Finite Group Databasebeta

← #29583813

Subgroups — #29583813

Order 15616.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839958C211yesmaximal, characteristic
2#21446624C211yesmaximal, characteristic, complemented
3#21446612C211yesmaximal, characteristic, complemented
4#21445816C211yesmaximal, characteristic, complemented
5C2×#16839512C211yesmaximal, characteristic, complemented
6C2×#16839505C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×D488—21no—
9C2×#14519774C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839958—22no—
12#16839958—22no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519699—21no—
15C2×#14519697—21no—
16C2×#14519697—21no—
17C2×#14519697—21no—
18C2×#14519689—21no—
19C2×#14519689—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839524—21no—
22#16839512—22no—
23#16839505—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#384C2211yescharacteristic
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C2×D488—24no—
33C2×D488—42no—
34C2×D488—42no—
35C22×#92418—21no—
36C22×#92418D411yescharacteristic
37C22×#92418D411yescharacteristic
38#14519774—21no—
39#14519774—21no—
40#14519774—21no—
41#14519774D412yes—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758198—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519699—24no—
51#14519697—42no—
52#14519697—42no—
53#14519697—42no—
54#14519689—42no—
55#14519689—42no—
56C4×#92418—21no—
57C4×#92418—21no—
58C22×C8×C61—21no—
59C22×C8×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61D412yes—
68C23×D61—21no—
69C23×D61—41no—
70C22×C4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C22×Dic61—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—22no—
80C2×D244—22no—
81C2×D244—21no—
82C2×D244—22no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—81no—
95C2×D244—81no—
96C2×D244SD1612yes—
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×C8×C61—22no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—81no—
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C42×C61#4111yescharacteristic
118#11758198—41no—
119#11758198—41no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418D812yescomplemented
131D488—48no—
132C23×C61#12111yescharacteristic
133C22×D61—22no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—42no—
141C22×D61—81no—
142C22×D61—81no—
143C22×D61—81no—
144C22×D61—81no—
145C22×D61—81no—
146C22×D61—81no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—81no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×C4×C61#12311yescharacteristic
157C2×C4×C61#12411yescharacteristic
158C2×C4×C61C2×D811yescharacteristic
159C2×C4×C61C2×SD1611yescharacteristic
160C2×C4×C61#13511yescharacteristic
161C2×C4×C61#13511yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169D244—22no—
170D244—22no—
171D244—41no—
172D244—42no—
173D244—42no—
174D244—42no—
175D244—42no—
176D244—41no—
177D244—82no—
178D244—82no—
179D244—81no—
180D244—81no—
181D244—81no—
182D244—81no—
183C4×D61—81no—
184C4×D61—81no—
185C4×D61—81no—
186C4×D61—81no—
187C8×C61—42no—
188C8×C61—81no—
189#92418—22no—
190#92418—41no—
191#92418—81no—
192#10473—611nomaximal, Sylow
193C22×C61#39411yescharacteristic
194C22×C61#45911yescharacteristic
195C22×C61#46311yescharacteristic
196C22×C61#46511yescharacteristic
197C22×C61#46911yescharacteristic
198C22×C61#47111yescharacteristic
199C22×C61#47211yescharacteristic
200C2×D61—42no—
201C2×D61—42no—
202C2×D61—42no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—82no—
208C2×D61—82no—
209C2×D61—82no—
210C2×D61—161no—
211C2×D61—161no—
212C2×D61—161no—
213C2×D61—161no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—161no—
217C4×C61#44911yescharacteristic
218C4×C61#45011yescharacteristic
219C4×C61#45911yescharacteristic
220C4×C61#46311yescharacteristic
221C4×C61#46611yescharacteristic
222C4×C61#46911yescharacteristic
223C4×C61#48111yescharacteristic
224C4×C61#48211yescharacteristic
225Dic61—81no—
226C2×#459—611no—
227#1957—611no—
228#1954—611no—
229#1802—611no—
230C2×#334—611no—
231C2×#331—611no—
232#1296D6111yescharacteristic, complemented
233C2×C61#166511yescharacteristic
234C2×C61#167711yescharacteristic
235C2×C61#168711yescharacteristic
236C2×C61#170111yescharacteristic
237C2×C61#203411yescharacteristic
238C2×C61#205111yescharacteristic
239C2×C61#205411yescharacteristic
240D61—82no—
241D61—162no—
242C22×D8—1221no—
243C2×#127—611no—
244C2×C4×D4—611no—
245#459—1222no—
246#459—1222no—
247C2×C4⋊C8—611no—
248C2×C4⋊C8C2×D6111yescharacteristic
249C2×C4⋊C8C2×D6111yescharacteristic
250C2×#102—1221no—
251C2×#102—1221no—
252C2×#102—1221no—
253C2×#102—1221no—
254C2×C22⋊C8—1221no—
255C2×C22⋊C8—1221no—
256C2×C4×C8—611no—
257#384C2×D6111yescharacteristic
258#340—1221no—
259#334—1222no—
260#331—1222no—
261C61#1047311yescharacteristic, complemented, Sylow
262C22×D4—611no—
263C22×D4—1221no—
264C22×D4—1221no—
265C22×D4—1221no—
266C23×C4—1221no—
267C2×D8—1224no—
268C2×D8—2442no—
269C2×D8—2442no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—611no—
273C22×C8—611no—
274C22×C8—1221no—
275#127—612no—
276#127—1221no—
277#127—1221no—
278#127—1221no—
279C4×D4—1221no—
280C4×D4—1221no—
281C4×D4—1221no—
282C4×D4—1221no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—611no—
287C2×C22⋊C4—1221no—
288C2×C42C22×D6111yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—1221no—
293C4⋊C8—1221no—
294C4⋊C8D24412yes—
295#102—1224no—
296#102—2442no—
297#102—2442no—
298#102—2442no—
299C22⋊C8—2442no—
300C22⋊C8—2442no—
301C4×C8—1221no—
302C4×C8—1221no—
303C24—1221no—
304C24—2441no—
305C2×D4—612no—
306C2×D4—1221no—
307C2×D4—1222no—
308C2×D4—1222no—
309C2×D4—1221no—
310C2×D4—1222no—
311C2×D4—1221no—
312C2×D4—1221no—
313C2×D4—1221no—
314C2×D4—4881no—
315C2×D4—4881no—
316C2×D4—2441no—
317C2×D4—2441no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327C22×C4—41no—
328C22×C4—1221no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4#1175822211yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4D4×D6111yescharacteristic
338D8—2448no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—612no—
346C2×C8—1221no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—2441no—
352C2×C8—2441no—
353C2×C8—2441no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—81no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C22⋊C4—2441no—
362C22⋊C4—2441no—
363C42C2×D24411yescharacteristic
364C42#1175822211yescharacteristic
365C42D4×D6111yescharacteristic
366C42#1175822611yescharacteristic
367C23—1222no—
368C23—4881no—
369C23—4881no—
370C23—4881no—
371C23—4881no—
372C23—4881no—
373C23—4881no—
374C23—2442no—
375C23—2441no—
376C23—2441no—
377C23—2441no—
378C23—2441no—
379C23—2441no—
380C23—2441no—
381C23#1451975011yescharacteristic
382D4—1222no—
383D4—1222no—
384D4—4882no—
385D4—4882no—
386D4—4881no—
387D4—4881no—
388D4—4881no—
389D4—4881no—
390D4—2442no—
391D4—2442no—
392D4—2441no—
393D4—2442no—
394D4—2441no—
395D4—2442no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4#1451974711yescharacteristic
409C2×C4#1451975011yescharacteristic
410C2×C4#1451975211yescharacteristic
411C2×C4#1451976211yescharacteristic
412C2×C4#1451976211yescharacteristic
413C2×C4#1451976511yescharacteristic
414C2×C4D8×D6111yescharacteristic
415C2×C4SD16×D6111yescharacteristic
416C2×C4#1451980011yescharacteristic
417C2×C4#1451980011yescharacteristic
418C2×C4#1451980111yescharacteristic
419C2×C4#1451980411yescharacteristic
420C2×C4#1451980411yescharacteristic
421C2×C4#1451980411yescharacteristic
422C8—42no—
423C8—81no—
424C8—1222no—
425C8—4881no—
426C8—2441no—
427C22—9761no—
428C22—9761no—
429C22—9761no—
430C22—9761no—
431C22—4882no—
432C22—4882no—
433C22—4882no—
434C22—4881no—
435C22—4881no—
436C22—4881no—
437C22—4881no—
438C22—2442no—
439C22—2442no—
440C22—2442no—
441C22#1683968011yescharacteristic
442C22#1683995611yescharacteristic
443C22#1683998011yescharacteristic
444C22#1683999411yescharacteristic
445C22#1684001411yescharacteristic
446C22#1684002811yescharacteristic
447C22#1684003111yescharacteristic
448C4—21no—
449C4—21no—
450C4—161no—
451C4—4881no—
452C4#1683991011yescharacteristic
453C4#1683991411yescharacteristic
454C4#1683995611yescharacteristic
455C4#1683998011yescharacteristic
456C4#1683999911yescharacteristic
457C4#1684001611yescharacteristic
458C4#1684008211yescharacteristic
459C4#1684008911yescharacteristic
460C2—9762no—
461C2—4882no—
462C2#2144516311yescharacteristic
463C2#2144523111yescharacteristic
464C2#2144529711yescharacteristic
465C2#2144538311yescharacteristic
466C2#2144701111yescharacteristic
467C2#2144711411yescharacteristic
468C2#2144713111yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC2×#16839958C2
hypercenter#1296D61
hypocenterC61#10473
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. #21446624C2semidirect
3. #21446612C2semidirect
4. #21445816C2semidirect
5. C2×#16839512C2semidirect
6. C2×#16839505C2semidirect
7. C61×#1296C2semidirect
130. C2×#92418D8semidirect
232. #1296D61semidirect
261. C61#10473semidirect

Maximal subgroups

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

subgroupindex
C2×#168399582
#214466242
#214466122
#214458162
C2×#168395122
C2×#168395052
C61×#12962
#1047361