Finite Group Databasebeta

← #29574623

Subgroups — #29574623

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×C4×#11758201C211yesmaximal, characteristic
2#21446613C211yesmaximal, characteristic
3C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic
5#21443653C211yesmaximal, characteristic, complemented
6#21443646C211yesmaximal, characteristic, complemented
7C2×C61×#446C211yesmaximal, characteristic, complemented
8C22×#11758201C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10C4×#11758201—22no—
11C4×#11758201—22no—
12C2×#14519708C411yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519701C411yescharacteristic
15C2×#14519697C411yescharacteristic
16C2×#14519689—21no—
17C2×#14519689—21no—
18C2×C4×#92418C2211yescharacteristic
19C2×C4×#92418C2211yescharacteristic
20Q8⋊#92418—22no—
21#16839489—22no—
22C2×C4×Q8×C61C2211yescharacteristic
23C61×#446—22no—
24C61×#446—22no—
25C2×C4⋊C8×C61—21no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×#97×C61—21no—
28C2×C4×C8×C61C2211yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758201—22no—
32C2×#11758201—22no—
33C2×#11758201—22no—
34C22×#92418—21no—
35C22×#92418—21no—
36C22×#92418C2×C411yescharacteristic
37C22×#92418C2×C411yescharacteristic
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758198—21no—
44#14519708—22no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47#14519701—22no—
48#14519697—22no—
49#14519689—42no—
50#14519689—42no—
51C4×#92418—21no—
52C4×#92418—21no—
53C4×#92418—21no—
54C4×#92418—21no—
55C22×Q8×C61C2×C411yescharacteristic
56C22×C8×C61—21no—
57C22×C8×C61D411yescharacteristic
58C22×C8×C61D411yescharacteristic
59C4×Q8×C61—21no—
60C4×Q8×C61—21no—
61C4×Q8×C61D412yes—
62C4×Q8×C61D412yes—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61C2×C411yescharacteristic
65C2×C42×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—24no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61D412yes—
70#97×C61—24no—
71C4×C8×C61—21no—
72C4×C8×C61—21no—
73C23×D61—21no—
74C2×Q8×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61C22⋊C412yes—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C22×Dic61—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244M1612yes—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
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×C61SD1612yescomplemented
107C4⋊C4×C61—21no—
108C4⋊C4×C61—22no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61C22⋊C412yes—
111C42×C61—22no—
112C42×C61—22no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117#11758201—28no—
118#11758198—41no—
119#11758198—41no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—22no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418M1612yes—
134C23×C61C4×D411yescharacteristic
135C22×D61—22no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142Q8×C61—22no—
143Q8×C61—22no—
144Q8×C61—41no—
145Q8×C61—41no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×C4×C61C2×M1611yescharacteristic
161C2×C4×C61C2×M1611yescharacteristic
162C2×C4×C61#13111yescharacteristic
163C2×C4×C61#13111yescharacteristic
164C2×C4×C61C2×SD1611yescharacteristic
165C2×C4×C61#13511yescharacteristic
166C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C61#13711yescharacteristic
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171D244—22no—
172D244—22no—
173D244—41no—
174D244—41no—
175C4×D61—81no—
176C4×D61—81no—
177C4×D61—81no—
178C4×D61—81no—
179C8×C61—22no—
180C8×C61—41no—
181C8×C61—42no—
182#92418—22no—
183#92418—42no—
184#92418—41no—
185#92418—81no—
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—42no—
204C4×C61—42no—
205C4×C61#40711yescharacteristic
206C4×C61#40811yescharacteristic
207C4×C61#43511yescharacteristic
208C4×C61#43611yescharacteristic
209C4×C61#44811yescharacteristic
210C4×C61#44911yescharacteristic
211C4×C61#46011yescharacteristic
212C4×C61#46411yescharacteristic
213Dic61—81no—
214C2×#446D6111yescharacteristic, complemented
215C2×C4×SD16—611no—
216#1954—611no—
217C2×Q8⋊C8—611no—
218C2×D4⋊C8—611no—
219#1277—611no—
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×Q8C2×D6111yescharacteristic
231C2×C4×D4—611no—
232#446—22no—
233#446—22no—
234C4×SD16—1222no—
235C4×SD16—1222no—
236C2×#106—611no—
237C2×C4⋊C8—21no—
238C2×C4⋊C8—611no—
239C2×C4⋊C8C2×D6111yescharacteristic
240C2×#103—611no—
241C2×#102—611no—
242C2×C22⋊C8—1221no—
243C2×C22⋊C8—1221no—
244C2×#97—21no—
245C2×C4×C8—611no—
246C2×C4×C8—611no—
247C2×C4×C8C2×D6111yescharacteristic
248Q8⋊C8—1222no—
249D4⋊C8—1222no—
250C61#895211yescharacteristic, complemented, Sylow
251C22×Q8C4×D6111yescharacteristic
252C22×D4—611no—
253C23×C4—1221no—
254C2×SD16—1222no—
255C2×SD16—1222no—
256C2×SD16—1222no—
257C22×C8—21no—
258C22×C8—611no—
259C22×C8—611no—
260C22×C8—1221no—
261C22×C8—1221no—
262C22×C8C22⋊D6111yescharacteristic
263C22×C8C22⋊D6111yescharacteristic
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8D24412yes—
267C4×Q8C22⋊D6112yes—
268C4×D4—1221no—
269C4×D4—1221no—
270C4×D4—1221no—
271C4×D4—1221no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4C4×D6111yescharacteristic
275C2×C22⋊C4—1221no—
276C2×C42—21no—
277C2×C42C22×D6111yescharacteristic
278#106—1222no—
279C4⋊C8—24no—
280C4⋊C8—21no—
281C4⋊C8—1221no—
282C4⋊C8—1221no—
283C4⋊C8C22⋊D6112yes—
284#103—1222no—
285#102—1222no—
286C22⋊C8—2442no—
287C22⋊C8—2442no—
288#97—24no—
289C4×C8—21no—
290C4×C8—21no—
291C4×C8—1221no—
292C4×C8—1221no—
293C4×C8—1221no—
294C4×C8—1221no—
295C24—1221no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8#1175819812yes—
302C2×D4—612no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1221no—
308C22×C4—21no—
309C22×C4—21no—
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×C4#1175822211yescharacteristic
319C22×C4C2×C22⋊D6111yescharacteristic
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—612no—
330C2×C8—1221no—
331C2×C8—1221no—
332C2×C8—1222no—
333C2×C8—1221no—
334C2×C8—1221no—
335C2×C8—1221no—
336C2×C8—2441no—
337C2×C8—2441no—
338C2×C8—2441no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8#1175820112yescomplemented
342C4⋊C4—21no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4#1175819812yes—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C42—22no—
351C42—22no—
352C42C2×D24411yescharacteristic
353C42#1175822211yescharacteristic
354C42C2×C22⋊D6111yescharacteristic
355C42C2×C22⋊D6111yescharacteristic
356C23—1222no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23C4×C22⋊D6111yescharacteristic
364Q8—22no—
365Q8—22no—
366Q8—41no—
367Q8—41no—
368D4—1222no—
369D4—1222no—
370D4—2441no—
371D4—2441no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—4881no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4C2×#1175819811yescharacteristic
388C2×C4C4×C22⋊D6111yescharacteristic
389C2×C4#1451974611yescharacteristic
390C2×C4#1451975111yescharacteristic
391C2×C4#1451975111yescharacteristic
392C2×C4#1451976011yescharacteristic
393C2×C4M16×D6111yescharacteristic
394C2×C4M16×D6111yescharacteristic
395C2×C4#1451978511yescharacteristic
396C2×C4#1451978511yescharacteristic
397C2×C4C2×#1175820111yescharacteristic
398C2×C4#1451979711yescharacteristic
399C2×C4#1451980211yescharacteristic
400C2×C4#1451980811yescharacteristic
401C8—22no—
402C8—41no—
403C8—42no—
404C8—1222no—
405C8—4881no—
406C8—2442no—
407C8—2441no—
408C22—4881no—
409C22—4881no—
410C22—4881no—
411C22—4881no—
412C22—2442no—
413C22—2442no—
414C22—2442no—
415C22#1683964111yescharacteristic
416C22#1683983111yescharacteristic
417C22#1683983811yescharacteristic
418C22C4×#1175820111yescharacteristic
419C22#1683986011yescharacteristic
420C22#1683987711yescharacteristic
421C22#1683988211yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—42no—
426C4—4881no—
427C4#1683972511yescharacteristic
428C4#1683973011yescharacteristic
429C4#1683983111yescharacteristic
430C4#1683983811yescharacteristic
431C4#1683990111yescharacteristic
432C4#1683990711yescharacteristic
433C4#1683996211yescharacteristic
434C4#1683998411yescharacteristic
435C2—4882no—
436C2#2144465311yescharacteristic
437C2#2144467411yescharacteristic
438C2#2144470911yescharacteristic
439C2#2144471911yescharacteristic
440C2#2144611611yescharacteristic
441C2#2144614611yescharacteristic
442C2#2144617411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#446C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenterC2×#446D61
hypocenterC61#8952
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊#92418C2semidirect
5. #21443653C2semidirect
6. #21443646C2semidirect
7. C2×C61×#446C2semidirect
106. C2×C8×C61SD16semidirect
214. C2×#446D61semidirect
250. C61#8952semidirect
341. C2×C8#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582012
#214466132
C2×Q8⋊#924182
C2×#168394892
#214436532
#214436462
C2×C61×#4462
#895261