Finite Group Databasebeta

← #23767729

Subgroups — #23767729

Order 10112.

546 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579143C211yesmaximal, characteristic
2C2×#14579139C211yesmaximal, characteristic, complemented
3#19098504C211yesmaximal, characteristic, complemented
4#19098503C211yesmaximal, characteristic, complemented
5#19098475C211yesmaximal, characteristic, complemented
6#19098467C211yesmaximal, characteristic, complemented
7#19098457C211yesmaximal, characteristic, complemented
8#19098451C211yesmaximal, characteristic, complemented
9#19098439C211yesmaximal, characteristic
10#19098439C211yesmaximal, characteristic
11#19098428C211yesmaximal, characteristic, complemented
12#19098425C211yesmaximal, characteristic, complemented
13#19098410C211yesmaximal, characteristic, complemented
14#95×D79C211yesmaximal, characteristic, complemented
15#397×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C22×C4×D79C2211yescharacteristic
21#14579143—24no—
22#14579139—24no—
23C2×C4⋊Dic79C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×C4×Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
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—22no—
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C2×C4×D79—22no—
68C2×C4×D79—22no—
69C2×C4×D79—22no—
70C2×C4×D79—22no—
71C2×C4×D79—22no—
72C2×C4×D79—22no—
73C2×C4×D79—22no—
74C2×C4×D79—41no—
75C2×C4×D79—41no—
76C4⋊Dic79—22no—
77Dic79⋊C4—22no—
78Dic79⋊C4—22no—
79Dic79⋊C4—22no—
80C22⋊Dic79—22no—
81C22⋊Dic79—22no—
82C22⋊Dic79—22no—
83(C2×D79)⋊C4—22no—
84(C2×D79)⋊C4—22no—
85(C2×D79)⋊C4D414yes—
86C4×Dic79—22no—
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—22no—
96C22⋊C4×C79—22no—
97C22⋊C4×C79—41no—
98C22⋊C4×C79—41no—
99C23×C79—21no—
100C23×C79—21no—
101C23×C79—21no—
102C23×C79—21no—
103C23×C79—21no—
104C23×C79—21no—
105C23×C79—21no—
106C23×C79C2411yescharacteristic
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79—21no—
111C22×D79C2×D412yes—
112C22×D79#4112yes—
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×C79C2×D412yes—
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×Dic79C2×D412yes—
152C2×Dic79#4112yes—
153C2×Dic79#4112yes—
154C4×D79—44no—
155C4×D79—44no—
156C4×D79—44no—
157Dic158—44no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79C22×D411yescharacteristic
166C22×C79C2×#4111yescharacteristic
167C22×C79C2×#4111yescharacteristic
168C22×C79C2×#4111yescharacteristic
169C22×C79C2×#4111yescharacteristic
170C22×C79H(5,𝔽2)11yescharacteristic
171C22×C792−1+411yescharacteristic
172C2×D79—22no—
173C2×D79—22no—
174C2×D79—22no—
175C2×D79—22no—
176C2×D79—22no—
177C2×D79—22no—
178C2×D79#12414yes—
179C4×C79—22no—
180C4×C79—41no—
181C4×C79—41no—
182C4×C79—41no—
183C4×C79—41no—
184C4×C79—41no—
185Dic79—22no—
186Dic79—22no—
187Dic79—22no—
188Dic79—41no—
189Dic79—41no—
190Dic79—41no—
191Dic79—41no—
192C2×C79—81no—
193C2×C79C2×#12411yescharacteristic
194C2×C79#52911yescharacteristic
195C2×C79#53911yescharacteristic
196C2×C79#54611yescharacteristic
197C2×C79#54711yescharacteristic
198C2×C79#55111yescharacteristic
199C2×C79#55211yescharacteristic
200D79—24no—
201#2488—791nomaximal, Sylow
202C79#248811yescharacteristic, complemented, Sylow
203C2×#123—791no—
204C2×C22⋊Q8—791no—
205#400—791no—
206#400—791no—
207#397D7911yescharacteristic, complemented
208#393—791no—
209#391—791no—
210#388—791no—
211#388—791no—
212#386—791no—
213#386—791no—
214#382—791no—
215#381—791no—
216C4×C22⋊C4—791no—
217C2×#95—791no—
218C22×Q8—791no—
219C22×D4—791no—
220C23×C4—791no—
221C23×C4—791no—
222C23×C4—791no—
223#123—1584no—
224C22⋊Q8—1584no—
225C2×C4⋊C4—791no—
226C2×C4⋊C4—791no—
227C2×C4⋊C4—791no—
228C2×C4⋊C4—791no—
229C2×C4⋊C4C2×D7911yescharacteristic
230C2×C22⋊C4—791no—
231C2×C22⋊C4—791no—
232C2×C22⋊C4—791no—
233C2×C22⋊C4—791no—
234C2×C22⋊C4—791no—
235C2×C22⋊C4—791no—
236C2×C22⋊C4C2×D7911yescharacteristic
237C2×C22⋊C4C2×D7911yescharacteristic
238C2×C22⋊C4C2×D7911yescharacteristic
239C2×C42—791no—
240C2×C42—791no—
241#95—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#95—791no—
252#95C2×D7911yescharacteristic
253#95C2×D7911yescharacteristic
254#95C2×D7911yescharacteristic
255C24—791no—
256C24C22×D7911yescharacteristic
257C2×Q8—3161no—
258C2×Q8—1582no—
259C2×Q8—1582no—
260C2×D4—1582no—
261C2×D4—1582no—
262C2×D4—1582no—
263C22×C4—3161no—
264C22×C4—3161no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—791no—
268C22×C4—791no—
269C22×C4—791no—
270C22×C4—791no—
271C22×C4—791no—
272C22×C4—1582no—
273C22×C4—1582no—
274C22×C4—1582no—
275C22×C4—1582no—
276C22×C4—1582no—
277C22×C4—1582no—
278C22×C4—1582no—
279C22×C4C22×D7911yescharacteristic
280C22×C4C22×D7911yescharacteristic
281C22×C4C22×D7911yescharacteristic
282C22×C4C22×D7911yescharacteristic
283C22×C4C22×D7911yescharacteristic
284C22×C4C22×D7911yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—1582no—
287C4⋊C4—1582no—
288C4⋊C4—1582no—
289C4⋊C4—1582no—
290C22⋊C4—22no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—794no—
294C22⋊C4—1582no—
295C22⋊C4—1582no—
296C22⋊C4—1582no—
297C22⋊C4—1582no—
298C22⋊C4—1582no—
299C42—3161no—
300C42—1582no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—792no—
309C23—792no—
310C23—792no—
311C23—1581no—
312C23—1581no—
313C23—1581no—
314C23—1581no—
315C23C23×D7911yescharacteristic
316Q8—3164no—
317D4—3164no—
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—3164no—
338C2×C4—792no—
339C2×C4—792no—
340C2×C4—792no—
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—
358C2×C4—1581no—
359C2×C4D4×D7912yes—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—794no—
368C22—1582no—
369C22—1582no—
370C22—1582no—
371C22—1582no—
372C22—1582no—
373C22—1582no—
374C22C2×D4×D7911yescharacteristic
375C22#41×D7911yescharacteristic
376C22#41×D7911yescharacteristic
377C22#41×D7911yescharacteristic
378C22#41×D7911yescharacteristic
379C22#1457920611yescharacteristic
380C22#1457920811yescharacteristic
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—3161no—
388C4—3161no—
389C4—3161no—
390C4—3161no—
391C4—1582no—
392C4—1582no—
393C4—1582no—
394C2—81no—
395C2—1584no—
396C2#124×D7911yescharacteristic
397C2#1909909611yescharacteristic
398C2#1909915611yescharacteristic
399C2#1909921011yescharacteristic
400C2#1909921111yescharacteristic
401C2#1909924111yescharacteristic
402C2#1909924911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#397×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#397D79
hypocenterC79#2488
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#14579139C2semidirect
3. #19098504C2semidirect
4. #19098503C2semidirect
5. #19098475C2semidirect
6. #19098467C2semidirect
7. #19098457C2semidirect
8. #19098451C2semidirect
11. #19098428C2semidirect
12. #19098425C2semidirect
13. #19098410C2semidirect
14. #95×D79C2semidirect
15. #397×C79C2semidirect
202. C79#2488semidirect
207. #397D79semidirect