Finite Group Databasebeta

← #29574624

Subgroups — #29574624

Order 15616.

560 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839889C211yesmaximal, characteristic, complemented
2C2×C4×#11758190C211yesmaximal, characteristic
3#21446612C211yesmaximal, characteristic
4C2×#16839492C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic
6#21443646C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C22×#11758190C411yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839889—22no—
12#16839889—22no—
13C4×#11758190—22no—
14C4×#11758190—22no—
15C2×#14519709C411yescharacteristic
16C2×#14519706—21no—
17C2×#14519702C411yescharacteristic
18C2×#14519699C411yescharacteristic
19C2×#14519689—21no—
20C2×#14519689—21no—
21C2×#14519687—21no—
22C2×C4×#92418C2211yescharacteristic
23C2×C4×#92418C2211yescharacteristic
24#16839492—22no—
25#16839489—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4×C8×C61C2211yescharacteristic
29C22×Dic122C2×C411yescharacteristic
30C22×D244C2×C411yescharacteristic
31C22×C4×D61—21no—
32C2×#11758190—22no—
33C2×#11758190—22no—
34C2×#11758190—22no—
35C22×#92418—21no—
36C22×#92418D411yescharacteristic
37C22×#92418D411yescharacteristic
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122D412yes—
41C4×Dic122D412yes—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—21no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
51#14519709—22no—
52#14519706—24no—
53#14519702—22no—
54#14519699—22no—
55#14519689—42no—
56#14519689—42no—
57#14519687—24no—
58C4×#92418—21no—
59C4×#92418—21no—
60C4×#92418—21no—
61C4×#92418—21no—
62C22×C8×C61—21no—
63C22×C8×C61—21no—
64C22×C8×C61C2×C411yescharacteristic
65C22×C8×C61C2×C411yescharacteristic
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D412yes—
71C4×C8×C61—21no—
72C4×C8×C61—21no—
73C23×D61—21no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244M1612yes—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122C22⋊C412yes—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—22no—
102C2×C8×C61—21no—
103C2×C8×C61—21no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61M1612yes—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61#4111yescharacteristic
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61C22⋊C412yes—
120#11758196—22no—
121#11758196—22no—
122C4×Dic61—22no—
123C4×Dic61—22no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—22no—
127C2×#92418—21no—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418SD1612yescomplemented
133#11758190—28no—
134C23×C61C4×D411yescharacteristic
135C22×D61—22no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61C4×D411yescharacteristic
146C2×C4×C61#12011yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12311yescharacteristic
150C2×C4×C61C2×M1611yescharacteristic
151C2×C4×C61C2×M1611yescharacteristic
152C2×C4×C61#13111yescharacteristic
153C2×C4×C61#13111yescharacteristic
154C2×C4×C61C2×SD1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61#13711yescharacteristic
158C2×Dic61—22no—
159C2×Dic61—22no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167D244—22no—
168D244—22no—
169D244—41no—
170D244—41no—
171C4×D61—81no—
172C4×D61—81no—
173C4×D61—81no—
174C4×D61—81no—
175Dic122—22no—
176Dic122—22no—
177Dic122—41no—
178Dic122—41no—
179C8×C61—22no—
180C8×C61—41no—
181C8×C61—42no—
182C8×C61—81no—
183#92418—22no—
184#92418—42no—
185#92418—41no—
186#8952—611nomaximal, Sylow
187C22×C61#38611yescharacteristic
188C22×C61#43511yescharacteristic
189C22×C61#43611yescharacteristic
190C22×C61C4×SD1611yescharacteristic
191C22×C61#44011yescharacteristic
192C22×C61#44311yescharacteristic
193C22×C61#44411yescharacteristic
194C2×D61—42no—
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61#40711yescharacteristic
204C4×C61#40811yescharacteristic
205C4×C61#43511yescharacteristic
206C4×C61#43611yescharacteristic
207C4×C61#44811yescharacteristic
208C4×C61#44911yescharacteristic
209C4×C61#46011yescharacteristic
210C4×C61#46411yescharacteristic
211Dic61—42no—
212Dic61—42no—
213Dic61—81no—
214C2×#446—611no—
215C2×C4×SD16—611no—
216#1954—611no—
217C2×Q8⋊C8—611no—
218C2×D4⋊C8—611no—
219#1277D6111yescharacteristic, complemented
220#1273—611no—
221C2×C61#158211yescharacteristic
222C2×C61#158511yescharacteristic
223C2×C61#159011yescharacteristic
224C2×C61#159211yescharacteristic
225C2×C61#187011yescharacteristic
226C2×C61#187611yescharacteristic
227C2×C61#188011yescharacteristic
228D61—82no—
229C22×SD16—611no—
230C2×C4×Q8—611no—
231C2×C4×D4—611no—
232#446—1222no—
233#446—1222no—
234C4×SD16—1222no—
235C4×SD16—1222no—
236C2×#106—611no—
237C2×C4⋊C8—1221no—
238C2×C4⋊C8C2×D6111yescharacteristic
239C2×C4⋊C8C2×D6111yescharacteristic
240C2×#103—611no—
241C2×#102—611no—
242C2×C22⋊C8—1221no—
243C2×C22⋊C8—1221no—
244C2×#97—1221no—
245C2×C4×C8—611no—
246C2×C4×C8—611no—
247C2×C4×C8C2×D6111yescharacteristic
248Q8⋊C8—1222no—
249D4⋊C8—1222no—
250C61#895211yescharacteristic, complemented, Sylow
251C22×Q8—611no—
252C22×D4—611no—
253C23×C4—1221no—
254C2×SD16—1222no—
255C2×SD16—1222no—
256C2×SD16—1222no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—611no—
260C22×C8—611no—
261C22×C8—1221no—
262C22×C8C4×D6111yescharacteristic
263C22×C8C4×D6111yescharacteristic
264C4×Q8—612no—
265C4×Q8—612no—
266C4×Q8—1221no—
267C4×Q8—1221no—
268C4×D4—1221no—
269C4×D4—1221no—
270C4×D4—1221no—
271C4×D4—1221no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C42—1221no—
277C2×C42C22×D6111yescharacteristic
278#106—1222no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—1224no—
283C4⋊C8D24412yes—
284#103—1222no—
285#102—1222no—
286C22⋊C8—2442no—
287C22⋊C8—2442no—
288#97—1224no—
289C4×C8—21no—
290C4×C8—21no—
291C4×C8—1221no—
292C4×C8—1221no—
293C4×C8—1221no—
294C4×C8—1221no—
295C24—1221no—
296C2×Q8—612no—
297C2×Q8—1221no—
298C2×Q8—1221no—
299C2×Q8—1221no—
300C2×Q8—1221no—
301C2×Q8—1221no—
302C2×D4—612no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4C2×C4×D6111yescharacteristic
318C22×C4D4×D6111yescharacteristic
319C22×C4#1175822611yescharacteristic
320SD16—1228no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—22no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—612no—
333C2×C8—1221no—
334C2×C8—1221no—
335C2×C8—1222no—
336C2×C8—1221no—
337C2×C8—1221no—
338C2×C8—1221no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8#1175818912yes—
342C4⋊C4—612no—
343C4⋊C4—1221no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C42—1222no—
351C42—1222no—
352C42C2×D24411yescharacteristic
353C42#1175822211yescharacteristic
354C42D4×D6111yescharacteristic
355C42D4×D6111yescharacteristic
356C23—1222no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23#1451973911yescharacteristic
364Q8—1222no—
365Q8—1222no—
366Q8—2441no—
367Q8—2441no—
368D4—1222no—
369D4—1222no—
370D4—2441no—
371D4—2441no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4C22⋊C4×D6111yescharacteristic
388C2×C4C4×D24411yescharacteristic
389C2×C4#1451974711yescharacteristic
390C2×C4#1451975011yescharacteristic
391C2×C4#1451975211yescharacteristic
392C2×C4#1451976211yescharacteristic
393C2×C4M16×D6111yescharacteristic
394C2×C4C2×#1175818911yescharacteristic
395C2×C4#1451978311yescharacteristic
396C2×C4#1451978511yescharacteristic
397C2×C4SD16×D6111yescharacteristic
398C2×C4#1451979811yescharacteristic
399C2×C4#1451980111yescharacteristic
400C2×C4#1451980911yescharacteristic
401C8—22no—
402C8—41no—
403C8—42no—
404C8—81no—
405C8—1222no—
406C8—2442no—
407C8—2441no—
408C22—4881no—
409C22—4881no—
410C22—4881no—
411C22—4881no—
412C22—2442no—
413C22—2442no—
414C22—2442no—
415C22#1683964011yescharacteristic
416C22#1683983211yescharacteristic
417C22#1683983911yescharacteristic
418C22#1683984911yescharacteristic
419C22#1683986111yescharacteristic
420C22#1683987811yescharacteristic
421C22#1683988311yescharacteristic
422C4—21no—
423C4—21no—
424C4—4881no—
425C4—2442no—
426C4—2442no—
427C4#1683972411yescharacteristic
428C4#1683972711yescharacteristic
429C4#1683983511yescharacteristic
430C4#1683984111yescharacteristic
431C4#1683990211yescharacteristic
432C4#1683990811yescharacteristic
433C4#1683996111yescharacteristic
434C4#1683998711yescharacteristic
435C2—4882no—
436C2#2144465411yescharacteristic
437C2#2144467511yescharacteristic
438C2#2144470811yescharacteristic
439C2#2144472011yescharacteristic
440C2#2144611511yescharacteristic
441C2#2144614711yescharacteristic
442C2#2144617511yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#8952
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
1. C2×#16839889C2semidirect
4. C2×#16839492C2semidirect
6. #21443646C2semidirect
7. C61×#1277C2semidirect
132. C2×#92418SD16semidirect
219. #1277D61semidirect
250. C61#8952semidirect

Maximal subgroups

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

subgroupindex
C2×#168398892
C2×C4×#117581902
#214466122
C2×#168394922
C2×#168394892
#214436462
C61×#12772
#895261