Finite Group Databasebeta

← #29597557

Subgroups — #29597557

Order 15616.

752 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 107 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#21449434C211yesmaximal, characteristic
2C2×#16839558C212yesmaximal, complemented
3#21445747C211yesmaximal, characteristic, complemented
4#21443945C212yesmaximal, complemented
5C2×C61×#413C211yesmaximal, characteristic, complemented
6C2×#14519773C411yescharacteristic
7C2×#14519766C2211yescharacteristic
8C2×#14519751C411yescharacteristic
9C2×#14519696C2212yes—
10C2×#14519694—21no—
11#16839726—21no—
12#16839670—21no—
13#16839670—21no—
14#16839669C2211yescharacteristic
15#16839665C411yescharacteristic
16#16839641—21no—
17#16839641—21no—
18C4×C22⋊Dic61C411yescharacteristic
19#16839558—24no—
20C22×#41×C61C2211yescharacteristic
21C22×M16×C61—21no—
22C61×#413—24no—
23C2×#101×C61C2212yes—
24C2×#100×C61—21no—
25C22×D244C2×C411yescharacteristic
26C22×C22⋊D61—21no—
27C22×C22⋊D61—21no—
28C22×C22⋊D61—21no—
29C2×#11758194—22no—
30#14519773—42no—
31#14519766—22no—
32#14519766—22no—
33#14519751—41no—
34#14519751—41no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61C2×C411yescharacteristic
44#14519696—22no—
45#14519696—22no—
46#14519694—42no—
47C22⋊#92418—41no—
48C22⋊#92418—41no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C2×#41×C61—22no—
53C2×#41×C61—22no—
54C2×#41×C61—41no—
55C2×#41×C61—41no—
56C2×#41×C61—42no—
57C22×Q8×C61C2311yescharacteristic
58C22×D4×C61C2×C411yescharacteristic
59C22×D4×C61D411yescharacteristic
60C22×D4×C61D411yescharacteristic
61C23×C4×C61C2×C411yescharacteristic
62C23×C4×C61D411yescharacteristic
63C23×C4×C61D411yescharacteristic
64C2×M16×C61—24no—
65C2×M16×C61—22no—
66C2×M16×C61—42no—
67C2×M16×C61—41no—
68C22×C8×C61—41no—
69#101×C61—22no—
70#101×C61D414yescomplemented
71#100×C61—24no—
72C24×C61C22⋊C411yescharacteristic
73C24×C61C22⋊C411yescharacteristic
74C24×C61C22⋊C411yescharacteristic
75C23×D61—21no—
76#41×C61—44no—
77#41×C61—44no—
78#41×C61—44no—
79#41×C61—44no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C2×Q8×C61C2×D412yes—
83C2×Q8×C61#4112yes—
84C2×D4×C61—22no—
85C2×D4×C61—22no—
86C2×D4×C61—22no—
87C2×D4×C61—21no—
88C2×D4×C61—22no—
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C22×C4×C61—22no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61C22⋊C411yescharacteristic
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C2×C22⋊D61—42no—
112C2×C22⋊D61—42no—
113C2×C22⋊D61—42no—
114C2×C22⋊D61—42no—
115C2×C22⋊D61—42no—
116C2×C22⋊D61—81no—
117C2×C22⋊D61—81no—
118C2×C22⋊D61—81no—
119C2×C22⋊D61—81no—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—21no—
123C2×D244—22no—
124C2×D244—41no—
125C2×D244—41no—
126M16×C61—24no—
127M16×C61—44no—
128M16×C61—42no—
129C2×C8×C61—44no—
130C2×C8×C61—42no—
131C22⋊Dic61—42no—
132C22⋊Dic61—81no—
133C22⋊Dic61—81no—
134#11758198—41no—
135#11758198—41no—
136#11758198—41no—
137#11758198—42no—
138#11758198—41no—
139C4⋊Dic61—41no—
140C4×Dic61—22no—
141C4×Dic61—41no—
142#11758194—42no—
143#11758194—42no—
144C2×#92418—42no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61#9912yes—
160C23×C61C2×C22⋊C411yescharacteristic
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168Q8×C61—42no—
169Q8×C61—42no—
170D4×C61—44no—
171D4×C61—44no—
172D4×C61—42no—
173D4×C61—42no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61#9911yescharacteristic
191C2×C4×C61#9911yescharacteristic
192C2×C4×C61C4×D412yes—
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#12112yes—
195C2×C4×C61#12311yescharacteristic
196C22⋊D61—84no—
197C22⋊D61—84no—
198C22⋊D61—84no—
199C2×Dic61—22no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208D244—82no—
209C8×C61—44no—
210#92418—82no—
211#13093—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—22no—
215C22×C61—42no—
216C22×C61—42no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—41no—
222C22×C61—41no—
223C22×C61—41no—
224C22×C61—41no—
225C22×C61—81no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61—81no—
229C22×C61#38611yescharacteristic
230C22×C61C2×#9911yescharacteristic
231C22×C61C2×#9911yescharacteristic
232C2×D61—81no—
233C2×D61—81no—
234C2×D61—81no—
235C2×D61—81no—
236C2×D61—81no—
237C2×D61—81no—
238C2×D61—81no—
239C4×C61—22no—
240C4×C61—21no—
241C4×C61—22no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245Dic61—42no—
246Dic61—81no—
247Dic61—81no—
248C2×#413D6111yescharacteristic, complemented
249#2431—611no—
250C2×#355—612no—
251#1785—611no—
252#1394—612no—
253C2×C61—21no—
254C2×C61—21no—
255C2×C61—42no—
256C2×C61—81no—
257C2×C61—81no—
258C2×C61#189811yescharacteristic
259C2×C61#213211yescharacteristic
260C2×C61#213411yescharacteristic
261D61—161no—
262C22×#41C2×D6111yescharacteristic
263C22×M16—21no—
264C2×#127—611no—
265C2×#124—611no—
266C2×#121—611no—
267#413—24no—
268C2×#101—612no—
269C2×#101C2×D6112yes—
270C2×#100—21no—
271C2×#100—1221no—
272#407—1221no—
273#392—1221no—
274#392—1221no—
275#391—611no—
276#390—611no—
277#386—1221no—
278#386—1221no—
279C4×C22⋊C4—611no—
280#355—1224no—
281C61#1309311yescharacteristic, complemented, Sylow
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—41no—
285C2×#41—41no—
286C2×#41—42no—
287C22×Q8C22×D6111yescharacteristic
288C22×D4—611no—
289C22×D4—1221no—
290C22×D4—1221no—
291C22×D4—1221no—
292C22×D4C4×D6111yescharacteristic
293C22×D4D24411yescharacteristic
294C22×D4C22⋊D6111yescharacteristic
295C23×C4C4×D6111yescharacteristic
296C23×C4D24411yescharacteristic
297C23×C4C22⋊D6111yescharacteristic
298C2×M16—24no—
299C2×M16—22no—
300C2×M16—42no—
301C2×M16—41no—
302C2×M16—1222no—
303C22×C8—41no—
304#127—2442no—
305#124—1222no—
306#124—1222no—
307#121—2441no—
308#121—2441no—
309C2×C4⋊C4—611no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1221no—
316C2×C42—611no—
317C2×C42—611no—
318#101—22no—
319#101—1222no—
320#101—1222no—
321#101C22⋊D6114yescomplemented
322#100—24no—
323#100—2442no—
324C22⋊C8—2441no—
325C22⋊C8—2441no—
326#95—1221no—
327#95—1221no—
328#95—1221no—
329C24—1221no—
330C24#1175819811yescharacteristic
331C24#1175819811yescharacteristic
332C24#1175819811yescharacteristic
333#41—44no—
334#41—44no—
335#41—44no—
336#41—44no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×Q8#1175822212yes—
340C2×Q8C2×C22⋊D6112yes—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—1222no—
352C2×D4—4881no—
353C2×D4—4881no—
354C2×D4—4881no—
355C2×D4—4881no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2442no—
359C2×D4—2442no—
360C2×D4—2442no—
361C2×D4—2442no—
362C2×D4—2442no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4#1175819811yescharacteristic
380C22×C4C2×C4×D6111yescharacteristic
381C22×C4C2×D24411yescharacteristic
382C22×C4C2×C22⋊D6111yescharacteristic
383M16—24no—
384M16—44no—
385M16—42no—
386M16—2442no—
387M16—2442no—
388C2×C8—44no—
389C2×C8—42no—
390C2×C8—2442no—
391C4⋊C4—2441no—
392C22⋊C4—4881no—
393C22⋊C4—4881no—
394C22⋊C4—2442no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2442no—
399C22⋊C4—2441no—
400C42—1222no—
401C42—2441no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—2441no—
417C23—2441no—
418C23—2441no—
419C23—2441no—
420C23—2441no—
421C23—2441no—
422C23—2441no—
423C23#1451969112yes—
424C23C2×#1175819811yescharacteristic
425Q8—42no—
426Q8—42no—
427D4—44no—
428D4—44no—
429D4—42no—
430D4—42no—
431D4—4882no—
432D4—4884no—
433D4—4884no—
434D4—4884no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—1222no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4#1451969111yescharacteristic
461C2×C4#1451969111yescharacteristic
462C2×C4C4×C22⋊D6112yes—
463C2×C4#1451974611yescharacteristic
464C2×C4#1451975112yes—
465C2×C4#1451976011yescharacteristic
466C8—44no—
467C8—4882no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—42no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—4881no—
486C22—4881no—
487C22—4881no—
488C22—4881no—
489C22—4881no—
490C22—4881no—
491C22—4881no—
492C22#1683964111yescharacteristic
493C22C2×#1451969111yescharacteristic
494C22C2×#1451969111yescharacteristic
495C4—21no—
496C4—22no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—22no—
501C4—4881no—
502C4—4881no—
503C4—2442no—
504C2—21no—
505C2—21no—
506C2—42no—
507C2—81no—
508C2—81no—
509C2—9761no—
510C2#2144627211yescharacteristic
511C2#2144750211yescharacteristic
512C2#2144751011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC2×C61×#413C2
socleC22×C61C2×#99
prime radical#21449434C2
cosocleC22×Q8×C61C23
hypercenterC2×#413D61
hypocenterC61#13093
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#16839558C2semidirect
3. #21445747C2semidirect
4. #21443945C2semidirect
5. C2×C61×#413C2semidirect
70. #101×C61D4semidirect
248. C2×#413D61semidirect
281. C61#13093semidirect
321. #101C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214494342
C2×#168395582
#214457472
#214439452
C2×C61×#4132
#1309361