Finite Group Databasebeta

← #29574910

Subgroups — #29574910

Order 15616.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455268C211yesmaximal, characteristic
2#21454484C211yesmaximal, characteristic, complemented
3#21444270C211yesmaximal, characteristic, complemented
4#21444199C211yesmaximal, characteristic, complemented
5#21443715C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1480C211yesmaximal, characteristic, complemented
8C2×#14519797—21no—
9C4×#11758222C2211yescharacteristic
10#16839981—21no—
11#16839974—21no—
12#16839969C411yescharacteristic
13#16839964C411yescharacteristic
14#16839959C411yescharacteristic
15#16839954C411yescharacteristic
16#16839822—22no—
17#16839818—21no—
18#16839814—21no—
19#16839786C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21#16839758—21no—
22#16839728—21no—
23#16839717—21no—
24C2×C4×#92418C2211yescharacteristic
25#16839492—21no—
26D4⋊#92418—22no—
27#16839489—21no—
28C61×#532C2211yescharacteristic
29C61×#431C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C61×D4⋊C8—21no—
32C61×D4⋊C8—21no—
33C2×#11758222D411yescharacteristic
34#14519797—42no—
35#14519797—42no—
36C2×#11758202—21no—
37C2×#11758200—21no—
38C2×#11758201—21no—
39C2×#11758199—21no—
40C2×#11758194—21no—
41C22×#92418—21no—
42C22×#92418—21no—
43C4×Dic122C2×C411yescharacteristic
44C4×Dic122D411yescharacteristic
45C4×D244C2×C411yescharacteristic
46C4×D244D411yescharacteristic
47C4×C22⋊D61—21no—
48C4×C22⋊D61—21no—
49#14519736D411yescharacteristic
50#14519734—21no—
51C42×D61—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418C2×C411yescharacteristic
55C4⋊#92418C2×C411yescharacteristic
56C4⋊#92418D412yes—
57#14519701—21no—
58#14519701—21no—
59#14519698—21no—
60#14519698—21no—
61#14519689—22no—
62#14519689—22no—
63#14519687—22no—
64C4×#92418—21no—
65C4×#92418—21no—
66C8×Dic61—22no—
67C2×#41×C61—21no—
68C22×C8×C61—21no—
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×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61D411yescharacteristic
80C4⋊C8×C61D411yescharacteristic
81C22⋊C8×C61—21no—
82C4×C8×C61—21no—
83#41×C61—41no—
84#41×C61—41no—
85#41×C61—41no—
86#41×C61—41no—
87C2×Q8×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C2×C22⋊D61—21no—
97#11758222—21no—
98#11758222—21no—
99#11758222—21no—
100#11758222—21no—
101C2×D244C22⋊C411yescharacteristic
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×Dic122C22⋊C411yescharacteristic
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C22⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C42×C61C22×C411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C22⋊Dic61—21no—
120#11758202—42no—
121#11758201—42no—
122#11758200—42no—
123#11758199—42no—
124#11758198—21no—
125#11758198—21no—
126C4⋊Dic61C22⋊C411yescharacteristic
127C4⋊Dic61C22⋊C411yescharacteristic
128#11758196—21no—
129#11758196—21no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133#11758194—41no—
134#11758194—41no—
135C2×#92418—22no—
136C2×#92418—21no—
137C2×#92418—21no—
138C2×#92418—22no—
139C2×#92418—41no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C23×C61—41no—
144C23×C61#12311yescharacteristic
145C22×D61—21no—
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—41no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61C2×C22⋊C411yescharacteristic
162C2×C4×C61C4×D411yescharacteristic
163C2×C4×C61C4×D411yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#13511yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C22⋊D61—41no—
172C22⋊D61—41no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176D244—21no—
177D244—21no—
178C4×D61—41no—
179C4×D61—41no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—81no—
183Dic122—21no—
184Dic122—21no—
185C8×C61—41no—
186C8×C61—41no—
187C8×C61—81no—
188#92418—42no—
189#92418—41no—
190#92418—41no—
191#92418—42no—
192#8996—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61#38611yescharacteristic
199C22×C61#48211yescharacteristic
200C22×C61#48211yescharacteristic
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—81no—
208C4×C61#41611yescharacteristic
209C4×C61#41811yescharacteristic
210C4×C61#44311yescharacteristic
211C4×C61#44411yescharacteristic
212C4×C61#44911yescharacteristic
213C4×C61#44911yescharacteristic
214Dic61—41no—
215Dic61—41no—
216Dic61—41no—
217#3035—611no—
218#2925—611no—
219#1492—611no—
220#1480D6111yescharacteristic, complemented
221#1476—611no—
222#1301—611no—
223#1277—611no—
224C2×C61—21no—
225C2×C61—21no—
226C2×C61—161no—
227C2×C61#187511yescharacteristic
228C2×C61#187611yescharacteristic
229C2×C61#188111yescharacteristic
230D61—81no—
231C2×#135—1221no—
232#532C2×D6111yescharacteristic
233C4×#41—611no—
234#464—1221no—
235#463—1221no—
236#462—611no—
237#461—611no—
238#460—611no—
239#459—611no—
240#433—1222no—
241#432—1221no—
242#431—1221no—
243#431C2×D6111yescharacteristic
244#423—611no—
245C2×C4⋊C8—611no—
246C2×C4⋊C8C2×D6111yescharacteristic
247#416—1221no—
248#408—1221no—
249#405—1221no—
250C2×C4×C8—611no—
251Q8⋊C8—1221no—
252D4⋊C8—21no—
253D4⋊C8—21no—
254D4⋊C8—1221no—
255D4⋊C8—1222no—
256C61#899611yescharacteristic, complemented, Sylow
257C2×#41—21no—
258C2×#41—611no—
259#135—2442no—
260#135—2442no—
261C2×Q16—1221no—
262C2×SD16—1221no—
263C2×SD16—1221no—
264C2×D8—1221no—
265C2×M16—1221no—
266C22×C8—21no—
267C22×C8—1221no—
268C22×C8—1221no—
269C4⋊Q8C4×D6111yescharacteristic
270#127C4×D6111yescharacteristic
271#124—21no—
272#121—21no—
273#121—21no—
274C4×Q8—611no—
275C4×Q8—611no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—611no—
279C4×D4—611no—
280C4×D4—1221no—
281C4×D4—1221no—
282#117—611no—
283#117—1221no—
284C2×C42—1221no—
285C2×C42C22×D6111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—611no—
289C4⋊C8—611no—
290C4⋊C8—612no—
291C4⋊C8—1221no—
292C4⋊C8—1221no—
293C4⋊C8C22⋊D6111yescharacteristic
294C4⋊C8C22⋊D6111yescharacteristic
295#103—1221no—
296#103—1221no—
297#102—1221no—
298#102—1221no—
299C22⋊C8—21no—
300C22⋊C8—1222no—
301C22⋊C8—1222no—
302#97—1222no—
303C4×C8—21no—
304C4×C8—1222no—
305C4×C8—1221no—
306C4×C8—1221no—
307#41—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—1221no—
312#41—1221no—
313#41—1221no—
314#41—1221no—
315C2×Q8—21no—
316C2×Q8—611no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—611no—
322C2×D4—1221no—
323C22×C4—41no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4#1175822211yescharacteristic
328C22×C4D4×D6111yescharacteristic
329C22×C4#1175822411yescharacteristic
330Q16—2442no—
331SD16—2442no—
332SD16—2442no—
333D8—2442no—
334M16—2441no—
335M16—2441no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—1222no—
342C2×C8—1221no—
343C2×C8—1221no—
344C2×C8—1222no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—611no—
352C4⋊C4—611no—
353C4⋊C4—1221no—
354C4⋊C4—1221no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C42—1221no—
361C42—1221no—
362C42—1221no—
363C42C2×C4×D6111yescharacteristic
364C42D4×D6111yescharacteristic
365C42D4×D6111yescharacteristic
366C42C2×C22⋊D6111yescharacteristic
367C23—41no—
368C23—1221no—
369C23#1451975911yescharacteristic
370Q8—41no—
371Q8—41no—
372Q8—1221no—
373Q8—1221no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381D4—1221no—
382D4—1221no—
383D4—2441no—
384D4—2441no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—4881no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4C22⋊C4×D6111yescharacteristic
400C2×C4#1451973711yescharacteristic
401C2×C4C4×C22⋊D6111yescharacteristic
402C2×C4#1451974511yescharacteristic
403C2×C4#1451974811yescharacteristic
404C2×C4#1451975011yescharacteristic
405C2×C4#1451979611yescharacteristic
406C2×C4#1451979811yescharacteristic
407C2×C4#1451980111yescharacteristic
408C2×C4#1451980411yescharacteristic
409C8—41no—
410C8—41no—
411C8—81no—
412C8—2442no—
413C8—2441no—
414C8—2441no—
415C8—2442no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—2441no—
422C22—2441no—
423C22—2441no—
424C22#1683963811yescharacteristic
425C22#1684008411yescharacteristic
426C22#1684008511yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—81no—
431C4—2441no—
432C4—2441no—
433C4—2441no—
434C4#1683975511yescharacteristic
435C4#1683976511yescharacteristic
436C4#1683987711yescharacteristic
437C4#1683988211yescharacteristic
438C4#1683990411yescharacteristic
439C4#1683990611yescharacteristic
440C2—21no—
441C2—21no—
442C2—161no—
443C2—4881no—
444C2#2144613811yescharacteristic
445C2#2144614911yescharacteristic
446C2#2144617811yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1480C2
socleC22×C61#386
prime radical#21455268C2
cosocleC2×C42×C61C23
hypercenter#1480D61
hypocenterC61#8996
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #21454484C2semidirect
3. #21444270C2semidirect
4. #21444199C2semidirect
5. #21443715C2semidirect
6. #21443653C2semidirect
7. C61×#1480C2semidirect
220. #1480D61semidirect
256. C61#8996semidirect

Maximal subgroups

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

subgroupindex
#214552682
#214544842
#214442702
#214441992
#214437152
#214436532
C61×#14802
#899661