Finite Group Databasebeta

← #29595663

Subgroups — #29595663

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519800C211yesmaximal, characteristic
2C2×#16839566C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic, complemented
6#21445845C211yesmaximal, characteristic, complemented
7C2×C61×#358C211yesmaximal, characteristic, complemented
8C22×#11758226—21no—
9C2×#14519800—22no—
10C2×#14519800—22no—
11C2×#14519800—22no—
12C2×#14519800—22no—
13C2×#14519800—22no—
14C2×#14519800C414yescomplemented
15C22×#11758201—21no—
16C22×D488C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×#11758185C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20#16839619—21no—
21#16839566—22no—
22#16839564—22no—
23#16839562—22no—
24#16839541—22no—
25#16839524—21no—
26C22×Q16×C61C2211yescharacteristic
27C22×C16×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C61×#358—22no—
30C2×#11758226—24no—
31C2×#11758226—24no—
32C2×#11758226—24no—
33C2×#11758226—42no—
34C2×#11758226—42no—
35C2×#11758226—42no—
36C22×D244—21no—
37C22×D244—41no—
38C22×C4×D61—41no—
39C22×C4×D61D411yescharacteristic
40#14519800—28no—
41#14519800—28no—
42#14519800—28no—
43#14519800—28no—
44C2×#11758201—24no—
45C2×#11758201—24no—
46C2×#11758201—24no—
47C2×D488—21no—
48C2×D488—21no—
49C2×D488—21no—
50C2×D488C2×C412yes—
51C2×D488D412yes—
52C2×D488D412yes—
53C22×#92418D411yescharacteristic
54C2×C8×D61—21no—
55C2×C8×D61—21no—
56C2×C8×D61—21no—
57C2×C8×D61—21no—
58C2×C8×D61C2×C412yes—
59C2×C8×D61D412yes—
60C2×C4⋊Dic61—21no—
61C2×#11758198—41no—
62C2×#11758185—21no—
63C2×#11758185—21no—
64C2×#11758185—21no—
65#14519711—21no—
66#14519711—21no—
67#14519684—41no—
68C22×Q8×C61—21no—
69C2×Q16×C61—21no—
70C2×Q16×C61—21no—
71C2×Q16×C61—21no—
72C2×Q16×C61C2×C412yes—
73C2×Q16×C61D412yes—
74C2×Q16×C61D412yes—
75C22×C8×C61C2311yescharacteristic
76C2×C4⋊C4×C61—21no—
77C2×C16×C61—21no—
78C2×C16×C61—21no—
79C2×C16×C61—21no—
80#107×C61—21no—
81#107×C61—21no—
82C23×D61—41no—
83C23×D61D811yescharacteristic
84C2×Q8×C61—22no—
85C2×Q8×C61—22no—
86C2×Q8×C61—22no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C2×Q8×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C2×D411yescharacteristic
93C22×Dic61—41no—
94C22×Dic61D811yescharacteristic
95#11758226—216no—
96#11758226—48no—
97#11758226—48no—
98#11758226—48no—
99C2×D244—22no—
100C2×D244—22no—
101C2×D244—22no—
102C2×D244—44no—
103C2×D244—44no—
104C2×D244—44no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—41no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—44no—
113C2×C4×D61—44no—
114C2×C4×D61—44no—
115C2×C4×D61C22⋊C412yes—
116C2×C4×D61SD1612yes—
117Q16×C61—22no—
118Q16×C61—22no—
119Q16×C61—22no—
120Q16×C61C22⋊C414yescomplemented
121C2×C8×C61C22×C411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129#11758201—216no—
130#11758198—82no—
131C4⋊Dic61—41no—
132C4⋊Dic61—41no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418C22⋊C412yes—
136D488—22no—
137D488—22no—
138D488—22no—
139D488C22⋊C414yescomplemented
140C8×D61—22no—
141C8×D61—22no—
142C8×D61—22no—
143C8×D61—22no—
144C16×C61—41no—
145#11758185—41no—
146C23×C61C2×D811yescharacteristic
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—42no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61—81no—
157C22×D61—81no—
158C22×D61—81no—
159C22×D61—81no—
160C22×D61#10212yes—
161Q8×C61—24no—
162Q8×C61—42no—
163Q8×C61—42no—
164Q8×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61C2×C22⋊C411yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61C2×SD1611yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182C2×Dic61#10212yes—
183D244—24no—
184D244—416no—
185D244—42no—
186D244—42no—
187D244—42no—
188C4×D61—22no—
189C4×D61—22no—
190C4×D61—22no—
191C4×D61—22no—
192C4×D61—416no—
193C8×C61C2×C22⋊C411yescharacteristic
194C8×C61C2×C22⋊C411yescharacteristic
195C8×C61#12011yescharacteristic
196C8×C61#12011yescharacteristic
197#92418—22no—
198#12733—611nomaximal, Sylow
199C22×C61C2×#10211yescharacteristic
200C22×C61#44711yescharacteristic
201C22×C61#44711yescharacteristic
202C22×C61#50811yescharacteristic
203C22×C61#50811yescharacteristic
204C22×C61#50911yescharacteristic
205C22×C61#51011yescharacteristic
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—22no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—44no—
214C2×D61—82no—
215C2×D61—82no—
216C2×D61—82no—
217C2×D61—82no—
218C2×D61—82no—
219C2×D61—82no—
220C4×C61—44no—
221C4×C61—161no—
222C4×C61#37911yescharacteristic
223C4×C61#41811yescharacteristic
224C4×C61#45011yescharacteristic
225C4×C61#45011yescharacteristic
226Dic61—22no—
227Dic61—161no—
228C22×#135—611no—
229C2×#358—611no—
230C2×#358D6111yescharacteristic, complemented
231C2×#357—611no—
232C2×#357—611no—
233C2×C22⋊C16—611no—
234#1808—611no—
235C2×C61#178611yescharacteristic
236C2×C61#213811yescharacteristic
237C2×C61#213911yescharacteristic
238C2×C61#218611yescharacteristic
239C2×C61#218611yescharacteristic
240C2×C61#218911yescharacteristic
241C2×C61#218911yescharacteristic
242D61—42no—
243D61—84no—
244C22×#41—1221no—
245C2×#135—614no—
246C2×#135—1222no—
247C2×#135—1222no—
248C2×#135—1222no—
249C2×#135—1222no—
250C2×#135—1222no—
251C22×Q16C2×D6111yescharacteristic
252C22×SD16—1221no—
253C22×D8—611no—
254C23×C8—611no—
255C22×C16—611no—
256C22×C16C2×D6111yescharacteristic
257C2×#107—611no—
258C2×#107C2×D6111yescharacteristic
259#380—1221no—
260#358—22no—
261#358—1222no—
262#357—1222no—
263#357—1222no—
264C22⋊C16—1222no—
265#340—1221no—
266C61#1273311yescharacteristic, complemented, Sylow
267C2×#41—1224no—
268C2×#41—1224no—
269C2×#41—1224no—
270C2×#41—2442no—
271C2×#41—2442no—
272C2×#41—2442no—
273C22×Q8—21no—
274C22×D4—1221no—
275C22×D4—2441no—
276C23×C4—611no—
277C23×C4—2441no—
278#135—1228no—
279#135—1228no—
280#135—1228no—
281#135—1228no—
282C2×Q16—21no—
283C2×Q16—21no—
284C2×Q16—21no—
285C2×Q16C4×D6112yes—
286C2×Q16D24412yes—
287C2×Q16C22⋊D6112yes—
288C2×SD16—1224no—
289C2×SD16—1224no—
290C2×SD16—1224no—
291C2×D8—612no—
292C2×D8—612no—
293C2×D8—612no—
294C2×D8—1221no—
295C2×D8—1221no—
296C2×D8—1221no—
297C22×C8—611no—
298C22×C8—612no—
299C22×C8—612no—
300C22×C8—1221no—
301C22×C8—1221no—
302C22×C8—1221no—
303C22×C8—1221no—
304C22×C8C22×D6111yescharacteristic
305C2×C4⋊C4—21no—
306C2×C4⋊C4—1221no—
307C2×C22⋊C4—2441no—
308C2×C16—21no—
309C2×C16—21no—
310C2×C16—21no—
311C2×C16—1221no—
312C2×C16—1221no—
313C2×C16—1221no—
314#107—21no—
315#107—21no—
316#107—1221no—
317#107—1221no—
318#95—2441no—
319C24—611no—
320C24—2441no—
321#41—12216no—
322#41—2448no—
323#41—2448no—
324#41—2448no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—41no—
329C2×Q8—41no—
330C2×Q8—41no—
331C2×D4—1222no—
332C2×D4—1222no—
333C2×D4—1222no—
334C2×D4—2444no—
335C2×D4—2444no—
336C2×D4—2444no—
337C2×D4—2441no—
338C2×D4—2441no—
339C2×D4—2441no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—611no—
343C22×C4—612no—
344C22×C4—612no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—2444no—
350C22×C4—2444no—
351C22×C4—2444no—
352C22×C4—2441no—
353C22×C4D4×D6111yescharacteristic
354Q16—22no—
355Q16—22no—
356Q16—22no—
357Q16#1175819814yescomplemented
358SD16—12216no—
359D8—614no—
360D8—1222no—
361D8—1222no—
362D8—1222no—
363C2×C8—612no—
364C2×C8—1221no—
365C2×C8—1221no—
366C2×C8—1222no—
367C2×C8—1222no—
368C2×C8—1222no—
369C2×C8—1222no—
370C2×C8C2×C4×D6111yescharacteristic
371C2×C8C2×D24411yescharacteristic
372C2×C8D4×D6111yescharacteristic
373C2×C8D4×D6111yescharacteristic
374C2×C8D4×D6111yescharacteristic
375C2×C8C2×C22⋊D6111yescharacteristic
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C22⋊C4—4882no—
381C16—41no—
382C16—2441no—
383C23—612no—
384C23—1221no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23—1221no—
390C23—4881no—
391C23—4881no—
392C23—4881no—
393C23—4881no—
394C23—2442no—
395C23—2442no—
396C23—2442no—
397C23D8×D6111yescharacteristic
398Q8—24no—
399Q8—42no—
400Q8—42no—
401Q8—42no—
402D4—1224no—
403D4—24416no—
404D4—2442no—
405D4—2442no—
406D4—2442no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—612no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—1222no—
417C2×C4—1222no—
418C2×C4—1222no—
419C2×C4—1222no—
420C2×C4—4881no—
421C2×C4—4881no—
422C2×C4—4881no—
423C2×C4—24416no—
424C2×C4C22⋊C4×D6111yescharacteristic
425C2×C4#1451974511yescharacteristic
426C2×C4#1451974711yescharacteristic
427C2×C4SD16×D6111yescharacteristic
428C2×C4#1451980111yescharacteristic
429C2×C4#1451980411yescharacteristic
430C8—1222no—
431C8C22⋊C4×D6111yescharacteristic
432C8C2×#1175819811yescharacteristic
433C8#1451974511yescharacteristic
434C8#1451974711yescharacteristic
435C22—1222no—
436C22—1222no—
437C22—1222no—
438C22—4882no—
439C22—4882no—
440C22—4882no—
441C22—4882no—
442C22—4882no—
443C22—4882no—
444C22—2444no—
445C22—2441no—
446C22—2441no—
447C22—2441no—
448C22—2441no—
449C22#102×D6111yescharacteristic
450C22#1683989411yescharacteristic
451C22#1683989711yescharacteristic
452C22#1684019311yescharacteristic
453C22#1684019511yescharacteristic
454C22#1684019911yescharacteristic
455C22#1684020411yescharacteristic
456C4—44no—
457C4—161no—
458C4—1222no—
459C4—9761no—
460C4#1683961711yescharacteristic
461C4#1683976511yescharacteristic
462C4#1683991111yescharacteristic
463C4#1683991411yescharacteristic
464C2—4884no—
465C2—2442no—
466C2#2144574811yescharacteristic
467C2#2144752511yescharacteristic
468C2#2144753011yescharacteristic
469C2#2144774111yescharacteristic
470C2#2144774511yescharacteristic
471C2#2144775811yescharacteristic
472C2#2144776211yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC22×#14519800C2
cosocleC22×C8×C61C23
hypercenterC2×#358D61
hypocenterC61#12733
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#16839566C2semidirect
3. C2×#16839564C2semidirect
4. C2×#16839562C2semidirect
5. C2×#16839541C2semidirect
6. #21445845C2semidirect
7. C2×C61×#358C2semidirect
14. C2×#14519800C4semidirect
120. Q16×C61C22⋊C4semidirect
139. D488C22⋊C4semidirect
230. C2×#358D61semidirect
266. C61#12733semidirect
357. Q16#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145198002
C2×#168395662
C2×#168395642
C2×#168395622
C2×#168395412
#214458452
C2×C61×#3582
#1273361