Finite Group Databasebeta

← #29598779

Subgroups — #29598779

Order 15616.

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

normal subgroups only

This group has 604 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
1#21455424C211yesmaximal, characteristic, complemented
2C2×#16840012C211yesmaximal, characteristic, complemented
3C2×#16839572C211yesmaximal, characteristic, complemented
4#21447535C211yesmaximal, characteristic, complemented
5C2×#16839543C211yesmaximal, characteristic, complemented
6#21443925C211yesmaximal, characteristic, complemented
7C2×C61×#509C211yesmaximal, characteristic, complemented
8C22×#11758189C2211yescharacteristic
9#16840269—21no—
10C2×#14519748—21no—
11C2×#14519717C2211yescharacteristic
12#16840017—21no—
13#16840012—22no—
14#16840012—22no—
15#16840012—21no—
16#16840005—22no—
17#16839800C2211yescharacteristic
18C2×#14519709C2211yescharacteristic
19#16839758—21no—
20C2×#14519698—21no—
21#16839572—22no—
22#16839563—22no—
23#16839543—22no—
24C2×#135×C61C2211yescharacteristic
25C22×D8×C61C2211yescharacteristic
26C61×#509—22no—
27C61×#509—22no—
28C2×SD32×C61—21no—
29C2×D16×C61—21no—
30C2×M32×C61C2211yescharacteristic
31C22×C22⋊D61—41no—
32C22×C4×D61D411yescharacteristic
33C2×#11758189—21no—
34C2×#11758189—21no—
35C2×#11758189—21no—
36C2×#11758189—21no—
37C2×#11758189—21no—
38C2×#11758189—21no—
39C22×#92418D411yescharacteristic
40#14519758—41no—
41#14519753—22no—
42#14519748—24no—
43#14519748—22no—
44#14519748—42no—
45#14519745—41no—
46C4×C22⋊D61—42no—
47#14519736—21no—
48C2×C4⋊Dic61—21no—
49C2×C22⋊Dic61—41no—
50#14519717—21no—
51#14519717—21no—
52C2×#11758185—21no—
53#14519711D412yescomplemented
54#14519709—21no—
55#14519709—21no—
56#14519709D412yescomplemented
57#14519701—22no—
58#14519698—24no—
59#14519698—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×C61D412yescomplemented
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—
82C23×D61D811yescharacteristic
83#41×C61—41no—
84#41×C61—41no—
85#41×C61—41no—
86#41×C61—41no—
87C2×Q8×C61—21no—
88C2×D4×C61—22no—
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61C2×D411yescharacteristic
98C2×C22⋊D61—44no—
99C2×C22⋊D61—42no—
100C2×C22⋊D61—84no—
101C22×Dic61—41no—
102C22×Dic61D811yescharacteristic
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109Q16×C61—21no—
110Q16×C61—21no—
111SD16×C61—41no—
112SD16×C61—41no—
113D8×C61—21no—
114D8×C61—22no—
115D8×C61—22no—
116D8×C61—21no—
117D8×C61—41no—
118D8×C61—41no—
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61#4111yescharacteristic
125C22⋊Dic61—44no—
126C22⋊Dic61—42no—
127C22⋊Dic61—41no—
128#11758198—42no—
129C4⋊Dic61—22no—
130C4⋊Dic61—22no—
131C4⋊Dic61—41no—
132#11758196—42no—
133C4×Dic61—41no—
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418—21no—
137#11758189—41no—
138#11758189—41no—
139#11758189—41no—
140#11758189—41no—
141C16×C61—22no—
142#11758185—41no—
143C23×C61—41no—
144C23×C61—42no—
145C23×C61—82no—
146C23×C61—82no—
147C23×C61—81no—
148C23×C61—81no—
149C23×C61C2×D811yescharacteristic
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—42no—
154Q8×C61—41no—
155Q8×C61—41no—
156D4×C61—42no—
157D4×C61—41no—
158D4×C61—42no—
159D4×C61—41no—
160D4×C61—81no—
161D4×C61—81no—
162D4×C61—81no—
163D4×C61—81no—
164C2×C4×C61—41no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C22⋊D61—84no—
174C22⋊D61—88no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—82no—
181C4×D61—41no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—41no—
185C8×C61#12011yescharacteristic
186C8×C61#12111yescharacteristic
187C8×C61#12111yescharacteristic
188C8×C61#12711yescharacteristic
189#92418—41no—
190#13316—611nomaximal, Sylow
191C22×C61—22no—
192C22×C61—82no—
193C22×C61—82no—
194C22×C61—82no—
195C22×C61—81no—
196C22×C61—82no—
197C22×C61—162no—
198C22×C61—162no—
199C22×C61#44711yescharacteristic
200C22×C61#44711yescharacteristic
201C22×C61#46611yescharacteristic
202C2×D61—42no—
203C2×D61—42no—
204C2×D61—41no—
205C2×D61—81no—
206C4×C61—81no—
207C4×C61#39211yescharacteristic
208C4×C61#44911yescharacteristic
209C4×C61#44911yescharacteristic
210C4×C61#46911yescharacteristic
211Dic61—41no—
212Dic61—82no—
213Dic61—82no—
214C2×#509D6111yescharacteristic, complemented
215#3054—611no—
216C2×#469—611no—
217C2×#360—611no—
218#2140—611no—
219C2×#349—611no—
220#1386—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—161no—
224C2×C61—162no—
225C2×C61#199911yescharacteristic
226C2×C61#219012yes—
227D61—81no—
228C2×#135C2×D6111yescharacteristic
229C22×D8C2×D6111yescharacteristic
230C22×M16—611no—
231#525—1221no—
232C2×#121—1221no—
233#509—22no—
234#509—22no—
235C2×SD32—21no—
236C2×D16—21no—
237C2×M32—611no—
238C2×M32C2×D6111yescharacteristic
239#470—1221no—
240#469—1222no—
241#469—1222no—
242#469—1221no—
243#468—1222no—
244#427—611no—
245C2×#106—611no—
246#416—1221no—
247C2×#102—1221no—
248#360—1222no—
249#357—1222no—
250#349—1222no—
251C61#1331611yescharacteristic, complemented, Sylow
252C2×#41—21no—
253C22×D4—21no—
254C22×D4—2441no—
255C23×C4—611no—
256#135—21no—
257#135—21no—
258#135—21no—
259#135—21no—
260C2×Q16C22⋊D6111yescharacteristic, complemented
261C2×SD16—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8C22⋊D6112yescomplemented
268C2×D8C22⋊D6111yescharacteristic, complemented
269C2×M16—1221no—
270C2×M16—1221no—
271C2×M16—1221no—
272C2×M16—1221no—
273C2×M16—1221no—
274C2×M16—1221no—
275C22×C8—611no—
276C22×C8C22×D6111yescharacteristic
277#123—2441no—
278C22⋊Q8—1222no—
279#121—1224no—
280#121—1222no—
281#121—2442no—
282#120—2441no—
283C4×D4—2442no—
284#117—1221no—
285C2×C4⋊C4—1221no—
286C2×C22⋊C4—2441no—
287SD32—24no—
288D16—24no—
289M32—21no—
290M32—1221no—
291M32—1221no—
292M32C22⋊D6112yescomplemented
293C2×C16—21no—
294C2×C16—1221no—
295#107—612no—
296#106—612no—
297#106—1221no—
298#106—1221no—
299#103—1222no—
300#102—1224no—
301#102—1222no—
302C24—41no—
303C24—611no—
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—4884no—
318C2×D4—2442no—
319C2×D4—2444no—
320C22×C4—41no—
321C22×C4—611no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—2441no—
329C22×C4D4×D6111yescharacteristic
330Q16—21no—
331Q16—21no—
332SD16—41no—
333SD16—41no—
334D8—21no—
335D8—22no—
336D8—22no—
337D8—21no—
338D8—41no—
339D8—41no—
340M16—2441no—
341M16—2441no—
342M16—2441no—
343M16—2441no—
344C2×C8—1221no—
345C2×C8—1221no—
346C2×C8—1221no—
347C2×C8D4×D6111yescharacteristic
348C2×C8D4×D6111yescharacteristic
349C2×C8#1175822411yescharacteristic
350C2×C8C2×C22⋊D6111yescharacteristic
351C2×C8C2×C22⋊D6111yescharacteristic
352C2×C8C2×C22⋊D6111yescharacteristic
353C4⋊C4—1222no—
354C4⋊C4—1222no—
355C4⋊C4—2442no—
356C4⋊C4—2441no—
357C22⋊C4—2442no—
358C22⋊C4—2444no—
359C22⋊C4—2442no—
360C22⋊C4—2441no—
361C42—2441no—
362C16—22no—
363C16—2441no—
364C23—42no—
365C23—41no—
366C23—82no—
367C23—82no—
368C23—81no—
369C23—81no—
370C23—1221no—
371C23—1221no—
372C23—1221no—
373C23—2442no—
374C23D8×D6111yescharacteristic
375Q8—41no—
376Q8—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—4888no—
386D4—4884no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—4882no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4#1451974511yescharacteristic
401C2×C4#1451974511yescharacteristic
402C2×C4#1451974811yescharacteristic
403C2×C4#1451979611yescharacteristic
404C2×C4#1451980111yescharacteristic
405C2×C4#1451980111yescharacteristic
406C8—2441no—
407C8#1451974611yescharacteristic
408C8#1451974911yescharacteristic
409C8#1451974911yescharacteristic
410C8#1451977311yescharacteristic
411C22—22no—
412C22—82no—
413C22—82no—
414C22—82no—
415C22—81no—
416C22—82no—
417C22—162no—
418C22—162no—
419C22—4881no—
420C22—2442no—
421C22—2442no—
422C22—2441no—
423C22#1683989411yescharacteristic
424C22#1683989411yescharacteristic
425C22#1683999511yescharacteristic
426C4—81no—
427C4—4882no—
428C4—4882no—
429C4—2441no—
430C4#1683967011yescharacteristic
431C4#1683990411yescharacteristic
432C4#1683990411yescharacteristic
433C4#1684001211yescharacteristic
434C2—21no—
435C2—21no—
436C2—162no—
437C2—161no—
438C2—4881no—
439C2#2144681411yescharacteristic
440C2#2144776312yes—
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#509C2
socleC22×C61#447
hypercenterC2×#509D61
hypocenterC61#13316
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. #21455424C2semidirect
2. C2×#16840012C2semidirect
3. C2×#16839572C2semidirect
4. #21447535C2semidirect
5. C2×#16839543C2semidirect
6. #21443925C2semidirect
7. C2×C61×#509C2semidirect
53. #14519711D4semidirect
56. #14519709D4semidirect
66. C2×Q16×C61D4semidirect
73. C2×D8×C61D4semidirect
74. C2×D8×C61D4semidirect
79. M32×C61D4semidirect
214. C2×#509D61semidirect
251. C61#13316semidirect
260. C2×Q16C22⋊D61semidirect
267. C2×D8C22⋊D61semidirect
268. C2×D8C22⋊D61semidirect
292. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214554242
C2×#168400122
C2×#168395722
#214475352
C2×#168395432
#214439252
C2×C61×#5092
#1331661