Finite Group Databasebeta

← #29575622

Subgroups — #29575622

Order 15616.

614 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839714C211yesmaximal, characteristic
2#21454130C211yesmaximal, characteristic
3#21445582C211yesmaximal, characteristic
4C2×#16839503C211yesmaximal, characteristic, complemented
5C2×#16839503C211yesmaximal, characteristic, complemented
6#21443700C211yesmaximal, characteristic, complemented
7C61×#1295C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519769C2211yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×#14519689—21no—
12#16839714—22no—
13#16839714—22no—
14C2×#14519688C2211yescharacteristic
15C2×#14519688C2211yescharacteristic
16C2×C8×Dic61—21no—
17#16839661C411yescharacteristic
18#16839661C411yescharacteristic
19#16839647—21no—
20#16839647—21no—
21#16839636—21no—
22#16839636—21no—
23#16839619C411yescharacteristic
24#16839619C411yescharacteristic
25#16839516—21no—
26#16839503—22no—
27#16839503—22no—
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#382C2211yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×#11758189—24no—
35C2×#11758189—24no—
36C2×#11758189—24no—
37C22×#92418—21no—
38C22×#92418—21no—
39#14519769—21no—
40#14519769—21no—
41#14519769—21no—
42#14519769—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C42×D61—21no—
55C42×D61—21no—
56C42×D61—21no—
57C42×D61—21no—
58#14519689—24no—
59#14519688—21no—
60#14519688—21no—
61#14519688—21no—
62#14519688D412yes—
63C8×Dic61—24no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C2×C4⋊C4×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C42×C61C2311yescharacteristic
73#97×C61—21no—
74#97×C61—21no—
75#97×C61—21no—
76#97×C61D412yes—
77#95×C61—21no—
78#95×C61—21no—
79C23×D61C22⋊C411yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×C4×D61—22no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—22no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C8×C61—22no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C42×C61#4111yescharacteristic
114#11758198—42no—
115#11758198—42no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—42no—
121C4⋊Dic61—42no—
122#11758196—41no—
123#11758196—41no—
124#11758196—41no—
125#11758196—41no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C2×#92418—22no—
133C2×#92418—22no—
134C2×#92418—22no—
135C2×#92418—22no—
136C2×#92418—41no—
137C2×#92418—41no—
138#11758189—216no—
139C23×C61C2×C22⋊C411yescharacteristic
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61#10412yes—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61C4×D411yescharacteristic
161C2×C4×C61#12011yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12311yescharacteristic
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61#10112yes—
178C2×Dic61#10412yes—
179C2×Dic61#10412yes—
180C4×D61—24no—
181C4×D61—24no—
182C4×D61—42no—
183C4×D61—42no—
184C4×D61—42no—
185C4×D61—42no—
186C8×C61—24no—
187C8×C61—42no—
188#92418—24no—
189#92418—42no—
190#9122—611nomaximal, Sylow
191C22×C61#38611yescharacteristic
192C22×C61C2×#10111yescharacteristic
193C22×C61#41311yescharacteristic
194C22×C61C2×#10411yescharacteristic
195C22×C61C2×#10411yescharacteristic
196C22×C61C2×#10411yescharacteristic
197C22×C61#42111yescharacteristic
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—81no—
212C4×C61—81no—
213Dic61—22no—
214Dic61—22no—
215Dic61—22no—
216Dic61—81no—
217Dic61—81no—
218C2×C4×M16—611no—
219#2851—611no—
220#1749—611no—
221C2×#330—611no—
222C2×#330—611no—
223#1295—611no—
224#1295D6111yescharacteristic, complemented
225C2×C61#152411yescharacteristic
226C2×C61#152611yescharacteristic
227C2×C61#152811yescharacteristic
228C2×C61#152911yescharacteristic
229C2×C61#187111yescharacteristic
230C2×C61#189611yescharacteristic
231C2×C61#190111yescharacteristic
232D61—42no—
233C22×M16—1221no—
234C2×#125—611no—
235C22×C42—611no—
236C2×C22⋊C8—1221no—
237C4×M16—1222no—
238C4×M16—1222no—
239C2×#97—611no—
240C2×#97—611no—
241C2×#97C2×D6111yescharacteristic
242C2×#97C2×D6111yescharacteristic
243C2×C4×C8—1221no—
244#389—611no—
245#389—611no—
246#387—1221no—
247#387—1221no—
248#385—1221no—
249#385—1221no—
250#382C2×D6111yescharacteristic
251#380—611no—
252#380—611no—
253#336—1221no—
254#330—1222no—
255#330—1222no—
256C61#912211yescharacteristic, complemented, Sylow
257C23×C4—611no—
258C23×C4—611no—
259C23×C4—611no—
260C2×M16—1224no—
261C2×M16—1224no—
262C2×M16—1224no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—1221no—
266C22×C8—1221no—
267#125—1221no—
268#125—1221no—
269#125—1221no—
270#125—1221no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4C4×D6111yescharacteristic
278C2×C4⋊C4C4×D6111yescharacteristic
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C42—611no—
282C2×C42—611no—
283C2×C42—611no—
284C2×C42—1221no—
285C2×C42—1221no—
286C2×C42—1221no—
287C2×C42—1221no—
288C2×C42C22×D6111yescharacteristic
289C22⋊C8—1224no—
290#97—21no—
291#97—21no—
292#97—21no—
293#97—612no—
294#97—1221no—
295#97—1221no—
296#97—1221no—
297#97D24412yes—
298C4×C8—1224no—
299#95—21no—
300#95—21no—
301#95—1221no—
302#95—1221no—
303#95—1221no—
304#95—1221no—
305C24—611no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1222no—
312C22×C4—1222no—
313C22×C4—1222no—
314C22×C4—1222no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4C2×C4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327C22×C4D4×D6111yescharacteristic
328M16—12216no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—1222no—
338C2×C8—1222no—
339C2×C8—2441no—
340C2×C8—2441no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—1221no—
344C4⋊C4—1221no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—2442no—
348C4⋊C4—2442no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C4⋊C4—2441no—
353C22⋊C4—2442no—
354C22⋊C4—2442no—
355C42—1221no—
356C42—1221no—
357C42—1221no—
358C42—1221no—
359C42—1221no—
360C42—1221no—
361C42C2×D24411yescharacteristic
362C42#1175822211yescharacteristic
363C42D4×D6111yescharacteristic
364C42#1175822611yescharacteristic
365C23—612no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—1221no—
372C23C22⋊C4×D6111yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—612no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—1224no—
389C2×C4—1224no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4#1451973911yescharacteristic
407C2×C4C4×D24411yescharacteristic
408C2×C4#1451974711yescharacteristic
409C2×C4#1451975011yescharacteristic
410C2×C4#1451975211yescharacteristic
411C2×C4#1451976211yescharacteristic
412C8—24no—
413C8—42no—
414C8—1224no—
415C8—2442no—
416C22—1222no—
417C22—1222no—
418C22—1222no—
419C22—2441no—
420C22—2441no—
421C22—2441no—
422C22—2441no—
423C22#1683964011yescharacteristic
424C22#101×D6111yescharacteristic
425C22#1683974311yescharacteristic
426C22#104×D6111yescharacteristic
427C22#104×D6111yescharacteristic
428C22#104×D6111yescharacteristic
429C22#1683977711yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—1222no—
439C4—1222no—
440C4—1222no—
441C4—4881no—
442C4—4881no—
443C2—2442no—
444C2#2144440411yescharacteristic
445C2#2144441211yescharacteristic
446C2#2144441911yescharacteristic
447C2#2144442311yescharacteristic
448C2#2144612011yescharacteristic
449C2#2144626111yescharacteristic
450C2#2144628611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#9122
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. C2×#16839503C2semidirect
5. C2×#16839503C2semidirect
6. #21443700C2semidirect
7. C61×#1295C2semidirect
224. #1295D61semidirect
256. C61#9122semidirect

Maximal subgroups

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

subgroupindex
C2×#168397142
#214541302
#214455822
C2×#168395032
#214437002
C61×#12952
#912261