Finite Group Databasebeta

← #29595682

Subgroups — #29595682

Order 15616.

926 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519796C211yesmaximal, characteristic
2C2×#16839579C211yesmaximal, characteristic, complemented
3C2×#16839577C211yesmaximal, characteristic, complemented
4C2×#16839575C211yesmaximal, characteristic, complemented
5#21447429C211yesmaximal, characteristic, complemented
6#21445854C211yesmaximal, characteristic, complemented
7C2×C61×#361C211yesmaximal, characteristic, complemented
8C22×#11758224—21no—
9C2×#14519796—22no—
10C2×#14519796—22no—
11C2×#14519796—22no—
12C2×#14519796—22no—
13C2×#14519796—22no—
14C2×#14519796C414yes—
15C22×Dic244C2211yescharacteristic
16C22×#11758200—21no—
17C22×C8×D61C2211yescharacteristic
18C2×#14519717C2211yescharacteristic
19C2×#14519713C2211yescharacteristic
20#16839725—21no—
21#16839579—22no—
22#16839577—22no—
23#16839575—22no—
24#16839541—22no—
25#16839526—21no—
26C22×D8×C61C2211yescharacteristic
27C2×M32×C61C2211yescharacteristic
28C2×#108×C61C2211yescharacteristic
29C61×#361—22no—
30C2×#11758224—24no—
31C2×#11758224—24no—
32C2×#11758224—24no—
33C2×#11758224—42no—
34C2×#11758224—42no—
35C2×#11758224—42no—
36C22×Dic122—21no—
37C22×C22⋊D61—41no—
38C23×Dic61—41no—
39C22×C4×D61D411yescharacteristic
40#14519796—28no—
41#14519796—28no—
42#14519796—28no—
43#14519796—28no—
44C2×Dic244—21no—
45C2×Dic244—21no—
46C2×Dic244—21no—
47C2×Dic244C2×C412yes—
48C2×Dic244D412yes—
49C2×Dic244D412yes—
50C2×#11758200—24no—
51C2×#11758200—24no—
52C2×#11758200—24no—
53C2×#11758194—21no—
54C22×#92418D411yescharacteristic
55C2×C8×D61—21no—
56C2×C8×D61—21no—
57C2×C8×D61—21no—
58C2×C8×D61—21no—
59C2×C8×D61C2×C412yes—
60C2×C8×D61D412yes—
61#14519717—21no—
62#14519717—21no—
63C2×#11758185—21no—
64#14519713—21no—
65#14519713—21no—
66#14519689—42no—
67C22×D4×C61—21no—
68C2×D8×C61—21no—
69C2×D8×C61—21no—
70C2×D8×C61—21no—
71C2×D8×C61C2×C412yes—
72C2×D8×C61D412yes—
73C2×D8×C61D412yes—
74C2×M16×C61—21no—
75C22×C8×C61C2311yescharacteristic
76M32×C61—21no—
77M32×C61—21no—
78C2×C16×C61—21no—
79#108×C61—21no—
80#108×C61—21no—
81C24×C61—41no—
82C23×D61SD1611yescharacteristic
83C2×D4×C61—22no—
84C2×D4×C61—22no—
85C2×D4×C61—22no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C22×C4×C61C2×D411yescharacteristic
90C2×C22⋊D61—44no—
91C2×C22⋊D61—44no—
92C2×C22⋊D61—44no—
93C22×Dic61—44no—
94C22×Dic61—44no—
95C22×Dic61—41no—
96C22×Dic61—44no—
97C22×Dic61SD1611yescharacteristic
98#11758224—216no—
99#11758224—48no—
100#11758224—48no—
101#11758224—48no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61C22⋊C412yes—
107C2×C4×D61D812yes—
108C2×Dic122—22no—
109C2×Dic122—22no—
110C2×Dic122—22no—
111C2×Dic122—41no—
112C2×Dic122—41no—
113C2×Dic122—41no—
114D8×C61—22no—
115D8×C61—22no—
116D8×C61—22no—
117D8×C61C22⋊C414yes—
118M16×C61—41no—
119M16×C61—41no—
120C2×C8×C61—41no—
121C2×C8×C61C22×C411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127#11758200—216no—
128#11758194—41no—
129#11758194—41no—
130C2×#92418—21no—
131C2×#92418—21no—
132C2×#92418—41no—
133C2×#92418C22⋊C412yes—
134Dic244—22no—
135Dic244—22no—
136Dic244—22no—
137Dic244C22⋊C414yes—
138C8×D61—22no—
139C8×D61—22no—
140C8×D61—22no—
141C8×D61—22no—
142C16×C61—41no—
143#11758185—41no—
144C23×C61—42no—
145C23×C61—42no—
146C23×C61—42no—
147C23×C61—84no—
148C23×C61C2×SD1611yescharacteristic
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—42no—
152C22×D61#10212yes—
153D4×C61—24no—
154D4×C61—42no—
155D4×C61—42no—
156D4×C61—42no—
157C2×C4×C61C2×C22⋊C411yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12011yescharacteristic
160C2×C4×C61C2×D811yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C22⋊D61—416no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—416no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61#10212yes—
171C4×D61—22no—
172C4×D61—22no—
173C4×D61—22no—
174C4×D61—22no—
175Dic122—24no—
176Dic122—42no—
177Dic122—42no—
178Dic122—42no—
179C8×C61—81no—
180C8×C61C2×C22⋊C411yescharacteristic
181C8×C61C2×C22⋊C411yescharacteristic
182C8×C61#12011yescharacteristic
183C8×C61#12011yescharacteristic
184#92418—22no—
185#92418—81no—
186#12738—611nomaximal, Sylow
187C22×C61—22no—
188C22×C61—44no—
189C22×C61—84no—
190C22×C61—84no—
191C22×C61—84no—
192C22×C61C2×#10211yescharacteristic
193C22×C61#45011yescharacteristic
194C22×C61#45011yescharacteristic
195C2×D61—24no—
196C2×D61—22no—
197C2×D61—42no—
198C2×D61—42no—
199C4×C61#37911yescharacteristic
200C4×C61#41811yescharacteristic
201C4×C61#44711yescharacteristic
202C4×C61#44711yescharacteristic
203Dic61—22no—
204Dic61—44no—
205C22×#135—611no—
206C2×#362—611no—
207C2×#362—611no—
208C2×#361—611no—
209C2×#361D6111yescharacteristic, complemented
210#2112—611no—
211#1810—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—84no—
215C2×C61#178611yescharacteristic
216C2×C61#214812yes—
217D61—42no—
218C22×#41—1221no—
219C2×#135—614no—
220C2×#135—1222no—
221C2×#135—1222no—
222C2×#135—1222no—
223C2×#135—1222no—
224C2×#135—1222no—
225C22×Q16—611no—
226C22×SD16—1221no—
227C22×D8C2×D6111yescharacteristic
228C23×C8—611no—
229C2×M32—611no—
230C2×M32C2×D6111yescharacteristic
231C2×#108—611no—
232C2×#108C2×D6111yescharacteristic
233#407—1221no—
234#362—1222no—
235#362—1222no—
236#361—22no—
237#361—1222no—
238C22⋊C16—1222no—
239#341—1221no—
240C61#1273811yescharacteristic, complemented, Sylow
241C2×#41—1224no—
242C2×#41—1224no—
243C2×#41—1224no—
244C2×#41—2442no—
245C2×#41—2442no—
246C2×#41—2442no—
247C22×Q8—1221no—
248C22×D4—21no—
249C22×D4—2441no—
250C23×C4—611no—
251C23×C4—2441no—
252#135—1228no—
253#135—1228no—
254#135—1228no—
255#135—1228no—
256C2×Q16—612no—
257C2×Q16—612no—
258C2×Q16—612no—
259C2×Q16—1221no—
260C2×Q16—1221no—
261C2×Q16—1221no—
262C2×SD16—1224no—
263C2×SD16—1224no—
264C2×SD16—1224no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8C4×D6112yes—
269C2×D8D24412yes—
270C2×D8C22⋊D6112yes—
271C2×M16—21no—
272C2×M16—1221no—
273C22×C8—611no—
274C22×C8—612no—
275C22×C8—612no—
276C22×C8—1221no—
277C22×C8—1221no—
278C22×C8—1221no—
279C22×C8—1221no—
280C22×C8C22×D6111yescharacteristic
281M32—21no—
282M32—21no—
283M32—1221no—
284M32—1221no—
285C2×C16—21no—
286C2×C16—1221no—
287#108—21no—
288#108—21no—
289#108—1221no—
290#108—1221no—
291C22⋊C8—2442no—
292C24—41no—
293C24—611no—
294#41—12216no—
295#41—2448no—
296#41—2448no—
297#41—2448no—
298C2×Q8—1222no—
299C2×Q8—1222no—
300C2×Q8—1222no—
301C2×Q8—2441no—
302C2×Q8—2441no—
303C2×Q8—2441no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—2444no—
311C2×D4—2444no—
312C2×D4—2444no—
313C22×C4—611no—
314C22×C4—612no—
315C22×C4—612no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—2444no—
321C22×C4—2444no—
322C22×C4—2444no—
323C22×C4—2441no—
324C22×C4D4×D6111yescharacteristic
325Q16—614no—
326Q16—1222no—
327Q16—1222no—
328Q16—1222no—
329SD16—12216no—
330D8—22no—
331D8—22no—
332D8—22no—
333D8#1175819814yes—
334M16—41no—
335M16—41no—
336M16—2441no—
337M16—2441no—
338C2×C8—41no—
339C2×C8—612no—
340C2×C8—1221no—
341C2×C8—1221no—
342C2×C8—1222no—
343C2×C8—1222no—
344C2×C8—1222no—
345C2×C8—1222no—
346C2×C8—2441no—
347C2×C8C2×C4×D6111yescharacteristic
348C2×C8C2×D24411yescharacteristic
349C2×C8D4×D6111yescharacteristic
350C2×C8D4×D6111yescharacteristic
351C2×C8D4×D6111yescharacteristic
352C2×C8C2×C22⋊D6111yescharacteristic
353C16—41no—
354C16—2441no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—84no—
359C23—612no—
360C23—1221no—
361C23—1221no—
362C23—2442no—
363C23SD16×D6111yescharacteristic
364Q8—1224no—
365Q8—2442no—
366Q8—2442no—
367Q8—2442no—
368D4—24no—
369D4—42no—
370D4—42no—
371D4—42no—
372D4—24416no—
373C2×C4—612no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1222no—
377C2×C4—1222no—
378C2×C4—1222no—
379C2×C4—1222no—
380C2×C4—24416no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4C22⋊C4×D6111yescharacteristic
385C2×C4#1451974511yescharacteristic
386C2×C4#1451974711yescharacteristic
387C2×C4D8×D6111yescharacteristic
388C2×C4#1451980111yescharacteristic
389C2×C4#1451980411yescharacteristic
390C8—81no—
391C8—1222no—
392C8—4881no—
393C8C22⋊C4×D6111yescharacteristic
394C8C2×#1175819811yescharacteristic
395C8#1451974511yescharacteristic
396C8#1451974711yescharacteristic
397C22—22no—
398C22—44no—
399C22—84no—
400C22—84no—
401C22—84no—
402C22—1222no—
403C22—1224no—
404C22—2442no—
405C22—2442no—
406C22#102×D6111yescharacteristic
407C22#1683991111yescharacteristic
408C22#1683991411yescharacteristic
409C4—1222no—
410C4—2444no—
411C4#1683961711yescharacteristic
412C4#1683976511yescharacteristic
413C4#1683989411yescharacteristic
414C4#1683989711yescharacteristic
415C2—21no—
416C2—21no—
417C2—84no—
418C2—2442no—
419C2#2144574811yescharacteristic
420C2#2144756512yes—
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#361C2
socleC22×C61C2×#102
prime radicalC22×#14519796C2
cosocleC22×C8×C61C23
hypercenterC2×#361D61
hypocenterC61#12738
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C2×#16839579C2semidirect
3. C2×#16839577C2semidirect
4. C2×#16839575C2semidirect
5. #21447429C2semidirect
6. #21445854C2semidirect
7. C2×C61×#361C2semidirect
209. C2×#361D61semidirect
240. C61#12738semidirect

Maximal subgroups

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

subgroupindex
C22×#145197962
C2×#168395792
C2×#168395772
C2×#168395752
#214474292
#214458542
C2×C61×#3612
#1273861