Finite Group Databasebeta

← #29597610

Subgroups — #29597610

Order 15616.

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

normal subgroups only

This group has 630 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#21454281C211yesmaximal, characteristic
3#21447473C211yesmaximal, characteristic, complemented
4#21445792C211yesmaximal, characteristic
5#21443947C211yesmaximal, characteristic, complemented
6#21443939C211yesmaximal, characteristic, complemented
7C61×#2129C211yesmaximal, characteristic, complemented
8C2×#14519824C2211yescharacteristic
9C2×#14519808C411yescharacteristic, complemented
10C22×#11758202C411yescharacteristic, complemented
11#16840239—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#16839736C2211yescharacteristic
22#16839735—21no—
23#16839734—22no—
24#16839734—22no—
25#16839729C2211yescharacteristic
26#16839552—22no—
27C61×#536C2211yescharacteristic
28C61×#410C2211yescharacteristic
29C61×#410C2211yescharacteristic
30C61×#354—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—
49C2×#11758194—21no—
50C2×#11758194C2×C411yescharacteristic
51C22×#92418C2×C411yescharacteristic
52C4×Dic122—42no—
53#14519742—42no—
54#14519736—21no—
55#14519733—24no—
56#14519705—42no—
57#14519700—21no—
58#14519700—21no—
59#14519700—21no—
60#14519700—42no—
61#14519697—21no—
62#14519696—21no—
63#14519694—21no—
64#14519692—21no—
65#14519692D412yes—
66#14519691—24no—
67C22⋊#92418—21no—
68C22⋊#92418—21no—
69C2×#41×C61C2311yescharacteristic
70C22×Q8×C61C2×C411yescharacteristic
71C4⋊Q8×C61—21no—
72#124×C61—21no—
73#123×C61—21no—
74#123×C61—21no—
75C22⋊Q8×C61—21no—
76C22⋊Q8×C61—21no—
77#117×C61—21no—
78#117×C61—21no—
79#117×C61C2×C411yescharacteristic
80#99×C61—21no—
81#99×C61—21no—
82#99×C61—21no—
83#99×C61D412yes—
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×C61#4111yescharacteristic
91C2×D4×C61C2×D411yescharacteristic
92C2×D4×C61C2×D411yescharacteristic
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—41no—
111#11758222—41no—
112#11758222—41no—
113#11758222—41no—
114C2×D244C22⋊C411yescharacteristic
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×Dic122—21no—
119C2×Dic122—22no—
120C2×Dic122—22no—
121C2×Dic122—22no—
122C2×Dic122—22no—
123C2×Dic122—21no—
124C2×Dic122—21no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127C2×Dic122C22⋊C411yescharacteristic
128C2×Dic122C22⋊C411yescharacteristic
129C2×Dic122C22⋊C411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C22⋊C4×C61—21no—
136C22⋊C4×C61—22no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C42×C61—21no—
141C42×C61—41no—
142C42×C61—41no—
143C22⋊Dic61—22no—
144#11758202—42no—
145#11758202—42no—
146#11758202—42no—
147#11758201—42no—
148C4⋊Dic61—41no—
149#11758196—44no—
150C4×Dic61—44no—
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×C61C4×D411yescharacteristic
160C23×C61#12011yescharacteristic
161C23×C61#12111yescharacteristic
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—42no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—81no—
180C2×C4×C61—81no—
181C2×C4×C61C2×C22⋊C411yescharacteristic
182C2×C4×C61C4×D411yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12311yescharacteristic
185C22⋊D61—42no—
186C22⋊D61—42no—
187C22⋊D61—42no—
188C2×Dic61—24no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195D244—21no—
196D244—21no—
197C4×D61—42no—
198C4×D61—42no—
199C4×D61—42no—
200Dic122—24no—
201Dic122—21no—
202Dic122—21no—
203Dic122—21no—
204Dic122—21no—
205Dic122—42no—
206Dic122—42no—
207Dic122#9912yes—
208Dic122#9912yes—
209#92418—41no—
210#92418—41no—
211#92418—81no—
212#13101—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—41no—
221C2×D61—81no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—81no—
226C4×C61—82no—
227C4×C61—81no—
228C4×C61—161no—
229C4×C61C2×#9911yescharacteristic
230C4×C61C2×#9911yescharacteristic
231Dic61—22no—
232Dic61—22no—
233Dic61—41no—
234Dic61—82no—
235#3011—611no—
236#2884—611no—
237#2129D6111yescharacteristic, complemented
238#2123—611no—
239#1796—611no—
240#1395—611no—
241#1391—611no—
242C2×C61—21no—
243C2×C61—41no—
244C2×C61—41no—
245C2×C61—41no—
246C2×C61#189811yescharacteristic
247D61—81no—
248C2×2−1+4—611no—
249C2×#137—611no—
250C22×Q16—611no—
251#536C2×D6111yescharacteristic
252#519—1221no—
253#452—1221no—
254#452—1221no—
255#451—1221no—
256#451—1221no—
257#421—1221no—
258#419—611no—
259#419—1221no—
260#416—611no—
261#413—611no—
262#410—611no—
263#410—1222no—
264#410—1221no—
265#410—1222no—
266#410C2×D6111yescharacteristic
267#410C2×D6111yescharacteristic
268#408—611no—
269#354—22no—
270#352—1222no—
271C61#1310111yescharacteristic, complemented, Sylow
2722−1+4—2442no—
2732−1+4—2442no—
274C2×#41—611no—
275C2×#41—611no—
276C2×#41—611no—
277C2×#41—1221no—
278C2×#41—1221no—
279C2×#41—1221no—
280C2×#41C22×D6111yescharacteristic
281C22×Q8—611no—
282C22×Q8—611no—
283C22×Q8—611no—
284C22×Q8—1221no—
285C22×Q8C4×D6111yescharacteristic
286#137—2442no—
287C2×Q16—1221no—
288C2×Q16—1221no—
289C2×Q16—1221no—
290C2×Q16—2442no—
291C2×SD16—1221no—
292C2×M16—611no—
293C2×M16—1221no—
294C22×C8—611no—
295C4⋊Q8—21no—
296#124—21no—
297#123—21no—
298#123—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C4×Q8—2442no—
302C4×Q8—2442no—
303#117—21no—
304#117—21no—
305#117—1224no—
306#117—1221no—
307#117C4×D6111yescharacteristic
308#104—2442no—
309#103—1221no—
310#103—1221no—
311#103—1221no—
312#103—2442no—
313#102—1221no—
314#101—1221no—
315#100—1221no—
316#99—21no—
317#99—21no—
318#99—21no—
319#99—612no—
320#99—1224no—
321#99—1221no—
322#99C22⋊D6112yes—
323C22⋊C8—1221no—
324C22⋊C8—1221no—
325#41—41no—
326#41—41no—
327#41—1222no—
328#41—1222no—
329#41—2441no—
330#41—2441no—
331#41—2441no—
332#41—2441no—
333#41—2444no—
334#41—2444no—
335#41—2444no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8—611no—
341C2×Q8—611no—
342C2×Q8—611no—
343C2×Q8—1222no—
344C2×Q8—1222no—
345C2×Q8—1222no—
346C2×Q8—1222no—
347C2×Q8—1221no—
348C2×Q8—1221no—
349C2×Q8—1221no—
350C2×Q8—2441no—
351C2×Q8—2441no—
352C2×Q8—2444no—
353C2×Q8#1175822211yescharacteristic
354C2×D4—611no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4—1221no—
358C2×D4D4×D6111yescharacteristic
359C2×D4#1175822411yescharacteristic
360C2×D4C2×C22⋊D6111yescharacteristic
361C22×C4—21no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—1221no—
368C22×C4C2×C4×D6111yescharacteristic
369C22×C4D4×D6111yescharacteristic
370C22×C4D4×D6111yescharacteristic
371Q16—2442no—
372Q16—2442no—
373Q16—2442no—
374SD16—2442no—
375M16—2441no—
376M16—2441no—
377M16—2441no—
378C2×C8—1221no—
379C2×C8—1221no—
380C2×C8—2441no—
381C2×C8—2441no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—2441no—
388C4⋊C4—2444no—
389C22⋊C4—21no—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—1222no—
395C42—21no—
396C42—41no—
397C42—41no—
398C42—2441no—
399C42—2444no—
400C23—1221no—
401C23#1451973711yescharacteristic
402C23#1451974511yescharacteristic
403C23#1451974811yescharacteristic
404Q8—41no—
405Q8—41no—
406Q8—41no—
407Q8—81no—
408Q8—612no—
409Q8—612no—
410Q8—1224no—
411Q8—1221no—
412Q8—1221no—
413Q8—1221no—
414Q8—1221no—
415Q8—2442no—
416Q8—2442no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—1221no—
421D4—1221no—
422D4—2442no—
423D4—2442no—
424D4—2442no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—1224no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4C22⋊C4×D6111yescharacteristic
447C2×C4C4×C22⋊D6111yescharacteristic
448C2×C4#1451975011yescharacteristic
449C2×C4#1451975911yescharacteristic
450C8—4881no—
451C8—2441no—
452C8—2441no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—4881no—
460C22—2441no—
461C22#1683963811yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—81no—
466C4—82no—
467C4—81no—
468C4—161no—
469C4—1222no—
470C4—1222no—
471C4—4882no—
472C4—2441no—
473C4#99×D6111yescharacteristic
474C4#99×D6111yescharacteristic
475C2—21no—
476C2—41no—
477C2—41no—
478C2—41no—
479C2—4881no—
480C2#2144626911yescharacteristic
subgroupG/H
centerC2#21446269
commutatorC22×C4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#2129C2
socleC2×C61#1898
prime radicalC2×#14519824C22
cosocleC2×#41×C61C23
hypercenter#2129D61
hypocenterC61#13101
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2129

Complements

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

NH ≅ G/Ntype
3. #21447473C2semidirect
5. #21443947C2semidirect
6. #21443939C2semidirect
7. C61×#2129C2semidirect
9. C2×#14519808C4semidirect
10. C22×#11758202C4semidirect
18. #16839770C4semidirect
19. #16839756C4semidirect
237. #2129D61semidirect
271. C61#13101semidirect

Maximal subgroups

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

subgroupindex
#214551122
#214542812
#214474732
#214457922
#214439472
#214439392
C61×#21292
#1310161