Finite Group Databasebeta

← #29580587

Subgroups — #29580587

Order 15616.

658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16840098C211yesmaximal, characteristic, complemented
2C2×#16840081C211yesmaximal, characteristic
3#21451747C211yesmaximal, characteristic
4C2×#16839500C211yesmaximal, characteristic, complemented
5C2×#16839497C211yesmaximal, characteristic
6#21444088C211yesmaximal, characteristic, complemented
7C61×#1280C211yesmaximal, characteristic, complemented
8C2×#14519756C2211yescharacteristic
9C2×#14519751C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11#16840098—22no—
12#16840098—22no—
13#16840081—22no—
14#16840081—22no—
15C2×#14519711—21no—
16C2×#14519709—21no—
17C2×#14519702—21no—
18C2×#14519699—21no—
19#16839702—21no—
20#16839689—21no—
21#16839680—21no—
22#16839675—21no—
23#16839641—22no—
24C2×#14519684—22no—
25C2×#14519684C2211yescharacteristic
26#16839500—22no—
27#16839497—22no—
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C22×D244D411yescharacteristic
33C22×C22⋊D61—21no—
34C23×Dic61—21no—
35C23×Dic61—21no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43#14519751—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61D411yescharacteristic
50C2×C4⋊Dic61D412yes—
51C2×C4⋊Dic61D411yescharacteristic
52C2×#11758196—21no—
53C2×C22⋊Dic61—21no—
54C2×#11758198—21no—
55C2×#11758198—22no—
56C2×#11758198—22no—
57#14519711—24no—
58#14519709—24no—
59#14519702—24no—
60#14519699—24no—
61#14519684—22no—
62#14519684—22no—
63#14519684—21no—
64#14519684—21no—
65#14519684—44no—
66C23×C4×C61D412yes—
67C23×C4×C61C2311yescharacteristic
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61D412yes—
73C22⋊C8×C61D412yes—
74#95×C61—21no—
75#95×C61—21no—
76C24×C61C2×D411yescharacteristic
77C23×D61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—42no—
82C22×C4×C61—42no—
83C22×C4×C61—42no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—42no—
93C2×C22⋊D61—42no—
94C22×Dic61—22no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—22no—
99C22×Dic61—41no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61—42no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C22×Dic61—42no—
107C2×D244—21no—
108C2×D244—21no—
109C2×D244—42no—
110C2×Dic122—21no—
111C2×Dic122—21no—
112C2×Dic122—42no—
113C2×C8×C61—22no—
114C2×C8×C61—22no—
115C2×C8×C61—42no—
116C2×C8×C61—42no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119#11758198—41no—
120#11758198—41no—
121#11758198—82no—
122#11758198—82no—
123C4⋊Dic61—22no—
124C4⋊Dic61—22no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—41no—
130C4⋊Dic61—41no—
131#11758196—41no—
132#11758196—41no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—22no—
136C23×C61#12011yescharacteristic
137C23×C61#12111yescharacteristic
138C23×C61#12711yescharacteristic
139C23×C61#13512yes—
140C23×C61#13712yes—
141C22×D61—41no—
142C22×D61—42no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—42no—
146C2×C4×C61—22no—
147C2×C4×C61—22no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—44no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—82no—
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C22⋊D61—82no—
162C22⋊D61—81no—
163C22⋊D61—81no—
164C2×Dic61—44no—
165C2×Dic61—42no—
166C2×Dic61—44no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—42no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—42no—
175C2×Dic61—82no—
176C2×Dic61—81no—
177C2×Dic61—82no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181D244—42no—
182D244—81no—
183Dic122—42no—
184Dic122—81no—
185C8×C61—42no—
186C8×C61—42no—
187#9969—611nomaximal, Sylow
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—22no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61#39211yescharacteristic
197C22×C61#45212yes—
198C22×C61#45311yescharacteristic
199C22×C61#45411yescharacteristic
200C22×C61#45812yes—
201C22×C61#46412yes—
202C22×C61#49511yescharacteristic
203C22×C61#49711yescharacteristic
204C2×D61—82no—
205C2×D61—82no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—82no—
214Dic61—82no—
215Dic61—81no—
216Dic61—82no—
217Dic61—81no—
218Dic61—81no—
219C2×#484—611no—
220C2×#481—611no—
221#2639—611no—
222C2×#328—611no—
223C2×#327—611no—
224#1445—611no—
225#1280D6111yescharacteristic, complemented
226C2×C61—21no—
227C2×C61—22no—
228C2×C61—21no—
229C2×C61#161512yes—
230C2×C61#161812yes—
231C2×C61#200611yescharacteristic
232C2×C61#201511yescharacteristic
233C2×C61#202211yescharacteristic
234D61—161no—
235C2×C22⋊Q8—611no—
236C2×#121—611no—
237C22×C4⋊C4—611no—
238#484—1222no—
239#484—1222no—
240#481—1222no—
241#481—1222no—
242C2×#107—1221no—
243C2×#106—1221no—
244C2×#103—1221no—
245C2×#102—1221no—
246C2×C22⋊C8C2×D6111yescharacteristic
247C2×C22⋊C8C2×D6111yescharacteristic
248#400—1221no—
249#397—1221no—
250#394—1221no—
251#393—1221no—
252#386—1222no—
253C2×#95—611no—
254C2×#95—1222no—
255C2×#95C2×D6111yescharacteristic
256#328—1222no—
257#327—1222no—
258C61#996911yescharacteristic, complemented, Sylow
259C22×Q8—611no—
260C22×D4—611no—
261C22×D4—1221no—
262C23×C4—1221no—
263C23×C4—1221no—
264C23×C4D24412yes—
265C23×C4C22×D6111yescharacteristic
266C22×C8—21no—
267C22×C8—21no—
268C22⋊Q8—1221no—
269C22⋊Q8—1221no—
270C22⋊Q8—1221no—
271C22⋊Q8—1221no—
272#121—1221no—
273#121—1221no—
274#121—1221no—
275#121—1221no—
276C2×C4⋊C4—612no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1221no—
285C2×C22⋊C4—1222no—
286C2×C22⋊C4—1222no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289#107—1224no—
290#106—1224no—
291#103—1224no—
292#102—1224no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8D24412yes—
296C22⋊C8D24412yes—
297#95—21no—
298#95—21no—
299#95—1222no—
300#95—1222no—
301#95—1221no—
302#95—1221no—
303#95—2444no—
304C24—1221no—
305C24C2×D24411yescharacteristic
306C2×Q8—1221no—
307C2×Q8—1221no—
308C2×Q8—2442no—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—2442no—
312C2×D4—2442no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2442no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—1222no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1222no—
327C22×C4—2442no—
328C22×C4—2441no—
329C22×C4—2442no—
330C22×C4—2442no—
331C22×C4—2441no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4—2442no—
335C22×C4C2×D24411yescharacteristic
336C22×C4C2×D24411yescharacteristic
337C22×C4D4×D6111yescharacteristic
338C22×C4D4×D6111yescharacteristic
339C22×C4D4×D6111yescharacteristic
340C22×C4#1175822611yescharacteristic
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—42no—
344C2×C8—42no—
345C4⋊C4—1222no—
346C4⋊C4—1222no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—2441no—
352C4⋊C4—2441no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C22⋊C4—4882no—
356C22⋊C4—4882no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C23—21no—
362C23—22no—
363C23—21no—
364C23—2441no—
365C23—2442no—
366C23—2442no—
367C23—2441no—
368C23—2441no—
369C23#1451974711yescharacteristic
370C23#1451975211yescharacteristic
371C23#1451977411yescharacteristic
372C23#1451979912yes—
373C23#1451981012yes—
374Q8—4881no—
375Q8—2442no—
376D4—4881no—
377D4—4882no—
378D4—4881no—
379D4—4881no—
380D4—2442no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—82no—
392C2×C4—4881no—
393C2×C4—4882no—
394C2×C4—4882no—
395C2×C4—4881no—
396C2×C4—4881no—
397C2×C4—4881no—
398C2×C4—2444no—
399C2×C4—2442no—
400C2×C4—2444no—
401C2×C4—2441no—
402C2×C4—2442no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2442no—
408C2×C4—2441no—
409C2×C4#1451974711yescharacteristic
410C2×C4#1451974711yescharacteristic
411C2×C4#1451975211yescharacteristic
412C2×C4#1451975211yescharacteristic
413C8—42no—
414C8—42no—
415C22—22no—
416C22—22no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—22no—
423C22—4881no—
424C22—4882no—
425C22—4881no—
426C22—4881no—
427C22—4882no—
428C22#1683967211yescharacteristic
429C22#1683992612yes—
430C22#1683993211yescharacteristic
431C22#1683993711yescharacteristic
432C22#1683995312yes—
433C22#1683998512yes—
434C22#1684014611yescharacteristic
435C22#1684015611yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—4882no—
442C4—4881no—
443C4—4881no—
444C4—4882no—
445C4—4881no—
446C2—21no—
447C2—22no—
448C2—21no—
449C2—9761no—
450C2#2144485212yes—
451C2#2144486912yes—
452C2#2144686311yescharacteristic
453C2#2144691611yescharacteristic
454C2#2144695111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenter#1280D61
hypocenterC61#9969
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
1. C2×#16840098C2semidirect
4. C2×#16839500C2semidirect
6. #21444088C2semidirect
7. C61×#1280C2semidirect
225. #1280D61semidirect
258. C61#9969semidirect

Maximal subgroups

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

subgroupindex
C2×#168400982
C2×#168400812
#214517472
C2×#168395002
C2×#168394972
#214440882
C61×#12802
#996961