Finite Group Databasebeta

← #34207620

Subgroups — #34207620

Order 20224.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098947C211yesmaximal, characteristic
2C2×#19098366C211yesmaximal, characteristic, complemented
3C2×#19098366C211yesmaximal, characteristic, complemented
4C2×#19098363C211yesmaximal, characteristic
5C2×#19098363C211yesmaximal, characteristic
6#23761478C211yesmaximal, characteristic, complemented
7C79×#1942C211yesmaximal, characteristic, complemented
8C22×Dic316C2211yescharacteristic
9C22×#11929613—21no—
10C22×D632C2211yescharacteristic
11C2×#14579149—21no—
12C22×C79⋊C16C2211yescharacteristic
13C22×C79⋊C16C2211yescharacteristic
14#19098947—22no—
15#19098947—22no—
16#19098366—22no—
17#19098366—22no—
18#19098363—22no—
19#19098363—22no—
20C2×#107×C79C2211yescharacteristic
21C2×#107×C79C2211yescharacteristic
22C2×C4×C8×C79C2211yescharacteristic
23#389×C79—21no—
24#340×C79—21no—
25C22×Dic158—21no—
26C22×D316—21no—
27C2×Dic316—21no—
28C2×Dic316—21no—
29C2×Dic316—21no—
30C2×Dic316—21no—
31C2×Dic316—21no—
32C2×Dic316D412yes—
33C2×#11929613—24no—
34C2×#11929613—42no—
35C2×#11929613—42no—
36C2×D632—21no—
37C2×D632—21no—
38C2×D632—21no—
39C2×D632—21no—
40C2×D632—21no—
41C2×D632D412yes—
42#14579149—24no—
43#14579149—42no—
44C2×(C2×D79)⋊C4—41no—
45C2×(C2×D79)⋊C4—41no—
46C2×C79⋊C16—21no—
47C2×C79⋊C16—21no—
48C2×C79⋊C16—21no—
49C2×C79⋊C16—21no—
50C2×C79⋊C16—21no—
51C2×C79⋊C16—21no—
52C22×C8×C79D411yescharacteristic
53C22×C8×C79C2311yescharacteristic
54C2×C4⋊C4×C79—21no—
55C2×C4⋊C4×C79—21no—
56C2×C4⋊C4×C79—41no—
57C2×C42×C79D411yescharacteristic
58#107×C79—21no—
59#107×C79—21no—
60#107×C79—21no—
61#107×C79D412yes—
62C4×C8×C79—21no—
63C4×C8×C79—21no—
64#95×C79—41no—
65C23×D79—41no—
66C2×Dic158—22no—
67C2×Dic158—41no—
68C2×Dic158—41no—
69C2×Dic158—41no—
70C2×Dic158—41no—
71C2×Dic158—41no—
72C2×D316—22no—
73C2×D316—41no—
74C2×D316—41no—
75C2×D316—41no—
76C2×D316—41no—
77C2×D316—41no—
78C22×Dic79—41no—
79Dic316—22no—
80Dic316—22no—
81Dic316—41no—
82Dic316—41no—
83#11929613—48no—
84D632—22no—
85D632—22no—
86D632—41no—
87D632—41no—
88(C2×D79)⋊C4—44no—
89(C2×D79)⋊C4—44no—
90C79⋊C16—41no—
91C79⋊C16—41no—
92C22×C4×C79—41no—
93C22×C4×C79—41no—
94C22×C4×C79D811yescharacteristic
95C22×C4×C79D811yescharacteristic
96C22×C4×C79C2×D411yescharacteristic
97C2×C8×C79—21no—
98C2×C8×C79—21no—
99C2×C8×C79SD1612yes—
100C2×C8×C79C2×D411yescharacteristic
101C2×C8×C79C2×D411yescharacteristic
102C2×C8×C79C2×D411yescharacteristic
103C2×C8×C79#4111yescharacteristic
104C2×C8×C79#4111yescharacteristic
105C2×C8×C79#4111yescharacteristic
106C4⋊C4×C79—22no—
107C4⋊C4×C79—41no—
108C4⋊C4×C79—41no—
109C4⋊C4×C79—41no—
110C4⋊C4×C79—82no—
111C42×C79—21no—
112C42×C79—21no—
113C23×C79C2×D811yescharacteristic
114C22×D79—42no—
115C22×D79—81no—
116C22×D79—81no—
117C22×D79—81no—
118C22×D79—81no—
119C22×D79—81no—
120C22×D79—81no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—42no—
128C2×C4×C79—81no—
129C2×C4×C79—81no—
130C2×C4×C79—81no—
131C2×C4×C79—81no—
132C2×C4×C79—81no—
133C2×C4×C79#12011yescharacteristic
134C2×C4×C79#12111yescharacteristic
135C2×C4×C79#12411yescharacteristic
136C2×C4×C79C2×SD1611yescharacteristic
137C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
139C2×Dic79—42no—
140C2×Dic79—81no—
141C2×Dic79—81no—
142D316—42no—
143D316—42no—
144D316—81no—
145D316—81no—
146Dic158—42no—
147Dic158—42no—
148Dic158—81no—
149Dic158—81no—
150C8×C79—22no—
151C8×C79#12111yescharacteristic
152C8×C79#12111yescharacteristic
153C8×C79#12311yescharacteristic
154C8×C79#12311yescharacteristic
155C22×C79#44711yescharacteristic
156C22×C79#45911yescharacteristic
157C22×C79#48611yescharacteristic
158C22×C79#50811yescharacteristic
159C22×C79#50811yescharacteristic
160C22×C79#50911yescharacteristic
161C22×C79#51011yescharacteristic
162C2×D79—82no—
163C2×D79—82no—
164C2×D79—82no—
165C2×D79—161no—
166C2×D79—161no—
167C2×D79—161no—
168C2×D79—161no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79—82no—
172C4×C79—161no—
173C4×C79#39411yescharacteristic
174C4×C79#45011yescharacteristic
175C4×C79#46011yescharacteristic
176C4×C79#49011yescharacteristic
177Dic79—82no—
178#13408—791nomaximal, Sylow
179C2×C79#204111yescharacteristic
180C2×C79#218611yescharacteristic
181C2×C79#218911yescharacteristic
182C2×C79#221011yescharacteristic
183C2×C79#221111yescharacteristic
184C2×C79#224211yescharacteristic
185C2×C79#224311yescharacteristic
186D79—162no—
187C2×#495—791no—
188C2×#358—791no—
189C2×#358—791no—
190C2×#357—791no—
191C2×#357—791no—
192#1942D7911yescharacteristic, complemented
193#1374—791no—
194C79#1340811yescharacteristic, complemented, Sylow
195C22×Q16—791no—
196C22×SD16—1581no—
197C22×D8—791no—
198C2×#124—1581no—
199C22×C16—791no—
200C22×C16—791no—
201#495—1582no—
202#495—1582no—
203C2×#107C2×D7911yescharacteristic
204C2×#107C2×D7911yescharacteristic
205C2×C4×C8C2×D7911yescharacteristic
206#389—21no—
207#358—1582no—
208#358—1582no—
209#357—1582no—
210#357—1582no—
211#340—21no—
212C22×Q8—1581no—
213C22×D4—1581no—
214C2×Q16—792no—
215C2×Q16—1581no—
216C2×Q16—1581no—
217C2×Q16—1581no—
218C2×Q16—1581no—
219C2×Q16—1581no—
220C2×SD16—3162no—
221C2×SD16—3162no—
222C2×SD16—1584no—
223C2×D8—792no—
224C2×D8—1581no—
225C2×D8—1581no—
226C2×D8—1581no—
227C2×D8—1581no—
228C2×D8—1581no—
229C22×C8C22⋊D7911yescharacteristic
230C22×C8C22×D7911yescharacteristic
231#124—3162no—
232#124—1584no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C22⋊C4—3161no—
237C2×C22⋊C4—3161no—
238C2×C42C22⋊D7911yescharacteristic
239C2×C16—1581no—
240C2×C16—1581no—
241C2×C16—1581no—
242C2×C16—1581no—
243C2×C16—1581no—
244C2×C16—1581no—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D31612yes—
249C4×C8—21no—
250C4×C8—21no—
251#95—41no—
252C24—3161no—
253C2×Q8—3161no—
254C2×Q8—3161no—
255C2×Q8—3161no—
256C2×Q8—3161no—
257C2×Q8—3161no—
258C2×Q8—1582no—
259C2×D4—3161no—
260C2×D4—3161no—
261C2×D4—3161no—
262C2×D4—3161no—
263C2×D4—3161no—
264C2×D4—1582no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—3161no—
268C22×C4#1192960911yescharacteristic
269C22×C4#1192960911yescharacteristic
270C22×C4C2×C22⋊D7911yescharacteristic
271Q16—3161no—
272Q16—3161no—
273Q16—1582no—
274Q16—1582no—
275SD16—3168no—
276D8—3161no—
277D8—3161no—
278D8—1582no—
279D8—1582no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8#1192961112yes—
283C2×C8D4×D7911yescharacteristic
284C2×C8D4×D7911yescharacteristic
285C2×C8C2×D31611yescharacteristic
286C2×C8#1192962411yescharacteristic
287C2×C8#1192962511yescharacteristic
288C2×C8#1192962511yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C22⋊C4—3164no—
295C22⋊C4—3164no—
296C42—21no—
297C42—21no—
298C16—3161no—
299C16—3161no—
300C23—3162no—
301C23—6321no—
302C23—6321no—
303C23—6321no—
304C23—6321no—
305C23—6321no—
306C23—6321no—
307C23C2×#1192960911yescharacteristic
308Q8—3162no—
309Q8—3162no—
310Q8—6321no—
311Q8—6321no—
312D4—3162no—
313D4—3162no—
314D4—6321no—
315D4—6321no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—3162no—
329C2×C4—6321no—
330C2×C4—6321no—
331C2×C4#1457912911yescharacteristic
332C2×C4#1457913511yescharacteristic
333C2×C4#1457915011yescharacteristic
334C2×C4C2×#1192961111yescharacteristic
335C2×C4#1457918611yescharacteristic
336C2×C4#1457918611yescharacteristic
337C8—22no—
338C8#1457913611yescharacteristic
339C8#1457913611yescharacteristic
340C8#1457914611yescharacteristic
341C8#1457914611yescharacteristic
342C22—6322no—
343C22—6322no—
344C22—6322no—
345C22—12641no—
346C22—12641no—
347C22—12641no—
348C22—12641no—
349C22#1909869611yescharacteristic
350C22#1909875811yescharacteristic
351C22#1909891111yescharacteristic
352C22#1909899311yescharacteristic
353C22#1909899311yescharacteristic
354C22#1909899911yescharacteristic
355C22#1909900411yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—161no—
360C4—6322no—
361C4#1909848011yescharacteristic
362C4#1909871311yescharacteristic
363C4#1909876311yescharacteristic
364C4#1909892911yescharacteristic
365C2—12642no—
366C2#2376463411yescharacteristic
367C2#2376532111yescharacteristic
368C2#2376533811yescharacteristic
369C2#2376545511yescharacteristic
370C2#2376546211yescharacteristic
371C2#2376563411yescharacteristic
372C2#2376563911yescharacteristic
subgroupG/H
centerC23C2×#11929609
commutator, cosocleC22×C8×C79C23
FrattiniC22×C8C22×D79
FittingC79×#1942C2
socleC23×C79C2×D8
prime radicalC22×D632C22
hypercenter#1942D79
hypocenterC79#13408
LCSG ▷ C22×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C2×#19098366C2semidirect
3. C2×#19098366C2semidirect
6. #23761478C2semidirect
7. C79×#1942C2semidirect
192. #1942D79semidirect
194. C79#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#190989472
C2×#190983662
C2×#190983632
#237614782
C79×#19422
#1340879