Finite Group Databasebeta

← #30600172

Subgroups — #30600172

Order 15616.

690 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840781C211yesmaximal, characteristic, complemented
2#21461674C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448327C211yesmaximal, characteristic
6#16840781—24no—
7C2×C4⋊#92420—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—
27C4⋊#92420—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#14519752—22no—
42#14519739—22no—
43#14519739—22no—
44#14519739—42no—
45#14519739—42no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×C4×Dic61—21no—
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61C2311yescharacteristic
56C42×D61—22no—
57C42×D61—22no—
58#14519684—21no—
59#14519684—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C42×C61C2×C411yescharacteristic
64#95×C61—21no—
65C23×D61—21no—
66C23×D61C22⋊C411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×D244—22no—
77C2×D244—22no—
78C2×D244—24no—
79C2×D244—21no—
80C2×D244—42no—
81C2×D244—42no—
82C2×D244M1612yes—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—22no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—42no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—42no—
97C2×C4×D61D812yes—
98C2×C4×D61SD1612yes—
99C2×#92420—24no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C2×#92420—42no—
104C2×#92420—42no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—42no—
108C4⋊C4×C61M1612yes—
109C42×C61—22no—
110#11758198—24no—
111#11758198—42no—
112#11758198—42no—
113#11758198—42no—
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—22no—
117C4×Dic61—21no—
118C4×Dic61—22no—
119C4×Dic61—21no—
120C4×Dic61—41no—
121C4×Dic61—41no—
122C4×Dic61C2×D412yes—
123C4×Dic61#4112yes—
124C23×C61C2×C22⋊C411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—22no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61#10212yes—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—22no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61#10212yes—
151C2×C4×C61C4×D412yes—
152C2×C4×C61C2×M1611yescharacteristic
153C2×C4×C61C2×M1611yescharacteristic
154C2×C4×C61#13112yes—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61#12011yescharacteristic
164C2×Dic61#12112yes—
165C2×Dic61#12311yescharacteristic
166C2×Dic61C2×D811yescharacteristic
167C2×Dic61C2×SD1611yescharacteristic
168C2×Dic61#13512yes—
169D244—24no—
170D244—48no—
171D244—42no—
172C4×D61—24no—
173C4×D61—24no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—42no—
177C4×D61—42no—
178C4×D61—82no—
179C4×D61—82no—
180#92420—44no—
181#92420—82no—
182#9076—611nomaximal, Sylow
183C22×C61#38611yescharacteristic
184C22×C61#40711yescharacteristic
185C22×C61#40811yescharacteristic
186C22×C61C2×#10211yescharacteristic
187C22×C61#41611yescharacteristic
188C22×C61#42111yescharacteristic
189C22×C61#42111yescharacteristic
190C2×D61—22no—
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—42no—
198C2×D61—42no—
199C2×D61—42no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C4×C61—22no—
205C4×C61—41no—
206C4×C61—42no—
207C4×C61—81no—
208C4×C61#43512yes—
209C4×C61#43612yes—
210Dic61—21no—
211Dic61—21no—
212Dic61—41no—
213Dic61—81no—
214Dic61#46512yes—
215Dic61#46612yes—
216C2×#431—611no—
217C4×#121—611no—
218#1797—611no—
219C2×D4⋊C8—612no—
220#1279—612no—
221C2×C61#148011yescharacteristic
222C2×C61#148211yescharacteristic
223C2×C61#148611yescharacteristic
224C2×C61#148811yescharacteristic
225C2×C61#187011yescharacteristic
226C2×C61#189311yescharacteristic
227C2×C61#189711yescharacteristic
228D61—42no—
229D61—82no—
230C2×#121—611no—
231C2×C4×D4—611no—
232C2×C4×D4—1221no—
233C22×C42—611no—
234#431—1224no—
235C2×C4⋊C8—612no—
236C2×C4⋊C8—1221no—
237C2×C22⋊C8—1221no—
238C2×C22⋊C8—1221no—
239C2×C4×C8—612no—
240#390—611no—
241#389#692311yescharacteristic
242#388—1221no—
243#386—1221no—
244#380—611no—
245C4×C4⋊C4—611no—
246C4×C22⋊C4—1221no—
247#336—1221no—
248D4⋊C8—1224no—
249C61#907611yescharacteristic, complemented, Sylow
250C22×D4—611no—
251C22×D4—1221no—
252C23×C4—611no—
253C23×C4—611no—
254C23×C4—611no—
255C23×C4—1221no—
256C22×C8—1222no—
257C22×C8—1222no—
258#121—1222no—
259#121—1222no—
260C4×D4—1222no—
261C4×D4—1222no—
262C4×D4—2442no—
263C4×D4—2442no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4C2×#692311yescharacteristic
267C2×C4⋊C4C2×#692311yescharacteristic
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C42—611no—
274C2×C42—611no—
275C2×C42—611no—
276C2×C42—1222no—
277C2×C42—1222no—
278C2×C42—1221no—
279C2×C42C2×#692311yescharacteristic
280C4⋊C8—1222no—
281C4⋊C8—1222no—
282C4⋊C8—1224no—
283C22⋊C8—1224no—
284C22⋊C8—2442no—
285C4×C8—614no—
286C4×C8—1222no—
287#95—21no—
288#95—1221no—
289#95—1221no—
290C24—611no—
291C24—1221no—
292C2×D4—612no—
293C2×D4—1224no—
294C2×D4—1222no—
295C2×D4—1221no—
296C2×D4—1222no—
297C2×D4—2442no—
298C2×D4—2442no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—611no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1222no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1222no—
314C22×C4—1221no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2442no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4—2442no—
321C22×C4C22⋊#692311yescharacteristic
322C22×C4C22⋊#692311yescharacteristic
323C22×C4C22×#692311yescharacteristic
324C2×C8—1224no—
325C2×C8—2442no—
326C2×C8—2442no—
327C2×C8—2442no—
328C2×C8—2442no—
329C2×C8—2442no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—42no—
333C4⋊C4—1222no—
334C4⋊C4#1175821312yes—
335C22⋊C4—1224no—
336C22⋊C4—2442no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C42—22no—
342C42—612no—
343C42—612no—
344C42—1221no—
345C42—1221no—
346C42—1222no—
347C42—2441no—
348C42—2441no—
349C23—612no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—1222no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23C2×C22⋊#692311yescharacteristic
364D4—1224no—
365D4—2448no—
366D4—2442no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—612no—
379C2×C4—611no—
380C2×C4—611no—
381C2×C4—612no—
382C2×C4—611no—
383C2×C4—611no—
384C2×C4—1224no—
385C2×C4—1224no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—4882no—
392C2×C4—4882no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4#1451983912yes—
401C2×C4D4×#692312yes—
402C2×C4D61⋊M1611yescharacteristic
403C2×C4C2×#1175821311yescharacteristic
404C2×C4#1451986512yes—
405C8—4882no—
406C8—2444no—
407C22—1222no—
408C22—1222no—
409C22—1222no—
410C22—4881no—
411C22—4881no—
412C22—4881no—
413C22—4881no—
414C22—2442no—
415C22—2442no—
416C22—2442no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22—2441no—
421C22#1684071011yescharacteristic
422C22#1684073311yescharacteristic
423C22#1684073711yescharacteristic
424C22C2×#1451983911yescharacteristic
425C22#1684075211yescharacteristic
426C22#1684075911yescharacteristic
427C22#1684076111yescharacteristic
428C4—22no—
429C4—41no—
430C4—42no—
431C4—81no—
432C4—612no—
433C4—612no—
434C4—1221no—
435C4—1221no—
436C4—4881no—
437C4—2441no—
438C4#1684079212yes—
439C4#1684079612yes—
440C2—4882no—
441C2—2442no—
442C2#2146112611yescharacteristic
443C2#2146113311yescharacteristic
444C2#2146114511yescharacteristic
445C2#2146115311yescharacteristic
446C2#2146179911yescharacteristic
447C2#2146183311yescharacteristic
448C2#2146183811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9076
LCSG ▷ C22×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×#16840781C2semidirect
2. #21461674C2semidirect
3. C2×#16840610C2semidirect
4. #21460655C2semidirect
33. C4×#92420D4semidirect
249. C61#9076semidirect

Maximal subgroups

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

subgroupindex
C2×#168407812
#214616742
C2×#168406102
#214606552
#214483272
#907661