Finite Group Databasebeta

← #29576252

Subgroups — #29576252

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×#16839840C211yesmaximal, characteristic, complemented
2#21446626C211yesmaximal, characteristic, complemented
3#21445819C211yesmaximal, characteristic, complemented
4C2×#16839506C211yesmaximal, characteristic, complemented
5#21443703C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C2×C61×#459C211yesmaximal, characteristic
8C22×#11758194—21no—
9#16839840—22no—
10#16839840—22no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519698—21no—
14C2×#14519698—21no—
15C2×#14519698—21no—
16C2×C22⋊#92418—21no—
17C2×C4×#92418C2211yescharacteristic
18#16839632C2211yescharacteristic
19#16839524—21no—
20#16839506—22no—
21C22×D8×C61—21no—
22C2×#127×C61C2211yescharacteristic
23C2×C4×D4×C61C2211yescharacteristic
24C61×#459—22no—
25C61×#459C414yescomplemented
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×#102×C61—21no—
28C2×#11758194—24no—
29C2×#11758194—42no—
30C2×#11758194—42no—
31C22×#92418—21no—
32C22×#92418—21no—
33C22×#92418D411yescharacteristic
34C22×#92418D411yescharacteristic
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418D412yes—
42#14519698—42no—
43#14519698—42no—
44#14519698—42no—
45C22⋊#92418—24no—
46C4×#92418—21no—
47C4×#92418—21no—
48C22×D4×C61—21no—
49C22×D4×C61—21no—
50C22×D4×C61—21no—
51C22×D4×C61D411yescharacteristic
52C23×C4×C61—21no—
53C2×D8×C61—24no—
54C2×D8×C61—42no—
55C2×D8×C61—42no—
56C22×C8×C61—21no—
57#127×C61—21no—
58#127×C61—21no—
59#127×C61—21no—
60#127×C61C2×C412yes—
61C4×D4×C61—21no—
62C4×D4×C61—21no—
63C4×D4×C61C2×C412yes—
64C4×D4×C61D412yes—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61C2×C412yes—
70#102×C61—24no—
71C24×C61—21no—
72C24×C61—41no—
73C2×D4×C61—22no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
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—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—81no—
93C2×D4×C61—81no—
94C2×D4×C61C22⋊C412yes—
95C22×C4×C61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61#4111yescharacteristic
105C22×Dic61—41no—
106D8×C61—48no—
107C2×C8×C61—22no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61C22⋊C412yes—
112C22⋊C4×C61—22no—
113C22⋊C4×C61—22no—
114C42×C61C22×C411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—81no—
123#11758194—48no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—22no—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—41no—
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—42no—
144C23×C61—81no—
145C23×C61—81no—
146C23×C61—81no—
147C23×C61—81no—
148C23×C61—81no—
149C23×C61—81no—
150C23×C61#12111yescharacteristic
151D4×C61—22no—
152D4×C61—22no—
153D4×C61—42no—
154D4×C61—42no—
155D4×C61—42no—
156D4×C61—42no—
157D4×C61—41no—
158D4×C61—41no—
159D4×C61—82no—
160D4×C61—82no—
161D4×C61—81no—
162D4×C61—81no—
163D4×C61—81no—
164D4×C61—81no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—22no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61C2×C22⋊C411yescharacteristic
175C2×C4×C61C4×D411yescharacteristic
176C2×C4×C61C4×D411yescharacteristic
177C2×C4×C61#12011yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12311yescharacteristic
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61#13511yescharacteristic
182C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C61#13711yescharacteristic
188C2×Dic61—81no—
189C2×Dic61—81no—
190C2×Dic61—81no—
191C8×C61—42no—
192#92418—22no—
193#92418—42no—
194#92418—41no—
195#92418—81no—
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—82no—
205C22×C61—82no—
206C22×C61—82no—
207C22×C61—161no—
208C22×C61—161no—
209C22×C61—161no—
210C22×C61—161no—
211C22×C61#38611yescharacteristic
212C22×C61#45911yescharacteristic
213C22×C61#46311yescharacteristic
214C22×C61#46811yescharacteristic
215C22×C61#46911yescharacteristic
216C22×C61#47111yescharacteristic
217C22×C61#47211yescharacteristic
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—42no—
221C4×C61#41711yescharacteristic
222C4×C61#41811yescharacteristic
223C4×C61C4×D811yescharacteristic
224C4×C61#44211yescharacteristic
225C4×C61#44711yescharacteristic
226C4×C61#44911yescharacteristic
227C4×C61#46811yescharacteristic
228C4×C61#46911yescharacteristic
229Dic61—161no—
230C2×#459D6111yescharacteristic
231C2×#436—611no—
232#1957—611no—
233#1802—611no—
234C2×#331—611no—
235#1296—611no—
236#1277—611no—
237C2×C61—82no—
238C2×C61—162no—
239C2×C61#168511yescharacteristic
240C2×C61#168711yescharacteristic
241C2×C61#169711yescharacteristic
242C2×C61#170111yescharacteristic
243C2×C61#187911yescharacteristic
244C2×C61#189511yescharacteristic
245C2×C61#190711yescharacteristic
246C22×D8—21no—
247C22×M16—1221no—
248C2×#127C2×D6111yescharacteristic
249C2×C4×D4C2×D6111yescharacteristic
250#459—22no—
251#459Dic6114yescomplemented
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#384—611no—
264#340—1221no—
265#331—1222no—
266C61#922911yescharacteristic, complemented, Sylow
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4C22⋊D6111yescharacteristic
271C23×C4—21no—
272C2×D8—24no—
273C2×D8—42no—
274C2×D8—42no—
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—21no—
284#127—21no—
285#127—21no—
286#127C2×Dic6112yes—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4C2×Dic6112yes—
290C4×D4C22⋊D6112yes—
291C2×C4⋊C4—1221no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4C22⋊D6111yescharacteristic
295C2×C22⋊C4—21no—
296C2×C42C22×D6111yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—612no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301C4⋊C8—1221no—
302C4⋊C8C2×Dic6112yes—
303#102—24no—
304#102—2442no—
305#102—2442no—
306#102—2442no—
307C22⋊C8—1224no—
308C4×C8—1221no—
309C4×C8—1221no—
310C24—21no—
311C24—41no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—81no—
332C2×D4—81no—
333C2×D4C22⋊Dic6112yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—2441no—
342C22×C4D4×D6111yescharacteristic
343C22×C4#1175822411yescharacteristic
344C22×C4C2×C22⋊D6111yescharacteristic
345D8—48no—
346M16—2448no—
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—612no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—1222no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—2441no—
358C2×C8—2441no—
359C2×C8—2441no—
360C2×C8—2441no—
361C2×C8—2441no—
362C4⋊C4—21no—
363C4⋊C4—4881no—
364C4⋊C4—2441no—
365C4⋊C4—2441no—
366C4⋊C4—2441no—
367C4⋊C4—2441no—
368C4⋊C4C22⋊Dic6112yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C42D4×D6111yescharacteristic
372C42#1175822411yescharacteristic
373C42C22×Dic6111yescharacteristic
374C42C2×C22⋊D6111yescharacteristic
375C23—22no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—81no—
386C23—81no—
387C23—81no—
388C23—81no—
389C23#1451974911yescharacteristic
390D4—22no—
391D4—22no—
392D4—41no—
393D4—41no—
394D4—42no—
395D4—42no—
396D4—42no—
397D4—42no—
398D4—82no—
399D4—82no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—81no—
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—4881no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4C2×C22⋊Dic6111yescharacteristic
417C2×C4D4×Dic6111yescharacteristic
418C2×C4D4×Dic6111yescharacteristic
419C2×C4#1451974511yescharacteristic
420C2×C4#1451974911yescharacteristic
421C2×C4#1451975811yescharacteristic
422C2×C4D8×D6111yescharacteristic
423C2×C4#1451979611yescharacteristic
424C2×C4#1451980111yescharacteristic
425C2×C4#1451980111yescharacteristic
426C2×C4#1451980211yescharacteristic
427C2×C4#1451980311yescharacteristic
428C2×C4#1451980311yescharacteristic
429C2×C4#1451980711yescharacteristic
430C8—42no—
431C8—1222no—
432C8—4881no—
433C8—2442no—
434C8—2441no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—161no—
446C22—161no—
447C22—161no—
448C22—161no—
449C22#1683964211yescharacteristic
450C22#1683995511yescharacteristic
451C22#1683997511yescharacteristic
452C22#1684000611yescharacteristic
453C22#1684001311yescharacteristic
454C22#1684002311yescharacteristic
455C22#1684003011yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—9761no—
460C4#1683976311yescharacteristic
461C4#1683976711yescharacteristic
462C4D8×Dic6111yescharacteristic
463C4#1683987411yescharacteristic
464C4#1683989411yescharacteristic
465C4#1683990411yescharacteristic
466C4#1684000611yescharacteristic
467C4#1684001311yescharacteristic
468C2—82no—
469C2—162no—
470C2#2144528211yescharacteristic
471C2#2144529611yescharacteristic
472C2#2144535011yescharacteristic
473C2#2144537811yescharacteristic
474C2#2144616911yescharacteristic
475C2#2144625811yescharacteristic
476C2#2144632911yescharacteristic
subgroupG/H
centerC23#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
Fitting, prime radicalC2×C61×#459C2
socleC23×C61#121
cosocleC2×C42×C61C23
hypercenterC2×#459D61
hypocenterC61#9229
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16839840C2semidirect
2. #21446626C2semidirect
3. #21445819C2semidirect
4. C2×#16839506C2semidirect
5. #21443703C2semidirect
6. #21443653C2semidirect
25. C61×#459C4semidirect
135. C2×#92418D8semidirect
251. #459Dic61semidirect
266. C61#9229semidirect

Maximal subgroups

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

subgroupindex
C2×#168398402
#214466262
#214458192
C2×#168395062
#214437032
#214436532
C2×C61×#4592
#922961