Finite Group Databasebeta

← #29597572

Subgroups — #29597572

Order 15616.

624 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 103 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#21455114C211yesmaximal, characteristic
2#21447513C211yesmaximal, characteristic, complemented
3#21447474C211yesmaximal, characteristic, complemented
4#21445794C211yesmaximal, characteristic
5#21443949C211yesmaximal, characteristic, complemented
6#21443941C211yesmaximal, characteristic, complemented
7C61×#2889C211yesmaximal, characteristic
8C2×#14519807C411yescharacteristic, complemented
9C22×#11758202C411yescharacteristic, complemented
10#16840333C2211yescharacteristic
11#16839924—21no—
12#16839924—21no—
13#16839918—21no—
14#16839918—21no—
15#16839779—21no—
16#16839771—21no—
17#16839771C411yescharacteristic, complemented
18#16839758C411yescharacteristic, complemented
19#16839746C2211yescharacteristic
20#16839736C2211yescharacteristic
21#16839729C2211yescharacteristic
22#16839560—22no—
23#16839553—22no—
24C2×2−1+4×C61C2211yescharacteristic
25C61×#568—21no—
26C61×#413—22no—
27C61×#413C2211yescharacteristic
28C61×#413C2211yescharacteristic
29C2×#101×C61—21no—
30C2×#101×C61—22no—
31C22×Dic122C2×C411yescharacteristic
32#14519807—42no—
33C2×#11758202—21no—
34C2×#11758202—21no—
35C2×#11758202—21no—
36C2×#11758202—42no—
37C2×#11758200—21no—
38C2×#11758194—21no—
39C2×#11758194C2×C411yescharacteristic
40C22×#92418C2×C411yescharacteristic
41#14519775—21no—
42#14519764—21no—
43#14519758—21no—
44#14519758—21no—
45#14519756—21no—
46#14519756—21no—
47#14519736—21no—
48#14519736C2×C411yescharacteristic
49#14519704—42no—
50#14519701—21no—
51#14519701—21no—
52#14519701—21no—
53#14519701—42no—
54#14519698—21no—
55#14519696—21no—
56#14519694—21no—
57#14519692—21no—
58#14519692—21no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
612−1+4×C61—42no—
622−1+4×C61—42no—
63C2×#41×C61—21no—
64C2×#41×C61—21no—
65C2×#41×C61—21no—
66C2×#41×C61C2×C411yescharacteristic
67C2×#41×C61D411yescharacteristic
68C2×#41×C61D411yescharacteristic
69C2×#41×C61C2311yescharacteristic
70C22×Q8×C61—21no—
71C22×Q8×C61C2×C411yescharacteristic
72C22×Q8×C61D411yescharacteristic
73C22×Q8×C61D411yescharacteristic
74#131×C61—42no—
75#131×C61—42no—
76C2×M16×C61—24no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79#101×C61—24no—
80#101×C61—21no—
81#101×C61D412yes—
82#100×C61—21no—
83#100×C61D412yes—
84#41×C61—22no—
85#41×C61—22no—
86#41×C61—22no—
87#41×C61—22no—
88#41×C61—41no—
89#41×C61—41no—
90#41×C61—41no—
91#41×C61—41no—
92#41×C61—44no—
93#41×C61—44no—
94#41×C61—44no—
95C2×Q8×C61—21no—
96C2×Q8×C61—21no—
97C2×Q8×C61—21no—
98C2×Q8×C61—22no—
99C2×Q8×C61—22no—
100C2×Q8×C61—41no—
101C2×Q8×C61—41no—
102C2×Q8×C61—41no—
103C2×Q8×C61—41no—
104C2×Q8×C61—44no—
105C2×Q8×C61C22⋊C411yescharacteristic
106C2×Q8×C61C22⋊C411yescharacteristic
107C2×Q8×C61C22⋊C411yescharacteristic
108C2×Q8×C61C2×D411yescharacteristic
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61C22⋊C411yescharacteristic
113C2×D4×C61C2×D411yescharacteristic
114C2×D4×C61#4111yescharacteristic
115C2×D4×C61#4111yescharacteristic
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×Dic61—21no—
126C2×Dic122—21no—
127C2×Dic122—21no—
128C2×Dic122—41no—
129C2×Dic122—41no—
130M16×C61—22no—
131M16×C61—22no—
132M16×C61—44no—
133M16×C61—41no—
134M16×C61—41no—
135C2×C8×C61—44no—
136C2×C8×C61—41no—
137C2×C8×C61—41no—
138C22⋊Dic61—21no—
139C22⋊Dic61—41no—
140C22⋊Dic61—41no—
141C22⋊Dic61—41no—
142#11758202—42no—
143#11758202—42no—
144#11758202—42no—
145#11758200—42no—
146C4⋊Dic61—21no—
147C4⋊Dic61—41no—
148#11758196—41no—
149#11758196—41no—
150C4×Dic61—21no—
151C4×Dic61—41no—
152#11758194—41no—
153#11758194—41no—
154#11758194—41no—
155C2×#92418—21no—
156C2×#92418—21no—
157C2×#92418—41no—
158C2×#92418—41no—
159C23×C61—21no—
160C23×C61C4×D411yescharacteristic
161C23×C61#12111yescharacteristic
162C23×C61#12311yescharacteristic
163Q8×C61—21no—
164Q8×C61—21no—
165Q8×C61—21no—
166Q8×C61—21no—
167Q8×C61—21no—
168Q8×C61—41no—
169Q8×C61—42no—
170Q8×C61—42no—
171Q8×C61—42no—
172Q8×C61#9912yes—
173D4×C61—24no—
174D4×C61—21no—
175D4×C61—41no—
176D4×C61—41no—
177D4×C61—41no—
178D4×C61—42no—
179D4×C61—42no—
180D4×C61#9912yes—
181C2×C4×C61—24no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61C2×C22⋊C411yescharacteristic
197C2×C4×C61C4×D411yescharacteristic
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61#12111yescharacteristic
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—81no—
203C2×Dic61—81no—
204Dic122—41no—
205Dic122—41no—
206Dic122—81no—
207C8×C61—42no—
208C8×C61—42no—
209#92418—41no—
210#92418—41no—
211#92418—81no—
212#13096—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—22no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—81no—
221C22×C61#38611yescharacteristic
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—22no—
226C4×C61—41no—
227C4×C61—41no—
228C4×C61C2×#9911yescharacteristic
229C4×C61C2×#9911yescharacteristic
230Dic61—81no—
231Dic61—81no—
232Dic61—161no—
233#3011—611no—
234#2889D6111yescharacteristic
235#2135—611no—
236#2123—611no—
237#1796—611no—
238#1395—611no—
239#1392—611no—
240C2×C61—21no—
241C2×C61—41no—
242C2×C61—41no—
243C2×C61—41no—
244C2×C61—42no—
245C2×C61#189811yescharacteristic
246C2×2−1+4C2×D6111yescharacteristic
247C2×#137—611no—
248C22×Q16—611no—
249#568—21no—
250#536—611no—
251#452—1221no—
252#452—1221no—
253#451—1221no—
254#451—1221no—
255#421—1221no—
256#419—611no—
257#419—1221no—
258#416—611no—
259#413—22no—
260#413—611no—
261#413C2×D6111yescharacteristic
262#413C2×D6111yescharacteristic
263C2×#101—21no—
264C2×#101—22no—
265#410—611no—
266#408—611no—
267#356—1222no—
268#352—1222no—
269C61#1309611yescharacteristic, complemented, Sylow
2702−1+4—42no—
2712−1+4—42no—
272C2×#41—21no—
273C2×#41—21no—
274C2×#41—21no—
275C2×#41C4×D6111yescharacteristic
276C2×#41D24411yescharacteristic
277C2×#41C22⋊D6111yescharacteristic
278C2×#41C22×D6111yescharacteristic
279C22×Q8—21no—
280C22×Q8—611no—
281C22×Q8C4×D6111yescharacteristic
282C22×Q8D24411yescharacteristic
283C22×Q8C22⋊D6111yescharacteristic
284#137—2442no—
285C2×Q16—1221no—
286C2×Q16—1221no—
287C2×Q16—1221no—
288C2×Q16—2442no—
289C2×SD16—1221no—
290#131—42no—
291#131—42no—
292C2×M16—24no—
293C2×M16—21no—
294C2×M16—21no—
295C2×M16—611no—
296C2×M16—1221no—
297C22×C8—611no—
298C4⋊Q8—1221no—
299#124—1221no—
300#123—1221no—
301#123—1221no—
302C22⋊Q8—1221no—
303C22⋊Q8—1221no—
304#117—611no—
305#117—1221no—
306#104—2442no—
307#103—1221no—
308#103—1221no—
309#103—1221no—
310#103—2442no—
311#102—1221no—
312#101—24no—
313#101—21no—
314#101—1221no—
315#101C22⋊D6112yes—
316#100—21no—
317#100—1221no—
318#100C22⋊D6112yes—
319#99—1221no—
320#99—1221no—
321C22⋊C8—1221no—
322C22⋊C8—1221no—
323#41—22no—
324#41—22no—
325#41—22no—
326#41—22no—
327#41—41no—
328#41—41no—
329#41—41no—
330#41—41no—
331#41—44no—
332#41—44no—
333#41—44no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—44no—
344C2×Q8—1221no—
345C2×Q8—1221no—
346C2×Q8—2441no—
347C2×Q8—2441no—
348C2×Q8#1175819811yescharacteristic
349C2×Q8#1175819811yescharacteristic
350C2×Q8#1175819811yescharacteristic
351C2×Q8C2×C22⋊D6111yescharacteristic
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4#1175819811yescharacteristic
356C2×D4#1175822211yescharacteristic
357C2×D4#1175822211yescharacteristic
358C2×D4C2×C22⋊D6111yescharacteristic
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—1221no—
366C22×C4C2×C4×D6111yescharacteristic
367C22×C4C2×D24411yescharacteristic
368C22×C4C2×C22⋊D6111yescharacteristic
369Q16—2442no—
370Q16—2442no—
371Q16—2442no—
372SD16—2442no—
373M16—22no—
374M16—22no—
375M16—44no—
376M16—41no—
377M16—41no—
378M16—2441no—
379M16—2441no—
380M16—2441no—
381C2×C8—44no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—1221no—
385C2×C8—1221no—
386C2×C8—2441no—
387C2×C8—2441no—
388C4⋊C4—1221no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C22⋊C4—1221no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C42—1221no—
397C42—2441no—
398C23—21no—
399C23C4×C22⋊D6111yescharacteristic
400C23#1451975111yescharacteristic
401C23#1451976011yescharacteristic
402Q8—21no—
403Q8—21no—
404Q8—21no—
405Q8—21no—
406Q8—21no—
407Q8—41no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—4881no—
412Q8—2441no—
413Q8—2441no—
414Q8#1451969112yes—
415D4—24no—
416D4—21no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—42no—
421D4—42no—
422D4#1451969112yes—
423C2×C4—24no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—4881no—
439C2×C4—4881no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4C2×#1175819811yescharacteristic
443C2×C4C4×C22⋊D6111yescharacteristic
444C2×C4#1451974611yescharacteristic
445C2×C4#1451975111yescharacteristic
446C8—42no—
447C8—42no—
448C8—4881no—
449C8—2441no—
450C8—2441no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—81no—
459C22#1683964111yescharacteristic
460C4—21no—
461C4—21no—
462C4—22no—
463C4—21no—
464C4—41no—
465C4—41no—
466C4—9761no—
467C4—4881no—
468C4—4881no—
469C4C2×#1451969111yescharacteristic
470C4C2×#1451969111yescharacteristic
471C2—21no—
472C2—41no—
473C2—41no—
474C2—41no—
475C2—42no—
476C2#2144627211yescharacteristic
subgroupG/H
centerC2#21446272
commutatorC22×C4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#2889C2
socleC2×C61#1898
prime radicalC2×2−1+4×C61C22
cosocleC2×#41×C61C23
hypercenter#2889D61
hypocenterC61#13096
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×2−1+4 ◁ #2889

Complements

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

NH ≅ G/Ntype
2. #21447513C2semidirect
3. #21447474C2semidirect
5. #21443949C2semidirect
6. #21443941C2semidirect
8. C2×#14519807C4semidirect
9. C22×#11758202C4semidirect
17. #16839771C4semidirect
18. #16839758C4semidirect
269. C61#13096semidirect

Maximal subgroups

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

subgroupindex
#214551142
#214475132
#214474742
#214457942
#214439492
#214439412
C61×#28892
#1309661