Finite Group Databasebeta

← #11889327

Subgroups — #11889327

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#552C211yesmaximal, characteristic
2D4×#634C211yesmaximal, characteristic
3#10592768C211yesmaximal, characteristic, complemented
4#10592762C211yesmaximal, characteristic, complemented
5#10592751C211yesmaximal, characteristic, complemented
6#10592750C211yesmaximal, characteristic, complemented
7#10592749C211yesmaximal, characteristic, complemented
8#10592749C211yesmaximal, characteristic, complemented
9#10592730C211yesmaximal, characteristic, complemented
10#10592729C211yesmaximal, characteristic, complemented
11#10592710C211yesmaximal, characteristic
12#10592703C211yesmaximal, characteristic, complemented
13#10592695C211yesmaximal, characteristic, complemented
14#10592670C211yesmaximal, characteristic, complemented
15C2×#63637C211yesmaximal, characteristic, complemented
16#83603—34nomaximal
17C22×#634C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C32×#126—21no—
20C32×#125—21no—
21C32×#125C2211yescharacteristic
22C32×#123—21no—
23C32×C22⋊Q8C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C32×C4×D4C2211yescharacteristic
27C32×#117—21no—
28C32×#117C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×#3756C2211yescharacteristic
31C2×#3756C2211yescharacteristic
32C2×#3756C2211yescharacteristic
33D4×C3⋊Dic3—21no—
34#64133C2211yescharacteristic
35#64133C2211yescharacteristic
36C2×#3748C2211yescharacteristic
37C22×C3⋊(C3⋊C8)C2211yescharacteristic
38#64097—21no—
39#64087—21no—
40#64087—21no—
41#64078C2211yescharacteristic
42C4×#634C2211yescharacteristic
43#63662C2211yescharacteristic
44#63657C2211yescharacteristic
45#63657C2211yescharacteristic
46#63637C2211yescharacteristic
47#63637C2211yescharacteristic
48#63637C2211yescharacteristic
49#63637C2211yescharacteristic
50#63637C2211yescharacteristic
51#63637C2211yescharacteristic
52#63637C2211yescharacteristic
53#63637C2211yescharacteristic
54#63637C2211yescharacteristic
55#63635C2211yescharacteristic
56#63635C2211yescharacteristic
57#63634C2211yescharacteristic
58C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
59#63630C2211yescharacteristic
60C3×#552D314yes—
61D4×Dic6—34no—
62#5069—34no—
63#5063—34no—
64#5052—34no—
65#5051—34no—
66#5050—34no—
67#5050—34no—
68#5031—34no—
69#5030—34no—
70#5011—34no—
71#5004—34no—
72#4996—34no—
73#4971—34no—
74C2×#810—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4D411yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3—21no—
81C22×C3⋊Dic3—21no—
82C2×#634—22no—
83C2×#634—22no—
84C2×#634—21no—
85C2×#634—21no—
86C2×#634—41no—
87C2×#634—41no—
88C2×#634C2311yescharacteristic
89C2×#634C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C32×C4⋊C4—21no—
92C32×C4⋊C4—21no—
93C32×C4⋊C4—21no—
94C32×C4⋊C4—21no—
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4D411yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C22⋊C4—21no—
104C32×C22⋊C4D411yescharacteristic
105C32×C22⋊C4D411yescharacteristic
106C32×C42—21no—
107C32×C42—21no—
108C32×C42C2311yescharacteristic
109#3757—21no—
110#3757—21no—
111#3756—22no—
112#3756—41no—
113#3756—41no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121#3748—41no—
122C2×C3⋊(C3⋊C8)—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3312—91noSylow
128C22×Dic6—34no—
129C22×Dic6—34no—
130C3×#126—24no—
131C3×#125—24no—
132C3×#125C2×D314yes—
133C3×#123—24no—
134C3×C22⋊Q8C2×D314yes—
135C3×C22⋊Q8C2×D314yes—
136C3×C4×Q8C2×D314yes—
137C3×C4×D4C2×D314yes—
138C3×#117—24no—
139C3×#117C2×D314yes—
140C2×C3×C4⋊C4C2×D314yes—
141C2×#216—34no—
142C2×#216—34no—
143C2×#216—34no—
144D4×Dic3—64no—
145#924—34no—
146#924—34no—
147C2×#208—34no—
148C22×C3⋊C8—34no—
149#888—64no—
150#878—64no—
151#878—64no—
152#869—34no—
153C4×Dic6—34no—
154#835—34no—
155#830—34no—
156#830—34no—
157#810—34no—
158#810—34no—
159#810—34no—
160#810—34no—
161#810—34no—
162#810—34no—
163#810—34no—
164#810—34no—
165#810—34no—
166#808—34no—
167#808—34no—
168#807—34no—
169C4⋊(C3⋊C8)—34no—
170#803—34no—
171C23×C32C2×D411yescharacteristic
172C23×C32C2×D411yescharacteristic
173C32×Q8—21no—
174C32×Q8—21no—
175C32×D4—22no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—42no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—42no—
195C2×C3⋊Dic3—42no—
196#634—21no—
197#634—21no—
198#634—21no—
199#634—21no—
200#634—21no—
201#634—42no—
202#634—42no—
203#634#4112yes—
204C3⋊(C3⋊C8)—21no—
205C3⋊(C3⋊C8)—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208#552C3⋊D311yescharacteristic
209D4×Q8—91no—
210#491—91no—
211#485—91no—
212#483—91no—
213#479—91no—
214#470—91no—
215#467—91no—
216#462—91no—
217#451—91no—
218#451—91no—
219#441—91no—
220#435—91no—
221#419—91no—
222C2×#103—91no—
223C2×C3×Q8C22×D314yes—
224C2×C3×D4#6714yes—
225C22×C3×C4—24no—
226C22×C3×C4C22×D314yes—
227C22×C3×C4C22×D314yes—
228C22×Dic3—64no—
229C22×Dic3—64no—
230C2×Dic6—34no—
231C2×Dic6—34no—
232C2×Dic6—34no—
233C2×Dic6—68no—
234C2×Dic6—68no—
235C2×Dic6—64no—
236C2×Dic6—64no—
237C2×Dic6—124no—
238C2×Dic6—124no—
239C3×C4⋊C4—24no—
240C3×C4⋊C4—24no—
241C3×C4⋊C4—24no—
242C3×C4⋊C4—24no—
243C3×C4⋊C4—24no—
244C3×C4⋊C4—24no—
245C3×C4⋊C4#6714yes—
246C3×C4⋊C4C22×D314yes—
247C3×C4⋊C4C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C22⋊C4—24no—
250C3×C22⋊C4—24no—
251C3×C22⋊C4—24no—
252C3×C22⋊C4#6714yes—
253C3×C22⋊C4#6714yes—
254C3×C42—24no—
255C3×C42—24no—
256C3×C42C22×D314yes—
257#217—64no—
258#217—64no—
259#216—68no—
260#216—124no—
261#216—124no—
262C4⋊Dic3—34no—
263C4⋊Dic3—64no—
264C4⋊Dic3—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268C4×Dic3—64no—
269#208—124no—
270C2×C3⋊C8—34no—
271C2×C3⋊C8—34no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—124no—
275C22×C32—21no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32#13712yes—
281C22×C32C22×D411yescharacteristic
282C32×C4—21no—
283C32×C4—21no—
284C32×C4—21no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—22no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C22×Q8—91no—
297C22×Q8—91no—
298C2×Q16—91no—
299C2×Q16—91no—
300C2×Q16—91no—
301C2×M16—91no—
302C22×C8—91no—
303C4⋊Q8—91no—
304C4⋊Q8—181no—
305#126—21no—
306#125—21no—
307#125C2×C3⋊D311yescharacteristic
308#123—21no—
309C22⋊Q8—91no—
310C22⋊Q8—91no—
311C22⋊Q8—181no—
312C22⋊Q8—181no—
313C22⋊Q8C2×C3⋊D311yescharacteristic
314C22⋊Q8C2×C3⋊D311yescharacteristic
315C4×Q8—91no—
316C4×Q8C2×C3⋊D311yescharacteristic
317C4×D4—181no—
318C4×D4C2×C3⋊D311yescharacteristic
319#117—21no—
320#117C2×C3⋊D311yescharacteristic
321C2×C4⋊C4C2×C3⋊D311yescharacteristic
322#107—91no—
323#106—91no—
324#106—91no—
325C4⋊C8—91no—
326#103—91no—
327#103—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336C22⋊C8—91no—
337C22⋊C8—91no—
338#97—91no—
339C23×C3C2×#6714yes—
340C23×C3C2×#6714yes—
341C3×Q8—24no—
342C3×Q8—24no—
343C3×D4—28no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—48no—
353C2×C3×C4C2×#6714yes—
354C2×C3×C4C2×#6714yes—
355C2×C3×C4C2×#6714yes—
356C2×C3×C4C2×#6714yes—
357C2×C3×C4C23×D314yes—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—128no—
363C2×Dic3—128no—
364Dic6—38no—
365Dic6—64no—
366Dic6—64no—
367Dic6—64no—
368Dic6—64no—
369Dic6—64no—
370Dic6—128no—
371Dic6—128no—
372C3⋊C8—64no—
373C3⋊C8—64no—
374C3⋊C8—64no—
375C3⋊C8—64no—
376C2×C32—22no—
377C2×C32—41no—
378C2×C32#54611yescharacteristic
379C2×C32C2×#13711yescharacteristic
380C2×C32#57811yescharacteristic
381C2×Q8—91no—
382C2×Q8—91no—
383C2×Q8—91no—
384C2×Q8—182no—
385C2×Q8—182no—
386C2×Q8—181no—
387C2×Q8—181no—
388C2×Q8—361no—
389C2×Q8—361no—
390C2×Q8C22×C3⋊D311yescharacteristic
391C2×D4#63811yescharacteristic
392C22×C4—21no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4C22×C3⋊D311yescharacteristic
396C22×C4C22×C3⋊D311yescharacteristic
397Q16—182no—
398Q16—361no—
399Q16—361no—
400M16—361no—
401C2×C8—91no—
402C2×C8—91no—
403C2×C8—91no—
404C2×C8—91no—
405C2×C8—361no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—91no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4#63811yescharacteristic
419C4⋊C4C22×C3⋊D311yescharacteristic
420C4⋊C4C22×C3⋊D311yescharacteristic
421C4⋊C4C22×C3⋊D311yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4#63811yescharacteristic
428C22⋊C4#63811yescharacteristic
429C42—21no—
430C42—21no—
431C42—181no—
432C42C22×C3⋊D311yescharacteristic
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—24no—
437C22×C3—24no—
438C22×C3#95118yes—
439C22×C3C22×#6714yes—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—24no—
443C3×C4—24no—
444C3×C4—44no—
445C3×C4—44no—
446C3×C4—44no—
447C3×C4—44no—
448C3×C4D3×#4114yes—
449C3×C4#100914yes—
450Dic3—68no—
451Dic3—124no—
452Dic3—124no—
453Dic3—124no—
454C32#331211yescharacteristic, complemented, Sylow
455C23C2×#63811yescharacteristic
456C23C2×#63811yescharacteristic
457Q8—21no—
458Q8—21no—
459Q8—92no—
460Q8—181no—
461Q8—181no—
462Q8—181no—
463Q8—181no—
464Q8—181no—
465Q8—362no—
466Q8—362no—
467D4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—42no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4C2×#63811yescharacteristic
484C2×C4C2×#63811yescharacteristic
485C2×C4C2×#63811yescharacteristic
486C2×C4C2×#63811yescharacteristic
487C2×C4C23×C3⋊D311yescharacteristic
488C8—181no—
489C8—181no—
490C8—181no—
491C8—181no—
492C2×C3—28no—
493C2×C3—44no—
494C2×C3C2×#95114yes—
495C2×C3#582914yes—
496C2×C3#583814yes—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22#6416012yes—
503C22C22×#63811yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—182no—
513C4—361no—
514C4—361no—
515C4—361no—
516C4#41×C3⋊D311yescharacteristic
517C4#6436611yescharacteristic
518C3#8360314yescomplemented
519C2—22no—
520C2—41no—
521C2C2×#6416011yescharacteristic
522C2#1059630011yescharacteristic
523C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#552C2
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenter#552C3⋊D3
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
3. #10592768C2semidirect
4. #10592762C2semidirect
5. #10592751C2semidirect
6. #10592750C2semidirect
7. #10592749C2semidirect
8. #10592749C2semidirect
9. #10592730C2semidirect
10. #10592729C2semidirect
12. #10592703C2semidirect
13. #10592695C2semidirect
14. #10592670C2semidirect
15. C2×#63637C2semidirect
454. C32#3312semidirect
518. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C32×#5522
D4×#6342
#105927682
#105927622
#105927512
#105927502
#105927492
#105927302
#105927292
#105927102
#105927032
#105926952
#105926702
C2×#636372
#836033