Finite Group Databasebeta

← #11785596

Subgroups — #11785596

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic
2C2×#63577C211yesmaximal, characteristic, complemented
3C2×#63573C211yesmaximal, characteristic, complemented
4#10591088C211yesmaximal, characteristic
5#10591087C211yesmaximal, characteristic
6#10589420C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#72015—31nomaximal
9#69000—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#907—22no—
18C3×#907C414yescomplemented
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21#63577—22no—
22#63573—21no—
23#63573—21no—
24#63566—21no—
25#63565—21no—
26#63563—21no—
27#63562—21no—
28C2×C3×#131—31no—
29C2×#907D311yescharacteristic
30#5232—31no—
31#5232—31no—
32#5133—31no—
33C2×#822—31no—
34C2×#819—31no—
35C2×#817—31no—
36#4966—31no—
37C2×#808—31no—
38C3×#343—31no—
39#4554—31no—
40#4554—31no—
41#4554—61no—
42#4554D311yescharacteristic, complemented
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235Q812yes—
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×M16—21no—
55C32×M16C2×C412yes—
56C2×C32×C8—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59#3748—21no—
60#3748—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×#208—21no—
65C3×#208—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8D411yescharacteristic
69C2×C3×C3⋊C8D411yescharacteristic
70C2×C3×C3⋊C8D412yes—
71C3×ΓL(1,𝔽25)—24no—
72C3×D3×C8—24no—
73#1815—91noSylow
74C2×C3×#41—31no—
75C2×#235C2×D311yescharacteristic
76C3×#131—34no—
77C3×#131—62no—
78C2×C3×M16—21no—
79C2×C3×M16—31no—
80C2×C3×M16—61no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C22×C3×C8—31no—
84C22×C3×C8—61no—
85C2×C3×C4⋊C4—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×#208—31no—
91C2×#208—31no—
92C2×#208—61no—
93C2×#208C2×D311yescharacteristic
94C22×C3⋊C8C2×D311yescharacteristic
95#907—22no—
96#907Dic314yescomplemented
97C2×ΓL(1,𝔽25)—21no—
98C2×D3×C8—21no—
99#835—61no—
100#835—61no—
101#832—61no—
102#832—61no—
103#822—62no—
104#821—61no—
105#819—62no—
106#817—61no—
107#817—61no—
108#816—61no—
109#810—61no—
110#809—61no—
111#808—61no—
112#808—61no—
113C23×C32#4111yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×Q811yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—81no—
123C3×#67—22no—
124C3×#67—22no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—81no—
128C3×D12—21no—
129C3×D12C4⋊C412yes—
130C3×C4×D3—22no—
131C3×C4×D3—22no—
132C3×Dic6—21no—
133C3×Dic6C4⋊C412yes—
134C32×C8—22no—
135C3⋊(C3⋊C8)—41no—
136C3×C3⋊C8—41no—
137C3×C3⋊C8C22⋊C412yes—
138C3×C3⋊C8C22⋊C412yes—
139C2×#131—31no—
140C2×#108—91no—
141C2×#106—91no—
142#417—91no—
143#417—91no—
144#343—31no—
145#343—91no—
146C3×#41—32no—
147C3×#41—32no—
148C3×#41—61no—
149C3×#41—61no—
150C2×C3×Q8—31no—
151C2×C3×D4—31no—
152C2×C3×D4—61no—
153C22×C3×C4—21no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—21no—
159C22×Dic3—21no—
160C22×Dic3—62no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163#235—21no—
164#235—21no—
165#235Dic612yes—
166#235C2×Dic312yes—
167C2×D12D1211yescharacteristic
168C2×C4×D3—21no—
169C2×Dic6D1211yescharacteristic
170C3×M16—21no—
171C3×M16—21no—
172C3×M16—22no—
173C3×M16—41no—
174C3×M16—64no—
175C3×M16—61no—
176C3×M16—61no—
177C3×M16C4×D312yes—
178C3×M16C2×Dic312yes—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—32no—
182C2×C3×C8—31no—
183C2×C3×C8—31no—
184C2×C3×C8—32no—
185C2×C3×C8—41no—
186C2×C3×C8—64no—
187C2×C3×C8—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—121no—
197C4⋊Dic3—121no—
198#208—21no—
199#208—21no—
200#208—62no—
201#208—61no—
202#208—61no—
203#208—61no—
204#208—61no—
205#208—121no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C2×C3⋊C8C2×Dic312yes—
211C2×C3⋊C8#6711yescharacteristic
212C2×C3⋊C8#6711yescharacteristic
213C2×C3⋊C8#6712yes—
214ΓL(1,𝔽25)—24no—
215D3×C8—24no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32#11711yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32C22⋊Q811yescharacteristic
221C2×C3×D3—22no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C32×C4C2×C22⋊C411yescharacteristic
225C32×C4C2×C4⋊C411yescharacteristic
226C32×C4#12111yescharacteristic
227C32×C4C22⋊Q811yescharacteristic
228C3⋊Dic3—81no—
229C3×Dic3—22no—
230C3×Dic3—81no—
231C2×#41—31no—
232#131—34no—
233#131—62no—
234C2×M16—31no—
235C2×M16—61no—
236C2×M16—91no—
237C2×M16D3211yescharacteristic
238C22×C8—31no—
239C22×C8—61no—
240C2×C4⋊C4—31no—
241C2×C4⋊C4—91no—
242#108—182no—
243#106—181no—
244#106—181no—
245#103—181no—
246#103—181no—
247#102—181no—
248#102—181no—
249C23×C3—21no—
250C23×C3—61no—
251C23×C3#23511yescharacteristic
252C23×C3#23511yescharacteristic
253C22×D3—21no—
254C3×Q8—32no—
255C3×Q8—61no—
256C3×D4—32no—
257C3×D4—62no—
258C3×D4—62no—
259C3×D4—61no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—61no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—121no—
270C2×C3×C4—241no—
271C2×C3×C4C2×Dic611yescharacteristic
272C2×C3×C4C2×C4×D311yescharacteristic
273C2×C3×C4C2×D1211yescharacteristic
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4#23511yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×Q811yescharacteristic
280C2×C3×C4C22×Dic311yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283#67—22no—
284#67—22no—
285C2×Dic3—21no—
286C2×Dic3—41no—
287C2×Dic3—81no—
288C2×Dic3—122no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—241no—
292C2×Dic3—241no—
293C2×Dic3—242no—
294D12—21no—
295D12C4⋊Dic312yes—
296C4×D3—22no—
297C4×D3—22no—
298Dic6—21no—
299Dic6C4⋊Dic312yes—
300C3×C8—22no—
301C3×C8—22no—
302C3×C8—32no—
303C3×C8—32no—
304C3×C8—42no—
305C3×C8—121no—
306C3⋊C8—41no—
307C3⋊C8—122no—
308C3⋊C8—121no—
309C3⋊C8—121no—
310C3⋊C8#21712yes—
311C3⋊C8#21712yes—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#38011yescharacteristic
315C2×C32#47111yescharacteristic
316C2×C32#47111yescharacteristic
317C3×D3—42no—
318#41—32no—
319#41—32no—
320#41—61no—
321#41—61no—
322C2×Q8—31no—
323C2×D4—31no—
324C2×D4—61no—
325C22×C4—61no—
326C22×C4—61no—
327C22×C4—181no—
328C22×C4C2×D3211yescharacteristic
329M16—21no—
330M16—64no—
331M16—61no—
332M16—61no—
333M16—181no—
334M16—181no—
335M16D3×Dic312yes—
336C2×C8—21no—
337C2×C8—32no—
338C2×C8—31no—
339C2×C8—31no—
340C2×C8—32no—
341C2×C8—64no—
342C2×C8—61no—
343C2×C8—181no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—62no—
358C22×C3—121no—
359C22×C3—121no—
360C22×C3#87211yescharacteristic
361C22×C3#88411yescharacteristic
362C22×C3#89611yescharacteristic
363C22×C3#92411yescharacteristic
364C22×C3#92611yescharacteristic
365C22×C3#93011yescharacteristic
366C2×D3—22no—
367C2×D3—41no—
368C2×D3—41no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—62no—
374C3×C4—241no—
375C3×C4D3×C22⋊C411yescharacteristic
376C3×C4#88411yescharacteristic
377C3×C4D3×C4⋊C411yescharacteristic
378C3×C4#89611yescharacteristic
379C3×C4#92411yescharacteristic
380C3×C4C2×C4⋊Dic311yescharacteristic
381C3×C4#93011yescharacteristic
382C3×C4C2×#21711yescharacteristic
383Dic3—22no—
384Dic3—81no—
385Dic3—242no—
386Dic3—241no—
387Dic3—241no—
388C32#181511yescharacteristic, complemented, Sylow
389C23—61no—
390C23#379811yescharacteristic
391Q8—32no—
392Q8—61no—
393D4—32no—
394D4—62no—
395D4—62no—
396D4—61no—
397C2×C4—61no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—121no—
401C2×C4—241no—
402C2×C4—361no—
403C2×C4—721no—
404C2×C4D3×Dic611yescharacteristic
405C2×C4#379811yescharacteristic
406C2×C4D3×D1211yescharacteristic
407C2×C4C2×D3×Dic311yescharacteristic
408C2×C4D3×#6711yescharacteristic
409C2×C4D3×#6711yescharacteristic
410C8—22no—
411C8—32no—
412C8—32no—
413C8—121no—
414C8—361no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—122no—
425C2×C3#466711yescharacteristic
426C2×C3#474811yescharacteristic
427C2×C3#475411yescharacteristic
428C2×C3#514111yescharacteristic
429C2×C3#514111yescharacteristic
430C2×C3#521211yescharacteristic
431D3—42no—
432C22—21no—
433C22—21no—
434C22—62no—
435C22—121no—
436C22—121no—
437C22#6385111yescharacteristic
438C22#6385511yescharacteristic
439C22#6390611yescharacteristic
440C4—62no—
441C4—241no—
442C4—721no—
443C4#6385111yescharacteristic
444C4D3×C4⋊Dic311yescharacteristic
445C4#6390611yescharacteristic
446C4D3×#21711yescharacteristic
447C3—21no—
448C3#6900011yescharacteristic, complemented
449C3#7201511yescharacteristic, complemented
450C2—21no—
451C2—21no—
452C2—122no—
453C2#1059099611yescharacteristic
454C2#1059099811yescharacteristic
455C2#1059129511yescharacteristic
subgroupG/H
centerC22#63906
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1815
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63577C2semidirect
3. C2×#63573C2semidirect
6. #10589420C2semidirect
7. C3×#4554C2semidirect
18. C3×#907C4semidirect
42. #4554D3semidirect
96. #907Dic3semidirect
388. C32#1815semidirect
448. C3#69000semidirect
449. C3#72015semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
C2×#635772
C2×#635732
#105910882
#105910872
#105894202
C3×#45542
#720153
#690003