Finite Group Databasebeta

← #11861194

Subgroups — #11861194

Order 1152.

1356 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#568C211yesmaximal, characteristic, complemented
2C2×#64159C211yesmaximal, characteristic
3#10596216C211yesmaximal, characteristic, complemented
4#10592935C211yesmaximal, characteristic, complemented
5#10592844C214yesmaximal, complemented
6#10592843C214yesmaximal, complemented
7#10592838C211yesmaximal, characteristic, complemented
8C2×#63649C211yesmaximal, characteristic, complemented
9#10592821C211yesmaximal, characteristic, complemented
10#83812—34nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C32×#131—22no—
14C32×#131C2214yescomplemented
15C2×C32×M16—22no—
16C2×C32×M16C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18#64159C412yescomplemented
19#64159C412yescomplemented
20#64159C2212yes—
21#64159C2212yes—
22C2×#3756C411yescharacteristic, complemented
23C2×#3755C411yescharacteristic, complemented
24C2×#3754C411yescharacteristic, complemented
25C2×#3753C411yescharacteristic, complemented
26#64135C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28C22×C3⋊(C3⋊C8)C2211yescharacteristic
29#64116—22no—
30M16×C3⋊D3—22no—
31#64110C2214yescomplemented
32#63664C2214yescomplemented
33#63652C2214yescomplemented
34#63649C2212yescomplemented
35#63649C2212yescomplemented
36#63642C2212yescomplemented
37C8×C3⋊Dic3C2212yescomplemented
38C3×#568D314yescomplemented
39C2×#950—34no—
40#5745—34no—
41#5236—34no—
42#5145—316no—
43#5144—316no—
44#5139—34no—
45C2×#822—34no—
46#5122—34no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41C2×C412yes—
50C32×#41C2312yes—
51C2×C32×Q8C2×C411yescharacteristic
52C2×C32×D4—21no—
53C2×C32×D4C2×C411yescharacteristic
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57#3828—21no—
58#3828—21no—
59#3828C2×C412yes—
60#3828C2312yes—
61C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×#634C2×C411yescharacteristic
64C32×M16—21no—
65C32×M16—24no—
66C32×M16D412yes—
67C32×M16D412yes—
68C32×M16C2312yes—
69C2×C32×C8—21no—
70C2×C32×C8—24no—
71C2×C32×C8C2312yes—
72#3757—21no—
73#3756C2×C412yes—
74#3756C2×C412yes—
75#3755C2×C412yes—
76#3755C2×C412yes—
77#3754C2×C412yes—
78#3754C2×C412yes—
79#3753C2×C412yes—
80#3753C2×C412yes—
81C4⋊(C3⋊Dic3)—21no—
82C4×C3⋊Dic3C2312yes—
83#3748—21no—
84#3748C2312yes—
85C2×C3⋊(C3⋊C8)—21no—
86C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
87C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
88C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
89C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92#3743—24no—
93C8×C3⋊D3—24no—
94#2957—91noSylow
95C2×C3×#41C2×D314yes—
96C2×#235—34no—
97C3×#131—28no—
98C3×#131C2×D3116yescomplemented
99C2×C3×M16—28no—
100C2×C3×M16C2×D314yes—
101C2×C3×M16C2×D314yes—
102#950—38no—
103#950—38no—
104#950—38no—
105#950—38no—
106C2×#216—34no—
107C2×#215—34no—
108C2×#214—34no—
109C2×#213—34no—
110#926—34no—
111C2×#208—34no—
112C22×C3⋊C8—34no—
113#907—68no—
114D3×M16—68no—
115#901—316no—
116#837—316no—
117#825—316no—
118#822—38no—
119#822—38no—
120#815—38no—
121C8×Dic3—38no—
122C23×C32—21no—
123C23×C32#4111yescharacteristic
124C22×C3⋊D3—21no—
125C32×Q8—21no—
126C32×Q8C22×C412yes—
127C32×D4—22no—
128C32×D4—22no—
129C32×D4—21no—
130C32×D4C22×C412yes—
131C2×C32×C4—21no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4C2411yescharacteristic
140#638—22no—
141#638—22no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—22no—
144C4⋊(C3⋊D3)—21no—
145C4⋊(C3⋊D3)C22×C412yes—
146C4×C3⋊D3—22no—
147C4×C3⋊D3—22no—
148#634—21no—
149#634C22×C412yes—
150C32×C8—22no—
151C32×C8C2×D414yes—
152C3⋊(C3⋊C8)—22no—
153C3⋊(C3⋊C8)C22×C411yescharacteristic
154C3⋊(C3⋊C8)C22×C411yescharacteristic
155C3⋊(C3⋊C8)C22×C411yescharacteristic
156C3⋊(C3⋊C8)C22×C411yescharacteristic
157C2×#135—91no—
158#568—91no—
159#568C3⋊D311yescharacteristic, complemented
160#444—94no—
161#443—94no—
162C2×#108—91no—
163#421—91no—
164#421—91no—
165#405—91no—
166C3×#41—24no—
167C3×#41—24no—
168C3×#41C4×D318yes—
169C3×#41C22×D318yes—
170C2×C3×Q8C4×D314yes—
171C2×C3×D4—24no—
172C2×C3×D4C4×D314yes—
173C22×C3×C4—24no—
174C22×C3×C4C22×D314yes—
175C2×#67—64no—
176#235—38no—
177#235—38no—
178#235—64no—
179#235—64no—
180C2×D12—34no—
181C2×C4×D3—64no—
182C2×Dic6—34no—
183C3×M16—24no—
184C3×M16—216no—
185C3×M16#6718yes—
186C3×M16#6718yes—
187C3×M16C22×D318yes—
188C2×C3×C8—24no—
189C2×C3×C8—216no—
190C2×C3×C8C22×D318yes—
191#217—64no—
192#216—38no—
193#216—38no—
194#215—38no—
195#215—38no—
196#214—38no—
197#214—38no—
198#213—38no—
199#213—38no—
200C4⋊Dic3—64no—
201C4×Dic3—38no—
202#208—38no—
203#208—64no—
204C2×C3⋊C8—34no—
205C2×C3⋊C8—34no—
206C2×C3⋊C8—34no—
207C2×C3⋊C8—34no—
208C2×C3⋊C8—34no—
209C2×C3⋊C8—34no—
210C2×C3⋊C8—64no—
211ΓL(1,𝔽25)—616no—
212D3×C8—616no—
213C22×C32—22no—
214C22×C32—41no—
215C22×C32—81no—
216C22×C32C4×D411yescharacteristic
217C22×C32C4×D411yescharacteristic
218C22×C32C2×#4111yescharacteristic
219C2×C3⋊D3—22no—
220C2×C3⋊D3—81no—
221C32×C4—22no—
222C32×C4C4×D411yescharacteristic
223C32×C4C4×D411yescharacteristic
224C32×C4C23×C411yescharacteristic
225C32×C4C22×D411yescharacteristic
226C3⋊Dic3—22no—
227C3⋊Dic3—42no—
228C2×#41—91no—
229C2×#41C2×C3⋊D311yescharacteristic
230#135—92no—
231#135—92no—
232#135—92no—
233#135—92no—
234C2×Q16—91no—
235C2×SD16—91no—
236C2×SD16—91no—
237C2×D8—91no—
238#131—22no—
239#131—94no—
240#131—182no—
241#131C2×C3⋊D314yescomplemented
242C2×M16—22no—
243C2×M16—91no—
244C2×M16—182no—
245C2×M16C2×C3⋊D311yescharacteristic
246C2×M16C2×C3⋊D311yescharacteristic
247C22×C8—91no—
248#117—91no—
249#108—92no—
250#108—92no—
251#104—94no—
252#104—94no—
253#97—92no—
254C4×C8—92no—
255C23×C3—24no—
256C23×C3#23514yes—
257C22×D3—64no—
258C3×Q8—24no—
259C3×Q8C2×C4×D318yes—
260C3×D4—28no—
261C3×D4—28no—
262C3×D4—24no—
263C3×D4C2×C4×D318yes—
264C2×C3×C4—24no—
265C2×C3×C4—28no—
266C2×C3×C4—28no—
267C2×C3×C4C2×C4×D314yes—
268C2×C3×C4C2×C4×D314yes—
269C2×C3×C4#23514yes—
270C2×C3×C4C2×#6714yes—
271C2×C3×C4C2×#6714yes—
272C2×C3×C4C23×D314yes—
273#67—68no—
274#67—68no—
275C2×Dic3—64no—
276C2×Dic3—68no—
277D12—38no—
278D12—64no—
279C4×D3—68no—
280C4×D3—68no—
281Dic6—38no—
282Dic6—64no—
283C3×C8—28no—
284C3×C8C2×#67116yes—
285C3⋊C8—34no—
286C3⋊C8—34no—
287C3⋊C8—34no—
288C3⋊C8—34no—
289C3⋊C8—68no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32—42no—
294C2×C32C2×C4×D411yescharacteristic
295C3⋊D3—42no—
296#41—21no—
297#41—21no—
298#41—92no—
299#41—92no—
300#41—181no—
301#41—181no—
302#41C4×C3⋊D312yes—
303#41C22×C3⋊D312yes—
304C2×Q8—91no—
305C2×Q8C4×C3⋊D311yescharacteristic
306C2×D4—21no—
307C2×D4—91no—
308C2×D4—181no—
309C2×D4C4×C3⋊D311yescharacteristic
310C22×C4—21no—
311C22×C4—181no—
312C22×C4C22×C3⋊D311yescharacteristic
313Q16—92no—
314Q16—92no—
315SD16—92no—
316SD16—92no—
317SD16—92no—
318SD16—92no—
319D8—92no—
320D8—92no—
321M16—21no—
322M16—24no—
323M16—92no—
324M16—181no—
325M16—184no—
326M16#63812yes—
327M16#63812yes—
328M16C22×C3⋊D312yes—
329C2×C8—21no—
330C2×C8—24no—
331C2×C8—91no—
332C2×C8—91no—
333C2×C8—91no—
334C2×C8—91no—
335C2×C8—91no—
336C2×C8—91no—
337C2×C8—181no—
338C2×C8—184no—
339C2×C8C22×C3⋊D312yes—
340C4⋊C4—181no—
341C22⋊C4—181no—
342C42—92no—
343C22×C3—28no—
344C22×C3—44no—
345C22×C3—84no—
346C22×C3C4×#6714yes—
347C22×C3C4×#6714yes—
348C22×C3C2×#23514yes—
349C2×D3—68no—
350C2×D3—244no—
351C3×C4—28no—
352C3×C4C4×#6714yes—
353C3×C4C4×#6714yes—
354C3×C4C22×C4×D314yes—
355C3×C4C22×#6714yes—
356Dic3—68no—
357Dic3—128no—
358C32#295711yescharacteristic, complemented, Sylow
359C23—21no—
360C23—181no—
361C23#382811yescharacteristic
362Q8—21no—
363Q8—92no—
364Q8—181no—
365Q8C2×C4×C3⋊D312yes—
366D4—22no—
367D4—22no—
368D4—21no—
369D4—92no—
370D4—182no—
371D4—182no—
372D4—181no—
373D4C2×C4×C3⋊D312yes—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—181no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4C2×C4×C3⋊D311yescharacteristic
382C2×C4C2×C4×C3⋊D311yescharacteristic
383C2×C4#382811yescharacteristic
384C2×C4C2×#63811yescharacteristic
385C2×C4C2×#63811yescharacteristic
386C2×C4C23×C3⋊D311yescharacteristic
387C8—22no—
388C8—91no—
389C8—91no—
390C8—91no—
391C8—91no—
392C8—182no—
393C8C2×#63814yes—
394C2×C3—24no—
395C2×C3—24no—
396C2×C3—24no—
397C2×C3—48no—
398C2×C3C2×C4×#6714yes—
399D3—128no—
400C22—22no—
401C22—41no—
402C22—81no—
403C22—182no—
404C22—721no—
405C22C4×#63811yescharacteristic
406C22C4×#63811yescharacteristic
407C22C2×#382811yescharacteristic
408C4—22no—
409C4—182no—
410C4—362no—
411C4C4×#63811yescharacteristic
412C4C4×#63811yescharacteristic
413C4C22×C4×C3⋊D311yescharacteristic
414C4C22×#63811yescharacteristic
415C3#8381214yescomplemented
416C2—21no—
417C2—21no—
418C2—21no—
419C2—42no—
420C2—362no—
421C2C2×C4×#63811yescharacteristic
subgroupG/H
centerC4C22×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#568C2
socleC2×C32C2×C4×D4
prime radicalC2×#64159C2
cosocleC2×C32×C4C24
hypercenter#568C3⋊D3
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×M16 ◁ #568

Complements

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

NH ≅ G/Ntype
1. C32×#568C2semidirect
3. #10596216C2semidirect
4. #10592935C2semidirect
5. #10592844C2semidirect
6. #10592843C2semidirect
7. #10592838C2semidirect
8. C2×#63649C2semidirect
9. #10592821C2semidirect
14. C32×#131C22semidirect
18. #64159C4semidirect
19. #64159C4semidirect
22. C2×#3756C4semidirect
23. C2×#3755C4semidirect
24. C2×#3754C4semidirect
25. C2×#3753C4semidirect
31. #64110C22semidirect
32. #63664C22semidirect
33. #63652C22semidirect
34. #63649C22semidirect
35. #63649C22semidirect
36. #63642C22semidirect
37. C8×C3⋊Dic3C22semidirect
38. C3×#568D3semidirect
98. C3×#131C2×D3semidirect
159. #568C3⋊D3semidirect
241. #131C2×C3⋊D3semidirect
358. C32#2957semidirect
415. C3#83812semidirect

Maximal subgroups

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

subgroupindex
C32×#5682
C2×#641592
#105962162
#105929352
#105928442
#105928432
#105928382
C2×#636492
#105928212
#838123