Finite Group Databasebeta

← #29597569

Subgroups — #29597569

Order 15616.

624 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 89 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#21455112C211yesmaximal, characteristic
2#21454300C211yesmaximal, characteristic
3#21447514C211yesmaximal, characteristic, complemented
4#21445792C211yesmaximal, characteristic
5#21443947C211yesmaximal, characteristic, complemented
6#21443941C211yesmaximal, characteristic, complemented
7C61×#2123C211yesmaximal, characteristic, complemented
8C2×#14519824C2211yescharacteristic
9C2×#14519808C411yescharacteristic, complemented
10C22×#11758202C411yescharacteristic, complemented
11#16840528—21no—
12#16839922—21no—
13#16839922—21no—
14#16839917—21no—
15#16839917—21no—
16#16839780—21no—
17#16839770—21no—
18#16839770C411yescharacteristic, complemented
19#16839756C411yescharacteristic, complemented
20#16839746C2211yescharacteristic
21#16839746C2211yescharacteristic
22#16839743—22no—
23C2×#14519695—21no—
24#101×D61—22no—
25#16839729C2211yescharacteristic
26#16839561—22no—
27C61×#536C2211yescharacteristic
28C61×#413C2211yescharacteristic
29C61×#410C2211yescharacteristic
30C61×#352—22no—
31#14519824—42no—
32#14519824—42no—
33C2×#11758222C2×C411yescharacteristic
34C2×#11758222D411yescharacteristic
35C2×#11758222D411yescharacteristic
36C2×#11758224—21no—
37C2×#11758224—21no—
38C2×#11758224—21no—
39C22×Dic122C2×C411yescharacteristic
40C22×Dic122D411yescharacteristic
41C22×Dic122D411yescharacteristic
42C2×Q8×D61—21no—
43#14519808—42no—
44C2×#11758202—21no—
45C2×#11758202—21no—
46C2×#11758202—21no—
47C2×#11758202—42no—
48C2×#11758201—21no—
49#14519785—42no—
50#14519783—42no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194C2×C411yescharacteristic
54M16×D61—24no—
55C22×#92418C2×C411yescharacteristic
56#14519705—42no—
57#14519700—21no—
58#14519700—21no—
59#14519700—21no—
60#14519700—42no—
61#14519697—21no—
62#14519696—21no—
63#14519696D412yes—
64#14519695—24no—
65#14519694—21no—
66#14519694—21no—
67C22⋊#92418—21no—
68C22⋊#92418—21no—
69C2×#41×C61C2311yescharacteristic
70C22×Q8×C61C2×C411yescharacteristic
71C2×M16×C61—21no—
72C4⋊Q8×C61—21no—
73#124×C61—21no—
74#123×C61—21no—
75#123×C61—21no—
76C22⋊Q8×C61—21no—
77C22⋊Q8×C61—21no—
78#117×C61—21no—
79#117×C61C2×C411yescharacteristic
80#101×C61—21no—
81#100×C61D412yes—
82#99×C61—21no—
83#99×C61—21no—
84#41×C61—41no—
85#41×C61—41no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61—41no—
89C2×Q8×C61—41no—
90C2×Q8×C61C2×D411yescharacteristic
91C2×D4×C61C2×D411yescharacteristic
92C2×D4×C61#4111yescharacteristic
93C2×D4×C61#4111yescharacteristic
94C22×C4×C61—21no—
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C2×C22⋊D61—21no—
99C2×C22⋊D61—21no—
100C2×C22⋊D61—21no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104Q8×D61—44no—
105#11758224—44no—
106#11758224—44no—
107#11758224—44no—
108#11758222—22no—
109#11758222—22no—
110#11758222—22no—
111#11758222—22no—
112#11758222—41no—
113#11758222—41no—
114C2×D244C22⋊C411yescharacteristic
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×Dic122—22no—
119C2×Dic122—22no—
120C2×Dic122—21no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—41no—
124C2×Dic122—41no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127C2×Dic122C22⋊C411yescharacteristic
128C2×Dic122C22⋊C411yescharacteristic
129C2×Dic122C22⋊C411yescharacteristic
130M16×C61—22no—
131M16×C61—41no—
132C2×C8×C61—41no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C22⋊C4×C61—21no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊C4×C61—41no—
141C42×C61—21no—
142C42×C61—41no—
143#11758202—42no—
144#11758202—42no—
145#11758202—42no—
146#11758201—42no—
147#11758194—22no—
148#11758194—41no—
149#11758194—41no—
150#11758194—41no—
151#11758194—41no—
152C2×#92418—21no—
153C2×#92418—21no—
154C2×#92418—41no—
155C2×#92418—41no—
156C2×#92418—41no—
157#11758189—44no—
158C8×D61—44no—
159C23×C61C4×D411yescharacteristic
160C23×C61#12111yescharacteristic
161C23×C61#12311yescharacteristic
162C22×D61—21no—
163Q8×C61—41no—
164Q8×C61—41no—
165Q8×C61—41no—
166Q8×C61—81no—
167D4×C61—41no—
168D4×C61—41no—
169D4×C61—41no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—81no—
179C2×C4×C61—81no—
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61C4×D411yescharacteristic
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C22⋊D61—24no—
185C22⋊D61—42no—
186C22⋊D61—42no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193D244—21no—
194D244#9912yes—
195C4×D61—24no—
196C4×D61—42no—
197C4×D61—42no—
198Dic122—21no—
199Dic122—21no—
200Dic122—21no—
201Dic122—21no—
202Dic122—21no—
203Dic122—42no—
204Dic122—42no—
205Dic122—42no—
206Dic122#9912yes—
207C8×C61—42no—
208#92418—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—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61#38611yescharacteristic
220C2×D61—22no—
221C2×D61—81no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61—161no—
228C4×C61C2×#9911yescharacteristic
229C4×C61C2×#9911yescharacteristic
230Dic61—22no—
231Dic61—41no—
232Dic61—41no—
233#3011—611no—
234#2889—611no—
235#2135—611no—
236#2123D6111yescharacteristic, complemented
237#1796—611no—
238#1395—611no—
239#1392—611no—
240C2×C61—21no—
241C2×C61—41no—
242C2×C61—41no—
243C2×C61—41no—
244C2×C61#189811yescharacteristic
245D61—42no—
246C2×2−1+4—611no—
247C2×#137—611no—
248C22×Q16—611no—
249#568—1221no—
250#536C2×D6111yescharacteristic
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—611no—
260#413—611no—
261#413—1222no—
262#413C2×D6111yescharacteristic
263C2×#101—1222no—
264C2×#101—1221no—
265#410C2×D6111yescharacteristic
266#408—611no—
267#356—1222no—
268#352—22no—
269C61#1309611yescharacteristic, complemented, Sylow
2702−1+4—2442no—
2712−1+4—2442no—
272C2×#41—611no—
273C2×#41—611no—
274C2×#41—611no—
275C2×#41—1221no—
276C2×#41—1221no—
277C2×#41—1221no—
278C2×#41C22×D6111yescharacteristic
279C22×Q8—611no—
280C22×Q8—611no—
281C22×Q8—611no—
282C22×Q8—1221no—
283C22×Q8C4×D6111yescharacteristic
284#137—2442no—
285C2×Q16—1221no—
286C2×Q16—1221no—
287C2×Q16—1221no—
288C2×Q16—2442no—
289C2×SD16—1221no—
290#131—2442no—
291#131—2442no—
292C2×M16—21no—
293C2×M16—611no—
294C2×M16—1224no—
295C2×M16—1221no—
296C2×M16—1221no—
297C22×C8—611no—
298C4⋊Q8—21no—
299#124—21no—
300#123—21no—
301#123—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304#117—21no—
305#117C4×D6111yescharacteristic
306#104—2442no—
307#103—1221no—
308#103—1221no—
309#103—1221no—
310#103—2442no—
311#102—1221no—
312#101—21no—
313#101—612no—
314#101—1224no—
315#101—1221no—
316#100—1221no—
317#100—1221no—
318#100C22⋊D6112yes—
319#99—21no—
320#99—21no—
321C22⋊C8—1221no—
322C22⋊C8—1221no—
323#41—41no—
324#41—41no—
325#41—1222no—
326#41—1222no—
327#41—1222no—
328#41—1222no—
329#41—2441no—
330#41—2441no—
331#41—2444no—
332#41—2444no—
333#41—2444no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×Q8—611no—
339C2×Q8—611no—
340C2×Q8—611no—
341C2×Q8—1222no—
342C2×Q8—1222no—
343C2×Q8—1221no—
344C2×Q8—1221no—
345C2×Q8—1221no—
346C2×Q8—2441no—
347C2×Q8—2441no—
348C2×Q8—2441no—
349C2×Q8—2441no—
350C2×Q8—2444no—
351C2×Q8D4×D6111yescharacteristic
352C2×D4—611no—
353C2×D4—1221no—
354C2×D4—1221no—
355C2×D4—1221no—
356C2×D4#1175822211yescharacteristic
357C2×D4#1175822411yescharacteristic
358C2×D4C2×C22⋊D6111yescharacteristic
359C22×C4—21no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4C2×C4×D6111yescharacteristic
367C22×C4D4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369Q16—2442no—
370Q16—2442no—
371Q16—2442no—
372SD16—2442no—
373M16—22no—
374M16—41no—
375M16—1222no—
376M16—2444no—
377M16—2441no—
378M16—2441no—
379M16—2441no—
380M16—2441no—
381C2×C8—41no—
382C2×C8—1221no—
383C2×C8—1221no—
384C2×C8—2444no—
385C2×C8—2441no—
386C2×C8—2441no—
387C2×C8—2441no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C22⋊C4—21no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C42—21no—
397C42—41no—
398C23—1221no—
399C23C4×C22⋊D6111yescharacteristic
400C23#1451974811yescharacteristic
401C23#1451975911yescharacteristic
402Q8—41no—
403Q8—41no—
404Q8—41no—
405Q8—81no—
406Q8—612no—
407Q8—1221no—
408Q8—1221no—
409Q8—1221no—
410Q8—1221no—
411Q8—1221no—
412Q8—2442no—
413Q8—2442no—
414Q8—2442no—
415D4—41no—
416D4—41no—
417D4—41no—
418D4—612no—
419D4—1224no—
420D4—1221no—
421D4—2442no—
422D4—2442no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—1224no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4C22⋊C4×D6111yescharacteristic
443C2×C4#1451973711yescharacteristic
444C2×C4#1451974511yescharacteristic
445C2×C4#1451975011yescharacteristic
446C8—42no—
447C8—4881no—
448C8—2442no—
449C8—2441no—
450C8—2441no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—1222no—
458C22—4881no—
459C22#1683963811yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—81no—
464C4—81no—
465C4—161no—
466C4—1222no—
467C4—2441no—
468C4—2441no—
469C4#99×D6111yescharacteristic
470C4#99×D6111yescharacteristic
471C2—21no—
472C2—41no—
473C2—41no—
474C2—41no—
475C2—2442no—
476C2#2144626911yescharacteristic
subgroupG/H
centerC2#21446269
commutatorC22×C4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#2123C2
socleC2×C61#1898
prime radicalC2×#14519824C22
cosocleC2×#41×C61C23
hypercenter#2123D61
hypocenterC61#13096
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2123

Complements

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

NH ≅ G/Ntype
3. #21447514C2semidirect
5. #21443947C2semidirect
6. #21443941C2semidirect
7. C61×#2123C2semidirect
9. C2×#14519808C4semidirect
10. C22×#11758202C4semidirect
18. #16839770C4semidirect
19. #16839756C4semidirect
236. #2123D61semidirect
269. C61#13096semidirect

Maximal subgroups

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

subgroupindex
#214551122
#214543002
#214475142
#214457922
#214439472
#214439412
C61×#21232
#1309661