Finite Group Databasebeta

← #29574605

Subgroups — #29574605

Order 15616.

584 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758201C211yesmaximal, characteristic
2C2×#16839841C211yesmaximal, characteristic
3C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic
5#21443653C211yesmaximal, characteristic, complemented
6#21443646C211yesmaximal, characteristic, complemented
7C61×#1984C211yesmaximal, characteristic, complemented
8C22×#11758201C411yescharacteristic
9C22×#11758189—21no—
10C2×C4×D244C2211yescharacteristic
11C4×#11758201—22no—
12C4×#11758201—22no—
13#16839841—22no—
14#16839841—22no—
15C2×#14519708C411yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519701C411yescharacteristic
18C2×#14519697C411yescharacteristic
19C2×#14519689—21no—
20C2×C4×#92418C2211yescharacteristic
21C2×C4×#92418C2211yescharacteristic
22Q8⋊#92418—22no—
23#16839489—22no—
24C2×C4×Q8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4×C8×C61C2211yescharacteristic
27C61×#336—21no—
28C61×#336—21no—
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758201—22no—
32C2×#11758201—22no—
33C2×#11758201—22no—
34C2×#11758189—24no—
35C2×#11758189—42no—
36C2×#11758189—42no—
37C22×#92418—21no—
38C22×#92418—21no—
39C22×#92418C2×C411yescharacteristic
40C22×#92418C2×C411yescharacteristic
41C4×D244—21no—
42C4×D244—21no—
43C4×D244D412yes—
44C4×D244D412yes—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47#14519708—22no—
48C4⋊#92418—21no—
49C4⋊#92418D412yes—
50#14519701—22no—
51#14519697—22no—
52#14519689—24no—
53C4×#92418—21no—
54C4×#92418—21no—
55C4×#92418—21no—
56C4×#92418—21no—
57C22×Q8×C61C2×C411yescharacteristic
58C22×C8×C61—21no—
59C22×C8×C61D411yescharacteristic
60C22×C8×C61D411yescharacteristic
61C4×Q8×C61—21no—
62C4×Q8×C61—21no—
63C4×Q8×C61—21no—
64C4×Q8×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61C2×C411yescharacteristic
67C2×C42×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
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×C61M1612yescomplemented
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×D244C22⋊C412yes—
92C2×C4×D61—22no—
93C2×C4×D61—22no—
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—21no—
102C2×C8×C61—21no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61SD1612yescomplemented
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C42×C61—41no—
112C42×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117#11758201—28no—
118#11758198—22no—
119#11758198—22no—
120C4⋊Dic61—21no—
121C4⋊Dic61C22⋊C412yes—
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—22no—
125C2×#92418—21no—
126C2×#92418—22no—
127C2×#92418—21no—
128C2×#92418—21no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418M1612yescomplemented
134#11758189—48no—
135C23×C61C4×D411yescharacteristic
136C22×D61—22no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143Q8×C61—22no—
144Q8×C61—22no—
145Q8×C61—41no—
146Q8×C61—41no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—22no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61C2×M1611yescharacteristic
162C2×C4×C61C2×M1611yescharacteristic
163C2×C4×C61#13111yescharacteristic
164C2×C4×C61#13111yescharacteristic
165C2×C4×C61C2×SD1611yescharacteristic
166C2×C4×C61#13511yescharacteristic
167C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C61#13711yescharacteristic
169C2×Dic61—22no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172D244—22no—
173D244—22no—
174D244—41no—
175D244—41no—
176C4×D61—42no—
177C4×D61—42no—
178C4×D61—42no—
179C4×D61—42no—
180C8×C61—22no—
181C8×C61—41no—
182C8×C61—81no—
183#92418—22no—
184#92418—42no—
185#92418—41no—
186#92418—42no—
187#8949—611nomaximal, Sylow
188C22×C61#38611yescharacteristic
189C22×C61#43511yescharacteristic
190C22×C61#43611yescharacteristic
191C22×C61C4×SD1611yescharacteristic
192C22×C61#44011yescharacteristic
193C22×C61#44311yescharacteristic
194C22×C61#44411yescharacteristic
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—42no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—42no—
205C4×C61—81no—
206C4×C61#40711yescharacteristic
207C4×C61#40811yescharacteristic
208C4×C61#43511yescharacteristic
209C4×C61#43611yescharacteristic
210C4×C61#45011yescharacteristic
211C4×C61#45211yescharacteristic
212C4×C61#46111yescharacteristic
213C4×C61#46311yescharacteristic
214Dic61—42no—
215C2×C4×SD16—611no—
216C2×#436—611no—
217#1984D6111yescharacteristic, complemented
218C2×Q8⋊C8—611no—
219C2×D4⋊C8—611no—
220#1277—611no—
221#1273—611no—
222C2×C61#158311yescharacteristic
223C2×C61#158811yescharacteristic
224C2×C61#159011yescharacteristic
225C2×C61#159211yescharacteristic
226C2×C61#187011yescharacteristic
227C2×C61#187611yescharacteristic
228C2×C61#187711yescharacteristic
229D61—82no—
230C22×SD16—611no—
231C22×M16—1221no—
232C2×C4×Q8C2×D6111yescharacteristic
233C2×C4×D4—611no—
234C4×SD16—1222no—
235C4×SD16—1222no—
236#436—1222no—
237#436—1222no—
238C2×#106—611no—
239C2×C4⋊C8—611no—
240C2×C4⋊C8C2×D6111yescharacteristic
241C2×#103—611no—
242C2×#102—611no—
243C2×C22⋊C8—1221no—
244C2×C4×C8—611no—
245C2×C4×C8—611no—
246C2×C4×C8C2×D6111yescharacteristic
247#336—21no—
248#336—21no—
249Q8⋊C8—1222no—
250D4⋊C8—1222no—
251C61#894911yescharacteristic, complemented, Sylow
252C22×Q8C4×D6111yescharacteristic
253C22×D4—611no—
254C23×C4—1221no—
255C2×SD16—1222no—
256C2×SD16—1222no—
257C2×SD16—1222no—
258C2×M16—1224no—
259C2×M16—2442no—
260C2×M16—2442no—
261C22×C8—21no—
262C22×C8—611no—
263C22×C8—611no—
264C22×C8—1221no—
265C22×C8—1221no—
266C22×C8C22⋊D6111yescharacteristic
267C22×C8C22⋊D6111yescharacteristic
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×D4—612no—
273C4×D4—612no—
274C4×D4—1221no—
275C4×D4—1221no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4C4×D6111yescharacteristic
279C2×C22⋊C4—1221no—
280C2×C42—21no—
281C2×C42C22×D6111yescharacteristic
282#106—1222no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—612no—
286C4⋊C8—1221no—
287#103—1222no—
288#102—1222no—
289C22⋊C8—1224no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—1221no—
293C4×C8—1221no—
294C4×C8—1221no—
295C4×C8—1221no—
296C24—1221no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8#1175818912yescomplemented
303C2×D4—612no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—1221no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—1221no—
312C22×C4—1222no—
313C22×C4—1222no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4C2×C4×D6111yescharacteristic
319C22×C4#1175822211yescharacteristic
320C22×C4C2×C22⋊D6111yescharacteristic
321SD16—1228no—
322M16—2448no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—612no—
332C2×C8—1221no—
333C2×C8—1221no—
334C2×C8—1222no—
335C2×C8—1221no—
336C2×C8—1222no—
337C2×C8—1221no—
338C2×C8—1221no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C2×C8—2441no—
343C2×C8#1175820112yescomplemented
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—612no—
349C4⋊C4—1221no—
350C22⋊C4—1222no—
351C22⋊C4—1222no—
352C42—41no—
353C42—41no—
354C42D4×D6111yescharacteristic
355C42D4×D6111yescharacteristic
356C42D4×D6111yescharacteristic
357C42#1175822411yescharacteristic
358C23—1222no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23—2441no—
365C23C4×C22⋊D6111yescharacteristic
366Q8—22no—
367Q8—22no—
368Q8—41no—
369Q8—41no—
370D4—1222no—
371D4—1222no—
372D4—2441no—
373D4—2441no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—1222no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4C22⋊C4×D6111yescharacteristic
390C2×C4#1451973711yescharacteristic
391C2×C4#1451974511yescharacteristic
392C2×C4#1451974811yescharacteristic
393C2×C4#1451975011yescharacteristic
394C2×C4#1451975911yescharacteristic
395C2×C4M16×D6111yescharacteristic
396C2×C4C2×#1175818911yescharacteristic
397C2×C4#1451978311yescharacteristic
398C2×C4#1451978511yescharacteristic
399C2×C4C2×#1175820111yescharacteristic
400C2×C4#1451979711yescharacteristic
401C2×C4#1451980211yescharacteristic
402C2×C4#1451980811yescharacteristic
403C8—22no—
404C8—41no—
405C8—81no—
406C8—1222no—
407C8—2442no—
408C8—2441no—
409C8—2442no—
410C22—4881no—
411C22—4881no—
412C22—4881no—
413C22—4881no—
414C22—2442no—
415C22—2442no—
416C22—2442no—
417C22#1683963811yescharacteristic
418C22#1683983311yescharacteristic
419C22#1683983811yescharacteristic
420C22C4×#1175820111yescharacteristic
421C22#1683986011yescharacteristic
422C22#1683987711yescharacteristic
423C22#1683988211yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—81no—
428C4—2442no—
429C4#1683972411yescharacteristic
430C4#1683972711yescharacteristic
431C4#1683983011yescharacteristic
432C4#1683983711yescharacteristic
433C4#1683991211yescharacteristic
434C4#1683992211yescharacteristic
435C4#1683996411yescharacteristic
436C4#1683997411yescharacteristic
437C2—4882no—
438C2#2144466211yescharacteristic
439C2#2144469711yescharacteristic
440C2#2144470911yescharacteristic
441C2#2144471911yescharacteristic
442C2#2144611311yescharacteristic
443C2#2144614911yescharacteristic
444C2#2144615611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1984C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1984D61
hypocenterC61#8949
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1984

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊#92418C2semidirect
5. #21443653C2semidirect
6. #21443646C2semidirect
7. C61×#1984C2semidirect
79. C2×Q8×C61M16semidirect
106. C2×C8×C61SD16semidirect
133. C2×#92418M16semidirect
217. #1984D61semidirect
251. C61#8949semidirect
302. C2×Q8#11758189semidirect
343. 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
C2×#168398412
C2×Q8⋊#924182
C2×#168394892
#214436532
#214436462
C61×#19842
#894961