Finite Group Databasebeta

← #29569199

Subgroups — #29569199

Order 15616.

478 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 81 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#21452844C211yesmaximal, characteristic
2#21447361C211yesmaximal, characteristic, complemented
3#21447224C211yesmaximal, characteristic, complemented
4#21447222C211yesmaximal, characteristic, complemented
5#21443644C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic, complemented
8C2×#14519763—21no—
9C2×#14519709—21no—
10C2×#14519702—21no—
11C2×#14519699—21no—
12C2×#14519698—21no—
13#16839678—21no—
14#16839671—21no—
15#16839670—21no—
16#16839668C2211yescharacteristic
17#16839664C2211yescharacteristic
18#16839655—21no—
19#16839652—21no—
20#16839632C2211yescharacteristic
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×C22⋊D61—21no—
30C22×C22⋊D61—21no—
31C22×#92418—21no—
32#14519763—42no—
33#14519763—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61—21no—
46#14519709—42no—
47#14519702—42no—
48#14519699—42no—
49#14519698—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×D4×C61D411yescharacteristic
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C24×C61—21no—
61C23×D61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C22×C4×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—42no—
71C2×C22⋊D61—81no—
72C2×C22⋊D61—81no—
73C2×C22⋊D61—81no—
74C2×C22⋊D61—81no—
75C2×C22⋊D61—81no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—41no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—41no—
83C2×D244—41no—
84C2×Dic122—21no—
85C2×Dic122—41no—
86C2×Dic122—41no—
87C2×Dic122SD1612yes—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C42×C61—41no—
100C22⋊Dic61—42no—
101C22⋊Dic61—81no—
102#11758198—42no—
103#11758198—41no—
104#11758198—41no—
105#11758198—41no—
106#11758198—41no—
107#11758198—81no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4×Dic61—42no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61#12011yescharacteristic
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135D4×C61—42no—
136D4×C61—81no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61C2×SD1611yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C22⋊D61—84no—
153C22⋊D61—84no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—81no—
164C2×Dic61—81no—
165C2×Dic61—81no—
166D244—42no—
167D244—81no—
168Dic122—42no—
169Dic122—81no—
170C8×C61—42no—
171C8×C61—81no—
172#92418—81no—
173#7810—611nomaximal, Sylow
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61#44911yescharacteristic
182C22×C61#44911yescharacteristic
183C22×C61#45011yescharacteristic
184C22×C61#45311yescharacteristic
185C22×C61#45511yescharacteristic
186C22×C61#45511yescharacteristic
187C22×C61#45811yescharacteristic
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—81no—
202Dic61—42no—
203Dic61—81no—
204Dic61—81no—
205Dic61—161no—
206#2733—611no—
207#2096—611no—
208#2071—611no—
209#2071—611no—
210#1272—611no—
211#1270—611no—
212#1270D6111yescharacteristic, complemented
213C2×C61—161no—
214C2×C61#161211yescharacteristic
215C2×C61#161211yescharacteristic
216C2×C61#161311yescharacteristic
217C2×C61#162411yescharacteristic
218C2×C61#164211yescharacteristic
219C2×C61#164211yescharacteristic
220C2×C61#165911yescharacteristic
221D61—161no—
222C2×#124—1221no—
223C2×#106—1221no—
224C2×#103—1221no—
225C2×#102—1221no—
226C2×#102—1221no—
227#394—1221no—
228#392—1221no—
229#392—1221no—
230#391—611no—
231#390—611no—
232#390C2×D6111yescharacteristic
233#388—1221no—
234#388—1221no—
235#384—611no—
236#340—1221no—
237#340—1221no—
238#336—611no—
239#336C2×D6111yescharacteristic
240#336C2×D6111yescharacteristic
241C61#781011yescharacteristic, complemented, Sylow
242C22×Q8—611no—
243C22×D4—611no—
244C22×D4—1221no—
245C22×D4—1221no—
246C22×D4D24411yescharacteristic
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—1221no—
250#124—2442no—
251#124—2442no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4D24411yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C42—1221no—
267C2×C42C22×D6111yescharacteristic
268#106—2442no—
269#103—2442no—
270#102—2442no—
271#102—2442no—
272#95—1221no—
273#95—1221no—
274#95—1221no—
275C24—21no—
276C24—1221no—
277C2×Q8—612no—
278C2×Q8—1221no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—4881no—
288C2×D4—4881no—
289C2×D4—4881no—
290C2×D4—4881no—
291C2×D4—4881no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2442no—
295C22×C4—21no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—2441no—
300C22×C4C2×D24411yescharacteristic
301C22×C4D4×D6111yescharacteristic
302C22×C4D4×D6111yescharacteristic
303C2×C8—22no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—2441no—
310C2×C8—2441no—
311C2×C8—2441no—
312C4⋊C4—41no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—4881no—
326C22⋊C4—4881no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C22⋊C4—2441no—
330C22⋊C4—2441no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C42—41no—
334C42—2442no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23#1451974711yescharacteristic
350Q8—4881no—
351Q8—2442no—
352D4—42no—
353D4—81no—
354D4—4881no—
355D4—4884no—
356D4—4884no—
357D4—2442no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—1222no—
368C2×C4—4881no—
369C2×C4—4881no—
370C2×C4—4881no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4SD16×D6111yescharacteristic
380C2×C4#1451979811yescharacteristic
381C2×C4#1451979911yescharacteristic
382C2×C4#1451980111yescharacteristic
383C2×C4#1451980111yescharacteristic
384C2×C4#1451980511yescharacteristic
385C8—42no—
386C8—81no—
387C8—4881no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—4881no—
396C22—4881no—
397C22—4881no—
398C22—4881no—
399C22—4881no—
400C22—4881no—
401C22—4881no—
402C22#1683990811yescharacteristic
403C22#1683990911yescharacteristic
404C22#1683991411yescharacteristic
405C22#1683993111yescharacteristic
406C22#1683994111yescharacteristic
407C22#1683994211yescharacteristic
408C22#1683995311yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—81no—
416C4—9761no—
417C4—4881no—
418C4—4881no—
419C4—2442no—
420C2—161no—
421C2—9761no—
422C2#2144483411yescharacteristic
423C2#2144483511yescharacteristic
424C2#2144484011yescharacteristic
425C2#2144490411yescharacteristic
426C2#2144502011yescharacteristic
427C2#2144502111yescharacteristic
428C2#2144512711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radical#21452844C2
hypercenter#1270D61
hypocenterC61#7810
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21447361C2semidirect
3. #21447224C2semidirect
4. #21447222C2semidirect
5. #21443644C2semidirect
6. #21443639C2semidirect
7. C61×#1270C2semidirect
212. #1270D61semidirect
241. C61#7810semidirect

Maximal subgroups

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

subgroupindex
#214528442
#214473612
#214472242
#214472222
#214436442
#214436392
C61×#12702
#781061