Finite Group Databasebeta

← #29579157

Subgroups — #29579157

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454120C211yesmaximal, characteristic
2#21445799C211yesmaximal, characteristic, complemented
3C2×#16839498C212yesmaximal, complemented
4C2×#16839495C212yesmaximal
5C61×#1434C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic, complemented
7C2×#14519756C2211yescharacteristic
8C2×#14519751C2211yescharacteristic
9C2×C4⋊#92418—21no—
10C2×C22⋊#92418C2212yes—
11#16839668C411yescharacteristic, complemented
12#16839664C411yescharacteristic, complemented
13#16839653—21no—
14#16839653—21no—
15#16839641—21no—
16#16839641—21no—
17#16839628C411yescharacteristic, complemented
18#16839517—21no—
19#16839498—24no—
20#16839495—24no—
21C22×C42×C61C2211yescharacteristic
22C2×#95×C61—21no—
23C2×#95×C61—21no—
24C2×#95×C61C2212yes—
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27C22×C22⋊D61—21no—
28C22×#92418—22no—
29#14519765—42no—
30#14519756—22no—
31#14519756—22no—
32#14519751—22no—
33#14519751—22no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C4⋊#92418—42no—
44C22⋊#92418—22no—
45C22⋊#92418—22no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61—22no—
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C23×C4×C61C2311yescharacteristic
54C2×C42×C61—42no—
55C2×C42×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59#95×C61—22no—
60#95×C61—42no—
61#95×C61—42no—
62#95×C61D414yes—
63C24×C61C2×D411yescharacteristic
64C23×D61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—24no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61—42no—
76C22×C4×C61—42no—
77C22×C4×C61—42no—
78C22×C4×C61—42no—
79C22×C4×C61—42no—
80C22×C4×C61—42no—
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D412yes—
88C22×C4×C61#4112yes—
89C2×C22⋊D61—42no—
90C2×C22⋊D61—42no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C2×D244—22no—
97C2×D244—41no—
98C2×D244—41no—
99C2×Dic122—22no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C42×C61—22no—
103C42×C61—22no—
104C42×C61—41no—
105C42×C61—41no—
106C22⋊Dic61—42no—
107#11758198—42no—
108#11758198—42no—
109#11758198—42no—
110#11758198—42no—
111#11758198—41no—
112#11758198—41no—
113C4⋊Dic61—22no—
114C4⋊Dic61—22no—
115#11758196—41no—
116#11758196—41no—
117C2×#92418—42no—
118C2×#92418—42no—
119C2×#92418—42no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61C2×C22⋊C411yescharacteristic
125C23×C61#12112yes—
126C23×C61#13512yes—
127C23×C61AGL(1,ℤ/8)11yescharacteristic
128C23×C61#13711yescharacteristic
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61—44no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—44no—
157C2×C4×C61—44no—
158C2×C4×C61—44no—
159C2×C4×C61—82no—
160C2×C4×C61—82no—
161C2×C4×C61—82no—
162C2×C4×C61—82no—
163C2×C4×C61#9912yes—
164C2×C4×C61C4×D412yes—
165C2×C4×C61#12411yescharacteristic
166C2×C4×C61#12711yescharacteristic
167C22⋊D61—82no—
168C22⋊D61—82no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178D244—82no—
179Dic122—82no—
180#92418—82no—
181#9716—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61#39011yescharacteristic
191C22×C61C2×#9911yescharacteristic
192C22×C61#41011yescharacteristic
193C22×C61#41611yescharacteristic
194C22×C61#41711yescharacteristic
195C22×C61#42111yescharacteristic
196C22×C61#42111yescharacteristic
197C22×C61#46312yes—
198C22×C61#46412yes—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C4×C61—21no—
207C4×C61—22no—
208C4×C61—21no—
209C4×C61—22no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—41no—
213C4×C61—84no—
214Dic61—81no—
215Dic61—81no—
216Dic61—81no—
217#2850—611no—
218#1797—611no—
219C2×#328—612no—
220C2×#327—612no—
221#1434D6111yescharacteristic, complemented
222C2×C61—22no—
223C2×C61—22no—
224C2×C61#151211yescharacteristic
225C2×C61#151311yescharacteristic
226C2×C61#151611yescharacteristic
227C2×C61#152111yescharacteristic
228C2×C61#196311yescharacteristic
229C2×C61#196411yescharacteristic
230C2×C61#198311yescharacteristic
231D61—161no—
232C2×#124—611no—
233C2×C22⋊Q8—611no—
234C2×#121—611no—
235C22×C42C2×D6111yescharacteristic
236C2×C4⋊C8—1221no—
237C2×C22⋊C8—612no—
238#391—611no—
239#390—611no—
240#388—1221no—
241#388—1221no—
242#386—1221no—
243#386—1221no—
244#382—611no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95C2×D6112yes—
248#336—1221no—
249#328—1224no—
250#327—1224no—
251C61#971611yescharacteristic, complemented, Sylow
252C22×Q8—611no—
253C22×D4—611no—
254C22×D4—1221no—
255C23×C4—22no—
256C23×C4C22⋊D6111yescharacteristic
257C23×C4C22⋊D6111yescharacteristic
258C23×C4C22×D6111yescharacteristic
259C22×C8—1222no—
260#124—2442no—
261C22⋊Q8—1222no—
262C22⋊Q8—1222no—
263#121—1222no—
264#121—1222no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C42—42no—
275C2×C42C4×D6111yescharacteristic
276C2×C42C4×D6111yescharacteristic
277C2×C42D24411yescharacteristic
278C2×C42D24411yescharacteristic
279C4⋊C8—2442no—
280C22⋊C8—1222no—
281C22⋊C8—1222no—
282#95—22no—
283#95—42no—
284#95—42no—
285#95—1221no—
286#95—1221no—
287#95—1221no—
288#95—1221no—
289#95D24414yes—
290C24—1221no—
291C24C2×C22⋊D6111yescharacteristic
292C2×Q8—1222no—
293C2×Q8—2441no—
294C2×Q8—2441no—
295C2×D4—1222no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2442no—
300C2×D4—2442no—
301C2×D4—2441no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4#1175819811yescharacteristic
322C22×C4#1175819811yescharacteristic
323C22×C4#1175819811yescharacteristic
324C22×C4#1175819811yescharacteristic
325C22×C4C2×C4×D6111yescharacteristic
326C22×C4C2×D24411yescharacteristic
327C22×C4C2×D24412yes—
328C22×C4#1175822212yes—
329C2×C8—2442no—
330C2×C8—2442no—
331C2×C8—2442no—
332C4⋊C4—1222no—
333C4⋊C4—1222no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C22⋊C4—2442no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C42—22no—
344C42—22no—
345C42—41no—
346C42—41no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23C2×#1175819811yescharacteristic
359C23#1451975112yes—
360C23#1451979712yes—
361C23#1451980311yescharacteristic
362C23#1451980811yescharacteristic
363Q8—4882no—
364D4—4882no—
365D4—4882no—
366D4—4882no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4#1451969112yes—
404C2×C4C4×D24412yes—
405C2×C4#1451976511yescharacteristic
406C2×C4#1451977411yescharacteristic
407C8—4882no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—4881no—
417C22—4881no—
418C22—4881no—
419C22—4881no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22#1683966411yescharacteristic
424C22C2×#1451969111yescharacteristic
425C22#1683973511yescharacteristic
426C22#1683975611yescharacteristic
427C22#1683976111yescharacteristic
428C22#1683978011yescharacteristic
429C22#1683978011yescharacteristic
430C22#1683997712yes—
431C22#1683998412yes—
432C4—22no—
433C4—21no—
434C4—22no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—84no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C2—22no—
444C2—22no—
445C2—9761no—
446C2#2144435511yescharacteristic
447C2#2144436011yescharacteristic
448C2#2144437311yescharacteristic
449C2#2144439411yescharacteristic
450C2#2144665111yescharacteristic
451C2#2144665511yescharacteristic
452C2#2144675111yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1434C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1434D61
hypocenterC61#9716
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #21445799C2semidirect
3. C2×#16839498C2semidirect
5. C61×#1434C2semidirect
6. C2×#14519765C4semidirect
11. #16839668C4semidirect
12. #16839664C4semidirect
17. #16839628C4semidirect
221. #1434D61semidirect
251. C61#9716semidirect

Maximal subgroups

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

subgroupindex
#214541202
#214457992
C2×#168394982
C2×#168394952
C61×#14342
#971661