Finite Group Databasebeta

← #11897667

Subgroups — #11897667

Order 1152.

734 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
1C3×#5543C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592707C211yesmaximal, characteristic
4C3×C4×#214C211yesmaximal, characteristic
5#10591440C212yesmaximal
6#10591410C212yesmaximal
7#10590491C212yesmaximal, complemented
8#10590419C212yesmaximal, complemented
9#10590311C211yesmaximal, characteristic, complemented
10#10590310C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83631—31nomaximal
13#79634—31nomaximal
14C32×C4×D4C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×D4×Dic3C2212yes—
17C2×C3×#214C2211yescharacteristic
18C2×C3×C4⋊Dic3—21no—
19C3×#924—21no—
20C3×#890C2212yes—
21C3×#878—22no—
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918—21no—
26#63918C2212yes—
27Dic3×Dic6—21no—
28Dic3×Dic6C2212yes—
29#63840—22no—
30#63659C2212yes—
31#63635C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2211yescharacteristic
34C3×#810C2211yescharacteristic
35C3×#808C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63576C2212yes—
38#63575C2212yes—
39#63575C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63565C2212yes—
42#63554C2212yes—
43C3×#554—31no—
44Q8×Dic6—31no—
45Q8×Dic6—31no—
46#5543D311yescharacteristic
47C3×C4×SD16—31no—
48#5164—32no—
49#5091—31no—
50#5078—31no—
51#5064—32no—
52#5063—32no—
53#5024—31no—
54#5021—31no—
55#5018—32no—
56C4×#214D311yescharacteristic
57#5008—31no—
58#5008—31no—
59#5008—61no—
60#5007—32no—
61#4856—32no—
62#4796—32no—
63#4759—32no—
64#4682—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634—21no—
69C22×C3×Dic3—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×#627—22no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#217—22no—
81C3×#214Q814yescomplemented
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3385—91noSylow
98C2×C3×SD16—31no—
99C3×C4⋊Q8—31no—
100C3×#125—32no—
101C3×C22⋊Q8—62no—
102C3×C22⋊Q8—61no—
103C3×C4×Q8—31no—
104C3×C4×Q8—31no—
105C3×C4×D4—21no—
106C3×C4×D4—32no—
107C3×C4×D4C2×D311yescharacteristic
108C3×C4×D4C2×D311yescharacteristic
109C2×C3×C4⋊C4—61no—
110Q8×Dic3—32no—
111Q8×Dic3—61no—
112D4×Dic3C2×D312yes—
113C2×#214C2×D311yescharacteristic
114C2×C4⋊Dic3—21no—
115#924—21no—
116#890C2×D312yes—
117#888—32no—
118#888—61no—
119#888—62no—
120#888—62no—
121#878—22no—
122#869—31no—
123#869—31no—
124#869—32no—
125#869—61no—
126#869—61no—
127#869C2×D311yescharacteristic
128C4×Dic6—32no—
129C4×Dic6—61no—
130C4×Dic6C2×D311yescharacteristic
131C4×Dic6C2×D311yescharacteristic
132C3×#106—31no—
133C3×#103—31no—
134C3×#102—31no—
135C3×C4×C8—31no—
136#835—32no—
137#832—32no—
138#832—32no—
139#832—62no—
140#832C2×D311yescharacteristic
141#818—32no—
142#818—32no—
143#815—32no—
144Dic3⋊C8—32no—
145#810—32no—
146#810C2×D311yescharacteristic
147#808—32no—
148#808—32no—
149#808—62no—
150#808C2×D311yescharacteristic
151#807—32no—
152#807—32no—
153#807—32no—
154#807—32no—
155C4⋊(C3⋊C8)—31no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)—61no—
159#803—32no—
160C4×C3⋊C8C2×D311yescharacteristic
161C23×C32—21no—
162C32×D4—21no—
163C32×D4C2×Q812yes—
164C2×C32×C4—21no—
165C2×C32×C4—42no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170#634—81no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—82no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×Dic6—22no—
178C3×Dic6—21no—
179C3×Dic6—81no—
180C3×Dic6C2×Q812yes—
181#627—82no—
182C3⋊(C3⋊C8)—22no—
183C3×C3⋊C8—21no—
184C3×C3⋊C8C2×Q812yes—
185Q82—91no—
186#554—31no—
187#501—92no—
188#500—91no—
189#479—92no—
190#477—91no—
191#476—91no—
192#474—92no—
193#446—91no—
194#440—92no—
195C4×SD16—31no—
196C2×C3×Q8—31no—
197C2×C3×Q8—31no—
198C2×C3×Q8—61no—
199C2×C3×D4—21no—
200C2×C3×D4C22×D311yescharacteristic
201C2×C3×D4C22×D311yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—41no—
205C22×C3×C4—62no—
206C22×Dic3—22no—
207C2×Dic6—21no—
208C2×Dic6—62no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—62no—
212C2×Dic6—121no—
213C2×Dic6#6711yescharacteristic
214C2×Dic6C22×D311yescharacteristic
215C3×SD16—34no—
216C2×C3×C8—31no—
217C2×C3×C8—31no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4C22×D311yescharacteristic
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—41no—
232C3×C22⋊C4—62no—
233C3×C42—21no—
234C3×C42—32no—
235C3×C42—61no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—22no—
239#214Dic614yescomplemented
240C4⋊Dic3—21no—
241C4⋊Dic3—22no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—62no—
245C4⋊Dic3—62no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—62no—
249C4⋊Dic3—121no—
250C4⋊Dic3#6711yescharacteristic
251C4⋊Dic3C22×D311yescharacteristic
252C4⋊Dic3C22×D312yes—
253Dic3⋊C4—21no—
254Dic3⋊C4—22no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4#6712yes—
258C4×Dic3—21no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3C22×D312yes—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267C22×C32—22no—
268C22×C32—41no—
269C22×C32—41no—
270C22×C32C22×D411yescharacteristic
271C32×C4—21no—
272C32×C4—41no—
273C32×C4#13712yes—
274C32×C4C22×Q811yescharacteristic
275C32×C42−1+411yescharacteristic
276C3⋊Dic3—42no—
277C3×Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—42no—
282C2×SD16—31no—
283C4⋊Q8—31no—
284C4⋊Q8—92no—
285C4⋊Q8—91no—
286C4⋊Q8—181no—
287C4⋊Q8—182no—
288#125—32no—
289C22⋊Q8—62no—
290C22⋊Q8—61no—
291C4×Q8—31no—
292C4×Q8—31no—
293C4×Q8—92no—
294C4×Q8—181no—
295C4×D4—32no—
296C4×D4D3211yescharacteristic
297C2×C4⋊C4—61no—
298#107—92no—
299#107—92no—
300#107—92no—
301#106—31no—
302#106—92no—
303C4⋊C8—92no—
304C4⋊C8—91no—
305#103—31no—
306#103—92no—
307#102—31no—
308#102—92no—
309#97—92no—
310C4×C8—31no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—41no—
314C3×Q8—32no—
315C3×Q8—62no—
316C3×Q8—61no—
317C3×Q8—241no—
318C3×D4—21no—
319C3×D4—21no—
320C3×D4—22no—
321C3×D4—41no—
322C3×D4C2×Dic612yes—
323C3×D4D3×Q812yes—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—41no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—61no—
335C2×C3×C4—62no—
336C2×C3×C4—61no—
337C2×C3×C4—82no—
338C2×C3×C4—242no—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—22no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—82no—
351C2×Dic3—122no—
352C2×Dic3C2×#6712yes—
353C2×Dic3C2×#6712yes—
354Dic6—22no—
355Dic6—21no—
356Dic6—81no—
357Dic6—242no—
358Dic6—242no—
359Dic6—241no—
360Dic6—241no—
361Dic6—242no—
362Dic6C2×Dic612yes—
363C3×C8—32no—
364C3×C8—61no—
365C3⋊C8—21no—
366C3⋊C8—62no—
367C3⋊C8—62no—
368C3⋊C8—122no—
369C3⋊C8C2×Dic612yes—
370C2×C32—42no—
371C2×C32D4×Q811yescharacteristic
372C2×C32C2×#13711yescharacteristic
373C2×C32#57611yescharacteristic
374C2×Q8—31no—
375C2×Q8—31no—
376C2×Q8—61no—
377C2×Q8—182no—
378C2×Q8—181no—
379C2×D4C2×D3211yescharacteristic
380C22×C4—21no—
381C22×C4—62no—
382SD16—34no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8—92no—
386C4⋊C4—31no—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—32no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—92no—
395C4⋊C4—182no—
396C4⋊C4—182no—
397C4⋊C4—181no—
398C4⋊C4C2×D3211yescharacteristic
399C22⋊C4—21no—
400C22⋊C4—62no—
401C42—32no—
402C42—61no—
403C42—182no—
404C42C2×D3211yescharacteristic
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—42no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×#6711yescharacteristic
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—22no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—62no—
426C3×C4—62no—
427C3×C4—62no—
428C3×C4—81no—
429C3×C4—122no—
430C3×C4—121no—
431C3×C4#91512yes—
432C3×C4#95112yes—
433C3×C4C22×Dic611yescharacteristic
434C3×C4C2×D3×Q811yescharacteristic
435C3×C4#100711yescharacteristic
436C3×C4#101011yescharacteristic
437Dic3—22no—
438Dic3—22no—
439Dic3—22no—
440Dic3—41no—
441Dic3—42no—
442Dic3—122no—
443Dic3—122no—
444Dic3—242no—
445C32#338511yescharacteristic, complemented, Sylow
446C23—21no—
447Q8—32no—
448Q8—61no—
449Q8—62no—
450Q8—241no—
451Q8—721no—
452Q8—722no—
453D4—21no—
454D4D3×Dic612yes—
455C2×C4—21no—
456C2×C4—32no—
457C2×C4—32no—
458C2×C4—42no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—62no—
462C2×C4—182no—
463C2×C4—242no—
464C2×C4D3×#6711yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C2×C4C22×D3211yescharacteristic
467C8—32no—
468C8—61no—
469C8—182no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—42no—
474C2×C3—42no—
475C2×C3—82no—
476C2×C3D4×Dic611yescharacteristic
477C2×C3C2×#91511yescharacteristic
478C2×C3#576911yescharacteristic
479C2×C3Q8×#6711yescharacteristic
480C2×C3C2×#95111yescharacteristic
481C2×C3#583511yescharacteristic
482C22—22no—
483C22—41no—
484C22—41no—
485C22C2×D3×#6711yescharacteristic
486C4—21no—
487C4—41no—
488C4—62no—
489C4—62no—
490C4—62no—
491C4—122no—
492C4—121no—
493C4—362no—
494C4#6392912yes—
495C4C2×D3×Dic611yescharacteristic
496C4#6429711yescharacteristic
497C3—21no—
498C3#7963411yescharacteristic, complemented
499C3#8363111yescharacteristic, complemented
500C2—42no—
501C2Dic6×#6711yescharacteristic
502C2C2×#6392911yescharacteristic
503C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×D4D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. Dic62C2semidirect
7. #10590491C2semidirect
8. #10590419C2semidirect
9. #10590311C2semidirect
10. #10590310C2semidirect
11. #10590258C2semidirect
81. C3×#214Q8semidirect
239. #214Dic6semidirect
445. C32#3385semidirect
498. C3#79634semidirect
499. C3#83631semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
Dic622
#105927072
C3×C4×#2142
#105914402
#105914102
#105904912
#105904192
#105903112
#105903102
#105902582
#836313
#796343