Finite Group Databasebeta

← #29598736

Subgroups — #29598736

Order 15616.

532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16840205C211yesmaximal, characteristic, complemented
2C2×#16840037C211yesmaximal, characteristic, complemented
3#21455489C211yesmaximal, characteristic
4C2×#16839570C211yesmaximal, characteristic, complemented
5C2×#16839567C211yesmaximal, characteristic, complemented
6#21443928C211yesmaximal, characteristic, complemented
7C2×C61×#350C211yesmaximal, characteristic, complemented
8C2×#14519807—21no—
9C2×#14519799C2211yescharacteristic
10C22×Dic244C2211yescharacteristic
11#16840340—21no—
12#16840205—22no—
13#16840205—22no—
14C2×Dic488—21no—
15C2×#14519722—21no—
16#16840037—22no—
17#16840037—22no—
18#16840008—22no—
19#16840003—21no—
20#16839998—21no—
21C2×#14519713C2211yescharacteristic
22C2×#14519711C2211yescharacteristic
23#16839764—21no—
24C2×#14519695—21no—
25#16839570—22no—
26#16839567—22no—
27C2×#131×C61C2211yescharacteristic
28C2×M32×C61C2211yescharacteristic
29C22×C16×C61C2211yescharacteristic
30C61×#350—22no—
31C2×#11758222—21no—
32C22×Dic122—21no—
33#14519807—24no—
34#14519807—42no—
35#14519799—21no—
36#14519799—21no—
37#14519799—21no—
38#14519799—21no—
39C2×Dic244—21no—
40C2×Dic244—21no—
41C2×Dic244—21no—
42C2×Dic244—21no—
43C2×Dic244—21no—
44C2×Dic244D411yescharacteristic
45C2×Dic244D412yescomplemented
46C2×#11758202—41no—
47C2×#11758190—21no—
48C2×#11758200—41no—
49C2×D488D411yescharacteristic
50C2×#11758194—21no—
51#14519756—22no—
52#14519753—41no—
53#14519751—22no—
54#14519749—42no—
55#14519748—41no—
56C2×C4⋊Dic61—21no—
57Dic488—24no—
58#14519722—24no—
59#14519713—21no—
60#14519713D412yescomplemented
61#14519711—21no—
62#14519711D412yes—
63#14519702—22no—
64#14519699—22no—
65#14519695—24no—
66C2×#41×C61D411yescharacteristic
67#131×C61—21no—
68#131×C61—21no—
69#131×C61—21no—
70#131×C61—21no—
71C2×M16×C61—21no—
72C2×M16×C61D411yescharacteristic
73C22×C8×C61—21no—
74C22×C8×C61C2311yescharacteristic
75M32×C61—21no—
76M32×C61D412yescomplemented
77C2×C16×C61—21no—
78C2×C16×C61—21no—
79C2×C16×C61—21no—
80C2×C16×C61—21no—
81#41×C61—21no—
82#41×C61—21no—
83#41×C61—21no—
84#41×C61—21no—
85C2×Q8×C61D811yescharacteristic
86C2×D4×C61—21no—
87C2×D4×C61D811yescharacteristic
88C22×C4×C61—21no—
89C22×C4×C61C2×D411yescharacteristic
90C2×C22⋊D61—41no—
91C2×C22⋊D61—42no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94#11758222—41no—
95#11758222—41no—
96#11758222—41no—
97#11758222—41no—
98C2×D244—21no—
99C2×C4×D61—41no—
100C2×Dic122—22no—
101C2×Dic122—21no—
102C2×Dic122—41no—
103C2×Dic122—41no—
104C2×Dic122—41no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107M16×C61—21no—
108M16×C61—21no—
109M16×C61—41no—
110M16×C61—41no—
111C2×C8×C61—21no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61#4111yescharacteristic
120C22⋊Dic61—42no—
121#11758202—44no—
122#11758200—44no—
123#11758198—42no—
124C4⋊Dic61—22no—
125C4⋊Dic61—41no—
126#11758196—42no—
127#11758194—22no—
128#11758194—41no—
129C2×#92418—41no—
130Dic244—22no—
131Dic244—21no—
132Dic244—22no—
133Dic244—21no—
134Dic244—41no—
135Dic244—41no—
136D488—21no—
137D488—21no—
138#11758190—41no—
139#11758190—41no—
140C16×C61—22no—
141C16×C61—41no—
142C23×C61—21no—
143C23×C61AGL(1,ℤ/8)11yescharacteristic
144C22×D61—41no—
145Q8×C61—21no—
146Q8×C61—21no—
147D4×C61—21no—
148D4×C61—21no—
149D4×C61—41no—
150D4×C61—41no—
151C2×C4×C61—21no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61#12011yescharacteristic
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61C2×D811yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C22⋊D61—81no—
161C22⋊D61—81no—
162C22⋊D61—162no—
163C2×Dic61—41no—
164C2×Dic61—42no—
165C2×Dic61—42no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—161no—
169D244—41no—
170D244—41no—
171C4×D61—81no—
172C4×D61—81no—
173Dic122—41no—
174Dic122—42no—
175Dic122—42no—
176Dic122—41no—
177Dic122—81no—
178Dic122—81no—
179C8×C61—41no—
180C8×C61#12011yescharacteristic
181C8×C61#12111yescharacteristic
182C8×C61#12111yescharacteristic
183C8×C61#12711yescharacteristic
184#92418—42no—
185#13308—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61#44711yescharacteristic
192C22×C61#44911yescharacteristic
193C22×C61#46911yescharacteristic
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C4×C61—41no—
198C4×C61#39211yescharacteristic
199C4×C61#44711yescharacteristic
200C4×C61#44911yescharacteristic
201C4×C61#46611yescharacteristic
202Dic61—82no—
203Dic61—82no—
204Dic61—81no—
205C2×#510—611no—
206C2×#473—611no—
207#3061—611no—
208C2×#359—611no—
209C2×#358—611no—
210C2×#350D6111yescharacteristic, complemented
211#1387—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—81no—
215C2×C61#199911yescharacteristic
216C2×C61#219411yescharacteristic
217C2×C61#219511yescharacteristic
218D61—161no—
219C2×#137—1221no—
220C2×#135—611no—
221C22×Q16—611no—
222C2×#131C2×D6111yescharacteristic
223#537—1221no—
224#510—1222no—
225#510—1222no—
226C2×Q32—1221no—
227C2×SD32—1221no—
228C2×M32C2×D6111yescharacteristic
229C22×C16C2×D6111yescharacteristic
230#473—1222no—
231#473—1222no—
232#468—1222no—
233#467—1221no—
234#466—1221no—
235C2×#108—611no—
236C2×#107—611no—
237#417—1221no—
238C2×#101—1221no—
239#359—1222no—
240#358—1222no—
241#350—22no—
242C61#1330811yescharacteristic, complemented, Sylow
243C2×#41—1221no—
244C2×#41D24411yescharacteristic
245C22×Q8—1221no—
246#137—1224no—
247#137—2442no—
248#135—1221no—
249#135—1221no—
250#135—1221no—
251#135—1221no—
252C2×Q16—612no—
253C2×Q16—611no—
254C2×Q16—1221no—
255C2×Q16—1221no—
256C2×Q16—1221no—
257C2×Q16—1221no—
258C2×Q16—1221no—
259C2×Q16—2441no—
260C2×SD16—1221no—
261C2×SD16—2441no—
262C2×D8—611no—
263#131—21no—
264#131—21no—
265#131—21no—
266#131—21no—
267C2×M16—21no—
268C2×M16—1221no—
269C2×M16D24411yescharacteristic
270C22×C8—21no—
271C22×C8C22×D6111yescharacteristic
272C22⋊Q8—1222no—
273C22⋊Q8—2441no—
274#121—1222no—
275#121—2442no—
276#121—2441no—
277C2×C4⋊C4—1221no—
278Q32—1224no—
279SD32—1224no—
280M32—21no—
281M32C22⋊D6112yescomplemented
282C2×C16—21no—
283C2×C16—21no—
284C2×C16—21no—
285C2×C16—21no—
286#108—612no—
287#108—1221no—
288#107—612no—
289#107—1221no—
290#103—1222no—
291#102—1222no—
292#101—1224no—
293#41—21no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—2441no—
298#41—2441no—
299#41—2441no—
300#41—2441no—
301C2×Q8—1222no—
302C2×Q8—1221no—
303C2×Q8—2441no—
304C2×Q8—2441no—
305C2×Q8—2441no—
306C2×Q8—2441no—
307C2×Q8—2441no—
308C2×Q8D48811yescharacteristic
309C2×D4—21no—
310C2×D4—1221no—
311C2×D4—2442no—
312C2×D4—2441no—
313C2×D4D48811yescharacteristic
314C22×C4—21no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4C2×D24411yescharacteristic
319Q16—1222no—
320Q16—1221no—
321Q16—1222no—
322Q16—1221no—
323Q16—2444no—
324Q16—2441no—
325Q16—2441no—
326SD16—2444no—
327SD16—2441no—
328SD16—2441no—
329D8—1221no—
330D8—1221no—
331M16—21no—
332M16—21no—
333M16—41no—
334M16—41no—
335M16—1222no—
336M16—2441no—
337C2×C8—21no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—2441no—
341C2×C8#1175822211yescharacteristic
342C2×C8D4×D6111yescharacteristic
343C2×C8D4×D6111yescharacteristic
344C2×C8D4×D6111yescharacteristic
345C2×C8D4×D6111yescharacteristic
346C2×C8C2×C22⋊D6111yescharacteristic
347C4⋊C4—1222no—
348C4⋊C4—2442no—
349C4⋊C4—2441no—
350C22⋊C4—2442no—
351C22⋊C4—2442no—
352C16—22no—
353C16—41no—
354C23—21no—
355C23—2441no—
356C23#1451980511yescharacteristic
357Q8—21no—
358Q8—21no—
359Q8—4881no—
360Q8—4881no—
361Q8—2442no—
362Q8—2441no—
363Q8—2441no—
364Q8—2442no—
365D4—21no—
366D4—21no—
367D4—41no—
368D4—41no—
369D4—9762no—
370D4—4881no—
371D4—4881no—
372D4—2441no—
373D4—2441no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—9761no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—2442no—
383C2×C4—2441no—
384C2×C4—2442no—
385C2×C4#1451974711yescharacteristic
386C2×C4#1451974711yescharacteristic
387C2×C4#1451975111yescharacteristic
388C2×C4C2×D48811yescharacteristic
389C2×C4#1451979911yescharacteristic
390C2×C4#1451980511yescharacteristic
391C8—41no—
392C8—2442no—
393C8#1451974511yescharacteristic
394C8#1451975011yescharacteristic
395C8#1451975011yescharacteristic
396C8#1451977311yescharacteristic
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22#1683989811yescharacteristic
406C22#1683990911yescharacteristic
407C22#1684001511yescharacteristic
408C4—41no—
409C4—4882no—
410C4—4881no—
411C4—4882no—
412C4#1683967111yescharacteristic
413C4#1683989811yescharacteristic
414C4#1683990911yescharacteristic
415C4#1683999811yescharacteristic
416C2—21no—
417C2—21no—
418C2—81no—
419C2—9761no—
420C2#2144681711yescharacteristic
421C2#2144779211yescharacteristic
422C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#350C2
socleC22×C61#447
prime radical#21455489C2
hypercenterC2×#350D61
hypocenterC61#13308
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. C2×#16840205C2semidirect
2. C2×#16840037C2semidirect
4. C2×#16839570C2semidirect
5. C2×#16839567C2semidirect
6. #21443928C2semidirect
7. C2×C61×#350C2semidirect
45. C2×Dic244D4semidirect
60. #14519713D4semidirect
76. M32×C61D4semidirect
210. C2×#350D61semidirect
242. C61#13308semidirect
281. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402052
C2×#168400372
#214554892
C2×#168395702
C2×#168395672
#214439282
C2×C61×#3502
#1330861