Finite Group Databasebeta

← #29580627

Subgroups — #29580627

Order 15616.

544 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456567C211yesmaximal, characteristic
2#21455759C211yesmaximal, characteristic, complemented
3#21445890C211yesmaximal, characteristic, complemented
4#21444180C211yesmaximal, characteristic, complemented
5#21444179C211yesmaximal, characteristic, complemented
6#21443695C211yesmaximal, characteristic, complemented
7C61×#3094C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9#16840086—22no—
10#16840080—21no—
11#16840075—21no—
12#16840075—21no—
13#16840073—21no—
14#16839996—22no—
15#16839896—21no—
16#16839895—21no—
17#16839805—21no—
18#16839766—21no—
19#16839726C2211yescharacteristic
20C2×C22⋊#92418C2211yescharacteristic
21C2×C22⋊#92418C2211yescharacteristic
22#16839517—22no—
23#16839486—22no—
24#16839485—22no—
25C2×#121×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#482—22no—
28C61×#481—21no—
29C61×#480—21no—
30C61×#428—21no—
31C61×#418—21no—
32C61×#407C2211yescharacteristic
33C22×D244D411yescharacteristic
34C22×C22⋊D61—21no—
35C2×#11758199—22no—
36C2×#11758194—21no—
37C22×#92418—21no—
38C22×#92418D412yes—
39#14519751—21no—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758198—21no—
45#14519710—22no—
46#14519710—22no—
47#14519708—22no—
48#14519698—22no—
49#14519697—22no—
50#14519697—22no—
51#14519697—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418D412yes—
58C22×D4×C61—21no—
59C22×D4×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C2×M16×C61—21no—
62#121×C61—21no—
63#121×C61—21no—
64#121×C61—21no—
65#121×C61—21no—
66#117×C61—21no—
67#117×C61—21no—
68#117×C61—21no—
69#117×C61—21no—
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C42×C61—21no—
76#107×C61—22no—
77#106×C61—22no—
78#102×C61—22no—
79#102×C61—22no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61D412yes—
82C24×C61—21no—
83C24×C61#4111yescharacteristic
84C23×D61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—42no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—82no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—42no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—82no—
104C22×Dic61—21no—
105C2×D244—21no—
106C2×D244—21no—
107C2×D244—42no—
108M16×C61—42no—
109C2×C8×C61—22no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C42×C61—41no—
121C42×C61—41no—
122#11758199—82no—
123#11758198—41no—
124#11758198—41no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127#11758194—42no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—42no—
131C2×#92418—42no—
132C2×#92418—41no—
133C23×C61—22no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—42no—
137C23×C61—41no—
138C23×C61—81no—
139C23×C61—81no—
140C23×C61#12111yescharacteristic
141C23×C61#12111yescharacteristic
142C23×C61#12111yescharacteristic
143C22×D61—41no—
144C22×D61—42no—
145C22×D61—81no—
146C22×D61—81no—
147D4×C61—42no—
148D4×C61—42no—
149D4×C61—82no—
150D4×C61—82no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—42no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—81no—
163C2×C4×C61#12011yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12011yescharacteristic
166C2×C4×C61#12711yescharacteristic
167C22⋊D61—82no—
168C22⋊D61—82no—
169C2×Dic61—41no—
170C2×Dic61—81no—
171D244—42no—
172D244—42no—
173C8×C61—42no—
174#92418—42no—
175#92418—42no—
176#92418—81no—
177#9977—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—82no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—162no—
191C22×C61#39211yescharacteristic
192C22×C61#47212yes—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—162no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—81no—
201C4×C61—81no—
202C4×C61—81no—
203C4×C61#45812yes—
204Dic61—81no—
205#3186—611no—
206#3094—611no—
207#3094D6111yescharacteristic, complemented
208#1818—611no—
209#1471—611no—
210#1471—611no—
211#1293—611no—
212C2×C61—22no—
213C2×C61—41no—
214C2×C61—41no—
215C2×C61—161no—
216C2×C61#201711yescharacteristic
217C2×C61#201811yescharacteristic
218C2×C61#202211yescharacteristic
219D61—161no—
220C2×#121—611no—
221C2×#121C2×D6111yescharacteristic
222C2×#117C2×D6111yescharacteristic
223#482—22no—
224#482—1222no—
225#481—21no—
226#481—1221no—
227#480—21no—
228#480—1221no—
229#480—1221no—
230#480—1221no—
231#466—1222no—
232#447—1221no—
233#447—1221no—
234#428—21no—
235#428—1221no—
236#418—21no—
237#418—1221no—
238#407—611no—
239#407C2×D6111yescharacteristic
240C2×C22⋊C8—611no—
241C2×C22⋊C8—611no—
242#336—1222no—
243#323—1222no—
244#323—1222no—
245C61#997711yescharacteristic, complemented, Sylow
246C22×D4—21no—
247C22×D4—611no—
248C22×D4—1221no—
249C22×D4C22⋊D6111yescharacteristic
250C23×C4C22×D6111yescharacteristic
251C2×D8—1222no—
252C2×M16—21no—
253C2×M16—1221no—
254C22×C8—612no—
255C22×C8—1221no—
256#121—21no—
257#121—21no—
258#121—21no—
259#121—21no—
260#121—1221no—
261#121—1221no—
262#121—1221no—
263#121—1221no—
264#117—21no—
265#117—21no—
266#117—21no—
267#117—21no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4C22⋊D6111yescharacteristic
270C2×C4⋊C4C22⋊D6111yescharacteristic
271C2×C4⋊C4C22⋊D6111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—1221no—
275C2×C42—21no—
276#107—22no—
277#107—1222no—
278#107—1222no—
279#106—22no—
280#106—1222no—
281#102—22no—
282#102—22no—
283#102—1222no—
284#102—1222no—
285#102—1222no—
286#102—1222no—
287C22⋊C8—21no—
288C22⋊C8—612no—
289C22⋊C8—1221no—
290C22⋊C8—1221no—
291C22⋊C8—1221no—
292C22⋊C8—1221no—
293C22⋊C8—1221no—
294C22⋊C8C22⋊D6112yes—
295C24—21no—
296C24—1221no—
297C24#1175822411yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—82no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—4882no—
307C2×D4—2442no—
308C2×D4—2441no—
309C2×D4—2441no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—1221no—
315C22×C4D4×D6111yescharacteristic
316C22×C4D4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318C22×C4C2×C22⋊D6111yescharacteristic
319C22×C4C2×C22⋊D6111yescharacteristic
320C22×C4C2×C22⋊D6111yescharacteristic
321D8—4882no—
322M16—42no—
323M16—2442no—
324C2×C8—22no—
325C2×C8—1222no—
326C2×C8—1222no—
327C2×C8—2442no—
328C2×C8—2441no—
329C2×C8—2442no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C42—41no—
345C42—41no—
346C23—22no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—41no—
351C23—81no—
352C23—81no—
353C23—4881no—
354C23—4881no—
355C23—2442no—
356C23—2441no—
357C23#1451974811yescharacteristic
358C23#1451974911yescharacteristic
359C23#1451974911yescharacteristic
360D4—42no—
361D4—42no—
362D4—82no—
363D4—82no—
364D4—4882no—
365D4—4882no—
366D4—2442no—
367D4—2442no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—4881no—
381C2×C4—2441no—
382C2×C4#1451974511yescharacteristic
383C2×C4#1451974511yescharacteristic
384C2×C4#1451974611yescharacteristic
385C2×C4#1451977311yescharacteristic
386C8—42no—
387C8—4881no—
388C8—2442no—
389C8—2442no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—82no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—162no—
403C22—9762no—
404C22—4881no—
405C22—4881no—
406C22—4881no—
407C22#1683967011yescharacteristic
408C22#1684003012yes—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—4881no—
416C4#1683995112yes—
417C2—22no—
418C2—41no—
419C2—41no—
420C2—161no—
421C2—9761no—
422C2#2144692211yescharacteristic
423C2#2144692511yescharacteristic
424C2#2144694711yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#3094C2
socleC22×C61#392
prime radical#21456567C2
hypercenter#3094D61
hypocenterC61#9977
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
2. #21455759C2semidirect
3. #21445890C2semidirect
4. #21444180C2semidirect
5. #21444179C2semidirect
6. #21443695C2semidirect
7. C61×#3094C2semidirect
207. #3094D61semidirect
245. C61#9977semidirect

Maximal subgroups

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

subgroupindex
#214565672
#214557592
#214458902
#214441802
#214441792
#214436952
C61×#30942
#997761