Finite Group Databasebeta

← #29580258

Subgroups — #29580258

Order 15616.

672 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840080C211yesmaximal, characteristic
2#21451561C211yesmaximal, characteristic
3#21445909C211yesmaximal, characteristic, complemented
4C2×#16839495C211yesmaximal, characteristic
5C2×#16839488C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C2×C61×#400C211yesmaximal, characteristic, complemented
8C2×#14519760—21no—
9C2×#14519751C2211yescharacteristic
10#16840080—22no—
11#16840080—22no—
12C2×#14519708—21no—
13C2×#14519697—21no—
14C2×C22⋊#92418C2211yescharacteristic
15C2×C22⋊#92418C2211yescharacteristic
16#16839692—21no—
17#16839684—22no—
18#16839679—21no—
19#16839641—21no—
20#16839622C2211yescharacteristic
21#16839524—22no—
22#16839495—22no—
23#16839488—22no—
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C61×#400—22no—
27C61×#400—22no—
28C2×#95×C61—21no—
29C2×#95×C61—21no—
30C2×#95×C61C2211yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35#14519760—42no—
36#14519760—42no—
37#14519751—21no—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D412yes—
43C2×#11758196—22no—
44C2×C22⋊Dic61—21no—
45C2×#11758198—22no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48#14519708—24no—
49#14519697—24no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418D412yes—
54#14519684—22no—
55#14519684—21no—
56C23×C4×C61—21no—
57C23×C4×C61—21no—
58C23×C4×C61D411yescharacteristic
59C23×C4×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61D412yes—
73#95×C61—24no—
74#95×C61—24no—
75#95×C61—21no—
76#95×C61D412yes—
77C24×C61C2×D411yescharacteristic
78C23×D61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—22no—
86C22×C4×C61—21no—
87C22×C4×C61—22no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—42no—
91C22×C4×C61—42no—
92C22×C4×C61—42no—
93C22×C4×C61—42no—
94C22×C4×C61—44no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61SD1612yes—
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61#4111yescharacteristic
106C2×C22⋊D61—41no—
107C2×C22⋊D61—41no—
108C2×C22⋊D61—41no—
109C2×C22⋊D61—41no—
110C2×C22⋊D61—41no—
111C2×C22⋊D61—41no—
112C22×Dic61—21no—
113C22×Dic61—22no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—42no—
117C4⋊C4×C61—22no—
118C4⋊C4×C61—22no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61—41no—
124C4⋊C4×C61—41no—
125C22⋊Dic61—41no—
126C22⋊Dic61—41no—
127#11758198—44no—
128#11758198—41no—
129#11758198—41no—
130#11758198—82no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133C4⋊Dic61—42no—
134#11758196—44no—
135C2×#92418—22no—
136C2×#92418—42no—
137C2×#92418—42no—
138C2×#92418—41no—
139C23×C61—22no—
140C23×C61—22no—
141C23×C61#12011yescharacteristic
142C23×C61#12011yescharacteristic
143C23×C61#12111yescharacteristic
144C23×C61C2×SD1611yescharacteristic
145C23×C61#13511yescharacteristic
146C23×C61AGL(1,ℤ/8)11yescharacteristic
147C23×C61#13711yescharacteristic
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—42no—
152C22×D61—42no—
153C2×C4×C61—22no—
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—44no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—82no—
175C2×C4×C61—82no—
176C2×C4×C61—82no—
177C2×C4×C61—82no—
178C2×C4×C61—81no—
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12711yescharacteristic
183C22⋊D61—81no—
184C22⋊D61—81no—
185C22⋊D61—81no—
186C22⋊D61—81no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—42no—
190C2×Dic61—41no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193D244—42no—
194D244—81no—
195#92418—42no—
196#92418—81no—
197#9921—611nomaximal, Sylow
198C22×C61—22no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—22no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61#39211yescharacteristic
207C22×C61#44811yescharacteristic
208C22×C61#44911yescharacteristic
209C22×C61#45011yescharacteristic
210C22×C61#45211yescharacteristic
211C22×C61#45412yes—
212C22×C61#45812yes—
213C22×C61#46511yescharacteristic
214C22×C61#46811yescharacteristic
215C2×D61—82no—
216C2×D61—82no—
217C2×D61—81no—
218C2×D61—81no—
219C2×D61—81no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—42no—
225C4×C61—82no—
226C4×C61—82no—
227C4×C61—81no—
228Dic61—82no—
229Dic61—81no—
230C2×#481—611no—
231#2618—611no—
232C2×#400D6111yescharacteristic, complemented
233#1824—611no—
234C2×#327—611no—
235C2×#324—611no—
236#1294—611no—
237C2×C61—21no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—21no—
241C2×C61#161512yes—
242C2×C61#161612yes—
243C2×C61#200011yescharacteristic
244C2×C61#200311yescharacteristic
245C2×C61#202211yescharacteristic
246D61—161no—
247C2×#123—1221no—
248C2×#121—611no—
249C22×C4⋊C4C2×D6111yescharacteristic
250C22×C4⋊C4C2×D6111yescharacteristic
251#481—1222no—
252#481—1222no—
253C2×#106—1221no—
254C2×#102—1221no—
255C2×C22⋊C8—611no—
256C2×C22⋊C8—611no—
257#400—22no—
258#400—22no—
259#398—1221no—
260#396—1222no—
261#394—1221no—
262#386—1221no—
263#380—611no—
264C2×#95—21no—
265C2×#95—21no—
266C2×#95C2×D6111yescharacteristic
267#340—1222no—
268#327—1222no—
269#324—1222no—
270C61#992111yescharacteristic, complemented, Sylow
271C22×D4—611no—
272C22×D4—1221no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4C22⋊D6111yescharacteristic
276C23×C4C22⋊D6111yescharacteristic
277C23×C4C22×D6111yescharacteristic
278C22×C8—1221no—
279C22×C8—1221no—
280#123—2442no—
281#123—2442no—
282#121—1221no—
283#121—1221no—
284#121—1221no—
285#121—1221no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—611no—
298C2×C4⋊C4—612no—
299C2×C4⋊C4—1222no—
300C2×C4⋊C4C22⋊D6112yes—
301C2×C22⋊C4—1222no—
302C2×C22⋊C4—1222no—
303C2×C22⋊C4—1221no—
304C2×C22⋊C4—1221no—
305#106—1224no—
306#102—1224no—
307C22⋊C8—612no—
308C22⋊C8—1221no—
309C22⋊C8—1221no—
310C22⋊C8—1221no—
311#95—24no—
312#95—24no—
313#95—21no—
314#95—1222no—
315#95—1221no—
316#95C22⋊D6112yes—
317C24—1221no—
318C24C2×C22⋊D6111yescharacteristic
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—2442no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327C2×D4—2441no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—44no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—1222no—
349C22×C4—1221no—
350C22×C4#1175820112yes—
351C22×C4D4×D6111yescharacteristic
352C22×C4D4×D6111yescharacteristic
353C22×C4D4×D6111yescharacteristic
354C22×C4#1175822411yescharacteristic
355C22×C4C2×C22⋊D6111yescharacteristic
356C22×C4C2×C22⋊D6111yescharacteristic
357C2×C8—1222no—
358C2×C8—2442no—
359C2×C8—2441no—
360C2×C8—2442no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—1221no—
370C4⋊C4—1221no—
371C4⋊C4—2442no—
372C4⋊C4—2444no—
373C22⋊C4—4882no—
374C22⋊C4—2444no—
375C22⋊C4—2441no—
376C22⋊C4—2441no—
377C22⋊C4—2441no—
378C22⋊C4—2441no—
379C23—22no—
380C23—22no—
381C23—2442no—
382C23—2441no—
383C23—2441no—
384C23—2441no—
385C23—2442no—
386C23#1451974511yescharacteristic
387C23#1451974611yescharacteristic
388C23#1451974911yescharacteristic
389C23C2×#1175820111yescharacteristic
390C23#1451979711yescharacteristic
391C23#1451980211yescharacteristic
392C23#1451980811yescharacteristic
393D4—4881no—
394D4—4881no—
395D4—4881no—
396D4—4881no—
397D4—4881no—
398D4—2442no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2442no—
431C2×C4#1451974511yescharacteristic
432C2×C4#1451974811yescharacteristic
433C2×C4#1451974911yescharacteristic
434C2×C4#1451977311yescharacteristic
435C8—4881no—
436C8—2442no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—4881no—
446C22—4881no—
447C22—4881no—
448C22—4882no—
449C22—4882no—
450C22#1683967011yescharacteristic
451C22#1683990111yescharacteristic
452C22#1683990711yescharacteristic
453C22#1683991211yescharacteristic
454C22#1683992211yescharacteristic
455C22#1683993412yes—
456C22#1683995112yes—
457C22#1683999311yescharacteristic
458C22#1684001011yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—82no—
465C4—81no—
466C4—82no—
467C4—4881no—
468C4—4882no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—9761no—
474C2#2144484812yes—
475C2#2144485512yes—
476C2#2144682011yescharacteristic
477C2#2144684111yescharacteristic
478C2#2144694711yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#400C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenterC2×#400D61
hypocenterC61#9921
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
3. #21445909C2semidirect
5. C2×#16839488C2semidirect
6. #21443698C2semidirect
7. C2×C61×#400C2semidirect
232. C2×#400D61semidirect
270. C61#9921semidirect

Maximal subgroups

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

subgroupindex
C2×#168400802
#214515612
#214459092
C2×#168394952
C2×#168394882
#214436982
C2×C61×#4002
#992161