Finite Group Databasebeta

← #29580288

Subgroups — #29580288

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839920C211yesmaximal, characteristic
2#21451632C211yesmaximal, characteristic
3C2×#16839682C211yesmaximal, characteristic
4#21445755C211yesmaximal, characteristic
5C2×#16839500C211yesmaximal, characteristic
6#21443699C211yesmaximal, characteristic
7C2×C61×#324C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C22×Dic244—21no—
10C2×#14519756C2211yescharacteristic
11C22×#11758196—21no—
12#16839920—22no—
13#16839920—22no—
14C2×#14519702—21no—
15C2×#14519702—22no—
16#16839701—21no—
17#16839695—22no—
18#16839682—22no—
19#16839682—22no—
20#16839682—21no—
21#16839635—21no—
22#16839625—21no—
23#16839622C2211yescharacteristic
24C2×#14519684—21no—
25C2×#14519684C2211yescharacteristic
26#16839500—22no—
27C22×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C61×#324—22no—
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—21no—
34C22×Dic122—21no—
35C22×Dic122—21no—
36C22×Dic122—44no—
37C22×Dic122D411yescharacteristic
38C22×Dic122D412yes—
39C23×Dic61—21no—
40C23×Dic61—21no—
41C2×Dic244—24no—
42C2×Dic244—44no—
43#14519756—21no—
44#14519756—21no—
45#14519756—21no—
46#14519756—21no—
47C2×C4⋊Dic61D411yescharacteristic
48C2×C4⋊Dic61D412yes—
49C2×#11758196—24no—
50C2×#11758196—21no—
51C2×#11758196—22no—
52C2×#11758196—44no—
53C2×C22⋊Dic61—21no—
54C2×C22⋊Dic61—21no—
55#14519702—24no—
56#14519702—44no—
57#14519684—24no—
58#14519684—22no—
59#14519684—22no—
60#14519684—22no—
61#14519684—21no—
62#14519684—21no—
63#14519684D412yes—
64C23×C4×C61D411yescharacteristic
65C23×C4×C61D411yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68C22×C8×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61D412yes—
79C24×C61C2×D411yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—42no—
90C22×C4×C61—42no—
91C22×C4×C61Q1612yescomplemented
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×Dic61—24no—
99C22×Dic61—24no—
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—22no—
105C22×Dic61—42no—
106C22×Dic61—42no—
107C22×Dic61—41no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C2×Dic122—24no—
112C2×Dic122—24no—
113C2×Dic122—22no—
114C2×Dic122—22no—
115C2×Dic122—21no—
116C2×Dic122—21no—
117C2×Dic122—44no—
118C2×Dic122—44no—
119C2×Dic122—44no—
120C2×Dic122—44no—
121C2×Dic122—42no—
122C2×Dic122—42no—
123C2×Dic122—41no—
124C2×Dic122—41no—
125C2×Dic122—42no—
126C2×C8×C61—22no—
127C2×C8×C61—42no—
128C2×C8×C61—42no—
129C2×C8×C61—41no—
130C4⋊C4×C61—41no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C22⋊Dic61—41no—
135C22⋊Dic61—41no—
136C22⋊Dic61—41no—
137C22⋊Dic61—41no—
138C4⋊Dic61—21no—
139C4⋊Dic61—21no—
140C4⋊Dic61—42no—
141#11758196—48no—
142#11758196—41no—
143#11758196—41no—
144#11758196—82no—
145Dic244—48no—
146C23×C61—22no—
147C23×C61—22no—
148C23×C61#12011yescharacteristic
149C23×C61#12011yescharacteristic
150C23×C61#12111yescharacteristic
151C23×C61C2×Q1611yescharacteristic
152C23×C61#13511yescharacteristic
153C23×C61#13711yescharacteristic
154C23×C61#13711yescharacteristic
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—42no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—81no—
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12711yescharacteristic
176C2×Dic61—24no—
177C2×Dic61—24no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—44no—
181C2×Dic61—44no—
182C2×Dic61—44no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—44no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193Dic122—24no—
194Dic122—24no—
195Dic122—42no—
196Dic122—44no—
197Dic122—42no—
198Dic122—44no—
199Dic122—42no—
200Dic122—81no—
201C8×C61—42no—
202C8×C61—81no—
203#9925—611nomaximal, Sylow
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—22no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61#39211yescharacteristic
213C22×C61#45111yescharacteristic
214C22×C61#45111yescharacteristic
215C22×C61#45211yescharacteristic
216C22×C61#45211yescharacteristic
217C22×C61#45612yes—
218C22×C61B(4,𝔽2)12yes—
219C22×C61#46711yescharacteristic
220C22×C61#47011yescharacteristic
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—42no—
226C4×C61—81no—
227Dic61—44no—
228Dic61—44no—
229Dic61—82no—
230Dic61—81no—
231Dic61—81no—
232C2×#451—611no—
233#2627—611no—
234C2×#395—611no—
235#1787—611no—
236C2×#328—611no—
237C2×#324D6111yescharacteristic
238#1294—611no—
239C2×C61—21no—
240C2×C61—21no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61#160312yes—
244C2×C61#160512yes—
245C2×C61#200111yescharacteristic
246C2×C61#200511yescharacteristic
247C2×C61#202111yescharacteristic
248C23×Q8—611no—
249C22×Q16—1221no—
250C2×C22⋊Q8—611no—
251C22×C4⋊C4—1221no—
252C22×C4⋊C4C2×D6111yescharacteristic
253#451—1222no—
254#451—1222no—
255C2×#103—1221no—
256C2×#103—1222no—
257C2×C22⋊C8C2×D6111yescharacteristic
258C2×C22⋊C8C2×D6111yescharacteristic
259#400—1221no—
260#398—1222no—
261#395—1222no—
262#395—1221no—
263#395—1222no—
264#385—1221no—
265#381—1221no—
266#380—611no—
267C2×#95—611no—
268C2×#95—1221no—
269#328—1222no—
270#324—22no—
271C61#992511yescharacteristic, complemented, Sylow
272C22×Q8—611no—
273C22×Q8—612no—
274C22×Q8—1221no—
275C22×Q8—1221no—
276C22×Q8—1221no—
277C22×Q8—1221no—
278C22×Q8—1221no—
279C22×Q8—2444no—
280C23×C4—1221no—
281C23×C4—1221no—
282C23×C4D24411yescharacteristic
283C23×C4D24411yescharacteristic
284C23×C4C22×D6111yescharacteristic
285C2×Q16—1224no—
286C2×Q16—2444no—
287C22×C8—21no—
288C22×C8—21no—
289C22⋊Q8—1221no—
290C22⋊Q8—1221no—
291C22⋊Q8—1221no—
292C22⋊Q8—1221no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—612no—
301C2×C4⋊C4—1222no—
302C2×C4⋊C4—1224no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—2444no—
305C2×C22⋊C4—1221no—
306C2×C22⋊C4—1221no—
307#103—1224no—
308#103—2444no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8C22⋊D6112yes—
313#95—612no—
314#95—1224no—
315#95—1222no—
316#95—1222no—
317#95—1222no—
318#95—1221no—
319#95—1221no—
320C24C2×D24411yescharacteristic
321C2×Q8—1224no—
322C2×Q8—1224no—
323C2×Q8—1222no—
324C2×Q8—1221no—
325C2×Q8—1222no—
326C2×Q8—1221no—
327C2×Q8—2442no—
328C2×Q8—2442no—
329C2×Q8—2442no—
330C2×Q8—2444no—
331C2×Q8—2444no—
332C2×Q8—2444no—
333C2×Q8—2444no—
334C2×Q8—2441no—
335C2×Q8—2441no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—1224no—
348C22×C4—1224no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—1221no—
354C22×C4—2442no—
355C22×C4—2442no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4Dic24412yescomplemented
361C22×C4#1175822211yescharacteristic
362C22×C4D4×D6111yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365C22×C4D4×D6111yescharacteristic
366C22×C4C2×C22⋊D6111yescharacteristic
367Q16—2448no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—42no—
371C2×C8—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4—4882no—
379C4⋊C4—2442no—
380C4⋊C4—2448no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C23—22no—
388C23—22no—
389C23#1451974711yescharacteristic
390C23#1451974711yescharacteristic
391C23#1451975111yescharacteristic
392C23C2×Dic24411yescharacteristic
393C23#1451979911yescharacteristic
394C23#1451981011yescharacteristic
395C23#1451981011yescharacteristic
396Q8—1224no—
397Q8—1224no—
398Q8—4881no—
399Q8—2442no—
400Q8—2442no—
401Q8—2444no—
402Q8—2442no—
403Q8—2444no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—81no—
421C2×C4—1224no—
422C2×C4—1224no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2442no—
431C2×C4—2444no—
432C2×C4—2444no—
433C2×C4—2442no—
434C2×C4—2444no—
435C2×C4—2444no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4#1451974511yescharacteristic
439C2×C4#1451975011yescharacteristic
440C2×C4#1451975011yescharacteristic
441C2×C4#1451977311yescharacteristic
442C8—42no—
443C8—81no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—21no—
451C22—21no—
452C22#1683967111yescharacteristic
453C22#1683992011yescharacteristic
454C22#1683992011yescharacteristic
455C22#1683992611yescharacteristic
456C22#1683992611yescharacteristic
457C22#1683994712yes—
458C22#1683995012yes—
459C22#1684000311yescharacteristic
460C22#1684002011yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—81no—
467C4—4881no—
468C4—4882no—
469C4—4881no—
470C4—2444no—
471C4—2444no—
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2#2144478412yes—
477C2#2144479512yes—
478C2#2144682911yescharacteristic
479C2#2144685711yescharacteristic
480C2#2144694411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#324D61
hypocenterC61#9925
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
91. C22×C4×C61Q16semidirect
271. C61#9925semidirect
360. C22×C4Dic244semidirect

Maximal subgroups

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

subgroupindex
C2×#168399202
#214516322
C2×#168396822
#214457552
C2×#168395002
#214436992
C2×C61×#3242
#992561