Finite Group Databasebeta

← #30597572

Subgroups — #30597572

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462276C211yesmaximal, characteristic
2#21461606C211yesmaximal, characteristic, complemented
3C4×C8×#6923C211yesmaximal, 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
10C2×#14519831—21no—
11C4×D61⋊C8C2211yescharacteristic
12C2×C8×#6923—22no—
13#16840714C412yes—
14#16840713C412yes—
15#16840712—22no—
16C4×C4⋊#6923C2211yescharacteristic
17C4×C22⋊#6923—21no—
18C42×#6923C2211yescharacteristic
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×#6923D412yes—
40C2×C4×#6923D411yescharacteristic
41C2×C4×#6923D411yescharacteristic
42#14519844—21no—
43C4⋊#92420C2×C412yes—
44#14519831—42no—
45C4×#92420—21no—
46C4×#92420C2×C412yes—
47C8×#6923—28no—
48(C2×#6923)⋊C4—22no—
49(C2×#6923)⋊C4—21no—
50C2×D4×D61C2×C411yescharacteristic
51C22×C4×D61—21no—
52C2×C8×D61—21no—
53C2×C8×D61—21no—
54C4×D244C2×C411yescharacteristic
55D4×Dic61C2×C411yescharacteristic
56#14519739C2×C411yescharacteristic
57C4×C22⋊D61—21no—
58#14519737—21no—
59C4⋊C4×D61C2×C411yescharacteristic
60C22⋊C4×D61—21no—
61C42×D61C2311yescharacteristic
62C4⋊#92418C2×C411yescharacteristic
63#14519706—21no—
64C4×#92418C2×C411yescharacteristic
65C8×Dic61—21no—
66C4×D4×C61C2×C411yescharacteristic
67C4⋊C8×C61C2×C411yescharacteristic
68C4×C8×C61C2×C411yescharacteristic
69C23×D61—21no—
70C22×#6923—22no—
71C22×#6923C22⋊C412yes—
72C22×#6923C22⋊C412yes—
73C2×D4×C61C4211yescharacteristic
74C22×C4×C61—21no—
75C2×C22⋊D61—21no—
76C22×Dic61—21no—
77D4×D61—22no—
78D4×D61—22no—
79C2×D244C4211yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61C22×C411yescharacteristic
88C2×C4×D61C2×D411yescharacteristic
89C2×C4×D61C2×D411yescharacteristic
90C22⋊#6923—44no—
91C22⋊#6923—44no—
92C2×#92420—22no—
93C2×#92420—22no—
94C4⋊#6923—22no—
95C4⋊#6923—22no—
96C4⋊#6923—44no—
97C4×#6923—24no—
98C4×#6923—22no—
99C4×#6923—22no—
100C4×#6923—21no—
101C4×#6923—21no—
102C4×#6923—41no—
103C4×#6923—41no—
104C4×#6923D812yes—
105C4×#6923SD1612yes—
106D61⋊C8—24no—
107D61⋊C8—41no—
108D61⋊C8—41no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C4⋊C4×C61C4211yescharacteristic
112C22⋊C4×C61—21no—
113C42×C61C22×C411yescharacteristic
114C22⋊Dic61—21no—
115#11758198—21no—
116#11758198—21no—
117C4⋊Dic61C4211yescharacteristic
118#11758196—21no—
119C4×Dic61C22×C411yescharacteristic
120C4×Dic61#4111yescharacteristic
121C4×Dic61#4111yescharacteristic
122C2×#92418—21no—
123C2×#92418—21no—
124C8×D61—24no—
125C8×D61—41no—
126C8×D61—41no—
127C23×C61—21no—
128C22×D61—21no—
129C22×D61—42no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—42no—
133C22×D61C2×C22⋊C411yescharacteristic
134C2×#6923—22no—
135C2×#6923—22no—
136C2×#6923—22no—
137C2×#6923—22no—
138C2×#6923—42no—
139C2×#6923—42no—
140C2×#6923—42no—
141C2×#6923#10214yes—
142C2×#6923#10414yes—
143D4×C61—21no—
144D4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61C2×C4211yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61C4×D411yescharacteristic
151C22⋊D61—42no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61#11711yescharacteristic
156C2×Dic61C4×D411yescharacteristic
157C2×Dic61C4×D411yescharacteristic
158D244—21no—
159D244—21no—
160C4×D61—22no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C4×D61—41no—
167C4×D61#13112yes—
168C4×D61#13112yes—
169C4×D61C2×D811yescharacteristic
170C4×D61C2×SD1611yescharacteristic
171C4×D61#13511yescharacteristic
172C4×D61#13511yescharacteristic
173#92420—24no—
174#92420—42no—
175C8×C61—22no—
176C8×C61—41no—
177#92418—22no—
178#92418—41no—
179#8177—611nomaximal, Sylow
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61C4×C22⋊C411yescharacteristic
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—82no—
188C2×D61—82no—
189C2×D61#40812yes—
190C2×D61C2×#10211yescharacteristic
191C2×D61#41611yescharacteristic
192C2×D61C2×#10412yes—
193#6923—24no—
194#6923—24no—
195#6923—82no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61#40511yescharacteristic
199C4×C61#40511yescharacteristic
200C4×C61C4×D811yescharacteristic
201C4×C61C4×SD1611yescharacteristic
202Dic61—21no—
203Dic61—41no—
204Dic61#43312yes—
205Dic61C4×D811yescharacteristic
206Dic61C4×SD1611yescharacteristic
207#2293—611no—
208#1767—611no—
209C42×C8—611no—
210C2×D4⋊C8—611no—
211C2×D4⋊C8—611no—
212#1279—611no—
213#1279—611no—
214C2×C61—81no—
215C2×C61#175011yescharacteristic
216C2×C61C4×#10411yescharacteristic
217C2×C61C4×#10211yescharacteristic
218D61—81no—
219D61#149212yes—
220D61#149412yes—
221C2×C4×D4—611no—
222C2×#117—1221no—
223C2×C4⋊C8—611no—
224C2×C4⋊C8—611no—
225C2×#97—1221no—
226C2×C4×C8—611no—
227C2×C4×C8—611no—
228C2×C4×C8—1222no—
229#390—612no—
230#389—612no—
231#388—1222no—
232C4×C4⋊C4—611no—
233C4×C22⋊C4—1221no—
234C43—611no—
235#336—1221no—
236D4⋊C8—612no—
237D4⋊C8—612no—
238D4⋊C8—611no—
239D4⋊C8—611no—
240D4⋊C8—611no—
241D4⋊C8#692311yescharacteristic, complemented
242C61#817711yescharacteristic, complemented, Sylow
243C22×D4—611no—
244C23×C4—1221no—
245C22×C8—1221no—
246C22×C8—1221no—
247C22×C8—1221no—
248C22×C8—1221no—
249C4×D4—611no—
250C4×D4—611no—
251C4×D4—611no—
252C4×D4—1221no—
253C4×D4—1221no—
254C4×D4C2×#692311yescharacteristic
255#117—2442no—
256#117—2442no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—612no—
259C2×C4⋊C4—1222no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1222no—
262C2×C22⋊C4—1222no—
263C2×C42—611no—
264C2×C42—611no—
265C2×C42—612no—
266C2×C42—611no—
267C2×C42—612no—
268C2×C42—1221no—
269C4⋊C8—612no—
270C4⋊C8—611no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8C2×#692311yescharacteristic
274#97—2442no—
275C4×C8—612no—
276C4×C8—611no—
277C4×C8—1221no—
278C4×C8—1221no—
279C4×C8—1228no—
280C4×C8C2×#692311yescharacteristic
281#95—1222no—
282#95—1221no—
283C24—1221no—
284C2×D4—611no—
285C2×D4—1222no—
286C2×D4—1222no—
287C2×D4—1221no—
288C2×D4C4×#692311yescharacteristic
289C22×C4—21no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—611no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1222no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4—2441no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—1224no—
307C2×C8—1222no—
308C2×C8—1224no—
309C2×C8—1221no—
310C2×C8—1222no—
311C2×C8—1221no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C4⋊C4—611no—
317C4⋊C4—1221no—
318C4⋊C4—1222no—
319C4⋊C4—1222no—
320C4⋊C4—2444no—
321C4⋊C4C4×#692311yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—2444no—
327C22⋊C4—2444no—
328C42—612no—
329C42—612no—
330C42—611no—
331C42—611no—
332C42—611no—
333C42—1224no—
334C42—1222no—
335C42—1222no—
336C42—1221no—
337C42—1221no—
338C42—2441no—
339C42—2441no—
340C42C22×#692311yescharacteristic
341C23—21no—
342C23—611no—
343C23—1221no—
344C23—2441no—
345C23—2442no—
346C23—2441no—
347C23—2442no—
348D4—21no—
349D4—21no—
350D4—1221no—
351D4—1221no—
352D4—2442no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—612no—
359C2×C4—612no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—614no—
365C2×C4—614no—
366C2×C4—611no—
367C2×C4—1222no—
368C2×C4—1222no—
369C2×C4—1222no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—1221no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4C2×C4×#692311yescharacteristic
385C2×C4D4×#692311yescharacteristic
386C2×C4D4×#692311yescharacteristic
387C8—22no—
388C8—41no—
389C8—1222no—
390C8—1224no—
391C8—2442no—
392C8—2441no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—612no—
397C22—612no—
398C22—611no—
399C22—611no—
400C22—4882no—
401C22—4882no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22C22⋊C4×#692311yescharacteristic
406C4—21no—
407C4—41no—
408C4—612no—
409C4—611no—
410C4—611no—
411C4—1224no—
412C4—1224no—
413C4—1221no—
414C4—4882no—
415C4—2441no—
416C4#1684072511yescharacteristic
417C4#1684072811yescharacteristic
418C4D8×#692311yescharacteristic
419C4SD16×#692311yescharacteristic
420C2—81no—
421C2—612no—
422C2—612no—
423C2—4881no—
424C2#2146155011yescharacteristic
425C2#104×#692311yescharacteristic
426C2#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#8177
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. #21461606C2semidirect
3. C4×C8×#6923C2semidirect
5. #21460654C2semidirect
6. #21460653C2semidirect
20. #16840610C4semidirect
21. D4⋊#92420C4semidirect
25. #16839491C4semidirect
26. D4⋊#92418C4semidirect
27. #16839489C4semidirect
28. C61×D4⋊C8C4semidirect
241. D4⋊C8#6923semidirect
242. C61#8177semidirect

Maximal subgroups

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

subgroupindex
#214622762
#214616062
C4×C8×#69232
D61⋊(D4⋊C8)2
#214606542
#214606532
D4⋊C8×D612
#817761