Finite Group Databasebeta

← #21449152

Subgroups — #21449152

Order 7808.

864 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11758222C211yesmaximal, characteristic
2C2×#14519762C211yesmaximal, characteristic, complemented
3C2×#14519759C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
5#16839683C211yesmaximal, characteristic, complemented
6#16839682C211yesmaximal, characteristic, complemented
7#16839678C211yesmaximal, characteristic, complemented
8#16839677C211yesmaximal, characteristic, complemented
9#16839640C211yesmaximal, characteristic, complemented
10#16839638C211yesmaximal, characteristic, complemented
11#16839636C211yesmaximal, characteristic, complemented
12#16839635C211yesmaximal, characteristic, complemented
13#16839633C211yesmaximal, characteristic, complemented
14#16839624C211yesmaximal, characteristic, complemented
15C61×#385C211yesmaximal, characteristic, complemented
16C2×#11758222—24no—
17C2×#11758222—24no—
18C2×#11758222—24no—
19C22×Dic122C2211yescharacteristic
20C22×D244C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic
24C22×C4×D61C2211yescharacteristic
25C22×C4×D61C2211yescharacteristic
26C22×C4×D61C2211yescharacteristic
27#14519762—24no—
28#14519759—24no—
29C2×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊Dic61C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758196C2211yescharacteristic
34C2×#11758196C2211yescharacteristic
35C4⋊C4×D61—24no—
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49#14519684C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic
51C2×C4⋊C4×C61C2211yescharacteristic
52C2×C4⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55#95×C61C2211yescharacteristic
56#95×C61C2211yescharacteristic
57C24×C61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C23×D61C2311yescharacteristic
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—22no—
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61D414yes—
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81#11758222—232no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244D414yes—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61D414yes—
97C2×Dic122—22no—
98C2×Dic122—22no—
99C2×Dic122—22no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—22no—
102C22⋊C4×C61—22no—
103C22⋊C4×C61—22no—
104C22⋊Dic61—22no—
105C22⋊Dic61—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198—22no—
112C4⋊Dic61—22no—
113C4⋊Dic61—22no—
114#11758196—22no—
115#11758196—22no—
116#11758196—22no—
117#11758196—22no—
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×D61C2×D412yes—
137C22×D61C2×D412yes—
138C22×D61C2×D412yes—
139C22×D61C2×D412yes—
140C2×C4×C61—28no—
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—21no—
156C2×C4×C61C2×D412yes—
157C2×C4×C61C2×D412yes—
158C2×C4×C61#4112yescomplemented
159C22⋊D61—28no—
160C22⋊D61—28no—
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×Dic61C2×D412yes—
177C2×Dic61C2×D412yes—
178C2×Dic61#4112yescomplemented
179D244—28no—
180C4×D61—28no—
181C4×D61—28no—
182C4×D61—28no—
183C4×D61—44no—
184Dic122—28no—
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—22no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61C22×D411yescharacteristic
193C22×C61C22×D411yescharacteristic
194C22×C61C22×D411yescharacteristic
195C22×C61C2×#4111yescharacteristic
196C22×C61C2×#4111yescharacteristic
197C22×C612−1+411yescharacteristic
198C22×C612−1+411yescharacteristic
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61#12014yes—
213C4×C61—22no—
214C4×C61—22no—
215C4×C61—22no—
216C4×C61—41no—
217C4×C61—41no—
218C4×C61—41no—
219Dic61—22no—
220Dic61—22no—
221Dic61—22no—
222Dic61—41no—
223Dic61—41no—
224Dic61—41no—
225#2406—611nomaximal, Sylow
226C2×C61—42no—
227C2×C61C2×#12011yescharacteristic
228C2×C61#52511yescharacteristic
229C2×C61#53611yescharacteristic
230C2×C61#54711yescharacteristic
231C2×C61#54711yescharacteristic
232C2×C61#54711yescharacteristic
233C2×C61#54711yescharacteristic
234D61—24no—
235D61—42no—
236C22×#41—611no—
237C2×#123—611no—
238C2×#123—611no—
239C22×C4⋊C4—611no—
240#395—611no—
241#395—611no—
242#394—611no—
243#394—611no—
244#386—611no—
245#386—611no—
246#385—611no—
247#385—611no—
248#385—611no—
249#385D6111yescharacteristic, complemented
250#381—611no—
251C61#240611yescharacteristic, complemented, Sylow
252C2×#41—1224no—
253C2×#41—1224no—
254C2×#41—1224no—
255C22×Q8—611no—
256C22×D4—611no—
257C22×D4—611no—
258C22×D4—611no—
259C23×C4—611no—
260C23×C4—611no—
261C23×C4—611no—
262C23×C4—611no—
263C23×C4C2×D6111yescharacteristic
264#123—1224no—
265#123—1224no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—1224no—
273C2×C4⋊C4C2×D6111yescharacteristic
274C2×C4⋊C4C2×D6111yescharacteristic
275C2×C22⋊C4—611no—
276C2×C22⋊C4—611no—
277C2×C22⋊C4—611no—
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4C2×D6111yescharacteristic
284C2×C22⋊C4C2×D6111yescharacteristic
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
296#41—12232no—
297C2×Q8—1222no—
298C2×Q8—1222no—
299C2×Q8—1222no—
300C2×D4—614no—
301C2×D4—614no—
302C2×D4—1222no—
303C2×D4—1222no—
304C2×D4—1222no—
305C2×D4—1222no—
306C2×D4—1222no—
307C2×D4—1222no—
308C2×D4—1222no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—611no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—614no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—1222no—
320C22×C4—1222no—
321C22×C4—1222no—
322C22×C4—1222no—
323C22×C4—1222no—
324C22×C4—1222no—
325C22×C4—1222no—
326C22×C4—1222no—
327C22×C4—1222no—
328C22×C4—1222no—
329C22×C4—1222no—
330C22×C4C22×D6111yescharacteristic
331C22×C4C22×D6111yescharacteristic
332C22×C4C22×D6111yescharacteristic
333C22×C4C22×D6111yescharacteristic
334C22×C4C22×D6111yescharacteristic
335C22×C4C22×D6111yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—1222no—
339C4⋊C4—1222no—
340C4⋊C4—1222no—
341C4⋊C4—1222no—
342C4⋊C4—1222no—
343C4⋊C4—1222no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—1222no—
347C22⋊C4—1222no—
348C22⋊C4—1222no—
349C22⋊C4—1222no—
350C22⋊C4—1222no—
351C22⋊C4—1222no—
352C22⋊C4—1222no—
353C22⋊C4—1222no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—612no—
361C23—612no—
362C23—612no—
363C23—612no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—1221no—
372C23—1221no—
373C23—1221no—
374C23D4×D6112yes—
375C23C23×D6111yescharacteristic
376Q8—1228no—
377D4—1228no—
378D4—1228no—
379D4—1228no—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
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—21no—
396C2×C4—612no—
397C2×C4—612no—
398C2×C4—612no—
399C2×C4—1228no—
400C2×C4—1228no—
401C2×C4—1228no—
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—2444no—
418C2×C4#1175822212yescomplemented
419C2×C4D4×D6112yes—
420C2×C4D4×D6112yes—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—614no—
429C22—1222no—
430C22—1222no—
431C22—1222no—
432C22—1222no—
433C22—1222no—
434C22—1222no—
435C22—1222no—
436C22—1222no—
437C22—1222no—
438C22—2441no—
439C22—2441no—
440C22—2441no—
441C22—2441no—
442C22C2×D4×D6111yescharacteristic
443C22C2×D4×D6111yescharacteristic
444C22C2×D4×D6111yescharacteristic
445C22#41×D6111yescharacteristic
446C22C2×#1175822211yescharacteristic
447C22#1451982411yescharacteristic
448C22#1451982511yescharacteristic
449C4—22no—
450C4—22no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—1222no—
456C4—1222no—
457C4—1222no—
458C4—2441no—
459C4—2441no—
460C4—2441no—
461C2—42no—
462C2—1224no—
463C2—2442no—
464C2#120×D6111yescharacteristic
465C2#1684027111yescharacteristic
466C2#1684033511yescharacteristic
467C2#1684041011yescharacteristic
468C2#1684041311yescharacteristic
469C2#1684041411yescharacteristic
470C2#1684041711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2406
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#14519762C2semidirect
3. C2×#14519759C2semidirect
4. C2×C4⋊C4×D61C2semidirect
5. #16839683C2semidirect
6. #16839682C2semidirect
7. #16839678C2semidirect
8. #16839677C2semidirect
9. #16839640C2semidirect
10. #16839638C2semidirect
11. #16839636C2semidirect
12. #16839635C2semidirect
13. #16839633C2semidirect
14. #16839624C2semidirect
15. C61×#385C2semidirect
158. C2×C4×C61#41semidirect
178. C2×Dic61#41semidirect
249. #385D61semidirect
251. C61#2406semidirect
418. C2×C4#11758222semidirect