Finite Group Databasebeta

← #29576239

Subgroups — #29576239

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840039C211yesmaximal, characteristic
2C2×#16839841C211yesmaximal, characteristic
3#21445816C211yesmaximal, characteristic
4C2×#16839508C211yesmaximal, characteristic, complemented
5#21443702C211yesmaximal, characteristic, complemented
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1956C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×C4×D244C2211yescharacteristic
10#16840039—22no—
11#16840039C414yescomplemented
12#16839841—22no—
13#16839841—22no—
14C2×#14519710—21no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519697—21no—
19C2×#14519697—21no—
20C2×#14519689—21no—
21#16839524—21no—
22#16839508—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×#103×C61—21no—
25C2×#103×C61—21no—
26C2×C4×C8×C61C2211yescharacteristic
27C61×#384C2211yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758189—24no—
31C2×#11758189—42no—
32C2×#11758189—42no—
33C22×#92418—21no—
34C22×#92418—21no—
35C22×#92418—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244C2×C412yes—
39C4×D244D412yes—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758198—21no—
42#14519710—24no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418C2×C412yes—
48C4⋊#92418D412yes—
49#14519697—24no—
50#14519697—42no—
51#14519689—24no—
52C22×Q8×C61—21no—
53C22×C8×C61D411yescharacteristic
54C22×C8×C61D411yescharacteristic
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61C2×C412yes—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C42×C61C2311yescharacteristic
65#103×C61—42no—
66#103×C61—42no—
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×C61D812yes—
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#11758198—22no—
114#11758198—22no—
115C4⋊Dic61—21no—
116C4⋊Dic61C22⋊C412yes—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126#11758189—48no—
127C23×C61#12111yescharacteristic
128C22×D61—22no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135Q8×C61—42no—
136Q8×C61—42no—
137Q8×C61—81no—
138Q8×C61—81no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—42no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12311yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61#13711yescharacteristic
159C2×C4×C61#13711yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C2×Dic61—22no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164D244—22no—
165D244—22no—
166D244—41no—
167D244—41no—
168C4×D61—42no—
169C4×D61—42no—
170C4×D61—42no—
171C4×D61—42no—
172C8×C61—22no—
173C8×C61—41no—
174#92418—42no—
175#92418—42no—
176#92418—81no—
177#9227—611nomaximal, Sylow
178C22×C61#38611yescharacteristic
179C22×C61#45911yescharacteristic
180C22×C61#46311yescharacteristic
181C22×C61#46811yescharacteristic
182C22×C61#47011yescharacteristic
183C22×C61#47111yescharacteristic
184C22×C61#47311yescharacteristic
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—82no—
195C4×C61—161no—
196C4×C61#41711yescharacteristic
197C4×C61#41911yescharacteristic
198C4×C61C4×D811yescharacteristic
199C4×C61#44211yescharacteristic
200C4×C61#44711yescharacteristic
201C4×C61#44911yescharacteristic
202C4×C61#46811yescharacteristic
203C4×C61#47011yescharacteristic
204Dic61—42no—
205C2×#474—611no—
206C2×#436—611no—
207#1956D6111yescharacteristic, complemented
208#1802—611no—
209C2×#332—611no—
210#1296—611no—
211#1277—611no—
212C2×C61#168511yescharacteristic
213C2×C61#168911yescharacteristic
214C2×C61#169911yescharacteristic
215C2×C61#170311yescharacteristic
216C2×C61#187911yescharacteristic
217C2×C61#189411yescharacteristic
218C2×C61#190811yescharacteristic
219D61—82no—
220C22×M16—1221no—
221C2×C4⋊Q8C2×D6111yescharacteristic
222C2×C4×D4—611no—
223#474—614no—
224#474—1222no—
225#436—1222no—
226#436—1222no—
227C2×#107—1221no—
228C2×C4⋊C8—611no—
229C2×C4⋊C8—611no—
230C2×C4⋊C8—611no—
231C2×#103—21no—
232C2×#103—21no—
233C2×#102—1221no—
234C2×#102—1221no—
235C2×C22⋊C8—1221no—
236C2×C4×C8C2×D6111yescharacteristic
237#384C2×D6111yescharacteristic
238#340—1221no—
239#332—1222no—
240C61#922711yescharacteristic, complemented, Sylow
241C22×Q8—21no—
242C22×D4—611no—
243C23×C4—1221no—
244C2×M16—1224no—
245C2×M16—2442no—
246C2×M16—2442no—
247C22×C8—1221no—
248C22×C8—1221no—
249C22×C8—1221no—
250C22×C8C22⋊D6111yescharacteristic
251C22×C8C22⋊D6111yescharacteristic
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8C4×D6112yes—
256C4×D4—612no—
257C4×D4—612no—
258C4×D4—1221no—
259C4×D4—1221no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—611no—
266C2×C22⋊C4—1221no—
267C2×C42C22×D6111yescharacteristic
268#107—1224no—
269C4⋊C8—612no—
270C4⋊C8—612no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275#103—42no—
276#103—42no—
277#102—1224no—
278#102—2442no—
279C22⋊C8—1224no—
280C4×C8—21no—
281C4×C8—21no—
282C24—1221no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—612no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—1221no—
298C22×C4—1222no—
299C22×C4—1222no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4D4×D6111yescharacteristic
305C22×C4#1175822411yescharacteristic
306C22×C4C2×C22⋊D6111yescharacteristic
307M16—2448no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—2441no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8#1175819912yes—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—81no—
332C4⋊C4—612no—
333C4⋊C4—1221no—
334C22⋊C4—1222no—
335C22⋊C4—1222no—
336C42C2×C4×D6111yescharacteristic
337C42#1175822211yescharacteristic
338C42D4×D6111yescharacteristic
339C42D4×D6111yescharacteristic
340C23—1222no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23#1451974811yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—1222no—
353D4—1222no—
354D4—2441no—
355D4—2441no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—1222no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4C22⋊C4×D6111yescharacteristic
372C2×C4#1451973711yescharacteristic
373C2×C4C4×C22⋊D6111yescharacteristic
374C2×C4#1451974511yescharacteristic
375C2×C4#1451975011yescharacteristic
376C2×C4#1451975911yescharacteristic
377C2×C4C2×#1175819911yescharacteristic
378C2×C4#1451979711yescharacteristic
379C2×C4#1451980211yescharacteristic
380C2×C4#1451980311yescharacteristic
381C2×C4#1451980411yescharacteristic
382C2×C4#1451980611yescharacteristic
383C2×C4#1451980911yescharacteristic
384C2×C4#1451980911yescharacteristic
385C8—22no—
386C8—41no—
387C8—4881no—
388C8—2442no—
389C8—2442no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—2442no—
395C22—2442no—
396C22—2442no—
397C22#1683963811yescharacteristic
398C22#1683995411yescharacteristic
399C22#1683997411yescharacteristic
400C22#1684000511yescharacteristic
401C22#1684001711yescharacteristic
402C22#1684002211yescharacteristic
403C22#1684003411yescharacteristic
404C4—21no—
405C4—21no—
406C4—82no—
407C4—161no—
408C4—2442no—
409C4#1683976211yescharacteristic
410C4#1683976911yescharacteristic
411C4C4×#1175819911yescharacteristic
412C4#1683987211yescharacteristic
413C4#1683989511yescharacteristic
414C4#1683990511yescharacteristic
415C4#1684001111yescharacteristic
416C4#1684001911yescharacteristic
417C2—4882no—
418C2#2144528111yescharacteristic
419C2#2144530511yescharacteristic
420C2#2144536311yescharacteristic
421C2#2144539111yescharacteristic
422C2#2144617011yescharacteristic
423C2#2144624911yescharacteristic
424C2#2144633711yescharacteristic
subgroupG/H
centerC23#14519748
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1956C2
socleC23×C61#121
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1956D61
hypocenterC61#9227
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
4. C2×#16839508C2semidirect
5. #21443702C2semidirect
6. #21443654C2semidirect
7. C61×#1956C2semidirect
11. #16840039C4semidirect
207. #1956D61semidirect
240. C61#9227semidirect

Maximal subgroups

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

subgroupindex
C2×#168400392
C2×#168398412
#214458162
C2×#168395082
#214437022
#214436542
C61×#19562
#922761