Finite Group Databasebeta

← #30603139

Subgroups — #30603139

Order 15616.

1446 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1446 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519838C212yesmaximal, complemented
2C22×#14519837C212yesmaximal
3#21461482C212yesmaximal, complemented
4C22×#14519763C211yesmaximal, characteristic
5C22×#11758217C2214yes—
6C2×#14519838—28no—
7C2×#14519838—24no—
8C2×#14519837—28no—
9C2×#14519837—24no—
10#16840628—24no—
11C23×Dic122C2211yescharacteristic
12C23×C22⋊D61C2211yescharacteristic
13C2×#14519763—24no—
14C2×#14519763—24no—
15C2×#14519763—24no—
16C22×C22⋊Dic61C411yescharacteristic
17C22×#11758198C411yescharacteristic
18C22×#11758198C411yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20C22×C22⋊C4×C61C411yescharacteristic
21C2×#11758217—24no—
22C2×#11758217—24no—
23C2×#11758217—24no—
24C2×#11758217—24no—
25C2×#11758217—24no—
26C2×#11758217D418yes—
27C22×#92420—24no—
28#14519838—216no—
29#14519837—216no—
30C24×D61C2×C411yescharacteristic
31C22×Dic122—24no—
32C22×Dic122—22no—
33C22×Dic122—22no—
34C22×Dic122—24no—
35C22×Dic122D414yes—
36C22×C22⋊D61—24no—
37C22×C22⋊D61—22no—
38C22×C22⋊D61—22no—
39C22×C22⋊D61—24no—
40C22×C22⋊D61D414yes—
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2311yescharacteristic
44#14519763—232no—
45C2×C22⋊Dic61—22no—
46C2×C22⋊Dic61—22no—
47C2×C22⋊Dic61—22no—
48C2×#11758198—22no—
49C2×#11758198—22no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×#11758198—22no—
53C2×#11758198—22no—
54C2×C4×Dic61—22no—
55C2×C4×Dic61—22no—
56C2×C4×Dic61D414yes—
57C25×C61C2×C411yescharacteristic
58C23×C4×C61C2×C411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—22no—
61C2×C22⋊C4×C61—22no—
62C2×C22⋊C4×C61—22no—
63C24×C61—21no—
64C24×C61—21no—
65C24×C61—24no—
66C24×C61—42no—
67C24×C61—42no—
68C24×C61C22⋊C412yes—
69C24×C61C22×C411yescharacteristic
70C23×D61—21no—
71C23×D61—21no—
72C23×D61—24no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61C22⋊C412yes—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—24no—
81C22×C4×C61—42no—
82C22×C4×C61C22⋊C412yes—
83C22×C4×C61C22⋊C412yes—
84C2×C22⋊D61—24no—
85C2×C22⋊D61—28no—
86C2×C22⋊D61—28no—
87C2×C22⋊D61—24no—
88C2×C22⋊D61—42no—
89C2×C22⋊D61—44no—
90C2×C22⋊D61—44no—
91C2×C22⋊D61—42no—
92C2×C22⋊D61—42no—
93C2×C22⋊D61—42no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—24no—
99C22×Dic61—42no—
100C22×Dic61C22⋊C412yes—
101C22×Dic61C22⋊C412yes—
102C22×Dic61C2×D412yes—
103C22×Dic61C2×D412yes—
104C22×Dic61C2×D414yes—
105C22×Dic61C2×D412yes—
106C22×Dic61#4114yes—
107C2×Dic122—24no—
108C2×Dic122—28no—
109C2×Dic122—28no—
110C2×Dic122—24no—
111C2×Dic122—42no—
112C2×Dic122—44no—
113C2×Dic122—44no—
114C2×Dic122—42no—
115C2×Dic122—42no—
116C2×Dic122—42no—
117#11758217—28no—
118#11758217—28no—
119#11758217—44no—
120#11758217—44no—
121C2×#92420—28no—
122C2×#92420—44no—
123C2×#92420—44no—
124C22⋊C4×C61—28no—
125C22⋊Dic61—28no—
126#11758198—28no—
127#11758198—28no—
128C4×Dic61—28no—
129C23×C61—22no—
130C23×C61—22no—
131C23×C61—22no—
132C23×C61—24no—
133C23×C61—42no—
134C23×C61—42no—
135C23×C61—42no—
136C23×C61—42no—
137C23×C61—42no—
138C23×C61—42no—
139C23×C61—42no—
140C23×C61—42no—
141C23×C61—88no—
142C23×C61C2×C22⋊C411yescharacteristic
143C23×C61C2×C22⋊C411yescharacteristic
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61C4×D414yes—
146C22×D61—22no—
147C22×D61—24no—
148C22×D61—42no—
149C22×D61—42no—
150C22×D61—42no—
151C22×D61—42no—
152C22×D61—42no—
153C22×D61—42no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61—88no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—24no—
160C2×C4×C61—24no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—42no—
165C22⋊D61—48no—
166C22⋊D61—48no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—24no—
170C2×Dic61—24no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61#12012yes—
176C2×Dic61#12012yes—
177C2×Dic61#12014yes—
178C2×Dic61#12114yes—
179C2×Dic61#12114yes—
180C2×Dic61#12114yes—
181C2×Dic61#12312yes—
182C2×Dic61#12312yes—
183C2×Dic61#12412yes—
184C2×Dic61#12712yes—
185Dic122—48no—
186Dic122—48no—
187#92420—48no—
188#10982—611nomaximal, Sylow
189C22×C61—28no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61—42no—
197C22×C61—84no—
198C22×C61—84no—
199C22×C61—84no—
200C22×C61#37911yescharacteristic
201C22×C61#38612yes—
202C22×C61#38612yes—
203C22×C61#39012yes—
204C22×C61#41312yes—
205C22×C61#41312yes—
206C2×D61—42no—
207C2×D61—42no—
208C2×D61—42no—
209C2×D61—84no—
210C2×D61—84no—
211C2×D61—84no—
212C4×C61—42no—
213C4×C61—42no—
214Dic61—42no—
215Dic61—42no—
216Dic61#39214yes—
217Dic61#39414yes—
218C22×#124—611no—
219C22×#101—612no—
220C22×#100—612no—
221#1728—612no—
222C2×C61—22no—
223C2×C61—22no—
224C2×C61—82no—
225C2×C61#143811yescharacteristic
226C2×C61#178511yescharacteristic
227C2×C61#178511yescharacteristic
228C2×C61#196714yes—
229D61—82no—
230C23×Q8—611no—
231C23×D4—611no—
232C22×M16—614no—
233C2×#124—1224no—
234C2×#124—1224no—
235C2×#124—1224no—
236C22×C22⋊C4—611no—
237C22×C22⋊C4—611no—
238C22×C22⋊C4—611no—
239C22×C22⋊C4#692311yescharacteristic
240C22×C42—611no—
241C2×#101—1228no—
242C2×#101—1224no—
243C2×#100—1228no—
244C2×#100—1224no—
245#336—1224no—
246C61#1098211yescharacteristic, complemented, Sylow
247C25—611no—
248C25C2×#692311yescharacteristic
249C22×Q8—614no—
250C22×Q8—1222no—
251C22×Q8—1222no—
252C22×Q8—1224no—
253C22×Q8—1224no—
254C22×D4—614no—
255C22×D4—1222no—
256C22×D4—1222no—
257C22×D4—1224no—
258C22×D4—1224no—
259C23×C4—611no—
260C23×C4—611no—
261C23×C4—611no—
262C23×C4C2×#692311yescharacteristic
263C23×C4C2×#692311yescharacteristic
264C2×M16—618no—
265C2×M16—1224no—
266C2×M16—1224no—
267C2×M16—1224no—
268C2×M16—1224no—
269C2×M16—1224no—
270C22×C8—1224no—
271#124—12232no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—1222no—
276C2×C22⋊C4—1222no—
277C2×C22⋊C4—1222no—
278C2×C22⋊C4—1222no—
279C2×C22⋊C4—1222no—
280C2×C22⋊C4—1222no—
281C2×C22⋊C4—1222no—
282C2×C22⋊C4—1222no—
283C2×C22⋊C4—1222no—
284C2×C42—614no—
285C2×C42—1222no—
286C2×C42—1222no—
287#101—12216no—
288#100—12216no—
289C24—21no—
290C24—21no—
291C24—24no—
292C24—42no—
293C24—42no—
294C24—612no—
295C24—1224no—
296C24—1221no—
297C24—1221no—
298C24—2442no—
299C24—2442no—
300C24C22⋊#692312yes—
301C24C22×#692311yescharacteristic
302C2×Q8—1224no—
303C2×Q8—1228no—
304C2×Q8—1228no—
305C2×Q8—1224no—
306C2×Q8—2442no—
307C2×Q8—2444no—
308C2×Q8—2442no—
309C2×Q8—2444no—
310C2×Q8—2442no—
311C2×Q8—2442no—
312C2×D4—1224no—
313C2×D4—1228no—
314C2×D4—1228no—
315C2×D4—1224no—
316C2×D4—2442no—
317C2×D4—2444no—
318C2×D4—2442no—
319C2×D4—2444no—
320C2×D4—2442no—
321C2×D4—2442no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—24no—
327C22×C4—42no—
328C22×C4—612no—
329C22×C4—612no—
330C22×C4—612no—
331C22×C4—614no—
332C22×C4—614no—
333C22×C4—612no—
334C22×C4—612no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1224no—
340C22×C4—2442no—
341C22×C4C22⋊#692312yes—
342C22×C4C22⋊#692312yes—
343M16—1228no—
344M16—1228no—
345M16—2444no—
346M16—2444no—
347C2×C8—1228no—
348C2×C8—2444no—
349C2×C8—2444no—
350C22⋊C4—28no—
351C22⋊C4—1228no—
352C22⋊C4—1228no—
353C22⋊C4—1228no—
354C42—1228no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—24no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—88no—
368C23—1224no—
369C23—1222no—
370C23—4888no—
371C23—2442no—
372C23—2442no—
373C23—2442no—
374C23—2442no—
375C23—2442no—
376C23—2442no—
377C23—2442no—
378C23—2442no—
379C23C2×C22⋊#692311yescharacteristic
380C23C2×C22⋊#692311yescharacteristic
381C23C2×C22⋊#692311yescharacteristic
382C23D4×#692314yes—
383Q8—2448no—
384Q8—2448no—
385D4—2448no—
386D4—2448no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—612no—
396C2×C4—612no—
397C2×C4—614no—
398C2×C4—614no—
399C2×C4—612no—
400C2×C4—612no—
401C2×C4—614no—
402C2×C4—612no—
403C2×C4—612no—
404C2×C4—614no—
405C2×C4—1224no—
406C2×C4—1224no—
407C2×C4—1222no—
408C2×C4—1222no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4—2442no—
413C8—2448no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—28no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—84no—
423C22—84no—
424C22—84no—
425C22—4884no—
426C22—4884no—
427C22—4884no—
428C22—2442no—
429C22—2442no—
430C22—2442no—
431C22#1684070311yescharacteristic
432C22#1684071012yes—
433C22#1684071012yes—
434C22#1684071412yes—
435C22#1684074812yes—
436C22#1684074912yes—
437C4—42no—
438C4—42no—
439C4—614no—
440C4—614no—
441C4—2442no—
442C4—2442no—
443C2—22no—
444C2—22no—
445C2—82no—
446C2—4882no—
447C2#2146100111yescharacteristic
448C2#2146165511yescharacteristic
449C2#2146165611yescharacteristic
450C2#2146196314yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#10982
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14519838C2semidirect
3. #21461482C2semidirect
246. C61#10982semidirect

Maximal subgroups

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

subgroupindex
C22×#145198382
C22×#145198372
#214614822
C22×#145197632
#1098261