Finite Group Databasebeta

← #11872427

Subgroups — #11872427

Order 1152.

1116 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596054C211yesmaximal, characteristic, complemented
2#10596045C211yesmaximal, characteristic
3C32×C4×Q16C211yesmaximal, characteristic, complemented
4#10592886C211yesmaximal, characteristic
5#10592881C211yesmaximal, characteristic, complemented
6#10592729C211yesmaximal, characteristic, complemented
7#10592725C211yesmaximal, characteristic, complemented
8#10592590C211yesmaximal, characteristic, complemented
9#10592583C211yesmaximal, characteristic, complemented
10#10592517C211yesmaximal, characteristic, complemented
11#10592507C211yesmaximal, characteristic
12#10592504C211yesmaximal, characteristic, complemented
13#10592498C211yesmaximal, characteristic, complemented
14C4×#3744C211yesmaximal, characteristic, complemented
15#10592389C211yesmaximal, characteristic, complemented
16#79748—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×C32×Q16C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21#64155C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64153C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26C2×#3744C2211yescharacteristic
27#64107—21no—
28#64106C2211yescharacteristic
29#64102—21no—
30#64102C2211yescharacteristic
31C4⋊C4×C3⋊D3—21no—
32C4⋊C4×C3⋊D3C2211yescharacteristic
33#64099C2211yescharacteristic
34#64098—21no—
35#64085—21no—
36C4×C4⋊(C3⋊D3)—21no—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38#64081—21no—
39#64081C2211yescharacteristic
40#64079—21no—
41C4×#634C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×C4×C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63648C2211yescharacteristic
49#63647C2211yescharacteristic
50#63647C2211yescharacteristic
51#63644C2211yescharacteristic
52#63643C2211yescharacteristic
53#63641C2211yescharacteristic
54#63641C2211yescharacteristic
55#63637C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63634C2211yescharacteristic
59#63630C2211yescharacteristic
60#5583—34no—
61#5574—34no—
62C3×C4×Q16D314yescomplemented
63#5187—34no—
64#5182—34no—
65#5030—34no—
66#5026—34no—
67#4891—34no—
68#4884—34no—
69#4818—34no—
70#4808—34no—
71#4805—34no—
72#4799—34no—
73C4×#204—34no—
74#4690—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77#3832—22no—
78#3832—22no—
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4×C3⋊D3—21no—
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×#634C2311yescharacteristic
87C32×Q16—22no—
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C4⋊C4C2311yescharacteristic
94C32×C42—21no—
95C32×C42—21no—
96C32×C42C2311yescharacteristic
97#3756—22no—
98#3755—22no—
99#3752—21no—
100#3752—21no—
101#3752—21no—
102#3752—21no—
103#3752D411yescharacteristic
104#3752D411yescharacteristic
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3744—22no—
124#3120—91noSylow
125C2×#239—34no—
126C2×C3×Q16C2×D314yes—
127C3×C4×Q8C2×D314yes—
128C3×C4×Q8C2×D314yes—
129#946—34no—
130Q8×Dic3—34no—
131#944—34no—
132C2×#216—34no—
133C2×#215—34no—
134C2×#204—34no—
135#898—64no—
136#897—34no—
137#893—34no—
138#893—64no—
139D3×C4⋊C4—34no—
140D3×C4⋊C4—64no—
141#890—34no—
142#889—64no—
143#876—64no—
144C4×D12—34no—
145C4×D12—64no—
146#872—34no—
147#872—64no—
148#870—64no—
149C4×Dic6—34no—
150C3×#107C2×D314yes—
151C3×#103C2×D314yes—
152C3×#103C2×D314yes—
153C3×C4×C8C2×D314yes—
154#835—34no—
155#835—34no—
156#821—34no—
157(C2×D3)⋊C8—34no—
158(C2×D3)⋊C8—34no—
159#817—34no—
160#816—34no—
161Dic3⋊C8—34no—
162Dic3⋊C8—34no—
163#810—34no—
164#809—34no—
165#808—34no—
166#807—34no—
167#803—34no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3C2×D411yescharacteristic
170C32×Q8—21no—
171C32×Q8—21no—
172C32×Q8—21no—
173C32×Q8#4112yes—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3C2×D411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C4⋊(C3⋊D3)—24no—
188C4⋊(C3⋊D3)—21no—
189C4⋊(C3⋊D3)#4112yes—
190C4×C3⋊D3—24no—
191C4×C3⋊D3—21no—
192C4×C3⋊D3—21no—
193C4×C3⋊D3—81no—
194C4×C3⋊D3—81no—
195C4×C3⋊D3—81no—
196#634—21no—
197#634—21no—
198C32×C8—21no—
199C32×C8—21no—
200C3⋊(C3⋊C8)—21no—
201C3⋊(C3⋊C8)—21no—
202#541—91no—
203#520—91no—
204#484—91no—
205#483—91no—
206#479—91no—
207#478—91no—
208#462—91no—
209#461—91no—
210#452—91no—
211#452—91no—
212#441—91no—
213#440—91no—
214C4×Q16C3⋊D311yescharacteristic, complemented
215C4×SD16—91no—
216#433—91no—
217C2×C3×Q8C22×D314yes—
218C2×C3×Q8C22×D314yes—
219#239—68no—
220#239—68no—
221C2×D12—34no—
222C2×D12—64no—
223C2×C4×D3—34no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×Dic6—34no—
229C3×Q16—28no—
230C2×C3×C8C22×D314yes—
231C2×C3×C8C22×D314yes—
232C3×C4⋊C4—24no—
233C3×C4⋊C4—24no—
234C3×C4⋊C4C22×D314yes—
235C3×C4⋊C4C22×D314yes—
236C3×C42—24no—
237C3×C42—24no—
238C3×C42C22×D314yes—
239#216—68no—
240#215—68no—
241(C2×D3)⋊C4—34no—
242(C2×D3)⋊C4—34no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—34no—
248C4⋊Dic3—34no—
249C4⋊Dic3—64no—
250C4⋊Dic3—64no—
251C4⋊Dic3—64no—
252Dic3⋊C4—34no—
253Dic3⋊C4—34no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260C4×Dic3—34no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C2×C3⋊C8—34no—
264C2×C3⋊C8—34no—
265#204—68no—
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—21no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—21no—
270C2×C3⋊D3—21no—
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C32×C4—22no—
274C32×C4—21no—
275C32×C4—21no—
276C32×C4—41no—
277C32×C4—41no—
278C32×C4—41no—
279C32×C4C2×#4111yescharacteristic
280C32×C4C2×#4111yescharacteristic
281C3⋊Dic3—21no—
282C3⋊Dic3—21no—
283C3⋊Dic3—21no—
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C2×#41—91no—
288C2×Q16—91no—
289C2×Q16C2×C3⋊D311yescharacteristic
290C2×SD16—91no—
291C2×SD16—91no—
292C4⋊Q8—91no—
293#126—181no—
294#126—181no—
295#125—91no—
296#125—181no—
297#125—181no—
298C22⋊Q8—91no—
299C22⋊Q8—91no—
300C4×Q8—91no—
301C4×Q8—91no—
302C4×Q8C2×C3⋊D311yescharacteristic
303C4×Q8C2×C3⋊D311yescharacteristic
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—181no—
307C4×D4—181no—
308#117—91no—
309#117—181no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—181no—
312#107—91no—
313#107C2×C3⋊D311yescharacteristic
314#106—91no—
315#106—91no—
316C4⋊C8—91no—
317C4⋊C8—91no—
318#103—91no—
319#103—91no—
320#103—91no—
321#103—91no—
322#103C2×C3⋊D311yescharacteristic
323#103C2×C3⋊D311yescharacteristic
324#102—91no—
325#102—91no—
326C22⋊C8—91no—
327C22⋊C8—91no—
328#97—91no—
329C4×C8C2×C3⋊D311yescharacteristic
330C22×D3—34no—
331C22×D3—64no—
332C3×Q8—24no—
333C3×Q8—24no—
334C3×Q8—24no—
335C3×Q8#23518yes—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4D3×D414yes—
341C2×C3×C4D3×D414yes—
342C2×C3×C4C23×D314yes—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—34no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349D12—38no—
350D12—616no—
351D12—64no—
352C4×D3—616no—
353C4×D3—64no—
354C4×D3—64no—
355C4×D3—244no—
356C4×D3—244no—
357C4×D3—244no—
358Dic6—64no—
359Dic6—64no—
360C3×C8—24no—
361C3×C8—24no—
362C3⋊C8—64no—
363C3⋊C8—64no—
364C2×C32#52511yescharacteristic
365C2×C32#57711yescharacteristic
366C2×C32#57811yescharacteristic
367C3⋊D3—41no—
368C3⋊D3—42no—
369#41—182no—
370#41—182no—
371C2×Q8—91no—
372C2×Q8C22×C3⋊D311yescharacteristic
373C2×Q8C22×C3⋊D311yescharacteristic
374C2×D4—91no—
375C2×D4—181no—
376C22×C4—91no—
377C22×C4—181no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4—181no—
381Q16—22no—
382Q16—182no—
383SD16—182no—
384SD16—182no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8C22×C3⋊D311yescharacteristic
388C2×C8C22×C3⋊D311yescharacteristic
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—91no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4—181no—
404C4⋊C4C22×C3⋊D311yescharacteristic
405C4⋊C4C22×C3⋊D311yescharacteristic
406C22⋊C4—91no—
407C22⋊C4—91no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—181no—
412C42—21no—
413C42—21no—
414C42—91no—
415C42—181no—
416C42—181no—
417C42C22×C3⋊D311yescharacteristic
418C22×C3C2×D3×D414yes—
419C2×D3—64no—
420C2×D3—64no—
421C2×D3—68no—
422C2×D3—64no—
423C2×D3—124no—
424C2×D3—124no—
425C3×C4—24no—
426C3×C4—24no—
427C3×C4—28no—
428C3×C4—44no—
429C3×C4—44no—
430C3×C4—44no—
431C3×C4C2×#23514yes—
432C3×C4D3×#4114yes—
433Dic3—64no—
434Dic3—64no—
435Dic3—64no—
436Dic3—124no—
437Dic3—124no—
438Dic3—124no—
439C32#312011yescharacteristic, complemented, Sylow
440C23—91no—
441C23—181no—
442Q8—21no—
443Q8—21no—
444Q8—21no—
445Q8—181no—
446Q8—181no—
447Q8#382812yes—
448D4—92no—
449D4—184no—
450D4—181no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—91no—
456C2×C4—91no—
457C2×C4—91no—
458C2×C4—184no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—721no—
465C2×C4—721no—
466C2×C4—721no—
467C2×C4D4×C3⋊D311yescharacteristic
468C2×C4D4×C3⋊D311yescharacteristic
469C2×C4C23×C3⋊D311yescharacteristic
470C8—21no—
471C8—21no—
472C8—181no—
473C8—181no—
474C2×C3#554714yes—
475C2×C3#576614yes—
476C2×C3#577014yes—
477D3—124no—
478D3—128no—
479C22—181no—
480C22—181no—
481C22—182no—
482C22—181no—
483C22—361no—
484C22—361no—
485C22C2×D4×C3⋊D311yescharacteristic
486C4—21no—
487C4—21no—
488C4—22no—
489C4—41no—
490C4—41no—
491C4—41no—
492C4—181no—
493C4—181no—
494C4—181no—
495C4—361no—
496C4—361no—
497C4—361no—
498C4C2×#382811yescharacteristic
499C4#41×C3⋊D311yescharacteristic
500C3#7974814yescomplemented
501C2—361no—
502C2—362no—
503C2#1059601811yescharacteristic
504C2#1059623711yescharacteristic
505C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC2×#3832C22
hypercenterC4×Q16C3⋊D3
hypocenterC32#3120
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #10596054C2semidirect
3. C32×C4×Q16C2semidirect
5. #10592881C2semidirect
6. #10592729C2semidirect
7. #10592725C2semidirect
8. #10592590C2semidirect
9. #10592583C2semidirect
10. #10592517C2semidirect
12. #10592504C2semidirect
13. #10592498C2semidirect
14. C4×#3744C2semidirect
15. #10592389C2semidirect
62. C3×C4×Q16D3semidirect
214. C4×Q16C3⋊D3semidirect
439. C32#3120semidirect
500. C3#79748semidirect

Maximal subgroups

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

subgroupindex
#105960542
#105960452
C32×C4×Q162
#105928862
#105928812
#105927292
#105927252
#105925902
#105925832
#105925172
#105925072
#105925042
#105924982
C4×#37442
#105923892
#797483