Finite Group Databasebeta

← #29594965

Subgroups — #29594965

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839736C211yesmaximal, characteristic
2#21448411C211yesmaximal, characteristic
3#21443938C214yesmaximal, complemented
4C2×C61×#413C211yesmaximal, characteristic
5C2×#14519736—21no—
6C2×#14519736C411yescharacteristic, complemented
7C22×C4⋊Dic61C411yescharacteristic, complemented
8#16839736—22no—
9#16839736C414yescomplemented
10C2×#14519692—21no—
11C2×#14519692C2212yes—
12#16839669—21no—
13#16839665—21no—
14#16839642C412yescomplemented
15#16839642C2212yes—
16#16839622—21no—
17#16839622—21no—
18C22×#41×C61C2211yescharacteristic
19C22×M16×C61—21no—
20C61×#413—22no—
21C61×#413C414yescomplemented
22C2×#101×C61—21no—
23C2×#100×C61C2212yes—
24C23×Dic61C2×C412yes—
25#14519736—24no—
26#14519736—42no—
27#14519736—42no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—41no—
32C2×C4⋊Dic61—41no—
33C2×C4⋊Dic61—41no—
34C2×C22⋊Dic61—22no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61C2×C412yes—
38C2×C4×Dic61—21no—
39C2×C4×Dic61—41no—
40#14519692—24no—
41#14519692—22no—
42#14519692C2×C414yes—
43#14519684—22no—
44#14519684—22no—
45C2×#41×C61—41no—
46C2×#41×C61—41no—
47C2×#41×C61—42no—
48C2×#41×C61C2×C412yes—
49C2×#41×C61C2×C412yes—
50C2×#41×C61D412yes—
51C2×#41×C61Q812yes—
52C22×Q8×C61D411yescharacteristic
53C22×D4×C61C2×C411yescharacteristic
54C22×D4×C61D411yescharacteristic
55C22×D4×C61C2311yescharacteristic
56C23×C4×C61C2×C411yescharacteristic
57C23×C4×C61D411yescharacteristic
58C23×C4×C61D411yescharacteristic
59C2×M16×C61—24no—
60C2×M16×C61—22no—
61C2×M16×C61—41no—
62C2×M16×C61—42no—
63C22×C8×C61—41no—
64#101×C61—24no—
65#100×C61—22no—
66#100×C61C2×C414yes—
67C24×C61C22⋊C411yescharacteristic
68C24×C61C22×C411yescharacteristic
69C24×C61C2×D411yescharacteristic
70#41×C61—42no—
71#41×C61—42no—
72#41×C61—42no—
73#41×C61—42no—
74#41×C61—42no—
75#41×C61—42no—
76#41×C61—42no—
77#41×C61—42no—
78C2×Q8×C61—41no—
79C2×Q8×C61—41no—
80C2×Q8×C61C22⋊C412yes—
81C2×Q8×C61C4⋊C412yes—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61C4212yes—
89C2×D4×C61C22⋊C412yes—
90C2×D4×C61C4⋊C412yes—
91C2×D4×C61C4⋊C412yes—
92C2×D4×C61C22×C411yescharacteristic
93C2×D4×C61C22×C411yescharacteristic
94C2×D4×C61C2×D411yescharacteristic
95C2×D4×C61C2×Q811yescharacteristic
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—22no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—22no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61C4212yes—
106C22×C4×C61C22⋊C411yescharacteristic
107C22×C4×C61C22⋊C411yescharacteristic
108C22×C4×C61C22⋊C412yes—
109C22×C4×C61C22⋊C412yes—
110C22×C4×C61C22⋊C411yescharacteristic
111C22×C4×C61C4⋊C412yes—
112C22×C4×C61C4⋊C412yes—
113C22×C4×C61C4⋊C412yes—
114C22×C4×C61C2×D411yescharacteristic
115C22×Dic61—22no—
116C22×Dic61—22no—
117C22×Dic61—42no—
118C22×Dic61—42no—
119C22×Dic61—82no—
120M16×C61—24no—
121M16×C61—42no—
122M16×C61—44no—
123C2×C8×C61—42no—
124C2×C8×C61—44no—
125C22⋊Dic61—24no—
126C22⋊Dic61—42no—
127C22⋊Dic61—42no—
128C22⋊Dic61—82no—
129C22⋊Dic61—82no—
130C4⋊Dic61—42no—
131C4⋊Dic61—44no—
132C4⋊Dic61—41no—
133C4⋊Dic61—41no—
134C4⋊Dic61—42no—
135C4×Dic61—42no—
136C4×Dic61—44no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—21no—
142C23×C61—21no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61#9512yes—
150C23×C61C2×C4211yescharacteristic
151C23×C61C2×C22⋊C411yescharacteristic
152C23×C61C2×C22⋊C411yescharacteristic
153C23×C61C2×C4⋊C411yescharacteristic
154C23×C61C2×C4⋊C411yescharacteristic
155Q8×C61—42no—
156Q8×C61—42no—
157D4×C61—42no—
158D4×C61—42no—
159D4×C61—42no—
160D4×C61—42no—
161D4×C61—41no—
162D4×C61—41no—
163D4×C61—41no—
164D4×C61—41no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61#9512yes—
184C2×C4×C61#9512yes—
185C2×C4×C61#9512yes—
186C2×C4×C61#9912yes—
187C2×C4×C61#9911yescharacteristic
188C2×C4×C61#9911yescharacteristic
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C2×C4⋊C411yescharacteristic
191C2×Dic61—44no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—82no—
199C2×Dic61—82no—
200C2×Dic61—84no—
201C8×C61—44no—
202#12575—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—22no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—42no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—42no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—41no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61C2×#9511yescharacteristic
225C22×C61C2×#9911yescharacteristic
226C22×C61C2×#9911yescharacteristic
227C4×C61—21no—
228C4×C61—22no—
229C4×C61—22no—
230C4×C61—21no—
231C4×C61#34212yes—
232C4×C61#34212yes—
233Dic61—82no—
234Dic61—84no—
235Dic61—82no—
236C2×#413D6111yescharacteristic
237C2×#410—611no—
238#2311—611no—
239#1390—614no—
240C2×C61—21no—
241C2×C61—21no—
242C2×C61—41no—
243C2×C61—41no—
244C2×C61—41no—
245C2×C61—42no—
246C2×C61—41no—
247C2×C61C2×#34211yescharacteristic
248C2×C61#212211yescharacteristic
249C2×C61#212311yescharacteristic
250C22×#41C2×D6111yescharacteristic
251C22×M16—21no—
252C2×#117—611no—
253C2×#117—1221no—
254C22×C4⋊C4—611no—
255#413—22no—
256#413Dic6114yescomplemented
257C2×#101—21no—
258C2×#100C2×D6112yes—
259#410—614no—
260#410—1222no—
261C2×#99—612no—
262C2×#99—1221no—
263#391—1221no—
264#390—1221no—
265#386—612no—
266#386—612no—
267#380—1221no—
268#380—1221no—
269C61#1257511yescharacteristic, complemented, Sylow
270C2×#41—41no—
271C2×#41—41no—
272C2×#41—42no—
273C2×#41Dic12212yes—
274C2×#41C4×D6112yes—
275C2×#41C2×Dic6112yes—
276C2×#41C22⋊D6112yes—
277C22×Q8C22⋊D6111yescharacteristic
278C22×D4C4×D6111yescharacteristic
279C22×D4D24411yescharacteristic
280C22×D4C22×D6111yescharacteristic
281C23×C4—612no—
282C23×C4C4×D6111yescharacteristic
283C23×C4D24411yescharacteristic
284C23×C4C22⋊D6111yescharacteristic
285C2×M16—24no—
286C2×M16—22no—
287C2×M16—41no—
288C2×M16—42no—
289C22×C8—41no—
290#117—1224no—
291#117—2442no—
292#117—2442no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—2441no—
297C2×C4⋊C4—2441no—
298C2×C4⋊C4—2441no—
299C2×C22⋊C4—612no—
300C2×C22⋊C4—1222no—
301C2×C22⋊C4—1222no—
302C2×C22⋊C4—1222no—
303C2×C42—1221no—
304C2×C42—2441no—
305#101—24no—
306#100—22no—
307#100C2×Dic6114yes—
308#99—614no—
309#99—1224no—
310#99—1222no—
311#95—1222no—
312#95—1222no—
313C24#1175819811yescharacteristic
314C24C2×C4×D6111yescharacteristic
315C24C2×D24411yescharacteristic
316#41—42no—
317#41—42no—
318#41—42no—
319#41—42no—
320#41—42no—
321#41—42no—
322#41—42no—
323#41—42no—
324C2×Q8—41no—
325C2×Q8—41no—
326C2×Q8#1175819612yes—
327C2×Q8C22⋊Dic6112yes—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4C4×Dic6112yes—
335C2×D4#1175819612yes—
336C2×D4C4⋊Dic6112yes—
337C2×D4#1175819812yes—
338C2×D4C2×Dic12211yescharacteristic
339C2×D4C2×C4×D6111yescharacteristic
340C2×D4C22×Dic6111yescharacteristic
341C2×D4C2×C22⋊D6111yescharacteristic
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—4882no—
354C22×C4—2442no—
355C22×C4—2442no—
356C22×C4C4×Dic6112yes—
357C22×C4#1175819612yes—
358C22×C4#1175819612yes—
359C22×C4C4⋊Dic6112yes—
360C22×C4#1175819811yescharacteristic
361C22×C4#1175819811yescharacteristic
362C22×C4#1175819812yes—
363C22×C4#1175819811yescharacteristic
364C22×C4C22⋊Dic6112yes—
365C22×C4C2×C22⋊D6111yescharacteristic
366M16—24no—
367M16—42no—
368M16—44no—
369C2×C8—42no—
370C2×C8—44no—
371C4⋊C4—2442no—
372C4⋊C4—2444no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2442no—
376C22⋊C4—1224no—
377C22⋊C4—4882no—
378C22⋊C4—4882no—
379C22⋊C4—2442no—
380C22⋊C4—2442no—
381C42—2442no—
382C42—2444no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23#1451968412yes—
396C23C2×C4×Dic6111yescharacteristic
397C23C2×#1175819811yescharacteristic
398C23C2×#1175819811yescharacteristic
399C23C2×#1175819611yescharacteristic
400C23C2×C4⋊Dic6111yescharacteristic
401Q8—42no—
402Q8—42no—
403D4—42no—
404D4—42no—
405D4—42no—
406D4—42no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—4882no—
430C2×C4—4882no—
431C2×C4—4884no—
432C2×C4—2444no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4#1451968412yes—
440C2×C4#1451968412yes—
441C2×C4#1451968412yes—
442C2×C4#1451969112yes—
443C2×C4#1451969111yescharacteristic
444C2×C4#1451969111yescharacteristic
445C2×C4C2×C22⋊Dic6111yescharacteristic
446C2×C4C2×#1175819611yescharacteristic
447C8—44no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—42no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—42no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22—81no—
469C22C2×#1451968411yescharacteristic
470C22C2×#1451969111yescharacteristic
471C22C2×#1451969111yescharacteristic
472C4—21no—
473C4—22no—
474C4—22no—
475C4—21no—
476C4—4882no—
477C4—4884no—
478C4—4882no—
479C4#1683952812yes—
480C4#1683952812yes—
481C2—21no—
482C2—21no—
483C2—41no—
484C2—41no—
485C2—41no—
486C2—42no—
487C2—41no—
488C2C2×#1683952811yescharacteristic
489C2#2144747011yescharacteristic
490C2#2144747411yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC23×C61C2×C42
FrattiniC22×D4C22×D61
FittingC2×C61×#413C2
socleC22×C61C2×#99
prime radicalC22×#41×C61C22
cosocleC22×D4×C61C23
hypercenterC2×#413D61
hypocenterC61#12575
LCSG ▷ C23×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
3. #21443938C2semidirect
6. C2×#14519736C4semidirect
7. C22×C4⋊Dic61C4semidirect
9. #16839736C4semidirect
14. #16839642C4semidirect
21. C61×#413C4semidirect
256. #413Dic61semidirect
269. C61#12575semidirect

Maximal subgroups

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

subgroupindex
C2×#168397362
#214484112
#214439382
C2×C61×#4132
#1257561