Finite Group Databasebeta

← #29576248

Subgroups — #29576248

Order 15616.

646 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×#16839957C211yesmaximal, characteristic
2C2×#16839840C211yesmaximal, characteristic, complemented
3#21446624C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic, complemented
5#21443702C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1802C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C22×#11758194—21no—
10C2×#14519774C2211yescharacteristic
11#16839957—22no—
12#16839957C414yescomplemented
13#16839840—22no—
14#16839840—22no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519697—21no—
18C2×#14519697—21no—
19C2×#14519697—21no—
20C2×C22⋊#92418—21no—
21C2×C4×#92418C2211yescharacteristic
22#16839505—22no—
23C2×C4×D4×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×#102×C61—21no—
26C61×#384C2211yescharacteristic
27C61×#340—21no—
28C22×D244—21no—
29C22×D244—21no—
30C22×D244—21no—
31C2×#11758199—24no—
32C2×#11758199—42no—
33C2×#11758199—42no—
34C2×#11758194—24no—
35C2×#11758194—42no—
36C2×#11758194—42no—
37C22×#92418—21no—
38C22×#92418—21no—
39C22×#92418D411yescharacteristic
40C22×#92418D411yescharacteristic
41#14519774—21no—
42#14519774—21no—
43#14519774—21no—
44#14519774C2×C412yes—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418C2×C412yes—
48C4⋊#92418D412yes—
49#14519697—24no—
50#14519697—42no—
51#14519697—42no—
52C22⋊#92418—24no—
53C4×#92418—21no—
54C4×#92418—21no—
55C22×D4×C61D411yescharacteristic
56C23×C4×C61—21no—
57C22×C8×C61—21no—
58C4×D4×C61—21no—
59C4×D4×C61—21no—
60C4×D4×C61C2×C412yes—
61C4×D4×C61D412yes—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70#102×C61—42no—
71C24×C61—21no—
72C23×D61—41no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61C22⋊C412yes—
79C22×C4×C61—21no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C2×D244—22no—
91C2×D244—22no—
92C2×D244—22no—
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—41no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244—81no—
105C2×D244—81no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—81no—
115C4⋊C4×C61C22⋊C412yes—
116C22⋊C4×C61—22no—
117C22⋊C4×C61—22no—
118C42×C61C22×C411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122#11758199—48no—
123#11758194—48no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—22no—
127C2×#92418—21no—
128C2×#92418—22no—
129C2×#92418—21no—
130C2×#92418—21no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418D812yescomplemented
136C23×C61—22no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61#12111yescharacteristic
144C22×D61—42no—
145C22×D61—81no—
146C22×D61—81no—
147C22×D61—81no—
148C22×D61—81no—
149C22×D61—81no—
150C22×D61—81no—
151D4×C61—22no—
152D4×C61—22no—
153D4×C61—41no—
154D4×C61—41no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—22no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61C2×C22⋊C411yescharacteristic
168C2×C4×C61C4×D411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12311yescharacteristic
173C2×C4×C61C2×D811yescharacteristic
174C2×C4×C61#13511yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C61#13711yescharacteristic
181D244—42no—
182D244—42no—
183D244—42no—
184D244—42no—
185D244—82no—
186D244—82no—
187D244—81no—
188D244—81no—
189D244—81no—
190D244—81no—
191C8×C61—81no—
192#92418—22no—
193#92418—42no—
194#92418—42no—
195#92418—41no—
196#9229—611nomaximal, Sylow
197C22×C61—42no—
198C22×C61—42no—
199C22×C61—42no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61—81no—
204C22×C61#38611yescharacteristic
205C22×C61#45911yescharacteristic
206C22×C61#46311yescharacteristic
207C22×C61#46811yescharacteristic
208C22×C61#46911yescharacteristic
209C22×C61#47111yescharacteristic
210C22×C61#47211yescharacteristic
211C2×D61—82no—
212C2×D61—82no—
213C2×D61—82no—
214C2×D61—161no—
215C2×D61—161no—
216C2×D61—161no—
217C2×D61—161no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—42no—
221C4×C61—161no—
222C4×C61#41711yescharacteristic
223C4×C61#41811yescharacteristic
224C4×C61C4×D811yescharacteristic
225C4×C61#44211yescharacteristic
226C4×C61#44711yescharacteristic
227C4×C61#44911yescharacteristic
228C4×C61#46811yescharacteristic
229C4×C61#46911yescharacteristic
230C2×#459—611no—
231C2×#436—611no—
232#1957—611no—
233#1802D6111yescharacteristic, complemented
234C2×#331—611no—
235#1296—611no—
236#1277—611no—
237C2×C61—82no—
238C2×C61#168511yescharacteristic
239C2×C61#168711yescharacteristic
240C2×C61#169711yescharacteristic
241C2×C61#170111yescharacteristic
242C2×C61#187911yescharacteristic
243C2×C61#189511yescharacteristic
244C2×C61#190711yescharacteristic
245D61—162no—
246C22×D8—1221no—
247C22×M16—1221no—
248C2×#127—611no—
249C2×C4×D4C2×D6111yescharacteristic
250#459—614no—
251#459—1222no—
252#436—1222no—
253#436—1222no—
254C2×C4⋊C8—611no—
255C2×C4⋊C8—611no—
256C2×C4⋊C8C2×D6111yescharacteristic
257C2×#102—21no—
258C2×#102—1221no—
259C2×#102—1221no—
260C2×#102—1221no—
261C2×C22⋊C8—1221no—
262C2×C4×C8—611no—
263#384C2×D6111yescharacteristic
264#340—21no—
265#331—1222no—
266C61#922911yescharacteristic, complemented, Sylow
267C22×D4—1221no—
268C22×D4—1221no—
269C22×D4—1221no—
270C22×D4C22⋊D6111yescharacteristic
271C23×C4—21no—
272C2×D8—1224no—
273C2×D8—2442no—
274C2×D8—2442no—
275C2×M16—1224no—
276C2×M16—2442no—
277C2×M16—2442no—
278C22×C8—21no—
279C22×C8—611no—
280C22×C8—611no—
281C22×C8—1221no—
282C22×C8—1221no—
283#127—612no—
284#127—1221no—
285#127—1221no—
286#127—1221no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4C4×D6112yes—
290C4×D4D24412yes—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4C22⋊D6111yescharacteristic
295C2×C22⋊C4—21no—
296C2×C42C22×D6111yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—612no—
300C4⋊C8—612no—
301C4⋊C8—1221no—
302C4⋊C8—1221no—
303#102—42no—
304#102—1224no—
305#102—2442no—
306#102—2442no—
307C22⋊C8—1224no—
308C4×C8—1221no—
309C4×C8—1221no—
310C24—21no—
311C24—2441no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—1222no—
318C2×D4—1222no—
319C2×D4—1222no—
320C2×D4—4881no—
321C2×D4—4881no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327C2×D4—2441no—
328C2×D4—2441no—
329C2×D4—2441no—
330C2×D4—2441no—
331C2×D4—2441no—
332C2×D4—2441no—
333C2×D4#1175819812yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4D4×D6111yescharacteristic
343C22×C4#1175822411yescharacteristic
344C22×C4C2×C22⋊D6111yescharacteristic
345D8—2448no—
346M16—2448no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—612no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1222no—
354C2×C8—1221no—
355C2×C8—1222no—
356C2×C8—1221no—
357C2×C8—1221no—
358C2×C8—2441no—
359C2×C8—2441no—
360C2×C8—2441no—
361C2×C8—2441no—
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—81no—
368C4⋊C4#1175819812yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C42C2×C4×D6111yescharacteristic
372C42C2×D24411yescharacteristic
373C42D4×D6111yescharacteristic
374C42#1175822411yescharacteristic
375C23—22no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—4881no—
383C23—4881no—
384C23—4881no—
385C23—4881no—
386C23—4881no—
387C23—4881no—
388C23—2442no—
389C23#1451974911yescharacteristic
390D4—22no—
391D4—22no—
392D4—41no—
393D4—41no—
394D4—4882no—
395D4—4882no—
396D4—4881no—
397D4—4881no—
398D4—4881no—
399D4—4881no—
400D4—2442no—
401D4—2442no—
402D4—2442no—
403D4—2442no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4C2×#1175819811yescharacteristic
417C2×C4#1451973711yescharacteristic
418C2×C4#1451973711yescharacteristic
419C2×C4#1451974711yescharacteristic
420C2×C4#1451974911yescharacteristic
421C2×C4#1451976111yescharacteristic
422C2×C4D8×D6111yescharacteristic
423C2×C4#1451979811yescharacteristic
424C2×C4#1451980111yescharacteristic
425C2×C4#1451980211yescharacteristic
426C2×C4#1451980211yescharacteristic
427C2×C4#1451980311yescharacteristic
428C2×C4#1451980411yescharacteristic
429C2×C4#1451980811yescharacteristic
430C8—81no—
431C8—1222no—
432C8—2442no—
433C8—2442no—
434C8—2441no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—9761no—
443C22—9761no—
444C22—9761no—
445C22—9761no—
446C22—4882no—
447C22—4882no—
448C22—4882no—
449C22#1683963911yescharacteristic
450C22#1683995511yescharacteristic
451C22#1683997911yescharacteristic
452C22#1684001011yescharacteristic
453C22#1684001311yescharacteristic
454C22#1684002711yescharacteristic
455C22#1684003011yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—161no—
460C4#1683976111yescharacteristic
461C4#1683976611yescharacteristic
462C4#1683984211yescharacteristic
463C4#1683987111yescharacteristic
464C4#1683989711yescharacteristic
465C4#1683990811yescharacteristic
466C4#1684001011yescharacteristic
467C4#1684001311yescharacteristic
468C2—82no—
469C2—9762no—
470C2#2144528611yescharacteristic
471C2#2144529611yescharacteristic
472C2#2144535411yescharacteristic
473C2#2144538211yescharacteristic
474C2#2144616511yescharacteristic
475C2#2144625511yescharacteristic
476C2#2144632511yescharacteristic
subgroupG/H
centerC23#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1802C2
socleC23×C61#121
prime radicalC2×#16839957C2
cosocleC2×C42×C61C23
hypercenter#1802D61
hypocenterC61#9229
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#16839840C2semidirect
3. #21446624C2semidirect
4. C2×#16839505C2semidirect
5. #21443702C2semidirect
6. #21443653C2semidirect
7. C61×#1802C2semidirect
12. #16839957C4semidirect
135. C2×#92418D8semidirect
233. #1802D61semidirect
266. C61#9229semidirect

Maximal subgroups

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

subgroupindex
C2×#168399572
C2×#168398402
#214466242
C2×#168395052
#214437022
#214436532
C61×#18022
#922961