Finite Group Databasebeta

← #21448505

Subgroups — #21448505

Order 7808.

668 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519749C211yesmaximal, characteristic
2C2×#14519737C211yesmaximal, characteristic, complemented
3C2×#14519733C211yesmaximal, characteristic, complemented
4#16839662C211yesmaximal, characteristic, complemented
5#16839662C211yesmaximal, characteristic, complemented
6#16839657C211yesmaximal, characteristic, complemented
7#16839656C211yesmaximal, characteristic, complemented
8#16839653C211yesmaximal, characteristic, complemented
9#16839642C211yesmaximal, characteristic, complemented
10#16839638C211yesmaximal, characteristic, complemented
11#16839634C211yesmaximal, characteristic, complemented
12#16839633C211yesmaximal, characteristic, complemented
13#16839620C211yesmaximal, characteristic, complemented
14C4×#11758196C211yesmaximal, characteristic, complemented
15C61×#390C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519749C418yescomplemented
22#14519737—24no—
23#14519733—24no—
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C22×D4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C42×C61C2211yescharacteristic
54C24×C61C2311yescharacteristic
55C24×C61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61C2×C414yescomplemented
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—22no—
66C2×C22⋊D61—22no—
67C2×C22⋊D61—41no—
68C2×C22⋊D61—41no—
69C2×C22⋊D61C2×C414yes—
70C2×C22⋊D61C2×C414yescomplemented
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61C2×C414yescomplemented
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C2×C4×D61—22no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C42×C61—41no—
93C22⋊Dic61—22no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61C2×C414yescomplemented
97#11758198—22no—
98#11758198—41no—
99#11758198—41no—
100#11758198C2×C414yescomplemented
101#11758196—22no—
102#11758196—22no—
103#11758196—22no—
104#11758196—22no—
105#11758196—41no—
106#11758196C2×C414yescomplemented
107C4×Dic61—22no—
108C4×Dic61—41no—
109C4×Dic61D414yescomplemented
110C23×C61—21no—
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×C61C22×C412yes—
123C23×C61C22×C412yes—
124C23×C61C2411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61C22×C412yes—
132D4×C61—44no—
133C2×C4×C61—21no—
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—21no—
146C2×C4×C61C22×C412yes—
147C2×C4×C61C2×D412yes—
148C22⋊D61—28no—
149C22⋊D61—44no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—28no—
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—44no—
167C2×Dic61C22×C412yes—
168C2×Dic61C22×C412yes—
169C2×Dic61C22×C412yes—
170C2×Dic61C2×D412yes—
171C2×Dic61C2×D412yes—
172C2×Dic61#4112yes—
173C4×D61—44no—
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61—22no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61C23×C411yescharacteristic
189C22×C61C22×D411yescharacteristic
190C22×C61C2×#4111yescharacteristic
191C22×C61H(5,𝔽2)11yescharacteristic
192C22×C61H(5,𝔽2)11yescharacteristic
193C22×C61H(5,𝔽2)11yescharacteristic
194C22×C612−1+411yescharacteristic
195C2×D61—22no—
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C4×C61—22no—
203C4×C61—22no—
204C4×C61—41no—
205C4×C61—41no—
206C4×C61—41no—
207Dic61—22no—
208Dic61—22no—
209Dic61—22no—
210Dic61—41no—
211Dic61—41no—
212Dic61—41no—
213Dic61C4×D414yes—
214#2324—611nomaximal, Sylow
215C2×C61—42no—
216C2×C61—42no—
217C2×C61C2×C4×D411yescharacteristic
218C2×C61#51811yescharacteristic
219C2×C61#52011yescharacteristic
220C2×C61#53511yescharacteristic
221C2×C61#53711yescharacteristic
222C2×C61#54011yescharacteristic
223C2×C61#54211yescharacteristic
224D61—42no—
225C2×#121—611no—
226C2×C4×D4—611no—
227C2×#117—611no—
228#390—611no—
229#390—611no—
230#390D6111yescharacteristic, complemented
231#389—611no—
232#388—611no—
233#388—611no—
234#386—611no—
235#386—611no—
236#385—611no—
237#385—611no—
238#380—611no—
239C4×C4⋊C4—611no—
240C61#232411yescharacteristic, complemented, Sylow
241C22×D4—611no—
242C22×D4—611no—
243C22×D4C2×D6111yescharacteristic
244C23×C4—611no—
245C23×C4—611no—
246C23×C4—611no—
247#121—618no—
248C4×D4—1224no—
249#117—1224no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4C2×D6111yescharacteristic
257C2×C22⋊C4—611no—
258C2×C22⋊C4—611no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4C2×D6111yescharacteristic
266C2×C22⋊C4C2×D6111yescharacteristic
267C2×C22⋊C4C2×D6111yescharacteristic
268C2×C22⋊C4C2×D6111yescharacteristic
269C2×C42—611no—
270C2×C42—611no—
271C2×C42—611no—
272C2×C42C2×D6111yescharacteristic
273#95—611no—
274#95—611no—
275#95—611no—
276#95—611no—
277#95—611no—
278#95—611no—
279C24—611no—
280C24C22×D6111yescharacteristic
281C24C22×D6111yescharacteristic
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—614no—
285C2×D4—614no—
286C2×D4—1222no—
287C2×D4—1222no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4C4×D6114yescomplemented
291C22×C4—611no—
292C22×C4—614no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—1222no—
300C22×C4—1222no—
301C22×C4—1222no—
302C22×C4—1222no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4C22×D6111yescharacteristic
308C22×C4C22×D6111yescharacteristic
309C22×C4C22×D6111yescharacteristic
310C22×C4C22×D6111yescharacteristic
311C22×C4C22×D6111yescharacteristic
312C4⋊C4—41no—
313C4⋊C4—614no—
314C4⋊C4—1222no—
315C4⋊C4—1222no—
316C4⋊C4—1222no—
317C4⋊C4—1222no—
318C4⋊C4—2441no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—614no—
324C22⋊C4—614no—
325C22⋊C4—1222no—
326C22⋊C4—1222no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C22⋊C4—2441no—
331C42—41no—
332C42—614no—
333C42—1222no—
334C42—2441no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—612no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23C2×C4×D6112yes—
355C23C2×C4×D6112yes—
356C23C23×D6111yescharacteristic
357D4—44no—
358D4—1228no—
359D4—2444no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
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—612no—
374C2×C4—612no—
375C2×C4—612no—
376C2×C4—612no—
377C2×C4—612no—
378C2×C4—612no—
379C2×C4—1228no—
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—2444no—
396C2×C4—2444no—
397C2×C4C2×C4×D6112yes—
398C2×C4D4×D6112yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—1222no—
414C22—1222no—
415C22—1222no—
416C22—2441no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22C22×C4×D6111yescharacteristic
421C22C2×D4×D6111yescharacteristic
422C22#41×D6111yescharacteristic
423C22#1451982211yescharacteristic
424C22#1451982211yescharacteristic
425C22#1451982211yescharacteristic
426C22#1451982411yescharacteristic
427C4—22no—
428C4—22no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—614no—
433C4—1222no—
434C4—1222no—
435C4—1222no—
436C4—2441no—
437C4—2441no—
438C4—2441no—
439C2—42no—
440C2—42no—
441C2—2442no—
442C2C4×D4×D6111yescharacteristic
443C2#1684023511yescharacteristic
444C2#1684024111yescharacteristic
445C2#1684032511yescharacteristic
446C2#1684033911yescharacteristic
447C2#1684036211yescharacteristic
448C2#1684037611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#390C2
socleC23×C61C24
hypercenter#390D61
hypocenterC61#2324
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#14519737C2semidirect
3. C2×#14519733C2semidirect
4. #16839662C2semidirect
5. #16839662C2semidirect
6. #16839657C2semidirect
7. #16839656C2semidirect
8. #16839653C2semidirect
9. #16839642C2semidirect
10. #16839638C2semidirect
11. #16839634C2semidirect
12. #16839633C2semidirect
13. #16839620C2semidirect
14. C4×#11758196C2semidirect
15. C61×#390C2semidirect
21. #14519749C4semidirect
59. C2×D4×C61C2×C4semidirect
70. C2×C22⋊D61C2×C4semidirect
76. C22×Dic61C2×C4semidirect
96. C22⋊Dic61C2×C4semidirect
100. #11758198C2×C4semidirect
106. #11758196C2×C4semidirect
109. C4×Dic61D4semidirect
230. #390D61semidirect
240. C61#2324semidirect
290. C2×D4C4×D61semidirect