Finite Group Databasebeta

← #11895873

Subgroups — #11895873

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2Dic6×D12C211yesmaximal, characteristic, complemented
3#10592778C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5#10591624C212yesmaximal, complemented
6#10591567C212yesmaximal
7#10591566C212yesmaximal, complemented
8#10591546C212yesmaximal, complemented
9C4×#3713C211yesmaximal, characteristic
10#10590272C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83668—31nomaximal
13#80416—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#947C2212yes—
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2212yes—
20C3×#898—22no—
21C3×#897—21no—
22C3×#892—21no—
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2212yes—
27#63893—22no—
28Dic3×D12C2212yes—
29#63857—21no—
30C2×#3713C2211yescharacteristic
31#63662C2212yes—
32#63662C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#835C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63576C2211yescharacteristic
37#63575C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42#63554C2212yes—
43C3×#556—31no—
44#5732D311yescharacteristic, complemented
45Q8×D12—31no—
46D4×Dic6—31no—
47C3×#461—31no—
48#5165—32no—
49#5164—32no—
50#5083D311yescharacteristic, complemented
51#5079—31no—
52#5079—31no—
53#5079—61no—
54#5057—32no—
55#5055—32no—
56#5026—32no—
57#5024—31no—
58#5021—32no—
59C4×#213—31no—
60C4×#213—31no—
61#5007—31no—
62#4846—31no—
63#4831—31no—
64#4794—32no—
65#4793—32no—
66C2×C32×Q8C2312yes—
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#627—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—44no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×#215—24no—
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3713—22no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×#126—62no—
107C3×#124—32no—
108C3×C22⋊Q8—61no—
109C3×C4×Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×D4—31no—
112C3×C4×D4—31no—
113C3×#117—61no—
114#947C2×D312yes—
115Q8×Dic3C2×D312yes—
116C2×#215C2×D312yes—
117D4×Dic3—32no—
118C2×#213—31no—
119C2×#213—31no—
120#924—61no—
121#898—22no—
122#897—21no—
123#897—62no—
124#897—61no—
125#892—21no—
126#888—32no—
127#878—62no—
128C4×D12—32no—
129C4×D12C2×D311yescharacteristic
130C4×D12C2×D311yescharacteristic
131#869—31no—
132#869—31no—
133#869—32no—
134#869—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—31no—
137C3×#103—32no—
138#835—32no—
139#835—32no—
140#835—32no—
141#835—32no—
142#835—62no—
143#835—62no—
144#835C2×D312yes—
145#832—31no—
146#832—31no—
147#832—32no—
148#821—32no—
149#818—32no—
150#815—32no—
151Dic3⋊C8—32no—
152#809—31no—
153#809—31no—
154#807—31no—
155#807—31no—
156#807—32no—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159#803—32no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C32×Q8—22no—
166C32×Q8—22no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172#634—42no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—21no—
180C3×D12#4112yes—
181C3×C4×D3—42no—
182C3×C4×D3—42no—
183C3×Dic6—22no—
184#627—44no—
185D3×Dic3—44no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—22no—
189#556—31no—
190D4×Q8—91no—
191#489—92no—
192#487—91no—
193#477—92no—
194#474—91no—
195#463—92no—
196#461—31no—
197#446—91no—
198#440—92no—
199C4×D8—91no—
200C2×C3×Q8—22no—
201C2×C3×Q8—31no—
202C2×C3×Q8C22×D312yes—
203C2×C3×Q8C22×D312yes—
204C2×C3×D4—31no—
205C2×C3×D4—31no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×Dic3—62no—
209D3×Q8—124no—
210C2×D12C22×D311yescharacteristic
211C2×D12C22×D311yescharacteristic
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—62no—
215C2×Dic6—62no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—62no—
219C2×Dic6—121no—
220C2×Dic6—124no—
221C2×Dic6#6711yescharacteristic
222C3×SD16—64no—
223C2×C3×C8—32no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—61no—
238C3×C22⋊C4—61no—
239C3×C42—21no—
240C3×C42—32no—
241C3×C42—62no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—62no—
245#215—24no—
246#213—62no—
247#213—62no—
248(C2×D3)⋊C4—21no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—62no—
253C4⋊Dic3—22no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—121no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3—22no—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8C22×D312yes—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C32×C4—21no—
283C32×C4—42no—
284C32×C4AGL(1,ℤ/8)12yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3⋊Dic3—42no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—41no—
292C22×Q8—181no—
293C2×SD16—32no—
294C2×D8—91no—
295C4⋊Q8—92no—
296C4⋊Q8—91no—
297C4⋊Q8D3211yescharacteristic
298#126—62no—
299#124—32no—
300C22⋊Q8—61no—
301C22⋊Q8—182no—
302C22⋊Q8—181no—
303C4×Q8—31no—
304C4×Q8—32no—
305C4×D4—31no—
306C4×D4—31no—
307C4×D4—92no—
308#117—61no—
309#107—91no—
310#107—92no—
311C4⋊C8—31no—
312C4⋊C8—92no—
313#103—32no—
314#103—92no—
315#103—92no—
316#102—91no—
317#102—91no—
318#102—92no—
319#97—92no—
320C4×C8—91no—
321C23×C3—61no—
322C23×C3—61no—
323C22×D3—21no—
324C22×D3—21no—
325C3×Q8—22no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—42no—
330C3×Q8—42no—
331C3×Q8—62no—
332C3×D4—32no—
333C3×D4—61no—
334C3×D4—61no—
335C3×D4—61no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—42no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—122no—
347C2×C3×C4—122no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—122no—
359C2×Dic3—124no—
360C2×Dic3C2×#6712yes—
361C2×Dic3C2×#6712yes—
362D12—21no—
363D12—21no—
364D12—21no—
365D12#23712yes—
366C4×D3—42no—
367C4×D3—42no—
368C4×D3—124no—
369Dic6—22no—
370Dic6—124no—
371Dic6—124no—
372Dic6—122no—
373Dic6—122no—
374Dic6—242no—
375C3×C8—62no—
376C3⋊C8—22no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C3⋊C8—121no—
382C3⋊C8—121no—
383C2×C32#54811yescharacteristic
384C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
385C2×C32#57811yescharacteristic
386C3×D3—42no—
387C3×D3—81no—
388C2×Q8—31no—
389C2×Q8—182no—
390C2×Q8—181no—
391C2×Q8—364no—
392C2×Q8C2×D3212yes—
393C2×D4—31no—
394C2×D4—31no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—182no—
398SD16—64no—
399D8—182no—
400C2×C8—32no—
401C2×C8—91no—
402C2×C8—91no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—31no—
409C4⋊C4—62no—
410C4⋊C4—92no—
411C4⋊C4—182no—
412C4⋊C4—181no—
413C22⋊C4—62no—
414C22⋊C4—62no—
415C22⋊C4—61no—
416C22⋊C4—61no—
417C22⋊C4—182no—
418C42—32no—
419C42—62no—
420C42C2×D3211yescharacteristic
421C22×C3—21no—
422C22×C3—62no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×#6711yescharacteristic
430C2×D3—22no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—82no—
447C3×C4—121no—
448C3×C4—121no—
449C3×C4#91412yes—
450C3×C4#94912yes—
451C3×C4C2×#23711yescharacteristic
452C3×C4D3×#4111yescharacteristic
453C3×C4#101011yescharacteristic
454C3×C4#101011yescharacteristic
455Dic3—22no—
456Dic3—22no—
457Dic3—41no—
458Dic3—41no—
459Dic3—122no—
460Dic3—122no—
461Dic3—242no—
462C32#336711yescharacteristic, complemented, Sylow
463C23—61no—
464C23—61no—
465Q8—22no—
466Q8—22no—
467Q8—62no—
468Q8—364no—
469Q8—362no—
470D4—32no—
471D4—61no—
472D4—61no—
473D4—61no—
474C2×C4—22no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—122no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—364no—
483C2×C4D3×#6711yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—62no—
487C8—181no—
488C8—181no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—122no—
493C2×C3—241no—
494C2×C3#559811yescharacteristic
495C2×C3C2×#91411yescharacteristic
496C2×C3#577911yescharacteristic
497C2×C3C2×#94911yescharacteristic
498C2×C3#583111yescharacteristic
499C2×C3#583811yescharacteristic
500D3—42no—
501D3—81no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22C2×D3×#6711yescharacteristic
509C4—21no—
510C4—42no—
511C4—62no—
512C4—62no—
513C4—121no—
514C4—121no—
515C4—362no—
516C4#6393912yes—
517C4#6430911yescharacteristic
518C4D3×#23711yescharacteristic
519C3—21no—
520C3#8041611yescharacteristic, complemented
521C3#8366811yescharacteristic, complemented
522C2—122no—
523C2—241no—
524C2#1059515711yescharacteristic
525C2C2×#6393911yescharacteristic
526C2#1059532811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4⋊Q8D32
hypocenterC32#3367
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
1. C3×#5732C2semidirect
2. Dic6×D12C2semidirect
3. #10592778C2semidirect
4. C3×#5083C2semidirect
5. #10591624C2semidirect
7. #10591566C2semidirect
8. #10591546C2semidirect
10. #10590272C2semidirect
11. #10590259C2semidirect
44. #5732D3semidirect
50. #5083D3semidirect
462. C32#3367semidirect
520. C3#80416semidirect
521. C3#83668semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
Dic6×D122
#105927782
C3×#50832
#105916242
#105915672
#105915662
#105915462
C4×#37132
#105902722
#105902592
#836683
#804163