Finite Group Databasebeta

← #30595711

Subgroups — #30595711

Order 15616.

568 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 124 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
2C2×#16840628C211yesmaximal, characteristic
3#21460638C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#21454169C211yesmaximal, characteristic
6C23×#92420—21no—
7C2×#14519844—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×#14519754—21no—
14C22×C4×Dic61C2211yescharacteristic
15#16839666—21no—
16#16839661C2211yescharacteristic
17#16839659—21no—
18#16839658C2211yescharacteristic
19#16839631C411yescharacteristic
20#16839622C411yescharacteristic
21#16839620—21no—
22C61×#380C411yescharacteristic
23C22×#92420—24no—
24C22×#92420—22no—
25C22×#92420—22no—
26C22×#92420—42no—
27C22×#92420—42no—
28#14519844—42no—
29C22⋊#92420—42no—
30C22×Dic122—21no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519776—42no—
34#14519754—42no—
35#14519754—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C23×C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56#95×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—41no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—41no—
70C22×Dic61—41no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61D812yes—
74C22×Dic61SD1612yes—
75C22×Dic61SD1612yes—
76C22×Dic61Q1612yes—
77C22×Dic61C2×D411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C2×Dic122—42no—
80C2×Dic122—42no—
81C2×Dic122—42no—
82C2×#92420—24no—
83C2×#92420—42no—
84C2×#92420—48no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—42no—
92C22⋊Dic61—42no—
93C4⋊Dic61—22no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97#11758196—42no—
98#11758196—42no—
99#11758196—42no—
100#11758196—41no—
101#11758196—41no—
102C4×Dic61—22no—
103C4×Dic61—22no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61#10112yes—
111C23×C61#10212yes—
112C23×C61#10312yes—
113C23×C61C2×C22⋊C411yescharacteristic
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—44no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61#13112yes—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—24no—
134C2×Dic61—24no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61#9912yes—
144C2×Dic61#10212yes—
145C2×Dic61#10312yes—
146C2×Dic61#10412yes—
147C2×Dic61C2×D811yescharacteristic
148C2×Dic61C2×SD1611yescharacteristic
149C2×Dic61C2×SD1611yescharacteristic
150C2×Dic61C2×Q1611yescharacteristic
151Dic122—84no—
152#92420—44no—
153#92420—82no—
154#7668—611nomaximal, Sylow
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—22no—
161C22×C61#33214yes—
162C22×C61#40811yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61C2×#10111yescharacteristic
165C22×C61C2×#10211yescharacteristic
166C22×C61C2×#10311yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C22×C61#42111yescharacteristic
169C4×C61—22no—
170C4×C61—41no—
171C4×C61—81no—
172C4×C61—81no—
173Dic61—21no—
174Dic61—21no—
175Dic61—21no—
176Dic61—22no—
177Dic61—21no—
178Dic61—81no—
179Dic61—81no—
180Dic61#32714yes—
181#2857—611no—
182#1797—611no—
183C2×#336—611no—
184#1271—612no—
185#1271—612no—
186C2×C61—24no—
187C2×C61#147211yescharacteristic
188C2×C61#148011yescharacteristic
189C2×C61#149311yescharacteristic
190C2×C61C2×#32711yescharacteristic
191C2×C61#152011yescharacteristic
192C2×C61#153111yescharacteristic
193C2×C61C2×#33211yescharacteristic
194C23×C8—1221no—
195C2×C4⋊Q8—611no—
196C2×C22⋊Q8—1221no—
197C22×C42—611no—
198C2×C4⋊C8—1221no—
199C2×C22⋊C8—1221no—
200#391—1221no—
201#389—611no—
202#389—611no—
203#389—1221no—
204#384—611no—
205#380—611no—
206#380—1221no—
207#380#692311yescharacteristic
208#336—612no—
209#336—612no—
210#336—1221no—
211C61#766811yescharacteristic, complemented, Sylow
212C22×Q8—1221no—
213C23×C4—611no—
214C23×C4—611no—
215C23×C4C2×#692311yescharacteristic
216C22×C8—1222no—
217C22×C8—1224no—
218C22×C8—1222no—
219C22×C8—2442no—
220C22×C8—2442no—
221C4⋊Q8—2442no—
222C22⋊Q8—2442no—
223C22⋊Q8—2442no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4C2×#692311yescharacteristic
232C2×C4⋊C4C2×#692311yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—1221no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—2442no—
240C4⋊C8—2442no—
241C22⋊C8—2442no—
242#95—21no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24C22⋊#692311yescharacteristic
247C2×Q8—2442no—
248C2×Q8—2442no—
249C2×Q8—2442no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—611no—
256C22×C4—612no—
257C22×C4—612no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—612no—
262C22×C4—612no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4C22⋊#692311yescharacteristic
270C22×C4C22×#692311yescharacteristic
271C2×C8—1224no—
272C2×C8—2442no—
273C2×C8—2442no—
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2448no—
277C2×C8—2442no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—1222no—
281C4⋊C4—2441no—
282C4⋊C4—2442no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2442no—
288C4⋊C4—2442no—
289C22⋊C4—42no—
290C22⋊C4—2442no—
291C42—1222no—
292C42—1222no—
293C42—2441no—
294C42—2441no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#1451983812yes—
300C23#1451983912yes—
301C23#1451984012yes—
302C23C2×C22⋊#692311yescharacteristic
303Q8—4884no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—612no—
317C2×C4—612no—
318C2×C4—612no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—612no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—1224no—
325C2×C4—1224no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451986412yes—
341C8—4882no—
342C8—2444no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22#1684062114yes—
350C22#1684073511yescharacteristic
351C22D61⋊#9911yescharacteristic
352C22C2×#1451983811yescharacteristic
353C22C2×#1451983911yescharacteristic
354C22C2×#1451984011yescharacteristic
355C22D61⋊#10411yescharacteristic
356C22#1684075911yescharacteristic
357C4—22no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—614no—
362C4—1221no—
363C4—1222no—
364C4—1221no—
365C4—1221no—
366C4—1221no—
367C4—4881no—
368C4—4881no—
369C2—24no—
370C2#2146109811yescharacteristic
371C2#2146112411yescharacteristic
372C2#2146116711yescharacteristic
373C2D61⋊#32711yescharacteristic
374C2#2146125711yescharacteristic
375C2#2146129111yescharacteristic
376C2C2×#1684062111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7668
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460638C2semidirect
4. #21460637C2semidirect
211. C61#7668semidirect

Maximal subgroups

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

subgroupindex
#214616752
C2×#168406282
#214606382
#214606372
#214541692
#766861