Finite Group Databasebeta

← #11897665

Subgroups — #11897665

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic
5#10591410C212yesmaximal
6#10591405C212yesmaximal
7#10590490C212yesmaximal, complemented
8#10590419C212yesmaximal, complemented
9#10590312C211yesmaximal, characteristic, complemented
10#10590284C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83631—31nomaximal
13#81056—31nomaximal
14C32×C4×D4C2211yescharacteristic
15C2×#3754C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C2×C3×C4⋊Dic3—21no—
19C3×#924—21no—
20C3×#890C2212yes—
21C3×#878—22no—
22C3×#869C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919—21no—
26#63918C2212yes—
27#63844C2212yes—
28#63843—21no—
29#63839—22no—
30#63659C2211yescharacteristic
31#63637C2211yescharacteristic
32#63635C2211yescharacteristic
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#832C2212yes—
35C3×#808C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63576C2212yes—
38#63576C2212yes—
39#63575C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63567C2212yes—
42#63554C2212yes—
43C3×#554—31no—
44#5722—31no—
45Q8×Dic6—31no—
46#5543D311yescharacteristic
47C3×#476—31no—
48#5091—31no—
49#5078—31no—
50#5078—31no—
51#5064—32no—
52#5063—32no—
53#5024—31no—
54#5018—32no—
55C4×#214—31no—
56C4×#214—31no—
57C4×#214—61no—
58#5008D311yescharacteristic
59#5007—32no—
60#4857—32no—
61#4856—32no—
62#4850—31no—
63#4831—31no—
64#4759—32no—
65#4757—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2311yescharacteristic
69C22×C3×Dic3—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#627—22no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3754Q814yescomplemented
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80C4×C3⋊Dic3—21no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×#217—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3385—91noSylow
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8—31no—
100C3×#125—32no—
101C3×C22⋊Q8—62no—
102C3×C22⋊Q8—61no—
103C3×C4×Q8—31no—
104C3×C4×D4—21no—
105C3×C4×D4—32no—
106C3×C4×D4C2×D311yescharacteristic
107C3×C4×D4C2×D311yescharacteristic
108C2×C3×C4⋊C4—61no—
109Q8×Dic3—61no—
110#944—62no—
111D4×Dic3C2×D312yes—
112C2×#214—31no—
113C2×#214—31no—
114C2×#214—61no—
115C2×C4⋊Dic3—21no—
116#924—21no—
117#890C2×D312yes—
118#888—32no—
119#888—61no—
120#888—62no—
121#888—61no—
122#887—32no—
123#887—61no—
124#878—22no—
125#869—32no—
126#869C2×D311yescharacteristic
127#869C2×D311yescharacteristic
128C4×Dic6—31no—
129C4×Dic6—31no—
130C4×Dic6—32no—
131C4×Dic6—61no—
132C4×Dic6C2×D311yescharacteristic
133C3×#106—32no—
134C3×C4⋊C8—31no—
135C3×#102—32no—
136#832—31no—
137#832—31no—
138#832—61no—
139#832C2×D312yes—
140#818—32no—
141#816—32no—
142#815—32no—
143Dic3⋊C8—32no—
144#810—31no—
145#810—31no—
146#810—32no—
147#810—61no—
148#808—31no—
149#808—31no—
150#808—61no—
151#808C2×D312yes—
152#807—32no—
153#807—32no—
154#807—32no—
155#807—32no—
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—
163C23×C32—21no—
164C32×D4—21no—
165C32×D4C2×Q812yes—
166C2×C32×C4—21no—
167C2×C32×C4—42no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173#634—21no—
174#634C2×Q812yes—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—82no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—81no—
182C3×Dic6—81no—
183#627—82no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)C2×Q812yes—
186C3×C3⋊C8—22no—
187Q82—91no—
188#554—31no—
189#501—92no—
190#500—91no—
191#479—92no—
192#477—91no—
193#476—31no—
194#474—92no—
195#446—91no—
196#440—92no—
197C4×SD16—91no—
198C2×C3×Q8—31no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×D4—21no—
202C2×C3×D4C22×D311yescharacteristic
203C2×C3×D4C22×D311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—41no—
207C22×C3×C4—62no—
208C22×Dic3—22no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6#6711yescharacteristic
217C2×C3×C8—32no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—32no—
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×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237#217—22no—
238#214—34no—
239#214—34no—
240#214—64no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—22no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3#6711yescharacteristic
249C4⋊Dic3C22×D312yes—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—22no—
252Dic3⋊C4—62no—
253Dic3⋊C4—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—121no—
258Dic3⋊C4#6712yes—
259C4×Dic3—62no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C4×Dic3—62no—
263C4×Dic3—121no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8C22×D312yes—
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C32×C4—21no—
277C32×C4—41no—
278C32×C4#13712yes—
279C32×C4C22×Q811yescharacteristic
280C32×C42−1+411yescharacteristic
281C3⋊Dic3—22no—
282C3⋊Dic3—41no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C2×SD16—91no—
288C4⋊Q8—31no—
289C4⋊Q8—31no—
290C4⋊Q8—92no—
291C4⋊Q8—181no—
292C4⋊Q8—182no—
293#125—32no—
294C22⋊Q8—62no—
295C22⋊Q8—61no—
296C4×Q8—31no—
297C4×Q8—92no—
298C4×Q8—91no—
299C4×Q8—181no—
300C4×D4—32no—
301C4×D4D3211yescharacteristic
302C2×C4⋊C4—61no—
303#107—92no—
304#107—92no—
305#107—92no—
306#106—32no—
307#106—91no—
308C4⋊C8—31no—
309C4⋊C8—92no—
310#103—92no—
311#103—91no—
312#102—32no—
313#102—91no—
314#97—92no—
315C4×C8—91no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—41no—
319C3×Q8—62no—
320C3×Q8—241no—
321C3×Q8—241no—
322C3×D4—21no—
323C3×D4—21no—
324C3×D4—22no—
325C3×D4—41no—
326C3×D4D3×Q812yes—
327C3×D4D3×Q812yes—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—41no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—82no—
341C2×C3×C4—242no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—82no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3C2×#6712yes—
358C2×Dic3C2×#6712yes—
359Dic6—22no—
360Dic6—32no—
361Dic6—32no—
362Dic6—62no—
363Dic6—61no—
364Dic6—61no—
365Dic6—81no—
366Dic6—81no—
367Dic6—121no—
368Dic6—242no—
369Dic6—242no—
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—32no—
373C3⋊C8—32no—
374C3⋊C8—62no—
375C3⋊C8—61no—
376C3⋊C8—61no—
377C3⋊C8—121no—
378C2×C32—42no—
379C2×C32D4×Q811yescharacteristic
380C2×C32C2×#13711yescharacteristic
381C2×C32#57611yescharacteristic
382C2×Q8—31no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—91no—
386C2×Q8—182no—
387C2×D4C2×D3211yescharacteristic
388C22×C4—21no—
389C22×C4—62no—
390SD16—94no—
391C2×C8—32no—
392C2×C8—91no—
393C2×C8—91no—
394C4⋊C4—31no—
395C4⋊C4—32no—
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—62no—
399C4⋊C4—62no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4—91no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—181no—
406C4⋊C4C2×D3211yescharacteristic
407C22⋊C4—21no—
408C22⋊C4—62no—
409C42—32no—
410C42—182no—
411C42—181no—
412C42C2×D3211yescharacteristic
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3—42no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—81no—
422C22×C3—81no—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C22×#6711yescharacteristic
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4—62no—
434C3×C4—62no—
435C3×C4—81no—
436C3×C4—122no—
437C3×C4—122no—
438C3×C4#91512yes—
439C3×C4#95112yes—
440C3×C4C2×D3×Q811yescharacteristic
441C3×C4C2×D3×Q811yescharacteristic
442C3×C4#100711yescharacteristic
443C3×C4#101011yescharacteristic
444Dic3—22no—
445Dic3—22no—
446Dic3—42no—
447Dic3—42no—
448Dic3—62no—
449Dic3—62no—
450Dic3—122no—
451Dic3—121no—
452Dic3—121no—
453Dic3—241no—
454C32#338511yescharacteristic, complemented, Sylow
455C23—21no—
456Q8—62no—
457Q8—92no—
458Q8—181no—
459Q8—241no—
460Q8—241no—
461Q8—722no—
462D4—21no—
463D4#379712yes—
464C2×C4—21no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—42no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—242no—
473C2×C4D3×#6711yescharacteristic
474C2×C4D3×#6711yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—62no—
477C8—92no—
478C8—181no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—42no—
483C2×C3—42no—
484C2×C3—82no—
485C2×C3#563211yescharacteristic
486C2×C3C2×#91511yescharacteristic
487C2×C3#577411yescharacteristic
488C2×C3Q8×#6711yescharacteristic
489C2×C3C2×#95111yescharacteristic
490C2×C3#583511yescharacteristic
491C22—22no—
492C22—41no—
493C22—41no—
494C22C2×D3×#6711yescharacteristic
495C4—21no—
496C4—41no—
497C4—62no—
498C4—62no—
499C4—122no—
500C4—122no—
501C4—182no—
502C4—361no—
503C4#6392912yes—
504C4#6429711yescharacteristic
505C4C2×#379711yescharacteristic
506C3—21no—
507C3#8105611yescharacteristic, complemented
508C3#8363111yescharacteristic, complemented
509C2—42no—
510C2#1059480311yescharacteristic
511C2C2×#6392911yescharacteristic
512C2#1059545411yescharacteristic
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. #10593856C2semidirect
7. #10590490C2semidirect
8. #10590419C2semidirect
9. #10590312C2semidirect
10. #10590284C2semidirect
11. #10590259C2semidirect
77. #3754Q8semidirect
454. C32#3385semidirect
507. C3#81056semidirect
508. C3#83631semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
#105938562
C4×#37542
C3×#50082
#105914102
#105914052
#105904902
#105904192
#105903122
#105902842
#105902592
#836313
#810563