Finite Group Databasebeta

← #21452059

Subgroups — #21452059

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×#14519760C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3C2×#14519751C211yesmaximal, characteristic, complemented
4C2×#14519750C211yesmaximal, characteristic, complemented
5#16839697C211yesmaximal, characteristic, complemented
6#16839695C211yesmaximal, characteristic, complemented
7#16839680C211yesmaximal, characteristic, complemented
8#16839679C211yesmaximal, characteristic, complemented
9#16839677C211yesmaximal, characteristic, complemented
10#16839671C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839638C211yesmaximal, characteristic, complemented
13#16839636C211yesmaximal, characteristic, complemented
14#16839621C211yesmaximal, characteristic, complemented
15C61×#385C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic
24#14519760—24no—
25#14519752—24no—
26#14519751—24no—
27#14519750—24no—
28C2×C4⋊Dic61C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48C23×C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C4⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—41no—
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C2×C22⋊D61—22no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61D414yescomplemented
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—22no—
85C2×D244—22no—
86C2×D244—22no—
87C2×D244—22no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×C4×D61—22no—
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—41no—
99C22⋊C4×C61—22no—
100C22⋊C4×C61—22no—
101C22⋊Dic61—22no—
102#11758198—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198—41no—
111#11758198D414yescomplemented
112C4⋊Dic61—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×C61C2×D412yes—
124C23×C61C2411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
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×D61C2×D412yes—
145C22×D61C2×D412yes—
146C2×C4×C61—21no—
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—
162C2×C4×C61—44no—
163C2×C4×C61C2×D412yes—
164C2×C4×C61#4112yes—
165C22⋊D61—44no—
166C22⋊D61—44no—
167C22⋊D61—44no—
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×Dic61C2×D412yes—
182C2×Dic61C2×D412yes—
183D244—44no—
184D244—44no—
185D244—44no—
186C4×D61—44no—
187C4×D61—44no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61C22×D411yescharacteristic
196C22×C61C22×D411yescharacteristic
197C22×C61C2×#4111yescharacteristic
198C22×C61H(5,𝔽2)11yescharacteristic
199C22×C61H(5,𝔽2)11yescharacteristic
200C22×C61H(5,𝔽2)11yescharacteristic
201C22×C612−1+411yescharacteristic
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
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—22no—
224C4×C61—22no—
225C4×C61—41no—
226C4×C61—41no—
227C4×C61—41no—
228C4×C61—41no—
229Dic61—22no—
230Dic61—22no—
231Dic61—41no—
232Dic61—41no—
233Dic61—41no—
234#2671—611nomaximal, Sylow
235C2×C61—42no—
236C2×C61#53411yescharacteristic
237C2×C61#53711yescharacteristic
238C2×C61#54011yescharacteristic
239C2×C61D4211yescharacteristic
240C2×C61#54611yescharacteristic
241C2×C61#54711yescharacteristic
242C2×C61#56211yescharacteristic
243D61—42no—
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#394—611no—
255#392—611no—
256#386—611no—
257#386—611no—
258#385—611no—
259#385D6111yescharacteristic, complemented
260#380—611no—
261C61#267111yescharacteristic, complemented, Sylow
262C22×D4—611no—
263C22×D4—611no—
264C22×D4—611no—
265C22×D4—611no—
266C22×D4—611no—
267C22×D4—611no—
268C23×C4—611no—
269C23×C4—611no—
270C23×C4C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
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#95C2×D6111yescharacteristic
300#95C2×D6111yescharacteristic
301C24—611no—
302C24—611no—
303C24—611no—
304C24C22×D6111yescharacteristic
305C2×D4—614no—
306C2×D4—1222no—
307C2×D4—1222no—
308C2×D4—1222no—
309C2×D4—1222no—
310C2×D4—1222no—
311C2×D4—1222no—
312C2×D4—1222no—
313C2×D4—1222no—
314C2×D4—1222no—
315C2×D4—2441no—
316C2×D4—2441no—
317C2×D4—2441no—
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—1222no—
332C22×C4—1222no—
333C22×C4—1222no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4C22×D6111yescharacteristic
338C22×C4C22×D6111yescharacteristic
339C22×C4C22×D6111yescharacteristic
340C22×C4C22×D6111yescharacteristic
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—41no—
345C4⋊C4—1222no—
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—2441no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—614no—
353C22⋊C4—1222no—
354C22⋊C4—1222no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—1222no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C22⋊C4—2441no—
362C22⋊C4—2441no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—612no—
370C23—612no—
371C23—1221no—
372C23—1221no—
373C23—1221no—
374C23—1221no—
375C23—1221no—
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—
389C23—1221no—
390C23D4×D6112yes—
391C23C23×D6111yescharacteristic
392D4—2444no—
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—21no—
414C2×C4—44no—
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—2444no—
431C2×C4—2444no—
432C2×C4#1175822212yes—
433C2×C4D4×D6112yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—1222no—
442C22—1222no—
443C22—1222no—
444C22—1222no—
445C22—1222no—
446C22—1222no—
447C22—2441no—
448C22—2441no—
449C22—2441no—
450C22—2441no—
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
464C22C2×#1175822211yescharacteristic
465C22#1451982211yescharacteristic
466C22#1451982311yescharacteristic
467C22#1451982311yescharacteristic
468C22#1451982511yescharacteristic
469C4—22no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—41no—
475C4—1222no—
476C4—1222no—
477C4—2441no—
478C4—2441no—
479C4—2441no—
480C2—42no—
481C2—4881no—
482C2—2442no—
483C2—2442no—
484C2#1684032311yescharacteristic
485C2#1684034211yescharacteristic
486C2#1684036311yescharacteristic
487C2#1684039411yescharacteristic
488C2#1684040811yescharacteristic
489C2#1684041311yescharacteristic
490C2#1684050811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2671
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14519760C2semidirect
2. C2×#14519752C2semidirect
3. C2×#14519751C2semidirect
4. C2×#14519750C2semidirect
5. #16839697C2semidirect
6. #16839695C2semidirect
7. #16839680C2semidirect
8. #16839679C2semidirect
9. #16839677C2semidirect
10. #16839671C2semidirect
11. #16839640C2semidirect
12. #16839638C2semidirect
13. #16839636C2semidirect
14. #16839621C2semidirect
15. C61×#385C2semidirect
76. C2×C22⋊D61D4semidirect
111. #11758198D4semidirect
259. #385D61semidirect
261. C61#2671semidirect