Finite Group Databasebeta

← #29568493

Subgroups — #29568493

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454168C211yesmaximal, characteristic
2#21445576C211yesmaximal, characteristic
3#21445511C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic, complemented
5#21443644C211yesmaximal, characteristic, complemented
6#21443644C211yesmaximal, characteristic, complemented
7C61×#1272C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519775C411yescharacteristic
10C2×#14519757C411yescharacteristic
11C2×#14519753C411yescharacteristic
12C2×C42×D61C2211yescharacteristic
13C2×#14519689—21no—
14C2×C8×Dic61—21no—
15#16839668C2211yescharacteristic
16#16839659—21no—
17#16839659—21no—
18#16839631C411yescharacteristic
19#16839621—21no—
20#16839621—21no—
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—24no—
32C2×#11758189—42no—
33C2×#11758189—42no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519775—42no—
37#14519757—42no—
38#14519753—42no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C42×D61—42no—
52#14519689—24no—
53C8×Dic61—42no—
54#14519684—21no—
55#14519684—21no—
56C22×Q8×C61C2×C411yescharacteristic
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C42×C61C2311yescharacteristic
61#95×C61—21no—
62#95×C61—21no—
63C23×D61C22⋊C411yescharacteristic
64C2×Q8×C61—21no—
65C2×Q8×C61—21no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61SD1612yes—
89C2×C4×D61Q1612yes—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61—41no—
102#11758198—42no—
103#11758198—42no—
104C4⋊Dic61—42no—
105C4⋊Dic61—41no—
106#11758196—42no—
107#11758196—42no—
108#11758196—42no—
109#11758196—42no—
110#11758196—42no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—41no—
114C2×#92418—22no—
115C2×#92418—22no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120#11758189—48no—
121C23×C61C2×C22⋊C411yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61#10312yes—
129Q8×C61—81no—
130Q8×C61—81no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61#13111yescharacteristic
144C2×C4×C61#13111yescharacteristic
145C2×C4×C61C2×SD1611yescharacteristic
146C2×C4×C61C2×Q1611yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61#9912yes—
160C2×Dic61#10012yes—
161C2×Dic61#10312yes—
162C2×Dic61#10412yes—
163C2×Dic61#10412yes—
164C4×D61—24no—
165C4×D61—24no—
166C4×D61—42no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—42no—
170Dic122—81no—
171Dic122—81no—
172C8×C61—42no—
173C8×C61—42no—
174#92418—42no—
175#92418—42no—
176#7687—611nomaximal, Sylow
177C22×C61#40811yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61C2×#10011yescharacteristic
180C22×C61C2×#10311yescharacteristic
181C22×C61#41911yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C22×C61C2×#10411yescharacteristic
184C2×D61—22no—
185C2×D61—22no—
186C2×D61—22no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—81no—
198C4×C61—81no—
199Dic61—22no—
200Dic61—22no—
201Dic61—81no—
202Dic61—81no—
203Dic61#32814yes—
204#2857—611no—
205C4×C22⋊C8—611no—
206#1728—611no—
207#1272—611no—
208#1272—611no—
209#1272—611no—
210#1272D6111yescharacteristic, complemented
211C2×C61#147111yescharacteristic
212C2×C61#148511yescharacteristic
213C2×C61#149311yescharacteristic
214C2×C61C2×#32811yescharacteristic
215C2×C61#150811yescharacteristic
216C2×C61#152511yescharacteristic
217C2×C61#154811yescharacteristic
218D61—42no—
219C22×M16—1221no—
220C2×C4⋊Q8—611no—
221C2×C22⋊Q8—611no—
222C2×C22⋊Q8—611no—
223C22×C42—611no—
224C2×C22⋊C8—1221no—
225C2×C4×C8—1221no—
226#391—611no—
227#391C2×D6111yescharacteristic
228#389—1221no—
229#389—1221no—
230#384—611no—
231#380—1221no—
232#380—1221no—
233#336—611no—
234#336—611no—
235#336—1221no—
236#336C2×D6111yescharacteristic
237#336C2×D6111yescharacteristic
238C61#768711yescharacteristic, complemented, Sylow
239C22×Q8—611no—
240C22×Q8C4×D6111yescharacteristic
241C23×C4—611no—
242C23×C4—611no—
243C23×C4—611no—
244C2×M16—1224no—
245C2×M16—2442no—
246C2×M16—2442no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—1221no—
250C22×C8—1221no—
251C4⋊Q8—2442no—
252C22⋊Q8—2442no—
253C22⋊Q8—2442no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4C4×D6111yescharacteristic
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C42—611no—
265C2×C42—611no—
266C2×C42—611no—
267C2×C42—2442no—
268C2×C42C22×D6111yescharacteristic
269C22⋊C8—1224no—
270C4×C8—2442no—
271#95—21no—
272#95—21no—
273#95—1221no—
274#95—1221no—
275C24—611no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—1221no—
281C2×Q8—1221no—
282C2×Q8—2441no—
283C2×Q8—2441no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—612no—
290C22×C4—612no—
291C22×C4—1222no—
292C22×C4—1222no—
293C22×C4—1222no—
294C22×C4—1222no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4C2×C4×D6111yescharacteristic
304C22×C4D4×D6111yescharacteristic
305C22×C4D4×D6111yescharacteristic
306M16—2448no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—2441no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C4⋊C4—41no—
320C4⋊C4—2441no—
321C4⋊C4—2442no—
322C4⋊C4—2442no—
323C4⋊C4—2442no—
324C4⋊C4—2442no—
325C4⋊C4—2442no—
326C4⋊C4—2442no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C42—41no—
330C42—1222no—
331C42—1222no—
332C42—2441no—
333C23—612no—
334C23—1221no—
335C23—1221no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23C22⋊C4×D6111yescharacteristic
341Q8—81no—
342Q8—81no—
343Q8—4881no—
344Q8—4881no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—612no—
358C2×C4—612no—
359C2×C4—612no—
360C2×C4—612no—
361C2×C4—612no—
362C2×C4—1224no—
363C2×C4—1224no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4#1451978311yescharacteristic
379C2×C4#1451978511yescharacteristic
380C2×C4SD16×D6111yescharacteristic
381C2×C4Q16×D6111yescharacteristic
382C2×C4#1451980611yescharacteristic
383C2×C4#1451980911yescharacteristic
384C8—42no—
385C8—42no—
386C8—2442no—
387C8—2442no—
388C22—1222no—
389C22—1222no—
390C22—1222no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22#1683972711yescharacteristic
396C22#99×D6111yescharacteristic
397C22#100×D6111yescharacteristic
398C22#103×D6111yescharacteristic
399C22#1683976911yescharacteristic
400C22#104×D6111yescharacteristic
401C22#104×D6111yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—614no—
411C4—1222no—
412C4—1222no—
413C4—4881no—
414C4—4881no—
415C2—2442no—
416C2#2144417711yescharacteristic
417C2#2144423811yescharacteristic
418C2#2144427211yescharacteristic
419C2#328×D6111yescharacteristic
420C2#2144433711yescharacteristic
421C2#2144440911yescharacteristic
422C2#2144449811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7687
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #21443645C2semidirect
5. #21443644C2semidirect
6. #21443644C2semidirect
7. C61×#1272C2semidirect
210. #1272D61semidirect
238. C61#7687semidirect

Maximal subgroups

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

subgroupindex
#214541682
#214455762
#214455112
#214436452
#214436442
C61×#12722
#768761