Finite Group Databasebeta

← #11788883

Subgroups — #11788883

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595042C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic, complemented
3#10592831C211yesmaximal, characteristic, complemented
4C2×C3×#823C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70089—31nomaximal
9#69040—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63977C414yes—
18#63916—22no—
19#63911—21no—
20#63860—21no—
21#63818—22no—
22#63817—22no—
23#63817—22no—
24#63651—21no—
25#63650—21no—
26C3×#823—22no—
27#63558—22no—
28#5805—31no—
29#5745—31no—
30#5745—31no—
31#5525—31no—
32C2×C3×#100—31no—
33C2×#833—31no—
34#5132—31no—
35#5132—31no—
36#5132—61no—
37C2×#823—31no—
38C2×#823D311yescharacteristic, complemented
39C3×#344—31no—
40#4559—31no—
41#4556D311yescharacteristic, complemented
42#4533—31no—
43C23×C3×D3C2×C412yes—
44C22×C32×C4C2311yescharacteristic
45C2×#638C2×C412yes—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3D412yes—
52C2×#634D411yescharacteristic
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×#626—24no—
60C32×M16—21no—
61C32×M16—21no—
62C2×C32×C8—21no—
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217C2×C412yes—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208D412yescomplemented
72C3×#208D412yescomplemented
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75(C2×D3)⋊Dic3—24no—
76#3712—24no—
77#3710—24no—
78#1914—91noSylow
79C22×C3×D4—31no—
80C2×#235—31no—
81C2×#235—31no—
82C2×#235—61no—
83C22×D12C2×D311yescharacteristic
84C2×C3×M16—21no—
85C2×C3×M16—31no—
86C2×C3×M16—31no—
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×M16C2×D311yescharacteristic
89C3×#117—31no—
90#953—34no—
91#940—61no—
92#938—62no—
93#936—61no—
94#926C2×D311yescharacteristic
95C2×#208—31no—
96C2×#208—31no—
97C2×#208—61no—
98C2×#208C2×D311yescharacteristic
99C2×#208C2×D311yescharacteristic
100#907—62no—
101#907—62no—
102D3×M16—62no—
103D3×M16—62no—
104#901—62no—
105#901—62no—
106#895—62no—
107#882—34no—
108#875—61no—
109#874—61no—
110C3×#100—62no—
111#833—62no—
112#824—61no—
113#824—61no—
114#824—62no—
115#823—22no—
116#823—61no—
117#823—61no—
118#823—62no—
119#823—62no—
120C23×C32C22×C411yescharacteristic
121C22×C3⋊D3C22⋊C412yes—
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—82no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132#638—22no—
133#638—22no—
134C2×C3⋊Dic3C22⋊C412yes—
135C4⋊(C3⋊D3)—21no—
136C4⋊(C3⋊D3)—21no—
137C4×C3⋊D3—22no—
138C4×C3⋊D3—22no—
139#634—21no—
140#634—21no—
141C2×C3×Dic3—22no—
142C3×D12—41no—
143C3×D12—41no—
144C3×D12—41no—
145C3×D12—41no—
146#626—84no—
147C32×C8—41no—
148C3⋊(C3⋊C8)—41no—
149C3×C3⋊C8—22no—
150C3×C3⋊C8—22no—
151#568—91no—
152#535—91no—
153#413—91no—
154C2×#100—31no—
155C2×#100—91no—
156#344—31no—
157#344—91no—
158C24×C3—32no—
159C23×D3C4×D312yes—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C22×C3×C4—21no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—32no—
170C2×#67—32no—
171C2×#67—62no—
172C2×#67—64no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177#235—61no—
178#235—61no—
179#235—61no—
180#235—61no—
181#235—121no—
182#235—121no—
183#235—121no—
184#235—121no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12—21no—
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—31no—
192C2×D12—31no—
193C2×D12—61no—
194C2×D12—64no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—62no—
198C2×Dic6—31no—
199C2×Dic6—31no—
200C2×Dic6—61no—
201C3×M16—22no—
202C3×M16—21no—
203C3×M16—21no—
204C3×M16—21no—
205C3×M16—21no—
206C3×M16—32no—
207C3×M16—32no—
208C3×M16—41no—
209C3×M16—61no—
210C3×M16—61no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—41no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C3×C4⋊C4—61no—
217C3×C22⋊C4—32no—
218C3×C42—61no—
219#217—64no—
220#217C4×D312yes—
221(C2×D3)⋊C4—64no—
222C4⋊Dic3—21no—
223C4×Dic3—21no—
224#208—21no—
225#208—21no—
226#208—62no—
227#208—61no—
228#208—61no—
229#208—61no—
230#208—61no—
231#208—121no—
232#208D1212yescomplemented
233#208#6712yescomplemented
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—121no—
239ΓL(1,𝔽25)—64no—
240ΓL(1,𝔽25)—64no—
241D3×C8—64no—
242D3×C8—64no—
243C22×C32—41no—
244C22×C32C2×C22⋊C411yescharacteristic
245C22×C32C4×D411yescharacteristic
246C22×C32C4×D411yescharacteristic
247C2×C3⋊D3—22no—
248C2×C3⋊D3—42no—
249C2×C3×D3—44no—
250C2×C3×D3—42no—
251C2×C3×D3—82no—
252C2×C3×D3—82no—
253C32×C4#12011yescharacteristic
254C32×C4#12111yescharacteristic
255C32×C4#12111yescharacteristic
256C32×C4#12311yescharacteristic
257C3⋊Dic3—22no—
258C3×Dic3—42no—
259C2×#41—91no—
260C22×D4—31no—
261#131—182no—
262#131—182no—
263C2×M16—31no—
264C2×M16—31no—
265C2×M16—91no—
266C2×M16—182no—
267C2×M16D3211yescharacteristic
268#127—181no—
269#124—181no—
270#121—182no—
271#120—94no—
272#117—31no—
273#101—181no—
274#100—62no—
275#100—181no—
276#100—182no—
277C23×C3—21no—
278C23×C3—62no—
279C23×C3—62no—
280C23×C3—62no—
281C23×C3—242no—
282C23×C3C2×C4×D311yescharacteristic
283C23×C3C2×C4×D311yescharacteristic
284C22×D3—22no—
285C22×D3—22no—
286C22×D3—22no—
287C22×D3—32no—
288C22×D3—32no—
289C22×D3—62no—
290C22×D3—82no—
291C3×D4—121no—
292C3×D4—121no—
293C3×D4—121no—
294C3×D4—121no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—62no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23911yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314#67—62no—
315#67—62no—
316#67—62no—
317#67—62no—
318#67—122no—
319#67—122no—
320#67—244no—
321C2×Dic3—22no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—62no—
325D12—41no—
326D12—41no—
327D12—41no—
328D12—41no—
329D12—61no—
330D12—61no—
331D12—61no—
332D12—61no—
333D12—121no—
334D12—121no—
335D12—244no—
336C4×D3—62no—
337C4×D3—62no—
338C4×D3—62no—
339C4×D3—62no—
340C4×D3—122no—
341C4×D3—122no—
342Dic6—61no—
343Dic6—61no—
344Dic6—61no—
345Dic6—61no—
346Dic6—121no—
347Dic6—121no—
348C3×C8—42no—
349C3×C8—41no—
350C3×C8—41no—
351C3×C8—62no—
352C3×C8—62no—
353C3⋊C8—22no—
354C3⋊C8—22no—
355C3⋊C8—122no—
356C3⋊C8—121no—
357C3⋊C8—121no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32#38611yescharacteristic
362C3⋊D3—42no—
363C3×D3—82no—
364C24—32no—
365#41—181no—
366#41—181no—
367#41—181no—
368#41—181no—
369C2×Q8—91no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—92no—
377C2×D4—91no—
378C2×D4—184no—
379C22×C4—92no—
380C22×C4C2×D3211yescharacteristic
381M16—21no—
382M16—21no—
383M16—32no—
384M16—32no—
385M16—61no—
386M16—61no—
387M16—184no—
388M16—181no—
389M16—181no—
390C2×C8—21no—
391C2×C8—61no—
392C2×C8—61no—
393C2×C8—184no—
394C2×C8—181no—
395C4⋊C4—61no—
396C22⋊C4—32no—
397C22⋊C4—184no—
398C42—61no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—81no—
405C22×C3—124no—
406C22×C3—122no—
407C22×C3—242no—
408C22×C3—242no—
409C22×C3C4×D1211yescharacteristic
410C22×C3D3×C22⋊C411yescharacteristic
411C22×C3D3×C22⋊C411yescharacteristic
412C22×C3#67⋊C411yescharacteristic
413C22×C3#89311yescharacteristic
414C22×C3C4×#6711yescharacteristic
415C2×D3—44no—
416C2×D3—42no—
417C2×D3—62no—
418C2×D3—62no—
419C2×D3—82no—
420C2×D3—82no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—242no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—122no—
430C3×C4#88211yescharacteristic
431C3×C4#88311yescharacteristic
432C3×C4#88411yescharacteristic
433C3×C4#88411yescharacteristic
434C3×C4#89411yescharacteristic
435C3×C4#89511yescharacteristic
436C3×C4#93711yescharacteristic
437C3×C4#93811yescharacteristic
438Dic3—42no—
439Dic3—62no—
440Dic3—62no—
441Dic3—122no—
442C32#191411yescharacteristic, complemented, Sylow
443C23—62no—
444C23—62no—
445C23—62no—
446C23—92no—
447C23—242no—
448C23C4×D3211yescharacteristic
449Q8—181no—
450Q8—181no—
451D4—121no—
452D4—121no—
453D4—121no—
454D4—121no—
455D4—182no—
456D4—182no—
457D4—181no—
458D4—181no—
459D4—724no—
460C2×C4—62no—
461C2×C4—92no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4#379911yescharacteristic
465C2×C4D3×D1211yescharacteristic
466C2×C4#380211yescharacteristic
467C2×C4#380411yescharacteristic
468C2×C4D3×#6711yescharacteristic
469C2×C4#381111yescharacteristic
470C8—41no—
471C8—62no—
472C8—62no—
473C8—361no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—41no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—242no—
485C2×C3#466511yescharacteristic
486C2×C3#495611yescharacteristic
487D3—82no—
488D3—122no—
489D3—122no—
490D3—242no—
491C22—41no—
492C22—124no—
493C22—122no—
494C22—182no—
495C22—242no—
496C22—242no—
497C22—362no—
498C22#6388011yescharacteristic
499C22#6390411yescharacteristic
500C22#6392111yescharacteristic
501C4—122no—
502C4—182no—
503C4#6385411yescharacteristic
504C4#6391011yescharacteristic
505C4#6392211yescharacteristic
506C4#6395811yescharacteristic
507C3—21no—
508C3#6904011yescharacteristic, complemented
509C3#7008911yescharacteristic, complemented
510C2—21no—
511C2—21no—
512C2—21no—
513C2—242no—
514C2—362no—
515C2#1059127511yescharacteristic
subgroupG/H
centerC2#10591275
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595042C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1914
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594780C2semidirect
3. #10592831C2semidirect
4. C2×C3×#823C2semidirect
5. C2×#63558C2semidirect
6. C3×#4556C2semidirect
7. #10589170C2semidirect
38. C2×#823D3semidirect
41. #4556D3semidirect
71. C3×#208D4semidirect
72. C3×#208D4semidirect
232. #208D12semidirect
233. #208#67semidirect
442. C32#1914semidirect
508. C3#69040semidirect
509. C3#70089semidirect

Maximal subgroups

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

subgroupindex
#105950422
#105947802
#105928312
C2×C3×#8232
C2×#635582
C3×#45562
#105891702
#700893
#690403