Finite Group Databasebeta

← #20250100

Subgroups — #20250100

Order 6016.

568 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094005C211yesmaximal, characteristic, complemented
2#15689061C211yesmaximal, characteristic, complemented
3#15689054C211yesmaximal, characteristic, complemented
4#15689051C211yesmaximal, characteristic, complemented
5#15689051C211yesmaximal, characteristic, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689037C211yesmaximal, characteristic, complemented
8#15689003C211yesmaximal, characteristic, complemented
9#15689003C211yesmaximal, characteristic, complemented
10#15689003C211yesmaximal, characteristic, complemented
11#15688996C211yesmaximal, characteristic, complemented
12#15688996C211yesmaximal, characteristic, complemented
13#15688995C211yesmaximal, characteristic, complemented
14#15688981C211yesmaximal, characteristic, complemented
15C2×#121×C47C211yesmaximal, characteristic
16C23×Dic47C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18#13094005—24no—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C22×D4×C47C2211yescharacteristic
46C22×D4×C47C2211yescharacteristic
47C22×D4×C47C2211yescharacteristic
48C23×C4×C47C2211yescharacteristic
49#121×C47—24no—
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C24×C47C2311yescharacteristic
56C2×D4×C47—22no—
57C2×D4×C47—22no—
58C2×D4×C47—22no—
59C2×D4×C47—22no—
60C2×D4×C47—41no—
61C2×D4×C47—41no—
62C2×D4×C47—41no—
63C2×D4×C47—41no—
64C2×D4×C47D414yes—
65C22×C4×C47—22no—
66C22×C4×C47—41no—
67C22×C4×C47—41no—
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C22×Dic47—22no—
73C22×Dic47—22no—
74C22×Dic47—41no—
75C22×Dic47—41no—
76C22×Dic47—41no—
77C22×Dic47—41no—
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C22×Dic47C2311yescharacteristic
84C22×Dic47C2311yescharacteristic
85C22×Dic47C2311yescharacteristic
86C4⋊C4×C47—22no—
87C22⋊C4×C47—22no—
88C22⋊C4×C47—22no—
89C22⋊Dic47—22no—
90C22⋊Dic47—22no—
91C22⋊Dic47—22no—
92C22⋊Dic47—22no—
93C22⋊Dic47—22no—
94C22⋊Dic47—22no—
95C22⋊Dic47—41no—
96C22⋊Dic47—41no—
97C22⋊Dic47—41no—
98C22⋊Dic47—41no—
99Dic47⋊C4—22no—
100Dic47⋊C4—22no—
101Dic47⋊C4—41no—
102Dic47⋊C4—41no—
103Dic47⋊C4—41no—
104Dic47⋊C4—41no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47C2×D412yes—
124C23×C47C2×D412yes—
125C23×C47#4112yes—
126C23×C47C2411yescharacteristic
127D4×C47—44no—
128D4×C47—44no—
129D4×C47—44no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—44no—
142C2×C4×C47C2×D412yes—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—44no—
167C2×Dic47—44no—
168C2×Dic47#4112yes—
169C22×C47—22no—
170C22×C47—22no—
171C22×C47—22no—
172C22×C47—22no—
173C22×C47—22no—
174C22×C47—22no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47—22no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47C22×D411yescharacteristic
191C22×C47C2×#4111yescharacteristic
192C22×C47C2×#4111yescharacteristic
193C22×C47H(5,𝔽2)11yescharacteristic
194C22×C47H(5,𝔽2)11yescharacteristic
195C22×C47H(5,𝔽2)11yescharacteristic
196C22×C472−1+411yescharacteristic
197C4×C47—22no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47—41no—
201Dic47—22no—
202Dic47—41no—
203Dic47—41no—
204Dic47—41no—
205Dic47—41no—
206Dic47—41no—
207Dic47—41no—
208Dic47—41no—
209#2708—471nomaximal, Sylow
210C2×C47—42no—
211C2×C47—42no—
212C2×C47—42no—
213C2×C47#53411yescharacteristic
214C2×C47#53811yescharacteristic
215C2×C47#53911yescharacteristic
216C2×C47#54611yescharacteristic
217C2×C47#54711yescharacteristic
218C2×C47#55311yescharacteristic
219C2×C47#56211yescharacteristic
220C2×#123—471no—
221C2×#121D4711yescharacteristic
222#400—471no—
223#398—471no—
224#397—471no—
225#397—471no—
226#394—471no—
227#394—471no—
228#386—471no—
229#386—471no—
230#386—471no—
231#385—471no—
232#385—471no—
233#385—471no—
234#380—471no—
235C47#270811yescharacteristic, complemented, Sylow
236C22×D4C2×D4711yescharacteristic
237C22×D4C2×D4711yescharacteristic
238C22×D4C2×D4711yescharacteristic
239C23×C4—471no—
240C23×C4—471no—
241C23×C4C2×D4711yescharacteristic
242#123—944no—
243#121—24no—
244C2×C4⋊C4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4—471no—
248C2×C4⋊C4—471no—
249C2×C4⋊C4—471no—
250C2×C4⋊C4C2×D4711yescharacteristic
251C2×C22⋊C4—471no—
252C2×C22⋊C4—471no—
253C2×C22⋊C4—471no—
254C2×C22⋊C4—471no—
255C2×C22⋊C4—471no—
256C2×C22⋊C4—471no—
257C2×C22⋊C4—471no—
258C2×C22⋊C4—471no—
259C2×C22⋊C4—471no—
260C2×C22⋊C4—471no—
261C2×C22⋊C4C2×D4711yescharacteristic
262C2×C22⋊C4C2×D4711yescharacteristic
263#95—471no—
264#95—471no—
265#95—471no—
266#95—471no—
267#95—471no—
268#95—471no—
269#95—471no—
270#95—471no—
271#95—471no—
272#95—471no—
273C24C22×D4711yescharacteristic
274C24C22×D4711yescharacteristic
275C24C22×D4711yescharacteristic
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4C22⋊D4714yes—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—471no—
291C22×C4—471no—
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—942no—
297C22×C4—942no—
298C22×C4—1881no—
299C22×C4—1881no—
300C22×C4—1881no—
301C22×C4—1881no—
302C22×C4C22×D4711yescharacteristic
303C22×C4C22×D4711yescharacteristic
304C22×C4C22×D4711yescharacteristic
305C22×C4C22×D4711yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—942no—
308C4⋊C4—942no—
309C4⋊C4—1881no—
310C4⋊C4—1881no—
311C4⋊C4—1881no—
312C4⋊C4—1881no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—942no—
316C22⋊C4—942no—
317C22⋊C4—942no—
318C22⋊C4—942no—
319C22⋊C4—942no—
320C22⋊C4—942no—
321C22⋊C4—1881no—
322C22⋊C4—1881no—
323C22⋊C4—1881no—
324C22⋊C4—1881no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23#1062535212yes—
344C23C2×C22⋊D4712yes—
345C23C2×C22⋊D4712yes—
346C23C23×D4711yescharacteristic
347D4—44no—
348D4—44no—
349D4—44no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—472no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—941no—
373C2×C4—941no—
374C2×C4—941no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—1884no—
387C2×C4—1884no—
388C2×C4C2×C22⋊D4712yes—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22C22×C22⋊D4711yescharacteristic
411C22#41×D4711yescharacteristic
412C22C2×#1062535211yescharacteristic
413C22#1309406911yescharacteristic
414C22#1309406911yescharacteristic
415C22#1309406911yescharacteristic
416C22#1309407111yescharacteristic
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—942no—
422C4—1881no—
423C4—1881no—
424C4—1881no—
425C4—1881no—
426C4—1881no—
427C4—1881no—
428C4—1881no—
429C2—42no—
430C2—42no—
431C2—42no—
432C2#1568968211yescharacteristic
433C2#1568970511yescharacteristic
434C2#1568971811yescharacteristic
435C2#1568976711yescharacteristic
436C2#1568977211yescharacteristic
437C2#1568981611yescharacteristic
438C2#1568986811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#121×C47C2
hypercenterC2×#121D47
hypocenterC47#2708
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13094005C2semidirect
2. #15689061C2semidirect
3. #15689054C2semidirect
4. #15689051C2semidirect
5. #15689051C2semidirect
6. #15689037C2semidirect
7. #15689037C2semidirect
8. #15689003C2semidirect
9. #15689003C2semidirect
10. #15689003C2semidirect
11. #15688996C2semidirect
12. #15688996C2semidirect
13. #15688995C2semidirect
14. #15688981C2semidirect
235. C47#2708semidirect