Finite Group Databasebeta

← #29598743

Subgroups — #29598743

Order 15616.

552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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#21455535C211yesmaximal, characteristic, complemented
2#21455463C211yesmaximal, characteristic, complemented
3C2×#16839575C211yesmaximal, characteristic, complemented
4#21447555C211yesmaximal, characteristic, complemented
5#21447448C211yesmaximal, characteristic, complemented
6#21443934C211yesmaximal, characteristic, complemented
7C2×C61×#509C211yesmaximal, characteristic, complemented
8#16840560—21no—
9C2×#14519783C2211yescharacteristic
10#16840329—21no—
11C2×#14519717C2211yescharacteristic
12#16840034—21no—
13#16840029—21no—
14#16840022—22no—
15#16840012—22no—
16#16839995—22no—
17C2×#14519713C2211yescharacteristic
18#16839800C2211yescharacteristic
19#16839767—21no—
20#16839746—21no—
21#16839575—22no—
22#16839572—22no—
23#16839547—22no—
24C2×#135×C61C2211yescharacteristic
25C22×D8×C61C2211yescharacteristic
26C61×#509—22no—
27C61×#509—22no—
28C2×SD32×C61—21no—
29C2×D16×C61—21no—
30C2×M32×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32#14519808—22no—
33#14519807—41no—
34#14519803—22no—
35#14519802—41no—
36#14519797—42no—
37#14519783—21no—
38#14519783—21no—
39#14519783—21no—
40#14519783—21no—
41C2×#11758194—21no—
42C2×#11758194D411yescharacteristic
43C2×#11758189—21no—
44C2×C8×D61—21no—
45#14519773—41no—
46#14519764—41no—
47#14519748—24no—
48#14519746—42no—
49#14519736—21no—
50#14519717—21no—
51#14519717—21no—
52C2×#11758185—21no—
53#14519713—21no—
54#14519713D412yescomplemented
55#14519711—21no—
56#14519709D412yes—
57#14519698—24no—
58#14519696—22no—
59#14519694—22no—
60C2×#41×C61—21no—
61C22×D4×C61—21no—
62#135×C61—21no—
63#135×C61—21no—
64#135×C61—21no—
65#135×C61—21no—
66C2×Q16×C61D411yescharacteristic, complemented
67C2×SD16×C61—21no—
68C2×D8×C61—21no—
69C2×D8×C61—21no—
70C2×D8×C61—21no—
71C2×D8×C61—21no—
72C2×D8×C61—21no—
73C2×D8×C61D412yes—
74C2×D8×C61D411yescharacteristic, complemented
75C22×C8×C61C2311yescharacteristic
76SD32×C61—24no—
77D16×C61—24no—
78M32×C61—21no—
79M32×C61D412yescomplemented
80C2×C16×C61—21no—
81C24×C61—41no—
82#41×C61—41no—
83#41×C61—41no—
84#41×C61—41no—
85#41×C61—41no—
86C2×Q8×C61—21no—
87C2×D4×C61—22no—
88C2×D4×C61—21no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61C2×D411yescharacteristic
97C2×C22⋊D61—21no—
98C2×C22⋊D61—44no—
99#11758222—21no—
100#11758222—21no—
101#11758222—21no—
102#11758222—21no—
103C2×D244D811yescharacteristic
104C2×C4×D61—21no—
105C2×Dic122D811yescharacteristic
106Q16×C61—21no—
107Q16×C61—21no—
108SD16×C61—41no—
109SD16×C61—41no—
110D8×C61—21no—
111D8×C61—22no—
112D8×C61—22no—
113D8×C61—21no—
114D8×C61—41no—
115D8×C61—41no—
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61#4111yescharacteristic
122C22⋊Dic61—44no—
123C22⋊Dic61—41no—
124#11758202—42no—
125#11758201—42no—
126#11758200—42no—
127#11758199—42no—
128C4⋊Dic61—22no—
129C4×Dic61—41no—
130#11758194—22no—
131#11758194—21no—
132#11758194—21no—
133#11758194—41no—
134C2×#92418—21no—
135C2×#92418—41no—
136#11758189—41no—
137#11758189—41no—
138C8×D61—41no—
139C8×D61—41no—
140C16×C61—22no—
141#11758185—41no—
142C23×C61—42no—
143C23×C61—41no—
144C23×C61—81no—
145C23×C61—81no—
146C23×C61—162no—
147C23×C61AGL(1,ℤ/8)11yescharacteristic
148C22×D61—21no—
149Q8×C61—41no—
150Q8×C61—41no—
151D4×C61—42no—
152D4×C61—41no—
153D4×C61—41no—
154D4×C61—42no—
155D4×C61—81no—
156D4×C61—81no—
157D4×C61—81no—
158D4×C61—81no—
159C2×C4×C61—41no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61#12011yescharacteristic
163C2×C4×C61#12011yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61C2×D811yescharacteristic
166C2×C4×C61#13511yescharacteristic
167C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
168C22⋊D61—41no—
169C22⋊D61—41no—
170C22⋊D61—164no—
171C2×Dic61—21no—
172C2×Dic61—42no—
173D244—21no—
174D244—21no—
175C4×D61—41no—
176C4×D61—41no—
177Dic122—21no—
178Dic122—21no—
179C8×C61#12011yescharacteristic
180C8×C61#12111yescharacteristic
181C8×C61#12111yescharacteristic
182C8×C61#12711yescharacteristic
183#92418—41no—
184#92418—42no—
185#13310—611nomaximal, Sylow
186C22×C61—41no—
187C22×C61—84no—
188C22×C61—81no—
189C22×C61—82no—
190C22×C61—161no—
191C22×C61—162no—
192C22×C61—162no—
193C22×C61#44711yescharacteristic
194C22×C61#44911yescharacteristic
195C22×C61#46911yescharacteristic
196C2×D61—42no—
197C2×D61—41no—
198C4×C61—81no—
199C4×C61#39211yescharacteristic
200C4×C61#44711yescharacteristic
201C4×C61#44911yescharacteristic
202C4×C61#46611yescharacteristic
203Dic61—41no—
204Dic61—82no—
205C2×#509D6111yescharacteristic, complemented
206#3067—611no—
207#3058—611no—
208C2×#361—611no—
209#2145—611no—
210#2117—611no—
211#1389—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—21no—
215C2×C61—162no—
216C2×C61—161no—
217C2×C61#199911yescharacteristic
218D61—81no—
219#575—1221no—
220C2×#135C2×D6111yescharacteristic
221C22×D8C2×D6111yescharacteristic
222C2×#131—611no—
223#535—1221no—
224#509—22no—
225#509—22no—
226C2×SD32—21no—
227C2×D16—21no—
228C2×M32—611no—
229C2×M32C2×D6111yescharacteristic
230#473—1221no—
231#472—1221no—
232#471—1222no—
233#469—1222no—
234#466—1222no—
235C2×#108—611no—
236#427—611no—
237#418—1221no—
238#413—1221no—
239#361—1222no—
240#360—1222no—
241#350—1222no—
242C61#1331011yescharacteristic, complemented, Sylow
243C2×#41—21no—
244C2×#41—611no—
245C22×D4—21no—
246#137—1222no—
247#137—2441no—
248AGL(1,ℤ/8)—1222no—
249AGL(1,ℤ/8)—2441no—
250#135—21no—
251#135—21no—
252#135—21no—
253#135—21no—
254#135—2442no—
255C2×Q16C22⋊D6111yescharacteristic, complemented
256C2×SD16—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—21no—
261C2×D8—21no—
262C2×D8C22⋊D6112yes—
263C2×D8C22⋊D6111yescharacteristic, complemented
264#131—1221no—
265#131—1221no—
266#131—1221no—
267#131—1221no—
268C2×M16—611no—
269C2×M16—1221no—
270C2×M16—1221no—
271C22×C8—1221no—
272C22×C8C22×D6111yescharacteristic
273#127—2441no—
274#124—2441no—
275#121—1224no—
276#120—2442no—
277#117—1221no—
278SD32—24no—
279D16—24no—
280M32—21no—
281M32—1221no—
282M32—1221no—
283M32C22⋊D6112yescomplemented
284C2×C16—21no—
285C2×C16—1221no—
286#108—612no—
287#108—1221no—
288#107—1221no—
289#106—612no—
290#102—1224no—
291#101—1222no—
292#100—1222no—
293C24—41no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302C2×Q8—21no—
303C2×Q8—611no—
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—611no—
313C2×D4—1221no—
314C2×D4—2444no—
315C22×C4—41no—
316C22×C4—1221no—
317C22×C4D4×D6111yescharacteristic
318Q16—21no—
319Q16—21no—
320Q16—2442no—
321SD16—41no—
322SD16—41no—
323SD16—2442no—
324SD16—2442no—
325D8—21no—
326D8—22no—
327D8—22no—
328D8—21no—
329D8—41no—
330D8—41no—
331D8—2442no—
332M16—1221no—
333M16—1222no—
334M16—1221no—
335M16—2441no—
336M16—2441no—
337M16—2441no—
338C2×C8—1221no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C2×C8D4×D6111yescharacteristic
343C2×C8D4×D6111yescharacteristic
344C2×C8#1175822411yescharacteristic
345C2×C8C2×C22⋊D6111yescharacteristic
346C2×C8C2×C22⋊D6111yescharacteristic
347C2×C8C2×C22⋊D6111yescharacteristic
348C4⋊C4—1222no—
349C22⋊C4—2444no—
350C22⋊C4—2441no—
351C42—2441no—
352C16—22no—
353C16—2441no—
354C23—42no—
355C23—41no—
356C23—81no—
357C23—81no—
358C23—162no—
359C23—1221no—
360C23#1451980111yescharacteristic
361Q8—41no—
362Q8—41no—
363Q8—1221no—
364Q8—1221no—
365D4—41no—
366D4—42no—
367D4—42no—
368D4—41no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4—1221no—
374D4—1221no—
375D4—9764no—
376D4—2441no—
377D4—2441no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—1221no—
382C2×C4—2442no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4#1451974511yescharacteristic
386C2×C4#1451974511yescharacteristic
387C2×C4#1451974811yescharacteristic
388C2×C4D8×D6111yescharacteristic
389C2×C4#1451979611yescharacteristic
390C2×C4#1451980111yescharacteristic
391C8—2442no—
392C8—2441no—
393C8#1451974611yescharacteristic
394C8#1451974911yescharacteristic
395C8#1451974911yescharacteristic
396C8#1451977311yescharacteristic
397C22—41no—
398C22—84no—
399C22—81no—
400C22—82no—
401C22—161no—
402C22—162no—
403C22—162no—
404C22—2442no—
405C22—2441no—
406C22#1683989411yescharacteristic
407C22#1683990411yescharacteristic
408C22#1684001211yescharacteristic
409C4—81no—
410C4—4882no—
411C4—2441no—
412C4#1683967011yescharacteristic
413C4#1683989411yescharacteristic
414C4#1683990411yescharacteristic
415C4#1683999511yescharacteristic
416C2—21no—
417C2—21no—
418C2—21no—
419C2—162no—
420C2—161no—
421C2—4881no—
422C2#2144681411yescharacteristic
subgroupG/H
centerC2#21446814
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#509C2
socleC2×C61#1999
hypercenterC2×#509D61
hypocenterC61#13310
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. #21455535C2semidirect
2. #21455463C2semidirect
3. C2×#16839575C2semidirect
4. #21447555C2semidirect
5. #21447448C2semidirect
6. #21443934C2semidirect
7. C2×C61×#509C2semidirect
54. #14519713D4semidirect
66. C2×Q16×C61D4semidirect
74. C2×D8×C61D4semidirect
79. M32×C61D4semidirect
205. C2×#509D61semidirect
242. C61#13310semidirect
255. C2×Q16C22⋊D61semidirect
263. C2×D8C22⋊D61semidirect
283. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214555352
#214554632
C2×#168395752
#214475552
#214474482
#214439342
C2×C61×#5092
#1331061