Finite Group Databasebeta

← #29582343

Subgroups — #29582343

Order 15616.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840043C211yesmaximal, characteristic
2C2×#16839972C211yesmaximal, characteristic, complemented
3#21450737C211yesmaximal, characteristic
4#21446780C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×#11758202—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519753—21no—
11C2×C4×D244C2211yescharacteristic
12#16840043—22no—
13#16840043—22no—
14#16839972—22no—
15#16839972—22no—
16C2×#14519711—21no—
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519700—21no—
19C2×#14519699—21no—
20#16839684—22no—
21#16839664—21no—
22#16839660—21no—
23#16839632C2211yescharacteristic
24#16839619—21no—
25#16839525—22no—
26#16839491—22no—
27C2×C4×Q8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×Dic122—21no—
32C22×D244D411yescharacteristic
33C22×C4×D61—21no—
34C2×#11758202—24no—
35C2×#11758202—42no—
36C2×#11758202—42no—
37C22×#92418—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777D412yes—
42#14519753—42no—
43#14519753—42no—
44C4×D244—21no—
45C4×D244—21no—
46C4×D244—21no—
47C4×D244—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61D411yescharacteristic
53C2×C4⋊Dic61D412yes—
54C2×#11758196—22no—
55C2×#11758198—22no—
56C2×#11758198—21no—
57C2×#11758198—22no—
58#14519711—24no—
59C4⋊#92418—21no—
60C4⋊#92418D412yes—
61#14519700—24no—
62#14519699—24no—
63#14519684—22no—
64C22×Q8×C61D411yescharacteristic
65C22×C8×C61—21no—
66C22×C8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C42×C61—21no—
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C4⋊C8×C61D412yes—
77C4×C8×C61—21no—
78C4×C8×C61—21no—
79C23×D61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61D812yes—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×Dic61—21no—
92C22×Dic61—22no—
93C22×Dic61—41no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244—21no—
98C2×D244—21no—
99C2×D244Q1612yescomplemented
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×Dic122—22no—
107C2×Dic122—41no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111C2×Dic122—41no—
112C2×C8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C42×C61—41no—
123C42×C61—41no—
124C42×C61C2×D411yescharacteristic
125C42×C61C2×D411yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61#4111yescharacteristic
128#11758202—48no—
129#11758198—44no—
130#11758198—41no—
131#11758198—41no—
132#11758198—82no—
133C4⋊Dic61—22no—
134C4⋊Dic61—21no—
135C4⋊Dic61—22no—
136C4⋊Dic61—21no—
137C4⋊Dic61—41no—
138C4⋊Dic61—41no—
139C4⋊Dic61—41no—
140C4⋊Dic61—41no—
141C4⋊Dic61—41no—
142C4⋊Dic61—41no—
143C4⋊Dic61—42no—
144#11758196—44no—
145C2×#92418—22no—
146C2×#92418—41no—
147C2×#92418—41no—
148C23×C61#12011yescharacteristic
149C22×D61—22no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156Q8×C61—22no—
157Q8×C61—22no—
158Q8×C61—41no—
159Q8×C61—41no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—22no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12011yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12711yescharacteristic
174C2×C4×C61C2×D811yescharacteristic
175C2×C4×C61C2×Q1611yescharacteristic
176C2×C4×C61#13511yescharacteristic
177C2×C4×C61#13511yescharacteristic
178C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C61#13711yescharacteristic
181C2×C4×C61#13711yescharacteristic
182C2×Dic61—42no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—42no—
186C2×Dic61—41no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—81no—
190C2×Dic61—81no—
191D244—22no—
192D244—22no—
193D244—41no—
194D244—41no—
195C4×D61—81no—
196C4×D61—81no—
197C4×D61—81no—
198C4×D61—81no—
199Dic122—42no—
200Dic122—42no—
201Dic122—81no—
202Dic122—81no—
203C8×C61—42no—
204C8×C61—42no—
205#92418—42no—
206#10233—611nomaximal, Sylow
207C22×C61#39211yescharacteristic
208C22×C61#44711yescharacteristic
209C22×C61#44911yescharacteristic
210C22×C61#45111yescharacteristic
211C22×C61#45211yescharacteristic
212C22×C61#45511yescharacteristic
213C22×C61#45611yescharacteristic
214C2×D61—42no—
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—81no—
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—42no—
224C4×C61—81no—
225C4×C61#44711yescharacteristic
226C4×C61#44911yescharacteristic
227C4×C61#45111yescharacteristic
228C4×C61#45211yescharacteristic
229C4×C61#46611yescharacteristic
230C4×C61#46711yescharacteristic
231C4×C61#46911yescharacteristic
232C4×C61#47011yescharacteristic
233Dic61—82no—
234Dic61—82no—
235Dic61—81no—
236C2×#474—611no—
237C2×#462—611no—
238#2538—611no—
239#1990—611no—
240C2×Q8⋊C8D6111yescharacteristic, complemented
241C2×D4⋊C8—611no—
242#1296—611no—
243C2×C61#164111yescharacteristic
244C2×C61#164411yescharacteristic
245C2×C61#164911yescharacteristic
246C2×C61#165211yescharacteristic
247C2×C61#199911yescharacteristic
248C2×C61#200111yescharacteristic
249C2×C61#200711yescharacteristic
250D61—82no—
251C22×Q16—1221no—
252C2×C4⋊Q8—611no—
253C2×C22⋊Q8—1221no—
254C2×C4×Q8C2×D6111yescharacteristic
255C2×C4×D4—611no—
256#474—1222no—
257#474—1222no—
258#462—1222no—
259#462—1222no—
260C2×#107—1221no—
261C2×C4⋊C8—611no—
262C2×C4⋊C8C2×D6111yescharacteristic
263C2×#103—1221no—
264C2×#102—1221no—
265C2×C4×C8C2×D6111yescharacteristic
266#396—1222no—
267#390—1221no—
268#389—1221no—
269#384—611no—
270#380—1221no—
271#340—1222no—
272Q8⋊C8—22no—
273D4⋊C8—1222no—
274C61#1023311yescharacteristic, complemented, Sylow
275C22×Q8—1221no—
276C22×Q8D24411yescharacteristic
277C22×D4—611no—
278C23×C4—1221no—
279C2×Q16—1224no—
280C2×Q16—2442no—
281C2×Q16—2442no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—1221no—
285C4⋊Q8—612no—
286C4⋊Q8—1221no—
287C4⋊Q8—1221no—
288C4⋊Q8—1221no—
289C22⋊Q8—2442no—
290C22⋊Q8—2442no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×D4—1221no—
296C4×D4—1221no—
297C4×D4—1221no—
298C4×D4—1221no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—612no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1222no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4D24411yescharacteristic
308C2×C22⋊C4—1222no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—1221no—
311C2×C42—21no—
312C2×C42C22×D6111yescharacteristic
313#107—1224no—
314C4⋊C8—21no—
315C4⋊C8—612no—
316C4⋊C8—1221no—
317C4⋊C8C22⋊D6112yes—
318#103—1224no—
319#102—1224no—
320C4×C8—21no—
321C4×C8—21no—
322#95—1222no—
323C24—1221no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—1222no—
330C2×Q8—2441no—
331C2×Q8—2441no—
332C2×Q8—2441no—
333C2×Q8—2441no—
334C2×Q8—2441no—
335C2×Q8D48812yes—
336C2×D4—612no—
337C2×D4—1221no—
338C2×D4—1221no—
339C2×D4—1221no—
340C2×D4—1221no—
341C2×D4—1221no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—1221no—
345C22×C4—1222no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4C2×D24411yescharacteristic
354C22×C4D4×D6111yescharacteristic
355C22×C4D4×D6111yescharacteristic
356Q16—2448no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—1222no—
364C2×C8—2441no—
365C2×C8—2441no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—1222no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—1222no—
374C4⋊C4—2442no—
375C4⋊C4—2444no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C22⋊C4—4882no—
383C22⋊C4—2444no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C42—41no—
387C42—41no—
388C42#1175822211yescharacteristic
389C42D4×D6111yescharacteristic
390C42D4×D6111yescharacteristic
391C42C2×C22⋊D6111yescharacteristic
392C23—1222no—
393C23—2441no—
394C23—2441no—
395C23—2441no—
396C23—2441no—
397C23—2441no—
398C23—2441no—
399C23#1451974711yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—41no—
403Q8—41no—
404Q8—4881no—
405Q8—4881no—
406Q8—2442no—
407Q8—2442no—
408D4—1222no—
409D4—1222no—
410D4—2441no—
411D4—2441no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—4881no—
421C2×C4—4881no—
422C2×C4—4881no—
423C2×C4—4881no—
424C2×C4—4881no—
425C2×C4—4881no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4#1451974511yescharacteristic
434C2×C4#1451974711yescharacteristic
435C2×C4#1451975011yescharacteristic
436C2×C4#1451975011yescharacteristic
437C2×C4#1451975111yescharacteristic
438C2×C4#1451977311yescharacteristic
439C2×C4C2×D48811yescharacteristic
440C2×C4Q16×D6111yescharacteristic
441C2×C4#1451979811yescharacteristic
442C2×C4#1451979911yescharacteristic
443C2×C4#1451980511yescharacteristic
444C2×C4#1451980511yescharacteristic
445C2×C4#1451980611yescharacteristic
446C2×C4#1451980911yescharacteristic
447C8—42no—
448C8—42no—
449C8—2442no—
450C22—4881no—
451C22—4881no—
452C22—4881no—
453C22—4881no—
454C22—2442no—
455C22—2442no—
456C22—2442no—
457C22#1683967111yescharacteristic
458C22#1683989811yescharacteristic
459C22#1683990911yescharacteristic
460C22#1683991911yescharacteristic
461C22#1683992711yescharacteristic
462C22#1683994111yescharacteristic
463C22#1683994611yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—4882no—
469C4—4881no—
470C4—4882no—
471C4#1683989811yescharacteristic
472C4#1683990911yescharacteristic
473C4#1683991611yescharacteristic
474C4#1683992111yescharacteristic
475C4#1683999811yescharacteristic
476C4#1684000211yescharacteristic
477C4#1684001511yescharacteristic
478C4#1684001911yescharacteristic
479C2—4882no—
480C2#2144501411yescharacteristic
481C2#2144503511yescharacteristic
482C2#2144507011yescharacteristic
483C2#2144509111yescharacteristic
484C2#2144681711yescharacteristic
485C2#2144682811yescharacteristic
486C2#2144686711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenterC2×Q8⋊C8D61
hypocenterC61#10233
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16839972C2semidirect
4. #21446780C2semidirect
6. #21443703C2semidirect
7. C2×C61×Q8⋊C8C2semidirect
99. C2×D244Q16semidirect
240. C2×Q8⋊C8D61semidirect
274. C61#10233semidirect

Maximal subgroups

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

subgroupindex
C2×#168400432
C2×#168399722
#214507372
#214467802
C2×#168394912
#214437032
C2×C61×Q8⋊C82
#1023361