Finite Group Databasebeta

← #34183469

Subgroups — #34183469

Order 20224.

476 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773404C211yesmaximal, characteristic
2#23764198C211yesmaximal, characteristic
3#23762057C211yesmaximal, characteristic, complemented
4#23761824C211yesmaximal, characteristic
5#23761295C211yesmaximal, characteristic, complemented
6#23761245C211yesmaximal, characteristic, complemented
7C79×#2961C211yesmaximal, characteristic, complemented
8C2×C4×D316C2211yescharacteristic
9#19098891C412yes—
10#19098850—21no—
11#19098765—21no—
12#19098713C412yes—
13C4×#11929611—22no—
14#19098616C2211yescharacteristic
15#19098616C2211yescharacteristic
16C2×C4⋊(C79⋊C8)C2211yescharacteristic
17C2×(C2×D79)⋊C8—21no—
18C2×(C2×D79)⋊C8—21no—
19#19098312—21no—
20#19098309—21no—
21#19098290—22no—
22#533×C79C2211yescharacteristic
23#446×C79—22no—
24#446×C79—22no—
25#424×C79—21no—
26#423×C79C2211yescharacteristic
27#405×C79—21no—
28C2×#97×C79C2211yescharacteristic
29C22×D316C2×C411yescharacteristic
30C22×C4×D79—21no—
31C2×#11929611—22no—
32C22×C79⋊C8—21no—
33C4×D316—21no—
34C4×D316—21no—
35C4×D316—21no—
36C4×D316—21no—
37C2×C4⋊Dic79C2×C411yescharacteristic
38C2×(C2×D79)⋊C4—21no—
39#14579092—22no—
40C4⋊(C79⋊C8)—21no—
41C4⋊(C79⋊C8)—21no—
42C4⋊(C79⋊C8)—21no—
43C4⋊(C79⋊C8)—21no—
44#14579085—22no—
45#14579081—22no—
46C22⋊(C79⋊C8)—21no—
47C22⋊(C79⋊C8)C2×C412yes—
48(C2×D79)⋊C8—42no—
49(C2×D79)⋊C8—42no—
50C4×C79⋊C8—21no—
51C4×C79⋊C8—21no—
52C2×M16×C79—21no—
53C22×C8×C79D411yescharacteristic
54C22×C8×C79D411yescharacteristic
55C4⋊Q8×C79D411yescharacteristic
56C4⋊Q8×C79D411yescharacteristic
57#125×C79—21no—
58C22⋊Q8×C79—21no—
59C22⋊Q8×C79C2×C412yes—
60C4×Q8×C79—21no—
61C4×Q8×C79D412yes—
62#117×C79—21no—
63C2×C42×C79C2311yescharacteristic
64C4⋊C8×C79—24no—
65C4⋊C8×C79—21no—
66C4⋊C8×C79D412yes—
67#97×C79—22no—
68#97×C79—21no—
69#97×C79—21no—
70C4×C8×C79—22no—
71C23×D79—21no—
72C2×D316—21no—
73C2×D316—21no—
74C2×D316—42no—
75C22×Dic79—21no—
76C2×C4×D79—41no—
77C2×C4×D79—41no—
78C2×C4×D79—41no—
79C2×C4×D79—41no—
80C2×C4×D79—41no—
81C2×C4×D79—41no—
82#11929611—44no—
83C2×C79⋊C8—22no—
84C2×C79⋊C8—41no—
85C2×C79⋊C8—41no—
86C2×C79⋊C8—41no—
87C2×C79⋊C8—41no—
88C4⋊Dic79—21no—
89C4⋊Dic79—21no—
90(C2×D79)⋊C4—41no—
91(C2×D79)⋊C4—41no—
92C2×Q8×C79—21no—
93C2×Q8×C79C22⋊C412yes—
94C22×C4×C79C22×C411yescharacteristic
95C22×C4×C79C2×D411yescharacteristic
96C22×C4×C79#4111yescharacteristic
97M16×C79—41no—
98M16×C79—41no—
99C2×C8×C79—21no—
100C2×C8×C79—22no—
101C2×C8×C79—21no—
102C2×C8×C79—21no—
103C2×C8×C79—21no—
104C2×C8×C79—21no—
105C2×C8×C79SD1612yescomplemented
106C4⋊C4×C79—22no—
107C4⋊C4×C79—21no—
108C4⋊C4×C79—21no—
109C4⋊C4×C79—21no—
110C4⋊C4×C79—22no—
111C4⋊C4×C79C22⋊C412yes—
112C22⋊C4×C79—22no—
113C42×C79—22no—
114C42×C79C2×D411yescharacteristic
115C42×C79C2×D411yescharacteristic
116C42×C79C2×D411yescharacteristic
117C42×C79#4111yescharacteristic
118C23×C79C4×D411yescharacteristic
119C22×D79—22no—
120C22×D79—41no—
121C22×D79—41no—
122C22×D79—41no—
123C22×D79—41no—
124C22×D79—41no—
125C22×D79—41no—
126Q8×C79—42no—
127Q8×C79—81no—
128C2×C4×C79—22no—
129C2×C4×C79—22no—
130C2×C4×C79—41no—
131C2×C4×C79—41no—
132C2×C4×C79C2×C22⋊C411yescharacteristic
133C2×C4×C79C4×D411yescharacteristic
134C2×C4×C79#12011yescharacteristic
135C2×C4×C79#12111yescharacteristic
136C2×C4×C79#12111yescharacteristic
137C2×C4×C79#12311yescharacteristic
138C2×C4×C79C2×SD1611yescharacteristic
139C2×C4×C79#13511yescharacteristic
140C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C79#13711yescharacteristic
142C2×Dic79—41no—
143C2×Dic79—41no—
144C2×Dic79—41no—
145D316—22no—
146D316—22no—
147D316—41no—
148D316—41no—
149C4×D79—81no—
150C4×D79—81no—
151C4×D79—81no—
152C4×D79—81no—
153C8×C79—22no—
154C8×C79—41no—
155C8×C79—42no—
156C79⋊C8—42no—
157C79⋊C8—81no—
158C79⋊C8—81no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79#38611yescharacteristic
162C22×C79C4×SD1611yescharacteristic
163C22×C79#44011yescharacteristic
164C2×D79—42no—
165C2×D79—42no—
166C2×D79—42no—
167C2×D79—81no—
168C2×D79—81no—
169C2×D79—81no—
170C2×D79—81no—
171C4×C79—21no—
172C4×C79—21no—
173C4×C79—21no—
174C4×C79—21no—
175C4×C79—42no—
176C4×C79—42no—
177C4×C79#44811yescharacteristic
178C4×C79#44911yescharacteristic
179C4×C79#46011yescharacteristic
180C4×C79#46411yescharacteristic
181Dic79—81no—
182#9050—791nomaximal, Sylow
183C2×C79—21no—
184C2×C79—21no—
185C2×C79#188011yescharacteristic
186C2×C79#188111yescharacteristic
187C2×C79#189111yescharacteristic
188D79—82no—
189#3101—791no—
190#2961D7911yescharacteristic, complemented
191#1955—791no—
192#1542—791no—
193#1486—791no—
194#1301—791no—
195#1281—791no—
196C79#905011yescharacteristic, complemented, Sylow
197#533C2×D7911yescharacteristic
198C2×C4×D4—791no—
199#483—792no—
200#476—1581no—
201#461—1581no—
202#450—792no—
203#446—22no—
204#446—22no—
205C4×SD16—1582no—
206#431—791no—
207#431—791no—
208#424—21no—
209#423C2×D7911yescharacteristic
210C2×C4⋊C8—791no—
211C2×C22⋊C8—1581no—
212C2×C22⋊C8—1581no—
213#405—21no—
214C2×#97C2×D7911yescharacteristic
215#333—1581no—
216#332—1581no—
217D4⋊C8—1582no—
218C22×D4—791no—
219C23×C4—1581no—
220C2×SD16—1582no—
221C2×M16—21no—
222C22×C8—1581no—
223C22×C8C22⋊D7911yescharacteristic
224C22×C8C22⋊D7911yescharacteristic
225C4⋊Q8D31611yescharacteristic
226C4⋊Q8D31611yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8C4×D7912yes—
230C4×Q8—21no—
231C4×Q8C22⋊D7912yes—
232C4×D4—1581no—
233C4×D4—1581no—
234C4×D4—1581no—
235C4×D4—1581no—
236#117—21no—
237C2×C4⋊C4—791no—
238C2×C22⋊C4—1581no—
239C2×C42C22×D7911yescharacteristic
240#106—1582no—
241C4⋊C8—24no—
242C4⋊C8—21no—
243C4⋊C8—1581no—
244C4⋊C8—1581no—
245C4⋊C8—1581no—
246C4⋊C8—1581no—
247C4⋊C8C22⋊D7912yes—
248#103—1582no—
249#102—1582no—
250C22⋊C8—3162no—
251C22⋊C8—3162no—
252C22⋊C8—792no—
253C22⋊C8—1581no—
254#97—22no—
255#97—21no—
256#97—21no—
257C4×C8—22no—
258C4×C8—1581no—
259C4×C8—1581no—
260C24—1581no—
261C2×Q8—21no—
262C2×Q8(C2×D79)⋊C412yes—
263C2×D4—3162no—
264C2×D4—1581no—
265C2×D4—1581no—
266C22×C4—3161no—
267C22×C4—3161no—
268C22×C4—3161no—
269C22×C4—3161no—
270C22×C4—3161no—
271C22×C4—3161no—
272C22×C4—1581no—
273C22×C4C2×C4×D7911yescharacteristic
274C22×C4C2×C22⋊D7911yescharacteristic
275C22×C4#1192962411yescharacteristic
276SD16—3164no—
277M16—41no—
278M16—41no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—3161no—
286C2×C8—3161no—
287C2×C8—3161no—
288C2×C8—3161no—
289C2×C8—1582no—
290C2×C8#1192961112yescomplemented
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—1581no—
297C4⋊C4—1581no—
298C4⋊C4(C2×D79)⋊C412yes—
299C22⋊C4—22no—
300C22⋊C4—3161no—
301C22⋊C4—3161no—
302C42—22no—
303C42C2×C22⋊D7911yescharacteristic
304C42C2×C22⋊D7911yescharacteristic
305C42C2×D31611yescharacteristic
306C42#1192962411yescharacteristic
307C23—3161no—
308C23—3161no—
309C23—3161no—
310C23—3161no—
311C23—3161no—
312C23—3161no—
313C23—1582no—
314C23C4×C22⋊D7911yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—3161no—
318D4—3161no—
319D4—1582no—
320D4—1582no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—3161no—
326C2×C4—3161no—
327C2×C4—3161no—
328C2×C4—6321no—
329C2×C4—6321no—
330C2×C4—6321no—
331C2×C4—6321no—
332C2×C4C2×(C2×D79)⋊C411yescharacteristic
333C2×C4C4×C22⋊D7911yescharacteristic
334C2×C4#1457913011yescharacteristic
335C2×C4#1457913511yescharacteristic
336C2×C4#1457913511yescharacteristic
337C2×C4#1457914411yescharacteristic
338C2×C4C2×#1192961111yescharacteristic
339C2×C4#1457918111yescharacteristic
340C2×C4#1457918611yescharacteristic
341C2×C4#1457919211yescharacteristic
342C8—22no—
343C8—41no—
344C8—42no—
345C8—3162no—
346C8—6321no—
347C8—6321no—
348C22—21no—
349C22—21no—
350C22—3162no—
351C22—3162no—
352C22—3162no—
353C22—6321no—
354C22—6321no—
355C22—6321no—
356C22—6321no—
357C22#1909844211yescharacteristic
358C22C4×#1192961111yescharacteristic
359C22#1909866111yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—42no—
366C4—6321no—
367C4#1909870211yescharacteristic
368C4#1909870811yescharacteristic
369C4#1909876311yescharacteristic
370C4#1909878511yescharacteristic
371C2—21no—
372C2—21no—
373C2—6322no—
374C2#2376375511yescharacteristic
375C2#2376376211yescharacteristic
376C2#2376381811yescharacteristic
subgroupG/H
centerC2×C4#14579130
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#2961C2
socleC22×C79#386
prime radicalC22×D316C2×C4
cosocleC2×C42×C79C23
hypercenter#2961D79
hypocenterC79#9050
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #23762057C2semidirect
5. #23761295C2semidirect
6. #23761245C2semidirect
7. C79×#2961C2semidirect
105. C2×C8×C79SD16semidirect
190. #2961D79semidirect
196. C79#9050semidirect
290. C2×C8#11929611semidirect

Maximal subgroups

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

subgroupindex
#237734042
#237641982
#237620572
#237618242
#237612952
#237612452
C79×#29612
#905079