Finite Group Databasebeta

← #29834712

Subgroups — #29834712

Order 15616.

520 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456356C211yesmaximal, characteristic
2#21454682C211yesmaximal, characteristic
3#21447985C211yesmaximal, characteristic, complemented
4#21447982C211yesmaximal, characteristic, complemented
5#21447980C211yesmaximal, characteristic, complemented
6#21447972C211yesmaximal, characteristic, complemented
7#21447969C211yesmaximal, characteristic, complemented
8#21447961C211yesmaximal, characteristic, complemented
9#21447960C211yesmaximal, characteristic, complemented
10#21447606C211yesmaximal, characteristic
11#21447600C211yesmaximal, characteristic
12#21447576C211yesmaximal, characteristic
13#21447537C211yesmaximal, characteristic
14#358×D61C211yesmaximal, characteristic
15C61×#2229C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17#16840392—21no—
18#16840238—21no—
19C2×#14519716C2211yescharacteristic
20C2×C16×D61C2211yescharacteristic
21#16840172—21no—
22#16840169—21no—
23#16840167C2211yescharacteristic
24#16840166C2211yescharacteristic
25#16840163C2211yescharacteristic
26#16839867—21no—
27#16839866—21no—
28C4×Dic244C2211yescharacteristic
29Q16×Dic61C2211yescharacteristic
30#16839856C2211yescharacteristic
31#16839801—21no—
32#16839799C2211yescharacteristic
33#16839799C2211yescharacteristic
34#107×D61C2211yescharacteristic
35#16839769—21no—
36#16839716C2211yescharacteristic
37#16839589C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839567C2211yescharacteristic
47#16839567C2211yescharacteristic
48#16839566C2211yescharacteristic
49#16839566C2211yescharacteristic
50#16839565C2211yescharacteristic
51#16839565C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Q8×D61—21no—
60C2×Dic244C2311yescharacteristic
61C2×#11758202—21no—
62Q16×D61—22no—
63Q16×D61Q814yescomplemented
64C2×#11758189D411yescharacteristic
65C2×C8×D61C2311yescharacteristic
66#14519777—21no—
67#14519776—21no—
68#14519776—41no—
69#14519768—21no—
70#14519767—41no—
71#14519757—41no—
72#14519755—41no—
73Q8×Dic61—21no—
74C4×Dic122—21no—
75C4×Dic122—41no—
76#14519742—21no—
77#14519742—41no—
78#14519735—21no—
79#14519735—21no—
80#14519735—41no—
81#14519734—41no—
82#14519734D411yescharacteristic
83C4⋊C4×D61—21no—
84#14519716—22no—
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C16×D61—22no—
88#14519711—21no—
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519710—21no—
93#14519710—21no—
94#14519708—21no—
95#14519708—21no—
96#14519708—21no—
97#14519702—21no—
98#14519701—21no—
99#14519700—21no—
100#14519688D411yescharacteristic
101#14519687D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×Q16×C61C2311yescharacteristic
104#125×C61—21no—
105C4×Q8×C61—21no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#106×C61—21no—
112#103×C61—21no—
113C4×C8×C61C2311yescharacteristic
114C2×Q8×C61—21no—
115Q8×D61—24no—
116Q8×D61—42no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61C2×D411yescharacteristic
120C2×Dic122—21no—
121C2×Dic122—41no—
122C2×Dic122—41no—
123C2×Dic122—41no—
124Q16×C61—21no—
125Q16×C61C2×Q812yes—
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2411yescharacteristic
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C42×C61—41no—
135C42×C61C2×D411yescharacteristic
136#11758202—24no—
137#11758198—41no—
138#11758198—41no—
139#11758198D811yescharacteristic
140#11758198D811yescharacteristic
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61—41no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196D811yescharacteristic
153#11758196D811yescharacteristic
154C4×Dic61—41no—
155C4×Dic61—41no—
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162Dic244—21no—
163Dic244C2×Q812yes—
164#11758189—22no—
165C8×D61C2×Q812yes—
166C8×D61#4112yes—
167C16×C61—21no—
168C16×C61—21no—
169#11758185—21no—
170#11758185—21no—
171C22×D61C2×D811yescharacteristic
172Q8×C61—22no—
173Q8×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61C2×D811yescharacteristic
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61C2×D811yescharacteristic
186C2×Dic61C2×D811yescharacteristic
187C2×Dic61C2×D811yescharacteristic
188C4×D61—44no—
189C4×D61—161no—
190C4×D61C22⋊Q812yes—
191C4×D61#13712yes—
192Dic122—22no—
193Dic122—41no—
194Dic122—44no—
195Dic122—161no—
196Dic122—161no—
197C8×C61—21no—
198C8×C61C22×Q811yescharacteristic
199C8×C61C2×#4111yescharacteristic
200#92418—21no—
201#92418C22⋊Q812yes—
202#33632—611nomaximal, Sylow
203C22×C61C22×D811yescharacteristic
204C2×D61—21no—
205C2×D61—21no—
206C2×D61#47412yes—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—42no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61—81no—
213C4×C61C2×C22⋊Q811yescharacteristic
214C4×C61C2×#13711yescharacteristic
215Dic61—21no—
216Dic61—21no—
217Dic61—42no—
218Dic61—81no—
219Dic61—81no—
220Dic61—81no—
221Dic61#47412yes—
222#3164—611no—
223#2950—611no—
224#2229—611no—
225#2229—611no—
226#2229—611no—
227#2229D6111yescharacteristic, complemented
228#2227—611no—
229#2227—611no—
230#2225—611no—
231#2225—611no—
232#2159—611no—
233#2158—611no—
234#2151—611no—
235#2141—611no—
236C2×#358—611no—
237C2×C61C2×#47411yescharacteristic
238C2×C61#341611yescharacteristic
239C2×C61#341711yescharacteristic
240D61—22no—
241C22×Q16—611no—
242#544—1221no—
243#519—1221no—
244C2×M32—611no—
245C22×C16—611no—
246#501—1221no—
247#501—1221no—
248#500—611no—
249#500—611no—
250#499—611no—
251#499C2×D6111yescharacteristic
252#441—1221no—
253#441—1221no—
254C4×Q16—611no—
255C4×Q16—611no—
256C4×Q16—611no—
257C4×Q16C2×D6111yescharacteristic
258#428—1221no—
259#427—611no—
260#427—611no—
261C2×#107—611no—
262#419—1221no—
263#405—611no—
264#367—611no—
265#367—611no—
266#367—611no—
267#367C2×D6111yescharacteristic
268#366—611no—
269#366—611no—
270#366—611no—
271#366C2×D6111yescharacteristic
272C4⋊C16—611no—
273C4⋊C16—611no—
274C4⋊C16—611no—
275C4⋊C16C2×D6111yescharacteristic
276#358—611no—
277#358—611no—
278#358—611no—
279#358—611no—
280#358—611no—
281#358—611no—
282#358C2×D6111yescharacteristic
283#358C2×D6111yescharacteristic
284C61#3363211yescharacteristic, complemented, Sylow
285C22×Q8—1221no—
286C2×Q16—614no—
287C2×Q16—611no—
288C2×Q16—1222no—
289C2×Q16—1221no—
290C2×Q16C22×D6111yescharacteristic
291C2×M16—611no—
292C22×C8—611no—
293C4⋊Q8—1221no—
294C4⋊Q8—1221no—
295C4⋊Q8—2441no—
296#125—21no—
297#125—1221no—
298#125—2441no—
299C22⋊Q8—2441no—
300C22⋊Q8—2441no—
301C4×Q8—21no—
302C4×Q8—1221no—
303C4×Q8—1221no—
304C4×Q8—1221no—
305C4×Q8—2441no—
306C4×Q8—2441no—
307#117—611no—
308#117—1221no—
309#117—1221no—
310#117—2441no—
311#117—2441no—
312C2×C4⋊C4—1221no—
313M32—1222no—
314C2×C16—611no—
315C2×C16—611no—
316C2×C16—1222no—
317C2×C16C22×D6111yescharacteristic
318C2×C16C22×D6111yescharacteristic
319#107—611no—
320#107—611no—
321#107—611no—
322#107—1221no—
323#107—1221no—
324#107—1221no—
325#107C22×D6111yescharacteristic
326#107C22×D6111yescharacteristic
327#107C22×D6111yescharacteristic
328#106—21no—
329#106—1221no—
330#106—1221no—
331#106—1221no—
332#103—21no—
333#103—1221no—
334#103—1221no—
335#103—1221no—
336#97—611no—
337#97—611no—
338C4×C8—611no—
339C4×C8C22×D6111yescharacteristic
340C2×Q8—21no—
341C2×Q8—1224no—
342C2×Q8—1221no—
343C2×Q8—2441no—
344C2×Q8—2441no—
345C2×Q8—2442no—
346C2×Q8—2441no—
347C22×C4—611no—
348C22×C4—2441no—
349C22×C4—2441no—
350Q16—21no—
351Q16—612no—
352Q16—1224no—
353Q16—1221no—
354Q16Q8×D6112yes—
355M16—1222no—
356C2×C8—611no—
357C2×C8—612no—
358C2×C8—612no—
359C2×C8—611no—
360C2×C8D4×D6111yescharacteristic
361C2×C8C23×D6111yescharacteristic
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—611no—
369C4⋊C4—611no—
370C4⋊C4—1221no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C22⋊C4—611no—
382C22⋊C4—611no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C42—41no—
386C42—611no—
387C42—2441no—
388C42—2441no—
389C42—2441no—
390C42—2441no—
391C42—2441no—
392C42D4×D6111yescharacteristic
393C16—21no—
394C16—21no—
395C16—1221no—
396C16—1221no—
397C23—611no—
398Q8—22no—
399Q8—41no—
400Q8—1222no—
401Q8—9761no—
402Q8—9761no—
403Q8—2444no—
404Q8—2441no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—611no—
410C2×C4—612no—
411C2×C4—612no—
412C2×C4—611no—
413C2×C4—611no—
414C2×C4—9761no—
415C2×C4—2444no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4D8×D6111yescharacteristic
421C2×C4D8×D6111yescharacteristic
422C2×C4C2×D4×D6111yescharacteristic
423C8—21no—
424C8—612no—
425C8—1221no—
426C8C2×Q8×D6111yescharacteristic
427C8#41×D6111yescharacteristic
428C22—612no—
429C22—1221no—
430C22—1221no—
431C22C2×D8×D6111yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—612no—
439C4—1221no—
440C4—1221no—
441C4—4881no—
442C4—4881no—
443C4—4881no—
444C4—2442no—
445C4C22⋊Q8×D6111yescharacteristic
446C4#137×D6111yescharacteristic
447C2—1222no—
448C2#474×D6111yescharacteristic
449C2#2145896411yescharacteristic
450C2#2145896911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2229C2
socleC22×C61C22×D8
prime radicalC22×D61C2×D8
hypercenter#2229D61
hypocenterC61#33632
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #21447985C2semidirect
4. #21447982C2semidirect
5. #21447980C2semidirect
6. #21447972C2semidirect
7. #21447969C2semidirect
8. #21447961C2semidirect
9. #21447960C2semidirect
15. C61×#2229C2semidirect
63. Q16×D61Q8semidirect
227. #2229D61semidirect
284. C61#33632semidirect

Maximal subgroups

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

subgroupindex
#214563562
#214546822
#214479852
#214479822
#214479802
#214479722
#214479692
#214479612
#214479602
#214476062
#214476002
#214475762
#214475372
#358×D612
C61×#22292
#3363261