Finite Group Databasebeta

← #29595532

Subgroups — #29595532

Order 15616.

1154 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1154 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×#16840326C211yesmaximal, characteristic
2C2×#16839558C214yesmaximal, complemented
3#21445747C211yesmaximal, characteristic, complemented
4C61×#1785C211yesmaximal, characteristic, complemented
5C23×D244C411yescharacteristic
6#16840326—28no—
7C2×#14519773C412yes—
8C2×#14519766C2212yes—
9C2×#14519751—21no—
10C2×#14519751—21no—
11C2×#14519745—21no—
12C2×#14519745—21no—
13C2×#14519736C411yescharacteristic
14C2×#14519696C2212yescomplemented
15C2×#14519694—21no—
16#16839726—21no—
17#16839558—28no—
18C22×#41×C61C2211yescharacteristic
19C2×#101×C61C2212yescomplemented
20C2×#100×C61—21no—
21C61×#407—21no—
22C24×D61—21no—
23C22×D244—21no—
24C22×D244—24no—
25C22×D244—42no—
26C22×D244—42no—
27C22×D244C2×C412yes—
28C22×C22⋊D61—22no—
29C22×C22⋊D61—22no—
30C2×#11758194—22no—
31#14519773—24no—
32#14519773—24no—
33#14519766—24no—
34#14519766D418yes—
35#14519751—28no—
36#14519751—28no—
37#14519745—28no—
38#14519745—28no—
39#14519736—24no—
40C2×C4⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—22no—
43C2×#11758198—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
65C23×D61—22no—
66C23×D61—24no—
67C23×D61—42no—
68C23×D61—42no—
69C23×D61—84no—
70#41×C61—416no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C2×Q8×C61C2×D414yes—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61—22no—
77C2×D4×C61—22no—
78C2×D4×C61—22no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—22no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C22×C411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C2×C22⋊D61—28no—
97C2×C22⋊D61—28no—
98C2×C22⋊D61—84no—
99C2×C22⋊D61—84no—
100C22×Dic61—22no—
101C2×D244—24no—
102C2×D244—22no—
103C2×D244—416no—
104C2×D244—42no—
105C2×D244—42no—
106C2×D244—42no—
107C2×D244—42no—
108C2×D244C22⋊C414yes—
109M16×C61—42no—
110M16×C61—42no—
111C2×C8×C61—42no—
112C22⋊Dic61—24no—
113#11758198—28no—
114#11758198—28no—
115C4⋊Dic61—24no—
116C4×Dic61—22no—
117C4×Dic61C22⋊C414yes—
118#11758194—42no—
119#11758194—42no—
120C2×#92418—42no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—42no—
130C23×C61—42no—
131C23×C61—42no—
132C23×C61#9912yes—
133C23×C61C2×C22⋊C411yescharacteristic
134C22×D61—24no—
135C22×D61—48no—
136C22×D61—44no—
137C22×D61—44no—
138C22×D61—42no—
139C22×D61—42no—
140C22×D61—88no—
141C22×D61—88no—
142C22×D61—88no—
143Q8×C61—44no—
144D4×C61—44no—
145D4×C61—44no—
146D4×C61—44no—
147C2×C4×C61—28no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—44no—
157C2×C4×C61—44no—
158C2×C4×C61#9912yes—
159C2×C4×C61C2×C22⋊C412yes—
160C2×C4×C61#12012yes—
161C2×C4×C61#12012yes—
162C22⋊D61—88no—
163C22⋊D61—88no—
164C2×Dic61—24no—
165C2×Dic61—44no—
166D244—44no—
167D244—48no—
168D244—44no—
169C8×C61—82no—
170#92418—82no—
171#12703—611nomaximal, Sylow
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61—42no—
178C22×C61—42no—
179C22×C61—42no—
180C22×C61—42no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61#37911yescharacteristic
186C22×C61C2×#9911yescharacteristic
187C22×C61C2×#9911yescharacteristic
188C2×D61—44no—
189C2×D61—44no—
190C2×D61—44no—
191C2×D61—84no—
192C2×D61—816no—
193C2×D61—84no—
194C4×C61—22no—
195C4×C61—22no—
196C4×C61—22no—
197C4×C61—22no—
198Dic61—44no—
199C2×#535—611no—
200C2×#355—614no—
201#1785—611no—
202#1785D6111yescharacteristic, complemented
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—42no—
206C2×C61—81no—
207C2×C61—81no—
208C2×C61#178111yescharacteristic
209C2×C61#213412yes—
210D61—84no—
211C22×#41C2×D6111yescharacteristic
212C23×D4—611no—
213#535—1228no—
214C2×#127—612no—
215C2×#124—612no—
216C2×#121—1221no—
217C2×#121—1221no—
218C2×#120—1221no—
219C2×#120—1221no—
220C2×#117—611no—
221C2×#101—612no—
222C2×#101C2×D6112yescomplemented
223C2×#100—21no—
224C2×#100—1221no—
225#407—21no—
226#407—1221no—
227#355—1228no—
228C61#1270311yescharacteristic, complemented, Sylow
229C25—1221no—
230C2×#41—24no—
231C2×#41—42no—
232C2×#41—42no—
233C22×Q8C22×D6111yescharacteristic
234C22×D4—612no—
235C22×D4—1224no—
236C22×D4—1222no—
237C22×D4—1222no—
238C22×D4—1221no—
239C22×D4—2442no—
240C22×D4—2442no—
241C22×D4C4×D6111yescharacteristic
242C22×D4D24411yescharacteristic
243C22×D4C22⋊D6111yescharacteristic
244C23×C4C4×D6111yescharacteristic
245C23×C4D24411yescharacteristic
246C23×C4C22⋊D6111yescharacteristic
247C2×M16—22no—
248C2×M16—1222no—
249#127—1224no—
250#127—1224no—
251#124—618no—
252#124—1224no—
253#121—1228no—
254#121—1228no—
255#120—1228no—
256#120—1228no—
257#117—1224no—
258C2×C4⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1222no—
261C2×C22⋊C4—1222no—
262C2×C42—612no—
263#101—24no—
264#101—1224no—
265#100—42no—
266#100—2442no—
267C22⋊C8—42no—
268C22⋊C8—2442no—
269C24—1224no—
270C24—1222no—
271C24—4884no—
272C24—2442no—
273C24—2442no—
274C24#1175819811yescharacteristic
275C24#1175819811yescharacteristic
276C24#1175819811yescharacteristic
277#41—416no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8D4×D6114yes—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—614no—
291C2×D4—1224no—
292C2×D4—1228no—
293C2×D4—1228no—
294C2×D4—1222no—
295C2×D4—4884no—
296C2×D4—4884no—
297C2×D4—2442no—
298C2×D4—2442no—
299C2×D4—24416no—
300C2×D4—2442no—
301C2×D4—2442no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—1222no—
312C22×C4#1175819811yescharacteristic
313C22×C4C2×C4×D6111yescharacteristic
314C22×C4C2×D24411yescharacteristic
315C22×C4C2×C22⋊D6111yescharacteristic
316M16—42no—
317M16—42no—
318M16—2442no—
319M16—2442no—
320C2×C8—42no—
321C2×C8—2442no—
322C4⋊C4—1224no—
323C22⋊C4—1224no—
324C22⋊C4—1228no—
325C22⋊C4—1228no—
326C42—614no—
327C42—1222no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23—1224no—
340C23—4888no—
341C23—4888no—
342C23—4888no—
343C23—2444no—
344C23—2444no—
345C23—2448no—
346C23—2442no—
347C23—2442no—
348C23#1451969112yes—
349C23C2×#1175819811yescharacteristic
350Q8—44no—
351D4—44no—
352D4—44no—
353D4—44no—
354D4—4888no—
355D4—4888no—
356D4—2444no—
357D4—2448no—
358D4—2444no—
359C2×C4—28no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—1224no—
371C2×C4—2444no—
372C2×C4#1451969112yes—
373C2×C4C22⋊C4×D6112yes—
374C2×C4#1451974512yes—
375C2×C4#1451974712yes—
376C8—82no—
377C8—4882no—
378C22—22no—
379C22—22no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—81no—
391C22—4884no—
392C22—48816no—
393C22—4884no—
394C22—2444no—
395C22—2444no—
396C22—2444no—
397C22#1683961711yescharacteristic
398C22C2×#1451969111yescharacteristic
399C22C2×#1451969111yescharacteristic
400C4—22no—
401C4—22no—
402C4—22no—
403C4—22no—
404C4—2444no—
405C2—21no—
406C2—21no—
407C2—42no—
408C2—81no—
409C2—81no—
410C2—4884no—
411C2#2144573311yescharacteristic
412C2#2144751012yes—
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1785C2
socleC22×C61C2×#99
prime radicalC2×#16840326C2
cosocleC22×Q8×C61C23
hypercenter#1785D61
hypocenterC61#12703
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×#16839558C2semidirect
3. #21445747C2semidirect
4. C61×#1785C2semidirect
14. C2×#14519696C22semidirect
19. C2×#101×C61C22semidirect
202. #1785D61semidirect
222. C2×#101C2×D61semidirect
228. C61#12703semidirect

Maximal subgroups

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

subgroupindex
C2×#168403262
C2×#168395582
#214457472
C61×#17852
#1270361