Finite Group Databasebeta

← #29575662

Subgroups — #29575662

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839814C211yesmaximal, characteristic
2#21454172C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×#16839509C211yesmaximal, characteristic, complemented
5C2×#16839507C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519757—21no—
10C2×C42×D61C2211yescharacteristic
11#16839814—22no—
12#16839814—22no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519689—21no—
16C2×#14519689—21no—
17C2×C8×Dic61—21no—
18#16839667—21no—
19#16839661—21no—
20#16839661C412yes—
21#16839619—21no—
22#16839619C412yes—
23#16839516—21no—
24#16839509—22no—
25#16839507—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#384C2211yescharacteristic
29C22×Dic122—21no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×#92418—21no—
34C22×#92418—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519757—42no—
40#14519757—42no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61C2×C412yes—
44C2×#11758198—22no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C42×D61—21no—
49C42×D61—21no—
50C42×D61—21no—
51C42×D61—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C4⋊#92418D412yes—
56#14519689—24no—
57#14519689—42no—
58C8×Dic61—24no—
59#14519684—22no—
60#14519684—22no—
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61C2×C412yes—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D412yes—
71C23×D61C22⋊C411yescharacteristic
72C22×C4×C61—22no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—22no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—22no—
93C2×C4×D61—41no—
94C2×C4×D61D812yes—
95C2×C4×D61SD1612yes—
96C2×Dic122—41no—
97C2×Dic122—41no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C4⋊C4×C61—42no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C42×C61#4111yescharacteristic
117#11758198—44no—
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—44no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C2×#92418—22no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C23×C61C2×C22⋊C411yescharacteristic
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61#10212yes—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×C4×C61C2×D811yescharacteristic
155C2×C4×C61C2×SD1611yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61#13511yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C2×C4×C61#13711yescharacteristic
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61#10112yes—
173C2×Dic61#10212yes—
174C4×D61—22no—
175C4×D61—22no—
176C4×D61—22no—
177C4×D61—22no—
178C4×D61—42no—
179C4×D61—42no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184Dic122—81no—
185Dic122—81no—
186Dic122—81no—
187Dic122—81no—
188C8×C61—42no—
189C8×C61—81no—
190#92418—42no—
191#92418—81no—
192#9130—611nomaximal, Sylow
193C22×C61#38611yescharacteristic
194C22×C61C2×#10111yescharacteristic
195C22×C61#41311yescharacteristic
196C22×C61C2×#10211yescharacteristic
197C22×C61#41611yescharacteristic
198C22×C61#41611yescharacteristic
199C22×C61#41911yescharacteristic
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—22no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—82no—
210C4×C61#45211yescharacteristic
211C4×C61#45211yescharacteristic
212C4×C61#46511yescharacteristic
213C4×C61#46511yescharacteristic
214C4×C61#46611yescharacteristic
215C4×C61#46611yescharacteristic
216C4×C61#48511yescharacteristic
217C4×C61#48511yescharacteristic
218Dic61—22no—
219Dic61—22no—
220Dic61—41no—
221Dic61—82no—
222C2×#431—611no—
223#2857—611no—
224#1797—611no—
225C2×#332—611no—
226C2×#332—611no—
227#1296—611no—
228#1296D6111yescharacteristic, complemented
229C2×C61#154011yescharacteristic
230C2×C61#154411yescharacteristic
231C2×C61#154611yescharacteristic
232C2×C61#155411yescharacteristic
233C2×C61#187311yescharacteristic
234C2×C61#189311yescharacteristic
235C2×C61#190111yescharacteristic
236D61—42no—
237C2×C4⋊Q8—611no—
238C2×C22⋊Q8—1221no—
239C22×C42—611no—
240#431—1222no—
241#431—1222no—
242C2×C4⋊C8—611no—
243C2×C4⋊C8—611no—
244C2×C4⋊C8C2×D6111yescharacteristic
245C2×C4⋊C8C2×D6111yescharacteristic
246C2×C22⋊C8—1221no—
247C2×C22⋊C8—1221no—
248C2×C4×C8—1221no—
249#391—1221no—
250#389—612no—
251#389—1221no—
252#384C2×D6111yescharacteristic
253#380—612no—
254#380—1221no—
255#336—1221no—
256#332—1222no—
257#332—1222no—
258C61#913011yescharacteristic, complemented, Sylow
259C22×Q8—1221no—
260C23×C4—611no—
261C23×C4—611no—
262C23×C4—611no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—1221no—
266C22×C8—1221no—
267C4⋊Q8—1221no—
268C4⋊Q8—1221no—
269C4⋊Q8—1221no—
270C4⋊Q8—1221no—
271C22⋊Q8—2442no—
272C22⋊Q8—2442no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—612no—
276C2×C4⋊C4—1222no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4C4×D6112yes—
279C2×C22⋊C4—1222no—
280C2×C42—611no—
281C2×C42—611no—
282C2×C42—611no—
283C2×C42—1221no—
284C2×C42—1221no—
285C2×C42—1221no—
286C2×C42—1221no—
287C2×C42C22×D6111yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—612no—
292C4⋊C8—1221no—
293C4⋊C8—1221no—
294C4⋊C8—1221no—
295C4⋊C8D24412yes—
296C22⋊C8—1224no—
297C22⋊C8—2442no—
298C4×C8—1224no—
299#95—1222no—
300#95—1222no—
301C24—611no—
302C2×Q8—2441no—
303C2×Q8—2441no—
304C2×Q8—2441no—
305C2×Q8—2441no—
306C2×Q8—2441no—
307C2×Q8—2441no—
308C22×C4—22no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—612no—
312C22×C4—612no—
313C22×C4—611no—
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—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1222no—
328C22×C4—2441no—
329C22×C4C2×C4×D6111yescharacteristic
330C22×C4D4×D6111yescharacteristic
331C22×C4D4×D6111yescharacteristic
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—1222no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C2×C8—2441no—
343C2×C8—2441no—
344C4⋊C4—42no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—1222no—
350C4⋊C4—1222no—
351C4⋊C4—2444no—
352C4⋊C4—2441no—
353C4⋊C4—2441no—
354C22⋊C4—2444no—
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
373Q8—4881no—
374Q8—4881no—
375Q8—4881no—
376Q8—4881no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—612no—
383C2×C4—612no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1222no—
389C2×C4—1222no—
390C2×C4—1222no—
391C2×C4—1222no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—2442no—
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#1451973911yescharacteristic
405C2×C4C4×D24411yescharacteristic
406C2×C4#1451974711yescharacteristic
407C2×C4#1451975011yescharacteristic
408C2×C4#1451975211yescharacteristic
409C2×C4#1451976211yescharacteristic
410C2×C4D8×D6111yescharacteristic
411C2×C4SD16×D6111yescharacteristic
412C2×C4#1451979611yescharacteristic
413C2×C4#1451979811yescharacteristic
414C2×C4#1451979811yescharacteristic
415C2×C4#1451980011yescharacteristic
416C2×C4#1451980611yescharacteristic
417C2×C4#1451980911yescharacteristic
418C8—42no—
419C8—81no—
420C8—4881no—
421C8—2442no—
422C22—1222no—
423C22—1222no—
424C22—1222no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22#1683964011yescharacteristic
430C22#101×D6111yescharacteristic
431C22#1683974311yescharacteristic
432C22#102×D6111yescharacteristic
433C22#1683975511yescharacteristic
434C22#1683975711yescharacteristic
435C22#1683976911yescharacteristic
436C4—21no—
437C4—21no—
438C4—82no—
439C4—1222no—
440C4—1222no—
441C4—4882no—
442C4—2441no—
443C4#1683992511yescharacteristic
444C4#1683992711yescharacteristic
445C4#1683999211yescharacteristic
446C4#1683999411yescharacteristic
447C4#1683999711yescharacteristic
448C4#1683999911yescharacteristic
449C4#1684010511yescharacteristic
450C4#1684010611yescharacteristic
451C2—2442no—
452C2#2144446511yescharacteristic
453C2#2144448211yescharacteristic
454C2#2144448911yescharacteristic
455C2#2144452811yescharacteristic
456C2#2144613011yescharacteristic
457C2#2144624611yescharacteristic
458C2#2144628611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#9130
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C2×#16839509C2semidirect
5. C2×#16839507C2semidirect
6. #21443702C2semidirect
7. C61×#1296C2semidirect
228. #1296D61semidirect
258. C61#9130semidirect

Maximal subgroups

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

subgroupindex
C2×#168398142
#214541722
#214457962
C2×#168395092
C2×#168395072
#214437022
C61×#12962
#913061