Finite Group Databasebeta

← #29577193

Subgroups — #29577193

Order 15616.

732 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#21455079C211yesmaximal, characteristic
2#21448660C211yesmaximal, characteristic
3#21446804C211yesmaximal, characteristic, complemented
4#21444340C211yesmaximal, characteristic, complemented
5#21443726C211yesmaximal, characteristic, complemented
6#21443705C211yesmaximal, characteristic, complemented
7C61×#1789C211yesmaximal, characteristic
8C2×#14519807C412yescomplemented
9C2×#14519756C2211yescharacteristic
10C2×Q8×Dic61—21no—
11#16839924—22no—
12#16839918—21no—
13#16839913—21no—
14#16839763C412yescomplemented
15#16839726C2211yescharacteristic
16#16839665—22no—
17#16839665—21no—
18#16839622—21no—
19#16839622C2211yescharacteristic
20C4×C22⋊Dic61—21no—
21C4×C22⋊Dic61C2211yescharacteristic
22#16839528—22no—
23#16839500—21no—
24#16839500—21no—
25C22×#41×C61C2211yescharacteristic
26C2×#104×C61—22no—
27C61×#407C2211yescharacteristic
28C4×C22⋊C4×C61C2211yescharacteristic
29C22×Dic122C2×C411yescharacteristic
30#14519807—44no—
31C2×#11758202—22no—
32C2×#11758200—22no—
33C2×#11758194C2×C412yes—
34#14519756—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756—21no—
38Q8×Dic61—44no—
39C2×C4⋊Dic61—22no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—21no—
43C2×C22⋊Dic61—22no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—22no—
47C2×C22⋊Dic61D412yes—
48C2×C4×Dic61—22no—
49C2×C4×Dic61—21no—
50#14519701—22no—
51#14519698—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519684—21no—
55#14519684D411yescharacteristic
56#14519684D411yescharacteristic
57C2×#41×C61—21no—
58C2×#41×C61—21no—
59C2×#41×C61—44no—
60C2×#41×C61C2×C412yes—
61C2×#41×C61D412yes—
62C22×Q8×C61D411yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61D411yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C2×M16×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C42×C61—21no—
70#104×C61—44no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#95×C61—21no—
74C24×C61—21no—
75C24×C61C2×D411yescharacteristic
76#41×C61—24no—
77#41×C61—24no—
78#41×C61—42no—
79#41×C61—42no—
80#41×C61—44no—
81#41×C61—44no—
82C2×Q8×C61—24no—
83C2×Q8×C61—21no—
84C2×Q8×C61C22⋊C412yes—
85C2×D4×C61—22no—
86C2×D4×C61—22no—
87C2×D4×C61—21no—
88C2×D4×C61—42no—
89C2×D4×C61—44no—
90C2×D4×C61C22⋊C412yes—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—42no—
95C22×C4×C61—44no—
96C22×C4×C61—41no—
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61#4111yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×Dic61—21no—
104C22×Dic61—22no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C2×Dic122—21no—
109C2×Dic122—21no—
110C2×Dic122—42no—
111M16×C61—42no—
112C2×C8×C61—41no—
113C22⋊C4×C61—22no—
114C22⋊C4×C61—41no—
115C42×C61—42no—
116C22⋊Dic61—42no—
117C22⋊Dic61—44no—
118C22⋊Dic61—41no—
119C22⋊Dic61—41no—
120C22⋊Dic61—42no—
121C22⋊Dic61—82no—
122#11758202—44no—
123#11758200—44no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—44no—
127C4⋊Dic61—42no—
128#11758196—41no—
129#11758196—41no—
130C4×Dic61—44no—
131C4×Dic61—42no—
132#11758194—42no—
133C2×#92418—22no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—22no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61—42no—
140C23×C61—42no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61C4×D411yescharacteristic
144C23×C61#12011yescharacteristic
145C23×C61#12111yescharacteristic
146Q8×C61—24no—
147Q8×C61—22no—
148Q8×C61#9914yes—
149D4×C61—22no—
150D4×C61—22no—
151D4×C61—44no—
152D4×C61—44no—
153D4×C61—42no—
154C2×C4×C61—24no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—44no—
163C2×C4×C61—44no—
164C2×C4×C61—42no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61C2×C22⋊C411yescharacteristic
168C2×C4×C61C4×D411yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12311yescharacteristic
171C2×Dic61—22no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—42no—
175C2×Dic61—41no—
176C2×Dic61—42no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—42no—
181C2×Dic61—41no—
182C2×Dic61—81no—
183C2×Dic61—81no—
184Dic122—42no—
185Dic122—81no—
186C8×C61—81no—
187#92418—42no—
188#9364—611nomaximal, Sylow
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—42no—
198C22×C61—42no—
199C22×C61—42no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61—82no—
203C22×C61—82no—
204C22×C61#38611yescharacteristic
205C22×C61#45511yescharacteristic
206C22×C61#45611yescharacteristic
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—24no—
210C4×C61—21no—
211C4×C61—82no—
212C4×C61C2×#9912yes—
213Dic61—42no—
214Dic61—82no—
215Dic61—81no—
216Dic61—81no—
217Dic61—81no—
218#3007—611no—
219#2341—611no—
220#1996—611no—
221#1789D6111yescharacteristic
222#1508—611no—
223#1305—611no—
224#1297—611no—
225C2×C61—21no—
226C2×C61—21no—
227C2×C61—41no—
228C2×C61—41no—
229C2×C61—82no—
230C2×C61#188211yescharacteristic
231C2×C61#189811yescharacteristic
232C2×C61#190611yescharacteristic
233C22×#41C2×D6111yescharacteristic
234C2×#137—612no—
235C2×C22⋊Q8—611no—
236C2×C4×Q8—1221no—
237#452—1222no—
238#451—1221no—
239#450—1221no—
240C2×#104—22no—
241#417—612no—
242#407—611no—
243#407C2×D6111yescharacteristic
244#390—1222no—
245#390—1221no—
246#380—611no—
247#380—1221no—
248C4×C22⋊C4—611no—
249C4×C22⋊C4—1221no—
250C4×C22⋊C4C2×D6111yescharacteristic
251#342—1222no—
252#328—1221no—
253#328—1221no—
254C61#936411yescharacteristic, complemented, Sylow
255C2×#41—21no—
256C2×#41—21no—
257C2×#41—44no—
258C2×#41C4×D6112yes—
259C2×#41C22⋊D6112yes—
260C22×Q8—611no—
261C22×Q8D24411yescharacteristic
262C22×D4—21no—
263C22×D4D24411yescharacteristic
264C23×C4—21no—
265C23×C4C22×D6111yescharacteristic
266#137—2444no—
267C2×Q16—1222no—
268C2×SD16—1222no—
269C2×M16—21no—
270C2×M16—612no—
271C22⋊Q8—1221no—
272C22⋊Q8—1221no—
273C22⋊Q8—1221no—
274C22⋊Q8—1221no—
275C4×Q8—2444no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1222no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—612no—
282C2×C22⋊C4—1222no—
283C2×C22⋊C4—1222no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C42—21no—
287C2×C42—1222no—
288C2×C42—1221no—
289#104—44no—
290#103—1222no—
291#102—1222no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—1221no—
295C22⋊C8—1221no—
296#95—21no—
297#95—611no—
298#95—611no—
299#95—1221no—
300C24—21no—
301C24D4×D6111yescharacteristic
302#41—24no—
303#41—24no—
304#41—42no—
305#41—42no—
306#41—44no—
307#41—44no—
308C2×Q8—24no—
309C2×Q8—21no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—2442no—
313C2×Q8#1175819812yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—42no—
318C2×D4—44no—
319C2×D4#1175819812yes—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—42no—
324C22×C4—44no—
325C22×C4—41no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1222no—
331C22×C4C2×C4×D6111yescharacteristic
332C22×C4C2×D24411yescharacteristic
333C22×C4D4×D6111yescharacteristic
334C22×C4#1175822411yescharacteristic
335C22×C4#1175822411yescharacteristic
336C22×C4C2×C22⋊D6111yescharacteristic
337Q16—2444no—
338SD16—2444no—
339M16—42no—
340M16—2442no—
341C2×C8—41no—
342C2×C8—1222no—
343C4⋊C4—1221no—
344C4⋊C4—1221no—
345C4⋊C4—2444no—
346C4⋊C4—2442no—
347C4⋊C4—2441no—
348C4⋊C4—2441no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—4882no—
352C22⋊C4—2442no—
353C22⋊C4—2444no—
354C22⋊C4—2441no—
355C22⋊C4—2441no—
356C22⋊C4—2442no—
357C42—42no—
358C42—2444no—
359C42—2442no—
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23#1451973711yescharacteristic
370C23#1451974711yescharacteristic
371C23#1451974911yescharacteristic
372Q8—24no—
373Q8—22no—
374Q8—4881no—
375Q8—2442no—
376Q8#1451969114yes—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—44no—
381D4—42no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—1222no—
396C2×C4—4881no—
397C2×C4—4881no—
398C2×C4—2441no—
399C2×C4—2442no—
400C2×C4—2441no—
401C2×C4—2442no—
402C2×C4—2441no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4C2×#1175819811yescharacteristic
409C2×C4#1451973711yescharacteristic
410C2×C4#1451974911yescharacteristic
411C2×C4#1451976111yescharacteristic
412C8—81no—
413C8—2442no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22#1683963911yescharacteristic
430C22#1683994111yescharacteristic
431C22#1683994611yescharacteristic
432C4—21no—
433C4—24no—
434C4—21no—
435C4—21no—
436C4—82no—
437C4—4881no—
438C4—4882no—
439C4—4881no—
440C4—4881no—
441C4—2442no—
442C4C2×#1451969112yes—
443C2—21no—
444C2—21no—
445C2—41no—
446C2—41no—
447C2—82no—
448C2#2144618611yescharacteristic
449C2#2144627011yescharacteristic
450C2#2144631811yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1789C2
socleC22×C61#386
prime radicalC22×#41×C61C22
cosocleC23×C4×C61C23
hypercenter#1789D61
hypocenterC61#9364
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
3. #21446804C2semidirect
4. #21444340C2semidirect
5. #21443726C2semidirect
6. #21443705C2semidirect
8. C2×#14519807C4semidirect
14. #16839763C4semidirect
254. C61#9364semidirect

Maximal subgroups

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

subgroupindex
#214550792
#214486602
#214468042
#214443402
#214437262
#214437052
C61×#17892
#936461