Finite Group Databasebeta

← #30595352

Subgroups — #30595352

Order 15616.

680 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
1C4×C22⋊#92420C211yesmaximal, characteristic, complemented
2C2×#16840628C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21448325C211yesmaximal, characteristic
6C23×#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519751C411yescharacteristic
13C2×#14519739C411yescharacteristic
14C2×#14519737—21no—
15C22×C4×Dic61C2211yescharacteristic
16#16839663C2211yescharacteristic
17#16839658C2211yescharacteristic
18#16839651—21no—
19#16839639—21no—
20C4⋊C4×Dic61C411yescharacteristic
21#16839609—21no—
22C61×#380C411yescharacteristic
23C22×#92420—24no—
24C22×#92420—22no—
25C22×#92420—22no—
26C22×#92420—42no—
27C22×#92420—42no—
28C22⋊#92420—24no—
29C4×#92420—42no—
30C22×D244C2×C411yescharacteristic
31C22×C22⋊D61—21no—
32C23×Dic61D411yescharacteristic
33C23×Dic61D411yescharacteristic
34C22×C4×D61—21no—
35#14519751—22no—
36#14519751C814yescomplemented
37#14519739—42no—
38#14519737—42no—
39#14519737—42no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—42no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52#14519684—21no—
53#14519684—21no—
54C23×C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58#95×C61—21no—
59C24×C61C22⋊C411yescharacteristic
60C23×D61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C2×C812yes—
67C22×C4×C61M1612yes—
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—24no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61—42no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—21no—
76C22×Dic61—22no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61D812yes—
81C22×Dic61SD1612yes—
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C2×D244—21no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244C2×C812yescomplemented
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C2×C4×D61—42no—
91C2×#92420—24no—
92C2×#92420—24no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—48no—
96C2×#92420—42no—
97C2×#92420—42no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C22⋊C4×C61—42no—
101#11758198—24no—
102#11758198—42no—
103#11758198—41no—
104#11758198—41no—
105#11758198—42no—
106C4⋊Dic61—21no—
107C4⋊Dic61C2×C812yescomplemented
108#11758196—41no—
109#11758196—41no—
110C4×Dic61—22no—
111C4×Dic61—22no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C4×Dic61—42no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61C22⋊C812yes—
120C23×C61#10212yes—
121C23×C61#10412yes—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—22no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61C22⋊C812yes—
143C2×C4×C61C22×C811yescharacteristic
144C2×C4×C61C2×M1611yescharacteristic
145C22⋊D61—48no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—24no—
151C2×Dic61—24no—
152C2×Dic61—22no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—44no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61#9912yes—
160C2×Dic61#10212yes—
161C2×Dic61#10412yes—
162C2×Dic61C2×D811yescharacteristic
163C2×Dic61C2×SD1611yescharacteristic
164C2×Dic61#13512yes—
165D244—42no—
166D244—42no—
167C4×D61—84no—
168#92420—44no—
169#92420—44no—
170#7565—611nomaximal, Sylow
171C22×C61—22no—
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61D4⋊C814yes—
178C22×C61C2×C22⋊C811yescharacteristic
179C22×C61C2×#9911yescharacteristic
180C22×C61#41311yescharacteristic
181C22×C61C2×#10211yescharacteristic
182C22×C61#41611yescharacteristic
183C22×C61C2×#10411yescharacteristic
184C22×C61C2×#10411yescharacteristic
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—22no—
195C4×C61—81no—
196C4×C61—81no—
197Dic61—21no—
198Dic61—21no—
199Dic61—22no—
200Dic61—42no—
201Dic61—41no—
202Dic61#32714yes—
203C4×#121—611no—
204C4×C22⋊C8—611no—
205C2×#336—611no—
206#1271—612no—
207#1270—612no—
208C2×C61—24no—
209C2×C61#145911yescharacteristic
210C2×C61C2×D4⋊C811yescharacteristic
211C2×C61#147611yescharacteristic
212C2×C61C2×#32711yescharacteristic
213C2×C61#150111yescharacteristic
214C2×C61#152411yescharacteristic
215C2×C61#154011yescharacteristic
216D61—82no—
217C23×C8—1221no—
218C2×#121—611no—
219C2×C4×D4—611no—
220C2×C4×D4—1221no—
221C22×C42—611no—
222C2×C22⋊C8—1221no—
223C2×C4×C8—1221no—
224#390—611no—
225#389—611no—
226#388—1221no—
227#386—1221no—
228#380#692311yescharacteristic
229C4×C4⋊C4—611no—
230C4×C22⋊C4—1221no—
231#336—612no—
232#336—612no—
233#336—1221no—
234C61#756511yescharacteristic, complemented, Sylow
235C22×D4—611no—
236C22×D4—1221no—
237C23×C4—611no—
238C23×C4—611no—
239C23×C4—1221no—
240C23×C4C2×#692311yescharacteristic
241C22×C8—1222no—
242C22×C8—1222no—
243C22×C8—1224no—
244C22×C8—2442no—
245C22×C8—2442no—
246#121—614no—
247#121—1222no—
248C4×D4—2442no—
249C4×D4—2442no—
250C4×D4—2442no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4C2×#692311yescharacteristic
254C2×C4⋊C4C2×#692311yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C42—611no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—1221no—
265C2×C42—2442no—
266C22⋊C8—1224no—
267C4×C8—2442no—
268#95—21no—
269#95—1221no—
270#95—1221no—
271C24—1221no—
272C24C22⋊#692311yescharacteristic
273C2×D4—612no—
274C2×D4—1224no—
275C2×D4—1221no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2442no—
279C2×D4—2442no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—611no—
285C22×C4—612no—
286C22×C4—612no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—1222no—
291C22×C4—1222no—
292C22×C4—1222no—
293C22×C4—1222no—
294C22×C4—1221no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4—2442no—
298C22×C4—2441no—
299C22×C4D61⋊C812yes—
300C22×C4#1175821312yes—
301C22×C4C22⋊#692311yescharacteristic
302C22×C4C22×#692311yescharacteristic
303C2×C8—1224no—
304C2×C8—1224no—
305C2×C8—2442no—
306C2×C8—2442no—
307C2×C8—2442no—
308C2×C8—2448no—
309C2×C8—2442no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—612no—
313C4⋊C4—1221no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C22⋊C4—42no—
317C22⋊C4—1224no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2442no—
321C22⋊C4—2442no—
322C42—1222no—
323C42—1222no—
324C42—2441no—
325C42—2441no—
326C42—2442no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—1222no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23#1451983412yes—
339C23#1451983912yes—
340C23#1451984212yes—
341C23C2×C22⋊#692311yescharacteristic
342D4—2442no—
343D4—2442no—
344D4—2448no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—612no—
358C2×C4—612no—
359C2×C4—612no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—612no—
363C2×C4—1224no—
364C2×C4—1224no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1222no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—4884no—
374C2×C4—2444no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4#1451983412yes—
378C2×C4C2×D61⋊C811yescharacteristic
379C2×C4C2×#1175821311yescharacteristic
380C8—2444no—
381C8—2444no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—4881no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22—2442no—
393C22—2442no—
394C22—2442no—
395C22#1684061014yes—
396C22C2×#1451983411yescharacteristic
397C22D61⋊#9911yescharacteristic
398C22#1684074911yescharacteristic
399C22C2×#1451983911yescharacteristic
400C22#1684075211yescharacteristic
401C22D61⋊#10411yescharacteristic
402C22C2×#1451984211yescharacteristic
403C4—22no—
404C4—21no—
405C4—21no—
406C4—81no—
407C4—81no—
408C4—614no—
409C4—1221no—
410C4—1221no—
411C4—1222no—
412C4—2442no—
413C4—2441no—
414C2—24no—
415C2—4882no—
416C2#2146105711yescharacteristic
417C2C2×#1684061011yescharacteristic
418C2#2146111211yescharacteristic
419C2D61⋊#32711yescharacteristic
420C2#2146119711yescharacteristic
421C2#2146127211yescharacteristic
422C2#2146131711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7565
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C4×C22⋊#92420C2semidirect
2. C2×#16840628C2semidirect
3. #21460638C2semidirect
4. #21460636C2semidirect
36. #14519751C8semidirect
87. C2×D244C2×C8semidirect
107. C4⋊Dic61C2×C8semidirect
234. C61#7565semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#924202
C2×#168406282
#214606382
#214606362
#214483252
#756561