Finite Group Databasebeta

← #29596278

Subgroups — #29596278

Order 15616.

638 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 91 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#391×D61C211yesmaximal, characteristic
2#21445741C212yesmaximal
3#21443946C211yesmaximal, characteristic, complemented
4#21443945C212yesmaximal, complemented
5C61×#1394C211yesmaximal, characteristic, complemented
6C22×Q8×D61C2211yescharacteristic
7C2×C4⋊C4×D61C411yescharacteristic
8C2×C42×D61C411yescharacteristic
9C2×#14519696C2212yes—
10C2×#14519695—22no—
11#16839725—22no—
12#16839669C2211yescharacteristic
13#16839668C411yescharacteristic
14#16839667C411yescharacteristic
15#16839666—22no—
16#95×D61—22no—
17C2×#101×C61C2212yes—
18C61×#391C2211yescharacteristic
19C22×Dic122C2×C411yescharacteristic
20C22×Dic122D412yes—
21C2×Q8×D61—22no—
22C2×Q8×D61—21no—
23C2×Q8×D61—21no—
24C2×Q8×D61—42no—
25C2×Q8×D61—41no—
26C2×Q8×D61—41no—
27C22×C4×D61—21no—
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D412yes—
31C2×#11758194—22no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C4⋊C4×D61—41no—
35C4⋊C4×D61—41no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C42×D61—42no—
39#14519696—22no—
40#14519696—22no—
41#14519695—44no—
42#14519689—42no—
43#14519689—42no—
44#14519684—22no—
45#14519684—22no—
46#14519684—22no—
47C22×Q8×C61C2311yescharacteristic
48C2×M16×C61—22no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51#101×C61—22no—
52#101×C61—22no—
53#95×C61—22no—
54C23×D61C22⋊C411yescharacteristic
55C2×Q8×C61—41no—
56C2×Q8×C61—41no—
57C2×Q8×C61#4112yes—
58C2×Q8×C61#4111yescharacteristic
59C2×Q8×C61#4111yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D412yes—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C412yes—
67C22×Dic61C22⋊C411yescharacteristic
68Q8×D61—42no—
69Q8×D61—42no—
70Q8×D61—44no—
71Q8×D61—44no—
72Q8×D61—42no—
73Q8×D61—42no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—22no—
79C2×C4×D61—24no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—44no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—22no—
93C2×Dic122—22no—
94C2×Dic122—24no—
95C2×Dic122—41no—
96C2×Dic122—41no—
97C2×Dic122—42no—
98M16×C61—42no—
99M16×C61—42no—
100C2×C8×C61—42no—
101C4⋊C4×C61—41no—
102C42×C61—41no—
103C4⋊Dic61—41no—
104#11758196—42no—
105C4×Dic61—42no—
106C4×Dic61—41no—
107#11758194—42no—
108#11758194—42no—
109C2×#92418—42no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—22no—
114C22×D61—22no—
115C22×D61#9911yescharacteristic
116C22×D61#9911yescharacteristic
117Q8×C61—41no—
118Q8×C61—42no—
119Q8×C61—41no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—22no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—41no—
129C2×C4×C61#11711yescharacteristic
130C2×C4×C61#11711yescharacteristic
131C2×C4×C61#12312yes—
132C2×C4×C61#12312yes—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61#9912yes—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—48no—
153C4×D61—82no—
154C4×D61—82no—
155Dic122—44no—
156Dic122—44no—
157Dic122—42no—
158Dic122—42no—
159C8×C61—82no—
160#92418—82no—
161#12860—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61#38111yescharacteristic
165C22×C61C2×#9911yescharacteristic
166C22×C61C2×#9911yescharacteristic
167C2×D61—24no—
168C2×D61—24no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61#35512yes—
174C2×D61#35612yes—
175C4×C61—22no—
176C4×C61—22no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—42no—
180C4×C61—81no—
181Dic61—22no—
182Dic61—42no—
183Dic61—42no—
184Dic61—81no—
185C2×#391—611no—
186#1784—612no—
187#1394—612no—
188#1394—611no—
189#1394D6111yescharacteristic, complemented
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#181911yescharacteristic
193C2×C61C2×#35511yescharacteristic
194C2×C61C2×#35611yescharacteristic
195D61—22no—
196D61—22no—
197C23×Q8—611no—
198C22×C4⋊C4—611no—
199C22×C42—611no—
200C2×#101—612no—
201C2×#101—1222no—
202C2×#101C2×D6112yes—
203#407—1222no—
204#391—611no—
205#391—611no—
206#391—611no—
207#391—1222no—
208#391C2×D6111yescharacteristic
209C2×#95—1222no—
210C61#1286011yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C22×Q8—612no—
213C22×Q8—1222no—
214C22×Q8—1221no—
215C22×Q8—1221no—
216C22×Q8—2441no—
217C22×Q8—2441no—
218C22×Q8—2442no—
219C22×Q8C22×D6111yescharacteristic
220C23×C4—611no—
221C23×C4—612no—
222C23×C4—1221no—
223C23×C4—1221no—
224C2×M16—22no—
225C2×M16—1222no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—2441no—
229C2×C4⋊C4—2441no—
230C2×C4⋊C4C4×D6111yescharacteristic
231C2×C42—611no—
232C2×C42—1221no—
233C2×C42—2442no—
234C2×C42C4×D6111yescharacteristic
235#101—22no—
236#101—22no—
237#101—1222no—
238#101—1222no—
239#101—2444no—
240C22⋊C8—2442no—
241C22⋊C8—2442no—
242#95—22no—
243#95—1222no—
244#95—1222no—
245#95—1222no—
246C24—611no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—1224no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C2×Q8—1222no—
253C2×Q8—1222no—
254C2×Q8—2441no—
255C2×Q8—2441no—
256C2×Q8—2442no—
257C2×Q8—2444no—
258C2×Q8—2444no—
259C2×Q8—2442no—
260C2×Q8—2442no—
261C2×Q8—2442no—
262C2×Q8—2442no—
263C2×Q8#1175822212yes—
264C2×Q8#1175822411yescharacteristic
265C2×Q8#1175822611yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—611no—
269C22×C4—612no—
270C22×C4—1222no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4—1224no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—2442no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2444no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4C2×C4×D6111yescharacteristic
289C22×C4D4×D6112yes—
290M16—42no—
291M16—42no—
292M16—2442no—
293M16—2442no—
294C2×C8—42no—
295C2×C8—2442no—
296C4⋊C4—41no—
297C4⋊C4—2441no—
298C4⋊C4—2442no—
299C42—41no—
300C42—2441no—
301C42—2442no—
302C23—611no—
303C23—611no—
304C23—1222no—
305C23—1222no—
306C23—1221no—
307C23—1221no—
308C23C22⋊C4×D6111yescharacteristic
309Q8—42no—
310Q8—41no—
311Q8—41no—
312Q8—2444no—
313Q8—2444no—
314Q8—2442no—
315Q8—2442no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—612no—
326C2×C4—1222no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—4882no—
337C2×C4—4882no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2448no—
343C2×C4—2442no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4#1451973411yescharacteristic
348C2×C4#1451973511yescharacteristic
349C2×C4#1451975912yes—
350C2×C4#1451976212yes—
351C8—82no—
352C8—4882no—
353C22—21no—
354C22—21no—
355C22—612no—
356C22—612no—
357C22—1224no—
358C22—1224no—
359C22—1221no—
360C22—1221no—
361C22—1221no—
362C22—1221no—
363C22#1683962411yescharacteristic
364C22#99×D6111yescharacteristic
365C22#99×D6111yescharacteristic
366C4—22no—
367C4—22no—
368C4—21no—
369C4—21no—
370C4—42no—
371C4—81no—
372C4—1222no—
373C4—4881no—
374C4—2442no—
375C4—2442no—
376C2—21no—
377C2—21no—
378C2—1222no—
379C2—1222no—
380C2#2144589211yescharacteristic
381C2#355×D6111yescharacteristic
382C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1394C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC22×Q8×C61C23
hypercenter#1394D61
hypocenterC61#12860
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
3. #21443946C2semidirect
4. #21443945C2semidirect
5. C61×#1394C2semidirect
189. #1394D61semidirect
210. C61#12860semidirect

Maximal subgroups

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

subgroupindex
#391×D612
#214457412
#214439462
#214439452
C61×#13942
#1286061