Finite Group Databasebeta

← #34205346

Subgroups — #34205346

Order 20224.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic632C211yesmaximal, characteristic
2C2×C4×Dic316C211yesmaximal, characteristic
3C2×#19098368C211yesmaximal, characteristic
4C2×#19098368C211yesmaximal, characteristic
5#23764261C211yesmaximal, characteristic
6#23761492C211yesmaximal, characteristic
7C79×#1374C211yesmaximal, characteristic
8C22×Dic316C2211yescharacteristic
9C22×Dic316C2211yescharacteristic
10C2×C4×Dic158—21no—
11C2×Dic632—22no—
12C2×Dic632—22no—
13C2×Dic632C414yescomplemented
14C4×Dic316—22no—
15C4×Dic316—22no—
16C2×#14579095C2211yescharacteristic
17C2×#14579095C2211yescharacteristic
18C2×#14579086—21no—
19C2×#14579086—21no—
20#19098469—21no—
21#19098368—22no—
22#19098368—22no—
23C22×C16×C79C2211yescharacteristic
24C22×C16×C79C2211yescharacteristic
25C2×C4×C8×C79C2211yescharacteristic
26C22×Dic158—21no—
27C22×Dic158—21no—
28C2×Dic316—21no—
29C2×Dic316—21no—
30C2×Dic316—21no—
31C2×Dic316—21no—
32C2×Dic316—21no—
33C2×Dic316—21no—
34C2×Dic316—21no—
35C2×Dic316—21no—
36C2×Dic316C2×C412yes—
37C2×Dic316C2×C412yes—
38C2×Dic316D412yes—
39C2×Dic316D412yes—
40C4×Dic158—24no—
41C4×Dic158—42no—
42C2×C4⋊Dic79—21no—
43C2×C4⋊Dic79—21no—
44C2×Dic79⋊C4—41no—
45C2×C4×Dic79—41no—
46Dic632—28no—
47#14579095—21no—
48#14579095—21no—
49#14579095—21no—
50#14579095D412yes—
51#14579086—24no—
52#14579086—42no—
53C79⋊#95—41no—
54C79⋊#95—41no—
55C22×C8×C79D411yescharacteristic
56C22×C8×C79C2311yescharacteristic
57C2×C42×C79D411yescharacteristic
58C2×C16×C79—21no—
59C2×C16×C79—21no—
60C2×C16×C79—21no—
61C2×C16×C79—21no—
62C2×C16×C79—21no—
63C2×C16×C79C2×C412yes—
64C4×C8×C79—21no—
65C4×C8×C79—21no—
66C2×Dic158—22no—
67C2×Dic158—22no—
68C2×Dic158—22no—
69C2×Dic158—22no—
70C2×Dic158—41no—
71C2×Dic158—41no—
72C2×Dic158—41no—
73C2×Dic158—41no—
74C2×Dic158—41no—
75C2×Dic158—41no—
76C2×Dic158—41no—
77C2×Dic158—41no—
78C22×Dic79—41no—
79C22×Dic79—41no—
80C22×Dic79—41no—
81C22×Dic79—41no—
82Dic316—22no—
83Dic316—22no—
84Dic316—22no—
85Dic316—22no—
86Dic316—22no—
87Dic316—41no—
88Dic316—41no—
89Dic316C22⋊C414yes—
90C4⋊Dic79—22no—
91C4⋊Dic79—41no—
92C4⋊Dic79—41no—
93C4⋊Dic79—41no—
94Dic79⋊C4—44no—
95C4×Dic79—44no—
96C22×C4×C79D811yescharacteristic
97C22×C4×C79D811yescharacteristic
98C22×C4×C79C2×D411yescharacteristic
99C2×C8×C79—21no—
100C2×C8×C79—21no—
101C2×C8×C79—21no—
102C2×C8×C79C22×C411yescharacteristic
103C2×C8×C79C2×D411yescharacteristic
104C2×C8×C79C2×D411yescharacteristic
105C2×C8×C79C2×D411yescharacteristic
106C2×C8×C79#4111yescharacteristic
107C2×C8×C79#4111yescharacteristic
108C42×C79—21no—
109C42×C79—21no—
110C16×C79—22no—
111C16×C79—41no—
112C23×C79C2×D811yescharacteristic
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79Q3212yescomplemented
119C2×C4×C79C4×D411yescharacteristic
120C2×C4×C79#12011yescharacteristic
121C2×C4×C79#12111yescharacteristic
122C2×C4×C79#13511yescharacteristic
123C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
125C2×Dic79—42no—
126C2×Dic79—42no—
127C2×Dic79—42no—
128C2×Dic79—42no—
129C2×Dic79—42no—
130C2×Dic79—81no—
131C2×Dic79—81no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C2×Dic79—81no—
136C2×Dic79—81no—
137Dic158—24no—
138Dic158—42no—
139Dic158—42no—
140Dic158—42no—
141Dic158—42no—
142Dic158—42no—
143Dic158—81no—
144Dic158—81no—
145C8×C79—41no—
146C8×C79C2×C22⋊C411yescharacteristic
147C8×C79C4×D411yescharacteristic
148C8×C79#12111yescharacteristic
149C8×C79#12311yescharacteristic
150C22×C79C4×D811yescharacteristic
151C22×C79#44711yescharacteristic
152C22×C79#45911yescharacteristic
153C22×C79C2×Q3211yescharacteristic
154C22×C79#50811yescharacteristic
155C22×C79#51011yescharacteristic
156C22×C79#51011yescharacteristic
157C4×C79—22no—
158C4×C79—41no—
159C4×C79#38611yescharacteristic
160C4×C79#44211yescharacteristic
161C4×C79#44911yescharacteristic
162C4×C79#46311yescharacteristic
163Dic79—44no—
164Dic79—82no—
165Dic79—82no—
166Dic79—161no—
167#13015—791nomaximal, Sylow
168C2×C79#187911yescharacteristic
169C2×C79C4×Q3211yescharacteristic
170C2×C79#217611yescharacteristic
171C2×C79#218811yescharacteristic
172C2×C79#218911yescharacteristic
173C2×C79#220911yescharacteristic
174C2×C79#221111yescharacteristic
175C22×Q32—791no—
176C2×C4×Q16—791no—
177C2×#358—791no—
178C2×#358—791no—
179#1969—791no—
180#1380—791no—
181#1374D7911yescharacteristic
182C79#1301511yescharacteristic, complemented, Sylow
183C22×Q16—791no—
184C22×Q16—791no—
185C2×C4×Q8—1581no—
186C2×Q32—794no—
187C2×Q32—1582no—
188C2×Q32—1582no—
189C22×C16C2×D7911yescharacteristic
190C22×C16C2×D7911yescharacteristic
191C4×Q16—1582no—
192C4×Q16—1582no—
193C2×#107—791no—
194C2×#107—791no—
195C2×#103—1581no—
196C2×#103—1581no—
197C2×C4×C8C2×D7911yescharacteristic
198#391—1581no—
199#358—1582no—
200#358—1582no—
201C22×Q8—1581no—
202C22×Q8—1581no—
203C2×Q16—792no—
204C2×Q16—792no—
205C2×Q16—792no—
206C2×Q16—792no—
207C2×Q16—1581no—
208C2×Q16—1581no—
209C2×Q16—1581no—
210C2×Q16—1581no—
211C2×Q16—1581no—
212C2×Q16—1581no—
213C2×Q16—1581no—
214C2×Q16—1581no—
215C22×C8D31611yescharacteristic
216C22×C8C22×D7911yescharacteristic
217C4×Q8—3162no—
218C4×Q8—1584no—
219C2×C4⋊C4—3161no—
220C2×C4⋊C4—1581no—
221C2×C4⋊C4—1581no—
222C2×C42—3161no—
223C2×C42D31611yescharacteristic
224Q32—1588no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—21no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16C4×D7912yes—
231#107—792no—
232#107—1581no—
233#107—1581no—
234#107—1581no—
235#103—3162no—
236#103—1584no—
237C4×C8—21no—
238C4×C8—21no—
239#95—3161no—
240#95—3161no—
241C2×Q8—3161no—
242C2×Q8—3161no—
243C2×Q8—3161no—
244C2×Q8—3161no—
245C2×Q8—3161no—
246C2×Q8—3161no—
247C2×Q8—3161no—
248C2×Q8—3161no—
249C2×Q8—1582no—
250C2×Q8—1582no—
251C2×Q8—1582no—
252C2×Q8—1582no—
253C22×C4—3161no—
254C22×C4—3161no—
255C22×C4—3161no—
256C22×C4—3161no—
257C22×C4D63211yescharacteristic
258C22×C4D63211yescharacteristic
259C22×C4C2×D31611yescharacteristic
260Q16—3161no—
261Q16—3161no—
262Q16—794no—
263Q16—1582no—
264Q16—1582no—
265Q16—1582no—
266Q16—1582no—
267Q16—1582no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8C2×C4×D7911yescharacteristic
272C2×C8D4×D7911yescharacteristic
273C2×C8D4×D7911yescharacteristic
274C2×C8D4×D7911yescharacteristic
275C2×C8#1192962411yescharacteristic
276C2×C8#1192962511yescharacteristic
277C4⋊C4—3164no—
278C4⋊C4—3161no—
279C4⋊C4—3161no—
280C4⋊C4—3161no—
281C4⋊C4—1582no—
282C42—21no—
283C42—21no—
284C42—3164no—
285C16—22no—
286C16—41no—
287C23C2×D63211yescharacteristic
288Q8—3162no—
289Q8—3162no—
290Q8—3162no—
291Q8—3162no—
292Q8—3162no—
293Q8—6321no—
294Q8—6321no—
295Q8—1584no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—3162no—
302C2×C4—3162no—
303C2×C4—3162no—
304C2×C4—3162no—
305C2×C4—3162no—
306C2×C4—6321no—
307C2×C4—6321no—
308C2×C4—6321no—
309C2×C4—6321no—
310C2×C4—6321no—
311C2×C4—6321no—
312C2×C4—6321no—
313C2×C4Dic63212yescomplemented
314C2×C4C4×D31611yescharacteristic
315C2×C4#1457913111yescharacteristic
316C2×C4#1457913611yescharacteristic
317C2×C4#1457918311yescharacteristic
318C2×C4#1457918911yescharacteristic
319C2×C4#1457918911yescharacteristic
320C8—41no—
321C8C22⋊C4×D7911yescharacteristic
322C8#1457912311yescharacteristic
323C8#1457913411yescharacteristic
324C8#1457914611yescharacteristic
325C22C4×D63211yescharacteristic
326C22#1909869911yescharacteristic
327C22#1909875911yescharacteristic
328C22C2×Dic63211yescharacteristic
329C22#1909899511yescharacteristic
330C22#1909900611yescharacteristic
331C22#1909900611yescharacteristic
332C4—22no—
333C4—41no—
334C4—3164no—
335C4—6322no—
336C4—6322no—
337C4—12641no—
338C4#1909844111yescharacteristic
339C4#1909867611yescharacteristic
340C4#1909871011yescharacteristic
341C4#1909877911yescharacteristic
342C2#2376374711yescharacteristic
343C2C4×Dic63211yescharacteristic
344C2#2376527211yescharacteristic
345C2#2376533611yescharacteristic
346C2#2376534211yescharacteristic
347C2#2376545111yescharacteristic
348C2#2376546311yescharacteristic
subgroupG/H
centerC23C2×D632
commutatorC2×C8×C79C22×C4
FrattiniC22×C8C22×D79
FittingC79×#1374C2
socle, prime radicalC23×C79C2×D8
cosocleC22×C8×C79C23
hypercenter#1374D79
hypocenterC79#13015
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
13. C2×Dic632C4semidirect
118. C2×C4×C79Q32semidirect
182. C79#13015semidirect
313. C2×C4Dic632semidirect

Maximal subgroups

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

subgroupindex
C22×Dic6322
C2×C4×Dic3162
C2×#190983682
#237642612
#237614922
C79×#13742
#1301579