Finite Group Databasebeta

← #29580447

Subgroups — #29580447

Order 15616.

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

normal subgroups only

This group has 812 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#21456567C211yesmaximal, characteristic
2C2×#16839901C211yesmaximal, characteristic, complemented
3#21446655C211yesmaximal, characteristic, complemented
4#21445754C211yesmaximal, characteristic, complemented
5#21444387C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#2436C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×#14519751C2211yescharacteristic
10#16840075—21no—
11#16840073—21no—
12#16839996—22no—
13#16839901—22no—
14#16839901—22no—
15#16839896—21no—
16#16839895—21no—
17C2×#14519701—21no—
18C2×#14519701—22no—
19C2×#14519691—22no—
20C2×C22⋊#92418C2211yescharacteristic
21C2×C22⋊#92418C2211yescharacteristic
22#16839622C2211yescharacteristic
23#16839496—22no—
24C23×Q8×C61C2211yescharacteristic
25C2×#124×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C61×#393—22no—
28C61×#391—21no—
29C61×#386—22no—
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C2×#11758201—24no—
34C2×#11758201—44no—
35C2×#11758199—22no—
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#14519710—22no—
47#14519701—24no—
48#14519701—44no—
49#14519698—22no—
50#14519697—22no—
51#14519691—44no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418D412yes—
56#14519684—21no—
57C22×Q8×C61—21no—
58C22×Q8×C61—21no—
59C22×Q8×C61—21no—
60C22×Q8×C61—21no—
61C22×Q8×C61—21no—
62C22×Q8×C61—44no—
63C22×Q8×C61D412yes—
64C22×D4×C61—21no—
65C22×D4×C61D411yescharacteristic
66C23×C4×C61—21no—
67C23×C4×C61C2311yescharacteristic
68#124×C61—44no—
69#121×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—24no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61D412yes—
77C2×C42×C61—21no—
78#95×C61—24no—
79#95×C61—21no—
80C24×C61—21no—
81C24×C61C2×D411yescharacteristic
82C23×D61—21no—
83C2×Q8×C61—24no—
84C2×Q8×C61—24no—
85C2×Q8×C61—24no—
86C2×Q8×C61—22no—
87C2×Q8×C61—22no—
88C2×Q8×C61—44no—
89C2×Q8×C61—42no—
90C2×Q8×C61—42no—
91C2×Q8×C61—42no—
92C2×Q8×C61—44no—
93C2×Q8×C61—44no—
94C2×Q8×C61—41no—
95C2×Q8×C61—41no—
96C2×D4×C61—21no—
97C2×D4×C61—21no—
98C2×D4×C61—42no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—42no—
102C2×D4×C61—42no—
103C22×C4×C61—22no—
104C22×C4×C61—21no—
105C22×C4×C61—22no—
106C22×C4×C61—42no—
107C22×C4×C61—44no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C2×C22⋊D61—41no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61—42no—
119C2×C22⋊D61—42no—
120C22×Dic61—21no—
121C22×Dic61—41no—
122C2×D244—21no—
123C2×D244—21no—
124C2×D244—42no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C22⋊C4×C61—22no—
128C22⋊C4×C61—22no—
129C22⋊C4×C61—48no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C42×C61—42no—
133C22⋊Dic61—42no—
134#11758201—48no—
135#11758199—82no—
136#11758198—41no—
137#11758198—41no—
138C4⋊Dic61—21no—
139C4⋊Dic61—21no—
140C4⋊Dic61—42no—
141C2×#92418—22no—
142C2×#92418—22no—
143C2×#92418—42no—
144C2×#92418—42no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61—41no—
150C23×C61—42no—
151C23×C61#12011yescharacteristic
152C23×C61#12111yescharacteristic
153C23×C61#12711yescharacteristic
154C23×C61#13512yes—
155C23×C61AGL(1,ℤ/8)12yes—
156C22×D61—41no—
157C22×D61—42no—
158C22×D61—81no—
159C22×D61—81no—
160Q8×C61—24no—
161Q8×C61—24no—
162Q8×C61—42no—
163Q8×C61—44no—
164Q8×C61—42no—
165Q8×C61—44no—
166D4×C61—42no—
167D4×C61—81no—
168D4×C61—82no—
169D4×C61—81no—
170D4×C61—81no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—24no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—44no—
180C2×C4×C61—44no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61#12011yescharacteristic
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C22⋊D61—82no—
192C22⋊D61—81no—
193C22⋊D61—81no—
194C2×Dic61—41no—
195C2×Dic61—42no—
196C2×Dic61—81no—
197C2×Dic61—81no—
198C2×Dic61—81no—
199D244—42no—
200D244—42no—
201#92418—42no—
202#92418—42no—
203#9948—611nomaximal, Sylow
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—42no—
211C22×C61—42no—
212C22×C61—84no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61#39211yescharacteristic
217C22×C61#44912yes—
218C22×C61#46312yes—
219C22×C61#49511yescharacteristic
220C22×C61#49611yescharacteristic
221C2×D61—81no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—162no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—44no—
229C4×C61—82no—
230C4×C61—81no—
231C4×C61B(4,𝔽2)12yes—
232Dic61—81no—
233Dic61—161no—
234#3186—611no—
235C2×#448—611no—
236#2436D6111yescharacteristic, complemented
237#1964—611no—
238#1787—611no—
239#1519—611no—
240#1282—611no—
241C2×C61—21no—
242C2×C61—22no—
243C2×C61—22no—
244C2×C61—21no—
245C2×C61—161no—
246C2×C61#200911yescharacteristic
247C2×C61#201211yescharacteristic
248C2×C61#202111yescharacteristic
249D61—161no—
250C23×Q8C2×D6111yescharacteristic
251C22×SD16—1221no—
252C2×#124—21no—
253C2×#121—611no—
254C2×#121C2×D6111yescharacteristic
255#480—1221no—
256#480—1221no—
257#466—1222no—
258#448—1222no—
259#448—1222no—
260#447—1221no—
261#447—1221no—
262C2×#103—1221no—
263C2×#103—1222no—
264C2×#99—1222no—
265C2×C22⋊C8—611no—
266C2×C22⋊C8—611no—
267#393—22no—
268#391—21no—
269#386—22no—
270#380—611no—
271C4×C22⋊C4C2×D6111yescharacteristic
272#327—1222no—
273C61#994811yescharacteristic, complemented, Sylow
274C22×Q8—21no—
275C22×Q8—21no—
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8—21no—
279C22×Q8—44no—
280C22×Q8C22⋊D6112yes—
281C22×D4—21no—
282C22×D4—611no—
283C22×D4—1221no—
284C22×D4C22⋊D6111yescharacteristic
285C23×C4—21no—
286C23×C4C22×D6111yescharacteristic
287C2×SD16—1224no—
288C2×SD16—2444no—
289C2×D8—1222no—
290C22×C8—612no—
291C22×C8—1221no—
292#124—44no—
293#121—21no—
294#121—21no—
295#121—21no—
296#121—21no—
297#121—1221no—
298#121—1221no—
299#121—1221no—
300#121—1221no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4C22⋊D6111yescharacteristic
304C2×C22⋊C4—24no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4C22⋊D6112yes—
309C2×C42—21no—
310#107—1222no—
311#103—1224no—
312#103—2444no—
313#102—1222no—
314#102—1222no—
315#99—2444no—
316C22⋊C8—612no—
317C22⋊C8—1221no—
318C22⋊C8—1221no—
319C22⋊C8—1221no—
320#95—24no—
321#95—21no—
322#95—1221no—
323C24—21no—
324C24—1221no—
325C24C2×C22⋊D6111yescharacteristic
326C2×Q8—24no—
327C2×Q8—24no—
328C2×Q8—24no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—44no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—42no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—42no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—1221no—
347C2×D4—1221no—
348C2×D4—2442no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2442no—
352C2×D4—2442no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—42no—
357C22×C4—44no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—1221no—
361C22×C4—2441no—
362C22×C4D4×D6111yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365C22×C4#1175822411yescharacteristic
366C22×C4C2×C22⋊D6111yescharacteristic
367C22×C4C2×C22⋊D6111yescharacteristic
368SD16—2448no—
369D8—4882no—
370C2×C8—1222no—
371C2×C8—1222no—
372C2×C8—2442no—
373C2×C8—2442no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4—2442no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—48no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—2442no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C42—42no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—4881no—
395C23—4881no—
396C23—2442no—
397C23—2441no—
398C23#1451974611yescharacteristic
399C23#1451974811yescharacteristic
400C23#1451977311yescharacteristic
401C23#1451979712yes—
402C23#1451980212yes—
403Q8—24no—
404Q8—24no—
405Q8—42no—
406Q8—44no—
407Q8—42no—
408Q8—44no—
409D4—42no—
410D4—81no—
411D4—82no—
412D4—81no—
413D4—81no—
414D4—4881no—
415D4—4881no—
416D4—4882no—
417D4—2442no—
418D4—2442no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—4881no—
436C2×C4—4881no—
437C2×C4—4881no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4#1451974511yescharacteristic
441C2×C4#1451974511yescharacteristic
442C2×C4#1451974911yescharacteristic
443C2×C4#1451974911yescharacteristic
444C8—2442no—
445C8—2442no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—9762no—
459C22—4881no—
460C22—4881no—
461C22—4881no—
462C22#1683967011yescharacteristic
463C22#1683990712yes—
464C22#1683997412yes—
465C22#1684014411yescharacteristic
466C22#1684015211yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—44no—
471C4—82no—
472C4—81no—
473C4—9761no—
474C4—4881no—
475C4#1683994812yes—
476C2—22no—
477C2—21no—
478C2—22no—
479C2—21no—
480C2—161no—
481C2—9761no—
482C2#2144687911yescharacteristic
483C2#2144689611yescharacteristic
484C2#2144694211yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2436C2
socleC22×C61#392
prime radical#21456567C2
hypercenter#2436D61
hypocenterC61#9948
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2436

Complements

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

NH ≅ G/Ntype
2. C2×#16839901C2semidirect
3. #21446655C2semidirect
4. #21445754C2semidirect
5. #21444387C2semidirect
6. #21443667C2semidirect
7. C61×#2436C2semidirect
236. #2436D61semidirect
273. C61#9948semidirect

Maximal subgroups

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

subgroupindex
#214565672
C2×#168399012
#214466552
#214457542
#214443872
#214436672
C61×#24362
#994861