Finite Group Databasebeta

← #21452250

Subgroups — #21452250

Order 7808.

626 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519750C211yesmaximal, characteristic, complemented
2C2×#14519748C211yesmaximal, characteristic, complemented
3#16839704C211yesmaximal, characteristic, complemented
4#16839690C211yesmaximal, characteristic, complemented
5#16839690C211yesmaximal, characteristic, complemented
6#16839677C211yesmaximal, characteristic, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839670C211yesmaximal, characteristic, complemented
9#16839641C211yesmaximal, characteristic, complemented
10#16839641C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839638C211yesmaximal, characteristic, complemented
13#16839636C211yesmaximal, characteristic, complemented
14#16839624C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23#14519750—24no—
24#14519748—24no—
25C2×C4⋊Dic61C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C22×D4×C61C2211yescharacteristic
47C23×C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C24×C61C2311yescharacteristic
55C23×D61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C2×D4×C61—22no—
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C22×C4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61D414yescomplemented
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C22×Dic61C2311yescharacteristic
86C2×D244—22no—
87C2×D244—22no—
88C2×D244—41no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊Dic61—22no—
99C22⋊Dic61—22no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102#11758198—22no—
103#11758198—22no—
104#11758198—41no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—22no—
109#11758196—22no—
110#11758196—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×C61C2×D412yes—
125C23×C61C2411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61C2×D412yes—
139C22×D61#4112yes—
140D4×C61—44no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
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×C61—21no—
155C2×C4×C61—44no—
156C2×C4×C61#4112yes—
157C22⋊D61—44no—
158C22⋊D61—44no—
159C22⋊D61—44no—
160C22⋊D61—44no—
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—21no—
177C2×Dic61—21no—
178C2×Dic61C2×D412yes—
179D244—44no—
180C4×D61—44no—
181C4×D61—44no—
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
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×C61C22×D411yescharacteristic
197C22×C61C2×#4111yescharacteristic
198C22×C61C2×#4111yescharacteristic
199C22×C61H(5,𝔽2)11yescharacteristic
200C22×C61H(5,𝔽2)11yescharacteristic
201C22×C61H(5,𝔽2)11yescharacteristic
202C22×C61H(5,𝔽2)11yescharacteristic
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—22no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61—41no—
216C2×D61—41no—
217C4×C61—22no—
218C4×C61—41no—
219C4×C61—41no—
220C4×C61—41no—
221C4×C61—41no—
222Dic61—22no—
223Dic61—41no—
224Dic61—41no—
225Dic61—41no—
226Dic61—41no—
227Dic61—41no—
228#2688—611nomaximal, Sylow
229C2×C61—42no—
230C2×C61—81no—
231C2×C61#53411yescharacteristic
232C2×C61#53811yescharacteristic
233C2×C61#54011yescharacteristic
234C2×C61#54611yescharacteristic
235C2×C61#54611yescharacteristic
236C2×C61#55311yescharacteristic
237C2×C61#56011yescharacteristic
238D61—42no—
239D61—42no—
240C2×#121—611no—
241C2×#121—611no—
242#400—611no—
243#397—611no—
244#397—611no—
245#394—611no—
246#392—611no—
247#392—611no—
248#386—611no—
249#386—611no—
250#386—611no—
251#386—611no—
252#386D6111yescharacteristic, complemented
253#385—611no—
254#381—611no—
255C61#268811yescharacteristic, complemented, Sylow
256C22×D4—611no—
257C22×D4—611no—
258C22×D4—611no—
259C22×D4—611no—
260C22×D4—611no—
261C22×D4C2×D6111yescharacteristic
262C23×C4—611no—
263C23×C4—611no—
264C23×C4C2×D6111yescharacteristic
265#121—1224no—
266#121—1224no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—611no—
269C2×C4⋊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
283#95—611no—
284#95—611no—
285#95—611no—
286#95—611no—
287#95—611no—
288#95—611no—
289#95—611no—
290#95—611no—
291#95C2×D6111yescharacteristic
292#95C2×D6111yescharacteristic
293C24—611no—
294C24—611no—
295C24C22×D6111yescharacteristic
296C24C22×D6111yescharacteristic
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—41no—
300C2×D4—614no—
301C2×D4—1222no—
302C2×D4—1222no—
303C2×D4—1222no—
304C2×D4—1222no—
305C2×D4—1222no—
306C2×D4—1222no—
307C2×D4—2441no—
308C2×D4—2441no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—1222no—
325C22×C4—1222no—
326C22×C4—1222no—
327C22×C4—2441no—
328C22×C4—2441no—
329C22×C4—2441no—
330C22×C4C22×D6111yescharacteristic
331C22×C4C22×D6111yescharacteristic
332C22×C4C22×D6111yescharacteristic
333C22×C4C22×D6111yescharacteristic
334C22×C4C22×D6111yescharacteristic
335C4⋊C4—1222no—
336C4⋊C4—1222no—
337C4⋊C4—2441no—
338C22⋊C4—22no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—1222no—
342C22⋊C4—1222no—
343C22⋊C4—1222no—
344C22⋊C4—1222no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
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—612no—
365C23—612no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—1221no—
372C23—1221no—
373C23—1221no—
374C23—1221no—
375C23—1221no—
376C23—1221no—
377C23—1221no—
378C23D4×D6112yes—
379C23C23×D6111yescharacteristic
380D4—44no—
381D4—2444no—
382D4—2444no—
383D4—2444no—
384D4—2444no—
385D4—2444no—
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—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—44no—
401C2×C4—612no—
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—1221no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—2444no—
420C2×C4—2444no—
421C2×C4#1175822212yes—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—1222no—
437C22—1222no—
438C22—1222no—
439C22—1222no—
440C22—1222no—
441C22—1222no—
442C22—2441no—
443C22—2441no—
444C22—2441no—
445C22—2441no—
446C22—2441no—
447C22—2441no—
448C22—2441no—
449C22—2441no—
450C22C2×D4×D6111yescharacteristic
451C22#41×D6111yescharacteristic
452C22C2×#1175822211yescharacteristic
453C22#1451982211yescharacteristic
454C22#1451982211yescharacteristic
455C22#1451982211yescharacteristic
456C22#1451982311yescharacteristic
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—1222no—
463C4—2441no—
464C4—2441no—
465C4—2441no—
466C4—2441no—
467C4—2441no—
468C2—42no—
469C2—81no—
470C2—2442no—
471C2—2442no—
472C2#1684032011yescharacteristic
473C2#1684034811yescharacteristic
474C2#1684036311yescharacteristic
475C2#1684040111yescharacteristic
476C2#1684040211yescharacteristic
477C2#1684046211yescharacteristic
478C2#1684050111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2688
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14519750C2semidirect
2. C2×#14519748C2semidirect
3. #16839704C2semidirect
4. #16839690C2semidirect
5. #16839690C2semidirect
6. #16839677C2semidirect
7. #16839671C2semidirect
8. #16839670C2semidirect
9. #16839641C2semidirect
10. #16839641C2semidirect
11. #16839640C2semidirect
12. #16839638C2semidirect
13. #16839636C2semidirect
14. #16839624C2semidirect
15. C61×#386C2semidirect
79. C2×C22⋊D61D4semidirect
252. #386D61semidirect
255. C61#2688semidirect