Finite Group Databasebeta

← #29580286

Subgroups — #29580286

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839918C211yesmaximal, characteristic
2#21451632C211yesmaximal, characteristic
3#21445754C211yesmaximal, characteristic
4C2×#16839498C211yesmaximal, characteristic
5C2×#16839488C211yesmaximal, characteristic
6#21443698C211yesmaximal, characteristic
7C2×C61×#395C211yesmaximal, characteristic
8C22×#11758202—21no—
9C2×#14519756C2211yescharacteristic
10#16839918—22no—
11#16839918—22no—
12C2×#14519701—21no—
13C2×#14519701—22no—
14C2×C22⋊#92418C2211yescharacteristic
15C2×C22⋊#92418C2211yescharacteristic
16#16839701—21no—
17#16839695—22no—
18#16839682—21no—
19#16839635—21no—
20#16839625—21no—
21#16839622C2211yescharacteristic
22#16839498—22no—
23#16839488—22no—
24C23×Q8×C61C2211yescharacteristic
25C22×C4⋊C4×C61—21no—
26C22×C4⋊C4×C61C2211yescharacteristic
27C61×#395—22no—
28C61×#395—22no—
29C2×#95×C61—21no—
30C2×#95×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C2×#11758202—24no—
33C2×#11758202—44no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D412yes—
42C2×#11758196—21no—
43C2×#11758196—22no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46#14519701—24no—
47#14519701—44no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418D412yes—
52#14519684—22no—
53#14519684—22no—
54#14519684—22no—
55#14519684—21no—
56C22×Q8×C61—21no—
57C22×Q8×C61—21no—
58C22×Q8×C61—21no—
59C22×Q8×C61—21no—
60C22×Q8×C61—21no—
61C22×Q8×C61—44no—
62C22×Q8×C61D412yes—
63C23×C4×C61—21no—
64C23×C4×C61—21no—
65C23×C4×C61D411yescharacteristic
66C23×C4×C61D411yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C2×C4⋊C4×C61—24no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61—44no—
76#95×C61—24no—
77#95×C61—21no—
78#95×C61D412yes—
79C24×C61C2×D411yescharacteristic
80C2×Q8×C61—24no—
81C2×Q8×C61—24no—
82C2×Q8×C61—22no—
83C2×Q8×C61—22no—
84C2×Q8×C61—44no—
85C2×Q8×C61—42no—
86C2×Q8×C61—42no—
87C2×Q8×C61—44no—
88C2×Q8×C61—44no—
89C2×Q8×C61—44no—
90C2×Q8×C61—41no—
91C2×Q8×C61—41no—
92C22×C4×C61—24no—
93C22×C4×C61—24no—
94C22×C4×C61—21no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
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—21no—
104C22×C4×C61—21no—
105C22×C4×C61—42no—
106C22×C4×C61—42no—
107C22×C4×C61—42no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61—41no—
112C22×C4×C61—42no—
113C22×C4×C61Q1612yescomplemented
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—22no—
123C2×Dic122—21no—
124C2×Dic122—21no—
125C2×Dic122—42no—
126C4⋊C4×C61—48no—
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C4⋊C4×C61—41no—
131C22⋊Dic61—41no—
132C22⋊Dic61—41no—
133C22⋊Dic61—41no—
134C22⋊Dic61—41no—
135#11758202—48no—
136C4⋊Dic61—21no—
137C4⋊Dic61—21no—
138C4⋊Dic61—42no—
139#11758196—41no—
140#11758196—41no—
141#11758196—82no—
142C2×#92418—22no—
143C2×#92418—42no—
144C2×#92418—42no—
145C2×#92418—41no—
146C23×C61—22no—
147C23×C61—22no—
148C23×C61#12011yescharacteristic
149C23×C61#12011yescharacteristic
150C23×C61#12111yescharacteristic
151C23×C61C2×Q1611yescharacteristic
152C23×C61#13511yescharacteristic
153C23×C61#13711yescharacteristic
154C23×C61#13711yescharacteristic
155Q8×C61—24no—
156Q8×C61—24no—
157Q8×C61—42no—
158Q8×C61—44no—
159Q8×C61—44no—
160Q8×C61—42no—
161C2×C4×C61—22no—
162C2×C4×C61—22no—
163C2×C4×C61—24no—
164C2×C4×C61—24no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—44no—
174C2×C4×C61—44no—
175C2×C4×C61—42no—
176C2×C4×C61—44no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—42no—
182C2×C4×C61—44no—
183C2×C4×C61—41no—
184C2×C4×C61—42no—
185C2×C4×C61—41no—
186C2×C4×C61—42no—
187C2×C4×C61—81no—
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12711yescharacteristic
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199Dic122—42no—
200Dic122—81no—
201#92418—42no—
202#92418—81no—
203#9925—611nomaximal, Sylow
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—22no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61#39211yescharacteristic
213C22×C61#45111yescharacteristic
214C22×C61#45111yescharacteristic
215C22×C61#45211yescharacteristic
216C22×C61#45211yescharacteristic
217C22×C61#45612yes—
218C22×C61B(4,𝔽2)12yes—
219C22×C61#46711yescharacteristic
220C22×C61#47011yescharacteristic
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—44no—
226C4×C61—42no—
227C4×C61—44no—
228C4×C61—81no—
229Dic61—82no—
230Dic61—81no—
231Dic61—81no—
232C2×#451—611no—
233#2627—611no—
234C2×#395D6111yescharacteristic
235#1787—611no—
236C2×#328—611no—
237C2×#324—611no—
238#1294—611no—
239C2×C61—21no—
240C2×C61—21no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61#160312yes—
244C2×C61#160512yes—
245C2×C61#200111yescharacteristic
246C2×C61#200511yescharacteristic
247C2×C61#202111yescharacteristic
248C23×Q8C2×D6111yescharacteristic
249C22×Q16—1221no—
250C2×C22⋊Q8—611no—
251C22×C4⋊C4—21no—
252C22×C4⋊C4C2×D6111yescharacteristic
253#451—1222no—
254#451—1222no—
255C2×#103—1221no—
256C2×#103—1222no—
257C2×C22⋊C8—611no—
258C2×C22⋊C8—611no—
259#400—1221no—
260#398—1222no—
261#395—22no—
262#395—22no—
263#395—1221no—
264#385—1221no—
265#381—1221no—
266#380—611no—
267C2×#95—21no—
268C2×#95C2×D6111yescharacteristic
269#328—1222no—
270#324—1222no—
271C61#992511yescharacteristic, complemented, Sylow
272C22×Q8—21no—
273C22×Q8—21no—
274C22×Q8—21no—
275C22×Q8—21no—
276C22×Q8—21no—
277C22×Q8—44no—
278C22×Q8—611no—
279C22×Q8C22⋊D6112yes—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4C22⋊D6111yescharacteristic
283C23×C4C22⋊D6111yescharacteristic
284C23×C4C22×D6111yescharacteristic
285C2×Q16—1224no—
286C2×Q16—2444no—
287C22×C8—1221no—
288C22×C8—1221no—
289C22⋊Q8—1221no—
290C22⋊Q8—1221no—
291C22⋊Q8—1221no—
292C22⋊Q8—1221no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—612no—
303C2×C4⋊C4—1222no—
304C2×C4⋊C4—1221no—
305C2×C22⋊C4—1221no—
306C2×C22⋊C4—1221no—
307#103—1224no—
308#103—2444no—
309C22⋊C8—612no—
310C22⋊C8—1221no—
311C22⋊C8—1221no—
312C22⋊C8—1221no—
313#95—24no—
314#95—21no—
315#95—1222no—
316#95—1222no—
317#95—1222no—
318#95—1221no—
319#95C22⋊D6112yes—
320C24C2×C22⋊D6111yescharacteristic
321C2×Q8—24no—
322C2×Q8—24no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—44no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8—44no—
329C2×Q8—44no—
330C2×Q8—44no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—1221no—
334C2×Q8—1221no—
335C2×Q8—2442no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4—1221no—
358C22×C4—1222no—
359C22×C4—1221no—
360C22×C4#1175820212yescomplemented
361C22×C4D4×D6111yescharacteristic
362C22×C4D4×D6111yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4#1175822411yescharacteristic
365C22×C4C2×C22⋊D6111yescharacteristic
366C22×C4C2×C22⋊D6111yescharacteristic
367Q16—2448no—
368C2×C8—1222no—
369C2×C8—2442no—
370C2×C8—2441no—
371C2×C8—2442no—
372C4⋊C4—48no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—4882no—
380C4⋊C4—2442no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C23—22no—
388C23—22no—
389C23#1451974511yescharacteristic
390C23#1451974611yescharacteristic
391C23#1451974911yescharacteristic
392C23C2×#1175820211yescharacteristic
393C23#1451979711yescharacteristic
394C23#1451980711yescharacteristic
395C23#1451980811yescharacteristic
396Q8—24no—
397Q8—24no—
398Q8—44no—
399Q8—42no—
400Q8—44no—
401Q8—42no—
402Q8—4881no—
403Q8—2442no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—81no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4#1451974511yescharacteristic
439C2×C4#1451974811yescharacteristic
440C2×C4#1451974911yescharacteristic
441C2×C4#1451977311yescharacteristic
442C8—4881no—
443C8—2442no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—21no—
451C22—21no—
452C22#1683967011yescharacteristic
453C22#1683991711yescharacteristic
454C22#1683991811yescharacteristic
455C22#1683992211yescharacteristic
456C22#1683992411yescharacteristic
457C22#1683994412yes—
458C22#1683994812yes—
459C22#1684000111yescharacteristic
460C22#1684001811yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—44no—
466C4—44no—
467C4—42no—
468C4—81no—
469C4—4881no—
470C4—4882no—
471C4—4881no—
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2#2144478012yes—
477C2#2144479212yes—
478C2#2144682711yescharacteristic
479C2#2144685511yescharacteristic
480C2#2144694211yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#395C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#395D61
hypocenterC61#9925
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
113. C22×C4×C61Q16semidirect
271. C61#9925semidirect
360. C22×C4#11758202semidirect

Maximal subgroups

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

subgroupindex
C2×#168399182
#214516322
#214457542
C2×#168394982
C2×#168394882
#214436982
C2×C61×#3952
#992561