Finite Group Databasebeta

← #30610152

Subgroups — #30610152

Order 15616.

1314 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C212yesmaximal, complemented
2#21461088C218yesmaximal, complemented
3#21461066C212yesmaximal, complemented
4#21461064C212yesmaximal, complemented
5C22×#14519763C211yesmaximal, characteristic
6#16840783—22no—
7#16840782C2214yescomplemented
8#16840779—22no—
9#16840778C2214yescomplemented
10#16840765—22no—
11#16840732C2214yes—
12C4×#11758217—22no—
13#16840606C2218yescomplemented
14#16840605C2218yescomplemented
15C23×Dic122C411yescharacteristic
16C23×C22⋊D61C411yescharacteristic
17C2×#14519763—22no—
18C2×#14519763—22no—
19C2×#14519763—22no—
20C2×#14519763—22no—
21C2×#14519763C414yes—
22C2×#14519763C2214yes—
23C22×C22⋊Dic61C2211yescharacteristic
24C22×#11758198C411yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C22⋊C4×C61C411yescharacteristic
28C2×#11758217—24no—
29#14519844—24no—
30C4⋊#92420—24no—
31C22⋊#92420—24no—
32C22⋊#92420C2318yes—
33#14519832—24no—
34C4×#92420—24no—
35C24×D61C2×C411yescharacteristic
36C22×Dic122—21no—
37C22×Dic122—22no—
38C22×Dic122—21no—
39C22×Dic122—44no—
40C22×Dic122C2×C414yes—
41C22×C22⋊D61—21no—
42C22×C22⋊D61—22no—
43C22×C22⋊D61—21no—
44C22×C22⋊D61—44no—
45C22×C22⋊D61C2×C414yes—
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2311yescharacteristic
49#14519763—24no—
50#14519763—24no—
51#14519763—24no—
52#14519763—24no—
53#14519763—24no—
54#14519763—24no—
55#14519763—24no—
56#14519763—24no—
57C2×C22⋊Dic61—22no—
58C2×C22⋊Dic61—22no—
59C2×C22⋊Dic61C2×C412yes—
60C2×C22⋊Dic61C2312yes—
61C2×#11758198—21no—
62C2×#11758198—21no—
63C2×#11758198—22no—
64C2×#11758198—22no—
65C2×#11758198—22no—
66C2×#11758198C2×C414yes—
67C2×#11758198C2×C412yes—
68C2×#11758198C2312yes—
69C2×C4×Dic61C2×C412yes—
70C2×C4×Dic61D412yes—
71C2×C4×Dic61D412yes—
72C2×C4×Dic61D412yes—
73C2×C4×Dic61D412yes—
74C2×C4×Dic61C2312yes—
75C25×C61C2×C411yescharacteristic
76C23×C4×C61C2×C411yescharacteristic
77C23×C4×C61C2×C411yescharacteristic
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—21no—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61C2×C414yes—
82C24×C61—21no—
83C24×C61—21no—
84C24×C61—42no—
85C24×C61—42no—
86C24×C61—42no—
87C24×C61C22×C411yescharacteristic
88C24×C61C22×C412yes—
89C23×D61—21no—
90C23×D61—21no—
91C23×D61—42no—
92C23×D61—42no—
93C23×D61—42no—
94C23×D61C22×C412yes—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61C22⋊C411yescharacteristic
100C22×C4×C61C22⋊C411yescharacteristic
101C22×C4×C61C22⋊C412yes—
102C22×C4×C61C22×C412yes—
103C22×C4×C61C22×C412yes—
104C2×C22⋊D61—24no—
105C2×C22⋊D61—24no—
106C2×C22⋊D61—44no—
107C2×C22⋊D61—48no—
108C2×C22⋊D61—48no—
109C2×C22⋊D61—44no—
110C22×Dic61—24no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—42no—
114C22×Dic61—42no—
115C22×Dic61C22⋊C411yescharacteristic
116C22×Dic61C22⋊C412yes—
117C22×Dic61C22⋊C411yescharacteristic
118C22×Dic61C22×C412yes—
119C22×Dic61C22×C412yes—
120C22×Dic61C22×C411yescharacteristic
121C22×Dic61C2×D412yes—
122C22×Dic61C2×D412yes—
123C22×Dic61C2411yescharacteristic
124C2×Dic122—24no—
125C2×Dic122—24no—
126C2×Dic122—44no—
127C2×Dic122—48no—
128C2×Dic122—44no—
129C2×Dic122—48no—
130#11758217—48no—
131C2×#92420—28no—
132C22⋊C4×C61—24no—
133C22⋊C4×C61—24no—
134C22⋊Dic61—24no—
135C22⋊Dic61—24no—
136#11758198—24no—
137#11758198—24no—
138#11758198—24no—
139#11758198—24no—
140C4×Dic61C22⋊C412yes—
141C4×Dic61C22⋊C412yes—
142C4×Dic61C22⋊C412yes—
143C4×Dic61C22⋊C412yes—
144C4×Dic61C2×D412yes—
145C4×Dic61C2×D412yes—
146C4×Dic61C2×D412yes—
147C4×Dic61C2×D412yes—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—24no—
153C23×C61—42no—
154C23×C61—42no—
155C23×C61—42no—
156C23×C61—42no—
157C23×C61—42no—
158C23×C61—42no—
159C23×C61—42no—
160C23×C61—42no—
161C23×C61—88no—
162C23×C61C2×C22⋊C411yescharacteristic
163C23×C61C2×C22⋊C411yescharacteristic
164C23×C61C23×C411yescharacteristic
165C22×D61—22no—
166C22×D61—24no—
167C22×D61—42no—
168C22×D61—42no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—42no—
172C22×D61—42no—
173C22×D61—42no—
174C22×D61—42no—
175C22×D61—88no—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61C2×C22⋊C412yes—
185C2×C4×C61C2×C22⋊C412yes—
186C22⋊D61—48no—
187C22⋊D61—48no—
188C2×Dic61—24no—
189C2×Dic61—22no—
190C2×Dic61—24no—
191C2×Dic61—24no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—41no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61#10014yes—
200C2×Dic61C2×C22⋊C412yes—
201C2×Dic61C2×C22⋊C412yes—
202C2×Dic61C2×C22⋊C412yes—
203C2×Dic61C22×D412yes—
204Dic122—48no—
205Dic122—48no—
206#92420—48no—
207#17393—611nomaximal, Sylow
208C22×C61—28no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—42no—
216C22×C61—42no—
217C22×C61—42no—
218C22×C61—84no—
219C22×C61—84no—
220C22×C61—84no—
221C22×C61#41012yes—
222C22×C61C2×#10012yes—
223C22×C61C22×C22⋊C411yescharacteristic
224C22×C61#56812yes—
225C2×D61—42no—
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—84no—
229C2×D61—84no—
230C2×D61—84no—
231C4×C61—22no—
232C4×C61—22no—
233C4×C61—42no—
234Dic61—22no—
235Dic61—22no—
236Dic61—22no—
237Dic61—42no—
238Dic61C2×#10014yes—
239C22×#124—611no—
240#2920—612no—
241#1469—618no—
242#1462—612no—
243#1462—612no—
244C2×C61—22no—
245C2×C61—22no—
246C2×C61—22no—
247C2×C61—82no—
248C2×C61#287911yescharacteristic
249C2×C61C2×#41011yescharacteristic
250C2×C61C22×#10011yescharacteristic
251D61—82no—
252C23×Q8—611no—
253C23×D4—611no—
254C2×#124—614no—
255C2×#124—614no—
256C2×#124—1222no—
257C2×#124—1222no—
258C2×#124—1222no—
259C2×#124—1222no—
260C22×C22⋊C4—611no—
261C22×C22⋊C4—611no—
262C22×C22⋊C4—611no—
263C22×C22⋊C4#692311yescharacteristic
264C22×C42—611no—
265#432—614no—
266#432—1222no—
267#431—614no—
268#431—1222no—
269#423—1222no—
270#407—614no—
271C4×M16—1222no—
272#323—618no—
273#323—618no—
274C61#1739311yescharacteristic, complemented, Sylow
275C25—611no—
276C25C2×#692311yescharacteristic
277C22×Q8—614no—
278C22×Q8—1221no—
279C22×Q8—1222no—
280C22×Q8—1221no—
281C22×Q8—2444no—
282C22×D4—614no—
283C22×D4—1221no—
284C22×D4—1222no—
285C22×D4—1221no—
286C22×D4—2444no—
287C23×C4—611no—
288C23×C4—611no—
289C23×C4—611no—
290C23×C4C2×#692311yescharacteristic
291C23×C4C2×#692311yescharacteristic
292C2×M16—1224no—
293#124—1224no—
294#124—1224no—
295#124—1224no—
296#124—1224no—
297#124—1224no—
298#124—1224no—
299#124—1224no—
300#124—1224no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—612no—
305C2×C22⋊C4—612no—
306C2×C22⋊C4—612no—
307C2×C22⋊C4—612no—
308C2×C22⋊C4—614no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1222no—
312C2×C22⋊C4—1222no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1222no—
316C2×C22⋊C4C2×#692314yes—
317C2×C42—612no—
318C2×C42—612no—
319C2×C42—612no—
320C2×C42—612no—
321C2×C42—612no—
322C2×C42—612no—
323C4⋊C8—1224no—
324C4⋊C8—1224no—
325C22⋊C8—618no—
326C22⋊C8—1224no—
327#97—1224no—
328C4×C8—1224no—
329C24—21no—
330C24—21no—
331C24—42no—
332C24—42no—
333C24—42no—
334C24—612no—
335C24—1221no—
336C24—1221no—
337C24—2442no—
338C24—2442no—
339C24—2442no—
340C24C22×#692311yescharacteristic
341C24C22×#692312yes—
342C2×Q8—1224no—
343C2×Q8—1224no—
344C2×Q8—2444no—
345C2×Q8—2448no—
346C2×Q8—2448no—
347C2×Q8—2444no—
348C2×D4—1224no—
349C2×D4—1224no—
350C2×D4—2444no—
351C2×D4—2448no—
352C2×D4—2444no—
353C2×D4—2448no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—611no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—611no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—612no—
367C22×C4—1224no—
368C22×C4—1221no—
369C22×C4—1221no—
370C22×C4—2442no—
371C22×C4—2442no—
372C22×C4C22⋊#692311yescharacteristic
373C22×C4C22⋊#692311yescharacteristic
374C22×C4C22⋊#692312yes—
375C22×C4C22×#692312yes—
376C22×C4C22×#692312yes—
377M16—2448no—
378C2×C8—1228no—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—1224no—
382C22⋊C4—1224no—
383C22⋊C4—1224no—
384C22⋊C4—1224no—
385C22⋊C4—1224no—
386C22⋊C4—1224no—
387C42—612no—
388C42—612no—
389C42—612no—
390C42—612no—
391C42—612no—
392C42—612no—
393C42—612no—
394C42—612no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—24no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—88no—
409C23—1224no—
410C23—1222no—
411C23—4888no—
412C23—2442no—
413C23—2442no—
414C23—2442no—
415C23—2442no—
416C23—2442no—
417C23—2442no—
418C23—2442no—
419C23—2442no—
420C23C2×C22⋊#692311yescharacteristic
421C23C2×C22⋊#692311yescharacteristic
422C23C23×#692311yescharacteristic
423Q8—2448no—
424Q8—2448no—
425D4—2448no—
426D4—2448no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—614no—
436C2×C4—612no—
437C2×C4—612no—
438C2×C4—612no—
439C2×C4—612no—
440C2×C4—1224no—
441C2×C4—1224no—
442C2×C4—1224no—
443C2×C4—1222no—
444C2×C4—1222no—
445C2×C4—2441no—
446C2×C4—2442no—
447C2×C4—2441no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4C2×C22⋊#692312yes—
452C2×C4C2×C22⋊#692312yes—
453C8—2448no—
454C22—28no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—84no—
465C22—84no—
466C22—84no—
467C22—4884no—
468C22—4884no—
469C22—4884no—
470C22—2442no—
471C22—2442no—
472C22—2442no—
473C22#1684074112yes—
474C22D61⋊#10012yes—
475C22C22×C22⋊#692311yescharacteristic
476C22#1684084012yes—
477C4—22no—
478C4—22no—
479C4—42no—
480C4—614no—
481C4—1222no—
482C4—1222no—
483C4—1222no—
484C4—2442no—
485C2—22no—
486C2—22no—
487C2—22no—
488C2—82no—
489C2—4882no—
490C2#2146240311yescharacteristic
491C2C2×#1684074111yescharacteristic
492C2C2×D61⋊#10011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#17393
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. #21461088C2semidirect
3. #21461066C2semidirect
4. #21461064C2semidirect
7. #16840782C22semidirect
9. #16840778C22semidirect
13. #16840606C22semidirect
14. #16840605C22semidirect
274. C61#17393semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214610882
#214610662
#214610642
C22×#145197632
#1739361