Finite Group Databasebeta

← #29574882

Subgroups — #29574882

Order 15616.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455846C211yesmaximal, characteristic
2M16×Dic122C211yesmaximal, characteristic, complemented
3C4×#14519700C211yesmaximal, characteristic, complemented
4#21444270C211yesmaximal, characteristic
5#21443722C211yesmaximal, characteristic, complemented
6#21443657C211yesmaximal, characteristic, complemented
7C61×#1980C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16840078—21no—
10#16840044C411yescharacteristic, complemented
11#16840044C411yescharacteristic, complemented
12#16839959C411yescharacteristic, complemented
13#16839959C411yescharacteristic, complemented
14#16839900—21no—
15#16839892—21no—
16#16839890—22no—
17C8×Dic122—21no—
18C4×#11758200—21no—
19C4×#11758200—21no—
20#16839815C2211yescharacteristic
21#16839786C2211yescharacteristic
22#16839785—21no—
23C2×#14519700—21no—
24M16×Dic61—21no—
25C2×C4×#92418C2211yescharacteristic
26#16839524—21no—
27D4⋊#92418—22no—
28C61×#532C2211yescharacteristic
29C2×#104×C61—21no—
30C2×#104×C61—21no—
31C4×M16×C61C2211yescharacteristic
32C4×C4⋊C4×C61C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×#11758200—21no—
35C2×#11758200—21no—
36C2×#11758194—21no—
37C22×#92418—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122C2×C411yescharacteristic
41C4×Dic122C2×C411yescharacteristic
42C4×Dic122D411yescharacteristic
43C4×Dic122D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×C4×Dic61—21no—
47#14519708—21no—
48#14519708—21no—
49C4⋊#92418—21no—
50C4⋊#92418C2×C411yescharacteristic
51C4⋊#92418C2×C411yescharacteristic
52C4⋊#92418D412yes—
53#14519706—22no—
54#14519706—22no—
55#14519700—24no—
56#14519700—21no—
57#14519700—21no—
58#14519698—21no—
59#14519698—21no—
60C22⋊#92418—21no—
61#14519687—22no—
62C4×#92418—21no—
63C4×#92418—21no—
64C4×#92418—21no—
65C8×Dic61—22no—
66C2×#41×C61—21no—
67C2×M16×C61D411yescharacteristic
68C2×M16×C61D411yescharacteristic
69C4⋊Q8×C61C2×C411yescharacteristic
70#127×C61C2×C411yescharacteristic
71#124×C61—21no—
72#121×C61—21no—
73#121×C61—21no—
74C4×D4×C61—21no—
75C4×D4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C42×C61—21no—
78C2×C42×C61C2311yescharacteristic
79#104×C61—42no—
80#104×C61—42no—
81#97×C61—21no—
82C4×C8×C61—21no—
83#95×C61—21no—
84#41×C61—41no—
85#41×C61—41no—
86#41×C61—41no—
87#41×C61—41no—
88C2×Q8×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×Dic61—21no—
99C22×Dic61—21no—
100C2×Dic122—22no—
101C2×Dic122—21no—
102C2×Dic122—41no—
103C2×Dic122C22⋊C411yescharacteristic
104C2×Dic122C22⋊C411yescharacteristic
105M16×C61—21no—
106M16×C61—21no—
107M16×C61—21no—
108M16×C61SD1612yescomplemented
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C4⋊C4×C61—22no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C42×C61—41no—
118C42×C61—41no—
119C42×C61C22×C411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123#11758200—42no—
124#11758200—42no—
125C4⋊Dic61—21no—
126C4⋊Dic61C22⋊C411yescharacteristic
127C4⋊Dic61C22⋊C411yescharacteristic
128#11758196—21no—
129#11758196—21no—
130#11758196—21no—
131#11758196—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136#11758194—41no—
137#11758194—41no—
138C2×#92418—22no—
139C2×#92418—21no—
140C2×#92418—21no—
141C2×#92418—22no—
142C2×#92418—41no—
143C2×#92418—41no—
144C23×C61—41no—
145C23×C61#12111yescharacteristic
146Q8×C61—41no—
147Q8×C61—41no—
148D4×C61—42no—
149D4×C61—41no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—41no—
153D4×C61—81no—
154D4×C61—81no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—41no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61C2×C22⋊C411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12311yescharacteristic
170C2×C4×C61C2×SD1611yescharacteristic
171C2×C4×C61#13511yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C61#13711yescharacteristic
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—42no—
179C2×Dic61—81no—
180Dic122—21no—
181Dic122—21no—
182Dic122—21no—
183Dic122—42no—
184Dic122#10412yescomplemented
185C8×C61—22no—
186C8×C61—41no—
187#92418—42no—
188#92418—41no—
189#92418—41no—
190#92418—42no—
191#8992—611nomaximal, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61#38611yescharacteristic
198C22×C61#46011yescharacteristic
199C22×C61#46411yescharacteristic
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—82no—
204C4×C61—81no—
205C4×C61C2×#10411yescharacteristic
206C4×C61#42111yescharacteristic
207C4×C61C4×SD1611yescharacteristic
208C4×C61#44011yescharacteristic
209C4×C61#44811yescharacteristic
210C4×C61#44911yescharacteristic
211Dic61—22no—
212Dic61—41no—
213Dic61—41no—
214Dic61—41no—
215#3103—611no—
216Q8×M16—611no—
217#1980D6111yescharacteristic
218C4×#103—611no—
219#1492—611no—
220#1303—611no—
221#1278—611no—
222C2×C61—21no—
223C2×C61—21no—
224C2×C61—161no—
225C2×C61#187111yescharacteristic
226C2×C61#188011yescharacteristic
227C2×C61#188111yescharacteristic
228#532C2×D6111yescharacteristic
229C2×C4×Q8—611no—
230#481—1221no—
231#475—611no—
232#475—611no—
233#460—611no—
234#460—611no—
235#448—1221no—
236#446—1221no—
237#446—1222no—
238C8×Q8—1221no—
239C4×SD16—1221no—
240C4×SD16—1221no—
241#431—611no—
242#423—611no—
243#423—1221no—
244C2×#104—21no—
245C2×#104—21no—
246C2×#103—1221no—
247C4×M16—1221no—
248C4×M16C2×D6111yescharacteristic
249C2×C4×C8—611no—
250C4×C4⋊C4C2×D6111yescharacteristic
251#340—1221no—
252D4⋊C8—1222no—
253C61#899211yescharacteristic, complemented, Sylow
254C2×#41—21no—
255C22×Q8—611no—
256C2×SD16—1221no—
257C2×SD16—1221no—
258C2×M16—1221no—
259C2×M16C22⋊D6111yescharacteristic
260C2×M16C22⋊D6111yescharacteristic
261C22×C8—1221no—
262C4⋊Q8C4×D6111yescharacteristic
263#127C4×D6111yescharacteristic
264#124—21no—
265#121—21no—
266#121—21no—
267C4×Q8—611no—
268C4×Q8—611no—
269C4×Q8—611no—
270C4×Q8—611no—
271C4×Q8—1221no—
272C4×Q8—1221no—
273C4×D4—21no—
274C4×D4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1221no—
278C2×C42—21no—
279C2×C42—1221no—
280C2×C42C22×D6111yescharacteristic
281#106—1221no—
282#106—1221no—
283C4⋊C8—611no—
284C4⋊C8—611no—
285C4⋊C8—612no—
286C4⋊C8—1222no—
287C4⋊C8—1222no—
288C4⋊C8—1221no—
289#104—42no—
290#104—42no—
291#103—1221no—
292#103—1221no—
293#103—1224no—
294#102—1221no—
295#102—1221no—
296C22⋊C8—1221no—
297#97—21no—
298#97—1222no—
299C4×C8—21no—
300C4×C8—1222no—
301C4×C8—1221no—
302C4×C8—1221no—
303C4×C8—1221no—
304#95—21no—
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309C2×Q8—21no—
310C2×Q8—611no—
311C2×Q8—611no—
312C2×Q8—1222no—
313C2×Q8—1221no—
314C2×Q8—2441no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4D4×D6111yescharacteristic
324C22×C4#1175822411yescharacteristic
325C22×C4C2×C22⋊D6111yescharacteristic
326SD16—2442no—
327SD16—2442no—
328M16—21no—
329M16—21no—
330M16—21no—
331M16—2441no—
332M16—2441no—
333M16#1175820012yescomplemented
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—1222no—
337C2×C8—1221no—
338C2×C8—1221no—
339C2×C8—1222no—
340C2×C8—2441no—
341C2×C8—2441no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—611no—
347C4⋊C4—611no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—41no—
356C42—41no—
357C42—1221no—
358C42—1221no—
359C42—1221no—
360C42—1221no—
361C42C2×C4×D6111yescharacteristic
362C42#1175822211yescharacteristic
363C42D4×D6111yescharacteristic
364C42D4×D6111yescharacteristic
365C23—41no—
366C23#1451974811yescharacteristic
367Q8—41no—
368Q8—41no—
369Q8—612no—
370Q8—1221no—
371Q8—1221no—
372Q8—1221no—
373Q8—2442no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—4881no—
395C2×C4—2442no—
396C2×C4C22⋊C4×D6111yescharacteristic
397C2×C4#1451973711yescharacteristic
398C2×C4C4×C22⋊D6111yescharacteristic
399C2×C4#1451974511yescharacteristic
400C2×C4#1451975011yescharacteristic
401C2×C4#1451975911yescharacteristic
402C2×C4C2×#1175820011yescharacteristic
403C2×C4#1451979711yescharacteristic
404C2×C4#1451980311yescharacteristic
405C2×C4#1451980711yescharacteristic
406C8—22no—
407C8—41no—
408C8—2442no—
409C8—2441no—
410C8—2441no—
411C8—2442no—
412C22—21no—
413C22—21no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22#1683963811yescharacteristic
418C22#1683995911yescharacteristic
419C22#1683998111yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—82no—
424C4—81no—
425C4—1222no—
426C4—2441no—
427C4—2441no—
428C4—2441no—
429C4#104×D6111yescharacteristic
430C4#1683977711yescharacteristic
431C4C4×#1175820011yescharacteristic
432C4#1683986211yescharacteristic
433C4#1683990011yescharacteristic
434C4#1683990511yescharacteristic
435C2—21no—
436C2—21no—
437C2—161no—
438C2#2144611811yescharacteristic
439C2#2144617711yescharacteristic
440C2#2144617811yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1980C2
socleC22×C61#386
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1980D61
hypocenterC61#8992
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. M16×Dic122C2semidirect
3. C4×#14519700C2semidirect
5. #21443722C2semidirect
6. #21443657C2semidirect
10. #16840044C4semidirect
11. #16840044C4semidirect
12. #16839959C4semidirect
13. #16839959C4semidirect
108. M16×C61SD16semidirect
184. Dic122#104semidirect
253. C61#8992semidirect
333. M16#11758200semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214558462
M16×Dic1222
C4×#145197002
#214442702
#214437222
#214436572
C61×#19802
#899261