Finite Group Databasebeta

← #29577786

Subgroups — #29577786

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454841C211yesmaximal, characteristic
2#21450128C211yesmaximal, characteristic
3#21445906C211yesmaximal, characteristic, complemented
4#21445903C211yesmaximal, characteristic, complemented
5#21445804C211yesmaximal, characteristic
6#21443686C211yesmaximal, characteristic, complemented
7C61×#1289C211yesmaximal, characteristic, complemented
8C2×#14519761—21no—
9C2×C4×C22⋊D61C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C8×C22⋊D61—22no—
12#16839825—22no—
13#16839812—21no—
14C2×#14519691—21no—
15C2×C22⋊#92418C2211yescharacteristic
16C22⋊C8×D61—21no—
17#16839694C412yescomplemented
18#16839689C412yescomplemented
19#16839661—21no—
20#16839623—21no—
21#16839622C2211yescharacteristic
22#16839619—21no—
23#16839528—21no—
24#16839525—22no—
25#16839524—22no—
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C22×C22⋊D61D411yescharacteristic
30C23×Dic61—21no—
31C22×C4×D61D411yescharacteristic
32C22×#92418D412yes—
33C2×C8×D61—22no—
34#14519761—42no—
35#14519761—42no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39C4×C22⋊D61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61C2×C412yes—
48C2×#11758196C2×C411yescharacteristic
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61D411yescharacteristic
51C2×#11758198—22no—
52C2×#11758198C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519706—22no—
55#14519691—42no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58#14519689—22no—
59C8×Dic61—22no—
60#14519684—22no—
61#14519684—22no—
62#14519684—21no—
63C23×C4×C61C2311yescharacteristic
64C22×C8×C61D412yes—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71#95×C61—21no—
72#95×C61C2×C412yes—
73C24×C61C2×D411yescharacteristic
74C23×D61C22⋊C411yescharacteristic
75C22×C4×C61—22no—
76C22×C4×C61—42no—
77C22×C4×C61—41no—
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C2×C22⋊D61—21no—
85C2×C22⋊D61—21no—
86C2×C22⋊D61—21no—
87C2×C22⋊D61—21no—
88C2×C22⋊D61D812yes—
89C2×C22⋊D61SD1612yes—
90C22×Dic61—22no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—42no—
104C2×C8×C61—22no—
105C2×C8×C61—42no—
106C4⋊C4×C61—42no—
107C4⋊C4×C61—42no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊Dic61—21no—
113C22⋊Dic61—21no—
114C22⋊Dic61—41no—
115C22⋊Dic61—41no—
116#11758198—21no—
117#11758198—21no—
118#11758198—44no—
119C4⋊Dic61—22no—
120C4⋊Dic61—22no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—44no—
124C4⋊Dic61—42no—
125#11758196—21no—
126#11758196—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C2×#92418—22no—
130C2×#92418—42no—
131C8×D61—82no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61C2×C22⋊C411yescharacteristic
135C23×C61#12111yescharacteristic
136C23×C61#12111yescharacteristic
137C23×C61C2×D811yescharacteristic
138C23×C61C2×SD1611yescharacteristic
139C23×C61#13511yescharacteristic
140C23×C61#13511yescharacteristic
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61#10212yes—
146C2×C4×C61—22no—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61C4×D411yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61#12011yescharacteristic
161C2×C4×C61#12311yescharacteristic
162C22⋊D61—22no—
163C22⋊D61—22no—
164C22⋊D61—22no—
165C22⋊D61—22no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182C2×Dic61#10212yes—
183C4×D61—42no—
184C4×D61—81no—
185C8×C61—42no—
186#92418—42no—
187#9470—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61#38611yescharacteristic
199C22×C61C2×#10211yescharacteristic
200C22×C61#41611yescharacteristic
201C22×C61#46511yescharacteristic
202C22×C61#46511yescharacteristic
203C22×C61#46611yescharacteristic
204C22×C61#46611yescharacteristic
205C2×D61—22no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—42no—
209C2×D61—81no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—82no—
214C4×C61—161no—
215C4×C61#45812yes—
216Dic61—22no—
217Dic61—41no—
218Dic61—41no—
219Dic61—82no—
220Dic61—161no—
221#2972—611no—
222#2486—611no—
223#1823—611no—
224#1823—611no—
225#1799—611no—
226#1289—611no—
227#1289D6111yescharacteristic, complemented
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61#189011yescharacteristic
235C2×C61#189311yescharacteristic
236C2×C61#190911yescharacteristic
237D61—42no—
238C2×#123—1221no—
239C2×C4×D4—611no—
240C22×C4⋊C4—611no—
241C8×D4—1222no—
242C8×D4—1222no—
243#431—1221no—
244C2×#99—1221no—
245C2×C22⋊C8—611no—
246C2×C22⋊C8—1221no—
247C2×C22⋊C8C2×D6111yescharacteristic
248#398—612no—
249#397—612no—
250#389—1221no—
251#381—1221no—
252#380—611no—
253#380—1221no—
254#380C2×D6111yescharacteristic
255#380C2×D6111yescharacteristic
256#342—1221no—
257#340—1222no—
258#340—1222no—
259C61#947011yescharacteristic, complemented, Sylow
260C22×D4—611no—
261C23×C4—611no—
262C23×C4—1221no—
263C23×C4C22×D6111yescharacteristic
264C22×C8—612no—
265C22×C8—1222no—
266C22×C8D24412yes—
267#123—2442no—
268#123—2442no—
269C4×D4—1221no—
270C4×D4—1221no—
271C4×D4—1221no—
272C4×D4—1221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—612no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1222no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4—1221no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—1222no—
289C2×C22⋊C4—1221no—
290C2×C42—611no—
291C4⋊C8—1222no—
292#99—2442no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—1222no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298C4×C8—1222no—
299#95—21no—
300#95—1222no—
301#95—1222no—
302#95—1221no—
303#95C4×D6112yes—
304C24—611no—
305C24D4×D6111yescharacteristic
306C2×D4—612no—
307C2×D4—612no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—1221no—
312C22×C4—22no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1222no—
321C22×C4—2442no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4—2441no—
326C22×C4—2441no—
327C22×C4—2441no—
328C22×C4—2441no—
329C22×C4C2×C4×D6111yescharacteristic
330C22×C4C2×D24411yescharacteristic
331C22×C4#1175822211yescharacteristic
332C22×C4D4×D6111yescharacteristic
333C22×C4D4×D6111yescharacteristic
334C22×C4#1175822611yescharacteristic
335C2×C8—22no—
336C2×C8—42no—
337C2×C8—1222no—
338C2×C8—4882no—
339C2×C8—2442no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—2442no—
347C4⋊C4—2444no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—1221no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—2444no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C42—1221no—
362C42—1221no—
363C23—41no—
364C23—41no—
365C23—612no—
366C23—1221no—
367C23—1221no—
368C23—2441no—
369C23—2441no—
370C23C22⋊C4×D6111yescharacteristic
371C23#1451975011yescharacteristic
372C23#1451975211yescharacteristic
373C23D8×D6111yescharacteristic
374C23SD16×D6111yescharacteristic
375C23#1451979811yescharacteristic
376C23#1451980011yescharacteristic
377D4—1222no—
378D4—1222no—
379D4—1222no—
380D4—1222no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—612no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—4881no—
399C2×C4—4881no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—4881no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4#1451973911yescharacteristic
413C2×C4C4×D24411yescharacteristic
414C2×C4#1451974711yescharacteristic
415C2×C4#1451976211yescharacteristic
416C8—42no—
417C8—2442no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—1222no—
429C22—4881no—
430C22—2442no—
431C22—2441no—
432C22—2441no—
433C22#1683964011yescharacteristic
434C22#102×D6111yescharacteristic
435C22#1683975711yescharacteristic
436C22#1683999211yescharacteristic
437C22#1683999411yescharacteristic
438C22#1683999711yescharacteristic
439C22#1683999911yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—82no—
444C4—161no—
445C4—1222no—
446C4—9761no—
447C4—4882no—
448C4—2441no—
449C4—2441no—
450C4#1683995312yes—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—2442no—
458C2#2144623111yescharacteristic
459C2#2144624611yescharacteristic
460C2#2144634011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1289C2
socleC22×C61#386
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1289D61
hypocenterC61#9470
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
3. #21445906C2semidirect
4. #21445903C2semidirect
6. #21443686C2semidirect
7. C61×#1289C2semidirect
17. #16839694C4semidirect
18. #16839689C4semidirect
227. #1289D61semidirect
259. C61#9470semidirect

Maximal subgroups

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

subgroupindex
#214548412
#214501282
#214459062
#214459032
#214458042
#214436862
C61×#12892
#947061