Finite Group Databasebeta

← #29574591

Subgroups — #29574591

Order 15616.

672 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758199C211yesmaximal, characteristic
2C2×C8×D244C211yesmaximal, characteristic, complemented
3C2×D4⋊#92418C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic, complemented
5#21443653C211yesmaximal, characteristic, complemented
6#21443646C211yesmaximal, characteristic, complemented
7C61×#1954C211yesmaximal, characteristic, complemented
8C22×#11758199C411yescharacteristic
9C22×C8×D61—21no—
10C2×C4×D244C2211yescharacteristic
11C4×#11758199—22no—
12C4×#11758199—22no—
13C8×D244—22no—
14C8×D244—22no—
15C2×#14519710C411yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519698C411yescharacteristic
18C2×#14519697C411yescharacteristic
19C2×#14519689—21no—
20C2×C4×#92418C2211yescharacteristic
21C2×C4×#92418C2211yescharacteristic
22D4⋊#92418—22no—
23#16839489—22no—
24C2×C4×D4×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C22⋊C8×C61—21no—
27C2×C22⋊C8×C61—21no—
28C2×C4×C8×C61C2211yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758199—22no—
32C2×#11758199—22no—
33C2×#11758199C814yescomplemented
34C22×#92418—21no—
35C22×#92418—21no—
36C22×#92418C2×C411yescharacteristic
37C22×#92418C2×C411yescharacteristic
38C2×C8×D61—24no—
39C2×C8×D61—42no—
40C2×C8×D61—42no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244D412yes—
44C4×D244D412yes—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47#14519710—22no—
48C4⋊#92418—21no—
49C4⋊#92418D412yes—
50#14519698—22no—
51#14519697—22no—
52#14519689—24no—
53C4×#92418—21no—
54C4×#92418—21no—
55C4×#92418—21no—
56C4×#92418—21no—
57C22×D4×C61C2×C411yescharacteristic
58C23×C4×C61—21no—
59C22×C8×C61—21no—
60C22×C8×C61D411yescharacteristic
61C22×C8×C61D411yescharacteristic
62C4×D4×C61—21no—
63C4×D4×C61—21no—
64C4×D4×C61—21no—
65C4×D4×C61—21no—
66C2×C4⋊C4×C61C2×C411yescharacteristic
67C2×C22⋊C4×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C22⋊C8×C61—42no—
72C22⋊C8×C61—42no—
73C4×C8×C61—21no—
74C4×C8×C61—21no—
75C24×C61—21no—
76C23×D61—21no—
77C2×D4×C61—21no—
78C2×D4×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61C2×C812yescomplemented
83C22×C4×C61—21no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×Dic61—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244C22⋊C412yes—
98C2×D244C2×C812yes—
99C2×D244M1612yes—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C2×C8×C61D812yescomplemented
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123#11758199—28no—
124#11758198—22no—
125#11758198—22no—
126C4⋊Dic61—21no—
127C4⋊Dic61C22⋊C412yes—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—22no—
131C2×#92418—21no—
132C2×#92418—22no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138C2×#92418—41no—
139C2×#92418C2×C812yescomplemented
140C8×D61—48no—
141C23×C61—22no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61C4×D411yescharacteristic
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156D4×C61—22no—
157D4×C61—22no—
158D4×C61—41no—
159D4×C61—41no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61C2×C22⋊C411yescharacteristic
170C2×C4×C61C4×D411yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12311yescharacteristic
175C2×C4×C61C22×C811yescharacteristic
176C2×C4×C61C2×M1611yescharacteristic
177C2×C4×C61#13111yescharacteristic
178C2×C4×C61#13111yescharacteristic
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61#13511yescharacteristic
181C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
183C2×Dic61—22no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186D244—22no—
187D244—22no—
188D244—22no—
189D244C22⋊C814yescomplemented
190C4×D61—42no—
191C4×D61—42no—
192C4×D61—42no—
193C4×D61—42no—
194C8×C61—22no—
195C8×C61—41no—
196C8×C61—81no—
197#92418—22no—
198#92418—42no—
199#92418—41no—
200#92418—42no—
201#8947—611nomaximal, Sylow
202C22×C61—42no—
203C22×C61—42no—
204C22×C61—42no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61#38611yescharacteristic
210C22×C61C8×D411yescharacteristic
211C22×C61#43511yescharacteristic
212C22×C61C4×D811yescharacteristic
213C22×C61#44211yescharacteristic
214C22×C61#44311yescharacteristic
215C22×C61#44411yescharacteristic
216C2×D61—24no—
217C2×D61—42no—
218C2×D61—42no—
219C2×D61—42no—
220C2×D61—42no—
221C2×D61—42no—
222C2×D61—42no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—81no—
226C4×C61C2×C22⋊C811yescharacteristic
227C4×C61#40811yescharacteristic
228C4×C61C8×D411yescharacteristic
229C4×C61#43511yescharacteristic
230C4×C61#44711yescharacteristic
231C4×C61#44911yescharacteristic
232C4×C61#45911yescharacteristic
233C4×C61#46311yescharacteristic
234Dic61—42no—
235C2×C4×D8—611no—
236C2×C8×D4—611no—
237#1954D6111yescharacteristic, complemented
238C2×D4⋊C8—611no—
239C2×D4⋊C8—611no—
240#1277—611no—
241#1273—611no—
242C2×C61—82no—
243C2×C61C8×D811yescharacteristic
244C2×C61#158011yescharacteristic
245C2×C61#158111yescharacteristic
246C2×C61#158611yescharacteristic
247C2×C61#186911yescharacteristic
248C2×C61#187611yescharacteristic
249C2×C61#187911yescharacteristic
250D61—44no—
251C22×D8—611no—
252C23×C8—1221no—
253C2×C4×D4—611no—
254C2×C4×D4C2×D6111yescharacteristic
255C4×D8—1222no—
256C4×D8—1222no—
257C8×D4—1222no—
258C8×D4—1222no—
259C2×#107—611no—
260C2×C4⋊C8—611no—
261C2×C4⋊C8C2×D6111yescharacteristic
262C2×#102—611no—
263C2×#102—611no—
264C2×C22⋊C8—21no—
265C2×C22⋊C8—21no—
266C2×C22⋊C8—1221no—
267C2×C4×C8—611no—
268C2×C4×C8—611no—
269C2×C4×C8C2×D6111yescharacteristic
270D4⋊C8—1222no—
271D4⋊C8—1222no—
272C61#894711yescharacteristic, complemented, Sylow
273C22×D4—611no—
274C22×D4C4×D6111yescharacteristic
275C23×C4—21no—
276C23×C4—1221no—
277C2×D8—614no—
278C2×D8—1222no—
279C2×D8—1222no—
280C22×C8—21no—
281C22×C8—611no—
282C22×C8—611no—
283C22×C8—1224no—
284C22×C8—1221no—
285C22×C8—1221no—
286C22×C8—2442no—
287C22×C8—2442no—
288C22×C8C22⋊D6111yescharacteristic
289C22×C8C22⋊D6111yescharacteristic
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—612no—
295C4×D4—612no—
296C4×D4—1221no—
297C4×D4—1221no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4C4×D6111yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—1221no—
302C2×C42C22×D6111yescharacteristic
303#107—1222no—
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8—612no—
307C4⋊C8—1221no—
308#102—1222no—
309#102—1222no—
310C22⋊C8—42no—
311C22⋊C8—42no—
312C22⋊C8—1224no—
313C4×C8—21no—
314C4×C8—21no—
315C4×C8—1221no—
316C4×C8—1221no—
317C4×C8—1221no—
318C4×C8—1221no—
319C24—21no—
320C24—1221no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—612no—
327C2×D4—612no—
328C2×D4—612no—
329C2×D4—1221no—
330C2×D4—1221no—
331C2×D4—1221no—
332C2×D4C8×D6112yescomplemented
333C22×C4—21no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—1221no—
341C22×C4—1222no—
342C22×C4—1222no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4—2441no—
346C22×C4—2441no—
347C22×C4C2×C4×D6111yescharacteristic
348C22×C4#1175822211yescharacteristic
349C22×C4C2×C22⋊D6111yescharacteristic
350D8—1228no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—612no—
360C2×C8—1221no—
361C2×C8—1221no—
362C2×C8—1222no—
363C2×C8—1221no—
364C2×C8—1222no—
365C2×C8—1221no—
366C2×C8—1221no—
367C2×C8—2448no—
368C2×C8—2441no—
369C2×C8—2441no—
370C2×C8—2441no—
371C2×C8—2441no—
372C2×C8#1175819912yescomplemented
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—612no—
376C4⋊C4—1221no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C42D4×D6111yescharacteristic
382C42D4×D6111yescharacteristic
383C42D4×D6111yescharacteristic
384C42#1175822411yescharacteristic
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—1222no—
393C23—1222no—
394C23—1222no—
395C23—2441no—
396C23—2441no—
397C23—2441no—
398C23—2441no—
399C23C4×C22⋊D6111yescharacteristic
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—614no—
405D4—1222no—
406D4—1222no—
407D4—1222no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—1222no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4C22⋊C4×D6111yescharacteristic
425C2×C4#1451973711yescharacteristic
426C2×C4#1451974511yescharacteristic
427C2×C4#1451974811yescharacteristic
428C2×C4#1451975011yescharacteristic
429C2×C4#1451975911yescharacteristic
430C2×C4C2×C8×D6111yescharacteristic
431C2×C4M16×D6111yescharacteristic
432C2×C4#1451978311yescharacteristic
433C2×C4#1451978511yescharacteristic
434C2×C4C2×#1175819911yescharacteristic
435C2×C4#1451979711yescharacteristic
436C2×C4#1451980211yescharacteristic
437C2×C4#1451980311yescharacteristic
438C8—22no—
439C8—41no—
440C8—81no—
441C8—1222no—
442C8—2442no—
443C8—2441no—
444C8—2442no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—1224no—
453C22—2442no—
454C22—2442no—
455C22—2442no—
456C22—2442no—
457C22—2442no—
458C22—2442no—
459C22#1683963811yescharacteristic
460C22C8×C22⋊D6111yescharacteristic
461C22#1683983111yescharacteristic
462C22C4×#1175819911yescharacteristic
463C22#1683987211yescharacteristic
464C22#1683987711yescharacteristic
465C22#1683988211yescharacteristic
466C4—21no—
467C4—21no—
468C4—81no—
469C4—2442no—
470C4C22⋊C8×D6111yescharacteristic
471C4#1683972711yescharacteristic
472C4#1683982511yescharacteristic
473C4#1683983611yescharacteristic
474C4#1683989511yescharacteristic
475C4#1683990511yescharacteristic
476C4#1683995411yescharacteristic
477C4#1683997411yescharacteristic
478C2—82no—
479C2—2444no—
480C2C8×#1175819911yescharacteristic
481C2#2144464111yescharacteristic
482C2#2144464611yescharacteristic
483C2#2144468111yescharacteristic
484C2#2144610811yescharacteristic
485C2#2144614911yescharacteristic
486C2#2144617011yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1954C2
socleC23×C61C4×D4
prime radicalC22×#11758199C4
cosocleC2×C42×C61C23
hypercenter#1954D61
hypocenterC61#8947
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×C8×D244C2semidirect
3. C2×D4⋊#92418C2semidirect
4. C2×#16839489C2semidirect
5. #21443653C2semidirect
6. #21443646C2semidirect
7. C61×#1954C2semidirect
33. C2×#11758199C8semidirect
82. C2×D4×C61C2×C8semidirect
114. C2×C8×C61D8semidirect
139. C2×#92418C2×C8semidirect
189. D244C22⋊C8semidirect
237. #1954D61semidirect
272. C61#8947semidirect
332. C2×D4C8×D61semidirect
372. C2×C8#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581992
C2×C8×D2442
C2×D4⋊#924182
C2×#168394892
#214436532
#214436462
C61×#19542
#894761