Finite Group Databasebeta

← #29583801

Subgroups — #29583801

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×#16839954C211yesmaximal, characteristic
2#21446626C211yesmaximal, characteristic, complemented
3#21446612C211yesmaximal, characteristic, complemented
4#21445820C211yesmaximal, characteristic, complemented
5C2×#16839514C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×#331C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×C4×D244C2211yescharacteristic
10#16839954—22no—
11#16839954—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519699—21no—
14C2×#14519698—21no—
15C2×#14519698—21no—
16C2×#14519698—21no—
17C2×#14519689—21no—
18C2×#14519689—21no—
19C2×C4×#92418C2211yescharacteristic
20#16839632C2211yescharacteristic
21#16839525—21no—
22#16839514—22no—
23C2×#127×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#331—22no—
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C2×#11758199—24no—
30C2×#11758199—42no—
31C2×#11758199—42no—
32C22×#92418—21no—
33C22×#92418D411yescharacteristic
34C22×#92418D411yescharacteristic
35C4×D244—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44C4⋊#92418—21no—
45C4⋊#92418D412yes—
46#14519699—42no—
47#14519698—24no—
48#14519698—42no—
49#14519698—42no—
50#14519689—42no—
51#14519689—42no—
52C4×#92418—21no—
53C4×#92418—21no—
54C22×D4×C61—21no—
55C22×D4×C61—21no—
56C22×D4×C61—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59#127×C61—21no—
60#127×C61—21no—
61#127×C61—21no—
62#127×C61D412yes—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C24×C61—41no—
69C23×D61—21no—
70C2×D4×C61—22no—
71C2×D4×C61—22no—
72C2×D4×C61—22no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—81no—
85C2×D4×C61—81no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—41no—
91C2×D244—21no—
92C2×D244—21no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244D812yes—
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—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113#11758199—48no—
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—81no—
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—22no—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418—21no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418D812yescomplemented
132C23×C61—42no—
133C23×C61—81no—
134C23×C61—81no—
135C23×C61—81no—
136C23×C61—81no—
137C23×C61—81no—
138C23×C61—81no—
139C23×C61#12111yescharacteristic
140C22×D61—22no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—41no—
147D4×C61—42no—
148D4×C61—42no—
149D4×C61—42no—
150D4×C61—42no—
151D4×C61—82no—
152D4×C61—82no—
153D4×C61—81no—
154D4×C61—81no—
155D4×C61—81no—
156D4×C61—81no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61#12011yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12311yescharacteristic
163C2×C4×C61#12311yescharacteristic
164C2×C4×C61#12411yescharacteristic
165C2×C4×C61C2×D811yescharacteristic
166C2×C4×C61C2×D811yescharacteristic
167C2×C4×C61#13511yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61#13711yescharacteristic
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C2×Dic61—81no—
179D244—22no—
180D244—22no—
181D244—41no—
182D244—41no—
183C4×D61—81no—
184C4×D61—81no—
185C4×D61—81no—
186C4×D61—81no—
187C8×C61—81no—
188C8×C61—81no—
189#92418—22no—
190#92418—42no—
191#92418—41no—
192#10472—611nomaximal, Sylow
193C22×C61—82no—
194C22×C61—82no—
195C22×C61—82no—
196C22×C61—161no—
197C22×C61—161no—
198C22×C61—161no—
199C22×C61—161no—
200C22×C61#39411yescharacteristic
201C22×C61#45911yescharacteristic
202C22×C61#46311yescharacteristic
203C22×C61#46611yescharacteristic
204C22×C61#46811yescharacteristic
205C22×C61#47111yescharacteristic
206C22×C61#47211yescharacteristic
207C2×D61—42no—
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61—81no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61#44711yescharacteristic
217C4×C61#45211yescharacteristic
218C4×C61#45911yescharacteristic
219C4×C61#46311yescharacteristic
220C4×C61#46611yescharacteristic
221C4×C61#46911yescharacteristic
222C4×C61#48011yescharacteristic
223C4×C61#48211yescharacteristic
224Dic61—81no—
225Dic61—161no—
226C2×#459—611no—
227#1957—611no—
228#1954—611no—
229#1802—611no—
230C2×#335—611no—
231C2×#331D6111yescharacteristic, complemented
232#1296—611no—
233C2×C61—162no—
234C2×C61#166711yescharacteristic
235C2×C61#168111yescharacteristic
236C2×C61#168511yescharacteristic
237C2×C61#169711yescharacteristic
238C2×C61#203311yescharacteristic
239C2×C61#205111yescharacteristic
240C2×C61#205411yescharacteristic
241D61—82no—
242C22×D8—1221no—
243C2×#127C2×D6111yescharacteristic
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#384—611no—
258#340—1221no—
259#335—1222no—
260#331—22no—
261C61#1047211yescharacteristic, complemented, Sylow
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—611no—
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—21no—
276#127—21no—
277#127—21no—
278#127C22⋊D6112yes—
279C4×D4—1221no—
280C4×D4—1221no—
281C4×D4—1221no—
282C4×D4—1221no—
283C2×C4⋊C4—611no—
284C2×C4⋊C4—1221no—
285C2×C4⋊C4—1221no—
286C2×C4⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C42C22×D6111yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—612no—
294C4⋊C8—1221no—
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—41no—
304C24—1221no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—81no—
320C2×D4—81no—
321C2×D4—612no—
322C2×D4—1221no—
323C2×D4—1221no—
324C2×D4—1221no—
325C2×D4—1221no—
326C2×D4—1221no—
327C22×C4—1221no—
328C22×C4—2441no—
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—41no—
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—1222no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—2441no—
353C2×C8—2441no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C4⋊C4—4881no—
357C4⋊C4—2441no—
358C4⋊C4—2441no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C22⋊C4—2441no—
362C22⋊C4—2441no—
363C42#1175822211yescharacteristic
364C42D4×D6111yescharacteristic
365C42#1175822411yescharacteristic
366C42C2×C22⋊D6111yescharacteristic
367C23—42no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—1222no—
375C23—2441no—
376C23—2441no—
377C23—2441no—
378C23—2441no—
379C23—2441no—
380C23—2441no—
381C23#1451975011yescharacteristic
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392D4—1222no—
393D4—1222no—
394D4—2441no—
395D4—2441no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—4881no—
399C2×C4—4881no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4#1451974511yescharacteristic
409C2×C4#1451974911yescharacteristic
410C2×C4#1451975011yescharacteristic
411C2×C4#1451975911yescharacteristic
412C2×C4#1451976011yescharacteristic
413C2×C4#1451976311yescharacteristic
414C2×C4D8×D6111yescharacteristic
415C2×C4D8×D6111yescharacteristic
416C2×C4#1451979811yescharacteristic
417C2×C4#1451979811yescharacteristic
418C2×C4#1451980111yescharacteristic
419C2×C4#1451980111yescharacteristic
420C2×C4#1451980411yescharacteristic
421C2×C4#1451980611yescharacteristic
422C8—81no—
423C8—81no—
424C8—1222no—
425C8—2441no—
426C8—2442no—
427C22—82no—
428C22—82no—
429C22—82no—
430C22—161no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—4881no—
435C22—4881no—
436C22—4881no—
437C22—4881no—
438C22—2442no—
439C22—2442no—
440C22—2442no—
441C22#1683967711yescharacteristic
442C22#1683995611yescharacteristic
443C22#1683997611yescharacteristic
444C22#1683999711yescharacteristic
445C22#1684000711yescharacteristic
446C22#1684002411yescharacteristic
447C22#1684003111yescharacteristic
448C4—21no—
449C4—21no—
450C4—9761no—
451C4—4881no—
452C4#1683989411yescharacteristic
453C4#1683992111yescharacteristic
454C4#1683995511yescharacteristic
455C4#1683997911yescharacteristic
456C4#1683999711yescharacteristic
457C4#1684001411yescharacteristic
458C4#1684007411yescharacteristic
459C4#1684008511yescharacteristic
460C2—162no—
461C2—4882no—
462C2#2144517311yescharacteristic
463C2#2144525511yescharacteristic
464C2#2144528311yescharacteristic
465C2#2144535111yescharacteristic
466C2#2144699911yescharacteristic
467C2#2144711111yescharacteristic
468C2#2144712811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#331C2
socleC23×C61#121
prime radicalC2×#16839954C2
hypercenterC2×#331D61
hypocenterC61#10472
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #21446626C2semidirect
3. #21446612C2semidirect
4. #21445820C2semidirect
5. C2×#16839514C2semidirect
6. #21443703C2semidirect
7. C2×C61×#331C2semidirect
131. C2×#92418D8semidirect
231. C2×#331D61semidirect
261. C61#10472semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
#214466262
#214466122
#214458202
C2×#168395142
#214437032
C2×C61×#3312
#1047261