Finite Group Databasebeta

← #30597590

Subgroups — #30597590

Order 15616.

574 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462276C211yesmaximal, characteristic
2C4⋊C8×#6923C211yesmaximal, characteristic, complemented
3#21461532C211yesmaximal, characteristic, complemented
4D61⋊(D4⋊C8)C211yesmaximal, characteristic
5#21460654C211yesmaximal, characteristic, complemented
6#21460653C211yesmaximal, characteristic, complemented
7D4⋊C8×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9D61⋊(C4⋊C8)C2211yescharacteristic
10C4×D61⋊C8C2211yescharacteristic
11C2×C8×#6923—21no—
12#16840714C412yes—
13#16840713C412yes—
14#16840712—22no—
15C4×C4⋊#6923C2211yescharacteristic
16C4×C22⋊#6923—21no—
17C42×#6923C2211yescharacteristic
18(C2×#6923)⋊C8—22no—
19(C2×#6923)⋊C8—21no—
20#16840610C412yescomplemented
21D4⋊#92420C412yescomplemented
22C4×D4×D61C2211yescharacteristic
23C4⋊C8×D61C2211yescharacteristic
24C4×C8×D61C2211yescharacteristic
25#16839491C411yescharacteristic, complemented
26D4⋊#92418C411yescharacteristic, complemented
27#16839489C411yescharacteristic, complemented
28C61×D4⋊C8C411yescharacteristic, complemented
29C2×D61⋊C8—21no—
30C2×D61⋊C8—21no—
31#14519856—42no—
32#14519856—42no—
33C2×C4⋊#6923—22no—
34C2×C4⋊#6923C2×C412yes—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—21no—
38C2×C4×#6923C2×C412yes—
39C2×C4×#6923D411yescharacteristic
40C2×C4×#6923D412yes—
41C2×C4×#6923D411yescharacteristic
42#14519844—21no—
43C4⋊#92420C2×C412yes—
44C4×#92420—21no—
45C4×#92420C2×C412yes—
46C8×#6923—42no—
47(C2×#6923)⋊C4—22no—
48(C2×#6923)⋊C4—21no—
49C2×D4×D61C2×C411yescharacteristic
50C22×C4×D61—21no—
51C2×C8×D61—21no—
52C2×C8×D61—21no—
53C4×D244C2×C411yescharacteristic
54D4×Dic61C2×C411yescharacteristic
55#14519739C2×C411yescharacteristic
56C4×C22⋊D61—21no—
57#14519737—21no—
58C4⋊C4×D61C2×C411yescharacteristic
59C22⋊C4×D61—21no—
60C42×D61C2311yescharacteristic
61C4⋊#92418C2×C411yescharacteristic
62#14519706—21no—
63C4×#92418C2×C411yescharacteristic
64C8×Dic61—21no—
65C4×D4×C61C2×C411yescharacteristic
66C4⋊C8×C61C2×C411yescharacteristic
67C4×C8×C61C2×C411yescharacteristic
68C23×D61—21no—
69C22×#6923—22no—
70C22×#6923C22⋊C412yes—
71C22×#6923C22⋊C412yes—
72C2×D4×C61C4211yescharacteristic
73C22×C4×C61—21no—
74C2×C22⋊D61—21no—
75C22×Dic61—21no—
76D4×D61—22no—
77D4×D61—22no—
78C2×D244C4211yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61C22×C411yescharacteristic
87C2×C4×D61C2×D411yescharacteristic
88C2×C4×D61C2×D411yescharacteristic
89C22⋊#6923—44no—
90C22⋊#6923—44no—
91C2×#92420—22no—
92C2×#92420—22no—
93C4⋊#6923—22no—
94C4⋊#6923—22no—
95C4⋊#6923—44no—
96C4×#6923—22no—
97C4×#6923—22no—
98C4×#6923—21no—
99C4×#6923—21no—
100C4×#6923—42no—
101C4×#6923—41no—
102C4×#6923—41no—
103C4×#6923D812yes—
104C4×#6923SD1612yes—
105D61⋊C8—42no—
106D61⋊C8—41no—
107D61⋊C8—41no—
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C4⋊C4×C61C4211yescharacteristic
111C22⋊C4×C61—21no—
112C42×C61C22×C411yescharacteristic
113C22⋊Dic61—21no—
114#11758198—21no—
115#11758198—21no—
116C4⋊Dic61C4211yescharacteristic
117#11758196—21no—
118C4×Dic61C22×C411yescharacteristic
119C4×Dic61#4111yescharacteristic
120C4×Dic61#4111yescharacteristic
121C2×#92418—21no—
122C2×#92418—21no—
123C8×D61—42no—
124C8×D61—41no—
125C8×D61—41no—
126C23×C61—21no—
127C22×D61—21no—
128C22×D61—42no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—42no—
132C22×D61C2×C22⋊C411yescharacteristic
133C2×#6923—22no—
134C2×#6923—22no—
135C2×#6923—22no—
136C2×#6923—22no—
137C2×#6923—22no—
138C2×#6923—42no—
139C2×#6923—42no—
140C2×#6923—42no—
141C2×#6923#10214yes—
142D4×C61—21no—
143D4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61C2×C4211yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C22⋊D61—42no—
151C2×Dic61—21no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61#11711yescharacteristic
155C2×Dic61C4×D411yescharacteristic
156C2×Dic61C4×D411yescharacteristic
157D244—21no—
158D244—21no—
159C4×D61—22no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C4×D61#13112yes—
167C4×D61#13112yes—
168C4×D61C2×D811yescharacteristic
169C4×D61C2×SD1611yescharacteristic
170C4×D61#13511yescharacteristic
171C4×D61#13511yescharacteristic
172#92420—42no—
173#92420—42no—
174C8×C61—41no—
175C8×C61—41no—
176#92418—41no—
177#92418—41no—
178#8183—611nomaximal, Sylow
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61C4×C22⋊C411yescharacteristic
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—82no—
187C2×D61—82no—
188C2×D61#40812yes—
189C2×D61C2×#10211yescharacteristic
190C2×D61#41611yescharacteristic
191C2×D61#42112yes—
192#6923—24no—
193#6923—42no—
194#6923—82no—
195C4×C61—21no—
196C4×C61—41no—
197C4×C61#40511yescharacteristic
198C4×C61#40511yescharacteristic
199C4×C61C4×D811yescharacteristic
200C4×C61C4×SD1611yescharacteristic
201Dic61—21no—
202Dic61—41no—
203Dic61#43312yes—
204Dic61C4×D811yescharacteristic
205Dic61C4×SD1611yescharacteristic
206#2293—611no—
207C4×C4⋊C8—611no—
208#1744—611no—
209C2×D4⋊C8—611no—
210C2×D4⋊C8—611no—
211#1279—611no—
212#1279—611no—
213C2×C61—81no—
214C2×C61#175011yescharacteristic
215C2×C61#175911yescharacteristic
216C2×C61C4×#10211yescharacteristic
217D61—81no—
218D61#148012yes—
219D61#148212yes—
220C2×C4×D4—611no—
221C2×#117—1221no—
222C2×C4⋊C8—611no—
223C2×C4⋊C8—611no—
224C2×C4×C8—611no—
225C2×C4×C8—611no—
226C2×C4×C8—1221no—
227#390—612no—
228#389—612no—
229#388—1222no—
230C4×C4⋊C4—611no—
231C4×C22⋊C4—1221no—
232C43—611no—
233#336—1222no—
234#336—1221no—
235D4⋊C8—612no—
236D4⋊C8—612no—
237D4⋊C8—611no—
238D4⋊C8—611no—
239D4⋊C8—611no—
240D4⋊C8#692311yescharacteristic, complemented
241C61#818311yescharacteristic, complemented, Sylow
242C22×D4—611no—
243C23×C4—1221no—
244C22×C8—1221no—
245C22×C8—1221no—
246C22×C8—1221no—
247C22×C8—1221no—
248C4×D4—611no—
249C4×D4—611no—
250C4×D4—611no—
251C4×D4—1221no—
252C4×D4—1221no—
253C4×D4C2×#692311yescharacteristic
254#117—2442no—
255#117—2442no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—612no—
258C2×C4⋊C4—1222no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1222no—
261C2×C22⋊C4—1222no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—612no—
265C2×C42—611no—
266C2×C42—612no—
267C2×C42—1221no—
268C4⋊C8—612no—
269C4⋊C8—611no—
270C4⋊C8—1221no—
271C4⋊C8—1221no—
272C4⋊C8C2×#692311yescharacteristic
273C4×C8—612no—
274C4×C8—611no—
275C4×C8—1221no—
276C4×C8—1221no—
277C4×C8—2442no—
278C4×C8C2×#692311yescharacteristic
279#95—1222no—
280#95—1221no—
281C24—1221no—
282C2×D4—611no—
283C2×D4—1222no—
284C2×D4—1222no—
285C2×D4—1221no—
286C2×D4C4×#692311yescharacteristic
287C22×C4—21no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—612no—
291C22×C4—611no—
292C22×C4—612no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1222no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—1222no—
305C2×C8—1222no—
306C2×C8—1221no—
307C2×C8—1221no—
308C2×C8—2441no—
309C2×C8—2441no—
310C2×C8—2442no—
311C2×C8—2441no—
312C2×C8—2441no—
313C2×C8—2442no—
314C4⋊C4—611no—
315C4⋊C4—1221no—
316C4⋊C4—1222no—
317C4⋊C4—1222no—
318C4⋊C4—2444no—
319C4⋊C4C4×#692311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—2444no—
325C22⋊C4—2444no—
326C42—612no—
327C42—612no—
328C42—611no—
329C42—611no—
330C42—611no—
331C42—1222no—
332C42—1222no—
333C42—1221no—
334C42—1221no—
335C42—2441no—
336C42—2441no—
337C42—2442no—
338C42C22×#692311yescharacteristic
339C23—21no—
340C23—611no—
341C23—1221no—
342C23—2441no—
343C23—2442no—
344C23—2441no—
345C23—2442no—
346D4—21no—
347D4—21no—
348D4—1221no—
349D4—1221no—
350D4—2442no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—612no—
357C2×C4—612no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—614no—
363C2×C4—611no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—1222no—
367C2×C4—1222no—
368C2×C4—1222no—
369C2×C4—1222no—
370C2×C4—1221no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2442no—
378C2×C4—2442no—
379C2×C4—2442no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4C2×C4×#692311yescharacteristic
383C2×C4D4×#692311yescharacteristic
384C2×C4D4×#692311yescharacteristic
385C8—41no—
386C8—41no—
387C8—2441no—
388C8—2442no—
389C8—2442no—
390C8—2441no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—612no—
395C22—612no—
396C22—611no—
397C22—611no—
398C22—4882no—
399C22—4882no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22C22⋊C4×#692311yescharacteristic
404C4—21no—
405C4—41no—
406C4—612no—
407C4—611no—
408C4—611no—
409C4—1224no—
410C4—1221no—
411C4—4882no—
412C4—2442no—
413C4—2441no—
414C4#1684072511yescharacteristic
415C4#1684072811yescharacteristic
416C4D8×#692311yescharacteristic
417C4SD16×#692311yescharacteristic
418C2—81no—
419C2—612no—
420C2—612no—
421C2—4881no—
422C2#2146155011yescharacteristic
423C2#2146158411yescharacteristic
424C2#102×#692311yescharacteristic
subgroupG/H
centerC2×C4D4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×D4⋊C8C4
socleC22×C61C4×C22⋊C4
prime radicalC2×D4×D61C2×C4
cosocleC42×D61C23
hypercenterD4⋊C8#6923
hypocenterC61#8183
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×#6923C2semidirect
3. #21461532C2semidirect
5. #21460654C2semidirect
6. #21460653C2semidirect
20. #16840610C4semidirect
21. D4⋊#92420C4semidirect
25. #16839491C4semidirect
26. D4⋊#92418C4semidirect
27. #16839489C4semidirect
28. C61×D4⋊C8C4semidirect
240. D4⋊C8#6923semidirect
241. C61#8183semidirect

Maximal subgroups

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

subgroupindex
#214622762
C4⋊C8×#69232
#214615322
D61⋊(D4⋊C8)2
#214606542
#214606532
D4⋊C8×D612
#818361