Finite Group Databasebeta

← #30595515

Subgroups — #30595515

Order 15616.

656 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461675C211yesmaximal, characteristic, complemented
2#21461545C211yesmaximal, characteristic, complemented
3#21460640C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21448307C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9C2×#14519832—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C22×#11758222C411yescharacteristic
13C22×C4×Dic61C2211yescharacteristic
14#16839667C411yescharacteristic
15#16839667C2211yescharacteristic
16#16839663C411yescharacteristic
17#16839663C2211yescharacteristic
18#16839639—21no—
19#16839639—21no—
20C4×#11758198—21no—
21C4×#11758198—21no—
22C2×#117×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C22⋊#92420—24no—
27C22⋊#92420—42no—
28#14519832—42no—
29C2×#11758222—22no—
30C2×#11758222—22no—
31C2×#11758222—42no—
32C2×#11758222—42no—
33C22×Dic122C2×C411yescharacteristic
34C22×D244C2×C411yescharacteristic
35C22×C22⋊D61—21no—
36C23×Dic61D411yescharacteristic
37C23×Dic61D411yescharacteristic
38C22×C4×D61—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61—42no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C23×C4×C61C2×C411yescharacteristic
53#117×C61—42no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C42×C61—21no—
58C24×C61C22⋊C411yescharacteristic
59C23×D61—21no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C2×C22⋊D61—24no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C22×Dic61—21no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83#11758222—48no—
84#11758222—48no—
85C2×D244—21no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244M1612yes—
89C2×C4×D61—24no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×Dic122—21no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122M1612yes—
96C2×#92420—24no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—42no—
105C42×C61—42no—
106#11758198—42no—
107#11758198—42no—
108#11758198—42no—
109#11758198—41no—
110#11758198—41no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61#10012yes—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—22no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C2×C4×C61—24no—
131C2×C4×C61—24no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61#9912yes—
143C2×C4×C61C2×M1611yescharacteristic
144C2×C4×C61C2×M1611yescharacteristic
145C22⋊D61—48no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—22no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—44no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61#10412yes—
162C2×Dic61#13512yes—
163C2×Dic61AGL(1,ℤ/8)11yescharacteristic
164C2×Dic61#13711yescharacteristic
165D244—42no—
166D244—42no—
167C4×D61—48no—
168Dic122—42no—
169Dic122—42no—
170#92420—44no—
171#92420—82no—
172#7612—611nomaximal, Sylow
173C22×C61—22no—
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61#40711yescharacteristic
181C22×C61C2×#9911yescharacteristic
182C22×C61C2×#10011yescharacteristic
183C22×C61#41611yescharacteristic
184C22×C61#41711yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C22×C61#42111yescharacteristic
187C2×D61—42no—
188C2×D61—42no—
189C2×D61—42no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—22no—
197C4×C61—81no—
198C4×C61—81no—
199Dic61—22no—
200Dic61—22no—
201Dic61—21no—
202Dic61—21no—
203Dic61—42no—
204Dic61—41no—
205#2297—611no—
206#1797—611no—
207#1749—611no—
208#1272—612no—
209#1270—612no—
210C2×C61—42no—
211C2×C61#146211yescharacteristic
212C2×C61#148811yescharacteristic
213C2×C61#148911yescharacteristic
214C2×C61#150111yescharacteristic
215C2×C61#151311yescharacteristic
216C2×C61#153011yescharacteristic
217C2×C61#155111yescharacteristic
218D61—82no—
219C22×#41—611no—
220C2×#117#692311yescharacteristic
221C22×C42—611no—
222C2×C4⋊C8—1221no—
223C2×C22⋊C8—1221no—
224C2×C22⋊C8—1221no—
225C2×#97—1221no—
226#391—611no—
227#391—611no—
228#390—611no—
229#390—611no—
230#386—1221no—
231#386—1221no—
232C4×C22⋊C4—1221no—
233C4×C22⋊C4—1221no—
234#336—612no—
235#336—612no—
236C61#761211yescharacteristic, complemented, Sylow
237C2×#41—1222no—
238C2×#41—1222no—
239C2×#41—2442no—
240C2×#41—2442no—
241C22×Q8—611no—
242C22×D4—611no—
243C22×D4—1221no—
244C23×C4—611no—
245C23×C4—611no—
246C23×C4—1221no—
247C23×C4C2×#692311yescharacteristic
248C22×C8—1222no—
249C22×C8—1222no—
250#117—42no—
251C2×C4⋊C4C2×#692311yescharacteristic
252C2×C4⋊C4C2×#692311yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C42—21no—
259C2×C42—611no—
260C2×C42—611no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—2442no—
264C4⋊C8—2442no—
265C22⋊C8—1224no—
266C22⋊C8—2442no—
267#97—2442no—
268#95—1221no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272C24—1221no—
273C24C22⋊#692311yescharacteristic
274#41—2448no—
275#41—2448no—
276C2×Q8—612no—
277C2×Q8—1221no—
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×D4—612no—
281C2×D4—1224no—
282C2×D4—1221no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2442no—
286C2×D4—2442no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—1224no—
298C22×C4—1222no—
299C22×C4—1221no—
300C22×C4—1222no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—2442no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2442no—
308C22×C4C22⋊#692311yescharacteristic
309C22×C4C22×#692311yescharacteristic
310C2×C8—1224no—
311C2×C8—2442no—
312C2×C8—2442no—
313C2×C8—2442no—
314C2×C8—2442no—
315C2×C8—2442no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C22⋊C4—42no—
319C22⋊C4—2442no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C42—42no—
325C42—1222no—
326C42—1222no—
327C42—2441no—
328C42—2441no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—1222no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23#1451983712yes—
343C23C2×C22⋊#692311yescharacteristic
344Q8—2442no—
345Q8—2442no—
346D4—2442no—
347D4—2442no—
348D4—2448no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—612no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—612no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1222no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—2448no—
376C2×C4—2444no—
377C2×C4—2442no—
378C2×C4—2442no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4#1451983612yes—
382C2×C4D61⋊M1611yescharacteristic
383C2×C4D61⋊M1611yescharacteristic
384C8—4882no—
385C8—2444no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—4881no—
394C22—4881no—
395C22—4881no—
396C22—4881no—
397C22—2442no—
398C22—2442no—
399C22—2442no—
400C22#1684073411yescharacteristic
401C22C2×#1451983611yescharacteristic
402C22C2×#1451983711yescharacteristic
403C22#1684075211yescharacteristic
404C22#1684075311yescharacteristic
405C22D61⋊#10411yescharacteristic
406C22#1684075911yescharacteristic
407C4—22no—
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—1222no—
413C4—1222no—
414C4—1221no—
415C4—1221no—
416C4—2442no—
417C4—2441no—
418C2—42no—
419C2—4882no—
420C2#2146106611yescharacteristic
421C2#2146115211yescharacteristic
422C2#2146115611yescharacteristic
423C2#2146119611yescharacteristic
424C2#2146123611yescharacteristic
425C2#2146128811yescharacteristic
426C2#2146133811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758222C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#7612
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21461675C2semidirect
2. #21461545C2semidirect
3. #21460640C2semidirect
4. #21460636C2semidirect
236. C61#7612semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214615452
#214606402
#214606362
#214483072
#761261