Finite Group Databasebeta

← #29583519

Subgroups — #29583519

Order 15616.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445946C211yesmaximal, characteristic, complemented
2#21445819C211yesmaximal, characteristic, complemented
3#21445819C211yesmaximal, characteristic, complemented
4C2×D4⋊#92418C211yesmaximal, characteristic, complemented
5C2×D4⋊#92418C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#2537C211yesmaximal, characteristic
8C2×C4⋊#92418C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×#14519698—21no—
11C2×#14519698—21no—
12C2×C4×#92418C2211yescharacteristic
13#16839632C2211yescharacteristic
14#16839524—22no—
15#16839524—21no—
16#16839524—21no—
17D4⋊#92418—22no—
18D4⋊#92418—22no—
19C2×#121×C61—21no—
20C2×#121×C61—21no—
21C2×C4×D4×C61C2211yescharacteristic
22C2×C4×D4×C61C2211yescharacteristic
23C61×#394—22no—
24C61×#384C2211yescharacteristic
25C61×#380—21no—
26C61×#380—21no—
27C22×#92418—21no—
28C22×#92418—21no—
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37#14519698—42no—
38#14519698—42no—
39C4×#92418—21no—
40C4×#92418D412yescomplemented
41C22×D4×C61—22no—
42C22×D4×C61D411yescharacteristic
43C22×D4×C61D411yescharacteristic
44C23×C4×C61—21no—
45C23×C4×C61—21no—
46#121×C61—42no—
47#121×C61—42no—
48#121×C61—42no—
49#121×C61—42no—
50C4×D4×C61—21no—
51C4×D4×C61—21no—
52C4×D4×C61—21no—
53C4×D4×C61—21no—
54C4×D4×C61—21no—
55C4×D4×C61—21no—
56C4×D4×C61—21no—
57C4×D4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C4⋊C4×C61D412yes—
63C2×C22⋊C4×C61—22no—
64C2×C22⋊C4×C61—22no—
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68#95×C61—22no—
69C24×C61—21no—
70C24×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—44no—
82C2×D4×C61—44no—
83C2×D4×C61—82no—
84C2×D4×C61D812yes—
85C2×D4×C61SD1612yes—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×Dic61—41no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—42no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C22⋊C4×C61—44no—
115C22⋊C4×C61—44no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122C42×C61#4111yescharacteristic
123C42×C61#4111yescharacteristic
124C4⋊Dic61—42no—
125C4⋊Dic61—41no—
126C4⋊Dic61—41no—
127C4⋊Dic61—41no—
128C4⋊Dic61—41no—
129C2×#92418—22no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61#12011yescharacteristic
153D4×C61—22no—
154D4×C61—22no—
155D4×C61—22no—
156D4×C61—22no—
157D4×C61—41no—
158D4×C61—41no—
159D4×C61—41no—
160D4×C61—41no—
161D4×C61—88no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—42no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—81no—
174C2×C4×C61—81no—
175C2×C4×C61—81no—
176C2×C4×C61—81no—
177C2×C4×C61—81no—
178C2×C4×C61—81no—
179C2×C4×C61—81no—
180C2×C4×C61—81no—
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12311yescharacteristic
185C2×C4×C61#12311yescharacteristic
186C2×C4×C61#12411yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×SD1611yescharacteristic
189C2×C4×C61#13511yescharacteristic
190C2×C4×C61#13511yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C61#13711yescharacteristic
195C2×Dic61—81no—
196C2×Dic61—81no—
197C2×Dic61—81no—
198#92418—42no—
199#92418—81no—
200#92418—81no—
201#10431—611nomaximal, Sylow
202C22×C61—42no—
203C22×C61—42no—
204C22×C61—42no—
205C22×C61—42no—
206C22×C61—42no—
207C22×C61—42no—
208C22×C61—81no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61#39411yescharacteristic
217C22×C61#44711yescharacteristic
218C22×C61#44911yescharacteristic
219C22×C61#45011yescharacteristic
220C22×C61#45211yescharacteristic
221C22×C61#45411yescharacteristic
222C22×C61#45511yescharacteristic
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—82no—
226C4×C61—81no—
227C4×C61—81no—
228C4×C61#46511yescharacteristic
229C4×C61#46611yescharacteristic
230C4×C61#46811yescharacteristic
231C4×C61#46911yescharacteristic
232C4×C61#48011yescharacteristic
233C4×C61#48111yescharacteristic
234C4×C61#48211yescharacteristic
235C4×C61#48211yescharacteristic
236Dic61—161no—
237#2537D6111yescharacteristic
238#1834—611no—
239#1802—611no—
240#1802—611no—
241C2×D4⋊C8—611no—
242C2×D4⋊C8—611no—
243#1296—611no—
244C2×C61—82no—
245C2×C61—82no—
246C2×C61#162511yescharacteristic
247C2×C61#163511yescharacteristic
248C2×C61#163911yescharacteristic
249C2×C61#164611yescharacteristic
250C2×C61#203311yescharacteristic
251C2×C61#203411yescharacteristic
252C2×C61#204011yescharacteristic
253C2×#121—21no—
254C2×#121—21no—
255C2×C4×D4C2×D6111yescharacteristic
256C2×C4×D4C2×D6111yescharacteristic
257C2×C4⋊C8—611no—
258C2×C4⋊C8—611no—
259C2×#102—1221no—
260C2×#102—1221no—
261C2×C4×C8—611no—
262#394—22no—
263#384—611no—
264#384C2×D6111yescharacteristic
265#380—21no—
266#380—21no—
267#340—1221no—
268#340—1221no—
269#340—1222no—
270D4⋊C8—1222no—
271D4⋊C8—1222no—
272C61#1043111yescharacteristic, complemented, Sylow
273C22×D4—22no—
274C22×D4C22⋊D6111yescharacteristic
275C22×D4C22⋊D6111yescharacteristic
276C23×C4—21no—
277C23×C4—21no—
278C22×C8—1221no—
279C22×C8—1221no—
280C22×C8—1221no—
281#121—42no—
282#121—42no—
283#121—42no—
284#121—42no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4C22⋊D6111yescharacteristic
299C2×C4⋊C4C22⋊D6111yescharacteristic
300C2×C4⋊C4C22⋊D6112yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C42C22×D6111yescharacteristic
306C4⋊C8—1221no—
307C4⋊C8—1221no—
308C4⋊C8—1221no—
309C4⋊C8—1221no—
310#102—2442no—
311#102—2442no—
312C4×C8—612no—
313C4×C8—1221no—
314#95—22no—
315C24—21no—
316C24—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—44no—
328C2×D4—44no—
329C2×D4—82no—
330C2×D4#1175819912yes—
331C2×D4#1175820012yes—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—2441no—
348C22×C4C2×C22⋊D6111yescharacteristic
349C22×C4C2×C22⋊D6111yescharacteristic
350C22×C4C2×C22⋊D6111yescharacteristic
351C2×C8—1222no—
352C2×C8—2441no—
353C2×C8—2441no—
354C2×C8—2441no—
355C2×C8—2441no—
356C2×C8—2441no—
357C2×C8—2441no—
358C2×C8—2441no—
359C2×C8—2441no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—2442no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C42D4×D6111yescharacteristic
381C42#1175822411yescharacteristic
382C42#1175822411yescharacteristic
383C42#1175822411yescharacteristic
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23#1451974611yescharacteristic
399D4—22no—
400D4—22no—
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—88no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—4881no—
428C2×C4—4881no—
429C2×C4—4881no—
430C2×C4#1451974811yescharacteristic
431C2×C4#1451974911yescharacteristic
432C2×C4#1451974911yescharacteristic
433C2×C4#1451975811yescharacteristic
434C2×C4#1451975811yescharacteristic
435C2×C4#1451976411yescharacteristic
436C2×C4C2×#1175819911yescharacteristic
437C2×C4C2×#1175820011yescharacteristic
438C2×C4#1451979711yescharacteristic
439C2×C4#1451979711yescharacteristic
440C2×C4#1451980211yescharacteristic
441C2×C4#1451980311yescharacteristic
442C2×C4#1451980311yescharacteristic
443C2×C4#1451980711yescharacteristic
444C8—4881no—
445C8—4881no—
446C8—2442no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#1683967611yescharacteristic
462C22#1683989611yescharacteristic
463C22#1683990711yescharacteristic
464C22#1683991311yescharacteristic
465C22#1683992411yescharacteristic
466C22#1683993511yescharacteristic
467C22#1683994011yescharacteristic
468C4—21no—
469C4—21no—
470C4—81no—
471C4—81no—
472C4—82no—
473C4—9761no—
474C4#1683998911yescharacteristic
475C4#1683999611yescharacteristic
476C4#1684000611yescharacteristic
477C4#1684001311yescharacteristic
478C4#1684007311yescharacteristic
479C4#1684007811yescharacteristic
480C4#1684008311yescharacteristic
481C4#1684008311yescharacteristic
482C2—82no—
483C2—82no—
484C2#2144490811yescharacteristic
485C2#2144497011yescharacteristic
486C2#2144499811yescharacteristic
487C2#2144504711yescharacteristic
488C2#2144699811yescharacteristic
489C2#2144700511yescharacteristic
490C2#2144704511yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#2537C2
socleC23×C61#120
hypercenter#2537D61
hypocenterC61#10431
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #21445946C2semidirect
2. #21445819C2semidirect
3. #21445819C2semidirect
4. C2×D4⋊#92418C2semidirect
5. C2×D4⋊#92418C2semidirect
6. #21443702C2semidirect
40. C4×#92418D4semidirect
272. C61#10431semidirect

Maximal subgroups

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

subgroupindex
#214459462
#214458192
C2×D4⋊#924182
#214437022
C61×#25372
#1043161