Finite Group Databasebeta

← #29575014

Subgroups — #29575014

Order 15616.

836 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839673C211yesmaximal, characteristic
2#21448416C211yesmaximal, characteristic
3#21445754C211yesmaximal, characteristic, complemented
4C2×#16839485C211yesmaximal, characteristic
5#21443699C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1787C211yesmaximal, characteristic, complemented
8C22×#11758198—21no—
9C22×#11758198C2211yescharacteristic
10C2×#14519701—22no—
11C2×C22⋊#92418C2211yescharacteristic
12#16839673—22no—
13#16839673C414yescomplemented
14#16839654—22no—
15#16839652—22no—
16#16839622C2211yescharacteristic
17#16839617—21no—
18C22⋊C4×Dic61—21no—
19C2×#14519684—21no—
20C2×#14519684C2211yescharacteristic
21#16839485—22no—
22C23×Q8×C61C2211yescharacteristic
23C2×#103×C61—22no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C24×D61D411yescharacteristic
27C23×Dic61—21no—
28C23×Dic61D411yescharacteristic
29C22×#92418—21no—
30C2×C4⋊Dic61D412yes—
31C2×C22⋊Dic61—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—24no—
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198—44no—
40C2×#11758198C2×C412yes—
41C2×#11758198D412yes—
42C2×C4×Dic61—22no—
43#14519701—44no—
44C22⋊#92418—21no—
45C22⋊#92418—21no—
46#14519684—22no—
47#14519684—21no—
48#14519684—21no—
49#14519684—24no—
50#14519684C2×C412yes—
51C22×Q8×C61—21no—
52C22×Q8×C61—21no—
53C22×Q8×C61—21no—
54C22×Q8×C61—21no—
55C22×Q8×C61—21no—
56C22×Q8×C61—44no—
57C22×Q8×C61C2×C412yes—
58C23×C4×C61—21no—
59C23×C4×C61C2311yescharacteristic
60C22×C8×C61—21no—
61C2×C4⋊C4×C61D412yes—
62C2×C22⋊C4×C61—21no—
63#103×C61—44no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#95×C61—21no—
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C23×D61—21no—
70C23×D61—21no—
71C23×D61—21no—
72C23×D61—21no—
73C23×D61—21no—
74C23×D61—42no—
75C23×D61—42no—
76C23×D61C22⋊C412yes—
77C2×Q8×C61—24no—
78C2×Q8×C61—24no—
79C2×Q8×C61—22no—
80C2×Q8×C61—22no—
81C2×Q8×C61—44no—
82C2×Q8×C61—42no—
83C2×Q8×C61—42no—
84C2×Q8×C61—44no—
85C2×Q8×C61—44no—
86C2×Q8×C61—44no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C22×C4×C61—24no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—42no—
93C22×C4×C61—42no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×C4×C61#4111yescharacteristic
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—22no—
105C22×Dic61—22no—
106C22×Dic61—42no—
107C22×Dic61—42no—
108C22×Dic61—42no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61C22⋊C412yes—
112C2×C8×C61—42no—
113C2×C8×C61—41no—
114C4⋊C4×C61—42no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119#11758198—22no—
120#11758198—22no—
121#11758198—22no—
122#11758198—22no—
123#11758198—48no—
124#11758198—82no—
125#11758198—82no—
126C4⋊Dic61—42no—
127C4×Dic61—82no—
128C2×#92418—42no—
129C2×#92418—41no—
130C23×C61—22no—
131C23×C61—22no—
132C23×C61C2×C22⋊C411yescharacteristic
133C23×C61#12011yescharacteristic
134C23×C61#12311yescharacteristic
135C23×C61#13511yescharacteristic
136C23×C61#13511yescharacteristic
137C23×C61#13711yescharacteristic
138C23×C61#13711yescharacteristic
139C22×D61—22no—
140C22×D61—22no—
141C22×D61—22no—
142C22×D61—42no—
143C22×D61—42no—
144C22×D61—44no—
145C22×D61—44no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—42no—
149C22×D61—42no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—81no—
153C22×D61—81no—
154C22×D61—82no—
155C22×D61—82no—
156Q8×C61—24no—
157Q8×C61—24no—
158Q8×C61—44no—
159Q8×C61—44no—
160Q8×C61—42no—
161Q8×C61—42no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—24no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—44no—
171C2×C4×C61—42no—
172C2×C4×C61—44no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61C4×D411yescharacteristic
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×Dic61—22no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—81no—
190C2×Dic61—82no—
191C2×Dic61—82no—
192C8×C61—81no—
193#92418—81no—
194#9016—611nomaximal, Sylow
195C22×C61—22no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—22no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61#38611yescharacteristic
204C22×C61#41611yescharacteristic
205C22×C61#41911yescharacteristic
206C22×C61#45211yescharacteristic
207C22×C61#45211yescharacteristic
208C22×C61#45512yes—
209C22×C61B(4,𝔽2)12yes—
210C22×C61#48511yescharacteristic
211C22×C61#48511yescharacteristic
212C2×D61—44no—
213C2×D61—42no—
214C2×D61—42no—
215C2×D61—42no—
216C2×D61—82no—
217C2×D61—82no—
218C2×D61—82no—
219C2×D61—82no—
220C2×D61—82no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—44no—
226C4×C61—82no—
227Dic61—42no—
228Dic61—82no—
229Dic61—82no—
230C2×#393—611no—
231#2312—611no—
232#1787—611no—
233#1787D6111yescharacteristic, complemented
234C2×#323—611no—
235#1294—611no—
236#1294—611no—
237C2×C61—21no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—21no—
241C2×C61#160612yes—
242C2×C61#160612yes—
243C2×C61#187311yescharacteristic
244C2×C61#188511yescharacteristic
245C2×C61#188911yescharacteristic
246D61—82no—
247C23×Q8C2×D6111yescharacteristic
248C22×C22⋊C4—611no—
249C22×C22⋊C4—1221no—
250C2×#103—22no—
251C2×#103—1222no—
252C2×C22⋊C8—611no—
253C2×C22⋊C8C2×D6111yescharacteristic
254#393—614no—
255#393—1222no—
256#388—1222no—
257#388—1222no—
258#380—611no—
259#380C2×D6111yescharacteristic
260#379—1221no—
261C4×C22⋊C4—1221no—
262C2×#95—611no—
263C2×#95—1221no—
264#323—1222no—
265C61#901611yescharacteristic, complemented, Sylow
266C25—611no—
267C22×Q8—21no—
268C22×Q8—21no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—21no—
272C22×Q8—44no—
273C22×Q8C4×D6112yes—
274C23×C4—21no—
275C23×C4—611no—
276C23×C4—1221no—
277C23×C4C22×D6111yescharacteristic
278C22×C8—21no—
279C22×C8—1221no—
280C2×C4⋊C4—612no—
281C2×C4⋊C4C22⋊D6112yes—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—612no—
284C2×C22⋊C4—612no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1222no—
290C2×C22⋊C4—1222no—
291C2×C22⋊C4—1224no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—2444no—
294C2×C42—1222no—
295#103—44no—
296#103—2444no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—1221no—
300C22⋊C8—1221no—
301#95—21no—
302#95—612no—
303#95—1224no—
304#95—1222no—
305#95—1221no—
306#95—1221no—
307C24—612no—
308C24—1221no—
309C24—1221no—
310C24—1221no—
311C24—1221no—
312C24—1221no—
313C24—1221no—
314C24—2442no—
315C24—2442no—
316C24D4×D6111yescharacteristic
317C2×Q8—24no—
318C2×Q8—24no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—44no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8—44no—
325C2×Q8—44no—
326C2×Q8—44no—
327C2×Q8—41no—
328C2×Q8—41no—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—612no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1222no—
340C22×C4—1222no—
341C22×C4—2442no—
342C22×C4—2442no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4—2442no—
346C22×C4C2×C4×D6111yescharacteristic
347C22×C4#1175822211yescharacteristic
348C22×C4D4×D6111yescharacteristic
349C22×C4D4×D6111yescharacteristic
350C22×C4#1175822411yescharacteristic
351C22×C4C2×C22⋊D6111yescharacteristic
352C2×C8—42no—
353C2×C8—41no—
354C2×C8—2442no—
355C2×C8—2441no—
356C4⋊C4—42no—
357C4⋊C4—2442no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—1222no—
361C22⋊C4—1222no—
362C22⋊C4—1222no—
363C22⋊C4—1222no—
364C22⋊C4—4882no—
365C22⋊C4—4882no—
366C22⋊C4—2448no—
367C22⋊C4—2441no—
368C22⋊C4—2441no—
369C42—4882no—
370C23—22no—
371C23—22no—
372C23—1222no—
373C23—1222no—
374C23—1222no—
375C23—4882no—
376C23—4882no—
377C23—4881no—
378C23—4881no—
379C23—2444no—
380C23—2444no—
381C23—2442no—
382C23—2442no—
383C23—2442no—
384C23—2442no—
385C23—2441no—
386C23—2441no—
387C23—2441no—
388C23—2441no—
389C23C22⋊C4×D6111yescharacteristic
390C23#1451974511yescharacteristic
391C23#1451975911yescharacteristic
392C23#1451979811yescharacteristic
393C23#1451980011yescharacteristic
394C23#1451980611yescharacteristic
395C23#1451980911yescharacteristic
396Q8—24no—
397Q8—24no—
398Q8—44no—
399Q8—44no—
400Q8—42no—
401Q8—42no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—1222no—
417C2×C4—4882no—
418C2×C4—4882no—
419C2×C4—4881no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4#1451973711yescharacteristic
429C2×C4C4×C22⋊D6111yescharacteristic
430C2×C4#1451974811yescharacteristic
431C2×C4#1451975011yescharacteristic
432C8—81no—
433C8—4881no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—4882no—
443C22—4882no—
444C22—4882no—
445C22—4882no—
446C22—4882no—
447C22—2444no—
448C22—2442no—
449C22—2442no—
450C22—2442no—
451C22#1683963811yescharacteristic
452C22#1683975711yescharacteristic
453C22#1683976911yescharacteristic
454C22#1683992111yescharacteristic
455C22#1683992311yescharacteristic
456C22#1683993812yes—
457C22#1683994812yes—
458C22#1684010111yescharacteristic
459C22#1684010211yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—44no—
465C4—82no—
466C4—4882no—
467C4—4882no—
468C4—2442no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—4882no—
474C2#2144479612yes—
475C2#2144479812yes—
476C2#2144612811yescharacteristic
477C2#2144620411yescharacteristic
478C2#2144622411yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1787C2
socleC23×C61#120
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1787D61
hypocenterC61#9016
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
3. #21445754C2semidirect
5. #21443699C2semidirect
6. #21443697C2semidirect
7. C61×#1787C2semidirect
13. #16839673C4semidirect
233. #1787D61semidirect
265. C61#9016semidirect

Maximal subgroups

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

subgroupindex
C2×#168396732
#214484162
#214457542
C2×#168394852
#214436992
#214436972
C61×#17872
#901661