Finite Group Databasebeta

← #29576237

Subgroups — #29576237

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×#16840043C211yesmaximal, characteristic
2C2×#16839839C211yesmaximal, characteristic
3#21446620C211yesmaximal, characteristic, complemented
4#21445816C211yesmaximal, characteristic
5C2×#16839509C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519777C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16840043—22no—
12#16840043C414yescomplemented
13#16839839—22no—
14#16839839—22no—
15C2×#14519711—21no—
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519700—21no—
18C2×#14519700—21no—
19C2×#14519699—21no—
20C2×#14519697—21no—
21C2×#14519689—21no—
22C2×C4×#92418C2211yescharacteristic
23#16839524—21no—
24#16839509—22no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#384C2211yescharacteristic
28C22×Dic122—21no—
29C22×D244D411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758189—24no—
32C2×#11758189—42no—
33C2×#11758189—42no—
34C22×#92418—21no—
35C22×#92418D411yescharacteristic
36C22×#92418D411yescharacteristic
37#14519777—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777C2×C412yes—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244C2×C412yes—
44C4×D244D412yes—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61D411yescharacteristic
48C2×#11758198—21no—
49#14519711—24no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52#14519700—42no—
53#14519700—42no—
54#14519699—24no—
55#14519697—42no—
56#14519689—24no—
57C4×#92418—21no—
58C4×#92418—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61C2×C412yes—
68C4⋊C8×C61D412yes—
69C23×D61—21no—
70C22×C4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—41no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244C22⋊C412yes—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×Dic122—22no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—81no—
105C42×C61C22×C411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109#11758198—22no—
110#11758198—22no—
111C4⋊Dic61—21no—
112C4⋊Dic61—22no—
113C4⋊Dic61—22no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61C22⋊C412yes—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—21no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418D812yes—
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—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61#13711yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—42no—
158C2×Dic61—81no—
159C2×Dic61—81no—
160D244—22no—
161D244—22no—
162D244—41no—
163D244—41no—
164C4×D61—42no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—42no—
168Dic122—42no—
169Dic122—42no—
170Dic122—81no—
171Dic122—81no—
172C8×C61—42no—
173C8×C61—42no—
174#92418—22no—
175#92418—41no—
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—161no—
195C4×C61#41711yescharacteristic
196C4×C61#41911yescharacteristic
197C4×C61C4×D811yescharacteristic
198C4×C61#44211yescharacteristic
199C4×C61#44711yescharacteristic
200C4×C61#44911yescharacteristic
201C4×C61#46811yescharacteristic
202C4×C61#47011yescharacteristic
203Dic61—42no—
204Dic61—82no—
205C2×#474—611no—
206C2×#436—611no—
207#1956—611no—
208#1802—611no—
209C2×#332—611no—
210#1296D6111yescharacteristic, complemented
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⋊Q8—611no—
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⋊C8C2×D6111yescharacteristic
230C2×C4⋊C8C2×D6111yescharacteristic
231C2×#103—1221no—
232C2×#103—1221no—
233C2×#102—1221no—
234C2×#102—1221no—
235C2×C22⋊C8—1221no—
236C2×C4×C8—611no—
237#384C2×D6111yescharacteristic
238#340—1221no—
239#332—1222no—
240C61#922711yescharacteristic, complemented, Sylow
241C22×Q8—1221no—
242C22×D4—611no—
243C23×C4—1221no—
244C2×M16—1224no—
245C2×M16—2442no—
246C2×M16—2442no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—611no—
250C22×C8—611no—
251C22×C8—1221no—
252C4⋊Q8—612no—
253C4⋊Q8—1221no—
254C4⋊Q8—1221no—
255C4⋊Q8—1221no—
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—611no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C42C22×D6111yescharacteristic
268#107—1224no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8C4×D6112yes—
274C4⋊C8D24412yes—
275#103—2442no—
276#103—2442no—
277#102—1224no—
278#102—2442no—
279C22⋊C8—1224no—
280C4×C8—1221no—
281C4×C8—1221no—
282C24—1221no—
283C2×Q8—1222no—
284C2×Q8—2441no—
285C2×Q8—2441no—
286C2×Q8—2441no—
287C2×Q8—2441no—
288C2×Q8—2441no—
289C2×D4—612no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C22×C4—41no—
296C22×C4—1221no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4#1175822211yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4D4×D6111yescharacteristic
307M16—2448no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—612no—
315C2×C8—1221no—
316C2×C8—1221no—
317C2×C8—1221no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—81no—
328C4⋊C4—612no—
329C4⋊C4—1221no—
330C4⋊C4—1222no—
331C4⋊C4—1222no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C22⋊C4—1222no—
335C22⋊C4—1222no—
336C42C2×C4×D6111yescharacteristic
337C42C2×D24411yescharacteristic
338C42D4×D6111yescharacteristic
339C42#1175822611yescharacteristic
340C23—1222no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23#1451975011yescharacteristic
348Q8—4881no—
349Q8—4881no—
350Q8—2442no—
351Q8—2442no—
352D4—1222no—
353D4—1222no—
354D4—2441no—
355D4—2441no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—1222no—
362C2×C4—4881no—
363C2×C4—4881no—
364C2×C4—2442no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4C22⋊C4×D6111yescharacteristic
372C2×C4#1451973911yescharacteristic
373C2×C4C4×D24411yescharacteristic
374C2×C4#1451974711yescharacteristic
375C2×C4#1451975211yescharacteristic
376C2×C4#1451976211yescharacteristic
377C2×C4D8×D6111yescharacteristic
378C2×C4#1451980011yescharacteristic
379C2×C4#1451980111yescharacteristic
380C2×C4#1451980411yescharacteristic
381C2×C4#1451980411yescharacteristic
382C2×C4#1451980611yescharacteristic
383C2×C4#1451980611yescharacteristic
384C2×C4#1451980911yescharacteristic
385C8—42no—
386C8—42no—
387C8—1222no—
388C8—4881no—
389C8—2441no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—2442no—
395C22—2442no—
396C22—2442no—
397C22#1683964011yescharacteristic
398C22#1683995611yescharacteristic
399C22#1683998011yescharacteristic
400C22#1684000711yescharacteristic
401C22#1684001911yescharacteristic
402C22#1684002411yescharacteristic
403C22#1684003611yescharacteristic
404C4—21no—
405C4—21no—
406C4—161no—
407C4—4882no—
408C4—2442no—
409C4#1683976011yescharacteristic
410C4#1683976911yescharacteristic
411C4#1683984411yescharacteristic
412C4#1683987311yescharacteristic
413C4#1683989711yescharacteristic
414C4#1683991011yescharacteristic
415C4#1684000911yescharacteristic
416C4#1684002111yescharacteristic
417C2—4882no—
418C2#2144528311yescharacteristic
419C2#2144530711yescharacteristic
420C2#2144536911yescharacteristic
421C2#2144539711yescharacteristic
422C2#2144616811yescharacteristic
423C2#2144625111yescharacteristic
424C2#2144633511yescharacteristic
subgroupG/H
centerC23#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#9227
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #21446620C2semidirect
5. C2×#16839509C2semidirect
6. #21443653C2semidirect
7. C61×#1296C2semidirect
12. #16840043C4semidirect
210. #1296D61semidirect
240. C61#9227semidirect

Maximal subgroups

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

subgroupindex
C2×#168400432
C2×#168398392
#214466202
#214458162
C2×#168395092
#214436532
C61×#12962
#922761