Finite Group Databasebeta

← #22595039

Subgroups — #22595039

Order 9088.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556118C211yesmaximal, characteristic, complemented
2#17985932C211yesmaximal, characteristic, complemented
3#17985924C211yesmaximal, characteristic, complemented
4#17985922C211yesmaximal, characteristic, complemented
5#17985922C211yesmaximal, characteristic, complemented
6#17985922C211yesmaximal, characteristic, complemented
7#17985913C211yesmaximal, characteristic
8#17985902C211yesmaximal, characteristic
9#17985898C211yesmaximal, characteristic, complemented
10#17985893C211yesmaximal, characteristic, complemented
11#17985893C211yesmaximal, characteristic, complemented
12#17985880C211yesmaximal, characteristic, complemented
13#17985872C211yesmaximal, characteristic, complemented
14#17985859C211yesmaximal, characteristic, complemented
15C2×#123×C71C211yesmaximal, characteristic
16#14556118—24no—
17C2×C4⋊Dic71C2211yescharacteristic
18C2×C4⋊Dic71C2211yescharacteristic
19C2×C4⋊Dic71C2211yescharacteristic
20C2×C4⋊Dic71C2211yescharacteristic
21C2×Dic71⋊C4C2211yescharacteristic
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×Dic71⋊C4C2211yescharacteristic
26C2×Dic71⋊C4C2211yescharacteristic
27C2×C22⋊Dic71C2211yescharacteristic
28C2×C22⋊Dic71C2211yescharacteristic
29C2×C22⋊Dic71C2211yescharacteristic
30C2×C22⋊Dic71C2211yescharacteristic
31C2×C22⋊Dic71C2211yescharacteristic
32C2×C22⋊Dic71C2211yescharacteristic
33C2×C22⋊Dic71C2211yescharacteristic
34C2×C22⋊Dic71C2211yescharacteristic
35C2×C4×Dic71C2211yescharacteristic
36C2×C4×Dic71C2211yescharacteristic
37C71⋊#95C2211yescharacteristic
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C71⋊#95C2211yescharacteristic
45C22×D4×C71C2211yescharacteristic
46C23×C4×C71C2211yescharacteristic
47#123×C71—24no—
48C2×C4⋊C4×C71C2211yescharacteristic
49C2×C4⋊C4×C71C2211yescharacteristic
50C2×C22⋊C4×C71C2211yescharacteristic
51C2×C22⋊C4×C71C2211yescharacteristic
52C2×C22⋊C4×C71C2211yescharacteristic
53C22×Dic71C2311yescharacteristic
54C22×Dic71C2311yescharacteristic
55C22×Dic71C2311yescharacteristic
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C4⋊Dic71—22no—
62C4⋊Dic71—41no—
63C4⋊Dic71—41no—
64C4⋊Dic71—41no—
65Dic71⋊C4—22no—
66Dic71⋊C4—22no—
67Dic71⋊C4—22no—
68Dic71⋊C4—22no—
69Dic71⋊C4—22no—
70Dic71⋊C4—41no—
71C22⋊Dic71—22no—
72C22⋊Dic71—22no—
73C22⋊Dic71—22no—
74C22⋊Dic71—41no—
75C22⋊Dic71—41no—
76C22⋊Dic71—41no—
77C22⋊Dic71—41no—
78C22⋊Dic71—41no—
79C4×Dic71—22no—
80C4×Dic71—41no—
81C24×C71C2311yescharacteristic
82C24×C71C2311yescharacteristic
83C2×D4×C71—22no—
84C2×D4×C71—22no—
85C2×D4×C71—41no—
86C22×C4×C71—22no—
87C22×C4×C71—22no—
88C22×C4×C71—41no—
89C22×C4×C71C2311yescharacteristic
90C22×C4×C71C2311yescharacteristic
91C22×C4×C71C2311yescharacteristic
92C22×C4×C71C2311yescharacteristic
93C22×C4×C71C2311yescharacteristic
94C4⋊C4×C71—22no—
95C4⋊C4×C71D414yes—
96C22⋊C4×C71—22no—
97C22⋊C4×C71—22no—
98C22⋊C4×C71—22no—
99C23×C71—21no—
100C23×C71—21no—
101C23×C71—21no—
102C23×C71—21no—
103C23×C71—21no—
104C23×C71—21no—
105C23×C71—21no—
106C23×C71—21no—
107C23×C71—21no—
108C23×C71—21no—
109C23×C71—21no—
110C23×C71—21no—
111C23×C71—21no—
112C23×C71#4112yes—
113C23×C71C2411yescharacteristic
114D4×C71—44no—
115C2×C4×C71—21no—
116C2×C4×C71—21no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
126C2×C4×C71—21no—
127C2×C4×C71—44no—
128C2×C4×C71C2×D412yes—
129C2×C4×C71C2×D412yes—
130C2×C4×C71C2×D412yes—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—21no—
136C2×Dic71—21no—
137C2×Dic71—21no—
138C2×Dic71—21no—
139C2×Dic71—21no—
140C2×Dic71—21no—
141C2×Dic71—21no—
142C2×Dic71—21no—
143C2×Dic71—21no—
144C2×Dic71—21no—
145C2×Dic71—21no—
146C2×Dic71—21no—
147C2×Dic71—21no—
148C2×Dic71—21no—
149C2×Dic71—21no—
150C2×Dic71—21no—
151C2×Dic71—21no—
152C2×Dic71—21no—
153C2×Dic71—21no—
154C2×Dic71#4112yes—
155C22×C71—22no—
156C22×C71—22no—
157C22×C71—22no—
158C22×C71—41no—
159C22×C71—41no—
160C22×C71—41no—
161C22×C71—41no—
162C22×C71—41no—
163C22×C71—41no—
164C22×C71—41no—
165C22×C71—41no—
166C22×C71—41no—
167C22×C71—41no—
168C22×C71—41no—
169C22×C71C22×D411yescharacteristic
170C22×C71C2×#4111yescharacteristic
171C22×C71C2×#4111yescharacteristic
172C22×C71H(5,𝔽2)11yescharacteristic
173C22×C71H(5,𝔽2)11yescharacteristic
174C22×C712−1+411yescharacteristic
175C22×C712−1+411yescharacteristic
176C4×C71—22no—
177C4×C71—22no—
178C4×C71—22no—
179C4×C71—41no—
180C4×C71—41no—
181Dic71—22no—
182Dic71—41no—
183Dic71—41no—
184Dic71—41no—
185Dic71—41no—
186Dic71—41no—
187Dic71—41no—
188Dic71—41no—
189C2×C71—42no—
190C2×C71—81no—
191C2×C71#53711yescharacteristic
192C2×C71#53911yescharacteristic
193C2×C71#54011yescharacteristic
194C2×C71#54611yescharacteristic
195C2×C71#54811yescharacteristic
196C2×C71#55211yescharacteristic
197C2×C71#56311yescharacteristic
198#2707—711nomaximal, Sylow
199C71#270711yescharacteristic, complemented, Sylow
200C2×#125—711no—
201C2×#123D7111yescharacteristic
202#398—711no—
203#397—711no—
204#396—711no—
205#396—711no—
206#396—711no—
207#394—711no—
208#390—711no—
209#389—711no—
210#388—711no—
211#388—711no—
212#387—711no—
213#385—711no—
214#380—711no—
215C22×D4C2×D7111yescharacteristic
216C23×C4C2×D7111yescharacteristic
217#125—1424no—
218#123—24no—
219C2×C4⋊C4—711no—
220C2×C4⋊C4—711no—
221C2×C4⋊C4—711no—
222C2×C4⋊C4—711no—
223C2×C4⋊C4—711no—
224C2×C4⋊C4—711no—
225C2×C4⋊C4—711no—
226C2×C4⋊C4—711no—
227C2×C4⋊C4—711no—
228C2×C4⋊C4—711no—
229C2×C4⋊C4C2×D7111yescharacteristic
230C2×C4⋊C4C2×D7111yescharacteristic
231C2×C22⋊C4—711no—
232C2×C22⋊C4—711no—
233C2×C22⋊C4—711no—
234C2×C22⋊C4—711no—
235C2×C22⋊C4—711no—
236C2×C22⋊C4—711no—
237C2×C22⋊C4—711no—
238C2×C22⋊C4—711no—
239C2×C22⋊C4C2×D7111yescharacteristic
240C2×C22⋊C4C2×D7111yescharacteristic
241C2×C22⋊C4C2×D7111yescharacteristic
242C2×C42—711no—
243C2×C42—711no—
244#95—711no—
245#95—711no—
246#95—711no—
247#95—711no—
248#95—711no—
249#95—711no—
250#95—711no—
251#95—711no—
252C24C22×D7111yescharacteristic
253C24C22×D7111yescharacteristic
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—41no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—711no—
261C22×C4—711no—
262C22×C4—711no—
263C22×C4—711no—
264C22×C4—711no—
265C22×C4—711no—
266C22×C4—711no—
267C22×C4—711no—
268C22×C4C22×D7111yescharacteristic
269C22×C4C22×D7111yescharacteristic
270C22×C4C22×D7111yescharacteristic
271C22×C4C22×D7111yescharacteristic
272C22×C4C22×D7111yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—2841no—
275C4⋊C4—2841no—
276C4⋊C4—2841no—
277C4⋊C4—2841no—
278C4⋊C4—1422no—
279C4⋊C4—1422no—
280C4⋊C4—1422no—
281C4⋊C4—1422no—
282C4⋊C4—1422no—
283C4⋊C4—1422no—
284C4⋊C4C22⋊D7114yes—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—2841no—
289C22⋊C4—2841no—
290C22⋊C4—2841no—
291C22⋊C4—2841no—
292C22⋊C4—2841no—
293C22⋊C4—1422no—
294C22⋊C4—1422no—
295C22⋊C4—1422no—
296C42—2841no—
297C42—1422no—
298C23—21no—
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#1176586412yes—
312C23C23×D7111yescharacteristic
313D4—44no—
314C2×C4—21no—
315C2×C4—21no—
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—44no—
327C2×C4—712no—
328C2×C4—1421no—
329C2×C4—1421no—
330C2×C4—1421no—
331C2×C4—1421no—
332C2×C4—1421no—
333C2×C4—1421no—
334C2×C4—1421no—
335C2×C4—1421no—
336C2×C4—1421no—
337C2×C4—1421no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4—1421no—
342C2×C4—1421no—
343C2×C4—1421no—
344C2×C4—1421no—
345C2×C4—1421no—
346C2×C4—1421no—
347C2×C4—1421no—
348C2×C4—1421no—
349C2×C4—1421no—
350C2×C4—1421no—
351C2×C4C2×C22⋊D7112yes—
352C2×C4C2×C22⋊D7112yes—
353C2×C4C2×C22⋊D7112yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22C22×C22⋊D7111yescharacteristic
369C22#41×D7111yescharacteristic
370C22C2×#1176586411yescharacteristic
371C22#1455617311yescharacteristic
372C22#1455617411yescharacteristic
373C22#1455617511yescharacteristic
374C22#1455617511yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—2841no—
381C4—2841no—
382C4—2841no—
383C4—2841no—
384C4—2841no—
385C4—2841no—
386C4—2841no—
387C4—1422no—
388C2—42no—
389C2—81no—
390C2#1798657711yescharacteristic
391C2#1798659311yescharacteristic
392C2#1798660111yescharacteristic
393C2#1798664311yescharacteristic
394C2#1798665611yescharacteristic
395C2#1798668611yescharacteristic
396C2#1798675211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
FittingC2×#123×C71C2
hypercenterC2×#123D71
hypocenterC71#2707
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14556118C2semidirect
2. #17985932C2semidirect
3. #17985924C2semidirect
4. #17985922C2semidirect
5. #17985922C2semidirect
6. #17985922C2semidirect
9. #17985898C2semidirect
10. #17985893C2semidirect
11. #17985893C2semidirect
12. #17985880C2semidirect
13. #17985872C2semidirect
14. #17985859C2semidirect
199. C71#2707semidirect