Finite Group Databasebeta

← #29598342

Subgroups — #29598342

Order 15616.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#21450795C211yesmaximal, characteristic
2C2×#16839560C212yesmaximal, complemented
3C2×#16839558C212yesmaximal
4C4×#14519696C211yesmaximal, characteristic, complemented
5C61×#1801C211yesmaximal, characteristic, complemented
6C2×#14519775C2211yescharacteristic
7C2×#14519766C2211yescharacteristic
8C2×#14519765C411yescharacteristic
9C2×#14519696C2212yes—
10C4×#11758194—21no—
11#16839684—21no—
12#16839684—21no—
13#16839667C411yescharacteristic
14#16839663C411yescharacteristic
15#16839653—21no—
16#16839653—21no—
17C4×C4⋊Dic61C411yescharacteristic
18#16839560—24no—
19#16839558—24no—
20#16839531—21no—
21C2×C4×Q8×C61C2211yescharacteristic
22C61×#423—21no—
23C2×#101×C61C2212yes—
24C61×#343—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27C2×#11758194—22no—
28#14519775—22no—
29#14519775—22no—
30#14519766—22no—
31#14519766—22no—
32#14519765—41no—
33#14519765—41no—
34C2×C4⋊Dic61—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61C2×C411yescharacteristic
45#14519696—22no—
46#14519696D414yes—
47#14519688—41no—
48C4×#92418—41no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×Q8×C61C2311yescharacteristic
53C2×M16×C61—22no—
54C4×Q8×C61—41no—
55C4×Q8×C61—41no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61C2×C411yescharacteristic
60C2×C42×C61D411yescharacteristic
61C2×C42×C61D411yescharacteristic
62C4⋊C8×C61—41no—
63C4⋊C8×C61—41no—
64#101×C61—22no—
65#101×C61—22no—
66C23×D61—21no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61C2×D412yes—
70C2×Q8×C61#4112yes—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C2×D244—22no—
82C2×D244—41no—
83C2×D244—41no—
84C2×Dic122—22no—
85C2×Dic122—41no—
86C2×Dic122—41no—
87M16×C61—42no—
88M16×C61—42no—
89C2×C8×C61—42no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C42×C61—21no—
94C42×C61—21no—
95C42×C61—21no—
96C42×C61—21no—
97C42×C61—21no—
98C42×C61—21no—
99#11758198—42no—
100#11758198—42no—
101#11758198—42no—
102#11758198—41no—
103#11758198—41no—
104#11758198—42no—
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—42no—
108#11758196—42no—
109#11758196—41no—
110#11758196—41no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113#11758194—24no—
114#11758194—42no—
115C2×#92418—42no—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124Q8×C61—42no—
125Q8×C61—42no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61#9911yescharacteristic
140C2×C4×C61#9911yescharacteristic
141C2×C4×C61C4×D412yes—
142C2×C4×C61#12112yes—
143C2×C4×C61#12411yescharacteristic
144C2×C4×C61#12711yescharacteristic
145C2×Dic61—22no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154D244—82no—
155Dic122—82no—
156C8×C61—82no—
157#92418—44no—
158#13228—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#39011yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61#41011yescharacteristic
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—22no—
174C4×C61—21no—
175C4×C61—22no—
176C4×C61—21no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61—41no—
180Dic61—42no—
181Dic61—81no—
182Dic61—81no—
183#2545—611no—
184C2×#356—612no—
185C2×#355—612no—
186#1801D6111yescharacteristic, complemented
187C4×#101—611no—
188C2×C61—21no—
189C2×C61—21no—
190C2×C61#196411yescharacteristic
191C2×C61#213211yescharacteristic
192C2×C61#213311yescharacteristic
193D61—161no—
194C2×C4⋊Q8—611no—
195C2×#124—611no—
196C2×#124—611no—
197C2×C4×Q8C2×D6111yescharacteristic
198#423—21no—
199C2×#101—612no—
200C2×#101C2×D6112yes—
201C4×M16—1221no—
202#396—1221no—
203#396—1221no—
204#391—611no—
205#390—611no—
206#388—1221no—
207#388—1221no—
208C4×C4⋊C4—611no—
209#356—1224no—
210#355—1224no—
211#343—21no—
212#343—1221no—
213C61#1322811yescharacteristic, complemented, Sylow
214C22×Q8—611no—
215C22×Q8C22×D6111yescharacteristic
216C22×D4—611no—
217C2×M16—22no—
218C2×M16—1222no—
219C4⋊Q8—1222no—
220C4⋊Q8—1222no—
221#124—1222no—
222#124—1222no—
223#124—2441no—
224#124—2441no—
225C4×Q8—41no—
226C4×Q8—41no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4C4×D6111yescharacteristic
231C2×C4⋊C4D24411yescharacteristic
232C2×C4⋊C4C22⋊D6111yescharacteristic
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42C4×D6111yescharacteristic
242C2×C42D24411yescharacteristic
243C2×C42C22⋊D6111yescharacteristic
244C4⋊C8—41no—
245C4⋊C8—41no—
246#101—22no—
247#101—22no—
248#101—614no—
249#101—1222no—
250#97—2441no—
251C4×C8—2441no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255C24—1221no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—1222no—
259C2×Q8—2441no—
260C2×Q8—2441no—
261C2×Q8D4×D6112yes—
262C2×Q8#1175822612yes—
263C2×D4—1222no—
264C2×D4—2441no—
265C2×D4—2441no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4#1175819811yescharacteristic
270C22×C4#1175819811yescharacteristic
271C22×C4#1175819811yescharacteristic
272C22×C4#1175819811yescharacteristic
273C22×C4C2×C4×D6111yescharacteristic
274C22×C4C2×D24411yescharacteristic
275C22×C4C2×C22⋊D6111yescharacteristic
276M16—42no—
277M16—42no—
278M16—1224no—
279M16—2442no—
280C2×C8—42no—
281C2×C8—2442no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—2442no—
286C4⋊C4—2442no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C22⋊C4—2442no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2442no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—1222no—
304C42—1222no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23C2×#1175819811yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—4882no—
316D4—4882no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—1222no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4#1451969111yescharacteristic
340C2×C4#1451969111yescharacteristic
341C2×C4#1451973912yes—
342C2×C4#1451975212yes—
343C2×C4#1451976611yescharacteristic
344C2×C4#1451977311yescharacteristic
345C8—82no—
346C8—2444no—
347C22—21no—
348C22—21no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22#1683966311yescharacteristic
357C22C2×#1451969111yescharacteristic
358C22#1683973511yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—22no—
363C4—22no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—4881no—
369C4—4881no—
370C4—2442no—
371C2—21no—
372C2—21no—
373C2—9761no—
374C2#2144665411yescharacteristic
375C2#2144750211yescharacteristic
376C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1801C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC22×Q8×C61C23
hypercenter#1801D61
hypocenterC61#13228
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. C2×#16839560C2semidirect
4. C4×#14519696C2semidirect
5. C61×#1801C2semidirect
186. #1801D61semidirect
213. C61#13228semidirect

Maximal subgroups

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

subgroupindex
#214507952
C2×#168395602
C2×#168395582
C4×#145196962
C61×#18012
#1322861