Finite Group Databasebeta

← #30599625

Subgroups — #30599625

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462668C211yesmaximal, characteristic
2#21461794C211yesmaximal, characteristic
3#21461763C211yesmaximal, characteristic, complemented
4#21461762C211yesmaximal, characteristic, complemented
5#21460662C211yesmaximal, characteristic, complemented
6#21460662C211yesmaximal, characteristic, complemented
7#21445606C211yesmaximal, characteristic
8C23×#92420C2211yescharacteristic
9#16840789—21no—
10#16840789—21no—
11#16840789—21no—
12#16840789—21no—
13#16840779—21no—
14C2×#14519844—21no—
15C2×C4⋊#92420—21no—
16C2×#14519834—21no—
17D61⋊(C22⋊C8)—21no—
18C2×C22⋊#92420C2211yescharacteristic
19C2×C22⋊#92420C2211yescharacteristic
20C2×C22⋊#92420C2211yescharacteristic
21#16840628—21no—
22#16840628—21no—
23#16840628—21no—
24C2×#14519737C2211yescharacteristic
25C2×#14519691C411yescharacteristic
26C2×#14519691C411yescharacteristic
27C22⋊C4×Dic61C2211yescharacteristic
28C22⋊C4×Dic61C2211yescharacteristic
29#16839529C411yescharacteristic
30C61×#342C411yescharacteristic
31C2×D61⋊C8—21no—
32C2×D61⋊C8—21no—
33C22×#92420—21no—
34C22×#92420—21no—
35C22×#92420—21no—
36C22×#92420—21no—
37C22×#92420—42no—
38C22×#92420D411yescharacteristic
39C22×#92420D411yescharacteristic
40C22×#92420D411yescharacteristic
41C22×#92420D411yescharacteristic
42#14519844—21no—
43#14519844—21no—
44#14519844—42no—
45C4⋊#92420—42no—
46#14519834—21no—
47#14519834—21no—
48#14519834—42no—
49C22⋊#92420—21no—
50C22⋊#92420—21no—
51C22⋊#92420—21no—
52C22⋊#92420—21no—
53C22⋊#92420—21no—
54C22⋊#92420—21no—
55C4×#92420—21no—
56C4×#92420—21no—
57C22×C22⋊D61C2×C411yescharacteristic
58C23×Dic61C2311yescharacteristic
59C22×C4×D61D411yescharacteristic
60#14519737—21no—
61#14519737—21no—
62#14519737—21no—
63#14519737—21no—
64C2×#11758196Q811yescharacteristic
65C2×C22⋊Dic61C2×C411yescharacteristic
66C2×C22⋊Dic61C2×C411yescharacteristic
67C2×#11758198Q811yescharacteristic
68C2×C4×Dic61—21no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61D411yescharacteristic
71#14519691—22no—
72#14519691C814yescomplemented
73#14519684—21no—
74#14519684—21no—
75C2×C22⋊C4×C61C2×C411yescharacteristic
76C2×C22⋊C4×C61C2×C411yescharacteristic
77C2×C22⋊C4×C61C2×C411yescharacteristic
78C24×C61C22×C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C4⋊C411yescharacteristic
83C22×C4×C61C4⋊C411yescharacteristic
84C2×C22⋊D61—21no—
85C2×C22⋊D61—21no—
86C2×C22⋊D61—21no—
87C2×C22⋊D61—21no—
88C2×C22⋊D61C2×C812yes—
89C2×C22⋊D61M1612yes—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61C4⋊C411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×D411yescharacteristic
97C22×Dic61C2×D411yescharacteristic
98C22×Dic61C2×Q811yescharacteristic
99C22×Dic61#4111yescharacteristic
100C22×Dic61#4111yescharacteristic
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×#92420—22no—
106C2×#92420—22no—
107C2×#92420—22no—
108C2×#92420—21no—
109C2×#92420—21no—
110C2×#92420—21no—
111C2×#92420—21no—
112C2×#92420—41no—
113C2×#92420—41no—
114C2×#92420—41no—
115C2×#92420—41no—
116C2×#92420—41no—
117C2×#92420—41no—
118C2×#92420—41no—
119C2×#92420—41no—
120C2×#92420—41no—
121C2×#92420—41no—
122C2×#92420—41no—
123D61⋊C8—81no—
124D61⋊C8—81no—
125C22⋊C4×C61—21no—
126C22⋊C4×C61—21no—
127C22⋊C4×C61—21no—
128C22⋊C4×C61—21no—
129C22⋊C4×C61—21no—
130C22⋊C4×C61C2×C812yescomplemented
131C22⋊Dic61—21no—
132C22⋊Dic61—21no—
133C22⋊Dic61—21no—
134C22⋊Dic61C2×C812yescomplemented
135#11758198—21no—
136#11758198—21no—
137#11758196—21no—
138#11758196—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—41no—
142C4×Dic61—41no—
143C4×Dic61—41no—
144C4×Dic61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61C2×C4⋊C411yescharacteristic
148C23×C61C4×D411yescharacteristic
149C23×C61C4×D411yescharacteristic
150C23×C61C22×C811yescharacteristic
151C23×C61C2×M1611yescharacteristic
152C23×C61#13111yescharacteristic
153C23×C61#13111yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61C4⋊C812yescomplemented
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—22no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C22⋊D61—22no—
170C22⋊D61—22no—
171C22⋊D61—22no—
172C22⋊D61—22no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—22no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61C4⋊C812yescomplemented
191C2×Dic61#12011yescharacteristic
192C2×Dic61C22⋊Q811yescharacteristic
193C2×Dic61C22⋊Q811yescharacteristic
194C2×Dic61#12311yescharacteristic
195C4×D61—41no—
196C4×D61—41no—
197C4×D61—81no—
198#92420—41no—
199#92420—41no—
200#92420—42no—
201#92420—41no—
202#92420—41no—
203#92420—81no—
204#8851—611nomaximal, Sylow
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61#38511yescharacteristic
216C22×C61C2×C4⋊C811yescharacteristic
217C22×C61#42411yescharacteristic
218C22×C61C8×D411yescharacteristic
219C22×C61C8×D411yescharacteristic
220C22×C61#43511yescharacteristic
221C22×C61#43511yescharacteristic
222C2×D61—22no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—42no—
226C2×D61—81no—
227C4×C61—42no—
228C4×C61—41no—
229C4×C61—41no—
230C4×C61—81no—
231Dic61—22no—
232Dic61—21no—
233Dic61—21no—
234Dic61—21no—
235Dic61—42no—
236Dic61—81no—
237Dic61B(4,𝔽2)11yescharacteristic
238Dic61#45811yescharacteristic
239#2972—611no—
240#1869—611no—
241#1850—611no—
242#1850—611no—
243C4×#99—611no—
244#1282—611no—
245#1282—611no—
246C2×C61—21no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61#185011yescharacteristic
253C2×C61#186711yescharacteristic
254C2×C61#186811yescharacteristic
255D61—42no—
256C23×C8—611no—
257C2×C4×D4—611no—
258C8×D4—1221no—
259C8×D4—1221no—
260C8×D4—1221no—
261C8×D4—1221no—
262#431—1221no—
263C2×C4⋊C8—1221no—
264C2×C4⋊C8—1221no—
265C2×#99—611no—
266C2×#99—611no—
267C2×C22⋊C8—611no—
268C2×C22⋊C8—611no—
269C2×C22⋊C8—611no—
270C2×C22⋊C8—1221no—
271C2×C22⋊C8—1221no—
272C4×C22⋊C4—611no—
273C4×C22⋊C4—611no—
274#342—611no—
275#342#692311yescharacteristic
276#336—1221no—
277#336—1221no—
278#336—1221no—
279C61#885111yescharacteristic, complemented, Sylow
280C22×D4—611no—
281C23×C4—611no—
282C23×C4—611no—
283C22×C8—611no—
284C22×C8—611no—
285C22×C8—611no—
286C22×C8—611no—
287C22×C8—1221no—
288C22×C8—1221no—
289C22×C8—1221no—
290C22×C8—1221no—
291C22×C8—1221no—
292C22×C8—1221no—
293C22×C8—2442no—
294C4×D4—1221no—
295C4×D4—1221no—
296C4×D4—1221no—
297C4×D4—1221no—
298C2×C4⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4C2×#692311yescharacteristic
303C2×C22⋊C4C2×#692311yescharacteristic
304C2×C22⋊C4C2×#692311yescharacteristic
305C2×C42—611no—
306C2×C42—1221no—
307C2×C42—1221no—
308C4⋊C8—1221no—
309C4⋊C8—1221no—
310C4⋊C8—2442no—
311C4⋊C8—2442no—
312#99—614no—
313#99—1222no—
314C22⋊C8—1221no—
315C22⋊C8—1221no—
316C22⋊C8—1221no—
317C22⋊C8—1221no—
318C22⋊C8—1221no—
319C22⋊C8—1221no—
320C22⋊C8—1221no—
321C22⋊C8—1221no—
322C22⋊C8—2442no—
323C4×C8—1221no—
324C4×C8—1221no—
325#95—1221no—
326#95—1221no—
327C24—611no—
328C24C22×#692311yescharacteristic
329C2×D4—612no—
330C2×D4—612no—
331C2×D4—1221no—
332C2×D4—1221no—
333C2×D4—1221no—
334C2×D4—1221no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—1221no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4C4⋊#692311yescharacteristic
353C22×C4C4⋊#692311yescharacteristic
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—1221no—
358C2×C8—1222no—
359C2×C8—1222no—
360C2×C8—1222no—
361C2×C8—4881no—
362C2×C8—4881no—
363C2×C8—2441no—
364C2×C8—2441no—
365C2×C8—2441no—
366C2×C8—2441no—
367C2×C8—2441no—
368C2×C8—2441no—
369C2×C8—2441no—
370C2×C8—2441no—
371C2×C8—2441no—
372C2×C8—2441no—
373C2×C8—2441no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—612no—
382C22⋊C4—1221no—
383C22⋊C4—1221no—
384C22⋊C4—1221no—
385C22⋊C4—1221no—
386C22⋊C4—1221no—
387C22⋊C4D61⋊C812yescomplemented
388C42—1221no—
389C42—1221no—
390C42—2441no—
391C42—2441no—
392C42—2441no—
393C42—2441no—
394C23—41no—
395C23—41no—
396C23—612no—
397C23—1221no—
398C23—1221no—
399C23—2441no—
400C23—2441no—
401C23C2×C4⋊#692311yescharacteristic
402C23D4×#692311yescharacteristic
403C23D4×#692311yescharacteristic
404C23C2×D61⋊C811yescharacteristic
405C23D61⋊M1611yescharacteristic
406C23#1451986411yescharacteristic
407C23#1451986511yescharacteristic
408D4—1222no—
409D4—1222no—
410D4—1222no—
411D4—1222no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—611no—
423C2×C4—611no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—612no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1222no—
436C2×C4—4881no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C8—4881no—
448C8—2442no—
449C8—2441no—
450C8—2441no—
451C8—2441no—
452C8—2441no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—1222no—
464C22—4881no—
465C22—2442no—
466C22—2441no—
467C22—2441no—
468C22#1684070911yescharacteristic
469C22D61⋊(C4⋊C8)11yescharacteristic
470C22#1684076911yescharacteristic
471C22#1684078911yescharacteristic
472C22#1684079011yescharacteristic
473C22#1684079211yescharacteristic
474C22#1684079411yescharacteristic
475C4—42no—
476C4—41no—
477C4—41no—
478C4—81no—
479C4—611no—
480C4—611no—
481C4—1222no—
482C4—1221no—
483C4—1221no—
484C4—1221no—
485C4—4881no—
486C4—2442no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—2442no—
494C2#2146176411yescharacteristic
495C2#2146179011yescharacteristic
496C2#2146179111yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC61×#342C4
socleC22×C61#385
prime radicalC22×C22⋊D61C2×C4
cosocleC23×Dic61C23
hypercenter#342#6923
hypocenterC61#8851
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #21461763C2semidirect
4. #21461762C2semidirect
5. #21460662C2semidirect
6. #21460662C2semidirect
72. #14519691C8semidirect
130. C22⋊C4×C61C2×C8semidirect
134. C22⋊Dic61C2×C8semidirect
158. C22×D61C4⋊C8semidirect
190. C2×Dic61C4⋊C8semidirect
279. C61#8851semidirect
387. C22⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
#214626682
#214617942
#214617632
#214617622
#214606622
#214456062
#885161