Finite Group Databasebeta

← #21455132

Subgroups — #21455132

Order 7808.

712 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519824C211yesmaximal, characteristic, complemented
2C2×#14519806C211yesmaximal, characteristic, complemented
3C2×#14519796C211yesmaximal, characteristic, complemented
4#16840341C211yesmaximal, characteristic, complemented
5#16839925C211yesmaximal, characteristic, complemented
6#16839924C211yesmaximal, characteristic, complemented
7#16839920C211yesmaximal, characteristic, complemented
8#16839919C211yesmaximal, characteristic, complemented
9#16839904C211yesmaximal, characteristic, complemented
10#16839900C211yesmaximal, characteristic, complemented
11#16839899C211yesmaximal, characteristic, complemented
12#16839760C211yesmaximal, characteristic, complemented
13#103×D61C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16#14519824—24no—
17#14519824—24no—
18C2×#11758222—21no—
19C2×#11758222C2211yescharacteristic
20C2×#11758224—21no—
21C2×#11758224—21no—
22C2×#11758224C2211yescharacteristic
23C2×#11758224C2211yescharacteristic
24C2×#11758224C2211yescharacteristic
25C22×Dic122—21no—
26C22×Dic122C2211yescharacteristic
27C2×Q8×D61C2211yescharacteristic
28C2×Q8×D61C2211yescharacteristic
29#14519806—24no—
30#14519796—24no—
31C2×Dic244C2211yescharacteristic
32C2×Dic244C2211yescharacteristic
33C2×#11758202C2211yescharacteristic
34C2×#11758200C2211yescharacteristic
35C2×#11758200C2211yescharacteristic
36C2×#11758200C2211yescharacteristic
37C2×#11758189C2211yescharacteristic
38C2×C8×D61C2211yescharacteristic
39#14519757C2211yescharacteristic
40#14519756C2211yescharacteristic
41#14519754—21no—
42#14519750—21no—
43#14519749—21no—
44#14519748—21no—
45#14519748C2211yescharacteristic
46C4⋊C4×D61C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519700C2211yescharacteristic
51#14519700C2211yescharacteristic
52#14519698C2211yescharacteristic
53C22⋊#92418C2211yescharacteristic
54#14519689C2211yescharacteristic
55#14519689C2211yescharacteristic
56C2×#41×C61C2211yescharacteristic
57C2×SD16×C61C2211yescharacteristic
58C2×D8×C61C2211yescharacteristic
59#121×C61C2211yescharacteristic
60#103×C61C2211yescharacteristic
61#102×C61C2211yescharacteristic
62C22⋊C8×C61C2211yescharacteristic
63#41×C61—22no—
64#41×C61—22no—
65C2×Q8×C61C2311yescharacteristic
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C22×C4×C61—21no—
71C22×C4×C61C2311yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61D411yescharacteristic
77C2×C22⋊D61D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82Q8×D61—22no—
83Q8×D61—22no—
84Q8×D61—22no—
85Q8×D61D414yescomplemented
86#11758224—28no—
87#11758224—28no—
88#11758224—22no—
89#11758224—22no—
90#11758224—22no—
91#11758224—22no—
92#11758224—22no—
93#11758224D414yescomplemented
94#11758222—28no—
95#11758222—22no—
96#11758222—22no—
97C2×D244D411yescharacteristic
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61C2311yescharacteristic
102C2×C4×D61C2311yescharacteristic
103C2×Dic122—28no—
104C2×Dic122—21no—
105C2×Dic122—21no—
106C2×Dic122—21no—
107C2×Dic122—22no—
108C2×Dic122—22no—
109C2×Dic122D411yescharacteristic
110C2×Dic122C2311yescharacteristic
111C2×Dic122C2311yescharacteristic
112C2×Dic122C2311yescharacteristic
113SD16×C61—22no—
114D8×C61—22no—
115C2×C8×C61C2311yescharacteristic
116C2×C8×C61C2311yescharacteristic
117C4⋊C4×C61C2311yescharacteristic
118C22⋊C4×C61—21no—
119C22⋊Dic61—21no—
120C22⋊Dic61—21no—
121#11758202—22no—
122#11758200—22no—
123#11758200—22no—
124#11758200—22no—
125#11758198—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61C2311yescharacteristic
128#11758196—21no—
129#11758196—21no—
130C2×#92418C2311yescharacteristic
131C2×#92418C2311yescharacteristic
132Dic244—22no—
133Dic244—22no—
134#11758189—22no—
135C8×D61—22no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61C2×D411yescharacteristic
139C22×D61C2×D411yescharacteristic
140C22×D61C2×D411yescharacteristic
141Q8×C61—21no—
142Q8×C61C2×D412yes—
143D4×C61—24no—
144D4×C61—21no—
145D4×C61—21no—
146D4×C61—21no—
147D4×C61—81no—
148D4×C61C2×D412yes—
149C2×C4×C61—24no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61C2×D411yescharacteristic
155C2×C4×C61C2411yescharacteristic
156C22⋊D61—24no—
157C22⋊D61—22no—
158C22⋊D61—24no—
159C22⋊D61—22no—
160C22⋊D61—42no—
161C22⋊D61—81no—
162C2×Dic61—24no—
163C2×Dic61—24no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—24no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—42no—
170C2×Dic61C2×D411yescharacteristic
171C2×Dic61C2×D411yescharacteristic
172D244—22no—
173C4×D61—24no—
174C4×D61—24no—
175C4×D61—21no—
176C4×D61—21no—
177C4×D61—81no—
178C4×D61C2×D412yes—
179C4×D61C2×D412yes—
180Dic122—24no—
181Dic122—24no—
182Dic122—21no—
183Dic122—21no—
184Dic122—22no—
185Dic122—24no—
186Dic122—21no—
187Dic122—21no—
188Dic122C2×D412yes—
189Dic122C2×D412yes—
190C8×C61—21no—
191C8×C61—21no—
192#92418—21no—
193#92418—21no—
194C22×C61—21no—
195C22×C61—22no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61C22×D411yescharacteristic
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—21no—
209C2×D61#12012yes—
210C4×C61—21no—
211C4×C61—22no—
212C4×C61—41no—
213C4×C61C22×D411yescharacteristic
214C4×C61C22×D411yescharacteristic
215Dic61—21no—
216Dic61—22no—
217Dic61—22no—
218Dic61—41no—
219Dic61—41no—
220Dic61#12012yes—
221#3013—611nomaximal, Sylow
222C2×C61—41no—
223C2×C61—42no—
224C2×C61—81no—
225C2×C61C2×#12011yescharacteristic
226C2×C61#57711yescharacteristic
227C2×C61#57811yescharacteristic
228D61—22no—
229D61—41no—
230C2×2−1+4—611no—
231C2×#137—611no—
232C2×#135—611no—
233#537—611no—
234#452—611no—
235#452—611no—
236#451—611no—
237#451—611no—
238#449—611no—
239#449D6111yescharacteristic, complemented
240#448—611no—
241#448—611no—
242#417—611no—
243C2×#103—611no—
244#408—611no—
245C61#301311yescharacteristic, complemented, Sylow
2462−1+4—1224no—
2472−1+4—1224no—
248C2×#41—611no—
249C2×#41—611no—
250C2×#41—611no—
251C2×#41—611no—
252C2×#41—1221no—
253C2×#41—1221no—
254C2×#41—1221no—
255C2×#41C2×D6111yescharacteristic
256C22×Q8—611no—
257C22×Q8—611no—
258C22×Q8—611no—
259C22×Q8—1221no—
260#137—1224no—
261#135—1224no—
262C2×Q16—611no—
263C2×Q16—611no—
264C2×Q16—611no—
265C2×SD16—611no—
266C2×SD16—611no—
267C2×SD16—611no—
268C2×SD16C2×D6111yescharacteristic
269C2×D8C2×D6111yescharacteristic
270C2×M16—611no—
271C22×C8—611no—
272C22⋊Q8—611no—
273C22⋊Q8—611no—
274C22⋊Q8—1221no—
275#121—611no—
276#121—1221no—
277#121—1221no—
278#121—1221no—
279#121C2×D6111yescharacteristic
280C2×C4⋊C4—611no—
281#103—611no—
282#103—611no—
283#103—611no—
284#103—611no—
285#103—611no—
286#103C2×D6111yescharacteristic
287#102—611no—
288#102C2×D6111yescharacteristic
289C22⋊C8—611no—
290C22⋊C8—611no—
291C22⋊C8—611no—
292C22⋊C8C2×D6111yescharacteristic
293#41—22no—
294#41—22no—
295#41—614no—
296#41—1222no—
297#41—1222no—
298#41—1228no—
299#41—1222no—
300#41—1222no—
301#41—1222no—
302#41—1222no—
303#41—1228no—
304#41—1228no—
305#41—1222no—
306C2×Q8—611no—
307C2×Q8—614no—
308C2×Q8—611no—
309C2×Q8—611no—
310C2×Q8—611no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8—1222no—
314C2×Q8—1222no—
315C2×Q8—1228no—
316C2×Q8—1222no—
317C2×Q8—1222no—
318C2×Q8—1222no—
319C2×Q8—1221no—
320C2×Q8C22×D6111yescharacteristic
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—611no—
324C2×D4—611no—
325C2×D4—611no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4C22×D6111yescharacteristic
331C2×D4C22×D6111yescharacteristic
332C22×C4—21no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4C22×D6111yescharacteristic
343Q16—1222no—
344Q16—1222no—
345Q16—1222no—
346SD16—22no—
347SD16—1222no—
348SD16—1222no—
349SD16—1222no—
350D8—22no—
351M16—1222no—
352C2×C8—611no—
353C2×C8—611no—
354C2×C8—1222no—
355C2×C8C22×D6111yescharacteristic
356C2×C8C22×D6111yescharacteristic
357C4⋊C4—611no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4C22×D6111yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—1221no—
364C22⋊C4—1221no—
365C22⋊C4—1221no—
366C23—21no—
367C23—21no—
368C23—611no—
369C23—611no—
370C23D4×D6111yescharacteristic
371Q8—21no—
372Q8—612no—
373Q8—612no—
374Q8—1222no—
375Q8—1224no—
376Q8—1224no—
377Q8—1224no—
378Q8—1221no—
379Q8—1221no—
380Q8—1221no—
381Q8—1221no—
382Q8D4×D6112yes—
383D4—24no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—81no—
388D4—1222no—
389D4—1222no—
390D4—1222no—
391D4—1224no—
392D4—1224no—
393D4—4881no—
394D4—2442no—
395D4D4×D6112yes—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—611no—
402C2×C4—612no—
403C2×C4—612no—
404C2×C4—611no—
405C2×C4—1224no—
406C2×C4—1224no—
407C2×C4—1224no—
408C2×C4—1224no—
409C2×C4—1224no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—4881no—
417C2×C4—2442no—
418C2×C4D4×D6111yescharacteristic
419C2×C4C23×D6111yescharacteristic
420C8—21no—
421C8—21no—
422C8—1221no—
423C8—1221no—
424C22—21no—
425C22—22no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—612no—
434C22—1221no—
435C22—1221no—
436C22—1221no—
437C22—1221no—
438C22—1221no—
439C22C2×D4×D6111yescharacteristic
440C4—21no—
441C4—22no—
442C4—41no—
443C4—612no—
444C4—1221no—
445C4—1222no—
446C4—1222no—
447C4—2441no—
448C4—2441no—
449C4C2×D4×D6111yescharacteristic
450C4C2×D4×D6111yescharacteristic
451C2—41no—
452C2—42no—
453C2—81no—
454C2—1222no—
455C2—2441no—
456C2#120×D6111yescharacteristic
457C2#1684057211yescharacteristic
458C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3013
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14519824C2semidirect
2. C2×#14519806C2semidirect
3. C2×#14519796C2semidirect
4. #16840341C2semidirect
5. #16839925C2semidirect
6. #16839924C2semidirect
7. #16839920C2semidirect
8. #16839919C2semidirect
9. #16839904C2semidirect
10. #16839900C2semidirect
11. #16839899C2semidirect
12. #16839760C2semidirect
13. #103×D61C2semidirect
14. #16839727C2semidirect
15. C61×#449C2semidirect
85. Q8×D61D4semidirect
93. #11758224D4semidirect
239. #449D61semidirect
245. C61#3013semidirect