Finite Group Databasebeta

← #21449810

Subgroups — #21449810

Order 7808.

668 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519756C211yesmaximal, characteristic, complemented
2C2×#14519755C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
4#16839678C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic, complemented
6#16839674C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic
8#16839656C211yesmaximal, characteristic, complemented
9#16839653C211yesmaximal, characteristic, complemented
10#16839648C211yesmaximal, characteristic, complemented
11#16839646C211yesmaximal, characteristic, complemented
12#16839641C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839635C211yesmaximal, characteristic, complemented
15C2×C4×D4×C61C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519756—24no—
21#14519755—24no—
22C4×C22⋊D61—24no—
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C22×D4×C61C2211yescharacteristic
48C23×C4×C61C2211yescharacteristic
49C23×C4×C61C2211yescharacteristic
50C4×D4×C61—24no—
51C2×C4⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C42×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C2×D4×C61—22no—
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C2×C22⋊D61—22no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61—22no—
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—41no—
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×Dic122—22no—
89C2×Dic122—22no—
90C2×Dic122—41no—
91C4⋊C4×C61D414yescomplemented
92C22⋊C4×C61—22no—
93C22⋊C4×C61—22no—
94C42×C61—22no—
95C22⋊Dic61—22no—
96C22⋊Dic61—22no—
97C22⋊Dic61—22no—
98C22⋊Dic61—22no—
99C22⋊Dic61—22no—
100C22⋊Dic61—41no—
101#11758198—22no—
102#11758198—22no—
103#11758198—22no—
104#11758198—22no—
105C4⋊Dic61—22no—
106#11758196—22no—
107#11758196—22no—
108#11758196—22no—
109#11758196D414yescomplemented
110C4×Dic61—22no—
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#4112yes—
124C23×C61#4112yes—
125C23×C61C2411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61#4112yes—
133D4×C61—28no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—44no—
146C2×C4×C61—44no—
147C2×C4×C61C2×D412yes—
148C2×C4×C61C2×D412yes—
149C2×C4×C61C2×D412yes—
150C2×C4×C61C2×D412yes—
151C22⋊D61—28no—
152C22⋊D61—44no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
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×Dic61C2×D412yes—
173C2×Dic61C2×D412yes—
174C4×D61—44no—
175Dic122—44no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61—22no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61C22×D411yescharacteristic
191C22×C61C22×D411yescharacteristic
192C22×C61C2×#4111yescharacteristic
193C22×C61C2×#4111yescharacteristic
194C22×C61C2×#4111yescharacteristic
195C22×C61H(5,𝔽2)11yescharacteristic
196C22×C612−1+411yescharacteristic
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C4×C61—22no—
205C4×C61—22no—
206C4×C61—22no—
207C4×C61—22no—
208C4×C61—41no—
209Dic61—22no—
210Dic61—22no—
211Dic61—41no—
212Dic61—41no—
213Dic61—41no—
214Dic61—41no—
215Dic61—41no—
216#2463—611nomaximal, Sylow
217C2×C61—42no—
218C2×C61—42no—
219C2×C61#52511yescharacteristic
220C2×C61#52511yescharacteristic
221C2×C61#53911yescharacteristic
222C2×C61D4211yescharacteristic
223C2×C61#54811yescharacteristic
224C2×C61#54811yescharacteristic
225C2×C61#55111yescharacteristic
226D61—42no—
227C2×C22⋊Q8—611no—
228C2×C22⋊Q8—611no—
229C2×C4×D4—611no—
230C2×C4×D4D6111yescharacteristic, complemented
231#394—611no—
232#394—611no—
233#393—611no—
234#392—611no—
235#388—611no—
236#388—611no—
237#387—611no—
238#387—611no—
239#386—611no—
240#386—611no—
241#385—611no—
242C61#246311yescharacteristic, complemented, Sylow
243C22×Q8—611no—
244C22×D4—611no—
245C22×D4—611no—
246C22×D4C2×D6111yescharacteristic
247C23×C4—611no—
248C23×C4C2×D6111yescharacteristic
249C23×C4C2×D6111yescharacteristic
250C22⋊Q8—1224no—
251C22⋊Q8—1224no—
252C4×D4—24no—
253C4×D4—1224no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4C2×D6111yescharacteristic
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—611no—
266C2×C22⋊C4—611no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4C2×D6111yescharacteristic
271C2×C22⋊C4C2×D6111yescharacteristic
272C2×C42—611no—
273C2×C42C2×D6111yescharacteristic
274#95—611no—
275#95—611no—
276#95—611no—
277#95—611no—
278#95—611no—
279#95—611no—
280#95—611no—
281#95—611no—
282C24—611no—
283C24C22×D6111yescharacteristic
284C24C22×D6111yescharacteristic
285C2×Q8—1222no—
286C2×Q8—1222no—
287C2×Q8—2441no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—1222no—
292C2×D4—1222no—
293C2×D4—1222no—
294C2×D4—1222no—
295C2×D4—1222no—
296C2×D4—2441no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—1222no—
311C22×C4—1222no—
312C22×C4—2441no—
313C22×C4C22×D6111yescharacteristic
314C22×C4C22×D6111yescharacteristic
315C22×C4C22×D6111yescharacteristic
316C22×C4C22×D6111yescharacteristic
317C22×C4C22×D6111yescharacteristic
318C4⋊C4—614no—
319C4⋊C4—1222no—
320C4⋊C4—1222no—
321C4⋊C4—1222no—
322C4⋊C4—1222no—
323C4⋊C4C22⋊D6114yescomplemented
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—1222no—
327C22⋊C4—1222no—
328C22⋊C4—1222no—
329C22⋊C4—1222no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—1222no—
333C22⋊C4—1222no—
334C22⋊C4—1222no—
335C22⋊C4—2441no—
336C42—22no—
337C42—1222no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—612no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—1221no—
357C23#1175822212yes—
358C23#1175822212yes—
359C23C23×D6111yescharacteristic
360Q8—2444no—
361D4—28no—
362D4—1228no—
363D4—2444no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—612no—
378C2×C4—612no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—2444no—
399C2×C4D4×D6112yes—
400C2×C4C2×C22⋊D6112yes—
401C2×C4C2×C22⋊D6112yes—
402C2×C4C2×C22⋊D6112yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—1222no—
418C22—1222no—
419C22—1222no—
420C22—2441no—
421C22—2441no—
422C22—2441no—
423C22—2441no—
424C22C2×D4×D6111yescharacteristic
425C22C22×C22⋊D6111yescharacteristic
426C22#41×D6111yescharacteristic
427C22C2×#1175822211yescharacteristic
428C22C2×#1175822211yescharacteristic
429C22#1451982211yescharacteristic
430C22#1451982411yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—41no—
436C4—1222no—
437C4—1222no—
438C4—2441no—
439C4—2441no—
440C4—2441no—
441C4—2441no—
442C4—2441no—
443C2—42no—
444C2—42no—
445C2—2442no—
446C2#1684027111yescharacteristic
447C2#1684027311yescharacteristic
448C2#1684035411yescharacteristic
449C2D4×C22⋊D6111yescharacteristic
450C2#1684041911yescharacteristic
451C2#1684042111yescharacteristic
452C2#1684044111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×D4×C61C2
hypercenterC2×C4×D4D61
hypocenterC61#2463
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519756C2semidirect
2. C2×#14519755C2semidirect
3. C2×C4×C22⋊D61C2semidirect
4. #16839678C2semidirect
5. #16839676C2semidirect
6. #16839674C2semidirect
8. #16839656C2semidirect
9. #16839653C2semidirect
10. #16839648C2semidirect
11. #16839646C2semidirect
12. #16839641C2semidirect
13. #16839638C2semidirect
14. #16839635C2semidirect
15. C2×C4×D4×C61C2semidirect
91. C4⋊C4×C61D4semidirect
109. #11758196D4semidirect
230. C2×C4×D4D61semidirect
242. C61#2463semidirect
323. C4⋊C4C22⋊D61semidirect