Finite Group Databasebeta

← #30600179

Subgroups — #30600179

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758217C211yesmaximal, characteristic, complemented
2#21461673C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448325C211yesmaximal, characteristic
6C22×#11758217—21no—
7C2×C4⋊#92420C2212yes—
8C2×C22⋊#92420—21no—
9C4×#11758217—24no—
10C2×#14519832—21no—
11C2×C4×#92420C2212yes—
12#16840628—21no—
13#16840610—24no—
14C2×#14519751C411yescharacteristic
15C2×#14519739C2211yescharacteristic
16C2×#14519737—21no—
17C22×C4×Dic61C2211yescharacteristic
18#16839663C411yescharacteristic
19#16839658C411yescharacteristic
20#16839651—21no—
21#16839639—21no—
22C4⋊C4×Dic61C2211yescharacteristic
23#16839609—21no—
24C61×#380C411yescharacteristic
25C2×#11758217—24no—
26C2×#11758217—24no—
27C2×#11758217—24no—
28C22×#92420—22no—
29C22×#92420—22no—
30C4⋊#92420—22no—
31C4⋊#92420—22no—
32C22⋊#92420—42no—
33#14519832—24no—
34C4×#92420—22no—
35C4×#92420D414yescomplemented
36C22×D244C2×C411yescharacteristic
37C22×C22⋊D61—21no—
38C23×Dic61D411yescharacteristic
39C23×Dic61D411yescharacteristic
40C22×C4×D61—21no—
41#14519751—22no—
42#14519751—22no—
43#14519739—22no—
44#14519739—22no—
45#14519737—44no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×#11758196—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×C4×Dic61—22no—
53C2×C4×Dic61—22no—
54C2×C4×Dic61—21no—
55C2×C4×Dic61C2×C411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61C2311yescharacteristic
59#14519684—21no—
60#14519684—21no—
61C23×C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C22⋊C4×C61—21no—
65#95×C61—21no—
66C24×C61C22⋊C411yescharacteristic
67C23×D61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—22no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C2×C22⋊D61—24no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—22no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—21no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92C2×D244—22no—
93C2×D244—22no—
94C2×D244—21no—
95C2×D244M1612yescomplemented
96C2×C4×D61—42no—
97C2×C4×D61—41no—
98C2×C4×D61—42no—
99C2×C4×D61—41no—
100#11758217—216no—
101C2×#92420—24no—
102C2×#92420—24no—
103C2×#92420—24no—
104C2×#92420—42no—
105C2×#92420—42no—
106C2×#92420—42no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—22no—
109C22⋊C4×C61—42no—
110#11758198—24no—
111#11758198—42no—
112#11758198—42no—
113#11758198—41no—
114#11758198—41no—
115C4⋊Dic61—21no—
116C4⋊Dic61M1612yescomplemented
117#11758196—42no—
118C4×Dic61—22no—
119C4×Dic61—21no—
120C4×Dic61—22no—
121C4×Dic61—21no—
122C4×Dic61—42no—
123C4×Dic61C2×D412yes—
124C4×Dic61#4112yes—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61#10412yes—
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—22no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61C4×D412yes—
152C2×C4×C61C2×M1611yescharacteristic
153C2×C4×C61C2×M1611yescharacteristic
154C2×C4×C61#13112yes—
155C22⋊D61—48no—
156C2×Dic61—24no—
157C2×Dic61—24no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—22no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61#10412yes—
171C2×Dic61#12011yescharacteristic
172C2×Dic61#12112yes—
173C2×Dic61#12311yescharacteristic
174C2×Dic61AGL(1,ℤ/8)12yes—
175C2×Dic61AGL(1,ℤ/8)11yescharacteristic
176C2×Dic61#13711yescharacteristic
177D244—24no—
178D244—42no—
179C4×D61—82no—
180C4×D61—82no—
181#92420—28no—
182#92420—82no—
183#9078—611nomaximal, Sylow
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61#38611yescharacteristic
192C22×C61#40711yescharacteristic
193C22×C61#40811yescharacteristic
194C22×C61#41711yescharacteristic
195C22×C61#41811yescharacteristic
196C22×C61C2×#10411yescharacteristic
197C22×C61C2×#10411yescharacteristic
198C2×D61—42no—
199C2×D61—42no—
200C2×D61—42no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C4×C61—41no—
206C4×C61—81no—
207C4×C61—81no—
208C4×C61#43512yes—
209C4×C61#43612yes—
210Dic61—21no—
211Dic61—22no—
212Dic61—21no—
213Dic61—41no—
214Dic61—42no—
215Dic61#46812yes—
216Dic61#46912yes—
217C2×C4×M16—611no—
218C4×#121—611no—
219#1797—611no—
220C2×D4⋊C8—612no—
221#1279—612no—
222C2×C61—42no—
223C2×C61#148311yescharacteristic
224C2×C61#148411yescharacteristic
225C2×C61#148911yescharacteristic
226C2×C61#149011yescharacteristic
227C2×C61#187011yescharacteristic
228C2×C61#189511yescharacteristic
229C2×C61#189611yescharacteristic
230D61—82no—
231C22×M16—1221no—
232C2×#121—611no—
233C2×C4×D4—611no—
234C2×C4×D4—1221no—
235C22×C42—611no—
236C2×C4⋊C8—612no—
237C2×C22⋊C8—1221no—
238C4×M16—1224no—
239C2×#97—1221no—
240C2×C4×C8—612no—
241#390—611no—
242#389—611no—
243#388—1221no—
244#386—1221no—
245#380#692311yescharacteristic
246C4×C4⋊C4—611no—
247C4×C22⋊C4—1221no—
248#336—1221no—
249D4⋊C8—1224no—
250C61#907811yescharacteristic, complemented, Sylow
251C22×D4—611no—
252C22×D4—1221no—
253C23×C4—611no—
254C23×C4—611no—
255C23×C4—1221no—
256C23×C4C2×#692311yescharacteristic
257C2×M16—1224no—
258C2×M16—1224no—
259C2×M16—1224no—
260C22×C8—1222no—
261C22×C8—1222no—
262#121—1222no—
263#121—1222no—
264C4×D4—1222no—
265C4×D4—1222no—
266C4×D4—2444no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4C2×#692311yescharacteristic
270C2×C4⋊C4C2×#692311yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C42—611no—
277C2×C42—611no—
278C2×C42—611no—
279C2×C42—611no—
280C2×C42—1222no—
281C2×C42—1222no—
282C2×C42—1221no—
283C4⋊C8—1222no—
284C4⋊C8—1222no—
285C22⋊C8—2442no—
286#97—1224no—
287C4×C8—614no—
288C4×C8—1222no—
289#95—21no—
290#95—1221no—
291#95—1221no—
292C24—1221no—
293C24C22⋊#692311yescharacteristic
294C2×D4—612no—
295C2×D4—1224no—
296C2×D4—1222no—
297C2×D4—1221no—
298C2×D4—1222no—
299C2×D4—2442no—
300C2×D4—2442no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1222no—
314C22×C4—1221no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1221no—
318C22×C4—1222no—
319C22×C4—1221no—
320C22×C4—2442no—
321C22×C4—2442no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4C22⋊#692311yescharacteristic
325C22×C4C22×#692311yescharacteristic
326M16—12216no—
327C2×C8—1224no—
328C2×C8—1224no—
329C2×C8—1224no—
330C2×C8—2442no—
331C2×C8—2442no—
332C2×C8—2442no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—612no—
336C4⋊C4—1221no—
337C4⋊C4—2442no—
338C22⋊C4—42no—
339C22⋊C4—1224no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2442no—
343C22⋊C4—2442no—
344C42—612no—
345C42—612no—
346C42—1221no—
347C42—1222no—
348C42—1221no—
349C42—1222no—
350C42—2442no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—1222no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23#1451984212yes—
365C23C2×C22⋊#692311yescharacteristic
366D4—1224no—
367D4—2448no—
368D4—2442no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—612no—
381C2×C4—611no—
382C2×C4—611no—
383C2×C4—612no—
384C2×C4—611no—
385C2×C4—611no—
386C2×C4—612no—
387C2×C4—1224no—
388C2×C4—1224no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1222no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—4882no—
398C2×C4—4882no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4D4×#692312yes—
404C2×C4D61⋊M1611yescharacteristic
405C2×C4D61⋊M1611yescharacteristic
406C2×C4#1451986412yes—
407C8—1228no—
408C8—4882no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—4881no—
417C22—4881no—
418C22—4881no—
419C22—4881no—
420C22—2442no—
421C22—2442no—
422C22—2442no—
423C22#1684071011yescharacteristic
424C22#1684073411yescharacteristic
425C22#1684073511yescharacteristic
426C22#1684075311yescharacteristic
427C22#1684075411yescharacteristic
428C22D61⋊#10411yescharacteristic
429C22C2×#1451984211yescharacteristic
430C4—41no—
431C4—81no—
432C4—81no—
433C4—612no—
434C4—612no—
435C4—1221no—
436C4—1222no—
437C4—1221no—
438C4—2441no—
439C4—2442no—
440C4#1684079412yes—
441C4#1684079512yes—
442C2—42no—
443C2—4882no—
444C2#2146113611yescharacteristic
445C2#2146113811yescharacteristic
446C2#2146115611yescharacteristic
447C2#2146116011yescharacteristic
448C2#2146179811yescharacteristic
449C2#2146183511yescharacteristic
450C2#2146183611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#9078
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758217C2semidirect
2. #21461673C2semidirect
3. C2×#16840610C2semidirect
4. #21460655C2semidirect
35. C4×#92420D4semidirect
95. C2×D244M16semidirect
116. C4⋊Dic61M16semidirect
250. C61#9078semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582172
#214616732
C2×#168406102
#214606552
#214483252
#907861