Finite Group Databasebeta

← #23771417

Subgroups — #23771417

Order 10112.

478 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579142C211yesmaximal, characteristic
2C2×#14579138C211yesmaximal, characteristic, complemented
3#19098497C211yesmaximal, characteristic, complemented
4#19098497C211yesmaximal, characteristic, complemented
5#19098494C211yesmaximal, characteristic, complemented
6#19098491C211yesmaximal, characteristic, complemented
7#19098491C211yesmaximal, characteristic, complemented
8#19098488C211yesmaximal, characteristic, complemented
9#19098486C211yesmaximal, characteristic, complemented
10#19098486C211yesmaximal, characteristic, complemented
11#19098483C211yesmaximal, characteristic, complemented
12#19098477C211yesmaximal, characteristic
13#19098475C211yesmaximal, characteristic, complemented
14#19098421C211yesmaximal, characteristic, complemented
15#394×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C23×Dic79C2211yescharacteristic
18#14579142—24no—
19#14579138—24no—
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×Dic79⋊C4C2211yescharacteristic
30C2×C22⋊Dic79C2211yescharacteristic
31C2×C22⋊Dic79C2211yescharacteristic
32C2×C22⋊Dic79C2211yescharacteristic
33C2×C22⋊Dic79C2211yescharacteristic
34C2×C22⋊Dic79C2211yescharacteristic
35C2×C22⋊Dic79C2211yescharacteristic
36C2×C22⋊Dic79C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C22×D4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C22⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C2×Dic158—22no—
54C2×Dic158—41no—
55C2×Dic158—41no—
56C22×Dic79—41no—
57C22×Dic79—41no—
58C22×Dic79D414yes—
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C4⋊Dic79—22no—
68C4⋊Dic79—41no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4—22no—
72Dic79⋊C4—22no—
73Dic79⋊C4—41no—
74Dic79⋊C4—41no—
75Dic79⋊C4—41no—
76Dic79⋊C4—41no—
77C22⋊Dic79—22no—
78C22⋊Dic79—22no—
79C22⋊Dic79—22no—
80C22⋊Dic79—22no—
81C22⋊Dic79—41no—
82C22⋊Dic79—41no—
83C22⋊Dic79—41no—
84C24×C79C2311yescharacteristic
85C24×C79C2311yescharacteristic
86C2×D4×C79—22no—
87C2×D4×C79—41no—
88C2×D4×C79—41no—
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C4⋊C4×C79—41no—
95C22⋊C4×C79—22no—
96C22⋊C4×C79—41no—
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×C79—21no—
107C23×C79—21no—
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79C2×D412yes—
113C23×C79C2411yescharacteristic
114D4×C79—44no—
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×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
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—21no—
152C2×Dic79—44no—
153C2×Dic79C2×D412yes—
154C2×Dic79C2×D412yes—
155Dic158—44no—
156C22×C79—22no—
157C22×C79—22no—
158C22×C79—22no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79C22×D411yescharacteristic
171C22×C79H(5,𝔽2)11yescharacteristic
172C22×C79H(5,𝔽2)11yescharacteristic
173C22×C79H(5,𝔽2)11yescharacteristic
174C22×C792−1+411yescharacteristic
175C22×C792−1+411yescharacteristic
176C22×C792−1+411yescharacteristic
177C4×C79—41no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79—41no—
182Dic79—22no—
183Dic79—22no—
184Dic79—41no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188Dic79—41no—
189Dic79—41no—
190C2×C79—42no—
191C2×C79—81no—
192C2×C79#53411yescharacteristic
193C2×C79#53611yescharacteristic
194C2×C79#53711yescharacteristic
195C2×C79#56211yescharacteristic
196C2×C79#56211yescharacteristic
197C2×C79#56311yescharacteristic
198C2×C79#56311yescharacteristic
199#2814—791nomaximal, Sylow
200C79#281411yescharacteristic, complemented, Sylow
201C2×#123—791no—
202C2×C22⋊Q8—791no—
203#398—791no—
204#398—791no—
205#398—791no—
206#397—791no—
207#397—791no—
208#397—791no—
209#396—791no—
210#396—791no—
211#395—791no—
212#394—791no—
213#394D7911yescharacteristic
214#393—791no—
215#380—791no—
216C22×Q8—791no—
217C22×D4C2×D7911yescharacteristic
218C23×C4—791no—
219#123—1584no—
220C22⋊Q8—1584no—
221C2×C4⋊C4—791no—
222C2×C4⋊C4—791no—
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⋊C4—791no—
231C2×C4⋊C4C2×D7911yescharacteristic
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⋊C4—791no—
239C2×C22⋊C4C2×D7911yescharacteristic
240C2×C22⋊C4C2×D7911yescharacteristic
241C2×C22⋊C4C2×D7911yescharacteristic
242C2×C22⋊C4C2×D7911yescharacteristic
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
253C24C22×D7911yescharacteristic
254C24C22×D7911yescharacteristic
255C2×Q8—3161no—
256C2×Q8—3161no—
257C2×Q8—1582no—
258C2×D4—22no—
259C2×D4—41no—
260C2×D4—41no—
261C22×C4—3161no—
262C22×C4—3161no—
263C22×C4—794no—
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—791no—
268C22×C4—791no—
269C22×C4—791no—
270C22×C4—791no—
271C22×C4—791no—
272C22×C4C22×D7911yescharacteristic
273C22×C4C22×D7911yescharacteristic
274C22×C4C22×D7911yescharacteristic
275C22×C4C22×D7911yescharacteristic
276C22×C4C22×D7911yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—3161no—
279C4⋊C4—3161no—
280C4⋊C4—3161no—
281C4⋊C4—3161no—
282C4⋊C4—3161no—
283C4⋊C4—1582no—
284C4⋊C4—1582no—
285C4⋊C4—1582no—
286C4⋊C4—1582no—
287C4⋊C4—1582no—
288C22⋊C4—22no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—3161no—
293C22⋊C4—3161no—
294C22⋊C4—3161no—
295C22⋊C4—1582no—
296C22⋊C4—1582no—
297C22⋊C4—1582no—
298C22⋊C4—1582no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23D4×D7912yes—
313C23C23×D7911yescharacteristic
314Q8—3164no—
315D4—44no—
316C2×C4—21no—
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—3164no—
332C2×C4—792no—
333C2×C4—792no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
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—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C2×D4×D7911yescharacteristic
371C22#1457920611yescharacteristic
372C22#1457920611yescharacteristic
373C22#1457920611yescharacteristic
374C22#1457920811yescharacteristic
375C22#1457920811yescharacteristic
376C22#1457920811yescharacteristic
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3161no—
383C4—3161no—
384C4—3161no—
385C4—3161no—
386C4—3161no—
387C4—3161no—
388C4—1582no—
389C4—1582no—
390C2—42no—
391C2—81no—
392C2#1909912311yescharacteristic
393C2#1909913511yescharacteristic
394C2#1909914011yescharacteristic
395C2#1909930811yescharacteristic
396C2#1909930811yescharacteristic
397C2#1909931311yescharacteristic
398C2#1909931611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC22×D4×C79C22
hypercenter#394D79
hypocenterC79#2814
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14579138C2semidirect
3. #19098497C2semidirect
4. #19098497C2semidirect
5. #19098494C2semidirect
6. #19098491C2semidirect
7. #19098491C2semidirect
8. #19098488C2semidirect
9. #19098486C2semidirect
10. #19098486C2semidirect
11. #19098483C2semidirect
13. #19098475C2semidirect
14. #19098421C2semidirect
200. C79#2814semidirect