Finite Group Databasebeta

← #11918526

Subgroups — #11918526

Order 1152.

3253 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596756C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4#10595443C218yesmaximal, complemented
5#10595442C218yesmaximal, complemented
6#10594780C216yesmaximal, complemented
7C2×#63817C216yesmaximal, complemented
8#87166—31nomaximal
9#87160—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64367C414yes—
12#64366C414yes—
13#41×C3⋊D3C2218yes—
14#64364C412yes—
15#64361C416yes—
16C2×#3828C2216yes—
17C3×#948C2214yescomplemented
18C3×#948C2214yescomplemented
19C3×#948C2218yescomplemented
20C2×C3×#208C2213yescomplemented
21C2×C3×#208C2216yescomplemented
22C22×C3×C3⋊C8C2213yescomplemented
23C2×#3712C22112yescomplemented
24#63818C22124yescomplemented
25#63817C22112yescomplemented
26#63817C22124yescomplemented
27#63817C22112yescomplemented
28#63817C2214yescomplemented
29#63817C22112yescomplemented
30C2×#3710C22112yescomplemented
31#5964—31no—
32#5964—31no—
33#5964—61no—
34C3×#568—31no—
35C2×C3×#131—31no—
36#5819D311yescharacteristic, complemented
37C2×#948D311yescharacteristic, complemented
38#5750—38no—
39#5750—38no—
40D3×#131—38no—
41D3×#131—38no—
42#5745—36no—
43#5745—36no—
44C2×#907—36no—
45C2×#901—36no—
46C32×#41C2×C414yes—
47C32×#41C2314yes—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4C2×C413yes—
50C22×C32×C4C2313yes—
51C2×#638C2×C4112yes—
52#3832C2×C418yes—
53Q8×C3⋊D3C2×C418yes—
54#3830C2×C4124yes—
55D4×C3⋊D3C2×C4124yes—
56#3828C2×C4112yes—
57#3828C2×C4112yes—
58#3828C2314yes—
59#3828C23112yes—
60C2×C4⋊(C3⋊D3)C2×C416yes—
61C2×C4×C3⋊D3C23112yes—
62C2×#634C2×C416yes—
63C3×#208C2314yes—
64C3×#208C23112yes—
65C3×#208C23112yes—
66C2×C3×C3⋊C8C2311yescharacteristic
67C2×C3×C3⋊C8C2313yes—
68C2×C3×C3⋊C8C2316yes—
69C2×C3×C3⋊C8C2316yes—
70C2×C3×C3⋊C8C23112yes—
71#3712C23124yes—
72#3712C2318yes—
73#3710C2318yes—
74#3710C23124yes—
75#3573—91noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79#1010—34no—
80#1010—34no—
81#1010—64no—
82#1009—34no—
83#1009—34no—
84#1009—64no—
85D3×#41—38no—
86D3×#41—38no—
87D3×#41—68no—
88#1007—32no—
89#1007—32no—
90#1007—62no—
91#1004—36no—
92#1004—36no—
93#1004—66no—
94C2×#235—36no—
95C2×#235—36no—
96C2×#235—66no—
97C3×#131—34no—
98C3×#131—34no—
99C3×#131—38no—
100C2×C3×M16—33no—
101C2×C3×M16—36no—
102C22×C3×C8—33no—
103#948C2×D314yescomplemented
104#948C2×D318yescomplemented
105#948C2×D314yescomplemented
106C2×#208C2×D316yescomplemented
107C2×#208C2×D313yescomplemented
108C22×C3⋊C8C2×D313yescomplemented
109#907—34no—
110#907—312no—
111#907—312no—
112#907—312no—
113#907—324no—
114D3×M16—324no—
115D3×M16—324no—
116#901—34no—
117#901—312no—
118#901—312no—
119#901—312no—
120#901—324no—
121C2×ΓL(1,𝔽25)—312no—
122C2×ΓL(1,𝔽25)—312no—
123C2×D3×C8—312no—
124C2×D3×C8—312no—
125C23×C32C22×C413yes—
126C22×C3⋊D3C22×C4112yes—
127C32×Q8C22×C414yes—
128C32×D4C22×C4112yes—
129C2×C32×C4C22×C416yes—
130C2×C32×C4C22×C413yes—
131C2×C32×C4C2416yes—
132C2×C32×C4C2411yescharacteristic
133#638C22×C418yes—
134#638C22×C4124yes—
135C2×C3⋊Dic3C22×C4112yes—
136C4⋊(C3⋊D3)C22×C414yes—
137C4⋊(C3⋊D3)C22×C4112yes—
138C4×C3⋊D3C22×C4124yes—
139C4×C3⋊D3C2418yes—
140#634C22×C414yes—
141#634C22×C4112yes—
142C3×C3⋊C8C2411yescharacteristic
143C3×C3⋊C8C2418yes—
144C3×C3⋊C8C2416yes—
145C3×C3⋊C8C2411yescharacteristic
146#585—91no—
147#568—31no—
148#568—96no—
149#568—98no—
150C2×#131—31no—
151C2×#131—96no—
152C2×#131—98no—
153C3×#41—24no—
154C3×#41—24no—
155C3×#41C4×D314yes—
156C3×#41C4×D314yes—
157C3×#41C22×D314yes—
158C3×#41C22×D314yes—
159C2×C3×Q8—21no—
160C2×C3×Q8C4×D311yescharacteristic
161C2×C3×Q8C4×D311yescharacteristic
162C2×C3×D4—23no—
163C2×C3×D4C4×D313yes—
164C2×C3×D4C4×D313yes—
165C22×C3×C4—23no—
166C22×C3×C4C22×D313yes—
167C22×C3×C4C22×D313yes—
168C2×#67—312no—
169C2×#67—312no—
170C2×#67—612no—
171#239—38no—
172#239—38no—
173#239—68no—
174D3×Q8—38no—
175D3×Q8—38no—
176D3×Q8—68no—
177#237—324no—
178#237—324no—
179#237—624no—
180D3×D4—324no—
181D3×D4—324no—
182D3×D4—624no—
183#235—312no—
184#235—312no—
185#235—312no—
186#235—312no—
187#235—34no—
188#235—312no—
189#235—312no—
190#235—34no—
191#235—64no—
192#235—612no—
193#235—612no—
194#235—612no—
195C2×D12—36no—
196C2×D12—36no—
197C2×D12—66no—
198C2×C4×D3—312no—
199C2×C4×D3—312no—
200C2×C4×D3—612no—
201C2×Dic6—36no—
202C2×Dic6—36no—
203C2×Dic6—66no—
204C3×M16—312no—
205C3×M16—312no—
206C3×M16—34no—
207C2×C3×C8—36no—
208C2×C3×C8—312no—
209C2×C3×C8—36no—
210C2×C3×C8—31no—
211C2×C3×C8—33no—
212#208C22×D314yes—
213#208C22×D3112yes—
214#208C22×D3112yes—
215C2×C3⋊C8C22×D316yes—
216C2×C3⋊C8C22×D3112yes—
217C2×C3⋊C8C22×D316yes—
218C2×C3⋊C8C22×D311yescharacteristic
219C2×C3⋊C8C22×D313yes—
220ΓL(1,𝔽25)—38no—
221ΓL(1,𝔽25)—38no—
222ΓL(1,𝔽25)—324no—
223ΓL(1,𝔽25)—324no—
224D3×C8—38no—
225D3×C8—38no—
226D3×C8—324no—
227D3×C8—324no—
228C22×C32—43no—
229C22×C32C23×C416yes—
230C22×C32C23×C411yescharacteristic
231C2×C3⋊D3—412no—
232C2×C3⋊D3C23×C418yes—
233C32×C4C23×C411yescharacteristic
234C32×C4C23×C416yes—
235C32×C4C2511yescharacteristic
236C3⋊Dic3C23×C418yes—
2372−1+4—94no—
2382−1+4—92no—
239H(5,𝔽2)—94no—
240H(5,𝔽2)—96no—
241C2×#41—98no—
242C2×#41—96no—
243C2×#41D3211yescharacteristic
244#131—34no—
245#131—34no—
246#131—38no—
247#131—94no—
248#131—912no—
249#131—912no—
250#131—912no—
251#131—924no—
252C2×M16—33no—
253C2×M16—36no—
254C2×M16—912no—
255C2×M16—924no—
256C22×C8—33no—
257C22×C8—912no—
258C23×C3—23no—
259C23×C3C2×C4×D313yes—
260C23×C3C2×C4×D313yes—
261C22×D3—312no—
262C22×D3—312no—
263C22×D3—612no—
264C3×Q8—24no—
265C3×Q8C2×C4×D314yes—
266C3×Q8C2×C4×D314yes—
267C3×D4—212no—
268C3×D4C2×C4×D3112yes—
269C3×D4C2×C4×D3112yes—
270C2×C3×C4—26no—
271C2×C3×C4—21no—
272C2×C3×C4—26no—
273C2×C3×C4—23no—
274C2×C3×C4C2×C4×D316yes—
275C2×C3×C4C2×C4×D316yes—
276C2×C3×C4C2×C4×D313yes—
277C2×C3×C4C2×C4×D313yes—
278C2×C3×C4C23×D311yescharacteristic
279C2×C3×C4C23×D316yes—
280C2×C3×C4C23×D316yes—
281C2×C3×C4C23×D311yescharacteristic
282#67—38no—
283#67—38no—
284#67—324no—
285#67—324no—
286#67—68no—
287#67—624no—
288C2×Dic3—312no—
289C2×Dic3—312no—
290C2×Dic3—612no—
291D12—34no—
292D12—34no—
293D12—312no—
294D12—312no—
295D12—64no—
296D12—612no—
297C4×D3—324no—
298C4×D3—324no—
299C4×D3—38no—
300C4×D3—38no—
301C4×D3—624no—
302C4×D3—68no—
303Dic6—34no—
304Dic6—34no—
305Dic6—312no—
306Dic6—312no—
307Dic6—64no—
308Dic6—612no—
309C3×C8—31no—
310C3×C8—38no—
311C3×C8—36no—
312C3×C8—31no—
313C3⋊C8C23×D311yescharacteristic
314C3⋊C8C23×D318yes—
315C3⋊C8C23×D316yes—
316C3⋊C8C23×D311yescharacteristic
317C2×C32—26no—
318C2×C32—21no—
319C2×C32C24×C411yescharacteristic
320C3⋊D3—28no—
321#41—98no—
322#41—924no—
323#41—912no—
324#41—94no—
325#41—912no—
326#41—912no—
327#41#62414yes—
328#41C2×D3214yes—
329C2×Q8—98no—
330C2×Q8—96no—
331C2×Q8#62411yescharacteristic
332C2×D4—912no—
333C2×D4—924no—
334C2×D4—96no—
335C2×D4#62413yes—
336C22×C4—912no—
337C22×C4C2×D3213yes—
338M16—34no—
339M16—312no—
340M16—312no—
341M16—98no—
342M16—924no—
343C2×C8—31no—
344C2×C8—36no—
345C2×C8—33no—
346C2×C8—36no—
347C2×C8—312no—
348C2×C8—98no—
349C2×C8—924no—
350C22×C3—26no—
351C22×C3—21no—
352C22×C3—43no—
353C22×C3—43no—
354C22×C3—83no—
355C22×C3C22×C4×D316yes—
356C22×C3C22×C4×D316yes—
357C22×C3C22×C4×D311yescharacteristic
358C22×C3C22×C4×D311yescharacteristic
359C2×D3—38no—
360C2×D3—38no—
361C2×D3—68no—
362C2×D3—1212no—
363C2×D3—1212no—
364C2×D3—2412no—
365C3×C4—21no—
366C3×C4—26no—
367C3×C4—21no—
368C3×C4C22×C4×D311yescharacteristic
369C3×C4C22×C4×D311yescharacteristic
370C3×C4C22×C4×D316yes—
371C3×C4C22×C4×D316yes—
372C3×C4C24×D311yescharacteristic
373C3×C4C24×D311yescharacteristic
374Dic3—38no—
375Dic3—38no—
376Dic3—68no—
377C32#357311yescharacteristic, complemented, Sylow
378C23—912no—
379C23C2×#62413yes—
380Q8—912no—
381Q8—94no—
382Q8C2×#62414yes—
383D4—924no—
384D4—98no—
385D4—912no—
386D4—94no—
387D4C2×#624112yes—
388C2×C4—912no—
389C2×C4—924no—
390C2×C4—98no—
391C2×C4C2×#62416yes—
392C2×C4C2×#62413yes—
393C2×C4C22×D3216yes—
394C2×C4C22×D3211yescharacteristic
395C8—31no—
396C8—31no—
397C8—36no—
398C8—38no—
399C2×C3—26no—
400C2×C3—21no—
401C2×C3—26no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—46no—
405C2×C3—41no—
406C2×C3C23×C4×D311yescharacteristic
407C2×C3C23×C4×D311yescharacteristic
408D3—68no—
409D3—68no—
410D3—128no—
411C22—43no—
412C22—98no—
413C22—3612no—
414C22C22×#62416yes—
415C22C22×#62411yescharacteristic
416C4—98no—
417C4C22×#62416yes—
418C4C22×#62411yescharacteristic
419C4C23×D3211yescharacteristic
420C3—21no—
421C3#8716011yescharacteristic, complemented
422C3#8716611yescharacteristic, complemented
423C2—21no—
424C2—26no—
425C2—188no—
426C2C23×#62411yescharacteristic
subgroupG/H
center, FrattiniC4C23×D32
commutator, socleC2×C32C24×C4
FittingC2×C32×#41C22
prime radical#10596756C2
cosocleC32×C4C25
hypercenterC2×#41D32
hypocenterC32#3573
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5819C2semidirect
3. C2×C3×#948C2semidirect
4. #10595443C2semidirect
5. #10595442C2semidirect
6. #10594780C2semidirect
7. C2×#63817C2semidirect
17. C3×#948C22semidirect
18. C3×#948C22semidirect
19. C3×#948C22semidirect
20. C2×C3×#208C22semidirect
21. C2×C3×#208C22semidirect
22. C22×C3×C3⋊C8C22semidirect
23. C2×#3712C22semidirect
24. #63818C22semidirect
25. #63817C22semidirect
26. #63817C22semidirect
27. #63817C22semidirect
28. #63817C22semidirect
29. #63817C22semidirect
30. C2×#3710C22semidirect
36. #5819D3semidirect
37. C2×#948D3semidirect
103. #948C2×D3semidirect
104. #948C2×D3semidirect
105. #948C2×D3semidirect
106. C2×#208C2×D3semidirect
107. C2×#208C2×D3semidirect
108. C22×C3⋊C8C2×D3semidirect
377. C32#3573semidirect
421. C3#87160semidirect
422. C3#87166semidirect

Maximal subgroups

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

subgroupindex
#105967562
C3×#58192
C2×C3×#9482
#105954432
#105954422
#105947802
C2×#638172
#871663
#871603