Finite Group Databasebeta

← #29577334

Subgroups — #29577334

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454843C211yesmaximal, characteristic, complemented
2#21445807C211yesmaximal, characteristic, complemented
3#21444387C212yesmaximal, complemented
4#21443698C212yesmaximal, complemented
5C61×#2543C211yesmaximal, characteristic
6D4×#92418—24no—
7#16839815—21no—
8C2×#14519692—21no—
9C2×C22⋊#92418—21no—
10C2×C22⋊#92418C2212yes—
11#16839622C2212yes—
12#16839529—21no—
13#16839496—24no—
14C2×#121×C61—21no—
15C2×#121×C61C2211yescharacteristic
16C2×C4×D4×C61C2211yescharacteristic
17C61×#398C411yescharacteristic, complemented
18C61×#397C411yescharacteristic, complemented
19C61×#394C411yescharacteristic, complemented
20C61×#392C411yescharacteristic, complemented
21C61×#388—21no—
22C61×#386—21no—
23C61×#386—21no—
24C2×#95×C61C2211yescharacteristic
25C22×#92418—22no—
26C22×#92418—22no—
27C2×C4⋊Dic61—22no—
28C2×C22⋊Dic61—22no—
29C4⋊#92418—22no—
30#14519692—42no—
31C22⋊#92418—22no—
32C22⋊#92418—22no—
33C22⋊#92418D414yescomplemented
34C4×#92418—22no—
35#14519684—22no—
36C22×D4×C61—21no—
37C22×D4×C61—21no—
38C22×D4×C61C2×C411yescharacteristic
39C22×D4×C61D411yescharacteristic
40C23×C4×C61—21no—
41C23×C4×C61D411yescharacteristic
42C23×C4×C61C2311yescharacteristic
43#121×C61—22no—
44#121×C61—22no—
45#121×C61—42no—
46#121×C61—42no—
47C4×D4×C61—22no—
48C4×D4×C61—22no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64#95×C61C2×C411yescharacteristic
65C24×C61—21no—
66C24×C61C22⋊C411yescharacteristic
67C24×C61C2×D411yescharacteristic
68C2×D4×C61—22no—
69C2×D4×C61—22no—
70C2×D4×C61—22no—
71C2×D4×C61—42no—
72C2×D4×C61—42no—
73C2×D4×C61—42no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—42no—
77C2×D4×C61—81no—
78C2×D4×C61—81no—
79C2×D4×C61D812yes—
80C2×D4×C61SD1612yes—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—42no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—81no—
90C22×C4×C61—81no—
91C22×C4×C61—81no—
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C22⋊C411yescharacteristic
94C22×C4×C61C22⋊C411yescharacteristic
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C2×D412yes—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61#4112yes—
99C22×Dic61—42no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—42no—
103C22⋊C4×C61—22no—
104C22⋊C4×C61—22no—
105C22⋊C4×C61—42no—
106C22⋊C4×C61—42no—
107C22⋊C4×C61—42no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—81no—
111C42×C61—21no—
112C42×C61—21no—
113C22⋊Dic61—42no—
114C22⋊Dic61—42no—
115C4⋊Dic61—82no—
116C2×#92418—24no—
117C2×#92418—82no—
118C2×#92418—82no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61#10212yes—
133C23×C61C2×C22⋊C411yescharacteristic
134C23×C61#12112yes—
135C23×C61C2×D811yescharacteristic
136C23×C61C2×SD1611yescharacteristic
137C23×C61#13512yes—
138D4×C61—24no—
139D4×C61—24no—
140D4×C61—82no—
141D4×C61—84no—
142D4×C61—82no—
143D4×C61—82no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—22no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—81no—
165C2×C4×C61—82no—
166C2×C4×C61—82no—
167C2×C4×C61#10212yes—
168C2×C4×C61C4×D412yes—
169C2×C4×C61#12011yescharacteristic
170C2×C4×C61#12311yescharacteristic
171C2×Dic61—82no—
172C2×Dic61—82no—
173C2×Dic61—82no—
174#92418—44no—
175#9384—611nomaximal, Sylow
176C22×C61—22no—
177C22×C61—21no—
178C22×C61—22no—
179C22×C61—21no—
180C22×C61—22no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—42no—
184C22×C61—42no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61#38611yescharacteristic
196C22×C61C2×#10211yescharacteristic
197C22×C61#41611yescharacteristic
198C22×C61#46512yes—
199C22×C61#46612yes—
200C4×C61—22no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—22no—
204C4×C61—42no—
205C4×C61—41no—
206C4×C61—41no—
207C4×C61—81no—
208C4×C61—81no—
209Dic61—162no—
210#2972—611no—
211#2543D6111yescharacteristic
212#1799—611no—
213#1519—612no—
214#1294—612no—
215C2×C61—22no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—22no—
219C2×C61—42no—
220C2×C61—161no—
221C2×C61#188411yescharacteristic
222C2×C61#189311yescharacteristic
223C2×C61#191311yescharacteristic
224C2×#121—21no—
225C2×#121C2×D6111yescharacteristic
226C2×C4×D4C2×D6111yescharacteristic
227C8×D4—1224no—
228#431—1221no—
229C2×#99—1221no—
230C2×C22⋊C8—612no—
231C2×C22⋊C8—1221no—
232#398Dic6111yescharacteristic, complemented
233#397Dic6111yescharacteristic, complemented
234#394Dic6111yescharacteristic, complemented
235#392Dic6111yescharacteristic, complemented
236#388—21no—
237#386—21no—
238#386—21no—
239#380—612no—
240C2×#95C2×D6111yescharacteristic
241#342—1221no—
242#327—1224no—
243C61#938411yescharacteristic, complemented, Sylow
244C22×D4—21no—
245C22×D4—21no—
246C22×D4C2×Dic6111yescharacteristic
247C22×D4C22⋊D6111yescharacteristic
248C23×C4—21no—
249C23×C4C22⋊D6111yescharacteristic
250C23×C4C22×D6111yescharacteristic
251C22×C8—1222no—
252C22×C8—1222no—
253#121—22no—
254#121—22no—
255#121—42no—
256#121—42no—
257C4×D4—22no—
258C4×D4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—1222no—
261C2×C4⋊C4C2×Dic6111yescharacteristic
262C2×C4⋊C4C2×Dic6111yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—1222no—
269C2×C22⋊C4C2×Dic6111yescharacteristic
270C2×C22⋊C4C22⋊D6111yescharacteristic
271C2×C42C22⋊D6111yescharacteristic
272C4⋊C8—1222no—
273#99—2442no—
274C22⋊C8—614no—
275C22⋊C8—1222no—
276C22⋊C8—1222no—
277C4×C8—1222no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—1222no—
282#95C2×Dic6111yescharacteristic
283#95C2×Dic6111yescharacteristic
284C24—21no—
285C24C22⋊Dic6111yescharacteristic
286C24C2×C22⋊D6111yescharacteristic
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4#1175819912yes—
299C2×D4#1175820012yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—2442no—
312C22×C4C22⋊Dic6111yescharacteristic
313C22×C4C22⋊Dic6111yescharacteristic
314C22×C4C22⋊Dic6111yescharacteristic
315C22×C4D4×D6112yes—
316C22×C4#1175822412yes—
317C22×C4C22×Dic6111yescharacteristic
318C22×C4C2×C22⋊D6111yescharacteristic
319C2×C8—1224no—
320C2×C8—4882no—
321C2×C8—4882no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—42no—
325C4⋊C4—4882no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—81no—
334C22⋊C4—2442no—
335C22⋊C4—2442no—
336C42—21no—
337C42—21no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23#1451969812yes—
352C23C2×C22⋊Dic6111yescharacteristic
353C23#1451974912yes—
354C23C2×#1175819911yescharacteristic
355C23C2×#1175820011yescharacteristic
356C23#1451979712yes—
357D4—24no—
358D4—24no—
359D4—82no—
360D4—84no—
361D4—82no—
362D4—82no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—4882no—
387C2×C4—4882no—
388C2×C4—4882no—
389C2×C4#1451969812yes—
390C2×C4D4×Dic6112yes—
391C2×C4#1451974511yescharacteristic
392C2×C4#1451975811yescharacteristic
393C8—2444no—
394C22—21no—
395C22—22no—
396C22—21no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22#1683964211yescharacteristic
414C22C2×#1451969811yescharacteristic
415C22#1683975811yescharacteristic
416C22#1683998912yes—
417C22#1683999612yes—
418C4—22no—
419C4—21no—
420C4—21no—
421C4—22no—
422C4—42no—
423C4—41no—
424C4—41no—
425C4—81no—
426C4—81no—
427C4—9762no—
428C2—21no—
429C2—22no—
430C2—21no—
431C2—22no—
432C2—42no—
433C2—161no—
434C2#2144620311yescharacteristic
435C2#2144624811yescharacteristic
436C2#2144636211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#2543C2
socleC22×C61#386
cosocleC23×C4×C61C23
hypercenter#2543D61
hypocenterC61#9384
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2543

Complements

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

NH ≅ G/Ntype
1. #21454843C2semidirect
2. #21445807C2semidirect
3. #21444387C2semidirect
4. #21443698C2semidirect
17. C61×#398C4semidirect
18. C61×#397C4semidirect
19. C61×#394C4semidirect
20. C61×#392C4semidirect
33. C22⋊#92418D4semidirect
232. #398Dic61semidirect
233. #397Dic61semidirect
234. #394Dic61semidirect
235. #392Dic61semidirect
243. C61#9384semidirect

Maximal subgroups

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

subgroupindex
#214548432
#214458072
#214443872
#214436982
C61×#25432
#938461