Finite Group Databasebeta

← #29580260

Subgroups — #29580260

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×#16840081C211yesmaximal, characteristic
2#21451561C211yesmaximal, characteristic
3C2×#16839701C211yesmaximal, characteristic, complemented
4#21445910C211yesmaximal, characteristic, complemented
5C2×#16839497C211yesmaximal, characteristic
6#21443699C211yesmaximal, characteristic, complemented
7C2×C61×#324C211yesmaximal, characteristic, complemented
8C2×#14519760—21no—
9C2×#14519751C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11#16840081—22no—
12#16840081—22no—
13C2×#14519709—21no—
14C2×#14519699—21no—
15#16839701—22no—
16#16839701—22no—
17#16839692—21no—
18#16839684—22no—
19#16839679—21no—
20#16839641—21no—
21#16839622C2211yescharacteristic
22C2×#14519684—21no—
23C2×#14519684—21no—
24C2×#14519684C2211yescharacteristic
25#16839525—22no—
26#16839497—22no—
27C22×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C61×#324—22no—
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C23×Dic61—21no—
34C23×Dic61—21no—
35#14519760—42no—
36#14519760—42no—
37#14519751—21no—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×C4⋊Dic61D412yes—
48C2×C4⋊Dic61D412yes—
49C2×#11758196—22no—
50C2×C22⋊Dic61—21no—
51C2×#11758198—22no—
52C2×#11758198—21no—
53C2×#11758198—22no—
54#14519709—24no—
55#14519699—24no—
56#14519684—22no—
57#14519684—24no—
58#14519684—24no—
59#14519684—21no—
60#14519684—21no—
61#14519684D412yes—
62C23×C4×C61D411yescharacteristic
63C23×C4×C61D411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—21no—
66C22×C8×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×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×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—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61SD1612yes—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C22×Dic61—22no—
104C22×Dic61—22no—
105C22×Dic61—21no—
106C22×Dic61—22no—
107C22×Dic61—42no—
108C22×Dic61—42no—
109C22×Dic61—44no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—42no—
117C2×C8×C61—22no—
118C2×C8×C61—42no—
119C2×C8×C61—42no—
120C2×C8×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—22no—
132C4⋊Dic61—21no—
133C4⋊Dic61—22no—
134C4⋊Dic61—21no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C4⋊Dic61—42no—
138#11758196—44no—
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—41no—
168C2×C4×C61—42no—
169C2×C4×C61—81no—
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12711yescharacteristic
174C22⋊D61—81no—
175C22⋊D61—81no—
176C22⋊D61—81no—
177C22⋊D61—81no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—44no—
181C2×Dic61—42no—
182C2×Dic61—41no—
183C2×Dic61—42no—
184C2×Dic61—41no—
185C2×Dic61—42no—
186C2×Dic61—41no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—82no—
190C2×Dic61—82no—
191C2×Dic61—82no—
192C2×Dic61—82no—
193D244—42no—
194D244—81no—
195C8×C61—42no—
196C8×C61—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—81no—
226Dic61—82no—
227Dic61—82no—
228Dic61—81no—
229Dic61—82no—
230C2×#481—611no—
231#2618—611no—
232C2×#400—611no—
233#1824—611no—
234C2×#327—611no—
235C2×#324D6111yescharacteristic, complemented
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⋊C4—611no—
250C22×C4⋊C4C2×D6111yescharacteristic
251#481—1222no—
252#481—1222no—
253C2×#106—1221no—
254C2×#102—1221no—
255C2×C22⋊C8C2×D6111yescharacteristic
256C2×C22⋊C8C2×D6111yescharacteristic
257#400—1222no—
258#400—1222no—
259#398—1221no—
260#396—1222no—
261#394—1221no—
262#386—1221no—
263#380—611no—
264C2×#95—611no—
265C2×#95—1221no—
266C2×#95—1221no—
267#340—1222no—
268#327—1222no—
269#324—22no—
270C61#992111yescharacteristic, complemented, Sylow
271C22×D4—611no—
272C22×D4—1221no—
273C23×C4—1221no—
274C23×C4—1221no—
275C23×C4D24411yescharacteristic
276C23×C4D24411yescharacteristic
277C23×C4C22×D6111yescharacteristic
278C22×C8—21no—
279C22×C8—21no—
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—612no—
293C2×C4⋊C4—611no—
294C2×C4⋊C4—612no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—1221no—
299C2×C4⋊C4—1222no—
300C2×C4⋊C4—1221no—
301C2×C22⋊C4—1222no—
302C2×C22⋊C4—1222no—
303C2×C22⋊C4—1221no—
304C2×C22⋊C4—1221no—
305#106—1224no—
306#102—1224no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8C22⋊D6112yes—
311#95—612no—
312#95—1224no—
313#95—1224no—
314#95—1222no—
315#95—1221no—
316#95—1221no—
317C24—1221no—
318C24C2×D24411yescharacteristic
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—21no—
336C22×C4—21no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—1222no—
340C22×C4—1222no—
341C22×C4—1222no—
342C22×C4—1221no—
343C22×C4—2442no—
344C22×C4—2442no—
345C22×C4—2444no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4#1175819012yes—
351C22×C4#1175822211yescharacteristic
352C22×C4D4×D6111yescharacteristic
353C22×C4D4×D6111yescharacteristic
354C22×C4D4×D6111yescharacteristic
355C22×C4D4×D6111yescharacteristic
356C22×C4C2×C22⋊D6111yescharacteristic
357C2×C8—22no—
358C2×C8—42no—
359C2×C8—42no—
360C2×C8—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—1222no—
366C4⋊C4—1221no—
367C4⋊C4—1222no—
368C4⋊C4—1221no—
369C4⋊C4—2442no—
370C4⋊C4—2444no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
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—2442no—
383C23—2441no—
384C23—2441no—
385C23—2441no—
386C23#1451974711yescharacteristic
387C23#1451974711yescharacteristic
388C23#1451975111yescharacteristic
389C23C2×#1175819011yescharacteristic
390C23#1451979911yescharacteristic
391C23#1451980511yescharacteristic
392C23#1451981011yescharacteristic
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—41no—
415C2×C4—81no—
416C2×C4—4882no—
417C2×C4—4882no—
418C2×C4—4882no—
419C2×C4—4882no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2444no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2442no—
431C2×C4#1451974511yescharacteristic
432C2×C4#1451975011yescharacteristic
433C2×C4#1451975011yescharacteristic
434C2×C4#1451977311yescharacteristic
435C8—42no—
436C8—81no—
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#1683967111yescharacteristic
451C22#1683990311yescharacteristic
452C22#1683990911yescharacteristic
453C22#1683991511yescharacteristic
454C22#1683992611yescharacteristic
455C22#1683993712yes—
456C22#1683995312yes—
457C22#1683999111yescharacteristic
458C22#1684000811yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—81no—
465C4—4882no—
466C4—4881no—
467C4—4882no—
468C4—4882no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—9761no—
474C2#2144485212yes—
475C2#2144485812yes—
476C2#2144682411yescharacteristic
477C2#2144684311yescharacteristic
478C2#2144694911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenterC2×#324D61
hypocenterC61#9921
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. C2×#16839701C2semidirect
4. #21445910C2semidirect
6. #21443699C2semidirect
7. C2×C61×#324C2semidirect
235. C2×#324D61semidirect
270. C61#9921semidirect

Maximal subgroups

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

subgroupindex
C2×#168400812
#214515612
C2×#168397012
#214459102
C2×#168394972
#214436992
C2×C61×#3242
#992161