Finite Group Databasebeta

← #29576306

Subgroups — #29576306

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455819C211yesmaximal, characteristic
2#21446647C211yesmaximal, characteristic, complemented
3#21444313C211yesmaximal, characteristic, complemented
4#21444244C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443652C211yesmaximal, characteristic, complemented
7C61×#2293C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840075—21no—
10#16840042C412yescomplemented
11#16839957C412yescomplemented
12#16839896—21no—
13C4×#11758199—22no—
14#16839815C2211yescharacteristic
15#16839815C2211yescharacteristic
16#16839786C2211yescharacteristic
17C2×#14519705—21no—
18C2×#14519705—21no—
19#16839495—22no—
20D4⋊#92418—22no—
21C2×C4×D4×C61C2211yescharacteristic
22C2×#117×C61—21no—
23C61×#390—21no—
24C61×#389—21no—
25C61×#388—22no—
26C4×C4⋊C4×C61C2211yescharacteristic
27C4×C22⋊C4×C61—21no—
28C43×C61C2211yescharacteristic
29C2×#11758222—21no—
30C2×#11758199—22no—
31C2×#11758194—21no—
32#14519777C2×C411yescharacteristic
33#14519774C2×C411yescharacteristic
34#14519765—21no—
35#14519751—21no—
36#14519751—21no—
37C4×D244—21no—
38C4×D244—21no—
39#14519710—22no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418C2×C412yes—
44#14519705—42no—
45#14519705—42no—
46#14519698—22no—
47#14519697—22no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C4×#92418—21no—
51C4×#92418—21no—
52C22×D4×C61D411yescharacteristic
53C23×C4×C61—21no—
54C4×D4×C61—21no—
55C4×D4×C61—21no—
56C4×D4×C61C2×C412yes—
57C4×D4×C61D412yes—
58#117×C61—42no—
59#117×C61—42no—
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—22no—
65C2×C22⋊C4×C61—22no—
66C2×C42×C61—21no—
67C2×C42×C61—21no—
68C2×C42×C61—21no—
69C2×C42×C61D411yescharacteristic
70C2×C42×C61D411yescharacteristic
71C2×C42×C61C2311yescharacteristic
72#95×C61—22no—
73#95×C61D412yes—
74C24×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61—42no—
77C2×D4×C61C22⋊C412yes—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C2×C22⋊D61—41no—
92#11758222—41no—
93#11758222—41no—
94#11758222—41no—
95#11758222—41no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244—21no—
99C2×C4×D61—41no—
100C2×Dic122—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—42no—
103C4⋊C4×C61—44no—
104C4⋊C4×C61C22⋊C412yes—
105C22⋊C4×C61—22no—
106C22⋊C4×C61—22no—
107C22⋊C4×C61—44no—
108C22⋊C4×C61—44no—
109C42×C61—21no—
110C42×C61—21no—
111C42×C61—21no—
112C42×C61—42no—
113C42×C61—42no—
114C42×C61—41no—
115C42×C61—41no—
116C42×C61D812yescomplemented
117C42×C61C22×C411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61#4111yescharacteristic
120C42×C61#4111yescharacteristic
121#11758199—44no—
122#11758198—41no—
123#11758198—41no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126#11758194—41no—
127#11758194—41no—
128C2×#92418—22no—
129C2×#92418—41no—
130C2×#92418—41no—
131C23×C61—22no—
132C23×C61—42no—
133C23×C61—42no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61#12011yescharacteristic
137C22×D61—41no—
138D4×C61—22no—
139D4×C61—22no—
140D4×C61—42no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61—42no—
159C2×C4×C61C2×C22⋊C411yescharacteristic
160C2×C4×C61C4×D411yescharacteristic
161C2×C4×C61C4×D411yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12311yescharacteristic
165C2×C4×C61C2×D811yescharacteristic
166C2×C4×C61#13511yescharacteristic
167C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
169C22⋊D61—81no—
170C22⋊D61—81no—
171C2×Dic61—41no—
172D244—42no—
173D244—41no—
174D244—41no—
175D244—81no—
176C4×D61—81no—
177C4×D61—81no—
178Dic122—41no—
179Dic122—41no—
180#92418—42no—
181#92418—81no—
182#92418—81no—
183#9237—611nomaximal, Sylow
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—42no—
187C22×C61—42no—
188C22×C61—42no—
189C22×C61—82no—
190C22×C61—82no—
191C22×C61#38611yescharacteristic
192C22×C61#44711yescharacteristic
193C22×C61#44911yescharacteristic
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—42no—
201C4×C61—42no—
202C4×C61—42no—
203C4×C61—82no—
204C4×C61#42112yes—
205C4×C61C4×D811yescharacteristic
206C4×C61#44211yescharacteristic
207C4×C61#45911yescharacteristic
208C4×C61#46311yescharacteristic
209Dic61—81no—
210#3100—611no—
211#2293D6111yescharacteristic, complemented
212#1962—611no—
213#1502—611no—
214#1486—611no—
215#1303—611no—
216#1276—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—82no—
220C2×C61#187911yescharacteristic
221C2×C61#189711yescharacteristic
222C2×C61#190611yescharacteristic
223D61—161no—
224#532—611no—
225C2×C4×D4C2×D6111yescharacteristic
226C2×#117—21no—
227#480—1221no—
228#474—612no—
229#459—612no—
230#447—1221no—
231C4×D8—1222no—
232#431—611no—
233#431—611no—
234#423—611no—
235C2×#104—1221no—
236C2×#104—1221no—
237#390—21no—
238#389—21no—
239#388—22no—
240C4×C4⋊C4C2×D6111yescharacteristic
241C4×C22⋊C4—21no—
242C43C2×D6111yescharacteristic
243#327—1222no—
244D4⋊C8—1222no—
245C61#923711yescharacteristic, complemented, Sylow
246C2×#41—1221no—
247C22×D4C22⋊D6111yescharacteristic
248C23×C4—21no—
249C2×D8—1222no—
250C2×M16—1221no—
251C4⋊Q8—611no—
252#127—611no—
253#124—1221no—
254#121—1221no—
255#121—1221no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—1221no—
259C4×D4—1221no—
260C4×D4C4×D6112yes—
261C4×D4D24412yes—
262#117—42no—
263#117—42no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C22⋊D6111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42C22⋊D6111yescharacteristic
274C2×C42C22⋊D6111yescharacteristic
275C2×C42C22×D6111yescharacteristic
276#107—1222no—
277C4⋊C8—612no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281#104—2442no—
282#104—2442no—
283#102—1222no—
284#102—1222no—
285C22⋊C8—1221no—
286C22⋊C8—1221no—
287C4×C8—1221no—
288C4×C8—1221no—
289#95—22no—
290#95C22⋊D6112yes—
291C24—21no—
292#41—2441no—
293#41—2441no—
294#41—2441no—
295#41—2441no—
296C2×Q8—1221no—
297C2×D4—21no—
298C2×D4—42no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—2441no—
303C2×D4#1175819812yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—2441no—
315C22×C4C2×C22⋊D6111yescharacteristic
316C22×C4C2×C22⋊D6111yescharacteristic
317C22×C4C2×C22⋊D6111yescharacteristic
318D8—2444no—
319M16—2441no—
320M16—2441no—
321C2×C8—1222no—
322C2×C8—2441no—
323C2×C8—2441no—
324C4⋊C4—21no—
325C4⋊C4—44no—
326C4⋊C4—42no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4#1175819812yes—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—44no—
333C22⋊C4—44no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—42no—
340C42—42no—
341C42—41no—
342C42—41no—
343C42#1175819912yescomplemented
344C42C2×C4×D6111yescharacteristic
345C42C2×D24411yescharacteristic
346C42#1175822211yescharacteristic
347C42#1175822211yescharacteristic
348C23—22no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—2441no—
354C23#1451974611yescharacteristic
355Q8—2441no—
356Q8—2441no—
357D4—22no—
358D4—22no—
359D4—42no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—2442no—
364D4—2441no—
365D4—2441no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—4881no—
385C2×C4—4881no—
386C2×C4—2441no—
387C2×C4C2×#1175819811yescharacteristic
388C2×C4C4×C22⋊D6111yescharacteristic
389C2×C4C4×C22⋊D6111yescharacteristic
390C2×C4#1451975111yescharacteristic
391C2×C4#1451975111yescharacteristic
392C2×C4#1451976011yescharacteristic
393C2×C4C2×#1175819911yescharacteristic
394C2×C4#1451979711yescharacteristic
395C2×C4#1451980211yescharacteristic
396C2×C4#1451980311yescharacteristic
397C8—4881no—
398C8—4881no—
399C8—2442no—
400C22—21no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—82no—
406C22—82no—
407C22—4881no—
408C22—4881no—
409C22—4881no—
410C22#1683964111yescharacteristic
411C22#1683989611yescharacteristic
412C22#1683990711yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—42no—
418C4—42no—
419C4—82no—
420C4—4881no—
421C4#1683978012yes—
422C4C4×#1175819911yescharacteristic
423C4#1683987211yescharacteristic
424C4#1683995711yescharacteristic
425C4#1683997711yescharacteristic
426C2—21no—
427C2—21no—
428C2—82no—
429C2—9761no—
430C2#2144616711yescharacteristic
431C2#2144626711yescharacteristic
432C2#2144632011yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2293C2
socleC22×C61#386
prime radical#21455819C2
cosocleC2×C42×C61C23
hypercenter#2293D61
hypocenterC61#9237
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. #21446647C2semidirect
3. #21444313C2semidirect
4. #21444244C2semidirect
5. #21443722C2semidirect
6. #21443652C2semidirect
7. C61×#2293C2semidirect
10. #16840042C4semidirect
11. #16839957C4semidirect
116. C42×C61D8semidirect
211. #2293D61semidirect
245. C61#9237semidirect
343. C42#11758199semidirect

Maximal subgroups

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

subgroupindex
#214558192
#214466472
#214443132
#214442442
#214437222
#214436522
C61×#22932
#923761