Finite Group Databasebeta

← C2×#19099379 #23778166

Subgroups — C2×#19099379 #23778166

Order 10112.

1408 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579209C211yesmaximal, characteristic, complemented
2C2×#14579208C211yesmaximal, characteristic, complemented
3#19099379C2116yesmaximal, direct product factor
4C2×#14579194C211yesmaximal, characteristic, complemented
5C2×#14579193C212yesmaximal, complemented
6C2×#14579190C212yesmaximal, complemented
7C2×#14579182C212yesmaximal, complemented
8C2×#14579181C211yesmaximal, characteristic, complemented
9C22×#11929614C211yesmaximal, characteristic, complemented
10C2×Q16×D79C212yesmaximal, complemented
11C2×#14579169C211yesmaximal, characteristic, complemented
12C2×#137×C79C211yesmaximal, characteristic, complemented
13#14579209—24no—
14#14579209C2218yescomplemented
15#14579208—24no—
16#14579208C2218yescomplemented
17C2×#11929625—21no—
18C2×#11929625C2212yes—
19C2×#11929624—21no—
20C2×#11929624—22no—
21C2×#11929624C2211yescharacteristic
22C2×#11929624C2211yescharacteristic
23C2×#11929623—22no—
24C2×#11929623C2212yes—
25C22×Dic158—21no—
26C22×Dic158C2211yescharacteristic
27C2×Q8×D79—21no—
28C2×Q8×D79C2212yes—
29C2×Q8×D79C2212yes—
30#14579194C2218yescomplemented
31#14579193C22116yescomplemented
32#14579190C22116yescomplemented
33#14579182C22116yescomplemented
34#14579181C2218yescomplemented
35C2×Dic316C2212yes—
36C2×#11929614C2211yescharacteristic
37C2×#11929614C2212yes—
38C2×#11929614C2212yes—
39C2×#11929614C2218yescomplemented
40Q16×D79C22116yescomplemented
41C2×#11929613C2212yes—
42C2×#11929612C2211yescharacteristic
43C2×#11929611C2211yescharacteristic
44C2×#11929609C2211yescharacteristic
45#14579169C2218yescomplemented
46C2×#11929607C2212yes—
47C22×C79⋊C8C2211yescharacteristic
48C2×C8×D79C2212yes—
49C2×#41×C79C2211yescharacteristic
50C22×Q8×C79C2211yescharacteristic
51#137×C79C2218yescomplemented
52C2×Q16×C79C2212yes—
53C2×SD16×C79C2212yes—
54C2×M16×C79C2211yescharacteristic
55#11929625—28no—
56#11929625—24no—
57#11929625C2318yes—
58#11929624—28no—
59#11929624—22no—
60#11929624—216no—
61#11929624D414yes—
62#11929624C2314yes—
63#11929624C2314yes—
64#11929623—24no—
65#11929623—216no—
66#11929623C2318yes—
67C2×Dic158—22no—
68C2×Dic158—22no—
69C2×Dic158—28no—
70C2×Dic158—21no—
71C2×Dic158—22no—
72C2×Dic158D411yescharacteristic
73C2×Dic158C2311yescharacteristic
74C2×Dic158C2312yes—
75C2×Dic158C2314yes—
76Q8×D79—24no—
77Q8×D79—24no—
78Q8×D79—28no—
79Q8×D79C2318yes—
80Q8×D79C2318yes—
81C2×D316—22no—
82C2×D316D411yescharacteristic
83C2×D316C2311yescharacteristic
84C2×C22⋊D79—21no—
85C2×C22⋊D79—22no—
86C2×C22⋊D79D412yes—
87C22×Dic79—22no—
88C22×Dic79—21no—
89C2×C4×D79—22no—
90C2×C4×D79—22no—
91C2×C4×D79—22no—
92C2×C4×D79—21no—
93C2×C4×D79C2312yes—
94Dic316C2318yes—
95#11929614C2314yes—
96#11929614C2318yes—
97#11929614C2318yes—
98#11929613C2318yes—
99#11929612C2314yes—
100#11929611C2314yes—
101#11929609C2314yes—
102#11929607C2318yes—
103C2×C79⋊C8C2311yescharacteristic
104C2×C79⋊C8C2311yescharacteristic
105C2×C79⋊C8C2314yes—
106C8×D79C2318yes—
107#41×C79—22no—
108#41×C79C2314yes—
109C2×Q8×C79—21no—
110C2×Q8×C79—22no—
111C2×Q8×C79C2311yescharacteristic
112C2×Q8×C79C2312yes—
113C2×Q8×C79C2314yes—
114C2×D4×C79—21no—
115C2×D4×C79C2311yescharacteristic
116C22×C4×C79—21no—
117C22×C4×C79—21no—
118C22×C4×C79C2311yescharacteristic
119Q16×C79C2318yes—
120SD16×C79C2318yes—
121M16×C79C2314yes—
122C2×C8×C79C2312yes—
123C23×C79—21no—
124C23×C79C2×D411yescharacteristic
125C22×D79—21no—
126C22×D79C2×D412yes—
127Q8×C79—21no—
128Q8×C79—24no—
129Q8×C79—22no—
130Q8×C79C2412yes—
131Q8×C79C2414yes—
132D4×C79—24no—
133D4×C79—21no—
134D4×C79C2412yes—
135C2×C4×C79—22no—
136C2×C4×C79—21no—
137C2×C4×C79—24no—
138C2×C4×C79—24no—
139C2×C4×C79C2×D411yescharacteristic
140C2×C4×C79C2×D412yes—
141C2×C4×C79C2411yescharacteristic
142C2×C4×C79C2412yes—
143C22⋊D79—24no—
144C22⋊D79—28no—
145C22⋊D79C2×D418yes—
146C2×Dic79—21no—
147C2×Dic79—22no—
148C2×Dic79—24no—
149C2×Dic79—28no—
150C2×Dic79C2×D412yes—
151D316—28no—
152D316—21no—
153D316C2×D414yes—
154D316C2412yes—
155C4×D79—28no—
156C4×D79—28no—
157C4×D79—24no—
158C4×D79—28no—
159C4×D79C2×D414yes—
160C4×D79C2414yes—
161Dic158—21no—
162Dic158—22no—
163Dic158—24no—
164Dic158—28no—
165Dic158—28no—
166Dic158C2×D414yes—
167Dic158C2412yes—
168Dic158C2414yes—
169C8×C79C2414yes—
170C79⋊C8C2412yes—
171C79⋊C8C2412yes—
172C22×C79—22no—
173C22×C79—22no—
174C22×C79—42no—
175C22×C79C22×D412yes—
176C22×C79C22×D411yescharacteristic
177C2×D79—24no—
178C2×D79—22no—
179C2×D79—42no—
180C2×D79C22×D414yes—
181C4×C79—22no—
182C4×C79—24no—
183C4×C79C22×D412yes—
184C4×C79C22×D411yescharacteristic
185C4×C79C2511yescharacteristic
186Dic79—22no—
187Dic79—24no—
188Dic79C22×D414yes—
189C2×C79—22no—
190C2×C79—42no—
191C2×C79#57812yescomplemented
192C2×C79C23×D411yescharacteristic
193D79—24no—
194D79—42no—
195C2×#578—791nomaximal, Sylow
196C79C2×#57811yescharacteristic, complemented, Sylow
197C2×2−1+4—791no—
198C2×2−1+4—791no—
199#578—7916no—
200C2×#137—792no—
201C2×#137—792no—
202C2×#137—791no—
203C2×#137D7911yescharacteristic, complemented
204C2×#135—791no—
205C2×#135—792no—
206C22×Q16—791no—
207C22×Q16—792no—
208C2×#131—791no—
2092−1+4—798no—
2102−1+4—798no—
2112−1+4—1584no—
2122−1+4—1584no—
213C2×#41—791no—
214C2×#41—792no—
215C2×#41—792no—
216C2×#41—791no—
217C2×#41—1582no—
218C2×#41—1581no—
219C2×#41—1582no—
220C2×#41—1581no—
221C2×#41C2×D7911yescharacteristic
222C22×Q8—792no—
223C22×Q8—792no—
224C22×Q8—791no—
225C22×Q8—1581no—
226C22×Q8—1581no—
227C22×Q8C2×D7911yescharacteristic
228#137—7916no—
229#137—7916no—
230#137—798no—
231#137C2×D7918yescomplemented
232#135—798no—
233#135—7916no—
234C2×Q16—791no—
235C2×Q16—792no—
236C2×Q16—792no—
237C2×Q16—798no—
238C2×Q16—7916no—
239C2×Q16—792no—
240C2×Q16C2×D7912yes—
241C2×SD16—791no—
242C2×SD16—791no—
243C2×SD16—792no—
244C2×SD16C2×D7912yes—
245C2×D8—791no—
246#131—798no—
247C2×M16—792no—
248C2×M16C2×D7911yescharacteristic
249C22×C8—791no—
250C22×C8—792no—
251#41—22no—
252#41—794no—
253#41—794no—
254#41—798no—
255#41—798no—
256#41—794no—
257#41—15816no—
258#41—1588no—
259#41—1584no—
260#41—1584no—
261#41—15816no—
262#41—1588no—
263#41—1582no—
264#41C22×D7914yes—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—791no—
268C2×Q8—798no—
269C2×Q8—798no—
270C2×Q8—791no—
271C2×Q8—792no—
272C2×Q8—794no—
273C2×Q8—1582no—
274C2×Q8—1582no—
275C2×Q8—1588no—
276C2×Q8—1584no—
277C2×Q8—1584no—
278C2×Q8—1588no—
279C2×Q8—1581no—
280C2×Q8—1582no—
281C2×Q8C22×D7911yescharacteristic
282C2×Q8C22×D7912yes—
283C2×Q8C22×D7914yes—
284C2×D4—21no—
285C2×D4—792no—
286C2×D4—791no—
287C2×D4—791no—
288C2×D4—1582no—
289C2×D4—1582no—
290C2×D4—1581no—
291C2×D4C22×D7911yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—792no—
295C22×C4—1582no—
296C22×C4—1582no—
297C22×C4—1582no—
298C22×C4—1582no—
299C22×C4—1581no—
300C22×C4—1581no—
301C22×C4C22×D7911yescharacteristic
302Q16—794no—
303Q16—798no—
304Q16—798no—
305Q16—798no—
306Q16C22×D7918yes—
307SD16—794no—
308SD16—794no—
309SD16—798no—
310SD16C22×D7918yes—
311D8—794no—
312M16—798no—
313M16C22×D7914yes—
314C2×C8—791no—
315C2×C8—791no—
316C2×C8—794no—
317C2×C8—798no—
318C2×C8C22×D7912yes—
319C23—21no—
320C23—792no—
321C23—1581no—
322C23D4×D7911yescharacteristic
323Q8—24no—
324Q8—22no—
325Q8—21no—
326Q8—794no—
327Q8—792no—
328Q8—794no—
329Q8—1588no—
330Q8—1588no—
331Q8—1584no—
332Q8—1581no—
333Q8—1582no—
334Q8C23×D7912yes—
335Q8C23×D7914yes—
336D4—24no—
337D4—21no—
338D4—798no—
339D4—792no—
340D4—794no—
341D4—1588no—
342D4—1588no—
343D4—1584no—
344D4—1581no—
345D4C23×D7912yes—
346C2×C4—24no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—792no—
351C2×C4—794no—
352C2×C4—794no—
353C2×C4—1588no—
354C2×C4—1588no—
355C2×C4—1588no—
356C2×C4—1588no—
357C2×C4—1584no—
358C2×C4—1581no—
359C2×C4—1582no—
360C2×C4—1584no—
361C2×C4D4×D7912yes—
362C2×C4D4×D7911yescharacteristic
363C2×C4C23×D7912yes—
364C2×C4C23×D7911yescharacteristic
365C8—792no—
366C8—792no—
367C8C23×D7914yes—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—3162no—
372C22—794no—
373C22—1582no—
374C22—1584no—
375C22C2×D4×D7912yes—
376C22C2×D4×D7911yescharacteristic
377C4—22no—
378C4—24no—
379C4—794no—
380C4—1582no—
381C4—1584no—
382C4C2×D4×D7912yes—
383C4C2×D4×D7911yescharacteristic
384C4C24×D7911yescharacteristic
385C2—22no—
386C2—42no—
387C2—3162no—
388C2—1584no—
389C2#1909937912yesdirect product factor
390C2C22×D4×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC4×C79C25
FrattiniC4C24×D79
FittingC2×#137×C79C2
socleC22×C79C22×D4
hypercenterC2×#137D79
hypocenterC79C2×#578
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14579209C2semidirect
2. C2×#14579208C2semidirect
3. #19099379C2direct (N × H)
4. C2×#14579194C2semidirect
5. C2×#14579193C2semidirect
6. C2×#14579190C2semidirect
7. C2×#14579182C2semidirect
8. C2×#14579181C2semidirect
9. C22×#11929614C2semidirect
10. C2×Q16×D79C2semidirect
11. C2×#14579169C2semidirect
12. C2×#137×C79C2semidirect
14. #14579209C22semidirect
16. #14579208C22semidirect
30. #14579194C22semidirect
31. #14579193C22semidirect
32. #14579190C22semidirect
33. #14579182C22semidirect
34. #14579181C22semidirect
39. C2×#11929614C22semidirect
40. Q16×D79C22semidirect
45. #14579169C22semidirect
51. #137×C79C22semidirect
191. C2×C79#578semidirect
196. C79C2×#578semidirect
203. C2×#137D79semidirect
231. #137C2×D79semidirect
389. C2#19099379direct (N × H)