Finite Group Databasebeta

← #21449823

Subgroups — #21449823

Order 7808.

710 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×#14519761C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3C2×#14519750C211yesmaximal, characteristic, complemented
4C2×#14519737C211yesmaximal, characteristic, complemented
5#16839692C211yesmaximal, characteristic, complemented
6#16839680C211yesmaximal, characteristic, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839671C211yesmaximal, characteristic, complemented
9#16839664C211yesmaximal, characteristic, complemented
10#16839654C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839639C211yesmaximal, characteristic, complemented
13#16839636C211yesmaximal, characteristic, complemented
14C4×#11758198C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C23×Dic61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic
24C22×C4×D61C2211yescharacteristic
25#14519761—24no—
26#14519752—24no—
27#14519750—24no—
28#14519737—24no—
29C2×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊Dic61C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×C4×Dic61C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
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—22no—
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C22×Dic61—22no—
75C22×Dic61—22no—
76C22×Dic61—41no—
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—22no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C4⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61D414yescomplemented
101C42×C61—41no—
102#11758198—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—41no—
110#11758198—41no—
111#11758198D414yescomplemented
112C4⋊Dic61—22no—
113C4⋊Dic61—22no—
114#11758196—22no—
115#11758196—22no—
116C4×Dic61—22no—
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×D61#4112yes—
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×C61C2×D412yes—
162C2×C4×C61C2×D412yes—
163C2×C4×C61C2×D412yes—
164C22⋊D61—28no—
165C22⋊D61—44no—
166C22⋊D61—44no—
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—44no—
180C2×Dic61C2×D412yes—
181C2×Dic61#4112yes—
182C2×Dic61#4112yes—
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×C61C2×#4111yescharacteristic
199C22×C61C2×#4111yescharacteristic
200C22×C61H(5,𝔽2)11yescharacteristic
201C22×C61H(5,𝔽2)11yescharacteristic
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—22no—
226C4×C61—41no—
227C4×C61—41no—
228C4×C61—41no—
229Dic61—22no—
230Dic61—22no—
231Dic61—22no—
232Dic61—41no—
233Dic61—41no—
234#2464—611nomaximal, Sylow
235C2×C61—42no—
236C2×C61#52511yescharacteristic
237C2×C61#53211yescharacteristic
238C2×C61#54011yescharacteristic
239C2×C61D4211yescharacteristic
240C2×C61#54611yescharacteristic
241C2×C61#54611yescharacteristic
242C2×C61#55311yescharacteristic
243D61—42no—
244D61—42no—
245D61—81no—
246C2×#123—611no—
247C2×#121—611no—
248C2×#121—611no—
249C2×C4×D4—611no—
250#398—611no—
251#394—611no—
252#392—611no—
253#392—611no—
254#390—611no—
255#388—611no—
256#388D6111yescharacteristic, complemented
257#386—611no—
258#386—611no—
259#385—611no—
260C4×C22⋊C4—611no—
261C61#246411yescharacteristic, 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×C4—611no—
271#123—1224no—
272#121—1224no—
273#121—1224no—
274C4×D4—1224no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4C2×D6111yescharacteristic
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
291C2×C22⋊C4C2×D6111yescharacteristic
292C2×C22⋊C4C2×D6111yescharacteristic
293C2×C42—611no—
294C2×C42C2×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—1222no—
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—1222no—
316C2×D4—1222no—
317C2×D4—1222no—
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—1222no—
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×C4C22×D6111yescharacteristic
338C22×C4C22×D6111yescharacteristic
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—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—614no—
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⋊C4D24414yescomplemented
361C42—41no—
362C42—1222no—
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—
390C23C2×D24412yes—
391C23C23×D6111yescharacteristic
392D4—1228no—
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—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—2444no—
429C2×C4—2444no—
430C2×C4—2444no—
431C2×C4C2×D24412yes—
432C2×C4C2×D24412yes—
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
463C22C22×D24411yescharacteristic
464C22#41×D6111yescharacteristic
465C22#41×D6111yescharacteristic
466C22#41×D6111yescharacteristic
467C22#1451982211yescharacteristic
468C22#1451982311yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—41no—
474C4—41no—
475C4—1222no—
476C4—1222no—
477C4—1222no—
478C4—2441no—
479C4—2441no—
480C2—42no—
481C2—4881no—
482C2—2442no—
483C2—2442no—
484C2#1684027411yescharacteristic
485C2#1684031111yescharacteristic
486C2#1684036411yescharacteristic
487C2D4×D24411yescharacteristic
488C2#1684040111yescharacteristic
489C2#1684040711yescharacteristic
490C2#1684046311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2464
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14519761C2semidirect
2. C2×#14519752C2semidirect
3. C2×#14519750C2semidirect
4. C2×#14519737C2semidirect
5. #16839692C2semidirect
6. #16839680C2semidirect
7. #16839671C2semidirect
8. #16839671C2semidirect
9. #16839664C2semidirect
10. #16839654C2semidirect
11. #16839640C2semidirect
12. #16839639C2semidirect
13. #16839636C2semidirect
14. C4×#11758198C2semidirect
15. C61×#388C2semidirect
100. C22⋊C4×C61D4semidirect
111. #11758198D4semidirect
256. #388D61semidirect
261. C61#2464semidirect
360. C22⋊C4D244semidirect