Finite Group Databasebeta

← #30595914

Subgroups — #30595914

Order 15616.

634 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461710C211yesmaximal, characteristic, complemented
2#21461673C211yesmaximal, characteristic, complemented
3#21460636C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454162C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519773C411yescharacteristic
13C2×#14519751C411yescharacteristic
14C2×#14519749—21no—
15C2×#14519749—21no—
16C22×C4×Dic61C2211yescharacteristic
17#16839665C2211yescharacteristic
18#16839663C2211yescharacteristic
19#16839662—21no—
20#16839662—21no—
21#16839631C411yescharacteristic
22C2×#121×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C22⋊#92420—42no—
27C22⋊#92420—42no—
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C22×C22⋊D61—21no—
31C22×C22⋊D61—21no—
32C23×Dic61D411yescharacteristic
33C23×Dic61D411yescharacteristic
34#14519773—42no—
35#14519751—42no—
36#14519749—44no—
37#14519749—42no—
38#14519749—42no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—42no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52C22×D4×C61—21no—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61C2×C411yescharacteristic
55#121×C61—42no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C24×C61—21no—
59C24×C61C22⋊C411yescharacteristic
60C23×D61—21no—
61C2×D4×C61—22no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61—42no—
65C2×D4×C61—42no—
66C2×D4×C61—42no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C22×Dic61—22no—
83C22×Dic61—22no—
84C22×Dic61—21no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61D812yes—
91C22×Dic61SD1612yes—
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C2×D244—22no—
95C2×D244—41no—
96C2×D244—41no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—42no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61—42no—
108#11758198—42no—
109#11758198—41no—
110#11758198—41no—
111#11758198—42no—
112C4⋊Dic61—41no—
113#11758196—42no—
114#11758196—42no—
115C4×Dic61—22no—
116C4×Dic61—22no—
117C4×Dic61—41no—
118C4×Dic61—41no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61#10212yes—
133C23×C61C2×C22⋊C411yescharacteristic
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141D4×C61—82no—
142D4×C61—84no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—44no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61#10012yes—
152C2×C4×C61#13112yes—
153C22⋊D61—84no—
154C22⋊D61—84no—
155C22⋊D61—84no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—42no—
165C2×Dic61—42no—
166C2×Dic61—44no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61#9912yes—
171C2×Dic61#10212yes—
172C2×Dic61C2×D811yescharacteristic
173C2×Dic61C2×SD1611yescharacteristic
174C2×Dic61AGL(1,ℤ/8)12yes—
175D244—82no—
176#92420—82no—
177#92420—82no—
178#7724—611nomaximal, Sylow
179C22×C61—22no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61#40811yescharacteristic
194C22×C61C2×#9911yescharacteristic
195C22×C61C2×#10011yescharacteristic
196C22×C61C2×#10211yescharacteristic
197C22×C61#41811yescharacteristic
198C22×C61#42111yescharacteristic
199C22×C61#42111yescharacteristic
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C4×C61—22no—
208C4×C61—22no—
209C4×C61—81no—
210Dic61—22no—
211Dic61—22no—
212Dic61—21no—
213Dic61—22no—
214Dic61—21no—
215Dic61—81no—
216#2856—611no—
217#1817—611no—
218#1797—611no—
219#1270—612no—
220#1270—612no—
221C2×C61—42no—
222C2×C61—161no—
223C2×C61#147111yescharacteristic
224C2×C61#148011yescharacteristic
225C2×C61#149611yescharacteristic
226C2×C61#151011yescharacteristic
227C2×C61#151911yescharacteristic
228C2×C61#153611yescharacteristic
229C2×C61#154511yescharacteristic
230D61—161no—
231C2×#127—611no—
232C2×#121—611no—
233C2×#121—1221no—
234C2×#121—1221no—
235C2×#121#692311yescharacteristic
236C22×C42—611no—
237C2×C4⋊C8—1221no—
238C2×C22⋊C8—1221no—
239C2×C22⋊C8—1221no—
240#390—611no—
241#390—611no—
242#390—1221no—
243#390—1221no—
244#384—611no—
245#336—612no—
246#336—612no—
247#336—1221no—
248C61#772411yescharacteristic, complemented, Sylow
249C22×D4—21no—
250C22×D4—611no—
251C22×D4—1221no—
252C22×D4—1221no—
253C22×D4—1221no—
254C22×D4C2×#692311yescharacteristic
255C23×C4—611no—
256C23×C4—611no—
257C23×C4C2×#692311yescharacteristic
258C22×C8—1222no—
259C22×C8—1222no—
260#127—2442no—
261#121—42no—
262#121—2442no—
263#121—2442no—
264#121—2444no—
265#121—2442no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4C2×#692311yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C42—611no—
277C2×C42—611no—
278C2×C42—611no—
279C2×C42—611no—
280C2×C42—2442no—
281C4⋊C8—2442no—
282C22⋊C8—2442no—
283C22⋊C8—2442no—
284C24—21no—
285C24—1221no—
286C24C22⋊#692311yescharacteristic
287C2×D4—22no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—1222no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2442no—
297C2×D4—2442no—
298C2×D4—2442no—
299C2×D4—2442no—
300C2×D4—2442no—
301C2×D4—2442no—
302C2×D4—2442no—
303C2×D4—2442no—
304C2×D4—2442no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—612no—
314C22×C4—612no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1221no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4—2441no—
321C22×C4C22⋊#692311yescharacteristic
322C22×C4C22×#692311yescharacteristic
323C2×C8—2442no—
324C2×C8—2442no—
325C2×C8—2442no—
326C2×C8—2442no—
327C2×C8—2442no—
328C2×C8—2442no—
329C4⋊C4—41no—
330C4⋊C4—2441no—
331C4⋊C4—2442no—
332C4⋊C4—2442no—
333C22⋊C4—42no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2442no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C42—1222no—
342C42—1222no—
343C42—2441no—
344C42—2441no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23—2441no—
365C23#1451983912yes—
366C23C2×C22⋊#692311yescharacteristic
367D4—82no—
368D4—84no—
369D4—4882no—
370D4—4884no—
371D4—4884no—
372D4—4884no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—44no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—612no—
382C2×C4—612no—
383C2×C4—611no—
384C2×C4—611no—
385C2×C4—612no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2444no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4#1451983712yes—
401C2×C4#1451986412yes—
402C8—4882no—
403C8—4882no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—4881no—
419C22—4881no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22—4881no—
424C22—4881no—
425C22#1684073511yescharacteristic
426C22D61⋊#9911yescharacteristic
427C22C2×#1451983711yescharacteristic
428C22C2×#1451983911yescharacteristic
429C22#1684075411yescharacteristic
430C22#1684075911yescharacteristic
431C22#1684075911yescharacteristic
432C4—22no—
433C4—22no—
434C4—81no—
435C4—1221no—
436C4—1221no—
437C4—1222no—
438C4—1222no—
439C4—1222no—
440C4—4881no—
441C2—42no—
442C2—161no—
443C2—9761no—
444C2#2146109511yescharacteristic
445C2#2146112411yescharacteristic
446C2#2146117811yescharacteristic
447C2#2146122511yescharacteristic
448C2#2146125411yescharacteristic
449C2#2146130711yescharacteristic
450C2#2146132611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#121×C61C4
socleC23×C61C2×C22⋊C4
prime radical#21454162C2
cosocleC2×C4×Dic61C23
hypercenterC2×#121#6923
hypocenterC61#7724
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461710C2semidirect
2. #21461673C2semidirect
3. #21460636C2semidirect
4. #21460635C2semidirect
248. C61#7724semidirect

Maximal subgroups

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

subgroupindex
#214617102
#214616732
#214606362
#214606352
#214541622
#772461