Finite Group Databasebeta

← #29583525

Subgroups — #29583525

Order 15616.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450735C211yesmaximal, characteristic
2#21445946C211yesmaximal, characteristic, complemented
3#21445820C211yesmaximal, characteristic, complemented
4#21445820C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic, complemented
6C2×#16839489C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C2×#14519752—21no—
9C2×#14519752—21no—
10C2×C4×D244C2211yescharacteristic
11C2×C4×D244C2211yescharacteristic
12C2×#14519699—21no—
13C2×#14519699—21no—
14C2×C4×#92418C2211yescharacteristic
15#16839679—22no—
16#16839632C2211yescharacteristic
17#16839619—21no—
18#16839619—21no—
19#16839525—21no—
20#16839525—21no—
21#16839524—22no—
22#16839489—22no—
23#16839489—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#384C2211yescharacteristic
27C22×D244—22no—
28C22×D244D411yescharacteristic
29C22×D244D411yescharacteristic
30C22×C4×D61—21no—
31C22×C4×D61—21no—
32C22×#92418—21no—
33#14519752—42no—
34#14519752—42no—
35#14519752—42no—
36#14519752—42no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61D411yescharacteristic
49C2×C4⋊Dic61D411yescharacteristic
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54#14519699—42no—
55#14519699—42no—
56C4×#92418—21no—
57C4×#92418D412yescomplemented
58#14519684—22no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61D412yes—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C23×D61—21no—
70C23×D61—21no—
71C22×C4×C61—22no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—41no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—44no—
89C2×D244—44no—
90C2×D244—82no—
91C2×D244D812yes—
92C2×D244SD1612yes—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C4⋊C4×C61—42no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C42×C61#4111yescharacteristic
119C42×C61#4111yescharacteristic
120#11758198—44no—
121#11758198—44no—
122#11758198—41no—
123#11758198—41no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—42no—
131C4⋊Dic61—41no—
132C4⋊Dic61—41no—
133C4⋊Dic61—41no—
134C4⋊Dic61—41no—
135C2×#92418—22no—
136C2×#92418—41no—
137C2×#92418—41no—
138C23×C61#12011yescharacteristic
139C22×D61—22no—
140C22×D61—22no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12311yescharacteristic
162C2×C4×C61#12311yescharacteristic
163C2×C4×C61#12411yescharacteristic
164C2×C4×C61C2×D811yescharacteristic
165C2×C4×C61C2×SD1611yescharacteristic
166C2×C4×C61#13511yescharacteristic
167C2×C4×C61#13511yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61#13711yescharacteristic
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181D244—22no—
182D244—22no—
183D244—22no—
184D244—22no—
185D244—41no—
186D244—41no—
187D244—41no—
188D244—41no—
189D244—88no—
190C4×D61—81no—
191C4×D61—81no—
192C4×D61—81no—
193C4×D61—81no—
194C4×D61—81no—
195C4×D61—81no—
196C4×D61—81no—
197C4×D61—81no—
198C8×C61—81no—
199C8×C61—81no—
200#92418—42no—
201#10431—611nomaximal, Sylow
202C22×C61#39411yescharacteristic
203C22×C61#44711yescharacteristic
204C22×C61#44911yescharacteristic
205C22×C61#45011yescharacteristic
206C22×C61#45211yescharacteristic
207C22×C61#45411yescharacteristic
208C22×C61#45511yescharacteristic
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—42no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C2×D61—81no—
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—82no—
226C4×C61#46511yescharacteristic
227C4×C61#46611yescharacteristic
228C4×C61#46811yescharacteristic
229C4×C61#46911yescharacteristic
230C4×C61#48011yescharacteristic
231C4×C61#48111yescharacteristic
232C4×C61#48211yescharacteristic
233C4×C61#48211yescharacteristic
234Dic61—81no—
235Dic61—81no—
236Dic61—161no—
237#2537—611no—
238#1834—611no—
239#1802—611no—
240#1802—611no—
241C2×D4⋊C8—611no—
242C2×D4⋊C8—611no—
243#1296D6111yescharacteristic, complemented
244C2×C61#162511yescharacteristic
245C2×C61#163511yescharacteristic
246C2×C61#163911yescharacteristic
247C2×C61#164611yescharacteristic
248C2×C61#203311yescharacteristic
249C2×C61#203411yescharacteristic
250C2×C61#204011yescharacteristic
251D61—82no—
252D61—82no—
253C2×#121—1221no—
254C2×#121—1221no—
255C2×C4×D4—611no—
256C2×C4×D4—611no—
257C2×C4⋊C8C2×D6111yescharacteristic
258C2×C4⋊C8C2×D6111yescharacteristic
259C2×#102—1221no—
260C2×#102—1221no—
261C2×C4×C8—611no—
262#394—1222no—
263#384—611no—
264#384C2×D6111yescharacteristic
265#380—1221no—
266#380—1221no—
267#340—1221no—
268#340—1221no—
269#340—1222no—
270D4⋊C8—1222no—
271D4⋊C8—1222no—
272C61#1043111yescharacteristic, complemented, Sylow
273C22×D4—611no—
274C22×D4—611no—
275C22×D4—1222no—
276C23×C4—1221no—
277C23×C4—1221no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—1221no—
281#121—2442no—
282#121—2442no—
283#121—2442no—
284#121—2442no—
285C4×D4—1221no—
286C4×D4—1221no—
287C4×D4—1221no—
288C4×D4—1221no—
289C4×D4—1221no—
290C4×D4—1221no—
291C4×D4—1221no—
292C4×D4—1221no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—611no—
296C2×C4⋊C4—611no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—1221no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4D24412yes—
301C2×C22⋊C4—1222no—
302C2×C22⋊C4—1222no—
303C2×C22⋊C4—1221no—
304C2×C22⋊C4—1221no—
305C2×C42C22×D6111yescharacteristic
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310#102—2442no—
311#102—2442no—
312C4×C8—612no—
313C4×C8—1221no—
314#95—1222no—
315C24—1221no—
316C24—1221no—
317C2×D4—612no—
318C2×D4—612no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4—1221no—
323C2×D4—1221no—
324C2×D4—1221no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—4882no—
330C2×D4—2444no—
331C2×D4—2444no—
332C22×C4—22no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4—2441no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4C2×D24411yescharacteristic
349C22×C4D4×D6111yescharacteristic
350C22×C4D4×D6111yescharacteristic
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—1222no—
358C2×C8—2441no—
359C2×C8—2441no—
360C4⋊C4—42no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C4⋊C4—2442no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C22⋊C4—2444no—
375C22⋊C4—2444no—
376C22⋊C4—2441no—
377C22⋊C4—2441no—
378C22⋊C4—2441no—
379C22⋊C4—2441no—
380C42#1175822211yescharacteristic
381C42#1175822211yescharacteristic
382C42D4×D6111yescharacteristic
383C42#1175822611yescharacteristic
384C23—1222no—
385C23—1222no—
386C23—2441no—
387C23—2441no—
388C23—2441no—
389C23—2441no—
390C23—2441no—
391C23—2441no—
392C23—2441no—
393C23—2441no—
394C23—2441no—
395C23—2441no—
396C23—2441no—
397C23—2441no—
398C23#1451974711yescharacteristic
399D4—1222no—
400D4—1222no—
401D4—1222no—
402D4—1222no—
403D4—4888no—
404D4—2441no—
405D4—2441no—
406D4—2441no—
407D4—2441no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—4881no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—4881no—
417C2×C4—4881no—
418C2×C4—4881no—
419C2×C4—4881no—
420C2×C4—4881no—
421C2×C4—4881no—
422C2×C4—4881no—
423C2×C4—4881no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4#1451975011yescharacteristic
431C2×C4#1451975011yescharacteristic
432C2×C4#1451975211yescharacteristic
433C2×C4#1451976211yescharacteristic
434C2×C4#1451976211yescharacteristic
435C2×C4#1451976511yescharacteristic
436C2×C4D8×D6111yescharacteristic
437C2×C4SD16×D6111yescharacteristic
438C2×C4#1451979811yescharacteristic
439C2×C4#1451980011yescharacteristic
440C2×C4#1451980111yescharacteristic
441C2×C4#1451980411yescharacteristic
442C2×C4#1451980411yescharacteristic
443C2×C4#1451980911yescharacteristic
444C8—81no—
445C8—81no—
446C8—2442no—
447C22—4881no—
448C22—4881no—
449C22—4881no—
450C22—4881no—
451C22—4881no—
452C22—4881no—
453C22—4881no—
454C22—4881no—
455C22—2442no—
456C22—2442no—
457C22—2442no—
458C22—2442no—
459C22—2442no—
460C22—2442no—
461C22#1683968011yescharacteristic
462C22#1683989711yescharacteristic
463C22#1683991011yescharacteristic
464C22#1683991411yescharacteristic
465C22#1683992711yescharacteristic
466C22#1683993711yescharacteristic
467C22#1683994211yescharacteristic
468C4—21no—
469C4—21no—
470C4—82no—
471C4—9761no—
472C4—4881no—
473C4—4881no—
474C4#1683999411yescharacteristic
475C4#1683999711yescharacteristic
476C4#1684001111yescharacteristic
477C4#1684001411yescharacteristic
478C4#1684007711yescharacteristic
479C4#1684008211yescharacteristic
480C4#1684008811yescharacteristic
481C4#1684008911yescharacteristic
482C2—4882no—
483C2—4882no—
484C2#2144490911yescharacteristic
485C2#2144497111yescharacteristic
486C2#2144499911yescharacteristic
487C2#2144504811yescharacteristic
488C2#2144700411yescharacteristic
489C2#2144701111yescharacteristic
490C2#2144704911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#120
prime radical#21450735C2
hypercenter#1296D61
hypocenterC61#10431
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21445946C2semidirect
3. #21445820C2semidirect
4. #21445820C2semidirect
5. C2×#16839489C2semidirect
6. C2×#16839489C2semidirect
7. C61×#1296C2semidirect
57. C4×#92418D4semidirect
243. #1296D61semidirect
272. C61#10431semidirect

Maximal subgroups

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

subgroupindex
#214507352
#214459462
#214458202
C2×#168394892
C61×#12962
#1043161