Finite Group Databasebeta

← C2×#23776414 #35169207

Subgroups — C2×#23776414 #35169207

Order 20224.

2086 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
1C2×#19099299C212yesmaximal, complemented
2#23776414C2116yesmaximal, direct product factor
3C2×#19098946C212yesmaximal, complemented
4C2×#19098760C212yesmaximal, complemented
5C2×#19098776C214yesmaximal, complemented
6C2×C8×Dic158C211yesmaximal, characteristic, complemented
7C2×C4×Dic316C211yesmaximal, characteristic, complemented
8C2×D8×Dic79C212yesmaximal, complemented
9C2×#493×C79C211yesmaximal, characteristic
10C22×Dic316C2211yescharacteristic
11C22×#11929612C2214yes—
12#19099299—28no—
13#19099299C22116yescomplemented
14C2×#14579148—22no—
15C2×#14579148C2214yes—
16C2×#14579142—24no—
17C2×C4×Dic158C2211yescharacteristic
18C2×C4×Dic158C2212yes—
19C2×D4×Dic79—22no—
20C2×D4×Dic79C2214yes—
21#19098946C22116yescomplemented
22#19098776C22132yescomplemented
23#19098760C22116yescomplemented
24C8×Dic158C2218yescomplemented
25C4×Dic316C2218yescomplemented
26D8×Dic79C22116yescomplemented
27C2×#14579095C2211yescharacteristic
28C2×C4⋊(C79⋊C8)C2211yescharacteristic
29C2×Dic79⋊C8C2212yes—
30C2×#14579086C2212yes—
31C2×#14579082C2214yes—
32C2×C8×Dic79C2212yes—
33C22×D8×C79C2212yes—
34C22×D8×C79C2212yes—
35C2×#127×C79C2212yes—
36#493×C79C2218yes—
37C2×C4×C8×C79C2211yescharacteristic
38C22×Dic158D411yescharacteristic
39C22×Dic158C2312yes—
40C23×Dic79—24no—
41C2×Dic316—24no—
42C2×Dic316C2314yes—
43C2×#11929612—48no—
44C2×#11929612C23116yes—
45C22×C79⋊C8C2312yes—
46#14579148—216no—
47#14579148—28no—
48#14579148C23116yes—
49#14579142—232no—
50C4×Dic158—24no—
51C4×Dic158D414yes—
52C4×Dic158C2318yes—
53C4×Dic158C2314yes—
54D4×Dic79—216no—
55D4×Dic79—28no—
56D4×Dic79C23116yes—
57C2×C4⋊Dic79D411yescharacteristic
58C2×C4⋊Dic79C2312yes—
59C2×Dic79⋊C4—22no—
60C2×Dic79⋊C4D412yes—
61C2×C22⋊Dic79—24no—
62C2×C22⋊Dic79—24no—
63C2×C22⋊Dic79—24no—
64C2×C4×Dic79—22no—
65C2×C4×Dic79C2312yes—
66#14579095C2314yes—
67C4⋊(C79⋊C8)C2314yes—
68Dic79⋊C8C2318yes—
69#14579086C2318yes—
70#14579082C23116yes—
71C8×Dic79C2318yes—
72C22×D4×C79—22no—
73C22×D4×C79—22no—
74C22×D4×C79C2314yes—
75C2×D8×C79—28no—
76C2×D8×C79—44no—
77C2×D8×C79C2318yes—
78C2×D8×C79C2318yes—
79C22×C8×C79C2311yescharacteristic
80C22×C8×C79C2311yescharacteristic
81#127×C79—24no—
82#127×C79C2318yes—
83C2×C42×C79C2311yescharacteristic
84C4×C8×C79C2314yes—
85C2×Dic158—24no—
86C2×Dic158—22no—
87C2×Dic158—24no—
88C2×Dic158—24no—
89C2×Dic158C2×D414yes—
90C2×Dic158C2414yes—
91C22×Dic79—216no—
92C22×Dic79—22no—
93C22×Dic79—22no—
94C22×Dic79—88no—
95C22×Dic79C2×D412yes—
96C22×Dic79C2×D412yes—
97Dic316—28no—
98#11929612—416no—
99C2×C79⋊C8—24no—
100C2×C79⋊C8C2414yes—
101C4⋊Dic79—22no—
102C4⋊Dic79C2×D414yes—
103C4⋊Dic79C2414yes—
104Dic79⋊C4—28no—
105Dic79⋊C4C2×D418yes—
106C22⋊Dic79—216no—
107C22⋊Dic79—216no—
108C22⋊Dic79—216no—
109C4×Dic79—28no—
110C4×Dic79C2×D414yes—
111C4×Dic79C2414yes—
112C24×C79—24no—
113C2×D4×C79—24no—
114C2×D4×C79—28no—
115C2×D4×C79—28no—
116C2×D4×C79—28no—
117C2×D4×C79—28no—
118C2×D4×C79—48no—
119C2×D4×C79—84no—
120C2×D4×C79C2418yes—
121C22×C4×C79C2×D411yescharacteristic
122C22×C4×C79C2×D411yescharacteristic
123C22×C4×C79C2411yescharacteristic
124D8×C79—216no—
125D8×C79—48no—
126C2×C8×C79—22no—
127C2×C8×C79#4114yes—
128C2×C8×C79C2412yes—
129C2×C8×C79C2412yes—
130C42×C79C2×D412yes—
131C42×C79C2412yes—
132C23×C79—28no—
133C23×C79—48no—
134C23×C79—48no—
135C23×C79—48no—
136C23×C79C22×D411yescharacteristic
137D4×C79—28no—
138D4×C79—28no—
139D4×C79—48no—
140D4×C79—416no—
141D4×C79—88no—
142C2×C4×C79—22no—
143C2×C4×C79#13514yes—
144C2×C4×C79C22×D412yes—
145C2×C4×C79C22×D411yescharacteristic
146C2×C4×C79C22×D412yes—
147C2×C4×C79C2×#4112yes—
148C2×C4×C79H(5,𝔽2)12yes—
149C2×C4×C79C2511yescharacteristic
150C2×Dic79—24no—
151C2×Dic79—24no—
152C2×Dic79—24no—
153C2×Dic79—24no—
154C2×Dic79—44no—
155C2×Dic79—44no—
156C2×Dic79—816no—
157C2×Dic79C22×D414yes—
158C2×Dic79C22×D414yes—
159Dic158—28no—
160Dic158—24no—
161Dic158—24no—
162Dic158—44no—
163C8×C79—22no—
164C8×C79C2×#4114yes—
165C79⋊C8—24no—
166C22×C79—48no—
167C22×C79—48no—
168C22×C79—48no—
169C22×C79—816no—
170C22×C79#55012yes—
171C22×C79C2×#13512yes—
172C22×C79#57612yes—
173C22×C79C23×D411yescharacteristic
174C4×C79—22no—
175C4×C79#55012yes—
176C4×C79C2×#13514yes—
177C4×C79C22×#4111yescharacteristic
178C4×C79C2×H(5,𝔽2)11yescharacteristic
179Dic79—24no—
180Dic79—24no—
181Dic79—44no—
182Dic79—44no—
183C2×#3396—791nomaximal, Sylow
184C2×C79—88no—
185C2×C79#339614yescomplemented
186C2×C79C2×#55011yescharacteristic
187C2×C79C22×#13511yescharacteristic
188C2×C79C2×#57611yescharacteristic
189C2×#559—792no—
190#3396—7916no—
191C2×#495—792no—
192C2×#493D7911yescharacteristic
193C2×#460—792no—
194C2×#463—794no—
195C2×C8×Q8—791no—
196C2×C4×Q16—791no—
197C2×C4×D8—792no—
198C79C2×#339611yescharacteristic, complemented, Sylow
199C22×Q16—791no—
200C22×SD16—794no—
201C22×D8C2×D7912yes—
202C22×D8C2×D7912yes—
203#559—7916no—
204#559—1588no—
205C2×#127C2×D7912yes—
206C2×#124—794no—
207C2×#124—1582no—
208C2×#123—1584no—
209C2×C4×Q8—791no—
210C2×C4×Q8—792no—
211C2×C4×D4—794no—
212C2×C4×D4—1582no—
213#495—7916no—
214#493C2×D7918yes—
215#463—7932no—
216#460—7916no—
217C8×Q8—798no—
218C4×Q16—798no—
219C4×D8—7916no—
220C2×#107—791no—
221C2×C4⋊C8—792no—
222C2×C4⋊C8—791no—
223C2×#103—792no—
224C2×#102—794no—
225C2×C4×C8—792no—
226C2×C4×C8C2×D7911yescharacteristic
227C22×Q8—791no—
228C22×Q8—792no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4C22×D7914yes—
232C23×C4—1584no—
233C2×Q16—794no—
234C2×Q16—1584no—
235C2×SD16—3168no—
236C2×SD16—7916no—
237C2×D8—28no—
238C2×D8—44no—
239C2×D8C22×D7918yes—
240C2×D8C22×D7918yes—
241C22×C8—792no—
242C22×C8C22×D7911yescharacteristic
243C22×C8C22×D7911yescharacteristic
244#127—24no—
245#127C22×D7918yes—
246#124—7916no—
247#124—1588no—
248#124—15816no—
249#123—15832no—
250C4×Q8—794no—
251C4×Q8—794no—
252C4×Q8—798no—
253C4×Q8—1584no—
254C4×D4—7916no—
255C4×D4—1588no—
256C4×D4—15816no—
257C2×C4⋊C4—791no—
258C2×C4⋊C4—792no—
259C2×C4⋊C4—792no—
260C2×C4⋊C4—1582no—
261C2×C22⋊C4—1584no—
262C2×C22⋊C4—1584no—
263C2×C22⋊C4—1584no—
264C2×C42—792no—
265C2×C42—1582no—
266C2×C42C22×D7911yescharacteristic
267#107—794no—
268C4⋊C8—798no—
269C4⋊C8—794no—
270#103—798no—
271#102—7916no—
272C4×C8—798no—
273C4×C8C22×D7914yes—
274C24—24no—
275C2×Q8—794no—
276C2×Q8—794no—
277C2×Q8—1584no—
278C2×Q8—1584no—
279C2×Q8—1584no—
280C2×Q8—1582no—
281C2×D4—28no—
282C2×D4—28no—
283C2×D4—24no—
284C2×D4—28no—
285C2×D4—28no—
286C2×D4—48no—
287C2×D4—84no—
288C2×D4C23×D7918yes—
289C22×C4—792no—
290C22×C4—792no—
291C22×C4—6328no—
292C22×C4—1582no—
293C22×C4—1582no—
294C22×C4—15816no—
295C22×C4D4×D7911yescharacteristic
296C22×C4D4×D7911yescharacteristic
297C22×C4C23×D7911yescharacteristic
298Q16—1588no—
299SD16—31616no—
300D8—216no—
301D8—48no—
302C2×C8—22no—
303C2×C8—794no—
304C2×C8—1584no—
305C2×C8#1192962314yes—
306C2×C8C23×D7912yes—
307C2×C8C23×D7912yes—
308C4⋊C4—798no—
309C4⋊C4—794no—
310C4⋊C4—794no—
311C4⋊C4—1588no—
312C4⋊C4—1582no—
313C22⋊C4—15816no—
314C22⋊C4—15816no—
315C22⋊C4—15816no—
316C42—794no—
317C42—794no—
318C42—1588no—
319C42D4×D7912yes—
320C42C23×D7912yes—
321C23—28no—
322C23—48no—
323C23—48no—
324C23—48no—
325C23C2×D4×D7911yescharacteristic
326Q8—3164no—
327Q8—1584no—
328Q8—1584no—
329Q8—1588no—
330D4—28no—
331D4—28no—
332D4—48no—
333D4—416no—
334D4—88no—
335C2×C4—22no—
336C2×C4—3164no—
337C2×C4—3164no—
338C2×C4—794no—
339C2×C4—794no—
340C2×C4—63216no—
341C2×C4—1584no—
342C2×C4—1584no—
343C2×C4—1584no—
344C2×C4—1584no—
345C2×C4#1457918014yes—
346C2×C4C2×D4×D7912yes—
347C2×C4C2×D4×D7911yescharacteristic
348C2×C4C2×D4×D7912yes—
349C2×C4C2×#1192962312yes—
350C2×C4#1457920612yes—
351C2×C4C24×D7911yescharacteristic
352C8—22no—
353C8—1584no—
354C8C2×#1192962314yes—
355C22—48no—
356C22—48no—
357C22—48no—
358C22—816no—
359C22#1909923312yes—
360C22C2×#1457918012yes—
361C22#1909936412yes—
362C22C22×D4×D7911yescharacteristic
363C4—22no—
364C4—3164no—
365C4—3164no—
366C4—1584no—
367C4—1584no—
368C4#1909923312yes—
369C4C2×#1457918014yes—
370C4C22×#1192962311yescharacteristic
371C4C2×#1457920611yescharacteristic
372C2—88no—
373C2#2377641414yesdirect product factor
374C2C2×#1909923311yescharacteristic
375C2C22×#1457918011yescharacteristic
376C2C2×#1909936411yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
Fitting, prime radicalC2×#493×C79C2
socleC23×C79C22×D4
hypercenterC2×#493D79
hypocenterC79C2×#3396
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#19099299C2semidirect
2. #23776414C2direct (N × H)
3. C2×#19098946C2semidirect
4. C2×#19098760C2semidirect
5. C2×#19098776C2semidirect
6. C2×C8×Dic158C2semidirect
7. C2×C4×Dic316C2semidirect
8. C2×D8×Dic79C2semidirect
13. #19099299C22semidirect
21. #19098946C22semidirect
22. #19098776C22semidirect
23. #19098760C22semidirect
24. C8×Dic158C22semidirect
25. C4×Dic316C22semidirect
26. D8×Dic79C22semidirect
185. C2×C79#3396semidirect
198. C79C2×#3396semidirect
373. C2#23776414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992992
#237764142
C2×#190989462
C2×#190987602
C2×#190987762
C2×C8×Dic1582
C2×C4×Dic3162
C2×D8×Dic792
C2×#493×C792
C2×#339679