Finite Group Databasebeta

← #11868500

Subgroups — #11868500

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2#10593948C211yesmaximal, characteristic
3C3×#5022C212yesmaximal, complemented
4#10591615C212yesmaximal, complemented
5#10591552C211yesmaximal, characteristic
6#10591552C211yesmaximal, characteristic
7#10590575C211yesmaximal, characteristic
8#10590573C211yesmaximal, characteristic
9#10590434C212yesmaximal, complemented
10#10590331C211yesmaximal, characteristic
11#10590292C212yesmaximal, complemented
12D3×#479—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15Q8×C3⋊Dic3C2211yescharacteristic
16C4⋊C4×C3⋊D3—21no—
17C4⋊C4×C3⋊D3C2211yescharacteristic
18#64096—21no—
19#64096C2211yescharacteristic
20C42×C3⋊D3—21no—
21C42×C3⋊D3C2211yescharacteristic
22C4×#634—21no—
23C4×#634C2211yescharacteristic
24C3×#870C2212yes—
25#63900C2211yescharacteristic
26#63900C2211yescharacteristic
27#63883—21no—
28#63883—21no—
29#63872C2212yes—
30#63870—21no—
31#63870—21no—
32C2×#3710C2211yescharacteristic
33C2×#3710C2211yescharacteristic
34C3×#835C2212yes—
35C3×#835C2212yes—
36C3×#808C2212yes—
37C3×#807C2212yes—
38C3×C4⋊(C3⋊C8)C2212yes—
39#63575C2212yes—
40#63573C2212yes—
41#63572C2212yes—
42#63567C2212yes—
43#63567C2212yes—
44D3×#125—32no—
45C4×D3×Q8—32no—
46C4×D3×Q8—61no—
47C3×#479—32no—
48#5063—32no—
49#5022D312yescomplemented
50D3×#107—32no—
51#4877—32no—
52D3×#106—32no—
53#4857—32no—
54D3×C4⋊C8—32no—
55#4829—32no—
56D3×#103—32no—
57D3×#103—32no—
58#4799—32no—
59#4796—32no—
60C2×C32×Q8C2311yescharacteristic
61Q8×C3⋊D3—22no—
62Q8×C3⋊D3Q814yes—
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634—21no—
69C2×#634C2311yescharacteristic
70C2×#624—21no—
71C2×#624—21no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4C2311yescharacteristic
74C32×C42—21no—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79#3750—21no—
80#3750—21no—
81C4×C3⋊Dic3—21no—
82C4×C3⋊Dic3—21no—
83C4×C3⋊Dic3—21no—
84C4×C3⋊Dic3D411yescharacteristic
85C4×C3⋊Dic3D411yescharacteristic
86C4×C3⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3724—21no—
94#3724—21no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97#3710—22no—
98#3710—22no—
99C2×#479—91noSylow
100C2×D3×Q8—32no—
101C2×D3×Q8—61no—
102C3×#125—32no—
103C3×C4×Q8—21no—
104C3×C4×Q8C2×D312yes—
105Q8×Dic3—32no—
106Q8×Dic3—61no—
107C2×D3×C8—32no—
108C2×D3×C8—32no—
109D3×C4⋊C4—32no—
110D3×C4⋊C4—32no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—61no—
113D3×C4⋊C4—62no—
114D3×C4⋊C4—62no—
115D3×C4⋊C4—62no—
116D3×C4⋊C4—62no—
117#890—32no—
118#890—32no—
119#889—62no—
120#889—62no—
121#887—32no—
122#887—61no—
123#887—62no—
124#887—62no—
125C42×D3—32no—
126C42×D3—61no—
127C42×D3—62no—
128C42×D3—62no—
129#870C2×D312yes—
130C4×Dic6—32no—
131C4×Dic6—61no—
132C4×Dic6—62no—
133C4×Dic6—62no—
134C3×#107—32no—
135C3×#106—32no—
136C3×C4⋊C8—32no—
137C3×#103—32no—
138C3×#103—32no—
139#835C2×D312yes—
140#835C2×D312yes—
141#818—32no—
142#817—32no—
143#816—32no—
144#816—32no—
145Dic3⋊C8—32no—
146Dic3⋊C8—32no—
147#810—32no—
148#810—32no—
149#808—32no—
150#808C2×D312yes—
151#807—32no—
152#807C2×D312yes—
153C4⋊(C3⋊C8)C2×D312yes—
154C22×C3⋊D3C2×D411yescharacteristic
155C32×Q8—21no—
156C32×Q8C2×Q812yes—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2411yescharacteristic
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3C2×D411yescharacteristic
165C2×C3⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
167C4×C3⋊D3—24no—
168C4×C3⋊D3—22no—
169C4×C3⋊D3—22no—
170C4×C3⋊D3—42no—
171C4×C3⋊D3C2×Q812yes—
172C4×C3⋊D3#4112yes—
173#634—21no—
174#634—24no—
175#634C2×Q812yes—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178#624—42no—
179#624—42no—
180C3×C3⋊C8—22no—
181C3×C3⋊C8—22no—
182C2×#125—91no—
183C2×C4×Q8—91no—
184#479—32no—
185#479—92no—
186#479—92no—
187#479—92no—
188C2×#107—91no—
189C2×#106—91no—
190C2×C4⋊C8—91no—
191C2×#103—91no—
192C2×#103—91no—
193C2×C3×Q8—21no—
194C2×C3×Q8C22×D312yes—
195D3×Q8—38no—
196D3×Q8—64no—
197D3×Q8—64no—
198D3×Q8—64no—
199C2×C4×D3—32no—
200C2×C4×D3—32no—
201C2×C4×D3—32no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×Dic6—32no—
212C2×Dic6—61no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×C3×C8—32no—
216C2×C3×C8—32no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4C22×D312yes—
225C3×C42—22no—
226C3×C42—22no—
227C3×C42—21no—
228C3×C42C22×D312yes—
229C4⋊Dic3—32no—
230C4⋊Dic3—61no—
231C4⋊Dic3—62no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234C4⋊Dic3—62no—
235C4⋊Dic3C22×D312yes—
236C4⋊Dic3C22×D312yes—
237Dic3⋊C4—22no—
238Dic3⋊C4—22no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249C4×Dic3—32no—
250C4×Dic3—32no—
251C4×Dic3—32no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C2×C3⋊C8C22×D312yes—
262C2×C3⋊C8C22×D312yes—
263D3×C8—64no—
264D3×C8—64no—
265C22×C32C22×D411yescharacteristic
266C2×C3⋊D3C22⋊Q812yes—
267C2×C3⋊D3#13512yes—
268C2×C3⋊D3#13712yes—
269C32×C4—22no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—41no—
273C32×C4C22×Q811yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—22no—
276C3⋊Dic3—21no—
277C3⋊Dic3—21no—
278C3⋊Dic3—41no—
279C3⋊Dic3C22⋊Q812yes—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C22×Q8—91no—
283C22×C8—91no—
284C22×C8—91no—
285#125—32no—
286#125—92no—
287#125—181no—
288#125—181no—
289C4×Q8—91no—
290C4×Q8—91no—
291C4×Q8—91no—
292C4×Q8—181no—
293C4×Q8—181no—
294C4×Q8D3211yescharacteristic
295C2×C4⋊C4—91no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—181no—
299C2×C4⋊C4—181no—
300C2×C4⋊C4—181no—
301C2×C42—91no—
302C2×C42—181no—
303#107—32no—
304#107—92no—
305#106—32no—
306#106—92no—
307C4⋊C8—32no—
308C4⋊C8—92no—
309#103—32no—
310#103—32no—
311#103—92no—
312#103—92no—
313C22×D3—32no—
314C22×D3—61no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8D3×Q814yes—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4C23×D312yes—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—32no—
334C2×Dic3—32no—
335C2×Dic3—32no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C4×D3—34no—
344C4×D3—34no—
345C4×D3—62no—
346C4×D3—62no—
347C4×D3—64no—
348C4×D3—64no—
349C4×D3—68no—
350C4×D3—64no—
351C4×D3—68no—
352C4×D3—122no—
353C4×D3—124no—
354C4×D3—124no—
355C4×D3—124no—
356C4×D3—124no—
357Dic6—34no—
358Dic6—62no—
359Dic6—68no—
360Dic6—68no—
361Dic6—62no—
362Dic6—62no—
363C3×C8—62no—
364C3×C8—62no—
365C3⋊C8—22no—
366C3⋊C8—22no—
367C2×C32C2×C22⋊Q811yescharacteristic
368C2×C32C2×#13511yescharacteristic
369C2×C32C2×#13711yescharacteristic
370C3⋊D3#47914yescomplemented
371C2×Q8—94no—
372C2×Q8—91no—
373C2×Q8—181no—
374C2×Q8—182no—
375C2×Q8C2×D3211yescharacteristic
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—181no—
380C22×C4—181no—
381C22×C4—181no—
382C22×C4—181no—
383C2×C8—32no—
384C2×C8—32no—
385C2×C8—182no—
386C2×C8—182no—
387C4⋊C4—21no—
388C4⋊C4—32no—
389C4⋊C4—32no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—91no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—182no—
399C4⋊C4—182no—
400C4⋊C4—181no—
401C4⋊C4C2×D3211yescharacteristic
402C42—21no—
403C42—91no—
404C42—91no—
405C42—91no—
406C42—181no—
407C42—181no—
408C42—181no—
409C42C2×D3211yescharacteristic
410C22×C3—21no—
411C22×C3C2×D3×D412yes—
412C2×D3—34no—
413C2×D3—34no—
414C2×D3—34no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—62no—
418C3×C4—24no—
419C3×C4—22no—
420C3×C4—22no—
421C3×C4—22no—
422C3×C4—24no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—41no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—122no—
429C3×C4—122no—
430C3×C4C2×D3×Q812yes—
431C3×C4D3×#4112yes—
432Dic3—34no—
433Dic3—42no—
434Dic3—42no—
435Dic3—62no—
436Dic3—64no—
437Dic3—62no—
438Dic3—62no—
439Dic3—62no—
440Dic3—64no—
441Dic3—121no—
442Dic3—122no—
443Dic3—122no—
444C32C2×#47911yescharacteristic, complemented, Sylow
445C23—91no—
446Q8—21no—
447Q8—92no—
448Q8—184no—
449Q8—181no—
450Q8#379712yes—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—91no—
456C2×C4—92no—
457C2×C4—92no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—182no—
461C2×C4—182no—
462C2×C4—184no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—362no—
466C2×C4—362no—
467C2×C4—362no—
468C2×C4#381111yescharacteristic
469C2×C4#381111yescharacteristic
470C2×C4C22×D3211yescharacteristic
471C8—62no—
472C8—62no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3D3×C22⋊Q812yes—
477C2×C3D3×#13512yes—
478C2×C3D3×#13712yes—
479D3—38no—
480D3—64no—
481C22—92no—
482C22—92no—
483C22—92no—
484C22C2×#381111yescharacteristic
485C4—22no—
486C4—21no—
487C4—21no—
488C4—41no—
489C4—92no—
490C4—122no—
491C4—122no—
492C4—182no—
493C4—181no—
494C4—181no—
495C4—361no—
496C4C2×#379711yescharacteristic
497C4#6430611yescharacteristic
498C3—21no—
499C3D3×#47912yescomplemented
500C2—94no—
501C2#1059492511yescharacteristic
502C2#1059532211yescharacteristic
503C2#1059545911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×Q8D32
hypocenterC32C2×#479
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5022C2semidirect
4. #10591615C2semidirect
9. #10590434C2semidirect
11. #10590292C2semidirect
49. #5022D3semidirect
370. C3⋊D3#479semidirect
444. C32C2×#479semidirect
499. C3D3×#479semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105939482
C3×#50222
#105916152
#105915522
#105905752
#105905732
#105904342
#105903312
#105902922
D3×#4793