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22#385×C10311yescharacteristic
394C22#447×C10311yescharacteristic
395C22#448×C10311yescharacteristic
396C22#450×C10311yescharacteristic
397C22#452×C10311yescharacteristic
398C22#454×C10311yescharacteristic
399C22#455×C10311yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—82no—
406C4—161no—
407C4C2×#106×C10311yescharacteristic
408C4#428×C10311yescharacteristic
409C4C4×D8×C10311yescharacteristic
410C4#440×C10311yescharacteristic
411C4#474×C10311yescharacteristic
412C4#478×C10311yescharacteristic
413C4#481×C10311yescharacteristic
414C4#483×C10311yescharacteristic
415C2—44no—
416C2C103×#162711yescharacteristic
417C2C103×#163511yescharacteristic
418C2C103×#163911yescharacteristic
419C2C103×#164311yescharacteristic
420C2C103×#185311yescharacteristic
421C2C103×#186011yescharacteristic
422C2C103×#186211yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC22×D4×C103D4
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
2. C103×#1948C2semidirect
3. C103×#1834C2semidirect
6. C103×#1296C2semidirect
7. C103×#1279C2semidirect
25. D4⋊C8×C103C4semidirect
58. C4⋊C8×C103C2×C4semidirect
61. C4×C8×C103C2×C4semidirect
134. D4×C103#106semidirect
203. #8894C103direct (N × H)
213. #1948C2×C103semidirect
214. #1834C2×C103semidirect
217. #1296C2×C103semidirect
218. #1279C2×C103semidirect
219. C103#8894direct (N × H)
237. D4⋊C8C4×C103semidirect
270. C4⋊C8C2×C4×C103semidirect
273. C4×C8C2×C4×C103semidirect
346. D4#106×C103semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊C4×C1032
C103×#19482
C103×#18342
C103×#18022
C2×D4⋊C8×C1032
C103×#12962
C103×#12792
#8894103