Finite Group Databasebeta

← #34204577

Subgroups — #34204577

Order 20224.

442 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D79C211yesmaximal, characteristic
2#23765010C211yesmaximal, characteristic
3#23763435C211yesmaximal, characteristic
4#23761510C211yesmaximal, characteristic, complemented
5#23761509C211yesmaximal, characteristic, complemented
6#23761508C211yesmaximal, characteristic, complemented
7C79×#1387C211yesmaximal, characteristic, complemented
8C22×C8×D79C2211yescharacteristic
9C2×C4⋊C4×D79—21no—
10C2×#14579101C2211yescharacteristic
11C2×#14579097C2211yescharacteristic
12C2×#14579095C2211yescharacteristic
13C2×#14579094—21no—
14#107×D79—21no—
15#107×D79—21no—
16#107×D79C412yes—
17#107×D79C412yes—
18#19098526—21no—
19(C2×D79)⋊C16—21no—
20(C2×D79)⋊C16—21no—
21#19098327—21no—
22C2×M32×C79C2211yescharacteristic
23C2×#108×C79C2211yescharacteristic
24C2×#107×C79C2211yescharacteristic
25C22×C4×D79—41no—
26C22×C4×D79D411yescharacteristic
27C2×#11929608—21no—
28C22×C79⋊C8D411yescharacteristic
29C2×C8×D79—21no—
30C2×C8×D79—21no—
31C2×C8×D79—21no—
32C2×C8×D79—21no—
33C2×C8×D79C2×C411yescharacteristic
34C2×C8×D79C2×C411yescharacteristic
35C2×C8×D79D411yescharacteristic
36C2×C8×D79D411yescharacteristic
37C2×C4⋊Dic79—21no—
38C2×Dic79⋊C4—41no—
39C4⋊C4×D79—22no—
40C4⋊C4×D79—22no—
41C4⋊C4×D79—41no—
42C4⋊C4×D79—41no—
43#14579101—21no—
44#14579101—21no—
45C2×C79⋊C16—21no—
46#14579097—21no—
47#14579097—21no—
48#14579095—21no—
49#14579095C2×C412yes—
50#14579094—22no—
51#14579094—22no—
52(C2×D79)⋊C8—41no—
53(C2×D79)⋊C8—41no—
54C2×M16×C79—21no—
55C22×C8×C79C2311yescharacteristic
56C2×C4⋊C4×C79—21no—
57M32×C79—21no—
58M32×C79—21no—
59C2×C16×C79—21no—
60#108×C79—21no—
61#108×C79—21no—
62#107×C79—21no—
63#107×C79C2×C412yes—
64C23×D79SD1611yescharacteristic
65C22×Dic79—41no—
66C22×Dic79SD1611yescharacteristic
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—42no—
72C2×C4×D79—42no—
73C2×C4×D79—84no—
74C2×C4×D79C22⋊C411yescharacteristic
75C2×C4×D79C22⋊C411yescharacteristic
76C2×C4×D79D811yescharacteristic
77C2×C4×D79D811yescharacteristic
78#11929608—41no—
79#11929608—41no—
80C2×C79⋊C8—21no—
81C2×C79⋊C8—21no—
82C2×C79⋊C8—41no—
83C2×C79⋊C8C22⋊C411yescharacteristic
84C2×C79⋊C8C22⋊C411yescharacteristic
85C8×D79—21no—
86C8×D79—21no—
87C8×D79—21no—
88C8×D79—21no—
89C8×D79—21no—
90C8×D79—21no—
91C8×D79—21no—
92C8×D79—21no—
93C4⋊Dic79—22no—
94C4⋊Dic79—41no—
95Dic79⋊C4—42no—
96Dic79⋊C4—42no—
97C79⋊C16—41no—
98C22×C4×C79—41no—
99C22×C4×C79C2×D411yescharacteristic
100M16×C79—41no—
101M16×C79—41no—
102C2×C8×C79—41no—
103C2×C8×C79C22×C411yescharacteristic
104C2×C8×C79C2×D411yescharacteristic
105C2×C8×C79#4111yescharacteristic
106C2×C8×C79#4111yescharacteristic
107C2×C8×C79#4111yescharacteristic
108C2×C8×C79#4111yescharacteristic
109C4⋊C4×C79—22no—
110C4⋊C4×C79—41no—
111C16×C79—41no—
112C23×C79C2×SD1611yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—22no—
116C22×D79—22no—
117C22×D79#10211yescharacteristic
118C22×D79#10211yescharacteristic
119C2×C4×C79—42no—
120C2×C4×C79—82no—
121C2×C4×C79C2×C22⋊C411yescharacteristic
122C2×C4×C79#12311yescharacteristic
123C2×C4×C79#12311yescharacteristic
124C2×C4×C79C2×D811yescharacteristic
125C2×C4×C79#13711yescharacteristic
126C2×C4×C79#13711yescharacteristic
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—42no—
130C2×Dic79—82no—
131C2×Dic79#10211yescharacteristic
132C2×Dic79#10211yescharacteristic
133C4×D79—21no—
134C4×D79—21no—
135C4×D79—21no—
136C4×D79—21no—
137C4×D79—21no—
138C4×D79—21no—
139C4×D79—21no—
140C4×D79—21no—
141C4×D79—84no—
142C4×D79—84no—
143C8×C79—81no—
144C8×C79#11711yescharacteristic
145C8×C79#11711yescharacteristic
146C8×C79#12311yescharacteristic
147C8×C79#12311yescharacteristic
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—81no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79C2×#10211yescharacteristic
154C22×C79#48311yescharacteristic
155C22×C79#48311yescharacteristic
156C2×D79—24no—
157C2×D79—24no—
158C2×D79—21no—
159C2×D79—21no—
160C2×D79—21no—
161C2×D79—21no—
162C2×D79#36112yes—
163C2×D79#36212yes—
164C4×C79—82no—
165C4×C79#38111yescharacteristic
166C4×C79#41911yescharacteristic
167C4×C79#48011yescharacteristic
168C4×C79#48011yescharacteristic
169Dic79—21no—
170Dic79—21no—
171Dic79—82no—
172#12871—791nomaximal, Sylow
173C2×C79—21no—
174C2×C79—21no—
175C2×C79#182311yescharacteristic
176C2×C79C2×#36111yescharacteristic
177C2×C79C2×#36211yescharacteristic
178D79—22no—
179D79—22no—
180C22×#107—791no—
181#2112—791no—
182#1810—791no—
183#1387—791no—
184#1387—791no—
185#1387—791no—
186#1387D7911yescharacteristic, complemented
187C79#1287111yescharacteristic, complemented, Sylow
188C23×C8—791no—
189C22×C4⋊C4—1581no—
190C2×M32—791no—
191C2×M32C2×D7911yescharacteristic
192C2×#108—791no—
193C2×#108C2×D7911yescharacteristic
194C2×#107—791no—
195C2×#107—792no—
196C2×#107—792no—
197C2×#107—1581no—
198C2×#107—1581no—
199C2×#107—1581no—
200C2×#107C2×D7911yescharacteristic
201#407—1581no—
202C22⋊C16—1581no—
203C22⋊C16—1581no—
204#341—1581no—
205C23×C4—3161no—
206C23×C4—791no—
207C2×M16—21no—
208C2×M16—1581no—
209C22×C8—791no—
210C22×C8—791no—
211C22×C8—791no—
212C22×C8—791no—
213C22×C8—791no—
214C22×C8—1581no—
215C22×C8—1581no—
216C22×C8—1581no—
217C22×C8—1581no—
218C22×C8C22×D7911yescharacteristic
219C2×C4⋊C4—21no—
220C2×C4⋊C4—3161no—
221C2×C4⋊C4—3161no—
222C2×C4⋊C4—3161no—
223C2×C4⋊C4—1582no—
224C2×C4⋊C4—1582no—
225C2×C4⋊C4—1581no—
226M32—21no—
227M32—21no—
228M32—1581no—
229M32—1581no—
230C2×C16—21no—
231C2×C16—1581no—
232#108—21no—
233#108—21no—
234#108—1581no—
235#108—1581no—
236#107—21no—
237#107—792no—
238#107—1582no—
239#107—1582no—
240#107—1581no—
241#107C4×D7912yes—
242C22⋊C8—3161no—
243C22⋊C8—3161no—
244C24—791no—
245C22×C4—41no—
246C22×C4—3162no—
247C22×C4—3162no—
248C22×C4—3161no—
249C22×C4—791no—
250C22×C4—791no—
251C22×C4—791no—
252C22×C4—791no—
253C22×C4—791no—
254C22×C4—6324no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4—1581no—
258C22×C4—1581no—
259C22×C4D4×D7911yescharacteristic
260M16—41no—
261M16—41no—
262M16—3161no—
263M16—3161no—
264C2×C8—41no—
265C2×C8—3161no—
266C2×C8—791no—
267C2×C8—791no—
268C2×C8—1581no—
269C2×C8—1581no—
270C2×C8—1581no—
271C2×C8—1581no—
272C2×C8—1581no—
273C2×C8—1581no—
274C2×C8—1581no—
275C2×C8—1581no—
276C2×C8—1581no—
277C2×C8—1581no—
278C2×C8C2×C4×D7911yescharacteristic
279C2×C8D4×D7911yescharacteristic
280C2×C8#1192962311yescharacteristic
281C2×C8#1192962411yescharacteristic
282C2×C8#1192962411yescharacteristic
283C2×C8#1192962511yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—3162no—
287C4⋊C4—3162no—
288C4⋊C4—3161no—
289C4⋊C4—1582no—
290C16—41no—
291C16—3161no—
292C23—791no—
293C23—791no—
294C23—1582no—
295C23—1582no—
296C23—1581no—
297C23—1581no—
298C23SD16×D7911yescharacteristic
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—3162no—
302C2×C4—791no—
303C2×C4—791no—
304C2×C4—6324no—
305C2×C4—6324no—
306C2×C4—6322no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4C22⋊C4×D7911yescharacteristic
318C2×C4#1457914311yescharacteristic
319C2×C4#1457914611yescharacteristic
320C2×C4D8×D7911yescharacteristic
321C2×C4#1457919011yescharacteristic
322C2×C4#1457919311yescharacteristic
323C8—81no—
324C8—6321no—
325C8—1581no—
326C8—1581no—
327C8#1457911811yescharacteristic
328C8#1457911911yescharacteristic
329C8#1457914311yescharacteristic
330C8#1457914611yescharacteristic
331C22—21no—
332C22—21no—
333C22—792no—
334C22—792no—
335C22—1584no—
336C22—1584no—
337C22—1581no—
338C22—1581no—
339C22—1581no—
340C22—1581no—
341C22#102×D7911yescharacteristic
342C22#1909889211yescharacteristic
343C22#1909889511yescharacteristic
344C4—82no—
345C4—6322no—
346C4—1581no—
347C4—1581no—
348C4#1909842511yescharacteristic
349C4#1909857011yescharacteristic
350C4#1909887511yescharacteristic
351C4#1909887811yescharacteristic
352C2—21no—
353C2—21no—
354C2—1582no—
355C2—1582no—
356C2#2376348511yescharacteristic
357C2#361×D7911yescharacteristic
358C2#362×D7911yescharacteristic
subgroupG/H
centerC22#102×D79
commutatorC2×C8×C79C22×C4
FrattiniC22×C8C22×D79
FittingC79×#1387C2
socleC22×C79C2×#102
prime radicalC23×D79SD16
cosocleC22×C8×C79C23
hypercenter#1387D79
hypocenterC79#12871
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
4. #23761510C2semidirect
5. #23761509C2semidirect
6. #23761508C2semidirect
7. C79×#1387C2semidirect
186. #1387D79semidirect
187. C79#12871semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D792
#237650102
#237634352
#237615102
#237615092
#237615082
C79×#13872
#1287179