Finite Group Databasebeta

← #21449428

Subgroups — #21449428

Order 7808.

914 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11758222C211yesmaximal, characteristic, complemented
2C2×#14519762C211yesmaximal, characteristic, complemented
3C2×#14519752C211yesmaximal, characteristic, complemented
4C2×#14519750C211yesmaximal, characteristic, complemented
5#16839682C211yesmaximal, characteristic, complemented
6#16839677C211yesmaximal, characteristic, complemented
7#16839675C211yesmaximal, characteristic, complemented
8#16839671C211yesmaximal, characteristic, complemented
9#16839641C211yesmaximal, characteristic, complemented
10#16839640C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839638C211yesmaximal, characteristic, complemented
13#16839633C211yesmaximal, characteristic, complemented
14#95×D61C211yesmaximal, characteristic, complemented
15C61×#385C211yesmaximal, characteristic, complemented
16C2×#11758222—24no—
17C2×#11758222—24no—
18C2×#11758222—24no—
19C22×Dic122C2211yescharacteristic
20C22×D244C2211yescharacteristic
21C22×D244C2211yescharacteristic
22C22×D244C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic
24C22×C22⋊D61C2211yescharacteristic
25C22×C22⋊D61C2211yescharacteristic
26C22×C4×D61C2211yescharacteristic
27C22×C4×D61C2211yescharacteristic
28C22×C4×D61C2211yescharacteristic
29C22×C4×D61C2211yescharacteristic
30#14519762—24no—
31#14519752—24no—
32#14519750—24no—
33C2×#11758196C2211yescharacteristic
34C2×#11758196C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
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
60C23×D61C2311yescharacteristic
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
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—22no—
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61D414yescomplemented
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84#11758222—232no—
85C2×D244—22no—
86C2×D244—22no—
87C2×D244—22no—
88C2×D244—22no—
89C2×D244—22no—
90C2×D244—22no—
91C2×D244—22no—
92C2×D244—41no—
93C2×D244D414yescomplemented
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61D414yescomplemented
106C2×Dic122—22no—
107C2×Dic122—22no—
108C2×Dic122—22no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—22no—
111C22⋊C4×C61—22no—
112C22⋊C4×C61—22no—
113C22⋊Dic61—41no—
114#11758198—22no—
115#11758198—22no—
116#11758198—22no—
117#11758198—22no—
118#11758198—22no—
119#11758198—22no—
120#11758198—22no—
121#11758198—41no—
122#11758196—22no—
123#11758196—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61C2×D412yes—
131C23×C61C2411yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61C2×D412yes—
150C22×D61C2×D412yes—
151C22×D61C2×D412yes—
152C22×D61C2×D412yes—
153C2×C4×C61—28no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61C2×D412yes—
170C2×C4×C61C2×D412yes—
171C2×C4×C61#4112yescomplemented
172C22⋊D61—28no—
173C22⋊D61—28no—
174C22⋊D61—44no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61C2×D412yes—
188C2×Dic61C2×D412yes—
189C2×Dic61#4112yescomplemented
190D244—28no—
191D244—44no—
192D244—44no—
193C4×D61—28no—
194C4×D61—28no—
195C4×D61—44no—
196C4×D61—44no—
197Dic122—28no—
198C22×C61—22no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61C22×D411yescharacteristic
206C22×C61C22×D411yescharacteristic
207C22×C61C22×D411yescharacteristic
208C22×C61C2×#4111yescharacteristic
209C22×C61C2×#4111yescharacteristic
210C22×C61H(5,𝔽2)11yescharacteristic
211C22×C612−1+411yescharacteristic
212C2×D61—22no—
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—22no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C2×D61—41no—
229C2×D61—41no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61#12014yes—
233C4×C61—22no—
234C4×C61—22no—
235C4×C61—22no—
236C4×C61—41no—
237C4×C61—41no—
238C4×C61—41no—
239Dic61—22no—
240Dic61—22no—
241Dic61—22no—
242Dic61—41no—
243Dic61—41no—
244#2430—611nomaximal, Sylow
245C2×C61—42no—
246C2×C61C2×#12011yescharacteristic
247C2×C61#53211yescharacteristic
248C2×C61#53711yescharacteristic
249C2×C61#54611yescharacteristic
250C2×C61#54611yescharacteristic
251C2×C61#54711yescharacteristic
252C2×C61#54711yescharacteristic
253D61—24no—
254D61—42no—
255D61—81no—
256C22×#41—611no—
257C2×#123—611no—
258C2×#121—611no—
259C2×#121—611no—
260#395—611no—
261#394—611no—
262#393—611no—
263#392—611no—
264#386—611no—
265#386—611no—
266#386—611no—
267#386—611no—
268#385—611no—
269#385D6111yescharacteristic, complemented
270C2×#95—611no—
271C61#243011yescharacteristic, complemented, Sylow
272C2×#41—1224no—
273C2×#41—1224no—
274C2×#41—1224no—
275C22×Q8—611no—
276C22×D4—611no—
277C22×D4—611no—
278C22×D4—611no—
279C22×D4—611no—
280C22×D4—611no—
281C22×D4—611no—
282C23×C4—611no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4C2×D6111yescharacteristic
287#123—1224no—
288#121—1224no—
289#121—1224no—
290C2×C4⋊C4—611no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4C2×D6111yescharacteristic
293C2×C4⋊C4C2×D6111yescharacteristic
294C2×C22⋊C4—611no—
295C2×C22⋊C4—611no—
296C2×C22⋊C4—611no—
297C2×C22⋊C4—611no—
298C2×C22⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4C2×D6111yescharacteristic
304C2×C22⋊C4C2×D6111yescharacteristic
305#95—611no—
306#95—611no—
307#95—611no—
308#95—611no—
309#95—611no—
310#95—611no—
311#95C2×D6111yescharacteristic
312#95C2×D6111yescharacteristic
313C24—611no—
314C24—611no—
315C24—611no—
316C24C22×D6111yescharacteristic
317#41—12232no—
318C2×Q8—1222no—
319C2×Q8—1222no—
320C2×Q8—1222no—
321C2×D4—614no—
322C2×D4—614no—
323C2×D4—1222no—
324C2×D4—1222no—
325C2×D4—1222no—
326C2×D4—1222no—
327C2×D4—1222no—
328C2×D4—1222no—
329C2×D4—1222no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—1222no—
333C2×D4—1222no—
334C2×D4—1222no—
335C2×D4—1222no—
336C2×D4—1222no—
337C2×D4—2441no—
338C2×D4—2441no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—614no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4C22×D6111yescharacteristic
360C22×C4C22×D6111yescharacteristic
361C22×C4C22×D6111yescharacteristic
362C22×C4C22×D6111yescharacteristic
363C22×C4C22×D6111yescharacteristic
364C22×C4C22×D6111yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—1222no—
368C4⋊C4—1222no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C22⋊C4—1222no—
374C22⋊C4—1222no—
375C22⋊C4—1222no—
376C22⋊C4—1222no—
377C22⋊C4—1222no—
378C22⋊C4—2441no—
379C22⋊C4—2441no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—612no—
387C23—612no—
388C23—612no—
389C23—612no—
390C23—1221no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—1221no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23D4×D6112yes—
408C23C23×D6111yescharacteristic
409Q8—1228no—
410D4—1228no—
411D4—1228no—
412D4—1228no—
413D4—2444no—
414D4—2444no—
415D4—2444no—
416C2×C4—28no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—1228no—
436C2×C4—1228no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4—2444no—
450C2×C4—2444no—
451C2×C4#1175822212yescomplemented
452C2×C4D4×D6112yes—
453C2×C4D4×D6112yes—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—614no—
462C22—1222no—
463C22—1222no—
464C22—1222no—
465C22—1222no—
466C22—1222no—
467C22—1222no—
468C22—1222no—
469C22—1222no—
470C22—1222no—
471C22—2441no—
472C22—2441no—
473C22—2441no—
474C22—2441no—
475C22—2441no—
476C22—2441no—
477C22—2441no—
478C22—2441no—
479C22—2441no—
480C22—2441no—
481C22—2441no—
482C22C2×D4×D6111yescharacteristic
483C22C2×D4×D6111yescharacteristic
484C22C2×D4×D6111yescharacteristic
485C22#41×D6111yescharacteristic
486C22C2×#1175822211yescharacteristic
487C22#1451982311yescharacteristic
488C22#1451982511yescharacteristic
489C4—22no—
490C4—22no—
491C4—22no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—1222no—
496C4—1222no—
497C4—1222no—
498C4—2441no—
499C4—2441no—
500C2—42no—
501C2—1224no—
502C2—4881no—
503C2—2442no—
504C2#120×D6111yescharacteristic
505C2#1684030911yescharacteristic
506C2#1684034211yescharacteristic
507C2#1684040411yescharacteristic
508C2#1684040811yescharacteristic
509C2#1684041311yescharacteristic
510C2#1684041411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2430
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C22×#11758222C2semidirect
2. C2×#14519762C2semidirect
3. C2×#14519752C2semidirect
4. C2×#14519750C2semidirect
5. #16839682C2semidirect
6. #16839677C2semidirect
7. #16839675C2semidirect
8. #16839671C2semidirect
9. #16839641C2semidirect
10. #16839640C2semidirect
11. #16839640C2semidirect
12. #16839638C2semidirect
13. #16839633C2semidirect
14. #95×D61C2semidirect
15. C61×#385C2semidirect
78. C2×C22⋊D61D4semidirect
93. C2×D244D4semidirect
105. C2×C4×D61D4semidirect
171. C2×C4×C61#41semidirect
189. C2×Dic61#41semidirect
269. #385D61semidirect
271. C61#2430semidirect
451. C2×C4#11758222semidirect