Finite Group Databasebeta

← #29573380

Subgroups — #29573380

Order 15616.

496 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448215C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic
3C4×#14519689C211yesmaximal, characteristic
4#21443660C211yesmaximal, characteristic, complemented
5#21443659C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×C42×D61C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×#14519689—21no—
11C2×#14519689—21no—
12C2×C4×#92418C2211yescharacteristic
13#16839629—21no—
14#16839627C411yescharacteristic
15#16839627C411yescharacteristic
16#16839624—21no—
17#16839619C411yescharacteristic
18#16839619C411yescharacteristic
19C4×C4⋊Dic61C2211yescharacteristic
20C4×#11758198—21no—
21#16839608—21no—
22#16839516—21no—
23#16839516—21no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C4×C4⋊C4×C61C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C42×D61—21no—
41C42×D61—21no—
42C42×D61—21no—
43C42×D61—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46#14519689—24no—
47#14519689—42no—
48C4×#92418—21no—
49C4×#92418—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61—21no—
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4×C8×C61—21no—
66C4×C8×C61—21no—
67#95×C61—21no—
68C23×D61C22⋊C411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—41no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C42×C61—41no—
106C42×C61—41no—
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110C42×C61#4111yescharacteristic
111#11758198—42no—
112#11758198—42no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—41no—
124C4×Dic61—41no—
125C2×#92418—22no—
126C2×#92418—41no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C23×C61C2×C22⋊C411yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61#10412yes—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61#11711yescharacteristic
148C2×C4×C61#11711yescharacteristic
149C2×C4×C61#12311yescharacteristic
150C2×C4×C61#12311yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61#12311yescharacteristic
153C2×C4×C61#13111yescharacteristic
154C2×C4×C61#13111yescharacteristic
155C2×C4×C61#13111yescharacteristic
156C2×C4×C61#13111yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C4×D61—42no—
177C4×D61—42no—
178C4×D61—41no—
179C4×D61—41no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—41no—
186C8×C61—42no—
187C8×C61—81no—
188#92418—42no—
189#92418—81no—
190#8711—611nomaximal, Sylow
191C22×C61#38111yescharacteristic
192C22×C61#40811yescharacteristic
193C22×C61#40811yescharacteristic
194C22×C61#41611yescharacteristic
195C22×C61#41711yescharacteristic
196C22×C61C2×#10411yescharacteristic
197C22×C61#42111yescharacteristic
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—81no—
208C4×C61—81no—
209C4×C61#43311yescharacteristic
210C4×C61#43311yescharacteristic
211C4×C61#43311yescharacteristic
212C4×C61#43311yescharacteristic
213C4×C61#48211yescharacteristic
214C4×C61#48211yescharacteristic
215C4×C61#48511yescharacteristic
216C4×C61#48511yescharacteristic
217Dic61—41no—
218Dic61—41no—
219Dic61—41no—
220Dic61—81no—
221Dic61—81no—
222#2283—611no—
223#1797—611no—
224C4×C22⋊C8—611no—
225#1279—611no—
226#1279—611no—
227#1279—611no—
228#1279D6111yescharacteristic, complemented
229C2×C61#148211yescharacteristic
230C2×C61#148311yescharacteristic
231C2×C61#149411yescharacteristic
232C2×C61#149511yescharacteristic
233C2×C61#181811yescharacteristic
234C2×C61#182511yescharacteristic
235C2×C61#182611yescharacteristic
236D61—42no—
237C22×C42—611no—
238C2×C4⋊C8—611no—
239C2×C4⋊C8C2×D6111yescharacteristic
240C2×C22⋊C8—1221no—
241C2×C22⋊C8—1221no—
242C2×C4×C8—611no—
243C2×C4×C8C2×D6111yescharacteristic
244#383—1221no—
245#382—611no—
246#382—611no—
247#381—1221no—
248#380—611no—
249#380—611no—
250C4×C4⋊C4—611no—
251C4×C4⋊C4C2×D6111yescharacteristic
252C4×C22⋊C4—1221no—
253#376—1221no—
254#336—1221no—
255#336—1221no—
256C61#871111yescharacteristic, complemented, Sylow
257C23×C4—611no—
258C23×C4—611no—
259C23×C4—611no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—1221no—
263C22×C8—1221no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4C4×D6111yescharacteristic
267C2×C4⋊C4C4×D6111yescharacteristic
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C42—21no—
271C2×C42—611no—
272C2×C42—611no—
273C2×C42—611no—
274C2×C42—1221no—
275C2×C42—1221no—
276C2×C42—1221no—
277C2×C42—1221no—
278C2×C42—1221no—
279C2×C42C22×D6111yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—1221no—
283C4⋊C8—1221no—
284C22⋊C8—1224no—
285C22⋊C8—2442no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8—1221no—
289C4×C8—1221no—
290#95—21no—
291#95—1221no—
292#95—1221no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296#95—1221no—
297#95—1221no—
298C24—611no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—1222no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—2441no—
322C22×C4C2×C4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—1222no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8—2441no—
336C2×C8—2441no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—1221no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—1221no—
345C22⋊C4—2442no—
346C22⋊C4—2442no—
347C42—41no—
348C42—41no—
349C42—1221no—
350C42—1221no—
351C42—1221no—
352C42—1221no—
353C42—1221no—
354C42—1221no—
355C42—2441no—
356C42—2441no—
357C42#1175822211yescharacteristic
358C42#1175822211yescharacteristic
359C42#1175822411yescharacteristic
360C42#1175822611yescharacteristic
361C23—612no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23C22⋊C4×D6111yescharacteristic
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4#1451973411yescharacteristic
403C2×C4#1451973511yescharacteristic
404C2×C4#1451975911yescharacteristic
405C2×C4#1451975911yescharacteristic
406C2×C4#1451976211yescharacteristic
407C2×C4#1451976211yescharacteristic
408C2×C4#1451978311yescharacteristic
409C2×C4#1451978311yescharacteristic
410C2×C4#1451978511yescharacteristic
411C2×C4#1451978511yescharacteristic
412C2×C4#1451979611yescharacteristic
413C2×C4#1451979811yescharacteristic
414C2×C4#1451980411yescharacteristic
415C2×C4#1451980911yescharacteristic
416C8—42no—
417C8—81no—
418C8—4881no—
419C8—2442no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22#1683962411yescharacteristic
428C22#1683972711yescharacteristic
429C22#1683972711yescharacteristic
430C22#1683975511yescharacteristic
431C22#1683976211yescharacteristic
432C22#104×D6111yescharacteristic
433C22#1683977711yescharacteristic
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—4881no—
439C4—4881no—
440C4—2441no—
441C4—2441no—
442C4—2441no—
443C4#1683982111yescharacteristic
444C4#1683982211yescharacteristic
445C4#1683982211yescharacteristic
446C4#1683982411yescharacteristic
447C4#1684008411yescharacteristic
448C4#1684008811yescharacteristic
449C4#1684010111yescharacteristic
450C4#1684010511yescharacteristic
451C2—2442no—
452C2#2144422411yescharacteristic
453C2#2144423111yescharacteristic
454C2#2144427611yescharacteristic
455C2#2144428311yescharacteristic
456C2#2144588911yescharacteristic
457C2#2144591211yescharacteristic
458C2#2144591711yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8711
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #21443660C2semidirect
5. #21443659C2semidirect
6. #21443658C2semidirect
7. C61×#1279C2semidirect
228. #1279D61semidirect
256. C61#8711semidirect

Maximal subgroups

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

subgroupindex
#214482152
#214457962
C4×#145196892
#214436602
#214436592
#214436582
C61×#12792
#871161