Finite Group Databasebeta

← #29583804

Subgroups — #29583804

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×#16839957C211yesmaximal, characteristic
2#21446625C211yesmaximal, characteristic, complemented
3#21445819C211yesmaximal, characteristic, complemented
4C2×#16839515C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1954C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×#14519774C2211yescharacteristic
10#16839957—22no—
11#16839957—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519699—21no—
15C2×#14519699—21no—
16C2×#14519698—21no—
17C2×#14519697—21no—
18#16839632C2211yescharacteristic
19#16839524—21no—
20#16839515—22no—
21#16839505—22no—
22C2×C4×D4×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C22⋊C8×C61—21no—
25C2×C22⋊C8×C61—21no—
26C2×C4×C8×C61C2211yescharacteristic
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C2×#11758199—24no—
31C2×#11758199—42no—
32C2×#11758199—42no—
33C22×#92418—21no—
34C22×#92418—21no—
35#14519774—21no—
36#14519774—21no—
37#14519774—21no—
38#14519774D412yes—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418D412yes—
46#14519699—42no—
47#14519699—42no—
48#14519698—42no—
49#14519697—24no—
50C22×D4×C61D411yescharacteristic
51C23×C4×C61—21no—
52C22×C8×C61—21no—
53C22×C8×C61D411yescharacteristic
54C22×C8×C61D411yescharacteristic
55C4×D4×C61—21no—
56C4×D4×C61—21no—
57C4×D4×C61—21no—
58C4×D4×C61—21no—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C22⋊C8×C61—42no—
65C22⋊C8×C61—42no—
66C4×C8×C61—21no—
67C4×C8×C61—21no—
68C24×C61—21no—
69C23×D61—41no—
70C2×D4×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61D812yes—
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C22×Dic61—41no—
87C2×D244—22no—
88C2×D244—22no—
89C2×D244—22no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—41no—
99C2×D244—41no—
100C2×D244—41no—
101C2×D244—81no—
102C2×D244—81no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61D812yescomplemented
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61#4111yescharacteristic
119C42×C61#4111yescharacteristic
120#11758199—48no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61—81no—
126C2×#92418—22no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C23×C61—22no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61#12111yescharacteristic
140C22×D61—42no—
141C22×D61—81no—
142C22×D61—81no—
143C22×D61—81no—
144C22×D61—81no—
145C22×D61—81no—
146C22×D61—81no—
147D4×C61—22no—
148D4×C61—22no—
149D4×C61—41no—
150D4×C61—41no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61#12011yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12311yescharacteristic
164C2×C4×C61#12311yescharacteristic
165C2×C4×C61#12411yescharacteristic
166C2×C4×C61C2×D811yescharacteristic
167C2×C4×C61C2×D811yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C61#13711yescharacteristic
174C2×Dic61—81no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177D244—42no—
178D244—42no—
179D244—42no—
180D244—42no—
181D244—82no—
182D244—82no—
183D244—81no—
184D244—81no—
185D244—81no—
186D244—81no—
187C8×C61—22no—
188C8×C61—41no—
189C8×C61—81no—
190#92418—42no—
191#92418—81no—
192#10472—611nomaximal, Sylow
193C22×C61—42no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61#39411yescharacteristic
201C22×C61#45911yescharacteristic
202C22×C61#46311yescharacteristic
203C22×C61#46611yescharacteristic
204C22×C61#46811yescharacteristic
205C22×C61#47111yescharacteristic
206C22×C61#47211yescharacteristic
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—81no—
217C4×C61#44711yescharacteristic
218C4×C61#45211yescharacteristic
219C4×C61#45911yescharacteristic
220C4×C61#46311yescharacteristic
221C4×C61#46611yescharacteristic
222C4×C61#46911yescharacteristic
223C4×C61#48011yescharacteristic
224C4×C61#48211yescharacteristic
225Dic61—161no—
226C2×#459—611no—
227#1957—611no—
228#1954D6111yescharacteristic, complemented
229#1802—611no—
230C2×#335—611no—
231C2×#331—611no—
232#1296—611no—
233C2×C61—82no—
234C2×C61#166711yescharacteristic
235C2×C61#168111yescharacteristic
236C2×C61#168511yescharacteristic
237C2×C61#169711yescharacteristic
238C2×C61#203311yescharacteristic
239C2×C61#205111yescharacteristic
240C2×C61#205411yescharacteristic
241D61—162no—
242C22×D8—1221no—
243C2×#127—611no—
244C2×C4×D4C2×D6111yescharacteristic
245#459—1222no—
246#459—1222no—
247C2×C4⋊C8—611no—
248C2×C4⋊C8—611no—
249C2×C4⋊C8C2×D6111yescharacteristic
250C2×#102—1221no—
251C2×#102—1221no—
252C2×#102—1221no—
253C2×#102—1221no—
254C2×C22⋊C8—21no—
255C2×C22⋊C8—21no—
256C2×C4×C8C2×D6111yescharacteristic
257#384—611no—
258#340—1221no—
259#335—1222no—
260#331—1222no—
261C61#1047211yescharacteristic, complemented, Sylow
262C22×D4—1221no—
263C22×D4—1221no—
264C22×D4—1221no—
265C22×D4D24411yescharacteristic
266C23×C4—21no—
267C2×D8—1224no—
268C2×D8—2442no—
269C2×D8—2442no—
270C22×C8—21no—
271C22×C8—1221no—
272C22×C8—1221no—
273C22×C8C22⋊D6111yescharacteristic
274C22×C8C22⋊D6111yescharacteristic
275#127—612no—
276#127—1221no—
277#127—1221no—
278#127—1221no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1221no—
285C2×C4⋊C4—1221no—
286C2×C4⋊C4D24411yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C22×D6111yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—612no—
292C4⋊C8—1221no—
293C4⋊C8—1221no—
294C4⋊C8—1221no—
295#102—1224no—
296#102—2442no—
297#102—2442no—
298#102—2442no—
299C22⋊C8—42no—
300C22⋊C8—42no—
301C4×C8—21no—
302C4×C8—21no—
303C24—21no—
304C24—2441no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—1222no—
311C2×D4—1222no—
312C2×D4—1222no—
313C2×D4—4881no—
314C2×D4—4881no—
315C2×D4—2441no—
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×D4D48812yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—2441no—
335C22×C4C2×D24411yescharacteristic
336C22×C4#1175822211yescharacteristic
337C22×C4C2×C22⋊D6111yescharacteristic
338D8—2448no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—1222no—
348C2×C8—2441no—
349C2×C8—2441no—
350C2×C8—2441no—
351C2×C8—2441no—
352C2×C8—2441no—
353C2×C8#1175819912yescomplemented
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—4881no—
357C4⋊C4—2441no—
358C4⋊C4—2441no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42D4×D6111yescharacteristic
364C42D4×D6111yescharacteristic
365C42#1175822411yescharacteristic
366C42#1175822411yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—4881no—
375C23—4881no—
376C23—4881no—
377C23—4881no—
378C23—4881no—
379C23—4881no—
380C23—2442no—
381C23#1451975111yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—41no—
386D4—4882no—
387D4—4882no—
388D4—4881no—
389D4—4881no—
390D4—4881no—
391D4—4881no—
392D4—2442no—
393D4—2442no—
394D4—2442no—
395D4—2442no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—4881no—
406C2×C4—4881no—
407C2×C4—4881no—
408C2×C4#1451974711yescharacteristic
409C2×C4#1451974811yescharacteristic
410C2×C4#1451974911yescharacteristic
411C2×C4#1451975911yescharacteristic
412C2×C4#1451976111yescharacteristic
413C2×C4#1451976311yescharacteristic
414C2×C4C2×#1175819911yescharacteristic
415C2×C4C2×D48811yescharacteristic
416C2×C4#1451979711yescharacteristic
417C2×C4#1451979911yescharacteristic
418C2×C4#1451980211yescharacteristic
419C2×C4#1451980311yescharacteristic
420C2×C4#1451980511yescharacteristic
421C2×C4#1451981011yescharacteristic
422C8—22no—
423C8—41no—
424C8—81no—
425C8—4881no—
426C8—2442no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—9761no—
435C22—9761no—
436C22—9761no—
437C22—9761no—
438C22—4882no—
439C22—4882no—
440C22—4882no—
441C22#1683967811yescharacteristic
442C22#1683995711yescharacteristic
443C22#1683997711yescharacteristic
444C22#1683999811yescharacteristic
445C22#1684000811yescharacteristic
446C22#1684002511yescharacteristic
447C22#1684003211yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—9761no—
452C4#1683989811yescharacteristic
453C4#1683992611yescharacteristic
454C4#1683995411yescharacteristic
455C4#1683997411yescharacteristic
456C4#1683999611yescharacteristic
457C4#1684001311yescharacteristic
458C4#1684007611yescharacteristic
459C4#1684008711yescharacteristic
460C2—82no—
461C2—9762no—
462C2#2144517411yescharacteristic
463C2#2144525611yescharacteristic
464C2#2144528411yescharacteristic
465C2#2144535211yescharacteristic
466C2#2144700211yescharacteristic
467C2#2144711011yescharacteristic
468C2#2144712911yescharacteristic
subgroupG/H
centerC23#14519751
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1954C2
socleC23×C61#121
prime radicalC2×#16839957C2
hypercenter#1954D61
hypocenterC61#10472
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. #21446625C2semidirect
3. #21445819C2semidirect
4. C2×#16839515C2semidirect
5. C2×#16839505C2semidirect
6. #21443703C2semidirect
7. C61×#1954C2semidirect
111. C2×C8×C61D8semidirect
228. #1954D61semidirect
261. C61#10472semidirect
353. C2×C8#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168399572
#214466252
#214458192
C2×#168395152
C2×#168395052
#214437032
C61×#19542
#1047261