Finite Group Databasebeta

← #34206489

Subgroups — #34206489

Order 20224.

514 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098946C211yesmaximal, characteristic
2C2×#19098368C211yesmaximal, characteristic, complemented
3C2×#19098366C211yesmaximal, characteristic, complemented
4C2×#19098364C211yesmaximal, characteristic
5C2×C16×Dic79C211yesmaximal, characteristic, complemented
6#23763563C211yesmaximal, characteristic, complemented
7C2×#357×C79C211yesmaximal, characteristic
8C22×Dic316C2211yescharacteristic
9C22×#11929612—21no—
10C2×#14579148—21no—
11C22×C79⋊C16C2211yescharacteristic
12#19098946—22no—
13#19098946C414yescomplemented
14C2×#14579095C2211yescharacteristic
15C2×#14579092—21no—
16C2×C8×Dic79C2211yescharacteristic
17#19098428—21no—
18#19098368—22no—
19#19098366—22no—
20#19098364—22no—
21C16×Dic79—22no—
22C22×D8×C79C2211yescharacteristic
23C22×C16×C79C2211yescharacteristic
24C2×#107×C79C2211yescharacteristic
25#357×C79—22no—
26C22×Dic158—21no—
27C2×Dic316—21no—
28C2×Dic316—21no—
29C2×Dic316—21no—
30C2×Dic316—21no—
31C2×Dic316—21no—
32C2×Dic316C2×C412yes—
33C2×#11929612—24no—
34C2×#11929612—42no—
35C2×#11929612—42no—
36C22×C79⋊C8D411yescharacteristic
37#14579148—24no—
38#14579148—42no—
39C2×C4⋊Dic79—21no—
40C2×C22⋊Dic79—42no—
41C2×C4×Dic79D411yescharacteristic
42C2×C79⋊C16—21no—
43C2×C79⋊C16—21no—
44C2×C79⋊C16D412yes—
45#14579095—21no—
46#14579095—21no—
47#14579092—42no—
48C8×Dic79C2×C412yes—
49C8×Dic79D412yes—
50C79⋊#95—42no—
51C22×D4×C79—21no—
52C2×D8×C79—21no—
53C2×D8×C79—21no—
54C2×D8×C79—21no—
55C2×D8×C79—21no—
56C2×D8×C79—21no—
57C2×D8×C79C2×C412yes—
58C22×C8×C79C2311yescharacteristic
59C2×C4⋊C4×C79—21no—
60C2×C16×C79—21no—
61C2×C16×C79—21no—
62C2×C16×C79D412yes—
63#107×C79—21no—
64#107×C79—21no—
65C2×Dic158—22no—
66C2×Dic158—41no—
67C2×Dic158—41no—
68C2×Dic158—41no—
69C2×Dic158—41no—
70C2×Dic158—41no—
71C22×Dic79—41no—
72C22×Dic79—41no—
73C22×Dic79D812yes—
74Dic316—22no—
75Dic316—22no—
76Dic316—41no—
77Dic316—41no—
78#11929612—48no—
79C2×C79⋊C8C22⋊C412yes—
80C2×C79⋊C8D812yes—
81C2×C79⋊C8SD1612yes—
82C4⋊Dic79—41no—
83C4⋊Dic79—41no—
84C22⋊Dic79—48no—
85C4×Dic79C22⋊C412yes—
86C4×Dic79SD1612yes—
87C79⋊C16—22no—
88C24×C79—41no—
89C2×D4×C79—22no—
90C2×D4×C79—41no—
91C2×D4×C79—41no—
92C2×D4×C79—41no—
93C2×D4×C79—41no—
94C2×D4×C79—41no—
95C22×C4×C79—41no—
96C22×C4×C79C2×D411yescharacteristic
97D8×C79—22no—
98D8×C79—22no—
99D8×C79—41no—
100D8×C79—41no—
101C2×C8×C79C22×C411yescharacteristic
102C2×C8×C79C2×D411yescharacteristic
103C2×C8×C79C2×D411yescharacteristic
104C2×C8×C79C2×D411yescharacteristic
105C2×C8×C79#4111yescharacteristic
106C2×C8×C79#4111yescharacteristic
107C4⋊C4×C79—41no—
108C4⋊C4×C79—41no—
109C16×C79—22no—
110C23×C79—42no—
111C23×C79—81no—
112C23×C79—81no—
113C23×C79—82no—
114C23×C79—82no—
115C23×C79C2×D811yescharacteristic
116D4×C79—42no—
117D4×C79—42no—
118D4×C79—81no—
119D4×C79—81no—
120C2×C4×C79—81no—
121C2×C4×C79—82no—
122C2×C4×C79C2×C22⋊C411yescharacteristic
123C2×C4×C79#12411yescharacteristic
124C2×C4×C79#12711yescharacteristic
125C2×C4×C79C2×D811yescharacteristic
126C2×C4×C79C2×SD1611yescharacteristic
127C2×C4×C79C2×SD1611yescharacteristic
128C2×Dic79—22no—
129C2×Dic79—22no—
130C2×Dic79—42no—
131C2×Dic79—81no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79—82no—
135C2×Dic79#10214yes—
136Dic158—42no—
137Dic158—42no—
138Dic158—81no—
139Dic158—81no—
140C8×C79C4×D411yescharacteristic
141C8×C79C4×D411yescharacteristic
142C8×C79#12111yescharacteristic
143C8×C79#12111yescharacteristic
144C79⋊C8#10214yes—
145C22×C79—84no—
146C22×C79—82no—
147C22×C79—162no—
148C22×C79—161no—
149C22×C79—161no—
150C22×C79C2×#10211yescharacteristic
151C22×C79#48611yescharacteristic
152C22×C79#49311yescharacteristic
153C22×C79#50812yes—
154C22×C79#50812yes—
155C4×C79—161no—
156C4×C79#39011yescharacteristic
157C4×C79C2×#10211yescharacteristic
158C4×C79#48611yescharacteristic
159C4×C79#49211yescharacteristic
160Dic79—24no—
161Dic79—82no—
162Dic79—161no—
163#13204—791nomaximal, Sylow
164C2×C79—162no—
165C2×C79#195711yescharacteristic
166C2×C79#213812yes—
167C2×C79#224212yes—
168C2×C79#224911yescharacteristic
169C2×C79#224911yescharacteristic
170C2×#495—791no—
171C2×#358—791no—
172C2×#358—791no—
173C2×#357—791no—
174C2×#357D7911yescharacteristic
175C2×C4×C16—791no—
176#1846—791no—
177C79#1320411yescharacteristic, complemented, Sylow
178C22×Q16—791no—
179C22×SD16—1581no—
180C22×D8C2×D7911yescharacteristic
181C2×#124—1581no—
182C22×C16—791no—
183C22×C16C2×D7911yescharacteristic
184#495—794no—
185#495—1582no—
186C2×#107—791no—
187C2×#107C2×D7911yescharacteristic
188C2×#106—1581no—
189C2×C4×C8—791no—
190#382—1581no—
191#358—1582no—
192#358—1582no—
193#357—22no—
194#357—1582no—
195C4×C16—1582no—
196C22×Q8—1581no—
197C22×D4—21no—
198C2×Q16—792no—
199C2×Q16—1581no—
200C2×Q16—1581no—
201C2×Q16—1581no—
202C2×Q16—1581no—
203C2×Q16—1581no—
204C2×SD16—3162no—
205C2×SD16—3162no—
206C2×SD16—1584no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8C4×D7912yes—
213C22×C8—791no—
214C22×C8C22×D7911yescharacteristic
215#124—3162no—
216#124—1584no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—1581no—
219C2×C22⋊C4—3162no—
220C2×C42—791no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—792no—
224C2×C16—1581no—
225C2×C16—1581no—
226C2×C16C22⋊D7912yes—
227#107—21no—
228#107—21no—
229#107—1581no—
230#107—1581no—
231#106—3162no—
232C4×C8—792no—
233C4×C8—792no—
234#95—3162no—
235C24—41no—
236C2×Q8—3161no—
237C2×Q8—3161no—
238C2×Q8—3161no—
239C2×Q8—3161no—
240C2×Q8—3161no—
241C2×Q8—1582no—
242C2×D4—22no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—3161no—
250C22×C4—3161no—
251C22×C4—792no—
252C22×C4D4×D7911yescharacteristic
253Q16—3161no—
254Q16—3161no—
255Q16—1582no—
256Q16—1582no—
257SD16—3168no—
258D8—22no—
259D8—22no—
260D8—41no—
261D8—41no—
262C2×C8—792no—
263C2×C8—792no—
264C2×C8—792no—
265C2×C8C2×C4×D7911yescharacteristic
266C2×C8D4×D7911yescharacteristic
267C2×C8D4×D7911yescharacteristic
268C2×C8C2×C22⋊D7911yescharacteristic
269C2×C8#1192962311yescharacteristic
270C2×C8#1192962411yescharacteristic
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—3161no—
274C4⋊C4—3161no—
275C22⋊C4—3168no—
276C42—792no—
277C42—792no—
278C16—22no—
279C16—1582no—
280C23—42no—
281C23—81no—
282C23—81no—
283C23—82no—
284C23—82no—
285C23D8×D7911yescharacteristic
286Q8—3162no—
287Q8—3162no—
288Q8—6321no—
289Q8—6321no—
290D4—42no—
291D4—42no—
292D4—81no—
293D4—81no—
294C2×C4—81no—
295C2×C4—82no—
296C2×C4—3162no—
297C2×C4—794no—
298C2×C4—6321no—
299C2×C4—6321no—
300C2×C4—6321no—
301C2×C4—6322no—
302C2×C4—1582no—
303C2×C4—1582no—
304C2×C4C22⋊C4×D7911yescharacteristic
305C2×C4#1457914711yescharacteristic
306C2×C4#1457915711yescharacteristic
307C2×C4D8×D7911yescharacteristic
308C2×C4SD16×D7911yescharacteristic
309C2×C4SD16×D7911yescharacteristic
310C8—794no—
311C8(C22⋊D79)⋊C411yescharacteristic
312C8C4×C22⋊D7911yescharacteristic
313C8#1457913311yescharacteristic
314C8#1457913411yescharacteristic
315C22—84no—
316C22—82no—
317C22—162no—
318C22—161no—
319C22—161no—
320C22#102×D7911yescharacteristic
321C22#1909890811yescharacteristic
322C22#1909893811yescharacteristic
323C22#1909899212yes—
324C22#1909899412yes—
325C4—161no—
326C4—6322no—
327C4—1584no—
328C4—12641no—
329C4#1909846311yescharacteristic
330C4#102×D7911yescharacteristic
331C4#1909890811yescharacteristic
332C4#1909893411yescharacteristic
333C2—162no—
334C2#2376420411yescharacteristic
335C2#2376510412yes—
336C2#2376563012yes—
337C2#2376565811yescharacteristic
338C2#2376566011yescharacteristic
subgroupG/H
centerC23D8×D79
commutatorC2×C8×C79C22×C4
FrattiniC22×C8C22×D79
FittingC2×#357×C79C2
socleC23×C79C2×D8
prime radicalC22×D8×C79C22
cosocleC22×C8×C79C23
hypercenterC2×#357D79
hypocenterC79#13204
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#19098368C2semidirect
3. C2×#19098366C2semidirect
5. C2×C16×Dic79C2semidirect
6. #23763563C2semidirect
13. #19098946C4semidirect
177. C79#13204semidirect

Maximal subgroups

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

subgroupindex
C2×#190989462
C2×#190983682
C2×#190983662
C2×#190983642
C2×C16×Dic792
#237635632
C2×#357×C792
#1320479