Finite Group Databasebeta

← #30601661

Subgroups — #30601661

Order 15616.

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

normal subgroups only

This group has 920 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#21461675C211yesmaximal, characteristic, complemented
2#21461545C211yesmaximal, characteristic, complemented
3C2×#16840606C214yesmaximal, complemented
4C2×#16839663C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×C22⋊#92420C2212yes—
7C2×C22⋊#92420C2212yes—
8C2×#14519832—21no—
9#16840628—21no—
10#16840628—21no—
11#16840606—28no—
12C23×D244C411yescharacteristic
13C22×#11758198C412yes—
14C22×#11758198C2212yes—
15C22×C4×Dic61C2211yescharacteristic
16#16839663—21no—
17#16839663—21no—
18#16839663—21no—
19#16839663—21no—
20C22×C4⋊C4×C61C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23#14519844—42no—
24C22⋊#92420—22no—
25C22⋊#92420—24no—
26C22⋊#92420D414yescomplemented
27#14519832—42no—
28C24×D61C2×C412yes—
29C22×D244—24no—
30C22×D244—21no—
31C22×D244—21no—
32C22×D244—42no—
33C22×D244—42no—
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2311yescharacteristic
36C2×#11758198—22no—
37C2×#11758198—22no—
38C2×#11758198—24no—
39C2×#11758198—22no—
40C2×#11758198—22no—
41C2×#11758198—24no—
42C2×#11758198—44no—
43C2×C4×Dic61—42no—
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C23×C4×C61C2×C412yes—
49C23×C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—42no—
53C24×C61C22×C411yescharacteristic
54C23×D61—22no—
55C23×D61—22no—
56C23×D61—24no—
57C23×D61—24no—
58C23×D61—42no—
59C23×D61—42no—
60C23×D61—42no—
61C23×D61—42no—
62C23×D61M1614yes—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—24no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D412yes—
82C22×Dic61#4112yes—
83C2×D244—24no—
84C2×D244—24no—
85C2×D244—416no—
86C2×D244—42no—
87C2×D244—42no—
88C2×D244—42no—
89C2×D244—42no—
90C2×#92420—24no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C4⋊C4×C61—42no—
97C4⋊C4×C61—42no—
98#11758198—44no—
99#11758198—44no—
100#11758198—44no—
101#11758198—42no—
102#11758198—42no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61C2×C22⋊C411yescharacteristic
112C23×C61C4×D412yes—
113C23×C61C2×M1612yes—
114C23×C61#13112yes—
115C22×D61—24no—
116C22×D61—28no—
117C22×D61—44no—
118C22×D61—44no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61—44no—
126C22×D61—44no—
127C22×D61—44no—
128C22×D61—84no—
129C22×D61—84no—
130C22×D61—84no—
131C22×D61—84no—
132C2×C4×C61—28no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—84no—
141C2×C4×C61#9912yes—
142C2×C4×C61#10012yes—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—44no—
155C2×Dic61#10012yes—
156C2×Dic61#12112yes—
157C2×Dic61#12411yescharacteristic
158C2×Dic61#12711yescharacteristic
159D244—48no—
160D244—48no—
161#92420—44no—
162#92420—82no—
163#9653—611nomaximal, Sylow
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—22no—
170C22×C61#39011yescharacteristic
171C22×C61#40711yescharacteristic
172C22×C61#40811yescharacteristic
173C22×C61C2×#9911yescharacteristic
174C22×C61#41011yescharacteristic
175C22×C61C2×#10011yescharacteristic
176C22×C61C2×#10011yescharacteristic
177C22×C61#43514yes—
178C2×D61—44no—
179C2×D61—44no—
180C2×D61—44no—
181C2×D61—88no—
182C2×D61—82no—
183C2×D61—82no—
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—88no—
187C4×C61—22no—
188C4×C61—22no—
189C4×C61—82no—
190Dic61—22no—
191Dic61—21no—
192Dic61—21no—
193Dic61—22no—
194Dic61—41no—
195C2×#390—611no—
196#1797—611no—
197#1749—611no—
198C2×#323—614no—
199C2×C61—24no—
200C2×C61#146211yescharacteristic
201C2×C61#146611yescharacteristic
202C2×C61#146911yescharacteristic
203C2×C61#147111yescharacteristic
204C2×C61#195511yescharacteristic
205C2×C61#196411yescharacteristic
206C2×C61#196511yescharacteristic
207D61—84no—
208C23×D4—611no—
209C22×C4⋊C4#692311yescharacteristic
210C22×C22⋊C4—612no—
211C22×C22⋊C4—612no—
212C22×C42—611no—
213C2×C4⋊C8—1221no—
214C2×C22⋊C8—612no—
215C2×C22⋊C8—612no—
216C2×#97—1221no—
217#390—1221no—
218#390—1221no—
219#390—1221no—
220#390—1221no—
221#336—1221no—
222#336—1221no—
223#323—1228no—
224C61#965311yescharacteristic, complemented, Sylow
225C25—612no—
226C22×D4—1224no—
227C22×D4—1221no—
228C22×D4—1221no—
229C22×D4—2442no—
230C22×D4—2442no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4C2×#692312yes—
234C23×C4C2×#692311yescharacteristic
235C22×C8—1222no—
236C22×C8—1222no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—42no—
240C2×C22⋊C4—1224no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1222no—
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—1224no—
246C2×C22⋊C4—2444no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—2442no—
252C4⋊C8—2442no—
253C22⋊C8—614no—
254C22⋊C8—1222no—
255C22⋊C8—1224no—
256#97—2442no—
257C24—614no—
258C24—1224no—
259C24—1224no—
260C24—1222no—
261C24—1222no—
262C24—2442no—
263C24—2442no—
264C24—2442no—
265C24—2442no—
266C24C22×#692311yescharacteristic
267C2×D4—1224no—
268C2×D4—1224no—
269C2×D4—24416no—
270C2×D4—2442no—
271C2×D4—2442no—
272C2×D4—2442no—
273C2×D4—2442no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—612no—
285C22×C4—612no—
286C22×C4—611no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4C22⋊#692311yescharacteristic
293C22×C4C22⋊#692311yescharacteristic
294C2×C8—1224no—
295C2×C8—2442no—
296C2×C8—2442no—
297C2×C8—2442no—
298C2×C8—2442no—
299C2×C8—2442no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C22⋊C4—2444no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2444no—
306C22⋊C4—2444no—
307C42—1222no—
308C42—1222no—
309C42—2441no—
310C42—2441no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—1228no—
316C23—1224no—
317C23—4884no—
318C23—4884no—
319C23—4884no—
320C23—4884no—
321C23—2444no—
322C23—2444no—
323C23—2444no—
324C23—2444no—
325C23—2442no—
326C23—2442no—
327C23—2442no—
328C23—2442no—
329C23—2442no—
330C23—2442no—
331C23—2444no—
332C23C2×C22⋊#692311yescharacteristic
333C23D4×#692312yes—
334C23D61⋊M1612yes—
335C23#1451986512yes—
336D4—2448no—
337D4—2448no—
338C2×C4—28no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—84no—
347C2×C4—612no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—612no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2444no—
363C2×C4#1451983612yes—
364C2×C4#1451983712yes—
365C8—4882no—
366C8—2444no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—4888no—
374C22—4888no—
375C22—4882no—
376C22—4882no—
377C22—4882no—
378C22—4882no—
379C22—2444no—
380C22—2444no—
381C22—2444no—
382C22#1684071411yescharacteristic
383C22#1684073411yescharacteristic
384C22#1684073711yescharacteristic
385C22C2×#1451983611yescharacteristic
386C22#1684074311yescharacteristic
387C22C2×#1451983711yescharacteristic
388C22D61⋊#10011yescharacteristic
389C22#1684079214yes—
390C4—22no—
391C4—22no—
392C4—82no—
393C4—1222no—
394C4—1221no—
395C4—1222no—
396C4—1221no—
397C4—2441no—
398C2—24no—
399C2—4884no—
400C2#2146106611yescharacteristic
401C2#2146108011yescharacteristic
402C2#2146109011yescharacteristic
403C2#2146109611yescharacteristic
404C2#2146194511yescharacteristic
405C2#2146195911yescharacteristic
406C2#2146196111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#9653
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
1. #21461675C2semidirect
2. #21461545C2semidirect
3. C2×#16840606C2semidirect
26. C22⋊#92420D4semidirect
224. C61#9653semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214615452
C2×#168406062
C2×#168396632
#965361