Finite Group Databasebeta

← #29580806

Subgroups — #29580806

Order 15616.

566 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457009C211yesmaximal, characteristic, complemented
2#21455910C211yesmaximal, characteristic
3#21446737C211yesmaximal, characteristic, complemented
4#21444421C211yesmaximal, characteristic, complemented
5#21444262C211yesmaximal, characteristic, complemented
6#21443675C211yesmaximal, characteristic, complemented
7C61×#2562C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840172—21no—
10#16840128—21no—
11#16840080—21no—
12#16840080—21no—
13#16840075—21no—
14#16840059—22no—
15#16840052—21no—
16#16839957—21no—
17#16839896—21no—
18#16839872—22no—
19#16839819C2211yescharacteristic
20#16839819C2211yescharacteristic
21C2×#14519705—22no—
22C4×#11758194C2211yescharacteristic
23#16839504—22no—
24D4⋊#92418—22no—
25C2×#125×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#400—21no—
28C61×#394—21no—
29C61×#388—22no—
30C61×#380—21no—
31C61×#380—21no—
32C4×C4⋊C4×C61C2211yescharacteristic
33C2×#11758222—21no—
34C2×#11758199—22no—
35C2×#11758194—21no—
36#14519777D411yescharacteristic
37#14519774D411yescharacteristic
38#14519765—21no—
39#14519751—21no—
40#14519751—21no—
41C4×D244—21no—
42C4×D244—21no—
43#14519710—22no—
44#14519708—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418D412yes—
48#14519705—44no—
49#14519698—22no—
50#14519697—22no—
51#14519697—22no—
52#14519697—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55#14519688—21no—
56#14519688—21no—
57#14519688D412yes—
58C4×#92418—21no—
59C22×D4×C61D411yescharacteristic
60C23×C4×C61—21no—
61#125×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64#125×C61—21no—
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C22⋊C4×C61—22no—
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—22no—
78C2×C42×C61D412yes—
79C2×C42×C61C2311yescharacteristic
80#95×C61—22no—
81#95×C61—22no—
82#95×C61—21no—
83C24×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—42no—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—42no—
92C22×C4×C61—42no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C2×C22⋊D61—41no—
99#11758222—42no—
100#11758222—42no—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244—21no—
104C2×C4×D61—41no—
105C2×Dic122—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—42no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C22⋊C4×C61—44no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—82no—
121C42×C61—42no—
122C42×C61C2×D411yescharacteristic
123C42×C61C2×D411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61#4111yescharacteristic
126#11758199—44no—
127#11758198—41no—
128#11758198—41no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131#11758194—22no—
132#11758194—41no—
133C2×#92418—22no—
134C2×#92418—22no—
135C2×#92418—41no—
136C23×C61—22no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61#12011yescharacteristic
144C22×D61—41no—
145D4×C61—22no—
146D4×C61—22no—
147D4×C61—41no—
148D4×C61—41no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—22no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—82no—
165C2×C4×C61—82no—
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12711yescharacteristic
172C22⋊D61—81no—
173C22⋊D61—81no—
174C2×Dic61—41no—
175D244—42no—
176D244—42no—
177D244—42no—
178C4×D61—82no—
179Dic122—42no—
180#92418—42no—
181#92418—42no—
182#92418—42no—
183#10005—611nomaximal, Sylow
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—42no—
187C22×C61—42no—
188C22×C61—42no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61#39211yescharacteristic
194C22×C61#45311yescharacteristic
195C22×C61#45411yescharacteristic
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—82no—
205C4×C61—81no—
206C4×C61—81no—
207C4×C61—81no—
208C4×C61#45412yes—
209Dic61—81no—
210#3234—611no—
211#3109—611no—
212#2562D6111yescharacteristic, complemented
213#1980—611no—
214#1528—611no—
215#1490—611no—
216#1285—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—82no—
220C2×C61#200311yescharacteristic
221C2×C61#200611yescharacteristic
222C2×C61#201011yescharacteristic
223D61—161no—
224#532—611no—
225C2×#125C2×D6111yescharacteristic
226C2×C4×D4C2×D6111yescharacteristic
227#501—1221no—
228#490—1221no—
229#481—1221no—
230#481—1221no—
231#480—1221no—
232#478—1222no—
233#476—1221no—
234#459—1221no—
235#447—1221no—
236#442—1222no—
237#432—611no—
238#432—611no—
239C2×#104—1222no—
240C4×M16—611no—
241#400—21no—
242#394—21no—
243#388—22no—
244#380—21no—
245#380—21no—
246C4×C4⋊C4C2×D6111yescharacteristic
247#330—1222no—
248D4⋊C8—1222no—
249C61#1000511yescharacteristic, complemented, Sylow
250C2×#41—1221no—
251C22×D4C22⋊D6111yescharacteristic
252C23×C4—21no—
253C2×D8—1222no—
254C2×M16—1221no—
255C4⋊Q8—611no—
256#127—611no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#124—1221no—
262#121—1221no—
263#121—1221no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—1221no—
269C4×D4—1221no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4C22⋊D6111yescharacteristic
274C2×C4⋊C4C22⋊D6111yescharacteristic
275C2×C4⋊C4C22⋊D6111yescharacteristic
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—22no—
279C2×C42C22⋊D6112yes—
280C2×C42C22×D6111yescharacteristic
281#107—1222no—
282#106—1222no—
283#106—1222no—
284C4⋊C8—612no—
285C4⋊C8—1221no—
286#104—2444no—
287#102—1222no—
288#102—1222no—
289#102—1222no—
290#102—1222no—
291C22⋊C8—1221no—
292C22⋊C8—1221no—
293#97—612no—
294#97—1221no—
295#97—1221no—
296C4×C8—1221no—
297#95—22no—
298#95—22no—
299#95—21no—
300C24—21no—
301#41—2442no—
302#41—2442no—
303C2×Q8—1221no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—42no—
307C2×D4—1221no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—2441no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—2441no—
320C22×C4C2×C22⋊D6111yescharacteristic
321C22×C4C2×C22⋊D6111yescharacteristic
322C22×C4C2×C22⋊D6111yescharacteristic
323D8—2444no—
324M16—1222no—
325M16—2441no—
326C2×C8—1222no—
327C2×C8—1222no—
328C2×C8—2441no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—42no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C22⋊C4—44no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—82no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C42—42no—
349C42D4×D6111yescharacteristic
350C42D4×D6111yescharacteristic
351C42D4×D6111yescharacteristic
352C42#1175822411yescharacteristic
353C23—22no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—2441no—
361C23#1451974611yescharacteristic
362Q8—2442no—
363D4—22no—
364D4—22no—
365D4—41no—
366D4—41no—
367D4—4881no—
368D4—4881no—
369D4—2442no—
370D4—2442no—
371D4—2442no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—4882no—
390C2×C4—2441no—
391C2×C4#1451974511yescharacteristic
392C2×C4#1451974511yescharacteristic
393C2×C4#1451974811yescharacteristic
394C2×C4#1451974911yescharacteristic
395C2×C4#1451974911yescharacteristic
396C2×C4#1451977311yescharacteristic
397C8—2442no—
398C8—2442no—
399C8—2442no—
400C22—21no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—4881no—
410C22—4881no—
411C22—4881no—
412C22#1683967011yescharacteristic
413C22#1683993011yescharacteristic
414C22#1683993511yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—82no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—4881no—
425C4#1683993412yes—
426C2—21no—
427C2—21no—
428C2—82no—
429C2—9761no—
430C2#2144684111yescharacteristic
431C2#2144686111yescharacteristic
432C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2562C2
socleC22×C61#392
prime radical#21455910C2
hypercenter#2562D61
hypocenterC61#10005
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2562

Complements

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

NH ≅ G/Ntype
1. #21457009C2semidirect
3. #21446737C2semidirect
4. #21444421C2semidirect
5. #21444262C2semidirect
6. #21443675C2semidirect
7. C61×#2562C2semidirect
212. #2562D61semidirect
249. C61#10005semidirect

Maximal subgroups

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

subgroupindex
#214570092
#214559102
#214467372
#214444212
#214442622
#214436752
C61×#25622
#1000561