Finite Group Databasebeta

← #11878705

Subgroups — #11878705

Order 1152.

927 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5716C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic, complemented
3#10592775C211yesmaximal, characteristic, complemented
4C3×#5076C211yesmaximal, characteristic, complemented
5#10591517C214yesmaximal, complemented
6#10591489C214yesmaximal, complemented
7#10590290C211yesmaximal, characteristic, complemented
8#10590288C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic, complemented
10#83317—31nomaximal
11#81764—31nomaximal
12C2×C3×#237—21no—
13C2×D3×Dic6C2212yes—
14C32×#127C2211yescharacteristic
15C2×#3754C2214yes—
16#64078C2211yescharacteristic
17C3×#938—21no—
18C3×#938C2212yes—
19C3×#936—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C2×C3×#214C2214yes—
23C3×C42×D3C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63918—21no—
27#63918—21no—
28D3×C4⋊Dic3—21no—
29D3×C4⋊Dic3—21no—
30#63866C2212yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×C4×C3⋊C8C2211yescharacteristic
33Dic3⋊(C3⋊C8)C2212yes—
34#63567C2214yes—
35#63565C2214yes—
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C3×#532—31no—
38D3×C4⋊Q8—31no—
39#5716D311yescharacteristic
40C2×#869—31no—
41C3×#492—31no—
42#5170—34no—
43#5162—34no—
44#5093—31no—
45#5093—31no—
46#5079—31no—
47#5076—31no—
48#5076—31no—
49#5076—61no—
50#5076D311yescharacteristic, complemented
51#5040—34no—
52#5019—34no—
53#4925—31no—
54#4685—31no—
55#4681—31no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C2×#634C2312yes—
60C2×C3×#67—22no—
61C22×C3×Dic3—22no—
62C3×#237—44no—
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3C2311yescharacteristic
66C2×C3×Dic6—21no—
67C2×C3×Dic6C2312yes—
68C2×#627—22no—
69C2×D3×Dic3—22no—
70D3×Dic6—44no—
71C32×C42C2311yescharacteristic
72#3754—44no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—21no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#217—22no—
77C3×#217—22no—
78C3×#214—44no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3C2312yes—
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2312yes—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89#3206—91noSylow
90C2×C3×#41—61no—
91C2×D3×Q8—32no—
92C2×#237—21no—
93C22×Dic6—32no—
94C2×C3×SD16—34no—
95C3×C4⋊Q8—31no—
96C3×C4⋊Q8—31no—
97C3×#127—21no—
98C3×#127C2×D311yescharacteristic
99C3×#127C2×D311yescharacteristic
100C3×#124—61no—
101C3×#121—32no—
102C3×#121—61no—
103C3×C4×D4—32no—
104C3×C4×D4—61no—
105C2×C3×C42—31no—
106#944—32no—
107#938—21no—
108#938C2×D312yes—
109#936—21no—
110D4×Dic3—21no—
111D4×Dic3C2×D312yes—
112C2×#214—34no—
113C2×#214—34no—
114C2×#214—64no—
115C2×#214C2×D314yes—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3—61no—
118D3×C4⋊C4—61no—
119D3×C4⋊C4—61no—
120#888—61no—
121#888—61no—
122C42×D3C2×D311yescharacteristic
123#869—32no—
124#869—31no—
125#869—31no—
126#869—61no—
127#869—61no—
128#869—61no—
129#869C2×D311yescharacteristic
130#869C2×D311yescharacteristic
131C3×C4×C8—31no—
132#835—34no—
133#830—32no—
134(C2×D3)⋊C8—32no—
135#816—34no—
136Dic3⋊C8—32no—
137#810—34no—
138#810—34no—
139C4⋊(C3⋊C8)—32no—
140C4×C3⋊C8—31no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—61no—
143C4×C3⋊C8C2×D311yescharacteristic
144C23×C32—22no—
145C22×C3×D3C2×D411yescharacteristic
146C32×D4—24no—
147C32×D4—42no—
148C32×D4—42no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3—22no—
153#634—24no—
154C3×#67—44no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—44no—
158C2×C3×Dic3C2×D411yescharacteristic
159C2×C3×Dic3C2×D411yescharacteristic
160C2×C3×Dic3C2×D411yescharacteristic
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163C3×C4×D3SD1614yescomplemented
164C3×Dic6—24no—
165C3×Dic6—42no—
166#627—44no—
167D3×Dic3—44no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—22no—
170#532—31no—
171C2×C4⋊Q8—91no—
172#492—31no—
173#492—91no—
174#487—91no—
175#487—91no—
176#461—94no—
177#448—94no—
178#431—91no—
179C3×#41—124no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—22no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—62no—
190C2×C3×D4C22×D312yes—
191C2×C3×D4C22×D312yes—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—62no—
196C2×#67—22no—
197C22×Dic3—22no—
198C22×Dic3—62no—
199D3×Q8—124no—
200#237—44no—
201C2×C4×D3—62no—
202C2×C4×D3#6711yescharacteristic
203C2×C4×D3#6711yescharacteristic
204C2×C4×D3C22×D311yescharacteristic
205C2×Dic6—21no—
206C2×Dic6—32no—
207C2×Dic6—32no—
208C2×Dic6—62no—
209C2×Dic6—62no—
210C2×Dic6—62no—
211C2×Dic6—124no—
212C2×Dic6C22×D312yes—
213C3×SD16—124no—
214C2×C3×C8—32no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C22⋊C4—62no—
220C3×C22⋊C4—62no—
221C3×C42—21no—
222C3×C42—31no—
223C3×C42—31no—
224C3×C42—31no—
225C3×C42C22×D311yescharacteristic
226C3×C42C22×D311yescharacteristic
227#217—22no—
228#217—22no—
229#214—44no—
230#214—124no—
231#214—124no—
232#214—128no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4⋊Dic3—62no—
237C4⋊Dic3—62no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—121no—
243C4⋊Dic3—121no—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247C4×Dic3#6711yescharacteristic
248C4×Dic3#6711yescharacteristic
249C4×Dic3C22×D311yescharacteristic
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8C22×D312yes—
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—21no—
259C2×C3×D3—21no—
260C2×C3×D3C2×SD1612yes—
261C32×C4C2×SD1612yes—
262C32×C4#13712yes—
263C32×C4H(5,𝔽2)12yes—
264C3⋊Dic3—42no—
265C3×Dic3—21no—
266C3×Dic3—21no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C3×Dic3C2×SD1612yes—
270C2×#41—61no—
271C22×Q8—92no—
272C2×SD16—34no—
273C2×SD16—94no—
274C4⋊Q8—31no—
275C4⋊Q8—31no—
276C4⋊Q8—92no—
277C4⋊Q8—91no—
278C4⋊Q8—181no—
279C4⋊Q8—181no—
280#127D3211yescharacteristic
281#124—61no—
282#121—32no—
283#121—61no—
284C4×D4—32no—
285C4×D4—61no—
286C2×C4⋊C4—181no—
287C2×C4⋊C4—181no—
288C2×C42—31no—
289C4⋊C8—92no—
290#103—94no—
291#103—94no—
292C22⋊C8—92no—
293C4×C8—31no—
294C4×C8—91no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—31no—
298C23×C3—42no—
299C22×D3C2×#6711yescharacteristic
300C3×Q8—64no—
301C3×Q8—122no—
302C3×D4—24no—
303C3×D4—24no—
304C3×D4—44no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—42no—
308C3×D4—42no—
309C3×D4—82no—
310C3×D4—82no—
311C3×D4—124no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—31no—
316C2×C3×C4—34no—
317C2×C3×C4—31no—
318C2×C3×C4—31no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—124no—
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330#67—44no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—44no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—122no—
337C2×Dic3—124no—
338C2×Dic3C2×#6711yescharacteristic
339C2×Dic3C2×#6711yescharacteristic
340C2×Dic3C2×#6711yescharacteristic
341C4×D3—22no—
342C4×D3—22no—
343C4×D3—124no—
344C4×D3#21414yescomplemented
345Dic6—24no—
346Dic6—42no—
347Dic6—64no—
348Dic6—64no—
349Dic6—124no—
350Dic6—124no—
351Dic6—124no—
352C3×C8—62no—
353C3⋊C8—22no—
354C3⋊C8—64no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C2×C32—82no—
358C2×C32#53511yescharacteristic
359C2×C32C22×SD1611yescharacteristic
360C2×C32C2×#13711yescharacteristic
361C3×D3—22no—
362#41—124no—
363C2×Q8—32no—
364C2×Q8—61no—
365C2×Q8—92no—
366C2×Q8—182no—
367C2×Q8—364no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—62no—
371C2×D4C2×D3212yes—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—62no—
376C22×C4—182no—
377SD16—124no—
378SD16—364no—
379C2×C8—32no—
380C2×C8—92no—
381C4⋊C4—32no—
382C4⋊C4—61no—
383C4⋊C4—61no—
384C4⋊C4—61no—
385C4⋊C4—182no—
386C4⋊C4—182no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C22⋊C4—62no—
390C22⋊C4—62no—
391C42—31no—
392C42—31no—
393C42—31no—
394C42C2×D3211yescharacteristic
395C22×C3—21no—
396C22×C3—32no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—82no—
406C22×C3—82no—
407C22×C3—82no—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C22×#6711yescharacteristic
410C2×D3—21no—
411C2×D3—21no—
412C2×D3C2×#21412yes—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—32no—
417C3×C4—61no—
418C3×C4—61no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4D3×SD1612yes—
422C3×C4#91512yes—
423C3×C4C2×#21412yes—
424C3×C4#95112yes—
425C3×C4#100412yes—
426C3×C4#100912yes—
427Dic3—21no—
428Dic3—21no—
429Dic3—42no—
430Dic3—42no—
431Dic3—122no—
432Dic3—122no—
433Dic3—242no—
434Dic3C2×#21412yes—
435C32#320611yescharacteristic, complemented, Sylow
436C23—22no—
437C23—31no—
438Q8—64no—
439Q8—122no—
440Q8—184no—
441Q8—364no—
442D4—24no—
443D4—42no—
444D4—42no—
445D4—124no—
446C2×C4—31no—
447C2×C4—34no—
448C2×C4—31no—
449C2×C4—31no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—124no—
455C2×C4—182no—
456C2×C4—364no—
457C2×C4D3×#6711yescharacteristic
458C2×C4D3×#6711yescharacteristic
459C2×C4C22×D3211yescharacteristic
460C8—62no—
461C8—182no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—62no—
466C2×C3—82no—
467C2×C3—82no—
468C2×C3—162no—
469C2×C3#571511yescharacteristic
470C2×C3C2×D3×SD1611yescharacteristic
471C2×C3C2×#91511yescharacteristic
472C2×C3C22×#21411yescharacteristic
473C2×C3C2×#95111yescharacteristic
474C2×C3#583011yescharacteristic
475D3—22no—
476C22—32no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—61no—
481C22—61no—
482C22C2×D3×#6711yescharacteristic
483C4—32no—
484C4—61no—
485C4—61no—
486C4—122no—
487C4—122no—
488C4—362no—
489C4D3×#21412yes—
490C4#6392912yes—
491C4#6431412yes—
492C3—21no—
493C3#8176411yescharacteristic, complemented
494C3#8331711yescharacteristic, complemented
495C2—62no—
496C2—82no—
497C2C2×D3×#21411yescharacteristic
498C2C2×#6392911yescharacteristic
499C2#1059530311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5716C2
hypercenter#127D32
hypocenterC32#3206
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. D3×#869C2semidirect
3. #10592775C2semidirect
4. C3×#5076C2semidirect
5. #10591517C2semidirect
6. #10591489C2semidirect
7. #10590290C2semidirect
8. #10590288C2semidirect
9. #10590261C2semidirect
50. #5076D3semidirect
163. C3×C4×D3SD16semidirect
344. C4×D3#214semidirect
435. C32#3206semidirect
493. C3#81764semidirect
494. C3#83317semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
D3×#8692
#105927752
C3×#50762
#105915172
#105914892
#105902902
#105902882
#105902612
#833173
#817643