Finite Group Databasebeta

← #23769823

Subgroups — #23769823

Order 10112.

512 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579143C211yesmaximal, characteristic
2C2×#14579138C211yesmaximal, characteristic, complemented
3#19098505C211yesmaximal, characteristic, complemented
4#19098497C211yesmaximal, characteristic, complemented
5#19098496C211yesmaximal, characteristic, complemented
6#19098478C211yesmaximal, characteristic
7#19098476C211yesmaximal, characteristic, complemented
8#19098467C211yesmaximal, characteristic, complemented
9#19098457C211yesmaximal, characteristic, complemented
10#19098455C211yesmaximal, characteristic, complemented
11#19098440C211yesmaximal, characteristic
12#19098434C211yesmaximal, characteristic, complemented
13#19098424C211yesmaximal, characteristic, complemented
14#19098422C211yesmaximal, characteristic, complemented
15#397×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C23×Dic79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579143—24no—
21#14579138—24no—
22C2×C4⋊Dic79C2211yescharacteristic
23C2×C4⋊Dic79C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
30C2×C22⋊Dic79C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C2×Dic158—22no—
55C2×Dic158—22no—
56C2×Dic158—41no—
57C2×C22⋊D79—22no—
58C2×C22⋊D79—22no—
59C2×C22⋊D79—41no—
60C22×Dic79—22no—
61C22×Dic79—22no—
62C22×Dic79—41no—
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C2×C4×D79—22no—
71C2×C4×D79—22no—
72C2×C4×D79—41no—
73C4⋊Dic79—22no—
74C4⋊Dic79—22no—
75Dic79⋊C4—22no—
76Dic79⋊C4—22no—
77Dic79⋊C4—22no—
78Dic79⋊C4—41no—
79Dic79⋊C4—41no—
80C22⋊Dic79—41no—
81C22⋊Dic79D414yes—
82(C2×D79)⋊C4—22no—
83(C2×D79)⋊C4—22no—
84(C2×D79)⋊C4—22no—
85(C2×D79)⋊C4—41no—
86(C2×D79)⋊C4—41no—
87C4×Dic79—41no—
88C24×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C4⋊C4×C79—41no—
96C22⋊C4×C79—22no—
97C22⋊C4×C79—22no—
98C22⋊C4×C79—41no—
99C23×C79—21no—
100C23×C79—21no—
101C23×C79—21no—
102C23×C79—21no—
103C23×C79—21no—
104C23×C79—21no—
105C23×C79C2×D412yes—
106C23×C79C2411yescharacteristic
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—21no—
112C22×D79—21no—
113C22×D79#4112yes—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
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—
132C22⋊D79—44no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
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—44no—
152C2×Dic79C2×D412yes—
153C2×Dic79C2×D412yes—
154C2×Dic79#4112yes—
155C4×D79—44no—
156Dic158—44no—
157C22×C79—22no—
158C22×C79—22no—
159C22×C79—22no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C22×C79C2×#4111yescharacteristic
166C22×C79C2×#4111yescharacteristic
167C22×C79H(5,𝔽2)11yescharacteristic
168C22×C79H(5,𝔽2)11yescharacteristic
169C22×C792−1+411yescharacteristic
170C22×C792−1+411yescharacteristic
171C2×D79—22no—
172C2×D79—22no—
173C2×D79—22no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—41no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79—41no—
182C4×C79—41no—
183C4×C79—41no—
184Dic79—22no—
185Dic79—22no—
186Dic79—22no—
187Dic79—41no—
188Dic79—41no—
189Dic79—41no—
190Dic79—41no—
191C2×C79—42no—
192C2×C79#53611yescharacteristic
193C2×C79#53911yescharacteristic
194C2×C79#54211yescharacteristic
195C2×C79#54611yescharacteristic
196C2×C79#54611yescharacteristic
197C2×C79#55211yescharacteristic
198C2×C79#56211yescharacteristic
199D79—42no—
200#2687—791nomaximal, Sylow
201C79#268711yescharacteristic, complemented, Sylow
202C2×#123—791no—
203C2×C22⋊Q8—791no—
204#400—791no—
205#398—791no—
206#398—791no—
207#397D7911yescharacteristic, complemented
208#394—791no—
209#393—791no—
210#391—791no—
211#388—791no—
212#388—791no—
213#386—791no—
214#385—791no—
215#381—791no—
216#380—791no—
217C22×Q8—791no—
218C22×D4—791no—
219C23×C4—791no—
220C23×C4—791no—
221#123—1584no—
222C22⋊Q8—1584no—
223C2×C4⋊C4—791no—
224C2×C4⋊C4—791no—
225C2×C4⋊C4—791no—
226C2×C4⋊C4—791no—
227C2×C4⋊C4—791no—
228C2×C4⋊C4—791no—
229C2×C4⋊C4—791no—
230C2×C4⋊C4C2×D7911yescharacteristic
231C2×C22⋊C4—791no—
232C2×C22⋊C4—791no—
233C2×C22⋊C4—791no—
234C2×C22⋊C4—791no—
235C2×C22⋊C4—791no—
236C2×C22⋊C4—791no—
237C2×C22⋊C4—791no—
238C2×C22⋊C4C2×D7911yescharacteristic
239C2×C22⋊C4C2×D7911yescharacteristic
240C2×C22⋊C4C2×D7911yescharacteristic
241C2×C42—791no—
242#95—791no—
243#95—791no—
244#95—791no—
245#95—791no—
246#95—791no—
247#95—791no—
248#95—791no—
249#95—791no—
250#95—791no—
251#95C2×D7911yescharacteristic
252#95C2×D7911yescharacteristic
253#95C2×D7911yescharacteristic
254C24—791no—
255C24C22×D7911yescharacteristic
256C2×Q8—3161no—
257C2×Q8—1582no—
258C2×Q8—1582no—
259C2×D4—3161no—
260C2×D4—1582no—
261C2×D4—1582no—
262C22×C4—3161no—
263C22×C4—3161no—
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—791no—
268C22×C4—791no—
269C22×C4—791no—
270C22×C4—791no—
271C22×C4—1582no—
272C22×C4—1582no—
273C22×C4—1582no—
274C22×C4—1582no—
275C22×C4C22×D7911yescharacteristic
276C22×C4C22×D7911yescharacteristic
277C22×C4C22×D7911yescharacteristic
278C22×C4C22×D7911yescharacteristic
279C22×C4C22×D7911yescharacteristic
280C22×C4C22×D7911yescharacteristic
281C4⋊C4—41no—
282C4⋊C4—3161no—
283C4⋊C4—3161no—
284C4⋊C4—1582no—
285C4⋊C4—1582no—
286C4⋊C4—1582no—
287C4⋊C4—1582no—
288C4⋊C4—1582no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—41no—
292C22⋊C4—3161no—
293C22⋊C4—3161no—
294C22⋊C4—3161no—
295C22⋊C4—794no—
296C22⋊C4—1582no—
297C22⋊C4—1582no—
298C22⋊C4—1582no—
299C42—3161no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—792no—
307C23—1581no—
308C23—1581no—
309C23—1581no—
310C23—1581no—
311C23—1581no—
312C23—1581no—
313C23D4×D7912yes—
314C23C23×D7911yescharacteristic
315Q8—3164no—
316D4—3164no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—3164no—
336C2×C4—3164no—
337C2×C4—792no—
338C2×C4—792no—
339C2×C4—792no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
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—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22—3161no—
369C22—1582no—
370C22—1582no—
371C22—1582no—
372C22C2×D4×D7911yescharacteristic
373C22#41×D7911yescharacteristic
374C22#41×D7911yescharacteristic
375C22#1457920611yescharacteristic
376C22#1457920711yescharacteristic
377C22#1457920811yescharacteristic
378C22#1457920811yescharacteristic
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—3161no—
386C4—3161no—
387C4—3161no—
388C4—3161no—
389C4—1582no—
390C4—1582no—
391C4—1582no—
392C2—42no—
393C2—3162no—
394C2#1909913511yescharacteristic
395C2#1909915411yescharacteristic
396C2#1909918111yescharacteristic
397C2#1909920211yescharacteristic
398C2#1909920511yescharacteristic
399C2#1909924911yescharacteristic
400C2#1909930711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#397×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#397D79
hypocenterC79#2687
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#14579138C2semidirect
3. #19098505C2semidirect
4. #19098497C2semidirect
5. #19098496C2semidirect
7. #19098476C2semidirect
8. #19098467C2semidirect
9. #19098457C2semidirect
10. #19098455C2semidirect
12. #19098434C2semidirect
13. #19098424C2semidirect
14. #19098422C2semidirect
15. #397×C79C2semidirect
201. C79#2687semidirect
207. #397D79semidirect