Finite Group Databasebeta

← C31×#2038 #16841971

Subgroups — C31×#2038 #16841971

Order 3968.

278 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C31×#536C211yesmaximal, characteristic
2C31×#428C211yesmaximal, characteristic, complemented
3C2×C31×#104C211yesmaximal, characteristic
4C31×#417C211yesmaximal, characteristic
5C2×C31×#101C211yesmaximal, characteristic, complemented
6C31×#391C211yesmaximal, characteristic, complemented
7C31×#339C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C22×Q8×C31C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C31×C4⋊Q8—21no—
13C31×#124—21no—
14C31×#123—22no—
15C31×C22⋊Q8—21no—
16C31×C22⋊Q8—21no—
17C31×#117C2211yescharacteristic
18C2×C4⋊C4×C31C2211yescharacteristic
19C2×C42×C31C2211yescharacteristic
20C31×#107—21no—
21C31×#106—21no—
22C31×#104—22no—
23C31×#103—21no—
24C31×#102—21no—
25C31×#101—22no—
26C31×#95—22no—
27#41×C31—21no—
28#41×C31—21no—
29#41×C31—21no—
30#41×C31—21no—
31C2×Q8×C31—21no—
32C2×Q8×C31—21no—
33C2×Q8×C31—21no—
34C2×Q8×C31—21no—
35C2×Q8×C31—21no—
36C2×Q8×C31—21no—
37C2×Q8×C31D411yescharacteristic
38C2×D4×C31—21no—
39C2×D4×C31D411yescharacteristic
40C22×C4×C31—21no—
41C22×C4×C31—21no—
42C22×C4×C31—21no—
43C22×C4×C31D412yes—
44C22×C4×C31C2311yescharacteristic
45M16×C31—21no—
46M16×C31—21no—
47M16×C31—21no—
48M16×C31D412yes—
49C2×C8×C31—21no—
50C2×C8×C31—21no—
51C4⋊C4×C31—22no—
52C4⋊C4×C31—22no—
53C4⋊C4×C31—21no—
54C4⋊C4×C31—21no—
55C4⋊C4×C31D411yescharacteristic
56C4⋊C4×C31D411yescharacteristic
57C22⋊C4×C31—22no—
58C22⋊C4×C31—22no—
59C22⋊C4×C31—21no—
60C42×C31—21no—
61C42×C31—21no—
62C42×C31—21no—
63C23×C31—21no—
64C23×C31C2×D411yescharacteristic
65Q8×C31—21no—
66Q8×C31—21no—
67Q8×C31—41no—
68Q8×C31—41no—
69Q8×C31—41no—
70Q8×C31—41no—
71D4×C31—21no—
72D4×C31—21no—
73D4×C31—41no—
74D4×C31—41no—
75C2×C4×C31—22no—
76C2×C4×C31—21no—
77C2×C4×C31—21no—
78C2×C4×C31—22no—
79C2×C4×C31—21no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—41no—
83C2×C4×C31—41no—
84C2×C4×C31—41no—
85C2×C4×C31—41no—
86C2×C4×C31—42no—
87C2×C4×C31—41no—
88C2×C4×C31C2×D411yescharacteristic
89C2×C4×C31C2×D411yescharacteristic
90C2×C4×C31C2×D411yescharacteristic
91C2×C4×C31#4111yescharacteristic
92C2×C4×C31#4111yescharacteristic
93C2×C4×C31#4111yescharacteristic
94C8×C31—22no—
95C8×C31—41no—
96#2038C3111yesmaximal, characteristic, direct product factor, Sylow
97C22×C31—21no—
98C22×C31—21no—
99C22×C31—41no—
100C22×C31—41no—
101C22×C31—41no—
102C22×C31#12011yescharacteristic
103C22×C31#12111yescharacteristic
104C22×C31#12311yescharacteristic
105C4×C31—42no—
106C4×C31—42no—
107C4×C31—41no—
108C4×C31—41no—
109C4×C31—41no—
110C4×C31—81no—
111C4×C31#12111yescharacteristic
112C4×C31#12111yescharacteristic
113C4×C31#12311yescharacteristic
114C4×C31#12411yescharacteristic
115#536C2×C3111yescharacteristic
116#428C2×C3111yescharacteristic, complemented
117C2×#104C2×C3111yescharacteristic
118#417C2×C3111yescharacteristic
119C2×#101C2×C3111yescharacteristic, complemented
120#391C2×C3111yescharacteristic, complemented
121#339C2×C3111yescharacteristic, complemented
122C2×C31—21no—
123C2×C31—21no—
124C2×C31—81no—
125C2×C31#39411yescharacteristic
126C2×C31#45411yescharacteristic
127C2×C31#45611yescharacteristic
128C2×#41C22×C3111yescharacteristic
129C22×Q8C22×C3111yescharacteristic
130C2×M16C22×C3111yescharacteristic
131C2×M16C22×C3111yescharacteristic
132C4⋊Q8—21no—
133#124—21no—
134#123—22no—
135C22⋊Q8—21no—
136C22⋊Q8—21no—
137#117C22×C3111yescharacteristic
138C2×C4⋊C4C22×C3111yescharacteristic
139C2×C42C22×C3111yescharacteristic
140#107—21no—
141#106—21no—
142#104—22no—
143#103—21no—
144#102—21no—
145#101—22no—
146#95—22no—
147C31#203811yescharacteristic, direct product factor, Sylow
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8D4×C3111yescharacteristic
159C2×D4—21no—
160C2×D4D4×C3111yescharacteristic
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4D4×C3112yes—
165C22×C4C23×C3111yescharacteristic
166M16—21no—
167M16—21no—
168M16—21no—
169M16D4×C3112yes—
170C2×C8—21no—
171C2×C8—21no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4D4×C3111yescharacteristic
177C4⋊C4D4×C3111yescharacteristic
178C22⋊C4—22no—
179C22⋊C4—22no—
180C22⋊C4—21no—
181C42—21no—
182C42—21no—
183C42—21no—
184C23—21no—
185C23C2×D4×C3111yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4C2×D4×C3111yescharacteristic
210C2×C4C2×D4×C3111yescharacteristic
211C2×C4C2×D4×C3111yescharacteristic
212C2×C4#41×C3111yescharacteristic
213C2×C4#41×C3111yescharacteristic
214C2×C4#41×C3111yescharacteristic
215C8—22no—
216C8—41no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22C31×#12011yescharacteristic
223C22C31×#12111yescharacteristic
224C22C31×#12311yescharacteristic
225C4—42no—
226C4—41no—
227C4—41no—
228C4—42no—
229C4—41no—
230C4—81no—
231C4C31×#12111yescharacteristic
232C4C31×#12111yescharacteristic
233C4C31×#12311yescharacteristic
234C4C31×#12411yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2C31×#39411yescharacteristic
239C2C31×#45411yescharacteristic
240C2C31×#45611yescharacteristic
subgroupG/H
center, socleC22×C31#120
commutator, Frattini, cosocleC22×C4C23×C31
prime radicalC2×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#428C2semidirect
5. C2×C31×#101C2semidirect
6. C31×#391C2semidirect
7. C31×#339C2semidirect
96. #2038C31direct (N × H)
116. #428C2×C31semidirect
119. C2×#101C2×C31semidirect
120. #391C2×C31semidirect
121. #339C2×C31semidirect
147. C31#2038direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#5362
C31×#4282
C2×C31×#1042
C31×#4172
C2×C31×#1012
C31×#3912
C31×#3392
#203831