Finite Group Databasebeta

← #21452048

Subgroups — #21452048

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×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4C2×#14519749C211yesmaximal, characteristic, complemented
5#16839697C211yesmaximal, characteristic, complemented
6#16839696C211yesmaximal, characteristic, complemented
7#16839680C211yesmaximal, characteristic, complemented
8#16839678C211yesmaximal, characteristic, complemented
9#16839671C211yesmaximal, characteristic, complemented
10#16839639C211yesmaximal, characteristic, complemented
11#16839639C211yesmaximal, characteristic, complemented
12#16839634C211yesmaximal, characteristic, complemented
13#16839633C211yesmaximal, characteristic, complemented
14#16839620C211yesmaximal, characteristic, complemented
15C61×#394C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C23×Dic61C2211yescharacteristic
22C23×Dic61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic
24#14519759—24no—
25#14519750—24no—
26#14519749—24no—
27#14519749—24no—
28C2×C4⋊Dic61C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758196C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—22no—
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61D414yescomplemented
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—22no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C22×Dic61C2311yescharacteristic
90C22×Dic61C2311yescharacteristic
91C2×D244—22no—
92C2×D244—41no—
93C2×D244—41no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C4⋊C4×C61—41no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—22no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊Dic61—22no—
103C22⋊Dic61D414yescomplemented
104#11758198—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—41no—
110#11758198—41no—
111C4⋊Dic61—22no—
112#11758196—22no—
113#11758196—22no—
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×C61C2×D412yes—
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×D61C2×D412yes—
146D4×C61—44no—
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×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C22⋊D61—44no—
163C22⋊D61—44no—
164C22⋊D61—44no—
165C22⋊D61—44no—
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—44no—
181C2×Dic61—44no—
182C2×Dic61C2×D412yes—
183C2×Dic61C2×D412yes—
184C2×Dic61C2×D412yes—
185C2×Dic61#4112yes—
186D244—44no—
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×C61C22×D411yescharacteristic
203C22×C61C22×D411yescharacteristic
204C22×C61C2×#4111yescharacteristic
205C22×C61H(5,𝔽2)11yescharacteristic
206C22×C61H(5,𝔽2)11yescharacteristic
207C22×C61H(5,𝔽2)11yescharacteristic
208C22×C612−1+411yescharacteristic
209C2×D61—22no—
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C4×C61—41no—
224C4×C61—41no—
225C4×C61—41no—
226C4×C61—41no—
227C4×C61—41no—
228Dic61—22no—
229Dic61—22no—
230Dic61—22no—
231Dic61—22no—
232Dic61—41no—
233Dic61—41no—
234#2671—611nomaximal, Sylow
235C2×C61—42no—
236C2×C61—42no—
237C2×C61#53411yescharacteristic
238C2×C61#53711yescharacteristic
239C2×C61#54011yescharacteristic
240C2×C61D4211yescharacteristic
241C2×C61#54611yescharacteristic
242C2×C61#54711yescharacteristic
243C2×C61#56211yescharacteristic
244D61—42no—
245D61—81no—
246C2×#123—611no—
247C2×#121—611no—
248C2×#121—611no—
249C2×#121—611no—
250#399—611no—
251#398—611no—
252#394—611no—
253#394—611no—
254#394D6111yescharacteristic, complemented
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×D4—611no—
266C22×D4—611no—
267C22×D4C2×D6111yescharacteristic
268C23×C4—611no—
269C23×C4—611no—
270C23×C4—611no—
271#123—1224no—
272#121—1224no—
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⋊C4C2×D6111yescharacteristic
292C2×C22⋊C4C2×D6111yescharacteristic
293C2×C22⋊C4C2×D6111yescharacteristic
294C2×C22⋊C4C2×D6111yescharacteristic
295#95—611no—
296#95—611no—
297#95—611no—
298#95—611no—
299#95—611no—
300#95C2×D6111yescharacteristic
301C24—611no—
302C24—611no—
303C24C22×D6111yescharacteristic
304C24C22×D6111yescharacteristic
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—614no—
309C2×D4—1222no—
310C2×D4—1222no—
311C2×D4—1222no—
312C2×D4—1222no—
313C2×D4—1222no—
314C2×D4—1222no—
315C2×D4—1222no—
316C2×D4—2441no—
317C2×D4—2441no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C22×C4—611no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—1222no—
332C22×C4—1222no—
333C22×C4—1222no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4C22×D6111yescharacteristic
339C22×C4C22×D6111yescharacteristic
340C22×C4C22×D6111yescharacteristic
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C4⋊C4—41no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—2441no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—614no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—1222no—
359C22⋊C4—1222no—
360C22⋊C4—1222no—
361C22⋊C4—2441no—
362C22⋊C4—2441no—
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—612no—
376C23—1221no—
377C23—1221no—
378C23—1221no—
379C23—1221no—
380C23—1221no—
381C23—1221no—
382C23—1221no—
383C23—1221no—
384C23—1221no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23D4×D6112yes—
390C23D4×D6112yes—
391C23C23×D6111yescharacteristic
392D4—44no—
393D4—2444no—
394D4—2444no—
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—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—612no—
414C2×C4—612no—
415C2×C4—612no—
416C2×C4—612no—
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—1221no—
430C2×C4—1221no—
431C2×C4—2444no—
432C2×C4—2444no—
433C2×C4—2444no—
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—1222no—
449C22—1222no—
450C22—1222no—
451C22—2441no—
452C22—2441no—
453C22—2441no—
454C22—2441no—
455C22—2441no—
456C22—2441no—
457C22—2441no—
458C22—2441no—
459C22—2441no—
460C22—2441no—
461C22—2441no—
462C22C2×D4×D6111yescharacteristic
463C22C2×D4×D6111yescharacteristic
464C22#41×D6111yescharacteristic
465C22#1451982211yescharacteristic
466C22#1451982211yescharacteristic
467C22#1451982311yescharacteristic
468C22#1451982411yescharacteristic
469C4—41no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—1222no—
475C4—1222no—
476C4—1222no—
477C4—1222no—
478C4—2441no—
479C4—2441no—
480C2—42no—
481C2—42no—
482C2—4881no—
483C2—2442no—
484C2#1684032011yescharacteristic
485C2#1684033911yescharacteristic
486C2#1684036211yescharacteristic
487C2#1684039411yescharacteristic
488C2#1684040411yescharacteristic
489C2#1684041011yescharacteristic
490C2#1684050611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2671
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14519759C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519749C2semidirect
4. C2×#14519749C2semidirect
5. #16839697C2semidirect
6. #16839696C2semidirect
7. #16839680C2semidirect
8. #16839678C2semidirect
9. #16839671C2semidirect
10. #16839639C2semidirect
11. #16839639C2semidirect
12. #16839634C2semidirect
13. #16839633C2semidirect
14. #16839620C2semidirect
15. C61×#394C2semidirect
78. C2×C22⋊D61D4semidirect
103. C22⋊Dic61D4semidirect
254. #394D61semidirect
261. C61#2671semidirect