Finite Group Databasebeta

← #29574905

Subgroups — #29574905

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#21455274C211yesmaximal, characteristic
2#21454485C211yesmaximal, characteristic, complemented
3#21444271C211yesmaximal, characteristic, complemented
4#21444219C211yesmaximal, characteristic, complemented
5#21443715C211yesmaximal, characteristic, complemented
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1476C211yesmaximal, characteristic, complemented
8C2×#14519797—21no—
9#16840312C2211yescharacteristic
10#16839984—21no—
11#16839977—21no—
12#16839972C411yescharacteristic
13#16839967C411yescharacteristic
14#16839962C411yescharacteristic
15#16839957C411yescharacteristic
16#16839823—22no—
17#16839819—21no—
18#16839815—21no—
19#16839786C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22#16839756—21no—
23#16839729—21no—
24#16839718—21no—
25#16839491—21no—
26#16839491—21no—
27#16839491—22no—
28C4×#41×C61C2211yescharacteristic
29C61×#431C2211yescharacteristic
30C2×C4×C8×C61C2211yescharacteristic
31C61×Q8⋊C8—21no—
32C61×D4⋊C8—21no—
33C2×#11758222—21no—
34#14519797—42no—
35#14519797—42no—
36C2×#11758202—21no—
37C2×#11758200—21no—
38C2×#11758201—21no—
39C2×#11758199—21no—
40C2×#11758194—21no—
41C22×#92418—21no—
42C22×#92418—21no—
43#14519777C2×C411yescharacteristic
44#14519774C2×C411yescharacteristic
45#14519765—21no—
46#14519751—21no—
47#14519751—21no—
48C4×D244—21no—
49C4×D244—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418C2×C411yescharacteristic
54C4⋊#92418C2×C411yescharacteristic
55C4⋊#92418D411yescharacteristic
56C4⋊#92418D411yescharacteristic
57C4⋊#92418D412yes—
58#14519700—21no—
59#14519700—21no—
60#14519697—21no—
61#14519697—21no—
62C22⋊#92418—22no—
63C22⋊#92418—22no—
64#14519688—22no—
65C4×#92418—22no—
66C2×#41×C61D411yescharacteristic
67C22×C8×C61—21no—
68C4×Q8×C61C2×C411yescharacteristic
69C4×Q8×C61D411yescharacteristic
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61C2×C411yescharacteristic
73C4×D4×C61D411yescharacteristic
74#117×C61—21no—
75#117×C61D411yescharacteristic
76C2×C42×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C4×C8×C61—21no—
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83#41×C61—21no—
84#41×C61—21no—
85#41×C61—21no—
86#41×C61—21no—
87C2×Q8×C61C22⋊C411yescharacteristic
88C2×D4×C61—21no—
89C2×D4×C61C22⋊C411yescharacteristic
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C2×C22⋊D61—41no—
97#11758222—41no—
98#11758222—41no—
99#11758222—41no—
100#11758222—41no—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244—21no—
104C2×C4×D61—41no—
105C2×Dic122—21no—
106C2×C8×C61—22no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61C22⋊C411yescharacteristic
113C4⋊C4×C61C22⋊C411yescharacteristic
114C22⋊C4×C61—21no—
115C22⋊C4×C61—21no—
116C22⋊C4×C61—21no—
117C42×C61—21no—
118C42×C61—21no—
119C42×C61—21no—
120C42×C61C22×C411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61C2×D411yescharacteristic
124#11758202—42no—
125#11758201—42no—
126#11758200—42no—
127#11758199—42no—
128#11758198—41no—
129#11758198—41no—
130C4⋊Dic61—21no—
131C4⋊Dic61—21no—
132#11758194—41no—
133#11758194—41no—
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418—21no—
137C2×#92418—22no—
138C2×#92418—21no—
139C2×#92418—41no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C23×C61—21no—
144C23×C61#12311yescharacteristic
145C22×D61—41no—
146Q8×C61—21no—
147Q8×C61—21no—
148D4×C61—21no—
149D4×C61—21no—
150D4×C61—41no—
151D4×C61—41no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—81no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C22⋊D61—81no—
174C22⋊D61—81no—
175C2×Dic61—41no—
176D244—42no—
177D244—41no—
178D244—41no—
179D244—41no—
180D244—41no—
181C4×D61—81no—
182C4×D61—81no—
183Dic122—41no—
184Dic122—41no—
185C8×C61—42no—
186C8×C61—81no—
187#92418—41no—
188#92418—41no—
189#92418—41no—
190#92418—41no—
191#92418—42no—
192#8996—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61#38611yescharacteristic
199C22×C61#48211yescharacteristic
200C22×C61#48211yescharacteristic
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61#41611yescharacteristic
211C4×C61#41811yescharacteristic
212C4×C61#44311yescharacteristic
213C4×C61#44411yescharacteristic
214C4×C61#44911yescharacteristic
215C4×C61#44911yescharacteristic
216Dic61—81no—
217#3035—611no—
218#2925—611no—
219#1492—611no—
220#1480—611no—
221#1476D6111yescharacteristic, complemented
222#1301—611no—
223#1277—611no—
224C2×C61—21no—
225C2×C61—21no—
226C2×C61—81no—
227C2×C61#187511yescharacteristic
228C2×C61#187611yescharacteristic
229C2×C61#188111yescharacteristic
230D61—161no—
231C2×#135—1221no—
232#532—611no—
233C4×#41C2×D6111yescharacteristic
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#423—611no—
245C2×C4⋊C8—611no—
246C2×C4⋊C8—611no—
247#416—1221no—
248#408—1221no—
249#405—1221no—
250C2×C4×C8C2×D6111yescharacteristic
251Q8⋊C8—21no—
252D4⋊C8—21no—
253D4⋊C8—1221no—
254D4⋊C8—1221no—
255D4⋊C8—1222no—
256C61#899611yescharacteristic, complemented, Sylow
257C2×#41—1221no—
258C2×#41D24411yescharacteristic
259#135—2442no—
260#135—2442no—
261C2×Q16—1221no—
262C2×SD16—1221no—
263C2×SD16—1221no—
264C2×D8—1221no—
265C2×M16—1221no—
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×Q8C4×D6111yescharacteristic
275C4×Q8C22⋊D6111yescharacteristic
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—1221no—
279C4×D4—1221no—
280C4×D4C4×D6111yescharacteristic
281C4×D4C22⋊D6111yescharacteristic
282#117—21no—
283#117D24411yescharacteristic
284C2×C42—21no—
285C2×C42C22×D6111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—611no—
288C4⋊C8—611no—
289C4⋊C8—611no—
290C4⋊C8—611no—
291C4⋊C8—612no—
292C4⋊C8—1221no—
293C4⋊C8—1221no—
294C4⋊C8—1221no—
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—21no—
305C4×C8—21no—
306C4×C8—1222no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—2441no—
312#41—2441no—
313#41—2441no—
314#41—2441no—
315C2×Q8—1221no—
316C2×Q8#1175819811yescharacteristic
317C2×D4—21no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—2441no—
322C2×D4#1175819811yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—2441no—
327C22×C4C2×D24411yescharacteristic
328C22×C4#1175822411yescharacteristic
329C22×C4#1175822411yescharacteristic
330Q16—2442no—
331SD16—2442no—
332SD16—2442no—
333D8—2442no—
334M16—2441no—
335M16—2441no—
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—1221no—
341C2×C8—1221no—
342C2×C8—1221no—
343C2×C8—1222no—
344C2×C8—1221no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4#1175819811yescharacteristic
354C4⋊C4#1175819811yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42C2×C4×D6111yescharacteristic
364C42D4×D6111yescharacteristic
365C42D4×D6111yescharacteristic
366C42C2×C22⋊D6111yescharacteristic
367C23—21no—
368C23—2441no—
369C23#1451976111yescharacteristic
370Q8—21no—
371Q8—21no—
372Q8—2441no—
373Q8—2441no—
374D4—21no—
375D4—21no—
376D4—41no—
377D4—41no—
378D4—4881no—
379D4—4881no—
380D4—2442no—
381D4—2441no—
382D4—2441no—
383D4—2441no—
384D4—2441no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—4881no—
397C2×C4—4881no—
398C2×C4—2441no—
399C2×C4C2×#1175819811yescharacteristic
400C2×C4#1451973711yescharacteristic
401C2×C4#1451973711yescharacteristic
402C2×C4#1451974711yescharacteristic
403C2×C4#1451974911yescharacteristic
404C2×C4#1451974911yescharacteristic
405C2×C4#1451979911yescharacteristic
406C2×C4#1451979911yescharacteristic
407C2×C4#1451980511yescharacteristic
408C2×C4#1451980511yescharacteristic
409C8—42no—
410C8—81no—
411C8—2441no—
412C8—2441no—
413C8—2441no—
414C8—2441no—
415C8—2442no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—4881no—
422C22—4881no—
423C22—4881no—
424C22#1683963911yescharacteristic
425C22#1684008711yescharacteristic
426C22#1684008711yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—4881no—
434C4#1683975911yescharacteristic
435C4#1683976811yescharacteristic
436C4#1683987611yescharacteristic
437C4#1683988111yescharacteristic
438C4#1683990911yescharacteristic
439C4#1683990911yescharacteristic
440C2—21no—
441C2—21no—
442C2—81no—
443C2—9761no—
444C2#2144613911yescharacteristic
445C2#2144614411yescharacteristic
446C2#2144617911yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1476C2
socleC22×C61#386
prime radical#21455274C2
cosocleC2×C42×C61C23
hypercenter#1476D61
hypocenterC61#8996
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #21454485C2semidirect
3. #21444271C2semidirect
4. #21444219C2semidirect
5. #21443715C2semidirect
6. #21443654C2semidirect
7. C61×#1476C2semidirect
221. #1476D61semidirect
256. C61#8996semidirect

Maximal subgroups

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

subgroupindex
#214552742
#214544852
#214442712
#214442192
#214437152
#214436542
C61×#14762
#899661