Finite Group Databasebeta

← #29598368

Subgroups — #29598368

Order 15616.

448 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21447514C211yesmaximal, characteristic, complemented
2#21447511C211yesmaximal, characteristic
3#21447473C211yesmaximal, characteristic, complemented
4#21447469C211yesmaximal, characteristic
5#21445869C211yesmaximal, characteristic, complemented
6#21445619C211yesmaximal, characteristic, complemented
7C61×#3057C211yesmaximal, characteristic
8C2×#14519713—21no—
9#16839746C2211yescharacteristic
10#16839746C2211yescharacteristic
11#16839746C2211yescharacteristic
12#16839736C2211yescharacteristic
13#16839717—21no—
14#16839561—22no—
15#16839559—22no—
16#16839552—22no—
17#16839549—22no—
18#16839533—21no—
19#16839520—21no—
20C22×SD16×C61C411yescharacteristic, complemented
21C2×#131×C61C2211yescharacteristic
22C61×#536C2211yescharacteristic
23C61×#535C2211yescharacteristic
24C61×#468—21no—
25C61×#468—21no—
26C61×#465—21no—
27C61×#465—21no—
28C61×#427C411yescharacteristic, complemented
29C61×#419C411yescharacteristic, complemented
30C61×#418C411yescharacteristic, complemented
31C2×#11758194—21no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34#14519736—21no—
35#14519713—41no—
36#14519713—41no—
37#14519696—21no—
38#14519696—21no—
39#14519696D412yes—
40#14519694—21no—
41#14519694—21no—
42#14519694—21no—
43#14519692—21no—
44#14519692D412yes—
45#14519687—41no—
46C8×Dic61—41no—
47C2×#41×C61C2311yescharacteristic
48C22×Q8×C61C2×C411yescharacteristic
49C22×D4×C61C2×C411yescharacteristic
50C2×SD16×C61—21no—
51C2×SD16×C61—21no—
52C2×SD16×C61—41no—
53C2×SD16×C61—41no—
54#131×C61—41no—
55#131×C61—41no—
56C2×M16×C61C2×C411yescharacteristic
57C2×M16×C61D411yescharacteristic
58C2×M16×C61D411yescharacteristic
59C22×C8×C61C2×C411yescharacteristic
60C22×C8×C61D411yescharacteristic
61C22×C8×C61D411yescharacteristic
62C4⋊Q8×C61—21no—
63#127×C61—21no—
64#124×C61—21no—
65#124×C61—21no—
66#123×C61—21no—
67#123×C61—21no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72#120×C61—21no—
73#120×C61—21no—
74#117×C61C2×C411yescharacteristic
75#117×C61C2×C411yescharacteristic
76#107×C61—21no—
77#106×C61—21no—
78#103×C61—21no—
79#103×C61—21no—
80#102×C61—21no—
81#102×C61—21no—
82C24×C61—21no—
83#41×C61—41no—
84#41×C61—41no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C2×Q8×C61C2×D411yescharacteristic
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61C2×D411yescharacteristic
97C2×D4×C61#4111yescharacteristic
98C2×D4×C61#4111yescharacteristic
99C22×C4×C61—21no—
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103SD16×C61—42no—
104SD16×C61—41no—
105SD16×C61—41no—
106M16×C61—41no—
107M16×C61—41no—
108M16×C61—41no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61—21no—
114C2×C8×C61—21no—
115C2×C8×C61C22⋊C411yescharacteristic
116C2×C8×C61C22⋊C411yescharacteristic
117C2×C8×C61C22⋊C411yescharacteristic
118C2×C8×C61C22⋊C411yescharacteristic
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C22⋊C4×C61—21no—
124C22⋊C4×C61—21no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C42×C61—21no—
130C42×C61—21no—
131C22⋊Dic61—22no—
132C4⋊Dic61—41no—
133C4×Dic61—41no—
134#11758194—22no—
135#11758194—41no—
136#11758194—41no—
137#11758194—41no—
138#11758194—41no—
139#11758194—41no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C23×C61—41no—
144C23×C61—81no—
145C23×C61—161no—
146C23×C61C4×D411yescharacteristic
147C23×C61#12111yescharacteristic
148C23×C61#12411yescharacteristic
149Q8×C61—41no—
150Q8×C61—41no—
151Q8×C61—41no—
152Q8×C61—81no—
153D4×C61—41no—
154D4×C61—41no—
155D4×C61—41no—
156D4×C61—41no—
157D4×C61—41no—
158D4×C61—81no—
159D4×C61—161no—
160D4×C61—161no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—81no—
171C2×C4×C61C2×C22⋊C411yescharacteristic
172C2×C4×C61C4×D411yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12711yescharacteristic
175C2×Dic61—42no—
176C8×C61—21no—
177C8×C61—21no—
178C8×C61—21no—
179C8×C61#9911yescharacteristic
180C8×C61#9911yescharacteristic
181#92418—42no—
182#92418—81no—
183#92418—81no—
184#13232—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—162no—
195C22×C61#39011yescharacteristic
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—81no—
200C4×C61—81no—
201C4×C61—81no—
202C4×C61C2×#9911yescharacteristic
203C4×C61#41011yescharacteristic
204Dic61—82no—
205#3057D6111yescharacteristic
206#2135—611no—
207#2134—611no—
208#2123—611no—
209#2122—611no—
210#1813—611no—
211#1757—611no—
212C2×C61—21no—
213C2×C61—41no—
214C2×C61—41no—
215C2×C61—41no—
216C2×C61—161no—
217C2×C61#196411yescharacteristic
218C22×SD16Dic6111yescharacteristic, complemented
219C2×#131C2×D6111yescharacteristic
220#536C2×D6111yescharacteristic
221#535C2×D6111yescharacteristic
222#468—21no—
223#468—21no—
224#465—21no—
225#465—21no—
226C2×#108—1221no—
227#427Dic6111yescharacteristic, complemented
228#419Dic6111yescharacteristic, complemented
229#418Dic6111yescharacteristic, complemented
230#413—611no—
231#413—611no—
232#413—611no—
233#410—611no—
234#405—1221no—
235#356—1222no—
236#355—1222no—
237#352—1222no—
238AΣL(1,𝔽16)—1222no—
239#344—1221no—
240#338—1221no—
241C61#1323211yescharacteristic, complemented, Sylow
242C2×#41C22×D6111yescharacteristic
243C22×Q8C2×Dic6111yescharacteristic
244C22×D4C2×Dic6111yescharacteristic
245C2×SD16—21no—
246C2×SD16—21no—
247C2×SD16—41no—
248C2×SD16—41no—
249#131—41no—
250#131—41no—
251C2×M16—1221no—
252C2×M16—1221no—
253C2×M16—1221no—
254C2×M16C2×Dic6111yescharacteristic
255C2×M16C22⋊D6111yescharacteristic
256C2×M16C22⋊D6111yescharacteristic
257C22×C8C2×Dic6111yescharacteristic
258C22×C8C22⋊D6111yescharacteristic
259C22×C8C22⋊D6111yescharacteristic
260C4⋊Q8—21no—
261#127—21no—
262#124—21no—
263#124—21no—
264#123—21no—
265#123—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—21no—
269#121—21no—
270#120—21no—
271#120—21no—
272#117—1221no—
273#117C2×Dic6111yescharacteristic
274#117C2×Dic6111yescharacteristic
275#108—2441no—
276#108—2441no—
277#107—21no—
278#106—21no—
279#103—21no—
280#103—21no—
281#102—21no—
282#102—21no—
283#101—612no—
284#101—1221no—
285#101—1221no—
286#100—1221no—
287#100—1221no—
288#100—1221no—
289#99—612no—
290#99—1221no—
291#97—2441no—
292C4×C8—2441no—
293C24—21no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8D4×D6111yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4D4×D6111yescharacteristic
308C2×D4#1175822411yescharacteristic
309C2×D4#1175822411yescharacteristic
310C22×C4—21no—
311C22×C4C22×Dic6111yescharacteristic
312C22×C4C2×C22⋊D6111yescharacteristic
313C22×C4C2×C22⋊D6111yescharacteristic
314SD16—42no—
315SD16—41no—
316SD16—41no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—1222no—
321M16—2441no—
322M16—2441no—
323M16—2441no—
324M16—2441no—
325M16—2441no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8C22⋊Dic6111yescharacteristic
336C2×C8C22⋊Dic6111yescharacteristic
337C2×C8C22⋊Dic6111yescharacteristic
338C2×C8C22⋊Dic6111yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—2441no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—1222no—
351C42—21no—
352C42—21no—
353C42—2441no—
354C23—41no—
355C23—81no—
356C23—161no—
357C23D4×Dic6111yescharacteristic
358C23#1451974811yescharacteristic
359C23#1451976411yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—161no—
371D4—161no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—2442no—
383C2×C4C2×C22⋊Dic6111yescharacteristic
384C2×C4D4×Dic6111yescharacteristic
385C2×C4#1451974811yescharacteristic
386C2×C4#1451977311yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—4881no—
391C8—4881no—
392C8—2442no—
393C8#1451969211yescharacteristic
394C8#1451969211yescharacteristic
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—162no—
405C22#1683966511yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—4882no—
413C4C2×#1451969211yescharacteristic
414C4#1683973611yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—161no—
420C2#2144665611yescharacteristic
subgroupG/H
centerC2#21446656
commutatorC22×C4×C61C22×C4
FrattiniC2×#41C22×D61
FittingC61×#3057C2
socleC2×C61#1964
prime radicalC61×#535C22
cosocleC2×#41×C61C23
hypercenter#3057D61
hypocenterC61#13232
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #3057

Complements

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

NH ≅ G/Ntype
1. #21447514C2semidirect
3. #21447473C2semidirect
5. #21445869C2semidirect
6. #21445619C2semidirect
20. C22×SD16×C61C4semidirect
28. C61×#427C4semidirect
29. C61×#419C4semidirect
30. C61×#418C4semidirect
218. C22×SD16Dic61semidirect
227. #427Dic61semidirect
228. #419Dic61semidirect
229. #418Dic61semidirect
241. C61#13232semidirect

Maximal subgroups

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

subgroupindex
#214475142
#214475112
#214474732
#214474692
#214458692
#214456192
C61×#30572
#1323261