Finite Group Databasebeta

← #29597308

Subgroups — #29597308

Order 15616.

644 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 95 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#21455210C211yesmaximal, characteristic
2#21447460C211yesmaximal, characteristic, complemented
3#21445782C211yesmaximal, characteristic, complemented
4#21445769C211yesmaximal, characteristic, complemented
5#21443948C211yesmaximal, characteristic, complemented
6#21443940C211yesmaximal, characteristic, complemented
7C61×#2978C211yesmaximal, characteristic, complemented
8#16840598C2211yescharacteristic
9#16840273—21no—
10#16839951—21no—
11#16839951C412yescomplemented
12#16839948—21no—
13#16839948C412yescomplemented
14#16839778—21no—
15#16839759—21no—
16#16839746C2211yescharacteristic
17#16839744—21no—
18#16839736C2211yescharacteristic
19#16839736C2211yescharacteristic
20#16839735—21no—
21#16839728—21no—
22#16839552—21no—
23#16839549—21no—
24C61×#525C2211yescharacteristic
25C61×#436—21no—
26C61×#436—21no—
27C61×#435—21no—
28C61×#435—21no—
29C61×#433—21no—
30C61×#408C2211yescharacteristic
31C61×#408C2211yescharacteristic
32C61×#407—21no—
33#14519825—21no—
34#14519824—41no—
35#14519823—41no—
36#14519822—21no—
37#14519822—21no—
38#14519822C2×C412yes—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42#41×D61—42no—
43C2×#11758194—21no—
44#14519760—22no—
45#14519756—41no—
46#14519751—41no—
47#14519746—22no—
48C4×C22⋊D61—42no—
49#14519736—21no—
50#14519736—21no—
51#14519703—42no—
52#14519702—41no—
53#14519699—41no—
54#14519696—21no—
55#14519695—41no—
56#14519694—21no—
57#14519693—41no—
58#14519692—21no—
59#14519692—21no—
60#14519692—21no—
61#14519692C2×C412yes—
62#14519691—22no—
63#14519691—22no—
64#14519689—42no—
65C2×#41×C61C2311yescharacteristic
66C23×C4×C61D411yescharacteristic
67C2×M16×C61—21no—
68C2×M16×C61—21no—
69C2×M16×C61D411yescharacteristic, complemented
70C2×M16×C61D411yescharacteristic, complemented
71C22×C8×C61D411yescharacteristic, complemented
72C22×C8×C61D411yescharacteristic, complemented
73#123×C61C2×C411yescharacteristic
74#123×C61D411yescharacteristic
75C22⋊Q8×C61—21no—
76#121×C61—21no—
77#120×C61C2×C411yescharacteristic
78#120×C61D411yescharacteristic
79C4×D4×C61—21no—
80C4×D4×C61—21no—
81#117×C61D411yescharacteristic
82C4⋊C8×C61—21no—
83C4⋊C8×C61—21no—
84C22⋊C8×C61—21no—
85C22⋊C8×C61—21no—
86C22⋊C8×C61—21no—
87C22⋊C8×C61—21no—
88C22⋊C8×C61—21no—
89C22⋊C8×C61—21no—
90#97×C61—21no—
91C4×C8×C61—21no—
92C24×C61C22⋊C411yescharacteristic
93#41×C61—41no—
94#41×C61—41no—
95C2×Q8×C61#4111yescharacteristic
96C2×D4×C61—21no—
97C2×D4×C61—21no—
98C2×D4×C61C22×C411yescharacteristic
99C2×D4×C61C2×D411yescharacteristic
100C2×D4×C61#4111yescharacteristic
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61C22⋊C411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C2×C22⋊D61—22no—
110C2×C22⋊D61—22no—
111C2×C22⋊D61—41no—
112C2×C22⋊D61—42no—
113#11758226—42no—
114Q8×D61—42no—
115#11758224—42no—
116#11758224—42no—
117#11758224—42no—
118D4×D61—42no—
119D4×D61—42no—
120D4×D61—42no—
121#11758222—22no—
122#11758222—22no—
123#11758222—41no—
124#11758222—41no—
125#11758222—41no—
126#11758222—41no—
127#11758222—41no—
128#11758222—41no—
129#11758222—41no—
130#11758222—41no—
131C2×D244—21no—
132C2×D244—21no—
133C2×D244—21no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—41no—
137C2×Dic122—21no—
138C2×Dic122—21no—
139C2×Dic122—21no—
140M16×C61—41no—
141M16×C61—41no—
142M16×C61—81no—
143M16×C61—81no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—41no—
149C2×C8×C61—41no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C22⋊C4×C61—21no—
154C22⋊C4×C61—21no—
155C22⋊C4×C61—21no—
156C22⋊C4×C61—21no—
157C22⋊C4×C61C22⋊C411yescharacteristic
158C22⋊C4×C61C22⋊C411yescharacteristic
159C42×C61—21no—
160C22⋊Dic61—22no—
161C22⋊Dic61—42no—
162C22⋊Dic61—41no—
163#11758198—42no—
164C4⋊Dic61—41no—
165C4⋊Dic61—41no—
166#11758196—42no—
167C4×Dic61—41no—
168C4×Dic61—41no—
169#11758194—41no—
170#11758194—41no—
171C2×#92418—41no—
172C23×C61—21no—
173C23×C61—41no—
174C23×C61—81no—
175C23×C61C2×C22⋊C411yescharacteristic
176C23×C61C4×D411yescharacteristic
177C23×C61#12111yescharacteristic
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—41no—
181Q8×C61—41no—
182D4×C61—41no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—81no—
186D4×C61—81no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—81no—
200C2×C4×C61C4×D411yescharacteristic
201C2×C4×C61#12011yescharacteristic
202C2×C4×C61#12111yescharacteristic
203C2×C4×C61#12311yescharacteristic
204C22⋊D61—42no—
205C22⋊D61—42no—
206C22⋊D61—42no—
207C22⋊D61—42no—
208C22⋊D61—84no—
209C2×Dic61—22no—
210C2×Dic61—22no—
211C2×Dic61—41no—
212C2×Dic61—42no—
213C2×Dic61—81no—
214D244—22no—
215D244—41no—
216D244—41no—
217D244—41no—
218C4×D61—42no—
219C4×D61—42no—
220C4×D61—42no—
221C4×D61—42no—
222Dic122—22no—
223Dic122—41no—
224Dic122—41no—
225Dic122—41no—
226C8×C61—41no—
227C8×C61—41no—
228C8×C61—41no—
229C8×C61—41no—
230#92418—81no—
231#13046—611nomaximal, Sylow
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61—42no—
241C22×C61—41no—
242C22×C61—81no—
243C22×C61#38611yescharacteristic
244C2×D61—42no—
245C2×D61—82no—
246C2×D61—82no—
247C2×D61—161no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—41no—
252C4×C61—41no—
253C4×C61—41no—
254C4×C61B(4,𝔽2)11yescharacteristic
255C4×C61B(4,𝔽2)11yescharacteristic
256Dic61—42no—
257Dic61—82no—
258Dic61—161no—
259#3025—611no—
260#2978D6111yescharacteristic, complemented
261#2120—611no—
262#1794—611no—
263#1791—611no—
264#1395—611no—
265#1391—611no—
266C2×C61—21no—
267C2×C61—41no—
268C2×C61—41no—
269C2×C61—41no—
270C2×C61—81no—
271C2×C61#188911yescharacteristic
272D61—82no—
273#585—611no—
274#525—1221no—
275#525C2×D6111yescharacteristic
276#458—612no—
277#458—1221no—
278B(4,𝔽2)—612no—
279B(4,𝔽2)—1221no—
280#436—21no—
281#436—21no—
282#435—21no—
283#435—21no—
284#433—21no—
285#421—1221no—
286#416—1221no—
287#413—611no—
288#413—1221no—
289#410—611no—
290#410—611no—
291#410—1221no—
292#408—1221no—
293#408C2×D6111yescharacteristic
294#408C2×D6111yescharacteristic
295#407—21no—
296#352—1221no—
297AΣL(1,𝔽16)—1221no—
298C61#1304611yescharacteristic, complemented, Sylow
2992−1+4—1221no—
3002−1+4—2441no—
301H(5,𝔽2)—612no—
302H(5,𝔽2)—1221no—
303H(5,𝔽2)—1221no—
304H(5,𝔽2)—2441no—
305C2×#41—1221no—
306C2×#41—1221no—
307C2×#41—1221no—
308C2×#41—2442no—
309C2×#41C22×D6111yescharacteristic
310C23×C4C22⋊D6111yescharacteristic
311C2×M16—21no—
312C2×M16—21no—
313C2×M16—1221no—
314C2×M16C22⋊D6111yescharacteristic, complemented
315C2×M16C22⋊D6111yescharacteristic, complemented
316C22×C8C22⋊D6111yescharacteristic, complemented
317C22×C8C22⋊D6111yescharacteristic, complemented
318#123—1222no—
319#123C4×D6111yescharacteristic
320#123D24411yescharacteristic
321C22⋊Q8—21no—
322C22⋊Q8—2441no—
323#121—21no—
324#121—2441no—
325#120—1222no—
326#120C4×D6111yescharacteristic
327#120D24411yescharacteristic
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—2442no—
331#117—1221no—
332#117—1221no—
333#117C22⋊D6111yescharacteristic
334C4⋊C8—21no—
335C4⋊C8—21no—
336#104—2442no—
337#103—2441no—
338#102—2441no—
339#101—1221no—
340#101—2441no—
341#100—1221no—
342#100—2441no—
343#99—612no—
344#99—1221no—
345#99—1222no—
346#99—1222no—
347#99—1221no—
348#99—1221no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—2442no—
356#97—21no—
357C4×C8—21no—
358C24#1175819811yescharacteristic
359#41—41no—
360#41—41no—
361#41—1222no—
362#41—1222no—
363#41—2441no—
364#41—2441no—
365#41—2441no—
366#41—2441no—
367#41—2441no—
368#41—2442no—
369#41—2442no—
370#41—2442no—
371#41—2442no—
372#41—2441no—
373#41—2441no—
374#41—2441no—
375C2×Q8—1221no—
376C2×Q8—1221no—
377C2×Q8—1221no—
378C2×Q8—2442no—
379C2×Q8#1175822211yescharacteristic
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—1221no—
383C2×D4—1221no—
384C2×D4—1221no—
385C2×D4—1222no—
386C2×D4—1222no—
387C2×D4—2442no—
388C2×D4—2442no—
389C2×D4—2442no—
390C2×D4—2442no—
391C2×D4—2441no—
392C2×D4C2×C4×D6111yescharacteristic
393C2×D4C2×D24411yescharacteristic
394C2×D4#1175822211yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—1222no—
400C22×C4—1222no—
401C22×C4—2441no—
402C22×C4#1175819811yescharacteristic
403C22×C4C2×C22⋊D6111yescharacteristic
404C22×C4C2×C22⋊D6111yescharacteristic
405C22×C4C2×C22⋊D6111yescharacteristic
406M16—41no—
407M16—41no—
408M16—81no—
409M16—81no—
410M16—2441no—
411M16—2441no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—2441no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—2441no—
423C4⋊C4—2441no—
424C4⋊C4—2442no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—1222no—
430C22⋊C4—2442no—
431C22⋊C4—2442no—
432C22⋊C4—2441no—
433C22⋊C4#1175819811yescharacteristic
434C22⋊C4#1175819811yescharacteristic
435C42—21no—
436C42—2441no—
437C42—2441no—
438C23—21no—
439C23—41no—
440C23—81no—
441C23—1222no—
442C23—1222no—
443C23—2441no—
444C23C2×#1175819811yescharacteristic
445C23C4×C22⋊D6111yescharacteristic
446C23#1451975111yescharacteristic
447Q8—41no—
448Q8—1222no—
449Q8—2441no—
450Q8—2441no—
451Q8—2441no—
452D4—41no—
453D4—41no—
454D4—41no—
455D4—81no—
456D4—81no—
457D4—1222no—
458D4—4884no—
459D4—2441no—
460D4—2441no—
461D4—2442no—
462D4—2442no—
463D4—2442no—
464D4—2442no—
465D4—2441no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—81no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—4881no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2441no—
487C2×C4—2442no—
488C2×C4C4×C22⋊D6111yescharacteristic
489C2×C4#1451974611yescharacteristic
490C2×C4#1451975111yescharacteristic
491C2×C4#1451976011yescharacteristic
492C8—41no—
493C8—41no—
494C8—41no—
495C8—41no—
496C8—4881no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—41no—
507C22—81no—
508C22—9761no—
509C22—4882no—
510C22—4882no—
511C22—2442no—
512C22#1683964111yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—41no—
517C4—41no—
518C4—41no—
519C4—9761no—
520C4—4882no—
521C4—2442no—
522C4#1683994911yescharacteristic
523C4#1683994911yescharacteristic
524C2—21no—
525C2—41no—
526C2—41no—
527C2—41no—
528C2—81no—
529C2—4882no—
530C2#2144622711yescharacteristic
subgroupG/H
centerC4#16839949
commutatorC2×D4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#2978C2
socleC2×C61#1889
prime radical#21455210C2
cosocleC2×#41×C61C23
hypercenter#2978D61
hypocenterC61#13046
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2978

Complements

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

NH ≅ G/Ntype
2. #21447460C2semidirect
3. #21445782C2semidirect
4. #21445769C2semidirect
5. #21443948C2semidirect
6. #21443940C2semidirect
7. C61×#2978C2semidirect
11. #16839951C4semidirect
13. #16839948C4semidirect
69. C2×M16×C61D4semidirect
70. C2×M16×C61D4semidirect
71. C22×C8×C61D4semidirect
72. C22×C8×C61D4semidirect
260. #2978D61semidirect
298. C61#13046semidirect
314. C2×M16C22⋊D61semidirect
315. C2×M16C22⋊D61semidirect
316. C22×C8C22⋊D61semidirect
317. C22×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214552102
#214474602
#214457822
#214457692
#214439482
#214439402
C61×#29782
#1304661