Finite Group Databasebeta

← #11788674

Subgroups — #11788674

Order 1152.

705 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63833C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic
3#10592832C211yesmaximal, characteristic
4C2×C3×#824C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70123—31nomaximal
9#68949—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3719—21no—
18#63833—22no—
19#63833C414yescomplemented
20C2×#3717—21no—
21C2×#3712—21no—
22#63817—22no—
23#63817—22no—
24C2×#3710—21no—
25#63648—21no—
26#63643—21no—
27C3×#824—22no—
28#63566—21no—
29#63566—21no—
30C2×#942—31no—
31C2×#909—31no—
32C2×#907—31no—
33C2×#901—31no—
34C2×C3×#101—31no—
35C2×#835—31no—
36C2×#824D311yescharacteristic, complemented
37#5133—31no—
38#5133—31no—
39#5133—61no—
40C2×#816—31no—
41C3×#341—31no—
42#4558D311yescharacteristic, complemented
43#4554—31no—
44#4554—31no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48#3828—21no—
49#3828—21no—
50#3828C2×C412yes—
51#3828D412yes—
52C2×C4⋊(C3⋊D3)D411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634D411yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C32×M16—21no—
63C32×M16—21no—
64C2×C32×C8—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208C2×C412yes—
70C3×#208D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D411yescharacteristic
76C2×C3×C3⋊C8D411yescharacteristic
77#3719—24no—
78#3717—24no—
79#3712—24no—
80#3710—24no—
81#1908—91noSylow
82C22×C3×Q8—31no—
83C2×#235—31no—
84C2×#235—31no—
85C2×#235—61no—
86C22×Dic6C2×D311yescharacteristic
87C2×C3×M16—21no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C22×C3×C8—31no—
93C2×#216—61no—
94#942—34no—
95#942—62no—
96C2×#215—61no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×#208C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103#909—34no—
104#909—62no—
105#907—62no—
106#907—62no—
107C2×Dic12—61no—
108C2×#204—61no—
109#901—62no—
110#901—62no—
111C2×ΓL(1,𝔽25)—61no—
112C2×ΓL(1,𝔽25)—61no—
113C2×D3×C8—61no—
114C2×D3×C8—61no—
115C3×#101—62no—
116#835—61no—
117#835—61no—
118#824—22no—
119#821—61no—
120#821—61no—
121#821—62no—
122#816—61no—
123#816—61no—
124#816—62no—
125#816—61no—
126#816—61no—
127C23×C32#4111yescharacteristic
128C22×C3⋊D3—21no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135#638—22no—
136#638—22no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—81no—
140C4⋊(C3⋊D3)—21no—
141C4⋊(C3⋊D3)C22⋊C412yes—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—22no—
144#634—21no—
145#634C22⋊C412yes—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—41no—
152C3×Dic6—41no—
153C32×C8—41no—
154C3×C3⋊C8—22no—
155C3×C3⋊C8—21no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—21no—
158C2×#137—91no—
159C2×#131—91no—
160#417—91no—
161C2×#103—91no—
162C2×#101—31no—
163#343—91no—
164#341—31no—
165C2×C3×Q8—32no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C22×C3×C4—21no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—121no—
178C22×Dic3—21no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—121no—
182#235—32no—
183#235—32no—
184#235—32no—
185#235—32no—
186#235—62no—
187#235—62no—
188#235—61no—
189#235—61no—
190#235—61no—
191#235—61no—
192#235—121no—
193#235—121no—
194C2×D12—31no—
195C2×D12—31no—
196C2×D12—61no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—121no—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—31no—
206C2×Dic6—31no—
207C2×Dic6—61no—
208C2×Dic6C4×D312yes—
209C3×M16—21no—
210C3×M16—21no—
211C3×M16—21no—
212C3×M16—21no—
213C3×M16—32no—
214C3×M16—32no—
215C3×M16—41no—
216C3×M16—41no—
217C3×M16—61no—
218C3×M16—61no—
219C2×C3×C8—22no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228#216—64no—
229#215—64no—
230C4⋊Dic3—62no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—121no—
236#208—21no—
237#208—21no—
238#208C4×D312yes—
239#208#6712yes—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8D1211yescharacteristic
245C2×C3⋊C8D1211yescharacteristic
246Dic12—64no—
247#204—64no—
248ΓL(1,𝔽25)—64no—
249ΓL(1,𝔽25)—64no—
250D3×C8—64no—
251D3×C8—64no—
252C22×C32—21no—
253C22×C32—21no—
254C22×C32C4×D411yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#12311yescharacteristic
257C2×C3⋊D3—22no—
258C2×C3⋊D3—41no—
259C2×C3⋊D3—41no—
260C32×C4C2×C22⋊C411yescharacteristic
261C32×C4C4×D411yescharacteristic
262C32×C4#12011yescharacteristic
263C32×C4#12111yescharacteristic
264C3⋊Dic3—22no—
265C3⋊Dic3—81no—
266C3×Dic3—42no—
267C2×#41—91no—
268C22×Q8—31no—
269#137—94no—
270#137—182no—
271C2×Q16—181no—
272C2×SD16—181no—
273#131—182no—
274#131—182no—
275C2×M16—31no—
276C2×M16—31no—
277C2×M16—181no—
278C2×M16D3211yescharacteristic
279C22×C8—31no—
280C22×C8—181no—
281C2×C4⋊C4—91no—
282#103—181no—
283#103—181no—
284#103—181no—
285#102—181no—
286#101—62no—
287C23×C3—21no—
288C23×C3#23511yescharacteristic
289C23×C3#23911yescharacteristic
290C22×D3—61no—
291C22×D3—61no—
292C22×D3—121no—
293C3×Q8—62no—
294C3×Q8—62no—
295C3×Q8—121no—
296C3×Q8—121no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—62no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318#67—62no—
319#67—62no—
320#67—62no—
321#67—62no—
322#67—122no—
323#67—122no—
324C2×Dic3—22no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—121no—
330C2×Dic3—122no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—242no—
334C2×Dic3—241no—
335C2×Dic3—241no—
336D12—32no—
337D12—32no—
338D12—62no—
339D12—61no—
340D12—61no—
341D12—121no—
342C4×D3—62no—
343C4×D3—62no—
344C4×D3—62no—
345C4×D3—62no—
346C4×D3—122no—
347C4×D3—122no—
348Dic6—22no—
349Dic6—22no—
350Dic6—32no—
351Dic6—32no—
352Dic6—41no—
353Dic6—41no—
354Dic6—62no—
355Dic6—61no—
356Dic6—61no—
357Dic6—121no—
358C3×C8—42no—
359C3×C8—41no—
360C3×C8—41no—
361C3×C8—62no—
362C3×C8—62no—
363C3×C8—61no—
364C3×C8—61no—
365C3⋊C8—22no—
366C3⋊C8—21no—
367C3⋊C8—21no—
368C3⋊C8—22no—
369C2×C32—21no—
370C2×C32—21no—
371C2×C32#38611yescharacteristic
372C2×C32#47111yescharacteristic
373C2×C32#47311yescharacteristic
374C3⋊D3—42no—
375#41—92no—
376#41—92no—
377#41—181no—
378#41—181no—
379C2×Q8—32no—
380C2×Q8—61no—
381C2×Q8—61no—
382C2×Q8—61no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—91no—
386C2×D4—91no—
387C2×D4—181no—
388C22×C4—61no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—184no—
393SD16—184no—
394M16—21no—
395M16—21no—
396M16—32no—
397M16—32no—
398M16—61no—
399M16—61no—
400M16—184no—
401C2×C8—21no—
402C2×C8—31no—
403C2×C8—31no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—61no—
408C2×C8—184no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3#88311yescharacteristic
421C22×C3#88411yescharacteristic
422C22×C3#89311yescharacteristic
423C22×C3#89411yescharacteristic
424C22×C3#89511yescharacteristic
425C22×C3C4×#6711yescharacteristic
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—122no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—241no—
434C2×D3—241no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—122no—
440C3×C4C4×D1211yescharacteristic
441C3×C4D3×C22⋊C411yescharacteristic
442C3×C4D3×C22⋊C411yescharacteristic
443C3×C4#67⋊C411yescharacteristic
444C3×C4#88211yescharacteristic
445C3×C4#88411yescharacteristic
446C3×C4#93711yescharacteristic
447C3×C4#93811yescharacteristic
448Dic3—42no—
449Dic3—62no—
450Dic3—62no—
451Dic3—122no—
452Dic3—242no—
453Dic3—241no—
454Dic3—241no—
455C32#190811yescharacteristic, complemented, Sylow
456C23—181no—
457C23#379911yescharacteristic
458Q8—62no—
459Q8—62no—
460Q8—92no—
461Q8—121no—
462Q8—121no—
463Q8—181no—
464D4—92no—
465D4—182no—
466D4—182no—
467D4—181no—
468C2×C4—62no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—181no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—361no—
475C2×C4—721no—
476C2×C4C4×D3211yescharacteristic
477C2×C4D3×D1211yescharacteristic
478C2×C4#380211yescharacteristic
479C2×C4#380411yescharacteristic
480C2×C4D3×#6711yescharacteristic
481C2×C4#381111yescharacteristic
482C8—41no—
483C8—62no—
484C8—61no—
485C8—61no—
486C8—62no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—41no—
495C2×C3—41no—
496C2×C3#466511yescharacteristic
497C2×C3#475411yescharacteristic
498C2×C3#475511yescharacteristic
499C2×C3#489611yescharacteristic
500C2×C3#489811yescharacteristic
501C2×C3#495611yescharacteristic
502D3—122no—
503D3—122no—
504D3—242no—
505C22—21no—
506C22—21no—
507C22—182no—
508C22—361no—
509C22—361no—
510C22#6385411yescharacteristic
511C22#6390411yescharacteristic
512C22#6391011yescharacteristic
513C4—122no—
514C4—182no—
515C4—721no—
516C4#6388011yescharacteristic
517C4#6392111yescharacteristic
518C4#6392211yescharacteristic
519C4#6395811yescharacteristic
520C3—21no—
521C3#6894911yescharacteristic, complemented
522C3#7012311yescharacteristic, complemented
523C2—21no—
524C2—21no—
525C2—362no—
526C2#1059099011yescharacteristic
527C2#1059099211yescharacteristic
528C2#1059127511yescharacteristic
subgroupG/H
centerC22#63910
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1908
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
4. C2×C3×#824C2semidirect
5. C2×#63566C2semidirect
6. C3×#4558C2semidirect
7. #10589168C2semidirect
19. #63833C4semidirect
36. C2×#824D3semidirect
42. #4558D3semidirect
455. C32#1908semidirect
521. C3#68949semidirect
522. C3#70123semidirect

Maximal subgroups

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

subgroupindex
C2×#638332
C2×#638172
#105928322
C2×C3×#8242
C2×#635662
C3×#45582
#105891682
#701233
#689493