Finite Group Databasebeta

← #29584227

Subgroups — #29584227

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840135C211yesmaximal, characteristic
2#21446770C211yesmaximal, characteristic, complemented
3#21446745C211yesmaximal, characteristic
4#21446537C211yesmaximal, characteristic, complemented
5C2×#16839507C211yesmaximal, characteristic, complemented
6C2×#16839505C211yesmaximal, characteristic
7C61×#1277C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C22×#11758190—21no—
10C2×#14519777C2211yescharacteristic
11C2×#14519774C2211yescharacteristic
12#16840135—22no—
13#16840135—22no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519706—21no—
16C2×#14519699—21no—
17C2×#14519699—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839516—21no—
22#16839507—22no—
23#16839505—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4×C8×C61C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244—21no—
29C22×D244—21no—
30C22×D244—21no—
31C2×#11758190—24no—
32C2×#11758190—24no—
33C2×#11758190—42no—
34C2×#11758190—42no—
35C2×#11758190—42no—
36C2×#11758190—42no—
37C22×#92418—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777D412yes—
42#14519774—21no—
43#14519774—21no—
44#14519774—21no—
45#14519774D412yes—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61D411yescharacteristic
49C2×C4⋊Dic61D411yescharacteristic
50C2×C4×Dic61—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519706—42no—
54#14519699—42no—
55#14519699—42no—
56#14519684—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C22×C8×C61D411yescharacteristic
60C22×C8×C61D411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61—21no—
68C23×D61—41no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61#4111yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—41no—
75C2×D244—22no—
76C2×D244—22no—
77C2×D244—22no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—81no—
90C2×D244—81no—
91C2×Dic122—22no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122—41no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61D812yes—
108C2×C8×C61SD1612yes—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113C4⋊Dic61—21no—
114C4⋊Dic61—22no—
115C4⋊Dic61—22no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61SD1612yescomplemented
121C4×Dic61—41no—
122C4×Dic61—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126#11758190—48no—
127#11758190—48no—
128C23×C61#12111yescharacteristic
129C22×D61—42no—
130C22×D61—81no—
131C22×D61—81no—
132C22×D61—81no—
133C22×D61—81no—
134C22×D61—81no—
135C22×D61—81no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12311yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×C4×C61#12411yescharacteristic
144C2×C4×C61C2×D811yescharacteristic
145C2×C4×C61C2×SD1611yescharacteristic
146C2×C4×C61C2×SD1611yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61#13711yescharacteristic
152C2×Dic61—22no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—81no—
160C2×Dic61—81no—
161D244—42no—
162D244—42no—
163D244—42no—
164D244—42no—
165D244—82no—
166D244—82no—
167D244—81no—
168D244—81no—
169D244—81no—
170D244—81no—
171Dic122—42no—
172Dic122—42no—
173Dic122—81no—
174Dic122—81no—
175C8×C61—22no—
176C8×C61—22no—
177C8×C61—81no—
178C8×C61—81no—
179#92418—81no—
180#10537—611nomaximal, Sylow
181C22×C61#39411yescharacteristic
182C22×C61#45911yescharacteristic
183C22×C61#46011yescharacteristic
184C22×C61#46511yescharacteristic
185C22×C61#46811yescharacteristic
186C22×C61#47111yescharacteristic
187C22×C61#47111yescharacteristic
188C2×D61—82no—
189C2×D61—82no—
190C2×D61—82no—
191C2×D61—161no—
192C2×D61—161no—
193C2×D61—161no—
194C2×D61—161no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61#44711yescharacteristic
198C4×C61#45011yescharacteristic
199C4×C61#46011yescharacteristic
200C4×C61#46111yescharacteristic
201C4×C61#46311yescharacteristic
202C4×C61#46411yescharacteristic
203C4×C61#48611yescharacteristic
204C4×C61#49011yescharacteristic
205Dic61—42no—
206Dic61—81no—
207Dic61—82no—
208C2×#492—611no—
209#1988—611no—
210#1982—611no—
211#1939—611no—
212C2×#332—611no—
213C2×#331—611no—
214#1277D6111yescharacteristic, complemented
215C2×C61#166511yescharacteristic
216C2×C61#166611yescharacteristic
217C2×C61#168511yescharacteristic
218C2×C61#168611yescharacteristic
219C2×C61#204111yescharacteristic
220C2×C61#204611yescharacteristic
221C2×C61#205511yescharacteristic
222D61—162no—
223C22×SD16—1221no—
224C22×SD16—1221no—
225C2×C4⋊Q8—611no—
226C2×#127—611no—
227#492—1222no—
228#492—1222no—
229C2×C4⋊C8—611no—
230C2×C4⋊C8—1221no—
231C2×C4⋊C8C2×D6111yescharacteristic
232C2×C4⋊C8C2×D6111yescharacteristic
233C2×#102—1221no—
234C2×#102—1221no—
235C2×C4×C8C2×D6111yescharacteristic
236C4×C4⋊C4—611no—
237#340—1221no—
238#340—1221no—
239#336—1221no—
240#332—1222no—
241#331—1222no—
242C61#1053711yescharacteristic, complemented, Sylow
243C22×Q8—1221no—
244C22×D4—1221no—
245C22×D4—1221no—
246C22×D4—1221no—
247C2×SD16—1224no—
248C2×SD16—1224no—
249C2×SD16—2442no—
250C2×SD16—2442no—
251C2×SD16—2442no—
252C2×SD16—2442no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—1221no—
256C22×C8D24411yescharacteristic
257C22×C8D24411yescharacteristic
258C4⋊Q8—612no—
259C4⋊Q8—1221no—
260C4⋊Q8—1221no—
261C4⋊Q8—1221no—
262#127—612no—
263#127—1221no—
264#127—1221no—
265#127—1221no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C42—1221no—
271C2×C42C22×D6111yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C4⋊C8—2442no—
279#102—2442no—
280#102—2442no—
281C4×C8—21no—
282C4×C8—21no—
283#95—1221no—
284C24—2441no—
285C2×Q8—1222no—
286C2×Q8—2441no—
287C2×Q8—2441no—
288C2×Q8—2441no—
289C2×Q8—2441no—
290C2×Q8—2441no—
291C2×D4—1222no—
292C2×D4—1222no—
293C2×D4—1222no—
294C2×D4—4881no—
295C2×D4—4881no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4—2441no—
306C2×D4—2441no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—2441no—
310C22×C4C2×D24411yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4#1175822611yescharacteristic
313SD16—2448no—
314SD16—2448no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—2441no—
326C2×C8—2441no—
327C2×C8—2441no—
328C2×C8#1175819012yes—
329C2×C8D48812yes—
330C4⋊C4—612no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1222no—
334C4⋊C4—1222no—
335C4⋊C4—1221no—
336C4⋊C4—2441no—
337C4⋊C4—2441no—
338C42—2441no—
339C42—2441no—
340C42#1175822211yescharacteristic
341C42#1175822211yescharacteristic
342C42D4×D6111yescharacteristic
343C42D4×D6111yescharacteristic
344C23—4881no—
345C23—4881no—
346C23—4881no—
347C23—4881no—
348C23—4881no—
349C23—4881no—
350C23—2442no—
351C23#1451975211yescharacteristic
352Q8—4881no—
353Q8—4881no—
354Q8—2442no—
355Q8—2442no—
356D4—4882no—
357D4—4882no—
358D4—4881no—
359D4—4881no—
360D4—4881no—
361D4—4881no—
362D4—2442no—
363D4—2442no—
364D4—2442no—
365D4—2442no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—1222no—
369C2×C4—4881no—
370C2×C4—4881no—
371C2×C4—2442no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4#1451974711yescharacteristic
378C2×C4#1451975011yescharacteristic
379C2×C4#1451975011yescharacteristic
380C2×C4#1451976211yescharacteristic
381C2×C4#1451976211yescharacteristic
382C2×C4#1451976511yescharacteristic
383C2×C4C2×D48811yescharacteristic
384C2×C4SD16×D6111yescharacteristic
385C2×C4C2×#1175819011yescharacteristic
386C2×C4#1451979811yescharacteristic
387C2×C4#1451980111yescharacteristic
388C2×C4#1451980511yescharacteristic
389C2×C4#1451980511yescharacteristic
390C2×C4#1451980911yescharacteristic
391C8—22no—
392C8—22no—
393C8—81no—
394C8—81no—
395C8—4881no—
396C22—9761no—
397C22—9761no—
398C22—9761no—
399C22—9761no—
400C22—4882no—
401C22—4882no—
402C22—4882no—
403C22#1683968011yescharacteristic
404C22#1683995811yescharacteristic
405C22#1683996311yescharacteristic
406C22#1683999211yescharacteristic
407C22#1684000911yescharacteristic
408C22#1684002611yescharacteristic
409C22#1684002611yescharacteristic
410C4—21no—
411C4—21no—
412C4—4882no—
413C4—4881no—
414C4—2442no—
415C4#1683989811yescharacteristic
416C4#1683991511yescharacteristic
417C4#1683996111yescharacteristic
418C4#1683996611yescharacteristic
419C4#1683997611yescharacteristic
420C4#1683998711yescharacteristic
421C4#1684010911yescharacteristic
422C4#1684012711yescharacteristic
423C2—9762no—
424C2#2144516111yescharacteristic
425C2#2144516811yescharacteristic
426C2#2144528511yescharacteristic
427C2#2144529211yescharacteristic
428C2#2144705411yescharacteristic
429C2#2144708311yescharacteristic
430C2#2144713811yescharacteristic
subgroupG/H
centerC23#14519752
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1277D61
hypocenterC61#10537
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #21446770C2semidirect
4. #21446537C2semidirect
5. C2×#16839507C2semidirect
7. C61×#1277C2semidirect
120. C4⋊Dic61SD16semidirect
214. #1277D61semidirect
242. C61#10537semidirect

Maximal subgroups

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

subgroupindex
C2×#168401352
#214467702
#214467452
#214465372
C2×#168395072
C2×#168395052
C61×#12772
#1053761