Finite Group Databasebeta

← #34207422

Subgroups — #34207422

Order 20224.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098796C211yesmaximal, characteristic
2C2×#19098388C211yesmaximal, characteristic, complemented
3C2×#19098364C211yesmaximal, characteristic, complemented
4C2×(C2×D79)⋊C16C211yesmaximal, characteristic, complemented
5#23763426C211yesmaximal, characteristic, complemented
6#23761492C211yesmaximal, characteristic, complemented
7C2×#357×C79C211yesmaximal, characteristic, complemented
8C22×C8×D79C2211yescharacteristic
9C2×#14579132—21no—
10C22×C79⋊C16C2211yescharacteristic
11#19098796—22no—
12#19098796—22no—
13C2×#14579095C2211yescharacteristic
14C2×#14579095C2211yescharacteristic
15C2×#14579082—21no—
16#19098420—21no—
17#19098388—22no—
18#19098364—22no—
19(C2×D79)⋊C16—22no—
20#19098325—21no—
21C22×D8×C79C2211yescharacteristic
22C22×C16×C79C2211yescharacteristic
23C2×#107×C79C2211yescharacteristic
24#357×C79—22no—
25C22×C22⋊D79—41no—
26C22×C4×D79D411yescharacteristic
27C22×C79⋊C8D411yescharacteristic
28C2×C8×D79—21no—
29C2×C8×D79—21no—
30C2×C8×D79—21no—
31C2×C8×D79—21no—
32C2×C8×D79—21no—
33C2×C8×D79—21no—
34#14579132—24no—
35#14579132—42no—
36C2×C4⋊Dic79—21no—
37C2×C4⋊Dic79—21no—
38C2×C22⋊Dic79—41no—
39C2×(C2×D79)⋊C4—41no—
40C2×C79⋊C16—21no—
41C2×C79⋊C16—21no—
42C2×C79⋊C16D412yescomplemented
43#14579095—21no—
44#14579095—21no—
45#14579095—21no—
46#14579095D412yes—
47#14579082—24no—
48C79⋊#95—41no—
49C22×D4×C79—21no—
50C2×D8×C79—21no—
51C2×D8×C79—21no—
52C2×D8×C79—21no—
53C2×D8×C79—21no—
54C2×D8×C79—21no—
55C2×D8×C79D412yes—
56C22×C8×C79C2311yescharacteristic
57C2×C4⋊C4×C79—21no—
58C2×C16×C79—21no—
59C2×C16×C79—21no—
60C2×C16×C79—21no—
61#107×C79—21no—
62#107×C79—21no—
63C23×D79D811yescharacteristic
64C2×C22⋊D79—44no—
65C2×C22⋊D79—82no—
66C2×C22⋊D79—82no—
67C22×Dic79—41no—
68C22×Dic79—41no—
69C22×Dic79D811yescharacteristic
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C79⋊C8—21no—
77C2×C79⋊C8—21no—
78C2×C79⋊C8—21no—
79C8×D79—41no—
80C8×D79—41no—
81C8×D79—41no—
82C8×D79—41no—
83C4⋊Dic79—22no—
84C4⋊Dic79—41no—
85C4⋊Dic79—41no—
86C4⋊Dic79—41no—
87C22⋊Dic79—44no—
88(C2×D79)⋊C4—82no—
89C79⋊C16—22no—
90C24×C79—41no—
91C2×D4×C79—22no—
92C2×D4×C79—41no—
93C2×D4×C79—41no—
94C2×D4×C79—41no—
95C2×D4×C79—41no—
96C2×D4×C79—41no—
97C22×C4×C79—41no—
98C22×C4×C79C2×D411yescharacteristic
99D8×C79—22no—
100D8×C79—22no—
101D8×C79—41no—
102D8×C79—41no—
103C2×C8×C79C2×D411yescharacteristic
104C2×C8×C79C2×D411yescharacteristic
105C2×C8×C79C2×D411yescharacteristic
106C2×C8×C79#4111yescharacteristic
107C2×C8×C79#4111yescharacteristic
108C2×C8×C79#4111yescharacteristic
109C4⋊C4×C79—41no—
110C4⋊C4×C79—41no—
111C16×C79—41no—
112C23×C79—42no—
113C23×C79—81no—
114C23×C79—81no—
115C23×C79—81no—
116C23×C79—81no—
117C23×C79—81no—
118C23×C79—81no—
119C23×C79C2×D811yescharacteristic
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—21no—
123C22×D79—21no—
124C22×D79—21no—
125C22×D79—21no—
126C22×D79D1612yes—
127D4×C79—42no—
128D4×C79—42no—
129D4×C79—81no—
130D4×C79—81no—
131C2×C4×C79—81no—
132C2×C4×C79—81no—
133C2×C4×C79—81no—
134C2×C4×C79#12011yescharacteristic
135C2×C4×C79#12111yescharacteristic
136C2×C4×C79#12311yescharacteristic
137C2×C4×C79#13511yescharacteristic
138C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C79#13711yescharacteristic
140C22⋊D79—88no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—42no—
145C2×Dic79—81no—
146C2×Dic79—81no—
147C2×Dic79—81no—
148C2×Dic79—81no—
149C2×Dic79—81no—
150C4×D79—41no—
151C4×D79—41no—
152C4×D79—41no—
153C4×D79—41no—
154C8×C79#12111yescharacteristic
155C8×C79#12111yescharacteristic
156C8×C79#12311yescharacteristic
157C8×C79#12411yescharacteristic
158C79⋊C8—41no—
159C22×C79—82no—
160C22×C79—82no—
161C22×C79—82no—
162C22×C79—161no—
163C22×C79—161no—
164C22×C79—161no—
165C22×C79—161no—
166C22×C79#44711yescharacteristic
167C22×C79#46611yescharacteristic
168C22×C79#48011yescharacteristic
169C22×C79C2×D1611yescharacteristic
170C22×C79#50811yescharacteristic
171C22×C79#50911yescharacteristic
172C22×C79#51011yescharacteristic
173C2×D79—22no—
174C2×D79—22no—
175C2×D79—22no—
176C2×D79—41no—
177C2×D79—41no—
178C2×D79—41no—
179C2×D79—41no—
180C4×C79—161no—
181C4×C79#39411yescharacteristic
182C4×C79#45211yescharacteristic
183C4×C79#46811yescharacteristic
184C4×C79#48211yescharacteristic
185Dic79—41no—
186Dic79—82no—
187Dic79—161no—
188#13380—791nomaximal, Sylow
189C2×C79—162no—
190C2×C79#203311yescharacteristic
191C2×C79#218411yescharacteristic
192C2×C79#218911yescharacteristic
193C2×C79#221511yescharacteristic
194C2×C79#222011yescharacteristic
195C2×C79#223211yescharacteristic
196C2×C79#223411yescharacteristic
197D79—42no—
198C2×#466—791no—
199C2×#366—791no—
200C2×#357—791no—
201C2×#357D7911yescharacteristic, complemented
202C2×C22⋊C16—791no—
203#1808—791no—
204#1380—791no—
205C79#1338011yescharacteristic, complemented, Sylow
206C22×D8C2×D7911yescharacteristic
207C23×C8—791no—
208C2×#121—1581no—
209C22×C16—791no—
210C22×C16C2×D7911yescharacteristic
211#466—1582no—
212#466—1582no—
213C2×#107—791no—
214C2×#107—791no—
215C2×#107C2×D7911yescharacteristic
216C2×#102—1581no—
217#380—1581no—
218#366—1582no—
219#357—22no—
220#357—1582no—
221C22⋊C16—1582no—
222#340—1581no—
223C22×D4—21no—
224C22×D4—3161no—
225C23×C4—791no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8—21no—
231C2×D8C22⋊D7912yes—
232C22×C8—791no—
233C22×C8—1581no—
234C22×C8—1581no—
235C22×C8—1581no—
236C22×C8—1581no—
237C22×C8—1581no—
238C22×C8—1581no—
239C22×C8C22×D7911yescharacteristic
240#121—3162no—
241#121—1584no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—1581no—
244C2×C4⋊C4—1581no—
245C2×C22⋊C4—3161no—
246C2×C22⋊C4—3161no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—792no—
251C2×C16—1581no—
252C2×C16—1581no—
253#107—21no—
254#107—21no—
255#107—792no—
256#107—1581no—
257#107—1581no—
258#107—1581no—
259#102—1584no—
260#95—3161no—
261C24—41no—
262C24—791no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—3164no—
270C2×D4—6322no—
271C2×D4—6322no—
272C22×C4—41no—
273C22×C4—3161no—
274C22×C4—3161no—
275C22×C4—791no—
276C22×C4—1581no—
277C22×C4—1581no—
278C22×C4—1581no—
279C22×C4—1581no—
280C22×C4—1581no—
281C22×C4—1581no—
282C22×C4D4×D7911yescharacteristic
283D8—22no—
284D8—22no—
285D8—41no—
286D8—41no—
287C2×C8—3161no—
288C2×C8—3161no—
289C2×C8—3161no—
290C2×C8—3161no—
291C2×C8—1581no—
292C2×C8—1581no—
293C2×C8—1581no—
294C2×C8D4×D7911yescharacteristic
295C2×C8D4×D7911yescharacteristic
296C2×C8C2×C22⋊D7911yescharacteristic
297C2×C8#1192962311yescharacteristic
298C2×C8#1192962411yescharacteristic
299C2×C8#1192962411yescharacteristic
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—3161no—
303C4⋊C4—3161no—
304C4⋊C4—3161no—
305C4⋊C4—1582no—
306C22⋊C4—3164no—
307C22⋊C4—6322no—
308C16—41no—
309C16—1582no—
310C23—42no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—81no—
315C23—81no—
316C23—81no—
317C23—792no—
318C23—1581no—
319C23—1581no—
320C23—1581no—
321C23—1581no—
322C23—1581no—
323C23—1581no—
324C23D8×D7911yescharacteristic
325D4—42no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—6328no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—3161no—
334C2×C4—3161no—
335C2×C4—3161no—
336C2×C4—3161no—
337C2×C4—3162no—
338C2×C4—6321no—
339C2×C4—6321no—
340C2×C4—6321no—
341C2×C4—6321no—
342C2×C4—6321no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4#1457912911yescharacteristic
347C2×C4#1457913411yescharacteristic
348C2×C4#1457914311yescharacteristic
349C2×C4#1457918211yescharacteristic
350C2×C4#1457918511yescharacteristic
351C2×C4#1457919011yescharacteristic
352C8—3161no—
353C8#1457913311yescharacteristic
354C8#1457913411yescharacteristic
355C8#1457914411yescharacteristic
356C8#1457914711yescharacteristic
357C22—82no—
358C22—82no—
359C22—82no—
360C22—161no—
361C22—161no—
362C22—161no—
363C22—161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22—1582no—
369C22—1582no—
370C22—1582no—
371C22#1909869511yescharacteristic
372C22#1909879811yescharacteristic
373C22#1909887511yescharacteristic
374C22D16×D7911yescharacteristic
375C22#1909899411yescharacteristic
376C22#1909899711yescharacteristic
377C22#1909900211yescharacteristic
378C4—161no—
379C4—3161no—
380C4—6322no—
381C4—12641no—
382C4#1909847811yescharacteristic
383C4#1909872211yescharacteristic
384C4#1909880811yescharacteristic
385C4#1909888611yescharacteristic
386C2—162no—
387C2—3162no—
388C2#2376458011yescharacteristic
389C2#2376531011yescharacteristic
390C2#2376533711yescharacteristic
391C2#2376548511yescharacteristic
392C2#2376551211yescharacteristic
393C2#2376557911yescharacteristic
394C2#2376559011yescharacteristic
subgroupG/H
centerC23D8×D79
commutator, cosocleC22×C8×C79C23
FrattiniC22×C8C22×D79
FittingC2×#357×C79C2
socleC23×C79C2×D8
prime radicalC2×#19098796C2
hypercenterC2×#357D79
hypocenterC79#13380
LCSG ▷ C22×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#19098388C2semidirect
3. C2×#19098364C2semidirect
4. C2×(C2×D79)⋊C16C2semidirect
5. #23763426C2semidirect
6. #23761492C2semidirect
7. C2×#357×C79C2semidirect
42. C2×C79⋊C16D4semidirect
201. C2×#357D79semidirect
205. C79#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#190987962
C2×#190983882
C2×#190983642
C2×(C2×D79)⋊C162
#237634262
#237614922
C2×#357×C792
#1338079