Finite Group Databasebeta

← #30601646

Subgroups — #30601646

Order 15616.

936 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#21461673C211yesmaximal, characteristic, complemented
2C4×C22⋊#92420C211yesmaximal, characteristic, complemented
3C2×#16840606C214yesmaximal, complemented
4C2×#16839663C211yesmaximal, characteristic
5C2×C4⋊#92420—21no—
6C2×C22⋊#92420C2212yes—
7C2×C22⋊#92420C2212yes—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628—21no—
11#16840606—28no—
12C23×D244C411yescharacteristic
13C22×#11758198C412yes—
14C22×#11758198C2212yes—
15C22×C4×Dic61C2211yescharacteristic
16#16839663—21no—
17#16839663—21no—
18#16839663—21no—
19#16839663—21no—
20C22×C4⋊C4×C61C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23C4⋊#92420—42no—
24C22⋊#92420—22no—
25C22⋊#92420—24no—
26C22⋊#92420D414yescomplemented
27C4×#92420—42no—
28C24×D61C2×C412yes—
29C22×D244—21no—
30C22×D244—21no—
31C22×D244—22no—
32C22×D244—42no—
33C22×D244—42no—
34C22×D244C814yescomplemented
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61C2311yescharacteristic
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198—24no—
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×#11758198—24no—
43C2×#11758198—44no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C23×C4×C61C2×C412yes—
50C23×C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—42no—
54C24×C61C22×C411yescharacteristic
55C23×D61—22no—
56C23×D61—22no—
57C23×D61—24no—
58C23×D61—24no—
59C23×D61—42no—
60C23×D61—42no—
61C23×D61—42no—
62C23×D61—42no—
63C23×D61C2×C814yes—
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—24no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C2×C812yes—
73C22×C4×C61M1612yes—
74C22×Dic61—22no—
75C22×Dic61—22no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D412yes—
84C22×Dic61#4112yes—
85C2×D244—24no—
86C2×D244—24no—
87C2×D244—42no—
88C2×D244—42no—
89C2×D244—48no—
90C2×D244—42no—
91C2×D244—42no—
92C2×D244—48no—
93C2×#92420—24no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61—42no—
101#11758198—44no—
102#11758198—44no—
103#11758198—44no—
104#11758198—42no—
105#11758198—42no—
106C4×Dic61—22no—
107C4×Dic61—22no—
108C4×Dic61—41no—
109C4×Dic61—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61C2×C22⋊C411yescharacteristic
115C23×C61C4×D412yes—
116C23×C61C22×C811yescharacteristic
117C23×C61C2×M1611yescharacteristic
118C23×C61#13112yes—
119C22×D61—24no—
120C22×D61—28no—
121C22×D61—44no—
122C22×D61—44no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61—42no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—44no—
130C22×D61—44no—
131C22×D61—44no—
132C22×D61—84no—
133C22×D61—84no—
134C22×D61—84no—
135C22×D61—84no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—24no—
139C2×C4×C61—24no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—84no—
144C2×C4×C61C22⋊C812yes—
145C2×C4×C61C22⋊C812yes—
146C2×C4×C61#9912yes—
147C2×C4×C61#10012yes—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—44no—
160C2×Dic61#10012yes—
161C2×Dic61#12112yes—
162C2×Dic61#12411yescharacteristic
163C2×Dic61#12711yescharacteristic
164D244—48no—
165D244—48no—
166#92420—44no—
167#92420—82no—
168#9649—611nomaximal, Sylow
169C22×C61—22no—
170C22×C61—22no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61#39011yescharacteristic
178C22×C61C2×C22⋊C811yescharacteristic
179C22×C61#40811yescharacteristic
180C22×C61C2×#9911yescharacteristic
181C22×C61#41011yescharacteristic
182C22×C61C2×#10011yescharacteristic
183C22×C61C2×#10011yescharacteristic
184C22×C61C8×D412yes—
185C22×C61#43612yes—
186C2×D61—44no—
187C2×D61—44no—
188C2×D61—44no—
189C2×D61—88no—
190C2×D61—82no—
191C2×D61—82no—
192C2×D61—82no—
193C2×D61—82no—
194C2×D61—88no—
195C4×C61—22no—
196C4×C61—82no—
197C4×C61#32314yescomplemented
198Dic61—22no—
199Dic61—21no—
200Dic61—21no—
201Dic61—22no—
202Dic61—41no—
203C2×#390—611no—
204#1797—611no—
205C4×C22⋊C8—611no—
206C2×#323—614no—
207C2×C61—22no—
208C2×C61—22no—
209C2×C61C2×#32311yescharacteristic
210C2×C61#146011yescharacteristic
211C2×C61#146911yescharacteristic
212C2×C61#147111yescharacteristic
213C2×C61#195411yescharacteristic
214C2×C61#196411yescharacteristic
215C2×C61#196511yescharacteristic
216D61—84no—
217C23×D4—611no—
218C22×C4⋊C4#692311yescharacteristic
219C22×C22⋊C4—612no—
220C22×C22⋊C4—612no—
221C22×C42—611no—
222C2×C4⋊C8—1221no—
223C2×C22⋊C8—612no—
224C2×C22⋊C8—612no—
225C2×C4×C8—1221no—
226#390—1221no—
227#390—1221no—
228#390—1221no—
229#390—1221no—
230#336—1221no—
231#336—1221no—
232#323—1228no—
233C61#964911yescharacteristic, complemented, Sylow
234C25—612no—
235C22×D4—614no—
236C22×D4—1222no—
237C22×D4—1221no—
238C22×D4—1221no—
239C22×D4—2442no—
240C22×D4—2442no—
241C23×C4—611no—
242C23×C4—611no—
243C23×C4C2×#692312yes—
244C23×C4C2×#692311yescharacteristic
245C22×C8—1222no—
246C22×C8—1222no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—42no—
250C2×C22⋊C4—1224no—
251C2×C22⋊C4—1222no—
252C2×C22⋊C4—1222no—
253C2×C22⋊C4—1222no—
254C2×C22⋊C4—1222no—
255C2×C22⋊C4—1224no—
256C2×C22⋊C4—2444no—
257C2×C42—611no—
258C2×C42—611no—
259C2×C42—611no—
260C2×C42—611no—
261C2×C42—2442no—
262C4⋊C8—2442no—
263C22⋊C8—614no—
264C22⋊C8—1222no—
265C22⋊C8—1224no—
266C4×C8—2442no—
267C24—614no—
268C24—1224no—
269C24—1224no—
270C24—1222no—
271C24—1222no—
272C24—2442no—
273C24—2442no—
274C24—2442no—
275C24—2442no—
276C24C22×#692311yescharacteristic
277C2×D4—1224no—
278C2×D4—1224no—
279C2×D4—2442no—
280C2×D4—2442no—
281C2×D4—2448no—
282C2×D4—2448no—
283C2×D4—2442no—
284C2×D4—2442no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—612no—
295C22×C4—612no—
296C22×C4—611no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4D61⋊C812yes—
303C22×C4#1175821312yes—
304C22×C4C22⋊#692311yescharacteristic
305C22×C4C22⋊#692311yescharacteristic
306C2×C8—1224no—
307C2×C8—2442no—
308C2×C8—2442no—
309C2×C8—2442no—
310C2×C8—2442no—
311C2×C8—2442no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C22⋊C4—2444no—
315C22⋊C4—2442no—
316C22⋊C4—2442no—
317C22⋊C4—2444no—
318C22⋊C4—2444no—
319C42—1222no—
320C42—1222no—
321C42—2441no—
322C42—2441no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—1228no—
328C23—1224no—
329C23—4884no—
330C23—4884no—
331C23—4884no—
332C23—4884no—
333C23—2444no—
334C23—2444no—
335C23—2444no—
336C23—2444no—
337C23—2442no—
338C23—2442no—
339C23—2442no—
340C23—2442no—
341C23—2442no—
342C23—2442no—
343C23—2444no—
344C23C2×C22⋊#692311yescharacteristic
345C23D4×#692312yes—
346C23C2×D61⋊C811yescharacteristic
347C23C2×#1175821311yescharacteristic
348C23#1451986512yes—
349D4—2448no—
350D4—2448no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—84no—
359C2×C4—612no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—612no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—2442no—
373C2×C4—2442no—
374C2×C4—2444no—
375C2×C4#1451983412yes—
376C2×C4#1451983412yes—
377C2×C4#1451983612yes—
378C2×C4#1451983712yes—
379C8—4882no—
380C8—2444no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—4888no—
390C22—4888no—
391C22—4882no—
392C22—4882no—
393C22—4882no—
394C22—4882no—
395C22—2444no—
396C22—2444no—
397C22—2444no—
398C22#1684071411yescharacteristic
399C22C2×#1451983411yescharacteristic
400C22#1684073711yescharacteristic
401C22C2×#1451983611yescharacteristic
402C22#1684074311yescharacteristic
403C22C2×#1451983711yescharacteristic
404C22D61⋊#10011yescharacteristic
405C22#1684079012yes—
406C22#1684079612yes—
407C4—22no—
408C4—82no—
409C4—1222no—
410C4—1221no—
411C4—1222no—
412C4—1221no—
413C4—2441no—
414C4#1684060614yescomplemented
415C2—22no—
416C2—22no—
417C2—4884no—
418C2C2×#1684060611yescharacteristic
419C2#2146106011yescharacteristic
420C2#2146109011yescharacteristic
421C2#2146109611yescharacteristic
422C2#2146194111yescharacteristic
423C2#2146195911yescharacteristic
424C2#2146196111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#9649
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461673C2semidirect
2. C4×C22⋊#92420C2semidirect
3. C2×#16840606C2semidirect
26. C22⋊#92420D4semidirect
34. C22×D244C8semidirect
197. C4×C61#323semidirect
233. C61#9649semidirect
414. C4#16840606semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
C2×#168406062
C2×#168396632
#964961