Finite Group Databasebeta

← #11859342

Subgroups — #11859342

Order 1152.

1135 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic, complemented
2#10595034C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic, complemented
4#10592825C211yesmaximal, characteristic, complemented
5C3×#5119C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic, complemented
7#10591055C211yesmaximal, characteristic, complemented
8#10590738C214yesmaximal, complemented
9#10590720C214yesmaximal, complemented
10#83794—31nomaximal
11#79073—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#907—24no—
20C2×C3×ΓL(1,𝔽25)C2212yescomplemented
21C2×C3×D3×C8C2212yescomplemented
22#63981C412yes—
23#63962C412yes—
24#63916C412yes—
25C4×#626C2214yes—
26#63871C412yes—
27C2×#3710—24no—
28C2×#3710C2212yes—
29C2×#3710C2212yes—
30#63647C2214yes—
31C3×Dic3⋊C8C2214yescomplemented
32(C2×D3)⋊(C3⋊C8)C2214yescomplemented
33#63554C2212yescomplemented
34Dic3×C3⋊C8C2212yescomplemented
35C2×C3×#131—31no—
36#5828—31no—
37C2×#907D311yescharacteristic, complemented
38C22×D3×C8—31no—
39C22×D3×C8—31no—
40#5524—31no—
41C3×#424—31no—
42#5234—31no—
43#5127—34no—
44#5126—31no—
45#5126—31no—
46#5126—61no—
47#5119D311yescharacteristic, complemented
48#5110—31no—
49C8×#67—34no—
50#5101—31no—
51#4997—31no—
52#4836—34no—
53#4834—34no—
54C23×C3⋊D3C2×C411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2×C411yescharacteristic
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3C2×C412yes—
60C2×C4×C3⋊D3C2312yes—
61C2×C3×#67C2×C412yes—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12C2×C411yescharacteristic
65C2×C3×C4×D3C2312yes—
66C2×C3×Dic6C2×C411yescharacteristic
67C2×#626C2×C414yes—
68C32×M16—22no—
69C2×C32×C8C2312yes—
70#3748—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×#217C2×C412yes—
73C3×C4⋊Dic3C2×C412yes—
74C3×C4×Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8D414yescomplemented
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2311yescharacteristic
79C2×C3×C3⋊C8C2311yescharacteristic
80C3×ΓL(1,𝔽25)—24no—
81C3×D3×C8—24no—
82Dic3⋊Dic3C2×C414yes—
83#3722C2×C414yes—
84(C2×D3)⋊Dic3C2×C414yes—
85#3710—24no—
86#3710—24no—
87#2929—91noSylow
88C2×C3×#41—31no—
89C2×#235C2×D311yescharacteristic
90C22×C4×D3—31no—
91C22×C4×D3—31no—
92C22×C4×D3—61no—
93C3×#131—64no—
94C2×C3×M16—21no—
95C2×C3×M16—32no—
96C2×C3×M16C2×D311yescharacteristic
97C2×C3×M16C2×D311yescharacteristic
98C22×C3×C8—31no—
99C22×C3×C8—31no—
100C22×C3×C8—32no—
101C3×#117—31no—
102#946—32no—
103#938—32no—
104#937—32no—
105#935—32no—
106C4×#67—34no—
107#926C2×D311yescharacteristic
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
111C22×C3⋊C8C2×D311yescharacteristic
112C22×C3⋊C8C2×D311yescharacteristic
113#907—24no—
114C2×ΓL(1,𝔽25)C2×D312yescomplemented
115C2×D3×C8—32no—
116C2×D3×C8—32no—
117C2×D3×C8—32no—
118C2×D3×C8—32no—
119C2×D3×C8—64no—
120C2×D3×C8—64no—
121C2×D3×C8C2×D312yescomplemented
122#897—32no—
123#895—32no—
124#886—32no—
125#882—32no—
126C4×D12—34no—
127C3×C4⋊C8—34no—
128#830—34no—
129(C2×D3)⋊C8—34no—
130(C2×D3)⋊C8—34no—
131(C2×D3)⋊C8—34no—
132(C2×D3)⋊C8—64no—
133#815—32no—
134Dic3⋊C8C2×D314yescomplemented
135C8×Dic3—32no—
136#803—32no—
137C4×C3⋊C8—32no—
138C23×C32C22×C411yescharacteristic
139C22×C3⋊D3—22no—
140C22×C3⋊D3—24no—
141C22×C3⋊D3C22×C412yes—
142C22×C3×D3C22×C412yes—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3C22×C412yes—
149C4×C3⋊D3—24no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152C3×#67—24no—
153C2×C3×Dic3C22×C414yes—
154C2×C3×Dic3C22×C412yes—
155C3×D12—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×Dic6—22no—
159#626—28no—
160C32×C8—22no—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8C2×D412yes—
164C3×C3⋊C8C2×D412yes—
165C2×#131—31no—
166C23×C8—91no—
167#525—91no—
168#435—94no—
169C8×D4—94no—
170#424—31no—
171#408—91no—
172#407—91no—
173#405—91no—
174C23×D3—31no—
175C23×D3—31no—
176C23×D3—61no—
177C3×#41—62no—
178C3×#41—62no—
179C2×C3×Q8—31no—
180C2×C3×D4—32no—
181C2×C3×D4—31no—
182C22×C3×C4—21no—
183C22×C3×C4—32no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—34no—
187C2×#67C4×D312yes—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—61no—
191#235—22no—
192#235—22no—
193C2×D12—34no—
194C2×D12C4×D311yescharacteristic
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—122no—
206C2×C4×D3—122no—
207C2×C4×D3C22×D312yes—
208C2×Dic6C4×D311yescharacteristic
209C3×M16—22no—
210C3×M16—22no—
211C3×M16—42no—
212C3×M16—64no—
213C2×C3×C8—22no—
214C2×C3×C8—34no—
215C2×C3×C8—31no—
216C2×C3×C8—31no—
217C2×C3×C8—32no—
218C2×C3×C8—64no—
219C2×C3×C8—62no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C22×D312yes—
222C3×C4⋊C4—32no—
223C3×C22⋊C4—32no—
224C3×C42—32no—
225#217—34no—
226#217C4×D312yes—
227(C2×D3)⋊C4—34no—
228(C2×D3)⋊C4—34no—
229(C2×D3)⋊C4—34no—
230C4⋊Dic3—34no—
231C4⋊Dic3C4×D312yes—
232Dic3⋊C4—34no—
233C4×Dic3C22×D312yes—
234#208—62no—
235#208—62no—
236#208—122no—
237C2×C3⋊C8—22no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8#6714yescomplemented
242C2×C3⋊C8C22×D312yes—
243C2×C3⋊C8C22×D311yescharacteristic
244C2×C3⋊C8C22×D311yescharacteristic
245ΓL(1,𝔽25)—24no—
246D3×C8—24no—
247D3×C8—64no—
248D3×C8—64no—
249D3×C8—64no—
250D3×C8—64no—
251C22×C32—22no—
252C22×C32C4×D412yes—
253C22×C32C23×C411yescharacteristic
254C2×C3⋊D3—28no—
255C2×C3⋊D3—22no—
256C2×C3⋊D3—22no—
257C2×C3⋊D3#13114yescomplemented
258C2×C3×D3—22no—
259C2×C3×D3—24no—
260C32×C4C4×D412yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—24no—
266C2×#41—31no—
267C23×C4—91no—
268#131—64no—
269C2×M16—32no—
270C2×M16—91no—
271C2×M16D3211yescharacteristic
272C22×C8—31no—
273C22×C8—31no—
274C22×C8—32no—
275C22×C8—92no—
276C22×C8—92no—
277C22×C8—184no—
278#123—92no—
279C22⋊Q8—92no—
280#121—92no—
281#120—92no—
282C4×D4—94no—
283#117—31no—
284C4⋊C8—34no—
285C22⋊C8—94no—
286C22⋊C8—94no—
287#97—92no—
288C4×C8—92no—
289C23×C3—21no—
290C23×C3—32no—
291C23×C3C2×C4×D311yescharacteristic
292C23×C3C2×C4×D311yescharacteristic
293C22×D3—32no—
294C22×D3—32no—
295C22×D3—62no—
296C22×D3—64no—
297C22×D3—64no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—124no—
301C22×D3—122no—
302C22×D3C2×C4×D312yes—
303C3×Q8—62no—
304C3×D4—64no—
305C3×D4—62no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—32no—
311C2×C3×C4—34no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4#23512yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4#23912yes—
319C2×C3×C4C2×#6712yes—
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322#67—24no—
323#67—68no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—122no—
330C2×Dic3C2×C4×D314yes—
331C2×Dic3C2×C4×D312yes—
332D12—22no—
333D12—68no—
334C4×D3—22no—
335C4×D3—22no—
336C4×D3—64no—
337C4×D3—64no—
338C4×D3—62no—
339C4×D3—62no—
340C4×D3—62no—
341C4×D3—62no—
342C4×D3—122no—
343C4×D3—122no—
344C4×D3—124no—
345Dic6—22no—
346C3×C8—22no—
347C3×C8—22no—
348C3×C8—32no—
349C3×C8—32no—
350C3×C8—42no—
351C3×C8—62no—
352C3⋊C8—22no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—122no—
356C3⋊C8C2×#6712yes—
357C3⋊C8C2×#6712yes—
358C2×C32—22no—
359C2×C32C2×C4×D411yescharacteristic
360C2×C32C2×#13112yes—
361C3⋊D3—24no—
362C3×D3—42no—
363C24—91no—
364#41—62no—
365#41—62no—
366C2×Q8—31no—
367C2×D4—32no—
368C2×D4—31no—
369C2×D4—94no—
370C22×C4—32no—
371C22×C4—91no—
372C22×C4—92no—
373C22×C4—92no—
374C22×C4—182no—
375C22×C4—182no—
376C22×C4C2×D3211yescharacteristic
377M16—22no—
378M16—64no—
379M16—182no—
380C2×C8—31no—
381C2×C8—31no—
382C2×C8—34no—
383C2×C8—32no—
384C2×C8—64no—
385C2×C8—62no—
386C2×C8—92no—
387C2×C8—184no—
388C2×C8—184no—
389C2×C8C2×D3212yes—
390C4⋊C4—32no—
391C4⋊C4—94no—
392C22⋊C4—32no—
393C22⋊C4—94no—
394C22⋊C4—94no—
395C42—32no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—42no—
401C22×C3—64no—
402C22×C3—62no—
403C22×C3#89312yes—
404C22×C3C4×#6712yes—
405C22×C3C22×C4×D311yescharacteristic
406C22×C3C22×C4×D311yescharacteristic
407C2×D3—24no—
408C2×D3—22no—
409C2×D3—34no—
410C2×D3—34no—
411C2×D3—64no—
412C2×D3—68no—
413C2×D3—68no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—128no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—64no—
425C3×C4—62no—
426C3×C4#89312yes—
427C3×C4C4×#6712yes—
428C3×C4C2×#23511yescharacteristic
429C3×C4C2×D3×D411yescharacteristic
430C3×C4C2×#23911yescharacteristic
431C3×C4C22×#6711yescharacteristic
432Dic3—24no—
433Dic3—22no—
434Dic3—62no—
435Dic3—62no—
436Dic3—122no—
437C32#292911yescharacteristic, complemented, Sylow
438C23—32no—
439C23—92no—
440C23—184no—
441C23—182no—
442C23C4×D3211yescharacteristic
443Q8—62no—
444D4—64no—
445D4—62no—
446D4—188no—
447C2×C4—34no—
448C2×C4—32no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—92no—
452C2×C4—182no—
453C2×C4—182no—
454C2×C4—182no—
455C2×C4—184no—
456C2×C4#379912yes—
457C2×C4C4×D3211yescharacteristic
458C2×C4D3×#6712yes—
459C2×C4C22×D3211yescharacteristic
460C8—22no—
461C8—32no—
462C8—32no—
463C8—62no—
464C8—182no—
465C2×C3—22no—
466C2×C3—22no—
467C2×C3—22no—
468C2×C3—21no—
469C2×C3—42no—
470C2×C3—122no—
471C2×C3C2×#89311yescharacteristic
472C2×C3D3×#13112yes—
473C2×C3D3×#13112yes—
474C2×C3C2×C4×#6711yescharacteristic
475D3—42no—
476D3—64no—
477D3—64no—
478D3—124no—
479C22—22no—
480C22—64no—
481C22—62no—
482C22—94no—
483C22—188no—
484C22—182no—
485C22—182no—
486C22#6390412yes—
487C22C2×C4×D3211yescharacteristic
488C4—64no—
489C4—62no—
490C4—182no—
491C4#6390412yes—
492C4C2×#379911yescharacteristic
493C4C2×D3×#6711yescharacteristic
494C3—21no—
495C3#7907311yescharacteristic, complemented
496C3#8379411yescharacteristic, complemented
497C2—22no—
498C2—122no—
499C2—184no—
500C2#1059470712yes—
501C2C2×#6390411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radical#10595034C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#907C2semidirect
3. C22×#3710C2semidirect
4. #10592825C2semidirect
5. C3×#5119C2semidirect
6. #10591070C2semidirect
7. #10591055C2semidirect
8. #10590738C2semidirect
9. #10590720C2semidirect
20. C2×C3×ΓL(1,𝔽25)C22semidirect
21. C2×C3×D3×C8C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. (C2×D3)⋊(C3⋊C8)C22semidirect
33. #63554C22semidirect
34. Dic3×C3⋊C8C22semidirect
37. C2×#907D3semidirect
47. #5119D3semidirect
76. C2×C3×C3⋊C8D4semidirect
114. C2×ΓL(1,𝔽25)C2×D3semidirect
121. C2×D3×C8C2×D3semidirect
134. Dic3⋊C8C2×D3semidirect
241. C2×C3⋊C8#67semidirect
257. C2×C3⋊D3#131semidirect
437. C32#2929semidirect
495. C3#79073semidirect
496. C3#83794semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
#105950342
C22×#37102
#105928252
C3×#51192
#105910702
#105910552
#105907382
#105907202
#837943
#790733