Finite Group Databasebeta

← #29574908

Subgroups — #29574908

Order 15616.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455276C211yesmaximal, characteristic
2#21454487C211yesmaximal, characteristic, complemented
3#21444269C211yesmaximal, characteristic, complemented
4#21444219C211yesmaximal, characteristic, complemented
5#21444199C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1301C211yesmaximal, characteristic, complemented
8C2×#14519799—21no—
9#16840312C2211yescharacteristic
10C4×#11758222C2211yescharacteristic
11#16839985—21no—
12#16839978—21no—
13#16839973C411yescharacteristic
14#16839968C411yescharacteristic
15#16839963C411yescharacteristic
16#16839958C411yescharacteristic
17#16839822—22no—
18#16839818—21no—
19#16839814—21no—
20C2×C4⋊#92418C2211yescharacteristic
21#16839759—21no—
22#16839730—21no—
23#16839720—21no—
24C2×C4×#92418C2211yescharacteristic
25#16839492—21no—
26#16839491—21no—
27#16839491—21no—
28#16839489—21no—
29#16839489—22no—
30C61×#431C2211yescharacteristic
31C61×#423C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×#11758222—21no—
34C2×#11758222D411yescharacteristic
35#14519799—42no—
36#14519799—42no—
37C2×Dic244—21no—
38C2×#11758190—21no—
39C2×#11758190—21no—
40C2×D488—21no—
41C22×#92418—21no—
42C22×#92418—21no—
43#14519777C2×C411yescharacteristic
44#14519774C2×C411yescharacteristic
45#14519765—21no—
46#14519751—21no—
47#14519751—21no—
48C4×Dic122C2×C411yescharacteristic
49C4×Dic122D411yescharacteristic
50C4×D244—21no—
51C4×D244—21no—
52C4×D244C2×C411yescharacteristic
53C4×D244D411yescharacteristic
54C4×C22⋊D61—21no—
55C4×C22⋊D61—21no—
56#14519736D411yescharacteristic
57#14519734—21no—
58C42×D61—21no—
59C4⋊#92418—21no—
60C4⋊#92418D411yescharacteristic
61C4⋊#92418D411yescharacteristic
62#14519702—21no—
63#14519702—21no—
64#14519699—21no—
65#14519699—21no—
66#14519689—22no—
67#14519689—22no—
68#14519687—22no—
69C4×#92418—21no—
70C4×#92418—21no—
71C8×Dic61—22no—
72C2×M16×C61—21no—
73C22×C8×C61—21no—
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C4⋊C8×C61C2×C411yescharacteristic
79C4⋊C8×C61C2×C411yescharacteristic
80C4⋊C8×C61D412yes—
81C22⋊C8×C61—21no—
82C4×C8×C61—21no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C2×C22⋊D61—21no—
87C2×C22⋊D61—41no—
88#11758222—21no—
89#11758222—21no—
90#11758222—21no—
91#11758222—21no—
92#11758222—41no—
93#11758222—41no—
94#11758222—41no—
95#11758222—41no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244—21no—
99C2×D244C22⋊C411yescharacteristic
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—41no—
104C2×Dic122—21no—
105C2×Dic122C22⋊C411yescharacteristic
106M16×C61—41no—
107M16×C61—41no—
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61—22no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C42×C61C22×C411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C22⋊Dic61—21no—
119#11758198—21no—
120#11758198—21no—
121#11758198—41no—
122#11758198—41no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61C22⋊C411yescharacteristic
126C4⋊Dic61C22⋊C411yescharacteristic
127#11758196—21no—
128#11758196—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C2×#92418—22no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138C2×#92418—41no—
139Dic244—42no—
140D488—42no—
141#11758190—42no—
142#11758190—42no—
143C23×C61#12311yescharacteristic
144C22×D61—21no—
145C22×D61—41no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—41no—
149C2×C4×C61C2×C22⋊C411yescharacteristic
150C2×C4×C61C4×D411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C22⋊D61—41no—
160C22⋊D61—41no—
161C22⋊D61—81no—
162C22⋊D61—81no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167D244—21no—
168D244—21no—
169D244—42no—
170D244—41no—
171D244—41no—
172D244—41no—
173D244—41no—
174C4×D61—41no—
175C4×D61—41no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61—81no—
179C4×D61—81no—
180C4×D61—81no—
181Dic122—21no—
182Dic122—21no—
183Dic122—41no—
184Dic122—41no—
185C8×C61—41no—
186C8×C61—41no—
187C8×C61—42no—
188C8×C61—81no—
189#92418—42no—
190#92418—41no—
191#92418—41no—
192#8996—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61#38611yescharacteristic
196C22×C61#48211yescharacteristic
197C22×C61#48211yescharacteristic
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61#41611yescharacteristic
208C4×C61#41811yescharacteristic
209C4×C61#44311yescharacteristic
210C4×C61#44411yescharacteristic
211C4×C61#44911yescharacteristic
212C4×C61#44911yescharacteristic
213Dic61—41no—
214Dic61—41no—
215Dic61—41no—
216Dic61—81no—
217#3035—611no—
218#2925—611no—
219#1492—611no—
220#1480—611no—
221#1476—611no—
222#1301D6111yescharacteristic, complemented
223#1277—611no—
224C2×C61—21no—
225C2×C61—21no—
226C2×C61#187511yescharacteristic
227C2×C61#187611yescharacteristic
228C2×C61#188111yescharacteristic
229D61—81no—
230D61—161no—
231C2×#135—1221no—
232#532—611no—
233C4×#41—611no—
234#464—1221no—
235#463—1221no—
236#462—611no—
237#461—611no—
238#460—611no—
239#459—611no—
240#433—1222no—
241#432—1221no—
242#431—1221no—
243#431C2×D6111yescharacteristic
244#423C2×D6111yescharacteristic
245C2×C4⋊C8—611no—
246C2×C4⋊C8C2×D6111yescharacteristic
247#416—1221no—
248#408—1221no—
249#405—1221no—
250C2×C4×C8—611no—
251Q8⋊C8—1221no—
252D4⋊C8—1221no—
253D4⋊C8—1221no—
254D4⋊C8—1221no—
255D4⋊C8—1222no—
256C61#899611yescharacteristic, complemented, Sylow
257C2×#41—611no—
258C2×#41—1221no—
259#135—2442no—
260#135—2442no—
261C2×Q16—1221no—
262C2×SD16—1221no—
263C2×SD16—1221no—
264C2×D8—1221no—
265C2×M16—21no—
266C22×C8—21no—
267C22×C8—1221no—
268C22×C8—1221no—
269C4⋊Q8—611no—
270#127—611no—
271#124—1221no—
272#121—1221no—
273#121—1221no—
274C4×Q8—611no—
275C4×Q8—611no—
276C4×D4—611no—
277C4×D4—611no—
278C4×D4—1221no—
279C4×D4—1221no—
280C4×D4—1221no—
281C4×D4—1221no—
282#117—611no—
283#117—1221no—
284C2×C42—1221no—
285C2×C42C22×D6111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—611no—
290C4⋊C8—611no—
291C4⋊C8—1221no—
292C4⋊C8C4×D6111yescharacteristic
293C4⋊C8C4×D6111yescharacteristic
294C4⋊C8D24412yes—
295#103—1221no—
296#103—1221no—
297#102—1221no—
298#102—1221no—
299C22⋊C8—21no—
300C22⋊C8—1222no—
301C22⋊C8—1222no—
302#97—1222no—
303C4×C8—21no—
304C4×C8—1222no—
305C4×C8—1221no—
306C4×C8—1221no—
307#41—1221no—
308#41—1221no—
309#41—1221no—
310#41—1221no—
311#41—2441no—
312#41—2441no—
313#41—2441no—
314#41—2441no—
315C2×Q8—611no—
316C2×Q8—1221no—
317C2×D4—611no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4—2441no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—2441no—
327C22×C4#1175822211yescharacteristic
328C22×C4D4×D6111yescharacteristic
329C22×C4#1175822611yescharacteristic
330Q16—2442no—
331SD16—2442no—
332SD16—2442no—
333D8—2442no—
334M16—41no—
335M16—41no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—1222no—
343C2×C8—1221no—
344C2×C8—1221no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C4⋊C4—611no—
350C4⋊C4—611no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4—1221no—
354C4⋊C4—1221no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—1221no—
361C42—1221no—
362C42—1221no—
363C42C2×C4×D6111yescharacteristic
364C42C2×D24411yescharacteristic
365C42D4×D6111yescharacteristic
366C42D4×D6111yescharacteristic
367C23—1221no—
368C23—2441no—
369C23#1451976211yescharacteristic
370Q8—1221no—
371Q8—1221no—
372Q8—2441no—
373Q8—2441no—
374D4—1221no—
375D4—1221no—
376D4—4881no—
377D4—4881no—
378D4—2442no—
379D4—2441no—
380D4—2441no—
381D4—2441no—
382D4—2441no—
383D4—2441no—
384D4—2441no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4881no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4C22⋊C4×D6111yescharacteristic
400C2×C4#1451973911yescharacteristic
401C2×C4C4×D24411yescharacteristic
402C2×C4#1451974711yescharacteristic
403C2×C4#1451975011yescharacteristic
404C2×C4#1451975211yescharacteristic
405C2×C4#1451979811yescharacteristic
406C2×C4#1451980011yescharacteristic
407C2×C4#1451980111yescharacteristic
408C2×C4#1451980411yescharacteristic
409C8—41no—
410C8—41no—
411C8—42no—
412C8—81no—
413C8—2442no—
414C8—2441no—
415C8—2441no—
416C22—21no—
417C22—21no—
418C22—4881no—
419C22—4881no—
420C22—4881no—
421C22—2441no—
422C22—2441no—
423C22—2441no—
424C22#1683964011yescharacteristic
425C22#1684008811yescharacteristic
426C22#1684008911yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—4881no—
431C4—2441no—
432C4—2441no—
433C4—2441no—
434C4#1683975711yescharacteristic
435C4#1683976511yescharacteristic
436C4#1683987811yescharacteristic
437C4#1683988311yescharacteristic
438C4#1683990811yescharacteristic
439C4#1683991011yescharacteristic
440C2—21no—
441C2—21no—
442C2—9761no—
443C2—4881no—
444C2#2144614011yescharacteristic
445C2#2144614711yescharacteristic
446C2#2144618011yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#386
prime radical#21455276C2
cosocleC2×C42×C61C23
hypercenter#1301D61
hypocenterC61#8996
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
2. #21454487C2semidirect
3. #21444269C2semidirect
4. #21444219C2semidirect
5. #21444199C2semidirect
6. #21443653C2semidirect
7. C61×#1301C2semidirect
222. #1301D61semidirect
256. C61#8996semidirect

Maximal subgroups

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

subgroupindex
#214552762
#214544872
#214442692
#214442192
#214441992
#214436532
C61×#13012
#899661