Finite Group Databasebeta

← #11868681

Subgroups — #11868681

Order 1152.

1093 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic, complemented
3C3×#4924C211yesmaximal, characteristic, complemented
4#10591131C212yesmaximal, complemented
5#10591096C212yesmaximal
6#10590313C212yesmaximal, complemented
7#10590308C214yesmaximal, complemented
8#10590300C212yesmaximal, complemented
9#83350—31nomaximal
10#79059—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C2×C32×C42C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C4×C4⋊(C3⋊D3)—21no—
17C4×C4⋊(C3⋊D3)—21no—
18C4×C4⋊(C3⋊D3)C2212yes—
19C4×C4⋊(C3⋊D3)C2212yes—
20C3×#926C2212yes—
21C3×#924—21no—
22C3×#924—21no—
23C2×C3×#208C2212yes—
24C3×#870C2212yescomplemented
25C3×#869C2211yescharacteristic, complemented
26C3×#869C2211yescharacteristic, complemented
27C3×C4×Dic6—21no—
28C3×C4×Dic6—21no—
29C3×C4⋊(C3⋊C8)C2212yescomplemented
30C3×C4⋊(C3⋊C8)C2212yescomplemented
31#63575C2214yescomplemented
32#63573C2214yescomplemented
33#63564C2214yes—
34#63564C2214yes—
35C3×#533—31no—
36C2×C4×D12—31no—
37C2×C4×D12—31no—
38C2×C4×D12—61no—
39#5470D311yescharacteristic, complemented
40C3×#423—31no—
41#5131—32no—
42#5121—32no—
43#5087—32no—
44#5084—32no—
45#5066—34no—
46#5001—32no—
47#4995—32no—
48#4924D311yescharacteristic, complemented
49#4847—34no—
50#4846—32no—
51#4842—32no—
52C23×C3⋊D3—21no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)Q814yescomplemented
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—44no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C32×C42D411yescharacteristic
67C32×C42D411yescharacteristic
68C32×C42C2311yescharacteristic
69C32×C42C2311yescharacteristic
70#3752—22no—
71#3752—22no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C3×#217—22no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C3×#208—24no—
83C2×C3×C3⋊C8C2314yes—
84#3077—91noSylow
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×C4×D3—62no—
89C22×C4×D3—61no—
90C22×C4×D3—61no—
91C2×C3×M16—32no—
92C3×C4⋊Q8—31no—
93C3×C4⋊Q8—31no—
94C3×#125—32no—
95C3×C22⋊Q8—61no—
96C3×C22⋊Q8—61no—
97C3×C4×Q8—61no—
98C3×C4×Q8—61no—
99C3×#117—32no—
100C2×C3×C42—21no—
101C2×C3×C42C2×D311yescharacteristic
102C2×C3×C42C2×D311yescharacteristic
103C2×(C2×D3)⋊C4—62no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106#926C2×D312yes—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—61no—
110#924—21no—
111#924—21no—
112C2×#208C2×D312yes—
113C4×D12—32no—
114C4×D12—32no—
115C4×D12—32no—
116C4×D12—32no—
117C4×D12—62no—
118C4×D12—62no—
119C4×D12—62no—
120C4×D12—62no—
121C4×D12—61no—
122C4×D12—61no—
123C4×D12—61no—
124C4×D12—61no—
125#870C2×D312yescomplemented
126#869C2×D311yescharacteristic, complemented
127#869C2×D311yescharacteristic, complemented
128C4×Dic6—21no—
129C4×Dic6—21no—
130C3×C4⋊C8—32no—
131C3×C4⋊C8—32no—
132#821—34no—
133#821—34no—
134#818—34no—
135#817—34no—
136#809—34no—
137#809—34no—
138#808—34no—
139#807—34no—
140C4⋊(C3⋊C8)C2×D312yescomplemented
141C4⋊(C3⋊C8)C2×D312yescomplemented
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—24no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—42no—
147C2×C32×C4—22no—
148C2×C32×C4—41no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×Q812yes—
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—42no—
159C4⋊(C3⋊D3)—24no—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)C2×Q814yes—
162C4×C3⋊D3—44no—
163C4×C3⋊D3—44no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C3×Dic6—42no—
167C3×Dic6—42no—
168C3×C3⋊C8—24no—
169#533—31no—
170C2×C4×D4—91no—
171#478—94no—
172#476—92no—
173#474—92no—
174#428—92no—
175#423—31no—
176#418—92no—
177C23×D3—62no—
178C23×D3—61no—
179C23×D3—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4D1211yescharacteristic
186C22×C3×C4D1211yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—62no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C2×D12—34no—
195C2×D12—34no—
196C2×D12—32no—
197C2×D12—32no—
198C2×D12—62no—
199C2×D12—64no—
200C2×D12—62no—
201C2×D12—64no—
202C2×D12—61no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—61no—
206C2×C4×D3—64no—
207C2×C4×D3—64no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—128no—
213C2×C4×D3—124no—
214C2×C4×D3—124no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C3×M16—64no—
218C2×C3×C8—34no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C22⋊C4—62no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—21no—
229C3×C42—21no—
230C3×C42—62no—
231C3×C42D1211yescharacteristic
232C3×C42D1211yescharacteristic
233C3×C42#6711yescharacteristic
234C3×C42#6711yescharacteristic
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#217—22no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3C22×D312yes—
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4—22no—
257Dic3⋊C4—22no—
258C4×Dic3—22no—
259#208—24no—
260C2×C3⋊C8C22×D314yes—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32C22⋊Q812yes—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—24no—
266C2×C3⋊D3—48no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C32×C4—21no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4C22⋊Q812yes—
273C32×C4AGL(1,ℤ/8)12yes—
274C32×C4C22×Q811yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—42no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C22×D4—91no—
280C23×C4—181no—
281C2×M16—32no—
282C4⋊Q8—31no—
283C4⋊Q8—31no—
284#125—32no—
285C22⋊Q8—61no—
286C22⋊Q8—61no—
287C4×Q8—61no—
288C4×Q8—61no—
289C4×D4—92no—
290C4×D4—92no—
291C4×D4—181no—
292C4×D4—181no—
293#117—32no—
294C2×C4⋊C4—91no—
295C2×C22⋊C4—181no—
296C2×C42D3211yescharacteristic
297#107—94no—
298#106—94no—
299C4⋊C8—32no—
300C4⋊C8—32no—
301#102—94no—
302#102—94no—
303C23×C3—21no—
304C23×C3C2×D1211yescharacteristic
305C23×C3C2×#6711yescharacteristic
306C22×D3—64no—
307C22×D3—68no—
308C22×D3—64no—
309C22×D3—64no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—124no—
313C22×D3—122no—
314C22×D3—122no—
315C22×D3—124no—
316C22×D3—122no—
317C22×D3—122no—
318C3×Q8—122no—
319C3×Q8—122no—
320C2×C3×C4—24no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—42no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4#23712yes—
342C2×C3×C4D3×Q812yes—
343C2×C3×C4D3×Q812yes—
344C2×C3×C4#23912yes—
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—64no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—124no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360D12—34no—
361D12—34no—
362D12—64no—
363D12—64no—
364D12—68no—
365D12—64no—
366D12—64no—
367D12—62no—
368D12—62no—
369C4×D3—128no—
370C4×D3—124no—
371C4×D3—124no—
372C4×D3—128no—
373C4×D3—124no—
374C4×D3—124no—
375Dic6—42no—
376Dic6—42no—
377C3×C8—64no—
378C3⋊C8—24no—
379C2×C32—22no—
380C2×C32C2×C22⋊Q811yescharacteristic
381C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
382C2×C32#57511yescharacteristic
383C3⋊D3—44no—
384C24—181no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×D4—92no—
388C2×D4—94no—
389C2×D4—182no—
390C2×D4—181no—
391C22×C4—181no—
392C22×C4—182no—
393C22×C4—182no—
394C22×C4—364no—
395C22×C4#62611yescharacteristic
396C22×C4#62611yescharacteristic
397C22×C4C2×D3211yescharacteristic
398M16—64no—
399C2×C8—34no—
400C4⋊C4—32no—
401C4⋊C4—32no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4—92no—
407C4⋊C4—181no—
408C22⋊C4—62no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C42—62no—
412C42#62611yescharacteristic
413C42#62611yescharacteristic
414C42C2×D3211yescharacteristic
415C42C2×D3211yescharacteristic
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3#89712yes—
425C22×C3#94612yes—
426C22×C3C22×D1211yescharacteristic
427C22×C3C22×#6711yescharacteristic
428C2×D3—68no—
429C2×D3—64no—
430C2×D3—64no—
431C2×D3—124no—
432C2×D3—1216no—
433C2×D3—128no—
434C2×D3—128no—
435C2×D3—124no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—122no—
454C3×C4—122no—
455C3×C4#89712yes—
456C3×C4#90812yes—
457C3×C4#94612yes—
458C3×C4#94912yes—
459C3×C4C2×#23711yescharacteristic
460C3×C4C2×D3×Q811yescharacteristic
461C3×C4C2×D3×Q811yescharacteristic
462C3×C4C2×#23911yescharacteristic
463Dic3—42no—
464Dic3—42no—
465Dic3—124no—
466Dic3—122no—
467Dic3—122no—
468C32#307711yescharacteristic, complemented, Sylow
469C23—182no—
470C23—184no—
471C23—362no—
472C23—362no—
473C23C2×#62611yescharacteristic
474Q8—122no—
475Q8—122no—
476D4—94no—
477D4—182no—
478D4—184no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—182no—
484C2×C4—364no—
485C2×C4—362no—
486C2×C4—364no—
487C2×C4#379612yes—
488C2×C4#379712yes—
489C2×C4C2×#62611yescharacteristic
490C2×C4C2×#62611yescharacteristic
491C2×C4C2×#62611yescharacteristic
492C2×C4C2×#62611yescharacteristic
493C2×C4C2×#62611yescharacteristic
494C2×C4C22×D3211yescharacteristic
495C8—64no—
496C2×C3—24no—
497C2×C3—22no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3C2×#89711yescharacteristic
503C2×C3C2×#90811yescharacteristic
504C2×C3#574811yescharacteristic
505C2×C3C2×#94611yescharacteristic
506C2×C3C2×#94911yescharacteristic
507C2×C3#582211yescharacteristic
508D3—128no—
509D3—124no—
510D3—124no—
511C22—21no—
512C22—21no—
513C22—184no—
514C22—368no—
515C22—362no—
516C22—362no—
517C22#6387112yes—
518C22C22×#62611yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—122no—
523C4—122no—
524C4—362no—
525C4#6382512yes—
526C4#6387112yes—
527C4C2×#379611yescharacteristic
528C4C2×#379711yescharacteristic
529C3—21no—
530C3#7905911yescharacteristic, complemented
531C3#8335011yescharacteristic, complemented
532C2—22no—
533C2—364no—
534C2C2×#6382511yescharacteristic
535C2#1059479511yescharacteristic
536C2C2×#6387111yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#5470C2semidirect
3. C3×#4924C2semidirect
4. #10591131C2semidirect
6. #10590313C2semidirect
7. #10590308C2semidirect
8. #10590300C2semidirect
24. C3×#870C22semidirect
25. C3×#869C22semidirect
26. C3×#869C22semidirect
29. C3×C4⋊(C3⋊C8)C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. #63575C22semidirect
32. #63573C22semidirect
39. #5470D3semidirect
48. #4924D3semidirect
59. C2×C4⋊(C3⋊D3)Q8semidirect
125. #870C2×D3semidirect
126. #869C2×D3semidirect
127. #869C2×D3semidirect
140. C4⋊(C3⋊C8)C2×D3semidirect
141. C4⋊(C3⋊C8)C2×D3semidirect
468. C32#3077semidirect
530. C3#79059semidirect
531. C3#83350semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×#54702
C3×#49242
#105911312
#105910962
#105903132
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