Finite Group Databasebeta

← #29580440

Subgroups — #29580440

Order 15616.

930 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456572C211yesmaximal, characteristic, complemented
2C2×#16839896C211yesmaximal, characteristic
3#21446655C211yesmaximal, characteristic, complemented
4#21445750C211yesmaximal, characteristic, complemented
5#21444391C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#2435C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×#14519751C2211yescharacteristic
10#16840090—21no—
11#16840080—21no—
12#16839993—22no—
13#16839912—21no—
14#16839901—21no—
15#16839896—22no—
16#16839896—22no—
17C2×#14519698—21no—
18C2×#14519698—22no—
19C2×#14519691—22no—
20C2×C22⋊#92418C2211yescharacteristic
21C2×C22⋊#92418C2211yescharacteristic
22#16839622C2211yescharacteristic
23#16839499—22no—
24C23×D4×C61C2211yescharacteristic
25C2×#124×C61—21no—
26C2×C22⋊Q8×C61C2211yescharacteristic
27C61×#394—22no—
28C61×#390—21no—
29C61×#379—22no—
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C2×#11758201—22no—
34C2×#11758199—24no—
35C2×#11758199—44no—
36C22×#92418—21no—
37C22×#92418D412yes—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41#14519751—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×#11758198—21no—
46#14519708—22no—
47#14519701—22no—
48#14519698—24no—
49#14519698—44no—
50#14519697—22no—
51#14519691—44no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418D412yes—
56#14519684—21no—
57C25×C61—21no—
58C22×Q8×C61D411yescharacteristic
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—44no—
65C22×D4×C61D412yes—
66C23×C4×C61C2311yescharacteristic
67#124×C61—44no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70C22⋊Q8×C61—21no—
71C22⋊Q8×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—24no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—24no—
77C2×C22⋊C4×C61D412yes—
78C2×C42×C61—21no—
79#95×C61—21no—
80C24×C61—22no—
81C24×C61—44no—
82C24×C61—41no—
83C24×C61—41no—
84C24×C61—42no—
85C24×C61—42no—
86C24×C61—82no—
87C24×C61C2×D411yescharacteristic
88C23×D61—21no—
89C2×Q8×C61—21no—
90C2×Q8×C61—21no—
91C2×Q8×C61—42no—
92C2×D4×C61—24no—
93C2×D4×C61—24no—
94C2×D4×C61—24no—
95C2×D4×C61—22no—
96C2×D4×C61—22no—
97C2×D4×C61—42no—
98C2×D4×C61—42no—
99C2×D4×C61—42no—
100C2×D4×C61—44no—
101C2×D4×C61—44no—
102C2×D4×C61—44no—
103C2×D4×C61—41no—
104C2×D4×C61—41no—
105C22×C4×C61—22no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—42no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C2×C22⋊D61—41no—
116C2×C22⋊D61—41no—
117C2×C22⋊D61—42no—
118C2×C22⋊D61—42no—
119C22×Dic61—21no—
120C22×Dic61—41no—
121C2×D244—21no—
122C2×D244—21no—
123C2×D244—42no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—41no—
127C4⋊C4×C61—41no—
128C22⋊C4×C61—22no—
129C22⋊C4×C61—22no—
130C22⋊C4×C61—48no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—84no—
134C42×C61—42no—
135C22⋊Dic61—42no—
136#11758201—82no—
137#11758199—48no—
138#11758198—41no—
139#11758198—41no—
140C4⋊Dic61—21no—
141C4⋊Dic61—21no—
142C4⋊Dic61—42no—
143C2×#92418—22no—
144C2×#92418—22no—
145C2×#92418—42no—
146C2×#92418—42no—
147C23×C61—24no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—44no—
151C23×C61—44no—
152C23×C61—44no—
153C23×C61—42no—
154C23×C61—42no—
155C23×C61—44no—
156C23×C61—82no—
157C23×C61—82no—
158C23×C61—88no—
159C23×C61—88no—
160C23×C61—82no—
161C23×C61—81no—
162C23×C61—81no—
163C23×C61#12011yescharacteristic
164C23×C61#12111yescharacteristic
165C23×C61#12711yescharacteristic
166C23×C61#13512yes—
167C23×C61AGL(1,ℤ/8)12yes—
168C22×D61—41no—
169C22×D61—42no—
170C22×D61—81no—
171C22×D61—81no—
172Q8×C61—42no—
173Q8×C61—81no—
174D4×C61—24no—
175D4×C61—24no—
176D4×C61—42no—
177D4×C61—42no—
178D4×C61—44no—
179D4×C61—44no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#12011yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12111yescharacteristic
197C22⋊D61—82no—
198C22⋊D61—81no—
199C22⋊D61—81no—
200C2×Dic61—41no—
201C2×Dic61—42no—
202C2×Dic61—81no—
203C2×Dic61—81no—
204C2×Dic61—81no—
205D244—42no—
206D244—42no—
207#92418—42no—
208#92418—42no—
209#9947—611nomaximal, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—42no—
217C22×C61—42no—
218C22×C61—48no—
219C22×C61—44no—
220C22×C61—84no—
221C22×C61—84no—
222C22×C61—88no—
223C22×C61—84no—
224C22×C61—82no—
225C22×C61—82no—
226C22×C61#39211yescharacteristic
227C22×C61#44912yes—
228C22×C61#46312yes—
229C22×C61#49511yescharacteristic
230C22×C61#49611yescharacteristic
231C2×D61—81no—
232C2×D61—81no—
233C2×D61—81no—
234C2×D61—162no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—82no—
239C4×C61—81no—
240C4×C61—81no—
241C4×C61B(4,𝔽2)12yes—
242Dic61—81no—
243Dic61—161no—
244#3187—611no—
245C2×#447—611no—
246#2435D6111yescharacteristic, complemented
247#1964—611no—
248#1786—611no—
249#1520—611no—
250#1282—611no—
251C2×C61—21no—
252C2×C61—22no—
253C2×C61—22no—
254C2×C61—21no—
255C2×C61—84no—
256C2×C61#200811yescharacteristic
257C2×C61#201211yescharacteristic
258C2×C61#202111yescharacteristic
259D61—161no—
260C23×D4C2×D6111yescharacteristic
261C22×D8—1221no—
262C2×#124—21no—
263C2×C22⋊Q8C2×D6111yescharacteristic
264C2×#121—611no—
265#483—1221no—
266#481—1221no—
267#465—1222no—
268#450—1221no—
269#448—1221no—
270#447—1222no—
271#447—1222no—
272C2×#102—1221no—
273C2×#102—1222no—
274C2×#99—1222no—
275C2×C22⋊C8—611no—
276C2×C22⋊C8—611no—
277#394—22no—
278#390—21no—
279#380—611no—
280#379—22no—
281C4×C22⋊C4C2×D6111yescharacteristic
282#328—1222no—
283C61#994711yescharacteristic, complemented, Sylow
284C25—21no—
285C22×Q8C22⋊D6111yescharacteristic
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—44no—
292C22×D4—611no—
293C22×D4—1221no—
294C22×D4C22⋊D6112yes—
295C23×C4C22×D6111yescharacteristic
296C2×SD16—1222no—
297C2×D8—1224no—
298C2×D8—2444no—
299C22×C8—612no—
300C22×C8—1221no—
301#124—44no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306#121—1221no—
307#121—1221no—
308#121—1221no—
309#121—1221no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4C22⋊D6111yescharacteristic
314C2×C22⋊C4—24no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—1221no—
318C2×C22⋊C4—1221no—
319C2×C22⋊C4C22⋊D6112yes—
320C2×C42—21no—
321#106—1222no—
322#103—1222no—
323#102—1222no—
324#102—1224no—
325#102—2444no—
326#99—2444no—
327C22⋊C8—612no—
328C22⋊C8—1221no—
329C22⋊C8—1221no—
330C22⋊C8—1221no—
331#95—21no—
332#95—1221no—
333C24—22no—
334C24—44no—
335C24—41no—
336C24—41no—
337C24—42no—
338C24—42no—
339C24—82no—
340C24—1221no—
341C24C2×C22⋊D6111yescharacteristic
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—42no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—44no—
354C2×D4—44no—
355C2×D4—44no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—1221no—
359C2×D4—1221no—
360C2×D4—2442no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4—2442no—
364C2×D4—2442no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—42no—
369C22×C4—1221no—
370C22×C4—2441no—
371C22×C4D4×D6111yescharacteristic
372C22×C4D4×D6111yescharacteristic
373C22×C4D4×D6111yescharacteristic
374C22×C4#1175822411yescharacteristic
375C22×C4C2×C22⋊D6111yescharacteristic
376C22×C4C2×C22⋊D6111yescharacteristic
377SD16—4882no—
378D8—2448no—
379C2×C8—1222no—
380C2×C8—1222no—
381C2×C8—2442no—
382C2×C8—2442no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—1221no—
388C4⋊C4—1221no—
389C4⋊C4—2442no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—48no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—84no—
396C22⋊C4—2442no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C42—42no—
400C23—24no—
401C23—41no—
402C23—41no—
403C23—44no—
404C23—44no—
405C23—44no—
406C23—42no—
407C23—44no—
408C23—42no—
409C23—82no—
410C23—82no—
411C23—88no—
412C23—88no—
413C23—82no—
414C23—81no—
415C23—81no—
416C23—4881no—
417C23—4881no—
418C23—2442no—
419C23—2441no—
420C23#1451974611yescharacteristic
421C23#1451974811yescharacteristic
422C23#1451977311yescharacteristic
423C23#1451979712yes—
424C23#1451980212yes—
425Q8—42no—
426Q8—81no—
427D4—24no—
428D4—24no—
429D4—42no—
430D4—42no—
431D4—44no—
432D4—44no—
433D4—4881no—
434D4—4881no—
435D4—4882no—
436D4—2442no—
437D4—2442no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—4881no—
452C2×C4—4881no—
453C2×C4—4881no—
454C2×C4—2442no—
455C2×C4—2441no—
456C2×C4#1451974511yescharacteristic
457C2×C4#1451974511yescharacteristic
458C2×C4#1451974911yescharacteristic
459C2×C4#1451974911yescharacteristic
460C8—2442no—
461C8—2442no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—42no—
469C22—42no—
470C22—48no—
471C22—44no—
472C22—84no—
473C22—84no—
474C22—88no—
475C22—84no—
476C22—82no—
477C22—82no—
478C22—9762no—
479C22—4881no—
480C22—4881no—
481C22—4881no—
482C22#1683967011yescharacteristic
483C22#1683990712yes—
484C22#1683997412yes—
485C22#1684014411yescharacteristic
486C22#1684015211yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—82no—
491C4—81no—
492C4—81no—
493C4—9761no—
494C4—4881no—
495C4#1683994812yes—
496C2—22no—
497C2—21no—
498C2—22no—
499C2—21no—
500C2—84no—
501C2—9761no—
502C2#2144687211yescharacteristic
503C2#2144689611yescharacteristic
504C2#2144694211yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2435C2
socleC22×C61#392
prime radicalC2×#16839896C2
hypercenter#2435D61
hypocenterC61#9947
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2435

Complements

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

NH ≅ G/Ntype
1. #21456572C2semidirect
3. #21446655C2semidirect
4. #21445750C2semidirect
5. #21444391C2semidirect
6. #21443667C2semidirect
7. C61×#2435C2semidirect
246. #2435D61semidirect
283. C61#9947semidirect

Maximal subgroups

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

subgroupindex
#214565722
C2×#168398962
#214466552
#214457502
#214443912
#214436672
C61×#24352
#994761