Finite Group Databasebeta

← #11898393

Subgroups — #11898393

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595384C212yesmaximal, complemented
2Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#5191C211yesmaximal, characteristic
4C3×#5183C211yesmaximal, characteristic, complemented
5#10591612C212yesmaximal, complemented
6#10591578C212yesmaximal, complemented
7#10591564C212yesmaximal, complemented
8#10590869C211yesmaximal, characteristic
9Dic3×Dic12C211yesmaximal, characteristic, complemented
10C8×#627C211yesmaximal, characteristic, complemented
11Dic3×D24C211yesmaximal, characteristic
12#81813—31nomaximal
13#81795—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15Q8×C3⋊Dic3C2212yes—
16C3×#947C2212yes—
17C3×#944C2212yes—
18C2×C3×#216C2212yes—
19C2×C3×#215C2212yes—
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×D24C2211yescharacteristic
22C4×#627C2211yescharacteristic
23#63893—22no—
24Dic3×D12C2212yes—
25#63878—22no—
26#63863C2212yes—
27#63862—22no—
28#63861—22no—
29Dic3×Dic6C2212yes—
30C2×#3715C2212yes—
31#63662C2212yes—
32#63645C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63572C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39#63566C2212yes—
40#63563C2212yes—
41#5732—32no—
42#5671—32no—
43C3×#495—31no—
44C3×#494—31no—
45#5191—31no—
46#5191D311yescharacteristic
47#5185—32no—
48#5185—32no—
49#5183D311yescharacteristic, complemented
50Dic3×Q16—31no—
51Dic3×Q16—31no—
52Dic3×Q16—31no—
53Dic3×Q16—61no—
54#5166—32no—
55#5162—32no—
56#5155—31no—
57Dic3×D8—31no—
58#5083—32no—
59#5054—32no—
60C4×Dic12—31no—
61C4×D24—31no—
62C8×Dic6—31no—
63C8×Dic6—31no—
64C2×C32×Q8C2312yes—
65C2×C3×D12C2312yes—
66C2×C3×Dic6C2312yes—
67C2×#627D411yescharacteristic
68C2×D3×Dic3—22no—
69C32×Q16—22no—
70C2×C32×C8C2311yescharacteristic
71C4⋊(C3⋊Dic3)—22no—
72C4⋊(C3⋊Dic3)C2312yes—
73C4×C3⋊Dic3—22no—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C3×#216—42no—
77C3×#215—42no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3C2311yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C3×Dic12—22no—
87C3×D24—22no—
88#3724D411yescharacteristic
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3D411yescharacteristic
91Dic3⋊Dic3D411yescharacteristic
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3715—42no—
97#3393—91noSylow
98C2×C3×Q16—21no—
99C2×C3×Q16—32no—
100C2×C3×Q16—31no—
101C2×C3×Q16C2×D311yescharacteristic
102C2×C3×Q16C2×D311yescharacteristic
103C2×C3×SD16—32no—
104C2×C3×D8—31no—
105C3×C4⋊Q8—32no—
106C3×#124—32no—
107#947—32no—
108#947C2×D312yes—
109Q8×Dic3—32no—
110Q8×Dic3—32no—
111Q8×Dic3—32no—
112Q8×Dic3—62no—
113#944C2×D312yes—
114C2×#216C2×D312yes—
115C2×#215—32no—
116C2×#215C2×D312yes—
117#936—32no—
118D4×Dic3—32no—
119C2×#214—32no—
120C2×Dic12C2×D311yescharacteristic
121C2×D24C2×D311yescharacteristic
122#898—62no—
123#898—62no—
124#897—62no—
125#892—62no—
126#879—62no—
127#879—62no—
128#878—62no—
129#877—62no—
130C4×D12—32no—
131C4×Dic6—31no—
132C4×Dic6—31no—
133C4×Dic6—32no—
134C3×C4×C8—31no—
135C3×C4×C8—31no—
136#835—32no—
137#835—32no—
138#835—32no—
139#835—62no—
140#832—32no—
141#821—32no—
142#818—31no—
143#818—31no—
144#818—61no—
145#816—32no—
146Dic3⋊C8—31no—
147Dic3⋊C8—31no—
148Dic3⋊C8—31no—
149Dic3⋊C8—31no—
150C8×Dic3—31no—
151C8×Dic3—31no—
152C8×Dic3—61no—
153C8×Dic3C2×D311yescharacteristic
154C8×Dic3C2×D311yescharacteristic
155C4⋊(C3⋊C8)—31no—
156C4⋊(C3⋊C8)—31no—
157C22×C3×D3—22no—
158C32×Q8—22no—
159C32×Q8—22no—
160C2×C32×C4—22no—
161C2×C32×C4C2411yescharacteristic
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3C2×D411yescharacteristic
164C2×C3⋊Dic3C2×D411yescharacteristic
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D411yescharacteristic
167C2×C3×Dic3C2×D411yescharacteristic
168C2×C3×Dic3C2×D411yescharacteristic
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—22no—
171C3×D12—22no—
172C3×Dic6—22no—
173C3×Dic6—22no—
174#627—22no—
175D3×Dic3—44no—
176C32×C8#4112yes—
177C3⋊(C3⋊C8)—21no—
178C3×C3⋊C8—21no—
179C3×C3⋊C8—21no—
180#556—92no—
181#495—31no—
182#495—91no—
183#494—31no—
184#464—92no—
185#464—92no—
186#461—92no—
187C8×Q8—91no—
188C4×Q16—91no—
189C4×Q16—91no—
190C4×D8—91no—
191C2×C3×Q8—22no—
192C2×C3×Q8—32no—
193C2×C3×Q8C22×D312yes—
194C2×C3×Q8C22×D312yes—
195C2×C3×D4—32no—
196C22×Dic3—62no—
197C2×D12C22×D312yes—
198C2×C4×D3—62no—
199C2×Dic6—31no—
200C2×Dic6—31no—
201C2×Dic6C22×D312yes—
202C3×Q16—24no—
203C3×Q16—22no—
204C3×Q16—22no—
205C3×Q16—62no—
206C3×Q16—122no—
207C3×SD16—122no—
208C3×D8—62no—
209C2×C3×C8—21no—
210C2×C3×C8—31no—
211C2×C3×C8—31no—
212C2×C3×C8C22×D311yescharacteristic
213C2×C3×C8C22×D311yescharacteristic
214C3×C4⋊C4—62no—
215C3×C4⋊C4—62no—
216C3×C22⋊C4—62no—
217C3×C22⋊C4—62no—
218C3×C42—31no—
219C3×C42—31no—
220#217—62no—
221#217—62no—
222#217—62no—
223#216—42no—
224#215—42no—
225#215—122no—
226#214—122no—
227(C2×D3)⋊C4—22no—
228(C2×D3)⋊C4—22no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—62no—
232C4⋊Dic3—31no—
233C4⋊Dic3—31no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—62no—
237C4⋊Dic3—62no—
238C4⋊Dic3—62no—
239C4⋊Dic3—62no—
240C4⋊Dic3—122no—
241Dic3⋊C4—22no—
242Dic3⋊C4—22no—
243Dic3⋊C4—31no—
244Dic3⋊C4—31no—
245Dic3⋊C4—31no—
246Dic3⋊C4—31no—
247Dic3⋊C4—62no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—61no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3—122no—
256C4×Dic3C22×D311yescharacteristic
257C4×Dic3C22×D311yescharacteristic
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8C22×D311yescharacteristic
262C2×C3⋊C8C22×D311yescharacteristic
263Dic12—22no—
264D24—22no—
265C22×C32C22×D411yescharacteristic
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C32×C4—42no—
270C32×C4C2×#4111yescharacteristic
271C32×C4H(5,𝔽2)11yescharacteristic
272C3⋊Dic3—21no—
273C3⋊Dic3—21no—
274C3⋊Dic3—42no—
275C3×Dic3—21no—
276C3×Dic3—21no—
277C3×Dic3—21no—
278C3×Dic3—42no—
279C3×Dic3#13512yes—
280C2×Q16—32no—
281C2×Q16—31no—
282C2×Q16D3211yescharacteristic
283C2×SD16—32no—
284C2×SD16—92no—
285C2×D8—31no—
286C4⋊Q8—32no—
287#126—182no—
288#126—182no—
289#124—32no—
290#124—92no—
291C22⋊Q8—182no—
292C4×Q8—91no—
293C4×Q8—92no—
294C4×Q8—92no—
295C4×D4—92no—
296#117—182no—
297#107—91no—
298C4⋊C8—91no—
299C4⋊C8—91no—
300C4⋊C8—91no—
301#103—92no—
302#103—92no—
303#102—92no—
304C4×C8—31no—
305C4×C8—31no—
306C4×C8—91no—
307C23×C3—62no—
308C22×D3—22no—
309C3×Q8—24no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—42no—
315C3×Q8—62no—
316C3×Q8—62no—
317C3×D4—62no—
318C3×D4—62no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—42no—
327C2×C3×C4—62no—
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—31no—
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—122no—
340C2×Dic3—124no—
341C2×Dic3D3×D411yescharacteristic
342C2×Dic3D3×D411yescharacteristic
343C2×Dic3D3×D411yescharacteristic
344C2×Dic3D3×D411yescharacteristic
345D12—22no—
346D12—22no—
347C4×D3—124no—
348Dic6—22no—
349Dic6—22no—
350Dic6—62no—
351Dic6—62no—
352C3×C8—22no—
353C3×C8—61no—
354C3×C8—61no—
355C3×C8#23712yes—
356C3×C8#23712yes—
357C3⋊C8—21no—
358C3⋊C8—21no—
359C3⋊C8—61no—
360C3⋊C8—61no—
361C3⋊C8—121no—
362C2×C32#55011yescharacteristic
363C2×C32C2×#13511yescharacteristic
364C2×C32#57811yescharacteristic
365C3×D3—82no—
366C2×Q8—32no—
367C2×Q8—91no—
368C2×Q8C2×D3212yes—
369C2×D4—32no—
370C22×C4—182no—
371Q16—22no—
372Q16—62no—
373Q16—122no—
374SD16—122no—
375SD16—362no—
376D8—62no—
377C2×C8—31no—
378C2×C8—31no—
379C2×C8—91no—
380C2×C8C2×D3211yescharacteristic
381C4⋊C4—62no—
382C4⋊C4—62no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—91no—
386C4⋊C4—92no—
387C4⋊C4—182no—
388C4⋊C4—182no—
389C22⋊C4—62no—
390C22⋊C4—62no—
391C22⋊C4—182no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C42—31no—
395C42—31no—
396C42—91no—
397C42—182no—
398C42—182no—
399C22×C3—21no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3C2×D3×D411yescharacteristic
404C22×C3C2×D3×D411yescharacteristic
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—42no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—32no—
411C3×C4—44no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—61no—
415C3×C4—61no—
416C3×C4—61no—
417C3×C4—122no—
418C3×C4C2×#23711yescharacteristic
419C3×C4C2×#23711yescharacteristic
420C3×C4#100411yescharacteristic
421C3×C4#100411yescharacteristic
422Dic3—21no—
423Dic3—21no—
424Dic3—21no—
425Dic3—42no—
426Dic3—62no—
427Dic3—61no—
428Dic3—61no—
429Dic3—61no—
430Dic3—61no—
431Dic3—121no—
432Dic3—122no—
433Dic3—122no—
434Dic3—242no—
435Dic3#91912yes—
436C32#339311yescharacteristic, complemented, Sylow
437C23—62no—
438Q8—22no—
439Q8—22no—
440Q8—62no—
441Q8—62no—
442Q8—182no—
443D4—62no—
444D4—62no—
445C2×C4—22no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—31no—
449C2×C4—31no—
450C2×C4—62no—
451C2×C4—91no—
452C2×C4—91no—
453C2×C4—182no—
454C2×C4—364no—
455C2×C4C22×D3211yescharacteristic
456C8—61no—
457C8—61no—
458C8—181no—
459C8#380512yes—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—242no—
464C2×C3#571811yescharacteristic
465C2×C3#571811yescharacteristic
466C2×C3C2×#91911yescharacteristic
467C2×C3#576611yescharacteristic
468C2×C3D3×#13511yescharacteristic
469C2×C3#577111yescharacteristic
470D3—82no—
471C22—122no—
472C22—122no—
473C22—122no—
474C22D32×D411yescharacteristic
475C4—32no—
476C4—42no—
477C4—61no—
478C4—61no—
479C4—61no—
480C4—122no—
481C4—181no—
482C4—181no—
483C4—362no—
484C4#6431311yescharacteristic
485C4C2×#380511yescharacteristic
486C3—21no—
487C3#8179511yescharacteristic, complemented
488C3#8181311yescharacteristic, complemented
489C2—242no—
490C2D3×#91911yescharacteristic
491C2#1059476811yescharacteristic
492C2#1059514411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC2×Q16D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #10595384C2semidirect
2. Q16×C3⋊Dic3C2semidirect
4. C3×#5183C2semidirect
5. #10591612C2semidirect
6. #10591578C2semidirect
7. #10591564C2semidirect
9. Dic3×Dic12C2semidirect
10. C8×#627C2semidirect
49. #5183D3semidirect
436. C32#3393semidirect
487. C3#81795semidirect
488. C3#81813semidirect

Maximal subgroups

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

subgroupindex
#105953842
Q16×C3⋊Dic32
C3×#51912
C3×#51832
#105916122
#105915782
#105915642
#105908692
Dic3×Dic122
C8×#6272
Dic3×D242
#818133
#817953