Finite Group Databasebeta

← #23775590

Subgroups — #23775590

Order 10112.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099277C211yesmaximal, characteristic, complemented
2#19099220C211yesmaximal, characteristic, complemented
3#19098921C211yesmaximal, characteristic, complemented
4#19098905C211yesmaximal, characteristic, complemented
5#19098885C211yesmaximal, characteristic, complemented
6#19098846C211yesmaximal, characteristic, complemented
7#19098813C211yesmaximal, characteristic, complemented
8#19098790C211yesmaximal, characteristic, complemented
9#19098776C211yesmaximal, characteristic, complemented
10#19098700C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12#19098631C211yesmaximal, characteristic, complemented
13#19098570C211yesmaximal, characteristic, complemented
14#19098559C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18C2×#11929607C2211yescharacteristic
19C22×C79⋊C8C2211yescharacteristic
20#14579160C2211yescharacteristic
21#14579148—21no—
22#14579148—21no—
23#14579148C2211yescharacteristic
24#14579147—21no—
25#14579140—21no—
26#14579140C2211yescharacteristic
27#14579133—21no—
28#14579132—21no—
29#14579132C2211yescharacteristic
30#14579132C2211yescharacteristic
31Q8×Dic79C2211yescharacteristic
32D4×Dic79C2211yescharacteristic
33C4×C22⋊D79—21no—
34C4×C22⋊D79C2211yescharacteristic
35#14579120C2211yescharacteristic
36#14579119C2211yescharacteristic
37#14579117—21no—
38#14579095C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579084C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579082C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×D8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62Q8×D79—22no—
63Q8×D79—41no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79D411yescharacteristic
67C22×Dic79—21no—
68C2×C4×D79—21no—
69C2×C4×D79C2311yescharacteristic
70#11929612—41no—
71#11929607—41no—
72C2×C79⋊C8—41no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C4⋊Dic79—21no—
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4D411yescharacteristic
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79D411yescharacteristic
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4D411yescharacteristic
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96#41×C79—22no—
97#41×C79—41no—
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79—21no—
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79—21no—
104C22×C4×C79C2311yescharacteristic
105SD16×C79—22no—
106D8×C79—41no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C22×D79C2×D411yescharacteristic
115Q8×C79—21no—
116Q8×C79#4112yes—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—42no—
122D4×C79—81no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—42no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—41no—
131C22⋊D79—42no—
132C22⋊D79—81no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—42no—
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141C4×D79—21no—
142C4×D79—21no—
143C4×D79—42no—
144Dic158—21no—
145Dic158—21no—
146Dic158—42no—
147Dic158—81no—
148C8×C79—21no—
149C8×C79—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—21no—
165C4×C79—21no—
166C4×C79—22no—
167C4×C79—41no—
168C4×C79C2×#4111yescharacteristic
169C4×C79H(5,𝔽2)11yescharacteristic
170Dic79—21no—
171Dic79—21no—
172Dic79—21no—
173Dic79—41no—
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177C2×C79—41no—
178C2×C79—81no—
179C2×C79—81no—
180C2×C79#54611yescharacteristic
181C2×C79#57511yescharacteristic
182C2×C79#57711yescharacteristic
183D79—41no—
184#3321—791nomaximal, Sylow
185C79#332111yescharacteristic, complemented, Sylow
186#555—791no—
187#548—791no—
188#489—791no—
189#485—791no—
190#482—791no—
191#475—791no—
192#469—791no—
193#465—791no—
194#463—791no—
195#449D7911yescharacteristic, complemented
196#448—791no—
197#440—791no—
198#435—791no—
199#419—791no—
200#416—791no—
201C2×#41C2×D7911yescharacteristic
202C22×Q8—791no—
203C2×SD16—791no—
204C2×SD16C2×D7911yescharacteristic
205C2×D8C2×D7911yescharacteristic
206C2×M16—791no—
207C22×C8—791no—
208C4⋊Q8—791no—
209#124—791no—
210#124—1581no—
211#124—1581no—
212#124—1581no—
213C22⋊Q8—791no—
214C22⋊Q8—1581no—
215#121—791no—
216#121—791no—
217#121—1581no—
218#121—1581no—
219#121C2×D7911yescharacteristic
220C4×Q8—791no—
221C4×D4—791no—
222C4×D4—791no—
223C4×D4—1581no—
224#117—791no—
225#117—791no—
226#117—1581no—
227#107—791no—
228#106—791no—
229#106—791no—
230C4⋊C8—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#103C2×D7911yescharacteristic
237#102—791no—
238#102—791no—
239#102—791no—
240#102C2×D7911yescharacteristic
241C22⋊C8—791no—
242C22⋊C8C2×D7911yescharacteristic
243#97—791no—
244#41—22no—
245#41—41no—
246C2×Q8—3161no—
247C2×Q8—791no—
248C2×Q8—1581no—
249C2×Q8—1581no—
250C2×Q8—1582no—
251C2×Q8C22×D7911yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—791no—
255C2×D4—1581no—
256C2×D4—1581no—
257C2×D4C22×D7911yescharacteristic
258C2×D4C22×D7911yescharacteristic
259C22×C4—21no—
260C22×C4—791no—
261C22×C4—1581no—
262C22×C4—1581no—
263C22×C4C22×D7911yescharacteristic
264SD16—22no—
265SD16—3161no—
266D8—41no—
267M16—3161no—
268C2×C8—3161no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8C22×D7911yescharacteristic
272C2×C8C22×D7911yescharacteristic
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—791no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4C22×D7911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—791no—
283C22⋊C4—791no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C42—791no—
293C42—1581no—
294C42—1581no—
295C42—1581no—
296C23—21no—
297C23—21no—
298C23—791no—
299C23D4×D7911yescharacteristic
300Q8—21no—
301Q8—3162no—
302Q8—6321no—
303Q8—1581no—
304Q8—1581no—
305Q8#1192962312yes—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—3162no—
313D4—3161no—
314D4—6321no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—3162no—
321C2×C4—3162no—
322C2×C4—791no—
323C2×C4—791no—
324C2×C4—791no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4D4×D7911yescharacteristic
332C2×C4C23×D7911yescharacteristic
333C8—21no—
334C8—21no—
335C8—1581no—
336C8—1581no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—1581no—
347C22—1581no—
348C22—1581no—
349C22C2×D4×D7911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—3161no—
354C4—3161no—
355C4—3161no—
356C4—3161no—
357C4—1581no—
358C4—1581no—
359C4—1581no—
360C4C2×#1192962311yescharacteristic
361C4#1457920611yescharacteristic
362C2—41no—
363C2—81no—
364C2—81no—
365C2—3161no—
366C2#1909920011yescharacteristic
367C2#1909936011yescharacteristic
368C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3321
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #19099277C2semidirect
2. #19099220C2semidirect
3. #19098921C2semidirect
4. #19098905C2semidirect
5. #19098885C2semidirect
6. #19098846C2semidirect
7. #19098813C2semidirect
8. #19098790C2semidirect
9. #19098776C2semidirect
10. #19098700C2semidirect
11. #19098664C2semidirect
12. #19098631C2semidirect
13. #19098570C2semidirect
14. #19098559C2semidirect
15. #449×C79C2semidirect
185. C79#3321semidirect
195. #449D79semidirect