Finite Group Databasebeta

← #34206523

Subgroups — #34206523

Order 20224.

470 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×#19098941C211yesmaximal, characteristic
2C2×#19098380C211yesmaximal, characteristic
3C2×#19098379C211yesmaximal, characteristic
4C2×#19098378C211yesmaximal, characteristic
5M32×Dic79C211yesmaximal, characteristic
6#23763570C211yesmaximal, characteristic
7C2×#362×C79C211yesmaximal, characteristic
8C22×Dic316C2211yescharacteristic
9C22×#11929614—21no—
10C2×#14579159—21no—
11C2×#14579101C2211yescharacteristic
12#19098941—21no—
13#19098941—21no—
14#19098941C412yes—
15#19098941C412yes—
16C2×#14579097C2211yescharacteristic
17C2×#14579096—21no—
18#19098586—21no—
19C2×C8×Dic79C2211yescharacteristic
20#19098380—22no—
21#19098379—22no—
22#19098378—22no—
23#19098338—21no—
24C16×Dic79—21no—
25C22×Q16×C79C2211yescharacteristic
26C2×M32×C79C2211yescharacteristic
27C2×#108×C79C2211yescharacteristic
28#362×C79—22no—
29C22×Dic158—21no—
30C2×Dic316—21no—
31C2×Dic316—21no—
32C2×Dic316—21no—
33C2×Dic316—21no—
34C2×Dic316—21no—
35C2×Dic316C2×C412yes—
36C2×#11929614—22no—
37C2×#11929614—22no—
38C2×#11929614—42no—
39C2×#11929614—42no—
40C2×#11929608—21no—
41C22×C79⋊C8D411yescharacteristic
42#14579159—22no—
43#14579159—22no—
44#14579159—42no—
45C2×Dic79⋊C4—42no—
46C2×C4×Dic79D411yescharacteristic
47#14579101—21no—
48#14579101D412yes—
49C2×C79⋊C16—21no—
50#14579097—21no—
51#14579097—21no—
52#14579096—42no—
53Dic79⋊C8—42no—
54C8×Dic79C2×C411yescharacteristic
55C8×Dic79C2×C411yescharacteristic
56C8×Dic79D411yescharacteristic
57C8×Dic79D411yescharacteristic
58C22×Q8×C79—21no—
59C2×Q16×C79—21no—
60C2×Q16×C79—21no—
61C2×Q16×C79—21no—
62C2×Q16×C79—21no—
63C2×Q16×C79—21no—
64C2×Q16×C79C2×C412yes—
65C2×M16×C79—21no—
66C22×C8×C79C2311yescharacteristic
67M32×C79—21no—
68M32×C79D412yes—
69C2×C16×C79—21no—
70#108×C79—21no—
71#108×C79—21no—
72C2×Dic158—22no—
73C2×Dic158—41no—
74C2×Dic158—41no—
75C2×Dic158—41no—
76C2×Dic158—41no—
77C2×Dic158—41no—
78C22×Dic79—41no—
79C22×Dic79SD1612yes—
80Dic316—22no—
81Dic316—22no—
82Dic316—41no—
83Dic316—41no—
84#11929614—44no—
85#11929614—44no—
86#11929608—41no—
87#11929608—41no—
88C2×C79⋊C8—41no—
89C2×C79⋊C8C22⋊C411yescharacteristic
90C2×C79⋊C8C22⋊C411yescharacteristic
91C2×C79⋊C8D812yes—
92C2×C79⋊C8SD1612yes—
93Dic79⋊C4—44no—
94Dic79⋊C4—44no—
95C4×Dic79C22⋊C411yescharacteristic
96C4×Dic79C22⋊C411yescharacteristic
97C4×Dic79D812yes—
98C79⋊C16—22no—
99C2×Q8×C79—22no—
100C2×Q8×C79—41no—
101C2×Q8×C79—41no—
102C2×Q8×C79—41no—
103C2×Q8×C79—41no—
104C2×Q8×C79—41no—
105C22×C4×C79—41no—
106C22×C4×C79C2×D411yescharacteristic
107Q16×C79—22no—
108Q16×C79—22no—
109Q16×C79—41no—
110Q16×C79—41no—
111M16×C79—41no—
112M16×C79—41no—
113C2×C8×C79—41no—
114C2×C8×C79C22×C411yescharacteristic
115C2×C8×C79C2×D411yescharacteristic
116C2×C8×C79C2×D411yescharacteristic
117C2×C8×C79C2×D411yescharacteristic
118C2×C8×C79#4111yescharacteristic
119C2×C8×C79#4111yescharacteristic
120C16×C79—22no—
121C23×C79C2×SD1611yescharacteristic
122Q8×C79—42no—
123Q8×C79—42no—
124Q8×C79—81no—
125Q8×C79—81no—
126C2×C4×C79—42no—
127C2×C4×C79—81no—
128C2×C4×C79—81no—
129C2×C4×C79C2×C22⋊C411yescharacteristic
130C2×C4×C79#12411yescharacteristic
131C2×C4×C79#12711yescharacteristic
132C2×C4×C79C2×D811yescharacteristic
133C2×C4×C79C2×D811yescharacteristic
134C2×C4×C79C2×SD1611yescharacteristic
135C2×Dic79—24no—
136C2×Dic79—42no—
137C2×Dic79—81no—
138C2×Dic79—81no—
139C2×Dic79#10212yes—
140C2×Dic79#10212yes—
141Dic158—42no—
142Dic158—42no—
143Dic158—81no—
144Dic158—81no—
145C8×C79—81no—
146C8×C79C4×D411yescharacteristic
147C8×C79C4×D411yescharacteristic
148C8×C79#12111yescharacteristic
149C8×C79#12111yescharacteristic
150C79⋊C8—81no—
151C79⋊C8#10212yes—
152C79⋊C8#10212yes—
153C22×C79—22no—
154C22×C79C2×#10211yescharacteristic
155C22×C79#48611yescharacteristic
156C22×C79#49211yescharacteristic
157C4×C79—82no—
158C4×C79#39011yescharacteristic
159C4×C79C2×#10211yescharacteristic
160C4×C79#48611yescharacteristic
161C4×C79#49311yescharacteristic
162Dic79—22no—
163Dic79—82no—
164Dic79#36214yescomplemented
165#13212—791nomaximal, Sylow
166C2×C79—21no—
167C2×C79—21no—
168C2×C79#195711yescharacteristic
169C2×C79C2×#36212yes—
170C2×#494—791no—
171C2×#362—791no—
172C2×#362—791no—
173C2×#362—791no—
174C2×#362D7911yescharacteristic
175C4×M32—791no—
176#1848—791no—
177C79#1321211yescharacteristic, complemented, Sylow
178C22×Q16—791no—
179C22×Q16—1581no—
180C22×Q16C2×D7911yescharacteristic
181C2×C4⋊Q8—1581no—
182C2×M32—791no—
183C2×M32C2×D7911yescharacteristic
184#494—792no—
185#494—792no—
186#494—1581no—
187#494—1581no—
188C2×#108—791no—
189C2×#108—1581no—
190C2×#108C2×D7911yescharacteristic
191#423—1581no—
192C2×C4×C8—791no—
193#362—22no—
194#362—1582no—
195#362—1582no—
196#362—1582no—
197#346—1581no—
198C4×C16—1581no—
199C22×Q8—21no—
200C22×Q8—1581no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—3162no—
207C2×Q16—3162no—
208C2×Q16—792no—
209C2×Q16—1582no—
210C2×Q16—1582no—
211C2×Q16—1581no—
212C2×Q16—1581no—
213C2×Q16—1581no—
214C2×Q16—1581no—
215C2×Q16—1581no—
216C2×Q16C4×D7912yes—
217C2×M16—21no—
218C2×M16—1581no—
219C22×C8—791no—
220C22×C8C22×D7911yescharacteristic
221C4⋊Q8—3162no—
222C4⋊Q8—1582no—
223C4⋊Q8—1582no—
224C2×C4⋊C4—3162no—
225C2×C42—791no—
226M32—21no—
227M32—792no—
228M32—1581no—
229M32C22⋊D7912yes—
230C2×C16—21no—
231C2×C16—1581no—
232#108—21no—
233#108—21no—
234#108—3162no—
235#108—1581no—
236#108—1581no—
237C4⋊C8—3162no—
238C4×C8—791no—
239C4×C8—791no—
240C4×C8—791no—
241C4×C8—791no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—3161no—
249C2×Q8—3161no—
250C2×Q8—3161no—
251C2×Q8—3161no—
252C2×Q8—3161no—
253C2×Q8—1582no—
254C22×C4—41no—
255C22×C4—3161no—
256C22×C4—792no—
257C22×C4D4×D7911yescharacteristic
258Q16—22no—
259Q16—22no—
260Q16—41no—
261Q16—41no—
262Q16—3164no—
263Q16—3164no—
264Q16—3161no—
265Q16—3161no—
266Q16—1582no—
267Q16—1582no—
268M16—41no—
269M16—41no—
270M16—3161no—
271M16—3161no—
272C2×C8—41no—
273C2×C8—3161no—
274C2×C8—791no—
275C2×C8—791no—
276C2×C8—792no—
277C2×C8—792no—
278C2×C8C2×C4×D7911yescharacteristic
279C2×C8D4×D7911yescharacteristic
280C2×C8D4×D7911yescharacteristic
281C2×C8C2×C22⋊D7911yescharacteristic
282C2×C8#1192962311yescharacteristic
283C2×C8#1192962411yescharacteristic
284C4⋊C4—3164no—
285C4⋊C4—3164no—
286C42—791no—
287C42—791no—
288C42—792no—
289C16—22no—
290C16—1582no—
291C23SD16×D7911yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296Q8—3162no—
297Q8—3162no—
298Q8—6321no—
299Q8—6321no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—3162no—
304C2×C4—792no—
305C2×C4—792no—
306C2×C4—6321no—
307C2×C4—6321no—
308C2×C4—1584no—
309C2×C4C22⋊C4×D7911yescharacteristic
310C2×C4#1457914711yescharacteristic
311C2×C4#1457915711yescharacteristic
312C2×C4D8×D7911yescharacteristic
313C2×C4D8×D7911yescharacteristic
314C2×C4SD16×D7911yescharacteristic
315C8—81no—
316C8—792no—
317C8—792no—
318C8—6321no—
319C8(C22⋊D79)⋊C411yescharacteristic
320C8C4×C22⋊D7911yescharacteristic
321C8#1457913311yescharacteristic
322C8#1457913411yescharacteristic
323C22—22no—
324C22#102×D7911yescharacteristic
325C22#1909890811yescharacteristic
326C22#1909893411yescharacteristic
327C4—82no—
328C4—794no—
329C4—6322no—
330C4—1582no—
331C4#1909846311yescharacteristic
332C4#102×D7911yescharacteristic
333C4#1909890811yescharacteristic
334C4#1909893811yescharacteristic
335C2—21no—
336C2—21no—
337C2#2376420411yescharacteristic
338C2#362×D7912yes—
subgroupG/H
centerC22#102×D79
commutatorC2×C8×C79C22×C4
FrattiniC22×C8C22×D79
FittingC2×#362×C79C2
socleC22×C79C2×#102
prime radicalC23×C79C2×SD16
cosocleC22×C8×C79C23
hypercenterC2×#362D79
hypocenterC79#13212
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
164. Dic79#362semidirect
177. C79#13212semidirect

Maximal subgroups

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

subgroupindex
C2×#190989412
C2×#190983802
C2×#190983792
C2×#190983782
M32×Dic792
#237635702
C2×#362×C792
#1321279