Finite Group Databasebeta

← C101×#13362 #38795513

Subgroups — C101×#13362 #38795513

Order 25856.

670 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3202C211yesmaximal, characteristic, complemented
2C101×#3022C212yesmaximal
3C101×#2123C212yesmaximal, complemented
4C101×#1794C211yesmaximal, characteristic
5C101×#1392C211yesmaximal, characteristic, complemented
6#585×C101C2211yescharacteristic
7C2×#137×C101—22no—
8#536×C101C2212yes—
9#485×C101—22no—
10#470×C101—21no—
11#467×C101—21no—
12#456×C101—24no—
13#455×C101—24no—
14#451×C101—22no—
15#421×C101—22no—
16#421×C101—21no—
17#416×C101—21no—
18#413×C101C2212yes—
19#410×C101C2211yescharacteristic
20#408×C101C2211yescharacteristic
21#352×C101—24no—
222−1+4×C101—41no—
232−1+4×C101D412yes—
24H(5,𝔽2)×C101—22no—
25H(5,𝔽2)×C101—21no—
26H(5,𝔽2)×C101—41no—
27C2×#41×C101—21no—
28C2×#41×C101—22no—
29C2×#41×C101—42no—
30C2×#41×C101C2311yescharacteristic
31C22×Q8×C101D412yes—
32#137×C101—28no—
33#137×C101—44no—
34C2×Q16×C101—21no—
35C2×Q16×C101—21no—
36C2×Q16×C101—42no—
37C2×SD16×C101—42no—
38C2×M16×C101—22no—
39C2×M16×C101D411yescharacteristic
40C22×C8×C101D411yescharacteristic
41C4⋊Q8×C101—22no—
42#124×C101—22no—
43#123×C101—22no—
44#123×C101—22no—
45C22⋊Q8×C101—22no—
46C22⋊Q8×C101—22no—
47#117×C101—21no—
48#117×C101D412yes—
49#107×C101—21no—
50#106×C101—21no—
51#104×C101—28no—
52#104×C101—42no—
53#103×C101—22no—
54#103×C101—22no—
55#103×C101—41no—
56#102×C101—41no—
57#101×C101—22no—
58#100×C101D414yes—
59#99×C101—22no—
60C22⋊C8×C101—22no—
61#41×C101—22no—
62#41×C101—24no—
63#41×C101—24no—
64#41×C101—22no—
65#41×C101—41no—
66#41×C101—41no—
67#41×C101—41no—
68#41×C101—42no—
69#41×C101—42no—
70#41×C101—44no—
71#41×C101—42no—
72#41×C101—41no—
73C2×Q8×C101—21no—
74C2×Q8×C101—22no—
75C2×Q8×C101—22no—
76C2×Q8×C101—22no—
77C2×Q8×C101—42no—
78C2×Q8×C101—42no—
79C2×Q8×C101—42no—
80C2×Q8×C101C2×D411yescharacteristic
81C2×D4×C101—21no—
82C2×D4×C101—22no—
83C2×D4×C101—44no—
84C2×D4×C101—42no—
85C2×D4×C101—42no—
86C2×D4×C101—41no—
87C2×D4×C101C2×D412yes—
88C2×D4×C101#4111yescharacteristic
89C22×C4×C101—22no—
90C22×C4×C101—41no—
91C22×C4×C101—42no—
92C22×C4×C101C2×D412yes—
93C22×C4×C101C2×D411yescharacteristic
94Q16×C101—48no—
95Q16×C101—81no—
96Q16×C101—81no—
97SD16×C101—48no—
98M16×C101—24no—
99M16×C101—42no—
100M16×C101—41no—
101C2×C8×C101—21no—
102C2×C8×C101—21no—
103C2×C8×C101—42no—
104C2×C8×C101—41no—
105C4⋊C4×C101—22no—
106C4⋊C4×C101—41no—
107C4⋊C4×C101—42no—
108C4⋊C4×C101—42no—
109C22⋊C4×C101—22no—
110C22⋊C4×C101—42no—
111C22⋊C4×C101—42no—
112C22⋊C4×C101—41no—
113C42×C101—22no—
114C42×C101—41no—
115C23×C101—42no—
116C23×C101—41no—
117C23×C101#12112yes—
118C23×C101#12711yescharacteristic
119Q8×C101—24no—
120Q8×C101—22no—
121Q8×C101—41no—
122Q8×C101—44no—
123Q8×C101—41no—
124Q8×C101—42no—
125Q8×C101—42no—
126D4×C101—24no—
127D4×C101—22no—
128D4×C101—42no—
129D4×C101—41no—
130D4×C101—44no—
131D4×C101—42no—
132D4×C101—42no—
133D4×C101—41no—
134C2×C4×C101—21no—
135C2×C4×C101—21no—
136C2×C4×C101—22no—
137C2×C4×C101—22no—
138C2×C4×C101—44no—
139C2×C4×C101—42no—
140C2×C4×C101—42no—
141C2×C4×C101—41no—
142C2×C4×C101—42no—
143C2×C4×C101—42no—
144C2×C4×C101—42no—
145C2×C4×C101—82no—
146C2×C4×C101—81no—
147C2×C4×C101#12012yes—
148C2×C4×C101#12011yescharacteristic
149C2×C4×C101#12111yescharacteristic
150C8×C101—44no—
151C8×C101—41no—
152C8×C101—41no—
153C22×C101—22no—
154C22×C101—21no—
155C22×C101—42no—
156C22×C101—41no—
157C22×C101—42no—
158C22×C101—161no—
159C22×C101—162no—
160C22×C101#39211yescharacteristic
161C4×C101—22no—
162C4×C101—21no—
163C4×C101—42no—
164C4×C101—82no—
165C4×C101—82no—
166C4×C101—161no—
167C4×C101B(4,𝔽2)11yescharacteristic
168C4×C101B(4,𝔽2)11yescharacteristic
169#13362C10111yesmaximal, characteristic, direct product factor, Sylow
170C2×C101—21no—
171C2×C101—41no—
172C2×C101—42no—
173C2×C101—82no—
174C2×C101#202111yescharacteristic
175#3202C2×C10111yescharacteristic, complemented
176#3022C2×C10112yes—
177#2123C2×C10112yescomplemented
178#1794C2×C10111yescharacteristic
179#1392C2×C10111yescharacteristic, complemented
180C101#1336211yescharacteristic, direct product factor, Sylow
181#585C22×C10111yescharacteristic
182C2×#137—22no—
183#536C22×C10112yes—
184#485—22no—
185#470—21no—
186#467—21no—
187#456—24no—
188#455—24no—
189#451—22no—
190#421—22no—
191#421—21no—
192#416—21no—
193#413C22×C10112yes—
194#410C22×C10111yescharacteristic
195#408C22×C10111yescharacteristic
196#352—24no—
1972−1+4—41no—
1982−1+4D4×C10112yes—
199H(5,𝔽2)—22no—
200H(5,𝔽2)—21no—
201H(5,𝔽2)—41no—
202C2×#41—22no—
203C2×#41—21no—
204C2×#41—42no—
205C2×#41C23×C10111yescharacteristic
206C22×Q8D4×C10112yes—
207#137—28no—
208#137—44no—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16—42no—
212C2×SD16—42no—
213C2×M16—22no—
214C2×M16D4×C10111yescharacteristic
215C22×C8D4×C10111yescharacteristic
216C4⋊Q8—22no—
217#124—22no—
218#123—22no—
219#123—22no—
220C22⋊Q8—22no—
221C22⋊Q8—22no—
222#117—21no—
223#117D4×C10112yes—
224#107—21no—
225#106—21no—
226#104—28no—
227#104—42no—
228#103—22no—
229#103—22no—
230#103—41no—
231#102—41no—
232#101—22no—
233#100D4×C10114yes—
234#99—22no—
235C22⋊C8—22no—
236#41—22no—
237#41—24no—
238#41—24no—
239#41—22no—
240#41—41no—
241#41—41no—
242#41—41no—
243#41—42no—
244#41—42no—
245#41—44no—
246#41—42no—
247#41—41no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8C2×D4×C10111yescharacteristic
256C2×D4—21no—
257C2×D4—22no—
258C2×D4—44no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—41no—
262C2×D4C2×D4×C10112yes—
263C2×D4#41×C10111yescharacteristic
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4C2×D4×C10112yes—
268C22×C4C2×D4×C10111yescharacteristic
269Q16—48no—
270Q16—81no—
271Q16—81no—
272SD16—48no—
273M16—24no—
274M16—42no—
275M16—41no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—42no—
279C2×C8—41no—
280C4⋊C4—22no—
281C4⋊C4—41no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C22⋊C4—22no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C42—22no—
289C42—41no—
290C23—42no—
291C23—41no—
292C23#121×C10112yes—
293C23#127×C10111yescharacteristic
294Q8—24no—
295Q8—22no—
296Q8—41no—
297Q8—44no—
298Q8—41no—
299Q8—42no—
300Q8—42no—
301D4—24no—
302D4—22no—
303D4—42no—
304D4—41no—
305D4—44no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—82no—
321C2×C4—81no—
322C2×C4#120×C10112yes—
323C2×C4#120×C10111yescharacteristic
324C2×C4#121×C10111yescharacteristic
325C8—44no—
326C8—41no—
327C8—41no—
328C22—22no—
329C22—21no—
330C22—42no—
331C22—41no—
332C22—42no—
333C22—161no—
334C22—162no—
335C22#392×C10111yescharacteristic
336C4—22no—
337C4—21no—
338C4—42no—
339C4—82no—
340C4—82no—
341C4—161no—
342C4B(4,𝔽2)×C10111yescharacteristic
343C4B(4,𝔽2)×C10111yescharacteristic
344C2—21no—
345C2—41no—
346C2—42no—
347C2—82no—
348C2C101×#202111yescharacteristic
subgroupG/H
center, socleC2×C101#2021
commutator, Frattini, cosocleC2×#41C23×C101
prime radical#585×C101C22
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C2×C4×C101 ◁ C2×#41×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3202C2semidirect
3. C101×#2123C2semidirect
5. C101×#1392C2semidirect
169. #13362C101direct (N × H)
175. #3202C2×C101semidirect
177. #2123C2×C101semidirect
179. #1392C2×C101semidirect
180. C101#13362direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32022
C101×#30222
C101×#21232
C101×#17942
C101×#13922
#13362101