Finite Group Databasebeta

← #30602183

Subgroups — #30602183

Order 15616.

600 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461673C211yesmaximal, characteristic
2#21461545C211yesmaximal, characteristic
3#21460657C212yesmaximal
4#21460657C212yesmaximal
5C2×#16839657C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420C2212yes—
8C2×C22⋊#92420C2212yes—
9C2×#14519832—21no—
10#16840628—21no—
11#16840628—21no—
12C22×#11758196C411yescharacteristic
13C22×#11758196C411yescharacteristic
14C22×#11758196C411yescharacteristic
15C22×C4×Dic61C2211yescharacteristic
16#16839657—21no—
17#16839657—21no—
18#16839657—21no—
19#16839657—21no—
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2211yescharacteristic
22C22×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C22⋊#92420—22no—
27C22⋊#92420—24no—
28C22⋊#92420Q814yes—
29#14519832—42no—
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2311yescharacteristic
34C2×#11758196—22no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—22no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—42no—
43C2×#11758196—42no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C23×C4×C61C2×C411yescharacteristic
54C23×C4×C61C2×C411yescharacteristic
55C23×C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—42no—
59C24×C61C22×C411yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61M1612yes—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—22no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61M1612yes—
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×Q812yes—
94C22×Dic61#4112yes—
95C2×#92420—24no—
96C2×#92420—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101C4⋊C4×C61—42no—
102C4⋊C4×C61—42no—
103#11758196—24no—
104#11758196—24no—
105#11758196—42no—
106#11758196—42no—
107#11758196—42no—
108#11758196—42no—
109C4×Dic61—22no—
110C4×Dic61—22no—
111C4×Dic61—41no—
112C4×Dic61—41no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61C2×C22⋊C411yescharacteristic
118C23×C61C4×Q812yes—
119C23×C61C2×M1611yescharacteristic
120C23×C61C2×M1611yescharacteristic
121C23×C61#13112yes—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—44no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—82no—
137C2×C4×C61#10012yes—
138C2×Dic61—24no—
139C2×Dic61—24no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—22no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—42no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—82no—
159C2×Dic61#9912yes—
160C2×Dic61#10112yes—
161C2×Dic61C22⋊Q812yes—
162C2×Dic61#12411yescharacteristic
163C2×Dic61C4⋊Q811yescharacteristic
164#92420—44no—
165#92420—82no—
166#9883—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—22no—
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—22no—
175C22×C61#39111yescharacteristic
176C22×C61#40711yescharacteristic
177C22×C61#40811yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61#41011yescharacteristic
180C22×C61C2×#10011yescharacteristic
181C22×C61C2×#10111yescharacteristic
182C22×C61#44612yes—
183C22×C61#44612yes—
184C4×C61—22no—
185C4×C61—42no—
186C4×C61—41no—
187C4×C61—81no—
188Dic61—22no—
189Dic61—22no—
190Dic61—22no—
191Dic61—21no—
192Dic61—21no—
193Dic61—42no—
194Dic61—81no—
195C2×#389—611no—
196#1797—611no—
197#1749—611no—
198#1280—612no—
199#1280—612no—
200C2×C61—22no—
201C2×C61—22no—
202C2×C61#146311yescharacteristic
203C2×C61#146611yescharacteristic
204C2×C61#147011yescharacteristic
205C2×C61#147111yescharacteristic
206C2×C61#198511yescharacteristic
207C2×C61#199611yescharacteristic
208C2×C61#199711yescharacteristic
209C22×C4⋊C4—611no—
210C22×C4⋊C4—611no—
211C22×C4⋊C4—611no—
212C22×C4⋊C4#692311yescharacteristic
213C22×C42—611no—
214C2×C4⋊C8—1221no—
215C2×C22⋊C8—612no—
216C2×C22⋊C8—612no—
217C2×#97—1221no—
218#389—1221no—
219#389—1221no—
220#389—1221no—
221#389—1221no—
222C2×#95—611no—
223C2×#95—611no—
224#336—1221no—
225#336—1221no—
226C61#988311yescharacteristic, complemented, Sylow
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—611no—
231C23×C4C2×#692311yescharacteristic
232C23×C4C2×#692311yescharacteristic
233C23×C4C2×#692311yescharacteristic
234C22×C8—1222no—
235C22×C8—1222no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1222no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—2442no—
248C2×C4⋊C4—2442no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—2442no—
254C4⋊C8—2442no—
255C22⋊C8—614no—
256C22⋊C8—1222no—
257C22⋊C8—1224no—
258#97—2442no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263C24C22×#692311yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—612no—
280C22×C4—612no—
281C22×C4—612no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1222no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4#1175821312yes—
297C22×C4C22⋊#692311yescharacteristic
298C22×C4C22⋊#692311yescharacteristic
299C2×C8—1224no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8—2442no—
304C2×C8—2442no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—1224no—
308C4⋊C4—1224no—
309C4⋊C4—2442no—
310C4⋊C4—2442no—
311C4⋊C4—2442no—
312C4⋊C4—2442no—
313C42—1222no—
314C42—1222no—
315C42—2441no—
316C42—2441no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C22⋊#692311yescharacteristic
322C23Q8×#692312yes—
323C23D61⋊M1611yescharacteristic
324C23C2×#1175821311yescharacteristic
325C23#1451986412yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4—612no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—612no—
345C2×C4—612no—
346C2×C4—1224no—
347C2×C4—1224no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1222no—
357C2×C4—4882no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2442no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2442no—
367C2×C4#1451983712yes—
368C8—4882no—
369C8—2444no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22(C2×#6923)⋊Q811yescharacteristic
379C22#1684073311yescharacteristic
380C22#1684073511yescharacteristic
381C22D61⋊#9911yescharacteristic
382C22#1684074111yescharacteristic
383C22C2×#1451983711yescharacteristic
384C22D61⋊#10111yescharacteristic
385C22#1684081212yes—
386C22#1684081412yes—
387C4—22no—
388C4—42no—
389C4—41no—
390C4—81no—
391C4—1222no—
392C4—1222no—
393C4—1221no—
394C4—1222no—
395C4—1221no—
396C4—4881no—
397C4—2442no—
398C2—22no—
399C2—22no—
400C2#2146106811yescharacteristic
401C2#2146107811yescharacteristic
402C2#2146109111yescharacteristic
403C2#2146109511yescharacteristic
404C2#2146199211yescharacteristic
405C2#2146201011yescharacteristic
406C2#2146201111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#9883
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
226. C61#9883semidirect

Maximal subgroups

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

subgroupindex
#214616732
#214615452
#214606572
C2×#168396572
#988361