Finite Group Databasebeta

← #30600164

Subgroups — #30600164

Order 15616.

694 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×#16840780C211yesmaximal, characteristic, complemented
2#21461674C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448327C211yesmaximal, characteristic
6#16840780—24no—
7C2×#14519844—21no—
8C2×C4⋊#92420C2212yes—
9C2×#14519834—21no—
10C2×#14519834—21no—
11C2×C4×#92420C2212yes—
12#16840628—21no—
13#16840610—24no—
14C2×#14519752C411yescharacteristic
15C2×#14519739—21no—
16C2×#14519739C2211yescharacteristic
17C2×C42×D61C2211yescharacteristic
18#16839664C411yescharacteristic
19#16839652—21no—
20#16839640—21no—
21#16839619C411yescharacteristic
22C4⋊C4×Dic61C2211yescharacteristic
23#16839609—21no—
24C61×#389C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27#14519844—24no—
28C4⋊#92420—22no—
29C4⋊#92420—22no—
30#14519834—24no—
31#14519834—42no—
32C4×#92420—22no—
33C4×#92420D414yescomplemented
34C22×D244—21no—
35C22×D244C2×C411yescharacteristic
36C22×C4×D61—21no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40#14519752—22no—
41#14519752C814yescomplemented
42#14519739—22no—
43#14519739—22no—
44#14519739—44no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61C2311yescharacteristic
55C42×D61—22no—
56C42×D61—22no—
57#14519684—21no—
58#14519684—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C42×C61C2×C411yescharacteristic
63#95×C61—21no—
64C23×D61—21no—
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×D244—22no—
76C2×D244—22no—
77C2×D244—24no—
78C2×D244—21no—
79C2×D244—42no—
80C2×D244—42no—
81C2×D244C2×C812yes—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—21no—
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—22no—
89C2×C4×D61—21no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—42no—
93C2×C4×D61—41no—
94C2×C4×D61—42no—
95C2×C4×D61—41no—
96C2×C4×D61C2×C812yes—
97C2×C4×D61M1612yes—
98C2×#92420—24no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C2×#92420—42no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—42no—
107C4⋊C4×C61C2×C812yes—
108C42×C61—22no—
109#11758198—24no—
110#11758198—42no—
111#11758198—42no—
112#11758198—42no—
113#11758198—41no—
114#11758198—41no—
115C4⋊Dic61—22no—
116C4×Dic61—21no—
117C4×Dic61—22no—
118C4×Dic61—21no—
119C4×Dic61—42no—
120C4×Dic61C2×D412yes—
121C4×Dic61#4112yes—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—22no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61C22⋊C812yes—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—22no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61C4×D412yes—
150C2×C4×C61C22×C811yescharacteristic
151C2×C4×C61C2×M1611yescharacteristic
152C2×C4×C61#13112yes—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61C22⋊C812yes—
161C2×Dic61#12011yescharacteristic
162C2×Dic61#12112yes—
163C2×Dic61#12311yescharacteristic
164C2×Dic61AGL(1,ℤ/8)12yes—
165C2×Dic61AGL(1,ℤ/8)11yescharacteristic
166C2×Dic61#13711yescharacteristic
167D244—24no—
168D244—48no—
169D244—42no—
170C4×D61—24no—
171C4×D61—24no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—82no—
177C4×D61—82no—
178#92420—44no—
179#92420—82no—
180#9074—611nomaximal, Sylow
181C22×C61#38611yescharacteristic
182C22×C61C2×C22⋊C811yescharacteristic
183C22×C61#40811yescharacteristic
184C22×C61#41711yescharacteristic
185C22×C61#41811yescharacteristic
186C22×C61#42111yescharacteristic
187C22×C61#42111yescharacteristic
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—22no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—42no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61—42no—
205C4×C61—81no—
206C4×C61C8×D412yes—
207C4×C61#43512yes—
208Dic61—22no—
209Dic61—21no—
210Dic61—21no—
211Dic61—81no—
212Dic61#46812yes—
213Dic61#46912yes—
214C2×#431—611no—
215C4×#121—611no—
216#1797—611no—
217C2×D4⋊C8—612no—
218#1279—612no—
219C2×C61#147711yescharacteristic
220C2×C61#147811yescharacteristic
221C2×C61#149511yescharacteristic
222C2×C61#149611yescharacteristic
223C2×C61#186911yescharacteristic
224C2×C61#189511yescharacteristic
225C2×C61#189711yescharacteristic
226D61—42no—
227D61—82no—
228C2×#121—611no—
229C2×C4×D4—611no—
230C2×C4×D4—1221no—
231C22×C42—611no—
232#431—1224no—
233C2×C4⋊C8—612no—
234C2×C4⋊C8—1221no—
235C2×C22⋊C8—1221no—
236C2×C22⋊C8—1221no—
237C2×C4×C8—612no—
238#390—611no—
239#389#692311yescharacteristic
240#388—1221no—
241#386—1221no—
242#380—611no—
243C4×C4⋊C4—611no—
244C4×C22⋊C4—1221no—
245#336—1221no—
246D4⋊C8—1224no—
247C61#907411yescharacteristic, complemented, Sylow
248C22×D4—611no—
249C22×D4—1221no—
250C23×C4—611no—
251C23×C4—611no—
252C23×C4—611no—
253C23×C4—1221no—
254C22×C8—1222no—
255C22×C8—1222no—
256#121—614no—
257#121—1222no—
258C4×D4—1222no—
259C4×D4—1222no—
260C4×D4—2444no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4C2×#692311yescharacteristic
264C2×C4⋊C4C2×#692311yescharacteristic
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C42—611no—
271C2×C42—611no—
272C2×C42—611no—
273C2×C42—1222no—
274C2×C42—1222no—
275C2×C42—1221no—
276C2×C42C2×#692311yescharacteristic
277C4⋊C8—1222no—
278C4⋊C8—1222no—
279C4⋊C8—1224no—
280C22⋊C8—1224no—
281C22⋊C8—2442no—
282C4×C8—614no—
283C4×C8—1222no—
284#95—21no—
285#95—1221no—
286#95—1221no—
287C24—611no—
288C24—1221no—
289C2×D4—612no—
290C2×D4—1224no—
291C2×D4—1222no—
292C2×D4—1221no—
293C2×D4—1222no—
294C2×D4—2442no—
295C2×D4—2442no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—612no—
302C22×C4—612no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1222no—
306C22×C4—1221no—
307C22×C4—1222no—
308C22×C4—1221no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—1221no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4C22⋊#692311yescharacteristic
319C22×C4C22⋊#692311yescharacteristic
320C22×C4C22×#692311yescharacteristic
321C2×C8—1224no—
322C2×C8—2442no—
323C2×C8—2442no—
324C2×C8—2442no—
325C2×C8—2442no—
326C2×C8—2442no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—42no—
330C4⋊C4—1222no—
331C4⋊C4D61⋊C812yes—
332C22⋊C4—1224no—
333C22⋊C4—2442no—
334C22⋊C4—2442no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C22⋊C4—2442no—
338C42—22no—
339C42—612no—
340C42—612no—
341C42—1221no—
342C42—1222no—
343C42—1221no—
344C42—2442no—
345C23—612no—
346C23—1221no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1222no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23C2×C22⋊#692311yescharacteristic
360D4—1224no—
361D4—2448no—
362D4—2442no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—612no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—612no—
379C2×C4—611no—
380C2×C4—611no—
381C2×C4—612no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1224no—
387C2×C4—1224no—
388C2×C4—4882no—
389C2×C4—4882no—
390C2×C4—2442no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4D4×#692312yes—
398C2×C4C2×D61⋊C811yescharacteristic
399C2×C4D61⋊M1611yescharacteristic
400C2×C4#1451986512yes—
401C8—4882no—
402C8—2444no—
403C22—1222no—
404C22—1222no—
405C22—1222no—
406C22—4881no—
407C22—4881no—
408C22—4881no—
409C22—4881no—
410C22—2442no—
411C22—2442no—
412C22—2442no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22—2441no—
417C22#1684071011yescharacteristic
418C22D61⋊(C22⋊C8)11yescharacteristic
419C22#1684073711yescharacteristic
420C22#1684075311yescharacteristic
421C22#1684075411yescharacteristic
422C22#1684075911yescharacteristic
423C22#1684076111yescharacteristic
424C4—41no—
425C4—41no—
426C4—42no—
427C4—81no—
428C4—612no—
429C4—612no—
430C4—1222no—
431C4—1221no—
432C4—1221no—
433C4—4881no—
434C4#1684079012yes—
435C4#1684079212yes—
436C2—4882no—
437C2—2442no—
438C2#2146111711yescharacteristic
439C2#2146111911yescharacteristic
440C2#2146117711yescharacteristic
441C2#2146118011yescharacteristic
442C2#2146179511yescharacteristic
443C2#2146183511yescharacteristic
444C2#2146183811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9074
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#16840780C2semidirect
2. #21461674C2semidirect
3. C2×#16840610C2semidirect
4. #21460655C2semidirect
33. C4×#92420D4semidirect
41. #14519752C8semidirect
247. C61#9074semidirect

Maximal subgroups

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

subgroupindex
C2×#168407802
#214616742
C2×#168406102
#214606552
#214483272
#907461