Finite Group Databasebeta

← #21446880

Subgroups — #21446880

Order 7808.

348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#16840560C211yesmaximal, characteristic
2C2×#14519810C211yesmaximal, characteristic, complemented
3#16840333C211yesmaximal, characteristic, complemented
4#16839770C211yesmaximal, characteristic, complemented
5#16839735C211yesmaximal, characteristic, complemented
6#16839534C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519810—22no—
11#14519810—22no—
12#14519808—21no—
13#14519807—21no—
14#14519803—21no—
15#14519802—21no—
16#14519797—22no—
17C2×Dic244—21no—
18C2×#11758190—21no—
19C2×#11758194C2211yescharacteristic
20#14519775—21no—
21#14519764—21no—
22#14519758—22no—
23#14519756—22no—
24#14519736C2211yescharacteristic
25#14519700—22no—
26#14519691—22no—
27C2×#41×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#104×C61—22no—
31#41×C61—21no—
32#41×C61—21no—
33#41×C61—21no—
34#41×C61—21no—
35C2×Q8×C61D411yescharacteristic
36C2×D4×C61—21no—
37C2×D4×C61D411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—21no—
41C22×Dic61—21no—
42#11758222—21no—
43#11758222—21no—
44#11758222—21no—
45#11758222—21no—
46C2×D244D411yescharacteristic
47C2×C4×D61—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122—21no—
52C2×Dic122—21no—
53C2×Dic122D412yes—
54C2×Dic122D411yescharacteristic
55M16×C61—21no—
56M16×C61D412yes—
57C2×C8×C61—21no—
58C4⋊C4×C61—21no—
59C22⋊C4×C61—21no—
60C42×C61—21no—
61C22⋊Dic61—24no—
62C22⋊Dic61D412yes—
63#11758202—22no—
64#11758201—22no—
65#11758200—22no—
66#11758199—22no—
67C4⋊Dic61—21no—
68#11758196—24no—
69C4×Dic61—21no—
70#11758194—21no—
71#11758194—21no—
72C2×#92418D412yes—
73Dic244—24no—
74#11758190—24no—
75C23×C61—21no—
76C23×C61C2×D411yescharacteristic
77C22×D61—21no—
78Q8×C61—21no—
79Q8×C61—21no—
80D4×C61—21no—
81D4×C61—21no—
82D4×C61—41no—
83D4×C61—41no—
84C2×C4×C61—21no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61#4111yescharacteristic
94C22⋊D61—41no—
95C22⋊D61—41no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101D244—21no—
102D244—21no—
103C4×D61—41no—
104C4×D61—41no—
105Dic122—22no—
106Dic122—21no—
107Dic122—21no—
108Dic122—22no—
109Dic122—41no—
110Dic122—41no—
111C8×C61—22no—
112#92418—22no—
113C22×C61—41no—
114C22×C61—42no—
115C22×C61—41no—
116C22×C61#12011yescharacteristic
117C22×C61#12111yescharacteristic
118C22×C61#12711yescharacteristic
119C2×D61—41no—
120C2×D61—81no—
121C4×C61—41no—
122C4×C61—81no—
123C4×C61#12011yescharacteristic
124C4×C61#12011yescharacteristic
125C4×C61#12111yescharacteristic
126C4×C61#12111yescharacteristic
127Dic61—42no—
128Dic61—42no—
129Dic61—41no—
130#2009—611nomaximal, Sylow
131C2×C61—21no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61—81no—
135C2×C61#39211yescharacteristic
136D61—81no—
137#575—611no—
138C2×#137—611no—
139#536—611no—
140#421D6111yescharacteristic, complemented
141#419—611no—
142#410—611no—
143#344—611no—
144C61#200911yescharacteristic, complemented, Sylow
145C2×#41—611no—
146C2×#41C2×D6111yescharacteristic
147C22×Q8—611no—
148#137—1222no—
149#137—1221no—
150#137—1221no—
151#137—1222no—
152AGL(1,ℤ/8)—1221no—
153AGL(1,ℤ/8)—1221no—
154#135—1222no—
155C2×Q16—1221no—
156C2×SD16—1221no—
157C2×M16—611no—
158C2×M16C2×D6111yescharacteristic
159C4⋊Q8—1221no—
160#124—1221no—
161#123—1222no—
162C22⋊Q8—1222no—
163#117—611no—
164#117C2×D6111yescharacteristic
165#104—22no—
166#103—1222no—
167#99—1222no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—1221no—
173#41—1221no—
174#41—1221no—
175#41—1221no—
176C2×Q8—612no—
177C2×Q8—611no—
178C2×Q8—1221no—
179C2×Q8—1221no—
180C2×Q8—1221no—
181C2×Q8—1221no—
182C2×Q8—1221no—
183C2×Q8D24411yescharacteristic
184C2×D4—21no—
185C2×D4—611no—
186C2×D4—1221no—
187C2×D4D24411yescharacteristic
188C22×C4—21no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4C22×D6111yescharacteristic
192Q16—1224no—
193Q16—1222no—
194SD16—1224no—
195SD16—1222no—
196SD16—1222no—
197D8—1222no—
198M16—21no—
199M16—1221no—
200M16—1221no—
201M16C22⋊D6112yes—
202C2×C8—21no—
203C2×C8—612no—
204C4⋊C4—21no—
205C4⋊C4—1224no—
206C4⋊C4—1221no—
207C22⋊C4—21no—
208C22⋊C4—612no—
209C22⋊C4—1224no—
210C42—21no—
211C42—1221no—
212C23—21no—
213C23—1221no—
214C23D4×D6111yescharacteristic
215Q8—21no—
216Q8—21no—
217Q8—1222no—
218Q8—1221no—
219Q8—1221no—
220Q8—1222no—
221Q8—2441no—
222Q8—2441no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—1221no—
228D4—1221no—
229D4—2441no—
230D4—2441no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1221no—
238C2×C4—2441no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4C2×D24411yescharacteristic
243C2×C4#1175822211yescharacteristic
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4D4×D6111yescharacteristic
247C2×C4C2×C22⋊D6111yescharacteristic
248C8—22no—
249C8—1222no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—4881no—
254C22—2441no—
255C22#1451974711yescharacteristic
256C22#1451975011yescharacteristic
257C22#1451977311yescharacteristic
258C4—41no—
259C4—81no—
260C4—2442no—
261C4—2441no—
262C4—2442no—
263C4#1451974511yescharacteristic
264C4#1451974711yescharacteristic
265C4#1451975011yescharacteristic
266C4#1451975111yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—4881no—
272C2#1683967111yescharacteristic
subgroupG/H
centerC2#16839671
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#392
hypercenter#421D61
hypocenterC61#2009
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. C2×#14519810C2semidirect
3. #16840333C2semidirect
4. #16839770C2semidirect
5. #16839735C2semidirect
6. #16839534C2semidirect
7. C61×#421C2semidirect
140. #421D61semidirect
144. C61#2009semidirect