Finite Group Databasebeta

← C2×#23773980 #35158006

Subgroups — C2×#23773980 #35158006

Order 20224.

2566 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×#19099114C212yesmaximal, complemented
2#23773980C2116yesmaximal, direct product factor
3C2×#19098940C211yesmaximal, characteristic, complemented
4C2×#19098911C212yesmaximal, complemented
5C2×#19098800C214yesmaximal, complemented
6C2×#19098645C214yesmaximal, complemented
7C2×C4×C8×D79C211yesmaximal, characteristic, complemented
8C2×#500×C79C211yesmaximal, characteristic, complemented
9C22×#11929625—22no—
10C22×D632C2214yes—
11C22×C8×D79C2212yes—
12#19099114—28no—
13#19099114C22116yescomplemented
14C2×#14579158C2212yes—
15C2×#14579150—22no—
16C2×#14579136—22no—
17C2×#14579136C2214yes—
18C2×#14579123—22no—
19C2×#14579123C2214yes—
20C2×C42×D79C2211yescharacteristic
21#19098940C2218yescomplemented
22#19098911C22116yescomplemented
23#19098800C22132yescomplemented
24#19098645C22132yescomplemented
25C2×#14579081C2218yes—
26C2×C4×C79⋊C8C2211yescharacteristic
27C2×C8×Dic79C2212yes—
28C4×C8×D79C2218yescomplemented
29C2×C4⋊Q8×C79C2212yes—
30#500×C79C2218yescomplemented
31C2×#107×C79C2214yes—
32C2×C4×C8×C79C2211yescharacteristic
33C2×#11929625—216no—
34C2×#11929625—416no—
35C22×D316—22no—
36C22×D316—22no—
37C22×D316—24no—
38C22×D316C2314yes—
39C22×C4×D79—24no—
40C22×C4×D79D411yescharacteristic
41C22×C4×D79D411yescharacteristic
42C22×C4×D79C2311yescharacteristic
43C2×D632—216no—
44C2×D632C23116yes—
45C22×C79⋊C8C2312yes—
46C2×C8×D79—28no—
47C2×C8×D79C2318yes—
48#14579158—24no—
49#14579158C2318yes—
50#14579150—216no—
51#14579136—216no—
52#14579136—28no—
53#14579136C23116yes—
54#14579123—216no—
55#14579123—28no—
56#14579123C23116yes—
57C2×(C2×D79)⋊C4—24no—
58C2×(C2×D79)⋊C4—24no—
59C2×C4×Dic79D411yescharacteristic
60C2×C4×Dic79D411yescharacteristic
61C2×C4×Dic79C2311yescharacteristic
62C42×D79D414yes—
63C42×D79C2314yes—
64#14579081C23132yes—
65C4×C79⋊C8C2314yes—
66C8×Dic79C2318yes—
67C22×Q8×C79—22no—
68C22×C8×C79C2312yes—
69C4⋊Q8×C79—24no—
70C4⋊Q8×C79C2318yes—
71C2×C4⋊C4×C79—22no—
72C2×C4⋊C4×C79C2314yes—
73C2×C42×C79C2311yescharacteristic
74#107×C79C23116yes—
75C4×C8×C79C2314yes—
76C23×D79—24no—
77C23×D79C2×D411yescharacteristic
78#11929625—464no—
79C2×D316—216no—
80C2×D316—28no—
81C2×D316—24no—
82C2×D316—28no—
83C2×D316—216no—
84C2×D316—416no—
85C2×D316—48no—
86C2×D316—48no—
87C2×D316C2418yes—
88C22×Dic79C2×D411yescharacteristic
89C22×Dic79C2×D411yescharacteristic
90C22×Dic79C2×D411yescharacteristic
91C2×C4×D79—216no—
92C2×C4×D79—24no—
93C2×C4×D79—24no—
94C2×C4×D79—416no—
95C2×C4×D79D818yescomplemented
96C2×C4×D79C2×D412yes—
97C2×C4×D79C2×D414yes—
98C2×C4×D79C2×D414yes—
99C2×C4×D79C2412yes—
100D632—232no—
101C2×C79⋊C8—24no—
102C2×C79⋊C8C2414yes—
103C8×D79—216no—
104(C2×D79)⋊C4—216no—
105(C2×D79)⋊C4—216no—
106C4×Dic79C2×D412yes—
107C4×Dic79C2×D414yes—
108C4×Dic79C2×D414yes—
109C4×Dic79C2412yes—
110C2×Q8×C79—28no—
111C2×Q8×C79—48no—
112C22×C4×C79—24no—
113C22×C4×C79C2×D411yescharacteristic
114C22×C4×C79C2×D411yescharacteristic
115C22×C4×C79C2411yescharacteristic
116C2×C8×C79#4118yescomplemented
117C2×C8×C79C2414yes—
118C4⋊C4×C79—28no—
119C4⋊C4×C79—24no—
120C4⋊C4×C79C2418yes—
121C42×C79C2×D412yes—
122C42×C79C2412yes—
123C23×C79C22×D411yescharacteristic
124C22×D79—22no—
125C22×D79—22no—
126C22×D79—28no—
127C22×D79—48no—
128C22×D79—48no—
129C22×D79—48no—
130C22×D79C2×D814yes—
131C22×D79C22×D412yes—
132Q8×C79—416no—
133C2×C4×C79—28no—
134C2×C4×C79—48no—
135C2×C4×C79C2×D814yes—
136C2×C4×C79#13514yes—
137C2×C4×C79C22×D411yescharacteristic
138C2×C4×C79C22×D412yes—
139C2×C4×C79C22×D412yes—
140C2×C4×C79C2×#4114yes—
141C2×C4×C79C2511yescharacteristic
142C2×Dic79—22no—
143C2×Dic79—22no—
144C2×Dic79C2×D814yes—
145C2×Dic79C22×D412yes—
146C2×Dic79C22×D412yes—
147C2×Dic79C22×D412yes—
148D316—216no—
149D316—432no—
150D316—48no—
151D316—416no—
152D316—416no—
153C4×D79—24no—
154C4×D79—28no—
155C4×D79—24no—
156C4×D79—432no—
157C4×D79C2×D8116yescomplemented
158C8×C79C2×#4118yescomplemented
159C79⋊C8—24no—
160C22×C79#53212yes—
161C22×C79C22×D812yes—
162C22×C79C2×#13512yes—
163C22×C79C23×D411yescharacteristic
164C2×D79—28no—
165C2×D79—22no—
166C2×D79—22no—
167C2×D79—48no—
168C2×D79—48no—
169C2×D79—48no—
170C2×D79—816no—
171C2×D79C22×D814yes—
172C4×C79—48no—
173C4×C79#53212yes—
174C4×C79C22×D814yes—
175C4×C79C2×#13514yes—
176C4×C79C22×#4112yes—
177Dic79—22no—
178Dic79—22no—
179Dic79C22×D814yes—
180C2×#3169—791nomaximal, Sylow
181C2×C79#316914yescomplemented
182C2×C79C2×#53211yescharacteristic
183C2×C79C23×D811yescharacteristic
184C2×C79C22×#13511yescharacteristic
185D79—24no—
186D79—88no—
187C2×#532—792no—
188#3169—7916no—
189C2×#500D7911yescharacteristic, complemented
190C2×#493—791no—
191C2×#486—792no—
192C2×#466—794no—
193C2×C4×D8—794no—
194C22×C4×C8—791no—
195C79C2×#316911yescharacteristic, complemented, Sylow
196C22×#41—1582no—
197C22×D8—794no—
198C23×C8—792no—
199#532—7916no—
200#532—1588no—
201C2×C4⋊Q8C2×D7912yes—
202C2×#127—792no—
203C2×#124—1582no—
204C2×#121—794no—
205C2×#121—1582no—
206C2×C4×D4—794no—
207C2×C4×D4—1582no—
208C22×C42—791no—
209#500C2×D7918yescomplemented
210#493—798no—
211#486—7916no—
212#466—7932no—
213C4×D8—7932no—
214C2×#107C2×D7914yes—
215C2×#102—798no—
216C2×C4×C8—792no—
217C2×C4×C8—791no—
218C2×C4×C8—798no—
219C2×C4×C8C2×D7911yescharacteristic
220C2×#41—31616no—
221C2×#41—15816no—
222C22×Q8—22no—
223C22×D4—794no—
224C22×D4—1584no—
225C22×D4—1582no—
226C22×D4—1582no—
227C23×C4—791no—
228C23×C4—791no—
229C23×C4—791no—
230C23×C4—1584no—
231C2×D8—7916no—
232C2×D8—15816no—
233C22×C8—792no—
234C22×C8—798no—
235C22×C8—1588no—
236C22×C8C22×D7912yes—
237C4⋊Q8—24no—
238C4⋊Q8C22×D7918yes—
239#127—798no—
240#127—1584no—
241#124—15816no—
242#121—7916no—
243#121—1588no—
244#121—15816no—
245C4×D4—7916no—
246C4×D4—1588no—
247C4×D4—15816no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4C22×D7914yes—
250C2×C22⋊C4—1584no—
251C2×C22⋊C4—1584no—
252C2×C42—791no—
253C2×C42—791no—
254C2×C42—791no—
255C2×C42—794no—
256C2×C42—794no—
257C2×C42C22×D7911yescharacteristic
258#107C22×D79116yes—
259#102—7932no—
260C4×C8—798no—
261C4×C8—794no—
262C4×C8C22×D7914yes—
263C24—791no—
264C24—1584no—
265#41—31664no—
266C2×Q8—28no—
267C2×Q8—48no—
268C2×D4—31616no—
269C2×D4—3168no—
270C2×D4—3168no—
271C2×D4—798no—
272C2×D4—15816no—
273C2×D4—15816no—
274C2×D4—1588no—
275C2×D4—1584no—
276C2×D4—1588no—
277C22×C4—24no—
278C22×C4—31616no—
279C22×C4—791no—
280C22×C4—798no—
281C22×C4—794no—
282C22×C4—791no—
283C22×C4—791no—
284C22×C4—792no—
285C22×C4—794no—
286C22×C4—792no—
287C22×C4—15816no—
288C22×C4—1584no—
289C22×C4—1584no—
290C22×C4D4×D7911yescharacteristic
291C22×C4D4×D7911yescharacteristic
292C22×C4C23×D7911yescharacteristic
293D8—15832no—
294C2×C8—794no—
295C2×C8—1584no—
296C2×C8—15816no—
297C2×C8#1192962518yescomplemented
298C2×C8C23×D7914yes—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4C23×D7918yes—
302C22⋊C4—15816no—
303C22⋊C4—15816no—
304C42—792no—
305C42—794no—
306C42—792no—
307C42—794no—
308C42D4×D7912yes—
309C42C23×D7912yes—
310C23—3168no—
311C23—3168no—
312C23—3168no—
313C23—794no—
314C23—792no—
315C23—1588no—
316C23—1582no—
317C23—1582no—
318C23C2×D4×D7911yescharacteristic
319Q8—416no—
320D4—31632no—
321D4—31616no—
322D4—31616no—
323D4—3168no—
324D4—15816no—
325C2×C4—28no—
326C2×C4—48no—
327C2×C4—31632no—
328C2×C4—794no—
329C2×C4—792no—
330C2×C4—7916no—
331C2×C4—792no—
332C2×C4—792no—
333C2×C4—1582no—
334C2×C4—1582no—
335C2×C4—1588no—
336C2×C4—1584no—
337C2×C4—1584no—
338C2×C4D8×D7914yes—
339C2×C4#1457918414yes—
340C2×C4C2×D4×D7912yes—
341C2×C4C2×D4×D7912yes—
342C2×C4C2×D4×D7911yescharacteristic
343C2×C4C2×#1192962514yes—
344C2×C4C24×D7911yescharacteristic
345C8—1584no—
346C8C2×#1192962518yescomplemented
347C22—3168no—
348C22—3168no—
349C22—3168no—
350C22—794no—
351C22—63216no—
352C22—1588no—
353C22—1582no—
354C22—1582no—
355C22#1909911412yes—
356C22C2×D8×D7912yes—
357C22C2×#1457918412yes—
358C22C22×D4×D7911yescharacteristic
359C4—48no—
360C4—794no—
361C4—1582no—
362C4—1582no—
363C4#1909911412yes—
364C4C2×D8×D7914yes—
365C4C2×#1457918414yes—
366C4C22×#1192962512yes—
367C2—6328no—
368C2—1584no—
369C2#2377398014yesdirect product factor
370C2C2×#1909911411yescharacteristic
371C2C22×D8×D7911yescharacteristic
372C2C22×#1457918411yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#500×C79C2
socleC23×C79C22×D4
hypercenterC2×#500D79
hypocenterC79C2×#3169
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
1. C2×#19099114C2semidirect
2. #23773980C2direct (N × H)
3. C2×#19098940C2semidirect
4. C2×#19098911C2semidirect
5. C2×#19098800C2semidirect
6. C2×#19098645C2semidirect
7. C2×C4×C8×D79C2semidirect
8. C2×#500×C79C2semidirect
13. #19099114C22semidirect
21. #19098940C22semidirect
22. #19098911C22semidirect
23. #19098800C22semidirect
24. #19098645C22semidirect
28. C4×C8×D79C22semidirect
30. #500×C79C22semidirect
95. C2×C4×D79D8semidirect
116. C2×C8×C79#41semidirect
157. C4×D79C2×D8semidirect
158. C8×C79C2×#41semidirect
181. C2×C79#3169semidirect
189. C2×#500D79semidirect
195. C79C2×#3169semidirect
209. #500C2×D79semidirect
297. C2×C8#11929625semidirect
346. C8C2×#11929625semidirect
369. C2#23773980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991142
#237739802
C2×#190989402
C2×#190989112
C2×#190988002
C2×#190986452
C2×C4×C8×D792
C2×#500×C792
C2×#316979