Finite Group Databasebeta

← #29584223

Subgroups — #29584223

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×#16840136C211yesmaximal, characteristic
2#21446746C211yesmaximal, characteristic
3#21446538C211yesmaximal, characteristic, complemented
4C2×#16839508C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1988C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C22×#11758201—21no—
10C2×#14519774C2211yescharacteristic
11#16840136—22no—
12#16840136—22no—
13C2×C4⋊#92418—21no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×C4⋊#92418C2211yescharacteristic
16C2×#14519697—21no—
17C2×#14519697—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839517—21no—
20#16839508—22no—
21#16839505—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C61×#340—21no—
26C61×#340—21no—
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C2×#11758201—24no—
31C2×#11758201—24no—
32C2×#11758201—42no—
33C2×#11758201—42no—
34C2×#11758201—42no—
35C2×#11758201—42no—
36C22×#92418—21no—
37C22×#92418—21no—
38C22×#92418D411yescharacteristic
39C22×#92418D411yescharacteristic
40#14519774—21no—
41#14519774—21no—
42#14519774—21no—
43#14519774D412yes—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—42no—
49#14519697—42no—
50#14519697—42no—
51C4×#92418—21no—
52C4×#92418—21no—
53C22×Q8×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×C4⋊C4×C61D411yescharacteristic
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C42×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67#95×C61—21no—
68C23×D61—41no—
69C2×Q8×C61—22no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—81no—
96C2×D244—81no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61SD1612yescomplemented
108C42×C61—41no—
109C42×C61—41no—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C42×C61#4111yescharacteristic
114#11758201—48no—
115#11758201—48no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418D812yes—
127C2×#92418SD1612yes—
128C23×C61#12111yescharacteristic
129C22×D61—42no—
130C22×D61—81no—
131C22×D61—81no—
132C22×D61—81no—
133C22×D61—81no—
134C22×D61—81no—
135C22×D61—81no—
136Q8×C61—42no—
137Q8×C61—42no—
138Q8×C61—81no—
139Q8×C61—81no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—81no—
150C2×C4×C61—81no—
151C2×C4×C61#12011yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12311yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×C4×C61#12411yescharacteristic
157C2×C4×C61C2×D811yescharacteristic
158C2×C4×C61C2×SD1611yescharacteristic
159C2×C4×C61C2×SD1611yescharacteristic
160C2×C4×C61#13511yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61#13711yescharacteristic
165D244—42no—
166D244—42no—
167D244—42no—
168D244—42no—
169D244—82no—
170D244—82no—
171D244—81no—
172D244—81no—
173D244—81no—
174D244—81no—
175C8×C61—81no—
176#92418—22no—
177#92418—22no—
178#92418—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—42no—
198C4×C61—81no—
199C4×C61—82no—
200C4×C61#44711yescharacteristic
201C4×C61#45011yescharacteristic
202C4×C61#46011yescharacteristic
203C4×C61#46111yescharacteristic
204C4×C61#46311yescharacteristic
205C4×C61#46411yescharacteristic
206C4×C61#48611yescharacteristic
207C4×C61#49011yescharacteristic
208C2×#492—611no—
209#1988D6111yescharacteristic, complemented
210#1982—611no—
211#1939—611no—
212C2×#332—611no—
213C2×#331—611no—
214#1277—611no—
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⋊Q8C2×D6111yescharacteristic
226C2×#127—611no—
227#492—1222no—
228#492—1222no—
229C2×C4⋊C8—611no—
230C2×C4⋊C8—611no—
231C2×C4⋊C8—1221no—
232C2×C4⋊C8C2×D6111yescharacteristic
233C2×#102—1221no—
234C2×#102—1221no—
235C2×C4×C8—611no—
236C4×C4⋊C4C2×D6111yescharacteristic
237#340—21no—
238#340—21no—
239#336—1221no—
240#332—1222no—
241#331—1222no—
242C61#1053711yescharacteristic, complemented, Sylow
243C22×Q8—21no—
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—611no—
255C22×C8—611no—
256C22×C8—1221no—
257C22×C8—1221no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8D24412yes—
262#127—612no—
263#127—1221no—
264#127—1221no—
265#127—1221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4C22⋊D6111yescharacteristic
269C2×C4⋊C4C22⋊D6111yescharacteristic
270C2×C42—21no—
271C2×C42C22×D6111yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C4⋊C8—2442no—
279#102—2442no—
280#102—2442no—
281C4×C8—1221no—
282C4×C8—1221no—
283#95—21no—
284C24—2441no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
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—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4D4×D6111yescharacteristic
311C22×C4#1175822411yescharacteristic
312C22×C4C2×C22⋊D6111yescharacteristic
313SD16—2448no—
314SD16—2448no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—612no—
319C2×C8—612no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—1221no—
323C2×C8—1221no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8—2441no—
327C2×C8—2441no—
328C2×C8—2441no—
329C2×C8—2441no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4#1175820112yescomplemented
338C42—41no—
339C42—41no—
340C42C2×D24411yescharacteristic
341C42#1175822211yescharacteristic
342C42D4×D6111yescharacteristic
343C42#1175822411yescharacteristic
344C23—4881no—
345C23—4881no—
346C23—4881no—
347C23—4881no—
348C23—4881no—
349C23—4881no—
350C23—2442no—
351C23#1451974911yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—81no—
355Q8—81no—
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—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4#1451974711yescharacteristic
378C2×C4#1451974811yescharacteristic
379C2×C4#1451975111yescharacteristic
380C2×C4#1451975911yescharacteristic
381C2×C4#1451976111yescharacteristic
382C2×C4#1451976311yescharacteristic
383C2×C4D8×D6111yescharacteristic
384C2×C4SD16×D6111yescharacteristic
385C2×C4C2×#1175820111yescharacteristic
386C2×C4#1451979711yescharacteristic
387C2×C4#1451980111yescharacteristic
388C2×C4#1451980211yescharacteristic
389C2×C4#1451980411yescharacteristic
390C2×C4#1451980811yescharacteristic
391C8—81no—
392C8—1222no—
393C8—1222no—
394C8—4881no—
395C8—4881no—
396C22—9761no—
397C22—9761no—
398C22—9761no—
399C22—9761no—
400C22—4882no—
401C22—4882no—
402C22—4882no—
403C22#1683967811yescharacteristic
404C22#1683995511yescharacteristic
405C22#1683996011yescharacteristic
406C22#1683999311yescharacteristic
407C22#1684001011yescharacteristic
408C22#1684002711yescharacteristic
409C22#1684002711yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—82no—
414C4—81no—
415C4#1683989711yescharacteristic
416C4#1683991411yescharacteristic
417C4#1683996211yescharacteristic
418C4#1683996411yescharacteristic
419C4#1683997411yescharacteristic
420C4#1683998411yescharacteristic
421C4#1684010711yescharacteristic
422C4#1684012511yescharacteristic
423C2—9762no—
424C2#2144516211yescharacteristic
425C2#2144516911yescharacteristic
426C2#2144528611yescharacteristic
427C2#2144529311yescharacteristic
428C2#2144705211yescharacteristic
429C2#2144707911yescharacteristic
430C2#2144713411yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1988C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1988D61
hypocenterC61#10537
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
3. #21446538C2semidirect
4. C2×#16839508C2semidirect
6. #21443653C2semidirect
7. C61×#1988C2semidirect
107. C4⋊C4×C61SD16semidirect
209. #1988D61semidirect
242. C61#10537semidirect
337. C4⋊C4#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×#168401362
#214467462
#214465382
C2×#168395082
C2×#168395052
#214436532
C61×#19882
#1053761