Finite Group Databasebeta

← #29595535

Subgroups — #29595535

Order 15616.

962 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#16840333C211yesmaximal, characteristic
2C2×#16839560C214yesmaximal, complemented
3#21445747C211yesmaximal, characteristic
4C61×#1785C211yesmaximal, characteristic
5C23×Dic122C411yescharacteristic
6#16840333—28no—
7C2×#14519775C2212yes—
8C2×#14519764C412yes—
9C2×#14519758—21no—
10C2×#14519758—21no—
11C2×#14519756—21no—
12C2×#14519756—21no—
13C2×#14519736C411yescharacteristic
14C2×#14519696C2212yes—
15C2×#14519694—21no—
16#16839726—21no—
17#16839560—28no—
18C22×#41×C61C2211yescharacteristic
19C2×#101×C61C2212yes—
20C2×#100×C61—21no—
21C61×#407—21no—
22C22×Dic122—21no—
23C22×Dic122—24no—
24C22×Dic122—42no—
25C22×Dic122—42no—
26C22×Dic122C2×C412yes—
27C23×Dic61—21no—
28C2×#11758194—22no—
29#14519775—24no—
30#14519775D418yes—
31#14519764—24no—
32#14519764—24no—
33#14519758—28no—
34#14519758—28no—
35#14519756—28no—
36#14519756—28no—
37#14519736—24no—
38C2×C4⋊Dic61—21no—
39C2×#11758196—22no—
40C2×#11758196—22no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—22no—
43C2×C22⋊Dic61—22no—
44C2×C4×Dic61C2×C412yes—
45#14519696—24no—
46#14519694—42no—
47C22⋊#92418—42no—
48C2×#41×C61—24no—
49C2×#41×C61—42no—
50C2×#41×C61—42no—
51C22×Q8×C61C2311yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53C22×D4×C61D411yescharacteristic
54C22×D4×C61D411yescharacteristic
55C23×C4×C61C2×C411yescharacteristic
56C23×C4×C61D411yescharacteristic
57C23×C4×C61D411yescharacteristic
58C2×M16×C61—22no—
59#101×C61—24no—
60#100×C61—42no—
61C22⋊C8×C61—42no—
62C24×C61C22⋊C411yescharacteristic
63C24×C61C22⋊C411yescharacteristic
64C24×C61C22⋊C411yescharacteristic
65#41×C61—416no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61C2×D414yes—
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61—22no—
72C2×D4×C61—22no—
73C2×D4×C61—22no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×Dic61—24no—
92C22×Dic61—22no—
93C22×Dic61—22no—
94C22×Dic61—42no—
95C22×Dic61—42no—
96C2×Dic122—24no—
97C2×Dic122—22no—
98C2×Dic122—42no—
99C2×Dic122—416no—
100C2×Dic122—42no—
101C2×Dic122—42no—
102C2×Dic122—42no—
103C2×Dic122C22⋊C414yes—
104M16×C61—42no—
105M16×C61—42no—
106C2×C8×C61—42no—
107C22⋊Dic61—24no—
108C22⋊Dic61—28no—
109C22⋊Dic61—28no—
110C4⋊Dic61—24no—
111#11758196—28no—
112#11758196—28no—
113C4×Dic61—22no—
114C4×Dic61C22⋊C414yes—
115#11758194—42no—
116#11758194—42no—
117C2×#92418—42no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—42no—
129C23×C61#9912yes—
130C23×C61C2×C22⋊C411yescharacteristic
131Q8×C61—44no—
132D4×C61—44no—
133D4×C61—44no—
134D4×C61—44no—
135C2×C4×C61—28no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—44no—
145C2×C4×C61—44no—
146C2×C4×C61#9912yes—
147C2×C4×C61C2×C22⋊C412yes—
148C2×C4×C61#12012yes—
149C2×C4×C61#12012yes—
150C2×Dic61—24no—
151C2×Dic61—24no—
152C2×Dic61—48no—
153C2×Dic61—44no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156Dic122—48no—
157Dic122—44no—
158Dic122—44no—
159C8×C61—82no—
160#92418—82no—
161#12704—611nomaximal, Sylow
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61#37911yescharacteristic
176C22×C61C2×#9911yescharacteristic
177C22×C61C2×#9911yescharacteristic
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—22no—
181C4×C61—22no—
182Dic61—44no—
183Dic61—44no—
184C2×#536—611no—
185C2×#356—614no—
186#1785—611no—
187#1785D6111yescharacteristic
188C2×C61—21no—
189C2×C61—21no—
190C2×C61—42no—
191C2×C61—81no—
192C2×C61—81no—
193C2×C61#178111yescharacteristic
194C2×C61#213512yes—
195C22×#41C2×D6111yescharacteristic
196C23×Q8—611no—
197#536—1228no—
198C2×C4⋊Q8—612no—
199C2×#124—612no—
200C2×#123—1221no—
201C2×#123—1221no—
202C2×C22⋊Q8—1221no—
203C2×C22⋊Q8—1221no—
204C2×#117—611no—
205C2×#101—612no—
206C2×#101C2×D6112yes—
207C2×#100—21no—
208C2×#100—1221no—
209#407—21no—
210#407—1221no—
211#356—1228no—
212C61#1270411yescharacteristic, complemented, Sylow
213C2×#41—24no—
214C2×#41—42no—
215C2×#41—42no—
216C22×Q8—612no—
217C22×Q8—1224no—
218C22×Q8—1221no—
219C22×Q8—2442no—
220C22×Q8—2442no—
221C22×Q8C22×D6111yescharacteristic
222C22×D4C4×D6111yescharacteristic
223C22×D4D24411yescharacteristic
224C22×D4C22⋊D6111yescharacteristic
225C23×C4—1221no—
226C23×C4C4×D6111yescharacteristic
227C23×C4D24411yescharacteristic
228C23×C4C22⋊D6111yescharacteristic
229C2×M16—22no—
230C2×M16—1222no—
231C4⋊Q8—618no—
232C4⋊Q8—1224no—
233#124—1224no—
234#124—1224no—
235#123—1228no—
236#123—1228no—
237C22⋊Q8—1228no—
238C22⋊Q8—1228no—
239#117—1224no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1222no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—1222no—
246C2×C42—612no—
247#101—24no—
248#101—1224no—
249#100—42no—
250#100—2442no—
251C22⋊C8—42no—
252C22⋊C8—2442no—
253C24#1175819811yescharacteristic
254C24#1175819811yescharacteristic
255C24#1175819811yescharacteristic
256#41—416no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—614no—
260C2×Q8—1224no—
261C2×Q8—1222no—
262C2×Q8—24416no—
263C2×Q8—2442no—
264C2×Q8—2442no—
265C2×Q8—2442no—
266C2×Q8—2442no—
267C2×Q8D4×D6114yes—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—1224no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—2442no—
290C22×C4—2442no—
291C22×C4#1175819811yescharacteristic
292C22×C4C2×C4×D6111yescharacteristic
293C22×C4C2×D24411yescharacteristic
294C22×C4C2×C22⋊D6111yescharacteristic
295M16—42no—
296M16—42no—
297M16—2442no—
298M16—2442no—
299C2×C8—42no—
300C2×C8—2442no—
301C4⋊C4—1224no—
302C4⋊C4—1228no—
303C4⋊C4—1228no—
304C22⋊C4—1224no—
305C22⋊C4—1228no—
306C22⋊C4—1228no—
307C42—614no—
308C42—1222no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23#1451969112yes—
321C23C2×#1175819811yescharacteristic
322Q8—44no—
323Q8—2444no—
324Q8—2448no—
325Q8—2444no—
326D4—44no—
327D4—44no—
328D4—44no—
329C2×C4—28no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—1224no—
341C2×C4—1224no—
342C2×C4—2444no—
343C2×C4—2448no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4#1451969112yes—
347C2×C4C22⋊C4×D6112yes—
348C2×C4#1451974512yes—
349C2×C4#1451974712yes—
350C8—82no—
351C8—4882no—
352C22—22no—
353C22—22no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—41no—
362C22—41no—
363C22—81no—
364C22—81no—
365C22#1683961711yescharacteristic
366C22C2×#1451969111yescharacteristic
367C22C2×#1451969111yescharacteristic
368C4—22no—
369C4—22no—
370C4—22no—
371C4—22no—
372C4—2444no—
373C4—2444no—
374C2—21no—
375C2—21no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2#2144573311yescharacteristic
380C2#2144751312yes—
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1785C2
socleC22×C61C2×#99
prime radicalC22×#41×C61C22
cosocleC22×Q8×C61C23
hypercenter#1785D61
hypocenterC61#12704
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
2. C2×#16839560C2semidirect
212. C61#12704semidirect

Maximal subgroups

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

subgroupindex
C2×#168403332
C2×#168395602
#214457472
C61×#17852
#1270461