Finite Group Databasebeta

← C103×#33666 #39938941

Subgroups — C103×#33666 #39938941

Order 26368.

596 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3169C211yesmaximal, characteristic, complemented
2C4×#135×C103C211yesmaximal, characteristic, complemented
3C103×#2234C212yesmaximal, complemented
4C103×#2227C211yesmaximal, characteristic, complemented
5C103×#2226C211yesmaximal, characteristic, complemented
6C103×#2207C211yesmaximal, characteristic, complemented
7C103×#2206C211yesmaximal, characteristic, complemented
8C103×#2186C212yesmaximal, complemented
9C4×SD32×C103C212yesmaximal, complemented
10C4×D16×C103C212yesmaximal, complemented
11C103×#2162C211yesmaximal, characteristic, complemented
12C2×#135×C103C2211yescharacteristic
13#532×C103—21no—
14C4×#41×C103—21no—
15C2×SD32×C103C2212yes—
16C2×D16×C103C2212yes—
17#500×C103C2211yescharacteristic
18#493×C103C2211yescharacteristic
19#486×C103—21no—
20#466×C103—21no—
21#466×C103C2212yes—
22C4×Q16×C103C2211yescharacteristic
23C4×Q16×C103C2211yescharacteristic
24C4×SD16×C103—21no—
25C4×SD16×C103—21no—
26C4×D8×C103—21no—
27C4×D8×C103C2211yescharacteristic
28C4×D8×C103C2212yes—
29C4×D8×C103C2211yescharacteristic
30#427×C103C2211yescharacteristic
31#416×C103—21no—
32C2×C4×C8×C103C2211yescharacteristic
33#367×C103C2212yes—
34#366×C103C2212yes—
35C4⋊C16×C103C2211yescharacteristic
36C4⋊C16×C103C2211yescharacteristic
37#358×C103C2212yes—
38#357×C103C2212yes—
39#357×C103C2212yes—
40#357×C103C2212yes—
41C22⋊C16×C103C2212yes—
42C4×C16×C103C2212yes—
43C2×#41×C103—21no—
44C2×#41×C103—41no—
45#135×C103—22no—
46#135×C103—22no—
47C2×Q16×C103C2311yescharacteristic
48C2×SD16×C103—21no—
49C2×D8×C103—21no—
50C2×D8×C103C2312yes—
51C2×D8×C103C2311yescharacteristic
52C22×C8×C103D411yescharacteristic
53C22×C8×C103C2311yescharacteristic
54C4⋊Q8×C103—21no—
55#127×C103—21no—
56#124×C103—41no—
57#121×C103—22no—
58#121×C103—41no—
59C4×Q8×C103—21no—
60C4×Q8×C103—21no—
61C4×D4×C103—22no—
62C4×D4×C103—21no—
63C4×D4×C103—21no—
64C4×D4×C103—41no—
65C4×D4×C103—41no—
66C4×D4×C103—41no—
67#117×C103—21no—
68#117×C103—41no—
69C2×C42×C103—41no—
70C2×C42×C103D411yescharacteristic
71SD32×C103—24no—
72D16×C103—24no—
73C2×C16×C103C2312yes—
74C2×C16×C103C2312yes—
75#107×C103—21no—
76#107×C103C2311yescharacteristic
77#107×C103C2311yescharacteristic
78#107×C103C2312yes—
79#106×C103—21no—
80#103×C103—21no—
81#103×C103—21no—
82#102×C103—21no—
83#102×C103—21no—
84#102×C103—22no—
85#102×C103—22no—
86C4×C8×C103D411yescharacteristic
87C4×C8×C103D411yescharacteristic
88C4×C8×C103C2311yescharacteristic
89C4×C8×C103C2311yescharacteristic
90#41×C103—24no—
91#41×C103—42no—
92#41×C103—84no—
93C2×Q8×C103—21no—
94C2×Q8×C103—41no—
95C2×D4×C103—21no—
96C2×D4×C103—22no—
97C2×D4×C103—41no—
98C2×D4×C103—42no—
99C2×D4×C103—41no—
100C2×D4×C103—41no—
101C22×C4×C103—41no—
102C22×C4×C103—41no—
103C22×C4×C103—41no—
104C22×C4×C103—42no—
105C22×C4×C103D811yescharacteristic
106C22×C4×C103D811yescharacteristic
107C22×C4×C103C2×D411yescharacteristic
108Q16×C103—21no—
109Q16×C103#4112yescomplemented
110SD16×C103—24no—
111D8×C103—21no—
112D8×C103—22no—
113D8×C103—22no—
114D8×C103—42no—
115D8×C103#4112yescomplemented
116C2×C8×C103—21no—
117C2×C8×C103—21no—
118C2×C8×C103—41no—
119C2×C8×C103C2×D411yescharacteristic
120C2×C8×C103C2×D411yescharacteristic
121C2×C8×C103C2×D411yescharacteristic
122C2×C8×C103C2411yescharacteristic
123C4⋊C4×C103—22no—
124C4⋊C4×C103—21no—
125C4⋊C4×C103—21no—
126C4⋊C4×C103—41no—
127C4⋊C4×C103—41no—
128C4⋊C4×C103—41no—
129C22⋊C4×C103—41no—
130C22⋊C4×C103—41no—
131C22⋊C4×C103—41no—
132C22⋊C4×C103—42no—
133C22⋊C4×C103—42no—
134C42×C103—41no—
135C42×C103—41no—
136C42×C103—41no—
137C42×C103D811yescharacteristic
138C42×C103D811yescharacteristic
139C42×C103C2×D411yescharacteristic
140C42×C103C2×D411yescharacteristic
141C16×C103—22no—
142C16×C103—22no—
143C23×C103—41no—
144C23×C103—42no—
145C23×C103C2×D811yescharacteristic
146Q8×C103—22no—
147Q8×C103—41no—
148Q8×C103—82no—
149D4×C103—22no—
150D4×C103—44no—
151D4×C103—42no—
152D4×C103—41no—
153D4×C103—42no—
154D4×C103—82no—
155D4×C103—84no—
156D4×C103—82no—
157C2×C4×C103—21no—
158C2×C4×C103—21no—
159C2×C4×C103—22no—
160C2×C4×C103—22no—
161C2×C4×C103—44no—
162C2×C4×C103—41no—
163C2×C4×C103—41no—
164C2×C4×C103—41no—
165C2×C4×C103—42no—
166C2×C4×C103—82no—
167C2×C4×C103—82no—
168C2×C4×C103—84no—
169C2×C4×C103C2×D811yescharacteristic
170C2×C4×C103C2×D811yescharacteristic
171C2×C4×C103C2×D811yescharacteristic
172C2×C4×C103C2×D811yescharacteristic
173C2×C4×C103C2×D811yescharacteristic
174C2×C4×C103C22×D411yescharacteristic
175C8×C103—21no—
176C8×C103—21no—
177C8×C103—21no—
178C8×C103C2×#4111yescharacteristic
179C8×C103C2×#4111yescharacteristic
180C22×C103—21no—
181C22×C103—21no—
182C22×C103—21no—
183C22×C103—42no—
184C22×C103—81no—
185C22×C103—81no—
186C22×C103—82no—
187C22×C103—82no—
188C22×C103—82no—
189C22×C103C22×D811yescharacteristic
190C4×C103—21no—
191C4×C103—21no—
192C4×C103—21no—
193C4×C103—42no—
194C4×C103—81no—
195C4×C103—81no—
196C4×C103—82no—
197C4×C103#50812yes—
198C4×C103#50912yes—
199C4×C103#52511yescharacteristic
200C4×C103#57511yescharacteristic
201#33666C10311yesmaximal, characteristic, direct product factor, Sylow
202C2×C103—41no—
203C2×C103—82no—
204C2×C103—162no—
205C2×C103#310011yescharacteristic
206C2×C103C2×#50811yescharacteristic
207C2×C103C2×#50911yescharacteristic
208#3169C2×C10311yescharacteristic, complemented
209C4×#135C2×C10311yescharacteristic, complemented
210#2234C2×C10312yescomplemented
211#2227C2×C10311yescharacteristic, complemented
212#2226C2×C10311yescharacteristic, complemented
213#2207C2×C10311yescharacteristic, complemented
214#2206C2×C10311yescharacteristic, complemented
215#2186C2×C10312yescomplemented
216C4×SD32C2×C10312yescomplemented
217C4×D16C2×C10312yescomplemented
218#2162C2×C10311yescharacteristic, complemented
219C103#3366611yescharacteristic, direct product factor, Sylow
220C2×#135C22×C10311yescharacteristic
221#532—21no—
222C4×#41—21no—
223C2×SD32C22×C10312yes—
224C2×D16C22×C10312yes—
225#500C22×C10311yescharacteristic
226#493C22×C10311yescharacteristic
227#486—21no—
228#466—21no—
229#466C22×C10312yes—
230C4×Q16C22×C10311yescharacteristic
231C4×Q16C22×C10311yescharacteristic
232C4×SD16—21no—
233C4×SD16—21no—
234C4×D8—21no—
235C4×D8C22×C10312yes—
236C4×D8C22×C10311yescharacteristic
237C4×D8C22×C10311yescharacteristic
238#427C22×C10311yescharacteristic
239#416—21no—
240C2×C4×C8C22×C10311yescharacteristic
241#367C22×C10312yes—
242#366C22×C10312yes—
243C4⋊C16C22×C10311yescharacteristic
244C4⋊C16C22×C10311yescharacteristic
245#358C22×C10312yes—
246#357C22×C10312yes—
247#357C22×C10312yes—
248#357C22×C10312yes—
249C22⋊C16C22×C10312yes—
250C4×C16C22×C10312yes—
251C2×#41—21no—
252C2×#41—41no—
253#135—22no—
254#135—22no—
255C2×Q16C23×C10311yescharacteristic
256C2×SD16—21no—
257C2×D8—21no—
258C2×D8C23×C10312yes—
259C2×D8C23×C10311yescharacteristic
260C22×C8D4×C10311yescharacteristic
261C22×C8C23×C10311yescharacteristic
262C4⋊Q8—21no—
263#127—21no—
264#124—41no—
265#121—22no—
266#121—41no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—22no—
272C4×D4—41no—
273C4×D4—41no—
274C4×D4—41no—
275#117—21no—
276#117—41no—
277C2×C42—41no—
278C2×C42D4×C10311yescharacteristic
279SD32—24no—
280D16—24no—
281C2×C16C23×C10312yes—
282C2×C16C23×C10312yes—
283#107—21no—
284#107C23×C10311yescharacteristic
285#107C23×C10311yescharacteristic
286#107C23×C10312yes—
287#106—21no—
288#103—21no—
289#103—21no—
290#102—21no—
291#102—21no—
292#102—22no—
293#102—22no—
294C4×C8D4×C10311yescharacteristic
295C4×C8D4×C10311yescharacteristic
296C4×C8C23×C10311yescharacteristic
297C4×C8C23×C10311yescharacteristic
298#41—24no—
299#41—42no—
300#41—84no—
301C2×Q8—21no—
302C2×Q8—41no—
303C2×D4—21no—
304C2×D4—22no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4D8×C10311yescharacteristic
314C22×C4D8×C10311yescharacteristic
315C22×C4C2×D4×C10311yescharacteristic
316Q16—21no—
317Q16#41×C10312yescomplemented
318SD16—24no—
319D8—21no—
320D8—22no—
321D8—22no—
322D8—42no—
323D8#41×C10312yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—41no—
327C2×C8C2×D4×C10311yescharacteristic
328C2×C8C2×D4×C10311yescharacteristic
329C2×C8C2×D4×C10311yescharacteristic
330C2×C8C24×C10311yescharacteristic
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C42—41no—
343C42—41no—
344C42—41no—
345C42D8×C10311yescharacteristic
346C42D8×C10311yescharacteristic
347C42C2×D4×C10311yescharacteristic
348C42C2×D4×C10311yescharacteristic
349C16—22no—
350C16—22no—
351C23—41no—
352C23—42no—
353C23C2×D8×C10311yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—82no—
357D4—22no—
358D4—44no—
359D4—42no—
360D4—41no—
361D4—42no—
362D4—82no—
363D4—84no—
364D4—82no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—44no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—84no—
376C2×C4—82no—
377C2×C4C2×D8×C10311yescharacteristic
378C2×C4C2×D8×C10311yescharacteristic
379C2×C4C2×D8×C10311yescharacteristic
380C2×C4C2×D8×C10311yescharacteristic
381C2×C4C2×D8×C10311yescharacteristic
382C2×C4C22×D4×C10311yescharacteristic
383C8—21no—
384C8—21no—
385C8—21no—
386C8C2×#41×C10311yescharacteristic
387C8C2×#41×C10311yescharacteristic
388C22—21no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—81no—
393C22—81no—
394C22—82no—
395C22—82no—
396C22—82no—
397C22C22×D8×C10311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—81no—
403C4—82no—
404C4—81no—
405C4#508×C10312yes—
406C4#509×C10312yes—
407C4#525×C10311yescharacteristic
408C4#575×C10311yescharacteristic
409C2—41no—
410C2—82no—
411C2—162no—
412C2C103×#310011yescharacteristic
413C2C2×#508×C10311yescharacteristic
414C2C2×#509×C10311yescharacteristic
subgroupG/H
centerC2×C4×C103C2×D8
commutator, Frattini, cosocleC2×C8C24×C103
socleC22×C103C22×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3169C2semidirect
2. C4×#135×C103C2semidirect
3. C103×#2234C2semidirect
4. C103×#2227C2semidirect
5. C103×#2226C2semidirect
6. C103×#2207C2semidirect
7. C103×#2206C2semidirect
8. C103×#2186C2semidirect
9. C4×SD32×C103C2semidirect
10. C4×D16×C103C2semidirect
11. C103×#2162C2semidirect
109. Q16×C103#41semidirect
115. D8×C103#41semidirect
201. #33666C103direct (N × H)
208. #3169C2×C103semidirect
209. C4×#135C2×C103semidirect
210. #2234C2×C103semidirect
211. #2227C2×C103semidirect
212. #2226C2×C103semidirect
213. #2207C2×C103semidirect
214. #2206C2×C103semidirect
215. #2186C2×C103semidirect
216. C4×SD32C2×C103semidirect
217. C4×D16C2×C103semidirect
218. #2162C2×C103semidirect
219. C103#33666direct (N × H)
317. Q16#41×C103semidirect
323. D8#41×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31692
C4×#135×C1032
C103×#22342
C103×#22272
C103×#22262
C103×#22072
C103×#22062
C103×#21862
C4×SD32×C1032
C4×D16×C1032
C103×#21622
#33666103