Finite Group Databasebeta

← #30602422

Subgroups — #30602422

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840705C211yesmaximal, characteristic
2C2×#16840705C211yesmaximal, characteristic
3C2×#16840639C214yesmaximal
4C2×#117×D61C211yesmaximal, characteristic
5C22×C22⋊#6923C2212yes—
6C22×C22⋊#6923C2212yes—
7#16840705—22no—
8#16840705—21no—
9#16840705—21no—
10#16840705—21no—
11#16840705—21no—
12#16840705C414yescomplemented
13C2×(C2×#6923)⋊C4—22no—
14C2×(C2×#6923)⋊C4C414yescomplemented
15#16840639—28no—
16C23×C4×D61C2211yescharacteristic
17C2×#14519736C411yescharacteristic, complemented
18C2×#14519735—21no—
19C2×#14519734—21no—
20C2×#14519733C412yescomplemented
21#117×D61—28no—
22C2×C4⋊C4×D61—21no—
23C2×C22⋊C4×D61C2212yes—
24C2×C42×D61—21no—
25C2×#117×C61C411yescharacteristic, complemented
26C23×#6923—22no—
27C23×#6923C2×C414yes—
28C2×C22⋊#6923—24no—
29C2×C22⋊#6923—24no—
30C2×C22⋊#6923—22no—
31C2×C22⋊#6923—22no—
32C2×C22⋊#6923—22no—
33C2×C22⋊#6923—24no—
34C2×C22⋊#6923—24no—
35C2×C22⋊#6923C2×C414yes—
36(C2×#6923)⋊C4—24no—
37(C2×#6923)⋊C4—24no—
38(C2×#6923)⋊C4—24no—
39(C2×#6923)⋊C4—24no—
40C24×D61C2311yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C22×C4×D61—24no—
43C22×C4×D61—24no—
44C22×C4×D61—22no—
45C22×C4×D61C2×C412yes—
46C22×C4×D61C2×C412yes—
47C22×C4×D61D412yes—
48C22×C4×D61D411yescharacteristic
49C22×C4×D61D411yescharacteristic
50C22×C4×D61D411yescharacteristic
51C22×C4×D61D411yescharacteristic
52C22×C4×D61Q812yes—
53#14519736—24no—
54#14519735—28no—
55#14519734—28no—
56#14519733—24no—
57#14519733—24no—
58C2×C4⋊Dic61—21no—
59C2×#11758196—22no—
60C4⋊C4×D61—28no—
61C2×C22⋊Dic61C2×C412yes—
62C2×#11758198—22no—
63C22⋊C4×D61—24no—
64C22⋊C4×D61D418yes—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—22no—
67C42×D61—28no—
68C23×C4×C61C2×C411yescharacteristic
69#117×C61—24no—
70C2×C4⋊C4×C61—21no—
71C2×C22⋊C4×C61C2×C412yes—
72C2×C42×C61—21no—
73C24×C61C22×C411yescharacteristic
74C23×D61—44no—
75C23×D61C22×C411yescharacteristic
76C23×D61C22×C411yescharacteristic
77C23×D61C2×D411yescharacteristic
78C23×D61C2×D411yescharacteristic
79C23×D61C2×D411yescharacteristic
80C23×D61C2×D414yes—
81C23×D61C2×Q811yescharacteristic
82C23×D61#4114yes—
83C22×#6923—24no—
84C22×#6923—24no—
85C22×#6923—28no—
86C22×#6923—48no—
87C22×#6923—44no—
88C22×#6923—48no—
89C22×C4×C61—22no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61C4212yes—
93C22×C4×C61C22⋊C411yescharacteristic
94C22×C4×C61C22⋊C411yescharacteristic
95C22×C4×C61C4⋊C412yes—
96C22×Dic61—22no—
97C22×Dic61—22no—
98C22×Dic61—22no—
99C22×Dic61C4212yes—
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C4⋊C412yes—
103C2×C4×D61—28no—
104C2×C4×D61—28no—
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—28no—
110C2×C4×D61—28no—
111C2×C4×D61—22no—
112C2×C4×D61—22no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—28no—
116C2×C4×D61—48no—
117C2×C4×D61C22⋊C412yes—
118C2×C4×D61C22⋊C412yes—
119C2×C4×D61C22⋊C412yes—
120C2×C4×D61C22⋊C412yes—
121C2×C4×D61C4⋊C412yes—
122C2×C4×D61C4⋊C412yes—
123C2×C4×D61C4⋊C412yes—
124C2×C4×D61C4⋊C412yes—
125C22⋊#6923—28no—
126C22⋊#6923—42no—
127C22⋊#6923—42no—
128C22⋊#6923—44no—
129C22⋊#6923—42no—
130C22⋊#6923—42no—
131C4⋊C4×C61—24no—
132C22⋊C4×C61—22no—
133C22⋊C4×C61C22⋊C414yes—
134C42×C61—24no—
135C22⋊Dic61—22no—
136C22⋊Dic61C22⋊C414yes—
137#11758198—28no—
138C4⋊Dic61—24no—
139#11758196—28no—
140C4×Dic61—28no—
141C4×Dic61—24no—
142C23×C61—42no—
143C23×C61C2×C4211yescharacteristic
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61C2×C22⋊C412yes—
146C23×C61C2×C4⋊C411yescharacteristic
147C23×C61#11712yes—
148C22×D61—24no—
149C22×D61—24no—
150C22×D61—24no—
151C22×D61—48no—
152C22×D61—48no—
153C22×D61—42no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61C2×C22⋊C411yescharacteristic
157C22×D61C2×C22⋊C411yescharacteristic
158C22×D61C2×C4⋊C411yescharacteristic
159C22×D61C2×C4⋊C411yescharacteristic
160C22×D61C4×D414yes—
161C22×D61C4×D414yes—
162C22×D61#12012yes—
163C22×D61#12012yes—
164C22×D61#12114yes—
165C22×D61C22⋊Q814yes—
166C22×D61#12312yes—
167C22×D61#12312yes—
168C2×#6923—48no—
169C2×#6923—44no—
170C2×#6923—44no—
171C2×#6923—48no—
172C2×#6923—88no—
173C2×#6923—88no—
174C2×C4×C61—24no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—24no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—24no—
181C2×C4×C61—44no—
182C2×C4×C61#9512yes—
183C2×C4×C61#9512yes—
184C2×Dic61—24no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—24no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—24no—
191C2×Dic61—44no—
192C2×Dic61#9512yes—
193C2×Dic61#9512yes—
194C4×D61—24no—
195C4×D61—24no—
196C4×D61—24no—
197C4×D61—24no—
198C4×D61—24no—
199C4×D61—24no—
200C4×D61—24no—
201C4×D61—24no—
202C4×D61—416no—
203#10736—611nomaximal, Sylow
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—42no—
208C22×C61—42no—
209C22×C61C2×#9511yescharacteristic
210C22×C61C4×C22⋊C412yes—
211C22×C61#37911yescharacteristic
212C22×C61#38012yes—
213C22×C61#38111yescharacteristic
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—24no—
218C2×D61—28no—
219C2×D61—28no—
220C2×D61—24no—
221C2×D61—44no—
222C2×D61—42no—
223C2×D61—44no—
224C2×D61—42no—
225C2×D61#38512yes—
226C2×D61#38512yes—
227C2×D61#38612yes—
228C2×D61#38612yes—
229C2×D61#41014yes—
230#6923—84no—
231#6923—84no—
232C4×C61—22no—
233C4×C61—22no—
234C4×C61—44no—
235Dic61—22no—
236Dic61—22no—
237Dic61—44no—
238C22×#117—611no—
239C2×#381—611no—
240C2×#381—611no—
241C2×#342—614no—
242C2×C61—21no—
243C2×C61—22no—
244C2×C61—22no—
245C2×C61—21no—
246C2×C61C22⋊#9511yescharacteristic
247C2×C61#174012yes—
248D61—22no—
249D61—22no—
250D61—22no—
251D61#189914yes—
252C24×C4—611no—
253C2×#117—611no—
254C2×#117—612no—
255C2×#117—1221no—
256C2×#117—1228no—
257C2×#117—1221no—
258C2×#117#692311yescharacteristic, complemented
259C22×C4⋊C4—1221no—
260C22×C22⋊C4—612no—
261C22×C22⋊C4—612no—
262C22×C22⋊C4—612no—
263C22×C42—1221no—
264#381—614no—
265#381—1222no—
266#381—1221no—
267#381—1221no—
268#381—1221no—
269#381—1221no—
270C2×#95—614no—
271C2×#95—1222no—
272#342—1228no—
273C61#1073611yescharacteristic, complemented, Sylow
274C25—611no—
275C23×C4—611no—
276C23×C4—612no—
277C23×C4—612no—
278C23×C4—612no—
279C23×C4—612no—
280C23×C4—611no—
281C23×C4—611no—
282C23×C4—611no—
283C23×C4—611no—
284C23×C4—614no—
285C23×C4—1224no—
286C23×C4—1224no—
287C23×C4—1222no—
288C23×C4—1222no—
289C23×C4C2×#692311yescharacteristic
290#117—24no—
291#117—1228no—
292#117—1224no—
293#117—1224no—
294#117—1228no—
295#117—1224no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—1228no—
298C2×C4⋊C4—1222no—
299C2×C4⋊C4—1221no—
300C2×C22⋊C4—612no—
301C2×C22⋊C4—618no—
302C2×C22⋊C4—614no—
303C2×C22⋊C4—1224no—
304C2×C22⋊C4—1222no—
305C2×C22⋊C4—1224no—
306C2×C22⋊C4—1224no—
307C2×C22⋊C4—1224no—
308C2×C22⋊C4—1224no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1222no—
312C2×C22⋊C4C2×#692312yes—
313C2×C42—21no—
314C2×C42—1228no—
315C2×C42—1222no—
316C2×C42—1221no—
317#95—1224no—
318#95—1224no—
319#95—1224no—
320#95—1224no—
321C24—611no—
322C24—611no—
323C24—611no—
324C24—611no—
325C24—614no—
326C24—611no—
327C24—611no—
328C24—614no—
329C24—2444no—
330C24C22×#692311yescharacteristic
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—612no—
335C22×C4—611no—
336C22×C4—611no—
337C22×C4—612no—
338C22×C4—612no—
339C22×C4—612no—
340C22×C4—612no—
341C22×C4—612no—
342C22×C4—612no—
343C22×C4—612no—
344C22×C4—612no—
345C22×C4—612no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1228no—
351C22×C4—1228no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1228no—
357C22×C4—1228no—
358C22×C4—1228no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1222no—
362C22×C4—1228no—
363C22×C4—1224no—
364C22×C4—1224no—
365C22×C4—2448no—
366C22×C4—2444no—
367C22×C4—2448no—
368C22×C4—2448no—
369C22×C4C4×#692312yes—
370C22×C4C4⋊#692312yes—
371C22×C4C22⋊#692311yescharacteristic
372C22×C4C22⋊#692311yescharacteristic
373C4⋊C4—24no—
374C4⋊C4—1228no—
375C4⋊C4—1224no—
376C22⋊C4—22no—
377C22⋊C4—614no—
378C22⋊C4—1228no—
379C22⋊C4—1222no—
380C22⋊C4—1228no—
381C22⋊C4—2442no—
382C22⋊C4—2442no—
383C22⋊C4—2444no—
384C22⋊C4—2442no—
385C22⋊C4—2442no—
386C22⋊C4C22⋊#692314yes—
387C42—24no—
388C42—1224no—
389C42—1228no—
390C23—42no—
391C23—611no—
392C23—614no—
393C23—612no—
394C23—611no—
395C23—611no—
396C23—611no—
397C23—614no—
398C23—612no—
399C23—614no—
400C23—612no—
401C23—614no—
402C23—612no—
403C23—1224no—
404C23—1224no—
405C23—1224no—
406C23—2442no—
407C23—2442no—
408C23—2442no—
409C23—2448no—
410C23—2448no—
411C23C2×C4×#692311yescharacteristic
412C23C2×C22⋊#692311yescharacteristic
413C23C2×C22⋊#692312yes—
414C23C2×C4⋊#692311yescharacteristic
415C23#1451985612yes—
416C2×C4—24no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—44no—
424C2×C4—612no—
425C2×C4—612no—
426C2×C4—1224no—
427C2×C4—1224no—
428C2×C4—1224no—
429C2×C4—1224no—
430C2×C4—1224no—
431C2×C4—1224no—
432C2×C4—1224no—
433C2×C4—1224no—
434C2×C4—1224no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1224no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1224no—
441C2×C4—4888no—
442C2×C4—4888no—
443C2×C4—24416no—
444C2×C4—2444no—
445C2×C4—2444no—
446C2×C4—2448no—
447C2×C4—2448no—
448C2×C4—2444no—
449C2×C4(C2×#6923)⋊C412yes—
450C2×C4(C2×#6923)⋊C412yes—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—42no—
455C22—42no—
456C22—612no—
457C22—614no—
458C22—612no—
459C22—612no—
460C22—612no—
461C22—1228no—
462C22—1228no—
463C22—1224no—
464C22—1224no—
465C22—1222no—
466C22—1222no—
467C22—1222no—
468C22—2442no—
469C22—2444no—
470C22—2442no—
471C22—2444no—
472C22C2×(C2×#6923)⋊C411yescharacteristic
473C22C4×C22⋊#692312yes—
474C22#1684070311yescharacteristic
475C22#1684070412yes—
476C22#1684070511yescharacteristic
477C4—22no—
478C4—22no—
479C4—44no—
480C4—1222no—
481C4—1222no—
482C4—4884no—
483C4—4884no—
484C4—2444no—
485C2—21no—
486C2—22no—
487C2—21no—
488C2—22no—
489C2—614no—
490C2—1222no—
491C2—1222no—
492C2—1222no—
493C2#2146099311yescharacteristic
494C2#2146151712yes—
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#95
prime radical, cosocleC24×D61C23
hypercenterC2×#117#6923
hypocenterC61#10736
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
12. #16840705C4semidirect
14. C2×(C2×#6923)⋊C4C4semidirect
17. C2×#14519736C4semidirect
20. C2×#14519733C4semidirect
25. C2×#117×C61C4semidirect
258. C2×#117#6923semidirect
273. C61#10736semidirect

Maximal subgroups

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

subgroupindex
C2×#168407052
C2×#168406392
C2×#117×D612
#1073661