Finite Group Databasebeta

← #30600247

Subgroups — #30600247

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×#92420C211yesmaximal, characteristic, complemented
2#21461114C211yesmaximal, characteristic, complemented
3C2×#16840610C211yesmaximal, characteristic, complemented
4#21461060C211yesmaximal, characteristic, complemented
5#21460665C211yesmaximal, characteristic, complemented
6#21460652C211yesmaximal, characteristic, complemented
7#21454632C211yesmaximal, characteristic
8Q8×#92420—21no—
9D4×#92420—21no—
10D4×#92420—22no—
11#16840778—21no—
12#16840778C2211yescharacteristic
13#16840778C2211yescharacteristic
14C2×C4⋊#92420C2211yescharacteristic
15C2×C4×#92420—21no—
16C2×C4×#92420C2211yescharacteristic
17Q8⋊#92420—21no—
18#16840610—21no—
19#16840610—21no—
20D4⋊#92420—21no—
21#16840606—22no—
22C2×#14519802C411yescharacteristic
23#41×Dic61C2211yescharacteristic
24C2×#14519739C2211yescharacteristic
25#16839871—21no—
26#16839865—21no—
27#16839847—21no—
28#16839842—21no—
29#16839802C411yescharacteristic
30#16839768C411yescharacteristic
31M16×Dic61C2211yescharacteristic
32C61×#417C411yescharacteristic
33C22×#92420—22no—
34C22×#92420—21no—
35C22×#92420—21no—
36C4⋊#92420—22no—
37C4⋊#92420—21no—
38C4⋊#92420—21no—
39C4⋊#92420—21no—
40C4⋊#92420—21no—
41C22⋊#92420—22no—
42C22⋊#92420—21no—
43C22⋊#92420D412yes—
44C4×#92420—22no—
45C4×#92420—21no—
46C4×#92420—21no—
47C4×#92420—21no—
48C4×#92420D411yescharacteristic
49C4×#92420D411yescharacteristic
50C22×D244C2×C411yescharacteristic
51C22×C4×D61—21no—
52#14519802—22no—
53#14519802C814yescomplemented
54C2×#11758201—21no—
55C2×#11758199—21no—
56C2×#11758194C2×C411yescharacteristic
57Q8×Dic61D411yescharacteristic
58Q8×Dic61D411yescharacteristic
59D4×Dic61—21no—
60D4×Dic61—21no—
61D4×Dic61D411yescharacteristic
62D4×Dic61D411yescharacteristic
63#14519739—21no—
64#14519739—21no—
65#14519739—21no—
66#14519739—21no—
67#14519736—21no—
68#14519736C2×C411yescharacteristic
69C2×#11758198—21no—
70C2×C4×Dic61—21no—
71C2×C4×Dic61C2311yescharacteristic
72#14519710—21no—
73#14519708—21no—
74#14519699—21no—
75#14519699—21no—
76#14519687—21no—
77C8×Dic61—21no—
78C2×#41×C61C2×C411yescharacteristic
79C2×M16×C61C2×C411yescharacteristic
80C2×C4⋊C4×C61C2×C411yescharacteristic
81#103×C61—21no—
82#102×C61—21no—
83C23×D61—21no—
84#41×C61—21no—
85#41×C61—21no—
86#41×C61C2×C812yes—
87#41×C61M1612yes—
88C2×Q8×C61C22⋊C411yescharacteristic
89C2×D4×C61—21no—
90C2×D4×C61C22⋊C411yescharacteristic
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61C22×C411yescharacteristic
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61C2×D411yescharacteristic
97C22×Dic61#4111yescharacteristic
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244C2×C812yescomplemented
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—81no—
107C2×C4×D61—81no—
108C2×#92420—21no—
109C2×#92420—22no—
110C2×#92420—21no—
111C2×#92420—42no—
112C2×#92420—44no—
113C2×#92420—41no—
114C2×#92420—41no—
115C2×#92420—81no—
116M16×C61—21no—
117M16×C61—21no—
118C2×C8×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C22⋊Dic61—21no—
122C22⋊Dic61—21no—
123C22⋊Dic61—21no—
124#11758201—24no—
125#11758199—24no—
126#11758198—41no—
127#11758198—41no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61C22⋊C411yescharacteristic
131C4⋊Dic61C22⋊C411yescharacteristic
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61C2×D411yescharacteristic
136C4×Dic61C2×D411yescharacteristic
137C4×Dic61C2×D411yescharacteristic
138C4×Dic61#4111yescharacteristic
139#11758194—21no—
140#11758194C2×C812yescomplemented
141C2×#92418—21no—
142C23×C61—21no—
143C23×C61C4×D411yescharacteristic
144C22×D61—22no—
145C22×D61—41no—
146C22×D61—41no—
147C22×D61—81no—
148C22×D61—81no—
149Q8×C61—21no—
150Q8×C61C22⋊C812yes—
151D4×C61—22no—
152D4×C61—22no—
153D4×C61—21no—
154D4×C61C22⋊C812yes—
155C2×C4×C61—21no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—41no—
159C2×C4×C61—81no—
160C2×C4×C61C2×C22⋊C411yescharacteristic
161C2×C4×C61C4×D411yescharacteristic
162C2×C4×C61C22×C811yescharacteristic
163C2×C4×C61C2×M1611yescharacteristic
164C2×C4×C61#13111yescharacteristic
165C2×C4×C61#13111yescharacteristic
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61#12011yescharacteristic
175C2×Dic61#12111yescharacteristic
176C2×Dic61#12111yescharacteristic
177C2×Dic61#12311yescharacteristic
178D244—22no—
179D244—22no—
180D244—41no—
181D244—41no—
182C4×D61—82no—
183C4×D61—81no—
184C4×D61—81no—
185#92420—22no—
186#92420—42no—
187#92420—41no—
188#92420—81no—
189#92420—81no—
190C8×C61—41no—
191#92418—22no—
192#9095—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—22no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61#38611yescharacteristic
199C22×C61C8×D411yescharacteristic
200C22×C61#43511yescharacteristic
201C2×D61—42no—
202C2×D61—82no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—82no—
206C4×C61—22no—
207C4×C61—81no—
208C4×C61C2×C22⋊C811yescharacteristic
209C4×C61#40811yescharacteristic
210C4×C61C8×D411yescharacteristic
211C4×C61#43511yescharacteristic
212Dic61—21no—
213Dic61—21no—
214Dic61—21no—
215Dic61—41no—
216Dic61—41no—
217Dic61#47111yescharacteristic
218Dic61#47211yescharacteristic
219C8×#41—611no—
220C4×AGL(1,ℤ/8)—611no—
221#1477—611no—
222C2×D4⋊C8—611no—
223#1460—611no—
224#1283—611no—
225#1278—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—42no—
229C2×C61#186911yescharacteristic
230C2×C61#190611yescharacteristic
231C2×C61#190711yescharacteristic
232D61—82no—
233C2×AGL(1,ℤ/8)—611no—
234C4×#41—611no—
235C2×C4×D4—611no—
236C8×Q8—1221no—
237#442—1221no—
238#440—1221no—
239C4×SD16—1221no—
240C4×D8—1221no—
241C8×D4—1222no—
242C8×D4—1221no—
243#431—611no—
244#431—611no—
245#431—1221no—
246#428—611no—
247C2×C4⋊C8—611no—
248#418—611no—
249#417#692311yescharacteristic
250C4×M16—611no—
251C2×C4×C8—611no—
252C2×C4×C8—1221no—
253Q8⋊C8—1221no—
254D4⋊C8—1221no—
255D4⋊C8—1221no—
256D4⋊C8—1221no—
257#323—1222no—
258C61#909511yescharacteristic, complemented, Sylow
259C2×#41C2×#692311yescharacteristic
260C22×D4—611no—
261C23×C4—1221no—
262AGL(1,ℤ/8)—614no—
263AGL(1,ℤ/8)—1222no—
264C2×SD16—1221no—
265C2×D8—1221no—
266C2×M16—611no—
267C2×M16C2×#692311yescharacteristic
268C22×C8—1221no—
269C22×C8—1222no—
270C22×C8—1221no—
271C4×Q8—611no—
272C4×Q8—611no—
273C4×D4—611no—
274C4×D4—611no—
275C4×D4—1221no—
276C4×D4—1221no—
277C4×D4—1221no—
278C4×D4—1221no—
279C4×D4—1221no—
280C4×D4—1221no—
281#117—611no—
282#117—1221no—
283C2×C4⋊C4C2×#692311yescharacteristic
284C2×C22⋊C4—1221no—
285C2×C42—611no—
286C2×C42—1221no—
287#107—1221no—
288#106—1221no—
289C4⋊C8—1221no—
290C4⋊C8—1221no—
291C4⋊C8—1221no—
292C4⋊C8—1221no—
293C4⋊C8—1222no—
294#103—21no—
295#102—21no—
296#102—1221no—
297#102—1221no—
298C22⋊C8—612no—
299C22⋊C8—1222no—
300C22⋊C8—1221no—
301#97—1221no—
302C4×C8—611no—
303C4×C8—611no—
304C4×C8—1221no—
305C4×C8—1221no—
306C4×C8—1221no—
307C4×C8—1221no—
308C4×C8—1222no—
309C24—1221no—
310#41—21no—
311#41—21no—
312#41D61⋊C812yes—
313#41#1175821312yes—
314C2×Q8C22⋊#692311yescharacteristic
315C2×D4—21no—
316C2×D4—612no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—1221no—
322C2×D4C22⋊#692311yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—4881no—
330C22×C4—4881no—
331C22×C4—2441no—
332C22×C4—2441no—
333C22×C4C22×#692311yescharacteristic
334SD16—1224no—
335D8—1224no—
336M16—21no—
337M16—21no—
338M16—612no—
339M16—1221no—
340C2×C8—21no—
341C2×C8—1221no—
342C2×C8—1221no—
343C2×C8—1221no—
344C2×C8—1222no—
345C2×C8—4881no—
346C2×C8—2442no—
347C2×C8—2444no—
348C2×C8—2441no—
349C2×C8—2441no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—611no—
353C4⋊C4—611no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C42—611no—
362C42—611no—
363C42—611no—
364C42—611no—
365C42—1221no—
366C42—1221no—
367C42—1221no—
368C23—21no—
369C23—1222no—
370C23—4881no—
371C23—4881no—
372C23—2441no—
373C23—2441no—
374C23D4×#692311yescharacteristic
375Q8—21no—
376Q8#1451983412yes—
377D4—22no—
378D4—22no—
379D4—21no—
380D4—1222no—
381D4—1222no—
382D4—2441no—
383D4—2441no—
384D4#1451983412yes—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—611no—
391C2×C4—611no—
392C2×C4—611no—
393C2×C4—611no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—4881no—
399C2×C4—4881no—
400C2×C4—4882no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2442no—
405C2×C4C2×C22⋊#692311yescharacteristic
406C2×C4D4×#692311yescharacteristic
407C2×C4C2×D61⋊C811yescharacteristic
408C2×C4C2×#1175821311yescharacteristic
409C2×C4#1451986411yescharacteristic
410C2×C4#1451986411yescharacteristic
411C8—41no—
412C8—1222no—
413C8—1222no—
414C8—4881no—
415C8—4881no—
416C8—2441no—
417C8—2442no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—4882no—
424C22—4882no—
425C22—4881no—
426C22—4881no—
427C22—2442no—
428C22#1684071011yescharacteristic
429C22#1684078911yescharacteristic
430C22#1684079111yescharacteristic
431C4—22no—
432C4—81no—
433C4—611no—
434C4—611no—
435C4—1221no—
436C4—1221no—
437C4—1221no—
438C4—2441no—
439C4—2441no—
440C4C2×#1451983411yescharacteristic
441C4#1684073511yescharacteristic
442C4#1684078911yescharacteristic
443C4#1684079111yescharacteristic
444C2—21no—
445C2—21no—
446C2—42no—
447C2—4882no—
448C2#2146179411yescharacteristic
449C2#2146185711yescharacteristic
450C2#2146185811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#417C4
socleC22×C61#386
prime radicalC2×#14519802C4
cosocleC2×C4×Dic61C23
hypercenter#417#6923
hypocenterC61#9095
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #41×#92420C2semidirect
2. #21461114C2semidirect
3. C2×#16840610C2semidirect
4. #21461060C2semidirect
5. #21460665C2semidirect
6. #21460652C2semidirect
53. #14519802C8semidirect
103. C2×D244C2×C8semidirect
140. #11758194C2×C8semidirect
258. C61#9095semidirect

Maximal subgroups

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

subgroupindex
#41×#924202
#214611142
C2×#168406102
#214610602
#214606652
#214606522
#214546322
#909561