Finite Group Databasebeta

← #34207441

Subgroups — #34207441

Order 20224.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098805C211yesmaximal, characteristic
2C2×#19098390C211yesmaximal, characteristic, complemented
3C2×#19098368C211yesmaximal, characteristic, complemented
4C2×#19098366C211yesmaximal, characteristic, complemented
5C2×(C2×D79)⋊C16C211yesmaximal, characteristic
6#23763426C211yesmaximal, characteristic
7C79×#1380C211yesmaximal, characteristic, complemented
8C22×Dic316C2211yescharacteristic
9C22×C8×D79C2211yescharacteristic
10C2×#14579141—21no—
11C22×C79⋊C16C2211yescharacteristic
12#19098805—22no—
13#19098805—22no—
14C2×#14579095C2211yescharacteristic
15C2×#14579084—21no—
16#19098420—21no—
17#19098390—22no—
18#19098368—22no—
19#19098366—22no—
20(C2×D79)⋊C16—22no—
21#19098325—21no—
22C22×C16×C79C2211yescharacteristic
23C2×#107×C79C2211yescharacteristic
24C2×#107×C79C2211yescharacteristic
25C22×Dic158—21no—
26C22×C4×D79D411yescharacteristic
27C2×Dic316—21no—
28C2×Dic316—21no—
29C2×Dic316—21no—
30C2×Dic316—21no—
31C2×Dic316—21no—
32C2×Dic316D412yes—
33C22×C79⋊C8D411yescharacteristic
34C2×C8×D79—21no—
35C2×C8×D79—21no—
36C2×C8×D79—21no—
37C2×C8×D79—21no—
38C2×C8×D79—21no—
39C2×C8×D79—21no—
40#14579141—24no—
41#14579141—42no—
42C2×C4⋊Dic79—21no—
43C2×C4⋊Dic79—41no—
44C2×(C2×D79)⋊C4—41no—
45C2×(C2×D79)⋊C4—41no—
46C2×C79⋊C16—21no—
47C2×C79⋊C16—21no—
48C2×C79⋊C16D412yes—
49#14579095—21no—
50#14579095—21no—
51#14579084—24no—
52C79⋊#95—41no—
53C22×C8×C79C2311yescharacteristic
54C2×C4⋊C4×C79—21no—
55C2×C4⋊C4×C79—21no—
56C2×C16×C79—21no—
57C2×C16×C79—21no—
58C2×C16×C79—21no—
59#107×C79—21no—
60#107×C79—21no—
61#107×C79—21no—
62#107×C79D412yes—
63C23×D79D811yescharacteristic
64C2×Dic158—22no—
65C2×Dic158—41no—
66C2×Dic158—41no—
67C2×Dic158—41no—
68C2×Dic158—41no—
69C2×Dic158—41no—
70C22×Dic79—41no—
71C22×Dic79—41no—
72C22×Dic79D811yescharacteristic
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79—21no—
77C2×C4×D79—21no—
78C2×C4×D79—21no—
79Dic316—22no—
80Dic316—22no—
81Dic316—41no—
82Dic316—41no—
83C2×C79⋊C8—21no—
84C2×C79⋊C8—21no—
85C2×C79⋊C8—21no—
86C8×D79—41no—
87C8×D79—41no—
88C8×D79—41no—
89C8×D79—41no—
90C4⋊Dic79—44no—
91C4⋊Dic79—41no—
92C4⋊Dic79—41no—
93(C2×D79)⋊C4—44no—
94(C2×D79)⋊C4—82no—
95C79⋊C16—22no—
96C22×C4×C79—41no—
97C22×C4×C79—41no—
98C22×C4×C79C2×D411yescharacteristic
99C2×C8×C79C2×D411yescharacteristic
100C2×C8×C79C2×D411yescharacteristic
101C2×C8×C79C2×D411yescharacteristic
102C2×C8×C79#4111yescharacteristic
103C2×C8×C79#4111yescharacteristic
104C2×C8×C79#4111yescharacteristic
105C4⋊C4×C79—22no—
106C4⋊C4×C79—41no—
107C4⋊C4×C79—41no—
108C4⋊C4×C79—41no—
109C16×C79—41no—
110C23×C79C2×D811yescharacteristic
111C22×D79—21no—
112C22×D79—21no—
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79SD3212yes—
118C2×C4×C79—42no—
119C2×C4×C79—81no—
120C2×C4×C79—81no—
121C2×C4×C79—81no—
122C2×C4×C79—81no—
123C2×C4×C79—81no—
124C2×C4×C79#12011yescharacteristic
125C2×C4×C79#12111yescharacteristic
126C2×C4×C79#12311yescharacteristic
127C2×C4×C79#13511yescharacteristic
128C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C79#13711yescharacteristic
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—42no—
134C2×Dic79—81no—
135C2×Dic79—81no—
136C2×Dic79—81no—
137C2×Dic79—81no—
138C2×Dic79—81no—
139C4×D79—41no—
140C4×D79—41no—
141C4×D79—41no—
142C4×D79—41no—
143Dic158—42no—
144Dic158—42no—
145Dic158—81no—
146Dic158—81no—
147C8×C79#12111yescharacteristic
148C8×C79#12111yescharacteristic
149C8×C79#12311yescharacteristic
150C8×C79#12411yescharacteristic
151C79⋊C8—41no—
152C22×C79#44711yescharacteristic
153C22×C79#46611yescharacteristic
154C22×C79#48011yescharacteristic
155C22×C79C2×SD3211yescharacteristic
156C22×C79#50811yescharacteristic
157C22×C79#51011yescharacteristic
158C22×C79#51011yescharacteristic
159C2×D79—22no—
160C2×D79—22no—
161C2×D79—22no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—41no—
166C4×C79—82no—
167C4×C79—161no—
168C4×C79#39411yescharacteristic
169C4×C79#45211yescharacteristic
170C4×C79#46811yescharacteristic
171C4×C79#48211yescharacteristic
172Dic79—41no—
173Dic79—82no—
174Dic79—161no—
175#13382—791nomaximal, Sylow
176C2×C79#203311yescharacteristic
177C2×C79#218511yescharacteristic
178C2×C79#218911yescharacteristic
179C2×C79#221711yescharacteristic
180C2×C79#221911yescharacteristic
181C2×C79#223511yescharacteristic
182C2×C79#223711yescharacteristic
183D79—42no—
184C2×#467—791no—
185C2×#367—791no—
186C2×#358—791no—
187C2×#358—791no—
188C2×C22⋊C16—791no—
189#1808—791no—
190#1380D7911yescharacteristic, complemented
191C79#1338211yescharacteristic, complemented, Sylow
192C22×Q16—791no—
193C23×C8—791no—
194C2×C22⋊Q8—1581no—
195C22×C16—791no—
196C22×C16C2×D7911yescharacteristic
197#467—1582no—
198#467—1582no—
199C2×#107—791no—
200C2×#107C2×D7911yescharacteristic
201C2×#107C2×D7911yescharacteristic
202C2×#103—1581no—
203#380—1581no—
204#367—1582no—
205#358—1582no—
206#358—1582no—
207C22⋊C16—1582no—
208#340—1581no—
209C22×Q8—1581no—
210C23×C4—791no—
211C2×Q16—792no—
212C2×Q16—1581no—
213C2×Q16—1581no—
214C2×Q16—1581no—
215C2×Q16—1581no—
216C2×Q16—1581no—
217C22×C8—791no—
218C22×C8—1581no—
219C22×C8—1581no—
220C22×C8—1581no—
221C22×C8—1581no—
222C22×C8—1581no—
223C22×C8—1581no—
224C22×C8C22×D7911yescharacteristic
225C22⋊Q8—3162no—
226C22⋊Q8—1584no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—3161no—
230C2×C4⋊C4—1581no—
231C2×C22⋊C4—3161no—
232C2×C22⋊C4—3161no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16—792no—
237C2×C16—1581no—
238C2×C16—1581no—
239#107—21no—
240#107—21no—
241#107—21no—
242#107—1581no—
243#107—1581no—
244#107D31612yes—
245#103—1584no—
246#95—3161no—
247C24—791no—
248C2×Q8—3161no—
249C2×Q8—3161no—
250C2×Q8—3161no—
251C2×Q8—3161no—
252C2×Q8—3161no—
253C2×Q8—1582no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—3161no—
257C22×C4—3161no—
258C22×C4—791no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4—1581no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4D4×D7911yescharacteristic
266Q16—3161no—
267Q16—3161no—
268Q16—1582no—
269Q16—1582no—
270C2×C8—3161no—
271C2×C8—3161no—
272C2×C8—3161no—
273C2×C8—3161no—
274C2×C8—1581no—
275C2×C8—1581no—
276C2×C8—1581no—
277C2×C8D4×D7911yescharacteristic
278C2×C8D4×D7911yescharacteristic
279C2×C8C2×D31611yescharacteristic
280C2×C8#1192962411yescharacteristic
281C2×C8#1192962411yescharacteristic
282C2×C8#1192962511yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—3164no—
288C4⋊C4—3161no—
289C4⋊C4—3161no—
290C22⋊C4—3164no—
291C22⋊C4—6322no—
292C16—41no—
293C16—1582no—
294C23—792no—
295C23—1581no—
296C23—1581no—
297C23—1581no—
298C23—1581no—
299C23—1581no—
300C23—1581no—
301C23D8×D7911yescharacteristic
302Q8—3162no—
303Q8—3162no—
304Q8—6321no—
305Q8—6321no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—3161no—
313C2×C4—3161no—
314C2×C4—3161no—
315C2×C4—3161no—
316C2×C4—3162no—
317C2×C4—6321no—
318C2×C4—6321no—
319C2×C4—6321no—
320C2×C4—6321no—
321C2×C4—6321no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4—1581no—
325C2×C4#1457913111yescharacteristic
326C2×C4#1457913411yescharacteristic
327C2×C4#1457914611yescharacteristic
328C2×C4#1457918211yescharacteristic
329C2×C4#1457918811yescharacteristic
330C2×C4#1457919311yescharacteristic
331C8—3161no—
332C8#1457913411yescharacteristic
333C8#1457913611yescharacteristic
334C8#1457914611yescharacteristic
335C8#1457914911yescharacteristic
336C22—3161no—
337C22—3161no—
338C22—3161no—
339C22—3161no—
340C22—1582no—
341C22—1582no—
342C22—1582no—
343C22#1909869811yescharacteristic
344C22#1909879811yescharacteristic
345C22#1909887811yescharacteristic
346C22SD32×D7911yescharacteristic
347C22#1909899211yescharacteristic
348C22#1909900211yescharacteristic
349C22#1909900511yescharacteristic
350C4—82no—
351C4—161no—
352C4—3161no—
353C4—6322no—
354C4—12641no—
355C4#1909848111yescharacteristic
356C4#1909872811yescharacteristic
357C4#1909881211yescharacteristic
358C4#1909888911yescharacteristic
359C2—3162no—
360C2#2376458511yescharacteristic
361C2#2376531811yescharacteristic
362C2#2376534111yescharacteristic
363C2#2376549511yescharacteristic
364C2#2376550711yescharacteristic
365C2#2376559911yescharacteristic
366C2#2376561011yescharacteristic
subgroupG/H
centerC23D8×D79
commutator, cosocleC22×C8×C79C23
FrattiniC22×C8C22×D79
FittingC79×#1380C2
socleC23×C79C2×D8
prime radicalC23×D79D8
hypercenter#1380D79
hypocenterC79#13382
LCSG ▷ C22×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#19098390C2semidirect
3. C2×#19098368C2semidirect
4. C2×#19098366C2semidirect
7. C79×#1380C2semidirect
190. #1380D79semidirect
191. C79#13382semidirect

Maximal subgroups

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

subgroupindex
C2×#190988052
C2×#190983902
C2×#190983682
C2×#190983662
C2×(C2×D79)⋊C162
#237634262
C79×#13802
#1338279