Finite Group Databasebeta

← #29583885

Subgroups — #29583885

Order 15616.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840039C211yesmaximal, characteristic
2#21446622C211yesmaximal, characteristic, complemented
3#21446612C211yesmaximal, characteristic
4#21445820C211yesmaximal, characteristic
5C2×#16839512C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16840039—22no—
10#16840039—22no—
11C2×#14519710—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519701—21no—
14C2×#14519701—21no—
15C2×#14519699—21no—
16C2×#14519697—21no—
17C2×#14519689—21no—
18C2×#14519689—21no—
19C2×C4×#92418C2211yescharacteristic
20#16839632C2211yescharacteristic
21#16839525—21no—
22#16839512—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#332—22no—
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418D411yescharacteristic
31C22×#92418D411yescharacteristic
32C4×D244—21no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758198—21no—
41#14519710—24no—
42C4⋊#92418—21no—
43C4⋊#92418D412yes—
44#14519701—42no—
45#14519701—42no—
46#14519699—42no—
47#14519697—24no—
48#14519689—42no—
49#14519689—42no—
50C4×#92418—21no—
51C4×#92418—21no—
52C22×Q8×C61—21no—
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61D412yes—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C23×D61—21no—
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—41no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244SD1612yes—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61#4111yescharacteristic
104C42×C61#4111yescharacteristic
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61—81no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—22no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418D812yes—
123C23×C61#12111yescharacteristic
124C22×D61—22no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131Q8×C61—42no—
132Q8×C61—42no—
133Q8×C61—81no—
134Q8×C61—81no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—42no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61#12411yescharacteristic
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61C2×SD1611yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—81no—
158C2×Dic61—81no—
159C2×Dic61—81no—
160D244—22no—
161D244—22no—
162D244—41no—
163D244—41no—
164C4×D61—81no—
165C4×D61—81no—
166C4×D61—81no—
167C4×D61—81no—
168C8×C61—81no—
169C8×C61—81no—
170#92418—22no—
171#92418—42no—
172#92418—41no—
173#10484—611nomaximal, Sylow
174C22×C61#39411yescharacteristic
175C22×C61#45911yescharacteristic
176C22×C61#46311yescharacteristic
177C22×C61#46511yescharacteristic
178C22×C61#47011yescharacteristic
179C22×C61#47111yescharacteristic
180C22×C61#47311yescharacteristic
181C2×D61—42no—
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—82no—
191C4×C61#44811yescharacteristic
192C4×C61#45211yescharacteristic
193C4×C61#45911yescharacteristic
194C4×C61#46311yescharacteristic
195C4×C61#46611yescharacteristic
196C4×C61#46911yescharacteristic
197C4×C61#48311yescharacteristic
198C4×C61#48511yescharacteristic
199Dic61—81no—
200Dic61—161no—
201C2×#474—611no—
202#1956—611no—
203#1954—611no—
204#1802—611no—
205C2×#334—611no—
206C2×#332D6111yescharacteristic, complemented
207#1296—611no—
208C2×C61#166511yescharacteristic
209C2×C61#167911yescharacteristic
210C2×C61#168911yescharacteristic
211C2×C61#170311yescharacteristic
212C2×C61#203511yescharacteristic
213C2×C61#205211yescharacteristic
214C2×C61#205411yescharacteristic
215D61—82no—
216C2×C4⋊Q8C2×D6111yescharacteristic
217C2×C4×D4—611no—
218#474—1222no—
219#474—1222no—
220C2×#107—1221no—
221C2×C4⋊C8—611no—
222C2×C4⋊C8C2×D6111yescharacteristic
223C2×C4⋊C8C2×D6111yescharacteristic
224C2×#103—1221no—
225C2×#103—1221no—
226C2×#102—1221no—
227C2×#102—1221no—
228C2×C22⋊C8—1221no—
229C2×C22⋊C8—1221no—
230C2×C4×C8—611no—
231#384—611no—
232#340—1221no—
233#334—1222no—
234#332—22no—
235C61#1048411yescharacteristic, complemented, Sylow
236C22×Q8—21no—
237C22×D4—611no—
238C23×C4—1221no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—611no—
242C22×C8—611no—
243C22×C8—1221no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8C22⋊D6112yes—
248C4×D4—1221no—
249C4×D4—1221no—
250C4×D4—1221no—
251C4×D4—1221no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C42C22×D6111yescharacteristic
260#107—1224no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—612no—
266C4⋊C8—1221no—
267#103—2442no—
268#103—2442no—
269#102—1224no—
270#102—2442no—
271C22⋊C8—2442no—
272C22⋊C8—2442no—
273C4×C8—1221no—
274C4×C8—1221no—
275C24—1221no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—612no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C22×C4—41no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4#1175822211yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4D4×D6111yescharacteristic
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—612no—
307C2×C8—1221no—
308C2×C8—1221no—
309C2×C8—1222no—
310C2×C8—1221no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—2441no—
314C2×C8—2441no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C4⋊C4—4881no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C42#1175822211yescharacteristic
329C42D4×D6111yescharacteristic
330C42#1175822411yescharacteristic
331C42C2×C22⋊D6111yescharacteristic
332C23—1222no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23#1451975011yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—1222no—
345D4—1222no—
346D4—2441no—
347D4—2441no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—4881no—
354C2×C4—4881no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4#1451974511yescharacteristic
364C2×C4#1451974911yescharacteristic
365C2×C4#1451975011yescharacteristic
366C2×C4#1451975911yescharacteristic
367C2×C4#1451976011yescharacteristic
368C2×C4#1451976311yescharacteristic
369C2×C4D8×D6111yescharacteristic
370C2×C4SD16×D6111yescharacteristic
371C2×C4#1451979811yescharacteristic
372C2×C4#1451980011yescharacteristic
373C2×C4#1451980111yescharacteristic
374C2×C4#1451980411yescharacteristic
375C2×C4#1451980611yescharacteristic
376C2×C4#1451980911yescharacteristic
377C8—81no—
378C8—81no—
379C8—1222no—
380C8—2441no—
381C8—2442no—
382C22—4881no—
383C22—4881no—
384C22—4881no—
385C22—4881no—
386C22—2442no—
387C22—2442no—
388C22—2442no—
389C22#1683967711yescharacteristic
390C22#1683995611yescharacteristic
391C22#1683997611yescharacteristic
392C22#1683999411yescharacteristic
393C22#1684001911yescharacteristic
394C22#1684002811yescharacteristic
395C22#1684003611yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—9761no—
400C4—4881no—
401C4#1683989911yescharacteristic
402C4#1683992311yescharacteristic
403C4#1683995511yescharacteristic
404C4#1683997911yescharacteristic
405C4#1683999711yescharacteristic
406C4#1684001411yescharacteristic
407C4#1684009111yescharacteristic
408C4#1684010211yescharacteristic
409C2—4882no—
410C2#2144516311yescharacteristic
411C2#2144524111yescharacteristic
412C2#2144530711yescharacteristic
413C2#2144539311yescharacteristic
414C2#2144701311yescharacteristic
415C2#2144711811yescharacteristic
416C2#2144712811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenterC2×#332D61
hypocenterC61#10484
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #21446622C2semidirect
5. C2×#16839512C2semidirect
6. #21443703C2semidirect
7. C2×C61×#332C2semidirect
206. C2×#332D61semidirect
235. C61#10484semidirect

Maximal subgroups

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

subgroupindex
C2×#168400392
#214466222
#214466122
#214458202
C2×#168395122
#214437032
C2×C61×#3322
#1048461