Finite Group Databasebeta

← #29575615

Subgroups — #29575615

Order 15616.

626 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×#97×D61C211yesmaximal, characteristic
2#21454124C211yesmaximal, characteristic
3#21445582C211yesmaximal, characteristic
4C2×#16839504C211yesmaximal, characteristic, complemented
5#21443701C211yesmaximal, characteristic, complemented
6#21443701C211yesmaximal, characteristic, complemented
7C2×C61×#330C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×C42×D61C2211yescharacteristic
10C2×#14519689—21no—
11C2×#14519688C2211yescharacteristic
12C2×#14519688C2211yescharacteristic
13C2×#14519687—21no—
14#97×D61—22no—
15#97×D61—22no—
16#16839658C411yescharacteristic
17#16839658C411yescharacteristic
18#16839643—21no—
19#16839643—21no—
20#16839633—21no—
21#16839633—21no—
22#16839628C2211yescharacteristic
23#16839619C411yescharacteristic
24#16839619C411yescharacteristic
25#16839516—21no—
26#16839504—22no—
27C2×#125×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#330—22no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×#92418—21no—
35C22×#92418—21no—
36C2×C8×D61—24no—
37C2×C8×D61—24no—
38C2×C8×D61—24no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C42×D61—21no—
49C42×D61—21no—
50C42×D61—21no—
51C42×D61—21no—
52#14519689—24no—
53#14519688—21no—
54#14519688—21no—
55#14519688—21no—
56#14519688D412yes—
57#14519687—24no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66#125×C61—21no—
67#125×C61—21no—
68#125×C61—21no—
69#125×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75#97×C61—21no—
76#97×C61—21no—
77#97×C61—21no—
78#97×C61D412yes—
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—22no—
95C2×C4×D61—22no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
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—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61#4111yescharacteristic
119C42×C61#4111yescharacteristic
120#11758198—42no—
121#11758198—42no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124#11758196—42no—
125#11758196—42no—
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—
138C8×D61—216no—
139C23×C61C2×C22⋊C411yescharacteristic
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61#10112yes—
145C22×D61#10412yes—
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—21no—
172C2×Dic61—21no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
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#9121—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—22no—
202C2×D61—22no—
203C2×D61—22no—
204C2×D61#33014yescomplemented
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—41no—
215Dic61—41no—
216Dic61—81no—
217Dic61—81no—
218C22×#97—611no—
219#2851—611no—
220#1749—611no—
221C2×#330—611no—
222C2×#330D6111yescharacteristic, complemented
223#1295—611no—
224#1295—611no—
225C2×C61C2×#33011yescharacteristic
226C2×C61#152411yescharacteristic
227C2×C61#153111yescharacteristic
228C2×C61#153211yescharacteristic
229C2×C61#187111yescharacteristic
230C2×C61#189611yescharacteristic
231C2×C61#190111yescharacteristic
232D61—24no—
233C23×C8—1221no—
234C2×#125C2×D6111yescharacteristic
235C22×C42—611no—
236C2×C22⋊C8—1221no—
237C2×#97—611no—
238C2×#97—611no—
239C2×#97—1222no—
240C2×#97—1221no—
241C2×#97—1222no—
242C2×#97C2×D6111yescharacteristic
243C2×#97C2×D6111yescharacteristic
244#389—611no—
245#389—611no—
246#387—1221no—
247#387—1221no—
248#385—1221no—
249#385—1221no—
250#382—611no—
251#380—611no—
252#380—611no—
253#336—1221no—
254#330—22no—
255#330—1222no—
256C61#912111yescharacteristic, complemented, Sylow
257C23×C4—611no—
258C23×C4—611no—
259C23×C4—611no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—1224no—
263C22×C8—1224no—
264C22×C8—1224no—
265C22×C8—1221no—
266C22×C8—1221no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4—611no—
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—1224no—
295#97—1221no—
296#97—1221no—
297#97—1221no—
298#97C22⋊D6112yes—
299#95—1221no—
300#95—1221no—
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
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—12216no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—1222no—
338C2×C8—1222no—
339C2×C8—2441no—
340C2×C8—2441no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C4⋊C4—2442no—
352C4⋊C4—2442no—
353C22⋊C4—2442no—
354C22⋊C4—2442no—
355C42—1221no—
356C42—1221no—
357C42—1221no—
358C42—1221no—
359C42—1221no—
360C42—1221no—
361C42#1175822211yescharacteristic
362C42D4×D6111yescharacteristic
363C42#1175822411yescharacteristic
364C42C2×C22⋊D6111yescharacteristic
365C23—612no—
366C23—612no—
367C23—612no—
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—1224no—
387C2×C4—1224no—
388C2×C4—1221no—
389C2×C4—1221no—
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#1451973711yescharacteristic
407C2×C4C4×C22⋊D6111yescharacteristic
408C2×C4#1451974511yescharacteristic
409C2×C4#1451974811yescharacteristic
410C2×C4#1451975011yescharacteristic
411C2×C4#1451975911yescharacteristic
412C8—24no—
413C8—42no—
414C8—1224no—
415C8—2442no—
416C22—614no—
417C22—1222no—
418C22—1222no—
419C22—1222no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22#1683963811yescharacteristic
424C22#101×D6111yescharacteristic
425C22#1683974511yescharacteristic
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—4881no—
440C4—4881no—
441C4—2441no—
442C4—2441no—
443C2—1224no—
444C2#330×D6111yescharacteristic
445C2#2144440611yescharacteristic
446C2#2144443211yescharacteristic
447C2#2144443811yescharacteristic
448C2#2144611811yescharacteristic
449C2#2144625911yescharacteristic
450C2#2144628411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#330D61
hypocenterC61#9121
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
4. C2×#16839504C2semidirect
5. #21443701C2semidirect
6. #21443701C2semidirect
7. C2×C61×#330C2semidirect
204. C2×D61#330semidirect
222. C2×#330D61semidirect
256. C61#9121semidirect

Maximal subgroups

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

subgroupindex
C2×#97×D612
#214541242
#214455822
C2×#168395042
#214437012
C2×C61×#3302
#912161