Finite Group Databasebeta

← C4×#14579190 #23772214

Subgroups — C4×#14579190 #23772214

Order 10112.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579190C211yesmaximal, characteristic
2C4×#11929623C211yesmaximal, characteristic
3C4×Q8×D79C211yesmaximal, characteristic, complemented
4#19098669C211yesmaximal, characteristic, complemented
5#19098667C211yesmaximal, characteristic, complemented
6#19098664C211yesmaximal, characteristic, complemented
7#19098660C211yesmaximal, characteristic, complemented
8C4×Dic316C211yesmaximal, characteristic, complemented
9C4×#11929614C211yesmaximal, characteristic, complemented
10C4×#11929612C211yesmaximal, characteristic, complemented
11#19098602C211yesmaximal, characteristic, complemented
12#19098570C211yesmaximal, characteristic, complemented
13#19098561C211yesmaximal, characteristic
14C4×#11929607C211yesmaximal, characteristic, complemented
15C4×SD16×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18#14579190C418yesdirect product factor
19C2×Dic316C2211yescharacteristic
20C2×#11929614C2211yescharacteristic
21C2×#11929612C2211yescharacteristic
22C2×#11929607C2211yescharacteristic
23C2×#11929607C2211yescharacteristic
24Q8×Dic79C2211yescharacteristic
25C4×Dic158—21no—
26C4×Dic158C2211yescharacteristic
27C4×Dic158C2211yescharacteristic
28#14579126—21no—
29#14579126C2211yescharacteristic
30#14579126C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32C4×C22⋊D79—21no—
33(C22⋊D79)⋊C4—21no—
34#14579119C2211yescharacteristic
35#14579117—21no—
36C4⋊C4×D79—21no—
37C4⋊C4×D79C2211yescharacteristic
38C2×C4×Dic79—21no—
39C42×D79—21no—
40C42×D79C2211yescharacteristic
41#14579095C2211yescharacteristic
42#14579094C2211yescharacteristic
43#14579092C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579086C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579084C2211yescharacteristic
48#14579084C2211yescharacteristic
49#14579082C2211yescharacteristic
50#14579071C2211yescharacteristic
51#14579071C2211yescharacteristic
52C4×C79⋊C8C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59C4×C8×C79C2211yescharacteristic
60#11929623—22no—
61#11929623C2×C414yes—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65Q8×D79—22no—
66Q8×D79C2×C414yescomplemented
67C2×C22⋊D79—21no—
68C22×Dic79—21no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79D411yescharacteristic
73C2×C4×D79D411yescharacteristic
74C2×C4×D79C2311yescharacteristic
75Dic316C2×C414yescomplemented
76#11929614C2×C414yescomplemented
77#11929612C2×C414yescomplemented
78#11929607—22no—
79#11929607C2×C414yescomplemented
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90C22⋊Dic79—21no—
91(C2×D79)⋊C4—21no—
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79—21no—
98C4×Dic79D411yescharacteristic
99C4×Dic79D411yescharacteristic
100C4×Dic79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79—21no—
104SD16×C79C2×C414yescomplemented
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C42×C79—21no—
112C42×C79C2311yescharacteristic
113C23×C79—21no—
114C22×D79C2×D411yescharacteristic
115Q8×C79—21no—
116Q8×C79C22×C412yes—
117D4×C79—21no—
118D4×C79C22×C412yes—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—42no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C22⋊D79—24no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—24no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—42no—
133C2×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C4×D79—24no—
137C4×D79—22no—
138C4×D79—41no—
139C4×D79—42no—
140C4×D79C22×C412yes—
141C4×D79#4112yes—
142Dic158—21no—
143Dic158—21no—
144Dic158—24no—
145Dic158C22×C412yes—
146Dic158C22×C412yes—
147C8×C79—21no—
148C8×C79C22×C412yes—
149C79⋊C8—21no—
150C79⋊C8C22×C412yes—
151C22×C79—22no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79C22×D411yescharacteristic
155C2×D79—21no—
156C2×D79—21no—
157C2×D79C4×D412yes—
158C4×C79—22no—
159C4×C79—21no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79#13712yescomplemented
163C4×C79C23×C411yescharacteristic
164C4×C79C2×#4111yescharacteristic
165Dic79—22no—
166Dic79—22no—
167Dic79—21no—
168Dic79—21no—
169Dic79—41no—
170Dic79—41no—
171Dic79C4×D412yes—
172C2×C79—42no—
173C2×C79C2×C4×D411yescharacteristic
174C2×C79C2×#13711yescharacteristic
175C2×C79#57511yescharacteristic
176D79—22no—
177C4×#137—791nomaximal, Sylow
178C79C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—791no—
180C4×#41—791no—
181C2×C4×Q8—791no—
182#441—791no—
183#441—791no—
184#440—791no—
185#440—791no—
186C4×Q16—791no—
187C4×Q16—791no—
188C4×SD16—791no—
189C4×SD16D7911yescharacteristic, complemented
190#428—791no—
191#419—791no—
192#417—791no—
193C4×M16—791no—
194C2×#41—791no—
195C22×Q8—791no—
196#137—798no—
197C2×Q16—791no—
198C2×Q16—791no—
199C2×SD16—791no—
200C2×SD16C2×D7911yescharacteristic
201C2×M16—791no—
202C2×M16—791no—
203C4×Q8—791no—
204C4×Q8—791no—
205C4×Q8—791no—
206C4×Q8—791no—
207C4×Q8—791no—
208C4×Q8—1581no—
209C4×Q8—1581no—
210C4×Q8C2×D7911yescharacteristic
211C4×D4—791no—
212C4×D4—1581no—
213C4×D4—1581no—
214C4×D4C2×D7911yescharacteristic
215#117—791no—
216#117—1581no—
217C2×C4⋊C4—791no—
218C2×C4⋊C4—1581no—
219C2×C42—791no—
220C2×C42—1581no—
221C2×C42—1581no—
222#107—791no—
223#107—791no—
224#106—791no—
225#106C2×D7911yescharacteristic
226#103—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103C2×D7911yescharacteristic
232#102—791no—
233#102C2×D7911yescharacteristic
234#97—791no—
235#97—791no—
236C4×C8—791no—
237C4×C8C2×D7911yescharacteristic
238#41—794no—
239#41—1582no—
240C2×Q8—794no—
241C2×Q8—791no—
242C2×Q8—791no—
243C2×Q8—1581no—
244C2×Q8—1582no—
245C2×Q8C22×D7911yescharacteristic
246C2×D4—1581no—
247C2×D4C22×D7911yescharacteristic
248C22×C4—21no—
249C22×C4—791no—
250C22×C4—791no—
251C22×C4—791no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256Q16—794no—
257Q16—794no—
258SD16—794no—
259SD16C4×D7914yescomplemented
260M16—794no—
261M16—1582no—
262C2×C8—791no—
263C2×C8—791no—
264C2×C8C22×D7911yescharacteristic
265C2×C8C22×D7911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4C22×D7911yescharacteristic
276C4⋊C4C22×D7911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C42—21no—
281C42—791no—
282C42—791no—
283C42—791no—
284C42—1581no—
285C42—1581no—
286C42—1581no—
287C42—1581no—
288C42—1581no—
289C42—1581no—
290C42C22×D7911yescharacteristic
291C23—21no—
292C23—791no—
293Q8—21no—
294Q8—792no—
295Q8—792no—
296Q8—1584no—
297Q8—1581no—
298Q8—1581no—
299Q8C2×C4×D7912yes—
300D4—21no—
301D4—1584no—
302D4C2×C4×D7912yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—3161no—
308C2×C4—3162no—
309C2×C4—3162no—
310C2×C4—791no—
311C2×C4—792no—
312C2×C4—792no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—1584no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1584no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1582no—
322C2×C4D4×D7911yescharacteristic
323C2×C4D4×D7911yescharacteristic
324C2×C4C23×D7911yescharacteristic
325C8—21no—
326C8—792no—
327C8—1581no—
328C8C2×C4×D7912yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—792no—
333C22—1581no—
334C22—1581no—
335C22C2×D4×D7911yescharacteristic
336C4—22no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—3161no—
341C4—3161no—
342C4—792no—
343C4—1582no—
344C4—1582no—
345C4—1581no—
346C4—1581no—
347C4#1457919012yesdirect product factor
348C4C22×C4×D7911yescharacteristic
349C4#41×D7911yescharacteristic
350C2—42no—
351C2—1582no—
352C2C4×D4×D7911yescharacteristic
353C2C2×#1457919011yescharacteristic
354C2#1909936011yescharacteristic
subgroupG/H
centerC2×C4D4×D79
commutatorC4×C79C23×C4
FrattiniC2×C4C23×D79
FittingC4×SD16×C79C2
socleC22×C79C22×D4
prime radicalC2×#11929623C22
cosocleC2×C4×C79C24
hypercenterC4×SD16D79
hypocenterC79C4×#137
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D79C2semidirect
4. #19098669C2semidirect
5. #19098667C2semidirect
6. #19098664C2semidirect
7. #19098660C2semidirect
8. C4×Dic316C2semidirect
9. C4×#11929614C2semidirect
10. C4×#11929612C2semidirect
11. #19098602C2semidirect
12. #19098570C2semidirect
14. C4×#11929607C2semidirect
15. C4×SD16×C79C2semidirect
18. #14579190C4direct (N × H)
66. Q8×D79C2×C4semidirect
75. Dic316C2×C4semidirect
76. #11929614C2×C4semidirect
77. #11929612C2×C4semidirect
79. #11929607C2×C4semidirect
104. SD16×C79C2×C4semidirect
162. C4×C79#137semidirect
178. C79C4×#137semidirect
189. C4×SD16D79semidirect
259. SD16C4×D79semidirect
347. C4#14579190direct (N × H)