Finite Group Databasebeta

← #23767231

Subgroups — #23767231

Order 10112.

584 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×#14579139C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D79C211yesmaximal, characteristic
3#19098501C211yesmaximal, characteristic, complemented
4#19098493C211yesmaximal, characteristic, complemented
5#19098486C211yesmaximal, characteristic, complemented
6#19098475C211yesmaximal, characteristic, complemented
7#19098467C211yesmaximal, characteristic, complemented
8#19098445C211yesmaximal, characteristic, complemented
9#19098439C211yesmaximal, characteristic
10#19098439C211yesmaximal, characteristic
11#19098437C211yesmaximal, characteristic, complemented
12#19098436C211yesmaximal, characteristic, complemented
13#19098434C211yesmaximal, characteristic, complemented
14#95×D79C211yesmaximal, characteristic, complemented
15#380×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C22×C4×D79C2211yescharacteristic
21#14579139—24no—
22C4×C22⋊D79—24no—
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×C22⋊Dic79C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C23×C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C22⋊C4×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⋊D79Q814yescomplemented
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—41no—
73C2×C4×D79—41no—
74C2×C4×D79—41no—
75C2×C4×D79—41no—
76C4⋊Dic79—41no—
77Dic79⋊C4—22no—
78Dic79⋊C4—22no—
79Dic79⋊C4—22no—
80Dic79⋊C4—22no—
81Dic79⋊C4—41no—
82C22⋊Dic79—22no—
83C22⋊Dic79—22no—
84C22⋊Dic79—41no—
85(C2×D79)⋊C4—22no—
86(C2×D79)⋊C4—22no—
87(C2×D79)⋊C4D414yes—
88C4×Dic79—22no—
89C24×C79C2311yescharacteristic
90C22×C4×C79—22no—
91C22×C4×C79—22no—
92C22×C4×C79—41no—
93C22×C4×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C4⋊C4×C79—22no—
100C4⋊C4×C79—41no—
101C22⋊C4×C79—41no—
102C22⋊C4×C79—41no—
103C23×C79—21no—
104C23×C79—21no—
105C23×C79—21no—
106C23×C79—21no—
107C23×C79—21no—
108C23×C79—21no—
109C23×C79C2×Q812yes—
110C23×C79C2411yescharacteristic
111C22×D79—21no—
112C22×D79—21no—
113C22×D79—21no—
114C22×D79—21no—
115C22×D79C2×D412yes—
116C22×D79C2×Q812yes—
117C22×D79#4112yes—
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—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—44no—
135C2×C4×C79C2×D412yes—
136C2×C4×C79#4112yes—
137C22⋊D79—28no—
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×Dic79C2×D412yes—
157C2×Dic79C2×Q812yes—
158C2×Dic79#4112yes—
159C4×D79—44no—
160C4×D79—44no—
161C4×D79—44no—
162Dic158—44no—
163C22×C79—22no—
164C22×C79—22no—
165C22×C79—22no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79C22×D411yescharacteristic
171C22×C79C22×Q811yescharacteristic
172C22×C79C2×#4111yescharacteristic
173C22×C79C2×#4111yescharacteristic
174C22×C79C2×#4111yescharacteristic
175C22×C79H(5,𝔽2)11yescharacteristic
176C22×C79H(5,𝔽2)11yescharacteristic
177C2×D79—22no—
178C2×D79—22no—
179C2×D79—22no—
180C2×D79—22no—
181C2×D79—22no—
182C2×D79—22no—
183C2×D79C22⋊Q814yes—
184C4×C79—22no—
185C4×C79—22no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79—41no—
189C4×C79—41no—
190Dic79—22no—
191Dic79—22no—
192Dic79—22no—
193Dic79—41no—
194Dic79—41no—
195Dic79—41no—
196Dic79—41no—
197C2×C79—42no—
198C2×C79C2×C22⋊Q811yescharacteristic
199C2×C79#52911yescharacteristic
200C2×C79#53811yescharacteristic
201C2×C79#54611yescharacteristic
202C2×C79#54611yescharacteristic
203C2×C79#55411yescharacteristic
204C2×C79#55411yescharacteristic
205D79—24no—
206#2450—791nomaximal, Sylow
207C79#245011yescharacteristic, complemented, Sylow
208C2×C22⋊Q8—791no—
209C2×C4×D4—791no—
210#400—791no—
211#398—791no—
212#396—791no—
213#393—791no—
214#391—791no—
215#387—791no—
216#386—791no—
217#386—791no—
218#385—791no—
219#385—791no—
220#385—791no—
221#380D7911yescharacteristic, complemented
222C2×#95—791no—
223C22×Q8—791no—
224C22×D4—791no—
225C23×C4—791no—
226C23×C4—791no—
227C23×C4—791no—
228C23×C4C2×D7911yescharacteristic
229C22⋊Q8—1584no—
230C4×D4—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⋊C4C2×D7911yescharacteristic
238C2×C4⋊C4C2×D7911yescharacteristic
239C2×C22⋊C4—791no—
240C2×C22⋊C4—791no—
241C2×C22⋊C4—791no—
242C2×C22⋊C4—791no—
243C2×C22⋊C4—791no—
244C2×C22⋊C4—791no—
245C2×C22⋊C4C2×D7911yescharacteristic
246C2×C22⋊C4C2×D7911yescharacteristic
247C2×C42—791no—
248#95—791no—
249#95—791no—
250#95—791no—
251#95—791no—
252#95—791no—
253#95—791no—
254#95—791no—
255#95—791no—
256#95—791no—
257#95—791no—
258#95C2×D7911yescharacteristic
259#95C2×D7911yescharacteristic
260C24—791no—
261C24C22×D7911yescharacteristic
262C2×Q8—3161no—
263C2×Q8—1582no—
264C2×Q8—1582no—
265C2×D4—794no—
266C2×D4—1582no—
267C2×D4—1582no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—3161no—
272C22×C4—3161no—
273C22×C4—3161no—
274C22×C4—3161no—
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×C4—1582no—
285C22×C4—1582no—
286C22×C4—1582no—
287C22×C4C22×D7911yescharacteristic
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7911yescharacteristic
290C22×C4C22×D7911yescharacteristic
291C22×C4C22×D7911yescharacteristic
292C22×C4C22×D7911yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—3161no—
296C4⋊C4—3161no—
297C4⋊C4—1582no—
298C4⋊C4—1582no—
299C4⋊C4—1582no—
300C4⋊C4—1582no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—3161no—
304C22⋊C4—794no—
305C22⋊C4—1582no—
306C22⋊C4—1582no—
307C22⋊C4—1582no—
308C22⋊C4—1582no—
309C42—1582no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—792no—
317C23—792no—
318C23—792no—
319C23—1581no—
320C23—1581no—
321C23—1581no—
322C23—1581no—
323C23Q8×D7912yes—
324C23C23×D7911yescharacteristic
325Q8—3164no—
326D4—1588no—
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—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—3164no—
345C2×C4—3164no—
346C2×C4—3164no—
347C2×C4—792no—
348C2×C4—792no—
349C2×C4—792no—
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×C4D4×D7912yes—
369C2×C4#1192962412yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—794no—
378C22—1582no—
379C22—1582no—
380C22—1582no—
381C22—1582no—
382C22—1582no—
383C22—1582no—
384C22C2×D4×D7911yescharacteristic
385C22C2×Q8×D7911yescharacteristic
386C22#41×D7911yescharacteristic
387C22#41×D7911yescharacteristic
388C22C2×#1192962411yescharacteristic
389C22#1457920611yescharacteristic
390C22#1457920611yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—3161no—
398C4—3161no—
399C4—3161no—
400C4—3161no—
401C4—1582no—
402C4—1582no—
403C4—1582no—
404C2—42no—
405C2—1584no—
406C2C22⋊Q8×D7911yescharacteristic
407C2#1909909111yescharacteristic
408C2#1909914511yescharacteristic
409C2#1909920311yescharacteristic
410C2#1909921011yescharacteristic
411C2#1909926711yescharacteristic
412C2#1909926811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#380×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#380D79
hypocenterC79#2450
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14579139C2semidirect
3. #19098501C2semidirect
4. #19098493C2semidirect
5. #19098486C2semidirect
6. #19098475C2semidirect
7. #19098467C2semidirect
8. #19098445C2semidirect
11. #19098437C2semidirect
12. #19098436C2semidirect
13. #19098434C2semidirect
14. #95×D79C2semidirect
15. #380×C79C2semidirect
59. C2×C22⋊D79Q8semidirect
207. C79#2450semidirect
221. #380D79semidirect