Finite Group Databasebeta

← #29583528

Subgroups — #29583528

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450732C211yesmaximal, characteristic
2#21445976C211yesmaximal, characteristic, complemented
3#21445820C211yesmaximal, characteristic, complemented
4#21445819C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#14519751—21no—
9C2×#14519748—21no—
10C2×C4×D244C2211yescharacteristic
11C2×#14519709—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519699—21no—
14C2×#14519698—21no—
15#16839678—22no—
16#16839632C2211yescharacteristic
17#16839632C2211yescharacteristic
18#16839622—21no—
19#16839619—21no—
20#16839525—21no—
21#16839524—21no—
22#16839491—22no—
23C2×C4×D4×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C61×D4⋊C8—22no—
27C22×D244D411yescharacteristic
28C22×C22⋊D61—22no—
29C22×C4×D61—21no—
30C22×#92418—21no—
31#14519751—42no—
32#14519751—42no—
33#14519748—42no—
34#14519748—42no—
35C4×D244—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D412yes—
46C2×C22⋊Dic61—22no—
47C2×#11758198—22no—
48C2×#11758198—21no—
49#14519709—44no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52#14519699—42no—
53#14519698—42no—
54#14519684—22no—
55C22×D4×C61D411yescharacteristic
56C23×C4×C61—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C4×D4×C61—21no—
60C4×D4×C61—21no—
61C4×D4×C61—21no—
62C4×D4×C61—21no—
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C22⋊C4×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4×C8×C61—21no—
69C4×C8×C61D412yescomplemented
70C24×C61—21no—
71C23×D61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61—21no—
77C2×D4×C61SD1612yes—
78C22×C4×C61—21no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C2×C22⋊D61—44no—
89C2×C22⋊D61—44no—
90C2×C22⋊D61—82no—
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×D244SD1612yes—
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×C8×C61—22no—
107C2×C8×C61—22no—
108C2×C8×C61—22no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C42×C61#4111yescharacteristic
119C42×C61#4111yescharacteristic
120C22⋊Dic61—44no—
121#11758198—44no—
122#11758198—41no—
123#11758198—41no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—41no—
127C4⋊Dic61—41no—
128C4⋊Dic61—41no—
129C4⋊Dic61—41no—
130C4⋊Dic61—42no—
131C4⋊Dic61—42no—
132C4⋊Dic61—41no—
133C4⋊Dic61—41no—
134C4⋊Dic61—41no—
135C4⋊Dic61—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138C2×#92418—41no—
139C23×C61—22no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61#12011yescharacteristic
147C22×D61—22no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154D4×C61—22no—
155D4×C61—22no—
156D4×C61—41no—
157D4×C61—41no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12311yescharacteristic
171C2×C4×C61#12311yescharacteristic
172C2×C4×C61#12411yescharacteristic
173C2×C4×C61C2×SD1611yescharacteristic
174C2×C4×C61C2×SD1611yescharacteristic
175C2×C4×C61#13511yescharacteristic
176C2×C4×C61#13511yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
181C22⋊D61—88no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—41no—
187C2×Dic61—42no—
188C2×Dic61—81no—
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—
199C8×C61—24no—
200C8×C61—81no—
201#92418—81no—
202#10432—611nomaximal, Sylow
203C22×C61—42no—
204C22×C61—42no—
205C22×C61—42no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61—81no—
210C22×C61#39411yescharacteristic
211C22×C61#44911yescharacteristic
212C22×C61#44911yescharacteristic
213C22×C61#45011yescharacteristic
214C22×C61#45011yescharacteristic
215C22×C61#45311yescharacteristic
216C22×C61#45611yescharacteristic
217C2×D61—42no—
218C2×D61—42no—
219C2×D61—42no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C2×D61—81no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—81no—
227C4×C61#46511yescharacteristic
228C4×C61#46511yescharacteristic
229C4×C61#46911yescharacteristic
230C4×C61#46911yescharacteristic
231C4×C61#48111yescharacteristic
232C4×C61#48111yescharacteristic
233C4×C61#48211yescharacteristic
234C4×C61#48211yescharacteristic
235Dic61—82no—
236Dic61—81no—
237Dic61—161no—
238#2537—611no—
239#1844—611no—
240#1802—611no—
241#1802—611no—
242C2×D4⋊C8—611no—
243C2×D4⋊C8D6111yescharacteristic, complemented
244#1296—611no—
245C2×C61—82no—
246C2×C61#162411yescharacteristic
247C2×C61#162911yescharacteristic
248C2×C61#165411yescharacteristic
249C2×C61#165411yescharacteristic
250C2×C61#203411yescharacteristic
251C2×C61#203411yescharacteristic
252C2×C61#203911yescharacteristic
253D61—82no—
254C2×#121—1221no—
255C2×#121—1221no—
256C2×C4×D4—611no—
257C2×C4×D4C2×D6111yescharacteristic
258C2×#106—1222no—
259C2×C4⋊C8—611no—
260C2×C4⋊C8C2×D6111yescharacteristic
261C2×#102—1221no—
262C2×#102—1221no—
263C2×C4×C8C2×D6111yescharacteristic
264#394—1222no—
265#384—611no—
266#384—611no—
267#380—1221no—
268#380—1221no—
269#340—1221no—
270#340—1221no—
271D4⋊C8—22no—
272D4⋊C8—1222no—
273C61#1043211yescharacteristic, complemented, Sylow
274C22×D4—611no—
275C22×D4—1222no—
276C22×D4D24411yescharacteristic
277C23×C4—21no—
278C23×C4—1221no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—1221no—
282#121—2442no—
283#121—2442no—
284#121—2442no—
285#121—2442no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—1221no—
291C4×D4—1221no—
292C4×D4—1221no—
293C4×D4—1221no—
294C2×C4⋊C4—611no—
295C2×C4⋊C4—612no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—1221no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4D24411yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—1222no—
304C2×C22⋊C4—1222no—
305C2×C22⋊C4—1221no—
306C2×C42C22×D6111yescharacteristic
307#106—2444no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310C4⋊C8—1221no—
311C4⋊C8—1221no—
312#102—2442no—
313#102—2442no—
314C4×C8—21no—
315C4×C8C22⋊D6112yescomplemented
316#95—1222no—
317C24—21no—
318C24—1221no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—612no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—4882no—
331C2×D4—2444no—
332C2×D4—2444no—
333C2×D4#1175819012yes—
334C22×C4—21no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—1221no—
342C22×C4—1222no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4—2441no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4C2×D24411yescharacteristic
351C22×C4D4×D6111yescharacteristic
352C22×C4D4×D6111yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—2441no—
360C2×C8—2441no—
361C2×C8—2441no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—2442no—
367C4⋊C4—2442no—
368C4⋊C4—2441no—
369C4⋊C4—2441no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—2444no—
379C22⋊C4—2444no—
380C22⋊C4—2441no—
381C22⋊C4—2441no—
382C42#1175822211yescharacteristic
383C42#1175822411yescharacteristic
384C42#1175822411yescharacteristic
385C42C2×C22⋊D6111yescharacteristic
386C23—22no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—1222no—
394C23—2441no—
395C23—2441no—
396C23—2441no—
397C23—2441no—
398C23—2441no—
399C23—2441no—
400C23#1451974711yescharacteristic
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—1222no—
406D4—1222no—
407D4—4888no—
408D4—2441no—
409D4—2441no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—4881no—
420C2×C4—4881no—
421C2×C4—4881no—
422C2×C4—4881no—
423C2×C4—4881no—
424C2×C4—4881no—
425C2×C4—4881no—
426C2×C4—2441no—
427C2×C4—2442no—
428C2×C4—2441no—
429C2×C4—2442no—
430C2×C4—2442no—
431C2×C4—2441no—
432C2×C4#1451974811yescharacteristic
433C2×C4#1451974911yescharacteristic
434C2×C4#1451975111yescharacteristic
435C2×C4#1451975911yescharacteristic
436C2×C4#1451976111yescharacteristic
437C2×C4#1451976311yescharacteristic
438C2×C4SD16×D6111yescharacteristic
439C2×C4C2×#1175819011yescharacteristic
440C2×C4#1451979811yescharacteristic
441C2×C4#1451979911yescharacteristic
442C2×C4#1451980111yescharacteristic
443C2×C4#1451980111yescharacteristic
444C2×C4#1451980511yescharacteristic
445C2×C4#1451980511yescharacteristic
446C8—24no—
447C8—81no—
448C8—4881no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—4881no—
457C22—4881no—
458C22—4881no—
459C22—4881no—
460C22—2442no—
461C22—2442no—
462C22—2442no—
463C22#1683967811yescharacteristic
464C22#1683990811yescharacteristic
465C22#1683990911yescharacteristic
466C22#1683991411yescharacteristic
467C22#1683991511yescharacteristic
468C22#1683993111yescharacteristic
469C22#1683994611yescharacteristic
470C4—21no—
471C4—21no—
472C4—81no—
473C4—9761no—
474C4—4882no—
475C4—4881no—
476C4#1683998811yescharacteristic
477C4#1683999111yescharacteristic
478C4#1684001211yescharacteristic
479C4#1684001511yescharacteristic
480C4#1684007911yescharacteristic
481C4#1684008111yescharacteristic
482C4#1684008511yescharacteristic
483C4#1684008711yescharacteristic
484C2—82no—
485C2—4882no—
486C2#2144490411yescharacteristic
487C2#2144493711yescharacteristic
488C2#2144510511yescharacteristic
489C2#2144510611yescharacteristic
490C2#2144700711yescharacteristic
491C2#2144700911yescharacteristic
492C2#2144704211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radical#21450732C2
hypercenterC2×D4⋊C8D61
hypocenterC61#10432
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21445976C2semidirect
3. #21445820C2semidirect
4. #21445819C2semidirect
5. C2×#16839491C2semidirect
6. #21443703C2semidirect
7. C2×C61×D4⋊C8C2semidirect
69. C4×C8×C61D4semidirect
243. C2×D4⋊C8D61semidirect
273. C61#10432semidirect
315. C4×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214507322
#214459762
#214458202
#214458192
C2×#168394912
#214437032
C2×C61×D4⋊C82
#1043261