Finite Group Databasebeta

← C101×#7745 #38789896

Subgroups — C101×#7745 #38789896

Order 25856.

612 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2804C211yesmaximal, characteristic, complemented
2C101×#2014C212yesmaximal, complemented
3C101×#2011C211yesmaximal, characteristic
4C101×#1272C212yesmaximal, complemented
5C101×#1270C211yesmaximal, characteristic, complemented
6C22×SD16×C101—22no—
7C22×D8×C101—21no—
8C2×#127×C101C2211yescharacteristic
9C2×#102×C101—21no—
10C2×#102×C101—22no—
11#400×C101—21no—
12#393×C101—22no—
13#391×C101C2212yes—
14#390×C101C2211yescharacteristic
15#386×C101—21no—
16#385×C101—22no—
17#336×C101C2211yescharacteristic
18#336×C101C2212yes—
19C22×Q8×C101D412yes—
20C22×D4×C101—21no—
21C22×D4×C101—22no—
22C22×D4×C101D411yescharacteristic
23C23×C4×C101—21no—
24C2×SD16×C101—44no—
25C2×SD16×C101—44no—
26C2×SD16×C101—44no—
27C2×D8×C101—42no—
28C2×D8×C101—42no—
29C2×D8×C101—42no—
30C22×C8×C101—21no—
31C22×C8×C101—22no—
32#127×C101—42no—
33C2×C4⋊C4×C101—21no—
34C2×C4⋊C4×C101D411yescharacteristic
35C2×C4⋊C4×C101D412yes—
36C2×C22⋊C4×C101—22no—
37C2×C22⋊C4×C101—22no—
38C2×C22⋊C4×C101—21no—
39C2×C42×C101C2311yescharacteristic
40#102×C101—42no—
41#102×C101—44no—
42#95×C101—22no—
43#95×C101—21no—
44#95×C101—22no—
45#95×C101—22no—
46C24×C101—21no—
47C24×C101—41no—
48C2×Q8×C101—22no—
49C2×Q8×C101—22no—
50C2×Q8×C101—42no—
51C2×Q8×C101—42no—
52C2×D4×C101—22no—
53C2×D4×C101—24no—
54C2×D4×C101—21no—
55C2×D4×C101—41no—
56C2×D4×C101—41no—
57C2×D4×C101—41no—
58C2×D4×C101—42no—
59C2×D4×C101—41no—
60C2×D4×C101—42no—
61C2×D4×C101—41no—
62C2×D4×C101—42no—
63C2×D4×C101—41no—
64C2×D4×C101—42no—
65C2×D4×C101—42no—
66C2×D4×C101—41no—
67C2×D4×C101SD1612yescomplemented
68C22×C4×C101—22no—
69C22×C4×C101—21no—
70C22×C4×C101—22no—
71C22×C4×C101—82no—
72C22×C4×C101—81no—
73C22×C4×C101C2×D411yescharacteristic
74C22×C4×C101C2×D412yes—
75SD16×C101—416no—
76D8×C101—48no—
77C2×C8×C101—22no—
78C2×C8×C101—24no—
79C2×C8×C101—41no—
80C2×C8×C101—42no—
81C2×C8×C101—41no—
82C2×C8×C101—42no—
83C4⋊C4×C101—41no—
84C4⋊C4×C101—42no—
85C4⋊C4×C101—81no—
86C22⋊C4×C101—42no—
87C22⋊C4×C101—42no—
88C22⋊C4×C101—82no—
89C22⋊C4×C101—81no—
90C42×C101—41no—
91C23×C101—22no—
92C23×C101—42no—
93C23×C101—42no—
94C23×C101—41no—
95C23×C101—41no—
96C23×C101—42no—
97C23×C101—81no—
98C23×C101—82no—
99C23×C101—81no—
100C23×C101—82no—
101C23×C101#12011yescharacteristic
102Q8×C101—44no—
103Q8×C101—82no—
104D4×C101—42no—
105D4×C101—42no—
106D4×C101—44no—
107D4×C101—42no—
108D4×C101—44no—
109D4×C101—81no—
110D4×C101—81no—
111D4×C101—81no—
112D4×C101—82no—
113D4×C101—82no—
114C2×C4×C101—21no—
115C2×C4×C101—22no—
116C2×C4×C101—21no—
117C2×C4×C101—22no—
118C2×C4×C101—42no—
119C2×C4×C101—42no—
120C2×C4×C101—42no—
121C2×C4×C101—42no—
122C2×C4×C101—41no—
123C2×C4×C101—42no—
124C2×C4×C101—42no—
125C2×C4×C101—42no—
126C2×C4×C101—84no—
127C2×C4×C101C2×SD1611yescharacteristic
128C2×C4×C101#13512yes—
129C2×C4×C101AGL(1,ℤ/8)12yes—
130C2×C4×C101#13711yescharacteristic
131C8×C101—42no—
132C8×C101—44no—
133C22×C101—42no—
134C22×C101—44no—
135C22×C101—82no—
136C22×C101—81no—
137C22×C101—81no—
138C22×C101—82no—
139C22×C101—84no—
140C22×C101—161no—
141C22×C101—162no—
142C22×C101—161no—
143C22×C101#44811yescharacteristic
144C22×C101#44912yes—
145C22×C101#45311yescharacteristic
146C22×C101#45312yes—
147C22×C101B(4,𝔽2)11yescharacteristic
148C4×C101—21no—
149C4×C101—21no—
150C4×C101—22no—
151C4×C101—22no—
152C4×C101—82no—
153C4×C101—81no—
154C4×C101—82no—
155#7745C10111yesmaximal, characteristic, direct product factor, Sylow
156C2×C101—82no—
157C2×C101—162no—
158C2×C101#159611yescharacteristic
159C2×C101#160012yes—
160C2×C101#162011yescharacteristic
161C2×C101#162212yes—
162C2×C101#165511yescharacteristic
163#2804C2×C10111yescharacteristic, complemented
164#2014C2×C10112yescomplemented
165#2011C2×C10111yescharacteristic
166#1272C2×C10112yescomplemented
167#1270C2×C10111yescharacteristic, complemented
168C101#774511yescharacteristic, direct product factor, Sylow
169C22×SD16—22no—
170C22×D8—21no—
171C2×#127C22×C10111yescharacteristic
172C2×#102—21no—
173C2×#102—22no—
174#400—21no—
175#393—22no—
176#391C22×C10112yes—
177#390C22×C10111yescharacteristic
178#386—21no—
179#385—22no—
180#336C22×C10111yescharacteristic
181#336C22×C10112yes—
182C22×Q8D4×C10112yes—
183C22×D4—21no—
184C22×D4—22no—
185C22×D4D4×C10111yescharacteristic
186C23×C4—21no—
187C2×SD16—44no—
188C2×SD16—44no—
189C2×SD16—44no—
190C2×D8—42no—
191C2×D8—42no—
192C2×D8—42no—
193C22×C8—21no—
194C22×C8—22no—
195#127—42no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4D4×C10112yes—
198C2×C4⋊C4D4×C10111yescharacteristic
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—21no—
202C2×C42C23×C10111yescharacteristic
203#102—42no—
204#102—44no—
205#95—22no—
206#95—21no—
207#95—22no—
208#95—22no—
209C24—21no—
210C24—41no—
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—42no—
214C2×Q8—42no—
215C2×D4—22no—
216C2×D4—24no—
217C2×D4—21no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—42no—
222C2×D4—41no—
223C2×D4—42no—
224C2×D4—41no—
225C2×D4—42no—
226C2×D4—41no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—41no—
230C2×D4SD16×C10112yescomplemented
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—82no—
235C22×C4—81no—
236C22×C4C2×D4×C10111yescharacteristic
237C22×C4C2×D4×C10112yes—
238SD16—416no—
239D8—48no—
240C2×C8—22no—
241C2×C8—24no—
242C2×C8—41no—
243C2×C8—42no—
244C2×C8—41no—
245C2×C8—42no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—81no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—82no—
252C22⋊C4—81no—
253C42—41no—
254C23—22no—
255C23—42no—
256C23—42no—
257C23—41no—
258C23—41no—
259C23—42no—
260C23—81no—
261C23—82no—
262C23—81no—
263C23—82no—
264C23#120×C10111yescharacteristic
265Q8—44no—
266Q8—82no—
267D4—42no—
268D4—42no—
269D4—44no—
270D4—42no—
271D4—44no—
272D4—81no—
273D4—81no—
274D4—81no—
275D4—82no—
276D4—82no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—84no—
290C2×C4C2×SD16×C10111yescharacteristic
291C2×C4#135×C10112yes—
292C2×C4AGL(1,ℤ/8)×C10112yes—
293C2×C4#137×C10111yescharacteristic
294C8—42no—
295C8—44no—
296C22—44no—
297C22—42no—
298C22—81no—
299C22—82no—
300C22—81no—
301C22—82no—
302C22—84no—
303C22—162no—
304C22—161no—
305C22—161no—
306C22#448×C10111yescharacteristic
307C22#449×C10112yes—
308C22#453×C10112yes—
309C22#453×C10111yescharacteristic
310C22B(4,𝔽2)×C10111yescharacteristic
311C4—21no—
312C4—21no—
313C4—22no—
314C4—22no—
315C4—82no—
316C4—82no—
317C4—81no—
318C2—82no—
319C2—162no—
320C2C101×#159611yescharacteristic
321C2C101×#160012yes—
322C2C101×#162011yescharacteristic
323C2C101×#162212yes—
324C2C101×#165511yescharacteristic
subgroupG/H
center, socleC23×C101#120
commutator, Frattini, cosocleC2×C42C23×C101
prime radicalC101×#2011C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#2804C2semidirect
2. C101×#2014C2semidirect
4. C101×#1272C2semidirect
5. C101×#1270C2semidirect
67. C2×D4×C101SD16semidirect
155. #7745C101direct (N × H)
163. #2804C2×C101semidirect
164. #2014C2×C101semidirect
166. #1272C2×C101semidirect
167. #1270C2×C101semidirect
168. C101#7745direct (N × H)
230. C2×D4SD16×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#28042
C101×#20142
C101×#20112
C101×#12722
C101×#12702
#7745101