Finite Group Databasebeta

← #21452050

Subgroups — #21452050

Order 7808.

682 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519759C211yesmaximal, characteristic, complemented
2C2×#14519749C211yesmaximal, characteristic, complemented
3C2×#14519748C211yesmaximal, characteristic, complemented
4#16839698C211yesmaximal, characteristic, complemented
5#16839695C211yesmaximal, characteristic, complemented
6#16839678C211yesmaximal, characteristic, complemented
7#16839676C211yesmaximal, characteristic, complemented
8#16839676C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839642C211yesmaximal, characteristic, complemented
11#16839641C211yesmaximal, characteristic, complemented
12#16839637C211yesmaximal, characteristic, complemented
13#16839633C211yesmaximal, characteristic, complemented
14#16839622C211yesmaximal, characteristic, complemented
15C2×#121×C61C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519759—24no—
22#14519749—24no—
23#14519748—24no—
24C2×C4⋊Dic61C2211yescharacteristic
25C2×C4⋊Dic61C2211yescharacteristic
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C22×D4×C61C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic
51#121×C61—24no—
52C2×C4⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C24×C61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—22no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—41no—
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—22no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61D414yescomplemented
84C22×Dic61—22no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C22×Dic61C2311yescharacteristic
90C22×Dic61C2311yescharacteristic
91C22×Dic61C2311yescharacteristic
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C4⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61D414yescomplemented
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102C22⋊Dic61—22no—
103C22⋊Dic61—22no—
104C22⋊Dic61—41no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111C4⋊Dic61—22no—
112C4⋊Dic61—22no—
113C4⋊Dic61—41no—
114#11758196—22no—
115#11758196—22no—
116#11758196—41no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61C2×D412yes—
137C23×C61C2×D412yes—
138C23×C61C2411yescharacteristic
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61C2×D412yes—
146D4×C61—44no—
147D4×C61—44no—
148D4×C61—44no—
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×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—44no—
159C2×C4×C61C2×D412yes—
160C2×C4×C61C2×D412yes—
161C2×C4×C61#4112yes—
162C22⋊D61—44no—
163C22⋊D61—44no—
164C22⋊D61—44no—
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×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—44no—
186C2×Dic61C2×D412yes—
187C4×D61—44no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—22no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61C22×D411yescharacteristic
210C22×C61C22×D411yescharacteristic
211C22×C61C2×#4111yescharacteristic
212C22×C61H(5,𝔽2)11yescharacteristic
213C22×C61H(5,𝔽2)11yescharacteristic
214C22×C61H(5,𝔽2)11yescharacteristic
215C22×C612−1+411yescharacteristic
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C4×C61—22no—
224C4×C61—22no—
225C4×C61—22no—
226C4×C61—41no—
227Dic61—22no—
228Dic61—41no—
229Dic61—41no—
230Dic61—41no—
231Dic61—41no—
232Dic61—41no—
233Dic61—41no—
234#2671—611nomaximal, Sylow
235C2×C61—42no—
236C2×C61—42no—
237C2×C61—81no—
238C2×C61#53411yescharacteristic
239C2×C61#53711yescharacteristic
240C2×C61#54011yescharacteristic
241C2×C61D4211yescharacteristic
242C2×C61#54611yescharacteristic
243C2×C61#54711yescharacteristic
244C2×C61#56211yescharacteristic
245D61—42no—
246C2×#123—611no—
247C2×#121—611no—
248C2×#121—611no—
249C2×#121D6111yescharacteristic, complemented
250#399—611no—
251#398—611no—
252#394—611no—
253#394—611no—
254#394—611no—
255#392—611no—
256#386—611no—
257#386—611no—
258#385—611no—
259#385—611no—
260#380—611no—
261C61#267111yescharacteristic, complemented, Sylow
262C22×D4—611no—
263C22×D4—611no—
264C22×D4—611no—
265C22×D4C2×D6111yescharacteristic
266C22×D4C2×D6111yescharacteristic
267C22×D4C2×D6111yescharacteristic
268C23×C4—611no—
269C23×C4—611no—
270C23×C4C2×D6111yescharacteristic
271#123—1224no—
272#121—24no—
273#121—1224no—
274#121—1224no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4C2×D6111yescharacteristic
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—611no—
289C2×C22⋊C4—611no—
290C2×C22⋊C4—611no—
291C2×C22⋊C4—611no—
292C2×C22⋊C4—611no—
293C2×C22⋊C4C2×D6111yescharacteristic
294C2×C22⋊C4C2×D6111yescharacteristic
295#95—611no—
296#95—611no—
297#95—611no—
298#95—611no—
299#95—611no—
300#95—611no—
301C24—611no—
302C24C22×D6111yescharacteristic
303C24C22×D6111yescharacteristic
304C24C22×D6111yescharacteristic
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—614no—
315C2×D4—1222no—
316C2×D4—1222no—
317C2×D4—1222no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—41no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—611no—
333C22×C4—1222no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4C22×D6111yescharacteristic
340C22×C4C22×D6111yescharacteristic
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C22⋊C4—22no—
351C22⋊C4—1222no—
352C22⋊C4—1222no—
353C22⋊C4—1222no—
354C22⋊C4—1222no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C22⋊C4—2441no—
362C22⋊C4C22⋊D6114yescomplemented
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—612no—
383C23—1221no—
384C23—1221no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23D4×D6112yes—
390C23C2×C22⋊D6112yes—
391C23C23×D6111yescharacteristic
392D4—44no—
393D4—44no—
394D4—44no—
395D4—2444no—
396D4—2444no—
397D4—2444no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—44no—
408C2×C4—612no—
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—1221no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—2444no—
430C2×C4—2444no—
431C2×C4#1175822412yes—
432C2×C4C2×C22⋊D6112yes—
433C2×C4C2×C22⋊D6112yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—1222no—
456C22—1222no—
457C22—1222no—
458C22—2441no—
459C22—2441no—
460C22—2441no—
461C22—2441no—
462C22C2×D4×D6111yescharacteristic
463C22C22×C22⋊D6111yescharacteristic
464C22C2×#1175822411yescharacteristic
465C22#1451982211yescharacteristic
466C22#1451982211yescharacteristic
467C22#1451982311yescharacteristic
468C22#1451982411yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—1222no—
474C4—2441no—
475C4—2441no—
476C4—2441no—
477C4—2441no—
478C4—2441no—
479C4—2441no—
480C2—42no—
481C2—42no—
482C2—81no—
483C2—2442no—
484C2#1684032011yescharacteristic
485C2#1684034011yescharacteristic
486C2#1684036511yescharacteristic
487C2D4×C22⋊D6111yescharacteristic
488C2#1684040611yescharacteristic
489C2#1684041211yescharacteristic
490C2#1684050711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2671
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519759C2semidirect
2. C2×#14519749C2semidirect
3. C2×#14519748C2semidirect
4. #16839698C2semidirect
5. #16839695C2semidirect
6. #16839678C2semidirect
7. #16839676C2semidirect
8. #16839676C2semidirect
9. #16839670C2semidirect
10. #16839642C2semidirect
11. #16839641C2semidirect
12. #16839637C2semidirect
13. #16839633C2semidirect
14. #16839622C2semidirect
15. C2×#121×C61C2semidirect
83. C2×C22⋊D61D4semidirect
99. C22⋊C4×C61D4semidirect
249. C2×#121D61semidirect
261. C61#2671semidirect
362. C22⋊C4C22⋊D61semidirect