Finite Group Databasebeta

← #29576454

Subgroups — #29576454

Order 15616.

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

normal subgroups only

This group has 708 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×#16839920C211yesmaximal, characteristic
2#21448651C211yesmaximal, characteristic
3#21446803C211yesmaximal, characteristic
4#21445753C211yesmaximal, characteristic
5#21444390C211yesmaximal, characteristic
6#21443666C211yesmaximal, characteristic
7C61×#1289C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C22×Dic244C412yescomplemented
10C2×#14519756C2211yescharacteristic
11C2×#14519742—21no—
12#16839920—21no—
13#16839920—22no—
14#16839920—21no—
15C2×#14519702C412yescomplemented
16C2×#14519700—22no—
17C2×C22⋊#92418C2211yescharacteristic
18#16839667—21no—
19#16839666—22no—
20#16839620—21no—
21C22⋊C4×Dic61—21no—
22C4×C22⋊Dic61C2211yescharacteristic
23#16839528—21no—
24#16839528—21no—
25#16839498—22no—
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C22×Dic122—21no—
30C22×Dic122—21no—
31C22×Dic122—21no—
32C22×Dic122—44no—
33C22×Dic122C2×C412yes—
34C22×Dic122C2×C411yescharacteristic
35C22×Dic122D411yescharacteristic
36C22×Dic122D412yes—
37C22×Dic122D411yescharacteristic
38C23×Dic61—21no—
39C2×Dic244—22no—
40C2×Dic244—22no—
41C2×Dic244—44no—
42C22×#92418—21no—
43#14519756—21no—
44#14519756—21no—
45#14519756—21no—
46#14519756—21no—
47#14519742—44no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196—22no—
50C2×#11758196—21no—
51C2×C22⋊Dic61—21no—
52C2×C22⋊Dic61D411yescharacteristic
53C2×C22⋊Dic61D411yescharacteristic
54C2×C4×Dic61—22no—
55C2×C4×Dic61—21no—
56#14519702—22no—
57#14519702—22no—
58#14519700—44no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61#14519684—22no—
62#14519684—22no—
63#14519684—21no—
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61C2×C412yes—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72#95×C61—21no—
73#95×C61D412yes—
74C24×C61C2×D411yescharacteristic
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
84C22×Dic61—21no—
85C22×Dic61—22no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—22no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—44no—
93C2×Dic122—21no—
94C2×Dic122—24no—
95C2×Dic122—24no—
96C2×Dic122—24no—
97C2×Dic122—22no—
98C2×Dic122—22no—
99C2×Dic122—21no—
100C2×Dic122—21no—
101C2×Dic122—21no—
102C2×Dic122—42no—
103C2×Dic122—42no—
104C2×Dic122—42no—
105C2×Dic122—44no—
106C2×Dic122—44no—
107C2×Dic122—44no—
108C2×Dic122—42no—
109C2×Dic122C22⋊C412yes—
110C2×Dic122C22⋊C412yes—
111C2×C8×C61—22no—
112C2×C8×C61—42no—
113C4⋊C4×C61—42no—
114C4⋊C4×C61—42no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊Dic61—21no—
120C22⋊Dic61—21no—
121C22⋊Dic61—21no—
122C22⋊Dic61—41no—
123C22⋊Dic61—41no—
124C22⋊Dic61Q1612yescomplemented
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127#11758196—44no—
128#11758196—41no—
129#11758196—41no—
130C4×Dic61—44no—
131C4×Dic61—42no—
132C2×#92418—42no—
133C2×#92418—41no—
134Dic244—44no—
135Dic244—44no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61C4×D411yescharacteristic
139C23×C61#12011yescharacteristic
140C23×C61#12111yescharacteristic
141C23×C61C2×Q1611yescharacteristic
142C23×C61#13511yescharacteristic
143C23×C61#13711yescharacteristic
144C23×C61#13711yescharacteristic
145C2×C4×C61—22no—
146C2×C4×C61—22no—
147C2×C4×C61—22no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61C2×C22⋊C411yescharacteristic
158C2×C4×C61C4×D411yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×Dic61—24no—
162C2×Dic61—22no—
163C2×Dic61—22no—
164C2×Dic61—22no—
165C2×Dic61—44no—
166C2×Dic61—44no—
167C2×Dic61—41no—
168C2×Dic61—42no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177Dic122—24no—
178Dic122—22no—
179Dic122—22no—
180Dic122—22no—
181Dic122—44no—
182Dic122—44no—
183Dic122—42no—
184Dic122—42no—
185Dic122—81no—
186Dic122#9914yes—
187C8×C61—42no—
188#92418—81no—
189#9258—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61#38611yescharacteristic
201C22×C61C4×Q1611yescharacteristic
202C22×C61#44111yescharacteristic
203C22×C61#45111yescharacteristic
204C22×C61#45211yescharacteristic
205C22×C61#46211yescharacteristic
206C22×C61#46411yescharacteristic
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—82no—
211C4×C61—161no—
212C4×C61C2×#9912yes—
213Dic61—24no—
214Dic61—42no—
215Dic61—42no—
216Dic61—81no—
217Dic61—81no—
218Dic61—81no—
219C2×#451—611no—
220Q8×C22⋊C4—611no—
221#1996—611no—
222#1787—611no—
223#1520—611no—
224#1289D6111yescharacteristic
225#1282—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61#187811yescharacteristic
233C2×C61#189811yescharacteristic
234C2×C61#190511yescharacteristic
235C23×Q8—611no—
236C22×Q16—612no—
237C2×C22⋊Q8—611no—
238C2×C4×Q8—1221no—
239#451—1221no—
240#451—1222no—
241#451—1221no—
242C2×#103—612no—
243C2×#103—1222no—
244C2×C22⋊C8—611no—
245C2×C22⋊C8C2×D6111yescharacteristic
246#391—1221no—
247#391—1222no—
248#380—1221no—
249#380C2×D6111yescharacteristic
250#380C2×D6111yescharacteristic
251C4×C22⋊C4—611no—
252C4×C22⋊C4—1221no—
253#342—1221no—
254#342—1221no—
255#328—1222no—
256C61#925811yescharacteristic, complemented, Sylow
257C22×Q8—612no—
258C22×Q8—611no—
259C22×Q8—611no—
260C22×Q8—612no—
261C22×Q8—611no—
262C22×Q8—1221no—
263C22×Q8—1221no—
264C22×Q8—1221no—
265C22×Q8—2444no—
266C23×C4—1221no—
267C23×C4C22×D6111yescharacteristic
268C2×Q16—1222no—
269C2×Q16—1222no—
270C2×Q16—2444no—
271C22×C8—1221no—
272C22×C8C4×D6112yes—
273C22⋊Q8—1221no—
274C22⋊Q8—1221no—
275C22⋊Q8—1221no—
276C22⋊Q8—1221no—
277C4×Q8—2444no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—1222no—
282C2×C4⋊C4—1221no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—1221no—
288C2×C42—1222no—
289C2×C42—1221no—
290#103—1222no—
291#103—1222no—
292#103—2444no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—1221no—
296C22⋊C8—1221no—
297#95—21no—
298#95—1222no—
299#95—1222no—
300#95—1221no—
301#95D24412yes—
302C24D4×D6111yescharacteristic
303C2×Q8—612no—
304C2×Q8—612no—
305C2×Q8—1224no—
306C2×Q8—1224no—
307C2×Q8—1224no—
308C2×Q8—1222no—
309C2×Q8—1222no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8—2442no—
315C2×Q8—2442no—
316C2×Q8—2442no—
317C2×Q8—2442no—
318C2×Q8—2444no—
319C2×Q8—2444no—
320C2×Q8—2444no—
321C22×C4—22no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—1221no—
325C22×C4—1222no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1222no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—2444no—
333C22×C4C2×C4×D6111yescharacteristic
334C22×C4C2×D24411yescharacteristic
335C22×C4#1175822211yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4D4×D6111yescharacteristic
338C22×C4#1175822611yescharacteristic
339Q16—2444no—
340Q16—2444no—
341C2×C8—22no—
342C2×C8—42no—
343C2×C8—2442no—
344C2×C8—2441no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—2444no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—612no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C22⋊C4—2441no—
361C22⋊C4—2441no—
362C42—2442no—
363C42—2444no—
364C23—41no—
365C23—41no—
366C23#1451973911yescharacteristic
367C23#1451974711yescharacteristic
368C23#1451975011yescharacteristic
369C23Q16×D6111yescharacteristic
370C23#1451979611yescharacteristic
371C23#1451980611yescharacteristic
372C23#1451980611yescharacteristic
373Q8—614no—
374Q8—1224no—
375Q8—1222no—
376Q8—1222no—
377Q8—1222no—
378Q8—4881no—
379Q8—2444no—
380Q8—2444no—
381Q8—2442no—
382Q8—2442no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—1224no—
396C2×C4—1222no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—4881no—
400C2×C4—4881no—
401C2×C4—2444no—
402C2×C4—2444no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2442no—
411C2×C4C22⋊C4×D6111yescharacteristic
412C2×C4C4×D24411yescharacteristic
413C2×C4#1451975211yescharacteristic
414C2×C4#1451976211yescharacteristic
415C8—42no—
416C8—4881no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22#1683964011yescharacteristic
428C22#1683985611yescharacteristic
429C22#1683986811yescharacteristic
430C22#1683991911yescharacteristic
431C22#1683992511yescharacteristic
432C22#1683997111yescharacteristic
433C22#1683998311yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—82no—
438C4—161no—
439C4—1224no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C4—2442no—
444C4—2442no—
445C4#99×D6112yes—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2#2144616111yescharacteristic
453C2#2144627111yescharacteristic
454C2#2144631411yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1289C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1289D61
hypocenterC61#9258
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
9. C22×Dic244C4semidirect
15. C2×#14519702C4semidirect
124. C22⋊Dic61Q16semidirect
256. C61#9258semidirect

Maximal subgroups

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

subgroupindex
C2×#168399202
#214486512
#214468032
#214457532
#214443902
#214436662
C61×#12892
#925861