Finite Group Databasebeta

← #21452608

Subgroups — #21452608

Order 7808.

598 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519770C211yesmaximal, characteristic, complemented
2C2×#14519749C211yesmaximal, characteristic, complemented
3#16839689C211yesmaximal, characteristic, complemented
4#16839677C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic, complemented
6#16839670C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839665C211yesmaximal, characteristic, complemented
9#16839662C211yesmaximal, characteristic, complemented
10#16839662C211yesmaximal, characteristic, complemented
11#16839656C211yesmaximal, characteristic, complemented
12#16839644C211yesmaximal, characteristic, complemented
13#16839642C211yesmaximal, characteristic, complemented
14#16839634C211yesmaximal, characteristic, complemented
15C61×#392C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20#14519770—24no—
21#14519749—24no—
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C22×D4×C61C2211yescharacteristic
47C22×D4×C61C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C24×C61C2311yescharacteristic
55C24×C61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C2×D4×C61—22no—
58C2×D4×C61—22no—
59C2×D4×C61—22no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C22×Dic61—22no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C22⋊C4×C61—22no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊Dic61—22no—
93C22⋊Dic61—22no—
94C22⋊Dic61—22no—
95C22⋊Dic61—22no—
96C22⋊Dic61—22no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100#11758198—22no—
101#11758198—41no—
102#11758198—41no—
103#11758198—41no—
104C4⋊Dic61—22no—
105#11758196—22no—
106#11758196—41no—
107#11758196—41no—
108#11758196D414yescomplemented
109C4×Dic61—22no—
110C4×Dic61—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61#4112yes—
132C23×C61C2411yescharacteristic
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140D4×C61—44no—
141D4×C61—44no—
142D4×C61—44no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61C2×D412yes—
155C22⋊D61—44no—
156C22⋊D61—44no—
157C22⋊D61—44no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—44no—
177C2×Dic61C2×D412yes—
178C2×Dic61C2×D412yes—
179C2×Dic61#4112yes—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—22no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61C22×D411yescharacteristic
202C22×C61C2×#4111yescharacteristic
203C22×C61C2×#4111yescharacteristic
204C22×C61H(5,𝔽2)11yescharacteristic
205C22×C61H(5,𝔽2)11yescharacteristic
206C22×C61H(5,𝔽2)11yescharacteristic
207C22×C61H(5,𝔽2)11yescharacteristic
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C4×C61—22no—
216C4×C61—41no—
217C4×C61—41no—
218C4×C61—41no—
219Dic61—22no—
220Dic61—22no—
221Dic61—22no—
222Dic61—41no—
223Dic61—41no—
224Dic61—41no—
225Dic61—41no—
226#2714—611nomaximal, Sylow
227C2×C61—42no—
228C2×C61—81no—
229C2×C61—81no—
230C2×C61#53511yescharacteristic
231C2×C61#53811yescharacteristic
232C2×C61#53811yescharacteristic
233C2×C61#54611yescharacteristic
234C2×C61#55011yescharacteristic
235C2×C61#55311yescharacteristic
236C2×C61#56011yescharacteristic
237D61—81no—
238C2×#126—611no—
239C2×#121—611no—
240#397—611no—
241#394—611no—
242#394—611no—
243#392—611no—
244#392—611no—
245#392D6111yescharacteristic, complemented
246#390—611no—
247#390—611no—
248#390—611no—
249#388—611no—
250#387—611no—
251#386—611no—
252#385—611no—
253C61#271411yescharacteristic, complemented, Sylow
254C22×D4—611no—
255C22×D4—611no—
256C22×D4—611no—
257C22×D4C2×D6111yescharacteristic
258C22×D4C2×D6111yescharacteristic
259C22×D4C2×D6111yescharacteristic
260C23×C4—611no—
261#126—1224no—
262#121—1224no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4—611no—
277C2×C22⋊C4—611no—
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4C2×D6111yescharacteristic
281C2×C22⋊C4C2×D6111yescharacteristic
282C2×C22⋊C4C2×D6111yescharacteristic
283C2×C42—611no—
284C2×C42—611no—
285#95—611no—
286#95—611no—
287#95—611no—
288#95—611no—
289#95—611no—
290#95C2×D6111yescharacteristic
291C24—611no—
292C24C22×D6111yescharacteristic
293C24C22×D6111yescharacteristic
294C24C22×D6111yescharacteristic
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—1222no—
305C2×D4—1222no—
306C2×D4—1222no—
307C2×D4—1222no—
308C2×D4—2441no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—1222no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4C22×D6111yescharacteristic
324C22×C4C22×D6111yescharacteristic
325C22×C4C22×D6111yescharacteristic
326C22×C4C22×D6111yescharacteristic
327C4⋊C4—614no—
328C4⋊C4—1222no—
329C4⋊C4—1222no—
330C4⋊C4—2441no—
331C4⋊C4—2441no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—1222no—
336C22⋊C4—1222no—
337C22⋊C4—1222no—
338C22⋊C4—1222no—
339C22⋊C4—1222no—
340C22⋊C4—1222no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C42—1222no—
348C42—2441no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—1221no—
370C23—1221no—
371C23—1221no—
372C23—1221no—
373C23—1221no—
374C23—1221no—
375C23—1221no—
376C23#1175822412yes—
377C23C23×D6111yescharacteristic
378D4—44no—
379D4—44no—
380D4—44no—
381D4—2444no—
382D4—2444no—
383D4—2444no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—612no—
396C2×C4—612no—
397C2×C4—612no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—2444no—
417C2×C4D4×D6112yes—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—2441no—
440C22—2441no—
441C22—2441no—
442C22—2441no—
443C22—2441no—
444C22—2441no—
445C22—2441no—
446C22C2×D4×D6111yescharacteristic
447C22#41×D6111yescharacteristic
448C22C2×#1175822411yescharacteristic
449C22#1451982211yescharacteristic
450C22#1451982211yescharacteristic
451C22#1451982211yescharacteristic
452C22#1451982211yescharacteristic
453C4—22no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—1222no—
458C4—1222no—
459C4—1222no—
460C4—2441no—
461C4—2441no—
462C4—2441no—
463C4—2441no—
464C2—42no—
465C2—81no—
466C2—81no—
467C2—4881no—
468C2#1684032511yescharacteristic
469C2#1684034411yescharacteristic
470C2#1684034711yescharacteristic
471C2#1684039911yescharacteristic
472C2#1684043011yescharacteristic
473C2#1684045511yescharacteristic
474C2#1684050111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2714
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519770C2semidirect
2. C2×#14519749C2semidirect
3. #16839689C2semidirect
4. #16839677C2semidirect
5. #16839676C2semidirect
6. #16839670C2semidirect
7. #16839670C2semidirect
8. #16839665C2semidirect
9. #16839662C2semidirect
10. #16839662C2semidirect
11. #16839656C2semidirect
12. #16839644C2semidirect
13. #16839642C2semidirect
14. #16839634C2semidirect
15. C61×#392C2semidirect
108. #11758196D4semidirect
245. #392D61semidirect
253. C61#2714semidirect