Finite Group Databasebeta

← #23769737

Subgroups — #23769737

Order 10112.

568 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579142C211yesmaximal, characteristic
2C2×#14579140C211yesmaximal, characteristic, complemented
3C2×#14579138C211yesmaximal, characteristic, complemented
4#19098496C211yesmaximal, characteristic, complemented
5#19098494C211yesmaximal, characteristic, complemented
6#19098491C211yesmaximal, characteristic, complemented
7#19098488C211yesmaximal, characteristic, complemented
8#19098483C211yesmaximal, characteristic, complemented
9#19098477C211yesmaximal, characteristic
10#19098457C211yesmaximal, characteristic, complemented
11#19098456C211yesmaximal, characteristic, complemented
12#19098436C211yesmaximal, characteristic, complemented
13#19098435C211yesmaximal, characteristic, complemented
14#19098432C211yesmaximal, characteristic, complemented
15C2×#123×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C23×Dic79C2211yescharacteristic
18#14579142—24no—
19#14579140—24no—
20#14579138—24no—
21C2×C4⋊Dic79C2211yescharacteristic
22C2×C4⋊Dic79C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×Dic79⋊C4C2211yescharacteristic
30C2×Dic79⋊C4C2211yescharacteristic
31C2×C22⋊Dic79C2211yescharacteristic
32C2×C22⋊Dic79C2211yescharacteristic
33C2×C22⋊Dic79C2211yescharacteristic
34C2×C22⋊Dic79C2211yescharacteristic
35C2×C22⋊Dic79C2211yescharacteristic
36C2×C22⋊Dic79C2211yescharacteristic
37C2×C22⋊Dic79C2211yescharacteristic
38C2×C4×Dic79C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C79⋊#95C2211yescharacteristic
47C22×D4×C79C2211yescharacteristic
48C23×C4×C79C2211yescharacteristic
49#123×C79—24no—
50C2×C4⋊C4×C79C2211yescharacteristic
51C2×C4⋊C4×C79C2211yescharacteristic
52C2×C22⋊C4×C79C2211yescharacteristic
53C2×C22⋊C4×C79C2211yescharacteristic
54C2×C22⋊C4×C79C2211yescharacteristic
55C2×Dic158—22no—
56C2×Dic158—22no—
57C2×Dic158—41no—
58C22×Dic79—22no—
59C22×Dic79—22no—
60C22×Dic79—41no—
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C4⋊Dic79—22no—
70C4⋊Dic79—22no—
71Dic79⋊C4—22no—
72Dic79⋊C4—22no—
73Dic79⋊C4—22no—
74Dic79⋊C4—22no—
75Dic79⋊C4—22no—
76Dic79⋊C4—22no—
77Dic79⋊C4—41no—
78Dic79⋊C4—41no—
79C22⋊Dic79—22no—
80C22⋊Dic79—22no—
81C22⋊Dic79—22no—
82C22⋊Dic79—22no—
83C22⋊Dic79—22no—
84C22⋊Dic79—22no—
85C22⋊Dic79D414yes—
86C4×Dic79—22no—
87C24×C79C2311yescharacteristic
88C24×C79C2311yescharacteristic
89C2×D4×C79—22no—
90C2×D4×C79—22no—
91C2×D4×C79—41no—
92C22×C4×C79—22no—
93C22×C4×C79—22no—
94C22×C4×C79—41no—
95C22×C4×C79C2311yescharacteristic
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C4⋊C4×C79—22no—
101C4⋊C4×C79—22no—
102C22⋊C4×C79—22no—
103C22⋊C4×C79—22no—
104C22⋊C4×C79D414yes—
105C23×C79—21no—
106C23×C79—21no—
107C23×C79—21no—
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C23×C79C2×D412yes—
118C23×C79C2×D412yes—
119C23×C79C2411yescharacteristic
120D4×C79—44no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—44no—
135C2×C4×C79C2×D412yes—
136C2×C4×C79C2×D412yes—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—21no—
158C2×Dic79—44no—
159C2×Dic79C2×D412yes—
160C2×Dic79C2×D412yes—
161C2×Dic79#4112yes—
162Dic158—44no—
163C22×C79—22no—
164C22×C79—22no—
165C22×C79—22no—
166C22×C79—22no—
167C22×C79—22no—
168C22×C79—22no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79C22×D411yescharacteristic
178C22×C79C22×D411yescharacteristic
179C22×C79C2×#4111yescharacteristic
180C22×C79H(5,𝔽2)11yescharacteristic
181C22×C792−1+411yescharacteristic
182C22×C792−1+411yescharacteristic
183C22×C792−1+411yescharacteristic
184C4×C79—22no—
185C4×C79—22no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79—41no—
189Dic79—22no—
190Dic79—22no—
191Dic79—22no—
192Dic79—41no—
193Dic79—41no—
194Dic79—41no—
195Dic79—41no—
196Dic79—41no—
197C2×C79—42no—
198C2×C79—42no—
199C2×C79#53611yescharacteristic
200C2×C79#53611yescharacteristic
201C2×C79#53911yescharacteristic
202C2×C79D4211yescharacteristic
203C2×C79#54711yescharacteristic
204C2×C79#54711yescharacteristic
205C2×C79#56311yescharacteristic
206#2680—791nomaximal, Sylow
207C79#268011yescharacteristic, complemented, Sylow
208C2×#123—791no—
209C2×#123D7911yescharacteristic
210C2×C22⋊Q8—791no—
211C2×C22⋊Q8—791no—
212#398—791no—
213#398—791no—
214#397—791no—
215#397—791no—
216#395—791no—
217#394—791no—
218#388—791no—
219#388—791no—
220#385—791no—
221#385—791no—
222#384—791no—
223C22×Q8—791no—
224C22×D4C2×D7911yescharacteristic
225C23×C4—791no—
226C23×C4C2×D7911yescharacteristic
227#123—24no—
228#123—1584no—
229C22⋊Q8—1584no—
230C22⋊Q8—1584no—
231C2×C4⋊C4—791no—
232C2×C4⋊C4—791no—
233C2×C4⋊C4—791no—
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C4⋊C4—791no—
237C2×C4⋊C4—791no—
238C2×C4⋊C4—791no—
239C2×C4⋊C4—791no—
240C2×C4⋊C4—791no—
241C2×C4⋊C4C2×D7911yescharacteristic
242C2×C4⋊C4C2×D7911yescharacteristic
243C2×C22⋊C4—791no—
244C2×C22⋊C4—791no—
245C2×C22⋊C4—791no—
246C2×C22⋊C4—791no—
247C2×C22⋊C4—791no—
248C2×C22⋊C4—791no—
249C2×C22⋊C4—791no—
250C2×C22⋊C4C2×D7911yescharacteristic
251C2×C22⋊C4C2×D7911yescharacteristic
252C2×C22⋊C4C2×D7911yescharacteristic
253C2×C42—791no—
254#95—791no—
255#95—791no—
256#95—791no—
257#95—791no—
258#95—791no—
259#95—791no—
260#95—791no—
261#95—791no—
262C24C22×D7911yescharacteristic
263C24C22×D7911yescharacteristic
264C2×Q8—3161no—
265C2×Q8—1582no—
266C2×Q8—1582no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—41no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—3161no—
274C22×C4—791no—
275C22×C4—791no—
276C22×C4—791no—
277C22×C4—791no—
278C22×C4—791no—
279C22×C4—791no—
280C22×C4—791no—
281C22×C4—791no—
282C22×C4—1582no—
283C22×C4—1582no—
284C22×C4C22×D7911yescharacteristic
285C22×C4C22×D7911yescharacteristic
286C22×C4C22×D7911yescharacteristic
287C22×C4C22×D7911yescharacteristic
288C22×C4C22×D7911yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—3161no—
292C4⋊C4—3161no—
293C4⋊C4—1582no—
294C4⋊C4—1582no—
295C4⋊C4—1582no—
296C4⋊C4—1582no—
297C4⋊C4—1582no—
298C4⋊C4—1582no—
299C4⋊C4—1582no—
300C4⋊C4—1582no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—794no—
304C22⋊C4—1582no—
305C22⋊C4—1582no—
306C22⋊C4—1582no—
307C22⋊C4—1582no—
308C22⋊C4—1582no—
309C22⋊C4—1582no—
310C22⋊C4C22⋊D7914yes—
311C42—1582no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23D4×D7912yes—
325C23C2×C22⋊D7912yes—
326C23C23×D7911yescharacteristic
327Q8—3164no—
328D4—44no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—3164no—
344C2×C4—792no—
345C2×C4—792no—
346C2×C4—792no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4—1581no—
353C2×C4—1581no—
354C2×C4—1581no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4—1581no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4—1581no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4—1581no—
368C2×C4C2×C22⋊D7912yes—
369C2×C4C2×C22⋊D7912yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22C2×D4×D7911yescharacteristic
385C22C22×C22⋊D7911yescharacteristic
386C22#41×D7911yescharacteristic
387C22#1457920611yescharacteristic
388C22#1457920811yescharacteristic
389C22#1457920811yescharacteristic
390C22#1457920811yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—3161no—
397C4—3161no—
398C4—3161no—
399C4—3161no—
400C4—3161no—
401C4—1582no—
402C4—1582no—
403C4—1582no—
404C2—42no—
405C2—42no—
406C2#1909913411yescharacteristic
407C2#1909913511yescharacteristic
408C2#1909915611yescharacteristic
409C2D4×C22⋊D7911yescharacteristic
410C2#1909921111yescharacteristic
411C2#1909921211yescharacteristic
412C2#1909931611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#123×C79C2
prime radicalC22×D4×C79C22
hypercenterC2×#123D79
hypocenterC79#2680
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#14579140C2semidirect
3. C2×#14579138C2semidirect
4. #19098496C2semidirect
5. #19098494C2semidirect
6. #19098491C2semidirect
7. #19098488C2semidirect
8. #19098483C2semidirect
10. #19098457C2semidirect
11. #19098456C2semidirect
12. #19098436C2semidirect
13. #19098435C2semidirect
14. #19098432C2semidirect
207. C79#2680semidirect