Finite Group Databasebeta

← C101×#13421 #38795572

Subgroups — C101×#13421 #38795572

Order 25856.

496 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2724C211yesmaximal, characteristic
2C2×#352×C101C212yesmaximal
3C101×#1890C212yesmaximal
4C101×#1856C211yesmaximal, characteristic
5C101×#1393C211yesmaximal, characteristic
6C2×#123×C101C2212yes—
7#518×C101C2211yescharacteristic
8#428×C101—21no—
9C2×#100×C101C2211yescharacteristic
10C2×#99×C101C2212yes—
11#398×C101—21no—
12#397×C101—22no—
13#390×C101C2211yescharacteristic
14#389×C101—21no—
15#385×C101—22no—
16#381×C101—22no—
17#352×C101—24no—
18#342×C101—22no—
19#339×C101—21no—
20C22×D4×C101C2311yescharacteristic
21C23×C4×C101D412yes—
22C2×M16×C101—21no—
23#123×C101—22no—
24#123×C101—22no—
25#123×C101—22no—
26#123×C101—22no—
27C4×D4×C101—41no—
28C4×D4×C101—41no—
29#117×C101—21no—
30C2×C4⋊C4×C101—21no—
31C2×C4⋊C4×C101—22no—
32C2×C4⋊C4×C101—21no—
33C2×C4⋊C4×C101—21no—
34C2×C4⋊C4×C101D411yescharacteristic
35C2×C22⋊C4×C101—22no—
36C2×C22⋊C4×C101—22no—
37C2×C22⋊C4×C101—22no—
38C2×C22⋊C4×C101—22no—
39C2×C22⋊C4×C101D412yes—
40C2×C42×C101D411yescharacteristic
41#107×C101—41no—
42#106×C101—41no—
43#100×C101—21no—
44#100×C101D412yes—
45#99×C101—22no—
46#99×C101—22no—
47#95×C101—21no—
48#95×C101—22no—
49#95×C101—22no—
50#95×C101—42no—
51#95×C101—42no—
52C24×C101C2×D412yes—
53C2×D4×C101—41no—
54C2×D4×C101—41no—
55C2×D4×C101C2×D411yescharacteristic
56C2×D4×C101#4111yescharacteristic
57C2×D4×C101#4112yes—
58C22×C4×C101—21no—
59C22×C4×C101—21no—
60C22×C4×C101—22no—
61C22×C4×C101—22no—
62C22×C4×C101—22no—
63C22×C4×C101—22no—
64C22×C4×C101—22no—
65C22×C4×C101—22no—
66C22×C4×C101—42no—
67C22×C4×C101—42no—
68C22×C4×C101—42no—
69C22×C4×C101C2×D411yescharacteristic
70M16×C101—22no—
71M16×C101—41no—
72C2×C8×C101—41no—
73C4⋊C4×C101—21no—
74C4⋊C4×C101—21no—
75C4⋊C4×C101—41no—
76C4⋊C4×C101—42no—
77C4⋊C4×C101—42no—
78C4⋊C4×C101—42no—
79C4⋊C4×C101—81no—
80C4⋊C4×C101—81no—
81C22⋊C4×C101—22no—
82C22⋊C4×C101—22no—
83C22⋊C4×C101—44no—
84C22⋊C4×C101—42no—
85C22⋊C4×C101—41no—
86C22⋊C4×C101—42no—
87C22⋊C4×C101—42no—
88C22⋊C4×C101—42no—
89C22⋊C4×C101—42no—
90C42×C101—41no—
91C42×C101—41no—
92C23×C101—22no—
93C23×C101—22no—
94C23×C101—42no—
95C23×C101—42no—
96C23×C101#12011yescharacteristic
97C23×C101#12112yes—
98C23×C101#12312yes—
99D4×C101—41no—
100D4×C101—41no—
101D4×C101—42no—
102C2×C4×C101—21no—
103C2×C4×C101—21no—
104C2×C4×C101—22no—
105C2×C4×C101—41no—
106C2×C4×C101—41no—
107C2×C4×C101—42no—
108C2×C4×C101—42no—
109C2×C4×C101—42no—
110C2×C4×C101—44no—
111C2×C4×C101—42no—
112C2×C4×C101—42no—
113C2×C4×C101—41no—
114C2×C4×C101—41no—
115C2×C4×C101—41no—
116C2×C4×C101—42no—
117C2×C4×C101—42no—
118C2×C4×C101—82no—
119C2×C4×C101—82no—
120C2×C4×C101—82no—
121C2×C4×C101—82no—
122C2×C4×C101—82no—
123C2×C4×C101—82no—
124C2×C4×C101#12111yescharacteristic
125C2×C4×C101#12411yescharacteristic
126C8×C101—42no—
127C22×C101—21no—
128C22×C101—21no—
129C22×C101—22no—
130C22×C101—22no—
131C22×C101—42no—
132C22×C101—42no—
133C22×C101—42no—
134C22×C101—42no—
135C22×C101—82no—
136C22×C101#39411yescharacteristic
137C22×C101B(4,𝔽2)11yescharacteristic
138C22×C101#45811yescharacteristic
139C4×C101—21no—
140C4×C101—21no—
141C4×C101—42no—
142C4×C101—82no—
143C4×C101—81no—
144C4×C101—81no—
145C4×C101—81no—
146C4×C101—82no—
147C4×C101—162no—
148#13421C10111yesmaximal, characteristic, direct product factor, Sylow
149C2×C101—21no—
150C2×C101—21no—
151C2×C101—42no—
152C2×C101—42no—
153C2×C101#204411yescharacteristic
154C2×C101#219811yescharacteristic
155C2×C101#220111yescharacteristic
156#2724C2×C10111yescharacteristic
157C2×#352C2×C10112yes—
158#1890C2×C10112yes—
159#1856C2×C10111yescharacteristic
160#1393C2×C10111yescharacteristic
161C101#1342111yescharacteristic, direct product factor, Sylow
162C2×#123C22×C10112yes—
163#518C22×C10111yescharacteristic
164#428—21no—
165C2×#100C22×C10111yescharacteristic
166C2×#99C22×C10112yes—
167#398—21no—
168#397—22no—
169#390C22×C10111yescharacteristic
170#389—21no—
171#385—22no—
172#381—22no—
173#352—24no—
174#342—22no—
175#339—21no—
176C22×D4C23×C10111yescharacteristic
177C23×C4D4×C10112yes—
178C2×M16—21no—
179#123—22no—
180#123—22no—
181#123—22no—
182#123—22no—
183C4×D4—41no—
184C4×D4—41no—
185#117—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4D4×C10111yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4D4×C10112yes—
196C2×C42D4×C10111yescharacteristic
197#107—41no—
198#106—41no—
199#100—21no—
200#100D4×C10112yes—
201#99—22no—
202#99—22no—
203#95—22no—
204#95—22no—
205#95—21no—
206#95—42no—
207#95—42no—
208C24C2×D4×C10112yes—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4C2×D4×C10111yescharacteristic
212C2×D4#41×C10111yescharacteristic
213C2×D4#41×C10112yes—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C2×D4×C10111yescharacteristic
226M16—22no—
227M16—41no—
228C2×C8—41no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C22⋊C4—22no—
238C22⋊C4—22no—
239C22⋊C4—44no—
240C22⋊C4—42no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C42—41no—
247C42—41no—
248C23—22no—
249C23—22no—
250C23—42no—
251C23—42no—
252C23#120×C10111yescharacteristic
253C23#121×C10112yes—
254C23#123×C10112yes—
255D4—41no—
256D4—41no—
257D4—42no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4#121×C10111yescharacteristic
281C2×C4#124×C10111yescharacteristic
282C8—42no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—22no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—82no—
292C22#394×C10111yescharacteristic
293C22B(4,𝔽2)×C10111yescharacteristic
294C22#458×C10111yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—82no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—82no—
303C4—162no—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2C101×#204411yescharacteristic
309C2C101×#219811yescharacteristic
310C2C101×#220111yescharacteristic
subgroupG/H
center, socleC22×C101B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C101
prime radicalC22×D4×C101C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C101 ◁ C22×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
148. #13421C101direct (N × H)
161. C101#13421direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#27242
C2×#352×C1012
C101×#18902
C101×#18562
C101×#13932
#13421101