Finite Group Databasebeta

← #11895974

Subgroups — #11895974

Order 1152.

823 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5075C211yesmaximal, characteristic, complemented
5#10591477C212yesmaximal, complemented
6#10591440C212yesmaximal, complemented
7#10591438C212yesmaximal, complemented
8#10591411C212yesmaximal, complemented
9C4×#3715C211yesmaximal, characteristic, complemented
10#10590272C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83587—31nomaximal
13#80371—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#940C2212yes—
18C3×#939—22no—
19C3×#938—21no—
20C3×D4×Dic3C2212yes—
21C2×C3×#214C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63869C2212yes—
26#63866—21no—
27#63845—22no—
28#63844—21no—
29Dic3×Dic6C2212yes—
30C2×#3715C2211yescharacteristic
31#63659C2212yes—
32#63659C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#832C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63575C2212yes—
37#63574C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2211yescharacteristic
40#63563C2212yes—
41#63562C2211yescharacteristic
42#63554C2212yes—
43C3×#550—31no—
44#5718D311yescharacteristic
45#5570—31no—
46#5567—31no—
47C3×#460—31no—
48#5164—32no—
49#5163—32no—
50#5075—32no—
51#5075D311yescharacteristic, complemented
52#5071—32no—
53#5070—31no—
54#5070—31no—
55#5070—61no—
56C4×#215—31no—
57#5024—31no—
58#5018—32no—
59C4×#214—31no—
60#5009—32no—
61#5007—31no—
62#4846—31no—
63#4831—31no—
64#4766—32no—
65#4764—32no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634—21no—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×#217—22no—
84C3×#214—24no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3715—22no—
99#3368—91noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C2×C3×SD16—32no—
103C3×#127—21no—
104C3×#127—32no—
105C3×#127C2×D311yescharacteristic
106C3×#127C2×D311yescharacteristic
107C3×#121—61no—
108C3×#121—62no—
109C3×C4×Q8—31no—
110C3×C4×Q8—31no—
111C3×C4×D4—32no—
112C3×C4×D4—31no—
113Q8×Dic3—32no—
114#944—61no—
115C2×#215—31no—
116#940C2×D312yes—
117#939—22no—
118#938—21no—
119D4×Dic3C2×D312yes—
120C2×#214—31no—
121C2×#214C2×D312yes—
122#890—32no—
123#890—62no—
124#889—62no—
125#887—61no—
126C4×D12C2×D311yescharacteristic
127#870—32no—
128#869—31no—
129#869—31no—
130#869—61no—
131#869—61no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—31no—
137C3×#102—32no—
138#835—31no—
139#832—32no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—31no—
144#832—32no—
145#832—62no—
146#832—62no—
147#832C2×D312yes—
148#821—32no—
149#818—32no—
150#815—32no—
151Dic3⋊C8—32no—
152#810—31no—
153#809—31no—
154#808—31no—
155#808—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—
163C23×C32—22no—
164C22×C3×D3—21no—
165C32×D4—22no—
166C32×D4—22no—
167C32×D4—42no—
168C32×D4—81no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173#634—42no—
174C3×#67—44no—
175C3×#67—82no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—42no—
185C3×Dic6—22no—
186C3×Dic6—21no—
187C3×Dic6#4112yescomplemented
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3×C3⋊C8—22no—
191#557—91no—
192#550—31no—
193#490—92no—
194#486—91no—
195#478—92no—
196#474—91no—
197#460—31no—
198#460—92no—
199#446—91no—
200#440—92no—
201C4×SD16—91no—
202C3×#41—124no—
203C2×C3×Q8—31no—
204C2×C3×Q8—31no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—31no—
211C2×C3×D4—41no—
212C2×C3×D4—41no—
213C2×C3×D4—62no—
214C2×C3×D4—62no—
215C2×C3×D4C22×D312yes—
216C2×C3×D4C22×D312yes—
217C22×C3×C4—62no—
218C22×C3×C4—61no—
219C2×#67—22no—
220C2×#67—22no—
221C22×Dic3—22no—
222#237—44no—
223C2×D12C22×D311yescharacteristic
224C2×C4×D3—21no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6—121no—
228C2×Dic6#6711yescharacteristic
229C2×Dic6C22×D311yescharacteristic
230C3×SD16—64no—
231C2×C3×C8—32no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—61no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—61no—
239C3×C42—21no—
240C3×C42—32no—
241C3×C42—61no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—22no—
245#215—62no—
246#214—24no—
247#214—62no—
248(C2×D3)⋊C4—21no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—121no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260Dic3⋊C4—21no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3—21no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8C22×D312yes—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C32×C4—21no—
285C32×C4AGL(1,ℤ/8)12yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—42no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C2×#41—61no—
295C2×SD16—32no—
296C2×SD16—91no—
297C4⋊Q8—91no—
298C4⋊Q8—181no—
299#127—32no—
300#127D3211yescharacteristic
301#125—92no—
302#125—182no—
303#121—61no—
304#121—62no—
305C4×Q8—31no—
306C4×Q8—31no—
307C4×Q8—92no—
308C4×Q8—181no—
309C4×D4—32no—
310C4×D4—31no—
311#107—92no—
312#106—91no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315#103—91no—
316#102—32no—
317#102—91no—
318#102—92no—
319#102—92no—
320#102—92no—
321#97—92no—
322C4×C8—91no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—42no—
326C23×C3—61no—
327C22×D3—21no—
328C3×Q8—32no—
329C3×Q8—62no—
330C3×Q8—61no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—42no—
339C3×D4—61no—
340C3×D4—61no—
341C3×D4—82no—
342C3×D4—81no—
343C3×D4—81no—
344C3×D4—82no—
345C3×D4—124no—
346C3×D4—242no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—124no—
356C2×C3×C4—122no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363#67—44no—
364#67—82no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—44no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—122no—
372C2×Dic3C2×#6712yes—
373C2×Dic3C2×#6712yes—
374D12—21no—
375D12—21no—
376C4×D3—42no—
377Dic6—22no—
378Dic6—21no—
379Dic6—122no—
380Dic6—122no—
381Dic6—242no—
382Dic6#23712yescomplemented
383C3×C8—62no—
384C3⋊C8—22no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—121no—
390C3⋊C8—121no—
391C2×C32—82no—
392C2×C32#54811yescharacteristic
393C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
394C2×C32#57711yescharacteristic
395C3×D3—81no—
396#41—124no—
397C2×Q8—31no—
398C2×Q8—31no—
399C2×Q8—181no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—31no—
403C2×D4—62no—
404C2×D4—62no—
405C2×D4C2×D3212yes—
406C22×C4—62no—
407C22×C4—61no—
408SD16—64no—
409SD16—182no—
410C2×C8—32no—
411C2×C8—91no—
412C2×C8—91no—
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—31no—
416C4⋊C4—31no—
417C4⋊C4—61no—
418C4⋊C4—92no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C4⋊C4—181no—
423C22⋊C4—62no—
424C22⋊C4—61no—
425C42—32no—
426C42—61no—
427C42—182no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—82no—
437C22×C3—82no—
438C22×C3—82no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3C2×D3×D411yescharacteristic
443C22×C3C22×#6711yescharacteristic
444C2×D3—41no—
445C2×D3—41no—
446C2×D3—41no—
447C3×C4—22no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—62no—
456C3×C4—121no—
457C3×C4—121no—
458C3×C4#91412yes—
459C3×C4#93212yes—
460C3×C4C2×#23711yescharacteristic
461C3×C4D3×#4111yescharacteristic
462C3×C4#101011yescharacteristic
463C3×C4#101011yescharacteristic
464Dic3—22no—
465Dic3—22no—
466Dic3—22no—
467Dic3—41no—
468Dic3—41no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472C32#336811yescharacteristic, complemented, Sylow
473C23—22no—
474C23—61no—
475Q8—32no—
476Q8—61no—
477Q8—62no—
478Q8—362no—
479D4—22no—
480D4—22no—
481D4—42no—
482D4—61no—
483D4—61no—
484D4—81no—
485D4—124no—
486D4—242no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—124no—
493C2×C4—122no—
494C2×C4—182no—
495C2×C4D3×#6711yescharacteristic
496C2×C4D3×#6711yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—62no—
499C8—181no—
500C8—181no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—82no—
505C2×C3—82no—
506C2×C3—162no—
507C2×C3—241no—
508C2×C3#559811yescharacteristic
509C2×C3C2×#91411yescharacteristic
510C2×C3#577511yescharacteristic
511C2×C3C2×#93211yescharacteristic
512C2×C3#583111yescharacteristic
513C2×C3#583611yescharacteristic
514D3—81no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22C2×D3×#6711yescharacteristic
522C4—21no—
523C4—62no—
524C4—62no—
525C4—62no—
526C4—121no—
527C4—121no—
528C4—362no—
529C4#6393412yes—
530C4#6430911yescharacteristic
531C4D3×#23711yescharacteristic
532C3—21no—
533C3#8037111yescharacteristic, complemented
534C3#8358711yescharacteristic, complemented
535C2—82no—
536C2—241no—
537C2#1059510611yescharacteristic
538C2C2×#6393411yescharacteristic
539C2#1059515711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenter#127D32
hypocenterC32#3368
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. #10593860C2semidirect
3. #10592769C2semidirect
4. C3×#5075C2semidirect
5. #10591477C2semidirect
6. #10591440C2semidirect
7. #10591438C2semidirect
8. #10591411C2semidirect
9. C4×#3715C2semidirect
10. #10590272C2semidirect
11. #10590259C2semidirect
51. #5075D3semidirect
187. C3×Dic6#41semidirect
382. Dic6#237semidirect
472. C32#3368semidirect
533. C3#80371semidirect
534. C3#83587semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105938602
#105927692
C3×#50752
#105914772
#105914402
#105914382
#105914112
C4×#37152
#105902722
#105902592
#835873
#803713