Finite Group Databasebeta

← #29576225

Subgroups — #29576225

Order 15616.

578 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839964C211yesmaximal, characteristic
2C2×#16839841C211yesmaximal, characteristic
3#21445816C211yesmaximal, characteristic
4C2×#16839508C211yesmaximal, characteristic, complemented
5#21443702C211yesmaximal, characteristic, complemented
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1990C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C22×#11758189—21no—
10C2×C4×D244C2211yescharacteristic
11#16839964—22no—
12#16839964C414yescomplemented
13#16839841—22no—
14#16839841—22no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519701—21no—
19C2×#14519697—21no—
20C2×#14519689—21no—
21#16839524—21no—
22#16839508—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4×C8×C61C2211yescharacteristic
25C61×#384C2211yescharacteristic
26C61×#340—21no—
27C61×#340—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758201—24no—
31C2×#11758201—42no—
32C2×#11758201—42no—
33C2×#11758189—24no—
34C2×#11758189—42no—
35C2×#11758189—42no—
36C22×#92418—21no—
37C22×#92418—21no—
38C22×#92418—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244C2×C412yes—
42C4×D244D412yes—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758198—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418C2×C412yes—
50C4⋊#92418D412yes—
51#14519701—24no—
52#14519697—42no—
53#14519689—24no—
54C22×Q8×C61—21no—
55C22×C8×C61D411yescharacteristic
56C22×C8×C61D411yescharacteristic
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61C2×C412yes—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4×C8×C61—21no—
68C4×C8×C61—21no—
69C23×D61—21no—
70C2×Q8×C61—22no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×Dic61—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244C22⋊C412yes—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61SD1612yescomplemented
100C4⋊C4×C61—22no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—81no—
109C42×C61C22×C411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113#11758201—48no—
114#11758198—22no—
115#11758198—22no—
116C4⋊Dic61—21no—
117C4⋊Dic61C22⋊C412yes—
118C2×#92418—22no—
119C2×#92418—22no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127#11758189—48no—
128C23×C61#12111yescharacteristic
129C22×D61—22no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136Q8×C61—42no—
137Q8×C61—42no—
138Q8×C61—81no—
139Q8×C61—81no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—42no—
143C2×C4×C61—81no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61C4×D411yescharacteristic
151C2×C4×C61#12011yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×C4×C61C2×SD1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C2×C4×C61#13711yescharacteristic
162C2×Dic61—22no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165D244—22no—
166D244—22no—
167D244—41no—
168D244—41no—
169C4×D61—42no—
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—42no—
173C8×C61—22no—
174C8×C61—41no—
175#92418—42no—
176#92418—42no—
177#92418—81no—
178#9225—611nomaximal, Sylow
179C22×C61#38611yescharacteristic
180C22×C61#46111yescharacteristic
181C22×C61#46311yescharacteristic
182C22×C61#46811yescharacteristic
183C22×C61#46911yescharacteristic
184C22×C61#47111yescharacteristic
185C22×C61#47311yescharacteristic
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—42no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—82no—
196C4×C61—161no—
197C4×C61#41711yescharacteristic
198C4×C61#41811yescharacteristic
199C4×C61C4×SD1611yescharacteristic
200C4×C61#44011yescharacteristic
201C4×C61#45011yescharacteristic
202C4×C61#45211yescharacteristic
203C4×C61#46811yescharacteristic
204C4×C61#46911yescharacteristic
205Dic61—42no—
206C2×#461—611no—
207C2×#436—611no—
208#1990D6111yescharacteristic, complemented
209#1802—611no—
210C2×#332—611no—
211#1296—611no—
212#1277—611no—
213C2×C61#169111yescharacteristic
214C2×C61#169311yescharacteristic
215C2×C61#169911yescharacteristic
216C2×C61#170111yescharacteristic
217C2×C61#187711yescharacteristic
218C2×C61#189511yescharacteristic
219C2×C61#190811yescharacteristic
220D61—82no—
221C22×SD16—1221no—
222C22×M16—1221no—
223C2×C4⋊Q8C2×D6111yescharacteristic
224C2×C4×D4—611no—
225#461—614no—
226#461—1222no—
227#436—1222no—
228#436—1222no—
229C2×C4⋊C8—611no—
230C2×C4⋊C8—611no—
231C2×C4⋊C8—611no—
232C2×#103—1221no—
233C2×#102—1221no—
234C2×C22⋊C8—1221no—
235C2×C4×C8C2×D6111yescharacteristic
236#384C2×D6111yescharacteristic
237#340—21no—
238#340—21no—
239#340—1221no—
240#332—1222no—
241C61#922511yescharacteristic, complemented, Sylow
242C22×Q8—21no—
243C22×D4—611no—
244C23×C4—1221no—
245C2×SD16—1224no—
246C2×SD16—2442no—
247C2×SD16—2442no—
248C2×M16—1224no—
249C2×M16—2442no—
250C2×M16—2442no—
251C22×C8—1221no—
252C22×C8—1221no—
253C22×C8—1221no—
254C22×C8C22⋊D6111yescharacteristic
255C22×C8C22⋊D6111yescharacteristic
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8C4×D6112yes—
260C4×D4—612no—
261C4×D4—612no—
262C4×D4—1221no—
263C4×D4—1221no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—611no—
270C2×C22⋊C4—1221no—
271C2×C42C22×D6111yescharacteristic
272C4⋊C8—612no—
273C4⋊C8—612no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278#103—1224no—
279#102—2442no—
280C22⋊C8—1224no—
281C4×C8—21no—
282C4×C8—21no—
283C24—1221no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—612no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—1221no—
299C22×C4—1222no—
300C22×C4—1222no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4D4×D6111yescharacteristic
306C22×C4#1175822411yescharacteristic
307C22×C4C2×C22⋊D6111yescharacteristic
308SD16—2448no—
309M16—2448no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—1222no—
316C2×C8—1222no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8#1175820112yescomplemented
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C4⋊C4—612no—
335C4⋊C4—1221no—
336C22⋊C4—1222no—
337C22⋊C4—1222no—
338C42C2×C4×D6111yescharacteristic
339C42#1175822211yescharacteristic
340C42D4×D6111yescharacteristic
341C42D4×D6111yescharacteristic
342C23—1222no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23#1451974811yescharacteristic
350Q8—42no—
351Q8—42no—
352Q8—81no—
353Q8—81no—
354D4—1222no—
355D4—1222no—
356D4—2441no—
357D4—2441no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—1222no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4C22⋊C4×D6111yescharacteristic
374C2×C4#1451973711yescharacteristic
375C2×C4C4×C22⋊D6111yescharacteristic
376C2×C4#1451974511yescharacteristic
377C2×C4#1451975011yescharacteristic
378C2×C4#1451975911yescharacteristic
379C2×C4C2×#1175820111yescharacteristic
380C2×C4#1451979711yescharacteristic
381C2×C4#1451980111yescharacteristic
382C2×C4#1451980111yescharacteristic
383C2×C4#1451980211yescharacteristic
384C2×C4#1451980411yescharacteristic
385C2×C4#1451980611yescharacteristic
386C2×C4#1451980811yescharacteristic
387C8—22no—
388C8—41no—
389C8—4881no—
390C8—2442no—
391C8—2442no—
392C22—4881no—
393C22—4881no—
394C22—4881no—
395C22—4881no—
396C22—2442no—
397C22—2442no—
398C22—2442no—
399C22#1683963811yescharacteristic
400C22#1683996411yescharacteristic
401C22#1683997411yescharacteristic
402C22#1684000511yescharacteristic
403C22#1684001211yescharacteristic
404C22#1684002211yescharacteristic
405C22#1684003411yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—161no—
410C4—2442no—
411C4#1683976011yescharacteristic
412C4#1683976511yescharacteristic
413C4C4×#1175820111yescharacteristic
414C4#1683986011yescharacteristic
415C4#1683991211yescharacteristic
416C4#1683992211yescharacteristic
417C4#1684000711yescharacteristic
418C4#1684001411yescharacteristic
419C2—4882no—
420C2#2144531511yescharacteristic
421C2#2144532911yescharacteristic
422C2#2144536311yescharacteristic
423C2#2144537711yescharacteristic
424C2#2144615611yescharacteristic
425C2#2144625411yescharacteristic
426C2#2144633711yescharacteristic
subgroupG/H
centerC23#14519748
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1990C2
socleC23×C61#121
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1990D61
hypocenterC61#9225
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#16839508C2semidirect
5. #21443702C2semidirect
6. #21443654C2semidirect
7. C61×#1990C2semidirect
12. #16839964C4semidirect
99. C2×C8×C61SD16semidirect
208. #1990D61semidirect
241. C61#9225semidirect
324. C2×C8#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×#168399642
C2×#168398412
#214458162
C2×#168395082
#214437022
#214436542
C61×#19902
#922561