Finite Group Databasebeta

← #29576191

Subgroups — #29576191

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839954C211yesmaximal, characteristic
2C2×#16839827C211yesmaximal, characteristic, complemented
3#21446626C211yesmaximal, characteristic, complemented
4#21445820C211yesmaximal, characteristic, complemented
5#21443703C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C2×C61×#331C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C22×C8×D61—21no—
10C2×C4×D244C2211yescharacteristic
11#16839954—22no—
12#16839954C414yescomplemented
13#16839827—22no—
14#16839827—22no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×#14519699—21no—
17C2×#14519698—21no—
18C2×#14519698—21no—
19C2×#14519698—21no—
20C2×#14519689—21no—
21C2×C4×#92418C2211yescharacteristic
22#16839632C2211yescharacteristic
23#16839525—21no—
24C2×#127×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#331—22no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758199—24no—
31C2×#11758199—42no—
32C2×#11758199—42no—
33C22×#92418—21no—
34C22×#92418D411yescharacteristic
35C22×#92418D411yescharacteristic
36C2×C8×D61—24no—
37C2×C8×D61—42no—
38C2×C8×D61—42no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244C2×C412yes—
42C4×D244D412yes—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758198—21no—
48C4⋊#92418—21no—
49C4⋊#92418C2×C412yes—
50#14519699—42no—
51#14519698—24no—
52#14519698—42no—
53#14519698—42no—
54#14519689—24no—
55C4×#92418—21no—
56C4×#92418—21no—
57C22×D4×C61—21no—
58C22×D4×C61—21no—
59C22×D4×C61—21no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62#127×C61—21no—
63#127×C61—21no—
64#127×C61—21no—
65#127×C61C2×C412yes—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D412yes—
71C24×C61—41no—
72C23×D61—21no—
73C2×D4×C61—22no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
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—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—81no—
88C2×D4×C61—81no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61#4111yescharacteristic
92C22×Dic61—21no—
93C22×Dic61—41no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244C22⋊C412yes—
98C2×D244D812yes—
99C2×D244SD1612yes—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C8×C61—22no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C42×C61C22×C411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116#11758199—48no—
117#11758198—22no—
118#11758198—22no—
119C4⋊Dic61—21no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—81no—
125C4⋊Dic61C22⋊C412yes—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418—22no—
129C2×#92418—21no—
130C2×#92418—21no—
131C2×#92418—21no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418D812yescomplemented
135C8×D61—48no—
136C23×C61—42no—
137C23×C61—81no—
138C23×C61—81no—
139C23×C61—81no—
140C23×C61—81no—
141C23×C61—81no—
142C23×C61—81no—
143C23×C61#12111yescharacteristic
144C22×D61—22no—
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151D4×C61—42no—
152D4×C61—42no—
153D4×C61—42no—
154D4×C61—42no—
155D4×C61—82no—
156D4×C61—82no—
157D4×C61—81no—
158D4×C61—81no—
159D4×C61—81no—
160D4×C61—81no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12311yescharacteristic
169C2×C4×C61C2×D811yescharacteristic
170C2×C4×C61C2×D811yescharacteristic
171C2×C4×C61C2×SD1611yescharacteristic
172C2×C4×C61#13511yescharacteristic
173C2×C4×C61#13511yescharacteristic
174C2×C4×C61#13511yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C2×Dic61—22no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182C2×Dic61—81no—
183D244—22no—
184D244—22no—
185D244—22no—
186D244#10214yescomplemented
187C4×D61—42no—
188C4×D61—42no—
189C4×D61—42no—
190C4×D61—42no—
191C8×C61—42no—
192C8×C61—81no—
193#92418—22no—
194#92418—42no—
195#92418—41no—
196#9221—611nomaximal, Sylow
197C22×C61—82no—
198C22×C61—82no—
199C22×C61—82no—
200C22×C61—161no—
201C22×C61—161no—
202C22×C61—161no—
203C22×C61—161no—
204C22×C61#38611yescharacteristic
205C22×C61#45911yescharacteristic
206C22×C61#46311yescharacteristic
207C22×C61#46511yescharacteristic
208C22×C61#46611yescharacteristic
209C22×C61#47111yescharacteristic
210C22×C61#47211yescharacteristic
211C2×D61—24no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—42no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61C2×#10211yescharacteristic
221C4×C61#41611yescharacteristic
222C4×C61C4×D811yescharacteristic
223C4×C61#44211yescharacteristic
224C4×C61#44711yescharacteristic
225C4×C61#44911yescharacteristic
226C4×C61#46511yescharacteristic
227C4×C61#46611yescharacteristic
228Dic61—42no—
229Dic61—161no—
230C2×#459—611no—
231C2×C8×D4—611no—
232#1957—611no—
233#1802—611no—
234C2×#331D6111yescharacteristic, complemented
235#1296—611no—
236#1277—611no—
237C2×C61—162no—
238C2×C61#166511yescharacteristic
239C2×C61#166711yescharacteristic
240C2×C61#167711yescharacteristic
241C2×C61#168111yescharacteristic
242C2×C61#187911yescharacteristic
243C2×C61#189311yescharacteristic
244C2×C61#190711yescharacteristic
245D61—44no—
246C22×D8—1221no—
247C23×C8—1221no—
248C2×#127C2×D6111yescharacteristic
249C2×C4×D4—611no—
250#459—614no—
251#459—1222no—
252C8×D4—1222no—
253C8×D4—1222no—
254C2×C4⋊C8—611no—
255C2×C4⋊C8C2×D6111yescharacteristic
256C2×C4⋊C8C2×D6111yescharacteristic
257C2×#102—1221no—
258C2×#102—1221no—
259C2×#102—1221no—
260C2×#102—1221no—
261C2×C22⋊C8—1221no—
262C2×C4×C8—611no—
263#384—611no—
264#340—1221no—
265#331—22no—
266C61#922111yescharacteristic, complemented, Sylow
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—611no—
271C23×C4—1221no—
272C2×D8—1224no—
273C2×D8—2442no—
274C2×D8—2442no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—611no—
278C22×C8—611no—
279C22×C8—1224no—
280C22×C8—1221no—
281C22×C8—2442no—
282C22×C8—2442no—
283#127—21no—
284#127—21no—
285#127—21no—
286#127C4×D6112yes—
287C4×D4—612no—
288C4×D4—612no—
289C4×D4—1221no—
290C4×D4—1221no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42C22×D6111yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—612no—
301C4⋊C8—1221no—
302C4⋊C8C22⋊D6112yes—
303#102—1224no—
304#102—2442no—
305#102—2442no—
306#102—2442no—
307C22⋊C8—1224no—
308C4×C8—1221no—
309C4×C8—1221no—
310C24—41no—
311C24—1221no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—81no—
327C2×D4—81no—
328C2×D4—612no—
329C2×D4—612no—
330C2×D4—612no—
331C2×D4—1221no—
332C2×D4—1221no—
333C2×D4—1221no—
334C22×C4—1221no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4#1175822211yescharacteristic
343C22×C4D4×D6111yescharacteristic
344C22×C4D4×D6111yescharacteristic
345D8—2448no—
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—612no—
353C2×C8—1221no—
354C2×C8—1221no—
355C2×C8—1222no—
356C2×C8—1221no—
357C2×C8—1221no—
358C2×C8—1221no—
359C2×C8—2448no—
360C2×C8—2441no—
361C2×C8—2441no—
362C4⋊C4—612no—
363C4⋊C4—1221no—
364C4⋊C4—4881no—
365C4⋊C4—2441no—
366C4⋊C4—2441no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C42C2×C4×D6111yescharacteristic
372C42D4×D6111yescharacteristic
373C42#1175822411yescharacteristic
374C42C2×C22⋊D6111yescharacteristic
375C23—42no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—1222no—
383C23—1222no—
384C23—1222no—
385C23—2441no—
386C23—2441no—
387C23—2441no—
388C23—2441no—
389C23#1451975011yescharacteristic
390D4—42no—
391D4—42no—
392D4—42no—
393D4—42no—
394D4—82no—
395D4—82no—
396D4—81no—
397D4—81no—
398D4—81no—
399D4—81no—
400D4—614no—
401D4—1222no—
402D4—1222no—
403D4—1222no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—1222no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—4881no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4C22⋊C4×D6111yescharacteristic
417C2×C4#1451973711yescharacteristic
418C2×C4C4×C22⋊D6111yescharacteristic
419C2×C4#1451974511yescharacteristic
420C2×C4#1451974811yescharacteristic
421C2×C4#1451975911yescharacteristic
422C2×C4D8×D6111yescharacteristic
423C2×C4D8×D6111yescharacteristic
424C2×C4SD16×D6111yescharacteristic
425C2×C4#1451979611yescharacteristic
426C2×C4#1451979811yescharacteristic
427C2×C4#1451979811yescharacteristic
428C2×C4#1451980111yescharacteristic
429C2×C4#1451980411yescharacteristic
430C8—42no—
431C8—81no—
432C8—1222no—
433C8—2442no—
434C8—2441no—
435C22—82no—
436C22—82no—
437C22—82no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22—161no—
442C22—1224no—
443C22—2442no—
444C22—2442no—
445C22—2442no—
446C22—2442no—
447C22—2442no—
448C22—2442no—
449C22#1683963811yescharacteristic
450C22#1683995611yescharacteristic
451C22#1683997611yescharacteristic
452C22#1683999011yescharacteristic
453C22#1683999711yescharacteristic
454C22#1684002411yescharacteristic
455C22#1684003111yescharacteristic
456C4—21no—
457C4—21no—
458C4—9761no—
459C4—2442no—
460C4#102×D6111yescharacteristic
461C4#1683975511yescharacteristic
462C4#1683984211yescharacteristic
463C4#1683987111yescharacteristic
464C4#1683989411yescharacteristic
465C4#1683990611yescharacteristic
466C4#1683998811yescharacteristic
467C4#1683999511yescharacteristic
468C2—162no—
469C2—2444no—
470C2#2144515911yescharacteristic
471C2#2144517311yescharacteristic
472C2#2144522711yescharacteristic
473C2#2144525511yescharacteristic
474C2#2144616411yescharacteristic
475C2#2144624411yescharacteristic
476C2#2144632411yescharacteristic
subgroupG/H
centerC23#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#331C2
socleC23×C61#121
prime radicalC2×#16839954C2
cosocleC2×C42×C61C23
hypercenterC2×#331D61
hypocenterC61#9221
LCSG ▷ 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. C2×#16839827C2semidirect
3. #21446626C2semidirect
4. #21445820C2semidirect
5. #21443703C2semidirect
6. #21443653C2semidirect
7. C2×C61×#331C2semidirect
12. #16839954C4semidirect
134. C2×#92418D8semidirect
186. D244#102semidirect
234. C2×#331D61semidirect
266. C61#9221semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
C2×#168398272
#214466262
#214458202
#214437032
#214436532
C2×C61×#3312
#922161