Finite Group Databasebeta

← #30597940

Subgroups — #30597940

Order 15616.

474 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462542C211yesmaximal, characteristic
2#21461611C211yesmaximal, characteristic, complemented
3#21461317C211yesmaximal, characteristic
4#21461034C211yesmaximal, characteristic, complemented
5#21460717C211yesmaximal, characteristic, complemented
6#21460710C211yesmaximal, characteristic, complemented
7#21444312C211yesmaximal, characteristic
8C2×#14519864—21no—
9#16840797C411yescharacteristic, complemented
10#16840796C411yescharacteristic, complemented
11#16840795—21no—
12#16840790C411yescharacteristic, complemented
13#16840789—21no—
14D4×#92420C411yescharacteristic, complemented
15#16840779C2211yescharacteristic
16#16840765C2211yescharacteristic
17C2×#14519844C2211yescharacteristic
18#16840735—21no—
19C2×C4×#92420—21no—
20C2×C4×#92420C2211yescharacteristic
21#16840628—21no—
22#16840621C412yescomplemented
23#16840620C412yescomplemented
24#92420⋊C8—21no—
25#16840603—21no—
26#16840307C2211yescharacteristic
27#16839812C2211yescharacteristic
28#16839613C2211yescharacteristic
29#16839497C411yescharacteristic
30#16839496C411yescharacteristic
31#16839495C411yescharacteristic
32C61×#327C411yescharacteristic
33#14519864—42no—
34#14519864—42no—
35C2×#11758213—21no—
36C2×#11758217—21no—
37C2×#11758217—21no—
38C2×D61⋊C8—21no—
39C22×#92420—21no—
40C22×#92420—21no—
41C22×#92420D411yescharacteristic
42C22×#92420D411yescharacteristic
43#14519844—21no—
44#14519844—21no—
45#14519844C2×C412yes—
46#14519844C2×C412yes—
47C4⋊#92420C2×C411yescharacteristic
48C4⋊#92420C2×C411yescharacteristic
49#14519834—21no—
50#14519834—21no—
51C22⋊#92420—21no—
52C22⋊#92420—21no—
53C22⋊#92420—21no—
54C4×#92420—21no—
55C4×#92420—42no—
56C4×#92420C2×C411yescharacteristic
57C4×#92420C2×C411yescharacteristic
58C4×#92420D411yescharacteristic
59C4×#92420D411yescharacteristic
60C2×#11758224—21no—
61#14519776C2×C411yescharacteristic
62#14519773C2×C411yescharacteristic
63#14519763—21no—
64#14519751C2×C411yescharacteristic
65#14519749—21no—
66D4×Dic61C2×C411yescharacteristic
67#14519739C2×C411yescharacteristic
68#14519737—21no—
69C2×#11758196—21no—
70C2×C4×Dic61—21no—
71C2×C4×Dic61C2311yescharacteristic
72#14519706—21no—
73C22⋊#92418C2×C411yescharacteristic
74C8×Dic61—21no—
75#14519684C2×C411yescharacteristic
76#121×C61C2×C411yescharacteristic
77C22⋊C8×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C2×D4×C61—21no—
80C2×D4×C61C4211yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C2×C22⋊D61—21no—
84C2×C22⋊D61—21no—
85C2×C22⋊D61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61#4111yescharacteristic
90#11758224—41no—
91#11758224—41no—
92#11758224—41no—
93#11758224—41no—
94C2×D244C4211yescharacteristic
95C2×C4×D61—21no—
96C2×Dic122—21no—
97#11758217—42no—
98#11758217—41no—
99#11758217—41no—
100C2×#92420—21no—
101C2×#92420—21no—
102C2×#92420—21no—
103C2×#92420—21no—
104C2×#92420—21no—
105C2×#92420—21no—
106C2×#92420—22no—
107C2×#92420—22no—
108C2×#92420—42no—
109C2×#92420—41no—
110C2×#92420—41no—
111C2×#92420C22⋊C411yescharacteristic
112C2×#92420C22⋊C411yescharacteristic
113C2×#92420C22⋊C411yescharacteristic
114C2×#92420C22⋊C411yescharacteristic
115#11758213—42no—
116D61⋊C8—42no—
117C2×C8×C61—21no—
118C4⋊C4×C61C4211yescharacteristic
119C22⋊C4×C61—21no—
120C22⋊Dic61—21no—
121#11758198—21no—
122#11758198—21no—
123C4⋊Dic61C4211yescharacteristic
124#11758196—24no—
125#11758196—21no—
126C4×Dic61—41no—
127C4×Dic61—41no—
128C4×Dic61C22×C411yescharacteristic
129C4×Dic61C22×C411yescharacteristic
130C4×Dic61C2×D411yescharacteristic
131C4×Dic61#4111yescharacteristic
132C2×#92418—21no—
133C23×C61—21no—
134C23×C61C4×D411yescharacteristic
135C22×D61—21no—
136D4×C61—41no—
137D4×C61—41no—
138D4×C61—41no—
139C2×C4×C61—22no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61C2×C4211yescharacteristic
145C2×C4×C61C4×D411yescharacteristic
146C22⋊D61—41no—
147C22⋊D61—41no—
148C22⋊D61—41no—
149C22⋊D61—41no—
150C22⋊D61—42no—
151C2×Dic61—22no—
152C2×Dic61—22no—
153C2×Dic61—21no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61C2×C22⋊C411yescharacteristic
159C2×Dic61#11711yescharacteristic
160C2×Dic61C4×D411yescharacteristic
161C2×Dic61C4×D411yescharacteristic
162C2×Dic61AGL(1,ℤ/8)11yescharacteristic
163C2×Dic61AGL(1,ℤ/8)11yescharacteristic
164C2×Dic61AGL(1,ℤ/8)11yescharacteristic
165C2×Dic61#13711yescharacteristic
166D244—41no—
167C4×D61—41no—
168C4×D61—41no—
169Dic122—41no—
170Dic122—41no—
171#92420—21no—
172#92420—21no—
173#92420—21no—
174#92420—21no—
175#92420—41no—
176#92420—41no—
177#92420—42no—
178#92420—42no—
179C8×C61—41no—
180#92418—41no—
181#8257—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61C4×C22⋊C411yescharacteristic
188C22×C61#44011yescharacteristic
189C22×C61#44211yescharacteristic
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—42no—
196C4×C61—41no—
197Dic61—21no—
198Dic61—42no—
199Dic61—41no—
200Dic61#41711yescharacteristic
201Dic61#41811yescharacteristic
202Dic61#44011yescharacteristic
203Dic61#44211yescharacteristic
204Dic61#44312yes—
205#2931—611no—
206C8×C4⋊C4—611no—
207#1540—611no—
208#1502—611no—
209#1452—611no—
210#1303—611no—
211#1301—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—81no—
215C2×C61#175711yescharacteristic
216C2×C61#176211yescharacteristic
217C2×C61#176411yescharacteristic
218D61—81no—
219C2×#131—1221no—
220#532—611no—
221#436—611no—
222#436—611no—
223#436—1221no—
224C8×D4—611no—
225C8×D4—611no—
226C8×D4—1221no—
227#431—611no—
228#431—611no—
229#423—611no—
230C2×C4⋊C8—611no—
231#408—1221no—
232C2×C4×C8—611no—
233C2×C4×C8—1221no—
234C4×C4⋊C4—611no—
235#336—1221no—
236#332—612no—
237#331—612no—
238#327—611no—
239#327—611no—
240#327—611no—
241#327#692311yescharacteristic
242#322—1221no—
243#322—1221no—
244C61#825711yescharacteristic, complemented, Sylow
245C2×#41—1221no—
246#131—2442no—
247#131—2442no—
248C2×M16—1221no—
249C2×M16—1221no—
250C2×M16—1221no—
251C22×C8—611no—
252C22×C8—611no—
253C22×C8—1221no—
254C22×C8—1221no—
255C22×C8—1221no—
256C4⋊Q8—611no—
257#127—611no—
258#124—1221no—
259#121—611no—
260#121—1221no—
261#121C2×#692311yescharacteristic
262C4×D4—611no—
263C4×D4—611no—
264C4×D4—1221no—
265C2×C4⋊C4—1221no—
266C2×C42—611no—
267C2×C42—1221no—
268C4⋊C8—611no—
269C4⋊C8—611no—
270C4⋊C8—612no—
271C4⋊C8—612no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275C22⋊C8—611no—
276C22⋊C8—1221no—
277C22⋊C8—1221no—
278C22⋊C8—1221no—
279C22⋊C8—1221no—
280C22⋊C8—1221no—
281C22⋊C8C2×#692311yescharacteristic
282C4×C8—611no—
283C4×C8—611no—
284C4×C8—611no—
285C4×C8—611no—
286C4×C8—1221no—
287C4×C8—1221no—
288C4×C8—2442no—
289#95—611no—
290#95C2×#692311yescharacteristic
291#41—2441no—
292#41—2441no—
293#41—2441no—
294#41—2441no—
295C2×Q8—1221no—
296C2×D4—21no—
297C2×D4—611no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4C4×#692311yescharacteristic
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4C22×#692311yescharacteristic
309M16—2442no—
310M16—2442no—
311M16—2441no—
312M16—2441no—
313C2×C8—21no—
314C2×C8—611no—
315C2×C8—611no—
316C2×C8—611no—
317C2×C8—611no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—1222no—
323C2×C8—1221no—
324C2×C8—1221no—
325C2×C8—1222no—
326C2×C8—1221no—
327C2×C8—2442no—
328C2×C8—2442no—
329C2×C8—2441no—
330C2×C8—2441no—
331C4⋊C4—611no—
332C4⋊C4—1221no—
333C4⋊C4—1224no—
334C4⋊C4C4×#692311yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C42—611no—
340C42—611no—
341C42—611no—
342C42—611no—
343C42—2441no—
344C42—2441no—
345C23—21no—
346C23—1221no—
347C23D4×#692311yescharacteristic
348Q8—2441no—
349Q8—2441no—
350D4—41no—
351D4—41no—
352D4—41no—
353D4—2441no—
354D4—2442no—
355D4—2441no—
356D4—2441no—
357D4—2441no—
358D4—2441no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—611no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—1221no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4C2×C4×#692311yescharacteristic
382C2×C4D4×#692311yescharacteristic
383C8—41no—
384C8—1221no—
385C8—1221no—
386C8—1221no—
387C8—1221no—
388C8—2441no—
389C8—2442no—
390C8—2442no—
391C8—2441no—
392C8—2441no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22C22⋊C4×#692311yescharacteristic
402C22#1684080111yescharacteristic
403C22#1684080311yescharacteristic
404C4—21no—
405C4—21no—
406C4—42no—
407C4—41no—
408C4—611no—
409C4—611no—
410C4—611no—
411C4—611no—
412C4—612no—
413C4—1221no—
414C4—2442no—
415C4—2441no—
416C2—21no—
417C2—21no—
418C2—81no—
419C2—4881no—
420C2#2146157711yescharacteristic
421C2#2146159011yescharacteristic
422C2#2146159511yescharacteristic
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#327C4
socleC22×C61C4×C22⋊C4
prime radical#16840307C22
cosocleC2×C4×Dic61C23
hypercenter#327#6923
hypocenterC61#8257
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #21461611C2semidirect
4. #21461034C2semidirect
5. #21460717C2semidirect
6. #21460710C2semidirect
9. #16840797C4semidirect
10. #16840796C4semidirect
12. #16840790C4semidirect
14. D4×#92420C4semidirect
22. #16840621C4semidirect
23. #16840620C4semidirect
244. C61#8257semidirect

Maximal subgroups

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

subgroupindex
#214625422
#214616112
#214613172
#214610342
#214607172
#214607102
#214443122
#825761